diff --git "a/data/train/javascript-000.jsonl" "b/data/train/javascript-000.jsonl" new file mode 100644--- /dev/null +++ "b/data/train/javascript-000.jsonl" @@ -0,0 +1,362 @@ +{"question_id": 1, "task_id": "two-sum", "difficulty": "Easy", "problem_description": "Given an array of integers nums and an integer target, return indices of the two numbers such that they add up to target.\nYou may assume that each input would have exactly one solution, and you may not use the same element twice.\nYou can return the answer in any order.\n \nExample 1:\n\nInput: nums = [2,7,11,15], target = 9\nOutput: [0,1]\nExplanation: Because nums[0] + nums[1] == 9, we return [0, 1].\n\nExample 2:\n\nInput: nums = [3,2,4], target = 6\nOutput: [1,2]\n\nExample 3:\n\nInput: nums = [3,3], target = 6\nOutput: [0,1]\n\n \nConstraints:\n\n2 <= nums.length <= 104\n-109 <= nums[i] <= 109\n-109 <= target <= 109\nOnly one valid answer exists.\n\n \nFollow-up: Can you come up with an algorithm that is less than O(n2) time complexity?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [3, 3],target = 6) == [0, 1]\n assert candidate(nums = [-1, -2, -3, -4],target = -8) == None\n assert candidate(nums = [1000000000, 1000000000],target = 2000000000) == [0, 1]\n assert candidate(nums = [1, 5, 7, 9],target = 10) == [0, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 3) == [0, 1]\n assert candidate(nums = [0, 4, 3, 0],target = 0) == [0, 3]\n assert candidate(nums = [1000000000, -1000000000, 500000000, -500000000],target = 0) == [0, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 17) == [7, 8]\n assert candidate(nums = [1, 5, 7, 8],target = 15) == [2, 3]\n assert candidate(nums = [1000000000, -1000000000],target = 0) == [0, 1]\n assert candidate(nums = [2, 7, 11, 15],target = 9) == [0, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 19) == [8, 9]\n assert candidate(nums = [1, 5, 7, 11],target = 16) == [1, 3]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 10) == [0, 1]\n assert candidate(nums = [3, 2, 4],target = 6) == [1, 2]\n assert candidate(nums = [15, 11, 7, 2],target = 9) == [2, 3]\n assert candidate(nums = [1000000000, -1000000000, 2000000000, -2000000000],target = 0) == [0, 1]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000],target = 4000) == [18, 20]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99],target = 100) == [24, 25]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100],target = 199) == [98, 99]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = 0) == [4, 6]\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],target = -150) == [6, 7]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],target = -39) == [18, 19]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119],target = 110) == [26, 28]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 1100) == [4, 5]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 70) == [16, 18]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2],target = 3) == [18, 19]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500],target = 3000) == [13, 15]\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000],target = 30000) == [13, 15]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 39) == [18, 19]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 99) == [49, 50]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500],target = 900) == [43, 45]\n assert candidate(nums = [-1000000000, -2000000000, -3000000000, -4000000000, -5000000000, -6000000000, -7000000000, -8000000000, -9000000000, -10000000000],target = -15000000000) == [6, 7]\n assert candidate(nums = [23, 8, 15, 37, 48, 5, 21, 7, 40, 6],target = 33) == None\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 390) == [18, 19]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 1500) == [6, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 21) == [9, 10]\n assert candidate(nums = [2, 5, 1, 9, 3, 8, 7, 6, 4, 0],target = 17) == [3, 5]\n assert candidate(nums = [1000000000, -1000000000, 500000000, 500000000],target = 0) == [0, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 29) == [13, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 38) == [17, 19]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 78) == None\n assert candidate(nums = [-1000000000, 1000000000, 500000000, -500000000],target = 0) == [0, 1]\n assert candidate(nums = [1000000000, 999999999, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 1999999999) == [0, 1]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 300) == [13, 15]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],target = 100) == [24, 25]\n assert candidate(nums = [5, 12, 7, 3, 9, 14, 10, 23, 1, 11],target = 22) == [1, 6]\n assert candidate(nums = [-3, 4, 3, 90, -11, 23, -5, 67, 100, -45, 89],target = 53) == None\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56, -57, -58, -59, -60, -61, -62, -63, -64, -65, -66, -67, -68, -69, -70, -71, -72, -73, -74, -75, -76, -77, -78, -79, -80, -81, -82, -83, -84, -85, -86, -87, -88, -89, -90, -91, -92, -93, -94, -95, -96, -97, -98, -99, -100],target = -199) == [98, 99]\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1],target = 1) == [0, 1]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2],target = 3) == [23, 24]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 550, 560, 570, 580, 590, 600, 610, 620, 630, 640, 650, 660, 670, 680, 690, 700, 710, 720, 730, 740, 750, 760, 770, 780, 790, 800, 810, 820, 830, 840, 850, 860, 870, 880, 890, 900, 910, 920, 930, 940, 950, 960, 970, 980, 990, 1000],target = 1990) == [98, 99]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 59) == [29, 30]\n assert candidate(nums = [123456789, 987654321, 456789123, 321987654, 654321987, 789123456],target = 1111111110) == [0, 1]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [0, 1]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -11) == [4, 5]\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992],target = 1999999997) == [0, 1]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -15) == [6, 7]\n assert candidate(nums = [1000000000, -1000000000, 500000000, 500000000, -500000000, -500000000, 1, 2, 3, 4],target = 0) == [0, 1]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],target = 2000000000) == [0, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150],target = 299) == [148, 149]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 59) == [28, 29]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],target = -31) == [14, 15]\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000, 21000, 22000, 23000, 24000, 25000, 26000, 27000, 28000, 29000, 30000],target = 60000) == None\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 39) == [18, 19]\n assert candidate(nums = [1000000000, -500000000, 2000000000, -1000000000, 0, 500000000],target = 1000000000) == [2, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],target = 99) == [48, 49]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],target = 49) == [23, 24]\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990],target = 1999999989) == [4, 5]\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 513) == [0, 9]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -18) == [7, 9]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],target = 1300) == [5, 6]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -17) == [7, 8]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 1900) == [8, 9]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [0, 1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 79) == None\n assert candidate(nums = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 10000000000],target = 30000000000) == None\n assert candidate(nums = [-3, -1, 0, 2, 5, 7, 8, 10],target = 4) == [1, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],target = 100) == None\n assert candidate(nums = [29, 37, 10, 55, 44, 3, 67, 90, 11, 38, 2, 9, 100, 34, 65, 23, 89, 12, 33, 22],target = 62) == [0, 18]\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().twoSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var twoSum = function(nums, target) {", "container": null, "callable": "twoSum", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 2, "task_id": "add-two-numbers", "difficulty": "Medium", "problem_description": "You are given two non-empty linked lists representing two non-negative integers. The digits are stored in reverse order, and each of their nodes contains a single digit. Add the two numbers and return the sum as a linked list.\nYou may assume the two numbers do not contain any leading zero, except the number 0 itself.\n \nExample 1:\n\n\nInput: l1 = [2,4,3], l2 = [5,6,4]\nOutput: [7,0,8]\nExplanation: 342 + 465 = 807.\n\nExample 2:\n\nInput: l1 = [0], l2 = [0]\nOutput: [0]\n\nExample 3:\n\nInput: l1 = [9,9,9,9,9,9,9], l2 = [9,9,9,9]\nOutput: [8,9,9,9,0,0,0,1]\n\n \nConstraints:\n\nThe number of nodes in each linked list is in the range [1, 100].\n0 <= Node.val <= 9\nIt is guaranteed that the list represents a number that does not have leading zeros.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(l1 = list_node([9, 8, 7]),l2 = list_node([1, 2, 3])), list_node([0, 1, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),l2 = list_node([5, 6, 4])), list_node([6, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 6, 4])), list_node([6, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 3]),l2 = list_node([5, 6, 4, 1])), list_node([7, 0, 8, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([9, 8, 7, 6, 5])), list_node([0, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([5, 5, 5]),l2 = list_node([5, 5, 5, 5, 5])), list_node([0, 1, 1, 6, 5]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9]),l2 = list_node([9, 9, 9, 9])), list_node([8, 9, 9, 9, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([1])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9])), list_node([0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0]),l2 = list_node([9, 9, 9, 9])), list_node([0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),l2 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9])), list_node([0, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 8, 9]),l2 = list_node([0, 0, 9])), list_node([1, 8, 8, 1]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 3]),l2 = list_node([5, 6, 4])), list_node([7, 0, 8]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 6, 4])), list_node([6, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 6]),l2 = list_node([1, 3, 5])), list_node([3, 7, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 1, 1]),l2 = list_node([9, 9, 9])), list_node([0, 1, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 8]),l2 = list_node([0])), list_node([1, 8]))\n assert is_same_list(candidate(l1 = list_node([1, 8]),l2 = list_node([0])), list_node([1, 8]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),l2 = list_node([4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5])), list_node([5, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(l1 = list_node([1, 8, 9]),l2 = list_node([9, 1])), list_node([0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([7, 2, 4, 3]),l2 = list_node([5, 6, 4])), list_node([2, 9, 8, 3]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([1, 2, 3, 4, 5])), list_node([2, 2, 3, 4, 5]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([6, 4, 5]),l2 = list_node([0, 4, 5])), list_node([6, 8, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([5]),l2 = list_node([5])), list_node([0, 1]))\n assert is_same_list(candidate(l1 = list_node([7, 2, 4, 3]),l2 = list_node([5, 6, 4, 2])), list_node([2, 9, 8, 5]))\n assert is_same_list(candidate(l1 = list_node([1, 2]),l2 = list_node([3, 4, 5, 6])), list_node([4, 6, 5, 6]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9]),l2 = list_node([1])), list_node([0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([9, 9]),l2 = list_node([1])), list_node([0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9])), list_node([0, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([9, 8, 7])), list_node([0, 1, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([7, 8, 9])), list_node([8, 0, 3, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 6, 4])), list_node([6, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([4, 5, 6])), list_node([5, 7, 9]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([5, 4, 3, 2, 1])), list_node([6, 6, 6, 6, 6]))\n assert is_same_list(candidate(l1 = list_node([0, 0, 1]),l2 = list_node([0, 0, 1])), list_node([0, 0, 2]))\n assert is_same_list(candidate(l1 = list_node([9, 9]),l2 = list_node([1, 1, 1])), list_node([0, 1, 2]))\n assert is_same_list(candidate(l1 = list_node([6, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([3, 4, 2])), list_node([9, 8, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([9]),l2 = list_node([1])), list_node([0, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),l2 = list_node([1])), list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([4, 5, 6])), list_node([5, 7, 9]))\n assert is_same_list(candidate(l1 = list_node([1, 8, 9]),l2 = list_node([2, 5, 8])), list_node([3, 3, 8, 1]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9]),l2 = list_node([9, 9, 9, 9])), list_node([8, 9, 9, 9, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([3, 2, 1]),l2 = list_node([9, 8, 7])), list_node([2, 1, 9]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 6, 4])), list_node([6, 6, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6])), list_node([6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([1, 2, 3, 4, 5])), list_node([2, 4, 6, 8, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([0]),l2 = list_node([0])), list_node([0]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 9]),l2 = list_node([5, 6, 4, 9])), list_node([7, 0, 4, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 3]),l2 = list_node([5, 6, 4])), list_node([7, 0, 8]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 3, 2, 5, 5, 5]),l2 = list_node([5, 6, 4])), list_node([7, 0, 8, 2, 5, 5, 5]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0]),l2 = list_node([9, 9, 9, 9, 9])), list_node([0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 6, 8]),l2 = list_node([1, 3, 5, 7])), list_node([3, 7, 1, 6, 1]))\n assert is_same_list(candidate(l1 = list_node([9]),l2 = list_node([1, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]))\n assert is_same_list(candidate(l1 = list_node([0, 1]),l2 = list_node([0, 1])), list_node([0, 2]))\n assert is_same_list(candidate(l1 = list_node([7, 1, 6]),l2 = list_node([5, 9, 2])), list_node([2, 1, 9]))\n"}, "metadata": {"canonical_parameter_names": ["l1", "l2"], "leetcode_dataset_entry_point": "Solution().addTwoNumbers", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var addTwoNumbers = function(l1, l2) {", "container": null, "callable": "addTwoNumbers", "parameters": [{"name": "l1", "type": "ListNode"}, {"name": "l2", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 3, "task_id": "longest-substring-without-repeating-characters", "difficulty": "Medium", "problem_description": "Given a string s, find the length of the longest substring without repeating characters.\n \nExample 1:\n\nInput: s = \"abcabcbb\"\nOutput: 3\nExplanation: The answer is \"abc\", with the length of 3.\n\nExample 2:\n\nInput: s = \"bbbbb\"\nOutput: 1\nExplanation: The answer is \"b\", with the length of 1.\n\nExample 3:\n\nInput: s = \"pwwkew\"\nOutput: 3\nExplanation: The answer is \"wke\", with the length of 3.\nNotice that the answer must be a substring, \"pwke\" is a subsequence and not a substring.\n\n \nConstraints:\n\n0 <= s.length <= 5 * 104\ns consists of English letters, digits, symbols and spaces.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcabcbb\") == 3\n assert candidate(s = \"bbbbb\") == 1\n assert candidate(s = \"pwwkew\") == 3\n assert candidate(s = \"abcdabcabcabcd\") == 4\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefg\") == 7\n assert candidate(s = \"aabbccddeeff\") == 2\n assert candidate(s = \"sldfjldskfjdslkfjsdkljflkjsdfljfsdlkflskdjflsdjflskdjflsdkjflsdfjlsd\") == 6\n assert candidate(s = \"racecar\") == 4\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 26\n assert candidate(s = \"aabacbebebe\") == 4\n assert candidate(s = \"ekdvdfis\") == 5\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890abcdefghijklmnopqrstuvwxyz\") == 36\n assert candidate(s = \"abbaabbaabba\") == 2\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 2\n assert candidate(s = \"abcdefghihgfedcba\") == 9\n assert candidate(s = \"abcdeffedcba\") == 6\n assert candidate(s = \"aaaaaaaabbbbbbbccccccdddddeeeeeeffffffffggggggg\") == 2\n assert candidate(s = \"tmmzuxt\") == 5\n assert candidate(s = \"nfpdmpi\") == 5\n assert candidate(s = \"anviaj\") == 5\n assert candidate(s = \"abcdeabcde\") == 5\n assert candidate(s = \"abcdabcabcd\") == 4\n assert candidate(s = \"dvdf\") == 3\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(s = \"abcdabcdeabcdabcdeabcd\") == 5\n assert candidate(s = \"rjqzupkoz\") == 8\n assert candidate(s = \"ababababababababab\") == 2\n assert candidate(s = \"!@#$%^&*()_+!@#$%^&*()_+\") == 12\n assert candidate(s = \"cdddddddddddddd\") == 2\n assert candidate(s = \"wobgrovw\") == 6\n assert candidate(s = \"abba\") == 2\n assert candidate(s = \"abcbacabc\") == 3\n assert candidate(s = \"ohvhjdml\") == 6\n assert candidate(s = \"123456789012345678901234567890\") == 10\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890!@#$%^&*()_+\") == 23\n assert candidate(s = \"12345678901234567890\") == 10\n assert candidate(s = \"abcdabcabcabcd\") == 4\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefg\") == 7\n assert candidate(s = \"aabbccddeeff\") == 2\n assert candidate(s = \"sldfjldskfjdslkfjsdkljflkjsdfljfsdlkflskdjflsdjflskdjflsdkjflsdfjlsd\") == 6\n assert candidate(s = \"racecar\") == 4\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 26\n assert candidate(s = \"aabacbebebe\") == 4\n assert candidate(s = \"ekdvdfis\") == 5\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890abcdefghijklmnopqrstuvwxyz\") == 36\n assert candidate(s = \"abbaabbaabba\") == 2\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 2\n assert candidate(s = \"abcdefghihgfedcba\") == 9\n assert candidate(s = \"abcdeffedcba\") == 6\n assert candidate(s = \"aaaaaaaabbbbbbbccccccdddddeeeeeeffffffffggggggg\") == 2\n assert candidate(s = \"tmmzuxt\") == 5\n assert candidate(s = \"nfpdmpi\") == 5\n assert candidate(s = \"anviaj\") == 5\n assert candidate(s = \"abcdeabcde\") == 5\n assert candidate(s = \"abcdabcabcd\") == 4\n assert candidate(s = \"dvdf\") == 3\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(s = \"abcdabcdeabcdabcdeabcd\") == 5\n assert candidate(s = \"rjqzupkoz\") == 8\n assert candidate(s = \"ababababababababab\") == 2\n assert candidate(s = \"!@#$%^&*()_+!@#$%^&*()_+\") == 12\n assert candidate(s = \"cdddddddddddddd\") == 2\n assert candidate(s = \"wobgrovw\") == 6\n assert candidate(s = \"abba\") == 2\n assert candidate(s = \"abcbacabc\") == 3\n assert candidate(s = \"ohvhjdml\") == 6\n assert candidate(s = \"123456789012345678901234567890\") == 10\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890!@#$%^&*()_+\") == 23\n assert candidate(s = \"12345678901234567890\") == 10\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().lengthOfLongestSubstring", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var lengthOfLongestSubstring = function(s) {", "container": null, "callable": "lengthOfLongestSubstring", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 4, "task_id": "median-of-two-sorted-arrays", "difficulty": "Hard", "problem_description": "Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays.\nThe overall run time complexity should be O(log (m+n)).\n \nExample 1:\n\nInput: nums1 = [1,3], nums2 = [2]\nOutput: 2.00000\nExplanation: merged array = [1,2,3] and median is 2.\n\nExample 2:\n\nInput: nums1 = [1,2], nums2 = [3,4]\nOutput: 2.50000\nExplanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5.\n\n \nConstraints:\n\nnums1.length == m\nnums2.length == n\n0 <= m <= 1000\n0 <= n <= 1000\n1 <= m + n <= 2000\n-106 <= nums1[i], nums2[i] <= 106\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [100, 200, 300],nums2 = [150, 250, 350]) == 225.0\n assert candidate(nums1 = [2],nums2 = []) == 2.0\n assert candidate(nums1 = [1, 3],nums2 = [2]) == 2.0\n assert candidate(nums1 = [1],nums2 = [2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5.5\n assert candidate(nums1 = [1000000],nums2 = [-1000000]) == 0.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 10.0\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [2, 4, 6, 8]) == 4.5\n assert candidate(nums1 = [10, 20, 30],nums2 = [5, 15, 25, 35, 45]) == 22.5\n assert candidate(nums1 = [0, 0],nums2 = [0, 0]) == 0.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10.5\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10]) == 5.5\n assert candidate(nums1 = [1, 2, 3],nums2 = [0, 4, 5, 6]) == 3.0\n assert candidate(nums1 = [5, 6],nums2 = [1, 2, 3, 4, 7, 8]) == 4.5\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [2, 4, 6, 8, 10]) == 5.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6],nums2 = [0]) == 3.0\n assert candidate(nums1 = [1, 2, 3],nums2 = [4]) == 2.5\n assert candidate(nums1 = [1, 2],nums2 = [3]) == 2.0\n assert candidate(nums1 = [1, 3, 5],nums2 = [2, 4, 6]) == 3.5\n assert candidate(nums1 = [1],nums2 = [2, 3, 4]) == 2.5\n assert candidate(nums1 = [1, 2],nums2 = [3, 4]) == 2.5\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [5, 15, 25, 35, 45]) == 27.5\n assert candidate(nums1 = [],nums2 = [1]) == 1.0\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],nums2 = [2, 4, 6, 8, 10]) == 10.5\n assert candidate(nums1 = [1000000, 1000001, 1000002, 1000003, 1000004],nums2 = [999999, 1000000, 1000005, 1000010]) == 1000002.0\n assert candidate(nums1 = [-1000000, -999999, -999998],nums2 = [-1000001, -999997, -999995, -999993, -999991]) == -999997.5\n assert candidate(nums1 = [5, 9, 11, 19],nums2 = [1, 3, 4, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 18]) == 10.5\n assert candidate(nums1 = [-5, -3, -1],nums2 = [-6, -4, -2, 0]) == -3.0\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-7, -3, 2, 7, 12]) == 1.0\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 15.5\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10]) == 8.0\n assert candidate(nums1 = [-1000000],nums2 = [0, 1000000]) == 0.0\n assert candidate(nums1 = [1],nums2 = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10.5\n assert candidate(nums1 = [-10, -9, -8, -7, -6],nums2 = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == -2.5\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10.5\n assert candidate(nums1 = [1],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 15.0\n assert candidate(nums1 = [1, 5, 9, 13],nums2 = [2, 6, 10, 14, 18]) == 9.0\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 8.0\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 8.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 0.0\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 10.5\n assert candidate(nums1 = [-5, -3, -1, 1, 3, 5],nums2 = [-6, -4, -2, 0, 2, 4, 6]) == 0.0\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10, 12, 14, 16]) == 7.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10.5\n assert candidate(nums1 = [1],nums2 = [1000000]) == 500000.5\n assert candidate(nums1 = [5, 15, 25, 35, 45],nums2 = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 37.5\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],nums2 = [26, 27, 28, 29, 30]) == 15.5\n assert candidate(nums1 = [-1000000, -999999, -999998],nums2 = [-1000001, -1000000, -999999, -999998]) == -999999.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [16, 17, 18, 19, 20]) == 10.5\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [21, 22, 23, 24, 25]) == 13.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 25.5\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15],nums2 = [2, 4, 6, 8, 10, 12, 14, 16]) == 8.5\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 20.5\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [0, 2, 4, 6, 8]) == 4.5\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [5, 15, 25, 35, 45, 55]) == 55.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],nums2 = [31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 20.5\n assert candidate(nums1 = [],nums2 = [1, 3, 5, 7, 9]) == 5.0\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 15.5\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 20.5\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [50, 150, 250, 350, 450, 550]) == 300.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15.5\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 20.5\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [5, 15, 25, 35, 45, 55]) == 30.0\n assert candidate(nums1 = [1, 2, 3],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 4.0\n assert candidate(nums1 = [-1, -3, -5, -7, -9],nums2 = [-2, -4, -6, -8, -10]) == -5.5\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11],nums2 = [2, 4, 6, 8, 10, 12]) == 6.5\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [50, 150, 250, 350, 450, 550, 650]) == 325.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15.5\n assert candidate(nums1 = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],nums2 = [500, 1500, 2500, 3500, 4500, 5500, 6500, 7500, 8500, 9500, 10500]) == 5500.0\n assert candidate(nums1 = [-10, -8, -6, -4, -2],nums2 = [-9, -7, -5, -3, -1]) == -5.5\n assert candidate(nums1 = [1000000],nums2 = [999999]) == 999999.5\n assert candidate(nums1 = [-5, -3, -1, 1, 3],nums2 = [-10, -8, -6, -4, -2]) == -3.5\n assert candidate(nums1 = [],nums2 = [1, 2, 3, 4, 5]) == 3.0\n assert candidate(nums1 = [1, 5, 9, 13, 17],nums2 = [2, 6, 10, 14, 18]) == 9.5\n assert candidate(nums1 = [1000000, 1000001, 1000002],nums2 = [999999, 1000000, 1000001, 1000002]) == 1000001.0\n assert candidate(nums1 = [100000, 100001, 100002, 100003, 100004],nums2 = [100005, 100006, 100007, 100008, 100009]) == 100004.5\n assert candidate(nums1 = [-5, -4, -3, -2, -1],nums2 = [0, 1, 2, 3, 4, 5]) == 0.0\n assert candidate(nums1 = [100000],nums2 = [-100000, -99999, -99998, -99997, -99996, -99995]) == -99997.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = []) == 5.5\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = []) == 3.0\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],nums2 = [2, 4, 6, 8, 10]) == 15.0\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10]) == 5.5\n assert candidate(nums1 = [],nums2 = [1, 2, 3, 4, 5]) == 3.0\n assert candidate(nums1 = [-5, -3, 0, 8],nums2 = [-10, -4, 2, 6, 12]) == 0.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 13.0\n assert candidate(nums1 = [-1, 3, 5, 7, 9],nums2 = [-2, -4, -6, -8, -10]) == -5.5\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50]) == 25.5\n assert candidate(nums1 = [1, 2, 2, 3, 3],nums2 = [2, 2, 3, 3, 4, 4, 5, 5]) == 3.0\n assert candidate(nums1 = [100, 200, 300],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 6.5\n assert candidate(nums1 = [],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10.5\n assert candidate(nums1 = [],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5.5\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6, 7, 8, 9, 10]) == 5.5\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],nums2 = []) == 13.0\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [50, 150, 250, 350, 450, 550]) == 300.0\n assert candidate(nums1 = [-5, 0, 3, 8, 12],nums2 = [-10, -1, 2, 4, 9, 14]) == 3.0\n assert candidate(nums1 = [50, 60, 70, 80, 90],nums2 = [10, 20, 30, 40]) == 50.0\n assert candidate(nums1 = [1, 3, 5],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 18.0\n assert candidate(nums1 = [1, 5, 7, 9, 11, 13],nums2 = [2, 4, 6, 8, 10, 12, 14]) == 8.0\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-20, -15, -1, 1, 6, 11, 15, 20]) == 1.0\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10, 11, 12]) == 6.5\n assert candidate(nums1 = [-1, -2, -3, -4, -5],nums2 = [-10, -9, -8, -7, -6]) == -3.5\n assert candidate(nums1 = [0, 0, 0, 0],nums2 = [0, 0, 0, 0]) == 0.0\n assert candidate(nums1 = [5, 15, 25, 35, 45],nums2 = [10, 20, 30, 40, 50, 60]) == 30.0\n assert candidate(nums1 = [100, 200, 300],nums2 = [50, 150, 250, 350]) == 200.0\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26]) == 12.0\n assert candidate(nums1 = [1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1.0\n assert candidate(nums1 = [-100000, -99999, -99998],nums2 = [-99997, -99996, -99995, -99994, -99993, -99992]) == -99996.0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = []) == 10.5\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = []) == 3.0\n assert candidate(nums1 = [1],nums2 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53]) == 19.0\n assert candidate(nums1 = [1, 2, 2, 3, 4],nums2 = [2, 2, 3, 4, 5]) == 2.5\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10, 12, 14]) == 6.5\n assert candidate(nums1 = [100, 200, 300, 400],nums2 = [50, 150, 250, 350, 450, 550]) == 275.0\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2"], "leetcode_dataset_entry_point": "Solution().findMedianSortedArrays", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMedianSortedArrays = function(nums1, nums2) {", "container": null, "callable": "findMedianSortedArrays", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 5, "task_id": "longest-palindromic-substring", "difficulty": "Medium", "problem_description": "Given a string s, return the longest palindromic substring in s.\n \nExample 1:\n\nInput: s = \"babad\"\nOutput: \"bab\"\nExplanation: \"aba\" is also a valid answer.\n\nExample 2:\n\nInput: s = \"cbbd\"\nOutput: \"bb\"\n\n \nConstraints:\n\n1 <= s.length <= 1000\ns consist of only digits and English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abba\") == \"abba\"\n assert candidate(s = \"aaaa\") == \"aaaa\"\n assert candidate(s = \"abacdfgdcaba\") == \"aba\"\n assert candidate(s = \"ac\") == \"a\"\n assert candidate(s = \"babad\") == \"aba\"\n assert candidate(s = \"noon\") == \"noon\"\n assert candidate(s = \"cbbd\") == \"bb\"\n assert candidate(s = \"abcba\") == \"abcba\"\n assert candidate(s = \"bcbabcbabcba\") == \"bcbabcbabcb\"\n assert candidate(s = \"noonhighnoon\") == \"noon\"\n assert candidate(s = \"forgeeksskeegfor\") == \"geeksskeeg\"\n assert candidate(s = \"aaabaaaa\") == \"aaabaaa\"\n assert candidate(s = \"abcdedcba\") == \"abcdedcba\"\n assert candidate(s = \"aaa\") == \"aaa\"\n assert candidate(s = \"aaaaa\") == \"aaaaa\"\n assert candidate(s = \"racecar\") == \"racecar\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"abcdefg\") == \"a\"\n assert candidate(s = \"aabbccddeeeffgg\") == \"eee\"\n assert candidate(s = \"abcdedcba12321\") == \"abcdedcba\"\n assert candidate(s = \"xxyyyxyxyxyxyxyxxyyxyxyxyxyxyx\") == \"xyxyxyxyxyx\"\n assert candidate(s = \"thisisanexamplewithlongestpalindromeonyxdxyxdx\") == \"xdxyxdx\"\n assert candidate(s = \"12345678987654321\") == \"12345678987654321\"\n assert candidate(s = \"xyzaaazyxzyzyxyz\") == \"xyzaaazyx\"\n assert candidate(s = \"12321abcdcba45654\") == \"abcdcba\"\n assert candidate(s = \"012210\") == \"012210\"\n assert candidate(s = \"tattarrattat\") == \"tattarrattat\"\n assert candidate(s = \"aabbabbaa\") == \"aabbabbaa\"\n assert candidate(s = \"abacdfgdcaba12321\") == \"12321\"\n assert candidate(s = \"xyxxyxyxyxyxyxyx\") == \"xyxyxyxyxyxyx\"\n assert candidate(s = \"1234321abcdefghgfedcba\") == \"abcdefghgfedcba\"\n assert candidate(s = \"abababababababababababababababababababababababababababababababab\") == \"bababababababababababababababababababababababababababababababab\"\n assert candidate(s = \"abacdfgdcabaxxxabcdcba\") == \"abcdcba\"\n assert candidate(s = \"12321abccba45654\") == \"abccba\"\n assert candidate(s = \"12321abcdedcbavcvcv\") == \"abcdedcba\"\n assert candidate(s = \"abcbaekayakecivic\") == \"ekayake\"\n assert candidate(s = \"noonmoonnoon\") == \"oonnoo\"\n assert candidate(s = \"abcbaxxxxxabcdcba\") == \"cbaxxxxxabc\"\n assert candidate(s = \"noonhighnoonnoon\") == \"noonnoon\"\n assert candidate(s = \"noonmidnightnoon\") == \"noon\"\n assert candidate(s = \"abcba12321defedcba\") == \"defed\"\n assert candidate(s = \"aabbabaaaabbaaabaaabbbbbaaaaaabbbaaaabbbbaaabbaabbbaaaabbbaaabbbbaaabbaabbaabbab\") == \"bbaaabbbbaaabb\"\n assert candidate(s = \"ababababababababa\") == \"ababababababababa\"\n assert candidate(s = \"noonnoonnoonnoonnoonnoon\") == \"noonnoonnoonnoonnoonnoon\"\n assert candidate(s = \"abccbaabacdfgdcaba\") == \"abccba\"\n assert candidate(s = \"racecarxracecar\") == \"racecarxracecar\"\n assert candidate(s = \"madamracecarlevel\") == \"racecar\"\n assert candidate(s = \"babcbabcbabcba\") == \"abcbabcbabcba\"\n assert candidate(s = \"abacdfgdcabaabacdfgdcaba\") == \"dcabaabacd\"\n assert candidate(s = \"madamintanimadaminabba\") == \"animadamina\"\n assert candidate(s = \"noonracecarracecar\") == \"racecarracecar\"\n assert candidate(s = \"zzzzzzzzzzzz\") == \"zzzzzzzzzzzz\"\n assert candidate(s = \"racecar2racecar\") == \"racecar2racecar\"\n assert candidate(s = \"zxyabcddcbaabczyx\") == \"abcddcba\"\n assert candidate(s = \"deeee\") == \"eeee\"\n assert candidate(s = \"abacdfgdcabacdfgdcaba\") == \"dcabacd\"\n assert candidate(s = \"1234543216789876\") == \"123454321\"\n assert candidate(s = \"abcbaaabcba\") == \"abcbaaabcba\"\n assert candidate(s = \"abcdedcbaefghihgfexyzzyx\") == \"efghihgfe\"\n assert candidate(s = \"abcdefgfebac\") == \"efgfe\"\n assert candidate(s = \"levelhannahlevel\") == \"levelhannahlevel\"\n assert candidate(s = \"xxyyzzzyyxx\") == \"xxyyzzzyyxx\"\n assert candidate(s = \"abcddcbaabcddcbaxyzzyx\") == \"abcddcbaabcddcba\"\n assert candidate(s = \"racecar12321racecar\") == \"racecar12321racecar\"\n assert candidate(s = \"abcdeffedcba\") == \"abcdeffedcba\"\n assert candidate(s = \"civicracecar\") == \"racecar\"\n assert candidate(s = \"levelmadammadam\") == \"madammadam\"\n assert candidate(s = \"zxyaxzyaz\") == \"z\"\n assert candidate(s = \"abcdefedcba\") == \"abcdefedcba\"\n assert candidate(s = \"12321321321321321\") == \"12321\"\n assert candidate(s = \"xyzzyxcbaapqrqpabczyzyx\") == \"apqrqpa\"\n assert candidate(s = \"abacdfgdcaba123321\") == \"123321\"\n assert candidate(s = \"abacdfgdcabaxxxxxabcdcba\") == \"baxxxxxab\"\n assert candidate(s = \"aabcdcbadefedcbaa\") == \"abcdcba\"\n assert candidate(s = \"abcdefghijiklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == \"klmnopqrstuvwxyzzyxwvutsrqponmlk\"\n assert candidate(s = \"bananaananab\") == \"bananaananab\"\n assert candidate(s = \"aabbccddeedcba\") == \"deed\"\n assert candidate(s = \"noonhighnoonnoonhighnoon\") == \"hnoonnoonh\"\n assert candidate(s = \"babaddabba\") == \"baddab\"\n assert candidate(s = \"abababababababababababababababababababababababababababababababbababa\") == \"babababababababababababababababababababababababababababababab\"\n assert candidate(s = \"abcdeedcba1234321xyzzyx\") == \"abcdeedcba\"\n assert candidate(s = \"aabb\") == \"bb\"\n assert candidate(s = \"mamamamamamamamama\") == \"amamamamamamamama\"\n assert candidate(s = \"abcdefgfedcba\") == \"abcdefgfedcba\"\n assert candidate(s = \"abcbabcba\") == \"abcbabcba\"\n assert candidate(s = \"xyzzzzyxabcdefedcba\") == \"abcdefedcba\"\n assert candidate(s = \"banana\") == \"anana\"\n assert candidate(s = \"abcbcbcbcbcbcbcbcbcbcbcbcb\") == \"bcbcbcbcbcbcbcbcbcbcbcbcb\"\n assert candidate(s = \"anana\") == \"anana\"\n assert candidate(s = \"aabbccddeeeeddccbbbaa\") == \"bbccddeeeeddccbb\"\n assert candidate(s = \"12321abcdedcba45654\") == \"abcdedcba\"\n assert candidate(s = \"aabbccddeeffgg\") == \"gg\"\n assert candidate(s = \"levelracecardeifiedracecar\") == \"racecardeifiedracecar\"\n assert candidate(s = \"aaaaabbbbbaaaa\") == \"aaaabbbbbaaaa\"\n assert candidate(s = \"abccba\") == \"abccba\"\n assert candidate(s = \"abcdcba12321xyzzyx\") == \"abcdcba\"\n assert candidate(s = \"12321abcba21321\") == \"abcba\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"zz\"\n assert candidate(s = \"abcdcbaxxxabcdcbaabcdcbaxxxabcdcba\") == \"abcdcbaxxxabcdcbaabcdcbaxxxabcdcba\"\n assert candidate(s = \"xyzabcbaxyz\") == \"abcba\"\n assert candidate(s = \"racecarannakayak\") == \"racecar\"\n assert candidate(s = \"abacdfgdcab\") == \"aba\"\n assert candidate(s = \"abcdeedcbafedcbe\") == \"abcdeedcba\"\n assert candidate(s = \"a1b2c3d4c3b2a\") == \"a\"\n assert candidate(s = \"abccccba\") == \"abccccba\"\n assert candidate(s = \"noonnoonnoon\") == \"noonnoonnoon\"\n assert candidate(s = \"aabbccddeeeedddccbaa\") == \"ddeeeedd\"\n assert candidate(s = \"AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\") == \"A\"\n assert candidate(s = \"acbbac\") == \"bb\"\n assert candidate(s = \"noonlevelnoon\") == \"noonlevelnoon\"\n assert candidate(s = \"abbaabba\") == \"abbaabba\"\n assert candidate(s = \"rotor1234321rotor\") == \"rotor1234321rotor\"\n assert candidate(s = \"aaaaabaaa\") == \"aaabaaa\"\n assert candidate(s = \"abcdefghihgfedcba\") == \"abcdefghihgfedcba\"\n assert candidate(s = \"civicdeifiedrotorlevel\") == \"deified\"\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\") == \"a\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaedcba\") == \"z\"\n assert candidate(s = \"aabcddeffedcba\") == \"deffed\"\n assert candidate(s = \"pppppppppppppppppppppppppppppppp\") == \"pppppppppppppppppppppppppppppppp\"\n assert candidate(s = \"aabbccddeeeedddccbbaa\") == \"ddeeeedd\"\n assert candidate(s = \"a1b2c3d4e5f6g7h8i9j0j9i8h7g6f5e4d3c2b1a\") == \"a1b2c3d4e5f6g7h8i9j0j9i8h7g6f5e4d3c2b1a\"\n assert candidate(s = \"mississippi\") == \"ississi\"\n assert candidate(s = \"zxcvbnmlkjhgfdsapoiuytrewqpoiuytrewqpoiuytrewqpoiuytrewq\") == \"z\"\n assert candidate(s = \"deifiedrotorlevel\") == \"deified\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().longestPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestPalindrome = function(s) {", "container": null, "callable": "longestPalindrome", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 6, "task_id": "zigzag-conversion", "difficulty": "Medium", "problem_description": "The string \"PAYPALISHIRING\" is written in a zigzag pattern on a given number of rows like this: (you may want to display this pattern in a fixed font for better legibility)\n\nP A H N\nA P L S I I G\nY I R\n\nAnd then read line by line: \"PAHNAPLSIIGYIR\"\nWrite the code that will take a string and make this conversion given a number of rows:\n\nstring convert(string s, int numRows);\n\n \nExample 1:\n\nInput: s = \"PAYPALISHIRING\", numRows = 3\nOutput: \"PAHNAPLSIIGYIR\"\n\nExample 2:\n\nInput: s = \"PAYPALISHIRING\", numRows = 4\nOutput: \"PINALSIGYAHRPI\"\nExplanation:\nP I N\nA L S I G\nY A H R\nP I\n\nExample 3:\n\nInput: s = \"A\", numRows = 1\nOutput: \"A\"\n\n \nConstraints:\n\n1 <= s.length <= 1000\ns consists of English letters (lower-case and upper-case), ',' and '.'.\n1 <= numRows <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"PAYPALISHIRING\",numRows = 4) == \"PINALSIGYAHRPI\"\n assert candidate(s = \"ABCDEFGHI\",numRows = 3) == \"AEIBDFHCG\"\n assert candidate(s = \"A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z\",numRows = 5) == \"AEIMQUY,,,,,,,,,,,,,BDFHJLNPRTVXZ,,,,,,,,,,,,CGKOSW\"\n assert candidate(s = \"PAYPALISHIRING\",numRows = 3) == \"PAHNAPLSIIGYIR\"\n assert candidate(s = \"A\",numRows = 1) == \"A\"\n assert candidate(s = \"HELLO\",numRows = 5) == \"HELLO\"\n assert candidate(s = \"ABCDEF\",numRows = 2) == \"ACEBDF\"\n assert candidate(s = \"HELLO WORLD\",numRows = 5) == \"HREOLLWDL O\"\n assert candidate(s = \"a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z\",numRows = 20) == \"atM,,,,,bsuLN,,,,,crvKO,,,,,dqwJP,,,,,epxIQ,,,,,foyHR,,,,,gnzGSZ,,,,,,hmAFTY,,,,,,ilBEUX,,,,,,jkCDVW,,,\"\n assert candidate(s = \"AB\",numRows = 1) == \"AB\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\",numRows = 5) == \"AIQYBHJPRXZCGKOSWDFLNTVEMU\"\n assert candidate(s = \"ABCD\",numRows = 2) == \"ACBD\"\n assert candidate(s = \"ABCDEFGHIJKL\",numRows = 4) == \"AGBFHLCEIKDJ\"\n assert candidate(s = \"HELLO.WORLD.\",numRows = 3) == \"HOREL.OL.LWD\"\n assert candidate(s = \"ABC\",numRows = 2) == \"ACB\"\n assert candidate(s = \"ABCDEFG\",numRows = 1) == \"ABCDEFG\"\n assert candidate(s = \"A,B.C\",numRows = 3) == \"AC,.B\"\n assert candidate(s = \"A,B,C,D,E,F,G\",numRows = 3) == \"ACEG,,,,,,BDF\"\n assert candidate(s = \"ABCDEFGHIJKL\",numRows = 3) == \"AEIBDFHJLCGK\"\n assert candidate(s = \"\",numRows = 1) == \"\"\n assert candidate(s = \"COMPLEX.EXAMPLE\",numRows = 6) == \"CAOXMMEPP.LLXEE\"\n assert candidate(s = \"A,B,C.,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.\",numRows = 7) == \"A,,,,,FGLMRSXYB,,,,,,,,,EHKNQTWZC,,,,,,,..DIJOPUV,,,,\"\n assert candidate(s = \"..............................\",numRows = 10) == \"..............................\"\n assert candidate(s = \"ZIGZAG\",numRows = 6) == \"ZIGZAG\"\n assert candidate(s = \"ThisIsATestOfTheEmergencyBroadcastSystem\",numRows = 10) == \"TeshmrytiEgSeseetmIhnssTcaAfycTOBdetraso\"\n assert candidate(s = \"The quick brown fox jumps over the lazy dog.\",numRows = 3) == \"Tqkofjsehadh uc rw o up vrtelz o.eibnxmo yg\"\n assert candidate(s = \"WithSpecialCharacters!@#$%^&*()\",numRows = 5) == \"Wic$icaat#%telre@^)hpCar!&(Shs*\"\n assert candidate(s = \"The quick brown fox jumps over the lazy dog.\",numRows = 8) == \"Tneghw vro.eofo d ro t qbxshyu pezikjm acul\"\n assert candidate(s = \"This,is,a,longer,string,with,punctuation!\",numRows = 7) == \"Tnwthog,iaiilegtuos,rnhtn,a,i,c!i,srpnstu\"\n assert candidate(s = \"\",numRows = 5) == \"\"\n assert candidate(s = \"Short\",numRows = 1) == \"Short\"\n assert candidate(s = \"Lorem.ipsum.dolor.sit.amet.consectetur.adipiscing.elit\",numRows = 12) == \"Laso.micrtepieitinms.dg..ca.iro.eponrlslsuiuoettmdce.t\"\n assert candidate(s = \"ABCD\",numRows = 1) == \"ABCD\"\n assert candidate(s = \"ZigzagPatternConversionIsCool.\",numRows = 7) == \"ZnsirCICgeonoztnooatvilgaes.Pr\"\n assert candidate(s = \"ZIGZAGCONVERSION\",numRows = 6) == \"ZEIVRGNSZOIACOGN\"\n assert candidate(s = \".,,..,.\",numRows = 3) == \"..,.,,.\"\n assert candidate(s = \"1234567890\",numRows = 2) == \"1357924680\"\n assert candidate(s = \"a.b.c.d.e.f.g.h.i.j.k.l.m.n.o.p.q.r.s.t.u.v.w.x.y.z.\",numRows = 12) == \"alw.....bkmvx.....cjnuy.....diotz.....ehps....fgqr..\"\n assert candidate(s = \"HELLOALLOHELLOALLOHELLOALLO\",numRows = 2) == \"HLOLOELALHLOLOELALHLOLOELAL\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\",numRows = 10) == \"asKbrtJLcquIMdpvHNZeowGOYfnxFPXgmyEQWhlzDRVikACSUjBT\"\n assert candidate(s = \"AnotherExampleWithALongerStringThatShouldBeChallengingToFormatCorrectly\",numRows = 8) == \"AWieFyneirnBCoololttgdhTrttphSTlagmchmArhulnaeeaLeaolitrrxogthegCrEnSno\"\n assert candidate(s = \"A\",numRows = 5) == \"A\"\n assert candidate(s = \"SHORT\",numRows = 25) == \"SHORT\"\n assert candidate(s = \"Zigzag.patters.are.pretty.cool.and.fascinating\",numRows = 10) == \"Z.aiepfsgrr.czaedia.tnngstaa.ry.tpe.liatcontog\"\n assert candidate(s = \"ZigZagConversion\",numRows = 6) == \"ZeivrgnsZoiaCogn\"\n assert candidate(s = \"PYTHONISAWESOMELANGUAGEFORTACKLINGCOMPLEXPROBLEMS\",numRows = 6) == \"PEALXYWSUGKIEPTAOGECNLRSHSMNFAGPOMOIEAOTCMBENLROL\"\n assert candidate(s = \"PYTHONPROGRAMMING\",numRows = 5) == \"POGYRGNTPRIHNAMOM\"\n assert candidate(s = \"BUTTERTOOMELON\",numRows = 3) == \"BEOOUTROMLNTTE\"\n assert candidate(s = \"1234567890abcdefghijklmnopqrstuvwxyz\",numRows = 7) == \"1co2bdnpz3aemqy40flrx59gksw68hjtv7iu\"\n assert candidate(s = \"ZIGZAGCONVERSION\",numRows = 8) == \"ZOIINGSZRAEGVCNO\"\n assert candidate(s = \"HELLOPYTHONHELLOPYTHONHELLOPYTHONHELLOPYTHON\",numRows = 8) == \"HLYOELOPTHNLEPOHTLHYLOYONTLNPPOHEHOYHOHELTNL\"\n assert candidate(s = \"A.B.C.D.E.F.G.H.I.J.K.L.M.N.O.P.Q.R.S.T.U.V.W.X.Y.Z.\",numRows = 5) == \"AEIMQUY.............BDFHJLNPRTVXZ.............CGKOSW\"\n assert candidate(s = \"ALGORITHMSANDDATASTRUCTURES\",numRows = 8) == \"AALDTGDASONSERATRISRUTMUTHC\"\n assert candidate(s = \"A.B.C.D.E.F.G.H.I.J.K.L.M.N.O.P.Q.R.S.T.U.V.W.X.Y.Z.\",numRows = 10) == \"AJS.....BIKRT......CHLQUZ......DGMPVY......EFNOWX...\"\n assert candidate(s = \"A.B.C.D.E.F.G.H.I.J.K.L.M.N.O.P.Q.R.S.T.U.V.W.X.Y.Z.\",numRows = 6) == \"AFKPUZ...........BEGJLOQTVY..........CDHIMNRSWX.....\"\n assert candidate(s = \"ToCodeOrNotToCode.\",numRows = 2) == \"TCdONtooeooeroTCd.\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\",numRows = 11) == \"auObtvNPcswMQdrxLReqyKSfpzJTgoAIUhnBHVimCGWjlDFXZkEY\"\n assert candidate(s = \"HELLO.WORLD.THIS.IS.A.TEST\",numRows = 8) == \"HIEHSLT.L.ITODSS.L.EWRATO.\"\n assert candidate(s = \"Lorem ipsum dolor sit amet, consectetur adipiscing elit.\",numRows = 6) == \"Lmtna ou i os dgersdsacerinlepo m cupiimilre,ttict otes.\"\n assert candidate(s = \"Longer.string.for.testing.the.zigzag.conversion\",numRows = 2) == \"Lne.tigfrtsigtezga.ovrinogrsrn.o.etn.h.izgcneso\"\n assert candidate(s = \"THISISAMUCHLONGERSTRINGTHANTHEPREVIOUSONES\",numRows = 9) == \"TREHESRVIGTPISNREOIOIHUSLNTSAHGNOMCTANSUHE\"\n assert candidate(s = \"REPEATEREPEATEREPEATEREPEATEREPEAT\",numRows = 15) == \"RREEEPTPEAEAEATPTEERREEPTEAAETPEER\"\n assert candidate(s = \"1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz\",numRows = 12) == \"1Mi2LNhj3KOgk4JPfl5IQem6HRdnz7GScoy8FTbpx9EUaqw0DVZrvACWYsuBXt\"\n assert candidate(s = \"HELLOWORLDTHISISATEST\",numRows = 7) == \"HIEHSLTILDSOLATWRTSOE\"\n assert candidate(s = \"AQuickBrownFoxJumpsOverTheLazyDog\",numRows = 11) == \"AvQOeusripTcmhkueBJLrxaoozgwFyonD\"\n assert candidate(s = \"123456789012345678901234567890\",numRows = 5) == \"197528068463715937462402805319\"\n assert candidate(s = \"........................................\",numRows = 4) == \"........................................\"\n assert candidate(s = \"ThisIsALongStringToTestTheFunctionalityOfTheZigZagConversion\",numRows = 7) == \"TthiahSrTeltZgnigitFaygCosnnsunOioiIogenofZnssLTTciTevrAothe\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\",numRows = 8) == \"AOBNPCMQDLRZEKSYFJTXGIUWHV\"\n assert candidate(s = \"HELLO.,WORLD.,HELLO.,WORLD.,HELLO.,WORLD.\",numRows = 10) == \"HOOEL.WRLL,,LLEW.DOHOO..,RL,.LLWDDEOL.HR,\"\n assert candidate(s = \"Short.string\",numRows = 1) == \"Short.string\"\n assert candidate(s = \"THISISALONGSTRINGFORTHETESTCASE\",numRows = 7) == \"TTEHSRTSIGIETSNNHCIOGTASLFRSAOE\"\n assert candidate(s = \"12345678901234567890\",numRows = 10) == \"19280374655647382910\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789\",numRows = 7) == \"AMYBLNXZ9CKOW08DJPV17EIQU26FHRT35GS4\"\n assert candidate(s = \"ONETWO,THREE,FOUR,FIVE,SIX,SEVEN,EIGHT,NINE,TEN\",numRows = 12) == \"O,TNES,EEVIENTIXNWF,IO,SN,RE,TUVTHOEHRFNGE,,IEE\"\n assert candidate(s = \"THEQUICK.BROWN.FOX.JUMPS.OVER.THE.LAZY.DOG.\",numRows = 5) == \"T.O.EOHKBFXSOH.DGECR..PVTL..QIONJME.AYUWURZ\"\n assert candidate(s = \"ALGORITHMSAREFUN\",numRows = 6) == \"AALSRGMEOHFRTUIN\"\n assert candidate(s = \"123456789012345678901234567890\",numRows = 6) == \"111202020393939484848575757666\"\n assert candidate(s = \"This.is.a.test.string\",numRows = 5) == \"Tath..srist.isietn.sg\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ\",numRows = 12) == \"AWSBVXRTCUYQUDTZPVESAOWFRBNXGQCMYHPDLZIOEKJNFJKMGILH\"\n assert candidate(s = \"AQUICKMOVEMENTOFTHEBROWNFOX\",numRows = 9) == \"ATQFHUOEITBCNRKEOMMWXOENOVF\"\n assert candidate(s = \"OneTwoThreeFourFiveSixSevenEightNineTenElevenTwelveThirteenFourteenFifteen\",numRows = 9) == \"OiNlenFvtievteerehnwernTuSgeTTuFwoiiTnhoioFxEeeiFfTeSnnvrntheeeEeteenrvlee\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",numRows = 13) == \"aybxzcwdveuftgshriqjpkolnm\"\n assert candidate(s = \"AVERYLONGSTRINGTHATWILLBETESTEDTOENSURETHECORRECTNESSOFTHETEST\",numRows = 20) == \"AEVRTEUHRSEYNCLEOOORNTRGDESECTTTRSNIEENTSGESTBOTHLFSALTETIHTWE\"\n assert candidate(s = \"Python.is.awesome.and.fun\",numRows = 9) == \"Peym.toahsnoednw..afi.usn\"\n assert candidate(s = \"\",numRows = 3) == \"\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ.,\",numRows = 5) == \"AIQYBHJPRXZCGKOSW.DFLNTV,EMU\"\n assert candidate(s = \"PythonIsFun\",numRows = 5) == \"PFysutInhno\"\n assert candidate(s = \"COMPLEXTESTCASEWITHVARYINGCHARS,.,\",numRows = 9) == \"CI.OWT,,MEHSPSVRLAAAECRHXTYCTSIGEN\"\n assert candidate(s = \"Mississippi\",numRows = 2) == \"Msispiissip\"\n assert candidate(s = \"PythonProgrammingIsFunAndEducational!\",numRows = 7) == \"Pmd!yamnEltriAdahgnnunooguconrIFaiPst\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\",numRows = 10) == \"ASBRTCQUDPVEOWFNXGMYHLZIKJ\"\n assert candidate(s = \"zigzagzigzagzigzagzigzagzigzagzigzagzigzag\",numRows = 4) == \"zzzzzzzigigigigigigiggagagagagagagazzzzzzz\"\n assert candidate(s = \"SOMETIMESGOODPROGRAMSMAKEYOUCRY\",numRows = 2) == \"SMTMSODRGASAEOCYOEIEGOPORMMKYUR\"\n assert candidate(s = \"REPEATEDCHARACTERSTESTCASEEEEEEEEEEEEEEEEEEEEEE\",numRows = 15) == \"REEEEPEEEEEASETAEECEDTECSEHEEATEERSEEAREECEEETE\"\n assert candidate(s = \"TheQuickBrownFoxJumpsOverTheLazyDog\",numRows = 6) == \"ToszhrwpOayeBnmvLDQkFueeoucoJrhgixT\"\n assert candidate(s = \"HELLO.,WORLD.,HELLO.,WORLD.\",numRows = 5) == \"HOLLEWRELRDL,LHOO.L.D,.WO.,\"\n assert candidate(s = \"AABBAABBCCDDEEFFGGHHIIJJKKLLMMNNOOPPQQRRSSTTUUVVWWXXYYZZ\",numRows = 12) == \"AJUAIJTUBIKTVBHKSVAHLSWAGLRWBGMRXBFMQXCFNQYCENPYDEOPZDOZ\"\n assert candidate(s = \"PYTHON.IS.A.GREAT.LANGUAGE.\",numRows = 4) == \"P.GLGYNI.R.AAETOSAETNU.H.AG\"\n assert candidate(s = \"MULTIPLELINESAREHERE.FIXEDFONTISNEAT.\",numRows = 15) == \"MNUOTLFITDSIENPXELIAEFTL..IENREESHAER\"\n assert candidate(s = \"MixedCASEAndNumbers123\",numRows = 4) == \"MANsiCSdur1xdEnme2eAb3\"\n assert candidate(s = \"PythonIsFunAndChallenging\",numRows = 5) == \"PFagysuhlntInClihnAdegonn\"\n assert candidate(s = \"S.P.E.C.I.A.L.,C.H.A.R.A.C.T.E.R.S.\",numRows = 9) == \"S...CHRSP,.....AEEL....RTCA....ACI.\"\n assert candidate(s = \"OneMoreExampleHere\",numRows = 10) == \"OneerMeoHreelEpxma\"\n"}, "metadata": {"canonical_parameter_names": ["s", "numRows"], "leetcode_dataset_entry_point": "Solution().convert", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var convert = function(s, numRows) {", "container": null, "callable": "convert", "parameters": [{"name": "s", "type": "string"}, {"name": "numRows", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 7, "task_id": "reverse-integer", "difficulty": "Medium", "problem_description": "Given a signed 32-bit integer x, return x with its digits reversed. If reversing x causes the value to go outside the signed 32-bit integer range [-231, 231 - 1], then return 0.\nAssume the environment does not allow you to store 64-bit integers (signed or unsigned).\n \nExample 1:\n\nInput: x = 123\nOutput: 321\n\nExample 2:\n\nInput: x = -123\nOutput: -321\n\nExample 3:\n\nInput: x = 120\nOutput: 21\n\n \nConstraints:\n\n-231 <= x <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(x = -2147483412) == -2143847412\n assert candidate(x = 2147483647) == 0\n assert candidate(x = 120) == 21\n assert candidate(x = -123) == -321\n assert candidate(x = 1534236469) == 0\n assert candidate(x = 0) == 0\n assert candidate(x = -2147483648) == 0\n assert candidate(x = -1534236469) == 0\n assert candidate(x = 123) == 321\n assert candidate(x = -10) == -1\n assert candidate(x = -100000) == -1\n assert candidate(x = 10) == 1\n assert candidate(x = -999999999) == -999999999\n assert candidate(x = 1) == 1\n assert candidate(x = 2147483646) == 0\n assert candidate(x = -123000) == -321\n assert candidate(x = -900000) == -9\n assert candidate(x = -100100100) == -1001001\n assert candidate(x = -2147483647) == 0\n assert candidate(x = -1010101010) == -101010101\n assert candidate(x = 1000000001) == 1000000001\n assert candidate(x = -1) == -1\n assert candidate(x = 123000) == 321\n assert candidate(x = -2000000002) == -2000000002\n assert candidate(x = 101010101) == 101010101\n assert candidate(x = 1111111111) == 1111111111\n assert candidate(x = 2147447412) == 2147447412\n assert candidate(x = -101010101) == -101010101\n assert candidate(x = 900000) == 9\n assert candidate(x = 987654321) == 123456789\n assert candidate(x = 999999999) == 999999999\n assert candidate(x = -1000000000) == -1\n assert candidate(x = 1001001001) == 1001001001\n assert candidate(x = -987654321) == -123456789\n assert candidate(x = -1000000001) == -1000000001\n assert candidate(x = 10000000000) == 1\n assert candidate(x = 11000000001) == 0\n assert candidate(x = 876543210) == 12345678\n assert candidate(x = 2147483640) == 463847412\n assert candidate(x = 100100100) == 1001001\n assert candidate(x = 100000) == 1\n assert candidate(x = 2000000002) == 2000000002\n assert candidate(x = -9646324351) == -1534236469\n assert candidate(x = -123456789) == -987654321\n assert candidate(x = 7463847412) == 2147483647\n assert candidate(x = -1000000003) == 0\n assert candidate(x = -3000000001) == -1000000003\n assert candidate(x = -876543210) == -12345678\n assert candidate(x = -1111111111) == -1111111111\n assert candidate(x = -1001001001) == -1001001001\n assert candidate(x = 9646324351) == 1534236469\n assert candidate(x = 1010101010) == 101010101\n assert candidate(x = 123456789) == 987654321\n assert candidate(x = -10000000000) == -1\n assert candidate(x = -2147483640) == -463847412\n assert candidate(x = -7463847412) == -2147483647\n assert candidate(x = 3000000001) == 1000000003\n assert candidate(x = 1000000000) == 1\n assert candidate(x = 1000000003) == 0\n assert candidate(x = -214748364) == -463847412\n assert candidate(x = 9000000000) == 9\n"}, "metadata": {"canonical_parameter_names": ["x"], "leetcode_dataset_entry_point": "Solution().reverse", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverse = function(x) {", "container": null, "callable": "reverse", "parameters": [{"name": "x", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 8, "task_id": "string-to-integer-atoi", "difficulty": "Medium", "problem_description": "Implement the myAtoi(string s) function, which converts a string to a 32-bit signed integer.\nThe algorithm for myAtoi(string s) is as follows:\n\nWhitespace: Ignore any leading whitespace (\" \").\nSignedness: Determine the sign by checking if the next character is '-' or '+', assuming positivity if neither present.\nConversion: Read the integer by skipping leading zeros until a non-digit character is encountered or the end of the string is reached. If no digits were read, then the result is 0.\nRounding: If the integer is out of the 32-bit signed integer range [-231, 231 - 1], then round the integer to remain in the range. Specifically, integers less than -231 should be rounded to -231, and integers greater than 231 - 1 should be rounded to 231 - 1.\n\nReturn the integer as the final result.\n \nExample 1:\n\nInput: s = \"42\"\nOutput: 42\nExplanation:\n\nThe underlined characters are what is read in and the caret is the current reader position.\nStep 1: \"42\" (no characters read because there is no leading whitespace)\n ^\nStep 2: \"42\" (no characters read because there is neither a '-' nor '+')\n ^\nStep 3: \"42\" (\"42\" is read in)\n ^\n\n\nExample 2:\n\nInput: s = \" -042\"\nOutput: -42\nExplanation:\n\nStep 1: \" -042\" (leading whitespace is read and ignored)\n ^\nStep 2: \" -042\" ('-' is read, so the result should be negative)\n ^\nStep 3: \" -042\" (\"042\" is read in, leading zeros ignored in the result)\n ^\n\n\nExample 3:\n\nInput: s = \"1337c0d3\"\nOutput: 1337\nExplanation:\n\nStep 1: \"1337c0d3\" (no characters read because there is no leading whitespace)\n ^\nStep 2: \"1337c0d3\" (no characters read because there is neither a '-' nor '+')\n ^\nStep 3: \"1337c0d3\" (\"1337\" is read in; reading stops because the next character is a non-digit)\n ^\n\n\nExample 4:\n\nInput: s = \"0-1\"\nOutput: 0\nExplanation:\n\nStep 1: \"0-1\" (no characters read because there is no leading whitespace)\n ^\nStep 2: \"0-1\" (no characters read because there is neither a '-' nor '+')\n ^\nStep 3: \"0-1\" (\"0\" is read in; reading stops because the next character is a non-digit)\n ^\n\n\nExample 5:\n\nInput: s = \"words and 987\"\nOutput: 0\nExplanation:\nReading stops at the first non-digit character 'w'.\n\n \nConstraints:\n\n0 <= s.length <= 200\ns consists of English letters (lower-case and upper-case), digits (0-9), ' ', '+', '-', and '.'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"2147483647\") == 2147483647\n assert candidate(s = \"42 with words\") == 42\n assert candidate(s = \"20000000000000000000000000000000000000000\") == 2147483647\n assert candidate(s = \"-2147483649\") == -2147483648\n assert candidate(s = \"-21474836480\") == -2147483648\n assert candidate(s = \" 000000000000 \") == 0\n assert candidate(s = \"+1\") == 1\n assert candidate(s = \" - 42\") == 0\n assert candidate(s = \"words with 42\") == 0\n assert candidate(s = \" -042\") == -42\n assert candidate(s = \"0-1\") == 0\n assert candidate(s = \" 0\") == 0\n assert candidate(s = \"-5\") == -5\n assert candidate(s = \" -119197303367810844 \") == -2147483648\n assert candidate(s = \" -12345\") == -12345\n assert candidate(s = \" \") == 0\n assert candidate(s = \" -042\") == -42\n assert candidate(s = \" -88827 5655 U\") == -88827\n assert candidate(s = \"+-12\") == 0\n assert candidate(s = \" +0 123\") == 0\n assert candidate(s = \"+2\") == 2\n assert candidate(s = \" +0 91283472332\") == 0\n assert candidate(s = \" - 42\") == 0\n assert candidate(s = \"words and 987\") == 0\n assert candidate(s = \"3.14159\") == 3\n assert candidate(s = \" 20000000000000000000\") == 2147483647\n assert candidate(s = \"0000000000012345678\") == 12345678\n assert candidate(s = \".\") == 0\n assert candidate(s = \"2147483648\") == 2147483647\n assert candidate(s = \"\") == 0\n assert candidate(s = \" 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\") == 0\n assert candidate(s = \"-\") == 0\n assert candidate(s = \"42\") == 42\n assert candidate(s = \"-91283472332\") == -2147483648\n assert candidate(s = \"4193 with words\") == 4193\n assert candidate(s = \" 3.14159\") == 3\n assert candidate(s = \" +0 123\") == 0\n assert candidate(s = \" +123\") == 123\n assert candidate(s = \" +42\") == 42\n assert candidate(s = \" +12345\") == 12345\n assert candidate(s = \" +42\") == 42\n assert candidate(s = \"0000000000000\") == 0\n assert candidate(s = \" \") == 0\n assert candidate(s = \"00000000000000\") == 0\n assert candidate(s = \" +42\") == 42\n assert candidate(s = \"1337c0d3\") == 1337\n assert candidate(s = \" +0 91283472332 456\") == 0\n assert candidate(s = \" 21474836460\") == 2147483647\n assert candidate(s = \"+\") == 0\n assert candidate(s = \" -00130\") == -130\n assert candidate(s = \"00000000000123456789\") == 123456789\n assert candidate(s = \" -0012a42\") == -12\n assert candidate(s = \" +3.14\") == 3\n assert candidate(s = \"21474836478\") == 2147483647\n assert candidate(s = \"-2147483648\") == -2147483648\n assert candidate(s = \"-21474836489\") == -2147483648\n assert candidate(s = \" + 413\") == 0\n assert candidate(s = \" -2147483649\") == -2147483648\n assert candidate(s = \" 21474836470000000000000000\") == 2147483647\n assert candidate(s = \" 9223372036854775808\") == 2147483647\n assert candidate(s = \" 2147483647abc\") == 2147483647\n assert candidate(s = \" -123 456\") == -123\n assert candidate(s = \" 0000123\") == 123\n assert candidate(s = \" 21474836470000000000000000000000\") == 2147483647\n assert candidate(s = \" 2147483647000000000000000\") == 2147483647\n assert candidate(s = \" 2147483647 -\") == 2147483647\n assert candidate(s = \" 214748364700000000000000000000\") == 2147483647\n assert candidate(s = \" abcdefghijklmnopqrstuvwxyz\") == 0\n assert candidate(s = \" 21474836470000000000000000000\") == 2147483647\n assert candidate(s = \" 000000000000000000000000000000000000000000000000000 -123\") == 0\n assert candidate(s = \" +2147483649\") == 2147483647\n assert candidate(s = \" +0\") == 0\n assert candidate(s = \" 2147483648\") == 2147483647\n assert candidate(s = \" 2147483647000000000000000000000\") == 2147483647\n assert candidate(s = \" -21474836480000\") == -2147483648\n assert candidate(s = \" -214748364800000000000000000\") == -2147483648\n assert candidate(s = \" 9223372036854775807\") == 2147483647\n assert candidate(s = \" -214748364800000\") == -2147483648\n assert candidate(s = \" -21474836480000000000000000000000\") == -2147483648\n assert candidate(s = \" -21474836480000000\") == -2147483648\n assert candidate(s = \" -12345678901234567890123456789012345678901234567890\") == -2147483648\n assert candidate(s = \" -214748364800\") == -2147483648\n assert candidate(s = \" 2147483647000000000000000000000000000\") == 2147483647\n assert candidate(s = \" 0000000000000 +123abc\") == 0\n assert candidate(s = \" -214748364800000000\") == -2147483648\n assert candidate(s = \" -21474836480000000000000000000000000000\") == -2147483648\n assert candidate(s = \" 21474836470000000\") == 2147483647\n assert candidate(s = \" +000000000000000000000000000000123\") == 123\n assert candidate(s = \" 2147483647000000000000000000000000\") == 2147483647\n assert candidate(s = \" -0000000000000000000000000000000000000000000000000000000000000001\") == -1\n assert candidate(s = \" 000000000000000000000000000000000000000000000000000 123\") == 0\n assert candidate(s = \" -21474836480\") == -2147483648\n assert candidate(s = \" -2147483648000000000000\") == -2147483648\n assert candidate(s = \" -2147483648 0\") == -2147483648\n assert candidate(s = \" -214748364800000000000000000000\") == -2147483648\n assert candidate(s = \" -214748364800000000000000000000000000\") == -2147483648\n assert candidate(s = \" -9223372036854775808\") == -2147483648\n assert candidate(s = \" -214748364800000000000000000000000000000\") == -2147483648\n assert candidate(s = \" 21474836470000000000000000000000000\") == 2147483647\n assert candidate(s = \" -2147483648000\") == -2147483648\n assert candidate(s = \" -2147483648\") == -2147483648\n assert candidate(s = \" -2147483648extra\") == -2147483648\n assert candidate(s = \" -2147483648000000000000000000000000\") == -2147483648\n assert candidate(s = \" 214748364700000000000\") == 2147483647\n assert candidate(s = \" +2147483647extra\") == 2147483647\n assert candidate(s = \" -2147483648abc\") == -2147483648\n assert candidate(s = \" -2147483648\") == -2147483648\n assert candidate(s = \" 214748364700000000000000000000000\") == 2147483647\n assert candidate(s = \" +000\") == 0\n assert candidate(s = \" -9223372036854775809\") == -2147483648\n assert candidate(s = \" 214748364700000000000000\") == 2147483647\n assert candidate(s = \" 0000000000000000000000000000000000000000000000000001\") == 1\n assert candidate(s = \" -0\") == 0\n assert candidate(s = \" +0000000000000000000000000000000000000000000000000000000000000001\") == 1\n assert candidate(s = \" 010\") == 10\n assert candidate(s = \" 2147483647000000\") == 2147483647\n assert candidate(s = \" -21474836480000000000000000000\") == -2147483648\n assert candidate(s = \"000000000000000000000000000000000000000000000000000\") == 0\n assert candidate(s = \" -2147483648000000000000000\") == -2147483648\n assert candidate(s = \"-0000000000000000000000000000000000000000000000000001\") == -1\n assert candidate(s = \" -2147483648000000000000000000\") == -2147483648\n assert candidate(s = \" 2147483646\") == 2147483646\n assert candidate(s = \" 214748364700000000000000000000000000000\") == 2147483647\n assert candidate(s = \" 2147483647000\") == 2147483647\n assert candidate(s = \" 12345678901234567890123456789012345678901234567890\") == 2147483647\n assert candidate(s = \" 0000-123\") == 0\n assert candidate(s = \" -2147483648 -\") == -2147483648\n assert candidate(s = \" 000000000000000000000000000000000000000000000000000 +123\") == 0\n assert candidate(s = \" 123 456\") == 123\n assert candidate(s = \" +2147483647 0\") == 2147483647\n assert candidate(s = \" 2147483648\") == 2147483647\n assert candidate(s = \" 2147483647extra\") == 2147483647\n assert candidate(s = \" 2147483647000000000000\") == 2147483647\n assert candidate(s = \" 214748364700000000000000000\") == 2147483647\n assert candidate(s = \" 21474836470000\") == 2147483647\n assert candidate(s = \" 0000000000000000000000000000000000000000000000000000000000000000+1\") == 0\n assert candidate(s = \" -214748364800000000000000\") == -2147483648\n assert candidate(s = \" -2147483648000000\") == -2147483648\n assert candidate(s = \" -2147483648000000000000000000000\") == -2147483648\n assert candidate(s = \" -000000000000000000000000000000123\") == -123\n assert candidate(s = \" +2147483648\") == 2147483647\n assert candidate(s = \" 214748364700\") == 2147483647\n assert candidate(s = \" +2147483647 +\") == 2147483647\n assert candidate(s = \" 00000000000000000000000000000000000000000000000000000000000000001\") == 1\n assert candidate(s = \" +1234567890123456789012345678901234567890\") == 2147483647\n assert candidate(s = \" -214748364800000000000000000000000\") == -2147483648\n assert candidate(s = \" -2147483648000000000\") == -2147483648\n assert candidate(s = \" !@#$%^&*()_+\") == 0\n assert candidate(s = \" 0000+123\") == 0\n assert candidate(s = \" -21474836480000000000\") == -2147483648\n assert candidate(s = \" -1234567890123456789012345678901234567890\") == -2147483648\n assert candidate(s = \" -2147483646\") == -2147483646\n assert candidate(s = \" -21474836480000000000000000000000000\") == -2147483648\n assert candidate(s = \" 2147483647\") == 2147483647\n assert candidate(s = \" 214748364700000000000000000000000000\") == 2147483647\n assert candidate(s = \" -214748364800000000000\") == -2147483648\n assert candidate(s = \" +2147483647abc\") == 2147483647\n assert candidate(s = \" 21474836470\") == 2147483647\n assert candidate(s = \" 0000000000000 123abc\") == 0\n assert candidate(s = \" 21474836470000000000\") == 2147483647\n assert candidate(s = \" +123 456\") == 123\n assert candidate(s = \" 2147483647000000000000000000\") == 2147483647\n assert candidate(s = \" 0000000000000000000000000000000000000000000000000000000000000000-1\") == 0\n assert candidate(s = \" ABCDEFGHIJKLMNOPQRSTUVWXYZ\") == 0\n assert candidate(s = \" -2147483648000000000000000000000000000\") == -2147483648\n assert candidate(s = \" -2147483649\") == -2147483648\n assert candidate(s = \"-+12\") == 0\n assert candidate(s = \" +2147483647\") == 2147483647\n assert candidate(s = \" 18446744073709551616\") == 2147483647\n assert candidate(s = \" +0000000000000000000000000000000000000000000123\") == 123\n assert candidate(s = \" 00000000000000000000000000000000000000000000000000000000000000000\") == 0\n assert candidate(s = \" 21474836470000000000000\") == 2147483647\n assert candidate(s = \" 214748364700000\") == 2147483647\n assert candidate(s = \" 2147483647000000000\") == 2147483647\n assert candidate(s = \" 0000000000000 -123abc\") == 0\n assert candidate(s = \" 0000000000000 -00001\") == 0\n assert candidate(s = \" -000\") == 0\n assert candidate(s = \" 214748364700000000\") == 2147483647\n assert candidate(s = \" -2147483647\") == -2147483647\n assert candidate(s = \" 21474836470000000000000000000000000000\") == 2147483647\n assert candidate(s = \" -21474836480000000000000\") == -2147483648\n assert candidate(s = \" -21474836480000000000000000\") == -2147483648\n assert candidate(s = \" -2147483648 +\") == -2147483648\n assert candidate(s = \" 0000000000000 +00001\") == 0\n assert candidate(s = \" 2147483647\") == 2147483647\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().myAtoi", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var myAtoi = function(s) {", "container": null, "callable": "myAtoi", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 9, "task_id": "palindrome-number", "difficulty": "Easy", "problem_description": "Given an integer x, return true if x is a palindrome, and false otherwise.\n \nExample 1:\n\nInput: x = 121\nOutput: true\nExplanation: 121 reads as 121 from left to right and from right to left.\n\nExample 2:\n\nInput: x = -121\nOutput: false\nExplanation: From left to right, it reads -121. From right to left, it becomes 121-. Therefore it is not a palindrome.\n\nExample 3:\n\nInput: x = 10\nOutput: false\nExplanation: Reads 01 from right to left. Therefore it is not a palindrome.\n\n \nConstraints:\n\n-231 <= x <= 231 - 1\n\n \nFollow up: Could you solve it without converting the integer to a string?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(x = 1221) == True\n assert candidate(x = 10) == False\n assert candidate(x = 123421) == False\n assert candidate(x = 1) == True\n assert candidate(x = -121) == False\n assert candidate(x = 12345678987654321) == True\n assert candidate(x = 123456) == False\n assert candidate(x = -2147483648) == False\n assert candidate(x = 1000000001) == True\n assert candidate(x = 1111111111) == True\n assert candidate(x = 0) == True\n assert candidate(x = 123321) == True\n assert candidate(x = 2147483647) == False\n assert candidate(x = 1000021) == False\n assert candidate(x = -1000021) == False\n assert candidate(x = 12321) == True\n assert candidate(x = 1234321) == True\n assert candidate(x = -12321) == False\n assert candidate(x = 121) == True\n assert candidate(x = -1221) == False\n assert candidate(x = 999999999999999999) == True\n assert candidate(x = 123456789987654321) == True\n assert candidate(x = 10000000000000000000000000000000000001) == True\n assert candidate(x = 1100110011) == True\n assert candidate(x = 12210000221) == False\n assert candidate(x = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) == False\n assert candidate(x = 12345678987654322) == False\n assert candidate(x = 987656789) == True\n assert candidate(x = 100000000000000001) == True\n assert candidate(x = 1234567890987654321) == True\n assert candidate(x = 100000000000000000001) == True\n assert candidate(x = 101010101) == True\n assert candidate(x = 1001001) == True\n assert candidate(x = 12300321) == True\n assert candidate(x = 2147447412) == True\n assert candidate(x = 12345677654321) == True\n assert candidate(x = 98765432112345678) == False\n assert candidate(x = 10000000001) == True\n assert candidate(x = 10000000000000000000) == False\n assert candidate(x = 12345654321) == True\n assert candidate(x = 999999999) == True\n assert candidate(x = 987898789) == True\n assert candidate(x = 1000000000000000000000000000000000001) == True\n assert candidate(x = -1000000001) == False\n assert candidate(x = 1000000000000000001) == True\n assert candidate(x = 2121212121) == False\n assert candidate(x = 123321000) == False\n assert candidate(x = 1001) == True\n assert candidate(x = 1234567899876543210) == False\n assert candidate(x = 1230321) == True\n assert candidate(x = 12211221) == True\n assert candidate(x = 1002001) == True\n assert candidate(x = 10000200001) == True\n assert candidate(x = 98789) == True\n assert candidate(x = 123454321) == True\n assert candidate(x = 98765432123456789) == True\n assert candidate(x = 100000000000000000000000000000000000000000000000001) == True\n assert candidate(x = 100000000000000000000000000000000000000) == False\n assert candidate(x = 123321123321) == True\n assert candidate(x = 1111111111111111111) == True\n assert candidate(x = 1000000000) == False\n"}, "metadata": {"canonical_parameter_names": ["x"], "leetcode_dataset_entry_point": "Solution().isPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPalindrome = function(x) {", "container": null, "callable": "isPalindrome", "parameters": [{"name": "x", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 10, "task_id": "regular-expression-matching", "difficulty": "Hard", "problem_description": "Given an input string s and a pattern p, implement regular expression matching with support for '.' and '*' where:\n\n'.' Matches any single character.​​​​\n'*' Matches zero or more of the preceding element.\n\nThe matching should cover the entire input string (not partial).\n \nExample 1:\n\nInput: s = \"aa\", p = \"a\"\nOutput: false\nExplanation: \"a\" does not match the entire string \"aa\".\n\nExample 2:\n\nInput: s = \"aa\", p = \"a*\"\nOutput: true\nExplanation: '*' means zero or more of the preceding element, 'a'. Therefore, by repeating 'a' once, it becomes \"aa\".\n\nExample 3:\n\nInput: s = \"ab\", p = \".*\"\nOutput: true\nExplanation: \".*\" means \"zero or more (*) of any character (.)\".\n\n \nConstraints:\n\n1 <= s.length <= 20\n1 <= p.length <= 20\ns contains only lowercase English letters.\np contains only lowercase English letters, '.', and '*'.\nIt is guaranteed for each appearance of the character '*', there will be a previous valid character to match.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aa\",p = \"a*\") == True\n assert candidate(s = \"aab\",p = \"c*a*b\") == True\n assert candidate(s = \"ab\",p = \".*\") == True\n assert candidate(s = \"aa\",p = \"a\") == False\n assert candidate(s = \"mississippi\",p = \"mis*is*p*.\") == False\n assert candidate(s = \"aabbccddeeff\",p = \"a*b*c*d*e*f*f*\") == True\n assert candidate(s = \"abababa\",p = \"(ab)*a\") == False\n assert candidate(s = \"abcde\",p = \"a*.*e\") == True\n assert candidate(s = \"ababcd\",p = \"a.*a.*d\") == True\n assert candidate(s = \"aabbbbc\",p = \"a*b*c\") == True\n assert candidate(s = \"aaaaaa\",p = \"a*a*a*a*a*a\") == True\n assert candidate(s = \"aabb\",p = \"ab*a*b*\") == True\n assert candidate(s = \"abcccccaaaa\",p = \"ab*c*a*.*\") == True\n assert candidate(s = \"abcdef\",p = \"abc.*f\") == True\n assert candidate(s = \"ababab\",p = \"(ab)*\") == False\n assert candidate(s = \"ab\",p = \"a*b*c*d*.*e*\") == True\n assert candidate(s = \"xaymz\",p = \"x.*z\") == True\n assert candidate(s = \"xaybz\",p = \"xa*y*b*z\") == True\n assert candidate(s = \"abcdefgh\",p = \"a*d*fh\") == False\n assert candidate(s = \"aaa\",p = \"a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a*a\") == True\n assert candidate(s = \"mississippi\",p = \"mi*ss*is*si*p*i*\") == True\n assert candidate(s = \"zzzz\",p = \"z*\") == True\n assert candidate(s = \"abcdefgh\",p = \"a.h\") == False\n assert candidate(s = \"ababab\",p = \"(ab)*b*\") == False\n assert candidate(s = \"abcdefgh\",p = \"a.*h\") == True\n assert candidate(s = \"mississippi\",p = \"mi.*is.*p*i\") == True\n assert candidate(s = \"abcdefgh\",p = \"abcdefgh\") == True\n assert candidate(s = \"abcdefg\",p = \"a*bc.d*efg\") == True\n assert candidate(s = \"abcdefgh\",p = \"a*b*c*d*e*f*g*h\") == True\n assert candidate(s = \"abcdefgh\",p = \"a*b*c*d*e*f*g*h*\") == True\n assert candidate(s = \"abcd\",p = \"a.b.c.d\") == False\n assert candidate(s = \"aabbcc\",p = \"a*b*c*c\") == True\n assert candidate(s = \"abc\",p = \"abc.\") == False\n assert candidate(s = \"mississippi\",p = \"m*is*i*s*i*p*i\") == True\n assert candidate(s = \"mississippi\",p = \"m*i*ss*i*p*i*\") == False\n assert candidate(s = \"abcde\",p = \"a.*de\") == True\n assert candidate(s = \"abcdeabcde\",p = \"abc*de*abc*de*\") == True\n assert candidate(s = \"abcd\",p = \"a*b*c*d*\") == True\n assert candidate(s = \"abcde\",p = \"a*.b*c*e*\") == False\n assert candidate(s = \"aabbbcccddd\",p = \"a*b*c*d*\") == True\n assert candidate(s = \"abc\",p = \"a.b.c\") == False\n assert candidate(s = \"abababab\",p = \"(ab)*\") == False\n assert candidate(s = \"hello\",p = \"he*llo*\") == True\n assert candidate(s = \"hello\",p = \"he.*o\") == True\n assert candidate(s = \"abcd\",p = \"d*\") == False\n assert candidate(s = \"abcde\",p = \"a..de\") == True\n assert candidate(s = \"abcabcabcabc\",p = \"(abc)*d\") == False\n assert candidate(s = \"abcdabcd\",p = \"abcd*\") == False\n assert candidate(s = \"aabb\",p = \"aab*b*\") == True\n assert candidate(s = \"xyzzy\",p = \"x*zy\") == False\n assert candidate(s = \"abcd\",p = \"a.*d\") == True\n assert candidate(s = \"xxyyzz\",p = \"x*y*z*\") == True\n assert candidate(s = \"abc\",p = \"a.c\") == True\n assert candidate(s = \"xyxxyxyx\",p = \"(xy)*x\") == False\n assert candidate(s = \"aabbbccc\",p = \"a*b*c*\") == True\n assert candidate(s = \"abcabcabcabc\",p = \"(abc)*\") == False\n assert candidate(s = \"abcdef\",p = \"a*bcdef\") == True\n assert candidate(s = \"aaaab\",p = \"a*b*\") == True\n assert candidate(s = \"complex\",p = \"c*o*m*p*l*e*x*\") == True\n assert candidate(s = \"aaa\",p = \"a*a\") == True\n assert candidate(s = \"xyz\",p = \"x*y*z*\") == True\n assert candidate(s = \"abcdefgh\",p = \"a.*g\") == False\n assert candidate(s = \"abcde\",p = \"a*b.c*d*e*\") == True\n assert candidate(s = \"abcde\",p = \"a*b*c*d*e*\") == True\n assert candidate(s = \"zzzzzzzzzzzz\",p = \"z*z*z*z*z*z*z*z*z*z*z*z*z*z*z*z*z*\") == True\n assert candidate(s = \"aabbccddeeff\",p = \"a*b*c*d*e*f*\") == True\n assert candidate(s = \"hello\",p = \"he.*\") == True\n assert candidate(s = \"abcde\",p = \"a*b*c*d.e\") == False\n assert candidate(s = \"aaaaabbb\",p = \"a*b*.*\") == True\n assert candidate(s = \"aabbccddeeffgghh\",p = \"a*b*c*d*e*f*g*h*\") == True\n assert candidate(s = \"abbabb\",p = \"a*b*b*\") == False\n assert candidate(s = \"sequence\",p = \"s.e*q*u*e*n*c*e*\") == True\n assert candidate(s = \"abcdabcd\",p = \"a*b*c*d*\") == False\n assert candidate(s = \"abcdedef\",p = \"abcd*e*f*\") == False\n assert candidate(s = \"abcdefgh\",p = \"a.b.c.d.e.f.g.h\") == False\n assert candidate(s = \"mississippi\",p = \"mi.*.pi.*\") == True\n assert candidate(s = \"hello\",p = \"he*ll*o\") == True\n assert candidate(s = \"abcde\",p = \"a*bc.e*\") == True\n assert candidate(s = \"aaaab\",p = \"a*a*a*a\") == False\n assert candidate(s = \"abcde\",p = \"a.*e\") == True\n assert candidate(s = \"aabbb\",p = \"a*b*b\") == True\n assert candidate(s = \"regex\",p = \"r.e*g*e*x*\") == True\n assert candidate(s = \"abcdef\",p = \"a*b*c*d*e*f*\") == True\n assert candidate(s = \"aaaa\",p = \"a*a*a*a\") == True\n assert candidate(s = \"teststring\",p = \"te*t*st*ring\") == False\n assert candidate(s = \"abcde\",p = \"a*b*c*de\") == True\n assert candidate(s = \"bbbac\",p = \"ba*ac\") == False\n assert candidate(s = \"aabbccddeeffgg\",p = \"a*b*c*d*e*f*g*\") == True\n assert candidate(s = \"abcde\",p = \"a*bc*de\") == True\n assert candidate(s = \"xyxyxyxyxyx\",p = \"x.y.x.y.x.y.x.y.x.y.x\") == False\n assert candidate(s = \"a\",p = \"a*a*a*a*\") == True\n assert candidate(s = \"abababab\",p = \"a*b*a*b*a*b*a*b\") == True\n assert candidate(s = \"abcdeabcdeabcde\",p = \"abc*de*abc*de*abc*de*f*\") == True\n assert candidate(s = \"abbbba\",p = \"ab*ba\") == True\n assert candidate(s = \"teststring\",p = \"t.*st.*r.*ing\") == True\n assert candidate(s = \"abcabc\",p = \"abc*\") == False\n assert candidate(s = \"abcd\",p = \"a*b*c*d*.*\") == True\n assert candidate(s = \"zzzzzzzzzzzz\",p = \"z*\") == True\n assert candidate(s = \"mississippi\",p = \"m.*s*is*p*i*.*\") == True\n assert candidate(s = \"abcdefgh\",p = \".*\") == True\n assert candidate(s = \"abcdefg\",p = \".*f.*\") == True\n assert candidate(s = \"abccde\",p = \"abc*d*e\") == True\n assert candidate(s = \"aabbbccdd\",p = \"aa*bbb*cc*dd*\") == True\n assert candidate(s = \"foobar\",p = \"fo*oba*r\") == True\n assert candidate(s = \"abcde\",p = \"a.*f\") == False\n assert candidate(s = \"aabb\",p = \"a*b*b*a*\") == True\n assert candidate(s = \"zabczabcz\",p = \"z*abc*z*\") == False\n assert candidate(s = \"aaaabbbb\",p = \"a*b*b*\") == True\n assert candidate(s = \"aabbcc\",p = \"a*b*b*c*c*\") == True\n assert candidate(s = \"abc\",p = \"a*b*c*\") == True\n assert candidate(s = \"abcdeabcdeabcde\",p = \"abc*de*abc*de*abc*de*\") == True\n assert candidate(s = \"abcde\",p = \"a*c*e\") == False\n assert candidate(s = \"xyzzaz\",p = \"x*y*.*z*\") == True\n assert candidate(s = \"ababab\",p = \"(ab)*b\") == False\n assert candidate(s = \"abcdef\",p = \"abc.def\") == False\n assert candidate(s = \"xyx\",p = \"x*y*x*\") == True\n assert candidate(s = \"aaaaaa\",p = \"a*a*a*a*\") == True\n assert candidate(s = \"abbb\",p = \"ab*\") == True\n assert candidate(s = \"a\",p = \".\") == True\n assert candidate(s = \"abcdexyz\",p = \"abc.*xyz\") == True\n assert candidate(s = \"aabbcc\",p = \"a*b*c*\") == True\n assert candidate(s = \"leetcode\",p = \"le.*e.*tcode\") == True\n assert candidate(s = \"aaa\",p = \"ab*a*c*a\") == True\n assert candidate(s = \"abcd\",p = \"a.d\") == False\n assert candidate(s = \"xylophone\",p = \"x.l*o.h.p*ne\") == True\n assert candidate(s = \"abcde\",p = \".*\") == True\n assert candidate(s = \"abxyzbcd\",p = \"ab.*bc*d\") == True\n assert candidate(s = \"zzzzz\",p = \"z*\") == True\n assert candidate(s = \"aaa\",p = \"a*a*\") == True\n assert candidate(s = \"aaaaaaab\",p = \"a*a*a*a*a*a*a*b\") == True\n assert candidate(s = \"hello world\",p = \"h.*o w*r*d\") == False\n assert candidate(s = \"abcdefgh\",p = \"a.*b.*c.*d.*e.*f.*g.*h\") == True\n assert candidate(s = \"hello\",p = \"h.l.o\") == True\n assert candidate(s = \"abcd\",p = \"a.b*c.d\") == False\n assert candidate(s = \"abcdefgh\",p = \"abcdefgh.\") == False\n assert candidate(s = \"a\",p = \"ab*a\") == False\n assert candidate(s = \"patternmatching\",p = \"pat*tern*m*atching*\") == True\n assert candidate(s = \"abcabcabc\",p = \"(abc)*\") == False\n assert candidate(s = \"ababab\",p = \"(ab)*ab*\") == False\n assert candidate(s = \"abcd\",p = \"a.c*d*\") == True\n assert candidate(s = \"a\",p = \".*\") == True\n assert candidate(s = \"abcdef\",p = \"abcd.e*f\") == True\n assert candidate(s = \"aabb\",p = \"a*bb\") == True\n assert candidate(s = \"abcdefgh\",p = \"abcdefgh*\") == True\n assert candidate(s = \"aaa\",p = \"a*a*a*a*a*a*\") == True\n assert candidate(s = \"aaaaaa\",p = \"a*a*a*a*a*a*\") == True\n assert candidate(s = \"abab\",p = \"(ab)*\") == False\n assert candidate(s = \"mississippi\",p = \"mi*s*is*ip*pi*s*\") == True\n assert candidate(s = \"aaaaab\",p = \"a*ba*\") == True\n assert candidate(s = \"abc\",p = \".b.\") == True\n assert candidate(s = \"abcd\",p = \"a*b.c*d*\") == True\n"}, "metadata": {"canonical_parameter_names": ["s", "p"], "leetcode_dataset_entry_point": "Solution().isMatch", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isMatch = function(s, p) {", "container": null, "callable": "isMatch", "parameters": [{"name": "s", "type": "string"}, {"name": "p", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 11, "task_id": "container-with-most-water", "difficulty": "Medium", "problem_description": "You are given an integer array height of length n. There are n vertical lines drawn such that the two endpoints of the ith line are (i, 0) and (i, height[i]).\nFind two lines that together with the x-axis form a container, such that the container contains the most water.\nReturn the maximum amount of water a container can store.\nNotice that you may not slant the container.\n \nExample 1:\n\n\nInput: height = [1,8,6,2,5,4,8,3,7]\nOutput: 49\nExplanation: The above vertical lines are represented by array [1,8,6,2,5,4,8,3,7]. In this case, the max area of water (blue section) the container can contain is 49.\n\nExample 2:\n\nInput: height = [1,1]\nOutput: 1\n\n \nConstraints:\n\nn == height.length\n2 <= n <= 105\n0 <= height[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(height = [1, 1]) == 1\n assert candidate(height = [4, 3, 2, 1, 4]) == 16\n assert candidate(height = [8, 10, 14, 0, 13, 10, 9, 9, 8, 9]) == 72\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7]) == 49\n assert candidate(height = [2, 3, 4, 5, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 81\n assert candidate(height = [2, 3, 10, 5, 7, 8, 9]) == 36\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 25\n assert candidate(height = [1, 2, 4, 3]) == 4\n assert candidate(height = [1, 2, 3, 4, 5]) == 6\n assert candidate(height = [1, 3, 2, 5, 25, 24, 5]) == 24\n assert candidate(height = [1, 2, 1]) == 2\n assert candidate(height = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 25\n assert candidate(height = [1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1]) == 220000\n assert candidate(height = [5, 8, 6, 2, 5, 4, 8, 3, 7, 9, 10, 11, 10, 9, 7, 3, 8, 4, 5, 2, 6, 8, 5, 3, 7, 9, 1, 4, 6, 8]) == 224\n assert candidate(height = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 160\n assert candidate(height = [10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1]) == 180\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 120\n assert candidate(height = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 200\n assert candidate(height = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 56\n assert candidate(height = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == 50\n assert candidate(height = [5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5]) == 128\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 10000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 19\n assert candidate(height = [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000]) == 300000\n assert candidate(height = [1, 3, 2, 5, 25, 24, 5, 2, 3, 1]) == 24\n assert candidate(height = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 190\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 50\n assert candidate(height = [5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000, 5000]) == 45000\n assert candidate(height = [2, 1, 5, 6, 2, 3, 1, 4, 5, 1, 5, 6, 2, 3, 1, 4, 5, 1]) == 70\n assert candidate(height = [10000, 9000, 8000, 7000, 6000, 5000, 4000, 3000, 2000, 1000]) == 25000\n assert candidate(height = [10000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 25\n assert candidate(height = [5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 90\n assert candidate(height = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 180\n assert candidate(height = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 120\n assert candidate(height = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10]) == 66\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 100\n assert candidate(height = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 2000\n assert candidate(height = [1000, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 29\n assert candidate(height = [2, 3, 10, 5, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 240\n assert candidate(height = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 90\n assert candidate(height = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986]) == 139804\n assert candidate(height = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) == 19000\n assert candidate(height = [10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 100\n assert candidate(height = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 19000\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 400\n assert candidate(height = [50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 90, 80, 70, 60]) == 950\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 12, 4, 3, 2, 1, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 176\n assert candidate(height = [3, 9, 3, 4, 7, 2, 12, 6, 5, 10, 1, 8]) == 80\n assert candidate(height = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 180\n assert candidate(height = [5, 10, 8, 3, 7, 6, 10, 4, 1, 9]) == 72\n assert candidate(height = [100, 200, 300, 400, 300, 200, 100, 200, 300, 400, 300, 200, 100]) == 2400\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 10, 12, 11]) == 80\n assert candidate(height = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7]) == 36\n assert candidate(height = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 18, 16, 14, 12, 10]) == 100\n assert candidate(height = [1, 2, 3, 4, 5, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 56\n assert candidate(height = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 100\n assert candidate(height = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 500\n assert candidate(height = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) == 24000\n assert candidate(height = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 1539\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1000]) == 29\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 50\n assert candidate(height = [9985, 9984, 9983, 9982, 9981, 9980, 9979, 9978, 9977, 9976, 9975, 9974, 9973, 9972, 9971]) == 139594\n assert candidate(height = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 70\n assert candidate(height = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 250\n assert candidate(height = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 56\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 450\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 25, 7]) == 49\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 136\n assert candidate(height = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 80\n assert candidate(height = [10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000, 1, 10000]) == 240000\n assert candidate(height = [100, 200, 150, 300, 250, 400, 350, 500, 450, 600, 550, 700, 650, 800, 750, 900, 850, 1000]) == 5000\n assert candidate(height = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 9000, 8000, 7000, 6000, 5000, 4000, 3000, 2000, 1000]) == 50000\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 180\n assert candidate(height = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 95\n assert candidate(height = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1]) == 120\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10000]) == 25\n assert candidate(height = [1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 5, 4, 3, 2, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1]) == 75\n assert candidate(height = [2, 3, 4, 5, 6, 7, 8, 9, 10]) == 25\n assert candidate(height = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 16\n assert candidate(height = [1, 1, 1, 1, 100, 1, 1, 1, 1, 1, 100, 1, 1, 1, 1, 1, 100, 1, 1, 1]) == 1200\n assert candidate(height = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2]) == 48\n assert candidate(height = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 190\n assert candidate(height = [10, 9, 8, 10, 9, 8, 10, 9, 8, 10, 9, 8, 10, 9, 8, 10, 9, 8, 10]) == 180\n assert candidate(height = [1, 2, 3, 4, 5, 15, 5, 4, 3, 2, 1, 15, 1, 2, 3, 4, 5, 15, 5, 4, 3, 2, 1]) == 180\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 50\n assert candidate(height = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 36\n assert candidate(height = [5, 3, 8, 4, 2, 7, 9, 6, 1]) == 35\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 112\n assert candidate(height = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 120\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 100\n assert candidate(height = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 45\n assert candidate(height = [10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1]) == 140\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 100\n assert candidate(height = [12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 36\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 14\n assert candidate(height = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 6, 5, 7, 4, 8, 3, 9, 2, 10, 1]) == 170\n assert candidate(height = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2]) == 48\n assert candidate(height = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 90\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 200\n assert candidate(height = [8, 10, 12, 10, 6, 5, 4, 3, 2, 1]) == 25\n assert candidate(height = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 55\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 10, 2, 15, 1, 5, 3]) == 80\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == 180\n assert candidate(height = [100, 20, 300, 40, 500, 60, 700, 80, 900, 1000, 100, 900, 80, 700, 60, 500, 40, 300, 20, 100]) == 5500\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 44\n assert candidate(height = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 800\n assert candidate(height = [39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 190\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 200\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 9, 10, 11, 12, 13, 14]) == 104\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 29\n assert candidate(height = [1, 3, 5, 7, 9, 11, 13, 15, 13, 11, 9, 7, 5, 3, 1]) == 56\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 56\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 144\n assert candidate(height = [1, 2, 3, 100, 2, 3, 100, 2, 3, 100, 2, 3, 100, 2, 3, 100, 2, 3, 100]) == 1500\n assert candidate(height = [100, 50, 30, 60, 100, 40, 20, 80, 70, 90, 10]) == 810\n assert candidate(height = [8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7]) == 98\n assert candidate(height = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 36\n"}, "metadata": {"canonical_parameter_names": ["height"], "leetcode_dataset_entry_point": "Solution().maxArea", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxArea = function(height) {", "container": null, "callable": "maxArea", "parameters": [{"name": "height", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 12, "task_id": "integer-to-roman", "difficulty": "Medium", "problem_description": "Seven different symbols represent Roman numerals with the following values:\n\n\n\nSymbol\nValue\n\n\n\n\nI\n1\n\n\nV\n5\n\n\nX\n10\n\n\nL\n50\n\n\nC\n100\n\n\nD\n500\n\n\nM\n1000\n\n\n\nRoman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules:\n\nIf the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the remainder to a Roman numeral.\nIf the value starts with 4 or 9 use the subtractive form representing one symbol subtracted from the following symbol, for example, 4 is 1 (I) less than 5 (V): IV and 9 is 1 (I) less than 10 (X): IX. Only the following subtractive forms are used: 4 (IV), 9 (IX), 40 (XL), 90 (XC), 400 (CD) and 900 (CM).\nOnly powers of 10 (I, X, C, M) can be appended consecutively at most 3 times to represent multiples of 10. You cannot append 5 (V), 50 (L), or 500 (D) multiple times. If you need to append a symbol 4 times use the subtractive form.\n\nGiven an integer, convert it to a Roman numeral.\n \nExample 1:\n\nInput: num = 3749\nOutput: \"MMMDCCXLIX\"\nExplanation:\n\n3000 = MMM as 1000 (M) + 1000 (M) + 1000 (M)\n 700 = DCC as 500 (D) + 100 (C) + 100 (C)\n 40 = XL as 10 (X) less of 50 (L)\n 9 = IX as 1 (I) less of 10 (X)\nNote: 49 is not 1 (I) less of 50 (L) because the conversion is based on decimal places\n\n\nExample 2:\n\nInput: num = 58\nOutput: \"LVIII\"\nExplanation:\n\n50 = L\n 8 = VIII\n\n\nExample 3:\n\nInput: num = 1994\nOutput: \"MCMXCIV\"\nExplanation:\n\n1000 = M\n 900 = CM\n 90 = XC\n 4 = IV\n\n\n \nConstraints:\n\n1 <= num <= 3999\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 44) == \"XLIV\"\n assert candidate(num = 9) == \"IX\"\n assert candidate(num = 4) == \"IV\"\n assert candidate(num = 2023) == \"MMXXIII\"\n assert candidate(num = 589) == \"DLXXXIX\"\n assert candidate(num = 444) == \"CDXLIV\"\n assert candidate(num = 1000) == \"M\"\n assert candidate(num = 789) == \"DCCLXXXIX\"\n assert candidate(num = 58) == \"LVIII\"\n assert candidate(num = 3999) == \"MMMCMXCIX\"\n assert candidate(num = 399) == \"CCCXCIX\"\n assert candidate(num = 3749) == \"MMMDCCXLIX\"\n assert candidate(num = 1994) == \"MCMXCIV\"\n assert candidate(num = 1) == \"I\"\n assert candidate(num = 3549) == \"MMMDXLIX\"\n assert candidate(num = 944) == \"CMXLIV\"\n assert candidate(num = 199) == \"CXCIX\"\n assert candidate(num = 60) == \"LX\"\n assert candidate(num = 621) == \"DCXXI\"\n assert candidate(num = 3000) == \"MMM\"\n assert candidate(num = 1499) == \"MCDXCIX\"\n assert candidate(num = 1602) == \"MDCII\"\n assert candidate(num = 999) == \"CMXCIX\"\n assert candidate(num = 207) == \"CCVII\"\n assert candidate(num = 2078) == \"MMLXXVIII\"\n assert candidate(num = 894) == \"DCCCXCIV\"\n assert candidate(num = 2421) == \"MMCDXXI\"\n assert candidate(num = 2999) == \"MMCMXCIX\"\n assert candidate(num = 149) == \"CXLIX\"\n assert candidate(num = 3949) == \"MMMCMXLIX\"\n assert candidate(num = 99) == \"XCIX\"\n assert candidate(num = 1492) == \"MCDXCII\"\n assert candidate(num = 1234) == \"MCCXXXIV\"\n assert candidate(num = 647) == \"DCXLVII\"\n assert candidate(num = 844) == \"DCCCXLIV\"\n assert candidate(num = 798) == \"DCCXCVIII\"\n assert candidate(num = 1043) == \"MXLIII\"\n assert candidate(num = 3001) == \"MMMI\"\n assert candidate(num = 2345) == \"MMCCCXLV\"\n assert candidate(num = 500) == \"D\"\n assert candidate(num = 746) == \"DCCXLVI\"\n assert candidate(num = 2944) == \"MMCMXLIV\"\n assert candidate(num = 1500) == \"MD\"\n assert candidate(num = 3357) == \"MMMCCCLVII\"\n assert candidate(num = 3388) == \"MMMCCCLXXXVIII\"\n assert candidate(num = 1597) == \"MDXCVII\"\n assert candidate(num = 2737) == \"MMDCCXXXVII\"\n assert candidate(num = 40) == \"XL\"\n assert candidate(num = 2708) == \"MMDCCVIII\"\n assert candidate(num = 349) == \"CCCXLIX\"\n assert candidate(num = 799) == \"DCCXCIX\"\n assert candidate(num = 1001) == \"MI\"\n assert candidate(num = 583) == \"DLXXXIII\"\n assert candidate(num = 2422) == \"MMCDXXII\"\n assert candidate(num = 891) == \"DCCCXCI\"\n assert candidate(num = 39) == \"XXXIX\"\n assert candidate(num = 1444) == \"MCDXLIV\"\n assert candidate(num = 1094) == \"MXCIV\"\n assert candidate(num = 2751) == \"MMDCCLI\"\n assert candidate(num = 3888) == \"MMMDCCCLXXXVIII\"\n assert candidate(num = 2994) == \"MMCMXCIV\"\n assert candidate(num = 876) == \"DCCCLXXVI\"\n assert candidate(num = 1009) == \"MIX\"\n assert candidate(num = 1648) == \"MDCXLVIII\"\n assert candidate(num = 1066) == \"MLXVI\"\n assert candidate(num = 2349) == \"MMCCCXLIX\"\n assert candidate(num = 2763) == \"MMDCCLXIII\"\n assert candidate(num = 1646) == \"MDCXLVI\"\n assert candidate(num = 3499) == \"MMMCDXCIX\"\n assert candidate(num = 1529) == \"MDXXIX\"\n assert candidate(num = 1453) == \"MCDLIII\"\n assert candidate(num = 1099) == \"MXCIX\"\n assert candidate(num = 299) == \"CCXCIX\"\n assert candidate(num = 89) == \"LXXXIX\"\n assert candidate(num = 2074) == \"MMLXXIV\"\n assert candidate(num = 2549) == \"MMDXLIX\"\n assert candidate(num = 1423) == \"MCDXXIII\"\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().intToRoman", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var intToRoman = function(num) {", "container": null, "callable": "intToRoman", "parameters": [{"name": "num", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 13, "task_id": "roman-to-integer", "difficulty": "Easy", "problem_description": "Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.\n\nSymbol Value\nI 1\nV 5\nX 10\nL 50\nC 100\nD 500\nM 1000\nFor example, 2 is written as II in Roman numeral, just two ones added together. 12 is written as XII, which is simply X + II. The number 27 is written as XXVII, which is XX + V + II.\nRoman numerals are usually written largest to smallest from left to right. However, the numeral for four is not IIII. Instead, the number four is written as IV. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as IX. There are six instances where subtraction is used:\n\nI can be placed before V (5) and X (10) to make 4 and 9. \nX can be placed before L (50) and C (100) to make 40 and 90. \nC can be placed before D (500) and M (1000) to make 400 and 900.\n\nGiven a roman numeral, convert it to an integer.\n \nExample 1:\n\nInput: s = \"III\"\nOutput: 3\nExplanation: III = 3.\n\nExample 2:\n\nInput: s = \"LVIII\"\nOutput: 58\nExplanation: L = 50, V= 5, III = 3.\n\nExample 3:\n\nInput: s = \"MCMXCIV\"\nOutput: 1994\nExplanation: M = 1000, CM = 900, XC = 90 and IV = 4.\n\n \nConstraints:\n\n1 <= s.length <= 15\ns contains only the characters ('I', 'V', 'X', 'L', 'C', 'D', 'M').\nIt is guaranteed that s is a valid roman numeral in the range [1, 3999].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"XCIX\") == 99\n assert candidate(s = \"MMCMXCIX\") == 2999\n assert candidate(s = \"MMMCMXCIX\") == 3999\n assert candidate(s = \"DCXXI\") == 621\n assert candidate(s = \"XC\") == 90\n assert candidate(s = \"VIII\") == 8\n assert candidate(s = \"XV\") == 15\n assert candidate(s = \"XXVII\") == 27\n assert candidate(s = \"IX\") == 9\n assert candidate(s = \"DCCLXXIX\") == 779\n assert candidate(s = \"XX\") == 20\n assert candidate(s = \"CDXLIV\") == 444\n assert candidate(s = \"LVIII\") == 58\n assert candidate(s = \"CM\") == 900\n assert candidate(s = \"D\") == 500\n assert candidate(s = \"X\") == 10\n assert candidate(s = \"IV\") == 4\n assert candidate(s = \"XXV\") == 25\n assert candidate(s = \"XXX\") == 30\n assert candidate(s = \"XL\") == 40\n assert candidate(s = \"MMMDCCCLXXXVIII\") == 3888\n assert candidate(s = \"XXXIX\") == 39\n assert candidate(s = \"XLIV\") == 44\n assert candidate(s = \"CCCXCIX\") == 399\n assert candidate(s = \"CD\") == 400\n assert candidate(s = \"LXX\") == 70\n assert candidate(s = \"CCC\") == 300\n assert candidate(s = \"MMM\") == 3000\n assert candidate(s = \"MCMXCIV\") == 1994\n assert candidate(s = \"III\") == 3\n assert candidate(s = \"MDCCCLXXIV\") == 1874\n assert candidate(s = \"CMXCIX\") == 999\n assert candidate(s = \"MMCDXCIX\") == 2499\n assert candidate(s = \"M\") == 1000\n assert candidate(s = \"CCXLVI\") == 246\n assert candidate(s = \"CC\") == 200\n assert candidate(s = \"DCCLXXIV\") == 774\n assert candidate(s = \"MCCCLXXXIX\") == 1389\n assert candidate(s = \"CMLXXXVII\") == 987\n assert candidate(s = \"XCIV\") == 94\n assert candidate(s = \"MDCCLXXVI\") == 1776\n assert candidate(s = \"DCCLXXVI\") == 776\n assert candidate(s = \"CMXLVII\") == 947\n assert candidate(s = \"MMMCMLXXIV\") == 3974\n assert candidate(s = \"MDCCCLXXI\") == 1871\n assert candidate(s = \"MMMDCCCLXXVII\") == 3877\n assert candidate(s = \"MMMCMXCXCIX\") == 4089\n assert candidate(s = \"MMMLXXVIII\") == 3078\n assert candidate(s = \"CCCLXXIV\") == 374\n assert candidate(s = \"MCMXLIV\") == 1944\n assert candidate(s = \"MMCDLXXI\") == 2471\n assert candidate(s = \"DCCCLXXXVIII\") == 888\n assert candidate(s = \"MMDCCCLXXIV\") == 2874\n assert candidate(s = \"MMCDXLIV\") == 2444\n assert candidate(s = \"MMDCCCLXXVII\") == 2877\n assert candidate(s = \"MMMDCCCXCIX\") == 3899\n assert candidate(s = \"LXXXIX\") == 89\n assert candidate(s = \"DCCCLXXVIII\") == 878\n assert candidate(s = \"MMXXIII\") == 2023\n assert candidate(s = \"LXXXVII\") == 87\n assert candidate(s = \"MMMCMXCXC\") == 4080\n assert candidate(s = \"DCCCXC\") == 890\n assert candidate(s = \"MMCMCCXCIX\") == 3199\n assert candidate(s = \"MMMDCCCLXXX\") == 3880\n assert candidate(s = \"MDCCCCLXXV\") == 1975\n assert candidate(s = \"MCMXCMLXXIX\") == 2869\n assert candidate(s = \"MMMDCCCLXXIX\") == 3879\n assert candidate(s = \"CDXC\") == 490\n assert candidate(s = \"MCMLXXI\") == 1971\n assert candidate(s = \"MCMLIV\") == 1954\n assert candidate(s = \"MMDCCCXCIX\") == 2899\n assert candidate(s = \"CCXCIX\") == 299\n assert candidate(s = \"MMMCMXCCLXXVIII\") == 4168\n assert candidate(s = \"CDXCIX\") == 499\n assert candidate(s = \"MMMCMLXXIX\") == 3979\n assert candidate(s = \"DCCLXXVIII\") == 778\n assert candidate(s = \"MDCCCLXXVIII\") == 1878\n assert candidate(s = \"MMDCCCLXXXVIII\") == 2888\n assert candidate(s = \"MCMXLVII\") == 1947\n assert candidate(s = \"DCXXVIII\") == 628\n assert candidate(s = \"CCXLVIII\") == 248\n assert candidate(s = \"MMMCDXLIV\") == 3444\n assert candidate(s = \"DCCCXCIX\") == 899\n assert candidate(s = \"DCCCXCIV\") == 894\n assert candidate(s = \"DCCCLXXIV\") == 874\n assert candidate(s = \"MCMLXXIII\") == 1973\n assert candidate(s = \"MMMCDXCIX\") == 3499\n assert candidate(s = \"MMCDLXXVIII\") == 2478\n assert candidate(s = \"LVIV\") == 59\n assert candidate(s = \"MMCDXXI\") == 2421\n assert candidate(s = \"MDCCCLXXVII\") == 1877\n assert candidate(s = \"LXXXIV\") == 84\n assert candidate(s = \"CMXLIV\") == 944\n assert candidate(s = \"MCMLXXXIV\") == 1984\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().romanToInt", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var romanToInt = function(s) {", "container": null, "callable": "romanToInt", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 14, "task_id": "longest-common-prefix", "difficulty": "Easy", "problem_description": "Write a function to find the longest common prefix string amongst an array of strings.\nIf there is no common prefix, return an empty string \"\".\n \nExample 1:\n\nInput: strs = [\"flower\",\"flow\",\"flight\"]\nOutput: \"fl\"\n\nExample 2:\n\nInput: strs = [\"dog\",\"racecar\",\"car\"]\nOutput: \"\"\nExplanation: There is no common prefix among the input strings.\n\n \nConstraints:\n\n1 <= strs.length <= 200\n0 <= strs[i].length <= 200\nstrs[i] consists of only lowercase English letters if it is non-empty.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(strs = ['hello', 'helium', 'helper']) == \"hel\"\n assert candidate(strs = ['a']) == \"a\"\n assert candidate(strs = ['', '', '', '']) == \"\"\n assert candidate(strs = ['apple', 'app', 'apricot']) == \"ap\"\n assert candidate(strs = ['abcd', 'abce', 'abcf']) == \"abc\"\n assert candidate(strs = ['apple', 'app', 'application']) == \"app\"\n assert candidate(strs = ['interview', 'interrupt', 'inter']) == \"inter\"\n assert candidate(strs = ['test', 'testing', 'tester']) == \"test\"\n assert candidate(strs = ['hello', 'hell', 'hella']) == \"hell\"\n assert candidate(strs = ['flower', 'flow', 'flight']) == \"fl\"\n assert candidate(strs = ['same', 'same', 'same']) == \"same\"\n assert candidate(strs = ['single']) == \"single\"\n assert candidate(strs = ['ab', 'abc', 'abcd']) == \"ab\"\n assert candidate(strs = ['abc', 'abc', 'abc']) == \"abc\"\n assert candidate(strs = ['abcd', 'dcba', 'abdc']) == \"\"\n assert candidate(strs = ['', 'b', 'abc']) == \"\"\n assert candidate(strs = ['a', 'ab', 'abc']) == \"a\"\n assert candidate(strs = ['dog', 'racecar', 'car']) == \"\"\n assert candidate(strs = ['a', 'a', 'a', 'a']) == \"a\"\n assert candidate(strs = ['', '', 'abc']) == \"\"\n assert candidate(strs = ['abc', 'abcd', 'abcde']) == \"abc\"\n assert candidate(strs = ['abcd', 'abc', 'ab', 'a']) == \"a\"\n assert candidate(strs = ['banana', 'bandana', 'banner']) == \"ban\"\n assert candidate(strs = ['aaaa', 'aaab', 'aaac']) == \"aaa\"\n assert candidate(strs = ['mississippi', 'mississauga', 'mission', 'missed']) == \"miss\"\n assert candidate(strs = ['commonality', 'commonwealth', 'common', 'commons']) == \"common\"\n assert candidate(strs = ['different', 'prefixes', 'here']) == \"\"\n assert candidate(strs = ['repetition', 'repetitive', 'repeat', 'repel', 'repeal', 'repetend']) == \"repe\"\n assert candidate(strs = ['million', 'millionaire', 'millionth', 'millionfold']) == \"million\"\n assert candidate(strs = ['algorithm', 'algorithmic', 'algebra', 'alignment']) == \"al\"\n assert candidate(strs = ['difficult', 'difficulty', 'differ']) == \"diff\"\n assert candidate(strs = ['environment', 'environmental', 'envision', 'enzyme']) == \"en\"\n assert candidate(strs = ['a', 'aa', 'aaa', 'aaaa']) == \"a\"\n assert candidate(strs = ['xylophone', 'xylotomy', 'xylography', 'xylograph']) == \"xylo\"\n assert candidate(strs = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa']) == \"a\"\n assert candidate(strs = ['abcde', 'abc', 'ab', 'a', 'abcde']) == \"a\"\n assert candidate(strs = ['unique', 'unit', 'universe', 'unity', 'un']) == \"un\"\n assert candidate(strs = ['same', 'same', 'same', 'same']) == \"same\"\n assert candidate(strs = ['abcdef', 'abcde', 'abcd', 'abc', 'ab', 'a']) == \"a\"\n assert candidate(strs = ['short', 'small', 'shallow', 'shrink']) == \"s\"\n assert candidate(strs = ['zebra', 'zoo', 'zenith', 'zest', 'zone', 'zephyr']) == \"z\"\n assert candidate(strs = ['multidimensional', 'multidimensionalities', 'multidimensionally', 'multidimensionalization']) == \"multidimensional\"\n assert candidate(strs = ['computation', 'compute', 'computer', 'comedy']) == \"com\"\n assert candidate(strs = ['abcd', 'ab', 'a', 'abcde']) == \"a\"\n assert candidate(strs = ['abcde', 'abcdf', 'abcde', 'abcda', 'abcde', 'abcdf']) == \"abcd\"\n assert candidate(strs = ['zebra', 'zoo', 'zealot']) == \"z\"\n assert candidate(strs = ['abcd', 'abcde', 'ab', 'a']) == \"a\"\n assert candidate(strs = ['microphone', 'microwave', 'microscope', 'microbial']) == \"micro\"\n assert candidate(strs = ['longest', 'long', 'lonely']) == \"lon\"\n assert candidate(strs = ['prefix', 'preprocessor', 'prevent']) == \"pre\"\n assert candidate(strs = ['algorithm', 'algorithmically', '', 'algorithmic']) == \"\"\n assert candidate(strs = ['algorithm', 'alert', 'alibaba', 'allied']) == \"al\"\n assert candidate(strs = ['unbelievable', 'unbeliever', 'unbelievably', 'unbelievability']) == \"unbeliev\"\n assert candidate(strs = ['prefix', 'preposition', 'prevent', 'premier']) == \"pre\"\n assert candidate(strs = ['prefix', 'prefixes', 'prefixation', 'prefixed']) == \"prefix\"\n assert candidate(strs = ['a', 'b', 'c', 'd']) == \"\"\n assert candidate(strs = ['', 'same', 'same', 'same', 'same']) == \"\"\n assert candidate(strs = ['same', 'same', 'same', 'same', 'same']) == \"same\"\n assert candidate(strs = ['optimization', 'optimization', 'optimized', 'optimizer']) == \"optimiz\"\n assert candidate(strs = ['communication', 'communicate', 'commune', 'communist']) == \"commun\"\n assert candidate(strs = ['a', 'ab', 'abc', 'abcd', 'abcde', 'abcdef']) == \"a\"\n assert candidate(strs = ['algorithm', 'algorithmically', 'algebra', 'allegro']) == \"al\"\n assert candidate(strs = ['common', 'commotion', 'communicate', 'community']) == \"comm\"\n assert candidate(strs = ['flower', 'flow', 'flight', 'flew', 'flying', 'flowing']) == \"fl\"\n assert candidate(strs = ['single', 'singlehandedly', 'singlemindedness', 'singlehanded']) == \"single\"\n assert candidate(strs = ['algorithm', 'algebra', 'alaska']) == \"al\"\n assert candidate(strs = ['congratulations', 'congruity', 'congruent']) == \"congr\"\n assert candidate(strs = ['a', 'ab', 'abc', 'abcd']) == \"a\"\n assert candidate(strs = ['algorithm', 'algorithmic', 'algorithmically', 'algorithmically']) == \"algorithm\"\n assert candidate(strs = ['preference', 'prefix', 'prevent', 'prey']) == \"pre\"\n assert candidate(strs = ['abracadabra', 'abracadabras', 'abracadabaster', 'abracadabration']) == \"abracadab\"\n assert candidate(strs = ['supercalifragilisticexpialidocious', 'super', 'supersonic']) == \"super\"\n assert candidate(strs = ['unanimity', 'unanimous', 'unanimously', 'unanimated']) == \"unanim\"\n assert candidate(strs = ['orthogonal', 'orthodox', 'orthopedic', 'orthography']) == \"ortho\"\n assert candidate(strs = ['abcd', 'abcde', 'abcdef', 'abcdefg']) == \"abcd\"\n assert candidate(strs = ['programming', 'programmer', 'programmatic', 'program']) == \"program\"\n assert candidate(strs = ['sequential', 'sequence', 'sequent', 'sequel']) == \"seque\"\n assert candidate(strs = ['abracadabra', 'abr', 'abracadabrador', 'abrac']) == \"abr\"\n assert candidate(strs = ['consistent', 'consistency', 'consistently', 'consist']) == \"consist\"\n assert candidate(strs = ['common', 'community', 'comma', 'communist']) == \"comm\"\n assert candidate(strs = ['zebra', 'zoo', 'zealot', 'zest']) == \"z\"\n assert candidate(strs = ['a', 'a', 'a', 'a', 'a']) == \"a\"\n assert candidate(strs = ['algorithm', 'algebra', 'altitude', 'altimeter']) == \"al\"\n assert candidate(strs = ['supercalifragilisticexpialidocious', 'super', 'supercal']) == \"super\"\n assert candidate(strs = ['maximum', 'maximize', 'maximal']) == \"maxim\"\n assert candidate(strs = ['complex', 'complicated', 'complect', 'complete']) == \"compl\"\n assert candidate(strs = ['prefix', 'pre', 'preface', 'prefer', 'preference', 'prefixing']) == \"pre\"\n assert candidate(strs = ['abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi']) == \"abcd\"\n assert candidate(strs = ['abcdefghij', 'abcdefgh', 'abcdefg', 'abcdef', 'abcde', 'abcd', 'abc', 'ab', 'a']) == \"a\"\n assert candidate(strs = ['abcde', 'abcde', 'abcde', 'abcde']) == \"abcde\"\n assert candidate(strs = ['algorithm', 'algorhythm', 'algae']) == \"alg\"\n assert candidate(strs = ['', '', '', '', 'a']) == \"\"\n assert candidate(strs = ['xylophone', 'xylography', 'xylogen', 'xylophonist']) == \"xylo\"\n assert candidate(strs = ['onomatopoeia', 'onomatopoetic', 'onomatope', 'onomatologist']) == \"onomato\"\n assert candidate(strs = ['rehabilitation', 'rehabilitate', 'rehabilitative', 'rehabilitated']) == \"rehabilitat\"\n assert candidate(strs = ['mississippi', 'missile', 'mission', 'missive']) == \"missi\"\n assert candidate(strs = ['longest', 'longevity', 'longitudinal']) == \"long\"\n assert candidate(strs = ['psychological', 'psychologist', 'psychology', 'psychic']) == \"psych\"\n assert candidate(strs = ['environment', 'envelope', 'envoy', 'evening']) == \"e\"\n assert candidate(strs = ['short', 'shorthand', 'shortfall']) == \"short\"\n assert candidate(strs = ['parallel', 'parallelogram', 'parallactic', 'paralactic']) == \"paral\"\n assert candidate(strs = ['cryptography', 'cryptographic', 'cryptanalysis', 'cryptanalytic']) == \"crypt\"\n assert candidate(strs = ['zebra', 'zoo', 'zero', 'zapper']) == \"z\"\n assert candidate(strs = ['singleword', 'single', 'singleton']) == \"single\"\n assert candidate(strs = ['anthropomorphic', 'anthropologist', 'anthropology', 'anthropocentric']) == \"anthropo\"\n assert candidate(strs = ['', '', '', 'a']) == \"\"\n assert candidate(strs = ['a', 'ab', 'abc', 'abcd', 'abcde']) == \"a\"\n assert candidate(strs = ['common', 'commune', 'command', 'community']) == \"comm\"\n assert candidate(strs = ['same', 'samsung', 'sample', 'sand', 'satellite', 'saturn']) == \"sa\"\n assert candidate(strs = ['algorithm', 'algebra', 'altitude']) == \"al\"\n assert candidate(strs = ['implementation', 'implement', 'implementing', 'implementor']) == \"implement\"\n assert candidate(strs = ['abracadabra', 'abracadabra', 'abracadabra']) == \"abracadabra\"\n assert candidate(strs = ['reorganization', 'reorganize', 'reorganized', 'reorganizing']) == \"reorganiz\"\n assert candidate(strs = ['university', 'universe', 'unique', 'unicorn']) == \"uni\"\n assert candidate(strs = ['', 'longest', 'longevity', 'logistics']) == \"\"\n assert candidate(strs = ['', '', '', 'abc']) == \"\"\n assert candidate(strs = ['environment', 'envy', 'envelop', 'enviable']) == \"env\"\n assert candidate(strs = ['unique', 'unicorn', 'unify', 'unity']) == \"uni\"\n assert candidate(strs = ['aabbcc', 'aabbc', 'aabb', 'aab', 'aa']) == \"aa\"\n assert candidate(strs = ['zebra', 'zoo', 'zeal', 'zither']) == \"z\"\n assert candidate(strs = ['', 'a', 'ab', 'abc', 'abcd']) == \"\"\n assert candidate(strs = ['aardvark', 'aardwolf', 'aardvark', 'aard']) == \"aard\"\n assert candidate(strs = ['zzzzzzzz', 'zzzzz', 'zzzz', 'zzz', 'zz', 'z']) == \"z\"\n assert candidate(strs = ['separation', 'separately', 'separated', 'separating']) == \"separat\"\n assert candidate(strs = ['mississippi', 'missile', 'mission', 'miss']) == \"miss\"\n assert candidate(strs = ['algorithm', 'algebra', 'alien', 'alert']) == \"al\"\n assert candidate(strs = ['commonality', 'common', 'commune', 'community', 'communicate', 'commemorative']) == \"comm\"\n assert candidate(strs = ['supercalifragilisticexpialidocious', 'supercalifragilistic', 'supercalifragili', 'super']) == \"super\"\n assert candidate(strs = ['parallel', 'parallelepiped', 'paralleled', 'paralegal']) == \"paral\"\n assert candidate(strs = ['prefix', 'preference', 'presentation']) == \"pre\"\n assert candidate(strs = ['unified', 'uniform', 'universe', 'unique']) == \"uni\"\n assert candidate(strs = ['anagram', 'anagrams', 'anagrammatic', 'anagrammatical']) == \"anagram\"\n assert candidate(strs = ['environment', 'environmental', 'environments', 'environmentally']) == \"environment\"\n assert candidate(strs = ['xylophone', 'xylography', 'xylophonist', 'xylophonics']) == \"xylo\"\n assert candidate(strs = ['prefix', '', 'prefix', 'prefix']) == \"\"\n assert candidate(strs = ['algorithm', 'algebra', 'altimeter']) == \"al\"\n assert candidate(strs = ['recognition', 'recognizable', 'recognize', 'recognizably']) == \"recogni\"\n assert candidate(strs = ['prefix', 'preposition', 'presentation']) == \"pre\"\n assert candidate(strs = ['challenges', 'challenging', 'challenge', 'challengingly']) == \"challeng\"\n assert candidate(strs = ['universally', 'universe', 'universal', 'universality', 'universes', 'universally']) == \"univers\"\n assert candidate(strs = ['mississippi', 'missile', 'missionary', 'misspell']) == \"miss\"\n assert candidate(strs = ['photosynthesis', 'photosynthetic', 'photosynthesize', 'photosynthetically']) == \"photosynthe\"\n assert candidate(strs = ['apple', 'apply', 'appetite', 'apparatus']) == \"app\"\n assert candidate(strs = ['prefix', 'pretext', 'prevent']) == \"pre\"\n assert candidate(strs = ['development', 'develop', 'developer', 'developmental', 'developing', 'devel']) == \"devel\"\n assert candidate(strs = ['prefix', 'preference', 'presentation', 'president', 'pressure', 'premier']) == \"pre\"\n assert candidate(strs = ['', 'unique', 'unanimous', 'unicorn', 'unicycle', 'unify']) == \"\"\n assert candidate(strs = ['complex', 'complicated', 'completion']) == \"compl\"\n"}, "metadata": {"canonical_parameter_names": ["strs"], "leetcode_dataset_entry_point": "Solution().longestCommonPrefix", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestCommonPrefix = function(strs) {", "container": null, "callable": "longestCommonPrefix", "parameters": [{"name": "strs", "type": "string[]"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 15, "task_id": "3sum", "difficulty": "Medium", "problem_description": "Given an integer array nums, return all the triplets [nums[i], nums[j], nums[k]] such that i != j, i != k, and j != k, and nums[i] + nums[j] + nums[k] == 0.\nNotice that the solution set must not contain duplicate triplets.\n \nExample 1:\n\nInput: nums = [-1,0,1,2,-1,-4]\nOutput: [[-1,-1,2],[-1,0,1]]\nExplanation: \nnums[0] + nums[1] + nums[2] = (-1) + 0 + 1 = 0.\nnums[1] + nums[2] + nums[4] = 0 + 1 + (-1) = 0.\nnums[0] + nums[3] + nums[4] = (-1) + 2 + (-1) = 0.\nThe distinct triplets are [-1,0,1] and [-1,-1,2].\nNotice that the order of the output and the order of the triplets does not matter.\n\nExample 2:\n\nInput: nums = [0,1,1]\nOutput: []\nExplanation: The only possible triplet does not sum up to 0.\n\nExample 3:\n\nInput: nums = [0,0,0]\nOutput: [[0,0,0]]\nExplanation: The only possible triplet sums up to 0.\n\n \nConstraints:\n\n3 <= nums.length <= 3000\n-105 <= nums[i] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-2, 0, 0, 2, 2]) == [[-2, 0, 2]]\n assert candidate(nums = [0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4]) == [[-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-2, 0, 1, 1, 2]) == [[-2, 0, 2], [-2, 1, 1]]\n assert candidate(nums = [1, 2, -2, -1]) == []\n assert candidate(nums = [-1, 0, 0, 0, 1, 1, 2]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [1, -1, -1, 0]) == [[-1, 0, 1]]\n assert candidate(nums = [3, -2, 1, 0, -1, -2, 1, -2, 1, -2]) == [[-2, -1, 3], [-2, 1, 1], [-1, 0, 1]]\n assert candidate(nums = [-1, 0, 1, 0]) == [[-1, 0, 1]]\n assert candidate(nums = [-4, -2, -2, -2, 0, 1, 2, 2, 2, 3, 3, 4, 4, 6, 6]) == [[-4, -2, 6], [-4, 0, 4], [-4, 1, 3], [-4, 2, 2], [-2, -2, 4], [-2, 0, 2]]\n assert candidate(nums = [-1, 1, 0]) == [[-1, 0, 1]]\n assert candidate(nums = [0, 1, 1]) == []\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [-1, 0, 1, -1, 0, 1, -1, 0, 1]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-3, -3, -3, -3, 1, 2, 2, 3, 3, 3]) == [[-3, 1, 2]]\n assert candidate(nums = [-1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-3, -2, -1, 0, 0, 0, 1, 2, 3]) == [[-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-5, -3, -2, 0, 1, 2, 3, 5, 7]) == [[-5, -2, 7], [-5, 0, 5], [-5, 2, 3], [-3, -2, 5], [-3, 0, 3], [-3, 1, 2], [-2, 0, 2]]\n assert candidate(nums = [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2]) == [[-1, -1, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-4, -3, -2, -1, 0, 1, 2, 3, 4]) == [[-4, 0, 4], [-4, 1, 3], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [-1, -1, 0, 0, 1, 1, 2, -2, 3]) == [[-2, -1, 3], [-2, 0, 2], [-2, 1, 1], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, -1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4]) == [[-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, -1, 0, 1, 1, 2, 2, 3]) == [[-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-5, 2, 3, 0, -4, -6, 5, -7, 9, -3, -8, -1, 1, -7, -3, 1, -8, 5, -5, -7, 6, -3, 0, 6, -4, -8, -9, 7, 7, -4, -9, 1, -2, 6, 5, -3, -9, -1, 5, 4, -1, -2, -5, -2, -8, 8, 6, -7, -1, -2, 3, -3, 9, -4, 2, -3, 3, 2, 6, -9, -5, -3, 5, -8, 1, 8, -2, 5, -3, -8, 1, 8, -7, -4, 5, 5, -1, 6, 2, 2, -6, -1, -3, 2, -5, -7, -9, -7, 6, 2, 2, 1, 6, 5, -5, 0, -5, 8, -5, -7, 6, -2, -9, -1, -2, 7, 1, -7, 5, -3, -9, 2, -7, -8, -3, -7, -9, 0, 4, -1, 3, 8, -2, -7, 9, -9, -6, -7, 4, 3, 3, -9, -9, -9, 9, 0, 5, -2, -9, -9, -6, -1, 0, 1, 9, -8, -3, -2, -1, 6, 0, 8, 8, -7, -6, -2, -1, -2, -8, -4, 8, -6, -9, 7, -6, -4, 0, 7, 8, -9, 9, -9, -8, -3, -5, -7, -3, 9, 1, 6, -9, -2, -4, -4, -3, -1, 5, -4, -9, -9, 8, -2, -8, 1, 0, 3, 6, -1, 6, -8, -7, -2, -8, 1, 9, -3, -5, -1, -7, 8, -5, -6, -1, 8, 0, -2, -1, 1, 8, -4, 1, -4, 4, -3, -1, -4, 5, 9, 4, -9, -8, 2, -2, -7, -7, -8, -7, -3, 7, -5, -8, 2, -6, -1, -2, -4, -4, -6, -8, 5, -4, 7, 8, -4, 5, 0, -7, -8, -4, -6, -1, -3, 1, 3, -2, -1, -9, 0, 1, 2, -8, 5, 8, 7, -3, -1, -7, -9, -2, -4, -1, -5, -2, -5, -5, -9, -8, -6, 6, -2, -9, -7, -5, -9, 2, -3, 7, 0, -9, 7, -4, 3, -3, -4, -8, 1, -4, -6, -4, 3, 5, 0, 4, -5, -8, -5, -3, -7, -1, 0, -3, -8, 2, -4, -3, 6, -7, -6, -3, -1, -5, -8, -4, -3, -7, -9, -6, -6, 3, -9, -5, 7, -1, -5, -7, 4, 8, -5, -5, 2, -9, -3, -8, -3, 4, -6, 2, -8, -8, -1, -8, -8, -9, 7, -9, 1, -3, -4, -1, -3, -1, -8, 9, -6, -1, 3, 3, -9, -9, 7, -5, -1, -7, -4, -8, 2, 0, 5, -8, 8, -3, -6, -2, -8, -3, -3, -1, -7, 4, -4, 6, 3, -6, -1, -2, -8, -3, 2, -8, -2, 8, -4, -7, -8, -9, -6, -8, -9, 7, 1, -4, 1, -8, 2, -2, 4, -1, 9, -3, -5, -1, -6, -2, -8, 2, -2, -8, -4, -3, -7, -3, 0, -9, -2, -1, -7, -1, -9, -1, 7, -6, -5, -4, -8, -4, -2, -7, 5, -6, -5, -5, -5, -5, -3, 4, -9, -3, -2, -8, -1, -9, -4, -2, 5, -3, 1, -4, -1, 1, -3, -1, -3, 1, -3, -5, 7, -3, -7, -9, 9, -2, -9, 7, -7, -1, -4, -2, -5, -3, 8, -6, -2, 2, -7, -8, 6, 9, -9, -7, -3, -9, -8, -2, -7, -6, -9, -9, -1, -9, -9, -7, -1, -8, -7, -8, -6, -4, -2, -3, -2, -2, -6, -9, -8, -5, -3, -1, -1, -3, 3, -5, -1, -2, -5, -9, 0, -7, -1, -4, -3, -9, -7, -3, -7, -8, -7, -6, 0, 1, -2, 0, -4, -5, -5, -3, -9, 5, -1, -2, 8, -8, -1, -9, -7, -8, -9, -9, 0, -1, -3, -4, -3, -2, -4, -6, -2, 6, -4, -4, -3, 8, -9, -5, -9, -4, -9, -8, -7, -3, -1, -6, -9, 0, -7, -8, 2, -5, -4, -5, -3, -6, -7, -4, -7, 3, -3, -4, -2, -3, 8, -9, -5, -2, -6, -3, -8, -1, -3, -7, -1, -8, -5, -5, -1, -3, -7, -3, -5, -5, 2, -4, -9, -3, -6, -3, -8, -6, -9, -3, -1, -8, -8, -8, -8, -7, -7, -7, -7, -7, -6, -6, -6, -6, -5, -5, -5, -5, -4, -4, -4, -4, -3, -3, -3, -3, -2, -2, -2, -2, -1, -1, -1, -1, 0, 0, 0, 0]) == [[-9, 0, 9], [-9, 1, 8], [-9, 2, 7], [-9, 3, 6], [-9, 4, 5], [-8, -1, 9], [-8, 0, 8], [-8, 1, 7], [-8, 2, 6], [-8, 3, 5], [-8, 4, 4], [-7, -2, 9], [-7, -1, 8], [-7, 0, 7], [-7, 1, 6], [-7, 2, 5], [-7, 3, 4], [-6, -3, 9], [-6, -2, 8], [-6, -1, 7], [-6, 0, 6], [-6, 1, 5], [-6, 2, 4], [-6, 3, 3], [-5, -4, 9], [-5, -3, 8], [-5, -2, 7], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -4, 8], [-4, -3, 7], [-4, -2, 6], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-4, 2, 2], [-3, -3, 6], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -2, 4], [-2, -1, 3], [-2, 0, 2], [-2, 1, 1], [-1, -1, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-10, -10, -10, -1, 0, 0, 1, 10, 10, 10]) == [[-10, 0, 10], [-1, 0, 1]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, 3, 4, 5, -5]) == [[-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3, 4, 5]) == [[-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [1, 2, -2, -1, -1, -3, 3, 3, 2, -2]) == [[-3, 1, 2], [-2, -1, 3], [-1, -1, 2]]\n assert candidate(nums = [-1, -1, -1, 0, 0, 1, 1, 1]) == [[-1, 0, 1]]\n assert candidate(nums = [-5, 2, 5, -1, 1, 0, -2, 2, -3, 3]) == [[-5, 0, 5], [-5, 2, 3], [-3, -2, 5], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3]) == [[-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == [[-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, -3, 3, 0, 1, 2, -1, -4]) == [[-4, 1, 3], [-4, 2, 2], [-3, 0, 3], [-3, 1, 2], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, 1, 2, -2, 3, -3, 4, -4]) == [[-4, 1, 3], [-3, -1, 4], [-3, 1, 2], [-2, -1, 3]]\n assert candidate(nums = [-10, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [[-10, 0, 10], [-10, 1, 9], [-10, 2, 8], [-10, 3, 7], [-10, 4, 6], [-5, -3, 8], [-5, -2, 7], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [1, 2, -2, -1, 0, 0, 0]) == [[-2, 0, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-4, -2, -2, -2, 0, 1, 2, 2, 2, 3, 3, 4, 4]) == [[-4, 0, 4], [-4, 1, 3], [-4, 2, 2], [-2, -2, 4], [-2, 0, 2]]\n assert candidate(nums = [1, -1, -1, 1, 0, 0, 0]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-1, -2, -3, 4, 1, 3, 0]) == [[-3, -1, 4], [-3, 0, 3], [-2, -1, 3], [-1, 0, 1]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [1, 2, -2, -1, -1, -1, 0, 0, 0, 0]) == [[-2, 0, 2], [-1, -1, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-10, -9, -8, -7, 7, 8, 9, 10]) == []\n assert candidate(nums = [-10, 0, 10, 5, -5, 3, -3, 2, -2, 1, -1]) == [[-10, 0, 10], [-5, 0, 5], [-5, 2, 3], [-3, -2, 5], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [3, 0, -2, -1, 1, -2, 1, 0, -2, 1, 2]) == [[-2, -1, 3], [-2, 0, 2], [-2, 1, 1], [-1, 0, 1]]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20]) == [[-10, -5, 15], [-10, 0, 10], [-5, 0, 5]]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 0, 0, 0]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-10, 0, 10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80, 90, -90]) == [[-90, 0, 90], [-90, 10, 80], [-90, 20, 70], [-90, 30, 60], [-90, 40, 50], [-80, -10, 90], [-80, 0, 80], [-80, 10, 70], [-80, 20, 60], [-80, 30, 50], [-70, -20, 90], [-70, -10, 80], [-70, 0, 70], [-70, 10, 60], [-70, 20, 50], [-70, 30, 40], [-60, -30, 90], [-60, -20, 80], [-60, -10, 70], [-60, 0, 60], [-60, 10, 50], [-60, 20, 40], [-50, -40, 90], [-50, -30, 80], [-50, -20, 70], [-50, -10, 60], [-50, 0, 50], [-50, 10, 40], [-50, 20, 30], [-40, -30, 70], [-40, -20, 60], [-40, -10, 50], [-40, 0, 40], [-40, 10, 30], [-30, -20, 50], [-30, -10, 40], [-30, 0, 30], [-30, 10, 20], [-20, -10, 30], [-20, 0, 20], [-10, 0, 10]]\n assert candidate(nums = [-1, 0, 1, 0, -1, 1, -1, 0, 1]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-4, -2, -1, 0, 1, 2, 3, 5]) == [[-4, -1, 5], [-4, 1, 3], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, -1, -1, 0, 0, 1, 1, 2, 3]) == [[-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-3, -3, -3, 1, 2, 3, 4, 4, 4]) == [[-3, 1, 2]]\n assert candidate(nums = [-2, -3, 4, 3, 2, 1, 0, -1, -2, -3, 3, 2, 1]) == [[-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -2, 4], [-2, -1, 3], [-2, 0, 2], [-2, 1, 1], [-1, 0, 1]]\n assert candidate(nums = [-4, -2, -2, -2, 0, 1, 2, 2, 2, 3, 3, 4]) == [[-4, 0, 4], [-4, 1, 3], [-4, 2, 2], [-2, -2, 4], [-2, 0, 2]]\n assert candidate(nums = [-4, -1, -1, 0, 1, 2]) == [[-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, -2, -3, -4, -5, 5, 4, 3, 2, 1]) == [[-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 1, 2], [-2, -1, 3]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, 3, -2, 2]) == [[-4, 1, 3], [-4, 2, 2], [-2, -1, 3], [-2, 0, 2], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3]) == [[-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 1, 2, 3, 4, 5]) == [[-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 1, 2], [-2, -1, 3]]\n assert candidate(nums = [-1, -2, -3, 0, 1, 2, 3]) == [[-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [100000, -100000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[-100000, 0, 100000], [0, 0, 0]]\n assert candidate(nums = [3, -3, 4, -4, 5, -5, 6, -6, 0]) == [[-6, 0, 6], [-5, 0, 5], [-4, 0, 4], [-3, 0, 3]]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, -1, -2, -3, -4, -5]) == [[-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-6, -6, -4, -2, 0, 2, 4, 6, 6]) == [[-6, 0, 6], [-6, 2, 4], [-4, -2, 6], [-4, 0, 4], [-2, 0, 2]]\n assert candidate(nums = [1, 2, 3, -6, 4, -1, -3, 2, 0]) == [[-6, 2, 4], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-1, 0, 1]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [[-5, -4, 9], [-5, -3, 8], [-5, -2, 7], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -3, 7], [-4, -2, 6], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [2, 2, 2, 2, 2, -2, -2, -2, -2, -2]) == []\n assert candidate(nums = [-1, -1, -1, 0, 0, 1, 1, 2, 3]) == [[-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-5, -3, -1, 0, 0, 0, 0, 0, 1, 2, 3, 5]) == [[-5, 0, 5], [-5, 2, 3], [-3, 0, 3], [-3, 1, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == [[-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [[-10, 0, 10], [-10, 1, 9], [-10, 2, 8], [-10, 3, 7], [-10, 4, 6], [-9, -1, 10], [-9, 0, 9], [-9, 1, 8], [-9, 2, 7], [-9, 3, 6], [-9, 4, 5], [-8, -2, 10], [-8, -1, 9], [-8, 0, 8], [-8, 1, 7], [-8, 2, 6], [-8, 3, 5], [-7, -3, 10], [-7, -2, 9], [-7, -1, 8], [-7, 0, 7], [-7, 1, 6], [-7, 2, 5], [-7, 3, 4], [-6, -4, 10], [-6, -3, 9], [-6, -2, 8], [-6, -1, 7], [-6, 0, 6], [-6, 1, 5], [-6, 2, 4], [-5, -4, 9], [-5, -3, 8], [-5, -2, 7], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -3, 7], [-4, -2, 6], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, -1, -2, -3, -4, -5, -6]) == [[-6, 1, 5], [-6, 2, 4], [-5, -1, 6], [-5, 1, 4], [-5, 2, 3], [-4, -2, 6], [-4, -1, 5], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 1, 2], [-2, -1, 3]]\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6]) == [[-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-10, -5, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 6, 7, 8]) == [[-10, 2, 8], [-10, 3, 7], [-10, 4, 6], [-10, 5, 5], [-5, -3, 8], [-5, -2, 7], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [1, 2, -3, 4, -1, -2, 3, -4, 0, 0, 0, 0]) == [[-4, 0, 4], [-4, 1, 3], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-5, 2, 1, -2, 3, -1, 2, -3, 0, 0, 0]) == [[-5, 2, 3], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -4, -5, -6, -7, -8, -9]) == [[-9, 0, 9], [-9, 1, 8], [-9, 2, 7], [-9, 3, 6], [-9, 4, 5], [-8, -1, 9], [-8, 0, 8], [-8, 1, 7], [-8, 2, 6], [-8, 3, 5], [-7, -2, 9], [-7, -1, 8], [-7, 0, 7], [-7, 1, 6], [-7, 2, 5], [-7, 3, 4], [-6, -3, 9], [-6, -2, 8], [-6, -1, 7], [-6, 0, 6], [-6, 1, 5], [-6, 2, 4], [-5, -4, 9], [-5, -3, 8], [-5, -2, 7], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -3, 7], [-4, -2, 6], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-2, 0, 1, 1, 2, 3, 4, 5, -3, -4, -5, 6, 7, 8, 9, -6, -7, -8, -9]) == [[-9, 0, 9], [-9, 1, 8], [-9, 2, 7], [-9, 3, 6], [-9, 4, 5], [-8, 0, 8], [-8, 1, 7], [-8, 2, 6], [-8, 3, 5], [-7, -2, 9], [-7, 0, 7], [-7, 1, 6], [-7, 2, 5], [-7, 3, 4], [-6, -3, 9], [-6, -2, 8], [-6, 0, 6], [-6, 1, 5], [-6, 2, 4], [-5, -4, 9], [-5, -3, 8], [-5, -2, 7], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -3, 7], [-4, -2, 6], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, 0, 3], [-3, 1, 2], [-2, 0, 2], [-2, 1, 1]]\n assert candidate(nums = [3, -1, -3, 0, 1, 2, 4, -2, -4, 5, -5, 6, -6]) == [[-6, 0, 6], [-6, 1, 5], [-6, 2, 4], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -2, 6], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-5, -3, -1, 0, 0, 0, 1, 3, 5]) == [[-5, 0, 5], [-3, 0, 3], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [1, 2, -2, -1, 0, -1, 2]) == [[-2, 0, 2], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-7, -5, -5, -1, 0, 1, 1, 5, 7]) == [[-7, 0, 7], [-5, 0, 5], [-1, 0, 1]]\n assert candidate(nums = [-1, 0, 1, 0, 1, 0, -1, -1, -1, 0]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [1, 2, -2, -1, 0, 3, -3]) == [[-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 1, 1, 1]) == [[-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [1, 2, 3, 4, 5, -5, -4, -3, -2, -1]) == [[-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 1, 2], [-2, -1, 3]]\n assert candidate(nums = [-100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000, -100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[-100000, 0, 100000], [0, 0, 0]]\n assert candidate(nums = [100000, -100000, 0, -50000, 50000, -25000, 25000]) == [[-100000, 0, 100000], [-50000, 0, 50000], [-25000, 0, 25000]]\n assert candidate(nums = [-2, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == [[-2, 0, 2], [-2, 1, 1], [0, 0, 0]]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == [[-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 1, 2], [-2, -1, 3]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0]) == [[0, 0, 0]]\n assert candidate(nums = [-4, -2, -2, -1, 0, 1, 2, 2, 4]) == [[-4, 0, 4], [-4, 2, 2], [-2, -2, 4], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == []\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, 3, 4, -3, 2, -2, -5, 5]) == [[-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-4, 2, 2], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1]) == []\n assert candidate(nums = [-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6]) == [[-6, 0, 6], [-6, 1, 5], [-6, 2, 4], [-5, -1, 6], [-5, 0, 5], [-5, 1, 4], [-5, 2, 3], [-4, -2, 6], [-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-3, -2, 5], [-3, -1, 4], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n assert candidate(nums = [-4, -2, 1, -5, -4, -4, 4, -2, 0, 4, 0, -2, 3, 1, -5, 0]) == [[-5, 1, 4], [-4, 0, 4], [-4, 1, 3], [-2, -2, 4], [-2, 1, 1], [0, 0, 0]]\n assert candidate(nums = [-1, 2, 1, -4, 3, 0, -2, 1, 1, -1, 0, 0, 0, 0, 0]) == [[-4, 1, 3], [-2, -1, 3], [-2, 0, 2], [-2, 1, 1], [-1, -1, 2], [-1, 0, 1], [0, 0, 0]]\n assert candidate(nums = [-1, 2, 1, -4, 3, 0, -2, 2, 1, -1, -3, 3]) == [[-4, 1, 3], [-4, 2, 2], [-3, 0, 3], [-3, 1, 2], [-2, -1, 3], [-2, 0, 2], [-2, 1, 1], [-1, -1, 2], [-1, 0, 1]]\n assert candidate(nums = [-5, -3, -1, 0, 2, 4, 6]) == [[-5, -1, 6], [-3, -1, 4]]\n assert candidate(nums = [1, 2, -2, -1, 0, -4, 3, 4, 5]) == [[-4, -1, 5], [-4, 0, 4], [-4, 1, 3], [-2, -1, 3], [-2, 0, 2], [-1, 0, 1]]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().threeSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var threeSum = function(nums) {", "container": null, "callable": "threeSum", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 16, "task_id": "3sum-closest", "difficulty": "Medium", "problem_description": "Given an integer array nums of length n and an integer target, find three integers in nums such that the sum is closest to target.\nReturn the sum of the three integers.\nYou may assume that each input would have exactly one solution.\n \nExample 1:\n\nInput: nums = [-1,2,1,-4], target = 1\nOutput: 2\nExplanation: The sum that is closest to the target is 2. (-1 + 2 + 1 = 2).\n\nExample 2:\n\nInput: nums = [0,0,0], target = 1\nOutput: 0\nExplanation: The sum that is closest to the target is 0. (0 + 0 + 0 = 0).\n\n \nConstraints:\n\n3 <= nums.length <= 500\n-1000 <= nums[i] <= 1000\n-104 <= target <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128],target = 82) == 82\n assert candidate(nums = [1, 1, 1, 0],target = -100) == 2\n assert candidate(nums = [-10, -2, -5, -1],target = -12) == -13\n assert candidate(nums = [-5, -4, -3, -2, -1],target = -10) == -10\n assert candidate(nums = [0, 0, 0],target = 1) == 0\n assert candidate(nums = [1, 1, 1, 1],target = 3) == 3\n assert candidate(nums = [5, 5, 5, 5],target = 15) == 15\n assert candidate(nums = [-1, -2, -3, -4, -5],target = -10) == -10\n assert candidate(nums = [-1, 0, 1, 2, -1, -4],target = 1) == 1\n assert candidate(nums = [-1, 2, 1, -4],target = 1) == 2\n assert candidate(nums = [5, 1, 3, 4, 2],target = 7) == 7\n assert candidate(nums = [1, 1, 1, 1],target = 0) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9],target = 15) == 15\n assert candidate(nums = [1, 2, 3, 4, 5],target = 10) == 10\n assert candidate(nums = [-5, -4, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 4, 5],target = 0) == 0\n assert candidate(nums = [999, -999, 888, -888, 777, -777, 666, -666, 555, -555, 444, -444, 333, -333, 222, -222, 111, -111],target = 0) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 25) == 25\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 45) == 42\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 1500) == 1500\n assert candidate(nums = [5, 7, 7, 8, 8, 10, 12, 13, 15, 17, 19, 21, 23, 25, 27],target = 30) == 30\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 50) == 49\n assert candidate(nums = [-100, -200, -300, -400, -500, 100, 200, 300, 400, 500],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 45) == 45\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == 0\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],target = -100) == -57\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],target = -30) == -27\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100],target = 150) == 150\n assert candidate(nums = [-10, -20, -30, -40, -50, 1, 2, 3, 4, 5],target = -150) == -120\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 50) == 42\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 25) == 25\n assert candidate(nums = [3, 5, -4, 8, 11, 1, -1, 6],target = 10) == 10\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 125, -125],target = 100) == 125\n assert candidate(nums = [-3, -1, 0, 2, 4, 6, 9, 12],target = 14) == 14\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, 3, 4, 5, 6, 7, 8, 9, 10],target = 15) == 15\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100, -110, -120],target = -300) == -300\n assert candidate(nums = [-10, -20, -30, -40, -50, 50, 40, 30, 20, 10],target = 0) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 100) == 57\n assert candidate(nums = [-5, -2, -1, 0, 1, 2, 5],target = 0) == 0\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = -5) == -5\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],target = -150) == -150\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -25) == -25\n assert candidate(nums = [3, 5, 8, 9, 15, 1, 7, 6, 4, 10],target = 28) == 28\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 0, 1, -1],target = 100) == 1\n assert candidate(nums = [33, 55, 77, 99, 111, 133, 155, 177, 199, 221, 243, 265, 287, 309, 331, 353, 375, 397, 419, 441],target = 1200) == 1191\n assert candidate(nums = [100, 50, 25, 20, 10, 5, 1],target = 120) == 121\n assert candidate(nums = [-1, 0, 1, 0, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6],target = 0) == 0\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 15) == 15\n assert candidate(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90],target = 100) == 100\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9],target = 20) == 20\n assert candidate(nums = [999, 1000, -1000, 999, -999, 1, -1, 2, -2],target = 3000) == 2998\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15],target = -45) == -42\n assert candidate(nums = [-1, 2, -8, 4, 5, -10, 7, 0, 1],target = 0) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120],target = 300) == 300\n assert candidate(nums = [-1000, 1000, -500, 500, -250, 250, 0, 1, -1, 2, -2],target = 1001) == 1001\n assert candidate(nums = [-100, -200, -300, 400, 500, 600, 700],target = -150) == -100\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0],target = 1) == 0\n assert candidate(nums = [100, -200, 300, -400, 500, -600, 700, -800, 900, -1000, 1100, -1200, 1300, -1400, 1500],target = 500) == 500\n assert candidate(nums = [-1000, -999, -998, -997, 0, 997, 998, 999, 1000],target = 500) == 995\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 50) == 50\n assert candidate(nums = [-1, 0, 1, 0, -1, 0],target = 0) == 0\n assert candidate(nums = [-5, -3, -1, 0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],target = 0) == 0\n assert candidate(nums = [-15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 1) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],target = 100) == 100\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10],target = 0) == 0\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80],target = 0) == 0\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 125, -125],target = 50) == 125\n assert candidate(nums = [100, -100, 200, -200, 300, -300, 400, -400, 500, -500, 600, -600],target = 1000) == 1000\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],target = 9) == 9\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 1000) == 570\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],target = 50) == 50\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 15) == 15\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],target = -250) == -250\n assert candidate(nums = [-100, 100, -50, 50, -25, 25, 0],target = 0) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],target = 1) == 1\n assert candidate(nums = [100, 200, 300, 400, 500, -100, -200, -300, -400, -500],target = 0) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 30) == 30\n assert candidate(nums = [-999, -998, -997, -996, -995, -994, -993, -992, -991, -990, -989, -988, -987, -986, -985, -984, -983, -982, -981, -980],target = -3000) == -2994\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 30) == 30\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == 0\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 10) == 15\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900],target = 1500) == 1500\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],target = 15) == 9\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -25) == -25\n assert candidate(nums = [-1, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, -23, -25, -27, -29],target = -45) == -45\n assert candidate(nums = [-2, 0, 1, 1, 2],target = 0) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 250) == 250\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],target = 20) == 20\n assert candidate(nums = [-50, -30, -10, 0, 10, 30, 50],target = 40) == 40\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8],target = 0) == 0\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],target = -250) == -250\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 125, -125],target = 0) == -125\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 40) == 40\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 3) == 3\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 15) == 15\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3],target = 0) == 0\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 15) == 15\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128],target = 100) == 100\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],target = 15) == 14\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 150) == 87\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().threeSumClosest", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var threeSumClosest = function(nums, target) {", "container": null, "callable": "threeSumClosest", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 17, "task_id": "letter-combinations-of-a-phone-number", "difficulty": "Medium", "problem_description": "Given a string containing digits from 2-9 inclusive, return all possible letter combinations that the number could represent. Return the answer in any order.\nA mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters.\n\n \nExample 1:\n\nInput: digits = \"23\"\nOutput: [\"ad\",\"ae\",\"af\",\"bd\",\"be\",\"bf\",\"cd\",\"ce\",\"cf\"]\n\nExample 2:\n\nInput: digits = \"\"\nOutput: []\n\nExample 3:\n\nInput: digits = \"2\"\nOutput: [\"a\",\"b\",\"c\"]\n\n \nConstraints:\n\n0 <= digits.length <= 4\ndigits[i] is a digit in the range ['2', '9'].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(digits = \"5678\") == ['jmpt', 'jmpu', 'jmpv', 'jmqt', 'jmqu', 'jmqv', 'jmrt', 'jmru', 'jmrv', 'jmst', 'jmsu', 'jmsv', 'jnpt', 'jnpu', 'jnpv', 'jnqt', 'jnqu', 'jnqv', 'jnrt', 'jnru', 'jnrv', 'jnst', 'jnsu', 'jnsv', 'jopt', 'jopu', 'jopv', 'joqt', 'joqu', 'joqv', 'jort', 'joru', 'jorv', 'jost', 'josu', 'josv', 'kmpt', 'kmpu', 'kmpv', 'kmqt', 'kmqu', 'kmqv', 'kmrt', 'kmru', 'kmrv', 'kmst', 'kmsu', 'kmsv', 'knpt', 'knpu', 'knpv', 'knqt', 'knqu', 'knqv', 'knrt', 'knru', 'knrv', 'knst', 'knsu', 'knsv', 'kopt', 'kopu', 'kopv', 'koqt', 'koqu', 'koqv', 'kort', 'koru', 'korv', 'kost', 'kosu', 'kosv', 'lmpt', 'lmpu', 'lmpv', 'lmqt', 'lmqu', 'lmqv', 'lmrt', 'lmru', 'lmrv', 'lmst', 'lmsu', 'lmsv', 'lnpt', 'lnpu', 'lnpv', 'lnqt', 'lnqu', 'lnqv', 'lnrt', 'lnru', 'lnrv', 'lnst', 'lnsu', 'lnsv', 'lopt', 'lopu', 'lopv', 'loqt', 'loqu', 'loqv', 'lort', 'loru', 'lorv', 'lost', 'losu', 'losv']\n assert candidate(digits = \"2\") == ['a', 'b', 'c']\n assert candidate(digits = \"3\") == ['d', 'e', 'f']\n assert candidate(digits = \"9\") == ['w', 'x', 'y', 'z']\n assert candidate(digits = \"47\") == ['gp', 'gq', 'gr', 'gs', 'hp', 'hq', 'hr', 'hs', 'ip', 'iq', 'ir', 'is']\n assert candidate(digits = \"99\") == ['ww', 'wx', 'wy', 'wz', 'xw', 'xx', 'xy', 'xz', 'yw', 'yx', 'yy', 'yz', 'zw', 'zx', 'zy', 'zz']\n assert candidate(digits = \"234\") == ['adg', 'adh', 'adi', 'aeg', 'aeh', 'aei', 'afg', 'afh', 'afi', 'bdg', 'bdh', 'bdi', 'beg', 'beh', 'bei', 'bfg', 'bfh', 'bfi', 'cdg', 'cdh', 'cdi', 'ceg', 'ceh', 'cei', 'cfg', 'cfh', 'cfi']\n assert candidate(digits = \"299\") == ['aww', 'awx', 'awy', 'awz', 'axw', 'axx', 'axy', 'axz', 'ayw', 'ayx', 'ayy', 'ayz', 'azw', 'azx', 'azy', 'azz', 'bww', 'bwx', 'bwy', 'bwz', 'bxw', 'bxx', 'bxy', 'bxz', 'byw', 'byx', 'byy', 'byz', 'bzw', 'bzx', 'bzy', 'bzz', 'cww', 'cwx', 'cwy', 'cwz', 'cxw', 'cxx', 'cxy', 'cxz', 'cyw', 'cyx', 'cyy', 'cyz', 'czw', 'czx', 'czy', 'czz']\n assert candidate(digits = \"\") == []\n assert candidate(digits = \"79\") == ['pw', 'px', 'py', 'pz', 'qw', 'qx', 'qy', 'qz', 'rw', 'rx', 'ry', 'rz', 'sw', 'sx', 'sy', 'sz']\n assert candidate(digits = \"23\") == ['ad', 'ae', 'af', 'bd', 'be', 'bf', 'cd', 'ce', 'cf']\n assert candidate(digits = \"89\") == ['tw', 'tx', 'ty', 'tz', 'uw', 'ux', 'uy', 'uz', 'vw', 'vx', 'vy', 'vz']\n assert candidate(digits = \"456\") == ['gjm', 'gjn', 'gjo', 'gkm', 'gkn', 'gko', 'glm', 'gln', 'glo', 'hjm', 'hjn', 'hjo', 'hkm', 'hkn', 'hko', 'hlm', 'hln', 'hlo', 'ijm', 'ijn', 'ijo', 'ikm', 'ikn', 'iko', 'ilm', 'iln', 'ilo']\n assert candidate(digits = \"34\") == ['dg', 'dh', 'di', 'eg', 'eh', 'ei', 'fg', 'fh', 'fi']\n assert candidate(digits = \"3456\") == ['dgjm', 'dgjn', 'dgjo', 'dgkm', 'dgkn', 'dgko', 'dglm', 'dgln', 'dglo', 'dhjm', 'dhjn', 'dhjo', 'dhkm', 'dhkn', 'dhko', 'dhlm', 'dhln', 'dhlo', 'dijm', 'dijn', 'dijo', 'dikm', 'dikn', 'diko', 'dilm', 'diln', 'dilo', 'egjm', 'egjn', 'egjo', 'egkm', 'egkn', 'egko', 'eglm', 'egln', 'eglo', 'ehjm', 'ehjn', 'ehjo', 'ehkm', 'ehkn', 'ehko', 'ehlm', 'ehln', 'ehlo', 'eijm', 'eijn', 'eijo', 'eikm', 'eikn', 'eiko', 'eilm', 'eiln', 'eilo', 'fgjm', 'fgjn', 'fgjo', 'fgkm', 'fgkn', 'fgko', 'fglm', 'fgln', 'fglo', 'fhjm', 'fhjn', 'fhjo', 'fhkm', 'fhkn', 'fhko', 'fhlm', 'fhln', 'fhlo', 'fijm', 'fijn', 'fijo', 'fikm', 'fikn', 'fiko', 'film', 'filn', 'filo']\n assert candidate(digits = \"62\") == ['ma', 'mb', 'mc', 'na', 'nb', 'nc', 'oa', 'ob', 'oc']\n assert candidate(digits = \"4444\") == ['gggg', 'gggh', 'gggi', 'gghg', 'gghh', 'gghi', 'ggig', 'ggih', 'ggii', 'ghgg', 'ghgh', 'ghgi', 'ghhg', 'ghhh', 'ghhi', 'ghig', 'ghih', 'ghii', 'gigg', 'gigh', 'gigi', 'gihg', 'gihh', 'gihi', 'giig', 'giih', 'giii', 'hggg', 'hggh', 'hggi', 'hghg', 'hghh', 'hghi', 'hgig', 'hgih', 'hgii', 'hhgg', 'hhgh', 'hhgi', 'hhhg', 'hhhh', 'hhhi', 'hhig', 'hhih', 'hhii', 'higg', 'high', 'higi', 'hihg', 'hihh', 'hihi', 'hiig', 'hiih', 'hiii', 'iggg', 'iggh', 'iggi', 'ighg', 'ighh', 'ighi', 'igig', 'igih', 'igii', 'ihgg', 'ihgh', 'ihgi', 'ihhg', 'ihhh', 'ihhi', 'ihig', 'ihih', 'ihii', 'iigg', 'iigh', 'iigi', 'iihg', 'iihh', 'iihi', 'iiig', 'iiih', 'iiii']\n assert candidate(digits = \"223\") == ['aad', 'aae', 'aaf', 'abd', 'abe', 'abf', 'acd', 'ace', 'acf', 'bad', 'bae', 'baf', 'bbd', 'bbe', 'bbf', 'bcd', 'bce', 'bcf', 'cad', 'cae', 'caf', 'cbd', 'cbe', 'cbf', 'ccd', 'cce', 'ccf']\n assert candidate(digits = \"9753\") == ['wpjd', 'wpje', 'wpjf', 'wpkd', 'wpke', 'wpkf', 'wpld', 'wple', 'wplf', 'wqjd', 'wqje', 'wqjf', 'wqkd', 'wqke', 'wqkf', 'wqld', 'wqle', 'wqlf', 'wrjd', 'wrje', 'wrjf', 'wrkd', 'wrke', 'wrkf', 'wrld', 'wrle', 'wrlf', 'wsjd', 'wsje', 'wsjf', 'wskd', 'wske', 'wskf', 'wsld', 'wsle', 'wslf', 'xpjd', 'xpje', 'xpjf', 'xpkd', 'xpke', 'xpkf', 'xpld', 'xple', 'xplf', 'xqjd', 'xqje', 'xqjf', 'xqkd', 'xqke', 'xqkf', 'xqld', 'xqle', 'xqlf', 'xrjd', 'xrje', 'xrjf', 'xrkd', 'xrke', 'xrkf', 'xrld', 'xrle', 'xrlf', 'xsjd', 'xsje', 'xsjf', 'xskd', 'xske', 'xskf', 'xsld', 'xsle', 'xslf', 'ypjd', 'ypje', 'ypjf', 'ypkd', 'ypke', 'ypkf', 'ypld', 'yple', 'yplf', 'yqjd', 'yqje', 'yqjf', 'yqkd', 'yqke', 'yqkf', 'yqld', 'yqle', 'yqlf', 'yrjd', 'yrje', 'yrjf', 'yrkd', 'yrke', 'yrkf', 'yrld', 'yrle', 'yrlf', 'ysjd', 'ysje', 'ysjf', 'yskd', 'yske', 'yskf', 'ysld', 'ysle', 'yslf', 'zpjd', 'zpje', 'zpjf', 'zpkd', 'zpke', 'zpkf', 'zpld', 'zple', 'zplf', 'zqjd', 'zqje', 'zqjf', 'zqkd', 'zqke', 'zqkf', 'zqld', 'zqle', 'zqlf', 'zrjd', 'zrje', 'zrjf', 'zrkd', 'zrke', 'zrkf', 'zrld', 'zrle', 'zrlf', 'zsjd', 'zsje', 'zsjf', 'zskd', 'zske', 'zskf', 'zsld', 'zsle', 'zslf']\n assert candidate(digits = \"425\") == ['gaj', 'gak', 'gal', 'gbj', 'gbk', 'gbl', 'gcj', 'gck', 'gcl', 'haj', 'hak', 'hal', 'hbj', 'hbk', 'hbl', 'hcj', 'hck', 'hcl', 'iaj', 'iak', 'ial', 'ibj', 'ibk', 'ibl', 'icj', 'ick', 'icl']\n assert candidate(digits = \"8\") == ['t', 'u', 'v']\n assert candidate(digits = \"256\") == ['ajm', 'ajn', 'ajo', 'akm', 'akn', 'ako', 'alm', 'aln', 'alo', 'bjm', 'bjn', 'bjo', 'bkm', 'bkn', 'bko', 'blm', 'bln', 'blo', 'cjm', 'cjn', 'cjo', 'ckm', 'ckn', 'cko', 'clm', 'cln', 'clo']\n assert candidate(digits = \"8888\") == ['tttt', 'tttu', 'tttv', 'ttut', 'ttuu', 'ttuv', 'ttvt', 'ttvu', 'ttvv', 'tutt', 'tutu', 'tutv', 'tuut', 'tuuu', 'tuuv', 'tuvt', 'tuvu', 'tuvv', 'tvtt', 'tvtu', 'tvtv', 'tvut', 'tvuu', 'tvuv', 'tvvt', 'tvvu', 'tvvv', 'uttt', 'uttu', 'uttv', 'utut', 'utuu', 'utuv', 'utvt', 'utvu', 'utvv', 'uutt', 'uutu', 'uutv', 'uuut', 'uuuu', 'uuuv', 'uuvt', 'uuvu', 'uuvv', 'uvtt', 'uvtu', 'uvtv', 'uvut', 'uvuu', 'uvuv', 'uvvt', 'uvvu', 'uvvv', 'vttt', 'vttu', 'vttv', 'vtut', 'vtuu', 'vtuv', 'vtvt', 'vtvu', 'vtvv', 'vutt', 'vutu', 'vutv', 'vuut', 'vuuu', 'vuuv', 'vuvt', 'vuvu', 'vuvv', 'vvtt', 'vvtu', 'vvtv', 'vvut', 'vvuu', 'vvuv', 'vvvt', 'vvvu', 'vvvv']\n assert candidate(digits = \"38\") == ['dt', 'du', 'dv', 'et', 'eu', 'ev', 'ft', 'fu', 'fv']\n assert candidate(digits = \"5555\") == ['jjjj', 'jjjk', 'jjjl', 'jjkj', 'jjkk', 'jjkl', 'jjlj', 'jjlk', 'jjll', 'jkjj', 'jkjk', 'jkjl', 'jkkj', 'jkkk', 'jkkl', 'jklj', 'jklk', 'jkll', 'jljj', 'jljk', 'jljl', 'jlkj', 'jlkk', 'jlkl', 'jllj', 'jllk', 'jlll', 'kjjj', 'kjjk', 'kjjl', 'kjkj', 'kjkk', 'kjkl', 'kjlj', 'kjlk', 'kjll', 'kkjj', 'kkjk', 'kkjl', 'kkkj', 'kkkk', 'kkkl', 'kklj', 'kklk', 'kkll', 'kljj', 'kljk', 'kljl', 'klkj', 'klkk', 'klkl', 'kllj', 'kllk', 'klll', 'ljjj', 'ljjk', 'ljjl', 'ljkj', 'ljkk', 'ljkl', 'ljlj', 'ljlk', 'ljll', 'lkjj', 'lkjk', 'lkjl', 'lkkj', 'lkkk', 'lkkl', 'lklj', 'lklk', 'lkll', 'lljj', 'lljk', 'lljl', 'llkj', 'llkk', 'llkl', 'lllj', 'lllk', 'llll']\n assert candidate(digits = \"293\") == ['awd', 'awe', 'awf', 'axd', 'axe', 'axf', 'ayd', 'aye', 'ayf', 'azd', 'aze', 'azf', 'bwd', 'bwe', 'bwf', 'bxd', 'bxe', 'bxf', 'byd', 'bye', 'byf', 'bzd', 'bze', 'bzf', 'cwd', 'cwe', 'cwf', 'cxd', 'cxe', 'cxf', 'cyd', 'cye', 'cyf', 'czd', 'cze', 'czf']\n assert candidate(digits = \"273\") == ['apd', 'ape', 'apf', 'aqd', 'aqe', 'aqf', 'ard', 'are', 'arf', 'asd', 'ase', 'asf', 'bpd', 'bpe', 'bpf', 'bqd', 'bqe', 'bqf', 'brd', 'bre', 'brf', 'bsd', 'bse', 'bsf', 'cpd', 'cpe', 'cpf', 'cqd', 'cqe', 'cqf', 'crd', 'cre', 'crf', 'csd', 'cse', 'csf']\n assert candidate(digits = \"9999\") == ['wwww', 'wwwx', 'wwwy', 'wwwz', 'wwxw', 'wwxx', 'wwxy', 'wwxz', 'wwyw', 'wwyx', 'wwyy', 'wwyz', 'wwzw', 'wwzx', 'wwzy', 'wwzz', 'wxww', 'wxwx', 'wxwy', 'wxwz', 'wxxw', 'wxxx', 'wxxy', 'wxxz', 'wxyw', 'wxyx', 'wxyy', 'wxyz', 'wxzw', 'wxzx', 'wxzy', 'wxzz', 'wyww', 'wywx', 'wywy', 'wywz', 'wyxw', 'wyxx', 'wyxy', 'wyxz', 'wyyw', 'wyyx', 'wyyy', 'wyyz', 'wyzw', 'wyzx', 'wyzy', 'wyzz', 'wzww', 'wzwx', 'wzwy', 'wzwz', 'wzxw', 'wzxx', 'wzxy', 'wzxz', 'wzyw', 'wzyx', 'wzyy', 'wzyz', 'wzzw', 'wzzx', 'wzzy', 'wzzz', 'xwww', 'xwwx', 'xwwy', 'xwwz', 'xwxw', 'xwxx', 'xwxy', 'xwxz', 'xwyw', 'xwyx', 'xwyy', 'xwyz', 'xwzw', 'xwzx', 'xwzy', 'xwzz', 'xxww', 'xxwx', 'xxwy', 'xxwz', 'xxxw', 'xxxx', 'xxxy', 'xxxz', 'xxyw', 'xxyx', 'xxyy', 'xxyz', 'xxzw', 'xxzx', 'xxzy', 'xxzz', 'xyww', 'xywx', 'xywy', 'xywz', 'xyxw', 'xyxx', 'xyxy', 'xyxz', 'xyyw', 'xyyx', 'xyyy', 'xyyz', 'xyzw', 'xyzx', 'xyzy', 'xyzz', 'xzww', 'xzwx', 'xzwy', 'xzwz', 'xzxw', 'xzxx', 'xzxy', 'xzxz', 'xzyw', 'xzyx', 'xzyy', 'xzyz', 'xzzw', 'xzzx', 'xzzy', 'xzzz', 'ywww', 'ywwx', 'ywwy', 'ywwz', 'ywxw', 'ywxx', 'ywxy', 'ywxz', 'ywyw', 'ywyx', 'ywyy', 'ywyz', 'ywzw', 'ywzx', 'ywzy', 'ywzz', 'yxww', 'yxwx', 'yxwy', 'yxwz', 'yxxw', 'yxxx', 'yxxy', 'yxxz', 'yxyw', 'yxyx', 'yxyy', 'yxyz', 'yxzw', 'yxzx', 'yxzy', 'yxzz', 'yyww', 'yywx', 'yywy', 'yywz', 'yyxw', 'yyxx', 'yyxy', 'yyxz', 'yyyw', 'yyyx', 'yyyy', 'yyyz', 'yyzw', 'yyzx', 'yyzy', 'yyzz', 'yzww', 'yzwx', 'yzwy', 'yzwz', 'yzxw', 'yzxx', 'yzxy', 'yzxz', 'yzyw', 'yzyx', 'yzyy', 'yzyz', 'yzzw', 'yzzx', 'yzzy', 'yzzz', 'zwww', 'zwwx', 'zwwy', 'zwwz', 'zwxw', 'zwxx', 'zwxy', 'zwxz', 'zwyw', 'zwyx', 'zwyy', 'zwyz', 'zwzw', 'zwzx', 'zwzy', 'zwzz', 'zxww', 'zxwx', 'zxwy', 'zxwz', 'zxxw', 'zxxx', 'zxxy', 'zxxz', 'zxyw', 'zxyx', 'zxyy', 'zxyz', 'zxzw', 'zxzx', 'zxzy', 'zxzz', 'zyww', 'zywx', 'zywy', 'zywz', 'zyxw', 'zyxx', 'zyxy', 'zyxz', 'zyyw', 'zyyx', 'zyyy', 'zyyz', 'zyzw', 'zyzx', 'zyzy', 'zyzz', 'zzww', 'zzwx', 'zzwy', 'zzwz', 'zzxw', 'zzxx', 'zzxy', 'zzxz', 'zzyw', 'zzyx', 'zzyy', 'zzyz', 'zzzw', 'zzzx', 'zzzy', 'zzzz']\n assert candidate(digits = \"999\") == ['www', 'wwx', 'wwy', 'wwz', 'wxw', 'wxx', 'wxy', 'wxz', 'wyw', 'wyx', 'wyy', 'wyz', 'wzw', 'wzx', 'wzy', 'wzz', 'xww', 'xwx', 'xwy', 'xwz', 'xxw', 'xxx', 'xxy', 'xxz', 'xyw', 'xyx', 'xyy', 'xyz', 'xzw', 'xzx', 'xzy', 'xzz', 'yww', 'ywx', 'ywy', 'ywz', 'yxw', 'yxx', 'yxy', 'yxz', 'yyw', 'yyx', 'yyy', 'yyz', 'yzw', 'yzx', 'yzy', 'yzz', 'zww', 'zwx', 'zwy', 'zwz', 'zxw', 'zxx', 'zxy', 'zxz', 'zyw', 'zyx', 'zyy', 'zyz', 'zzw', 'zzx', 'zzy', 'zzz']\n assert candidate(digits = \"73\") == ['pd', 'pe', 'pf', 'qd', 'qe', 'qf', 'rd', 're', 'rf', 'sd', 'se', 'sf']\n assert candidate(digits = \"673\") == ['mpd', 'mpe', 'mpf', 'mqd', 'mqe', 'mqf', 'mrd', 'mre', 'mrf', 'msd', 'mse', 'msf', 'npd', 'npe', 'npf', 'nqd', 'nqe', 'nqf', 'nrd', 'nre', 'nrf', 'nsd', 'nse', 'nsf', 'opd', 'ope', 'opf', 'oqd', 'oqe', 'oqf', 'ord', 'ore', 'orf', 'osd', 'ose', 'osf']\n assert candidate(digits = \"9257\") == ['wajp', 'wajq', 'wajr', 'wajs', 'wakp', 'wakq', 'wakr', 'waks', 'walp', 'walq', 'walr', 'wals', 'wbjp', 'wbjq', 'wbjr', 'wbjs', 'wbkp', 'wbkq', 'wbkr', 'wbks', 'wblp', 'wblq', 'wblr', 'wbls', 'wcjp', 'wcjq', 'wcjr', 'wcjs', 'wckp', 'wckq', 'wckr', 'wcks', 'wclp', 'wclq', 'wclr', 'wcls', 'xajp', 'xajq', 'xajr', 'xajs', 'xakp', 'xakq', 'xakr', 'xaks', 'xalp', 'xalq', 'xalr', 'xals', 'xbjp', 'xbjq', 'xbjr', 'xbjs', 'xbkp', 'xbkq', 'xbkr', 'xbks', 'xblp', 'xblq', 'xblr', 'xbls', 'xcjp', 'xcjq', 'xcjr', 'xcjs', 'xckp', 'xckq', 'xckr', 'xcks', 'xclp', 'xclq', 'xclr', 'xcls', 'yajp', 'yajq', 'yajr', 'yajs', 'yakp', 'yakq', 'yakr', 'yaks', 'yalp', 'yalq', 'yalr', 'yals', 'ybjp', 'ybjq', 'ybjr', 'ybjs', 'ybkp', 'ybkq', 'ybkr', 'ybks', 'yblp', 'yblq', 'yblr', 'ybls', 'ycjp', 'ycjq', 'ycjr', 'ycjs', 'yckp', 'yckq', 'yckr', 'ycks', 'yclp', 'yclq', 'yclr', 'ycls', 'zajp', 'zajq', 'zajr', 'zajs', 'zakp', 'zakq', 'zakr', 'zaks', 'zalp', 'zalq', 'zalr', 'zals', 'zbjp', 'zbjq', 'zbjr', 'zbjs', 'zbkp', 'zbkq', 'zbkr', 'zbks', 'zblp', 'zblq', 'zblr', 'zbls', 'zcjp', 'zcjq', 'zcjr', 'zcjs', 'zckp', 'zckq', 'zckr', 'zcks', 'zclp', 'zclq', 'zclr', 'zcls']\n assert candidate(digits = \"33\") == ['dd', 'de', 'df', 'ed', 'ee', 'ef', 'fd', 'fe', 'ff']\n assert candidate(digits = \"555\") == ['jjj', 'jjk', 'jjl', 'jkj', 'jkk', 'jkl', 'jlj', 'jlk', 'jll', 'kjj', 'kjk', 'kjl', 'kkj', 'kkk', 'kkl', 'klj', 'klk', 'kll', 'ljj', 'ljk', 'ljl', 'lkj', 'lkk', 'lkl', 'llj', 'llk', 'lll']\n assert candidate(digits = \"7777\") == ['pppp', 'pppq', 'pppr', 'ppps', 'ppqp', 'ppqq', 'ppqr', 'ppqs', 'pprp', 'pprq', 'pprr', 'pprs', 'ppsp', 'ppsq', 'ppsr', 'ppss', 'pqpp', 'pqpq', 'pqpr', 'pqps', 'pqqp', 'pqqq', 'pqqr', 'pqqs', 'pqrp', 'pqrq', 'pqrr', 'pqrs', 'pqsp', 'pqsq', 'pqsr', 'pqss', 'prpp', 'prpq', 'prpr', 'prps', 'prqp', 'prqq', 'prqr', 'prqs', 'prrp', 'prrq', 'prrr', 'prrs', 'prsp', 'prsq', 'prsr', 'prss', 'pspp', 'pspq', 'pspr', 'psps', 'psqp', 'psqq', 'psqr', 'psqs', 'psrp', 'psrq', 'psrr', 'psrs', 'pssp', 'pssq', 'pssr', 'psss', 'qppp', 'qppq', 'qppr', 'qpps', 'qpqp', 'qpqq', 'qpqr', 'qpqs', 'qprp', 'qprq', 'qprr', 'qprs', 'qpsp', 'qpsq', 'qpsr', 'qpss', 'qqpp', 'qqpq', 'qqpr', 'qqps', 'qqqp', 'qqqq', 'qqqr', 'qqqs', 'qqrp', 'qqrq', 'qqrr', 'qqrs', 'qqsp', 'qqsq', 'qqsr', 'qqss', 'qrpp', 'qrpq', 'qrpr', 'qrps', 'qrqp', 'qrqq', 'qrqr', 'qrqs', 'qrrp', 'qrrq', 'qrrr', 'qrrs', 'qrsp', 'qrsq', 'qrsr', 'qrss', 'qspp', 'qspq', 'qspr', 'qsps', 'qsqp', 'qsqq', 'qsqr', 'qsqs', 'qsrp', 'qsrq', 'qsrr', 'qsrs', 'qssp', 'qssq', 'qssr', 'qsss', 'rppp', 'rppq', 'rppr', 'rpps', 'rpqp', 'rpqq', 'rpqr', 'rpqs', 'rprp', 'rprq', 'rprr', 'rprs', 'rpsp', 'rpsq', 'rpsr', 'rpss', 'rqpp', 'rqpq', 'rqpr', 'rqps', 'rqqp', 'rqqq', 'rqqr', 'rqqs', 'rqrp', 'rqrq', 'rqrr', 'rqrs', 'rqsp', 'rqsq', 'rqsr', 'rqss', 'rrpp', 'rrpq', 'rrpr', 'rrps', 'rrqp', 'rrqq', 'rrqr', 'rrqs', 'rrrp', 'rrrq', 'rrrr', 'rrrs', 'rrsp', 'rrsq', 'rrsr', 'rrss', 'rspp', 'rspq', 'rspr', 'rsps', 'rsqp', 'rsqq', 'rsqr', 'rsqs', 'rsrp', 'rsrq', 'rsrr', 'rsrs', 'rssp', 'rssq', 'rssr', 'rsss', 'sppp', 'sppq', 'sppr', 'spps', 'spqp', 'spqq', 'spqr', 'spqs', 'sprp', 'sprq', 'sprr', 'sprs', 'spsp', 'spsq', 'spsr', 'spss', 'sqpp', 'sqpq', 'sqpr', 'sqps', 'sqqp', 'sqqq', 'sqqr', 'sqqs', 'sqrp', 'sqrq', 'sqrr', 'sqrs', 'sqsp', 'sqsq', 'sqsr', 'sqss', 'srpp', 'srpq', 'srpr', 'srps', 'srqp', 'srqq', 'srqr', 'srqs', 'srrp', 'srrq', 'srrr', 'srrs', 'srsp', 'srsq', 'srsr', 'srss', 'sspp', 'sspq', 'sspr', 'ssps', 'ssqp', 'ssqq', 'ssqr', 'ssqs', 'ssrp', 'ssrq', 'ssrr', 'ssrs', 'sssp', 'sssq', 'sssr', 'ssss']\n assert candidate(digits = \"59\") == ['jw', 'jx', 'jy', 'jz', 'kw', 'kx', 'ky', 'kz', 'lw', 'lx', 'ly', 'lz']\n assert candidate(digits = \"369\") == ['dmw', 'dmx', 'dmy', 'dmz', 'dnw', 'dnx', 'dny', 'dnz', 'dow', 'dox', 'doy', 'doz', 'emw', 'emx', 'emy', 'emz', 'enw', 'enx', 'eny', 'enz', 'eow', 'eox', 'eoy', 'eoz', 'fmw', 'fmx', 'fmy', 'fmz', 'fnw', 'fnx', 'fny', 'fnz', 'fow', 'fox', 'foy', 'foz']\n assert candidate(digits = \"298\") == ['awt', 'awu', 'awv', 'axt', 'axu', 'axv', 'ayt', 'ayu', 'ayv', 'azt', 'azu', 'azv', 'bwt', 'bwu', 'bwv', 'bxt', 'bxu', 'bxv', 'byt', 'byu', 'byv', 'bzt', 'bzu', 'bzv', 'cwt', 'cwu', 'cwv', 'cxt', 'cxu', 'cxv', 'cyt', 'cyu', 'cyv', 'czt', 'czu', 'czv']\n assert candidate(digits = \"88\") == ['tt', 'tu', 'tv', 'ut', 'uu', 'uv', 'vt', 'vu', 'vv']\n assert candidate(digits = \"2222\") == ['aaaa', 'aaab', 'aaac', 'aaba', 'aabb', 'aabc', 'aaca', 'aacb', 'aacc', 'abaa', 'abab', 'abac', 'abba', 'abbb', 'abbc', 'abca', 'abcb', 'abcc', 'acaa', 'acab', 'acac', 'acba', 'acbb', 'acbc', 'acca', 'accb', 'accc', 'baaa', 'baab', 'baac', 'baba', 'babb', 'babc', 'baca', 'bacb', 'bacc', 'bbaa', 'bbab', 'bbac', 'bbba', 'bbbb', 'bbbc', 'bbca', 'bbcb', 'bbcc', 'bcaa', 'bcab', 'bcac', 'bcba', 'bcbb', 'bcbc', 'bcca', 'bccb', 'bccc', 'caaa', 'caab', 'caac', 'caba', 'cabb', 'cabc', 'caca', 'cacb', 'cacc', 'cbaa', 'cbab', 'cbac', 'cbba', 'cbbb', 'cbbc', 'cbca', 'cbcb', 'cbcc', 'ccaa', 'ccab', 'ccac', 'ccba', 'ccbb', 'ccbc', 'ccca', 'cccb', 'cccc']\n assert candidate(digits = \"97531\") == ['wpjdw', 'wpjdx', 'wpjdy', 'wpjdz', 'wpjew', 'wpjex', 'wpjey', 'wpjez', 'wpjfw', 'wpjfx', 'wpjfy', 'wpjfz', 'wpkdw', 'wpkdx', 'wpkdy', 'wpkdz', 'wpkew', 'wpkex', 'wpkey', 'wpkez', 'wpkfw', 'wpkfx', 'wpkfy', 'wpkfz', 'wpldw', 'wpldx', 'wpldy', 'wpldz', 'wplew', 'wplex', 'wpley', 'wplez', 'wplfw', 'wplfx', 'wplfy', 'wplfz', 'wqjdw', 'wqjdx', 'wqjdy', 'wqjdz', 'wqjew', 'wqjex', 'wqjey', 'wqjez', 'wqjfw', 'wqjfx', 'wqjfy', 'wqjfz', 'wqkdw', 'wqkdx', 'wqkdy', 'wqkdz', 'wqkew', 'wqkex', 'wqkey', 'wqkez', 'wqkfw', 'wqkfx', 'wqkfy', 'wqkfz', 'wqldw', 'wqldx', 'wqldy', 'wqldz', 'wqlew', 'wqlex', 'wqley', 'wqlez', 'wqlfw', 'wqlfx', 'wqlfy', 'wqlfz', 'wrjdw', 'wrjdx', 'wrjdy', 'wrjdz', 'wrjew', 'wrjex', 'wrjey', 'wrjez', 'wrjfw', 'wrjfx', 'wrjfy', 'wrjfz', 'wrkdw', 'wrkdx', 'wrkdy', 'wrkdz', 'wrkew', 'wrkex', 'wrkey', 'wrkez', 'wrkfw', 'wrkfx', 'wrkfy', 'wrkfz', 'wrldw', 'wrldx', 'wrldy', 'wrldz', 'wrlew', 'wrlex', 'wrley', 'wrlez', 'wrlfw', 'wrlfx', 'wrlfy', 'wrlfz', 'wsjdw', 'wsjdx', 'wsjdy', 'wsjdz', 'wsjew', 'wsjex', 'wsjey', 'wsjez', 'wsjfw', 'wsjfx', 'wsjfy', 'wsjfz', 'wskdw', 'wskdx', 'wskdy', 'wskdz', 'wskew', 'wskex', 'wskey', 'wskez', 'wskfw', 'wskfx', 'wskfy', 'wskfz', 'wsldw', 'wsldx', 'wsldy', 'wsldz', 'wslew', 'wslex', 'wsley', 'wslez', 'wslfw', 'wslfx', 'wslfy', 'wslfz', 'xpjdw', 'xpjdx', 'xpjdy', 'xpjdz', 'xpjew', 'xpjex', 'xpjey', 'xpjez', 'xpjfw', 'xpjfx', 'xpjfy', 'xpjfz', 'xpkdw', 'xpkdx', 'xpkdy', 'xpkdz', 'xpkew', 'xpkex', 'xpkey', 'xpkez', 'xpkfw', 'xpkfx', 'xpkfy', 'xpkfz', 'xpldw', 'xpldx', 'xpldy', 'xpldz', 'xplew', 'xplex', 'xpley', 'xplez', 'xplfw', 'xplfx', 'xplfy', 'xplfz', 'xqjdw', 'xqjdx', 'xqjdy', 'xqjdz', 'xqjew', 'xqjex', 'xqjey', 'xqjez', 'xqjfw', 'xqjfx', 'xqjfy', 'xqjfz', 'xqkdw', 'xqkdx', 'xqkdy', 'xqkdz', 'xqkew', 'xqkex', 'xqkey', 'xqkez', 'xqkfw', 'xqkfx', 'xqkfy', 'xqkfz', 'xqldw', 'xqldx', 'xqldy', 'xqldz', 'xqlew', 'xqlex', 'xqley', 'xqlez', 'xqlfw', 'xqlfx', 'xqlfy', 'xqlfz', 'xrjdw', 'xrjdx', 'xrjdy', 'xrjdz', 'xrjew', 'xrjex', 'xrjey', 'xrjez', 'xrjfw', 'xrjfx', 'xrjfy', 'xrjfz', 'xrkdw', 'xrkdx', 'xrkdy', 'xrkdz', 'xrkew', 'xrkex', 'xrkey', 'xrkez', 'xrkfw', 'xrkfx', 'xrkfy', 'xrkfz', 'xrldw', 'xrldx', 'xrldy', 'xrldz', 'xrlew', 'xrlex', 'xrley', 'xrlez', 'xrlfw', 'xrlfx', 'xrlfy', 'xrlfz', 'xsjdw', 'xsjdx', 'xsjdy', 'xsjdz', 'xsjew', 'xsjex', 'xsjey', 'xsjez', 'xsjfw', 'xsjfx', 'xsjfy', 'xsjfz', 'xskdw', 'xskdx', 'xskdy', 'xskdz', 'xskew', 'xskex', 'xskey', 'xskez', 'xskfw', 'xskfx', 'xskfy', 'xskfz', 'xsldw', 'xsldx', 'xsldy', 'xsldz', 'xslew', 'xslex', 'xsley', 'xslez', 'xslfw', 'xslfx', 'xslfy', 'xslfz', 'ypjdw', 'ypjdx', 'ypjdy', 'ypjdz', 'ypjew', 'ypjex', 'ypjey', 'ypjez', 'ypjfw', 'ypjfx', 'ypjfy', 'ypjfz', 'ypkdw', 'ypkdx', 'ypkdy', 'ypkdz', 'ypkew', 'ypkex', 'ypkey', 'ypkez', 'ypkfw', 'ypkfx', 'ypkfy', 'ypkfz', 'ypldw', 'ypldx', 'ypldy', 'ypldz', 'yplew', 'yplex', 'ypley', 'yplez', 'yplfw', 'yplfx', 'yplfy', 'yplfz', 'yqjdw', 'yqjdx', 'yqjdy', 'yqjdz', 'yqjew', 'yqjex', 'yqjey', 'yqjez', 'yqjfw', 'yqjfx', 'yqjfy', 'yqjfz', 'yqkdw', 'yqkdx', 'yqkdy', 'yqkdz', 'yqkew', 'yqkex', 'yqkey', 'yqkez', 'yqkfw', 'yqkfx', 'yqkfy', 'yqkfz', 'yqldw', 'yqldx', 'yqldy', 'yqldz', 'yqlew', 'yqlex', 'yqley', 'yqlez', 'yqlfw', 'yqlfx', 'yqlfy', 'yqlfz', 'yrjdw', 'yrjdx', 'yrjdy', 'yrjdz', 'yrjew', 'yrjex', 'yrjey', 'yrjez', 'yrjfw', 'yrjfx', 'yrjfy', 'yrjfz', 'yrkdw', 'yrkdx', 'yrkdy', 'yrkdz', 'yrkew', 'yrkex', 'yrkey', 'yrkez', 'yrkfw', 'yrkfx', 'yrkfy', 'yrkfz', 'yrldw', 'yrldx', 'yrldy', 'yrldz', 'yrlew', 'yrlex', 'yrley', 'yrlez', 'yrlfw', 'yrlfx', 'yrlfy', 'yrlfz', 'ysjdw', 'ysjdx', 'ysjdy', 'ysjdz', 'ysjew', 'ysjex', 'ysjey', 'ysjez', 'ysjfw', 'ysjfx', 'ysjfy', 'ysjfz', 'yskdw', 'yskdx', 'yskdy', 'yskdz', 'yskew', 'yskex', 'yskey', 'yskez', 'yskfw', 'yskfx', 'yskfy', 'yskfz', 'ysldw', 'ysldx', 'ysldy', 'ysldz', 'yslew', 'yslex', 'ysley', 'yslez', 'yslfw', 'yslfx', 'yslfy', 'yslfz', 'zpjdw', 'zpjdx', 'zpjdy', 'zpjdz', 'zpjew', 'zpjex', 'zpjey', 'zpjez', 'zpjfw', 'zpjfx', 'zpjfy', 'zpjfz', 'zpkdw', 'zpkdx', 'zpkdy', 'zpkdz', 'zpkew', 'zpkex', 'zpkey', 'zpkez', 'zpkfw', 'zpkfx', 'zpkfy', 'zpkfz', 'zpldw', 'zpldx', 'zpldy', 'zpldz', 'zplew', 'zplex', 'zpley', 'zplez', 'zplfw', 'zplfx', 'zplfy', 'zplfz', 'zqjdw', 'zqjdx', 'zqjdy', 'zqjdz', 'zqjew', 'zqjex', 'zqjey', 'zqjez', 'zqjfw', 'zqjfx', 'zqjfy', 'zqjfz', 'zqkdw', 'zqkdx', 'zqkdy', 'zqkdz', 'zqkew', 'zqkex', 'zqkey', 'zqkez', 'zqkfw', 'zqkfx', 'zqkfy', 'zqkfz', 'zqldw', 'zqldx', 'zqldy', 'zqldz', 'zqlew', 'zqlex', 'zqley', 'zqlez', 'zqlfw', 'zqlfx', 'zqlfy', 'zqlfz', 'zrjdw', 'zrjdx', 'zrjdy', 'zrjdz', 'zrjew', 'zrjex', 'zrjey', 'zrjez', 'zrjfw', 'zrjfx', 'zrjfy', 'zrjfz', 'zrkdw', 'zrkdx', 'zrkdy', 'zrkdz', 'zrkew', 'zrkex', 'zrkey', 'zrkez', 'zrkfw', 'zrkfx', 'zrkfy', 'zrkfz', 'zrldw', 'zrldx', 'zrldy', 'zrldz', 'zrlew', 'zrlex', 'zrley', 'zrlez', 'zrlfw', 'zrlfx', 'zrlfy', 'zrlfz', 'zsjdw', 'zsjdx', 'zsjdy', 'zsjdz', 'zsjew', 'zsjex', 'zsjey', 'zsjez', 'zsjfw', 'zsjfx', 'zsjfy', 'zsjfz', 'zskdw', 'zskdx', 'zskdy', 'zskdz', 'zskew', 'zskex', 'zskey', 'zskez', 'zskfw', 'zskfx', 'zskfy', 'zskfz', 'zsldw', 'zsldx', 'zsldy', 'zsldz', 'zslew', 'zslex', 'zsley', 'zslez', 'zslfw', 'zslfx', 'zslfy', 'zslfz']\n assert candidate(digits = \"2357\") == ['adjp', 'adjq', 'adjr', 'adjs', 'adkp', 'adkq', 'adkr', 'adks', 'adlp', 'adlq', 'adlr', 'adls', 'aejp', 'aejq', 'aejr', 'aejs', 'aekp', 'aekq', 'aekr', 'aeks', 'aelp', 'aelq', 'aelr', 'aels', 'afjp', 'afjq', 'afjr', 'afjs', 'afkp', 'afkq', 'afkr', 'afks', 'aflp', 'aflq', 'aflr', 'afls', 'bdjp', 'bdjq', 'bdjr', 'bdjs', 'bdkp', 'bdkq', 'bdkr', 'bdks', 'bdlp', 'bdlq', 'bdlr', 'bdls', 'bejp', 'bejq', 'bejr', 'bejs', 'bekp', 'bekq', 'bekr', 'beks', 'belp', 'belq', 'belr', 'bels', 'bfjp', 'bfjq', 'bfjr', 'bfjs', 'bfkp', 'bfkq', 'bfkr', 'bfks', 'bflp', 'bflq', 'bflr', 'bfls', 'cdjp', 'cdjq', 'cdjr', 'cdjs', 'cdkp', 'cdkq', 'cdkr', 'cdks', 'cdlp', 'cdlq', 'cdlr', 'cdls', 'cejp', 'cejq', 'cejr', 'cejs', 'cekp', 'cekq', 'cekr', 'ceks', 'celp', 'celq', 'celr', 'cels', 'cfjp', 'cfjq', 'cfjr', 'cfjs', 'cfkp', 'cfkq', 'cfkr', 'cfks', 'cflp', 'cflq', 'cflr', 'cfls']\n assert candidate(digits = \"29\") == ['aw', 'ax', 'ay', 'az', 'bw', 'bx', 'by', 'bz', 'cw', 'cx', 'cy', 'cz']\n assert candidate(digits = \"357\") == ['djp', 'djq', 'djr', 'djs', 'dkp', 'dkq', 'dkr', 'dks', 'dlp', 'dlq', 'dlr', 'dls', 'ejp', 'ejq', 'ejr', 'ejs', 'ekp', 'ekq', 'ekr', 'eks', 'elp', 'elq', 'elr', 'els', 'fjp', 'fjq', 'fjr', 'fjs', 'fkp', 'fkq', 'fkr', 'fks', 'flp', 'flq', 'flr', 'fls']\n assert candidate(digits = \"44\") == ['gg', 'gh', 'gi', 'hg', 'hh', 'hi', 'ig', 'ih', 'ii']\n assert candidate(digits = \"294\") == ['awg', 'awh', 'awi', 'axg', 'axh', 'axi', 'ayg', 'ayh', 'ayi', 'azg', 'azh', 'azi', 'bwg', 'bwh', 'bwi', 'bxg', 'bxh', 'bxi', 'byg', 'byh', 'byi', 'bzg', 'bzh', 'bzi', 'cwg', 'cwh', 'cwi', 'cxg', 'cxh', 'cxi', 'cyg', 'cyh', 'cyi', 'czg', 'czh', 'czi']\n assert candidate(digits = \"235\") == ['adj', 'adk', 'adl', 'aej', 'aek', 'ael', 'afj', 'afk', 'afl', 'bdj', 'bdk', 'bdl', 'bej', 'bek', 'bel', 'bfj', 'bfk', 'bfl', 'cdj', 'cdk', 'cdl', 'cej', 'cek', 'cel', 'cfj', 'cfk', 'cfl']\n assert candidate(digits = \"6789\") == ['mptw', 'mptx', 'mpty', 'mptz', 'mpuw', 'mpux', 'mpuy', 'mpuz', 'mpvw', 'mpvx', 'mpvy', 'mpvz', 'mqtw', 'mqtx', 'mqty', 'mqtz', 'mquw', 'mqux', 'mquy', 'mquz', 'mqvw', 'mqvx', 'mqvy', 'mqvz', 'mrtw', 'mrtx', 'mrty', 'mrtz', 'mruw', 'mrux', 'mruy', 'mruz', 'mrvw', 'mrvx', 'mrvy', 'mrvz', 'mstw', 'mstx', 'msty', 'mstz', 'msuw', 'msux', 'msuy', 'msuz', 'msvw', 'msvx', 'msvy', 'msvz', 'nptw', 'nptx', 'npty', 'nptz', 'npuw', 'npux', 'npuy', 'npuz', 'npvw', 'npvx', 'npvy', 'npvz', 'nqtw', 'nqtx', 'nqty', 'nqtz', 'nquw', 'nqux', 'nquy', 'nquz', 'nqvw', 'nqvx', 'nqvy', 'nqvz', 'nrtw', 'nrtx', 'nrty', 'nrtz', 'nruw', 'nrux', 'nruy', 'nruz', 'nrvw', 'nrvx', 'nrvy', 'nrvz', 'nstw', 'nstx', 'nsty', 'nstz', 'nsuw', 'nsux', 'nsuy', 'nsuz', 'nsvw', 'nsvx', 'nsvy', 'nsvz', 'optw', 'optx', 'opty', 'optz', 'opuw', 'opux', 'opuy', 'opuz', 'opvw', 'opvx', 'opvy', 'opvz', 'oqtw', 'oqtx', 'oqty', 'oqtz', 'oquw', 'oqux', 'oquy', 'oquz', 'oqvw', 'oqvx', 'oqvy', 'oqvz', 'ortw', 'ortx', 'orty', 'ortz', 'oruw', 'orux', 'oruy', 'oruz', 'orvw', 'orvx', 'orvy', 'orvz', 'ostw', 'ostx', 'osty', 'ostz', 'osuw', 'osux', 'osuy', 'osuz', 'osvw', 'osvx', 'osvy', 'osvz']\n assert candidate(digits = \"697\") == ['mwp', 'mwq', 'mwr', 'mws', 'mxp', 'mxq', 'mxr', 'mxs', 'myp', 'myq', 'myr', 'mys', 'mzp', 'mzq', 'mzr', 'mzs', 'nwp', 'nwq', 'nwr', 'nws', 'nxp', 'nxq', 'nxr', 'nxs', 'nyp', 'nyq', 'nyr', 'nys', 'nzp', 'nzq', 'nzr', 'nzs', 'owp', 'owq', 'owr', 'ows', 'oxp', 'oxq', 'oxr', 'oxs', 'oyp', 'oyq', 'oyr', 'oys', 'ozp', 'ozq', 'ozr', 'ozs']\n assert candidate(digits = \"57\") == ['jp', 'jq', 'jr', 'js', 'kp', 'kq', 'kr', 'ks', 'lp', 'lq', 'lr', 'ls']\n assert candidate(digits = \"237\") == ['adp', 'adq', 'adr', 'ads', 'aep', 'aeq', 'aer', 'aes', 'afp', 'afq', 'afr', 'afs', 'bdp', 'bdq', 'bdr', 'bds', 'bep', 'beq', 'ber', 'bes', 'bfp', 'bfq', 'bfr', 'bfs', 'cdp', 'cdq', 'cdr', 'cds', 'cep', 'ceq', 'cer', 'ces', 'cfp', 'cfq', 'cfr', 'cfs']\n assert candidate(digits = \"7\") == ['p', 'q', 'r', 's']\n assert candidate(digits = \"789\") == ['ptw', 'ptx', 'pty', 'ptz', 'puw', 'pux', 'puy', 'puz', 'pvw', 'pvx', 'pvy', 'pvz', 'qtw', 'qtx', 'qty', 'qtz', 'quw', 'qux', 'quy', 'quz', 'qvw', 'qvx', 'qvy', 'qvz', 'rtw', 'rtx', 'rty', 'rtz', 'ruw', 'rux', 'ruy', 'ruz', 'rvw', 'rvx', 'rvy', 'rvz', 'stw', 'stx', 'sty', 'stz', 'suw', 'sux', 'suy', 'suz', 'svw', 'svx', 'svy', 'svz']\n assert candidate(digits = \"777\") == ['ppp', 'ppq', 'ppr', 'pps', 'pqp', 'pqq', 'pqr', 'pqs', 'prp', 'prq', 'prr', 'prs', 'psp', 'psq', 'psr', 'pss', 'qpp', 'qpq', 'qpr', 'qps', 'qqp', 'qqq', 'qqr', 'qqs', 'qrp', 'qrq', 'qrr', 'qrs', 'qsp', 'qsq', 'qsr', 'qss', 'rpp', 'rpq', 'rpr', 'rps', 'rqp', 'rqq', 'rqr', 'rqs', 'rrp', 'rrq', 'rrr', 'rrs', 'rsp', 'rsq', 'rsr', 'rss', 'spp', 'spq', 'spr', 'sps', 'sqp', 'sqq', 'sqr', 'sqs', 'srp', 'srq', 'srr', 'srs', 'ssp', 'ssq', 'ssr', 'sss']\n assert candidate(digits = \"222\") == ['aaa', 'aab', 'aac', 'aba', 'abb', 'abc', 'aca', 'acb', 'acc', 'baa', 'bab', 'bac', 'bba', 'bbb', 'bbc', 'bca', 'bcb', 'bcc', 'caa', 'cab', 'cac', 'cba', 'cbb', 'cbc', 'cca', 'ccb', 'ccc']\n assert candidate(digits = \"94\") == ['wg', 'wh', 'wi', 'xg', 'xh', 'xi', 'yg', 'yh', 'yi', 'zg', 'zh', 'zi']\n assert candidate(digits = \"377\") == ['dpp', 'dpq', 'dpr', 'dps', 'dqp', 'dqq', 'dqr', 'dqs', 'drp', 'drq', 'drr', 'drs', 'dsp', 'dsq', 'dsr', 'dss', 'epp', 'epq', 'epr', 'eps', 'eqp', 'eqq', 'eqr', 'eqs', 'erp', 'erq', 'err', 'ers', 'esp', 'esq', 'esr', 'ess', 'fpp', 'fpq', 'fpr', 'fps', 'fqp', 'fqq', 'fqr', 'fqs', 'frp', 'frq', 'frr', 'frs', 'fsp', 'fsq', 'fsr', 'fss']\n assert candidate(digits = \"923\") == ['wad', 'wae', 'waf', 'wbd', 'wbe', 'wbf', 'wcd', 'wce', 'wcf', 'xad', 'xae', 'xaf', 'xbd', 'xbe', 'xbf', 'xcd', 'xce', 'xcf', 'yad', 'yae', 'yaf', 'ybd', 'ybe', 'ybf', 'ycd', 'yce', 'ycf', 'zad', 'zae', 'zaf', 'zbd', 'zbe', 'zbf', 'zcd', 'zce', 'zcf']\n assert candidate(digits = \"333\") == ['ddd', 'dde', 'ddf', 'ded', 'dee', 'def', 'dfd', 'dfe', 'dff', 'edd', 'ede', 'edf', 'eed', 'eee', 'eef', 'efd', 'efe', 'eff', 'fdd', 'fde', 'fdf', 'fed', 'fee', 'fef', 'ffd', 'ffe', 'fff']\n assert candidate(digits = \"888\") == ['ttt', 'ttu', 'ttv', 'tut', 'tuu', 'tuv', 'tvt', 'tvu', 'tvv', 'utt', 'utu', 'utv', 'uut', 'uuu', 'uuv', 'uvt', 'uvu', 'uvv', 'vtt', 'vtu', 'vtv', 'vut', 'vuu', 'vuv', 'vvt', 'vvu', 'vvv']\n assert candidate(digits = \"4826\") == ['gtam', 'gtan', 'gtao', 'gtbm', 'gtbn', 'gtbo', 'gtcm', 'gtcn', 'gtco', 'guam', 'guan', 'guao', 'gubm', 'gubn', 'gubo', 'gucm', 'gucn', 'guco', 'gvam', 'gvan', 'gvao', 'gvbm', 'gvbn', 'gvbo', 'gvcm', 'gvcn', 'gvco', 'htam', 'htan', 'htao', 'htbm', 'htbn', 'htbo', 'htcm', 'htcn', 'htco', 'huam', 'huan', 'huao', 'hubm', 'hubn', 'hubo', 'hucm', 'hucn', 'huco', 'hvam', 'hvan', 'hvao', 'hvbm', 'hvbn', 'hvbo', 'hvcm', 'hvcn', 'hvco', 'itam', 'itan', 'itao', 'itbm', 'itbn', 'itbo', 'itcm', 'itcn', 'itco', 'iuam', 'iuan', 'iuao', 'iubm', 'iubn', 'iubo', 'iucm', 'iucn', 'iuco', 'ivam', 'ivan', 'ivao', 'ivbm', 'ivbn', 'ivbo', 'ivcm', 'ivcn', 'ivco']\n assert candidate(digits = \"724\") == ['pag', 'pah', 'pai', 'pbg', 'pbh', 'pbi', 'pcg', 'pch', 'pci', 'qag', 'qah', 'qai', 'qbg', 'qbh', 'qbi', 'qcg', 'qch', 'qci', 'rag', 'rah', 'rai', 'rbg', 'rbh', 'rbi', 'rcg', 'rch', 'rci', 'sag', 'sah', 'sai', 'sbg', 'sbh', 'sbi', 'scg', 'sch', 'sci']\n assert candidate(digits = \"2793\") == ['apwd', 'apwe', 'apwf', 'apxd', 'apxe', 'apxf', 'apyd', 'apye', 'apyf', 'apzd', 'apze', 'apzf', 'aqwd', 'aqwe', 'aqwf', 'aqxd', 'aqxe', 'aqxf', 'aqyd', 'aqye', 'aqyf', 'aqzd', 'aqze', 'aqzf', 'arwd', 'arwe', 'arwf', 'arxd', 'arxe', 'arxf', 'aryd', 'arye', 'aryf', 'arzd', 'arze', 'arzf', 'aswd', 'aswe', 'aswf', 'asxd', 'asxe', 'asxf', 'asyd', 'asye', 'asyf', 'aszd', 'asze', 'aszf', 'bpwd', 'bpwe', 'bpwf', 'bpxd', 'bpxe', 'bpxf', 'bpyd', 'bpye', 'bpyf', 'bpzd', 'bpze', 'bpzf', 'bqwd', 'bqwe', 'bqwf', 'bqxd', 'bqxe', 'bqxf', 'bqyd', 'bqye', 'bqyf', 'bqzd', 'bqze', 'bqzf', 'brwd', 'brwe', 'brwf', 'brxd', 'brxe', 'brxf', 'bryd', 'brye', 'bryf', 'brzd', 'brze', 'brzf', 'bswd', 'bswe', 'bswf', 'bsxd', 'bsxe', 'bsxf', 'bsyd', 'bsye', 'bsyf', 'bszd', 'bsze', 'bszf', 'cpwd', 'cpwe', 'cpwf', 'cpxd', 'cpxe', 'cpxf', 'cpyd', 'cpye', 'cpyf', 'cpzd', 'cpze', 'cpzf', 'cqwd', 'cqwe', 'cqwf', 'cqxd', 'cqxe', 'cqxf', 'cqyd', 'cqye', 'cqyf', 'cqzd', 'cqze', 'cqzf', 'crwd', 'crwe', 'crwf', 'crxd', 'crxe', 'crxf', 'cryd', 'crye', 'cryf', 'crzd', 'crze', 'crzf', 'cswd', 'cswe', 'cswf', 'csxd', 'csxe', 'csxf', 'csyd', 'csye', 'csyf', 'cszd', 'csze', 'cszf']\n assert candidate(digits = \"8947\") == ['twgp', 'twgq', 'twgr', 'twgs', 'twhp', 'twhq', 'twhr', 'twhs', 'twip', 'twiq', 'twir', 'twis', 'txgp', 'txgq', 'txgr', 'txgs', 'txhp', 'txhq', 'txhr', 'txhs', 'txip', 'txiq', 'txir', 'txis', 'tygp', 'tygq', 'tygr', 'tygs', 'tyhp', 'tyhq', 'tyhr', 'tyhs', 'tyip', 'tyiq', 'tyir', 'tyis', 'tzgp', 'tzgq', 'tzgr', 'tzgs', 'tzhp', 'tzhq', 'tzhr', 'tzhs', 'tzip', 'tziq', 'tzir', 'tzis', 'uwgp', 'uwgq', 'uwgr', 'uwgs', 'uwhp', 'uwhq', 'uwhr', 'uwhs', 'uwip', 'uwiq', 'uwir', 'uwis', 'uxgp', 'uxgq', 'uxgr', 'uxgs', 'uxhp', 'uxhq', 'uxhr', 'uxhs', 'uxip', 'uxiq', 'uxir', 'uxis', 'uygp', 'uygq', 'uygr', 'uygs', 'uyhp', 'uyhq', 'uyhr', 'uyhs', 'uyip', 'uyiq', 'uyir', 'uyis', 'uzgp', 'uzgq', 'uzgr', 'uzgs', 'uzhp', 'uzhq', 'uzhr', 'uzhs', 'uzip', 'uziq', 'uzir', 'uzis', 'vwgp', 'vwgq', 'vwgr', 'vwgs', 'vwhp', 'vwhq', 'vwhr', 'vwhs', 'vwip', 'vwiq', 'vwir', 'vwis', 'vxgp', 'vxgq', 'vxgr', 'vxgs', 'vxhp', 'vxhq', 'vxhr', 'vxhs', 'vxip', 'vxiq', 'vxir', 'vxis', 'vygp', 'vygq', 'vygr', 'vygs', 'vyhp', 'vyhq', 'vyhr', 'vyhs', 'vyip', 'vyiq', 'vyir', 'vyis', 'vzgp', 'vzgq', 'vzgr', 'vzgs', 'vzhp', 'vzhq', 'vzhr', 'vzhs', 'vzip', 'vziq', 'vzir', 'vzis']\n assert candidate(digits = \"444\") == ['ggg', 'ggh', 'ggi', 'ghg', 'ghh', 'ghi', 'gig', 'gih', 'gii', 'hgg', 'hgh', 'hgi', 'hhg', 'hhh', 'hhi', 'hig', 'hih', 'hii', 'igg', 'igh', 'igi', 'ihg', 'ihh', 'ihi', 'iig', 'iih', 'iii']\n assert candidate(digits = \"397\") == ['dwp', 'dwq', 'dwr', 'dws', 'dxp', 'dxq', 'dxr', 'dxs', 'dyp', 'dyq', 'dyr', 'dys', 'dzp', 'dzq', 'dzr', 'dzs', 'ewp', 'ewq', 'ewr', 'ews', 'exp', 'exq', 'exr', 'exs', 'eyp', 'eyq', 'eyr', 'eys', 'ezp', 'ezq', 'ezr', 'ezs', 'fwp', 'fwq', 'fwr', 'fws', 'fxp', 'fxq', 'fxr', 'fxs', 'fyp', 'fyq', 'fyr', 'fys', 'fzp', 'fzq', 'fzr', 'fzs']\n assert candidate(digits = \"23579\") == ['adjpw', 'adjpx', 'adjpy', 'adjpz', 'adjqw', 'adjqx', 'adjqy', 'adjqz', 'adjrw', 'adjrx', 'adjry', 'adjrz', 'adjsw', 'adjsx', 'adjsy', 'adjsz', 'adkpw', 'adkpx', 'adkpy', 'adkpz', 'adkqw', 'adkqx', 'adkqy', 'adkqz', 'adkrw', 'adkrx', 'adkry', 'adkrz', 'adksw', 'adksx', 'adksy', 'adksz', 'adlpw', 'adlpx', 'adlpy', 'adlpz', 'adlqw', 'adlqx', 'adlqy', 'adlqz', 'adlrw', 'adlrx', 'adlry', 'adlrz', 'adlsw', 'adlsx', 'adlsy', 'adlsz', 'aejpw', 'aejpx', 'aejpy', 'aejpz', 'aejqw', 'aejqx', 'aejqy', 'aejqz', 'aejrw', 'aejrx', 'aejry', 'aejrz', 'aejsw', 'aejsx', 'aejsy', 'aejsz', 'aekpw', 'aekpx', 'aekpy', 'aekpz', 'aekqw', 'aekqx', 'aekqy', 'aekqz', 'aekrw', 'aekrx', 'aekry', 'aekrz', 'aeksw', 'aeksx', 'aeksy', 'aeksz', 'aelpw', 'aelpx', 'aelpy', 'aelpz', 'aelqw', 'aelqx', 'aelqy', 'aelqz', 'aelrw', 'aelrx', 'aelry', 'aelrz', 'aelsw', 'aelsx', 'aelsy', 'aelsz', 'afjpw', 'afjpx', 'afjpy', 'afjpz', 'afjqw', 'afjqx', 'afjqy', 'afjqz', 'afjrw', 'afjrx', 'afjry', 'afjrz', 'afjsw', 'afjsx', 'afjsy', 'afjsz', 'afkpw', 'afkpx', 'afkpy', 'afkpz', 'afkqw', 'afkqx', 'afkqy', 'afkqz', 'afkrw', 'afkrx', 'afkry', 'afkrz', 'afksw', 'afksx', 'afksy', 'afksz', 'aflpw', 'aflpx', 'aflpy', 'aflpz', 'aflqw', 'aflqx', 'aflqy', 'aflqz', 'aflrw', 'aflrx', 'aflry', 'aflrz', 'aflsw', 'aflsx', 'aflsy', 'aflsz', 'bdjpw', 'bdjpx', 'bdjpy', 'bdjpz', 'bdjqw', 'bdjqx', 'bdjqy', 'bdjqz', 'bdjrw', 'bdjrx', 'bdjry', 'bdjrz', 'bdjsw', 'bdjsx', 'bdjsy', 'bdjsz', 'bdkpw', 'bdkpx', 'bdkpy', 'bdkpz', 'bdkqw', 'bdkqx', 'bdkqy', 'bdkqz', 'bdkrw', 'bdkrx', 'bdkry', 'bdkrz', 'bdksw', 'bdksx', 'bdksy', 'bdksz', 'bdlpw', 'bdlpx', 'bdlpy', 'bdlpz', 'bdlqw', 'bdlqx', 'bdlqy', 'bdlqz', 'bdlrw', 'bdlrx', 'bdlry', 'bdlrz', 'bdlsw', 'bdlsx', 'bdlsy', 'bdlsz', 'bejpw', 'bejpx', 'bejpy', 'bejpz', 'bejqw', 'bejqx', 'bejqy', 'bejqz', 'bejrw', 'bejrx', 'bejry', 'bejrz', 'bejsw', 'bejsx', 'bejsy', 'bejsz', 'bekpw', 'bekpx', 'bekpy', 'bekpz', 'bekqw', 'bekqx', 'bekqy', 'bekqz', 'bekrw', 'bekrx', 'bekry', 'bekrz', 'beksw', 'beksx', 'beksy', 'beksz', 'belpw', 'belpx', 'belpy', 'belpz', 'belqw', 'belqx', 'belqy', 'belqz', 'belrw', 'belrx', 'belry', 'belrz', 'belsw', 'belsx', 'belsy', 'belsz', 'bfjpw', 'bfjpx', 'bfjpy', 'bfjpz', 'bfjqw', 'bfjqx', 'bfjqy', 'bfjqz', 'bfjrw', 'bfjrx', 'bfjry', 'bfjrz', 'bfjsw', 'bfjsx', 'bfjsy', 'bfjsz', 'bfkpw', 'bfkpx', 'bfkpy', 'bfkpz', 'bfkqw', 'bfkqx', 'bfkqy', 'bfkqz', 'bfkrw', 'bfkrx', 'bfkry', 'bfkrz', 'bfksw', 'bfksx', 'bfksy', 'bfksz', 'bflpw', 'bflpx', 'bflpy', 'bflpz', 'bflqw', 'bflqx', 'bflqy', 'bflqz', 'bflrw', 'bflrx', 'bflry', 'bflrz', 'bflsw', 'bflsx', 'bflsy', 'bflsz', 'cdjpw', 'cdjpx', 'cdjpy', 'cdjpz', 'cdjqw', 'cdjqx', 'cdjqy', 'cdjqz', 'cdjrw', 'cdjrx', 'cdjry', 'cdjrz', 'cdjsw', 'cdjsx', 'cdjsy', 'cdjsz', 'cdkpw', 'cdkpx', 'cdkpy', 'cdkpz', 'cdkqw', 'cdkqx', 'cdkqy', 'cdkqz', 'cdkrw', 'cdkrx', 'cdkry', 'cdkrz', 'cdksw', 'cdksx', 'cdksy', 'cdksz', 'cdlpw', 'cdlpx', 'cdlpy', 'cdlpz', 'cdlqw', 'cdlqx', 'cdlqy', 'cdlqz', 'cdlrw', 'cdlrx', 'cdlry', 'cdlrz', 'cdlsw', 'cdlsx', 'cdlsy', 'cdlsz', 'cejpw', 'cejpx', 'cejpy', 'cejpz', 'cejqw', 'cejqx', 'cejqy', 'cejqz', 'cejrw', 'cejrx', 'cejry', 'cejrz', 'cejsw', 'cejsx', 'cejsy', 'cejsz', 'cekpw', 'cekpx', 'cekpy', 'cekpz', 'cekqw', 'cekqx', 'cekqy', 'cekqz', 'cekrw', 'cekrx', 'cekry', 'cekrz', 'ceksw', 'ceksx', 'ceksy', 'ceksz', 'celpw', 'celpx', 'celpy', 'celpz', 'celqw', 'celqx', 'celqy', 'celqz', 'celrw', 'celrx', 'celry', 'celrz', 'celsw', 'celsx', 'celsy', 'celsz', 'cfjpw', 'cfjpx', 'cfjpy', 'cfjpz', 'cfjqw', 'cfjqx', 'cfjqy', 'cfjqz', 'cfjrw', 'cfjrx', 'cfjry', 'cfjrz', 'cfjsw', 'cfjsx', 'cfjsy', 'cfjsz', 'cfkpw', 'cfkpx', 'cfkpy', 'cfkpz', 'cfkqw', 'cfkqx', 'cfkqy', 'cfkqz', 'cfkrw', 'cfkrx', 'cfkry', 'cfkrz', 'cfksw', 'cfksx', 'cfksy', 'cfksz', 'cflpw', 'cflpx', 'cflpy', 'cflpz', 'cflqw', 'cflqx', 'cflqy', 'cflqz', 'cflrw', 'cflrx', 'cflry', 'cflrz', 'cflsw', 'cflsx', 'cflsy', 'cflsz']\n assert candidate(digits = \"6\") == ['m', 'n', 'o']\n assert candidate(digits = \"58\") == ['jt', 'ju', 'jv', 'kt', 'ku', 'kv', 'lt', 'lu', 'lv']\n assert candidate(digits = \"77\") == ['pp', 'pq', 'pr', 'ps', 'qp', 'qq', 'qr', 'qs', 'rp', 'rq', 'rr', 'rs', 'sp', 'sq', 'sr', 'ss']\n assert candidate(digits = \"56\") == ['jm', 'jn', 'jo', 'km', 'kn', 'ko', 'lm', 'ln', 'lo']\n assert candidate(digits = \"85\") == ['tj', 'tk', 'tl', 'uj', 'uk', 'ul', 'vj', 'vk', 'vl']\n assert candidate(digits = \"2345\") == ['adgj', 'adgk', 'adgl', 'adhj', 'adhk', 'adhl', 'adij', 'adik', 'adil', 'aegj', 'aegk', 'aegl', 'aehj', 'aehk', 'aehl', 'aeij', 'aeik', 'aeil', 'afgj', 'afgk', 'afgl', 'afhj', 'afhk', 'afhl', 'afij', 'afik', 'afil', 'bdgj', 'bdgk', 'bdgl', 'bdhj', 'bdhk', 'bdhl', 'bdij', 'bdik', 'bdil', 'begj', 'begk', 'begl', 'behj', 'behk', 'behl', 'beij', 'beik', 'beil', 'bfgj', 'bfgk', 'bfgl', 'bfhj', 'bfhk', 'bfhl', 'bfij', 'bfik', 'bfil', 'cdgj', 'cdgk', 'cdgl', 'cdhj', 'cdhk', 'cdhl', 'cdij', 'cdik', 'cdil', 'cegj', 'cegk', 'cegl', 'cehj', 'cehk', 'cehl', 'ceij', 'ceik', 'ceil', 'cfgj', 'cfgk', 'cfgl', 'cfhj', 'cfhk', 'cfhl', 'cfij', 'cfik', 'cfil']\n assert candidate(digits = \"9876\") == ['wtpm', 'wtpn', 'wtpo', 'wtqm', 'wtqn', 'wtqo', 'wtrm', 'wtrn', 'wtro', 'wtsm', 'wtsn', 'wtso', 'wupm', 'wupn', 'wupo', 'wuqm', 'wuqn', 'wuqo', 'wurm', 'wurn', 'wuro', 'wusm', 'wusn', 'wuso', 'wvpm', 'wvpn', 'wvpo', 'wvqm', 'wvqn', 'wvqo', 'wvrm', 'wvrn', 'wvro', 'wvsm', 'wvsn', 'wvso', 'xtpm', 'xtpn', 'xtpo', 'xtqm', 'xtqn', 'xtqo', 'xtrm', 'xtrn', 'xtro', 'xtsm', 'xtsn', 'xtso', 'xupm', 'xupn', 'xupo', 'xuqm', 'xuqn', 'xuqo', 'xurm', 'xurn', 'xuro', 'xusm', 'xusn', 'xuso', 'xvpm', 'xvpn', 'xvpo', 'xvqm', 'xvqn', 'xvqo', 'xvrm', 'xvrn', 'xvro', 'xvsm', 'xvsn', 'xvso', 'ytpm', 'ytpn', 'ytpo', 'ytqm', 'ytqn', 'ytqo', 'ytrm', 'ytrn', 'ytro', 'ytsm', 'ytsn', 'ytso', 'yupm', 'yupn', 'yupo', 'yuqm', 'yuqn', 'yuqo', 'yurm', 'yurn', 'yuro', 'yusm', 'yusn', 'yuso', 'yvpm', 'yvpn', 'yvpo', 'yvqm', 'yvqn', 'yvqo', 'yvrm', 'yvrn', 'yvro', 'yvsm', 'yvsn', 'yvso', 'ztpm', 'ztpn', 'ztpo', 'ztqm', 'ztqn', 'ztqo', 'ztrm', 'ztrn', 'ztro', 'ztsm', 'ztsn', 'ztso', 'zupm', 'zupn', 'zupo', 'zuqm', 'zuqn', 'zuqo', 'zurm', 'zurn', 'zuro', 'zusm', 'zusn', 'zuso', 'zvpm', 'zvpn', 'zvpo', 'zvqm', 'zvqn', 'zvqo', 'zvrm', 'zvrn', 'zvro', 'zvsm', 'zvsn', 'zvso']\n assert candidate(digits = \"666\") == ['mmm', 'mmn', 'mmo', 'mnm', 'mnn', 'mno', 'mom', 'mon', 'moo', 'nmm', 'nmn', 'nmo', 'nnm', 'nnn', 'nno', 'nom', 'non', 'noo', 'omm', 'omn', 'omo', 'onm', 'onn', 'ono', 'oom', 'oon', 'ooo']\n assert candidate(digits = \"4567\") == ['gjmp', 'gjmq', 'gjmr', 'gjms', 'gjnp', 'gjnq', 'gjnr', 'gjns', 'gjop', 'gjoq', 'gjor', 'gjos', 'gkmp', 'gkmq', 'gkmr', 'gkms', 'gknp', 'gknq', 'gknr', 'gkns', 'gkop', 'gkoq', 'gkor', 'gkos', 'glmp', 'glmq', 'glmr', 'glms', 'glnp', 'glnq', 'glnr', 'glns', 'glop', 'gloq', 'glor', 'glos', 'hjmp', 'hjmq', 'hjmr', 'hjms', 'hjnp', 'hjnq', 'hjnr', 'hjns', 'hjop', 'hjoq', 'hjor', 'hjos', 'hkmp', 'hkmq', 'hkmr', 'hkms', 'hknp', 'hknq', 'hknr', 'hkns', 'hkop', 'hkoq', 'hkor', 'hkos', 'hlmp', 'hlmq', 'hlmr', 'hlms', 'hlnp', 'hlnq', 'hlnr', 'hlns', 'hlop', 'hloq', 'hlor', 'hlos', 'ijmp', 'ijmq', 'ijmr', 'ijms', 'ijnp', 'ijnq', 'ijnr', 'ijns', 'ijop', 'ijoq', 'ijor', 'ijos', 'ikmp', 'ikmq', 'ikmr', 'ikms', 'iknp', 'iknq', 'iknr', 'ikns', 'ikop', 'ikoq', 'ikor', 'ikos', 'ilmp', 'ilmq', 'ilmr', 'ilms', 'ilnp', 'ilnq', 'ilnr', 'ilns', 'ilop', 'iloq', 'ilor', 'ilos']\n assert candidate(digits = \"5\") == ['j', 'k', 'l']\n assert candidate(digits = \"654321\") == ['mjgdaw', 'mjgdax', 'mjgday', 'mjgdaz', 'mjgdbw', 'mjgdbx', 'mjgdby', 'mjgdbz', 'mjgdcw', 'mjgdcx', 'mjgdcy', 'mjgdcz', 'mjgeaw', 'mjgeax', 'mjgeay', 'mjgeaz', 'mjgebw', 'mjgebx', 'mjgeby', 'mjgebz', 'mjgecw', 'mjgecx', 'mjgecy', 'mjgecz', 'mjgfaw', 'mjgfax', 'mjgfay', 'mjgfaz', 'mjgfbw', 'mjgfbx', 'mjgfby', 'mjgfbz', 'mjgfcw', 'mjgfcx', 'mjgfcy', 'mjgfcz', 'mjhdaw', 'mjhdax', 'mjhday', 'mjhdaz', 'mjhdbw', 'mjhdbx', 'mjhdby', 'mjhdbz', 'mjhdcw', 'mjhdcx', 'mjhdcy', 'mjhdcz', 'mjheaw', 'mjheax', 'mjheay', 'mjheaz', 'mjhebw', 'mjhebx', 'mjheby', 'mjhebz', 'mjhecw', 'mjhecx', 'mjhecy', 'mjhecz', 'mjhfaw', 'mjhfax', 'mjhfay', 'mjhfaz', 'mjhfbw', 'mjhfbx', 'mjhfby', 'mjhfbz', 'mjhfcw', 'mjhfcx', 'mjhfcy', 'mjhfcz', 'mjidaw', 'mjidax', 'mjiday', 'mjidaz', 'mjidbw', 'mjidbx', 'mjidby', 'mjidbz', 'mjidcw', 'mjidcx', 'mjidcy', 'mjidcz', 'mjieaw', 'mjieax', 'mjieay', 'mjieaz', 'mjiebw', 'mjiebx', 'mjieby', 'mjiebz', 'mjiecw', 'mjiecx', 'mjiecy', 'mjiecz', 'mjifaw', 'mjifax', 'mjifay', 'mjifaz', 'mjifbw', 'mjifbx', 'mjifby', 'mjifbz', 'mjifcw', 'mjifcx', 'mjifcy', 'mjifcz', 'mkgdaw', 'mkgdax', 'mkgday', 'mkgdaz', 'mkgdbw', 'mkgdbx', 'mkgdby', 'mkgdbz', 'mkgdcw', 'mkgdcx', 'mkgdcy', 'mkgdcz', 'mkgeaw', 'mkgeax', 'mkgeay', 'mkgeaz', 'mkgebw', 'mkgebx', 'mkgeby', 'mkgebz', 'mkgecw', 'mkgecx', 'mkgecy', 'mkgecz', 'mkgfaw', 'mkgfax', 'mkgfay', 'mkgfaz', 'mkgfbw', 'mkgfbx', 'mkgfby', 'mkgfbz', 'mkgfcw', 'mkgfcx', 'mkgfcy', 'mkgfcz', 'mkhdaw', 'mkhdax', 'mkhday', 'mkhdaz', 'mkhdbw', 'mkhdbx', 'mkhdby', 'mkhdbz', 'mkhdcw', 'mkhdcx', 'mkhdcy', 'mkhdcz', 'mkheaw', 'mkheax', 'mkheay', 'mkheaz', 'mkhebw', 'mkhebx', 'mkheby', 'mkhebz', 'mkhecw', 'mkhecx', 'mkhecy', 'mkhecz', 'mkhfaw', 'mkhfax', 'mkhfay', 'mkhfaz', 'mkhfbw', 'mkhfbx', 'mkhfby', 'mkhfbz', 'mkhfcw', 'mkhfcx', 'mkhfcy', 'mkhfcz', 'mkidaw', 'mkidax', 'mkiday', 'mkidaz', 'mkidbw', 'mkidbx', 'mkidby', 'mkidbz', 'mkidcw', 'mkidcx', 'mkidcy', 'mkidcz', 'mkieaw', 'mkieax', 'mkieay', 'mkieaz', 'mkiebw', 'mkiebx', 'mkieby', 'mkiebz', 'mkiecw', 'mkiecx', 'mkiecy', 'mkiecz', 'mkifaw', 'mkifax', 'mkifay', 'mkifaz', 'mkifbw', 'mkifbx', 'mkifby', 'mkifbz', 'mkifcw', 'mkifcx', 'mkifcy', 'mkifcz', 'mlgdaw', 'mlgdax', 'mlgday', 'mlgdaz', 'mlgdbw', 'mlgdbx', 'mlgdby', 'mlgdbz', 'mlgdcw', 'mlgdcx', 'mlgdcy', 'mlgdcz', 'mlgeaw', 'mlgeax', 'mlgeay', 'mlgeaz', 'mlgebw', 'mlgebx', 'mlgeby', 'mlgebz', 'mlgecw', 'mlgecx', 'mlgecy', 'mlgecz', 'mlgfaw', 'mlgfax', 'mlgfay', 'mlgfaz', 'mlgfbw', 'mlgfbx', 'mlgfby', 'mlgfbz', 'mlgfcw', 'mlgfcx', 'mlgfcy', 'mlgfcz', 'mlhdaw', 'mlhdax', 'mlhday', 'mlhdaz', 'mlhdbw', 'mlhdbx', 'mlhdby', 'mlhdbz', 'mlhdcw', 'mlhdcx', 'mlhdcy', 'mlhdcz', 'mlheaw', 'mlheax', 'mlheay', 'mlheaz', 'mlhebw', 'mlhebx', 'mlheby', 'mlhebz', 'mlhecw', 'mlhecx', 'mlhecy', 'mlhecz', 'mlhfaw', 'mlhfax', 'mlhfay', 'mlhfaz', 'mlhfbw', 'mlhfbx', 'mlhfby', 'mlhfbz', 'mlhfcw', 'mlhfcx', 'mlhfcy', 'mlhfcz', 'mlidaw', 'mlidax', 'mliday', 'mlidaz', 'mlidbw', 'mlidbx', 'mlidby', 'mlidbz', 'mlidcw', 'mlidcx', 'mlidcy', 'mlidcz', 'mlieaw', 'mlieax', 'mlieay', 'mlieaz', 'mliebw', 'mliebx', 'mlieby', 'mliebz', 'mliecw', 'mliecx', 'mliecy', 'mliecz', 'mlifaw', 'mlifax', 'mlifay', 'mlifaz', 'mlifbw', 'mlifbx', 'mlifby', 'mlifbz', 'mlifcw', 'mlifcx', 'mlifcy', 'mlifcz', 'njgdaw', 'njgdax', 'njgday', 'njgdaz', 'njgdbw', 'njgdbx', 'njgdby', 'njgdbz', 'njgdcw', 'njgdcx', 'njgdcy', 'njgdcz', 'njgeaw', 'njgeax', 'njgeay', 'njgeaz', 'njgebw', 'njgebx', 'njgeby', 'njgebz', 'njgecw', 'njgecx', 'njgecy', 'njgecz', 'njgfaw', 'njgfax', 'njgfay', 'njgfaz', 'njgfbw', 'njgfbx', 'njgfby', 'njgfbz', 'njgfcw', 'njgfcx', 'njgfcy', 'njgfcz', 'njhdaw', 'njhdax', 'njhday', 'njhdaz', 'njhdbw', 'njhdbx', 'njhdby', 'njhdbz', 'njhdcw', 'njhdcx', 'njhdcy', 'njhdcz', 'njheaw', 'njheax', 'njheay', 'njheaz', 'njhebw', 'njhebx', 'njheby', 'njhebz', 'njhecw', 'njhecx', 'njhecy', 'njhecz', 'njhfaw', 'njhfax', 'njhfay', 'njhfaz', 'njhfbw', 'njhfbx', 'njhfby', 'njhfbz', 'njhfcw', 'njhfcx', 'njhfcy', 'njhfcz', 'njidaw', 'njidax', 'njiday', 'njidaz', 'njidbw', 'njidbx', 'njidby', 'njidbz', 'njidcw', 'njidcx', 'njidcy', 'njidcz', 'njieaw', 'njieax', 'njieay', 'njieaz', 'njiebw', 'njiebx', 'njieby', 'njiebz', 'njiecw', 'njiecx', 'njiecy', 'njiecz', 'njifaw', 'njifax', 'njifay', 'njifaz', 'njifbw', 'njifbx', 'njifby', 'njifbz', 'njifcw', 'njifcx', 'njifcy', 'njifcz', 'nkgdaw', 'nkgdax', 'nkgday', 'nkgdaz', 'nkgdbw', 'nkgdbx', 'nkgdby', 'nkgdbz', 'nkgdcw', 'nkgdcx', 'nkgdcy', 'nkgdcz', 'nkgeaw', 'nkgeax', 'nkgeay', 'nkgeaz', 'nkgebw', 'nkgebx', 'nkgeby', 'nkgebz', 'nkgecw', 'nkgecx', 'nkgecy', 'nkgecz', 'nkgfaw', 'nkgfax', 'nkgfay', 'nkgfaz', 'nkgfbw', 'nkgfbx', 'nkgfby', 'nkgfbz', 'nkgfcw', 'nkgfcx', 'nkgfcy', 'nkgfcz', 'nkhdaw', 'nkhdax', 'nkhday', 'nkhdaz', 'nkhdbw', 'nkhdbx', 'nkhdby', 'nkhdbz', 'nkhdcw', 'nkhdcx', 'nkhdcy', 'nkhdcz', 'nkheaw', 'nkheax', 'nkheay', 'nkheaz', 'nkhebw', 'nkhebx', 'nkheby', 'nkhebz', 'nkhecw', 'nkhecx', 'nkhecy', 'nkhecz', 'nkhfaw', 'nkhfax', 'nkhfay', 'nkhfaz', 'nkhfbw', 'nkhfbx', 'nkhfby', 'nkhfbz', 'nkhfcw', 'nkhfcx', 'nkhfcy', 'nkhfcz', 'nkidaw', 'nkidax', 'nkiday', 'nkidaz', 'nkidbw', 'nkidbx', 'nkidby', 'nkidbz', 'nkidcw', 'nkidcx', 'nkidcy', 'nkidcz', 'nkieaw', 'nkieax', 'nkieay', 'nkieaz', 'nkiebw', 'nkiebx', 'nkieby', 'nkiebz', 'nkiecw', 'nkiecx', 'nkiecy', 'nkiecz', 'nkifaw', 'nkifax', 'nkifay', 'nkifaz', 'nkifbw', 'nkifbx', 'nkifby', 'nkifbz', 'nkifcw', 'nkifcx', 'nkifcy', 'nkifcz', 'nlgdaw', 'nlgdax', 'nlgday', 'nlgdaz', 'nlgdbw', 'nlgdbx', 'nlgdby', 'nlgdbz', 'nlgdcw', 'nlgdcx', 'nlgdcy', 'nlgdcz', 'nlgeaw', 'nlgeax', 'nlgeay', 'nlgeaz', 'nlgebw', 'nlgebx', 'nlgeby', 'nlgebz', 'nlgecw', 'nlgecx', 'nlgecy', 'nlgecz', 'nlgfaw', 'nlgfax', 'nlgfay', 'nlgfaz', 'nlgfbw', 'nlgfbx', 'nlgfby', 'nlgfbz', 'nlgfcw', 'nlgfcx', 'nlgfcy', 'nlgfcz', 'nlhdaw', 'nlhdax', 'nlhday', 'nlhdaz', 'nlhdbw', 'nlhdbx', 'nlhdby', 'nlhdbz', 'nlhdcw', 'nlhdcx', 'nlhdcy', 'nlhdcz', 'nlheaw', 'nlheax', 'nlheay', 'nlheaz', 'nlhebw', 'nlhebx', 'nlheby', 'nlhebz', 'nlhecw', 'nlhecx', 'nlhecy', 'nlhecz', 'nlhfaw', 'nlhfax', 'nlhfay', 'nlhfaz', 'nlhfbw', 'nlhfbx', 'nlhfby', 'nlhfbz', 'nlhfcw', 'nlhfcx', 'nlhfcy', 'nlhfcz', 'nlidaw', 'nlidax', 'nliday', 'nlidaz', 'nlidbw', 'nlidbx', 'nlidby', 'nlidbz', 'nlidcw', 'nlidcx', 'nlidcy', 'nlidcz', 'nlieaw', 'nlieax', 'nlieay', 'nlieaz', 'nliebw', 'nliebx', 'nlieby', 'nliebz', 'nliecw', 'nliecx', 'nliecy', 'nliecz', 'nlifaw', 'nlifax', 'nlifay', 'nlifaz', 'nlifbw', 'nlifbx', 'nlifby', 'nlifbz', 'nlifcw', 'nlifcx', 'nlifcy', 'nlifcz', 'ojgdaw', 'ojgdax', 'ojgday', 'ojgdaz', 'ojgdbw', 'ojgdbx', 'ojgdby', 'ojgdbz', 'ojgdcw', 'ojgdcx', 'ojgdcy', 'ojgdcz', 'ojgeaw', 'ojgeax', 'ojgeay', 'ojgeaz', 'ojgebw', 'ojgebx', 'ojgeby', 'ojgebz', 'ojgecw', 'ojgecx', 'ojgecy', 'ojgecz', 'ojgfaw', 'ojgfax', 'ojgfay', 'ojgfaz', 'ojgfbw', 'ojgfbx', 'ojgfby', 'ojgfbz', 'ojgfcw', 'ojgfcx', 'ojgfcy', 'ojgfcz', 'ojhdaw', 'ojhdax', 'ojhday', 'ojhdaz', 'ojhdbw', 'ojhdbx', 'ojhdby', 'ojhdbz', 'ojhdcw', 'ojhdcx', 'ojhdcy', 'ojhdcz', 'ojheaw', 'ojheax', 'ojheay', 'ojheaz', 'ojhebw', 'ojhebx', 'ojheby', 'ojhebz', 'ojhecw', 'ojhecx', 'ojhecy', 'ojhecz', 'ojhfaw', 'ojhfax', 'ojhfay', 'ojhfaz', 'ojhfbw', 'ojhfbx', 'ojhfby', 'ojhfbz', 'ojhfcw', 'ojhfcx', 'ojhfcy', 'ojhfcz', 'ojidaw', 'ojidax', 'ojiday', 'ojidaz', 'ojidbw', 'ojidbx', 'ojidby', 'ojidbz', 'ojidcw', 'ojidcx', 'ojidcy', 'ojidcz', 'ojieaw', 'ojieax', 'ojieay', 'ojieaz', 'ojiebw', 'ojiebx', 'ojieby', 'ojiebz', 'ojiecw', 'ojiecx', 'ojiecy', 'ojiecz', 'ojifaw', 'ojifax', 'ojifay', 'ojifaz', 'ojifbw', 'ojifbx', 'ojifby', 'ojifbz', 'ojifcw', 'ojifcx', 'ojifcy', 'ojifcz', 'okgdaw', 'okgdax', 'okgday', 'okgdaz', 'okgdbw', 'okgdbx', 'okgdby', 'okgdbz', 'okgdcw', 'okgdcx', 'okgdcy', 'okgdcz', 'okgeaw', 'okgeax', 'okgeay', 'okgeaz', 'okgebw', 'okgebx', 'okgeby', 'okgebz', 'okgecw', 'okgecx', 'okgecy', 'okgecz', 'okgfaw', 'okgfax', 'okgfay', 'okgfaz', 'okgfbw', 'okgfbx', 'okgfby', 'okgfbz', 'okgfcw', 'okgfcx', 'okgfcy', 'okgfcz', 'okhdaw', 'okhdax', 'okhday', 'okhdaz', 'okhdbw', 'okhdbx', 'okhdby', 'okhdbz', 'okhdcw', 'okhdcx', 'okhdcy', 'okhdcz', 'okheaw', 'okheax', 'okheay', 'okheaz', 'okhebw', 'okhebx', 'okheby', 'okhebz', 'okhecw', 'okhecx', 'okhecy', 'okhecz', 'okhfaw', 'okhfax', 'okhfay', 'okhfaz', 'okhfbw', 'okhfbx', 'okhfby', 'okhfbz', 'okhfcw', 'okhfcx', 'okhfcy', 'okhfcz', 'okidaw', 'okidax', 'okiday', 'okidaz', 'okidbw', 'okidbx', 'okidby', 'okidbz', 'okidcw', 'okidcx', 'okidcy', 'okidcz', 'okieaw', 'okieax', 'okieay', 'okieaz', 'okiebw', 'okiebx', 'okieby', 'okiebz', 'okiecw', 'okiecx', 'okiecy', 'okiecz', 'okifaw', 'okifax', 'okifay', 'okifaz', 'okifbw', 'okifbx', 'okifby', 'okifbz', 'okifcw', 'okifcx', 'okifcy', 'okifcz', 'olgdaw', 'olgdax', 'olgday', 'olgdaz', 'olgdbw', 'olgdbx', 'olgdby', 'olgdbz', 'olgdcw', 'olgdcx', 'olgdcy', 'olgdcz', 'olgeaw', 'olgeax', 'olgeay', 'olgeaz', 'olgebw', 'olgebx', 'olgeby', 'olgebz', 'olgecw', 'olgecx', 'olgecy', 'olgecz', 'olgfaw', 'olgfax', 'olgfay', 'olgfaz', 'olgfbw', 'olgfbx', 'olgfby', 'olgfbz', 'olgfcw', 'olgfcx', 'olgfcy', 'olgfcz', 'olhdaw', 'olhdax', 'olhday', 'olhdaz', 'olhdbw', 'olhdbx', 'olhdby', 'olhdbz', 'olhdcw', 'olhdcx', 'olhdcy', 'olhdcz', 'olheaw', 'olheax', 'olheay', 'olheaz', 'olhebw', 'olhebx', 'olheby', 'olhebz', 'olhecw', 'olhecx', 'olhecy', 'olhecz', 'olhfaw', 'olhfax', 'olhfay', 'olhfaz', 'olhfbw', 'olhfbx', 'olhfby', 'olhfbz', 'olhfcw', 'olhfcx', 'olhfcy', 'olhfcz', 'olidaw', 'olidax', 'oliday', 'olidaz', 'olidbw', 'olidbx', 'olidby', 'olidbz', 'olidcw', 'olidcx', 'olidcy', 'olidcz', 'olieaw', 'olieax', 'olieay', 'olieaz', 'oliebw', 'oliebx', 'olieby', 'oliebz', 'oliecw', 'oliecx', 'oliecy', 'oliecz', 'olifaw', 'olifax', 'olifay', 'olifaz', 'olifbw', 'olifbx', 'olifby', 'olifbz', 'olifcw', 'olifcx', 'olifcy', 'olifcz']\n assert candidate(digits = \"567\") == ['jmp', 'jmq', 'jmr', 'jms', 'jnp', 'jnq', 'jnr', 'jns', 'jop', 'joq', 'jor', 'jos', 'kmp', 'kmq', 'kmr', 'kms', 'knp', 'knq', 'knr', 'kns', 'kop', 'koq', 'kor', 'kos', 'lmp', 'lmq', 'lmr', 'lms', 'lnp', 'lnq', 'lnr', 'lns', 'lop', 'loq', 'lor', 'los']\n"}, "metadata": {"canonical_parameter_names": ["digits"], "leetcode_dataset_entry_point": "Solution().letterCombinations", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var letterCombinations = function(digits) {", "container": null, "callable": "letterCombinations", "parameters": [{"name": "digits", "type": "string"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 18, "task_id": "4sum", "difficulty": "Medium", "problem_description": "Given an array nums of n integers, return an array of all the unique quadruplets [nums[a], nums[b], nums[c], nums[d]] such that:\n\n0 <= a, b, c, d < n\na, b, c, and d are distinct.\nnums[a] + nums[b] + nums[c] + nums[d] == target\n\nYou may return the answer in any order.\n \nExample 1:\n\nInput: nums = [1,0,-1,0,-2,2], target = 0\nOutput: [[-2,-1,1,2],[-2,0,0,2],[-1,0,0,1]]\n\nExample 2:\n\nInput: nums = [2,2,2,2,2], target = 8\nOutput: [[2,2,2,2]]\n\n \nConstraints:\n\n1 <= nums.length <= 200\n-109 <= nums[i] <= 109\n-109 <= target <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 0, -1, 0, -2, 2],target = 0) == [[-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [-3, -1, 0, 2, 4, 5],target = 0) == [[-3, -1, 0, 4]]\n assert candidate(nums = [-1, -2, -3, -4, -5],target = -14) == [[-5, -4, -3, -2]]\n assert candidate(nums = [0, 0, 0, 0],target = 0) == [[0, 0, 0, 0]]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -20) == [[-10, -7, -2, -1], [-10, -6, -3, -1], [-10, -5, -4, -1], [-10, -5, -3, -2], [-9, -8, -2, -1], [-9, -7, -3, -1], [-9, -6, -4, -1], [-9, -6, -3, -2], [-9, -5, -4, -2], [-8, -7, -4, -1], [-8, -7, -3, -2], [-8, -6, -5, -1], [-8, -6, -4, -2], [-8, -5, -4, -3], [-7, -6, -5, -2], [-7, -6, -4, -3]]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000],target = 4000000000) == [[1000000000, 1000000000, 1000000000, 1000000000]]\n assert candidate(nums = [-1, -2, -3, -4, -5],target = -10) == [[-4, -3, -2, -1]]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000],target = 4000000000) == [[1000000000, 1000000000, 1000000000, 1000000000]]\n assert candidate(nums = [2, 2, 2, 2, 2],target = 8) == [[2, 2, 2, 2]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 20) == [[1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 6, 10], [1, 3, 7, 9], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 6, 8], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 5, 9], [2, 4, 6, 8], [2, 5, 6, 7], [3, 4, 5, 8], [3, 4, 6, 7]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = 0) == [[-5, -4, 4, 5], [-5, -3, 3, 5], [-5, -2, 2, 5], [-5, -2, 3, 4], [-5, -1, 1, 5], [-5, -1, 2, 4], [-5, 0, 1, 4], [-5, 0, 2, 3], [-4, -3, 2, 5], [-4, -3, 3, 4], [-4, -2, 1, 5], [-4, -2, 2, 4], [-4, -1, 0, 5], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 1, 3], [-3, -2, 0, 5], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 30) == [[3, 8, 9, 10], [4, 7, 9, 10], [5, 6, 9, 10], [5, 7, 8, 10], [6, 7, 8, 9]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8],target = 20) == [[1, 4, 7, 8], [1, 5, 6, 8], [2, 3, 7, 8], [2, 4, 6, 8], [2, 5, 6, 7], [3, 4, 5, 8], [3, 4, 6, 7]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4],target = -1) == [[-4, 0, 1, 2], [-1, -1, 0, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8],target = 10) == [[1, 2, 3, 4]]\n assert candidate(nums = [1, 2, 3, 4, 5],target = 10) == [[1, 2, 3, 4]]\n assert candidate(nums = [-3, -2, -1, 0, 0, 1, 2, 3, 4],target = 0) == [[-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [1, 0, -1, 0, -2, 2, -1, 1],target = 0) == [[-2, -1, 1, 2], [-2, 0, 0, 2], [-2, 0, 1, 1], [-1, -1, 0, 2], [-1, -1, 1, 1], [-1, 0, 0, 1]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = 0) == [[-5, -4, 4, 5], [-5, -3, 3, 5], [-5, -2, 2, 5], [-5, -2, 3, 4], [-5, -1, 1, 5], [-5, -1, 2, 4], [-5, 0, 1, 4], [-5, 0, 2, 3], [-4, -3, 2, 5], [-4, -3, 3, 4], [-4, -2, 1, 5], [-4, -2, 2, 4], [-4, -1, 0, 5], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 1, 3], [-3, -2, 0, 5], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2]]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 4) == [[1, 1, 1, 1]]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 300) == [[30, 80, 90, 100], [40, 70, 90, 100], [50, 60, 90, 100], [50, 70, 80, 100], [60, 70, 80, 90]]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20, 25, 30],target = 30) == [[-10, -5, 15, 30], [-10, -5, 20, 25], [-10, 0, 10, 30], [-10, 0, 15, 25], [-10, 5, 10, 25], [-10, 5, 15, 20], [-5, 0, 5, 30], [-5, 0, 10, 25], [-5, 0, 15, 20], [-5, 5, 10, 20], [0, 5, 10, 15]]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 20) == [[5, 5, 5, 5]]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],target = 12) == [[1, 1, 5, 5], [1, 2, 4, 5], [1, 3, 3, 5], [1, 3, 4, 4], [2, 2, 3, 5], [2, 2, 4, 4], [2, 3, 3, 4]]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1, -1, 2, -2],target = 4000000000) == [[1000000000, 1000000000, 1000000000, 1000000000]]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1],target = 0) == [[-1, -1, 1, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 35) == []\n assert candidate(nums = [-1, 2, 2, -5, 0, -1, 4],target = 3) == [[-5, 2, 2, 4], [-1, 0, 2, 2]]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],target = -20) == [[-10, -7, -2, -1], [-10, -6, -3, -1], [-10, -5, -4, -1], [-10, -5, -3, -2], [-9, -8, -2, -1], [-9, -7, -3, -1], [-9, -6, -4, -1], [-9, -6, -3, -2], [-9, -5, -4, -2], [-8, -7, -4, -1], [-8, -7, -3, -2], [-8, -6, -5, -1], [-8, -6, -4, -2], [-8, -5, -4, -3], [-7, -6, -5, -2], [-7, -6, -4, -3]]\n assert candidate(nums = [1, 0, -1, 0, -2, 2, 1, 0, -1, 0, -2, 2, 1, 0, -1, 0, -2, 2],target = 0) == [[-2, -2, 2, 2], [-2, -1, 1, 2], [-2, 0, 0, 2], [-2, 0, 1, 1], [-1, -1, 0, 2], [-1, -1, 1, 1], [-1, 0, 0, 1], [0, 0, 0, 0]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 1) == []\n assert candidate(nums = [1, -2, -5, -4, -3, 3, 3, 5],target = -11) == [[-5, -4, -3, 1]]\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 1, 1, 1],target = 0) == [[-1, -1, 1, 1], [-1, 0, 0, 1]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [[0, 0, 0, 0]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, -2, -3, 3, 0, 4],target = 0) == [[-4, -3, 3, 4], [-4, -2, 2, 4], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 0, 4], [-4, 0, 1, 3], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -1, -1, 4], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, -1, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 30) == [[1, 2, 12, 15], [1, 2, 13, 14], [1, 3, 11, 15], [1, 3, 12, 14], [1, 4, 10, 15], [1, 4, 11, 14], [1, 4, 12, 13], [1, 5, 9, 15], [1, 5, 10, 14], [1, 5, 11, 13], [1, 6, 8, 15], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 8, 9, 12], [1, 8, 10, 11], [2, 3, 10, 15], [2, 3, 11, 14], [2, 3, 12, 13], [2, 4, 9, 15], [2, 4, 10, 14], [2, 4, 11, 13], [2, 5, 8, 15], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 6, 7, 15], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 8, 9, 11], [3, 4, 8, 15], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 5, 7, 15], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 7, 8, 12], [3, 7, 9, 11], [3, 8, 9, 10], [4, 5, 6, 15], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 7, 8, 11], [4, 7, 9, 10], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 7, 8, 10], [6, 7, 8, 9]]\n assert candidate(nums = [-3, -1, 0, 1, 2, 3, 5, 6, -6, -5],target = 0) == [[-6, -5, 5, 6], [-6, -3, 3, 6], [-6, -1, 1, 6], [-6, -1, 2, 5], [-6, 0, 1, 5], [-6, 1, 2, 3], [-5, -3, 2, 6], [-5, -3, 3, 5], [-5, -1, 0, 6], [-5, -1, 1, 5], [-5, 0, 2, 3], [-3, -1, 1, 3], [-3, 0, 1, 2]]\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10],target = 0) == [[-10, -6, 7, 9], [-10, -4, 5, 9], [-10, -2, 3, 9], [-10, -2, 5, 7], [-8, -6, 5, 9], [-8, -4, 3, 9], [-8, -4, 5, 7], [-8, -2, 1, 9], [-8, -2, 3, 7], [-6, -4, 1, 9], [-6, -4, 3, 7], [-6, -2, 1, 7], [-6, -2, 3, 5], [-4, -2, 1, 5]]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],target = -70) == [[-20, -19, -18, -13], [-20, -19, -17, -14], [-20, -19, -16, -15], [-20, -18, -17, -15], [-19, -18, -17, -16]]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 600) == [[30, 180, 190, 200], [40, 170, 190, 200], [50, 160, 190, 200], [50, 170, 180, 200], [60, 150, 190, 200], [60, 160, 180, 200], [60, 170, 180, 190], [70, 140, 190, 200], [70, 150, 180, 200], [70, 160, 170, 200], [70, 160, 180, 190], [80, 130, 190, 200], [80, 140, 180, 200], [80, 150, 170, 200], [80, 150, 180, 190], [80, 160, 170, 190], [90, 120, 190, 200], [90, 130, 180, 200], [90, 140, 170, 200], [90, 140, 180, 190], [90, 150, 160, 200], [90, 150, 170, 190], [90, 160, 170, 180], [100, 110, 190, 200], [100, 120, 180, 200], [100, 130, 170, 200], [100, 130, 180, 190], [100, 140, 160, 200], [100, 140, 170, 190], [100, 150, 160, 190], [100, 150, 170, 180], [110, 120, 170, 200], [110, 120, 180, 190], [110, 130, 160, 200], [110, 130, 170, 190], [110, 140, 150, 200], [110, 140, 160, 190], [110, 140, 170, 180], [110, 150, 160, 180], [120, 130, 150, 200], [120, 130, 160, 190], [120, 130, 170, 180], [120, 140, 150, 190], [120, 140, 160, 180], [120, 150, 160, 170], [130, 140, 150, 180], [130, 140, 160, 170]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, -2, 2],target = 0) == [[-4, 0, 2, 2], [-2, -1, 1, 2], [-1, -1, 0, 2]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 90) == []\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],target = 5000000000) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1],target = 10) == [[-10, 1, 9, 10], [-10, 2, 8, 10], [-10, 3, 7, 10], [-10, 3, 8, 9], [-10, 4, 6, 10], [-10, 4, 7, 9], [-10, 5, 6, 9], [-10, 5, 7, 8], [-9, 1, 8, 10], [-9, 2, 7, 10], [-9, 2, 8, 9], [-9, 3, 6, 10], [-9, 3, 7, 9], [-9, 4, 5, 10], [-9, 4, 6, 9], [-9, 4, 7, 8], [-9, 5, 6, 8], [-8, -1, 9, 10], [-8, 1, 7, 10], [-8, 1, 8, 9], [-8, 2, 6, 10], [-8, 2, 7, 9], [-8, 3, 5, 10], [-8, 3, 6, 9], [-8, 3, 7, 8], [-8, 4, 5, 9], [-8, 4, 6, 8], [-8, 5, 6, 7], [-7, -2, 9, 10], [-7, -1, 8, 10], [-7, 1, 6, 10], [-7, 1, 7, 9], [-7, 2, 5, 10], [-7, 2, 6, 9], [-7, 2, 7, 8], [-7, 3, 4, 10], [-7, 3, 5, 9], [-7, 3, 6, 8], [-7, 4, 5, 8], [-7, 4, 6, 7], [-6, -3, 9, 10], [-6, -2, 8, 10], [-6, -1, 7, 10], [-6, -1, 8, 9], [-6, 1, 5, 10], [-6, 1, 6, 9], [-6, 1, 7, 8], [-6, 2, 4, 10], [-6, 2, 5, 9], [-6, 2, 6, 8], [-6, 3, 4, 9], [-6, 3, 5, 8], [-6, 3, 6, 7], [-6, 4, 5, 7], [-5, -4, 9, 10], [-5, -3, 8, 10], [-5, -2, 7, 10], [-5, -2, 8, 9], [-5, -1, 6, 10], [-5, -1, 7, 9], [-5, 1, 4, 10], [-5, 1, 5, 9], [-5, 1, 6, 8], [-5, 2, 3, 10], [-5, 2, 4, 9], [-5, 2, 5, 8], [-5, 2, 6, 7], [-5, 3, 4, 8], [-5, 3, 5, 7], [-5, 4, 5, 6], [-4, -3, 7, 10], [-4, -3, 8, 9], [-4, -2, 6, 10], [-4, -2, 7, 9], [-4, -1, 5, 10], [-4, -1, 6, 9], [-4, -1, 7, 8], [-4, 1, 3, 10], [-4, 1, 4, 9], [-4, 1, 5, 8], [-4, 1, 6, 7], [-4, 2, 3, 9], [-4, 2, 4, 8], [-4, 2, 5, 7], [-4, 3, 4, 7], [-4, 3, 5, 6], [-3, -2, 5, 10], [-3, -2, 6, 9], [-3, -2, 7, 8], [-3, -1, 4, 10], [-3, -1, 5, 9], [-3, -1, 6, 8], [-3, 1, 2, 10], [-3, 1, 3, 9], [-3, 1, 4, 8], [-3, 1, 5, 7], [-3, 2, 3, 8], [-3, 2, 4, 7], [-3, 2, 5, 6], [-3, 3, 4, 6], [-2, -1, 3, 10], [-2, -1, 4, 9], [-2, -1, 5, 8], [-2, -1, 6, 7], [-2, 1, 2, 9], [-2, 1, 3, 8], [-2, 1, 4, 7], [-2, 1, 5, 6], [-2, 2, 3, 7], [-2, 2, 4, 6], [-2, 3, 4, 5], [-1, 1, 2, 8], [-1, 1, 3, 7], [-1, 1, 4, 6], [-1, 2, 3, 6], [-1, 2, 4, 5], [1, 2, 3, 4]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 70) == [[13, 18, 19, 20], [14, 17, 19, 20], [15, 16, 19, 20], [15, 17, 18, 20], [16, 17, 18, 19]]\n assert candidate(nums = [-1000000000, -1000000000, 1000000000, 1000000000, -1000000000, 1000000000, 0, 0],target = 0) == [[-1000000000, -1000000000, 1000000000, 1000000000], [-1000000000, 0, 0, 1000000000]]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 4) == [[1, 1, 1, 1]]\n assert candidate(nums = [-1, -1, 2, 2, 3, 3, -3, -3, -2, -2, 1, 1, 0, 0, 0, 0],target = 0) == [[-3, -3, 3, 3], [-3, -2, 2, 3], [-3, -1, 1, 3], [-3, -1, 2, 2], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -2, 1, 3], [-2, -2, 2, 2], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-2, 0, 1, 1], [-1, -1, 0, 2], [-1, -1, 1, 1], [-1, 0, 0, 1], [0, 0, 0, 0]]\n assert candidate(nums = [1000000000, 1000000000, -1000000000, -1000000000, 500000000, -500000000],target = 0) == [[-1000000000, -1000000000, 1000000000, 1000000000], [-1000000000, -500000000, 500000000, 1000000000]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [[0, 0, 0, 0]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, -2, -2],target = -1) == [[-4, 0, 1, 2], [-2, -2, 1, 2], [-2, -1, 0, 2], [-1, -1, 0, 1]]\n assert candidate(nums = [2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 5) == [[1, 1, 1, 2]]\n assert candidate(nums = [1, 0, -1, 0, -2, 2, 3, 4, -3, -4, 5, -5],target = 1) == [[-5, -3, 4, 5], [-5, -2, 3, 5], [-5, -1, 2, 5], [-5, -1, 3, 4], [-5, 0, 1, 5], [-5, 0, 2, 4], [-5, 1, 2, 3], [-4, -3, 3, 5], [-4, -2, 2, 5], [-4, -2, 3, 4], [-4, -1, 1, 5], [-4, -1, 2, 4], [-4, 0, 0, 5], [-4, 0, 1, 4], [-4, 0, 2, 3], [-3, -2, 1, 5], [-3, -2, 2, 4], [-3, -1, 0, 5], [-3, -1, 1, 4], [-3, -1, 2, 3], [-3, 0, 0, 4], [-3, 0, 1, 3], [-2, -1, 0, 4], [-2, -1, 1, 3], [-2, 0, 0, 3], [-2, 0, 1, 2], [-1, 0, 0, 2]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 30) == [[-5, 8, 13, 14], [-5, 9, 12, 14], [-5, 10, 11, 14], [-5, 10, 12, 13], [-4, 7, 13, 14], [-4, 8, 12, 14], [-4, 9, 11, 14], [-4, 9, 12, 13], [-4, 10, 11, 13], [-3, 6, 13, 14], [-3, 7, 12, 14], [-3, 8, 11, 14], [-3, 8, 12, 13], [-3, 9, 10, 14], [-3, 9, 11, 13], [-3, 10, 11, 12], [-2, 5, 13, 14], [-2, 6, 12, 14], [-2, 7, 11, 14], [-2, 7, 12, 13], [-2, 8, 10, 14], [-2, 8, 11, 13], [-2, 9, 10, 13], [-2, 9, 11, 12], [-1, 4, 13, 14], [-1, 5, 12, 14], [-1, 6, 11, 14], [-1, 6, 12, 13], [-1, 7, 10, 14], [-1, 7, 11, 13], [-1, 8, 9, 14], [-1, 8, 10, 13], [-1, 8, 11, 12], [-1, 9, 10, 12], [0, 3, 13, 14], [0, 4, 12, 14], [0, 5, 11, 14], [0, 5, 12, 13], [0, 6, 10, 14], [0, 6, 11, 13], [0, 7, 9, 14], [0, 7, 10, 13], [0, 7, 11, 12], [0, 8, 9, 13], [0, 8, 10, 12], [0, 9, 10, 11], [1, 2, 13, 14], [1, 3, 12, 14], [1, 4, 11, 14], [1, 4, 12, 13], [1, 5, 10, 14], [1, 5, 11, 13], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 8, 9, 12], [1, 8, 10, 11], [2, 3, 11, 14], [2, 3, 12, 13], [2, 4, 10, 14], [2, 4, 11, 13], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 8, 9, 11], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 7, 8, 12], [3, 7, 9, 11], [3, 8, 9, 10], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 7, 8, 11], [4, 7, 9, 10], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 7, 8, 10], [6, 7, 8, 9]]\n assert candidate(nums = [5, 5, 3, 3, 2, 2, 1, 1, -1, -1, -2, -2, -3, -3, -5, -5],target = 0) == [[-5, -5, 5, 5], [-5, -3, 3, 5], [-5, -2, 2, 5], [-5, -1, 1, 5], [-5, -1, 3, 3], [-5, 1, 1, 3], [-5, 1, 2, 2], [-3, -3, 1, 5], [-3, -3, 3, 3], [-3, -2, 2, 3], [-3, -1, -1, 5], [-3, -1, 1, 3], [-3, -1, 2, 2], [-2, -2, -1, 5], [-2, -2, 1, 3], [-2, -2, 2, 2], [-2, -1, 1, 2], [-1, -1, 1, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 30) == [[3, 8, 9, 10], [4, 7, 9, 10], [5, 6, 9, 10], [5, 7, 8, 10], [6, 7, 8, 9]]\n assert candidate(nums = [1000000000, -1000000000, 2000000000, -2000000000, 500000000, -500000000],target = 0) == [[-2000000000, -1000000000, 1000000000, 2000000000], [-2000000000, -500000000, 500000000, 2000000000], [-1000000000, -500000000, 500000000, 1000000000]]\n assert candidate(nums = [1, 0, -1, 0, -2, 2, 3, -3, 4, -4],target = 0) == [[-4, -3, 3, 4], [-4, -2, 2, 4], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 0, 4], [-4, 0, 1, 3], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [-3, -2, -1, 0, 0, 1, 2, 3],target = 0) == [[-3, -2, 2, 3], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [-1, 0, 0, 1, 0, -1, 0, -1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0],target = 0) == [[-1, -1, 1, 1], [-1, 0, 0, 1], [0, 0, 0, 0]]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 600) == [[30, 180, 190, 200], [40, 170, 190, 200], [50, 160, 190, 200], [50, 170, 180, 200], [60, 150, 190, 200], [60, 160, 180, 200], [60, 170, 180, 190], [70, 140, 190, 200], [70, 150, 180, 200], [70, 160, 170, 200], [70, 160, 180, 190], [80, 130, 190, 200], [80, 140, 180, 200], [80, 150, 170, 200], [80, 150, 180, 190], [80, 160, 170, 190], [90, 120, 190, 200], [90, 130, 180, 200], [90, 140, 170, 200], [90, 140, 180, 190], [90, 150, 160, 200], [90, 150, 170, 190], [90, 160, 170, 180], [100, 110, 190, 200], [100, 120, 180, 200], [100, 130, 170, 200], [100, 130, 180, 190], [100, 140, 160, 200], [100, 140, 170, 190], [100, 150, 160, 190], [100, 150, 170, 180], [110, 120, 170, 200], [110, 120, 180, 190], [110, 130, 160, 200], [110, 130, 170, 190], [110, 140, 150, 200], [110, 140, 160, 190], [110, 140, 170, 180], [110, 150, 160, 180], [120, 130, 150, 200], [120, 130, 160, 190], [120, 130, 170, 180], [120, 140, 150, 190], [120, 140, 160, 180], [120, 150, 160, 170], [130, 140, 150, 180], [130, 140, 160, 170]]\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90],target = 0) == [[-100, -70, 80, 90], [-100, -60, 70, 90], [-100, -50, 60, 90], [-100, -50, 70, 80], [-100, -40, 50, 90], [-100, -40, 60, 80], [-100, -30, 40, 90], [-100, -30, 50, 80], [-100, -30, 60, 70], [-100, -20, 30, 90], [-100, -20, 40, 80], [-100, -20, 50, 70], [-100, -10, 20, 90], [-100, -10, 30, 80], [-100, -10, 40, 70], [-100, -10, 50, 60], [-100, 0, 10, 90], [-100, 0, 20, 80], [-100, 0, 30, 70], [-100, 0, 40, 60], [-100, 10, 20, 70], [-100, 10, 30, 60], [-100, 10, 40, 50], [-100, 20, 30, 50], [-90, -80, 80, 90], [-90, -70, 70, 90], [-90, -60, 60, 90], [-90, -60, 70, 80], [-90, -50, 50, 90], [-90, -50, 60, 80], [-90, -40, 40, 90], [-90, -40, 50, 80], [-90, -40, 60, 70], [-90, -30, 30, 90], [-90, -30, 40, 80], [-90, -30, 50, 70], [-90, -20, 20, 90], [-90, -20, 30, 80], [-90, -20, 40, 70], [-90, -20, 50, 60], [-90, -10, 10, 90], [-90, -10, 20, 80], [-90, -10, 30, 70], [-90, -10, 40, 60], [-90, 0, 10, 80], [-90, 0, 20, 70], [-90, 0, 30, 60], [-90, 0, 40, 50], [-90, 10, 20, 60], [-90, 10, 30, 50], [-90, 20, 30, 40], [-80, -70, 60, 90], [-80, -70, 70, 80], [-80, -60, 50, 90], [-80, -60, 60, 80], [-80, -50, 40, 90], [-80, -50, 50, 80], [-80, -50, 60, 70], [-80, -40, 30, 90], [-80, -40, 40, 80], [-80, -40, 50, 70], [-80, -30, 20, 90], [-80, -30, 30, 80], [-80, -30, 40, 70], [-80, -30, 50, 60], [-80, -20, 10, 90], [-80, -20, 20, 80], [-80, -20, 30, 70], [-80, -20, 40, 60], [-80, -10, 0, 90], [-80, -10, 10, 80], [-80, -10, 20, 70], [-80, -10, 30, 60], [-80, -10, 40, 50], [-80, 0, 10, 70], [-80, 0, 20, 60], [-80, 0, 30, 50], [-80, 10, 20, 50], [-80, 10, 30, 40], [-70, -60, 40, 90], [-70, -60, 50, 80], [-70, -60, 60, 70], [-70, -50, 30, 90], [-70, -50, 40, 80], [-70, -50, 50, 70], [-70, -40, 20, 90], [-70, -40, 30, 80], [-70, -40, 40, 70], [-70, -40, 50, 60], [-70, -30, 10, 90], [-70, -30, 20, 80], [-70, -30, 30, 70], [-70, -30, 40, 60], [-70, -20, 0, 90], [-70, -20, 10, 80], [-70, -20, 20, 70], [-70, -20, 30, 60], [-70, -20, 40, 50], [-70, -10, 0, 80], [-70, -10, 10, 70], [-70, -10, 20, 60], [-70, -10, 30, 50], [-70, 0, 10, 60], [-70, 0, 20, 50], [-70, 0, 30, 40], [-70, 10, 20, 40], [-60, -50, 20, 90], [-60, -50, 30, 80], [-60, -50, 40, 70], [-60, -50, 50, 60], [-60, -40, 10, 90], [-60, -40, 20, 80], [-60, -40, 30, 70], [-60, -40, 40, 60], [-60, -30, 0, 90], [-60, -30, 10, 80], [-60, -30, 20, 70], [-60, -30, 30, 60], [-60, -30, 40, 50], [-60, -20, -10, 90], [-60, -20, 0, 80], [-60, -20, 10, 70], [-60, -20, 20, 60], [-60, -20, 30, 50], [-60, -10, 0, 70], [-60, -10, 10, 60], [-60, -10, 20, 50], [-60, -10, 30, 40], [-60, 0, 10, 50], [-60, 0, 20, 40], [-60, 10, 20, 30], [-50, -40, 0, 90], [-50, -40, 10, 80], [-50, -40, 20, 70], [-50, -40, 30, 60], [-50, -40, 40, 50], [-50, -30, -10, 90], [-50, -30, 0, 80], [-50, -30, 10, 70], [-50, -30, 20, 60], [-50, -30, 30, 50], [-50, -20, -10, 80], [-50, -20, 0, 70], [-50, -20, 10, 60], [-50, -20, 20, 50], [-50, -20, 30, 40], [-50, -10, 0, 60], [-50, -10, 10, 50], [-50, -10, 20, 40], [-50, 0, 10, 40], [-50, 0, 20, 30], [-40, -30, -20, 90], [-40, -30, -10, 80], [-40, -30, 0, 70], [-40, -30, 10, 60], [-40, -30, 20, 50], [-40, -30, 30, 40], [-40, -20, -10, 70], [-40, -20, 0, 60], [-40, -20, 10, 50], [-40, -20, 20, 40], [-40, -10, 0, 50], [-40, -10, 10, 40], [-40, -10, 20, 30], [-40, 0, 10, 30], [-30, -20, -10, 60], [-30, -20, 0, 50], [-30, -20, 10, 40], [-30, -20, 20, 30], [-30, -10, 0, 40], [-30, -10, 10, 30], [-30, 0, 10, 20], [-20, -10, 0, 30], [-20, -10, 10, 20]]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = 10) == [[-2, 3, 4, 5], [-1, 2, 4, 5], [0, 1, 4, 5], [0, 2, 3, 5], [1, 2, 3, 4]]\n assert candidate(nums = [1, 0, -1, 0, -2, 2, 3, 4, -3, -4],target = 0) == [[-4, -3, 3, 4], [-4, -2, 2, 4], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 0, 4], [-4, 0, 1, 3], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [-1, 2, 2, -5, 0, 2, 4],target = 3) == [[-5, 2, 2, 4], [-1, 0, 2, 2]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 20) == [[1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 6, 10], [1, 3, 7, 9], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 6, 8], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 5, 9], [2, 4, 6, 8], [2, 5, 6, 7], [3, 4, 5, 8], [3, 4, 6, 7]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [[0, 0, 0, 0]]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 8) == [[2, 2, 2, 2]]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],target = -30) == [[-10, -9, -8, -3], [-10, -9, -7, -4], [-10, -9, -6, -5], [-10, -8, -7, -5], [-9, -8, -7, -6]]\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3],target = 8) == [[1, 1, 3, 3], [1, 2, 2, 3], [2, 2, 2, 2]]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == [[-10, -9, 9, 10], [-10, -8, 8, 10], [-10, -7, 7, 10], [-10, -7, 8, 9], [-10, -6, 6, 10], [-10, -6, 7, 9], [-10, -5, 5, 10], [-10, -5, 6, 9], [-10, -5, 7, 8], [-10, -4, 4, 10], [-10, -4, 5, 9], [-10, -4, 6, 8], [-10, -3, 3, 10], [-10, -3, 4, 9], [-10, -3, 5, 8], [-10, -3, 6, 7], [-10, -2, 2, 10], [-10, -2, 3, 9], [-10, -2, 4, 8], [-10, -2, 5, 7], [-10, -1, 1, 10], [-10, -1, 2, 9], [-10, -1, 3, 8], [-10, -1, 4, 7], [-10, -1, 5, 6], [-10, 0, 1, 9], [-10, 0, 2, 8], [-10, 0, 3, 7], [-10, 0, 4, 6], [-10, 1, 2, 7], [-10, 1, 3, 6], [-10, 1, 4, 5], [-10, 2, 3, 5], [-9, -8, 7, 10], [-9, -8, 8, 9], [-9, -7, 6, 10], [-9, -7, 7, 9], [-9, -6, 5, 10], [-9, -6, 6, 9], [-9, -6, 7, 8], [-9, -5, 4, 10], [-9, -5, 5, 9], [-9, -5, 6, 8], [-9, -4, 3, 10], [-9, -4, 4, 9], [-9, -4, 5, 8], [-9, -4, 6, 7], [-9, -3, 2, 10], [-9, -3, 3, 9], [-9, -3, 4, 8], [-9, -3, 5, 7], [-9, -2, 1, 10], [-9, -2, 2, 9], [-9, -2, 3, 8], [-9, -2, 4, 7], [-9, -2, 5, 6], [-9, -1, 0, 10], [-9, -1, 1, 9], [-9, -1, 2, 8], [-9, -1, 3, 7], [-9, -1, 4, 6], [-9, 0, 1, 8], [-9, 0, 2, 7], [-9, 0, 3, 6], [-9, 0, 4, 5], [-9, 1, 2, 6], [-9, 1, 3, 5], [-9, 2, 3, 4], [-8, -7, 5, 10], [-8, -7, 6, 9], [-8, -7, 7, 8], [-8, -6, 4, 10], [-8, -6, 5, 9], [-8, -6, 6, 8], [-8, -5, 3, 10], [-8, -5, 4, 9], [-8, -5, 5, 8], [-8, -5, 6, 7], [-8, -4, 2, 10], [-8, -4, 3, 9], [-8, -4, 4, 8], [-8, -4, 5, 7], [-8, -3, 1, 10], [-8, -3, 2, 9], [-8, -3, 3, 8], [-8, -3, 4, 7], [-8, -3, 5, 6], [-8, -2, 0, 10], [-8, -2, 1, 9], [-8, -2, 2, 8], [-8, -2, 3, 7], [-8, -2, 4, 6], [-8, -1, 0, 9], [-8, -1, 1, 8], [-8, -1, 2, 7], [-8, -1, 3, 6], [-8, -1, 4, 5], [-8, 0, 1, 7], [-8, 0, 2, 6], [-8, 0, 3, 5], [-8, 1, 2, 5], [-8, 1, 3, 4], [-7, -6, 3, 10], [-7, -6, 4, 9], [-7, -6, 5, 8], [-7, -6, 6, 7], [-7, -5, 2, 10], [-7, -5, 3, 9], [-7, -5, 4, 8], [-7, -5, 5, 7], [-7, -4, 1, 10], [-7, -4, 2, 9], [-7, -4, 3, 8], [-7, -4, 4, 7], [-7, -4, 5, 6], [-7, -3, 0, 10], [-7, -3, 1, 9], [-7, -3, 2, 8], [-7, -3, 3, 7], [-7, -3, 4, 6], [-7, -2, -1, 10], [-7, -2, 0, 9], [-7, -2, 1, 8], [-7, -2, 2, 7], [-7, -2, 3, 6], [-7, -2, 4, 5], [-7, -1, 0, 8], [-7, -1, 1, 7], [-7, -1, 2, 6], [-7, -1, 3, 5], [-7, 0, 1, 6], [-7, 0, 2, 5], [-7, 0, 3, 4], [-7, 1, 2, 4], [-6, -5, 1, 10], [-6, -5, 2, 9], [-6, -5, 3, 8], [-6, -5, 4, 7], [-6, -5, 5, 6], [-6, -4, 0, 10], [-6, -4, 1, 9], [-6, -4, 2, 8], [-6, -4, 3, 7], [-6, -4, 4, 6], [-6, -3, -1, 10], [-6, -3, 0, 9], [-6, -3, 1, 8], [-6, -3, 2, 7], [-6, -3, 3, 6], [-6, -3, 4, 5], [-6, -2, -1, 9], [-6, -2, 0, 8], [-6, -2, 1, 7], [-6, -2, 2, 6], [-6, -2, 3, 5], [-6, -1, 0, 7], [-6, -1, 1, 6], [-6, -1, 2, 5], [-6, -1, 3, 4], [-6, 0, 1, 5], [-6, 0, 2, 4], [-6, 1, 2, 3], [-5, -4, -1, 10], [-5, -4, 0, 9], [-5, -4, 1, 8], [-5, -4, 2, 7], [-5, -4, 3, 6], [-5, -4, 4, 5], [-5, -3, -2, 10], [-5, -3, -1, 9], [-5, -3, 0, 8], [-5, -3, 1, 7], [-5, -3, 2, 6], [-5, -3, 3, 5], [-5, -2, -1, 8], [-5, -2, 0, 7], [-5, -2, 1, 6], [-5, -2, 2, 5], [-5, -2, 3, 4], [-5, -1, 0, 6], [-5, -1, 1, 5], [-5, -1, 2, 4], [-5, 0, 1, 4], [-5, 0, 2, 3], [-4, -3, -2, 9], [-4, -3, -1, 8], [-4, -3, 0, 7], [-4, -3, 1, 6], [-4, -3, 2, 5], [-4, -3, 3, 4], [-4, -2, -1, 7], [-4, -2, 0, 6], [-4, -2, 1, 5], [-4, -2, 2, 4], [-4, -1, 0, 5], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 1, 3], [-3, -2, -1, 6], [-3, -2, 0, 5], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2]]\n assert candidate(nums = [1, 0, -1, 0, -2, 2, 3, 4, 5, 6, 7, 8, 9, -9, -8, -7, -6, -5, -4, -3, -2, -1],target = 0) == [[-9, -8, 8, 9], [-9, -7, 7, 9], [-9, -6, 6, 9], [-9, -6, 7, 8], [-9, -5, 5, 9], [-9, -5, 6, 8], [-9, -4, 4, 9], [-9, -4, 5, 8], [-9, -4, 6, 7], [-9, -3, 3, 9], [-9, -3, 4, 8], [-9, -3, 5, 7], [-9, -2, 2, 9], [-9, -2, 3, 8], [-9, -2, 4, 7], [-9, -2, 5, 6], [-9, -1, 1, 9], [-9, -1, 2, 8], [-9, -1, 3, 7], [-9, -1, 4, 6], [-9, 0, 0, 9], [-9, 0, 1, 8], [-9, 0, 2, 7], [-9, 0, 3, 6], [-9, 0, 4, 5], [-9, 1, 2, 6], [-9, 1, 3, 5], [-9, 2, 3, 4], [-8, -7, 6, 9], [-8, -7, 7, 8], [-8, -6, 5, 9], [-8, -6, 6, 8], [-8, -5, 4, 9], [-8, -5, 5, 8], [-8, -5, 6, 7], [-8, -4, 3, 9], [-8, -4, 4, 8], [-8, -4, 5, 7], [-8, -3, 2, 9], [-8, -3, 3, 8], [-8, -3, 4, 7], [-8, -3, 5, 6], [-8, -2, 1, 9], [-8, -2, 2, 8], [-8, -2, 3, 7], [-8, -2, 4, 6], [-8, -1, 0, 9], [-8, -1, 1, 8], [-8, -1, 2, 7], [-8, -1, 3, 6], [-8, -1, 4, 5], [-8, 0, 0, 8], [-8, 0, 1, 7], [-8, 0, 2, 6], [-8, 0, 3, 5], [-8, 1, 2, 5], [-8, 1, 3, 4], [-7, -6, 4, 9], [-7, -6, 5, 8], [-7, -6, 6, 7], [-7, -5, 3, 9], [-7, -5, 4, 8], [-7, -5, 5, 7], [-7, -4, 2, 9], [-7, -4, 3, 8], [-7, -4, 4, 7], [-7, -4, 5, 6], [-7, -3, 1, 9], [-7, -3, 2, 8], [-7, -3, 3, 7], [-7, -3, 4, 6], [-7, -2, 0, 9], [-7, -2, 1, 8], [-7, -2, 2, 7], [-7, -2, 3, 6], [-7, -2, 4, 5], [-7, -1, -1, 9], [-7, -1, 0, 8], [-7, -1, 1, 7], [-7, -1, 2, 6], [-7, -1, 3, 5], [-7, 0, 0, 7], [-7, 0, 1, 6], [-7, 0, 2, 5], [-7, 0, 3, 4], [-7, 1, 2, 4], [-6, -5, 2, 9], [-6, -5, 3, 8], [-6, -5, 4, 7], [-6, -5, 5, 6], [-6, -4, 1, 9], [-6, -4, 2, 8], [-6, -4, 3, 7], [-6, -4, 4, 6], [-6, -3, 0, 9], [-6, -3, 1, 8], [-6, -3, 2, 7], [-6, -3, 3, 6], [-6, -3, 4, 5], [-6, -2, -1, 9], [-6, -2, 0, 8], [-6, -2, 1, 7], [-6, -2, 2, 6], [-6, -2, 3, 5], [-6, -1, -1, 8], [-6, -1, 0, 7], [-6, -1, 1, 6], [-6, -1, 2, 5], [-6, -1, 3, 4], [-6, 0, 0, 6], [-6, 0, 1, 5], [-6, 0, 2, 4], [-6, 1, 2, 3], [-5, -4, 0, 9], [-5, -4, 1, 8], [-5, -4, 2, 7], [-5, -4, 3, 6], [-5, -4, 4, 5], [-5, -3, -1, 9], [-5, -3, 0, 8], [-5, -3, 1, 7], [-5, -3, 2, 6], [-5, -3, 3, 5], [-5, -2, -2, 9], [-5, -2, -1, 8], [-5, -2, 0, 7], [-5, -2, 1, 6], [-5, -2, 2, 5], [-5, -2, 3, 4], [-5, -1, -1, 7], [-5, -1, 0, 6], [-5, -1, 1, 5], [-5, -1, 2, 4], [-5, 0, 0, 5], [-5, 0, 1, 4], [-5, 0, 2, 3], [-4, -3, -2, 9], [-4, -3, -1, 8], [-4, -3, 0, 7], [-4, -3, 1, 6], [-4, -3, 2, 5], [-4, -3, 3, 4], [-4, -2, -2, 8], [-4, -2, -1, 7], [-4, -2, 0, 6], [-4, -2, 1, 5], [-4, -2, 2, 4], [-4, -1, -1, 6], [-4, -1, 0, 5], [-4, -1, 1, 4], [-4, -1, 2, 3], [-4, 0, 0, 4], [-4, 0, 1, 3], [-3, -2, -2, 7], [-3, -2, -1, 6], [-3, -2, 0, 5], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, -1, 5], [-3, -1, 0, 4], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -2, -1, 5], [-2, -2, 0, 4], [-2, -2, 1, 3], [-2, -1, -1, 4], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, -1, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 50) == [[1, 10, 19, 20], [1, 11, 18, 20], [1, 12, 17, 20], [1, 12, 18, 19], [1, 13, 16, 20], [1, 13, 17, 19], [1, 14, 15, 20], [1, 14, 16, 19], [1, 14, 17, 18], [1, 15, 16, 18], [2, 9, 19, 20], [2, 10, 18, 20], [2, 11, 17, 20], [2, 11, 18, 19], [2, 12, 16, 20], [2, 12, 17, 19], [2, 13, 15, 20], [2, 13, 16, 19], [2, 13, 17, 18], [2, 14, 15, 19], [2, 14, 16, 18], [2, 15, 16, 17], [3, 8, 19, 20], [3, 9, 18, 20], [3, 10, 17, 20], [3, 10, 18, 19], [3, 11, 16, 20], [3, 11, 17, 19], [3, 12, 15, 20], [3, 12, 16, 19], [3, 12, 17, 18], [3, 13, 14, 20], [3, 13, 15, 19], [3, 13, 16, 18], [3, 14, 15, 18], [3, 14, 16, 17], [4, 7, 19, 20], [4, 8, 18, 20], [4, 9, 17, 20], [4, 9, 18, 19], [4, 10, 16, 20], [4, 10, 17, 19], [4, 11, 15, 20], [4, 11, 16, 19], [4, 11, 17, 18], [4, 12, 14, 20], [4, 12, 15, 19], [4, 12, 16, 18], [4, 13, 14, 19], [4, 13, 15, 18], [4, 13, 16, 17], [4, 14, 15, 17], [5, 6, 19, 20], [5, 7, 18, 20], [5, 8, 17, 20], [5, 8, 18, 19], [5, 9, 16, 20], [5, 9, 17, 19], [5, 10, 15, 20], [5, 10, 16, 19], [5, 10, 17, 18], [5, 11, 14, 20], [5, 11, 15, 19], [5, 11, 16, 18], [5, 12, 13, 20], [5, 12, 14, 19], [5, 12, 15, 18], [5, 12, 16, 17], [5, 13, 14, 18], [5, 13, 15, 17], [5, 14, 15, 16], [6, 7, 17, 20], [6, 7, 18, 19], [6, 8, 16, 20], [6, 8, 17, 19], [6, 9, 15, 20], [6, 9, 16, 19], [6, 9, 17, 18], [6, 10, 14, 20], [6, 10, 15, 19], [6, 10, 16, 18], [6, 11, 13, 20], [6, 11, 14, 19], [6, 11, 15, 18], [6, 11, 16, 17], [6, 12, 13, 19], [6, 12, 14, 18], [6, 12, 15, 17], [6, 13, 14, 17], [6, 13, 15, 16], [7, 8, 15, 20], [7, 8, 16, 19], [7, 8, 17, 18], [7, 9, 14, 20], [7, 9, 15, 19], [7, 9, 16, 18], [7, 10, 13, 20], [7, 10, 14, 19], [7, 10, 15, 18], [7, 10, 16, 17], [7, 11, 12, 20], [7, 11, 13, 19], [7, 11, 14, 18], [7, 11, 15, 17], [7, 12, 13, 18], [7, 12, 14, 17], [7, 12, 15, 16], [7, 13, 14, 16], [8, 9, 13, 20], [8, 9, 14, 19], [8, 9, 15, 18], [8, 9, 16, 17], [8, 10, 12, 20], [8, 10, 13, 19], [8, 10, 14, 18], [8, 10, 15, 17], [8, 11, 12, 19], [8, 11, 13, 18], [8, 11, 14, 17], [8, 11, 15, 16], [8, 12, 13, 17], [8, 12, 14, 16], [8, 13, 14, 15], [9, 10, 11, 20], [9, 10, 12, 19], [9, 10, 13, 18], [9, 10, 14, 17], [9, 10, 15, 16], [9, 11, 12, 18], [9, 11, 13, 17], [9, 11, 14, 16], [9, 12, 13, 16], [9, 12, 14, 15], [10, 11, 12, 17], [10, 11, 13, 16], [10, 11, 14, 15], [10, 12, 13, 15], [11, 12, 13, 14]]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 0, 0, 0, 0],target = 3000000000) == [[0, 1000000000, 1000000000, 1000000000]]\n assert candidate(nums = [5, 5, 3, 5, 3, 3, 9, 0, 123, 1, 10, 10, 10, 10, 10],target = 30) == [[0, 10, 10, 10], [1, 9, 10, 10], [5, 5, 10, 10]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 50) == [[1, 10, 19, 20], [1, 11, 18, 20], [1, 12, 17, 20], [1, 12, 18, 19], [1, 13, 16, 20], [1, 13, 17, 19], [1, 14, 15, 20], [1, 14, 16, 19], [1, 14, 17, 18], [1, 15, 16, 18], [2, 9, 19, 20], [2, 10, 18, 20], [2, 11, 17, 20], [2, 11, 18, 19], [2, 12, 16, 20], [2, 12, 17, 19], [2, 13, 15, 20], [2, 13, 16, 19], [2, 13, 17, 18], [2, 14, 15, 19], [2, 14, 16, 18], [2, 15, 16, 17], [3, 8, 19, 20], [3, 9, 18, 20], [3, 10, 17, 20], [3, 10, 18, 19], [3, 11, 16, 20], [3, 11, 17, 19], [3, 12, 15, 20], [3, 12, 16, 19], [3, 12, 17, 18], [3, 13, 14, 20], [3, 13, 15, 19], [3, 13, 16, 18], [3, 14, 15, 18], [3, 14, 16, 17], [4, 7, 19, 20], [4, 8, 18, 20], [4, 9, 17, 20], [4, 9, 18, 19], [4, 10, 16, 20], [4, 10, 17, 19], [4, 11, 15, 20], [4, 11, 16, 19], [4, 11, 17, 18], [4, 12, 14, 20], [4, 12, 15, 19], [4, 12, 16, 18], [4, 13, 14, 19], [4, 13, 15, 18], [4, 13, 16, 17], [4, 14, 15, 17], [5, 6, 19, 20], [5, 7, 18, 20], [5, 8, 17, 20], [5, 8, 18, 19], [5, 9, 16, 20], [5, 9, 17, 19], [5, 10, 15, 20], [5, 10, 16, 19], [5, 10, 17, 18], [5, 11, 14, 20], [5, 11, 15, 19], [5, 11, 16, 18], [5, 12, 13, 20], [5, 12, 14, 19], [5, 12, 15, 18], [5, 12, 16, 17], [5, 13, 14, 18], [5, 13, 15, 17], [5, 14, 15, 16], [6, 7, 17, 20], [6, 7, 18, 19], [6, 8, 16, 20], [6, 8, 17, 19], [6, 9, 15, 20], [6, 9, 16, 19], [6, 9, 17, 18], [6, 10, 14, 20], [6, 10, 15, 19], [6, 10, 16, 18], [6, 11, 13, 20], [6, 11, 14, 19], [6, 11, 15, 18], [6, 11, 16, 17], [6, 12, 13, 19], [6, 12, 14, 18], [6, 12, 15, 17], [6, 13, 14, 17], [6, 13, 15, 16], [7, 8, 15, 20], [7, 8, 16, 19], [7, 8, 17, 18], [7, 9, 14, 20], [7, 9, 15, 19], [7, 9, 16, 18], [7, 10, 13, 20], [7, 10, 14, 19], [7, 10, 15, 18], [7, 10, 16, 17], [7, 11, 12, 20], [7, 11, 13, 19], [7, 11, 14, 18], [7, 11, 15, 17], [7, 12, 13, 18], [7, 12, 14, 17], [7, 12, 15, 16], [7, 13, 14, 16], [8, 9, 13, 20], [8, 9, 14, 19], [8, 9, 15, 18], [8, 9, 16, 17], [8, 10, 12, 20], [8, 10, 13, 19], [8, 10, 14, 18], [8, 10, 15, 17], [8, 11, 12, 19], [8, 11, 13, 18], [8, 11, 14, 17], [8, 11, 15, 16], [8, 12, 13, 17], [8, 12, 14, 16], [8, 13, 14, 15], [9, 10, 11, 20], [9, 10, 12, 19], [9, 10, 13, 18], [9, 10, 14, 17], [9, 10, 15, 16], [9, 11, 12, 18], [9, 11, 13, 17], [9, 11, 14, 16], [9, 12, 13, 16], [9, 12, 14, 15], [10, 11, 12, 17], [10, 11, 13, 16], [10, 11, 14, 15], [10, 12, 13, 15], [11, 12, 13, 14]]\n assert candidate(nums = [-3, -1, 0, 2, 4, 5, 6, 7],target = 10) == [[-3, 0, 6, 7], [-3, 2, 4, 7], [-3, 2, 5, 6], [-1, 0, 4, 7], [-1, 0, 5, 6], [-1, 2, 4, 5]]\n assert candidate(nums = [5, 5, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 20) == [[5, 5, 5, 5]]\n assert candidate(nums = [-10, -29, -2, -47, -82, 30, 3, 2, -8, -7, -33, 21, 45, 67, 90, 23, 4, 5, 6, 7],target = 20) == [[-82, -33, 45, 90], [-82, -10, 45, 67], [-82, 5, 7, 90], [-82, 5, 30, 67], [-47, -29, 6, 90], [-47, -8, 30, 45], [-47, -7, 7, 67], [-47, -2, 2, 67], [-33, -29, -8, 90], [-33, 2, 6, 45], [-33, 2, 21, 30], [-33, 3, 5, 45], [-29, -10, -8, 67], [-29, -2, 6, 45], [-29, -2, 21, 30], [-29, 5, 21, 23], [-10, -8, -7, 45], [-10, -7, 7, 30], [-10, -2, 2, 30], [-10, 2, 5, 23], [-10, 2, 7, 21], [-10, 3, 4, 23], [-10, 3, 6, 21], [-10, 4, 5, 21], [-8, -7, 5, 30], [-8, -2, 7, 23], [-8, 2, 3, 23], [-8, 2, 5, 21], [-8, 3, 4, 21], [-7, -2, 6, 23], [-7, 2, 4, 21], [2, 5, 6, 7], [3, 4, 6, 7]]\n assert candidate(nums = [-3, -2, -1, 0, 0, 1, 2, 3],target = 0) == [[-3, -2, 2, 3], [-3, -1, 1, 3], [-3, 0, 0, 3], [-3, 0, 1, 2], [-2, -1, 0, 3], [-2, -1, 1, 2], [-2, 0, 0, 2], [-1, 0, 0, 1]]\n assert candidate(nums = [-1, 0, 1, 0, -2, 2, -1, -4],target = -1) == [[-4, 0, 1, 2], [-2, -1, 0, 2], [-2, 0, 0, 1], [-1, -1, 0, 1]]\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 8) == [[2, 2, 2, 2]]\n assert candidate(nums = [-1, 0, 1, 2, -1, -4, 2, 3],target = 0) == [[-4, -1, 2, 3], [-4, 0, 1, 3], [-4, 0, 2, 2], [-1, -1, 0, 2]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [[0, 0, 0, 0]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [[0, 0, 0, 0]]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 20) == [[1, 1, 8, 10], [1, 1, 9, 9], [1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 6, 10], [1, 3, 7, 9], [1, 3, 8, 8], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 5, 9], [1, 5, 6, 8], [1, 5, 7, 7], [1, 6, 6, 7], [2, 2, 6, 10], [2, 2, 7, 9], [2, 2, 8, 8], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 4, 10], [2, 4, 5, 9], [2, 4, 6, 8], [2, 4, 7, 7], [2, 5, 5, 8], [2, 5, 6, 7], [3, 3, 4, 10], [3, 3, 5, 9], [3, 3, 6, 8], [3, 3, 7, 7], [3, 4, 4, 9], [3, 4, 5, 8], [3, 4, 6, 7], [3, 5, 5, 7], [3, 5, 6, 6], [4, 4, 5, 7], [4, 4, 6, 6], [4, 5, 5, 6]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 0) == []\n assert candidate(nums = [-1, -1, -1, -1, 1, 1, 1, 1],target = 0) == [[-1, -1, 1, 1]]\n assert candidate(nums = [2, 3, 1, 0, -4, -1, -2, -3, 4, 5, 6],target = 10) == [[-4, 3, 5, 6], [-3, 2, 5, 6], [-3, 3, 4, 6], [-2, 1, 5, 6], [-2, 2, 4, 6], [-2, 3, 4, 5], [-1, 0, 5, 6], [-1, 1, 4, 6], [-1, 2, 3, 6], [-1, 2, 4, 5], [0, 1, 3, 6], [0, 1, 4, 5], [0, 2, 3, 5], [1, 2, 3, 4]]\n assert candidate(nums = [1, 2, -1, -2, 3, 4, -3, -4],target = 0) == [[-4, -3, 3, 4], [-4, -2, 2, 4], [-4, -1, 1, 4], [-4, -1, 2, 3], [-3, -2, 1, 4], [-3, -2, 2, 3], [-3, -1, 1, 3], [-2, -1, 1, 2]]\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().fourSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var fourSum = function(nums, target) {", "container": null, "callable": "fourSum", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 19, "task_id": "remove-nth-node-from-end-of-list", "difficulty": "Medium", "problem_description": "Given the head of a linked list, remove the nth node from the end of the list and return its head.\n \nExample 1:\n\n\nInput: head = [1,2,3,4,5], n = 2\nOutput: [1,2,3,5]\n\nExample 2:\n\nInput: head = [1], n = 1\nOutput: []\n\nExample 3:\n\nInput: head = [1,2], n = 1\nOutput: [1]\n\n \nConstraints:\n\nThe number of nodes in the list is sz.\n1 <= sz <= 30\n0 <= Node.val <= 100\n1 <= n <= sz\n\n \nFollow up: Could you do this in one pass?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([100, 90, 80, 70, 60]),n = 3), list_node([100, 90, 70, 60]))\n assert is_same_list(candidate(head = list_node([1, 2]),n = 1), list_node([1]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),n = 5), list_node([4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),n = 2), list_node([1, 2, 3, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),n = 5), list_node([1, 2, 3, 4, 5, 7, 8, 9, 10]))\n assert candidate(head = list_node([1]),n = 1) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3]),n = 3), list_node([2, 3]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]),n = 15), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),n = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),n = 5), list_node([10, 20, 30, 40, 50, 70, 80, 90, 100]))\n assert is_same_list(candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]),n = 1), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),n = 3), list_node([1, 2, 3, 4, 5, 6, 7, 9, 10]))\n assert is_same_list(candidate(head = list_node([30, 20, 10]),n = 2), list_node([30, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 29), list_node([1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 30), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98]),n = 13), list_node([7, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60]),n = 1), list_node([10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([2, 3, 4, 5]),n = 1), list_node([2, 3, 4]))\n assert is_same_list(candidate(head = list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0]),n = 2), list_node([1, 0, 1, 0, 1, 0, 1, 0, 0]))\n assert is_same_list(candidate(head = list_node([5, 10]),n = 2), list_node([10]))\n assert is_same_list(candidate(head = list_node([3, 2, 1]),n = 1), list_node([3, 2]))\n assert is_same_list(candidate(head = list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89]),n = 1), list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90]),n = 5), list_node([10, 20, 30, 40, 60, 70, 80, 90]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 10), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),n = 10), list_node([20, 30, 40, 50, 60, 70, 80, 90, 100]))\n assert candidate(head = list_node([5]),n = 1) == None\n assert is_same_list(candidate(head = list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 29), list_node([30, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45]),n = 7), list_node([3, 6, 9, 12, 15, 18, 21, 24, 30, 33, 36, 39, 42, 45]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 29), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 10), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60]),n = 30), list_node([4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),n = 10), list_node([2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]),n = 10), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 65, 70, 75, 80, 85, 90, 95, 100]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 30]),n = 16), list_node([3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 30]))\n assert is_same_list(candidate(head = list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 1), list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 5), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90]),n = 3), list_node([100, 99, 98, 97, 96, 95, 94, 93, 91, 90]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),n = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9]),n = 10), list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 6, 4, 3, 3, 8, 3, 2, 7, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 25), list_node([1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),n = 28), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),n = 10), list_node([1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1]),n = 29), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 20), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([3, 5, 1, 2, 4, 7, 6, 8, 9]),n = 3), list_node([3, 5, 1, 2, 4, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]),n = 1), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28]))\n assert is_same_list(candidate(head = list_node([1, 2]),n = 2), list_node([2]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]),n = 28), list_node([1, 3, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),n = 4), list_node([1, 2, 3, 4, 5, 6, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 4), list_node([9, 8, 7, 6, 5, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 15), list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]))\n assert is_same_list(candidate(head = list_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),n = 2), list_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([2, 3, 4, 5]),n = 4), list_node([3, 4, 5]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]),n = 14), list_node([10, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),n = 1), list_node([10, 20, 30, 40, 50, 60, 70, 80, 90]))\n assert is_same_list(candidate(head = list_node([29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 29), list_node([28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]),n = 15), list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 30), list_node([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),n = 25), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70]),n = 15), list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70]))\n assert is_same_list(candidate(head = list_node([6, 2, 8, 2, 8, 4, 1, 8, 5, 2, 8, 6, 4, 3, 2, 8, 6, 2, 4, 3, 8, 2, 6, 4, 3, 2, 8, 6, 2, 4]),n = 20), list_node([6, 2, 8, 2, 8, 4, 1, 8, 5, 2, 6, 4, 3, 2, 8, 6, 2, 4, 3, 8, 2, 6, 4, 3, 2, 8, 6, 2, 4]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),n = 20), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71]),n = 10), list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 79, 78, 77, 76, 75, 74, 73, 72, 71]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 10), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([99, 88, 77, 66, 55, 44, 33, 22, 11]),n = 9), list_node([88, 77, 66, 55, 44, 33, 22, 11]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 1), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]),n = 14), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]))\n assert is_same_list(candidate(head = list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]),n = 15), list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]))\n assert is_same_list(candidate(head = list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71]),n = 1), list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71]),n = 1), list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72]))\n assert is_same_list(candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 30), list_node([0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),n = 7), list_node([1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([3, 2, 1]),n = 2), list_node([3, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),n = 2), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),n = 8), list_node([1, 2, 2, 3, 4, 5, 5, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),n = 15), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),n = 9), list_node([8, 7, 6, 5, 4, 3, 2, 1]))\n"}, "metadata": {"canonical_parameter_names": ["head", "n"], "leetcode_dataset_entry_point": "Solution().removeNthFromEnd", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeNthFromEnd = function(head, n) {", "container": null, "callable": "removeNthFromEnd", "parameters": [{"name": "head", "type": "ListNode"}, {"name": "n", "type": "number"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 20, "task_id": "valid-parentheses", "difficulty": "Easy", "problem_description": "Given a string s containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.\nAn input string is valid if:\n\nOpen brackets must be closed by the same type of brackets.\nOpen brackets must be closed in the correct order.\nEvery close bracket has a corresponding open bracket of the same type.\n\n \nExample 1:\n\nInput: s = \"()\"\nOutput: true\n\nExample 2:\n\nInput: s = \"()[]{}\"\nOutput: true\n\nExample 3:\n\nInput: s = \"(]\"\nOutput: false\n\nExample 4:\n\nInput: s = \"([])\"\nOutput: true\n\n \nConstraints:\n\n1 <= s.length <= 104\ns consists of parentheses only '()[]{}'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"((((((()))))))\") == True\n assert candidate(s = \"{[()]}\") == True\n assert candidate(s = \"[[[[[[{{{{}}}}]]]]]]\") == True\n assert candidate(s = \"({[(])})\") == False\n assert candidate(s = \"([)]\") == False\n assert candidate(s = \")()()(\") == False\n assert candidate(s = \"({[({})]})\") == True\n assert candidate(s = \"\") == True\n assert candidate(s = \"(]\") == False\n assert candidate(s = \"{{{{{{}}}}}}\") == True\n assert candidate(s = \"{[(])}\") == False\n assert candidate(s = \"[[[[[[]]]]]]\") == True\n assert candidate(s = \"[({})]\") == True\n assert candidate(s = \"()[]{}\") == True\n assert candidate(s = \"([{}])\") == True\n assert candidate(s = \"()\") == True\n assert candidate(s = \"((({{[[]]}})))\") == True\n assert candidate(s = \"((()))\") == True\n assert candidate(s = \"([])\") == True\n assert candidate(s = \"({[{}]}){([{}])}\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()({})[({})]({})()()[({})]\") == True\n assert candidate(s = \"[[[[[[[[]]]]]]]]\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()\") == True\n assert candidate(s = \"({[()]})({[()]})({[()]})({[()]})({[()]})\") == True\n assert candidate(s = \"[[[[]]]]\") == True\n assert candidate(s = \"([{}])({[()]})\") == True\n assert candidate(s = \"({[([{([{}])()]})]})\") == False\n assert candidate(s = \"([])({})[]{}\") == True\n assert candidate(s = \"({[([{}])()]})\") == True\n assert candidate(s = \"({[({[({[({[({})]})]})]})]})\") == True\n assert candidate(s = \"({[([{([{}])()]})]})()[]{}\") == False\n assert candidate(s = \"({{{{{}}}}})\") == True\n assert candidate(s = \"(((((())))))\") == True\n assert candidate(s = \"([({})])\") == True\n assert candidate(s = \"({[()]})[({[()]})]\") == True\n assert candidate(s = \"({[({})]})({[{}]})\") == True\n assert candidate(s = \"[({[({[({[]})]})]})]({[({[]})]})\") == True\n assert candidate(s = \"({[()({[()]})]})\") == True\n assert candidate(s = \"((((((((((((())))))))))))\") == False\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})()\") == True\n assert candidate(s = \"({[([{}])()]}){([])}\") == True\n assert candidate(s = \"({[([{}])()]})()\") == True\n assert candidate(s = \"({[({[({[({[({[({})]})]})]})]})]})\") == True\n assert candidate(s = \"{}{}{}{}{}\") == True\n assert candidate(s = \"([({[({[()]})]})])\") == True\n assert candidate(s = \"{((({[({})]})()))}\") == True\n assert candidate(s = \"[{()}]\") == True\n assert candidate(s = \"(((((((({[({[({})]})]})()))))))\") == False\n assert candidate(s = \"([({[({[({[({[]})]})]})]})])\") == True\n assert candidate(s = \"({[({})]})({[({})]})({[({})]})({[({})]})\") == True\n assert candidate(s = \"({[({[({[({[]})]})]})]})\") == True\n assert candidate(s = \"{{{{{{{{}}}}}}}}}\") == False\n assert candidate(s = \"((((((((()))))))))\") == True\n assert candidate(s = \"{((((((((({[({[({[({[({})]})]})]})]))))))}\") == False\n assert candidate(s = \"{[({[({[({[]})]})]})]})({[({[({[({[]})]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})\") == False\n assert candidate(s = \"({[()({})({})({})({})]})\") == True\n assert candidate(s = \"((({{{[[[()]]]}}})))\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()({})[({})]({})()()\") == True\n assert candidate(s = \"({[({})]})({[({})]})({[({})]})({[({})]})({[({})]})({[({})]})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()({})\") == True\n assert candidate(s = \"{([({[({[({[]})]})]})]})({[({[({[({[]})]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})\") == False\n assert candidate(s = \"{(((((((({[({[({})]})]})()))))))}\") == False\n assert candidate(s = \"({[({[({[({[()]})]})]})]})\") == True\n assert candidate(s = \"({[({})({})({})({})({})({})({})({})({})({})({})({})({})({})({})({})({})({})({})({})]})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()({})[({})]({})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]\") == True\n assert candidate(s = \"({[({[({[({})]})]})]})\") == True\n assert candidate(s = \"[({}){()}]\") == True\n assert candidate(s = \"([{}])({[]})\") == True\n assert candidate(s = \"[({})](())\") == True\n assert candidate(s = \"{[({})]}[({})]\") == True\n assert candidate(s = \"[[{{}}]]\") == True\n assert candidate(s = \"({[({})]})({[({})]})\") == True\n assert candidate(s = \"({[({[({[()]}())]}())}())\") == False\n assert candidate(s = \"({[([{}])()]}){}\") == True\n assert candidate(s = \"({[({})]})({[({})]})({[({})]})\") == True\n assert candidate(s = \"{[(())[()]}\") == False\n assert candidate(s = \"({[({})({})({})({})({})({})({})({})]})\") == True\n assert candidate(s = \"((()))[({})]\") == True\n assert candidate(s = \"({[({})]({})})\") == True\n assert candidate(s = \"([])({[]}){([])}\") == True\n assert candidate(s = \"()()()()()()()()()()\") == True\n assert candidate(s = \"((((((())))))){}[]\") == True\n assert candidate(s = \"{[()]}{[()]}\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})()[]\") == True\n assert candidate(s = \"{({[({})]})}\") == True\n assert candidate(s = \"((({{{[[[]]]}}})))\") == True\n assert candidate(s = \"({[([{([{}])()]})]})()[]{}{([])[()]}\") == False\n assert candidate(s = \"((({[({})]})({[({})]}))({[({})]})({[({})]})({[({})]})\") == False\n assert candidate(s = \"({[({[({[()]}])}])})\") == False\n assert candidate(s = \"{{{{{{{{}}}}}}}}\") == True\n assert candidate(s = \"()()()()()()()\") == True\n assert candidate(s = \"({[()]})({[()]})({[()]})\") == True\n assert candidate(s = \"{[()]({[()]})}\") == True\n assert candidate(s = \"({[({[({[({[]}]})]})]})\") == False\n assert candidate(s = \"({[({[({})]})]})\") == True\n assert candidate(s = \"({[()]})\") == True\n assert candidate(s = \"({[(())]})\") == True\n assert candidate(s = \"({[()]}{[()]})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}\") == True\n assert candidate(s = \"([{}])((()))[{}]\") == True\n assert candidate(s = \"{([({[({[({[]})]})]})]})({[({[({[]})]})]})\") == False\n assert candidate(s = \"((({[({})]})()))\") == True\n assert candidate(s = \"[({})]({[()]})\") == True\n assert candidate(s = \"({[{({})}]})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()\") == True\n assert candidate(s = \"(((())))\") == True\n assert candidate(s = \"({[([{([{}])()]})]})()[]{}{([])[()]}{({})}\") == False\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()({})[({})]({})()\") == True\n assert candidate(s = \"(((((((())))))\") == False\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]\") == True\n assert candidate(s = \"()({})({[()]})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}\") == True\n assert candidate(s = \"{{[[(())]]}}\") == True\n assert candidate(s = \"{[({[({[({[]})]})]})]})({[({[({[({[]})]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})\") == False\n assert candidate(s = \"({[({})]})({})\") == True\n assert candidate(s = \"[({})]([])\") == True\n assert candidate(s = \"({[([{}])()]}){([])[()]}\") == True\n assert candidate(s = \"({[([{}])()]})[]\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()\") == True\n assert candidate(s = \"({[({[({[({[]})]})]})]})({[({[({[]})]})]})({[({[({[]})]})]})\") == True\n assert candidate(s = \"([({})({})])\") == True\n assert candidate(s = \"((((({{{[[[]]]}}}))))))\") == False\n assert candidate(s = \"[({[({})]})]\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})\") == True\n assert candidate(s = \"[[[({})]]]\") == True\n assert candidate(s = \"({[]})({})({[]})({})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})(){}[]()({})[({})]({})()[]{}()({})[({})]\") == True\n assert candidate(s = \"((()))[{}]\") == True\n assert candidate(s = \"(((((({[({[({})]})]})())))))\") == True\n assert candidate(s = \"[[[[[[[]]]]]]]\") == True\n assert candidate(s = \"({[({})]})({[({})]})({[({})]})({[({})]})({[({})]})\") == True\n assert candidate(s = \"((((({[({})]})()))))\") == True\n assert candidate(s = \"{[()]}{[()]}{[()]}\") == True\n assert candidate(s = \"(){}[]{}[]{}\") == True\n assert candidate(s = \"([{}])({[{}]})({[{}]})\") == True\n assert candidate(s = \"{{{{}}}}\") == True\n assert candidate(s = \"[{()}]{[()]}\") == True\n assert candidate(s = \"({[()()]})\") == True\n assert candidate(s = \"()[]{}()[]{}\") == True\n assert candidate(s = \"({[()]})({[()]})\") == True\n assert candidate(s = \"({[({[({[({[({[]})]})]})]})]})\") == True\n assert candidate(s = \"{[()]}({[()]}({[()]}))\") == True\n assert candidate(s = \"((({{[[(())]]}})))\") == True\n assert candidate(s = \"{(((((({[({[({})]})]})())))))}\") == True\n assert candidate(s = \"[[{{(())}}]]\") == True\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().isValid", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isValid = function(s) {", "container": null, "callable": "isValid", "parameters": [{"name": "s", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 21, "task_id": "merge-two-sorted-lists", "difficulty": "Easy", "problem_description": "You are given the heads of two sorted linked lists list1 and list2.\nMerge the two lists into one sorted list. The list should be made by splicing together the nodes of the first two lists.\nReturn the head of the merged linked list.\n \nExample 1:\n\n\nInput: list1 = [1,2,4], list2 = [1,3,4]\nOutput: [1,1,2,3,4,4]\n\nExample 2:\n\nInput: list1 = [], list2 = []\nOutput: []\n\nExample 3:\n\nInput: list1 = [], list2 = [0]\nOutput: [0]\n\n \nConstraints:\n\nThe number of nodes in both lists is in the range [0, 50].\n-100 <= Node.val <= 100\nBoth list1 and list2 are sorted in non-decreasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(list1 = list_node([1, 1, 1]),list2 = list_node([1, 1, 1])), list_node([1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30]),list2 = list_node([5, 15, 25, 35])), list_node([5, 10, 15, 20, 25, 30, 35]))\n assert is_same_list(candidate(list1 = list_node([-1, 0, 2]),list2 = list_node([-2, -1, 0])), list_node([-2, -1, -1, 0, 0, 2]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9]),list2 = list_node([2, 4, 6, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([10]),list2 = list_node([10])), list_node([10, 10]))\n assert is_same_list(candidate(list1 = list_node([100]),list2 = list_node([50, 75, 100])), list_node([50, 75, 100, 100]))\n assert is_same_list(candidate(list1 = list_node([-100, 0, 100]),list2 = list_node([-50, 50])), list_node([-100, -50, 0, 50, 100]))\n assert is_same_list(candidate(list1 = list_node([5]),list2 = list_node([4])), list_node([4, 5]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7]),list2 = list_node([2, 4, 6, 8])), list_node([1, 2, 3, 4, 5, 6, 7, 8]))\n assert candidate(list1 = list_node([]),list2 = list_node([])) == None\n assert is_same_list(candidate(list1 = list_node([5]),list2 = list_node([1, 2, 3])), list_node([1, 2, 3, 5]))\n assert is_same_list(candidate(list1 = list_node([-100, 0, 100]),list2 = list_node([-50, 50])), list_node([-100, -50, 0, 50, 100]))\n assert is_same_list(candidate(list1 = list_node([]),list2 = list_node([0])), list_node([0]))\n assert is_same_list(candidate(list1 = list_node([-10, -5, 0]),list2 = list_node([-20, -15, -10])), list_node([-20, -15, -10, -10, -5, 0]))\n assert is_same_list(candidate(list1 = list_node([1, 1, 1, 1]),list2 = list_node([1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(list1 = list_node([-1, -2, -3]),list2 = list_node([-4, -5, -6])), list_node([-4, -5, -6, -1, -2, -3]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 4]),list2 = list_node([1, 3, 4])), list_node([1, 1, 2, 3, 4, 4]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3]),list2 = list_node([4, 5, 6])), list_node([1, 2, 3, 4, 5, 6]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5]),list2 = list_node([6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),list2 = list_node([11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(list1 = list_node([-100, -50, 0, 50, 100]),list2 = list_node([-200, -150, -100, -50, 0])), list_node([-200, -150, -100, -100, -50, -50, 0, 0, 50, 100]))\n assert is_same_list(candidate(list1 = list_node([-99, -98, -97]),list2 = list_node([-96, -95, -94])), list_node([-99, -98, -97, -96, -95, -94]))\n assert is_same_list(candidate(list1 = list_node([-100, -99, -98]),list2 = list_node([-100, -99, -98])), list_node([-100, -100, -99, -99, -98, -98]))\n assert is_same_list(candidate(list1 = list_node([-10, -5, 0, 5, 10]),list2 = list_node([-20, -15, -10, -5, 0])), list_node([-20, -15, -10, -10, -5, -5, 0, 0, 5, 10]))\n assert is_same_list(candidate(list1 = list_node([30, 40, 50]),list2 = list_node([10, 20, 30, 40, 50, 60])), list_node([10, 20, 30, 30, 40, 40, 50, 50, 60]))\n assert is_same_list(candidate(list1 = list_node([2, 4, 6, 8]),list2 = list_node([1, 3, 5, 7, 9, 11, 13, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15]))\n assert is_same_list(candidate(list1 = list_node([-99, -50, -20, 0, 20, 50]),list2 = list_node([-98, -49, -19, -1, 19, 49])), list_node([-99, -98, -50, -49, -20, -19, -1, 0, 19, 20, 49, 50]))\n assert is_same_list(candidate(list1 = list_node([-10, -5, 0, 5, 10]),list2 = list_node([-11, -6, -1, 6, 11])), list_node([-11, -10, -6, -5, -1, 0, 5, 6, 10, 11]))\n assert is_same_list(candidate(list1 = list_node([1]),list2 = list_node([2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([0, 1, 2, 3, 4]),list2 = list_node([-4, -3, -2, -1, 0])), list_node([-4, -3, -2, -1, 0, 0, 1, 2, 3, 4]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9, 11, 13]),list2 = list_node([2, 4, 6, 8, 10, 12, 14])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]))\n assert is_same_list(candidate(list1 = list_node([50, 100, 150, 200, 250, 300]),list2 = list_node([25, 75, 125, 175, 225, 275, 325])), list_node([25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325]))\n assert is_same_list(candidate(list1 = list_node([50, 45, 40, 35, 30]),list2 = list_node([25, 20, 15, 10, 5, 0])), list_node([25, 20, 15, 10, 5, 0, 50, 45, 40, 35, 30]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),list2 = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(list1 = list_node([-1, 2, 4, 6, 8]),list2 = list_node([0, 3, 5, 7, 9])), list_node([-1, 0, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30, 40, 50]),list2 = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([2, 4, 6, 8, 10, 10, 12, 14, 16, 18, 20, 20, 30, 40, 50]))\n assert is_same_list(candidate(list1 = list_node([0, 2, 4, 6, 8, 10]),list2 = list_node([1, 3, 5, 7, 9])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([-1, -2, -3, -4, -5]),list2 = list_node([-5, -4, -3, -2, -1])), list_node([-5, -4, -3, -2, -1, -2, -3, -4, -5, -1]))\n assert is_same_list(candidate(list1 = list_node([-99, -98, -97, -96]),list2 = list_node([-95, -94, -93, -92])), list_node([-99, -98, -97, -96, -95, -94, -93, -92]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5]),list2 = list_node([0, -1, -2, -3, -4, -5])), list_node([0, -1, -2, -3, -4, -5, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(list1 = list_node([-5, -4, -3, -2, -1]),list2 = list_node([0, 1, 2, 3, 4, 5])), list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(list1 = list_node([-1, 2, -3, 4, -5]),list2 = list_node([1, -2, 3, -4, 5])), list_node([-1, 1, -2, 2, -3, 3, -4, 4, -5, 5]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),list2 = list_node([5, 15, 25, 35, 45, 55, 65, 75, 85, 95])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9]),list2 = list_node([10, 20, 30, 40, 50])), list_node([1, 3, 5, 7, 9, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(list1 = list_node([0, 2, 4, 6, 8]),list2 = list_node([1, 3, 5, 7, 9])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(list1 = list_node([-100, -50, 0, 50, 100]),list2 = list_node([])), list_node([-100, -50, 0, 50, 100]))\n assert is_same_list(candidate(list1 = list_node([-10, -8, -6, -4, -2]),list2 = list_node([-9, -7, -5, -3, -1])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(list1 = list_node([-100, -50, 0, 50, 100]),list2 = list_node([-75, -25, 25, 75])), list_node([-100, -75, -50, -25, 0, 25, 50, 75, 100]))\n assert is_same_list(candidate(list1 = list_node([1]),list2 = list_node([2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9]),list2 = list_node([1, 3, 5, 7, 9])), list_node([1, 1, 3, 3, 5, 5, 7, 7, 9, 9]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),list2 = list_node([11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(list1 = list_node([-50, -40, -30]),list2 = list_node([-20, -10, 0, 10, 20, 30])), list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9]),list2 = list_node([2, 4, 6, 8, 10, 12, 14])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14]))\n assert is_same_list(candidate(list1 = list_node([100, 101, 102, 103]),list2 = list_node([104, 105, 106, 107])), list_node([100, 101, 102, 103, 104, 105, 106, 107]))\n assert is_same_list(candidate(list1 = list_node([-100, -50, -10]),list2 = list_node([-200, -150, -100, -50, -10])), list_node([-200, -150, -100, -100, -50, -50, -10, -10]))\n assert is_same_list(candidate(list1 = list_node([1]),list2 = list_node([1, 2, 3, 4, 5])), list_node([1, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30]),list2 = list_node([5, 15, 25, 35, 45, 55, 65])), list_node([5, 10, 15, 20, 25, 30, 35, 45, 55, 65]))\n assert is_same_list(candidate(list1 = list_node([100, 90, 80, 70, 60]),list2 = list_node([50, 40, 30, 20, 10])), list_node([50, 40, 30, 20, 10, 100, 90, 80, 70, 60]))\n assert is_same_list(candidate(list1 = list_node([10]),list2 = list_node([5, 15, 25, 35, 45])), list_node([5, 10, 15, 25, 35, 45]))\n assert is_same_list(candidate(list1 = list_node([100, 200, 300]),list2 = list_node([50, 150, 250, 350])), list_node([50, 100, 150, 200, 250, 300, 350]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),list2 = list_node([5])), list_node([1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([-99, -50, 0, 25, 75, 100]),list2 = list_node([-100, -75, -25, -1, 50, 100])), list_node([-100, -99, -75, -50, -25, -1, 0, 25, 50, 75, 100, 100]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),list2 = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30]))\n assert is_same_list(candidate(list1 = list_node([2, 4, 6, 8, 10]),list2 = list_node([1, 3, 5, 7, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([100]),list2 = list_node([-100, -50, 0, 50, 75])), list_node([-100, -50, 0, 50, 75, 100]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3]),list2 = list_node([4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5]),list2 = list_node([])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(list1 = list_node([-1, 0, 1, 2, 3]),list2 = list_node([-3, -2, -1, 0, 1])), list_node([-3, -2, -1, -1, 0, 0, 1, 1, 2, 3]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30, 40, 50]),list2 = list_node([5, 15, 25, 35, 45])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9]),list2 = list_node([2, 4, 6, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(list1 = list_node([-1, -3, -5, -7, -9]),list2 = list_node([-2, -4, -6, -8, -10])), list_node([-2, -4, -6, -8, -10, -1, -3, -5, -7, -9]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30]),list2 = list_node([5, 15, 25, 35, 45])), list_node([5, 10, 15, 20, 25, 30, 35, 45]))\n assert is_same_list(candidate(list1 = list_node([-1, 0, 1]),list2 = list_node([-2, -1, 0, 1, 2])), list_node([-2, -1, -1, 0, 0, 1, 1, 2]))\n assert is_same_list(candidate(list1 = list_node([50]),list2 = list_node([50, 50, 50, 50, 50])), list_node([50, 50, 50, 50, 50, 50]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3]),list2 = list_node([1, 2, 3, 4, 5])), list_node([1, 1, 2, 2, 3, 3, 4, 5]))\n assert is_same_list(candidate(list1 = list_node([50]),list2 = list_node([-50, 0, 50, 100])), list_node([-50, 0, 50, 50, 100]))\n assert is_same_list(candidate(list1 = list_node([-5, -3, -1]),list2 = list_node([-4, -2, 0, 2, 4])), list_node([-5, -4, -3, -2, -1, 0, 2, 4]))\n assert is_same_list(candidate(list1 = list_node([5, 10, 15, 20]),list2 = list_node([25, 30, 35, 40, 45, 50])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50]))\n assert is_same_list(candidate(list1 = list_node([-99, -50, 0, 25, 75]),list2 = list_node([-100, -25, -1, 50, 100])), list_node([-100, -99, -50, -25, -1, 0, 25, 50, 75, 100]))\n assert is_same_list(candidate(list1 = list_node([-10, -5, 0, 5, 10]),list2 = list_node([-20, -15, -10, 0, 15, 20])), list_node([-20, -15, -10, -10, -5, 0, 0, 5, 10, 15, 20]))\n assert is_same_list(candidate(list1 = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),list2 = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),list2 = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(list1 = list_node([0, 0, 0, 0, 0]),list2 = list_node([0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9]),list2 = list_node([2, 4, 6, 8, 10, 11, 12])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]))\n assert is_same_list(candidate(list1 = list_node([-50, -40, -30, -20, -10]),list2 = list_node([-60, -55, -45, -35, -25])), list_node([-60, -55, -50, -45, -40, -35, -30, -25, -20, -10]))\n assert is_same_list(candidate(list1 = list_node([-3, -2, -1, 0, 1, 2, 3]),list2 = list_node([-4, -3, -2, -1, 0, 1, 2, 3, 4])), list_node([-4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4]))\n assert is_same_list(candidate(list1 = list_node([0, 0, 0, 0]),list2 = list_node([-1, -2, -3, -4])), list_node([-1, -2, -3, -4, 0, 0, 0, 0]))\n assert is_same_list(candidate(list1 = list_node([-10, -5, 0, 5, 10]),list2 = list_node([-20, -15, -10, -5, 0, 5, 10])), list_node([-20, -15, -10, -10, -5, -5, 0, 0, 5, 5, 10, 10]))\n assert is_same_list(candidate(list1 = list_node([-10, -5, 0, 5, 10]),list2 = list_node([-15, -10, -5, 0, 5])), list_node([-15, -10, -10, -5, -5, 0, 0, 5, 5, 10]))\n assert is_same_list(candidate(list1 = list_node([]),list2 = list_node([-50, -25, 0, 25, 50, 75])), list_node([-50, -25, 0, 25, 50, 75]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5]),list2 = list_node([5, 6, 7, 8, 9])), list_node([1, 2, 3, 4, 5, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(list1 = list_node([100, 200, 300]),list2 = list_node([50, 150, 250, 350])), list_node([50, 100, 150, 200, 250, 300, 350]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30, 40, 50]),list2 = list_node([5, 15, 25, 35, 45])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50]))\n assert is_same_list(candidate(list1 = list_node([-1, 0, 3, 10, 20, 30, 40, 50]),list2 = list_node([1, 2, 4, 5, 8, 13, 21, 25, 35, 45, 55])), list_node([-1, 0, 1, 2, 3, 4, 5, 8, 10, 13, 20, 21, 25, 30, 35, 40, 45, 50, 55]))\n assert is_same_list(candidate(list1 = list_node([-20, -10, 0, 10, 20]),list2 = list_node([-15, -5, 5, 15, 25])), list_node([-20, -15, -10, -5, 0, 5, 10, 15, 20, 25]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9, 11]),list2 = list_node([2, 4, 6, 8, 10, 12])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]),list2 = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30, 40, 50]),list2 = list_node([5, 15, 25, 35, 45, 55])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),list2 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(list1 = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),list2 = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(list1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),list2 = list_node([11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(list1 = list_node([-99, -98, -97, -96, -95]),list2 = list_node([-94, -93, -92, -91, -90])), list_node([-99, -98, -97, -96, -95, -94, -93, -92, -91, -90]))\n assert is_same_list(candidate(list1 = list_node([10, 20, 30, 40, 50]),list2 = list_node([25, 35, 45, 55, 65])), list_node([10, 20, 25, 30, 35, 40, 45, 50, 55, 65]))\n assert is_same_list(candidate(list1 = list_node([100]),list2 = list_node([-100])), list_node([-100, 100]))\n assert is_same_list(candidate(list1 = list_node([1, 4, 7, 10]),list2 = list_node([2, 5, 8, 11])), list_node([1, 2, 4, 5, 7, 8, 10, 11]))\n assert is_same_list(candidate(list1 = list_node([-1, 0, 1]),list2 = list_node([-2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-2, -3, -4, -5, -6, -7, -8, -9, -10, -1, 0, 1]))\n assert is_same_list(candidate(list1 = list_node([50, 60, 70, 80, 90]),list2 = list_node([40, 55, 65, 75, 85])), list_node([40, 50, 55, 60, 65, 70, 75, 80, 85, 90]))\n assert is_same_list(candidate(list1 = list_node([5, 10, 15, 20, 25]),list2 = list_node([3, 8, 13, 18, 23])), list_node([3, 5, 8, 10, 13, 15, 18, 20, 23, 25]))\n assert is_same_list(candidate(list1 = list_node([-1, -2, -3, -4, -5]),list2 = list_node([-1, -2, -3, -4, -5])), list_node([-1, -2, -3, -4, -5, -1, -2, -3, -4, -5]))\n assert is_same_list(candidate(list1 = list_node([-50, -40, -30, -20, -10]),list2 = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])), list_node([-50, -40, -30, -20, -10, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]))\n assert is_same_list(candidate(list1 = list_node([-10, -20, -30, -40, -50]),list2 = list_node([-5, -15, -25, -35, -45])), list_node([-10, -20, -30, -40, -50, -5, -15, -25, -35, -45]))\n"}, "metadata": {"canonical_parameter_names": ["list1", "list2"], "leetcode_dataset_entry_point": "Solution().mergeTwoLists", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var mergeTwoLists = function(list1, list2) {", "container": null, "callable": "mergeTwoLists", "parameters": [{"name": "list1", "type": "ListNode"}, {"name": "list2", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 22, "task_id": "generate-parentheses", "difficulty": "Medium", "problem_description": "Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.\n \nExample 1:\nInput: n = 3\nOutput: [\"((()))\",\"(()())\",\"(())()\",\"()(())\",\"()()()\"]\nExample 2:\nInput: n = 1\nOutput: [\"()\"]\n\n \nConstraints:\n\n1 <= n <= 8\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == ['(((((((())))))))', '((((((()()))))))', '((((((())())))))', '((((((()))()))))', '((((((())))())))', '((((((()))))()))', '((((((())))))())', '((((((()))))))()', '(((((()(()))))))', '(((((()()())))))', '(((((()())()))))', '(((((()()))())))', '(((((()())))()))', '(((((()()))))())', '(((((()())))))()', '(((((())(())))))', '(((((())()()))))', '(((((())())())))', '(((((())()))()))', '(((((())())))())', '(((((())()))))()', '(((((()))(()))))', '(((((()))()())))', '(((((()))())()))', '(((((()))()))())', '(((((()))())))()', '(((((())))(())))', '(((((())))()()))', '(((((())))())())', '(((((())))()))()', '(((((()))))(()))', '(((((()))))()())', '(((((()))))())()', '(((((())))))(())', '(((((())))))()()', '((((()((()))))))', '((((()(()())))))', '((((()(())()))))', '((((()(()))())))', '((((()(())))()))', '((((()(()))))())', '((((()(())))))()', '((((()()(())))))', '((((()()()()))))', '((((()()())())))', '((((()()()))()))', '((((()()())))())', '((((()()()))))()', '((((()())(()))))', '((((()())()())))', '((((()())())()))', '((((()())()))())', '((((()())())))()', '((((()()))(())))', '((((()()))()()))', '((((()()))())())', '((((()()))()))()', '((((()())))(()))', '((((()())))()())', '((((()())))())()', '((((()()))))(())', '((((()()))))()()', '((((())((())))))', '((((())(()()))))', '((((())(())())))', '((((())(()))()))', '((((())(())))())', '((((())(()))))()', '((((())()(()))))', '((((())()()())))', '((((())()())()))', '((((())()()))())', '((((())()())))()', '((((())())(())))', '((((())())()()))', '((((())())())())', '((((())())()))()', '((((())()))(()))', '((((())()))()())', '((((())()))())()', '((((())())))(())', '((((())())))()()', '((((()))((()))))', '((((()))(()())))', '((((()))(())()))', '((((()))(()))())', '((((()))(())))()', 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'()()((())()()())', '()()((())()())()', '()()((())())(())', '()()((())())()()', '()()((()))((()))', '()()((()))(()())', '()()((()))(())()', '()()((()))()(())', '()()((()))()()()', '()()(()(((()))))', '()()(()((()())))', '()()(()((())()))', '()()(()((()))())', '()()(()((())))()', '()()(()(()(())))', '()()(()(()()()))', '()()(()(()())())', '()()(()(()()))()', '()()(()(())(()))', '()()(()(())()())', '()()(()(())())()', '()()(()(()))(())', '()()(()(()))()()', '()()(()()((())))', '()()(()()(()()))', '()()(()()(())())', '()()(()()(()))()', '()()(()()()(()))', '()()(()()()()())', '()()(()()()())()', '()()(()()())(())', '()()(()()())()()', '()()(()())((()))', '()()(()())(()())', '()()(()())(())()', '()()(()())()(())', '()()(()())()()()', '()()(())(((())))', '()()(())((()()))', '()()(())((())())', '()()(())((()))()', '()()(())(()(()))', '()()(())(()()())', '()()(())(()())()', '()()(())(())(())', '()()(())(())()()', '()()(())()((()))', '()()(())()(()())', '()()(())()(())()', '()()(())()()(())', '()()(())()()()()', '()()()((((()))))', '()()()(((()())))', '()()()(((())()))', '()()()(((()))())', '()()()(((())))()', '()()()((()(())))', '()()()((()()()))', '()()()((()())())', '()()()((()()))()', '()()()((())(()))', '()()()((())()())', '()()()((())())()', '()()()((()))(())', '()()()((()))()()', '()()()(()((())))', '()()()(()(()()))', '()()()(()(())())', '()()()(()(()))()', '()()()(()()(()))', '()()()(()()()())', '()()()(()()())()', '()()()(()())(())', '()()()(()())()()', '()()()(())((()))', '()()()(())(()())', '()()()(())(())()', '()()()(())()(())', '()()()(())()()()', '()()()()(((())))', '()()()()((()()))', '()()()()((())())', '()()()()((()))()', '()()()()(()(()))', '()()()()(()()())', '()()()()(()())()', '()()()()(())(())', '()()()()(())()()', '()()()()()((()))', '()()()()()(()())', '()()()()()(())()', '()()()()()()(())', '()()()()()()()()']\n assert candidate(n = 3) == ['((()))', '(()())', '(())()', '()(())', '()()()']\n assert candidate(n = 4) == ['(((())))', '((()()))', '((())())', '((()))()', '(()(()))', '(()()())', '(()())()', '(())(())', '(())()()', '()((()))', '()(()())', '()(())()', '()()(())', '()()()()']\n assert candidate(n = 6) == ['(((((())))))', '((((()()))))', '((((())())))', '((((()))()))', '((((())))())', '((((()))))()', '(((()(()))))', '(((()()())))', '(((()())()))', '(((()()))())', '(((()())))()', '(((())(())))', '(((())()()))', '(((())())())', '(((())()))()', '(((()))(()))', '(((()))()())', '(((()))())()', '(((())))(())', '(((())))()()', '((()((()))))', '((()(()())))', '((()(())()))', '((()(()))())', '((()(())))()', '((()()(())))', '((()()()()))', '((()()())())', '((()()()))()', '((()())(()))', '((()())()())', '((()())())()', '((()()))(())', '((()()))()()', '((())((())))', '((())(()()))', '((())(())())', '((())(()))()', '((())()(()))', '((())()()())', '((())()())()', '((())())(())', '((())())()()', '((()))((()))', '((()))(()())', '((()))(())()', '((()))()(())', '((()))()()()', '(()(((()))))', '(()((()())))', '(()((())()))', '(()((()))())', '(()((())))()', '(()(()(())))', '(()(()()()))', '(()(()())())', '(()(()()))()', '(()(())(()))', '(()(())()())', '(()(())())()', '(()(()))(())', '(()(()))()()', '(()()((())))', '(()()(()()))', '(()()(())())', '(()()(()))()', '(()()()(()))', '(()()()()())', '(()()()())()', '(()()())(())', '(()()())()()', '(()())((()))', '(()())(()())', '(()())(())()', '(()())()(())', '(()())()()()', '(())(((())))', '(())((()()))', '(())((())())', '(())((()))()', '(())(()(()))', '(())(()()())', '(())(()())()', '(())(())(())', '(())(())()()', '(())()((()))', '(())()(()())', '(())()(())()', '(())()()(())', '(())()()()()', '()((((()))))', '()(((()())))', '()(((())()))', '()(((()))())', '()(((())))()', '()((()(())))', '()((()()()))', '()((()())())', '()((()()))()', '()((())(()))', '()((())()())', '()((())())()', '()((()))(())', '()((()))()()', '()(()((())))', '()(()(()()))', '()(()(())())', '()(()(()))()', '()(()()(()))', '()(()()()())', '()(()()())()', '()(()())(())', '()(()())()()', '()(())((()))', '()(())(()())', '()(())(())()', '()(())()(())', '()(())()()()', '()()(((())))', '()()((()()))', '()()((())())', '()()((()))()', '()()(()(()))', '()()(()()())', '()()(()())()', '()()(())(())', '()()(())()()', '()()()((()))', '()()()(()())', '()()()(())()', '()()()()(())', '()()()()()()']\n assert candidate(n = 2) == ['(())', '()()']\n assert candidate(n = 1) == ['()']\n assert candidate(n = 7) == ['((((((()))))))', '(((((()())))))', '(((((())()))))', '(((((()))())))', '(((((())))()))', '(((((()))))())', '(((((())))))()', '((((()(())))))', '((((()()()))))', '((((()())())))', '((((()()))()))', '((((()())))())', '((((()()))))()', '((((())(()))))', '((((())()())))', '((((())())()))', '((((())()))())', '((((())())))()', '((((()))(())))', '((((()))()()))', '((((()))())())', '((((()))()))()', '((((())))(()))', '((((())))()())', '((((())))())()', '((((()))))(())', '((((()))))()()', '(((()((())))))', '(((()(()()))))', '(((()(())())))', '(((()(()))()))', '(((()(())))())', '(((()(()))))()', '(((()()(()))))', '(((()()()())))', '(((()()())()))', '(((()()()))())', '(((()()())))()', '(((()())(())))', '(((()())()()))', '(((()())())())', '(((()())()))()', '(((()()))(()))', '(((()()))()())', '(((()()))())()', '(((()())))(())', '(((()())))()()', '(((())((()))))', '(((())(()())))', '(((())(())()))', '(((())(()))())', '(((())(())))()', '(((())()(())))', '(((())()()()))', '(((())()())())', '(((())()()))()', '(((())())(()))', '(((())())()())', '(((())())())()', '(((())()))(())', '(((())()))()()', '(((()))((())))', '(((()))(()()))', '(((()))(())())', '(((()))(()))()', '(((()))()(()))', '(((()))()()())', '(((()))()())()', '(((()))())(())', '(((()))())()()', '(((())))((()))', '(((())))(()())', '(((())))(())()', '(((())))()(())', '(((())))()()()', '((()(((())))))', '((()((()()))))', '((()((())())))', '((()((()))()))', '((()((())))())', '((()((()))))()', '((()(()(()))))', '((()(()()())))', '((()(()())()))', '((()(()()))())', '((()(()())))()', '((()(())(())))', '((()(())()()))', '((()(())())())', '((()(())()))()', '((()(()))(()))', '((()(()))()())', '((()(()))())()', '((()(())))(())', '((()(())))()()', '((()()((()))))', '((()()(()())))', '((()()(())()))', '((()()(()))())', '((()()(())))()', '((()()()(())))', '((()()()()()))', '((()()()())())', '((()()()()))()', '((()()())(()))', '((()()())()())', '((()()())())()', '((()()()))(())', '((()()()))()()', '((()())((())))', '((()())(()()))', '((()())(())())', '((()())(()))()', '((()())()(()))', '((()())()()())', '((()())()())()', '((()())())(())', '((()())())()()', '((()()))((()))', '((()()))(()())', '((()()))(())()', '((()()))()(())', '((()()))()()()', '((())(((()))))', '((())((()())))', '((())((())()))', '((())((()))())', '((())((())))()', '((())(()(())))', '((())(()()()))', '((())(()())())', '((())(()()))()', '((())(())(()))', '((())(())()())', '((())(())())()', '((())(()))(())', '((())(()))()()', '((())()((())))', '((())()(()()))', '((())()(())())', '((())()(()))()', '((())()()(()))', '((())()()()())', '((())()()())()', '((())()())(())', '((())()())()()', '((())())((()))', '((())())(()())', '((())())(())()', '((())())()(())', '((())())()()()', '((()))(((())))', '((()))((()()))', '((()))((())())', '((()))((()))()', '((()))(()(()))', '((()))(()()())', '((()))(()())()', '((()))(())(())', '((()))(())()()', '((()))()((()))', '((()))()(()())', '((()))()(())()', '((()))()()(())', '((()))()()()()', '(()((((())))))', '(()(((()()))))', '(()(((())())))', '(()(((()))()))', '(()(((())))())', '(()(((()))))()', '(()((()(()))))', '(()((()()())))', '(()((()())()))', '(()((()()))())', '(()((()())))()', '(()((())(())))', '(()((())()()))', '(()((())())())', '(()((())()))()', '(()((()))(()))', '(()((()))()())', '(()((()))())()', '(()((())))(())', '(()((())))()()', '(()(()((()))))', '(()(()(()())))', '(()(()(())()))', '(()(()(()))())', '(()(()(())))()', '(()(()()(())))', '(()(()()()()))', '(()(()()())())', '(()(()()()))()', '(()(()())(()))', '(()(()())()())', '(()(()())())()', '(()(()()))(())', '(()(()()))()()', '(()(())((())))', '(()(())(()()))', '(()(())(())())', '(()(())(()))()', '(()(())()(()))', '(()(())()()())', '(()(())()())()', '(()(())())(())', '(()(())())()()', '(()(()))((()))', '(()(()))(()())', '(()(()))(())()', '(()(()))()(())', '(()(()))()()()', '(()()(((()))))', '(()()((()())))', '(()()((())()))', '(()()((()))())', '(()()((())))()', '(()()(()(())))', '(()()(()()()))', '(()()(()())())', '(()()(()()))()', '(()()(())(()))', '(()()(())()())', '(()()(())())()', '(()()(()))(())', '(()()(()))()()', '(()()()((())))', '(()()()(()()))', '(()()()(())())', '(()()()(()))()', '(()()()()(()))', '(()()()()()())', '(()()()()())()', '(()()()())(())', '(()()()())()()', '(()()())((()))', '(()()())(()())', '(()()())(())()', '(()()())()(())', '(()()())()()()', '(()())(((())))', '(()())((()()))', '(()())((())())', '(()())((()))()', '(()())(()(()))', '(()())(()()())', '(()())(()())()', '(()())(())(())', '(()())(())()()', '(()())()((()))', '(()())()(()())', '(()())()(())()', '(()())()()(())', '(()())()()()()', '(())((((()))))', '(())(((()())))', '(())(((())()))', '(())(((()))())', '(())(((())))()', '(())((()(())))', '(())((()()()))', '(())((()())())', '(())((()()))()', '(())((())(()))', '(())((())()())', '(())((())())()', '(())((()))(())', '(())((()))()()', '(())(()((())))', '(())(()(()()))', '(())(()(())())', '(())(()(()))()', '(())(()()(()))', '(())(()()()())', '(())(()()())()', '(())(()())(())', '(())(()())()()', '(())(())((()))', '(())(())(()())', '(())(())(())()', '(())(())()(())', '(())(())()()()', '(())()(((())))', '(())()((()()))', '(())()((())())', '(())()((()))()', '(())()(()(()))', '(())()(()()())', '(())()(()())()', '(())()(())(())', '(())()(())()()', '(())()()((()))', '(())()()(()())', '(())()()(())()', '(())()()()(())', '(())()()()()()', '()(((((())))))', '()((((()()))))', '()((((())())))', '()((((()))()))', '()((((())))())', '()((((()))))()', '()(((()(()))))', '()(((()()())))', '()(((()())()))', '()(((()()))())', '()(((()())))()', '()(((())(())))', '()(((())()()))', '()(((())())())', '()(((())()))()', '()(((()))(()))', '()(((()))()())', '()(((()))())()', '()(((())))(())', '()(((())))()()', '()((()((()))))', '()((()(()())))', '()((()(())()))', '()((()(()))())', '()((()(())))()', '()((()()(())))', '()((()()()()))', '()((()()())())', '()((()()()))()', '()((()())(()))', '()((()())()())', '()((()())())()', '()((()()))(())', '()((()()))()()', '()((())((())))', '()((())(()()))', '()((())(())())', '()((())(()))()', '()((())()(()))', '()((())()()())', '()((())()())()', '()((())())(())', '()((())())()()', '()((()))((()))', '()((()))(()())', '()((()))(())()', '()((()))()(())', '()((()))()()()', '()(()(((()))))', '()(()((()())))', '()(()((())()))', '()(()((()))())', '()(()((())))()', '()(()(()(())))', '()(()(()()()))', '()(()(()())())', '()(()(()()))()', '()(()(())(()))', '()(()(())()())', '()(()(())())()', '()(()(()))(())', '()(()(()))()()', '()(()()((())))', '()(()()(()()))', '()(()()(())())', '()(()()(()))()', '()(()()()(()))', '()(()()()()())', '()(()()()())()', '()(()()())(())', '()(()()())()()', '()(()())((()))', '()(()())(()())', '()(()())(())()', '()(()())()(())', '()(()())()()()', '()(())(((())))', '()(())((()()))', '()(())((())())', '()(())((()))()', '()(())(()(()))', '()(())(()()())', '()(())(()())()', '()(())(())(())', '()(())(())()()', '()(())()((()))', '()(())()(()())', '()(())()(())()', '()(())()()(())', '()(())()()()()', '()()((((()))))', '()()(((()())))', '()()(((())()))', '()()(((()))())', '()()(((())))()', '()()((()(())))', '()()((()()()))', '()()((()())())', '()()((()()))()', '()()((())(()))', '()()((())()())', '()()((())())()', '()()((()))(())', '()()((()))()()', '()()(()((())))', '()()(()(()()))', '()()(()(())())', '()()(()(()))()', '()()(()()(()))', '()()(()()()())', '()()(()()())()', '()()(()())(())', '()()(()())()()', '()()(())((()))', '()()(())(()())', '()()(())(())()', '()()(())()(())', '()()(())()()()', '()()()(((())))', '()()()((()()))', '()()()((())())', '()()()((()))()', '()()()(()(()))', '()()()(()()())', '()()()(()())()', '()()()(())(())', '()()()(())()()', '()()()()((()))', '()()()()(()())', '()()()()(())()', '()()()()()(())', '()()()()()()()']\n assert candidate(n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n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().generateParenthesis", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var generateParenthesis = function(n) {", "container": null, "callable": "generateParenthesis", "parameters": [{"name": "n", "type": "number"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 23, "task_id": "merge-k-sorted-lists", "difficulty": "Hard", "problem_description": "You are given an array of k linked-lists lists, each linked-list is sorted in ascending order.\nMerge all the linked-lists into one sorted linked-list and return it.\n \nExample 1:\n\nInput: lists = [[1,4,5],[1,3,4],[2,6]]\nOutput: [1,1,2,3,4,4,5,6]\nExplanation: The linked-lists are:\n[\n 1->4->5,\n 1->3->4,\n 2->6\n]\nmerging them into one sorted list:\n1->1->2->3->4->4->5->6\n\nExample 2:\n\nInput: lists = []\nOutput: []\n\nExample 3:\n\nInput: lists = [[]]\nOutput: []\n\n \nConstraints:\n\nk == lists.length\n0 <= k <= 104\n0 <= lists[i].length <= 500\n-104 <= lists[i][j] <= 104\nlists[i] is sorted in ascending order.\nThe sum of lists[i].length will not exceed 104.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(lists = []) == None\n assert candidate(lists = [[],[],[],[]]) == None\n assert candidate(lists = [[]]) == None\n"}, "metadata": {"canonical_parameter_names": ["lists"], "leetcode_dataset_entry_point": "Solution().mergeKLists", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var mergeKLists = function(lists) {", "container": null, "callable": "mergeKLists", "parameters": [{"name": "lists", "type": "ListNode[]"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 24, "task_id": "swap-nodes-in-pairs", "difficulty": "Medium", "problem_description": "Given a linked list, swap every two adjacent nodes and return its head. You must solve the problem without modifying the values in the list's nodes (i.e., only nodes themselves may be changed.)\n \nExample 1:\n\nInput: head = [1,2,3,4]\nOutput: [2,1,4,3]\nExplanation:\n\n\nExample 2:\n\nInput: head = []\nOutput: []\n\nExample 3:\n\nInput: head = [1]\nOutput: [1]\n\nExample 4:\n\nInput: head = [1,2,3]\nOutput: [2,1,3]\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 100].\n0 <= Node.val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4])), list_node([2, 1, 4, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3])), list_node([2, 1, 3]))\n assert candidate(head = list_node([])) == None\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21])), list_node([3, 1, 7, 5, 11, 9, 15, 13, 19, 17, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6])), list_node([2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 6]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186, 197, 208])), list_node([21, 10, 43, 32, 65, 54, 87, 76, 109, 98, 131, 120, 153, 142, 175, 164, 197, 186, 208]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 9]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25])), list_node([3, 1, 7, 5, 11, 9, 15, 13, 19, 17, 23, 21, 25]))\n assert is_same_list(candidate(head = list_node([5])), list_node([5]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1])), list_node([4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 1, 2, 1, 2, 1, 2, 1, 2])), list_node([2, 1, 2, 1, 2, 1, 2, 1, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 10]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81])), list_node([99, 100, 97, 98, 95, 96, 93, 94, 91, 92, 89, 90, 87, 88, 85, 86, 83, 84, 81, 82]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60])), list_node([20, 10, 40, 30, 60, 50]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([99, 100, 97, 98, 95, 96, 93, 94, 91, 92, 89, 90, 87, 88, 85, 86, 83, 84, 81, 82, 79, 80, 77, 78, 75, 76, 73, 74, 71, 72, 69, 70, 67, 68, 65, 66, 63, 64, 61, 62, 59, 60, 57, 58, 55, 56, 53, 54, 51, 52, 49, 50, 47, 48, 45, 46, 43, 44, 41, 42, 39, 40, 37, 38, 35, 36, 33, 34, 31, 32, 29, 30, 27, 28, 25, 26, 23, 24, 21, 22, 19, 20, 17, 18, 15, 16, 13, 14, 11, 12, 9, 10, 7, 8, 5, 6, 3, 4, 1, 2]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([9, 10, 7, 8, 5, 6, 3, 4, 1, 2, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29]))\n assert is_same_list(candidate(head = list_node([7, 8, 9, 10, 11, 12, 13, 14])), list_node([8, 7, 10, 9, 12, 11, 14, 13]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90])), list_node([20, 10, 40, 30, 60, 50, 80, 70, 90]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0]))\n assert is_same_list(candidate(head = list_node([7, 6, 5, 4, 3, 2, 1])), list_node([6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([50, 25, 75, 100, 5, 20, 30, 40, 60, 80, 90, 10])), list_node([25, 50, 100, 75, 20, 5, 40, 30, 80, 60, 10, 90]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 21])), list_node([4, 2, 8, 6, 12, 10, 16, 14, 20, 18, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70])), list_node([20, 10, 40, 30, 60, 50, 70]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20])), list_node([3, 1, 7, 5, 11, 9, 15, 13, 19, 17, 20]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 1, 3, 3, 4, 4, 5, 5])), list_node([2, 1, 1, 2, 3, 3, 4, 4, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([42])), list_node([42]))\n assert is_same_list(candidate(head = list_node([1, 2])), list_node([2, 1]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50])), list_node([20, 10, 40, 30, 50]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21])), list_node([3, 1, 7, 5, 11, 9, 15, 13, 19, 17, 21]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([9, 10, 7, 8, 5, 6, 3, 4, 1, 2]))\n assert is_same_list(candidate(head = list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 11]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22])), list_node([4, 2, 8, 6, 12, 10, 16, 14, 20, 18, 22]))\n assert is_same_list(candidate(head = list_node([2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 11]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 1, 3, 4, 4, 3, 5, 6, 6, 5])), list_node([2, 1, 1, 2, 4, 3, 3, 4, 6, 5, 5, 6]))\n assert is_same_list(candidate(head = list_node([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 15]))\n assert is_same_list(candidate(head = list_node([100, 0, 100, 0, 100, 0, 100, 0])), list_node([0, 100, 0, 100, 0, 100, 0, 100]))\n assert is_same_list(candidate(head = list_node([25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([24, 25, 22, 23, 20, 21, 18, 19, 16, 17, 14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24])), list_node([4, 2, 8, 6, 12, 10, 16, 14, 20, 18, 24, 22]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([8, 9, 6, 7, 4, 5, 2, 3, 0, 1, -2, -1, -4, -3, -6, -5, -8, -7, -10, -9]))\n assert is_same_list(candidate(head = list_node([42, 42])), list_node([42, 42]))\n assert is_same_list(candidate(head = list_node([100, 1, 99, 2, 98, 3, 97, 4, 96, 5])), list_node([1, 100, 2, 99, 3, 98, 4, 97, 5, 96]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 6, 7])), list_node([4, 5, 2, 3, 6, 1, 7]))\n assert is_same_list(candidate(head = list_node([2, 3, 4, 5, 6, 7, 8, 9, 10, 11])), list_node([3, 2, 5, 4, 7, 6, 9, 8, 11, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29]))\n assert is_same_list(candidate(head = list_node([19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([18, 19, 16, 17, 14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81])), list_node([99, 100, 97, 98, 95, 96, 93, 94, 91, 92, 89, 90, 87, 88, 85, 86, 83, 84, 81, 82]))\n assert is_same_list(candidate(head = list_node([2, 5, 3, 4, 1, 6, 8, 7])), list_node([5, 2, 4, 3, 6, 1, 7, 8]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([5, 4])), list_node([4, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 6, 2])), list_node([1, 5, 6, 9, 2]))\n assert is_same_list(candidate(head = list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2])), list_node([2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([4, 2, 8, 6, 12, 10, 16, 14, 20, 18]))\n assert is_same_list(candidate(head = list_node([1, 2])), list_node([2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 15]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0])), list_node([1, 0, 1, 0, 1, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8])), list_node([3, 1, 7, 5, 2, 9, 6, 4, 8]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80])), list_node([20, 10, 40, 30, 60, 50, 80, 70]))\n assert is_same_list(candidate(head = list_node([21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([20, 21, 18, 19, 16, 17, 14, 15, 12, 13, 10, 11, 8, 9, 6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6])), list_node([4, 5, 2, 3, 10, 1, 8, 9, 6, 7]))\n assert is_same_list(candidate(head = list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90])), list_node([98, 99, 96, 97, 94, 95, 92, 93, 90, 91]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8])), list_node([2, 1, 4, 3, 6, 5, 8, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([2, 1, 4, 3, 5]))\n assert is_same_list(candidate(head = list_node([5, 10])), list_node([10, 5]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19])), list_node([3, 1, 7, 5, 11, 9, 15, 13, 19, 17]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16])), list_node([4, 2, 8, 6, 12, 10, 16, 14]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100])), list_node([20, 10, 40, 30, 60, 50, 80, 70, 100, 90]))\n assert is_same_list(candidate(head = list_node([1, 4, 3, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([4, 1, 2, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 8, 2])), list_node([1, 5, 8, 9, 2]))\n assert is_same_list(candidate(head = list_node([11, 22, 33, 44, 55, 66, 77, 88, 99, 100])), list_node([22, 11, 44, 33, 66, 55, 88, 77, 100, 99]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7])), list_node([2, 1, 4, 3, 6, 5, 7]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91])), list_node([99, 100, 97, 98, 95, 96, 93, 94, 91, 92]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([8, 9, 6, 7, 4, 5, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1])), list_node([19, 21, 15, 17, 11, 13, 7, 9, 3, 5, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19])), list_node([3, 1, 7, 5, 11, 9, 15, 13, 19, 17]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11])), list_node([2, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11]))\n assert is_same_list(candidate(head = list_node([7, 6, 5, 4, 3, 2, 1, 0])), list_node([6, 7, 4, 5, 2, 3, 0, 1]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().swapPairs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var swapPairs = function(head) {", "container": null, "callable": "swapPairs", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 25, "task_id": "reverse-nodes-in-k-group", "difficulty": "Hard", "problem_description": "Given the head of a linked list, reverse the nodes of the list k at a time, and return the modified list.\nk is a positive integer and is less than or equal to the length of the linked list. If the number of nodes is not a multiple of k then left-out nodes, in the end, should remain as it is.\nYou may not alter the values in the list's nodes, only nodes themselves may be changed.\n \nExample 1:\n\n\nInput: head = [1,2,3,4,5], k = 2\nOutput: [2,1,4,3,5]\n\nExample 2:\n\n\nInput: head = [1,2,3,4,5], k = 3\nOutput: [3,2,1,4,5]\n\n \nConstraints:\n\nThe number of nodes in the list is n.\n1 <= k <= n <= 5000\n0 <= Node.val <= 1000\n\n \nFollow-up: Can you solve the problem in O(1) extra memory space?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([1, 2]),k = 2), list_node([2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6]),k = 4), list_node([4, 3, 2, 1, 5, 6]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7]),k = 3), list_node([3, 2, 1, 6, 5, 4, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6]))\n assert candidate(head = list_node([]),k = 1) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),k = 5), list_node([5, 4, 3, 2, 1, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]),k = 4), list_node([4, 3, 2, 1, 8, 7, 6, 5, 9, 10, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),k = 2), list_node([2, 1, 4, 3, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6]),k = 2), list_node([2, 1, 4, 3, 6, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]),k = 2), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6]),k = 3), list_node([3, 2, 1, 6, 5, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),k = 3), list_node([3, 2, 1, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2]),k = 1), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([1]),k = 1), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8]),k = 4), list_node([4, 3, 2, 1, 8, 7, 6, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),k = 1), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),k = 3), list_node([3, 2, 1, 6, 5, 4, 9, 8, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 18, 17, 16, 15, 14, 13, 19, 20, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]),k = 13), list_node([13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 53, 54, 55, 56, 57, 58, 59, 60]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 4), list_node([4, 3, 2, 1, 8, 7, 6, 5, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 18, 17, 16, 15, 14, 13, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 11), list_node([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([9, 1, 7, 3, 8, 4, 6, 2, 5, 0]),k = 3), list_node([7, 1, 9, 4, 8, 3, 5, 2, 6, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),k = 12), list_node([12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 21, 20, 19, 18, 17, 16, 15, 28, 27, 26, 25, 24, 23, 22, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),k = 4), list_node([4, 3, 2, 1, 8, 7, 6, 5, 12, 11, 10, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),k = 10), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),k = 3), list_node([3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]),k = 11), list_node([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]),k = 50), list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 3), list_node([3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13, 18, 17, 16, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]),k = 20), list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 22, 23, 24, 25, 26, 27]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 13), list_node([13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]),k = 10), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4]),k = 4), list_node([4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]),k = 16), list_node([16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 18, 19, 20, 21, 22, 23]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11, 12]))\n assert is_same_list(candidate(head = list_node([42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]),k = 6), list_node([42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 7, 4, 6, 2, 3]),k = 2), list_node([1, 5, 7, 9, 6, 4, 3, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]),k = 11), list_node([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 34, 35, 36, 37, 38, 39, 40]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]),k = 19), list_node([19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 21, 22, 23, 24, 25, 26]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]),k = 12), list_node([12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 49, 50]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 9), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 8, 9, 10, 11, 12, 13]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]),k = 3), list_node([3, 2, 1, 6, 5, 4, 9, 8, 7, 10, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11, 12, 13, 14]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]),k = 4), list_node([4, 3, 2, 1, 8, 7, 6, 5, 12, 11, 10, 9, 13]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]),k = 14), list_node([14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 16, 17, 18, 19, 20, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11, 20, 19, 18, 17, 16, 25, 24, 23, 22, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]),k = 11), list_node([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 13, 14, 15, 16]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]),k = 11), list_node([11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 13, 14, 15, 16, 17, 18]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 8), list_node([8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1000, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980, 979, 978, 977, 976, 975, 974, 973, 972, 971, 970, 969, 968, 967, 966, 965, 964, 963, 962, 961, 960]),k = 3), list_node([998, 999, 1000, 995, 996, 997, 992, 993, 994, 989, 990, 991, 986, 987, 988, 983, 984, 985, 980, 981, 982, 977, 978, 979, 974, 975, 976, 971, 972, 973, 968, 969, 970, 965, 966, 967, 962, 963, 964, 961, 960]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75]),k = 15), list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800]),k = 5), list_node([500, 400, 300, 200, 100, 600, 700, 800]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]),k = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11, 12, 13]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]),k = 21), list_node([21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 23, 24, 25, 26, 27, 28]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 18), list_node([18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 20, 21, 22, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 4), list_node([10, 9, 8, 7, 14, 13, 12, 11, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]),k = 10), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 13, 14, 15, 16, 17]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15, 16]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]),k = 8), list_node([8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7]),k = 1), list_node([1, 2, 3, 4, 5, 6, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),k = 10), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 31]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]),k = 22), list_node([22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 23, 24, 25, 26, 27, 28, 29]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 9), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 19, 20, 21, 22, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 13]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 8), list_node([8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 24, 23, 22, 21, 20, 19, 18, 17, 25]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]),k = 14), list_node([14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 29, 30, 31, 32, 33, 34, 35, 36]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 19), list_node([19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8]),k = 2), list_node([2, 1, 4, 3, 6, 5, 8, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),k = 9), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 27, 26, 25, 24, 23, 22, 21, 20, 19, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 21, 20, 19, 18, 17, 16, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]),k = 3), list_node([3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13, 16]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),k = 13), list_node([13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 27, 28, 29, 30, 31]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]),k = 9), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]),k = 5), list_node([1, 2, 3, 4, 5, -4, -3, -2, -1, 0, -5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]),k = 2), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]),k = 6), list_node([6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7, 13, 14, 15, 16, 17]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 15), list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11]),k = 7), list_node([-1, 0, 1, 2, 3, 4, 5, -8, -7, -6, -5, -4, -3, -2, -9, -10, -11]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),k = 5), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130]),k = 3), list_node([30, 20, 10, 60, 50, 40, 90, 80, 70, 120, 110, 100, 130]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]),k = 10), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]),k = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]),k = 9), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110]),k = 5), list_node([50, 40, 30, 20, 10, 100, 90, 80, 70, 60, 110]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 14, 13, 12, 11, 10, 9, 8, 15, 16, 17]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]),k = 9), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 17, 16, 15, 14, 13, 12, 11, 10, 27, 26, 25, 24, 23, 22, 21, 20, 19, 36, 35, 34, 33, 32, 31, 30, 29, 28, 37, 38, 39, 40]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 13), list_node([13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),k = 5), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11, 20, 19, 18, 17, 16, 25, 24, 23, 22, 21, 30, 29, 28, 27, 26, 31]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 2), list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),k = 2), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1000, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980, 979, 978, 977, 976, 975, 974, 973, 972, 971, 970, 969, 968, 967, 966, 965, 964, 963, 962, 961, 960]),k = 20), list_node([981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 960]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]),k = 12), list_node([12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 14, 15, 16, 17, 18, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]),k = 15), list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 16, 17, 18, 19, 20, 21, 22]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 8), list_node([8, 7, 6, 5, 4, 3, 2, 1, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]),k = 17), list_node([17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 19, 20, 21, 22, 23, 24]))\n assert is_same_list(candidate(head = list_node([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80]),k = 15), list_node([85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 84, 83, 82, 81, 80]))\n"}, "metadata": {"canonical_parameter_names": ["head", "k"], "leetcode_dataset_entry_point": "Solution().reverseKGroup", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverseKGroup = function(head, k) {", "container": null, "callable": "reverseKGroup", "parameters": [{"name": "head", "type": "ListNode"}, {"name": "k", "type": "number"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 26, "task_id": "remove-duplicates-from-sorted-array", "difficulty": "Easy", "problem_description": "Given an integer array nums sorted in non-decreasing order, remove the duplicates in-place such that each unique element appears only once. The relative order of the elements should be kept the same. Then return the number of unique elements in nums.\nConsider the number of unique elements of nums to be k, to get accepted, you need to do the following things:\n\nChange the array nums such that the first k elements of nums contain the unique elements in the order they were present in nums initially. The remaining elements of nums are not important as well as the size of nums.\nReturn k.\n\nCustom Judge:\nThe judge will test your solution with the following code:\n\nint[] nums = [...]; // Input array\nint[] expectedNums = [...]; // The expected answer with correct length\n\nint k = removeDuplicates(nums); // Calls your implementation\n\nassert k == expectedNums.length;\nfor (int i = 0; i < k; i++) {\n assert nums[i] == expectedNums[i];\n}\n\nIf all assertions pass, then your solution will be accepted.\n \nExample 1:\n\nInput: nums = [1,1,2]\nOutput: 2, nums = [1,2,_]\nExplanation: Your function should return k = 2, with the first two elements of nums being 1 and 2 respectively.\nIt does not matter what you leave beyond the returned k (hence they are underscores).\n\nExample 2:\n\nInput: nums = [0,0,1,1,1,2,2,3,3,4]\nOutput: 5, nums = [0,1,2,3,4,_,_,_,_,_]\nExplanation: Your function should return k = 5, with the first five elements of nums being 0, 1, 2, 3, and 4 respectively.\nIt does not matter what you leave beyond the returned k (hence they are underscores).\n\n \nConstraints:\n\n1 <= nums.length <= 3 * 104\n-100 <= nums[i] <= 100\nnums is sorted in non-decreasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [-100, 0, 100]) == 3\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 5]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4]) == 5\n assert candidate(nums = [-1, -1, -1, -1, -1]) == 1\n assert candidate(nums = [-1, -1, 0, 0, 1, 1, 2]) == 4\n assert candidate(nums = [-10, -10, -9, -9, -8, -7, -6, -6, -6, -5]) == 6\n assert candidate(nums = [-100, -100, -50, -50, 0, 0, 50, 50, 100, 100]) == 5\n assert candidate(nums = [0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5]) == 5\n assert candidate(nums = [1, 1, 2]) == 2\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 7\n assert candidate(nums = [-100, -100, -99, -99, 0, 0, 1, 1, 2, 2, 3, 3]) == 6\n assert candidate(nums = [-100, 100]) == 2\n assert candidate(nums = [0, 0, 1, 1, 1, 2, 2, 3, 3, 4]) == 5\n assert candidate(nums = [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 5\n assert candidate(nums = [-1, -1, 0, 0, 1, 2, 2, 3, 4]) == 6\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == 15\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9]) == 9\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8]) == 8\n assert candidate(nums = [0, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 9, 10, 10, 10]) == 11\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9]) == 9\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 4]) == 4\n assert candidate(nums = [-100, -99, -98, -98, -97, -97, -96, -95, -94, -94, -93, -92, -91, -90, -89, -89, -88, -87, -86, -85]) == 16\n assert candidate(nums = [-1, -1, 0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10]) == 12\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]) == 5\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 9\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7]) == 7\n assert candidate(nums = [-10, -10, -9, -9, -8, -8, -7, -7, -6, -6, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 10\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 21\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 2\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == 15\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == 8\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == 20\n assert candidate(nums = [-100, -100, -50, -50, -50, -50, -50, 0, 0, 0, 0, 0, 0, 50, 50, 50, 50, 50, 100, 100, 100, 100, 100]) == 5\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [-10, -10, -5, -5, -1, 0, 0, 0, 3, 3, 3, 3, 3, 5, 5, 8]) == 7\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9]) == 9\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 10, 10]) == 10\n assert candidate(nums = [-100, -50, 0, 50, 100]) == 5\n assert candidate(nums = [-100, -100, -50, -50, 0, 0, 0, 10, 10, 20, 20, 20, 50, 50, 100, 100]) == 7\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3]) == 3\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-1, -1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 11\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10]) == 10\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7]) == 7\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5]) == 5\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4]) == 5\n assert candidate(nums = [1, 1, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 7, 8, 8, 9, 10, 10, 11]) == 11\n assert candidate(nums = [-50, -50, -50, -25, -25, -25, 0, 0, 25, 25, 50, 50, 50]) == 5\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10]) == 10\n assert candidate(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 16\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9]) == 9\n assert candidate(nums = [-1, -1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3]) == 5\n assert candidate(nums = [0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 30\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 10]) == 12\n assert candidate(nums = [-100, -100, -50, -50, 0, 0, 50, 50, 100, 100]) == 5\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1\n assert candidate(nums = [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6]) == 7\n assert candidate(nums = [-5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, 0, 0, 0, 1, 2, 3, 4, 5]) == 7\n assert candidate(nums = [-10, -5, -3, -3, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 16\n assert candidate(nums = [0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9]) == 10\n assert candidate(nums = [1, 2, 3, 3, 3, 4, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10]) == 10\n assert candidate(nums = [0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9]) == 10\n assert candidate(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 1\n assert candidate(nums = [-100, -50, -50, -50, -25, -10, 0, 0, 0, 0, 5, 10, 10, 25, 50, 50, 50, 100, 100]) == 10\n assert candidate(nums = [0, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9, 10, 10, 10, 10]) == 11\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [1, 2, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [-5, -5, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == 14\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [-5, -4, -4, -3, -2, -2, -1, 0, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 7, 8, 8, 9, 10]) == 16\n assert candidate(nums = [-5, -4, -4, -4, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4]) == 10\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [-100, -100, -99, -98, -98, -97, -97, -97, -96]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-100, -100, -50, -50, 0, 0, 0, 50, 50, 50, 100, 100]) == 5\n assert candidate(nums = [-1, -1, -1, -1, -1, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 7\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11]) == 2\n assert candidate(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 1\n assert candidate(nums = [-1, -1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 9, 10]) == 12\n assert candidate(nums = [-1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4]) == 4\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [-100, -100, -50, -50, 0, 0, 0, 50, 50, 100, 100]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 15, 16, 17]) == 17\n assert candidate(nums = [-10, -10, -10, -10, -10, -9, -9, -9, -8, -8, -7, -7, -6, -6, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3]) == 14\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9]) == 9\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12]) == 12\n assert candidate(nums = [-100, -50, -50, -25, -25, -10, -10, 0, 0, 50, 50, 100, 100]) == 7\n assert candidate(nums = [-100, -50, -50, 0, 0, 0, 25, 25, 50, 75, 75, 100]) == 7\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -95, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83]) == 18\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6]) == 6\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81]) == 20\n assert candidate(nums = [-10, -10, -9, -9, -8, -8, -7, -7, -6, -6, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 21\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [-50, -50, -50, -25, -25, -25, -10, -10, -10, 0, 0, 0, 50, 50, 50, 100, 100, 100]) == 6\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().removeDuplicates", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeDuplicates = function(nums) {", "container": null, "callable": "removeDuplicates", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 27, "task_id": "remove-element", "difficulty": "Easy", "problem_description": "Given an integer array nums and an integer val, remove all occurrences of val in nums in-place. The order of the elements may be changed. Then return the number of elements in nums which are not equal to val.\nConsider the number of elements in nums which are not equal to val be k, to get accepted, you need to do the following things:\n\nChange the array nums such that the first k elements of nums contain the elements which are not equal to val. The remaining elements of nums are not important as well as the size of nums.\nReturn k.\n\nCustom Judge:\nThe judge will test your solution with the following code:\n\nint[] nums = [...]; // Input array\nint val = ...; // Value to remove\nint[] expectedNums = [...]; // The expected answer with correct length.\n // It is sorted with no values equaling val.\n\nint k = removeElement(nums, val); // Calls your implementation\n\nassert k == expectedNums.length;\nsort(nums, 0, k); // Sort the first k elements of nums\nfor (int i = 0; i < actualLength; i++) {\n assert nums[i] == expectedNums[i];\n}\n\nIf all assertions pass, then your solution will be accepted.\n \nExample 1:\n\nInput: nums = [3,2,2,3], val = 3\nOutput: 2, nums = [2,2,_,_]\nExplanation: Your function should return k = 2, with the first two elements of nums being 2.\nIt does not matter what you leave beyond the returned k (hence they are underscores).\n\nExample 2:\n\nInput: nums = [0,1,2,2,3,0,4,2], val = 2\nOutput: 5, nums = [0,1,4,0,3,_,_,_]\nExplanation: Your function should return k = 5, with the first five elements of nums containing 0, 0, 1, 3, and 4.\nNote that the five elements can be returned in any order.\nIt does not matter what you leave beyond the returned k (hence they are underscores).\n\n \nConstraints:\n\n0 <= nums.length <= 100\n0 <= nums[i] <= 50\n0 <= val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [],val = 1) == 0\n assert candidate(nums = [0, 0, 0, 0, 0],val = 0) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],val = 5) == 9\n assert candidate(nums = [5, 5, 5, 5, 5, 5],val = 5) == 0\n assert candidate(nums = [0, 1, 2, 2, 3, 0, 4, 2],val = 2) == 5\n assert candidate(nums = [50, 49, 48, 47, 46],val = 46) == 4\n assert candidate(nums = [1, 1, 1, 1, 1],val = 1) == 0\n assert candidate(nums = [3, 2, 2, 3],val = 3) == 2\n assert candidate(nums = [1, 2, 3, 4, 5],val = 6) == 5\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],val = 5) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],val = 0) == 0\n assert candidate(nums = [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0],val = 25) == 49\n assert candidate(nums = [42, 27, 15, 42, 27, 15, 42, 27, 15, 42],val = 42) == 6\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],val = 2) == 19\n assert candidate(nums = [42],val = 100) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],val = 1) == 0\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6],val = 5) == 10\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],val = 0) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],val = 12) == 24\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],val = 2) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50, 10, 20, 30, 40, 50],val = 50) == 12\n assert candidate(nums = [3, 3, 3, 3, 3, 2, 2, 1, 1, 0, 0],val = 3) == 6\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75],val = 25) == 14\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],val = 1) == 18\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],val = 5) == 10\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1],val = 0) == 10\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31],val = 46) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],val = 10) == 19\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41],val = 21) == 20\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 9, 0, 0],val = 9) == 39\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [10, 20, 10, 30, 10, 40, 50, 10],val = 10) == 4\n assert candidate(nums = [42],val = 42) == 0\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],val = 1) == 8\n assert candidate(nums = [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],val = 33) == 14\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 6],val = 2) == 5\n assert candidate(nums = [7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9],val = 8) == 8\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],val = 3) == 19\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],val = 5) == 18\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41],val = 43) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],val = 10) == 19\n assert candidate(nums = [1, 3, 3, 3, 2, 2, 2, 4, 4, 4, 5, 5, 5, 6, 6, 6],val = 3) == 13\n assert candidate(nums = [1, 2, 3, 4, 5, 2, 2, 2, 3, 4, 5],val = 2) == 7\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2],val = 2) == 10\n assert candidate(nums = [3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1],val = 1) == 16\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50],val = 50) == 0\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],val = 10) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],val = 11) == 10\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],val = 10) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],val = 15) == 24\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22],val = 2) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],val = 7) == 14\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9],val = 0) == 18\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],val = 20) == 19\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],val = 0) == 0\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50],val = 25) == 18\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 3, 2, 1, 0, 3],val = 3) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1],val = 2) == 6\n assert candidate(nums = [30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2],val = 28) == 14\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],val = 3) == 18\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],val = 40) == 20\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],val = 8) == 14\n assert candidate(nums = [42, 24, 42, 24, 42, 24, 42, 24],val = 24) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],val = 15) == 19\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41],val = 41) == 9\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],val = 0) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],val = 1) == 29\n assert candidate(nums = [7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10],val = 7) == 6\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20],val = 15) == 38\n assert candidate(nums = [10, 20, 10, 30, 10, 40, 10, 50],val = 10) == 4\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50, 60],val = 10) == 9\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50],val = 50) == 0\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31],val = 46) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],val = 15) == 19\n assert candidate(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25],val = 25) == 0\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [10, 20, 30, 10, 20, 30, 10, 20, 30, 10],val = 10) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],val = 1) == 18\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],val = 11) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],val = 50) == 49\n assert candidate(nums = [3, 1, 3, 3, 2, 3, 3, 3, 3, 3],val = 3) == 2\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5],val = 5) == 8\n assert candidate(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10],val = 0) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3],val = 2) == 10\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],val = 50) == 19\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0],val = 42) == 50\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],val = 1) == 19\n assert candidate(nums = [10, 20, 30, 20, 10, 30, 40, 20],val = 20) == 5\n assert candidate(nums = [1, 2, 3, 4, 5],val = 6) == 5\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],val = 5) == 18\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],val = 20) == 19\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50],val = 30) == 8\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31],val = 40) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1],val = 1) == 9\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],val = 22) == 14\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],val = 1) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 50, 40, 30, 20, 10],val = 10) == 8\n assert candidate(nums = [10, 10, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9],val = 10) == 9\n assert candidate(nums = [10, 10, 10, 9, 9, 8, 8, 8, 7, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 1],val = 10) == 18\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],val = 10) == 14\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],val = 11) == 10\n assert candidate(nums = [10, 1, 10, 2, 10, 3, 10, 4],val = 10) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],val = 13) == 14\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42],val = 42) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],val = 15) == 14\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],val = 7) == 0\n assert candidate(nums = [1, 1, 2, 3, 3, 4, 4, 5, 5, 5],val = 3) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],val = 7) == 14\n"}, "metadata": {"canonical_parameter_names": ["nums", "val"], "leetcode_dataset_entry_point": "Solution().removeElement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeElement = function(nums, val) {", "container": null, "callable": "removeElement", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "val", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 28, "task_id": "find-the-index-of-the-first-occurrence-in-a-string", "difficulty": "Easy", "problem_description": "Given two strings needle and haystack, return the index of the first occurrence of needle in haystack, or -1 if needle is not part of haystack.\n \nExample 1:\n\nInput: haystack = \"sadbutsad\", needle = \"sad\"\nOutput: 0\nExplanation: \"sad\" occurs at index 0 and 6.\nThe first occurrence is at index 0, so we return 0.\n\nExample 2:\n\nInput: haystack = \"leetcode\", needle = \"leeto\"\nOutput: -1\nExplanation: \"leeto\" did not occur in \"leetcode\", so we return -1.\n\n \nConstraints:\n\n1 <= haystack.length, needle.length <= 104\nhaystack and needle consist of only lowercase English characters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(haystack = \"ababcabcabababd\",needle = \"ababd\") == 10\n assert candidate(haystack = \"abcde\",needle = \"f\") == -1\n assert candidate(haystack = \"mississippi\",needle = \"issi\") == 1\n assert candidate(haystack = \"sadbutsad\",needle = \"sad\") == 0\n assert candidate(haystack = \"abababa\",needle = \"aba\") == 0\n assert candidate(haystack = \"abcdefgh\",needle = \"efg\") == 4\n assert candidate(haystack = \"abc\",needle = \"c\") == 2\n assert candidate(haystack = \"aaaaa\",needle = \"bba\") == -1\n assert candidate(haystack = \"mississippi\",needle = \"issip\") == 4\n assert candidate(haystack = \"abc\",needle = \"d\") == -1\n assert candidate(haystack = \"a\",needle = \"a\") == 0\n assert candidate(haystack = \"hello\",needle = \"ll\") == 2\n assert candidate(haystack = \"leetcode\",needle = \"leeto\") == -1\n assert candidate(haystack = \"ababababab\",needle = \"aba\") == 0\n assert candidate(haystack = \"randomrandomrandom\",needle = \"random\") == 0\n assert candidate(haystack = \"abcdefgabcdefgabcdefg\",needle = \"efg\") == 4\n assert candidate(haystack = \"abcdefg\",needle = \"\") == 0\n assert candidate(haystack = \"a quick brown fox jumps over the lazy dog\",needle = \"quack\") == -1\n assert candidate(haystack = \"abracadabra\",needle = \"cad\") == 4\n assert candidate(haystack = \"aaaaaaabc\",needle = \"aaaaaab\") == 1\n assert candidate(haystack = \"level\",needle = \"eve\") == 1\n assert candidate(haystack = \"aaaaaa\",needle = \"aaa\") == 0\n assert candidate(haystack = \"abababab\",needle = \"aba\") == 0\n assert candidate(haystack = \"abcde\",needle = \"\") == 0\n assert candidate(haystack = \"xylophone\",needle = \"phone\") == 4\n assert candidate(haystack = \"abcdeabcdeabcde\",needle = \"deabc\") == 3\n assert candidate(haystack = \"quickbrownfox\",needle = \"quick\") == 0\n assert candidate(haystack = \"repeatedstringrepeatedstring\",needle = \"string\") == 8\n assert candidate(haystack = \"abcde\",needle = \"abcde\") == 0\n assert candidate(haystack = \"noinneedlehere\",needle = \"needle\") == 4\n assert candidate(haystack = \"banana\",needle = \"ana\") == 1\n assert candidate(haystack = \"abcdefghijklmnopqrstuvwxyz\",needle = \"mnop\") == 12\n assert candidate(haystack = \"abcabcabcabcabcabc\",needle = \"abcabc\") == 0\n assert candidate(haystack = \"boundarycase\",needle = \"boundarycase\") == 0\n assert candidate(haystack = \"abcabcabcabc\",needle = \"bcabc\") == 1\n assert candidate(haystack = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",needle = \"mnopqrstuv\") == -1\n assert candidate(haystack = \"sequence\",needle = \"qu\") == 2\n assert candidate(haystack = \"bananananana\",needle = \"nan\") == 2\n assert candidate(haystack = \"aaaaaaaaaaaaaaaaaa\",needle = \"aaaaaaaaaa\") == 0\n assert candidate(haystack = \"abcdefghij\",needle = \"jihgfedcba\") == -1\n assert candidate(haystack = \"abcdefghij\",needle = \"abcdefghij\") == 0\n assert candidate(haystack = \"thisisaverylongstringwithsomecharacters\",needle = \"characters\") == 29\n assert candidate(haystack = \"thisisaverylongstringwithsomerepeatingpatterns\",needle = \"patterns\") == 38\n assert candidate(haystack = \"thesamethesame\",needle = \"thesame\") == 0\n assert candidate(haystack = \"noon\",needle = \"noon\") == 0\n assert candidate(haystack = \"hellohellohellohellohello\",needle = \"hellohello\") == 0\n assert candidate(haystack = \"nnnnnnnnnn\",needle = \"nnnn\") == 0\n assert candidate(haystack = \"12345678901234567890\",needle = \"56789012\") == 4\n assert candidate(haystack = \"12345678901234567890\",needle = \"56789\") == 4\n assert candidate(haystack = \"abcabcabcabcabc\",needle = \"cab\") == 2\n assert candidate(haystack = \"thisisaverylonghaystack\",needle = \"averylong\") == 6\n assert candidate(haystack = \"hellohellohello\",needle = \"hellohello\") == 0\n assert candidate(haystack = \"singleletter\",needle = \"a\") == -1\n assert candidate(haystack = \"oneonetwoonethreeonethreeone\",needle = \"three\") == 12\n assert candidate(haystack = \"abcabcabcabcabcabc\",needle = \"cab\") == 2\n assert candidate(haystack = \"pythonprogrammingpython\",needle = \"thonpro\") == 2\n assert candidate(haystack = \"repeatedcharactersequenceeeeeeeeeeeeeee\",needle = \"eeeeeeee\") == 24\n assert candidate(haystack = \"abcdabcyabcdabc\",needle = \"abcdabc\") == 0\n assert candidate(haystack = \"mississippi\",needle = \"issipp\") == 4\n assert candidate(haystack = \"aaaaabaaaabaaaaabaaaabaaaaabaaaabaaaaabaaaab\",needle = \"baaab\") == -1\n assert candidate(haystack = \"aaaaaa\",needle = \"aaaaaaa\") == -1\n assert candidate(haystack = \"abcdefghijklmnopqrstuvwxyz\",needle = \"xyz\") == 23\n assert candidate(haystack = \"overlaplaplaplaplap\",needle = \"lap\") == 4\n assert candidate(haystack = \"aaaaabaaaaaa\",needle = \"aaaaab\") == 0\n assert candidate(haystack = \"helloworldhelloworld\",needle = \"worldhello\") == 5\n assert candidate(haystack = \"abracadabra\",needle = \"abra\") == 0\n assert candidate(haystack = \"abababababababababab\",needle = \"ababab\") == 0\n assert candidate(haystack = \"aabbccddeeffgghhiijjkk\",needle = \"eeffgg\") == 8\n assert candidate(haystack = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",needle = \"mnop\") == -1\n assert candidate(haystack = \"mississippiissippi\",needle = \"issip\") == 4\n assert candidate(haystack = \"aquickbrownfoxjumpsoverthelazydog\",needle = \"dog\") == 30\n assert candidate(haystack = \"abababababababab\",needle = \"ababab\") == 0\n assert candidate(haystack = \"almostsameprefixalmost\",needle = \"almost\") == 0\n assert candidate(haystack = \"qwertyuiopasdfghjklzxcvbnm\",needle = \"qwertyuiop\") == 0\n assert candidate(haystack = \"ananananananan\",needle = \"anana\") == 0\n assert candidate(haystack = \"averylongstringwithrepeatedcharactersaaaaaaaaa\",needle = \"aaaaaaaa\") == 37\n assert candidate(haystack = \"\",needle = \"\") == 0\n assert candidate(haystack = \"findinganoccurrenceinanarray\",needle = \"anoccurrence\") == 7\n assert candidate(haystack = \"repeatedrepeatedrepeated\",needle = \"repeated\") == 0\n assert candidate(haystack = \"pythonprogramming\",needle = \"programming\") == 6\n assert candidate(haystack = \"palindrome\",needle = \"alin\") == 1\n assert candidate(haystack = \"singleletter\",needle = \"s\") == 0\n assert candidate(haystack = \"aaaaaabaaaaaab\",needle = \"aaaaaab\") == 0\n assert candidate(haystack = \"thisisaverylongstringthatwilltestouralgorithm\",needle = \"longstring\") == 11\n assert candidate(haystack = \"this is a simple test\",needle = \"simple\") == 10\n assert candidate(haystack = \"aaaaabaaaabaaaaabaaaab\",needle = \"aaaab\") == 1\n assert candidate(haystack = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",needle = \"zzzzzzzzzz\") == 0\n assert candidate(haystack = \"repeatedrepeatedrepeated\",needle = \"repeatedre\") == 0\n assert candidate(haystack = \"thelastwordisneedle\",needle = \"needle\") == 13\n assert candidate(haystack = \"hellohellohello\",needle = \"lohe\") == 3\n assert candidate(haystack = \"abababababab\",needle = \"ababab\") == 0\n assert candidate(haystack = \"abababababab\",needle = \"bababa\") == 1\n assert candidate(haystack = \"thisisaverylongstringforatest\",needle = \"avery\") == 6\n assert candidate(haystack = \"overlappingoverlap\",needle = \"lapping\") == 4\n assert candidate(haystack = \"findthehiddenpattern\",needle = \"hidden\") == 7\n assert candidate(haystack = \"ababababab\",needle = \"abab\") == 0\n assert candidate(haystack = \"asubstringrightattheend\",needle = \"end\") == 20\n assert candidate(haystack = \"longstringthatcontainsavarietyofcharacters\",needle = \"characters\") == 32\n assert candidate(haystack = \"bananaanabanana\",needle = \"anaban\") == 6\n assert candidate(haystack = \"racecar\",needle = \"race\") == 0\n assert candidate(haystack = \"longstringwithnokeyword\",needle = \"keyword\") == 16\n assert candidate(haystack = \"abcdefghij\",needle = \"gh\") == 6\n assert candidate(haystack = \"mississippi\",needle = \"pi\") == 9\n assert candidate(haystack = \"verylonghaystackwithrepeatingcharactersaaaaaaaaaaa\",needle = \"aaaaa\") == 39\n assert candidate(haystack = \"\",needle = \"a\") == -1\n assert candidate(haystack = \"a\",needle = \"\") == 0\n assert candidate(haystack = \"09876543210987654321\",needle = \"654321\") == 4\n assert candidate(haystack = \"hellohellohello\",needle = \"hello\") == 0\n assert candidate(haystack = \"aaaaaaaaaaa\",needle = \"aaaaaa\") == 0\n assert candidate(haystack = \"thisisaverylongstringthatcontainsmultiplesubstrings\",needle = \"substring\") == 41\n assert candidate(haystack = \"uniquecharacters\",needle = \"characters\") == 6\n assert candidate(haystack = \"aaaaaaab\",needle = \"aaaab\") == 3\n assert candidate(haystack = \"almosttherealmost\",needle = \"almostthere\") == 0\n assert candidate(haystack = \"aaaaaaaaaab\",needle = \"aaaaaab\") == 4\n assert candidate(haystack = \"aaaaabaaaaabaaaaab\",needle = \"aaaaab\") == 0\n assert candidate(haystack = \"a quick brown fox jumps over the lazy dog\",needle = \"quick\") == 2\n assert candidate(haystack = \"thisisaverylongstringwithrepeatedpatterns\",needle = \"repeated\") == 25\n assert candidate(haystack = \"thisisaverylonghaystackthatcontainsavariablesubstring\",needle = \"substring\") == 44\n assert candidate(haystack = \"xxyyzzxxyyzzxxyyzz\",needle = \"xxyyzz\") == 0\n assert candidate(haystack = \"aaaaa\",needle = \"aa\") == 0\n assert candidate(haystack = \"ababababababababa\",needle = \"abab\") == 0\n assert candidate(haystack = \"a quick brown fox jumps over the lazy dog\",needle = \"lazy\") == 33\n assert candidate(haystack = \"needleinthestack\",needle = \"needle\") == 0\n assert candidate(haystack = \"aaaaaaaaaaaaaaaaaaaa\",needle = \"aaaaaaaaa\") == 0\n assert candidate(haystack = \"aaaaaaab\",needle = \"aaaaaab\") == 1\n assert candidate(haystack = \"aaaa\",needle = \"aaaaa\") == -1\n assert candidate(haystack = \"substring\",needle = \"string\") == 3\n assert candidate(haystack = \"xyzxyzxyzxyz\",needle = \"zyx\") == -1\n assert candidate(haystack = \"abababababababababab\",needle = \"abab\") == 0\n assert candidate(haystack = \"oneonetwoonetwothree\",needle = \"twone\") == -1\n assert candidate(haystack = \"bananananana\",needle = \"anan\") == 1\n assert candidate(haystack = \"xyxxyxyxyxyxyxyx\",needle = \"xyxyx\") == 3\n assert candidate(haystack = \"aaaaabaaaa\",needle = \"aaab\") == 2\n assert candidate(haystack = \"abcdefghij\",needle = \"efgh\") == 4\n assert candidate(haystack = \"overlaplaplaplap\",needle = \"laplap\") == 4\n assert candidate(haystack = \"thisisaverylongstringforsearching\",needle = \"searching\") == 24\n assert candidate(haystack = \"bananabananabanana\",needle = \"nan\") == 2\n assert candidate(haystack = \"longhaystackwithaveryspecificsubstring\",needle = \"averyspecific\") == 16\n assert candidate(haystack = \"aaaaaaa\",needle = \"aaaaaa\") == 0\n assert candidate(haystack = \"abcdefabcdefabcdefabcdef\",needle = \"cdef\") == 2\n assert candidate(haystack = \"aaaaabaaaaabaaaaabaaaaab\",needle = \"aaaab\") == 1\n assert candidate(haystack = \"hellohellohello\",needle = \"lohel\") == 3\n assert candidate(haystack = \"abcdabcdabcd\",needle = \"cdab\") == 2\n assert candidate(haystack = \"banana\",needle = \"na\") == 2\n"}, "metadata": {"canonical_parameter_names": ["haystack", "needle"], "leetcode_dataset_entry_point": "Solution().strStr", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var strStr = function(haystack, needle) {", "container": null, "callable": "strStr", "parameters": [{"name": "haystack", "type": "string"}, {"name": "needle", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 29, "task_id": "divide-two-integers", "difficulty": "Medium", "problem_description": "Given two integers dividend and divisor, divide two integers without using multiplication, division, and mod operator.\nThe integer division should truncate toward zero, which means losing its fractional part. For example, 8.345 would be truncated to 8, and -2.7335 would be truncated to -2.\nReturn the quotient after dividing dividend by divisor.\nNote: Assume we are dealing with an environment that could only store integers within the 32-bit signed integer range: [−231, 231 − 1]. For this problem, if the quotient is strictly greater than 231 - 1, then return 231 - 1, and if the quotient is strictly less than -231, then return -231.\n \nExample 1:\n\nInput: dividend = 10, divisor = 3\nOutput: 3\nExplanation: 10/3 = 3.33333.. which is truncated to 3.\n\nExample 2:\n\nInput: dividend = 7, divisor = -3\nOutput: -2\nExplanation: 7/-3 = -2.33333.. which is truncated to -2.\n\n \nConstraints:\n\n-231 <= dividend, divisor <= 231 - 1\ndivisor != 0\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(dividend = 10,divisor = 3) == 3\n assert candidate(dividend = -2147483648,divisor = 2) == -1073741824\n assert candidate(dividend = -2147483648,divisor = -1) == 2147483647\n assert candidate(dividend = -1,divisor = -1) == 1\n assert candidate(dividend = 2147483647,divisor = 1) == 2147483647\n assert candidate(dividend = 1,divisor = 1) == 1\n assert candidate(dividend = 1000000000,divisor = 3) == 333333333\n assert candidate(dividend = 7,divisor = -3) == -2\n assert candidate(dividend = -2147483648,divisor = 1) == -2147483648\n assert candidate(dividend = 100,divisor = 7) == 14\n assert candidate(dividend = -5,divisor = 2) == -2\n assert candidate(dividend = 1,divisor = -1) == -1\n assert candidate(dividend = 2147483647,divisor = 2) == 1073741823\n assert candidate(dividend = 0,divisor = 1) == 0\n assert candidate(dividend = 1,divisor = 2) == 0\n assert candidate(dividend = -1,divisor = 1) == -1\n assert candidate(dividend = -7,divisor = 3) == -2\n assert candidate(dividend = -1000000000,divisor = 1000000000) == -1\n assert candidate(dividend = 15,divisor = 6) == 2\n assert candidate(dividend = 1,divisor = -2147483648) == 0\n assert candidate(dividend = -15,divisor = -5) == 3\n assert candidate(dividend = 1000000000,divisor = 500000000) == 2\n assert candidate(dividend = 2147483647,divisor = -1) == -2147483647\n assert candidate(dividend = 123456789,divisor = 987654321) == 0\n assert candidate(dividend = 1,divisor = 999999998) == 0\n assert candidate(dividend = -15,divisor = -6) == 2\n assert candidate(dividend = -1024,divisor = -2) == 512\n assert candidate(dividend = -15,divisor = 3) == -5\n assert candidate(dividend = -5,divisor = -2) == 2\n assert candidate(dividend = 1024,divisor = 10) == 102\n assert candidate(dividend = -1000000000,divisor = -1000000000) == 1\n assert candidate(dividend = -1000000000,divisor = -987654321) == 1\n assert candidate(dividend = -1500000000,divisor = -4) == 375000000\n assert candidate(dividend = -1023,divisor = 10) == -102\n assert candidate(dividend = -1000000000,divisor = 3) == -333333333\n assert candidate(dividend = 15,divisor = -5) == -3\n assert candidate(dividend = -1000000000,divisor = -3) == 333333333\n assert candidate(dividend = 1023,divisor = 10) == 102\n assert candidate(dividend = -10,divisor = 1) == -10\n assert candidate(dividend = 1000000000,divisor = 123456789) == 8\n assert candidate(dividend = -1024,divisor = 1024) == -1\n assert candidate(dividend = -1,divisor = 2147483648) == 0\n assert candidate(dividend = -15,divisor = 5) == -3\n assert candidate(dividend = -1000000000,divisor = 987654321) == -1\n assert candidate(dividend = 1024,divisor = -10) == -102\n assert candidate(dividend = 15,divisor = -4) == -3\n assert candidate(dividend = 15,divisor = -6) == -2\n assert candidate(dividend = 5,divisor = -2) == -2\n assert candidate(dividend = -15,divisor = 4) == -3\n assert candidate(dividend = -15,divisor = -4) == 3\n assert candidate(dividend = -15,divisor = -3) == 5\n assert candidate(dividend = -123456789,divisor = 987654321) == 0\n assert candidate(dividend = 100,divisor = -7) == -14\n assert candidate(dividend = 999999999,divisor = 1) == 999999999\n assert candidate(dividend = -1024,divisor = -10) == 102\n assert candidate(dividend = 10,divisor = -1) == -10\n assert candidate(dividend = 1000000000,divisor = 25) == 40000000\n assert candidate(dividend = 123456789,divisor = -987654321) == 0\n assert candidate(dividend = 1500000000,divisor = 3) == 500000000\n assert candidate(dividend = 15,divisor = 4) == 3\n assert candidate(dividend = -2147483648,divisor = 3) == -715827882\n assert candidate(dividend = -1024,divisor = 10) == -102\n assert candidate(dividend = 1,divisor = 999999999) == 0\n assert candidate(dividend = -100,divisor = 7) == -14\n assert candidate(dividend = 1024,divisor = 2) == 512\n assert candidate(dividend = 1024,divisor = 1024) == 1\n assert candidate(dividend = 15,divisor = 5) == 3\n assert candidate(dividend = 1025,divisor = 3) == 341\n assert candidate(dividend = -123456789,divisor = -987654321) == 0\n assert candidate(dividend = -1025,divisor = -3) == 341\n assert candidate(dividend = -1,divisor = 999999999) == 0\n assert candidate(dividend = 1000000000,divisor = -1000000000) == -1\n assert candidate(dividend = -1000000000,divisor = -25) == 40000000\n assert candidate(dividend = 2147483647,divisor = -2147483648) == 0\n assert candidate(dividend = 150,divisor = 3) == 50\n assert candidate(dividend = 100,divisor = 1) == 100\n assert candidate(dividend = 1023,divisor = -10) == -102\n assert candidate(dividend = -1000000000,divisor = 25) == -40000000\n assert candidate(dividend = -1023,divisor = -2) == 511\n assert candidate(dividend = -1,divisor = 999999998) == 0\n assert candidate(dividend = -999999999,divisor = 999999999) == -1\n assert candidate(dividend = -1,divisor = 2147483647) == 0\n assert candidate(dividend = 15,divisor = 3) == 5\n assert candidate(dividend = 1000000000,divisor = 1000000000) == 1\n assert candidate(dividend = 1000000000,divisor = -25) == -40000000\n assert candidate(dividend = -1023,divisor = -10) == 102\n assert candidate(dividend = -2147483648,divisor = -2147483648) == 1\n assert candidate(dividend = 2147483647,divisor = 2147483647) == 1\n assert candidate(dividend = 100,divisor = -1) == -100\n assert candidate(dividend = 2147483647,divisor = 3) == 715827882\n assert candidate(dividend = -2147483648,divisor = -3) == 715827882\n assert candidate(dividend = 999999999,divisor = 999999999) == 1\n assert candidate(dividend = 15,divisor = -3) == -5\n assert candidate(dividend = -2147483648,divisor = 2147483647) == -1\n assert candidate(dividend = 1000000000,divisor = -3) == -333333333\n assert candidate(dividend = -1000000000,divisor = -500000000) == 2\n assert candidate(dividend = 1,divisor = 100) == 0\n assert candidate(dividend = -15,divisor = 6) == -2\n assert candidate(dividend = -999999999,divisor = 1) == -999999999\n assert candidate(dividend = 1023,divisor = 2) == 511\n assert candidate(dividend = -100,divisor = -7) == 14\n assert candidate(dividend = 5,divisor = 2) == 2\n assert candidate(dividend = 10,divisor = -3) == -3\n assert candidate(dividend = -50,divisor = -10) == 5\n assert candidate(dividend = 100,divisor = 10) == 10\n assert candidate(dividend = -1000,divisor = 5) == -200\n assert candidate(dividend = -1000,divisor = -5) == 200\n assert candidate(dividend = 100,divisor = -2) == -50\n assert candidate(dividend = 56,divisor = 7) == 8\n assert candidate(dividend = -50,divisor = 10) == -5\n assert candidate(dividend = -50,divisor = 5) == -10\n assert candidate(dividend = 15,divisor = 2) == 7\n assert candidate(dividend = -1,divisor = -2147483648) == 0\n assert candidate(dividend = -10,divisor = 3) == -3\n assert candidate(dividend = 100,divisor = 33) == 3\n assert candidate(dividend = 150,divisor = 6) == 25\n assert candidate(dividend = 1,divisor = 2147483647) == 0\n assert candidate(dividend = -100,divisor = -5) == 20\n assert candidate(dividend = -7,divisor = -3) == 2\n assert candidate(dividend = -100,divisor = 10) == -10\n assert candidate(dividend = 100,divisor = -10) == -10\n assert candidate(dividend = -2147483647,divisor = 2) == -1073741823\n assert candidate(dividend = -56,divisor = -7) == 8\n assert candidate(dividend = 100,divisor = 2) == 50\n assert candidate(dividend = -100,divisor = -2) == 50\n assert candidate(dividend = 100,divisor = -5) == -20\n assert candidate(dividend = 100,divisor = 5) == 20\n assert candidate(dividend = 0,divisor = 5) == 0\n assert candidate(dividend = -100,divisor = -10) == 10\n assert candidate(dividend = -100,divisor = 2) == -50\n assert candidate(dividend = -100,divisor = 5) == -20\n assert candidate(dividend = 0,divisor = -1) == 0\n assert candidate(dividend = 1000,divisor = 5) == 200\n assert candidate(dividend = 1000,divisor = -5) == -200\n assert candidate(dividend = 1000,divisor = 3) == 333\n"}, "metadata": {"canonical_parameter_names": ["dividend", "divisor"], "leetcode_dataset_entry_point": "Solution().divide", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var divide = function(dividend, divisor) {", "container": null, "callable": "divide", "parameters": [{"name": "dividend", "type": "number"}, {"name": "divisor", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 30, "task_id": "substring-with-concatenation-of-all-words", "difficulty": "Hard", "problem_description": "You are given a string s and an array of strings words. All the strings of words are of the same length.\nA concatenated string is a string that exactly contains all the strings of any permutation of words concatenated.\n\nFor example, if words = [\"ab\",\"cd\",\"ef\"], then \"abcdef\", \"abefcd\", \"cdabef\", \"cdefab\", \"efabcd\", and \"efcdab\" are all concatenated strings. \"acdbef\" is not a concatenated string because it is not the concatenation of any permutation of words.\n\nReturn an array of the starting indices of all the concatenated substrings in s. You can return the answer in any order.\n \nExample 1:\n\nInput: s = \"barfoothefoobarman\", words = [\"foo\",\"bar\"]\nOutput: [0,9]\nExplanation:\nThe substring starting at 0 is \"barfoo\". It is the concatenation of [\"bar\",\"foo\"] which is a permutation of words.\nThe substring starting at 9 is \"foobar\". It is the concatenation of [\"foo\",\"bar\"] which is a permutation of words.\n\nExample 2:\n\nInput: s = \"wordgoodgoodgoodbestword\", words = [\"word\",\"good\",\"best\",\"word\"]\nOutput: []\nExplanation:\nThere is no concatenated substring.\n\nExample 3:\n\nInput: s = \"barfoofoobarthefoobarman\", words = [\"bar\",\"foo\",\"the\"]\nOutput: [6,9,12]\nExplanation:\nThe substring starting at 6 is \"foobarthe\". It is the concatenation of [\"foo\",\"bar\",\"the\"].\nThe substring starting at 9 is \"barthefoo\". It is the concatenation of [\"bar\",\"the\",\"foo\"].\nThe substring starting at 12 is \"thefoobar\". It is the concatenation of [\"the\",\"foo\",\"bar\"].\n\n \nConstraints:\n\n1 <= s.length <= 104\n1 <= words.length <= 5000\n1 <= words[i].length <= 30\ns and words[i] consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"wordgoodgoodgoodbestword\",words = ['word', 'good', 'best', 'word']) == []\n assert candidate(s = \"a\",words = ['a', 'a', 'a']) == []\n assert candidate(s = \"abababab\",words = ['a', 'b', 'a', 'b']) == [0, 1, 2, 3, 4]\n assert candidate(s = \"lingmindraboofooowingdingbarrwingmonkeypoundcake\",words = ['fooo', 'barr', 'wing', 'ding', 'wing']) == [13]\n assert candidate(s = \"barfoothefoobarman\",words = ['foo', 'bar']) == [0, 9]\n assert candidate(s = \"barfoofoobarthefoobarman\",words = ['bar', 'foo', 'the']) == [6, 9, 12]\n assert candidate(s = \"aaa\",words = ['a', 'a']) == [0, 1]\n assert candidate(s = \"thisisjustafancysentencewithallthesewordsin\",words = ['this', 'is', 'a', 'just', 'fancy', 'sentence', 'with', 'all', 'these', 'words', 'in']) == []\n assert candidate(s = \"overlaplaplaplaplaplaplaplaplaplap\",words = ['lap', 'laplap', 'laplap', 'laplap', 'laplap', 'laplap', 'laplap', 'laplap']) == []\n assert candidate(s = \"abcdefabcdefabcdefabcdefabcdef\",words = ['abcdef', 'abcdef', 'abcdef', 'abcdef', 'abcdef']) == [0]\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",words = ['aabb', 'ccdd', 'eefg', 'ghhi', 'jklk', 'llmm', 'nnoo', 'pqqr', 'rstt', 'uuvv', 'wwxx', 'yyzz']) == []\n assert candidate(s = \"oneonetwoonethreetwothreeonetwothreeone\",words = ['one', 'two', 'three']) == []\n assert candidate(s = \"abcdefgabcdefgabcdefg\",words = ['abc', 'def', 'gab', 'cde', 'fgh']) == []\n assert candidate(s = \"zazbzczdzazbzczdzaz\",words = ['zaz', 'bz', 'cz', 'dz', 'az', 'bz', 'cz', 'dz']) == []\n assert candidate(s = \"onetwothreefourfivesixseveneightnine\",words = ['onetwo', 'threefour', 'fivesix', 'seveneight', 'ninetwo', 'threefour', 'fivesix']) == []\n assert candidate(s = \"zzzzzzzzzzzzzzzzzz\",words = ['zzz', 'zzz', 'zzz', 'zzz']) == [0, 3, 6, 1, 4, 2, 5]\n assert candidate(s = \"abcdefghijabcdefghijabcdefghij\",words = ['abc', 'def', 'ghi', 'jkl', 'abc', 'def', 'ghi', 'jkl', 'abc', 'def']) == []\n assert candidate(s = \"abcdabcdabcdabcd\",words = ['abcd', 'dcba', 'abdc', 'bacd']) == []\n assert candidate(s = \"testtesttesttest\",words = ['test', 'test', 'test']) == [0, 4]\n assert candidate(s = \"alibabacloudisfastgrowing\",words = ['ali', 'ba', 'ba', 'cloud', 'is', 'fast', 'grow', 'ing']) == []\n assert candidate(s = \"mississippiissippi\",words = ['mis', 'iss', 'ssi', 'ipp', 'ppi', 'ippi', 'ippi', 'ippi', 'ippi', 'ippi', 'ippi', 'ippi', 'ippi', 'ippi', 'ippi']) == []\n assert candidate(s = \"thisisaverylongstringthatcontainsmanywordsandwordstogether\",words = ['this', 'is', 'avery', 'long', 'string', 'that', 'contains', 'many', 'words', 'and', 'words', 'together']) == []\n assert candidate(s = \"catdogcatdogcatdogcat\",words = ['cat', 'dog', 'cat', 'dog', 'cat']) == [0, 6]\n assert candidate(s = \"abcdefghabcdefghabcdefgh\",words = ['abcdef', 'ghabcd', 'efghab', 'cdefgh', 'defghi', 'efghab', 'fghabc']) == []\n assert candidate(s = \"repeatedrepeatedrepeated\",words = ['repeated', 'repe', 'atedre', 'peated']) == []\n assert candidate(s = \"xylophoneclarinetxylophoneclarinet\",words = ['xylo', 'phone', 'clar', 'inet']) == []\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",words = ['quick', 'brown', 'fox', 'jump', 'over', 'the', 'lazy', 'dog']) == []\n assert candidate(s = \"repeatedrepeatedrepeatedword\",words = ['repeated', 'repeated', 'repeated', 'word']) == []\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",words = ['quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog']) == []\n assert candidate(s = \"onetwothreefour\",words = ['one', 'two', 'three', 'four']) == []\n assert candidate(s = \"loremipsumdolorsitamet\",words = ['lorem', 'ipsum', 'dolor', 'sit', 'amet']) == []\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",words = ['aabb', 'ccdd', 'eefg', 'ghhi', 'ijjk', 'kllm', 'mnnm', 'nnoo', 'ppqq', 'rrss', 'ttuu', 'vvww', 'xxyy', 'zzaa']) == []\n assert candidate(s = \"ababababababababababababababababab\",words = ['aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab']) == []\n assert candidate(s = \"onetwothreefourfivesixseveneightnine\",words = ['one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine']) == []\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiii\",words = ['aabb', 'bbcc', 'ccdd', 'ddeeff', 'ffgg', 'gghh', 'hhiiaa']) == []\n assert candidate(s = \"aabbccddeeffgghhiijj\",words = ['aabb', 'ccdd', 'eeff', 'gghh', 'iijj']) == [0]\n assert candidate(s = \"mississippi\",words = ['issi', 'ippi']) == []\n assert candidate(s = \"aaaaaaaaaaaabbbbbbbbbbbcccccccccccddddddddddd\",words = ['aaaaa', 'bbbbb', 'ccccc', 'ddddd', 'aaaaa', 'bbbbb', 'ccccc', 'ddddd', 'aaaaa', 'bbbbb']) == []\n assert candidate(s = \"complexcomplexcomplexcomplex\",words = ['com', 'ple', 'xco', 'mple', 'com', 'ple', 'xco', 'mple']) == []\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",words = ['abc', 'def', 'ghi', 'jkl', 'mno', 'pqr', 'stu', 'vwx', 'yz', 'zz']) == []\n assert candidate(s = \"pythonprogramminglanguage\",words = ['py', 'thon', 'pro', 'gram', 'ming', 'lan', 'guag', 'e']) == []\n assert candidate(s = \"exampleexampleexampleexample\",words = ['example', 'example', 'example', 'example']) == [0]\n assert candidate(s = \"abcdefghabcdefgh\",words = ['abcd', 'efgh', 'efgh', 'abcd']) == [0]\n assert candidate(s = \"hellohellohellohellohello\",words = ['hello', 'hello', 'hello', 'hello', 'hello']) == [0]\n assert candidate(s = \"xxyyyzzzzzyyyxx\",words = ['xx', 'yy', 'zz', 'yy', 'xx']) == []\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",words = ['abc', 'def', 'ghi', 'jkl', 'mno', 'pqr', 'stu', 'vwx', 'yz']) == []\n assert candidate(s = \"hellohellohellohellohellohellohello\",words = ['hello', 'hello']) == [0, 5, 10, 15, 20, 25]\n assert candidate(s = \"concatenationconcatenationconcatenation\",words = ['concat', 'enationc', 'ationc', 'tenation', 'enationc', 'oncatena']) == []\n assert candidate(s = \"overlapoverlappingoverlapping\",words = ['over', 'lap', 'over', 'lapping']) == []\n assert candidate(s = \"xxyyzzxxyyzzxxyyzzxxyyzz\",words = ['xxyy', 'yyzz', 'xxyy', 'yyzz', 'xxyy', 'yyzz']) == []\n assert candidate(s = \"abcdefgabcdefgabcdefg\",words = ['abc', 'def', 'gab']) == [0, 7]\n assert candidate(s = \"aabbccddeeff\",words = ['abc', 'def', 'abb']) == []\n assert candidate(s = \"mississippiissississippi\",words = ['issi', 'ssis', 'siss', 'issi', 'ssis', 'siss', 'issi', 'ssis', 'siss']) == []\n assert candidate(s = \"abcdefghijklmno\",words = ['abc', 'def', 'ghi', 'jkl', 'mno']) == [0]\n assert candidate(s = \"xyzxyzxyzxyzxyz\",words = ['xyz', 'zyx', 'yzx', 'xzy', 'zxy']) == []\n assert candidate(s = \"abcdefabcdefabcdefabcdefabcdefabcdef\",words = ['abcdef', 'abcdef', 'abcdef', 'abcdef', 'abcdef', 'abcdef']) == [0]\n assert candidate(s = \"thisisatargetstringwithtargetstring\",words = ['this', 'is', 'a', 'target', 'string']) == []\n assert candidate(s = \"thisisanexamplethisisanexamplethisisanexample\",words = ['this', 'isan', 'example', 'isan', 'example']) == []\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",words = ['zzzz', 'zzzz', 'zzzz', 'zzzz', 'zzzz', 'zzzz', 'zzzz', 'zzzz', 'zzzz', 'zzzz']) == [0, 4, 1, 5, 2, 6, 3]\n assert candidate(s = \"abcdabcdabcdabcdabcdabcd\",words = ['abcd', 'dcba', 'abdc', 'bacd', 'cdab']) == []\n assert candidate(s = \"abcdefghijabcdefghijabcdefghij\",words = ['abc', 'def', 'ghi', 'jabc', 'def', 'ghij', 'abc', 'def', 'ghi', 'j']) == []\n assert candidate(s = \"abcdefghiabcdefghiabcdefghi\",words = ['abc', 'def', 'ghi', 'abc', 'def', 'ghi', 'abc', 'def', 'ghi']) == [0]\n assert candidate(s = \"abcdefghijabcdefghijabcdefghijabcdefghij\",words = ['abc', 'def', 'ghi', 'jabc', 'def', 'ghi', 'jabc', 'def', 'ghi', 'j']) == []\n assert candidate(s = \"aaaaaaaaaaaaaaaaaab\",words = ['aaaa', 'aaaa', 'aaaa', 'aaaa', 'aaaa', 'aaaa', 'aaaa', 'aaaa', 'aaaa', 'a']) == []\n assert candidate(s = \"onetwothreefourfivesix\",words = ['one', 'two', 'three', 'four', 'five', 'six']) == []\n assert candidate(s = \"ababababababababababababababab\",words = ['aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab', 'aba', 'bab']) == [0]\n assert candidate(s = \"abracadabra\",words = ['bra', 'cad']) == [1]\n assert candidate(s = \"amazinganduniquestring\",words = ['amazing', 'and', 'unique', 'string']) == []\n assert candidate(s = \"mississippiississi\",words = ['issi', 'ssis', 'siss', 'issi']) == []\n assert candidate(s = \"abcdefabcdefabcdef\",words = ['abc', 'def', 'cba', 'fed']) == []\n assert candidate(s = \"abcdefghij\",words = ['abc', 'def', 'ghi', 'j']) == []\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\",words = ['aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa']) == []\n assert candidate(s = \"mnopqrstuvmnopqrstuv\",words = ['mnop', 'qrst', 'uv', 'mnop', 'qrst', 'uv']) == []\n assert candidate(s = \"lmnopqrlmnopqrlmnopqr\",words = ['lmnop', 'qr', 'lmnop', 'qr', 'lmnop', 'qr']) == []\n assert candidate(s = \"xyzzxyzzxyzzxyzzxyzzxyzzxyzz\",words = ['xyz', 'zxy', 'zzx', 'xyz', 'zxy', 'zzx', 'xyz', 'zxy', 'zzx', 'xyz', 'zxy', 'zzx']) == []\n assert candidate(s = \"abcdefghijabcdefghijabcdefghij\",words = ['abcdefghij', 'abcdefghij', 'abcdefghij']) == [0]\n assert candidate(s = \"anananananananananananananananananan\",words = ['ana', 'nan', 'ana']) == [0, 6, 12, 18, 24, 4, 10, 16, 22, 2, 8, 14, 20, 26]\n assert candidate(s = \"hellohellohellohello\",words = ['hello', 'hello', 'hello']) == [0, 5]\n assert candidate(s = \"abcdefabcdefabcdefabcdefabcdef\",words = ['abc', 'def']) == [0, 3, 6, 9, 12, 15, 18, 21, 24]\n assert candidate(s = \"qwertyqwertyqwertyqwertyqwertyqwertyqwertyqwertyqwertyqwertyqwertyqwerty\",words = ['qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty', 'qwe', 'rty']) == [0, 3, 6, 9, 12]\n assert candidate(s = \"aaaabbbbccccaaaabbbbcccc\",words = ['aaaa', 'bbbb', 'cccc', 'aaaa', 'bbbb', 'cccc']) == [0]\n assert candidate(s = \"concatenatedsubstringthatappearsmultipleconcatenatedsubstring\",words = ['concatenated', 'substring', 'that', 'appears', 'multiple']) == []\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc\",words = ['abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc']) == []\n assert candidate(s = \"mississippiissimissing\",words = ['issi', 'ssis', 'ippi', 'ssip']) == []\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",words = ['abc', 'def', 'ghi', 'jkl', 'mno', 'pqr', 'stu', 'vwx', 'yz']) == []\n assert candidate(s = \"longstringwithmanywordsoflengthfive\",words = ['fivel', 'ength', 'withm', 'nword', 'stringw', 'ongst', 'rings', 'words', 'thefa']) == []\n assert candidate(s = \"xxyzxyzyxzyzyzxzy\",words = ['xyz', 'zyx', 'zyz', 'zxy']) == []\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",words = ['abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc', 'abc']) == [0]\n assert candidate(s = \"qwertyuiopqwertyuiopqwertyuiop\",words = ['qwerty', 'uiop', 'qwerty', 'uiop', 'qwerty', 'uiop']) == []\n assert candidate(s = \"mississippiississippi\",words = ['miss', 'issi', 'ssip', 'ippi']) == []\n assert candidate(s = \"abcdefghijabcdefghijabcdefghijabcdefghijabcdefghijabcdefghijabcdefghij\",words = ['abc', 'def', 'ghi', 'jabc', 'def', 'ghi', 'jabc', 'def', 'ghi', 'jabc', 'def', 'ghi', 'jabc', 'def', 'ghi', 'j']) == []\n assert candidate(s = \"aaaaaabbbbccccdddd\",words = ['aaaa', 'bbbb', 'cccc', 'dddd']) == [2]\n assert candidate(s = \"xyzxyzxyzxyz\",words = ['xyz', 'xyz', 'xyz', 'xyz']) == [0]\n assert candidate(s = \"mississippiissimissing\",words = ['issi', 'ssis', 'ippi', 'ssim']) == []\n"}, "metadata": {"canonical_parameter_names": ["s", "words"], "leetcode_dataset_entry_point": "Solution().findSubstring", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findSubstring = function(s, words) {", "container": null, "callable": "findSubstring", "parameters": [{"name": "s", "type": "string"}, {"name": "words", "type": "string[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 32, "task_id": "longest-valid-parentheses", "difficulty": "Hard", "problem_description": "Given a string containing just the characters '(' and ')', return the length of the longest valid (well-formed) parentheses substring.\n \nExample 1:\n\nInput: s = \"(()\"\nOutput: 2\nExplanation: The longest valid parentheses substring is \"()\".\n\nExample 2:\n\nInput: s = \")()())\"\nOutput: 4\nExplanation: The longest valid parentheses substring is \"()()\".\n\nExample 3:\n\nInput: s = \"\"\nOutput: 0\n\n \nConstraints:\n\n0 <= s.length <= 3 * 104\ns[i] is '(', or ')'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"(()())\") == 6\n assert candidate(s = \"())\") == 2\n assert candidate(s = \"())(()\") == 2\n assert candidate(s = \"((((((()))))))\") == 14\n assert candidate(s = \"((())()())()\") == 12\n assert candidate(s = \")()(()(()))\") == 10\n assert candidate(s = \"(()(()(()(()))))\") == 16\n assert candidate(s = \")()())\") == 4\n assert candidate(s = \"()()()()()()()()\") == 16\n assert candidate(s = \"()(()(()))\") == 10\n assert candidate(s = \"()()(())\") == 8\n assert candidate(s = \"\") == 0\n assert candidate(s = \"(()))()\") == 4\n assert candidate(s = \"(()))(()))\") == 4\n assert candidate(s = \"(()))\") == 4\n assert candidate(s = \"(()(()))\") == 8\n assert candidate(s = \"((()))(())()()\") == 14\n assert candidate(s = \"((())()())\") == 10\n assert candidate(s = \"(()(())())()()\") == 14\n assert candidate(s = \"()(()(()(()(()(()))))\") == 18\n assert candidate(s = \"((((((((((()))))))))))\") == 22\n assert candidate(s = \"())()(()\") == 2\n assert candidate(s = \"()(()\") == 2\n assert candidate(s = \"(()\") == 2\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 72\n assert candidate(s = \"(((())))()()()\") == 14\n assert candidate(s = \"(()((())()())())\") == 16\n assert candidate(s = \"()()()()()()()()()\") == 18\n assert candidate(s = \"((())((()))\") == 10\n assert candidate(s = \"((()))\") == 6\n assert candidate(s = \"(()))(()())\") == 6\n assert candidate(s = \"()()\") == 4\n assert candidate(s = \"()()()()\") == 8\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()\") == 36\n assert candidate(s = \"()()()()()()()()()()()()()()()()()\") == 34\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 80\n assert candidate(s = \"(()(()(()(()(())))))\") == 20\n assert candidate(s = \"()(()(()))()()\") == 14\n assert candidate(s = \"(()((())()()))\") == 14\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 60\n assert candidate(s = \"((((()))))((((()))))((((()))))\") == 30\n assert candidate(s = \"(()((((())))))\") == 14\n assert candidate(s = \"(((((((((((((())))))))))()))))))))))))))))))()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 60\n assert candidate(s = \"((())()(()))\") == 12\n assert candidate(s = \"(((((())))))\") == 12\n assert candidate(s = \"(()((())())())\") == 14\n assert candidate(s = \"()((((((()))))))()\") == 18\n assert candidate(s = \"(((()(()(()(()(()(()()))))))))\") == 30\n assert candidate(s = \"((((()))))(((())))\") == 18\n assert candidate(s = \"(((())))(((())))(((())))(((())))\") == 32\n assert candidate(s = \"((((((((((())))))))))))\") == 22\n assert candidate(s = \"()(()(((()))()))\") == 16\n assert candidate(s = \"(((((())))))(((((())))))\") == 24\n assert candidate(s = \"()()(()(()))(()(()))()()\") == 24\n assert candidate(s = \"(()(()(()(()(()))))())\") == 22\n assert candidate(s = \"(()())(()())(()())\") == 18\n assert candidate(s = \"()()()(()(()(()(()(()()))))\") == 20\n assert candidate(s = \"(()(()))(()(()))(()(()))(()(()))\") == 32\n assert candidate(s = \"((((((((()))))))))\") == 18\n assert candidate(s = \"((()()()()()()))((()()()()()()))\") == 32\n assert candidate(s = \"()((()))()(()(()))()\") == 20\n assert candidate(s = \"(((((()(()(()(()(()(()()))))))))))()()()\") == 40\n assert candidate(s = \"(()(()(()(()(()(()(()(())))))))()()\") == 34\n assert candidate(s = \"(()(()(()(()))()))\") == 18\n assert candidate(s = \"()(()())(()(()))\") == 16\n assert candidate(s = \"(()(()(()(()(()(()(()(())))))))))\") == 32\n assert candidate(s = \"()(()(()(()(()(()(()(()(()))()))))))()()\") == 40\n assert candidate(s = \"()(()(()))()()()\") == 16\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(()))))))))))))))\") == 44\n assert candidate(s = \"((()))((()))\") == 12\n assert candidate(s = \"((()()(()())))()()\") == 18\n assert candidate(s = \"()(()(()(()(()(()(()(()))))))))))))()(()(()(()))()()()()()()()()\") == 30\n assert candidate(s = \"(()((())((()))(((())))))\") == 24\n assert candidate(s = \"()()()()()()()()()()\") == 20\n assert candidate(s = \"((((((((()))))))(()(()(()(()(()(()(()))))))))()()\") == 48\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(())))))()))))))))\") == 46\n assert candidate(s = \"(()(()(()(()(()(()()))))))\") == 26\n assert candidate(s = \"(()(()(()(()(()(()))))))\") == 24\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(()()))))))))))()())\") == 50\n assert candidate(s = \"()(()(()(()(()(())))))\") == 22\n assert candidate(s = \"(((()(()))(()(()))))\") == 20\n assert candidate(s = \"()((((()))))()(()(()))\") == 22\n assert candidate(s = \"(()((((()))))))()()\") == 14\n assert candidate(s = \"((((()))))(()(()))\") == 18\n assert candidate(s = \"(()(()(()(()(()(()))))())()()\") == 28\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()(()(()(()(()))()))))))))))))))))))\") == 54\n assert candidate(s = \"(()(()(()(()(()(()(()))))))))))))()(()(()(()))\") == 28\n assert candidate(s = \"(()(()(()))(()(())))\") == 20\n assert candidate(s = \"(()(()))(()(()))\") == 16\n assert candidate(s = \"(((()()(()())()(()(())))))()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()()\") == 126\n assert candidate(s = \"(()(()(()(()(()(()(()(()(())))))))))\") == 36\n assert candidate(s = \"(()(()))()(()())\") == 16\n assert candidate(s = \"()((((((((())))))))))()()\") == 20\n assert candidate(s = \"()(()(()(()(()(()(())))))()()()\") == 28\n assert candidate(s = \"(()(()(()(()(()(()(()()))))))))\") == 30\n assert candidate(s = \"((())())(()(()(()())))\") == 22\n assert candidate(s = \"((()))((()))((()))((()))\") == 24\n assert candidate(s = \"((()))()((()))()((()))\") == 22\n assert candidate(s = \"(()(()(()(()(()(()(()))))))))))))()\") == 28\n assert candidate(s = \"(()(())((())))\") == 14\n assert candidate(s = \"((((((((()))))))))))))))\") == 18\n assert candidate(s = \"(()(()(()(()(()(()(())))))))\") == 28\n assert candidate(s = \"(()(()(()(()(()(()(()))))))())\") == 30\n assert candidate(s = \"()()(()(()(()(()()))))\") == 22\n assert candidate(s = \"()(()))(()(()))\") == 8\n assert candidate(s = \"(()(()(()(()(()(()(()(())))))())))\") == 34\n assert candidate(s = \"(()(()(()(()(()(()(()(()(()))))))))))))()(()(()(()))()()()()()()()()(()(()(())))\") == 38\n assert candidate(s = \"()(()(()(()(()(()(()(())))))))\") == 30\n assert candidate(s = \"(()()(()))((())())\") == 18\n assert candidate(s = \"(((((())))))(((()(()))(()))(()(()))(()(()))(()(()))(()(())))\") == 60\n assert candidate(s = \"(()(()(()(()(()(()(())))))())()()()\") == 34\n assert candidate(s = \"()(()(()(()(()(())))))()()\") == 26\n assert candidate(s = \"((()))(()(()))\") == 14\n assert candidate(s = \"())(()())(()(()()(())))\") == 20\n assert candidate(s = \"((())())(()(()(()(()))))\") == 24\n assert candidate(s = \"(((()))(()))(()())\") == 18\n assert candidate(s = \"((())())(()(()))\") == 16\n assert candidate(s = \"(()(()))(()(()))(()(()))\") == 24\n assert candidate(s = \"(()(()(())))()()()(()(()))\") == 26\n assert candidate(s = \"()()()()()()()()()()()()\") == 24\n assert candidate(s = \"(((((()(()))(()(())))))())\") == 26\n assert candidate(s = \"()(()(()(()(()(()(()(()))))))))\") == 30\n assert candidate(s = \"((())((()))(()(()))(()))\") == 24\n assert candidate(s = \"()(()()(()(()())))\") == 18\n assert candidate(s = \"((()(()())))()((()(())))\") == 24\n assert candidate(s = \"((((()))()()()(()))\") == 18\n assert candidate(s = \"((((((()))))))(()(()(())))\") == 26\n assert candidate(s = \"(((()(()(()(()())))))()())\") == 26\n assert candidate(s = \"()(()(()(()(()(()(())))))\") == 22\n assert candidate(s = \"()()()()()()()()()()()()()()()()()()()()\") == 40\n assert candidate(s = \"()()()()()()()()()()()()()()()\") == 30\n assert candidate(s = \"((((((()))))))(()(()(()(()))))\") == 30\n assert candidate(s = \"(()())(())(()(()(()(())))())\") == 28\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().longestValidParentheses", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestValidParentheses = function(s) {", "container": null, "callable": "longestValidParentheses", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 33, "task_id": "search-in-rotated-sorted-array", "difficulty": "Medium", "problem_description": "There is an integer array nums sorted in ascending order (with distinct values).\nPrior to being passed to your function, nums is possibly rotated at an unknown pivot index k (1 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed). For example, [0,1,2,4,5,6,7] might be rotated at pivot index 3 and become [4,5,6,7,0,1,2].\nGiven the array nums after the possible rotation and an integer target, return the index of target if it is in nums, or -1 if it is not in nums.\nYou must write an algorithm with O(log n) runtime complexity.\n \nExample 1:\nInput: nums = [4,5,6,7,0,1,2], target = 0\nOutput: 4\nExample 2:\nInput: nums = [4,5,6,7,0,1,2], target = 3\nOutput: -1\nExample 3:\nInput: nums = [1], target = 0\nOutput: -1\n\n \nConstraints:\n\n1 <= nums.length <= 5000\n-104 <= nums[i] <= 104\nAll values of nums are unique.\nnums is an ascending array that is possibly rotated.\n-104 <= target <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3],target = 3) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 10) == 9\n assert candidate(nums = [5, 1, 3],target = 1) == 1\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 3) == -1\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 0) == 4\n assert candidate(nums = [6, 7, 8, 9, 1, 2, 3, 4, 5],target = 6) == 0\n assert candidate(nums = [2, 5, 6, 0, 1, 3, 4],target = 1) == -1\n assert candidate(nums = [3, 5, 1],target = 3) == 0\n assert candidate(nums = [11, 13, 15, 17],target = 11) == 0\n assert candidate(nums = [15, 1, 3, 5, 7, 9, 11, 13],target = 7) == 4\n assert candidate(nums = [5, 1, 2, 3, 4],target = 1) == 1\n assert candidate(nums = [5, 1, 2, 3, 4],target = 6) == -1\n assert candidate(nums = [3, 1],target = 1) == 1\n assert candidate(nums = [15, 17, 11, 13],target = 11) == 2\n assert candidate(nums = [5, 1, 3],target = 3) == 2\n assert candidate(nums = [11, 13, 15, 17],target = 10) == -1\n assert candidate(nums = [4, 5, 6, 7, 8, 1, 2, 3],target = 8) == 4\n assert candidate(nums = [2, 1],target = 1) == 1\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 0, 1],target = 5) == 3\n assert candidate(nums = [3, 5, 1],target = 1) == 2\n assert candidate(nums = [7, 0, 1, 2, 3, 4, 5, 6],target = 5) == 6\n assert candidate(nums = [11, 13, 15, 17],target = 13) == 1\n assert candidate(nums = [11, 13, 15, 17],target = 18) == -1\n assert candidate(nums = [5, 1, 3],target = 5) == 0\n assert candidate(nums = [1, 3, 5],target = 1) == 0\n assert candidate(nums = [1],target = 0) == -1\n assert candidate(nums = [6, 7, 8, 9, 1, 2, 3, 4, 5],target = 5) == 8\n assert candidate(nums = [1, 3, 5],target = 5) == 2\n assert candidate(nums = [11, 13, 15, 17],target = 17) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 3) == 2\n assert candidate(nums = [99, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98],target = 50) == 50\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 65) == -1\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 1019) == 19\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0, 1, 2, 3, 4],target = 49) == 44\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 90) == 75\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 3) == 15\n assert candidate(nums = [999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 1095) == 96\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 29) == 19\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 29) == 14\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 145) == 45\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 47) == 2\n assert candidate(nums = [6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5],target = 0) == 5\n assert candidate(nums = [20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 19) == 19\n assert candidate(nums = [47, 48, 49, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46],target = 45) == 48\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 1, 2],target = 2) == 10\n assert candidate(nums = [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7],target = 29) == 21\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 0],target = 0) == 99\n assert candidate(nums = [15, 16, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 20) == 4\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4],target = 1) == 26\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 0],target = 15) == 13\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3],target = 1) == 11\n assert candidate(nums = [6, 7, 8, 9, 10, 1, 2, 3, 4, 5],target = 10) == 4\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3],target = 10) == 6\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2],target = 11) == -1\n assert candidate(nums = [11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 1, 3, 5, 7, 9],target = 25) == 7\n assert candidate(nums = [11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 20) == -1\n assert candidate(nums = [11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 1, 3, 5, 7, 9],target = 29) == 9\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 29) == 14\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 18) == -1\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 43) == 78\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 70) == 25\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39],target = 0) == 0\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3],target = 11) == -1\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 100) == -1\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2],target = 15) == 12\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3],target = 0) == 16\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 198) == 98\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2],target = 19) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 15) == 14\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 16) == 7\n assert candidate(nums = [47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46],target = 97) == 50\n assert candidate(nums = [11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 15) == 4\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3],target = 3) == 30\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98],target = 99) == 49\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 0) == 11\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28],target = 25) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 31) == -1\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 1, 2],target = 10) == -1\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3],target = 19) == 15\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 20) == 5\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 1014) == 14\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1],target = 0) == 18\n assert candidate(nums = [30, 40, 50, 60, 70, 80, 90, 10, 20],target = 50) == 2\n assert candidate(nums = [15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 19) == 4\n assert candidate(nums = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5],target = 0) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == 9\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 9) == 19\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8, 10],target = 19) == 4\n assert candidate(nums = [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 49) == 15\n assert candidate(nums = [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 50) == -1\n assert candidate(nums = [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 0) == 11\n assert candidate(nums = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 25) == -1\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 35) == 15\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150],target = 75) == 75\n assert candidate(nums = [29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28],target = 14) == 15\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 50) == 50\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 100, 200, 300, 400, 500, 600, 700, 800],target = 900) == 8\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 0) == 51\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 2) == 13\n assert candidate(nums = [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7],target = 30) == 22\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6],target = 1) == 25\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3],target = 10) == 6\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 105) == 5\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2],target = 0) == 15\n assert candidate(nums = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0, 1, 2, 3, 4, 5],target = 18) == -1\n assert candidate(nums = [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49],target = 35) == 85\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 2, 4, 6, 8],target = 97) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 0],target = 0) == 50\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3],target = 7) == 3\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 151) == -1\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 1) == 77\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 1) == -1\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1, 2, 3],target = 99) == 95\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 3, 5, 7],target = 15) == 2\n assert candidate(nums = [15, 16, 19, 20, 25, 1, 3, 4, 5, 7, 10, 14],target = 5) == 8\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 37) == 17\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 0) == 31\n assert candidate(nums = [33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],target = 61) == 14\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8],target = 5) == 16\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 5, 7, 9],target = 17) == 3\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8],target = 7) == -1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38],target = 39) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 0],target = 50) == 49\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2],target = 2) == 29\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 1, 2],target = 0) == -1\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 0, 1, 2],target = 30) == 27\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44],target = 0) == 6\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49],target = 25) == 25\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2],target = 21) == -1\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 110) == 10\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99],target = 999) == -1\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().search", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var search = function(nums, target) {", "container": null, "callable": "search", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 34, "task_id": "find-first-and-last-position-of-element-in-sorted-array", "difficulty": "Medium", "problem_description": "Given an array of integers nums sorted in non-decreasing order, find the starting and ending position of a given target value.\nIf target is not found in the array, return [-1, -1].\nYou must write an algorithm with O(log n) runtime complexity.\n \nExample 1:\nInput: nums = [5,7,7,8,8,10], target = 8\nOutput: [3,4]\nExample 2:\nInput: nums = [5,7,7,8,8,10], target = 6\nOutput: [-1,-1]\nExample 3:\nInput: nums = [], target = 0\nOutput: [-1,-1]\n\n \nConstraints:\n\n0 <= nums.length <= 105\n-109 <= nums[i] <= 109\nnums is a non-decreasing array.\n-109 <= target <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 6]\n assert candidate(nums = [2, 2, 2, 2, 3, 3, 4, 4, 4, 4],target = 2) == [0, 3]\n assert candidate(nums = [1, 2, 3, 4, 5],target = 5) == [4, 4]\n assert candidate(nums = [5, 7, 7, 8, 8, 10],target = 8) == [3, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 1) == [0, 0]\n assert candidate(nums = [-10, -5, -3, 0, 3, 5, 9, 10],target = 3) == [4, 4]\n assert candidate(nums = [1, 3, 5, 7, 9],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 5],target = 2) == [1, 3]\n assert candidate(nums = [1],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 5, 6],target = 4) == [4, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 7) == [6, 6]\n assert candidate(nums = [5, 7, 7, 8, 8, 10],target = 6) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7],target = 5) == [4, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == [4, 4]\n assert candidate(nums = [1, 1, 1, 1, 1],target = 1) == [0, 4]\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5],target = 2) == [1, 4]\n assert candidate(nums = [1, 3, 5, 7, 9],target = 2) == [-1, -1]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 9]\n assert candidate(nums = [],target = 0) == [-1, -1]\n assert candidate(nums = [1],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5],target = 1) == [0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9],target = 10) == [-1, -1]\n assert candidate(nums = [1],target = 2) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 20) == [19, 19]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 4) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 6) == [5, 5]\n assert candidate(nums = [-10, -8, -5, -3, -1, 0, 1, 3, 5, 7, 9, 11, 13],target = 15) == [-1, -1]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 5) == [9, 11]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 5],target = 2) == [1, 3]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = 5) == [6, 8]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 7) == [11, 12]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 9, 10],target = 5) == [6, 9]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 0) == [-1, -1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 4) == [-1, -1]\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10],target = 4) == [15, 19]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [0, 9]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5],target = 3) == [4, 7]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [0, 7]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 3) == [3, 4]\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],target = -100) == [0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 19]\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 7, 8, 9],target = 4) == [4, 9]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 21) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 16) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7],target = 5) == [7, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 1) == [0, 0]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 2) == [2, 4]\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 10],target = 3) == [2, 5]\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5],target = 2) == [1, 4]\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 6],target = 2) == [1, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 4) == [5, 6]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 10) == [22, 22]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = -6) == [-1, -1]\n assert candidate(nums = [1, 3, 3, 3, 3, 5, 7, 9],target = 3) == [1, 4]\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 10],target = 5) == [7, 9]\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 22) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7],target = 4) == [4, 6]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -1) == [-1, -1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 15) == [7, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 2) == [1, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 10, 10],target = 7) == [18, 19]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = -5) == [1, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == [9, 9]\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90],target = -90) == [10, 10]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10],target = 1) == [0, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 0) == [-1, -1]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = 20) == [6, 6]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 1) == [0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 13) == [6, 6]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 2) == [1, 2]\n assert candidate(nums = [-10, -5, -5, -1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = -5) == [1, 2]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8],target = 5) == [8, 11]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 5) == [7, 8]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10, 10, 10],target = 10) == [12, 15]\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [1, 20]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 10) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 8) == [13, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == [9, 9]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 10) == [9, 9]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 19]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [0, 31]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == [-1, -1]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = 0) == [4, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 15) == [14, 14]\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [1, 12]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 10) == [17, 18]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 6) == [9, 10]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -10) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 7) == [6, 6]\n assert candidate(nums = [-10, -8, -5, -3, -1, 0, 1, 3, 5, 7, 9, 11, 13],target = -3) == [3, 3]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 29) == [14, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 5) == [4, 4]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = 0) == [2, 2]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 21) == [10, 10]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 2) == [1, 2]\n assert candidate(nums = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5],target = 3) == [1, 21]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4],target = 3) == [6, 8]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 14]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 0) == [-1, -1]\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = 25) == [-1, -1]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 8, 9],target = 5) == [7, 10]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 25) == [12, 12]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 7) == [6, 6]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 9) == [8, 8]\n assert candidate(nums = [1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 8, 8, 9],target = 8) == [13, 16]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],target = 10) == [0, 14]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10],target = 5) == [8, 12]\n assert candidate(nums = [-10, -5, -5, -5, 0, 0, 0, 1, 2, 3, 3, 3, 3, 4, 5, 6],target = -5) == [1, 3]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 0) == [-1, -1]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == [0, 9]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10],target = 5) == [12, 16]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 1) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 21) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 4, 5, 6],target = 3) == [2, 5]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 6) == [10, 11]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = 9) == [9, 9]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 29]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 0) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 25) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 10) == [9, 9]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 11) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 11) == [10, 10]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 3) == [-1, -1]\n assert candidate(nums = [-10, -5, -5, -5, 0, 3, 5, 5, 5, 9],target = -10) == [0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 0) == [0, 4]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 5],target = 3) == [3, 8]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6],target = 7) == [-1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == [4, 4]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 1) == [0, 10]\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().searchRange", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var searchRange = function(nums, target) {", "container": null, "callable": "searchRange", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 35, "task_id": "search-insert-position", "difficulty": "Easy", "problem_description": "Given a sorted array of distinct integers and a target value, return the index if the target is found. If not, return the index where it would be if it were inserted in order.\nYou must write an algorithm with O(log n) runtime complexity.\n \nExample 1:\n\nInput: nums = [1,3,5,6], target = 5\nOutput: 2\n\nExample 2:\n\nInput: nums = [1,3,5,6], target = 2\nOutput: 1\n\nExample 3:\n\nInput: nums = [1,3,5,6], target = 7\nOutput: 4\n\n \nConstraints:\n\n1 <= nums.length <= 104\n-104 <= nums[i] <= 104\nnums contains distinct values sorted in ascending order.\n-104 <= target <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-10, 0, 5, 10],target = 0) == 1\n assert candidate(nums = [1, 2, 4, 6, 7, 9],target = 3) == 2\n assert candidate(nums = [1, 3, 5],target = 4) == 2\n assert candidate(nums = [1, 3, 5, 6],target = 2) == 1\n assert candidate(nums = [-10, -5, -3, 2, 3, 4, 5],target = -4) == 2\n assert candidate(nums = [-10, 0, 10, 20, 30, 40, 50],target = -5) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11],target = 10) == 5\n assert candidate(nums = [1],target = 1) == 0\n assert candidate(nums = [-10, 0, 10, 20, 30, 40, 50],target = 25) == 4\n assert candidate(nums = [1, 3],target = 2) == 1\n assert candidate(nums = [-10, 0, 5, 10],target = 15) == 4\n assert candidate(nums = [1, 3, 5, 6],target = 7) == 4\n assert candidate(nums = [1, 3, 5, 6],target = 5) == 2\n assert candidate(nums = [1, 3],target = 4) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == 4\n assert candidate(nums = [1, 3, 4, 5, 6, 8, 9, 11, 13, 15],target = 7) == 5\n assert candidate(nums = [1, 2, 4, 6, 8, 10],target = 5) == 3\n assert candidate(nums = [1],target = 0) == 0\n assert candidate(nums = [1],target = 2) == 1\n assert candidate(nums = [-10, -5, -3, 2, 3, 4, 5],target = 3) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == 10\n assert candidate(nums = [1, 3, 5, 6],target = 0) == 0\n assert candidate(nums = [-10, 0, 5, 10],target = -5) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 256) == 8\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 5) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],target = 14) == 7\n assert candidate(nums = [10000],target = 9999) == 0\n assert candidate(nums = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100],target = -550) == 5\n assert candidate(nums = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 15) == 7\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10],target = -85) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 12) == 11\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 20) == 10\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 29) == 29\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 155) == 15\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 15) == 7\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],target = 27) == 5\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41],target = 39) == 13\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5.5) == 5\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 27) == 8\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000],target = 500000) == 6\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = 200) == 14\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 33) == 6\n assert candidate(nums = [-10000, 10000],target = 10000) == 1\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24],target = 11) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 19) == 18\n assert candidate(nums = [-10000, 10000],target = 0) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 10) == 5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 0) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 20) == 10\n assert candidate(nums = [-10, -5, -3, -1, 0, 2, 4, 6, 8, 10],target = -6) == 1\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],target = 26) == 9\n assert candidate(nums = [50, 60, 70, 80, 90, 100, 110, 120, 130, 140],target = 145) == 10\n assert candidate(nums = [-10, -5, -3, 0, 4, 8, 12],target = 3) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],target = 12) == 6\n assert candidate(nums = [10000],target = 10001) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 512) == 9\n assert candidate(nums = [-10, -5, 0, 3, 9, 12, 15],target = 1) == 3\n assert candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500],target = -350) == 2\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256],target = 64) == 6\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100],target = 50) == 7\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80],target = 67) == 13\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 10) == 5\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58],target = 59) == 20\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 1) == 0\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],target = 100) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 500) == 4\n assert candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500],target = -250) == 3\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5.5) == 6\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20, 25, 30],target = 12) == 5\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 5500) == 5\n assert candidate(nums = [-1000, -500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500, 1000],target = -750) == 1\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20],target = -3) == 2\n assert candidate(nums = [1, 3, 5, 7, 9],target = 6) == 3\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 100) == 0\n assert candidate(nums = [1, 10, 100, 1000, 10000],target = 500) == 3\n assert candidate(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50],target = -35) == 2\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59],target = 3) == 1\n assert candidate(nums = [-10, -5, 0, 5, 10],target = -7) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 8) == 7\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 1500) == 1\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19],target = 18) == 6\n assert candidate(nums = [-10000, 10000],target = -10000) == 0\n assert candidate(nums = [-999, -998, -997, -996, -995, -994, -993, -992, -991, -990],target = -993) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],target = 20) == 10\n assert candidate(nums = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = 1024) == 32\n assert candidate(nums = [-1000, -500, -250, -125, -62, -31, -15, -7, -3, -1],target = -10) == 7\n assert candidate(nums = [-10000, -9000, -8000, -7000, -6000, -5000, -4000, -3000, -2000, -1000],target = -7500) == 3\n assert candidate(nums = [2, 4, 6, 8, 10],target = 5) == 2\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 11) == 11\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 29) == 9\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 93) == 18\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 550) == 5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 20) == 10\n assert candidate(nums = [1, 10, 100, 1000, 10000],target = 5000) == 4\n assert candidate(nums = [-10000, -9000, -8000, -7000, -6000, -5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],target = 5000) == 15\n assert candidate(nums = [-10, -5, -3, -1, 0, 2, 4, 6, 8, 10],target = -4) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 14) == 7\n assert candidate(nums = [-5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000],target = -2500) == 3\n assert candidate(nums = [-10, -5, 0, 2, 5, 9, 11, 20],target = 3) == 4\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58],target = 26) == 9\n assert candidate(nums = [10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000],target = 55000) == 5\n assert candidate(nums = [-500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500],target = -75) == 3\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],target = 31) == 15\n assert candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = -45) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],target = 44) == 22\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25],target = 15) == 5\n assert candidate(nums = [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023],target = 1024) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],target = 1150) == 11\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],target = 15) == 5\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 100) == 6\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000],target = 10000000) == 7\n assert candidate(nums = [100, 200, 300, 400, 500],target = 250) == 2\n assert candidate(nums = [-100, -50, 0, 50, 100],target = -75) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 15) == 14\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 19) == 9\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 257) == 9\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90],target = 5) == 0\n assert candidate(nums = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024],target = -1) == 0\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().searchInsert", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var searchInsert = function(nums, target) {", "container": null, "callable": "searchInsert", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 36, "task_id": "valid-sudoku", "difficulty": "Medium", "problem_description": "Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:\n\nEach row must contain the digits 1-9 without repetition.\nEach column must contain the digits 1-9 without repetition.\nEach of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.\n\nNote:\n\nA Sudoku board (partially filled) could be valid but is not necessarily solvable.\nOnly the filled cells need to be validated according to the mentioned rules.\n\n \nExample 1:\n\n\nInput: board = \n[[\"5\",\"3\",\".\",\".\",\"7\",\".\",\".\",\".\",\".\"]\n,[\"6\",\".\",\".\",\"1\",\"9\",\"5\",\".\",\".\",\".\"]\n,[\".\",\"9\",\"8\",\".\",\".\",\".\",\".\",\"6\",\".\"]\n,[\"8\",\".\",\".\",\".\",\"6\",\".\",\".\",\".\",\"3\"]\n,[\"4\",\".\",\".\",\"8\",\".\",\"3\",\".\",\".\",\"1\"]\n,[\"7\",\".\",\".\",\".\",\"2\",\".\",\".\",\".\",\"6\"]\n,[\".\",\"6\",\".\",\".\",\".\",\".\",\"2\",\"8\",\".\"]\n,[\".\",\".\",\".\",\"4\",\"1\",\"9\",\".\",\".\",\"5\"]\n,[\".\",\".\",\".\",\".\",\"8\",\".\",\".\",\"7\",\"9\"]]\nOutput: true\n\nExample 2:\n\nInput: board = \n[[\"8\",\"3\",\".\",\".\",\"7\",\".\",\".\",\".\",\".\"]\n,[\"6\",\".\",\".\",\"1\",\"9\",\"5\",\".\",\".\",\".\"]\n,[\".\",\"9\",\"8\",\".\",\".\",\".\",\".\",\"6\",\".\"]\n,[\"8\",\".\",\".\",\".\",\"6\",\".\",\".\",\".\",\"3\"]\n,[\"4\",\".\",\".\",\"8\",\".\",\"3\",\".\",\".\",\"1\"]\n,[\"7\",\".\",\".\",\".\",\"2\",\".\",\".\",\".\",\"6\"]\n,[\".\",\"6\",\".\",\".\",\".\",\".\",\"2\",\"8\",\".\"]\n,[\".\",\".\",\".\",\"4\",\"1\",\"9\",\".\",\".\",\"5\"]\n,[\".\",\".\",\".\",\".\",\"8\",\".\",\".\",\"7\",\"9\"]]\nOutput: false\nExplanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.\n\n \nConstraints:\n\nboard.length == 9\nboard[i].length == 9\nboard[i][j] is a digit 1-9 or '.'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = [['8', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '5', '1', '9'], ['.', '9', '.', '.', '5', '.', '.', '.', '.'], ['.', '.', '.', '2', '.', '4', '.', '.', '.'], ['4', '.', '.', '.', '.', '.', '1', '.', '.'], ['.', '.', '.', '.', '.', '.', '7', '.', '3'], ['.', '.', '2', '.', '.', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '.', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '5', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['1', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '2', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '3', '.', '.', '.', '.', '.', '.'], ['4', '.', '.', '5', '.', '.', '.', '.', '.'], ['.', '5', '.', '.', '6', '.', '.', '.', '.'], ['.', '.', '6', '.', '.', '7', '.', '.', '.'], ['7', '.', '.', '.', '.', '.', '8', '.', '.'], ['.', '8', '.', '.', '.', '.', '.', '9', '.'], ['.', '.', '9', '.', '.', '.', '.', '.', '1']]) == True\n assert candidate(board = [['.', '.', '.', '.', '5', '.', '.', '1', '.'], ['.', '4', '.', '3', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '3', '.', '.', '1'], ['8', '.', '.', '.', '.', '.', '.', '2', '.'], ['.', '.', '2', '.', '7', '.', '4', '.', '.'], ['.', '1', '.', '.', '.', '.', '.', '.', '8'], ['9', '.', '.', '1', '.', '.', '.', '.', '.'], ['.', '.', '8', '.', '.', '8', '.', '7', '.'], ['.', '5', '.', '.', '9', '.', '.', '.', '.']]) == False\n assert candidate(board = [['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['4', '5', '6', '7', '8', '9', '1', '2', '3'], ['7', '8', '9', '1', '2', '3', '4', '5', '6'], ['2', '3', '4', '5', '6', '7', '8', '9', '1'], ['5', '6', '7', '8', '9', '1', '2', '3', '4'], ['8', '9', '1', '2', '3', '4', '5', '6', '7'], ['3', '4', '5', '6', '7', '8', '9', '1', '2'], ['6', '7', '8', '9', '1', '2', '3', '4', '5'], ['9', '1', '2', '3', '4', '5', '6', '7', '8']]) == True\n assert candidate(board = [['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['9', '8', '7', '6', '5', '4', '3', '2', '1'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == False\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['2', '3', '4', '5', '6', '7', '8', '9', '1'], ['3', '4', '5', '6', '7', '8', '9', '1', '2'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == False\n assert candidate(board = [['.', '.', '9', '7', '4', '8', '.', '.', '.'], ['7', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '2', '.', '1', '.', '9', '.', '.', '.'], ['.', '.', '7', '.', '.', '.', '2', '4', '.'], ['.', '6', '4', '.', '1', '.', '5', '9', '.'], ['.', '9', '8', '.', '.', '.', '3', '.', '.'], ['.', '.', '.', '8', '.', '3', '.', '2', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '6'], ['.', '.', '.', '2', '7', '5', '9', '.', '.']]) == True\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '5']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '9', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '4', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['5', '3', '4', '6', '7', '8', '9', '1', '2'], ['6', '7', '2', '1', '9', '5', '3', '4', '8'], ['1', '9', '8', '3', '4', '2', '5', '6', '7'], ['8', '5', '9', '7', '6', '1', '4', '2', '3'], ['4', '2', '6', '8', '5', '3', '7', '9', '1'], ['7', '1', '3', '9', '2', '4', '8', '5', '6'], ['9', '6', '1', '5', '3', '7', '2', '8', '4'], ['2', '8', '7', '4', '1', '9', '6', '3', '5'], ['3', '4', '5', '2', '8', '6', '1', '7', '9']]) == True\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == True\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '9'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '.', '7', '9']]) == False\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['2', '.', '.', '.', '8', '.', '.', '7', '9']]) == True\n assert candidate(board = [['5', '3', '.', '.', '7', '.', '.', '.', '.'], ['6', '.', '.', '1', '9', '5', '.', '.', '.'], ['.', '9', '8', '.', '.', '.', '.', '6', '.'], ['8', '.', '.', '.', '6', '.', '.', '.', '3'], ['4', '.', '.', '8', '.', '3', '.', '.', '1'], ['7', '.', '.', '.', '2', '.', '.', '.', '6'], ['.', '6', '.', '.', '.', '.', '2', '8', '.'], ['.', '.', '.', '4', '1', '9', '.', '.', '5'], ['.', '.', '.', '.', '8', '.', '5', '7', '9']]) == False\n assert candidate(board = [['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9'], ['1', '2', '3', '4', '5', '6', '7', '8', '9']]) == False\n"}, "metadata": {"canonical_parameter_names": ["board"], "leetcode_dataset_entry_point": "Solution().isValidSudoku", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isValidSudoku = function(board) {", "container": null, "callable": "isValidSudoku", "parameters": [{"name": "board", "type": "character[][]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 38, "task_id": "count-and-say", "difficulty": "Medium", "problem_description": "The count-and-say sequence is a sequence of digit strings defined by the recursive formula:\n\ncountAndSay(1) = \"1\"\ncountAndSay(n) is the run-length encoding of countAndSay(n - 1).\n\nRun-length encoding (RLE) is a string compression method that works by replacing consecutive identical characters (repeated 2 or more times) with the concatenation of the character and the number marking the count of the characters (length of the run). For example, to compress the string \"3322251\" we replace \"33\" with \"23\", replace \"222\" with \"32\", replace \"5\" with \"15\" and replace \"1\" with \"11\". Thus the compressed string becomes \"23321511\".\nGiven a positive integer n, return the nth element of the count-and-say sequence.\n \nExample 1:\n\nInput: n = 4\nOutput: \"1211\"\nExplanation:\n\ncountAndSay(1) = \"1\"\ncountAndSay(2) = RLE of \"1\" = \"11\"\ncountAndSay(3) = RLE of \"11\" = \"21\"\ncountAndSay(4) = RLE of \"21\" = \"1211\"\n\n\nExample 2:\n\nInput: n = 1\nOutput: \"1\"\nExplanation:\nThis is the base case.\n\n \nConstraints:\n\n1 <= n <= 30\n\n \nFollow up: Could you solve it iteratively?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == \"1113213211\"\n assert candidate(n = 3) == \"21\"\n assert candidate(n = 30) == \"3113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321223112111311222112132113213221133122211311221122111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321132132211322132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331222113321112131122211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112112322211322311311222113111231133211121312211231131112311211232221121113122113121113222123211211131221132211131221121321131211132221123113112211121312211231131122113221122112133221121321132132211331121321231231121113121113122122311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312211322311211133112111312211213211311123113223112111321322123122113222122211211232221121113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123112221221321132132211231131122211331121321232221121113122113121113222123211211131211121332211213111213122112132113121113222112132113213221232112111312111213322112132113213221133112132123123112111311222112132113311213211221121332211231131122211311123113321112131221123113112221132231131122211211131221131112311332211213211321223112111311222112132113212221132221222112112322211211131221131211132221232112111312111213111213211231131112311311221122132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132122311211131122211213211321222113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213213211221113122113121113222112132113213221232112111312111213322112132113213221133112132123123112111312211322311211133112111312212221121123222112132113213221133112132123222113223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211\"\n assert candidate(n = 15) == \"311311222113111231131112132112311321322112111312211312111322212311322113212221\"\n assert candidate(n = 4) == \"1211\"\n assert candidate(n = 9) == \"31131211131221\"\n assert candidate(n = 6) == \"312211\"\n assert candidate(n = 20) == \"11131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113121113123112112322111213211322211312113211\"\n assert candidate(n = 2) == \"11\"\n assert candidate(n = 25) == \"132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113212231121113112221121321132132211231232112311321322112311311222113111231133221121113122113121113221112131221123113111231121123222112132113213221133112132123123112111312111312212231131122211311123113322112111312211312111322111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312212221121123222112132113213221133112132123123112111311222112132113213221132213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121132211332113221122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321231231121113112221121321132122311211131122211211131221131211322113322112111312211322132113213221123113112221131112311311121321122112132231121113122113322113111221131221\"\n assert candidate(n = 1) == \"1\"\n assert candidate(n = 7) == \"13112221\"\n assert candidate(n = 10) == \"13211311123113112211\"\n assert candidate(n = 5) == \"111221\"\n assert candidate(n = 29) == \"11131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211132221121311121312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221231122212213211321322112311311222113311213212322211211131221131211132221232112111312111213322112131112131221121321131211132221121321132132212321121113121112133221121321132132211331121321231231121113112221121321133112132112211213322112311311222113111231133211121312211231131122211322311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122111213122112311311222113111221131221221321132132211331121321231231121113112221121321133112132112211213322112311311222113111231133211121312211231131122211322311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122111213122112311311222112111331121113112221121113122113121113222112132113213221232112111312111213322112311311222113111221221113122112132113121113222112311311222113111221132221231221132221222112112322211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312111322212321121113121112133221132211131221131211132221232112111312111213322112132113213221133112132113221321123113213221121113122123211211131221222112112322211231131122211311123113321112132132112211131221131211132221121321132132212321121113121112133221123113112221131112311332111213211322111213111213211231131211132211121311222113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131211131221223113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331121321231231121113112221121321133112132112211213322112312321123113213221123113112221133112132123222112311311222113111231132231121113112221121321133112132112211213322112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312111322212311222122132113213221123113112221133112132123222112311311222113111231133211121321132211121311121321122112133221123113112221131112311332211322111312211312111322212321121113121112133221121321132132211331121321231231121113112221121321132122311211131122211211131221131211322113322112111312211322132113213221123113112221131112311311121321122112132231121113122113322113111221131221\"\n assert candidate(n = 11) == \"11131221133112132113212221\"\n assert candidate(n = 22) == \"132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113213221133122112231131122211211131221131112311332211211131221131211132221232112111312111213322112132113213221133112132113221321123113213221121113122123211211131221222112112322211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211\"\n assert candidate(n = 12) == \"3113112221232112111312211312113211\"\n assert candidate(n = 27) == \"31131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122211211133112111311222112111312211312111322211213211321322123211211131211121332211231131122211311122122111312211213211312111322211231131122211311123113322112111331121113112221121113122113111231133221121113122113121113222123211211131211121332211213211321322113311213211322132112311321322112111312212321121113122122211211232221123113112221131112311332111213122112311311123112111331121113122112132113311213211321222122111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112132113213221133112132123123112111311222112132113311213211231232112311311222112111312211311123113322112132113212231121113112221121321132122211322212221121123222112311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311123113322113223113112221131112311332211211131221131211132211121312211231131112311211232221121321132132211331221122311311222112111312211311123113322112132113213221133122211332111213112221133211322112211213322112111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122211331121321232221121113122113121122132112311321322112111312211312111322211213111213122112132113121113222112132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212321121113121112133221121311121312211213211312111322211213211321322123211211131211121332211213211321322113311213212312311211131122211213211331121321122112133221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311222113111221221113122112132113121113222112132113213221133122211332111213322112132113213221132231131122211311123113322112111312211312111322212321121113122123211231131122113221123113221113122112132113213211121332212311322113212221\"\n assert candidate(n = 26) == \"1113122113121113222123211211131211121311121321123113213221121113122123211211131221121311121312211213211321322112311311222113311213212322211211131221131211221321123113213221121113122113121113222112131112131221121321131211132221121321132132211331121321232221123113112221131112311322311211131122211213211331121321122112133221121113122113121113222123211211131211121311121321123113111231131122112213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211231131122211311123113321112131221123113111231121113311211131221121321131211132221123113112211121312211231131122113221122112133221121113122113121113222123211211131211121311121321123113213221121113122113121113222113221113122113121113222112132113213221232112111312111213322112311311222113111221221113122112132113121113222112311311222113111221132221231221132221222112112322211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312111213111213211231132132211211131221131211221321123113213221123113112221131112211322212322211231131122211322111312211312111322211213211321322113311213211331121113122122211211132213211231131122212322211331222113112211\"\n assert candidate(n = 14) == \"11131221131211131231121113112221121321132132211331222113112211\"\n assert candidate(n = 21) == \"311311222113111231133211121312211231131112311211133112111312211213211312111322211231131122211311122122111312211213211312111322211213211321322113311213212322211231131122211311123113223112111311222112132113311213211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221131112311311121321122112132231121113122113322113111221131221\"\n assert candidate(n = 17) == \"11131221131211132221232112111312212321123113112221121113122113111231133221121321132132211331121321231231121113122113322113111221131221\"\n assert candidate(n = 18) == \"31131122211311123113321112131221123113112211121312211213211321322112311311222113311213212322211211131221131211132221232112111312111213111213211231131122212322211331222113112211\"\n assert candidate(n = 13) == \"1321132132111213122112311311222113111221131221\"\n assert candidate(n = 23) == \"111312211312111322212321121113121112131112132112311321322112111312212321121113122112131112131221121321132132211231131122211331121321232221121113122113121113222123112221221321132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322212321121113122123211231131122113221123113221113122112132113213211121332212311322113212221\"\n assert candidate(n = 19) == \"1321132132211331121321231231121113112221121321132122311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112311332111213122112311311123112111331121113122112132113213211121332212311322113212221\"\n assert candidate(n = 28) == \"13211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321223112111311222112132113213221123123211231132132211231131122211311123113322112111312211312111322111213122112311311123112112322211213211321322113312211223113112221121113122113111231133221121321132132211331121321232221123123211231132132211231131122211331121321232221123113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221232112111312211312113211223113112221131112311332111213122112311311123112112322211211131221131211132221232112111312211322111312211213211312111322211231131122111213122112311311221132211221121332211211131221131211132221232112111312111213111213211231132132211211131221232112111312211213111213122112132113213221123113112221133112132123222112111312211312112213211231132132211211131221131211322113321132211221121332211213211321322113311213212312311211131122211213211331121321123123211231131122211211131221131112311332211213211321322113311213212322211322132113213221133112132123222112311311222113111231132231121113112221121321133112132112211213322112111312211312111322212311222122132113213221123113112221133112132123222112111312211312111322212311322123123112111321322123122113222122211211232221123113112221131112311332111213122112311311123112111331121113122112132113121113222112311311221112131221123113112221121113311211131122211211131221131211132221121321132132212321121113121112133221123113112221131112212211131221121321131211132221123113112221131112311332211211133112111311222112111312211311123113322112111312211312111322212321121113121112133221121321132132211331121321132213211231132132211211131221232112111312212221121123222112311311222113111231133211121321321122111312211312111322211213211321322123211211131211121332211231131122211311123113321112131221123113111231121123222112111331121113112221121113122113111231133221121113122113121113221112131221123113111231121123222112111312211312111322212321121113121112131112132112311321322112111312212321121113122122211211232221121321132132211331121321231231121113112221121321133112132112312321123113112221121113122113111231133221121321132132211331221122311311222112111312211311123113322112111312211312111322212311322123123112112322211211131221131211132221132213211321322113311213212322211231131122211311123113321112131221123113112211121312211213211321222113222112132113223113112221121113122113121113123112112322111213211322211312113211\"\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countAndSay", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countAndSay = function(n) {", "container": null, "callable": "countAndSay", "parameters": [{"name": "n", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 39, "task_id": "combination-sum", "difficulty": "Medium", "problem_description": "Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.\nThe same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.\nThe test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.\n \nExample 1:\n\nInput: candidates = [2,3,6,7], target = 7\nOutput: [[2,2,3],[7]]\nExplanation:\n2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times.\n7 is a candidate, and 7 = 7.\nThese are the only two combinations.\n\nExample 2:\n\nInput: candidates = [2,3,5], target = 8\nOutput: [[2,2,2,2],[2,3,3],[3,5]]\n\nExample 3:\n\nInput: candidates = [2], target = 1\nOutput: []\n\n \nConstraints:\n\n1 <= candidates.length <= 30\n2 <= candidates[i] <= 40\nAll elements of candidates are distinct.\n1 <= target <= 40\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(candidates = [2, 5, 2, 1, 2],target = 5) == [[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 1, 2], [1, 1, 1, 2], [1, 2, 2], [1, 2, 2], [1, 2, 2], [1, 2, 2], [1, 2, 2], [1, 2, 2], [5]]\n assert candidate(candidates = [8, 7, 4, 3],target = 11) == [[3, 4, 4], [3, 8], [4, 7]]\n assert candidate(candidates = [2, 5, 10],target = 10) == [[2, 2, 2, 2, 2], [5, 5], [10]]\n assert candidate(candidates = [2, 5, 10],target = 15) == [[2, 2, 2, 2, 2, 5], [5, 5, 5], [5, 10]]\n assert candidate(candidates = [3, 5, 7],target = 10) == [[3, 7], [5, 5]]\n assert candidate(candidates = [2, 3, 5],target = 8) == [[2, 2, 2, 2], [2, 3, 3], [3, 5]]\n assert candidate(candidates = [8, 2, 3],target = 11) == [[2, 2, 2, 2, 3], [2, 3, 3, 3], [3, 8]]\n assert candidate(candidates = [3, 5, 8],target = 11) == [[3, 3, 5], [3, 8]]\n assert candidate(candidates = [3, 5, 7, 8, 9],target = 15) == [[3, 3, 3, 3, 3], [3, 3, 9], [3, 5, 7], [5, 5, 5], [7, 8]]\n assert candidate(candidates = [4, 2, 1],target = 10) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 2, 4], [1, 1, 2, 2, 2, 2], [1, 1, 2, 2, 4], [1, 1, 4, 4], [2, 2, 2, 2, 2], [2, 2, 2, 4], [2, 4, 4]]\n assert candidate(candidates = [10, 20, 30],target = 20) == [[10, 10], [20]]\n assert candidate(candidates = [3, 12, 9, 11, 6, 7, 8, 5, 4],target = 15) == [[3, 3, 3, 3, 3], [3, 3, 3, 6], [3, 3, 4, 5], [3, 3, 9], [3, 4, 4, 4], [3, 4, 8], [3, 5, 7], [3, 6, 6], [3, 12], [4, 4, 7], [4, 5, 6], [4, 11], [5, 5, 5], [6, 9], [7, 8]]\n assert candidate(candidates = [7, 6, 5],target = 17) == [[5, 5, 7], [5, 6, 6]]\n assert candidate(candidates = [10, 15, 3, 7],target = 25) == [[3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 10], [3, 7, 15], [10, 15]]\n assert candidate(candidates = [7, 14],target = 30) == []\n assert candidate(candidates = [1],target = 1) == [[1]]\n assert candidate(candidates = [1, 2, 3],target = 5) == [[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 1, 3], [1, 2, 2], [2, 3]]\n assert candidate(candidates = [4, 6, 8],target = 12) == [[4, 4, 4], [4, 8], [6, 6]]\n assert candidate(candidates = [2],target = 1) == []\n assert candidate(candidates = [3, 5, 7],target = 11) == [[3, 3, 5]]\n assert candidate(candidates = [1, 2],target = 4) == [[1, 1, 1, 1], [1, 1, 2], [2, 2]]\n assert candidate(candidates = [1, 2, 5],target = 5) == [[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [5]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5],target = 8) == [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 5], [1, 1, 2, 2, 2], [1, 1, 6], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 5], [1, 1, 2, 2, 2], [1, 1, 6], [1, 2, 5], [1, 7], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 5], [1, 1, 2, 2, 2], [1, 1, 6], [1, 2, 5], [1, 7], [2, 2, 2, 2], [2, 6]]\n assert candidate(candidates = [1],target = 2) == [[1, 1]]\n assert candidate(candidates = [2, 3, 6, 7],target = 7) == [[2, 2, 3], [7]]\n assert candidate(candidates = [4, 7, 10, 13, 16, 19, 22, 25, 28, 31],target = 80) == [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 16], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 13], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 10], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 10], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 28], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 25], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 22], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 13, 19], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 16, 16], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 22], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 10, 19], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 13, 16], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 10, 16], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 13, 13], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 19], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 10, 16], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 13, 13], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 10, 10, 13], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 10, 10, 10], [4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 16], [4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 10, 13], [4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 10, 10, 10], [4, 4, 4, 4, 4, 4, 4, 4, 4, 13, 31], [4, 4, 4, 4, 4, 4, 4, 4, 4, 16, 28], [4, 4, 4, 4, 4, 4, 4, 4, 4, 19, 25], [4, 4, 4, 4, 4, 4, 4, 4, 4, 22, 22], [4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 13], [4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 10, 10], [4, 4, 4, 4, 4, 4, 4, 4, 7, 10, 31], [4, 4, 4, 4, 4, 4, 4, 4, 7, 13, 28], [4, 4, 4, 4, 4, 4, 4, 4, 7, 16, 25], [4, 4, 4, 4, 4, 4, 4, 4, 7, 19, 22], [4, 4, 4, 4, 4, 4, 4, 4, 10, 10, 28], [4, 4, 4, 4, 4, 4, 4, 4, 10, 13, 25], [4, 4, 4, 4, 4, 4, 4, 4, 10, 16, 22], [4, 4, 4, 4, 4, 4, 4, 4, 10, 19, 19], [4, 4, 4, 4, 4, 4, 4, 4, 13, 13, 22], [4, 4, 4, 4, 4, 4, 4, 4, 13, 16, 19], [4, 4, 4, 4, 4, 4, 4, 4, 16, 16, 16], [4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 10], [4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 31], [4, 4, 4, 4, 4, 4, 4, 7, 7, 10, 28], [4, 4, 4, 4, 4, 4, 4, 7, 7, 13, 25], [4, 4, 4, 4, 4, 4, 4, 7, 7, 16, 22], [4, 4, 4, 4, 4, 4, 4, 7, 7, 19, 19], [4, 4, 4, 4, 4, 4, 4, 7, 10, 10, 25], [4, 4, 4, 4, 4, 4, 4, 7, 10, 13, 22], [4, 4, 4, 4, 4, 4, 4, 7, 10, 16, 19], [4, 4, 4, 4, 4, 4, 4, 7, 13, 13, 19], [4, 4, 4, 4, 4, 4, 4, 7, 13, 16, 16], [4, 4, 4, 4, 4, 4, 4, 10, 10, 10, 22], [4, 4, 4, 4, 4, 4, 4, 10, 10, 13, 19], [4, 4, 4, 4, 4, 4, 4, 10, 10, 16, 16], [4, 4, 4, 4, 4, 4, 4, 10, 13, 13, 16], [4, 4, 4, 4, 4, 4, 4, 13, 13, 13, 13], [4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7], [4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 28], [4, 4, 4, 4, 4, 4, 7, 7, 7, 10, 25], [4, 4, 4, 4, 4, 4, 7, 7, 7, 13, 22], [4, 4, 4, 4, 4, 4, 7, 7, 7, 16, 19], [4, 4, 4, 4, 4, 4, 7, 7, 10, 10, 22], [4, 4, 4, 4, 4, 4, 7, 7, 10, 13, 19], [4, 4, 4, 4, 4, 4, 7, 7, 10, 16, 16], [4, 4, 4, 4, 4, 4, 7, 7, 13, 13, 16], [4, 4, 4, 4, 4, 4, 7, 10, 10, 10, 19], [4, 4, 4, 4, 4, 4, 7, 10, 10, 13, 16], [4, 4, 4, 4, 4, 4, 7, 10, 13, 13, 13], [4, 4, 4, 4, 4, 4, 10, 10, 10, 10, 16], [4, 4, 4, 4, 4, 4, 10, 10, 10, 13, 13], [4, 4, 4, 4, 4, 4, 25, 31], [4, 4, 4, 4, 4, 4, 28, 28], [4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 25], [4, 4, 4, 4, 4, 7, 7, 7, 7, 10, 22], [4, 4, 4, 4, 4, 7, 7, 7, 7, 13, 19], [4, 4, 4, 4, 4, 7, 7, 7, 7, 16, 16], [4, 4, 4, 4, 4, 7, 7, 7, 10, 10, 19], [4, 4, 4, 4, 4, 7, 7, 7, 10, 13, 16], [4, 4, 4, 4, 4, 7, 7, 7, 13, 13, 13], [4, 4, 4, 4, 4, 7, 7, 10, 10, 10, 16], [4, 4, 4, 4, 4, 7, 7, 10, 10, 13, 13], [4, 4, 4, 4, 4, 7, 10, 10, 10, 10, 13], [4, 4, 4, 4, 4, 7, 22, 31], [4, 4, 4, 4, 4, 7, 25, 28], [4, 4, 4, 4, 4, 10, 10, 10, 10, 10, 10], [4, 4, 4, 4, 4, 10, 19, 31], [4, 4, 4, 4, 4, 10, 22, 28], [4, 4, 4, 4, 4, 10, 25, 25], [4, 4, 4, 4, 4, 13, 16, 31], [4, 4, 4, 4, 4, 13, 19, 28], [4, 4, 4, 4, 4, 13, 22, 25], [4, 4, 4, 4, 4, 16, 16, 28], [4, 4, 4, 4, 4, 16, 19, 25], [4, 4, 4, 4, 4, 16, 22, 22], [4, 4, 4, 4, 4, 19, 19, 22], [4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 22], [4, 4, 4, 4, 7, 7, 7, 7, 7, 10, 19], [4, 4, 4, 4, 7, 7, 7, 7, 7, 13, 16], [4, 4, 4, 4, 7, 7, 7, 7, 10, 10, 16], [4, 4, 4, 4, 7, 7, 7, 7, 10, 13, 13], [4, 4, 4, 4, 7, 7, 7, 10, 10, 10, 13], [4, 4, 4, 4, 7, 7, 10, 10, 10, 10, 10], [4, 4, 4, 4, 7, 7, 19, 31], [4, 4, 4, 4, 7, 7, 22, 28], [4, 4, 4, 4, 7, 7, 25, 25], [4, 4, 4, 4, 7, 10, 16, 31], [4, 4, 4, 4, 7, 10, 19, 28], [4, 4, 4, 4, 7, 10, 22, 25], [4, 4, 4, 4, 7, 13, 13, 31], [4, 4, 4, 4, 7, 13, 16, 28], [4, 4, 4, 4, 7, 13, 19, 25], [4, 4, 4, 4, 7, 13, 22, 22], [4, 4, 4, 4, 7, 16, 16, 25], [4, 4, 4, 4, 7, 16, 19, 22], [4, 4, 4, 4, 7, 19, 19, 19], [4, 4, 4, 4, 10, 10, 13, 31], [4, 4, 4, 4, 10, 10, 16, 28], [4, 4, 4, 4, 10, 10, 19, 25], [4, 4, 4, 4, 10, 10, 22, 22], [4, 4, 4, 4, 10, 13, 13, 28], [4, 4, 4, 4, 10, 13, 16, 25], [4, 4, 4, 4, 10, 13, 19, 22], [4, 4, 4, 4, 10, 16, 16, 22], [4, 4, 4, 4, 10, 16, 19, 19], [4, 4, 4, 4, 13, 13, 13, 25], [4, 4, 4, 4, 13, 13, 16, 22], [4, 4, 4, 4, 13, 13, 19, 19], [4, 4, 4, 4, 13, 16, 16, 19], [4, 4, 4, 4, 16, 16, 16, 16], [4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 19], [4, 4, 4, 7, 7, 7, 7, 7, 7, 10, 16], [4, 4, 4, 7, 7, 7, 7, 7, 7, 13, 13], [4, 4, 4, 7, 7, 7, 7, 7, 10, 10, 13], [4, 4, 4, 7, 7, 7, 7, 10, 10, 10, 10], [4, 4, 4, 7, 7, 7, 16, 31], [4, 4, 4, 7, 7, 7, 19, 28], [4, 4, 4, 7, 7, 7, 22, 25], [4, 4, 4, 7, 7, 10, 13, 31], [4, 4, 4, 7, 7, 10, 16, 28], [4, 4, 4, 7, 7, 10, 19, 25], [4, 4, 4, 7, 7, 10, 22, 22], [4, 4, 4, 7, 7, 13, 13, 28], [4, 4, 4, 7, 7, 13, 16, 25], [4, 4, 4, 7, 7, 13, 19, 22], [4, 4, 4, 7, 7, 16, 16, 22], [4, 4, 4, 7, 7, 16, 19, 19], [4, 4, 4, 7, 10, 10, 10, 31], [4, 4, 4, 7, 10, 10, 13, 28], [4, 4, 4, 7, 10, 10, 16, 25], [4, 4, 4, 7, 10, 10, 19, 22], [4, 4, 4, 7, 10, 13, 13, 25], [4, 4, 4, 7, 10, 13, 16, 22], [4, 4, 4, 7, 10, 13, 19, 19], [4, 4, 4, 7, 10, 16, 16, 19], [4, 4, 4, 7, 13, 13, 13, 22], [4, 4, 4, 7, 13, 13, 16, 19], [4, 4, 4, 7, 13, 16, 16, 16], [4, 4, 4, 10, 10, 10, 10, 28], [4, 4, 4, 10, 10, 10, 13, 25], [4, 4, 4, 10, 10, 10, 16, 22], [4, 4, 4, 10, 10, 10, 19, 19], [4, 4, 4, 10, 10, 13, 13, 22], [4, 4, 4, 10, 10, 13, 16, 19], [4, 4, 4, 10, 10, 16, 16, 16], [4, 4, 4, 10, 13, 13, 13, 19], [4, 4, 4, 10, 13, 13, 16, 16], [4, 4, 4, 13, 13, 13, 13, 16], [4, 4, 7, 7, 7, 7, 7, 7, 7, 7, 16], [4, 4, 7, 7, 7, 7, 7, 7, 7, 10, 13], [4, 4, 7, 7, 7, 7, 7, 7, 10, 10, 10], [4, 4, 7, 7, 7, 7, 13, 31], [4, 4, 7, 7, 7, 7, 16, 28], [4, 4, 7, 7, 7, 7, 19, 25], [4, 4, 7, 7, 7, 7, 22, 22], [4, 4, 7, 7, 7, 10, 10, 31], [4, 4, 7, 7, 7, 10, 13, 28], [4, 4, 7, 7, 7, 10, 16, 25], [4, 4, 7, 7, 7, 10, 19, 22], [4, 4, 7, 7, 7, 13, 13, 25], [4, 4, 7, 7, 7, 13, 16, 22], [4, 4, 7, 7, 7, 13, 19, 19], [4, 4, 7, 7, 7, 16, 16, 19], [4, 4, 7, 7, 10, 10, 10, 28], [4, 4, 7, 7, 10, 10, 13, 25], [4, 4, 7, 7, 10, 10, 16, 22], [4, 4, 7, 7, 10, 10, 19, 19], [4, 4, 7, 7, 10, 13, 13, 22], [4, 4, 7, 7, 10, 13, 16, 19], [4, 4, 7, 7, 10, 16, 16, 16], [4, 4, 7, 7, 13, 13, 13, 19], [4, 4, 7, 7, 13, 13, 16, 16], [4, 4, 7, 10, 10, 10, 10, 25], [4, 4, 7, 10, 10, 10, 13, 22], [4, 4, 7, 10, 10, 10, 16, 19], [4, 4, 7, 10, 10, 13, 13, 19], [4, 4, 7, 10, 10, 13, 16, 16], [4, 4, 7, 10, 13, 13, 13, 16], [4, 4, 7, 13, 13, 13, 13, 13], [4, 4, 10, 10, 10, 10, 10, 22], [4, 4, 10, 10, 10, 10, 13, 19], [4, 4, 10, 10, 10, 10, 16, 16], [4, 4, 10, 10, 10, 13, 13, 16], [4, 4, 10, 10, 13, 13, 13, 13], [4, 4, 10, 31, 31], [4, 4, 13, 28, 31], [4, 4, 16, 25, 31], [4, 4, 16, 28, 28], [4, 4, 19, 22, 31], [4, 4, 19, 25, 28], [4, 4, 22, 22, 28], [4, 4, 22, 25, 25], [4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 13], [4, 7, 7, 7, 7, 7, 7, 7, 7, 10, 10], [4, 7, 7, 7, 7, 7, 10, 31], [4, 7, 7, 7, 7, 7, 13, 28], [4, 7, 7, 7, 7, 7, 16, 25], [4, 7, 7, 7, 7, 7, 19, 22], [4, 7, 7, 7, 7, 10, 10, 28], [4, 7, 7, 7, 7, 10, 13, 25], [4, 7, 7, 7, 7, 10, 16, 22], [4, 7, 7, 7, 7, 10, 19, 19], [4, 7, 7, 7, 7, 13, 13, 22], [4, 7, 7, 7, 7, 13, 16, 19], [4, 7, 7, 7, 7, 16, 16, 16], [4, 7, 7, 7, 10, 10, 10, 25], [4, 7, 7, 7, 10, 10, 13, 22], [4, 7, 7, 7, 10, 10, 16, 19], [4, 7, 7, 7, 10, 13, 13, 19], [4, 7, 7, 7, 10, 13, 16, 16], [4, 7, 7, 7, 13, 13, 13, 16], [4, 7, 7, 10, 10, 10, 10, 22], [4, 7, 7, 10, 10, 10, 13, 19], [4, 7, 7, 10, 10, 10, 16, 16], [4, 7, 7, 10, 10, 13, 13, 16], [4, 7, 7, 10, 13, 13, 13, 13], [4, 7, 7, 31, 31], [4, 7, 10, 10, 10, 10, 10, 19], [4, 7, 10, 10, 10, 10, 13, 16], [4, 7, 10, 10, 10, 13, 13, 13], [4, 7, 10, 28, 31], [4, 7, 13, 25, 31], [4, 7, 13, 28, 28], [4, 7, 16, 22, 31], [4, 7, 16, 25, 28], [4, 7, 19, 19, 31], [4, 7, 19, 22, 28], [4, 7, 19, 25, 25], [4, 7, 22, 22, 25], [4, 10, 10, 10, 10, 10, 10, 16], [4, 10, 10, 10, 10, 10, 13, 13], [4, 10, 10, 25, 31], [4, 10, 10, 28, 28], [4, 10, 13, 22, 31], [4, 10, 13, 25, 28], [4, 10, 16, 19, 31], [4, 10, 16, 22, 28], [4, 10, 16, 25, 25], [4, 10, 19, 19, 28], [4, 10, 19, 22, 25], [4, 10, 22, 22, 22], [4, 13, 13, 19, 31], [4, 13, 13, 22, 28], [4, 13, 13, 25, 25], [4, 13, 16, 16, 31], [4, 13, 16, 19, 28], [4, 13, 16, 22, 25], [4, 13, 19, 19, 25], [4, 13, 19, 22, 22], [4, 16, 16, 16, 28], [4, 16, 16, 19, 25], [4, 16, 16, 22, 22], [4, 16, 19, 19, 22], [4, 19, 19, 19, 19], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 10], [7, 7, 7, 7, 7, 7, 7, 31], [7, 7, 7, 7, 7, 7, 10, 28], [7, 7, 7, 7, 7, 7, 13, 25], [7, 7, 7, 7, 7, 7, 16, 22], [7, 7, 7, 7, 7, 7, 19, 19], [7, 7, 7, 7, 7, 10, 10, 25], [7, 7, 7, 7, 7, 10, 13, 22], [7, 7, 7, 7, 7, 10, 16, 19], [7, 7, 7, 7, 7, 13, 13, 19], [7, 7, 7, 7, 7, 13, 16, 16], [7, 7, 7, 7, 10, 10, 10, 22], [7, 7, 7, 7, 10, 10, 13, 19], [7, 7, 7, 7, 10, 10, 16, 16], [7, 7, 7, 7, 10, 13, 13, 16], [7, 7, 7, 7, 13, 13, 13, 13], [7, 7, 7, 10, 10, 10, 10, 19], [7, 7, 7, 10, 10, 10, 13, 16], [7, 7, 7, 10, 10, 13, 13, 13], [7, 7, 7, 28, 31], [7, 7, 10, 10, 10, 10, 10, 16], [7, 7, 10, 10, 10, 10, 13, 13], [7, 7, 10, 25, 31], [7, 7, 10, 28, 28], [7, 7, 13, 22, 31], [7, 7, 13, 25, 28], [7, 7, 16, 19, 31], [7, 7, 16, 22, 28], [7, 7, 16, 25, 25], [7, 7, 19, 19, 28], [7, 7, 19, 22, 25], [7, 7, 22, 22, 22], [7, 10, 10, 10, 10, 10, 10, 13], [7, 10, 10, 22, 31], [7, 10, 10, 25, 28], [7, 10, 13, 19, 31], [7, 10, 13, 22, 28], [7, 10, 13, 25, 25], [7, 10, 16, 16, 31], [7, 10, 16, 19, 28], [7, 10, 16, 22, 25], [7, 10, 19, 19, 25], [7, 10, 19, 22, 22], [7, 13, 13, 16, 31], [7, 13, 13, 19, 28], [7, 13, 13, 22, 25], [7, 13, 16, 16, 28], [7, 13, 16, 19, 25], [7, 13, 16, 22, 22], [7, 13, 19, 19, 22], [7, 16, 16, 16, 25], [7, 16, 16, 19, 22], [7, 16, 19, 19, 19], [10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 19, 31], [10, 10, 10, 22, 28], [10, 10, 10, 25, 25], [10, 10, 13, 16, 31], [10, 10, 13, 19, 28], [10, 10, 13, 22, 25], [10, 10, 16, 16, 28], [10, 10, 16, 19, 25], [10, 10, 16, 22, 22], [10, 10, 19, 19, 22], [10, 13, 13, 13, 31], [10, 13, 13, 16, 28], [10, 13, 13, 19, 25], [10, 13, 13, 22, 22], [10, 13, 16, 16, 25], [10, 13, 16, 19, 22], [10, 13, 19, 19, 19], [10, 16, 16, 16, 22], [10, 16, 16, 19, 19], [13, 13, 13, 13, 28], [13, 13, 13, 16, 25], [13, 13, 13, 19, 22], [13, 13, 16, 16, 22], [13, 13, 16, 19, 19], [13, 16, 16, 16, 19], [16, 16, 16, 16, 16]]\n assert candidate(candidates = [1, 4, 7, 10, 13, 16, 19],target = 50) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 10, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 10, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 13, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 10, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 19], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 7, 16], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 10, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4], [1, 1, 1, 1, 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1, 1, 1, 4, 4, 7, 7, 7, 7, 10], [1, 1, 1, 1, 4, 4, 19, 19], [1, 1, 1, 1, 4, 7, 7, 7, 7, 7, 7], [1, 1, 1, 1, 4, 7, 16, 19], [1, 1, 1, 1, 4, 10, 13, 19], [1, 1, 1, 1, 4, 10, 16, 16], [1, 1, 1, 1, 4, 13, 13, 16], [1, 1, 1, 1, 7, 7, 13, 19], [1, 1, 1, 1, 7, 7, 16, 16], [1, 1, 1, 1, 7, 10, 10, 19], [1, 1, 1, 1, 7, 10, 13, 16], [1, 1, 1, 1, 7, 13, 13, 13], [1, 1, 1, 1, 10, 10, 10, 16], [1, 1, 1, 1, 10, 10, 13, 13], [1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7], [1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 19], [1, 1, 1, 4, 4, 4, 4, 4, 4, 7, 16], [1, 1, 1, 4, 4, 4, 4, 4, 4, 10, 13], [1, 1, 1, 4, 4, 4, 4, 4, 7, 7, 13], [1, 1, 1, 4, 4, 4, 4, 4, 7, 10, 10], [1, 1, 1, 4, 4, 4, 4, 7, 7, 7, 10], [1, 1, 1, 4, 4, 4, 7, 7, 7, 7, 7], [1, 1, 1, 4, 4, 4, 16, 19], [1, 1, 1, 4, 4, 7, 13, 19], [1, 1, 1, 4, 4, 7, 16, 16], [1, 1, 1, 4, 4, 10, 10, 19], [1, 1, 1, 4, 4, 10, 13, 16], [1, 1, 1, 4, 4, 13, 13, 13], [1, 1, 1, 4, 7, 7, 10, 19], [1, 1, 1, 4, 7, 7, 13, 16], [1, 1, 1, 4, 7, 10, 10, 16], [1, 1, 1, 4, 7, 10, 13, 13], [1, 1, 1, 4, 10, 10, 10, 13], [1, 1, 1, 7, 7, 7, 7, 19], [1, 1, 1, 7, 7, 7, 10, 16], [1, 1, 1, 7, 7, 7, 13, 13], [1, 1, 1, 7, 7, 10, 10, 13], [1, 1, 1, 7, 10, 10, 10, 10], [1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 16], [1, 1, 4, 4, 4, 4, 4, 4, 4, 7, 13], [1, 1, 4, 4, 4, 4, 4, 4, 4, 10, 10], [1, 1, 4, 4, 4, 4, 4, 4, 7, 7, 10], [1, 1, 4, 4, 4, 4, 4, 7, 7, 7, 7], [1, 1, 4, 4, 4, 4, 13, 19], [1, 1, 4, 4, 4, 4, 16, 16], [1, 1, 4, 4, 4, 7, 10, 19], [1, 1, 4, 4, 4, 7, 13, 16], [1, 1, 4, 4, 4, 10, 10, 16], [1, 1, 4, 4, 4, 10, 13, 13], [1, 1, 4, 4, 7, 7, 7, 19], [1, 1, 4, 4, 7, 7, 10, 16], [1, 1, 4, 4, 7, 7, 13, 13], [1, 1, 4, 4, 7, 10, 10, 13], [1, 1, 4, 4, 10, 10, 10, 10], [1, 1, 4, 7, 7, 7, 7, 16], [1, 1, 4, 7, 7, 7, 10, 13], [1, 1, 4, 7, 7, 10, 10, 10], [1, 1, 7, 7, 7, 7, 7, 13], [1, 1, 7, 7, 7, 7, 10, 10], [1, 1, 10, 19, 19], [1, 1, 13, 16, 19], [1, 1, 16, 16, 16], [1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 13], [1, 4, 4, 4, 4, 4, 4, 4, 4, 7, 10], [1, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7], [1, 4, 4, 4, 4, 4, 10, 19], [1, 4, 4, 4, 4, 4, 13, 16], [1, 4, 4, 4, 4, 7, 7, 19], [1, 4, 4, 4, 4, 7, 10, 16], [1, 4, 4, 4, 4, 7, 13, 13], [1, 4, 4, 4, 4, 10, 10, 13], [1, 4, 4, 4, 7, 7, 7, 16], [1, 4, 4, 4, 7, 7, 10, 13], [1, 4, 4, 4, 7, 10, 10, 10], [1, 4, 4, 7, 7, 7, 7, 13], [1, 4, 4, 7, 7, 7, 10, 10], [1, 4, 7, 7, 7, 7, 7, 10], [1, 4, 7, 19, 19], [1, 4, 10, 16, 19], [1, 4, 13, 13, 19], [1, 4, 13, 16, 16], [1, 7, 7, 7, 7, 7, 7, 7], [1, 7, 7, 16, 19], [1, 7, 10, 13, 19], [1, 7, 10, 16, 16], [1, 7, 13, 13, 16], [1, 10, 10, 10, 19], [1, 10, 10, 13, 16], [1, 10, 13, 13, 13], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10], [4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7], [4, 4, 4, 4, 4, 4, 7, 19], [4, 4, 4, 4, 4, 4, 10, 16], [4, 4, 4, 4, 4, 4, 13, 13], [4, 4, 4, 4, 4, 7, 7, 16], [4, 4, 4, 4, 4, 7, 10, 13], [4, 4, 4, 4, 4, 10, 10, 10], [4, 4, 4, 4, 7, 7, 7, 13], [4, 4, 4, 4, 7, 7, 10, 10], [4, 4, 4, 7, 7, 7, 7, 10], [4, 4, 4, 19, 19], [4, 4, 7, 7, 7, 7, 7, 7], [4, 4, 7, 16, 19], [4, 4, 10, 13, 19], [4, 4, 10, 16, 16], [4, 4, 13, 13, 16], [4, 7, 7, 13, 19], [4, 7, 7, 16, 16], [4, 7, 10, 10, 19], [4, 7, 10, 13, 16], [4, 7, 13, 13, 13], [4, 10, 10, 10, 16], [4, 10, 10, 13, 13], [7, 7, 7, 10, 19], [7, 7, 7, 13, 16], [7, 7, 10, 10, 16], [7, 7, 10, 13, 13], [7, 10, 10, 10, 13], [10, 10, 10, 10, 10]]\n assert candidate(candidates = [11, 22, 33, 44, 55, 66, 77, 88, 99],target = 100) == []\n assert candidate(candidates = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],target = 100) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 35], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 40], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 35], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 45], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 40], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 35], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 25, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 50], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 15, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 35], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 45], [5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 40], [5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 35], [5, 5, 5, 5, 5, 5, 5, 5, 5, 25, 30], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 30], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 15, 25], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 40], [5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 15, 20], [5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 35], [5, 5, 5, 5, 5, 5, 5, 5, 10, 20, 30], [5, 5, 5, 5, 5, 5, 5, 5, 10, 25, 25], [5, 5, 5, 5, 5, 5, 5, 5, 10, 50], [5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 15, 15, 30], [5, 5, 5, 5, 5, 5, 5, 5, 15, 20, 25], [5, 5, 5, 5, 5, 5, 5, 5, 15, 45], [5, 5, 5, 5, 5, 5, 5, 5, 20, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 20, 40], [5, 5, 5, 5, 5, 5, 5, 5, 25, 35], [5, 5, 5, 5, 5, 5, 5, 5, 30, 30], [5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 15], [5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 25], [5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 15, 20], [5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 35], [5, 5, 5, 5, 5, 5, 5, 10, 10, 15, 15, 15], [5, 5, 5, 5, 5, 5, 5, 10, 10, 15, 30], [5, 5, 5, 5, 5, 5, 5, 10, 10, 20, 25], [5, 5, 5, 5, 5, 5, 5, 10, 10, 45], [5, 5, 5, 5, 5, 5, 5, 10, 15, 15, 25], [5, 5, 5, 5, 5, 5, 5, 10, 15, 20, 20], [5, 5, 5, 5, 5, 5, 5, 10, 15, 40], [5, 5, 5, 5, 5, 5, 5, 10, 20, 35], [5, 5, 5, 5, 5, 5, 5, 10, 25, 30], [5, 5, 5, 5, 5, 5, 5, 15, 15, 15, 20], [5, 5, 5, 5, 5, 5, 5, 15, 15, 35], [5, 5, 5, 5, 5, 5, 5, 15, 20, 30], [5, 5, 5, 5, 5, 5, 5, 15, 25, 25], [5, 5, 5, 5, 5, 5, 5, 15, 50], [5, 5, 5, 5, 5, 5, 5, 20, 20, 25], [5, 5, 5, 5, 5, 5, 5, 20, 45], [5, 5, 5, 5, 5, 5, 5, 25, 40], [5, 5, 5, 5, 5, 5, 5, 30, 35], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 15, 15], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 30], [5, 5, 5, 5, 5, 5, 10, 10, 10, 15, 25], [5, 5, 5, 5, 5, 5, 10, 10, 10, 20, 20], [5, 5, 5, 5, 5, 5, 10, 10, 10, 40], [5, 5, 5, 5, 5, 5, 10, 10, 15, 15, 20], [5, 5, 5, 5, 5, 5, 10, 10, 15, 35], [5, 5, 5, 5, 5, 5, 10, 10, 20, 30], [5, 5, 5, 5, 5, 5, 10, 10, 25, 25], [5, 5, 5, 5, 5, 5, 10, 10, 50], [5, 5, 5, 5, 5, 5, 10, 15, 15, 15, 15], [5, 5, 5, 5, 5, 5, 10, 15, 15, 30], [5, 5, 5, 5, 5, 5, 10, 15, 20, 25], [5, 5, 5, 5, 5, 5, 10, 15, 45], [5, 5, 5, 5, 5, 5, 10, 20, 20, 20], [5, 5, 5, 5, 5, 5, 10, 20, 40], [5, 5, 5, 5, 5, 5, 10, 25, 35], [5, 5, 5, 5, 5, 5, 10, 30, 30], [5, 5, 5, 5, 5, 5, 15, 15, 15, 25], [5, 5, 5, 5, 5, 5, 15, 15, 20, 20], [5, 5, 5, 5, 5, 5, 15, 15, 40], [5, 5, 5, 5, 5, 5, 15, 20, 35], [5, 5, 5, 5, 5, 5, 15, 25, 30], [5, 5, 5, 5, 5, 5, 20, 20, 30], [5, 5, 5, 5, 5, 5, 20, 25, 25], [5, 5, 5, 5, 5, 5, 20, 50], [5, 5, 5, 5, 5, 5, 25, 45], [5, 5, 5, 5, 5, 5, 30, 40], [5, 5, 5, 5, 5, 5, 35, 35], [5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 15], [5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 25], [5, 5, 5, 5, 5, 10, 10, 10, 10, 15, 20], [5, 5, 5, 5, 5, 10, 10, 10, 10, 35], [5, 5, 5, 5, 5, 10, 10, 10, 15, 15, 15], [5, 5, 5, 5, 5, 10, 10, 10, 15, 30], [5, 5, 5, 5, 5, 10, 10, 10, 20, 25], [5, 5, 5, 5, 5, 10, 10, 10, 45], [5, 5, 5, 5, 5, 10, 10, 15, 15, 25], [5, 5, 5, 5, 5, 10, 10, 15, 20, 20], [5, 5, 5, 5, 5, 10, 10, 15, 40], [5, 5, 5, 5, 5, 10, 10, 20, 35], [5, 5, 5, 5, 5, 10, 10, 25, 30], [5, 5, 5, 5, 5, 10, 15, 15, 15, 20], [5, 5, 5, 5, 5, 10, 15, 15, 35], [5, 5, 5, 5, 5, 10, 15, 20, 30], [5, 5, 5, 5, 5, 10, 15, 25, 25], [5, 5, 5, 5, 5, 10, 15, 50], [5, 5, 5, 5, 5, 10, 20, 20, 25], [5, 5, 5, 5, 5, 10, 20, 45], [5, 5, 5, 5, 5, 10, 25, 40], [5, 5, 5, 5, 5, 10, 30, 35], [5, 5, 5, 5, 5, 15, 15, 15, 15, 15], [5, 5, 5, 5, 5, 15, 15, 15, 30], [5, 5, 5, 5, 5, 15, 15, 20, 25], [5, 5, 5, 5, 5, 15, 15, 45], [5, 5, 5, 5, 5, 15, 20, 20, 20], [5, 5, 5, 5, 5, 15, 20, 40], [5, 5, 5, 5, 5, 15, 25, 35], [5, 5, 5, 5, 5, 15, 30, 30], [5, 5, 5, 5, 5, 20, 20, 35], [5, 5, 5, 5, 5, 20, 25, 30], [5, 5, 5, 5, 5, 25, 25, 25], [5, 5, 5, 5, 5, 25, 50], [5, 5, 5, 5, 5, 30, 45], [5, 5, 5, 5, 5, 35, 40], [5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 20], [5, 5, 5, 5, 10, 10, 10, 10, 10, 15, 15], [5, 5, 5, 5, 10, 10, 10, 10, 10, 30], [5, 5, 5, 5, 10, 10, 10, 10, 15, 25], [5, 5, 5, 5, 10, 10, 10, 10, 20, 20], [5, 5, 5, 5, 10, 10, 10, 10, 40], [5, 5, 5, 5, 10, 10, 10, 15, 15, 20], [5, 5, 5, 5, 10, 10, 10, 15, 35], [5, 5, 5, 5, 10, 10, 10, 20, 30], [5, 5, 5, 5, 10, 10, 10, 25, 25], [5, 5, 5, 5, 10, 10, 10, 50], [5, 5, 5, 5, 10, 10, 15, 15, 15, 15], [5, 5, 5, 5, 10, 10, 15, 15, 30], [5, 5, 5, 5, 10, 10, 15, 20, 25], [5, 5, 5, 5, 10, 10, 15, 45], [5, 5, 5, 5, 10, 10, 20, 20, 20], [5, 5, 5, 5, 10, 10, 20, 40], [5, 5, 5, 5, 10, 10, 25, 35], [5, 5, 5, 5, 10, 10, 30, 30], [5, 5, 5, 5, 10, 15, 15, 15, 25], [5, 5, 5, 5, 10, 15, 15, 20, 20], [5, 5, 5, 5, 10, 15, 15, 40], [5, 5, 5, 5, 10, 15, 20, 35], [5, 5, 5, 5, 10, 15, 25, 30], [5, 5, 5, 5, 10, 20, 20, 30], [5, 5, 5, 5, 10, 20, 25, 25], [5, 5, 5, 5, 10, 20, 50], [5, 5, 5, 5, 10, 25, 45], [5, 5, 5, 5, 10, 30, 40], [5, 5, 5, 5, 10, 35, 35], [5, 5, 5, 5, 15, 15, 15, 15, 20], [5, 5, 5, 5, 15, 15, 15, 35], [5, 5, 5, 5, 15, 15, 20, 30], [5, 5, 5, 5, 15, 15, 25, 25], [5, 5, 5, 5, 15, 15, 50], [5, 5, 5, 5, 15, 20, 20, 25], [5, 5, 5, 5, 15, 20, 45], [5, 5, 5, 5, 15, 25, 40], [5, 5, 5, 5, 15, 30, 35], [5, 5, 5, 5, 20, 20, 20, 20], [5, 5, 5, 5, 20, 20, 40], [5, 5, 5, 5, 20, 25, 35], [5, 5, 5, 5, 20, 30, 30], [5, 5, 5, 5, 25, 25, 30], [5, 5, 5, 5, 30, 50], [5, 5, 5, 5, 35, 45], [5, 5, 5, 5, 40, 40], [5, 5, 5, 10, 10, 10, 10, 10, 10, 10, 15], [5, 5, 5, 10, 10, 10, 10, 10, 10, 25], [5, 5, 5, 10, 10, 10, 10, 10, 15, 20], [5, 5, 5, 10, 10, 10, 10, 10, 35], [5, 5, 5, 10, 10, 10, 10, 15, 15, 15], [5, 5, 5, 10, 10, 10, 10, 15, 30], [5, 5, 5, 10, 10, 10, 10, 20, 25], [5, 5, 5, 10, 10, 10, 10, 45], [5, 5, 5, 10, 10, 10, 15, 15, 25], [5, 5, 5, 10, 10, 10, 15, 20, 20], [5, 5, 5, 10, 10, 10, 15, 40], [5, 5, 5, 10, 10, 10, 20, 35], [5, 5, 5, 10, 10, 10, 25, 30], [5, 5, 5, 10, 10, 15, 15, 15, 20], [5, 5, 5, 10, 10, 15, 15, 35], [5, 5, 5, 10, 10, 15, 20, 30], [5, 5, 5, 10, 10, 15, 25, 25], [5, 5, 5, 10, 10, 15, 50], [5, 5, 5, 10, 10, 20, 20, 25], [5, 5, 5, 10, 10, 20, 45], [5, 5, 5, 10, 10, 25, 40], [5, 5, 5, 10, 10, 30, 35], [5, 5, 5, 10, 15, 15, 15, 15, 15], [5, 5, 5, 10, 15, 15, 15, 30], [5, 5, 5, 10, 15, 15, 20, 25], [5, 5, 5, 10, 15, 15, 45], [5, 5, 5, 10, 15, 20, 20, 20], [5, 5, 5, 10, 15, 20, 40], [5, 5, 5, 10, 15, 25, 35], [5, 5, 5, 10, 15, 30, 30], [5, 5, 5, 10, 20, 20, 35], [5, 5, 5, 10, 20, 25, 30], [5, 5, 5, 10, 25, 25, 25], [5, 5, 5, 10, 25, 50], [5, 5, 5, 10, 30, 45], [5, 5, 5, 10, 35, 40], [5, 5, 5, 15, 15, 15, 15, 25], [5, 5, 5, 15, 15, 15, 20, 20], [5, 5, 5, 15, 15, 15, 40], [5, 5, 5, 15, 15, 20, 35], [5, 5, 5, 15, 15, 25, 30], [5, 5, 5, 15, 20, 20, 30], [5, 5, 5, 15, 20, 25, 25], [5, 5, 5, 15, 20, 50], [5, 5, 5, 15, 25, 45], [5, 5, 5, 15, 30, 40], [5, 5, 5, 15, 35, 35], [5, 5, 5, 20, 20, 20, 25], [5, 5, 5, 20, 20, 45], [5, 5, 5, 20, 25, 40], [5, 5, 5, 20, 30, 35], [5, 5, 5, 25, 25, 35], [5, 5, 5, 25, 30, 30], [5, 5, 5, 35, 50], [5, 5, 5, 40, 45], [5, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10], [5, 5, 10, 10, 10, 10, 10, 10, 10, 20], [5, 5, 10, 10, 10, 10, 10, 10, 15, 15], [5, 5, 10, 10, 10, 10, 10, 10, 30], [5, 5, 10, 10, 10, 10, 10, 15, 25], [5, 5, 10, 10, 10, 10, 10, 20, 20], [5, 5, 10, 10, 10, 10, 10, 40], [5, 5, 10, 10, 10, 10, 15, 15, 20], [5, 5, 10, 10, 10, 10, 15, 35], [5, 5, 10, 10, 10, 10, 20, 30], [5, 5, 10, 10, 10, 10, 25, 25], [5, 5, 10, 10, 10, 10, 50], [5, 5, 10, 10, 10, 15, 15, 15, 15], [5, 5, 10, 10, 10, 15, 15, 30], [5, 5, 10, 10, 10, 15, 20, 25], [5, 5, 10, 10, 10, 15, 45], [5, 5, 10, 10, 10, 20, 20, 20], [5, 5, 10, 10, 10, 20, 40], [5, 5, 10, 10, 10, 25, 35], [5, 5, 10, 10, 10, 30, 30], [5, 5, 10, 10, 15, 15, 15, 25], [5, 5, 10, 10, 15, 15, 20, 20], [5, 5, 10, 10, 15, 15, 40], [5, 5, 10, 10, 15, 20, 35], [5, 5, 10, 10, 15, 25, 30], [5, 5, 10, 10, 20, 20, 30], [5, 5, 10, 10, 20, 25, 25], [5, 5, 10, 10, 20, 50], [5, 5, 10, 10, 25, 45], [5, 5, 10, 10, 30, 40], [5, 5, 10, 10, 35, 35], [5, 5, 10, 15, 15, 15, 15, 20], [5, 5, 10, 15, 15, 15, 35], [5, 5, 10, 15, 15, 20, 30], [5, 5, 10, 15, 15, 25, 25], [5, 5, 10, 15, 15, 50], [5, 5, 10, 15, 20, 20, 25], [5, 5, 10, 15, 20, 45], [5, 5, 10, 15, 25, 40], [5, 5, 10, 15, 30, 35], [5, 5, 10, 20, 20, 20, 20], [5, 5, 10, 20, 20, 40], [5, 5, 10, 20, 25, 35], [5, 5, 10, 20, 30, 30], [5, 5, 10, 25, 25, 30], [5, 5, 10, 30, 50], [5, 5, 10, 35, 45], [5, 5, 10, 40, 40], [5, 5, 15, 15, 15, 15, 15, 15], [5, 5, 15, 15, 15, 15, 30], [5, 5, 15, 15, 15, 20, 25], [5, 5, 15, 15, 15, 45], [5, 5, 15, 15, 20, 20, 20], [5, 5, 15, 15, 20, 40], [5, 5, 15, 15, 25, 35], [5, 5, 15, 15, 30, 30], [5, 5, 15, 20, 20, 35], [5, 5, 15, 20, 25, 30], [5, 5, 15, 25, 25, 25], [5, 5, 15, 25, 50], [5, 5, 15, 30, 45], [5, 5, 15, 35, 40], [5, 5, 20, 20, 20, 30], [5, 5, 20, 20, 25, 25], [5, 5, 20, 20, 50], [5, 5, 20, 25, 45], [5, 5, 20, 30, 40], [5, 5, 20, 35, 35], [5, 5, 25, 25, 40], [5, 5, 25, 30, 35], [5, 5, 30, 30, 30], [5, 5, 40, 50], [5, 5, 45, 45], [5, 10, 10, 10, 10, 10, 10, 10, 10, 15], [5, 10, 10, 10, 10, 10, 10, 10, 25], [5, 10, 10, 10, 10, 10, 10, 15, 20], [5, 10, 10, 10, 10, 10, 10, 35], [5, 10, 10, 10, 10, 10, 15, 15, 15], [5, 10, 10, 10, 10, 10, 15, 30], [5, 10, 10, 10, 10, 10, 20, 25], [5, 10, 10, 10, 10, 10, 45], [5, 10, 10, 10, 10, 15, 15, 25], [5, 10, 10, 10, 10, 15, 20, 20], [5, 10, 10, 10, 10, 15, 40], [5, 10, 10, 10, 10, 20, 35], [5, 10, 10, 10, 10, 25, 30], [5, 10, 10, 10, 15, 15, 15, 20], [5, 10, 10, 10, 15, 15, 35], [5, 10, 10, 10, 15, 20, 30], [5, 10, 10, 10, 15, 25, 25], [5, 10, 10, 10, 15, 50], [5, 10, 10, 10, 20, 20, 25], [5, 10, 10, 10, 20, 45], [5, 10, 10, 10, 25, 40], [5, 10, 10, 10, 30, 35], [5, 10, 10, 15, 15, 15, 15, 15], [5, 10, 10, 15, 15, 15, 30], [5, 10, 10, 15, 15, 20, 25], [5, 10, 10, 15, 15, 45], [5, 10, 10, 15, 20, 20, 20], [5, 10, 10, 15, 20, 40], [5, 10, 10, 15, 25, 35], [5, 10, 10, 15, 30, 30], [5, 10, 10, 20, 20, 35], [5, 10, 10, 20, 25, 30], [5, 10, 10, 25, 25, 25], [5, 10, 10, 25, 50], [5, 10, 10, 30, 45], [5, 10, 10, 35, 40], [5, 10, 15, 15, 15, 15, 25], [5, 10, 15, 15, 15, 20, 20], [5, 10, 15, 15, 15, 40], [5, 10, 15, 15, 20, 35], [5, 10, 15, 15, 25, 30], [5, 10, 15, 20, 20, 30], [5, 10, 15, 20, 25, 25], [5, 10, 15, 20, 50], [5, 10, 15, 25, 45], [5, 10, 15, 30, 40], [5, 10, 15, 35, 35], [5, 10, 20, 20, 20, 25], [5, 10, 20, 20, 45], [5, 10, 20, 25, 40], [5, 10, 20, 30, 35], [5, 10, 25, 25, 35], [5, 10, 25, 30, 30], [5, 10, 35, 50], [5, 10, 40, 45], [5, 15, 15, 15, 15, 15, 20], [5, 15, 15, 15, 15, 35], [5, 15, 15, 15, 20, 30], [5, 15, 15, 15, 25, 25], [5, 15, 15, 15, 50], [5, 15, 15, 20, 20, 25], [5, 15, 15, 20, 45], [5, 15, 15, 25, 40], [5, 15, 15, 30, 35], [5, 15, 20, 20, 20, 20], [5, 15, 20, 20, 40], [5, 15, 20, 25, 35], [5, 15, 20, 30, 30], [5, 15, 25, 25, 30], [5, 15, 30, 50], [5, 15, 35, 45], [5, 15, 40, 40], [5, 20, 20, 20, 35], [5, 20, 20, 25, 30], [5, 20, 25, 25, 25], [5, 20, 25, 50], [5, 20, 30, 45], [5, 20, 35, 40], [5, 25, 25, 45], [5, 25, 30, 40], [5, 25, 35, 35], [5, 30, 30, 35], [5, 45, 50], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 10, 10, 10, 15, 15], [10, 10, 10, 10, 10, 10, 10, 30], [10, 10, 10, 10, 10, 10, 15, 25], [10, 10, 10, 10, 10, 10, 20, 20], [10, 10, 10, 10, 10, 10, 40], [10, 10, 10, 10, 10, 15, 15, 20], [10, 10, 10, 10, 10, 15, 35], [10, 10, 10, 10, 10, 20, 30], [10, 10, 10, 10, 10, 25, 25], [10, 10, 10, 10, 10, 50], [10, 10, 10, 10, 15, 15, 15, 15], [10, 10, 10, 10, 15, 15, 30], [10, 10, 10, 10, 15, 20, 25], [10, 10, 10, 10, 15, 45], [10, 10, 10, 10, 20, 20, 20], [10, 10, 10, 10, 20, 40], [10, 10, 10, 10, 25, 35], [10, 10, 10, 10, 30, 30], [10, 10, 10, 15, 15, 15, 25], [10, 10, 10, 15, 15, 20, 20], [10, 10, 10, 15, 15, 40], [10, 10, 10, 15, 20, 35], [10, 10, 10, 15, 25, 30], [10, 10, 10, 20, 20, 30], [10, 10, 10, 20, 25, 25], [10, 10, 10, 20, 50], [10, 10, 10, 25, 45], [10, 10, 10, 30, 40], [10, 10, 10, 35, 35], [10, 10, 15, 15, 15, 15, 20], [10, 10, 15, 15, 15, 35], [10, 10, 15, 15, 20, 30], [10, 10, 15, 15, 25, 25], [10, 10, 15, 15, 50], [10, 10, 15, 20, 20, 25], [10, 10, 15, 20, 45], [10, 10, 15, 25, 40], [10, 10, 15, 30, 35], [10, 10, 20, 20, 20, 20], [10, 10, 20, 20, 40], [10, 10, 20, 25, 35], [10, 10, 20, 30, 30], [10, 10, 25, 25, 30], [10, 10, 30, 50], [10, 10, 35, 45], [10, 10, 40, 40], [10, 15, 15, 15, 15, 15, 15], [10, 15, 15, 15, 15, 30], [10, 15, 15, 15, 20, 25], [10, 15, 15, 15, 45], [10, 15, 15, 20, 20, 20], [10, 15, 15, 20, 40], [10, 15, 15, 25, 35], [10, 15, 15, 30, 30], [10, 15, 20, 20, 35], [10, 15, 20, 25, 30], [10, 15, 25, 25, 25], [10, 15, 25, 50], [10, 15, 30, 45], [10, 15, 35, 40], [10, 20, 20, 20, 30], [10, 20, 20, 25, 25], [10, 20, 20, 50], [10, 20, 25, 45], [10, 20, 30, 40], [10, 20, 35, 35], [10, 25, 25, 40], [10, 25, 30, 35], [10, 30, 30, 30], [10, 40, 50], [10, 45, 45], [15, 15, 15, 15, 15, 25], [15, 15, 15, 15, 20, 20], [15, 15, 15, 15, 40], [15, 15, 15, 20, 35], [15, 15, 15, 25, 30], [15, 15, 20, 20, 30], [15, 15, 20, 25, 25], [15, 15, 20, 50], [15, 15, 25, 45], [15, 15, 30, 40], [15, 15, 35, 35], [15, 20, 20, 20, 25], [15, 20, 20, 45], [15, 20, 25, 40], [15, 20, 30, 35], [15, 25, 25, 35], [15, 25, 30, 30], [15, 35, 50], [15, 40, 45], [20, 20, 20, 20, 20], [20, 20, 20, 40], [20, 20, 25, 35], [20, 20, 30, 30], [20, 25, 25, 30], [20, 30, 50], [20, 35, 45], [20, 40, 40], [25, 25, 25, 25], [25, 25, 50], [25, 30, 45], [25, 35, 40], [30, 30, 40], [30, 35, 35], [50, 50]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13],target = 20) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 3, 9], [1, 1, 1, 1, 1, 1, 1, 1, 5, 7], [1, 1, 1, 1, 1, 1, 1, 3, 3, 7], [1, 1, 1, 1, 1, 1, 1, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 13], [1, 1, 1, 1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 3, 11], [1, 1, 1, 1, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 3, 3, 9], [1, 1, 1, 1, 1, 3, 5, 7], [1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 3, 3, 3, 7], [1, 1, 1, 1, 3, 3, 5, 5], [1, 1, 1, 1, 3, 13], [1, 1, 1, 1, 5, 11], [1, 1, 1, 1, 7, 9], [1, 1, 1, 3, 3, 3, 3, 5], [1, 1, 1, 3, 3, 11], [1, 1, 1, 3, 5, 9], [1, 1, 1, 3, 7, 7], [1, 1, 1, 5, 5, 7], [1, 1, 3, 3, 3, 3, 3, 3], [1, 1, 3, 3, 3, 9], [1, 1, 3, 3, 5, 7], [1, 1, 3, 5, 5, 5], [1, 1, 5, 13], [1, 1, 7, 11], [1, 1, 9, 9], [1, 3, 3, 3, 3, 7], [1, 3, 3, 3, 5, 5], [1, 3, 3, 13], [1, 3, 5, 11], [1, 3, 7, 9], [1, 5, 5, 9], [1, 5, 7, 7], [3, 3, 3, 3, 3, 5], [3, 3, 3, 11], [3, 3, 5, 9], [3, 3, 7, 7], [3, 5, 5, 7], [5, 5, 5, 5], [7, 13], [9, 11]]\n assert candidate(candidates = [6, 13, 17, 19, 23, 29, 31],target = 65) == [[6, 6, 6, 6, 6, 6, 6, 6, 17], [6, 6, 6, 6, 6, 6, 6, 23], [6, 6, 6, 6, 6, 6, 29], [6, 6, 6, 13, 17, 17], [6, 6, 13, 17, 23], [6, 6, 17, 17, 19], [6, 13, 17, 29], [6, 13, 23, 23], [6, 17, 19, 23], [13, 13, 13, 13, 13], [13, 23, 29], [17, 17, 31], [17, 19, 29], [19, 23, 23]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 18) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6], [1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 2, 8], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 4, 6], [1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 10], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 1, 1, 1, 1, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 2, 3, 6], [1, 1, 1, 1, 1, 1, 1, 2, 4, 5], [1, 1, 1, 1, 1, 1, 1, 2, 9], [1, 1, 1, 1, 1, 1, 1, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 3, 4, 4], [1, 1, 1, 1, 1, 1, 1, 3, 8], [1, 1, 1, 1, 1, 1, 1, 4, 7], [1, 1, 1, 1, 1, 1, 1, 5, 6], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4], [1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 1, 1, 1, 2, 2, 2, 6], [1, 1, 1, 1, 1, 1, 2, 2, 3, 5], [1, 1, 1, 1, 1, 1, 2, 2, 4, 4], [1, 1, 1, 1, 1, 1, 2, 2, 8], [1, 1, 1, 1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 1, 1, 1, 2, 3, 7], [1, 1, 1, 1, 1, 1, 2, 4, 6], [1, 1, 1, 1, 1, 1, 2, 5, 5], [1, 1, 1, 1, 1, 1, 2, 10], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 3, 3, 6], [1, 1, 1, 1, 1, 1, 3, 4, 5], [1, 1, 1, 1, 1, 1, 3, 9], [1, 1, 1, 1, 1, 1, 4, 4, 4], [1, 1, 1, 1, 1, 1, 4, 8], [1, 1, 1, 1, 1, 1, 5, 7], [1, 1, 1, 1, 1, 1, 6, 6], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3], [1, 1, 1, 1, 1, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 1, 1, 2, 2, 2, 7], [1, 1, 1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 1, 1, 2, 2, 3, 6], [1, 1, 1, 1, 1, 2, 2, 4, 5], [1, 1, 1, 1, 1, 2, 2, 9], [1, 1, 1, 1, 1, 2, 3, 3, 5], [1, 1, 1, 1, 1, 2, 3, 4, 4], [1, 1, 1, 1, 1, 2, 3, 8], [1, 1, 1, 1, 1, 2, 4, 7], [1, 1, 1, 1, 1, 2, 5, 6], [1, 1, 1, 1, 1, 3, 3, 3, 4], [1, 1, 1, 1, 1, 3, 3, 7], [1, 1, 1, 1, 1, 3, 4, 6], [1, 1, 1, 1, 1, 3, 5, 5], [1, 1, 1, 1, 1, 3, 10], [1, 1, 1, 1, 1, 4, 4, 5], [1, 1, 1, 1, 1, 4, 9], [1, 1, 1, 1, 1, 5, 8], [1, 1, 1, 1, 1, 6, 7], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2, 2, 4], [1, 1, 1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 1, 1, 2, 2, 2, 2, 6], [1, 1, 1, 1, 2, 2, 2, 3, 5], [1, 1, 1, 1, 2, 2, 2, 4, 4], [1, 1, 1, 1, 2, 2, 2, 8], [1, 1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 1, 2, 2, 3, 7], [1, 1, 1, 1, 2, 2, 4, 6], [1, 1, 1, 1, 2, 2, 5, 5], [1, 1, 1, 1, 2, 2, 10], [1, 1, 1, 1, 2, 3, 3, 3, 3], [1, 1, 1, 1, 2, 3, 3, 6], [1, 1, 1, 1, 2, 3, 4, 5], [1, 1, 1, 1, 2, 3, 9], [1, 1, 1, 1, 2, 4, 4, 4], [1, 1, 1, 1, 2, 4, 8], [1, 1, 1, 1, 2, 5, 7], [1, 1, 1, 1, 2, 6, 6], [1, 1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 1, 3, 3, 4, 4], [1, 1, 1, 1, 3, 3, 8], [1, 1, 1, 1, 3, 4, 7], [1, 1, 1, 1, 3, 5, 6], [1, 1, 1, 1, 4, 4, 6], [1, 1, 1, 1, 4, 5, 5], [1, 1, 1, 1, 4, 10], [1, 1, 1, 1, 5, 9], [1, 1, 1, 1, 6, 8], [1, 1, 1, 1, 7, 7], [1, 1, 1, 2, 2, 2, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 2, 2, 5], [1, 1, 1, 2, 2, 2, 2, 3, 4], [1, 1, 1, 2, 2, 2, 2, 7], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 6], [1, 1, 1, 2, 2, 2, 4, 5], [1, 1, 1, 2, 2, 2, 9], [1, 1, 1, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 3, 8], [1, 1, 1, 2, 2, 4, 7], [1, 1, 1, 2, 2, 5, 6], [1, 1, 1, 2, 3, 3, 3, 4], [1, 1, 1, 2, 3, 3, 7], [1, 1, 1, 2, 3, 4, 6], [1, 1, 1, 2, 3, 5, 5], [1, 1, 1, 2, 3, 10], [1, 1, 1, 2, 4, 4, 5], [1, 1, 1, 2, 4, 9], [1, 1, 1, 2, 5, 8], [1, 1, 1, 2, 6, 7], [1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 3, 3, 3, 6], [1, 1, 1, 3, 3, 4, 5], [1, 1, 1, 3, 3, 9], [1, 1, 1, 3, 4, 4, 4], [1, 1, 1, 3, 4, 8], [1, 1, 1, 3, 5, 7], [1, 1, 1, 3, 6, 6], [1, 1, 1, 4, 4, 7], [1, 1, 1, 4, 5, 6], [1, 1, 1, 5, 5, 5], [1, 1, 1, 5, 10], [1, 1, 1, 6, 9], [1, 1, 1, 7, 8], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2, 4], [1, 1, 2, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 2, 6], [1, 1, 2, 2, 2, 2, 3, 5], [1, 1, 2, 2, 2, 2, 4, 4], [1, 1, 2, 2, 2, 2, 8], [1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 2, 2, 2, 3, 7], [1, 1, 2, 2, 2, 4, 6], [1, 1, 2, 2, 2, 5, 5], [1, 1, 2, 2, 2, 10], [1, 1, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 3, 3, 6], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 9], [1, 1, 2, 2, 4, 4, 4], [1, 1, 2, 2, 4, 8], [1, 1, 2, 2, 5, 7], [1, 1, 2, 2, 6, 6], [1, 1, 2, 3, 3, 3, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 8], [1, 1, 2, 3, 4, 7], [1, 1, 2, 3, 5, 6], [1, 1, 2, 4, 4, 6], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 10], [1, 1, 2, 5, 9], [1, 1, 2, 6, 8], [1, 1, 2, 7, 7], [1, 1, 3, 3, 3, 3, 4], [1, 1, 3, 3, 3, 7], [1, 1, 3, 3, 4, 6], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 10], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 9], [1, 1, 3, 5, 8], [1, 1, 3, 6, 7], [1, 1, 4, 4, 4, 4], [1, 1, 4, 4, 8], [1, 1, 4, 5, 7], [1, 1, 4, 6, 6], [1, 1, 5, 5, 6], [1, 1, 6, 10], [1, 1, 7, 9], [1, 1, 8, 8], [1, 2, 2, 2, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2, 2, 5], [1, 2, 2, 2, 2, 2, 3, 4], [1, 2, 2, 2, 2, 2, 7], [1, 2, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 3, 6], [1, 2, 2, 2, 2, 4, 5], [1, 2, 2, 2, 2, 9], [1, 2, 2, 2, 3, 3, 5], [1, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 3, 8], [1, 2, 2, 2, 4, 7], [1, 2, 2, 2, 5, 6], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 7], [1, 2, 2, 3, 4, 6], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 10], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 9], [1, 2, 2, 5, 8], [1, 2, 2, 6, 7], [1, 2, 3, 3, 3, 3, 3], [1, 2, 3, 3, 3, 6], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 9], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 8], [1, 2, 3, 5, 7], [1, 2, 3, 6, 6], [1, 2, 4, 4, 7], [1, 2, 4, 5, 6], [1, 2, 5, 5, 5], [1, 2, 5, 10], [1, 2, 6, 9], [1, 2, 7, 8], [1, 3, 3, 3, 3, 5], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 8], [1, 3, 3, 4, 7], [1, 3, 3, 5, 6], [1, 3, 4, 4, 6], [1, 3, 4, 5, 5], [1, 3, 4, 10], [1, 3, 5, 9], [1, 3, 6, 8], [1, 3, 7, 7], [1, 4, 4, 4, 5], [1, 4, 4, 9], [1, 4, 5, 8], [1, 4, 6, 7], [1, 5, 5, 7], [1, 5, 6, 6], [1, 7, 10], [1, 8, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 4, 4], [2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 3, 3, 4], [2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 4, 6], [2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 10], [2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 3, 3, 6], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 9], [2, 2, 2, 4, 4, 4], [2, 2, 2, 4, 8], [2, 2, 2, 5, 7], [2, 2, 2, 6, 6], [2, 2, 3, 3, 3, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 8], [2, 2, 3, 4, 7], [2, 2, 3, 5, 6], [2, 2, 4, 4, 6], [2, 2, 4, 5, 5], [2, 2, 4, 10], [2, 2, 5, 9], [2, 2, 6, 8], [2, 2, 7, 7], [2, 3, 3, 3, 3, 4], [2, 3, 3, 3, 7], [2, 3, 3, 4, 6], [2, 3, 3, 5, 5], [2, 3, 3, 10], [2, 3, 4, 4, 5], [2, 3, 4, 9], [2, 3, 5, 8], [2, 3, 6, 7], [2, 4, 4, 4, 4], [2, 4, 4, 8], [2, 4, 5, 7], [2, 4, 6, 6], [2, 5, 5, 6], [2, 6, 10], [2, 7, 9], [2, 8, 8], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 6], [3, 3, 3, 4, 5], [3, 3, 3, 9], [3, 3, 4, 4, 4], [3, 3, 4, 8], [3, 3, 5, 7], [3, 3, 6, 6], [3, 4, 4, 7], [3, 4, 5, 6], [3, 5, 5, 5], [3, 5, 10], [3, 6, 9], [3, 7, 8], [4, 4, 4, 6], [4, 4, 5, 5], [4, 4, 10], [4, 5, 9], [4, 6, 8], [4, 7, 7], [5, 5, 8], [5, 6, 7], [6, 6, 6], [8, 10], [9, 9]]\n assert candidate(candidates = [2, 5, 10, 20, 50],target = 100) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 20, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 20, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 20, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 20, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 20, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 10, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 20, 20, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 20, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20, 20, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 50], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 10, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10, 50], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 20, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 10, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10, 50], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 20, 20, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 20, 50], [2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 10, 20, 20], [2, 2, 2, 2, 2, 5, 5, 10, 10, 10, 50], [2, 2, 2, 2, 2, 5, 5, 10, 10, 20, 20, 20], [2, 2, 2, 2, 2, 5, 5, 10, 20, 50], [2, 2, 2, 2, 2, 5, 5, 20, 20, 20, 20], [2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10, 10, 10, 10], [2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 10, 10, 20], [2, 2, 2, 2, 2, 10, 10, 10, 10, 10, 20, 20], [2, 2, 2, 2, 2, 10, 10, 10, 10, 50], [2, 2, 2, 2, 2, 10, 10, 10, 20, 20, 20], [2, 2, 2, 2, 2, 10, 10, 20, 50], [2, 2, 2, 2, 2, 10, 20, 20, 20, 20], [2, 2, 2, 2, 2, 20, 20, 50], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 50], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 10, 50], [5, 5, 5, 5, 5, 5, 5, 5, 20, 20, 20], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 10, 10, 10, 20, 20], [5, 5, 5, 5, 5, 5, 10, 10, 50], [5, 5, 5, 5, 5, 5, 10, 20, 20, 20], [5, 5, 5, 5, 5, 5, 20, 50], [5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 20], [5, 5, 5, 5, 10, 10, 10, 10, 20, 20], [5, 5, 5, 5, 10, 10, 10, 50], [5, 5, 5, 5, 10, 10, 20, 20, 20], [5, 5, 5, 5, 10, 20, 50], [5, 5, 5, 5, 20, 20, 20, 20], [5, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10], [5, 5, 10, 10, 10, 10, 10, 10, 10, 20], [5, 5, 10, 10, 10, 10, 10, 20, 20], [5, 5, 10, 10, 10, 10, 50], [5, 5, 10, 10, 10, 20, 20, 20], [5, 5, 10, 10, 20, 50], [5, 5, 10, 20, 20, 20, 20], [5, 5, 20, 20, 50], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 10, 10, 20, 20], [10, 10, 10, 10, 10, 50], [10, 10, 10, 10, 20, 20, 20], [10, 10, 10, 20, 50], [10, 10, 20, 20, 20, 20], [10, 20, 20, 50], [20, 20, 20, 20, 20], [50, 50]]\n assert candidate(candidates = [2, 5, 10, 15, 20, 25],target = 40) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 15], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 5, 5, 5, 15], [2, 2, 2, 2, 2, 5, 5, 10, 10], [2, 2, 2, 2, 2, 5, 5, 20], [2, 2, 2, 2, 2, 5, 10, 15], [2, 2, 2, 2, 2, 5, 25], [2, 2, 2, 2, 2, 10, 10, 10], [2, 2, 2, 2, 2, 10, 20], [2, 2, 2, 2, 2, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 20], [5, 5, 5, 10, 15], [5, 5, 5, 25], [5, 5, 10, 10, 10], [5, 5, 10, 20], [5, 5, 15, 15], [5, 10, 10, 15], [5, 10, 25], [5, 15, 20], [10, 10, 10, 10], [10, 10, 20], [10, 15, 15], [15, 25], [20, 20]]\n assert candidate(candidates = [13, 17, 19, 23, 29, 31, 37],target = 60) == [[13, 13, 17, 17], [23, 37], [29, 31]]\n assert candidate(candidates = [10, 20, 30, 40, 50],target = 100) == [[10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 10, 10, 10, 30], [10, 10, 10, 10, 10, 10, 20, 20], [10, 10, 10, 10, 10, 10, 40], [10, 10, 10, 10, 10, 20, 30], [10, 10, 10, 10, 10, 50], [10, 10, 10, 10, 20, 20, 20], [10, 10, 10, 10, 20, 40], [10, 10, 10, 10, 30, 30], [10, 10, 10, 20, 20, 30], [10, 10, 10, 20, 50], [10, 10, 10, 30, 40], [10, 10, 20, 20, 20, 20], [10, 10, 20, 20, 40], [10, 10, 20, 30, 30], [10, 10, 30, 50], [10, 10, 40, 40], [10, 20, 20, 20, 30], [10, 20, 20, 50], [10, 20, 30, 40], [10, 30, 30, 30], [10, 40, 50], [20, 20, 20, 20, 20], [20, 20, 20, 40], [20, 20, 30, 30], [20, 30, 50], [20, 40, 40], [30, 30, 40], [50, 50]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 20) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 3, 9], [1, 1, 1, 1, 1, 1, 1, 1, 5, 7], [1, 1, 1, 1, 1, 1, 1, 3, 3, 7], [1, 1, 1, 1, 1, 1, 1, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 13], [1, 1, 1, 1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 3, 11], [1, 1, 1, 1, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 3, 3, 9], [1, 1, 1, 1, 1, 3, 5, 7], [1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 1, 15], [1, 1, 1, 1, 3, 3, 3, 7], [1, 1, 1, 1, 3, 3, 5, 5], [1, 1, 1, 1, 3, 13], [1, 1, 1, 1, 5, 11], [1, 1, 1, 1, 7, 9], [1, 1, 1, 3, 3, 3, 3, 5], [1, 1, 1, 3, 3, 11], [1, 1, 1, 3, 5, 9], [1, 1, 1, 3, 7, 7], [1, 1, 1, 5, 5, 7], [1, 1, 1, 17], [1, 1, 3, 3, 3, 3, 3, 3], [1, 1, 3, 3, 3, 9], [1, 1, 3, 3, 5, 7], [1, 1, 3, 5, 5, 5], [1, 1, 3, 15], [1, 1, 5, 13], [1, 1, 7, 11], [1, 1, 9, 9], [1, 3, 3, 3, 3, 7], [1, 3, 3, 3, 5, 5], [1, 3, 3, 13], [1, 3, 5, 11], [1, 3, 7, 9], [1, 5, 5, 9], [1, 5, 7, 7], [1, 19], [3, 3, 3, 3, 3, 5], [3, 3, 3, 11], [3, 3, 5, 9], [3, 3, 7, 7], [3, 5, 5, 7], [3, 17], [5, 5, 5, 5], [5, 15], [7, 13], [9, 11]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 20) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 6], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 6], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 6], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 8], [1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 6], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 2, 10], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 6], [1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 5], [1, 1, 1, 1, 1, 1, 1, 1, 3, 9], [1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4], [1, 1, 1, 1, 1, 1, 1, 1, 4, 8], [1, 1, 1, 1, 1, 1, 1, 1, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 6, 6], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 6], [1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 5], [1, 1, 1, 1, 1, 1, 1, 2, 2, 9], [1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4], [1, 1, 1, 1, 1, 1, 1, 2, 3, 8], [1, 1, 1, 1, 1, 1, 1, 2, 4, 7], [1, 1, 1, 1, 1, 1, 1, 2, 5, 6], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 4], [1, 1, 1, 1, 1, 1, 1, 3, 3, 7], [1, 1, 1, 1, 1, 1, 1, 3, 4, 6], [1, 1, 1, 1, 1, 1, 1, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 3, 10], [1, 1, 1, 1, 1, 1, 1, 4, 4, 5], [1, 1, 1, 1, 1, 1, 1, 4, 9], [1, 1, 1, 1, 1, 1, 1, 5, 8], [1, 1, 1, 1, 1, 1, 1, 6, 7], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 4], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 6], [1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 5], [1, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4], [1, 1, 1, 1, 1, 1, 2, 2, 2, 8], [1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 1, 1, 1, 2, 2, 3, 7], [1, 1, 1, 1, 1, 1, 2, 2, 4, 6], [1, 1, 1, 1, 1, 1, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 2, 2, 10], [1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 2, 3, 3, 6], [1, 1, 1, 1, 1, 1, 2, 3, 4, 5], [1, 1, 1, 1, 1, 1, 2, 3, 9], [1, 1, 1, 1, 1, 1, 2, 4, 4, 4], [1, 1, 1, 1, 1, 1, 2, 4, 8], [1, 1, 1, 1, 1, 1, 2, 5, 7], [1, 1, 1, 1, 1, 1, 2, 6, 6], [1, 1, 1, 1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 3, 3, 4, 4], [1, 1, 1, 1, 1, 1, 3, 3, 8], [1, 1, 1, 1, 1, 1, 3, 4, 7], [1, 1, 1, 1, 1, 1, 3, 5, 6], [1, 1, 1, 1, 1, 1, 4, 4, 6], [1, 1, 1, 1, 1, 1, 4, 5, 5], [1, 1, 1, 1, 1, 1, 4, 10], [1, 1, 1, 1, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 6, 8], [1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4], [1, 1, 1, 1, 1, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 1, 1, 2, 2, 2, 3, 6], [1, 1, 1, 1, 1, 2, 2, 2, 4, 5], [1, 1, 1, 1, 1, 2, 2, 2, 9], [1, 1, 1, 1, 1, 2, 2, 3, 3, 5], [1, 1, 1, 1, 1, 2, 2, 3, 4, 4], [1, 1, 1, 1, 1, 2, 2, 3, 8], [1, 1, 1, 1, 1, 2, 2, 4, 7], [1, 1, 1, 1, 1, 2, 2, 5, 6], [1, 1, 1, 1, 1, 2, 3, 3, 3, 4], [1, 1, 1, 1, 1, 2, 3, 3, 7], [1, 1, 1, 1, 1, 2, 3, 4, 6], [1, 1, 1, 1, 1, 2, 3, 5, 5], [1, 1, 1, 1, 1, 2, 3, 10], [1, 1, 1, 1, 1, 2, 4, 4, 5], [1, 1, 1, 1, 1, 2, 4, 9], [1, 1, 1, 1, 1, 2, 5, 8], [1, 1, 1, 1, 1, 2, 6, 7], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 3, 3, 3, 6], [1, 1, 1, 1, 1, 3, 3, 4, 5], [1, 1, 1, 1, 1, 3, 3, 9], [1, 1, 1, 1, 1, 3, 4, 4, 4], [1, 1, 1, 1, 1, 3, 4, 8], [1, 1, 1, 1, 1, 3, 5, 7], [1, 1, 1, 1, 1, 3, 6, 6], [1, 1, 1, 1, 1, 4, 4, 7], [1, 1, 1, 1, 1, 4, 5, 6], [1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 1, 5, 10], [1, 1, 1, 1, 1, 6, 9], [1, 1, 1, 1, 1, 7, 8], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 4], [1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3], [1, 1, 1, 1, 2, 2, 2, 2, 2, 6], [1, 1, 1, 1, 2, 2, 2, 2, 3, 5], [1, 1, 1, 1, 2, 2, 2, 2, 4, 4], [1, 1, 1, 1, 2, 2, 2, 2, 8], [1, 1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 1, 2, 2, 2, 3, 7], [1, 1, 1, 1, 2, 2, 2, 4, 6], [1, 1, 1, 1, 2, 2, 2, 5, 5], [1, 1, 1, 1, 2, 2, 2, 10], [1, 1, 1, 1, 2, 2, 3, 3, 3, 3], [1, 1, 1, 1, 2, 2, 3, 3, 6], [1, 1, 1, 1, 2, 2, 3, 4, 5], [1, 1, 1, 1, 2, 2, 3, 9], [1, 1, 1, 1, 2, 2, 4, 4, 4], [1, 1, 1, 1, 2, 2, 4, 8], [1, 1, 1, 1, 2, 2, 5, 7], [1, 1, 1, 1, 2, 2, 6, 6], [1, 1, 1, 1, 2, 3, 3, 3, 5], [1, 1, 1, 1, 2, 3, 3, 4, 4], [1, 1, 1, 1, 2, 3, 3, 8], [1, 1, 1, 1, 2, 3, 4, 7], [1, 1, 1, 1, 2, 3, 5, 6], [1, 1, 1, 1, 2, 4, 4, 6], [1, 1, 1, 1, 2, 4, 5, 5], [1, 1, 1, 1, 2, 4, 10], [1, 1, 1, 1, 2, 5, 9], [1, 1, 1, 1, 2, 6, 8], [1, 1, 1, 1, 2, 7, 7], [1, 1, 1, 1, 3, 3, 3, 3, 4], [1, 1, 1, 1, 3, 3, 3, 7], [1, 1, 1, 1, 3, 3, 4, 6], [1, 1, 1, 1, 3, 3, 5, 5], [1, 1, 1, 1, 3, 3, 10], [1, 1, 1, 1, 3, 4, 4, 5], [1, 1, 1, 1, 3, 4, 9], [1, 1, 1, 1, 3, 5, 8], [1, 1, 1, 1, 3, 6, 7], [1, 1, 1, 1, 4, 4, 4, 4], [1, 1, 1, 1, 4, 4, 8], [1, 1, 1, 1, 4, 5, 7], [1, 1, 1, 1, 4, 6, 6], [1, 1, 1, 1, 5, 5, 6], [1, 1, 1, 1, 6, 10], [1, 1, 1, 1, 7, 9], [1, 1, 1, 1, 8, 8], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 2, 2, 2, 2, 2, 3, 4], [1, 1, 1, 2, 2, 2, 2, 2, 7], [1, 1, 1, 2, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3, 6], [1, 1, 1, 2, 2, 2, 2, 4, 5], [1, 1, 1, 2, 2, 2, 2, 9], [1, 1, 1, 2, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 8], [1, 1, 1, 2, 2, 2, 4, 7], [1, 1, 1, 2, 2, 2, 5, 6], [1, 1, 1, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 7], [1, 1, 1, 2, 2, 3, 4, 6], [1, 1, 1, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 3, 10], [1, 1, 1, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 4, 9], [1, 1, 1, 2, 2, 5, 8], [1, 1, 1, 2, 2, 6, 7], [1, 1, 1, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 3, 3, 3, 6], [1, 1, 1, 2, 3, 3, 4, 5], [1, 1, 1, 2, 3, 3, 9], [1, 1, 1, 2, 3, 4, 4, 4], [1, 1, 1, 2, 3, 4, 8], [1, 1, 1, 2, 3, 5, 7], [1, 1, 1, 2, 3, 6, 6], [1, 1, 1, 2, 4, 4, 7], [1, 1, 1, 2, 4, 5, 6], [1, 1, 1, 2, 5, 5, 5], [1, 1, 1, 2, 5, 10], [1, 1, 1, 2, 6, 9], [1, 1, 1, 2, 7, 8], [1, 1, 1, 3, 3, 3, 3, 5], [1, 1, 1, 3, 3, 3, 4, 4], [1, 1, 1, 3, 3, 3, 8], [1, 1, 1, 3, 3, 4, 7], [1, 1, 1, 3, 3, 5, 6], [1, 1, 1, 3, 4, 4, 6], [1, 1, 1, 3, 4, 5, 5], [1, 1, 1, 3, 4, 10], [1, 1, 1, 3, 5, 9], [1, 1, 1, 3, 6, 8], [1, 1, 1, 3, 7, 7], [1, 1, 1, 4, 4, 4, 5], [1, 1, 1, 4, 4, 9], [1, 1, 1, 4, 5, 8], [1, 1, 1, 4, 6, 7], [1, 1, 1, 5, 5, 7], [1, 1, 1, 5, 6, 6], [1, 1, 1, 7, 10], [1, 1, 1, 8, 9], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2, 2, 4], [1, 1, 2, 2, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 2, 2, 6], [1, 1, 2, 2, 2, 2, 2, 3, 5], [1, 1, 2, 2, 2, 2, 2, 4, 4], [1, 1, 2, 2, 2, 2, 2, 8], [1, 1, 2, 2, 2, 2, 3, 3, 4], [1, 1, 2, 2, 2, 2, 3, 7], [1, 1, 2, 2, 2, 2, 4, 6], [1, 1, 2, 2, 2, 2, 5, 5], [1, 1, 2, 2, 2, 2, 10], [1, 1, 2, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3, 6], [1, 1, 2, 2, 2, 3, 4, 5], [1, 1, 2, 2, 2, 3, 9], [1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 2, 2, 2, 4, 8], [1, 1, 2, 2, 2, 5, 7], [1, 1, 2, 2, 2, 6, 6], [1, 1, 2, 2, 3, 3, 3, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 8], [1, 1, 2, 2, 3, 4, 7], [1, 1, 2, 2, 3, 5, 6], [1, 1, 2, 2, 4, 4, 6], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 10], [1, 1, 2, 2, 5, 9], [1, 1, 2, 2, 6, 8], [1, 1, 2, 2, 7, 7], [1, 1, 2, 3, 3, 3, 3, 4], [1, 1, 2, 3, 3, 3, 7], [1, 1, 2, 3, 3, 4, 6], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 10], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 9], [1, 1, 2, 3, 5, 8], [1, 1, 2, 3, 6, 7], [1, 1, 2, 4, 4, 4, 4], [1, 1, 2, 4, 4, 8], [1, 1, 2, 4, 5, 7], [1, 1, 2, 4, 6, 6], [1, 1, 2, 5, 5, 6], [1, 1, 2, 6, 10], [1, 1, 2, 7, 9], [1, 1, 2, 8, 8], [1, 1, 3, 3, 3, 3, 3, 3], [1, 1, 3, 3, 3, 3, 6], [1, 1, 3, 3, 3, 4, 5], [1, 1, 3, 3, 3, 9], [1, 1, 3, 3, 4, 4, 4], [1, 1, 3, 3, 4, 8], [1, 1, 3, 3, 5, 7], [1, 1, 3, 3, 6, 6], [1, 1, 3, 4, 4, 7], [1, 1, 3, 4, 5, 6], [1, 1, 3, 5, 5, 5], [1, 1, 3, 5, 10], [1, 1, 3, 6, 9], [1, 1, 3, 7, 8], [1, 1, 4, 4, 4, 6], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 10], [1, 1, 4, 5, 9], [1, 1, 4, 6, 8], [1, 1, 4, 7, 7], [1, 1, 5, 5, 8], [1, 1, 5, 6, 7], [1, 1, 6, 6, 6], [1, 1, 8, 10], [1, 1, 9, 9], [1, 2, 2, 2, 2, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2, 2, 2, 5], [1, 2, 2, 2, 2, 2, 2, 3, 4], [1, 2, 2, 2, 2, 2, 2, 7], [1, 2, 2, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 2, 3, 6], [1, 2, 2, 2, 2, 2, 4, 5], [1, 2, 2, 2, 2, 2, 9], [1, 2, 2, 2, 2, 3, 3, 5], [1, 2, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 2, 3, 8], [1, 2, 2, 2, 2, 4, 7], [1, 2, 2, 2, 2, 5, 6], [1, 2, 2, 2, 3, 3, 3, 4], [1, 2, 2, 2, 3, 3, 7], [1, 2, 2, 2, 3, 4, 6], [1, 2, 2, 2, 3, 5, 5], [1, 2, 2, 2, 3, 10], [1, 2, 2, 2, 4, 4, 5], [1, 2, 2, 2, 4, 9], [1, 2, 2, 2, 5, 8], [1, 2, 2, 2, 6, 7], [1, 2, 2, 3, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3, 6], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 9], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 8], [1, 2, 2, 3, 5, 7], [1, 2, 2, 3, 6, 6], [1, 2, 2, 4, 4, 7], [1, 2, 2, 4, 5, 6], [1, 2, 2, 5, 5, 5], [1, 2, 2, 5, 10], [1, 2, 2, 6, 9], [1, 2, 2, 7, 8], [1, 2, 3, 3, 3, 3, 5], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 8], [1, 2, 3, 3, 4, 7], [1, 2, 3, 3, 5, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 10], [1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 3, 7, 7], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 9], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 5, 5, 7], [1, 2, 5, 6, 6], [1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 3, 3, 3, 3, 4], [1, 3, 3, 3, 3, 7], [1, 3, 3, 3, 4, 6], [1, 3, 3, 3, 5, 5], [1, 3, 3, 3, 10], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 9], [1, 3, 3, 5, 8], [1, 3, 3, 6, 7], [1, 3, 4, 4, 4, 4], [1, 3, 4, 4, 8], [1, 3, 4, 5, 7], [1, 3, 4, 6, 6], [1, 3, 5, 5, 6], [1, 3, 6, 10], [1, 3, 7, 9], [1, 3, 8, 8], [1, 4, 4, 4, 7], [1, 4, 4, 5, 6], [1, 4, 5, 5, 5], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 5, 9], [1, 5, 6, 8], [1, 5, 7, 7], [1, 6, 6, 7], [1, 9, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 4, 4], [2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 3, 3, 4], [2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 4, 6], [2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 6], [2, 2, 2, 2, 3, 4, 5], [2, 2, 2, 2, 3, 9], [2, 2, 2, 2, 4, 4, 4], [2, 2, 2, 2, 4, 8], [2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 6, 6], [2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 8], [2, 2, 2, 3, 4, 7], [2, 2, 2, 3, 5, 6], [2, 2, 2, 4, 4, 6], [2, 2, 2, 4, 5, 5], [2, 2, 2, 4, 10], [2, 2, 2, 5, 9], [2, 2, 2, 6, 8], [2, 2, 2, 7, 7], [2, 2, 3, 3, 3, 3, 4], [2, 2, 3, 3, 3, 7], [2, 2, 3, 3, 4, 6], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 10], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 9], [2, 2, 3, 5, 8], [2, 2, 3, 6, 7], [2, 2, 4, 4, 4, 4], [2, 2, 4, 4, 8], [2, 2, 4, 5, 7], [2, 2, 4, 6, 6], [2, 2, 5, 5, 6], [2, 2, 6, 10], [2, 2, 7, 9], [2, 2, 8, 8], [2, 3, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3, 6], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 9], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 8], [2, 3, 3, 5, 7], [2, 3, 3, 6, 6], [2, 3, 4, 4, 7], [2, 3, 4, 5, 6], [2, 3, 5, 5, 5], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 4, 4, 6], [2, 4, 4, 5, 5], [2, 4, 4, 10], [2, 4, 5, 9], [2, 4, 6, 8], [2, 4, 7, 7], [2, 5, 5, 8], [2, 5, 6, 7], [2, 6, 6, 6], [2, 8, 10], [2, 9, 9], [3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 4, 4], [3, 3, 3, 3, 8], [3, 3, 3, 4, 7], [3, 3, 3, 5, 6], [3, 3, 4, 4, 6], [3, 3, 4, 5, 5], [3, 3, 4, 10], [3, 3, 5, 9], [3, 3, 6, 8], [3, 3, 7, 7], [3, 4, 4, 4, 5], [3, 4, 4, 9], [3, 4, 5, 8], [3, 4, 6, 7], [3, 5, 5, 7], [3, 5, 6, 6], [3, 7, 10], [3, 8, 9], [4, 4, 4, 4, 4], [4, 4, 4, 8], [4, 4, 5, 7], [4, 4, 6, 6], [4, 5, 5, 6], [4, 6, 10], [4, 7, 9], [4, 8, 8], [5, 5, 5, 5], [5, 5, 10], [5, 6, 9], [5, 7, 8], [6, 6, 8], [6, 7, 7], [10, 10]]\n assert candidate(candidates = [1, 18, 25, 37, 41, 52],target = 80) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 18], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 37], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 41], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 25], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 25], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 52], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 18, 18], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 37], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 41], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 18, 25], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 37], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 41], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 25, 25], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 52], [1, 1, 1, 1, 1, 1, 1, 1, 18, 18, 18, 18], [1, 1, 1, 1, 1, 1, 1, 18, 18, 37], [1, 1, 1, 1, 1, 1, 37, 37], [1, 1, 1, 1, 1, 25, 25, 25], [1, 1, 1, 18, 18, 41], [1, 1, 1, 25, 52], [1, 1, 37, 41], [1, 18, 18, 18, 25], [18, 25, 37]]\n assert candidate(candidates = [18, 22, 30, 26, 25, 27, 32],target = 50) == [[18, 32], [25, 25]]\n assert candidate(candidates = [7, 14, 21, 28, 35, 42, 49],target = 140) == [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 42], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 49], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 42], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 28, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 49], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 42], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 28, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 42], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 28, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 21, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 49], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 28, 42], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 35, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 21, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 49], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 42], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 28, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 21, 35], [7, 7, 7, 7, 7, 7, 7, 7, 7, 21, 28, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 28, 49], [7, 7, 7, 7, 7, 7, 7, 7, 7, 35, 42], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 28], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 42], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 21, 35], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 28, 28], [7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 21, 28], [7, 7, 7, 7, 7, 7, 7, 7, 14, 21, 49], [7, 7, 7, 7, 7, 7, 7, 7, 14, 28, 42], [7, 7, 7, 7, 7, 7, 7, 7, 14, 35, 35], [7, 7, 7, 7, 7, 7, 7, 7, 21, 21, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 21, 21, 42], [7, 7, 7, 7, 7, 7, 7, 7, 21, 28, 35], [7, 7, 7, 7, 7, 7, 7, 7, 28, 28, 28], [7, 7, 7, 7, 7, 7, 7, 7, 35, 49], [7, 7, 7, 7, 7, 7, 7, 7, 42, 42], [7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 21], [7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 35], [7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 21, 28], [7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 49], [7, 7, 7, 7, 7, 7, 7, 14, 14, 21, 21, 21], [7, 7, 7, 7, 7, 7, 7, 14, 14, 21, 42], [7, 7, 7, 7, 7, 7, 7, 14, 14, 28, 35], [7, 7, 7, 7, 7, 7, 7, 14, 21, 21, 35], [7, 7, 7, 7, 7, 7, 7, 14, 21, 28, 28], [7, 7, 7, 7, 7, 7, 7, 14, 28, 49], [7, 7, 7, 7, 7, 7, 7, 14, 35, 42], [7, 7, 7, 7, 7, 7, 7, 21, 21, 21, 28], [7, 7, 7, 7, 7, 7, 7, 21, 21, 49], [7, 7, 7, 7, 7, 7, 7, 21, 28, 42], [7, 7, 7, 7, 7, 7, 7, 21, 35, 35], [7, 7, 7, 7, 7, 7, 7, 28, 28, 35], [7, 7, 7, 7, 7, 7, 7, 42, 49], [7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 14], [7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 28], [7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 21, 21], [7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 42], [7, 7, 7, 7, 7, 7, 14, 14, 14, 21, 35], [7, 7, 7, 7, 7, 7, 14, 14, 14, 28, 28], [7, 7, 7, 7, 7, 7, 14, 14, 21, 21, 28], [7, 7, 7, 7, 7, 7, 14, 14, 21, 49], [7, 7, 7, 7, 7, 7, 14, 14, 28, 42], [7, 7, 7, 7, 7, 7, 14, 14, 35, 35], [7, 7, 7, 7, 7, 7, 14, 21, 21, 21, 21], [7, 7, 7, 7, 7, 7, 14, 21, 21, 42], [7, 7, 7, 7, 7, 7, 14, 21, 28, 35], [7, 7, 7, 7, 7, 7, 14, 28, 28, 28], [7, 7, 7, 7, 7, 7, 14, 35, 49], [7, 7, 7, 7, 7, 7, 14, 42, 42], [7, 7, 7, 7, 7, 7, 21, 21, 21, 35], [7, 7, 7, 7, 7, 7, 21, 21, 28, 28], [7, 7, 7, 7, 7, 7, 21, 28, 49], [7, 7, 7, 7, 7, 7, 21, 35, 42], [7, 7, 7, 7, 7, 7, 28, 28, 42], [7, 7, 7, 7, 7, 7, 28, 35, 35], [7, 7, 7, 7, 7, 7, 49, 49], [7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 21], [7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 35], [7, 7, 7, 7, 7, 14, 14, 14, 14, 21, 28], [7, 7, 7, 7, 7, 14, 14, 14, 14, 49], [7, 7, 7, 7, 7, 14, 14, 14, 21, 21, 21], [7, 7, 7, 7, 7, 14, 14, 14, 21, 42], [7, 7, 7, 7, 7, 14, 14, 14, 28, 35], [7, 7, 7, 7, 7, 14, 14, 21, 21, 35], [7, 7, 7, 7, 7, 14, 14, 21, 28, 28], [7, 7, 7, 7, 7, 14, 14, 28, 49], [7, 7, 7, 7, 7, 14, 14, 35, 42], [7, 7, 7, 7, 7, 14, 21, 21, 21, 28], [7, 7, 7, 7, 7, 14, 21, 21, 49], [7, 7, 7, 7, 7, 14, 21, 28, 42], [7, 7, 7, 7, 7, 14, 21, 35, 35], [7, 7, 7, 7, 7, 14, 28, 28, 35], [7, 7, 7, 7, 7, 14, 42, 49], [7, 7, 7, 7, 7, 21, 21, 21, 21, 21], [7, 7, 7, 7, 7, 21, 21, 21, 42], [7, 7, 7, 7, 7, 21, 21, 28, 35], [7, 7, 7, 7, 7, 21, 28, 28, 28], [7, 7, 7, 7, 7, 21, 35, 49], [7, 7, 7, 7, 7, 21, 42, 42], [7, 7, 7, 7, 7, 28, 28, 49], [7, 7, 7, 7, 7, 28, 35, 42], [7, 7, 7, 7, 7, 35, 35, 35], [7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 14, 14], [7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 28], [7, 7, 7, 7, 14, 14, 14, 14, 14, 21, 21], [7, 7, 7, 7, 14, 14, 14, 14, 14, 42], [7, 7, 7, 7, 14, 14, 14, 14, 21, 35], [7, 7, 7, 7, 14, 14, 14, 14, 28, 28], [7, 7, 7, 7, 14, 14, 14, 21, 21, 28], [7, 7, 7, 7, 14, 14, 14, 21, 49], [7, 7, 7, 7, 14, 14, 14, 28, 42], [7, 7, 7, 7, 14, 14, 14, 35, 35], [7, 7, 7, 7, 14, 14, 21, 21, 21, 21], [7, 7, 7, 7, 14, 14, 21, 21, 42], [7, 7, 7, 7, 14, 14, 21, 28, 35], [7, 7, 7, 7, 14, 14, 28, 28, 28], [7, 7, 7, 7, 14, 14, 35, 49], [7, 7, 7, 7, 14, 14, 42, 42], [7, 7, 7, 7, 14, 21, 21, 21, 35], [7, 7, 7, 7, 14, 21, 21, 28, 28], [7, 7, 7, 7, 14, 21, 28, 49], [7, 7, 7, 7, 14, 21, 35, 42], [7, 7, 7, 7, 14, 28, 28, 42], [7, 7, 7, 7, 14, 28, 35, 35], [7, 7, 7, 7, 14, 49, 49], [7, 7, 7, 7, 21, 21, 21, 21, 28], [7, 7, 7, 7, 21, 21, 21, 49], [7, 7, 7, 7, 21, 21, 28, 42], [7, 7, 7, 7, 21, 21, 35, 35], [7, 7, 7, 7, 21, 28, 28, 35], [7, 7, 7, 7, 21, 42, 49], [7, 7, 7, 7, 28, 28, 28, 28], [7, 7, 7, 7, 28, 35, 49], [7, 7, 7, 7, 28, 42, 42], [7, 7, 7, 7, 35, 35, 42], [7, 7, 7, 14, 14, 14, 14, 14, 14, 14, 21], [7, 7, 7, 14, 14, 14, 14, 14, 14, 35], [7, 7, 7, 14, 14, 14, 14, 14, 21, 28], [7, 7, 7, 14, 14, 14, 14, 14, 49], [7, 7, 7, 14, 14, 14, 14, 21, 21, 21], [7, 7, 7, 14, 14, 14, 14, 21, 42], [7, 7, 7, 14, 14, 14, 14, 28, 35], [7, 7, 7, 14, 14, 14, 21, 21, 35], [7, 7, 7, 14, 14, 14, 21, 28, 28], [7, 7, 7, 14, 14, 14, 28, 49], [7, 7, 7, 14, 14, 14, 35, 42], [7, 7, 7, 14, 14, 21, 21, 21, 28], [7, 7, 7, 14, 14, 21, 21, 49], [7, 7, 7, 14, 14, 21, 28, 42], [7, 7, 7, 14, 14, 21, 35, 35], [7, 7, 7, 14, 14, 28, 28, 35], [7, 7, 7, 14, 14, 42, 49], [7, 7, 7, 14, 21, 21, 21, 21, 21], [7, 7, 7, 14, 21, 21, 21, 42], [7, 7, 7, 14, 21, 21, 28, 35], [7, 7, 7, 14, 21, 28, 28, 28], [7, 7, 7, 14, 21, 35, 49], [7, 7, 7, 14, 21, 42, 42], [7, 7, 7, 14, 28, 28, 49], [7, 7, 7, 14, 28, 35, 42], [7, 7, 7, 14, 35, 35, 35], [7, 7, 7, 21, 21, 21, 21, 35], [7, 7, 7, 21, 21, 21, 28, 28], [7, 7, 7, 21, 21, 28, 49], [7, 7, 7, 21, 21, 35, 42], [7, 7, 7, 21, 28, 28, 42], [7, 7, 7, 21, 28, 35, 35], [7, 7, 7, 21, 49, 49], [7, 7, 7, 28, 28, 28, 35], [7, 7, 7, 28, 42, 49], [7, 7, 7, 35, 35, 49], [7, 7, 7, 35, 42, 42], [7, 7, 14, 14, 14, 14, 14, 14, 14, 14, 14], [7, 7, 14, 14, 14, 14, 14, 14, 14, 28], [7, 7, 14, 14, 14, 14, 14, 14, 21, 21], [7, 7, 14, 14, 14, 14, 14, 14, 42], [7, 7, 14, 14, 14, 14, 14, 21, 35], [7, 7, 14, 14, 14, 14, 14, 28, 28], [7, 7, 14, 14, 14, 14, 21, 21, 28], [7, 7, 14, 14, 14, 14, 21, 49], [7, 7, 14, 14, 14, 14, 28, 42], [7, 7, 14, 14, 14, 14, 35, 35], [7, 7, 14, 14, 14, 21, 21, 21, 21], [7, 7, 14, 14, 14, 21, 21, 42], [7, 7, 14, 14, 14, 21, 28, 35], [7, 7, 14, 14, 14, 28, 28, 28], [7, 7, 14, 14, 14, 35, 49], [7, 7, 14, 14, 14, 42, 42], [7, 7, 14, 14, 21, 21, 21, 35], [7, 7, 14, 14, 21, 21, 28, 28], [7, 7, 14, 14, 21, 28, 49], [7, 7, 14, 14, 21, 35, 42], [7, 7, 14, 14, 28, 28, 42], [7, 7, 14, 14, 28, 35, 35], [7, 7, 14, 14, 49, 49], [7, 7, 14, 21, 21, 21, 21, 28], [7, 7, 14, 21, 21, 21, 49], [7, 7, 14, 21, 21, 28, 42], [7, 7, 14, 21, 21, 35, 35], [7, 7, 14, 21, 28, 28, 35], [7, 7, 14, 21, 42, 49], [7, 7, 14, 28, 28, 28, 28], [7, 7, 14, 28, 35, 49], [7, 7, 14, 28, 42, 42], [7, 7, 14, 35, 35, 42], [7, 7, 21, 21, 21, 21, 21, 21], [7, 7, 21, 21, 21, 21, 42], [7, 7, 21, 21, 21, 28, 35], [7, 7, 21, 21, 28, 28, 28], [7, 7, 21, 21, 35, 49], [7, 7, 21, 21, 42, 42], [7, 7, 21, 28, 28, 49], [7, 7, 21, 28, 35, 42], [7, 7, 21, 35, 35, 35], [7, 7, 28, 28, 28, 42], [7, 7, 28, 28, 35, 35], [7, 7, 28, 49, 49], [7, 7, 35, 42, 49], [7, 7, 42, 42, 42], [7, 14, 14, 14, 14, 14, 14, 14, 14, 21], [7, 14, 14, 14, 14, 14, 14, 14, 35], [7, 14, 14, 14, 14, 14, 14, 21, 28], [7, 14, 14, 14, 14, 14, 14, 49], [7, 14, 14, 14, 14, 14, 21, 21, 21], [7, 14, 14, 14, 14, 14, 21, 42], [7, 14, 14, 14, 14, 14, 28, 35], [7, 14, 14, 14, 14, 21, 21, 35], [7, 14, 14, 14, 14, 21, 28, 28], [7, 14, 14, 14, 14, 28, 49], [7, 14, 14, 14, 14, 35, 42], [7, 14, 14, 14, 21, 21, 21, 28], [7, 14, 14, 14, 21, 21, 49], [7, 14, 14, 14, 21, 28, 42], [7, 14, 14, 14, 21, 35, 35], [7, 14, 14, 14, 28, 28, 35], [7, 14, 14, 14, 42, 49], [7, 14, 14, 21, 21, 21, 21, 21], [7, 14, 14, 21, 21, 21, 42], [7, 14, 14, 21, 21, 28, 35], [7, 14, 14, 21, 28, 28, 28], [7, 14, 14, 21, 35, 49], [7, 14, 14, 21, 42, 42], [7, 14, 14, 28, 28, 49], [7, 14, 14, 28, 35, 42], [7, 14, 14, 35, 35, 35], [7, 14, 21, 21, 21, 21, 35], [7, 14, 21, 21, 21, 28, 28], [7, 14, 21, 21, 28, 49], [7, 14, 21, 21, 35, 42], [7, 14, 21, 28, 28, 42], [7, 14, 21, 28, 35, 35], [7, 14, 21, 49, 49], [7, 14, 28, 28, 28, 35], [7, 14, 28, 42, 49], [7, 14, 35, 35, 49], [7, 14, 35, 42, 42], [7, 21, 21, 21, 21, 21, 28], [7, 21, 21, 21, 21, 49], [7, 21, 21, 21, 28, 42], [7, 21, 21, 21, 35, 35], [7, 21, 21, 28, 28, 35], [7, 21, 21, 42, 49], [7, 21, 28, 28, 28, 28], [7, 21, 28, 35, 49], [7, 21, 28, 42, 42], [7, 21, 35, 35, 42], [7, 28, 28, 28, 49], [7, 28, 28, 35, 42], [7, 28, 35, 35, 35], [7, 35, 49, 49], [7, 42, 42, 49], [14, 14, 14, 14, 14, 14, 14, 14, 14, 14], [14, 14, 14, 14, 14, 14, 14, 14, 28], [14, 14, 14, 14, 14, 14, 14, 21, 21], [14, 14, 14, 14, 14, 14, 14, 42], [14, 14, 14, 14, 14, 14, 21, 35], [14, 14, 14, 14, 14, 14, 28, 28], [14, 14, 14, 14, 14, 21, 21, 28], [14, 14, 14, 14, 14, 21, 49], [14, 14, 14, 14, 14, 28, 42], [14, 14, 14, 14, 14, 35, 35], [14, 14, 14, 14, 21, 21, 21, 21], [14, 14, 14, 14, 21, 21, 42], [14, 14, 14, 14, 21, 28, 35], [14, 14, 14, 14, 28, 28, 28], [14, 14, 14, 14, 35, 49], [14, 14, 14, 14, 42, 42], [14, 14, 14, 21, 21, 21, 35], [14, 14, 14, 21, 21, 28, 28], [14, 14, 14, 21, 28, 49], [14, 14, 14, 21, 35, 42], [14, 14, 14, 28, 28, 42], [14, 14, 14, 28, 35, 35], [14, 14, 14, 49, 49], [14, 14, 21, 21, 21, 21, 28], [14, 14, 21, 21, 21, 49], [14, 14, 21, 21, 28, 42], [14, 14, 21, 21, 35, 35], [14, 14, 21, 28, 28, 35], [14, 14, 21, 42, 49], [14, 14, 28, 28, 28, 28], [14, 14, 28, 35, 49], [14, 14, 28, 42, 42], [14, 14, 35, 35, 42], [14, 21, 21, 21, 21, 21, 21], [14, 21, 21, 21, 21, 42], [14, 21, 21, 21, 28, 35], [14, 21, 21, 28, 28, 28], [14, 21, 21, 35, 49], [14, 21, 21, 42, 42], [14, 21, 28, 28, 49], [14, 21, 28, 35, 42], [14, 21, 35, 35, 35], [14, 28, 28, 28, 42], [14, 28, 28, 35, 35], [14, 28, 49, 49], [14, 35, 42, 49], [14, 42, 42, 42], [21, 21, 21, 21, 21, 35], [21, 21, 21, 21, 28, 28], [21, 21, 21, 28, 49], [21, 21, 21, 35, 42], [21, 21, 28, 28, 42], [21, 21, 28, 35, 35], [21, 21, 49, 49], [21, 28, 28, 28, 35], [21, 28, 42, 49], [21, 35, 35, 49], [21, 35, 42, 42], [28, 28, 28, 28, 28], [28, 28, 35, 49], [28, 28, 42, 42], [28, 35, 35, 42], [35, 35, 35, 35], [42, 49, 49]]\n assert candidate(candidates = [8, 16, 24, 32, 40, 48],target = 64) == [[8, 8, 8, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 8, 16], [8, 8, 8, 8, 8, 24], [8, 8, 8, 8, 16, 16], [8, 8, 8, 8, 32], [8, 8, 8, 16, 24], [8, 8, 8, 40], [8, 8, 16, 16, 16], [8, 8, 16, 32], [8, 8, 24, 24], [8, 8, 48], [8, 16, 16, 24], [8, 16, 40], [8, 24, 32], [16, 16, 16, 16], [16, 16, 32], [16, 24, 24], [16, 48], [24, 40], [32, 32]]\n assert candidate(candidates = [29, 26, 23, 20, 17, 14, 11, 8, 5, 2],target = 50) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 8, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 26], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 23], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 14, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 8, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 8, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 8, 8, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 14], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 8, 11], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 8, 8, 8], [2, 2, 2, 2, 2, 2, 2, 2, 5, 29], [2, 2, 2, 2, 2, 2, 2, 2, 8, 26], [2, 2, 2, 2, 2, 2, 2, 2, 11, 23], [2, 2, 2, 2, 2, 2, 2, 2, 14, 20], [2, 2, 2, 2, 2, 2, 2, 2, 17, 17], [2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 8, 8], [2, 2, 2, 2, 2, 2, 2, 5, 5, 26], [2, 2, 2, 2, 2, 2, 2, 5, 8, 23], [2, 2, 2, 2, 2, 2, 2, 5, 11, 20], [2, 2, 2, 2, 2, 2, 2, 5, 14, 17], [2, 2, 2, 2, 2, 2, 2, 8, 8, 20], [2, 2, 2, 2, 2, 2, 2, 8, 11, 17], [2, 2, 2, 2, 2, 2, 2, 8, 14, 14], [2, 2, 2, 2, 2, 2, 2, 11, 11, 14], [2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 8], [2, 2, 2, 2, 2, 2, 5, 5, 5, 23], [2, 2, 2, 2, 2, 2, 5, 5, 8, 20], [2, 2, 2, 2, 2, 2, 5, 5, 11, 17], [2, 2, 2, 2, 2, 2, 5, 5, 14, 14], [2, 2, 2, 2, 2, 2, 5, 8, 8, 17], [2, 2, 2, 2, 2, 2, 5, 8, 11, 14], [2, 2, 2, 2, 2, 2, 5, 11, 11, 11], [2, 2, 2, 2, 2, 2, 8, 8, 8, 14], [2, 2, 2, 2, 2, 2, 8, 8, 11, 11], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 5, 5, 5, 8, 17], [2, 2, 2, 2, 2, 5, 5, 5, 11, 14], [2, 2, 2, 2, 2, 5, 5, 8, 8, 14], [2, 2, 2, 2, 2, 5, 5, 8, 11, 11], [2, 2, 2, 2, 2, 5, 8, 8, 8, 11], [2, 2, 2, 2, 2, 8, 8, 8, 8, 8], [2, 2, 2, 2, 2, 11, 29], [2, 2, 2, 2, 2, 14, 26], [2, 2, 2, 2, 2, 17, 23], [2, 2, 2, 2, 2, 20, 20], [2, 2, 2, 2, 5, 5, 5, 5, 5, 17], [2, 2, 2, 2, 5, 5, 5, 5, 8, 14], [2, 2, 2, 2, 5, 5, 5, 5, 11, 11], [2, 2, 2, 2, 5, 5, 5, 8, 8, 11], [2, 2, 2, 2, 5, 5, 8, 8, 8, 8], [2, 2, 2, 2, 5, 8, 29], [2, 2, 2, 2, 5, 11, 26], [2, 2, 2, 2, 5, 14, 23], [2, 2, 2, 2, 5, 17, 20], [2, 2, 2, 2, 8, 8, 26], [2, 2, 2, 2, 8, 11, 23], [2, 2, 2, 2, 8, 14, 20], [2, 2, 2, 2, 8, 17, 17], [2, 2, 2, 2, 11, 11, 20], [2, 2, 2, 2, 11, 14, 17], [2, 2, 2, 2, 14, 14, 14], [2, 2, 2, 5, 5, 5, 5, 5, 5, 14], [2, 2, 2, 5, 5, 5, 5, 5, 8, 11], [2, 2, 2, 5, 5, 5, 5, 8, 8, 8], [2, 2, 2, 5, 5, 5, 29], [2, 2, 2, 5, 5, 8, 26], [2, 2, 2, 5, 5, 11, 23], [2, 2, 2, 5, 5, 14, 20], [2, 2, 2, 5, 5, 17, 17], [2, 2, 2, 5, 8, 8, 23], [2, 2, 2, 5, 8, 11, 20], [2, 2, 2, 5, 8, 14, 17], [2, 2, 2, 5, 11, 11, 17], [2, 2, 2, 5, 11, 14, 14], [2, 2, 2, 8, 8, 8, 20], [2, 2, 2, 8, 8, 11, 17], [2, 2, 2, 8, 8, 14, 14], [2, 2, 2, 8, 11, 11, 14], [2, 2, 2, 11, 11, 11, 11], [2, 2, 5, 5, 5, 5, 5, 5, 5, 11], [2, 2, 5, 5, 5, 5, 5, 5, 8, 8], [2, 2, 5, 5, 5, 5, 26], [2, 2, 5, 5, 5, 8, 23], [2, 2, 5, 5, 5, 11, 20], [2, 2, 5, 5, 5, 14, 17], [2, 2, 5, 5, 8, 8, 20], [2, 2, 5, 5, 8, 11, 17], [2, 2, 5, 5, 8, 14, 14], [2, 2, 5, 5, 11, 11, 14], [2, 2, 5, 8, 8, 8, 17], [2, 2, 5, 8, 8, 11, 14], [2, 2, 5, 8, 11, 11, 11], [2, 2, 8, 8, 8, 8, 14], [2, 2, 8, 8, 8, 11, 11], [2, 2, 17, 29], [2, 2, 20, 26], [2, 2, 23, 23], [2, 5, 5, 5, 5, 5, 5, 5, 5, 8], [2, 5, 5, 5, 5, 5, 23], [2, 5, 5, 5, 5, 8, 20], [2, 5, 5, 5, 5, 11, 17], [2, 5, 5, 5, 5, 14, 14], [2, 5, 5, 5, 8, 8, 17], [2, 5, 5, 5, 8, 11, 14], [2, 5, 5, 5, 11, 11, 11], [2, 5, 5, 8, 8, 8, 14], [2, 5, 5, 8, 8, 11, 11], [2, 5, 8, 8, 8, 8, 11], [2, 5, 14, 29], [2, 5, 17, 26], [2, 5, 20, 23], [2, 8, 8, 8, 8, 8, 8], [2, 8, 11, 29], [2, 8, 14, 26], [2, 8, 17, 23], [2, 8, 20, 20], [2, 11, 11, 26], [2, 11, 14, 23], [2, 11, 17, 20], [2, 14, 14, 20], [2, 14, 17, 17], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 8, 17], [5, 5, 5, 5, 5, 11, 14], [5, 5, 5, 5, 8, 8, 14], [5, 5, 5, 5, 8, 11, 11], [5, 5, 5, 8, 8, 8, 11], [5, 5, 8, 8, 8, 8, 8], [5, 5, 11, 29], [5, 5, 14, 26], [5, 5, 17, 23], [5, 5, 20, 20], [5, 8, 8, 29], [5, 8, 11, 26], [5, 8, 14, 23], [5, 8, 17, 20], [5, 11, 11, 23], [5, 11, 14, 20], [5, 11, 17, 17], [5, 14, 14, 17], [8, 8, 8, 26], [8, 8, 11, 23], [8, 8, 14, 20], [8, 8, 17, 17], [8, 11, 11, 20], [8, 11, 14, 17], [8, 14, 14, 14], [11, 11, 11, 17], [11, 11, 14, 14]]\n assert candidate(candidates = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45],target = 60) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 21], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 24], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 21], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 27], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 12, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 24], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 21], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 15, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 30], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 9, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 21], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 12, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 27], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 12, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 24], [3, 3, 3, 3, 3, 3, 3, 3, 3, 12, 21], [3, 3, 3, 3, 3, 3, 3, 3, 3, 15, 18], [3, 3, 3, 3, 3, 3, 3, 3, 3, 33], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 12], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 18], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 9, 15], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 12, 12], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 24], [3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 9, 12], [3, 3, 3, 3, 3, 3, 3, 3, 6, 9, 21], [3, 3, 3, 3, 3, 3, 3, 3, 6, 12, 18], [3, 3, 3, 3, 3, 3, 3, 3, 6, 15, 15], [3, 3, 3, 3, 3, 3, 3, 3, 6, 30], [3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 9, 9, 18], [3, 3, 3, 3, 3, 3, 3, 3, 9, 12, 15], [3, 3, 3, 3, 3, 3, 3, 3, 9, 27], [3, 3, 3, 3, 3, 3, 3, 3, 12, 12, 12], [3, 3, 3, 3, 3, 3, 3, 3, 12, 24], [3, 3, 3, 3, 3, 3, 3, 3, 15, 21], [3, 3, 3, 3, 3, 3, 3, 3, 18, 18], [3, 3, 3, 3, 3, 3, 3, 3, 36], [3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 9], [3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 15], [3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 9, 12], [3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 21], [3, 3, 3, 3, 3, 3, 3, 6, 6, 9, 9, 9], [3, 3, 3, 3, 3, 3, 3, 6, 6, 9, 18], [3, 3, 3, 3, 3, 3, 3, 6, 6, 12, 15], [3, 3, 3, 3, 3, 3, 3, 6, 6, 27], [3, 3, 3, 3, 3, 3, 3, 6, 9, 9, 15], [3, 3, 3, 3, 3, 3, 3, 6, 9, 12, 12], [3, 3, 3, 3, 3, 3, 3, 6, 9, 24], [3, 3, 3, 3, 3, 3, 3, 6, 12, 21], [3, 3, 3, 3, 3, 3, 3, 6, 15, 18], [3, 3, 3, 3, 3, 3, 3, 6, 33], [3, 3, 3, 3, 3, 3, 3, 9, 9, 9, 12], [3, 3, 3, 3, 3, 3, 3, 9, 9, 21], [3, 3, 3, 3, 3, 3, 3, 9, 12, 18], [3, 3, 3, 3, 3, 3, 3, 9, 15, 15], [3, 3, 3, 3, 3, 3, 3, 9, 30], [3, 3, 3, 3, 3, 3, 3, 12, 12, 15], [3, 3, 3, 3, 3, 3, 3, 12, 27], [3, 3, 3, 3, 3, 3, 3, 15, 24], [3, 3, 3, 3, 3, 3, 3, 18, 21], [3, 3, 3, 3, 3, 3, 3, 39], [3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 12], [3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 9, 9], [3, 3, 3, 3, 3, 3, 6, 6, 6, 6, 18], [3, 3, 3, 3, 3, 3, 6, 6, 6, 9, 15], [3, 3, 3, 3, 3, 3, 6, 6, 6, 12, 12], [3, 3, 3, 3, 3, 3, 6, 6, 6, 24], [3, 3, 3, 3, 3, 3, 6, 6, 9, 9, 12], [3, 3, 3, 3, 3, 3, 6, 6, 9, 21], [3, 3, 3, 3, 3, 3, 6, 6, 12, 18], [3, 3, 3, 3, 3, 3, 6, 6, 15, 15], [3, 3, 3, 3, 3, 3, 6, 6, 30], [3, 3, 3, 3, 3, 3, 6, 9, 9, 9, 9], [3, 3, 3, 3, 3, 3, 6, 9, 9, 18], [3, 3, 3, 3, 3, 3, 6, 9, 12, 15], [3, 3, 3, 3, 3, 3, 6, 9, 27], [3, 3, 3, 3, 3, 3, 6, 12, 12, 12], [3, 3, 3, 3, 3, 3, 6, 12, 24], [3, 3, 3, 3, 3, 3, 6, 15, 21], [3, 3, 3, 3, 3, 3, 6, 18, 18], [3, 3, 3, 3, 3, 3, 6, 36], [3, 3, 3, 3, 3, 3, 9, 9, 9, 15], [3, 3, 3, 3, 3, 3, 9, 9, 12, 12], [3, 3, 3, 3, 3, 3, 9, 9, 24], [3, 3, 3, 3, 3, 3, 9, 12, 21], [3, 3, 3, 3, 3, 3, 9, 15, 18], [3, 3, 3, 3, 3, 3, 9, 33], [3, 3, 3, 3, 3, 3, 12, 12, 18], [3, 3, 3, 3, 3, 3, 12, 15, 15], [3, 3, 3, 3, 3, 3, 12, 30], [3, 3, 3, 3, 3, 3, 15, 27], [3, 3, 3, 3, 3, 3, 18, 24], [3, 3, 3, 3, 3, 3, 21, 21], [3, 3, 3, 3, 3, 3, 42], [3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 9], [3, 3, 3, 3, 3, 6, 6, 6, 6, 6, 15], [3, 3, 3, 3, 3, 6, 6, 6, 6, 9, 12], [3, 3, 3, 3, 3, 6, 6, 6, 6, 21], [3, 3, 3, 3, 3, 6, 6, 6, 9, 9, 9], [3, 3, 3, 3, 3, 6, 6, 6, 9, 18], [3, 3, 3, 3, 3, 6, 6, 6, 12, 15], [3, 3, 3, 3, 3, 6, 6, 6, 27], [3, 3, 3, 3, 3, 6, 6, 9, 9, 15], [3, 3, 3, 3, 3, 6, 6, 9, 12, 12], [3, 3, 3, 3, 3, 6, 6, 9, 24], [3, 3, 3, 3, 3, 6, 6, 12, 21], [3, 3, 3, 3, 3, 6, 6, 15, 18], [3, 3, 3, 3, 3, 6, 6, 33], [3, 3, 3, 3, 3, 6, 9, 9, 9, 12], [3, 3, 3, 3, 3, 6, 9, 9, 21], [3, 3, 3, 3, 3, 6, 9, 12, 18], [3, 3, 3, 3, 3, 6, 9, 15, 15], [3, 3, 3, 3, 3, 6, 9, 30], [3, 3, 3, 3, 3, 6, 12, 12, 15], [3, 3, 3, 3, 3, 6, 12, 27], [3, 3, 3, 3, 3, 6, 15, 24], [3, 3, 3, 3, 3, 6, 18, 21], [3, 3, 3, 3, 3, 6, 39], [3, 3, 3, 3, 3, 9, 9, 9, 9, 9], [3, 3, 3, 3, 3, 9, 9, 9, 18], [3, 3, 3, 3, 3, 9, 9, 12, 15], [3, 3, 3, 3, 3, 9, 9, 27], [3, 3, 3, 3, 3, 9, 12, 12, 12], [3, 3, 3, 3, 3, 9, 12, 24], [3, 3, 3, 3, 3, 9, 15, 21], [3, 3, 3, 3, 3, 9, 18, 18], [3, 3, 3, 3, 3, 9, 36], [3, 3, 3, 3, 3, 12, 12, 21], [3, 3, 3, 3, 3, 12, 15, 18], [3, 3, 3, 3, 3, 12, 33], [3, 3, 3, 3, 3, 15, 15, 15], [3, 3, 3, 3, 3, 15, 30], [3, 3, 3, 3, 3, 18, 27], [3, 3, 3, 3, 3, 21, 24], [3, 3, 3, 3, 3, 45], [3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6], [3, 3, 3, 3, 6, 6, 6, 6, 6, 6, 12], [3, 3, 3, 3, 6, 6, 6, 6, 6, 9, 9], [3, 3, 3, 3, 6, 6, 6, 6, 6, 18], [3, 3, 3, 3, 6, 6, 6, 6, 9, 15], [3, 3, 3, 3, 6, 6, 6, 6, 12, 12], [3, 3, 3, 3, 6, 6, 6, 6, 24], [3, 3, 3, 3, 6, 6, 6, 9, 9, 12], [3, 3, 3, 3, 6, 6, 6, 9, 21], [3, 3, 3, 3, 6, 6, 6, 12, 18], [3, 3, 3, 3, 6, 6, 6, 15, 15], [3, 3, 3, 3, 6, 6, 6, 30], [3, 3, 3, 3, 6, 6, 9, 9, 9, 9], [3, 3, 3, 3, 6, 6, 9, 9, 18], [3, 3, 3, 3, 6, 6, 9, 12, 15], [3, 3, 3, 3, 6, 6, 9, 27], [3, 3, 3, 3, 6, 6, 12, 12, 12], [3, 3, 3, 3, 6, 6, 12, 24], [3, 3, 3, 3, 6, 6, 15, 21], [3, 3, 3, 3, 6, 6, 18, 18], [3, 3, 3, 3, 6, 6, 36], [3, 3, 3, 3, 6, 9, 9, 9, 15], [3, 3, 3, 3, 6, 9, 9, 12, 12], [3, 3, 3, 3, 6, 9, 9, 24], [3, 3, 3, 3, 6, 9, 12, 21], [3, 3, 3, 3, 6, 9, 15, 18], [3, 3, 3, 3, 6, 9, 33], [3, 3, 3, 3, 6, 12, 12, 18], [3, 3, 3, 3, 6, 12, 15, 15], [3, 3, 3, 3, 6, 12, 30], [3, 3, 3, 3, 6, 15, 27], [3, 3, 3, 3, 6, 18, 24], [3, 3, 3, 3, 6, 21, 21], [3, 3, 3, 3, 6, 42], [3, 3, 3, 3, 9, 9, 9, 9, 12], [3, 3, 3, 3, 9, 9, 9, 21], [3, 3, 3, 3, 9, 9, 12, 18], [3, 3, 3, 3, 9, 9, 15, 15], [3, 3, 3, 3, 9, 9, 30], [3, 3, 3, 3, 9, 12, 12, 15], [3, 3, 3, 3, 9, 12, 27], [3, 3, 3, 3, 9, 15, 24], [3, 3, 3, 3, 9, 18, 21], [3, 3, 3, 3, 9, 39], [3, 3, 3, 3, 12, 12, 12, 12], [3, 3, 3, 3, 12, 12, 24], [3, 3, 3, 3, 12, 15, 21], [3, 3, 3, 3, 12, 18, 18], [3, 3, 3, 3, 12, 36], [3, 3, 3, 3, 15, 15, 18], [3, 3, 3, 3, 15, 33], [3, 3, 3, 3, 18, 30], [3, 3, 3, 3, 21, 27], [3, 3, 3, 3, 24, 24], [3, 3, 3, 6, 6, 6, 6, 6, 6, 6, 9], [3, 3, 3, 6, 6, 6, 6, 6, 6, 15], [3, 3, 3, 6, 6, 6, 6, 6, 9, 12], [3, 3, 3, 6, 6, 6, 6, 6, 21], [3, 3, 3, 6, 6, 6, 6, 9, 9, 9], [3, 3, 3, 6, 6, 6, 6, 9, 18], [3, 3, 3, 6, 6, 6, 6, 12, 15], [3, 3, 3, 6, 6, 6, 6, 27], [3, 3, 3, 6, 6, 6, 9, 9, 15], [3, 3, 3, 6, 6, 6, 9, 12, 12], [3, 3, 3, 6, 6, 6, 9, 24], [3, 3, 3, 6, 6, 6, 12, 21], [3, 3, 3, 6, 6, 6, 15, 18], [3, 3, 3, 6, 6, 6, 33], [3, 3, 3, 6, 6, 9, 9, 9, 12], [3, 3, 3, 6, 6, 9, 9, 21], [3, 3, 3, 6, 6, 9, 12, 18], [3, 3, 3, 6, 6, 9, 15, 15], [3, 3, 3, 6, 6, 9, 30], [3, 3, 3, 6, 6, 12, 12, 15], [3, 3, 3, 6, 6, 12, 27], [3, 3, 3, 6, 6, 15, 24], [3, 3, 3, 6, 6, 18, 21], [3, 3, 3, 6, 6, 39], [3, 3, 3, 6, 9, 9, 9, 9, 9], [3, 3, 3, 6, 9, 9, 9, 18], [3, 3, 3, 6, 9, 9, 12, 15], [3, 3, 3, 6, 9, 9, 27], [3, 3, 3, 6, 9, 12, 12, 12], [3, 3, 3, 6, 9, 12, 24], [3, 3, 3, 6, 9, 15, 21], [3, 3, 3, 6, 9, 18, 18], [3, 3, 3, 6, 9, 36], [3, 3, 3, 6, 12, 12, 21], [3, 3, 3, 6, 12, 15, 18], [3, 3, 3, 6, 12, 33], [3, 3, 3, 6, 15, 15, 15], [3, 3, 3, 6, 15, 30], [3, 3, 3, 6, 18, 27], [3, 3, 3, 6, 21, 24], [3, 3, 3, 6, 45], [3, 3, 3, 9, 9, 9, 9, 15], [3, 3, 3, 9, 9, 9, 12, 12], [3, 3, 3, 9, 9, 9, 24], [3, 3, 3, 9, 9, 12, 21], [3, 3, 3, 9, 9, 15, 18], [3, 3, 3, 9, 9, 33], [3, 3, 3, 9, 12, 12, 18], [3, 3, 3, 9, 12, 15, 15], [3, 3, 3, 9, 12, 30], [3, 3, 3, 9, 15, 27], [3, 3, 3, 9, 18, 24], [3, 3, 3, 9, 21, 21], [3, 3, 3, 9, 42], [3, 3, 3, 12, 12, 12, 15], [3, 3, 3, 12, 12, 27], [3, 3, 3, 12, 15, 24], [3, 3, 3, 12, 18, 21], [3, 3, 3, 12, 39], [3, 3, 3, 15, 15, 21], [3, 3, 3, 15, 18, 18], [3, 3, 3, 15, 36], [3, 3, 3, 18, 33], [3, 3, 3, 21, 30], [3, 3, 3, 24, 27], [3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6], [3, 3, 6, 6, 6, 6, 6, 6, 6, 12], [3, 3, 6, 6, 6, 6, 6, 6, 9, 9], [3, 3, 6, 6, 6, 6, 6, 6, 18], [3, 3, 6, 6, 6, 6, 6, 9, 15], [3, 3, 6, 6, 6, 6, 6, 12, 12], [3, 3, 6, 6, 6, 6, 6, 24], [3, 3, 6, 6, 6, 6, 9, 9, 12], [3, 3, 6, 6, 6, 6, 9, 21], [3, 3, 6, 6, 6, 6, 12, 18], [3, 3, 6, 6, 6, 6, 15, 15], [3, 3, 6, 6, 6, 6, 30], [3, 3, 6, 6, 6, 9, 9, 9, 9], [3, 3, 6, 6, 6, 9, 9, 18], [3, 3, 6, 6, 6, 9, 12, 15], [3, 3, 6, 6, 6, 9, 27], [3, 3, 6, 6, 6, 12, 12, 12], [3, 3, 6, 6, 6, 12, 24], [3, 3, 6, 6, 6, 15, 21], [3, 3, 6, 6, 6, 18, 18], [3, 3, 6, 6, 6, 36], [3, 3, 6, 6, 9, 9, 9, 15], [3, 3, 6, 6, 9, 9, 12, 12], [3, 3, 6, 6, 9, 9, 24], [3, 3, 6, 6, 9, 12, 21], [3, 3, 6, 6, 9, 15, 18], [3, 3, 6, 6, 9, 33], [3, 3, 6, 6, 12, 12, 18], [3, 3, 6, 6, 12, 15, 15], [3, 3, 6, 6, 12, 30], [3, 3, 6, 6, 15, 27], [3, 3, 6, 6, 18, 24], [3, 3, 6, 6, 21, 21], [3, 3, 6, 6, 42], [3, 3, 6, 9, 9, 9, 9, 12], [3, 3, 6, 9, 9, 9, 21], [3, 3, 6, 9, 9, 12, 18], [3, 3, 6, 9, 9, 15, 15], [3, 3, 6, 9, 9, 30], [3, 3, 6, 9, 12, 12, 15], [3, 3, 6, 9, 12, 27], [3, 3, 6, 9, 15, 24], [3, 3, 6, 9, 18, 21], [3, 3, 6, 9, 39], [3, 3, 6, 12, 12, 12, 12], [3, 3, 6, 12, 12, 24], [3, 3, 6, 12, 15, 21], [3, 3, 6, 12, 18, 18], [3, 3, 6, 12, 36], [3, 3, 6, 15, 15, 18], [3, 3, 6, 15, 33], [3, 3, 6, 18, 30], [3, 3, 6, 21, 27], [3, 3, 6, 24, 24], [3, 3, 9, 9, 9, 9, 9, 9], [3, 3, 9, 9, 9, 9, 18], [3, 3, 9, 9, 9, 12, 15], [3, 3, 9, 9, 9, 27], [3, 3, 9, 9, 12, 12, 12], [3, 3, 9, 9, 12, 24], [3, 3, 9, 9, 15, 21], [3, 3, 9, 9, 18, 18], [3, 3, 9, 9, 36], [3, 3, 9, 12, 12, 21], [3, 3, 9, 12, 15, 18], [3, 3, 9, 12, 33], [3, 3, 9, 15, 15, 15], [3, 3, 9, 15, 30], [3, 3, 9, 18, 27], [3, 3, 9, 21, 24], [3, 3, 9, 45], [3, 3, 12, 12, 12, 18], [3, 3, 12, 12, 15, 15], [3, 3, 12, 12, 30], [3, 3, 12, 15, 27], [3, 3, 12, 18, 24], [3, 3, 12, 21, 21], [3, 3, 12, 42], [3, 3, 15, 15, 24], [3, 3, 15, 18, 21], [3, 3, 15, 39], [3, 3, 18, 18, 18], [3, 3, 18, 36], [3, 3, 21, 33], [3, 3, 24, 30], [3, 3, 27, 27], [3, 6, 6, 6, 6, 6, 6, 6, 6, 9], [3, 6, 6, 6, 6, 6, 6, 6, 15], [3, 6, 6, 6, 6, 6, 6, 9, 12], [3, 6, 6, 6, 6, 6, 6, 21], [3, 6, 6, 6, 6, 6, 9, 9, 9], [3, 6, 6, 6, 6, 6, 9, 18], [3, 6, 6, 6, 6, 6, 12, 15], [3, 6, 6, 6, 6, 6, 27], [3, 6, 6, 6, 6, 9, 9, 15], [3, 6, 6, 6, 6, 9, 12, 12], [3, 6, 6, 6, 6, 9, 24], [3, 6, 6, 6, 6, 12, 21], [3, 6, 6, 6, 6, 15, 18], [3, 6, 6, 6, 6, 33], [3, 6, 6, 6, 9, 9, 9, 12], [3, 6, 6, 6, 9, 9, 21], [3, 6, 6, 6, 9, 12, 18], [3, 6, 6, 6, 9, 15, 15], [3, 6, 6, 6, 9, 30], [3, 6, 6, 6, 12, 12, 15], [3, 6, 6, 6, 12, 27], [3, 6, 6, 6, 15, 24], [3, 6, 6, 6, 18, 21], [3, 6, 6, 6, 39], [3, 6, 6, 9, 9, 9, 9, 9], [3, 6, 6, 9, 9, 9, 18], [3, 6, 6, 9, 9, 12, 15], [3, 6, 6, 9, 9, 27], [3, 6, 6, 9, 12, 12, 12], [3, 6, 6, 9, 12, 24], [3, 6, 6, 9, 15, 21], [3, 6, 6, 9, 18, 18], [3, 6, 6, 9, 36], [3, 6, 6, 12, 12, 21], [3, 6, 6, 12, 15, 18], [3, 6, 6, 12, 33], [3, 6, 6, 15, 15, 15], [3, 6, 6, 15, 30], [3, 6, 6, 18, 27], [3, 6, 6, 21, 24], [3, 6, 6, 45], [3, 6, 9, 9, 9, 9, 15], [3, 6, 9, 9, 9, 12, 12], [3, 6, 9, 9, 9, 24], [3, 6, 9, 9, 12, 21], [3, 6, 9, 9, 15, 18], [3, 6, 9, 9, 33], [3, 6, 9, 12, 12, 18], [3, 6, 9, 12, 15, 15], [3, 6, 9, 12, 30], [3, 6, 9, 15, 27], [3, 6, 9, 18, 24], [3, 6, 9, 21, 21], [3, 6, 9, 42], [3, 6, 12, 12, 12, 15], [3, 6, 12, 12, 27], [3, 6, 12, 15, 24], [3, 6, 12, 18, 21], [3, 6, 12, 39], [3, 6, 15, 15, 21], [3, 6, 15, 18, 18], [3, 6, 15, 36], [3, 6, 18, 33], [3, 6, 21, 30], [3, 6, 24, 27], [3, 9, 9, 9, 9, 9, 12], [3, 9, 9, 9, 9, 21], [3, 9, 9, 9, 12, 18], [3, 9, 9, 9, 15, 15], [3, 9, 9, 9, 30], [3, 9, 9, 12, 12, 15], [3, 9, 9, 12, 27], [3, 9, 9, 15, 24], [3, 9, 9, 18, 21], [3, 9, 9, 39], [3, 9, 12, 12, 12, 12], [3, 9, 12, 12, 24], [3, 9, 12, 15, 21], [3, 9, 12, 18, 18], [3, 9, 12, 36], [3, 9, 15, 15, 18], [3, 9, 15, 33], [3, 9, 18, 30], [3, 9, 21, 27], [3, 9, 24, 24], [3, 12, 12, 12, 21], [3, 12, 12, 15, 18], [3, 12, 12, 33], [3, 12, 15, 15, 15], [3, 12, 15, 30], [3, 12, 18, 27], [3, 12, 21, 24], [3, 12, 45], [3, 15, 15, 27], [3, 15, 18, 24], [3, 15, 21, 21], [3, 15, 42], [3, 18, 18, 21], [3, 18, 39], [3, 21, 36], [3, 24, 33], [3, 27, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 12], [6, 6, 6, 6, 6, 6, 6, 9, 9], [6, 6, 6, 6, 6, 6, 6, 18], [6, 6, 6, 6, 6, 6, 9, 15], [6, 6, 6, 6, 6, 6, 12, 12], [6, 6, 6, 6, 6, 6, 24], [6, 6, 6, 6, 6, 9, 9, 12], [6, 6, 6, 6, 6, 9, 21], [6, 6, 6, 6, 6, 12, 18], [6, 6, 6, 6, 6, 15, 15], [6, 6, 6, 6, 6, 30], [6, 6, 6, 6, 9, 9, 9, 9], [6, 6, 6, 6, 9, 9, 18], [6, 6, 6, 6, 9, 12, 15], [6, 6, 6, 6, 9, 27], [6, 6, 6, 6, 12, 12, 12], [6, 6, 6, 6, 12, 24], [6, 6, 6, 6, 15, 21], [6, 6, 6, 6, 18, 18], [6, 6, 6, 6, 36], [6, 6, 6, 9, 9, 9, 15], [6, 6, 6, 9, 9, 12, 12], [6, 6, 6, 9, 9, 24], [6, 6, 6, 9, 12, 21], [6, 6, 6, 9, 15, 18], [6, 6, 6, 9, 33], [6, 6, 6, 12, 12, 18], [6, 6, 6, 12, 15, 15], [6, 6, 6, 12, 30], [6, 6, 6, 15, 27], [6, 6, 6, 18, 24], [6, 6, 6, 21, 21], [6, 6, 6, 42], [6, 6, 9, 9, 9, 9, 12], [6, 6, 9, 9, 9, 21], [6, 6, 9, 9, 12, 18], [6, 6, 9, 9, 15, 15], [6, 6, 9, 9, 30], [6, 6, 9, 12, 12, 15], [6, 6, 9, 12, 27], [6, 6, 9, 15, 24], [6, 6, 9, 18, 21], [6, 6, 9, 39], [6, 6, 12, 12, 12, 12], [6, 6, 12, 12, 24], [6, 6, 12, 15, 21], [6, 6, 12, 18, 18], [6, 6, 12, 36], [6, 6, 15, 15, 18], [6, 6, 15, 33], [6, 6, 18, 30], [6, 6, 21, 27], [6, 6, 24, 24], [6, 9, 9, 9, 9, 9, 9], [6, 9, 9, 9, 9, 18], [6, 9, 9, 9, 12, 15], [6, 9, 9, 9, 27], [6, 9, 9, 12, 12, 12], [6, 9, 9, 12, 24], [6, 9, 9, 15, 21], [6, 9, 9, 18, 18], [6, 9, 9, 36], [6, 9, 12, 12, 21], [6, 9, 12, 15, 18], [6, 9, 12, 33], [6, 9, 15, 15, 15], [6, 9, 15, 30], [6, 9, 18, 27], [6, 9, 21, 24], [6, 9, 45], [6, 12, 12, 12, 18], [6, 12, 12, 15, 15], [6, 12, 12, 30], [6, 12, 15, 27], [6, 12, 18, 24], [6, 12, 21, 21], [6, 12, 42], [6, 15, 15, 24], [6, 15, 18, 21], [6, 15, 39], [6, 18, 18, 18], [6, 18, 36], [6, 21, 33], [6, 24, 30], [6, 27, 27], [9, 9, 9, 9, 9, 15], [9, 9, 9, 9, 12, 12], [9, 9, 9, 9, 24], [9, 9, 9, 12, 21], [9, 9, 9, 15, 18], [9, 9, 9, 33], [9, 9, 12, 12, 18], [9, 9, 12, 15, 15], [9, 9, 12, 30], [9, 9, 15, 27], [9, 9, 18, 24], [9, 9, 21, 21], [9, 9, 42], [9, 12, 12, 12, 15], [9, 12, 12, 27], [9, 12, 15, 24], [9, 12, 18, 21], [9, 12, 39], [9, 15, 15, 21], [9, 15, 18, 18], [9, 15, 36], [9, 18, 33], [9, 21, 30], [9, 24, 27], [12, 12, 12, 12, 12], [12, 12, 12, 24], [12, 12, 15, 21], [12, 12, 18, 18], [12, 12, 36], [12, 15, 15, 18], [12, 15, 33], [12, 18, 30], [12, 21, 27], [12, 24, 24], [15, 15, 15, 15], [15, 15, 30], [15, 18, 27], [15, 21, 24], [15, 45], [18, 18, 24], [18, 21, 21], [18, 42], [21, 39], [24, 36], [27, 33], [30, 30]]\n assert candidate(candidates = [18, 14, 9, 7, 3, 2, 1],target = 30) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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2], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 9], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 7, 7], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 14], [1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 7], [1, 1, 1, 1, 2, 2, 2, 2, 2, 7, 9], [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 9], [1, 1, 1, 1, 2, 2, 2, 2, 9, 9], [1, 1, 1, 1, 2, 2, 2, 2, 18], [1, 1, 1, 1, 2, 2, 2, 3, 3, 7, 7], [1, 1, 1, 1, 2, 2, 2, 3, 3, 14], [1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 7], [1, 1, 1, 1, 2, 2, 3, 3, 7, 9], [1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 9], [1, 1, 1, 1, 2, 3, 3, 9, 9], [1, 1, 1, 1, 2, 3, 3, 18], [1, 1, 1, 1, 2, 3, 7, 7, 7], [1, 1, 1, 1, 2, 3, 7, 14], [1, 1, 1, 1, 3, 3, 3, 3, 7, 7], [1, 1, 1, 1, 3, 3, 3, 3, 14], [1, 1, 1, 1, 3, 7, 7, 9], [1, 1, 1, 1, 3, 9, 14], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7], [1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 9], [1, 1, 1, 2, 2, 2, 2, 2, 3, 7, 7], [1, 1, 1, 2, 2, 2, 2, 2, 3, 14], [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 7], [1, 1, 1, 2, 2, 2, 2, 3, 7, 9], [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 9], [1, 1, 1, 2, 2, 2, 3, 9, 9], [1, 1, 1, 2, 2, 2, 3, 18], [1, 1, 1, 2, 2, 2, 7, 7, 7], [1, 1, 1, 2, 2, 2, 7, 14], [1, 1, 1, 2, 2, 3, 3, 3, 7, 7], [1, 1, 1, 2, 2, 3, 3, 3, 14], [1, 1, 1, 2, 2, 7, 7, 9], [1, 1, 1, 2, 2, 9, 14], [1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 7], [1, 1, 1, 2, 3, 3, 3, 7, 9], [1, 1, 1, 2, 7, 9, 9], [1, 1, 1, 2, 7, 18], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 3, 3, 3, 3, 3, 3, 9], [1, 1, 1, 3, 3, 3, 9, 9], [1, 1, 1, 3, 3, 3, 18], [1, 1, 1, 3, 3, 7, 7, 7], [1, 1, 1, 3, 3, 7, 14], [1, 1, 1, 9, 9, 9], [1, 1, 1, 9, 18], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 9], [1, 1, 2, 2, 2, 2, 2, 2, 2, 7, 7], [1, 1, 2, 2, 2, 2, 2, 2, 2, 14], [1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [1, 1, 2, 2, 2, 2, 2, 2, 7, 9], [1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 9], [1, 1, 2, 2, 2, 2, 2, 9, 9], [1, 1, 2, 2, 2, 2, 2, 18], [1, 1, 2, 2, 2, 2, 3, 3, 7, 7], [1, 1, 2, 2, 2, 2, 3, 3, 14], [1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 7], [1, 1, 2, 2, 2, 3, 3, 7, 9], [1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 2, 2, 3, 3, 3, 3, 3, 9], [1, 1, 2, 2, 3, 3, 9, 9], [1, 1, 2, 2, 3, 3, 18], [1, 1, 2, 2, 3, 7, 7, 7], [1, 1, 2, 2, 3, 7, 14], [1, 1, 2, 3, 3, 3, 3, 7, 7], [1, 1, 2, 3, 3, 3, 3, 14], [1, 1, 2, 3, 7, 7, 9], [1, 1, 2, 3, 9, 14], [1, 1, 3, 3, 3, 3, 3, 3, 3, 7], [1, 1, 3, 3, 3, 3, 7, 9], [1, 1, 3, 7, 9, 9], [1, 1, 3, 7, 18], [1, 1, 7, 7, 7, 7], [1, 1, 7, 7, 14], [1, 1, 14, 14], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 9], [1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7], [1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], [1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 9], [1, 2, 2, 2, 2, 2, 2, 3, 7, 7], [1, 2, 2, 2, 2, 2, 2, 3, 14], [1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7], [1, 2, 2, 2, 2, 2, 3, 7, 9], [1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3, 3, 3, 9], [1, 2, 2, 2, 2, 3, 9, 9], [1, 2, 2, 2, 2, 3, 18], [1, 2, 2, 2, 2, 7, 7, 7], [1, 2, 2, 2, 2, 7, 14], [1, 2, 2, 2, 3, 3, 3, 7, 7], [1, 2, 2, 2, 3, 3, 3, 14], [1, 2, 2, 2, 7, 7, 9], [1, 2, 2, 2, 9, 14], [1, 2, 2, 3, 3, 3, 3, 3, 3, 7], [1, 2, 2, 3, 3, 3, 7, 9], [1, 2, 2, 7, 9, 9], [1, 2, 2, 7, 18], [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 2, 3, 3, 3, 3, 3, 3, 9], [1, 2, 3, 3, 3, 9, 9], [1, 2, 3, 3, 3, 18], [1, 2, 3, 3, 7, 7, 7], [1, 2, 3, 3, 7, 14], [1, 2, 9, 9, 9], [1, 2, 9, 18], [1, 3, 3, 3, 3, 3, 7, 7], [1, 3, 3, 3, 3, 3, 14], [1, 3, 3, 7, 7, 9], [1, 3, 3, 9, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 9], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 14], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 7, 9], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 3, 3, 3, 9], [2, 2, 2, 2, 2, 2, 9, 9], [2, 2, 2, 2, 2, 2, 18], [2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 3, 3, 14], [2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 3, 3, 7, 9], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 3, 9], [2, 2, 2, 3, 3, 9, 9], [2, 2, 2, 3, 3, 18], [2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 3, 7, 14], [2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 3, 3, 3, 3, 14], [2, 2, 3, 7, 7, 9], [2, 2, 3, 9, 14], [2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 3, 3, 3, 3, 7, 9], [2, 3, 7, 9, 9], [2, 3, 7, 18], [2, 7, 7, 7, 7], [2, 7, 7, 14], [2, 14, 14], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 9, 9], [3, 3, 3, 3, 18], [3, 3, 3, 7, 7, 7], [3, 3, 3, 7, 14], [3, 9, 9, 9], [3, 9, 18], [7, 7, 7, 9], [7, 9, 14]]\n assert candidate(candidates = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29],target = 50) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 23], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 23], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 11, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 23], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 23], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 13, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 11, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 29], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 13, 19], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 3, 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5, 5, 5, 5, 13], [3, 3, 3, 3, 5, 5, 5, 5, 7, 11], [3, 3, 3, 3, 5, 5, 5, 23], [3, 3, 3, 3, 5, 5, 7, 7, 7, 7], [3, 3, 3, 3, 5, 5, 11, 17], [3, 3, 3, 3, 5, 7, 7, 19], [3, 3, 3, 3, 5, 7, 13, 13], [3, 3, 3, 3, 5, 11, 11, 11], [3, 3, 3, 3, 7, 7, 7, 17], [3, 3, 3, 3, 7, 7, 11, 13], [3, 3, 3, 3, 19, 19], [3, 3, 3, 5, 5, 5, 5, 5, 5, 11], [3, 3, 3, 5, 5, 5, 5, 7, 7, 7], [3, 3, 3, 5, 5, 5, 7, 19], [3, 3, 3, 5, 5, 5, 13, 13], [3, 3, 3, 5, 5, 7, 7, 17], [3, 3, 3, 5, 5, 7, 11, 13], [3, 3, 3, 5, 7, 7, 11, 11], [3, 3, 3, 5, 7, 29], [3, 3, 3, 5, 13, 23], [3, 3, 3, 5, 17, 19], [3, 3, 3, 7, 7, 7, 7, 13], [3, 3, 3, 7, 11, 23], [3, 3, 3, 7, 17, 17], [3, 3, 3, 11, 11, 19], [3, 3, 3, 11, 13, 17], [3, 3, 5, 5, 5, 5, 5, 5, 7, 7], [3, 3, 5, 5, 5, 5, 5, 19], [3, 3, 5, 5, 5, 5, 7, 17], [3, 3, 5, 5, 5, 5, 11, 13], [3, 3, 5, 5, 5, 7, 11, 11], [3, 3, 5, 5, 5, 29], [3, 3, 5, 5, 7, 7, 7, 13], [3, 3, 5, 5, 11, 23], [3, 3, 5, 5, 17, 17], [3, 3, 5, 7, 7, 7, 7, 11], [3, 3, 5, 7, 13, 19], [3, 3, 5, 11, 11, 17], [3, 3, 5, 13, 13, 13], [3, 3, 7, 7, 7, 23], [3, 3, 7, 7, 11, 19], [3, 3, 7, 7, 13, 17], [3, 3, 7, 11, 13, 13], [3, 3, 11, 11, 11, 11], [3, 5, 5, 5, 5, 5, 5, 5, 5, 7], [3, 5, 5, 5, 5, 5, 5, 17], [3, 5, 5, 5, 5, 5, 11, 11], [3, 5, 5, 5, 5, 7, 7, 13], [3, 5, 5, 5, 7, 7, 7, 11], [3, 5, 5, 5, 13, 19], [3, 5, 5, 7, 7, 23], [3, 5, 5, 7, 11, 19], [3, 5, 5, 7, 13, 17], [3, 5, 5, 11, 13, 13], [3, 5, 7, 7, 7, 7, 7, 7], [3, 5, 7, 7, 11, 17], [3, 5, 7, 11, 11, 13], [3, 5, 13, 29], [3, 5, 19, 23], [3, 7, 7, 7, 7, 19], [3, 7, 7, 7, 13, 13], [3, 7, 7, 11, 11, 11], [3, 7, 11, 29], [3, 7, 17, 23], [3, 11, 13, 23], [3, 11, 17, 19], [3, 13, 17, 17], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 7, 13], [5, 5, 5, 5, 5, 7, 7, 11], [5, 5, 5, 5, 7, 23], [5, 5, 5, 5, 11, 19], [5, 5, 5, 5, 13, 17], [5, 5, 5, 7, 7, 7, 7, 7], [5, 5, 5, 7, 11, 17], [5, 5, 5, 11, 11, 13], [5, 5, 7, 7, 7, 19], [5, 5, 7, 7, 13, 13], [5, 5, 7, 11, 11, 11], [5, 5, 11, 29], [5, 5, 17, 23], [5, 7, 7, 7, 7, 17], [5, 7, 7, 7, 11, 13], [5, 7, 19, 19], [5, 11, 11, 23], [5, 11, 17, 17], [5, 13, 13, 19], [7, 7, 7, 7, 11, 11], [7, 7, 7, 29], [7, 7, 13, 23], [7, 7, 17, 19], [7, 11, 13, 19], [7, 13, 13, 17], [11, 11, 11, 17], [11, 13, 13, 13]]\n assert candidate(candidates = [2, 5, 10, 15],target = 20) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 10], [5, 5, 5, 5], [5, 5, 10], [5, 15], [10, 10]]\n assert candidate(candidates = [18, 27, 36, 45, 54],target = 126) == [[18, 18, 18, 18, 18, 18, 18], [18, 18, 18, 18, 18, 36], [18, 18, 18, 18, 27, 27], [18, 18, 18, 18, 54], [18, 18, 18, 27, 45], [18, 18, 18, 36, 36], [18, 18, 27, 27, 36], [18, 18, 36, 54], [18, 18, 45, 45], [18, 27, 27, 27, 27], [18, 27, 27, 54], [18, 27, 36, 45], [18, 36, 36, 36], [18, 54, 54], [27, 27, 27, 45], [27, 27, 36, 36], [27, 45, 54], [36, 36, 54], [36, 45, 45]]\n assert candidate(candidates = [5, 10, 20, 25, 30, 35, 40],target = 70) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 25], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 30], [5, 5, 5, 5, 5, 5, 5, 10, 25], [5, 5, 5, 5, 5, 5, 5, 35], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 10, 10, 20], [5, 5, 5, 5, 5, 5, 10, 30], [5, 5, 5, 5, 5, 5, 20, 20], [5, 5, 5, 5, 5, 5, 40], [5, 5, 5, 5, 5, 10, 10, 25], [5, 5, 5, 5, 5, 10, 35], [5, 5, 5, 5, 5, 20, 25], [5, 5, 5, 5, 10, 10, 10, 10, 10], [5, 5, 5, 5, 10, 10, 10, 20], [5, 5, 5, 5, 10, 10, 30], [5, 5, 5, 5, 10, 20, 20], [5, 5, 5, 5, 10, 40], [5, 5, 5, 5, 20, 30], [5, 5, 5, 5, 25, 25], [5, 5, 5, 10, 10, 10, 25], [5, 5, 5, 10, 10, 35], [5, 5, 5, 10, 20, 25], [5, 5, 5, 20, 35], [5, 5, 5, 25, 30], [5, 5, 10, 10, 10, 10, 10, 10], [5, 5, 10, 10, 10, 10, 20], [5, 5, 10, 10, 10, 30], [5, 5, 10, 10, 20, 20], [5, 5, 10, 10, 40], [5, 5, 10, 20, 30], [5, 5, 10, 25, 25], [5, 5, 20, 20, 20], [5, 5, 20, 40], [5, 5, 25, 35], [5, 5, 30, 30], [5, 10, 10, 10, 10, 25], [5, 10, 10, 10, 35], [5, 10, 10, 20, 25], [5, 10, 20, 35], [5, 10, 25, 30], [5, 20, 20, 25], [5, 25, 40], [5, 30, 35], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 30], [10, 10, 10, 20, 20], [10, 10, 10, 40], [10, 10, 20, 30], [10, 10, 25, 25], [10, 20, 20, 20], [10, 20, 40], [10, 25, 35], [10, 30, 30], [20, 20, 30], [20, 25, 25], [30, 40], [35, 35]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 25) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 9], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 9], [1, 1, 1, 1, 1, 1, 1, 1, 3, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 17], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 9], [1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 7], [1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 3, 15], [1, 1, 1, 1, 1, 1, 1, 5, 13], [1, 1, 1, 1, 1, 1, 1, 7, 11], [1, 1, 1, 1, 1, 1, 1, 9, 9], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 7], [1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 3, 3, 13], [1, 1, 1, 1, 1, 1, 3, 5, 11], [1, 1, 1, 1, 1, 1, 3, 7, 9], [1, 1, 1, 1, 1, 1, 5, 5, 9], [1, 1, 1, 1, 1, 1, 5, 7, 7], [1, 1, 1, 1, 1, 1, 19], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 3, 3, 3, 11], [1, 1, 1, 1, 1, 3, 3, 5, 9], [1, 1, 1, 1, 1, 3, 3, 7, 7], [1, 1, 1, 1, 1, 3, 5, 5, 7], [1, 1, 1, 1, 1, 3, 17], [1, 1, 1, 1, 1, 5, 5, 5, 5], [1, 1, 1, 1, 1, 5, 15], [1, 1, 1, 1, 1, 7, 13], [1, 1, 1, 1, 1, 9, 11], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 3, 3, 3, 3, 9], [1, 1, 1, 1, 3, 3, 3, 5, 7], [1, 1, 1, 1, 3, 3, 5, 5, 5], [1, 1, 1, 1, 3, 3, 15], [1, 1, 1, 1, 3, 5, 13], [1, 1, 1, 1, 3, 7, 11], [1, 1, 1, 1, 3, 9, 9], [1, 1, 1, 1, 5, 5, 11], [1, 1, 1, 1, 5, 7, 9], [1, 1, 1, 1, 7, 7, 7], [1, 1, 1, 3, 3, 3, 3, 3, 7], [1, 1, 1, 3, 3, 3, 3, 5, 5], [1, 1, 1, 3, 3, 3, 13], [1, 1, 1, 3, 3, 5, 11], [1, 1, 1, 3, 3, 7, 9], [1, 1, 1, 3, 5, 5, 9], [1, 1, 1, 3, 5, 7, 7], [1, 1, 1, 3, 19], [1, 1, 1, 5, 5, 5, 7], [1, 1, 1, 5, 17], [1, 1, 1, 7, 15], [1, 1, 1, 9, 13], [1, 1, 1, 11, 11], [1, 1, 3, 3, 3, 3, 3, 3, 5], [1, 1, 3, 3, 3, 3, 11], [1, 1, 3, 3, 3, 5, 9], [1, 1, 3, 3, 3, 7, 7], [1, 1, 3, 3, 5, 5, 7], [1, 1, 3, 3, 17], [1, 1, 3, 5, 5, 5, 5], [1, 1, 3, 5, 15], [1, 1, 3, 7, 13], [1, 1, 3, 9, 11], [1, 1, 5, 5, 13], [1, 1, 5, 7, 11], [1, 1, 5, 9, 9], [1, 1, 7, 7, 9], [1, 3, 3, 3, 3, 3, 3, 3, 3], [1, 3, 3, 3, 3, 3, 9], [1, 3, 3, 3, 3, 5, 7], [1, 3, 3, 3, 5, 5, 5], [1, 3, 3, 3, 15], [1, 3, 3, 5, 13], [1, 3, 3, 7, 11], [1, 3, 3, 9, 9], [1, 3, 5, 5, 11], [1, 3, 5, 7, 9], [1, 3, 7, 7, 7], [1, 5, 5, 5, 9], [1, 5, 5, 7, 7], [1, 5, 19], [1, 7, 17], [1, 9, 15], [1, 11, 13], [3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 13], [3, 3, 3, 5, 11], [3, 3, 3, 7, 9], [3, 3, 5, 5, 9], [3, 3, 5, 7, 7], [3, 3, 19], [3, 5, 5, 5, 7], [3, 5, 17], [3, 7, 15], [3, 9, 13], [3, 11, 11], [5, 5, 5, 5, 5], [5, 5, 15], [5, 7, 13], [5, 9, 11], [7, 7, 11], [7, 9, 9]]\n assert candidate(candidates = [8, 15, 7, 9, 10, 1],target = 31) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 9], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 8], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 15], [1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 9], [1, 1, 1, 1, 1, 1, 1, 1, 7, 8, 8], [1, 1, 1, 1, 1, 1, 1, 1, 8, 15], [1, 1, 1, 1, 1, 1, 1, 7, 7, 10], [1, 1, 1, 1, 1, 1, 1, 7, 8, 9], [1, 1, 1, 1, 1, 1, 1, 8, 8, 8], [1, 1, 1, 1, 1, 1, 1, 9, 15], [1, 1, 1, 1, 1, 1, 7, 8, 10], [1, 1, 1, 1, 1, 1, 7, 9, 9], [1, 1, 1, 1, 1, 1, 8, 8, 9], [1, 1, 1, 1, 1, 1, 10, 15], [1, 1, 1, 1, 1, 7, 9, 10], [1, 1, 1, 1, 1, 8, 8, 10], [1, 1, 1, 1, 1, 8, 9, 9], [1, 1, 1, 1, 7, 10, 10], [1, 1, 1, 1, 8, 9, 10], [1, 1, 1, 1, 9, 9, 9], [1, 1, 1, 7, 7, 7, 7], [1, 1, 1, 8, 10, 10], [1, 1, 1, 9, 9, 10], [1, 1, 7, 7, 7, 8], [1, 1, 7, 7, 15], [1, 1, 9, 10, 10], [1, 7, 7, 7, 9], [1, 7, 7, 8, 8], [1, 7, 8, 15], [1, 10, 10, 10], [1, 15, 15], [7, 7, 7, 10], [7, 7, 8, 9], [7, 8, 8, 8], [7, 9, 15], [8, 8, 15]]\n assert candidate(candidates = [5, 10, 15, 20, 25],target = 50) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 10, 15], [5, 5, 5, 5, 5, 25], [5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 10, 20], [5, 5, 5, 5, 15, 15], [5, 5, 5, 10, 10, 15], [5, 5, 5, 10, 25], [5, 5, 5, 15, 20], [5, 5, 10, 10, 10, 10], [5, 5, 10, 10, 20], [5, 5, 10, 15, 15], [5, 5, 15, 25], [5, 5, 20, 20], [5, 10, 10, 10, 15], [5, 10, 10, 25], [5, 10, 15, 20], [5, 15, 15, 15], [5, 20, 25], [10, 10, 10, 10, 10], [10, 10, 10, 20], [10, 10, 15, 15], [10, 15, 25], [10, 20, 20], [15, 15, 20], [25, 25]]\n assert candidate(candidates = [7, 14, 21, 28, 35],target = 70) == [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 14], [7, 7, 7, 7, 7, 7, 7, 21], [7, 7, 7, 7, 7, 7, 14, 14], [7, 7, 7, 7, 7, 7, 28], [7, 7, 7, 7, 7, 14, 21], [7, 7, 7, 7, 7, 35], [7, 7, 7, 7, 14, 14, 14], [7, 7, 7, 7, 14, 28], [7, 7, 7, 7, 21, 21], [7, 7, 7, 14, 14, 21], [7, 7, 7, 14, 35], [7, 7, 7, 21, 28], [7, 7, 14, 14, 14, 14], [7, 7, 14, 14, 28], [7, 7, 14, 21, 21], [7, 7, 21, 35], [7, 7, 28, 28], [7, 14, 14, 14, 21], [7, 14, 14, 35], [7, 14, 21, 28], [7, 21, 21, 21], [7, 28, 35], [14, 14, 14, 14, 14], [14, 14, 14, 28], [14, 14, 21, 21], [14, 21, 35], [14, 28, 28], [21, 21, 28], [35, 35]]\n assert candidate(candidates = [6, 12, 18, 24, 30, 36],target = 60) == [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 12], [6, 6, 6, 6, 6, 6, 6, 18], [6, 6, 6, 6, 6, 6, 12, 12], [6, 6, 6, 6, 6, 6, 24], [6, 6, 6, 6, 6, 12, 18], [6, 6, 6, 6, 6, 30], [6, 6, 6, 6, 12, 12, 12], [6, 6, 6, 6, 12, 24], [6, 6, 6, 6, 18, 18], [6, 6, 6, 6, 36], [6, 6, 6, 12, 12, 18], [6, 6, 6, 12, 30], [6, 6, 6, 18, 24], [6, 6, 12, 12, 12, 12], [6, 6, 12, 12, 24], [6, 6, 12, 18, 18], [6, 6, 12, 36], [6, 6, 18, 30], [6, 6, 24, 24], [6, 12, 12, 12, 18], [6, 12, 12, 30], [6, 12, 18, 24], [6, 18, 18, 18], [6, 18, 36], [6, 24, 30], [12, 12, 12, 12, 12], [12, 12, 12, 24], [12, 12, 18, 18], [12, 12, 36], [12, 18, 30], [12, 24, 24], [18, 18, 24], [24, 36], [30, 30]]\n assert candidate(candidates = [29, 23, 17, 11, 5, 3, 1],target = 47) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 29], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 29], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 29], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 29], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 11, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 17, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 29], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 23], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 11, 17], [1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 11, 11, 11], [1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 29], [1, 1, 1, 1, 1, 1, 1, 1, 5, 11, 23], [1, 1, 1, 1, 1, 1, 1, 1, 5, 17, 17], [1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 17], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 11], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 17], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 11, 11], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 23], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 11, 17], [1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 29], [1, 1, 1, 1, 1, 1, 1, 3, 3, 11, 23], [1, 1, 1, 1, 1, 1, 1, 3, 3, 17, 17], [1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 5, 17], [1, 1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 11, 11], [1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 11, 29], [1, 1, 1, 1, 1, 1, 1, 17, 23], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 17], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 23], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 5, 11], [1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 29], [1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 5, 17], [1, 1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 11, 11], [1, 1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 3, 5, 5, 5, 23], [1, 1, 1, 1, 1, 1, 3, 5, 5, 11, 17], [1, 1, 1, 1, 1, 1, 3, 5, 11, 11, 11], [1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5, 5, 11], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 17], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 11, 11], [1, 1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 3, 3, 3, 5, 5, 23], [1, 1, 1, 1, 1, 3, 3, 3, 5, 11, 17], [1, 1, 1, 1, 1, 3, 3, 3, 11, 11, 11], [1, 1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 5, 11], [1, 1, 1, 1, 1, 3, 5, 5, 29], [1, 1, 1, 1, 1, 3, 5, 11, 23], [1, 1, 1, 1, 1, 3, 5, 17, 17], [1, 1, 1, 1, 1, 3, 11, 11, 17], [1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 17], [1, 1, 1, 1, 1, 5, 5, 5, 5, 11, 11], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 11], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 5, 17], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 11, 11], [1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5], [1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 23], [1, 1, 1, 1, 3, 3, 3, 3, 3, 11, 17], [1, 1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 5, 11], [1, 1, 1, 1, 3, 3, 3, 5, 29], [1, 1, 1, 1, 3, 3, 3, 11, 23], [1, 1, 1, 1, 3, 3, 3, 17, 17], [1, 1, 1, 1, 3, 3, 5, 5, 5, 5, 17], [1, 1, 1, 1, 3, 3, 5, 5, 5, 11, 11], [1, 1, 1, 1, 3, 5, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 1, 3, 11, 29], [1, 1, 1, 1, 3, 17, 23], [1, 1, 1, 1, 5, 5, 5, 5, 23], [1, 1, 1, 1, 5, 5, 5, 11, 17], [1, 1, 1, 1, 5, 5, 11, 11, 11], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 17], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 23], [1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 11], [1, 1, 1, 3, 3, 3, 3, 3, 29], [1, 1, 1, 3, 3, 3, 3, 5, 5, 5, 17], [1, 1, 1, 3, 3, 3, 3, 5, 5, 11, 11], [1, 1, 1, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5], [1, 1, 1, 3, 3, 5, 5, 5, 23], [1, 1, 1, 3, 3, 5, 5, 11, 17], [1, 1, 1, 3, 3, 5, 11, 11, 11], [1, 1, 1, 3, 5, 5, 5, 5, 5, 5, 11], [1, 1, 1, 5, 5, 5, 29], [1, 1, 1, 5, 5, 11, 23], [1, 1, 1, 5, 5, 17, 17], [1, 1, 1, 5, 11, 11, 17], [1, 1, 1, 11, 11, 11, 11], [1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 11], [1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 17], [1, 1, 3, 3, 3, 3, 3, 3, 5, 11, 11], [1, 1, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5], [1, 1, 3, 3, 3, 3, 5, 5, 23], [1, 1, 3, 3, 3, 3, 5, 11, 17], [1, 1, 3, 3, 3, 3, 11, 11, 11], [1, 1, 3, 3, 3, 5, 5, 5, 5, 5, 11], [1, 1, 3, 3, 5, 5, 29], [1, 1, 3, 3, 5, 11, 23], [1, 1, 3, 3, 5, 17, 17], [1, 1, 3, 3, 11, 11, 17], [1, 1, 3, 5, 5, 5, 5, 5, 17], [1, 1, 3, 5, 5, 5, 5, 11, 11], [1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5], [1, 1, 5, 11, 29], [1, 1, 5, 17, 23], [1, 1, 11, 11, 23], [1, 1, 11, 17, 17], [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 11], [1, 3, 3, 3, 3, 3, 3, 3, 3, 5, 17], [1, 3, 3, 3, 3, 3, 3, 3, 3, 11, 11], [1, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5], [1, 3, 3, 3, 3, 3, 3, 5, 23], [1, 3, 3, 3, 3, 3, 3, 11, 17], [1, 3, 3, 3, 3, 3, 5, 5, 5, 5, 11], [1, 3, 3, 3, 3, 5, 29], [1, 3, 3, 3, 3, 11, 23], [1, 3, 3, 3, 3, 17, 17], [1, 3, 3, 3, 5, 5, 5, 5, 17], [1, 3, 3, 3, 5, 5, 5, 11, 11], [1, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5], [1, 3, 3, 11, 29], [1, 3, 3, 17, 23], [1, 3, 5, 5, 5, 5, 23], [1, 3, 5, 5, 5, 11, 17], [1, 3, 5, 5, 11, 11, 11], [1, 5, 5, 5, 5, 5, 5, 5, 11], [1, 17, 29], [1, 23, 23], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [3, 3, 3, 3, 3, 3, 3, 3, 23], [3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 11], [3, 3, 3, 3, 3, 3, 29], [3, 3, 3, 3, 3, 5, 5, 5, 17], [3, 3, 3, 3, 3, 5, 5, 11, 11], [3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5], [3, 3, 3, 5, 5, 5, 23], [3, 3, 3, 5, 5, 11, 17], [3, 3, 3, 5, 11, 11, 11], [3, 3, 5, 5, 5, 5, 5, 5, 11], [3, 5, 5, 5, 29], [3, 5, 5, 11, 23], [3, 5, 5, 17, 17], [3, 5, 11, 11, 17], [3, 11, 11, 11, 11], [5, 5, 5, 5, 5, 5, 17], [5, 5, 5, 5, 5, 11, 11]]\n assert candidate(candidates = [5, 10, 15, 20, 25],target = 50) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 10, 15], [5, 5, 5, 5, 5, 25], [5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 10, 20], [5, 5, 5, 5, 15, 15], [5, 5, 5, 10, 10, 15], [5, 5, 5, 10, 25], [5, 5, 5, 15, 20], [5, 5, 10, 10, 10, 10], [5, 5, 10, 10, 20], [5, 5, 10, 15, 15], [5, 5, 15, 25], [5, 5, 20, 20], [5, 10, 10, 10, 15], [5, 10, 10, 25], [5, 10, 15, 20], [5, 15, 15, 15], [5, 20, 25], [10, 10, 10, 10, 10], [10, 10, 10, 20], [10, 10, 15, 15], [10, 15, 25], [10, 20, 20], [15, 15, 20], [25, 25]]\n assert candidate(candidates = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 150) == [[10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 30], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 40], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 30], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 50], [10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 20], [10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 40], [10, 10, 10, 10, 10, 10, 10, 10, 10, 30, 30], [10, 10, 10, 10, 10, 10, 10, 10, 10, 60], [10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 30], [10, 10, 10, 10, 10, 10, 10, 10, 20, 50], [10, 10, 10, 10, 10, 10, 10, 10, 30, 40], [10, 10, 10, 10, 10, 10, 10, 10, 70], [10, 10, 10, 10, 10, 10, 10, 20, 20, 20, 20], [10, 10, 10, 10, 10, 10, 10, 20, 20, 40], [10, 10, 10, 10, 10, 10, 10, 20, 30, 30], [10, 10, 10, 10, 10, 10, 10, 20, 60], [10, 10, 10, 10, 10, 10, 10, 30, 50], [10, 10, 10, 10, 10, 10, 10, 40, 40], [10, 10, 10, 10, 10, 10, 10, 80], [10, 10, 10, 10, 10, 10, 20, 20, 20, 30], [10, 10, 10, 10, 10, 10, 20, 20, 50], [10, 10, 10, 10, 10, 10, 20, 30, 40], [10, 10, 10, 10, 10, 10, 20, 70], [10, 10, 10, 10, 10, 10, 30, 30, 30], [10, 10, 10, 10, 10, 10, 30, 60], [10, 10, 10, 10, 10, 10, 40, 50], [10, 10, 10, 10, 10, 10, 90], [10, 10, 10, 10, 10, 20, 20, 20, 20, 20], [10, 10, 10, 10, 10, 20, 20, 20, 40], [10, 10, 10, 10, 10, 20, 20, 30, 30], [10, 10, 10, 10, 10, 20, 20, 60], [10, 10, 10, 10, 10, 20, 30, 50], [10, 10, 10, 10, 10, 20, 40, 40], [10, 10, 10, 10, 10, 20, 80], [10, 10, 10, 10, 10, 30, 30, 40], [10, 10, 10, 10, 10, 30, 70], [10, 10, 10, 10, 10, 40, 60], [10, 10, 10, 10, 10, 50, 50], [10, 10, 10, 10, 10, 100], [10, 10, 10, 10, 20, 20, 20, 20, 30], [10, 10, 10, 10, 20, 20, 20, 50], [10, 10, 10, 10, 20, 20, 30, 40], [10, 10, 10, 10, 20, 20, 70], [10, 10, 10, 10, 20, 30, 30, 30], [10, 10, 10, 10, 20, 30, 60], [10, 10, 10, 10, 20, 40, 50], [10, 10, 10, 10, 20, 90], [10, 10, 10, 10, 30, 30, 50], [10, 10, 10, 10, 30, 40, 40], [10, 10, 10, 10, 30, 80], [10, 10, 10, 10, 40, 70], [10, 10, 10, 10, 50, 60], [10, 10, 10, 20, 20, 20, 20, 20, 20], [10, 10, 10, 20, 20, 20, 20, 40], [10, 10, 10, 20, 20, 20, 30, 30], [10, 10, 10, 20, 20, 20, 60], [10, 10, 10, 20, 20, 30, 50], [10, 10, 10, 20, 20, 40, 40], [10, 10, 10, 20, 20, 80], [10, 10, 10, 20, 30, 30, 40], [10, 10, 10, 20, 30, 70], [10, 10, 10, 20, 40, 60], [10, 10, 10, 20, 50, 50], [10, 10, 10, 20, 100], [10, 10, 10, 30, 30, 30, 30], [10, 10, 10, 30, 30, 60], [10, 10, 10, 30, 40, 50], [10, 10, 10, 30, 90], [10, 10, 10, 40, 40, 40], [10, 10, 10, 40, 80], [10, 10, 10, 50, 70], [10, 10, 10, 60, 60], [10, 10, 20, 20, 20, 20, 20, 30], [10, 10, 20, 20, 20, 20, 50], [10, 10, 20, 20, 20, 30, 40], [10, 10, 20, 20, 20, 70], [10, 10, 20, 20, 30, 30, 30], [10, 10, 20, 20, 30, 60], [10, 10, 20, 20, 40, 50], [10, 10, 20, 20, 90], [10, 10, 20, 30, 30, 50], [10, 10, 20, 30, 40, 40], [10, 10, 20, 30, 80], [10, 10, 20, 40, 70], [10, 10, 20, 50, 60], [10, 10, 30, 30, 30, 40], [10, 10, 30, 30, 70], [10, 10, 30, 40, 60], [10, 10, 30, 50, 50], [10, 10, 30, 100], [10, 10, 40, 40, 50], [10, 10, 40, 90], [10, 10, 50, 80], [10, 10, 60, 70], [10, 20, 20, 20, 20, 20, 20, 20], [10, 20, 20, 20, 20, 20, 40], [10, 20, 20, 20, 20, 30, 30], [10, 20, 20, 20, 20, 60], [10, 20, 20, 20, 30, 50], [10, 20, 20, 20, 40, 40], [10, 20, 20, 20, 80], [10, 20, 20, 30, 30, 40], [10, 20, 20, 30, 70], [10, 20, 20, 40, 60], [10, 20, 20, 50, 50], [10, 20, 20, 100], [10, 20, 30, 30, 30, 30], [10, 20, 30, 30, 60], [10, 20, 30, 40, 50], [10, 20, 30, 90], [10, 20, 40, 40, 40], [10, 20, 40, 80], [10, 20, 50, 70], [10, 20, 60, 60], [10, 30, 30, 30, 50], [10, 30, 30, 40, 40], [10, 30, 30, 80], [10, 30, 40, 70], [10, 30, 50, 60], [10, 40, 40, 60], [10, 40, 50, 50], [10, 40, 100], [10, 50, 90], [10, 60, 80], [10, 70, 70], [20, 20, 20, 20, 20, 20, 30], [20, 20, 20, 20, 20, 50], [20, 20, 20, 20, 30, 40], [20, 20, 20, 20, 70], [20, 20, 20, 30, 30, 30], [20, 20, 20, 30, 60], [20, 20, 20, 40, 50], [20, 20, 20, 90], [20, 20, 30, 30, 50], [20, 20, 30, 40, 40], [20, 20, 30, 80], [20, 20, 40, 70], [20, 20, 50, 60], [20, 30, 30, 30, 40], [20, 30, 30, 70], [20, 30, 40, 60], [20, 30, 50, 50], [20, 30, 100], [20, 40, 40, 50], [20, 40, 90], [20, 50, 80], [20, 60, 70], [30, 30, 30, 30, 30], [30, 30, 30, 60], [30, 30, 40, 50], [30, 30, 90], [30, 40, 40, 40], [30, 40, 80], [30, 50, 70], [30, 60, 60], [40, 40, 70], [40, 50, 60], [50, 50, 50], [50, 100], [60, 90], [70, 80]]\n assert candidate(candidates = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29],target = 40) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 19], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 2, 2, 2, 2, 2, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 2, 2, 2, 2, 2, 5, 19], [2, 2, 2, 2, 2, 2, 2, 2, 7, 17], [2, 2, 2, 2, 2, 2, 2, 2, 11, 13], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 17], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 3, 7, 13], [2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 13], [2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 11], [2, 2, 2, 2, 2, 2, 2, 3, 23], [2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 11], [2, 2, 2, 2, 2, 2, 2, 5, 7, 7, 7], [2, 2, 2, 2, 2, 2, 2, 7, 19], [2, 2, 2, 2, 2, 2, 2, 13, 13], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 13], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 11], [2, 2, 2, 2, 2, 2, 3, 3, 3, 5, 7, 7], [2, 2, 2, 2, 2, 2, 3, 3, 3, 19], [2, 2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 7], [2, 2, 2, 2, 2, 2, 3, 3, 5, 17], [2, 2, 2, 2, 2, 2, 3, 3, 11, 11], [2, 2, 2, 2, 2, 2, 3, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 3, 5, 7, 13], [2, 2, 2, 2, 2, 2, 3, 7, 7, 11], [2, 2, 2, 2, 2, 2, 5, 5, 5, 13], [2, 2, 2, 2, 2, 2, 5, 5, 7, 11], [2, 2, 2, 2, 2, 2, 5, 23], [2, 2, 2, 2, 2, 2, 7, 7, 7, 7], [2, 2, 2, 2, 2, 2, 11, 17], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 7], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5], [2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 13], [2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 11], [2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 11], [2, 2, 2, 2, 2, 3, 3, 3, 7, 7, 7], [2, 2, 2, 2, 2, 3, 3, 5, 5, 7, 7], [2, 2, 2, 2, 2, 3, 3, 5, 19], [2, 2, 2, 2, 2, 3, 3, 7, 17], [2, 2, 2, 2, 2, 3, 3, 11, 13], [2, 2, 2, 2, 2, 3, 5, 5, 5, 5, 7], [2, 2, 2, 2, 2, 3, 5, 5, 17], [2, 2, 2, 2, 2, 3, 5, 11, 11], [2, 2, 2, 2, 2, 3, 7, 7, 13], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 7, 13], [2, 2, 2, 2, 2, 5, 7, 7, 11], [2, 2, 2, 2, 2, 7, 23], [2, 2, 2, 2, 2, 11, 19], [2, 2, 2, 2, 2, 13, 17], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 11], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7], [2, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 7], [2, 2, 2, 2, 3, 3, 3, 3, 3, 17], [2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 5], [2, 2, 2, 2, 3, 3, 3, 3, 7, 13], [2, 2, 2, 2, 3, 3, 3, 5, 5, 13], [2, 2, 2, 2, 3, 3, 3, 5, 7, 11], [2, 2, 2, 2, 3, 3, 3, 23], [2, 2, 2, 2, 3, 3, 5, 5, 5, 11], [2, 2, 2, 2, 3, 3, 5, 7, 7, 7], [2, 2, 2, 2, 3, 3, 7, 19], [2, 2, 2, 2, 3, 3, 13, 13], [2, 2, 2, 2, 3, 5, 5, 5, 7, 7], [2, 2, 2, 2, 3, 5, 5, 19], [2, 2, 2, 2, 3, 5, 7, 17], [2, 2, 2, 2, 3, 5, 11, 13], [2, 2, 2, 2, 3, 7, 11, 11], [2, 2, 2, 2, 3, 29], [2, 2, 2, 2, 5, 5, 5, 5, 5, 7], [2, 2, 2, 2, 5, 5, 5, 17], [2, 2, 2, 2, 5, 5, 11, 11], [2, 2, 2, 2, 5, 7, 7, 13], [2, 2, 2, 2, 7, 7, 7, 11], [2, 2, 2, 2, 13, 19], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 13], [2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 11], [2, 2, 2, 3, 3, 3, 3, 3, 5, 7, 7], [2, 2, 2, 3, 3, 3, 3, 3, 19], [2, 2, 2, 3, 3, 3, 3, 5, 5, 5, 7], [2, 2, 2, 3, 3, 3, 3, 5, 17], [2, 2, 2, 3, 3, 3, 3, 11, 11], [2, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5], [2, 2, 2, 3, 3, 3, 5, 7, 13], [2, 2, 2, 3, 3, 3, 7, 7, 11], [2, 2, 2, 3, 3, 5, 5, 5, 13], [2, 2, 2, 3, 3, 5, 5, 7, 11], [2, 2, 2, 3, 3, 5, 23], [2, 2, 2, 3, 3, 7, 7, 7, 7], [2, 2, 2, 3, 3, 11, 17], [2, 2, 2, 3, 5, 5, 5, 5, 11], [2, 2, 2, 3, 5, 5, 7, 7, 7], [2, 2, 2, 3, 5, 7, 19], [2, 2, 2, 3, 5, 13, 13], [2, 2, 2, 3, 7, 7, 17], [2, 2, 2, 3, 7, 11, 13], [2, 2, 2, 5, 5, 5, 5, 7, 7], [2, 2, 2, 5, 5, 5, 19], [2, 2, 2, 5, 5, 7, 17], [2, 2, 2, 5, 5, 11, 13], [2, 2, 2, 5, 7, 11, 11], [2, 2, 2, 5, 29], [2, 2, 2, 7, 7, 7, 13], [2, 2, 2, 11, 23], [2, 2, 2, 17, 17], [2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 7], [2, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5], [2, 2, 3, 3, 3, 3, 3, 3, 5, 13], [2, 2, 3, 3, 3, 3, 3, 3, 7, 11], [2, 2, 3, 3, 3, 3, 3, 5, 5, 11], [2, 2, 3, 3, 3, 3, 3, 7, 7, 7], [2, 2, 3, 3, 3, 3, 5, 5, 7, 7], [2, 2, 3, 3, 3, 3, 5, 19], [2, 2, 3, 3, 3, 3, 7, 17], [2, 2, 3, 3, 3, 3, 11, 13], [2, 2, 3, 3, 3, 5, 5, 5, 5, 7], [2, 2, 3, 3, 3, 5, 5, 17], [2, 2, 3, 3, 3, 5, 11, 11], [2, 2, 3, 3, 3, 7, 7, 13], [2, 2, 3, 3, 5, 5, 5, 5, 5, 5], [2, 2, 3, 3, 5, 5, 7, 13], [2, 2, 3, 3, 5, 7, 7, 11], [2, 2, 3, 3, 7, 23], [2, 2, 3, 3, 11, 19], [2, 2, 3, 3, 13, 17], [2, 2, 3, 5, 5, 5, 5, 13], [2, 2, 3, 5, 5, 5, 7, 11], [2, 2, 3, 5, 5, 23], [2, 2, 3, 5, 7, 7, 7, 7], [2, 2, 3, 5, 11, 17], [2, 2, 3, 7, 7, 19], [2, 2, 3, 7, 13, 13], [2, 2, 3, 11, 11, 11], [2, 2, 5, 5, 5, 5, 5, 11], [2, 2, 5, 5, 5, 7, 7, 7], [2, 2, 5, 5, 7, 19], [2, 2, 5, 5, 13, 13], [2, 2, 5, 7, 7, 17], [2, 2, 5, 7, 11, 13], [2, 2, 7, 7, 11, 11], [2, 2, 7, 29], [2, 2, 13, 23], [2, 2, 17, 19], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [2, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 7], [2, 3, 3, 3, 3, 3, 3, 3, 17], [2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [2, 3, 3, 3, 3, 3, 3, 7, 13], [2, 3, 3, 3, 3, 3, 5, 5, 13], [2, 3, 3, 3, 3, 3, 5, 7, 11], [2, 3, 3, 3, 3, 3, 23], [2, 3, 3, 3, 3, 5, 5, 5, 11], [2, 3, 3, 3, 3, 5, 7, 7, 7], [2, 3, 3, 3, 3, 7, 19], [2, 3, 3, 3, 3, 13, 13], [2, 3, 3, 3, 5, 5, 5, 7, 7], [2, 3, 3, 3, 5, 5, 19], [2, 3, 3, 3, 5, 7, 17], [2, 3, 3, 3, 5, 11, 13], [2, 3, 3, 3, 7, 11, 11], [2, 3, 3, 3, 29], [2, 3, 3, 5, 5, 5, 5, 5, 7], [2, 3, 3, 5, 5, 5, 17], [2, 3, 3, 5, 5, 11, 11], [2, 3, 3, 5, 7, 7, 13], [2, 3, 3, 7, 7, 7, 11], [2, 3, 3, 13, 19], [2, 3, 5, 5, 5, 5, 5, 5, 5], [2, 3, 5, 5, 5, 7, 13], [2, 3, 5, 5, 7, 7, 11], [2, 3, 5, 7, 23], [2, 3, 5, 11, 19], [2, 3, 5, 13, 17], [2, 3, 7, 7, 7, 7, 7], [2, 3, 7, 11, 17], [2, 3, 11, 11, 13], [2, 5, 5, 5, 5, 5, 13], [2, 5, 5, 5, 5, 7, 11], [2, 5, 5, 5, 23], [2, 5, 5, 7, 7, 7, 7], [2, 5, 5, 11, 17], [2, 5, 7, 7, 19], [2, 5, 7, 13, 13], [2, 5, 11, 11, 11], [2, 7, 7, 7, 17], [2, 7, 7, 11, 13], [2, 19, 19], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 13], [3, 3, 3, 3, 3, 3, 3, 3, 5, 11], [3, 3, 3, 3, 3, 3, 3, 5, 7, 7], [3, 3, 3, 3, 3, 3, 3, 19], [3, 3, 3, 3, 3, 3, 5, 5, 5, 7], [3, 3, 3, 3, 3, 3, 5, 17], [3, 3, 3, 3, 3, 3, 11, 11], [3, 3, 3, 3, 3, 5, 5, 5, 5, 5], [3, 3, 3, 3, 3, 5, 7, 13], [3, 3, 3, 3, 3, 7, 7, 11], [3, 3, 3, 3, 5, 5, 5, 13], [3, 3, 3, 3, 5, 5, 7, 11], [3, 3, 3, 3, 5, 23], [3, 3, 3, 3, 7, 7, 7, 7], [3, 3, 3, 3, 11, 17], [3, 3, 3, 5, 5, 5, 5, 11], [3, 3, 3, 5, 5, 7, 7, 7], [3, 3, 3, 5, 7, 19], [3, 3, 3, 5, 13, 13], [3, 3, 3, 7, 7, 17], [3, 3, 3, 7, 11, 13], [3, 3, 5, 5, 5, 5, 7, 7], [3, 3, 5, 5, 5, 19], [3, 3, 5, 5, 7, 17], [3, 3, 5, 5, 11, 13], [3, 3, 5, 7, 11, 11], [3, 3, 5, 29], [3, 3, 7, 7, 7, 13], [3, 3, 11, 23], [3, 3, 17, 17], [3, 5, 5, 5, 5, 5, 5, 7], [3, 5, 5, 5, 5, 17], [3, 5, 5, 5, 11, 11], [3, 5, 5, 7, 7, 13], [3, 5, 7, 7, 7, 11], [3, 5, 13, 19], [3, 7, 7, 23], [3, 7, 11, 19], [3, 7, 13, 17], [3, 11, 13, 13], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 7, 13], [5, 5, 5, 7, 7, 11], [5, 5, 7, 23], [5, 5, 11, 19], [5, 5, 13, 17], [5, 7, 7, 7, 7, 7], [5, 7, 11, 17], [5, 11, 11, 13], [7, 7, 7, 19], [7, 7, 13, 13], [7, 11, 11, 11], [11, 29], [17, 23]]\n assert candidate(candidates = [8, 16, 32, 64, 128],target = 255) == []\n assert candidate(candidates = [3, 7, 11, 13, 17, 19, 23, 29],target = 50) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 13], [3, 3, 3, 3, 3, 3, 3, 3, 3, 23], [3, 3, 3, 3, 3, 3, 3, 3, 7, 19], [3, 3, 3, 3, 3, 3, 3, 3, 13, 13], [3, 3, 3, 3, 3, 3, 3, 7, 11, 11], [3, 3, 3, 3, 3, 3, 3, 29], [3, 3, 3, 3, 3, 3, 7, 7, 7, 11], [3, 3, 3, 3, 3, 3, 13, 19], [3, 3, 3, 3, 3, 7, 7, 7, 7, 7], [3, 3, 3, 3, 3, 7, 11, 17], [3, 3, 3, 3, 3, 11, 11, 13], [3, 3, 3, 3, 7, 7, 7, 17], [3, 3, 3, 3, 7, 7, 11, 13], [3, 3, 3, 3, 19, 19], [3, 3, 3, 7, 7, 7, 7, 13], [3, 3, 3, 7, 11, 23], [3, 3, 3, 7, 17, 17], [3, 3, 3, 11, 11, 19], [3, 3, 3, 11, 13, 17], [3, 3, 7, 7, 7, 23], [3, 3, 7, 7, 11, 19], [3, 3, 7, 7, 13, 17], [3, 3, 7, 11, 13, 13], [3, 3, 11, 11, 11, 11], [3, 7, 7, 7, 7, 19], [3, 7, 7, 7, 13, 13], [3, 7, 7, 11, 11, 11], [3, 7, 11, 29], [3, 7, 17, 23], [3, 11, 13, 23], [3, 11, 17, 19], [3, 13, 17, 17], [7, 7, 7, 7, 11, 11], [7, 7, 7, 29], [7, 7, 13, 23], [7, 7, 17, 19], [7, 11, 13, 19], [7, 13, 13, 17], [11, 11, 11, 17], [11, 13, 13, 13]]\n assert candidate(candidates = [11, 13, 17, 19, 23, 29],target = 50) == [[11, 11, 11, 17], [11, 13, 13, 13]]\n assert candidate(candidates = [2, 5, 10, 20, 50],target = 50) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 20], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 20], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5], [2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 10, 10], [2, 2, 2, 2, 2, 5, 5, 5, 5, 20], [2, 2, 2, 2, 2, 5, 5, 10, 10, 10], [2, 2, 2, 2, 2, 5, 5, 10, 20], [2, 2, 2, 2, 2, 10, 10, 10, 10], [2, 2, 2, 2, 2, 10, 10, 20], [2, 2, 2, 2, 2, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 10, 20], [5, 5, 10, 10, 10, 10], [5, 5, 10, 10, 20], [5, 5, 20, 20], [10, 10, 10, 10, 10], [10, 10, 10, 20], [10, 20, 20], [50]]\n assert candidate(candidates = [3, 5, 7, 11, 13, 17, 19, 23],target = 50) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 13], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 13], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 7, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 23], [3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 11], [3, 3, 3, 3, 3, 3, 3, 3, 5, 7, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 7, 19], [3, 3, 3, 3, 3, 3, 3, 3, 13, 13], [3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 7, 7], [3, 3, 3, 3, 3, 3, 3, 5, 5, 19], [3, 3, 3, 3, 3, 3, 3, 5, 7, 17], [3, 3, 3, 3, 3, 3, 3, 5, 11, 13], [3, 3, 3, 3, 3, 3, 3, 7, 11, 11], [3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7], [3, 3, 3, 3, 3, 3, 5, 5, 5, 17], [3, 3, 3, 3, 3, 3, 5, 5, 11, 11], [3, 3, 3, 3, 3, 3, 5, 7, 7, 13], [3, 3, 3, 3, 3, 3, 7, 7, 7, 11], [3, 3, 3, 3, 3, 3, 13, 19], [3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5], [3, 3, 3, 3, 3, 5, 5, 5, 7, 13], [3, 3, 3, 3, 3, 5, 5, 7, 7, 11], [3, 3, 3, 3, 3, 5, 7, 23], [3, 3, 3, 3, 3, 5, 11, 19], [3, 3, 3, 3, 3, 5, 13, 17], [3, 3, 3, 3, 3, 7, 7, 7, 7, 7], [3, 3, 3, 3, 3, 7, 11, 17], [3, 3, 3, 3, 3, 11, 11, 13], [3, 3, 3, 3, 5, 5, 5, 5, 5, 13], [3, 3, 3, 3, 5, 5, 5, 5, 7, 11], [3, 3, 3, 3, 5, 5, 5, 23], [3, 3, 3, 3, 5, 5, 7, 7, 7, 7], [3, 3, 3, 3, 5, 5, 11, 17], [3, 3, 3, 3, 5, 7, 7, 19], [3, 3, 3, 3, 5, 7, 13, 13], [3, 3, 3, 3, 5, 11, 11, 11], [3, 3, 3, 3, 7, 7, 7, 17], [3, 3, 3, 3, 7, 7, 11, 13], [3, 3, 3, 3, 19, 19], [3, 3, 3, 5, 5, 5, 5, 5, 5, 11], [3, 3, 3, 5, 5, 5, 5, 7, 7, 7], [3, 3, 3, 5, 5, 5, 7, 19], [3, 3, 3, 5, 5, 5, 13, 13], [3, 3, 3, 5, 5, 7, 7, 17], [3, 3, 3, 5, 5, 7, 11, 13], [3, 3, 3, 5, 7, 7, 11, 11], [3, 3, 3, 5, 13, 23], [3, 3, 3, 5, 17, 19], [3, 3, 3, 7, 7, 7, 7, 13], [3, 3, 3, 7, 11, 23], [3, 3, 3, 7, 17, 17], [3, 3, 3, 11, 11, 19], [3, 3, 3, 11, 13, 17], [3, 3, 5, 5, 5, 5, 5, 5, 7, 7], [3, 3, 5, 5, 5, 5, 5, 19], [3, 3, 5, 5, 5, 5, 7, 17], [3, 3, 5, 5, 5, 5, 11, 13], [3, 3, 5, 5, 5, 7, 11, 11], [3, 3, 5, 5, 7, 7, 7, 13], [3, 3, 5, 5, 11, 23], [3, 3, 5, 5, 17, 17], [3, 3, 5, 7, 7, 7, 7, 11], [3, 3, 5, 7, 13, 19], [3, 3, 5, 11, 11, 17], [3, 3, 5, 13, 13, 13], [3, 3, 7, 7, 7, 23], [3, 3, 7, 7, 11, 19], [3, 3, 7, 7, 13, 17], [3, 3, 7, 11, 13, 13], [3, 3, 11, 11, 11, 11], [3, 5, 5, 5, 5, 5, 5, 5, 5, 7], [3, 5, 5, 5, 5, 5, 5, 17], [3, 5, 5, 5, 5, 5, 11, 11], [3, 5, 5, 5, 5, 7, 7, 13], [3, 5, 5, 5, 7, 7, 7, 11], [3, 5, 5, 5, 13, 19], [3, 5, 5, 7, 7, 23], [3, 5, 5, 7, 11, 19], [3, 5, 5, 7, 13, 17], [3, 5, 5, 11, 13, 13], [3, 5, 7, 7, 7, 7, 7, 7], [3, 5, 7, 7, 11, 17], [3, 5, 7, 11, 11, 13], [3, 5, 19, 23], [3, 7, 7, 7, 7, 19], [3, 7, 7, 7, 13, 13], [3, 7, 7, 11, 11, 11], [3, 7, 17, 23], [3, 11, 13, 23], [3, 11, 17, 19], [3, 13, 17, 17], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 7, 13], [5, 5, 5, 5, 5, 7, 7, 11], [5, 5, 5, 5, 7, 23], [5, 5, 5, 5, 11, 19], [5, 5, 5, 5, 13, 17], [5, 5, 5, 7, 7, 7, 7, 7], [5, 5, 5, 7, 11, 17], [5, 5, 5, 11, 11, 13], [5, 5, 7, 7, 7, 19], [5, 5, 7, 7, 13, 13], [5, 5, 7, 11, 11, 11], [5, 5, 17, 23], [5, 7, 7, 7, 7, 17], [5, 7, 7, 7, 11, 13], [5, 7, 19, 19], [5, 11, 11, 23], [5, 11, 17, 17], [5, 13, 13, 19], [7, 7, 7, 7, 11, 11], [7, 7, 13, 23], [7, 7, 17, 19], [7, 11, 13, 19], [7, 13, 13, 17], [11, 11, 11, 17], [11, 13, 13, 13]]\n assert candidate(candidates = [11, 22, 33, 44, 55, 66, 77, 88, 99],target = 198) == [[11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 44], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 55], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 22], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 44], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 33, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 66], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 55], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 33, 44], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 77], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 22], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 44], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 33, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 66], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 33, 55], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 44, 44], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 88], [11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 55], [11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 33, 44], [11, 11, 11, 11, 11, 11, 11, 11, 11, 22, 77], [11, 11, 11, 11, 11, 11, 11, 11, 11, 33, 33, 33], [11, 11, 11, 11, 11, 11, 11, 11, 11, 33, 66], [11, 11, 11, 11, 11, 11, 11, 11, 11, 44, 55], [11, 11, 11, 11, 11, 11, 11, 11, 11, 99], [11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 22, 22], [11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 44], [11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 33, 33], [11, 11, 11, 11, 11, 11, 11, 11, 22, 22, 66], [11, 11, 11, 11, 11, 11, 11, 11, 22, 33, 55], [11, 11, 11, 11, 11, 11, 11, 11, 22, 44, 44], [11, 11, 11, 11, 11, 11, 11, 11, 22, 88], [11, 11, 11, 11, 11, 11, 11, 11, 33, 33, 44], [11, 11, 11, 11, 11, 11, 11, 11, 33, 77], [11, 11, 11, 11, 11, 11, 11, 11, 44, 66], [11, 11, 11, 11, 11, 11, 11, 11, 55, 55], [11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 22, 33], [11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 55], [11, 11, 11, 11, 11, 11, 11, 22, 22, 33, 44], [11, 11, 11, 11, 11, 11, 11, 22, 22, 77], [11, 11, 11, 11, 11, 11, 11, 22, 33, 33, 33], [11, 11, 11, 11, 11, 11, 11, 22, 33, 66], [11, 11, 11, 11, 11, 11, 11, 22, 44, 55], [11, 11, 11, 11, 11, 11, 11, 22, 99], [11, 11, 11, 11, 11, 11, 11, 33, 33, 55], [11, 11, 11, 11, 11, 11, 11, 33, 44, 44], [11, 11, 11, 11, 11, 11, 11, 33, 88], [11, 11, 11, 11, 11, 11, 11, 44, 77], [11, 11, 11, 11, 11, 11, 11, 55, 66], [11, 11, 11, 11, 11, 11, 22, 22, 22, 22, 22, 22], [11, 11, 11, 11, 11, 11, 22, 22, 22, 22, 44], [11, 11, 11, 11, 11, 11, 22, 22, 22, 33, 33], [11, 11, 11, 11, 11, 11, 22, 22, 22, 66], [11, 11, 11, 11, 11, 11, 22, 22, 33, 55], [11, 11, 11, 11, 11, 11, 22, 22, 44, 44], [11, 11, 11, 11, 11, 11, 22, 22, 88], [11, 11, 11, 11, 11, 11, 22, 33, 33, 44], [11, 11, 11, 11, 11, 11, 22, 33, 77], [11, 11, 11, 11, 11, 11, 22, 44, 66], [11, 11, 11, 11, 11, 11, 22, 55, 55], [11, 11, 11, 11, 11, 11, 33, 33, 33, 33], [11, 11, 11, 11, 11, 11, 33, 33, 66], [11, 11, 11, 11, 11, 11, 33, 44, 55], [11, 11, 11, 11, 11, 11, 33, 99], [11, 11, 11, 11, 11, 11, 44, 44, 44], [11, 11, 11, 11, 11, 11, 44, 88], [11, 11, 11, 11, 11, 11, 55, 77], [11, 11, 11, 11, 11, 11, 66, 66], [11, 11, 11, 11, 11, 22, 22, 22, 22, 22, 33], [11, 11, 11, 11, 11, 22, 22, 22, 22, 55], [11, 11, 11, 11, 11, 22, 22, 22, 33, 44], [11, 11, 11, 11, 11, 22, 22, 22, 77], [11, 11, 11, 11, 11, 22, 22, 33, 33, 33], [11, 11, 11, 11, 11, 22, 22, 33, 66], [11, 11, 11, 11, 11, 22, 22, 44, 55], [11, 11, 11, 11, 11, 22, 22, 99], [11, 11, 11, 11, 11, 22, 33, 33, 55], [11, 11, 11, 11, 11, 22, 33, 44, 44], [11, 11, 11, 11, 11, 22, 33, 88], [11, 11, 11, 11, 11, 22, 44, 77], [11, 11, 11, 11, 11, 22, 55, 66], [11, 11, 11, 11, 11, 33, 33, 33, 44], [11, 11, 11, 11, 11, 33, 33, 77], [11, 11, 11, 11, 11, 33, 44, 66], [11, 11, 11, 11, 11, 33, 55, 55], [11, 11, 11, 11, 11, 44, 44, 55], [11, 11, 11, 11, 11, 44, 99], [11, 11, 11, 11, 11, 55, 88], [11, 11, 11, 11, 11, 66, 77], [11, 11, 11, 11, 22, 22, 22, 22, 22, 22, 22], [11, 11, 11, 11, 22, 22, 22, 22, 22, 44], [11, 11, 11, 11, 22, 22, 22, 22, 33, 33], [11, 11, 11, 11, 22, 22, 22, 22, 66], [11, 11, 11, 11, 22, 22, 22, 33, 55], [11, 11, 11, 11, 22, 22, 22, 44, 44], [11, 11, 11, 11, 22, 22, 22, 88], [11, 11, 11, 11, 22, 22, 33, 33, 44], [11, 11, 11, 11, 22, 22, 33, 77], [11, 11, 11, 11, 22, 22, 44, 66], [11, 11, 11, 11, 22, 22, 55, 55], [11, 11, 11, 11, 22, 33, 33, 33, 33], [11, 11, 11, 11, 22, 33, 33, 66], [11, 11, 11, 11, 22, 33, 44, 55], [11, 11, 11, 11, 22, 33, 99], [11, 11, 11, 11, 22, 44, 44, 44], [11, 11, 11, 11, 22, 44, 88], [11, 11, 11, 11, 22, 55, 77], [11, 11, 11, 11, 22, 66, 66], [11, 11, 11, 11, 33, 33, 33, 55], [11, 11, 11, 11, 33, 33, 44, 44], [11, 11, 11, 11, 33, 33, 88], [11, 11, 11, 11, 33, 44, 77], [11, 11, 11, 11, 33, 55, 66], [11, 11, 11, 11, 44, 44, 66], [11, 11, 11, 11, 44, 55, 55], [11, 11, 11, 11, 55, 99], [11, 11, 11, 11, 66, 88], [11, 11, 11, 11, 77, 77], [11, 11, 11, 22, 22, 22, 22, 22, 22, 33], [11, 11, 11, 22, 22, 22, 22, 22, 55], [11, 11, 11, 22, 22, 22, 22, 33, 44], [11, 11, 11, 22, 22, 22, 22, 77], [11, 11, 11, 22, 22, 22, 33, 33, 33], [11, 11, 11, 22, 22, 22, 33, 66], [11, 11, 11, 22, 22, 22, 44, 55], [11, 11, 11, 22, 22, 22, 99], [11, 11, 11, 22, 22, 33, 33, 55], [11, 11, 11, 22, 22, 33, 44, 44], [11, 11, 11, 22, 22, 33, 88], [11, 11, 11, 22, 22, 44, 77], [11, 11, 11, 22, 22, 55, 66], [11, 11, 11, 22, 33, 33, 33, 44], [11, 11, 11, 22, 33, 33, 77], [11, 11, 11, 22, 33, 44, 66], [11, 11, 11, 22, 33, 55, 55], [11, 11, 11, 22, 44, 44, 55], [11, 11, 11, 22, 44, 99], [11, 11, 11, 22, 55, 88], [11, 11, 11, 22, 66, 77], [11, 11, 11, 33, 33, 33, 33, 33], [11, 11, 11, 33, 33, 33, 66], [11, 11, 11, 33, 33, 44, 55], [11, 11, 11, 33, 33, 99], [11, 11, 11, 33, 44, 44, 44], [11, 11, 11, 33, 44, 88], [11, 11, 11, 33, 55, 77], [11, 11, 11, 33, 66, 66], [11, 11, 11, 44, 44, 77], [11, 11, 11, 44, 55, 66], [11, 11, 11, 55, 55, 55], [11, 11, 11, 66, 99], [11, 11, 11, 77, 88], [11, 11, 22, 22, 22, 22, 22, 22, 22, 22], [11, 11, 22, 22, 22, 22, 22, 22, 44], [11, 11, 22, 22, 22, 22, 22, 33, 33], [11, 11, 22, 22, 22, 22, 22, 66], [11, 11, 22, 22, 22, 22, 33, 55], [11, 11, 22, 22, 22, 22, 44, 44], [11, 11, 22, 22, 22, 22, 88], [11, 11, 22, 22, 22, 33, 33, 44], [11, 11, 22, 22, 22, 33, 77], [11, 11, 22, 22, 22, 44, 66], [11, 11, 22, 22, 22, 55, 55], [11, 11, 22, 22, 33, 33, 33, 33], [11, 11, 22, 22, 33, 33, 66], [11, 11, 22, 22, 33, 44, 55], [11, 11, 22, 22, 33, 99], [11, 11, 22, 22, 44, 44, 44], [11, 11, 22, 22, 44, 88], [11, 11, 22, 22, 55, 77], [11, 11, 22, 22, 66, 66], [11, 11, 22, 33, 33, 33, 55], [11, 11, 22, 33, 33, 44, 44], [11, 11, 22, 33, 33, 88], [11, 11, 22, 33, 44, 77], [11, 11, 22, 33, 55, 66], [11, 11, 22, 44, 44, 66], [11, 11, 22, 44, 55, 55], [11, 11, 22, 55, 99], [11, 11, 22, 66, 88], [11, 11, 22, 77, 77], [11, 11, 33, 33, 33, 33, 44], [11, 11, 33, 33, 33, 77], [11, 11, 33, 33, 44, 66], [11, 11, 33, 33, 55, 55], [11, 11, 33, 44, 44, 55], [11, 11, 33, 44, 99], [11, 11, 33, 55, 88], [11, 11, 33, 66, 77], [11, 11, 44, 44, 44, 44], [11, 11, 44, 44, 88], [11, 11, 44, 55, 77], [11, 11, 44, 66, 66], [11, 11, 55, 55, 66], [11, 11, 77, 99], [11, 11, 88, 88], [11, 22, 22, 22, 22, 22, 22, 22, 33], [11, 22, 22, 22, 22, 22, 22, 55], [11, 22, 22, 22, 22, 22, 33, 44], [11, 22, 22, 22, 22, 22, 77], [11, 22, 22, 22, 22, 33, 33, 33], [11, 22, 22, 22, 22, 33, 66], [11, 22, 22, 22, 22, 44, 55], [11, 22, 22, 22, 22, 99], [11, 22, 22, 22, 33, 33, 55], [11, 22, 22, 22, 33, 44, 44], [11, 22, 22, 22, 33, 88], [11, 22, 22, 22, 44, 77], [11, 22, 22, 22, 55, 66], [11, 22, 22, 33, 33, 33, 44], [11, 22, 22, 33, 33, 77], [11, 22, 22, 33, 44, 66], [11, 22, 22, 33, 55, 55], [11, 22, 22, 44, 44, 55], [11, 22, 22, 44, 99], [11, 22, 22, 55, 88], [11, 22, 22, 66, 77], [11, 22, 33, 33, 33, 33, 33], [11, 22, 33, 33, 33, 66], [11, 22, 33, 33, 44, 55], [11, 22, 33, 33, 99], [11, 22, 33, 44, 44, 44], [11, 22, 33, 44, 88], [11, 22, 33, 55, 77], [11, 22, 33, 66, 66], [11, 22, 44, 44, 77], [11, 22, 44, 55, 66], [11, 22, 55, 55, 55], [11, 22, 66, 99], [11, 22, 77, 88], [11, 33, 33, 33, 33, 55], [11, 33, 33, 33, 44, 44], [11, 33, 33, 33, 88], [11, 33, 33, 44, 77], [11, 33, 33, 55, 66], [11, 33, 44, 44, 66], [11, 33, 44, 55, 55], [11, 33, 55, 99], [11, 33, 66, 88], [11, 33, 77, 77], [11, 44, 44, 44, 55], [11, 44, 44, 99], [11, 44, 55, 88], [11, 44, 66, 77], [11, 55, 55, 77], [11, 55, 66, 66], [11, 88, 99], [22, 22, 22, 22, 22, 22, 22, 22, 22], [22, 22, 22, 22, 22, 22, 22, 44], [22, 22, 22, 22, 22, 22, 33, 33], [22, 22, 22, 22, 22, 22, 66], [22, 22, 22, 22, 22, 33, 55], [22, 22, 22, 22, 22, 44, 44], [22, 22, 22, 22, 22, 88], [22, 22, 22, 22, 33, 33, 44], [22, 22, 22, 22, 33, 77], [22, 22, 22, 22, 44, 66], [22, 22, 22, 22, 55, 55], [22, 22, 22, 33, 33, 33, 33], [22, 22, 22, 33, 33, 66], [22, 22, 22, 33, 44, 55], [22, 22, 22, 33, 99], [22, 22, 22, 44, 44, 44], [22, 22, 22, 44, 88], [22, 22, 22, 55, 77], [22, 22, 22, 66, 66], [22, 22, 33, 33, 33, 55], [22, 22, 33, 33, 44, 44], [22, 22, 33, 33, 88], [22, 22, 33, 44, 77], [22, 22, 33, 55, 66], [22, 22, 44, 44, 66], [22, 22, 44, 55, 55], [22, 22, 55, 99], [22, 22, 66, 88], [22, 22, 77, 77], [22, 33, 33, 33, 33, 44], [22, 33, 33, 33, 77], [22, 33, 33, 44, 66], [22, 33, 33, 55, 55], [22, 33, 44, 44, 55], [22, 33, 44, 99], [22, 33, 55, 88], [22, 33, 66, 77], [22, 44, 44, 44, 44], [22, 44, 44, 88], [22, 44, 55, 77], [22, 44, 66, 66], [22, 55, 55, 66], [22, 77, 99], [22, 88, 88], [33, 33, 33, 33, 33, 33], [33, 33, 33, 33, 66], [33, 33, 33, 44, 55], [33, 33, 33, 99], [33, 33, 44, 44, 44], [33, 33, 44, 88], [33, 33, 55, 77], [33, 33, 66, 66], [33, 44, 44, 77], [33, 44, 55, 66], [33, 55, 55, 55], [33, 66, 99], [33, 77, 88], [44, 44, 44, 66], [44, 44, 55, 55], [44, 55, 99], [44, 66, 88], [44, 77, 77], [55, 55, 88], [55, 66, 77], [66, 66, 66], [99, 99]]\n assert candidate(candidates = [13, 11, 7, 5, 2, 1],target = 30) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 13], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 7, 7], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 11], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 13], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 7, 11], [1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 13], [1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 7], [1, 1, 1, 1, 1, 1, 1, 1, 11, 11], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 11], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 13], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5, 5, 5], [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 5, 7], [1, 1, 1, 1, 1, 1, 1, 2, 2, 5, 7, 7], [1, 1, 1, 1, 1, 1, 1, 2, 5, 5, 11], [1, 1, 1, 1, 1, 1, 1, 2, 7, 7, 7], [1, 1, 1, 1, 1, 1, 1, 5, 5, 13], [1, 1, 1, 1, 1, 1, 1, 5, 7, 11], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 5, 5], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 7], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 7, 7], [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 5, 11], [1, 1, 1, 1, 1, 1, 2, 2, 2, 5, 13], [1, 1, 1, 1, 1, 1, 2, 2, 2, 7, 11], [1, 1, 1, 1, 1, 1, 2, 2, 5, 5, 5, 5], [1, 1, 1, 1, 1, 1, 2, 2, 7, 13], [1, 1, 1, 1, 1, 1, 2, 5, 5, 5, 7], [1, 1, 1, 1, 1, 1, 2, 11, 11], [1, 1, 1, 1, 1, 1, 5, 5, 7, 7], [1, 1, 1, 1, 1, 1, 11, 13], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 11], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 13], [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5, 5, 5], [1, 1, 1, 1, 1, 2, 2, 2, 2, 5, 5, 7], [1, 1, 1, 1, 1, 2, 2, 2, 5, 7, 7], [1, 1, 1, 1, 1, 2, 2, 5, 5, 11], [1, 1, 1, 1, 1, 2, 2, 7, 7, 7], [1, 1, 1, 1, 1, 2, 5, 5, 13], [1, 1, 1, 1, 1, 2, 5, 7, 11], [1, 1, 1, 1, 1, 5, 5, 5, 5, 5], [1, 1, 1, 1, 1, 5, 7, 13], [1, 1, 1, 1, 1, 7, 7, 11], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 5, 7], [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 7, 7], [1, 1, 1, 1, 2, 2, 2, 2, 2, 5, 11], [1, 1, 1, 1, 2, 2, 2, 2, 5, 13], [1, 1, 1, 1, 2, 2, 2, 2, 7, 11], [1, 1, 1, 1, 2, 2, 2, 5, 5, 5, 5], [1, 1, 1, 1, 2, 2, 2, 7, 13], [1, 1, 1, 1, 2, 2, 5, 5, 5, 7], [1, 1, 1, 1, 2, 2, 11, 11], [1, 1, 1, 1, 2, 5, 5, 7, 7], [1, 1, 1, 1, 2, 11, 13], [1, 1, 1, 1, 5, 5, 5, 11], [1, 1, 1, 1, 5, 7, 7, 7], [1, 1, 1, 1, 13, 13], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 11], [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 13], [1, 1, 1, 2, 2, 2, 2, 2, 2, 5, 5, 5], [1, 1, 1, 2, 2, 2, 2, 2, 5, 5, 7], [1, 1, 1, 2, 2, 2, 2, 5, 7, 7], [1, 1, 1, 2, 2, 2, 5, 5, 11], [1, 1, 1, 2, 2, 2, 7, 7, 7], [1, 1, 1, 2, 2, 5, 5, 13], [1, 1, 1, 2, 2, 5, 7, 11], [1, 1, 1, 2, 5, 5, 5, 5, 5], [1, 1, 1, 2, 5, 7, 13], [1, 1, 1, 2, 7, 7, 11], [1, 1, 1, 5, 5, 5, 5, 7], [1, 1, 1, 5, 11, 11], [1, 1, 1, 7, 7, 13], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [1, 1, 2, 2, 2, 2, 2, 2, 2, 7, 7], [1, 1, 2, 2, 2, 2, 2, 2, 5, 11], [1, 1, 2, 2, 2, 2, 2, 5, 13], [1, 1, 2, 2, 2, 2, 2, 7, 11], [1, 1, 2, 2, 2, 2, 5, 5, 5, 5], [1, 1, 2, 2, 2, 2, 7, 13], [1, 1, 2, 2, 2, 5, 5, 5, 7], [1, 1, 2, 2, 2, 11, 11], [1, 1, 2, 2, 5, 5, 7, 7], [1, 1, 2, 2, 11, 13], [1, 1, 2, 5, 5, 5, 11], [1, 1, 2, 5, 7, 7, 7], [1, 1, 2, 13, 13], [1, 1, 5, 5, 5, 13], [1, 1, 5, 5, 7, 11], [1, 1, 7, 7, 7, 7], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 11], [1, 2, 2, 2, 2, 2, 2, 2, 2, 13], [1, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5], [1, 2, 2, 2, 2, 2, 2, 5, 5, 7], [1, 2, 2, 2, 2, 2, 5, 7, 7], [1, 2, 2, 2, 2, 5, 5, 11], [1, 2, 2, 2, 2, 7, 7, 7], [1, 2, 2, 2, 5, 5, 13], [1, 2, 2, 2, 5, 7, 11], [1, 2, 2, 5, 5, 5, 5, 5], [1, 2, 2, 5, 7, 13], [1, 2, 2, 7, 7, 11], [1, 2, 5, 5, 5, 5, 7], [1, 2, 5, 11, 11], [1, 2, 7, 7, 13], [1, 5, 5, 5, 7, 7], [1, 5, 11, 13], [1, 7, 11, 11], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 11, 11], [2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 11, 13], [2, 2, 5, 5, 5, 11], [2, 2, 5, 7, 7, 7], [2, 2, 13, 13], [2, 5, 5, 5, 13], [2, 5, 5, 7, 11], [2, 7, 7, 7, 7], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11]]\n assert candidate(candidates = [8, 16, 24, 32, 40, 48, 56, 64],target = 100) == []\n assert candidate(candidates = [2, 4, 6, 8, 10, 12, 14],target = 32) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 12], [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 8], [2, 2, 2, 2, 2, 2, 2, 2, 2, 14], [2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 8], [2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 4, 12], [2, 2, 2, 2, 2, 2, 2, 2, 6, 10], [2, 2, 2, 2, 2, 2, 2, 2, 8, 8], [2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 6], [2, 2, 2, 2, 2, 2, 2, 4, 4, 10], [2, 2, 2, 2, 2, 2, 2, 4, 6, 8], [2, 2, 2, 2, 2, 2, 2, 4, 14], [2, 2, 2, 2, 2, 2, 2, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 6, 12], [2, 2, 2, 2, 2, 2, 2, 8, 10], [2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4], [2, 2, 2, 2, 2, 2, 4, 4, 4, 8], [2, 2, 2, 2, 2, 2, 4, 4, 6, 6], [2, 2, 2, 2, 2, 2, 4, 4, 12], [2, 2, 2, 2, 2, 2, 4, 6, 10], [2, 2, 2, 2, 2, 2, 4, 8, 8], [2, 2, 2, 2, 2, 2, 6, 6, 8], [2, 2, 2, 2, 2, 2, 6, 14], [2, 2, 2, 2, 2, 2, 8, 12], [2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 4, 4, 4, 4, 6], [2, 2, 2, 2, 2, 4, 4, 4, 10], [2, 2, 2, 2, 2, 4, 4, 6, 8], [2, 2, 2, 2, 2, 4, 4, 14], [2, 2, 2, 2, 2, 4, 6, 6, 6], [2, 2, 2, 2, 2, 4, 6, 12], [2, 2, 2, 2, 2, 4, 8, 10], [2, 2, 2, 2, 2, 6, 6, 10], [2, 2, 2, 2, 2, 6, 8, 8], [2, 2, 2, 2, 2, 8, 14], [2, 2, 2, 2, 2, 10, 12], [2, 2, 2, 2, 4, 4, 4, 4, 4, 4], [2, 2, 2, 2, 4, 4, 4, 4, 8], [2, 2, 2, 2, 4, 4, 4, 6, 6], [2, 2, 2, 2, 4, 4, 4, 12], [2, 2, 2, 2, 4, 4, 6, 10], [2, 2, 2, 2, 4, 4, 8, 8], [2, 2, 2, 2, 4, 6, 6, 8], [2, 2, 2, 2, 4, 6, 14], [2, 2, 2, 2, 4, 8, 12], [2, 2, 2, 2, 4, 10, 10], [2, 2, 2, 2, 6, 6, 6, 6], [2, 2, 2, 2, 6, 6, 12], [2, 2, 2, 2, 6, 8, 10], [2, 2, 2, 2, 8, 8, 8], [2, 2, 2, 2, 10, 14], [2, 2, 2, 2, 12, 12], [2, 2, 2, 4, 4, 4, 4, 4, 6], [2, 2, 2, 4, 4, 4, 4, 10], [2, 2, 2, 4, 4, 4, 6, 8], [2, 2, 2, 4, 4, 4, 14], [2, 2, 2, 4, 4, 6, 6, 6], [2, 2, 2, 4, 4, 6, 12], [2, 2, 2, 4, 4, 8, 10], [2, 2, 2, 4, 6, 6, 10], [2, 2, 2, 4, 6, 8, 8], [2, 2, 2, 4, 8, 14], [2, 2, 2, 4, 10, 12], [2, 2, 2, 6, 6, 6, 8], [2, 2, 2, 6, 6, 14], [2, 2, 2, 6, 8, 12], [2, 2, 2, 6, 10, 10], [2, 2, 2, 8, 8, 10], [2, 2, 2, 12, 14], [2, 2, 4, 4, 4, 4, 4, 4, 4], [2, 2, 4, 4, 4, 4, 4, 8], [2, 2, 4, 4, 4, 4, 6, 6], [2, 2, 4, 4, 4, 4, 12], [2, 2, 4, 4, 4, 6, 10], [2, 2, 4, 4, 4, 8, 8], [2, 2, 4, 4, 6, 6, 8], [2, 2, 4, 4, 6, 14], [2, 2, 4, 4, 8, 12], [2, 2, 4, 4, 10, 10], [2, 2, 4, 6, 6, 6, 6], [2, 2, 4, 6, 6, 12], [2, 2, 4, 6, 8, 10], [2, 2, 4, 8, 8, 8], [2, 2, 4, 10, 14], [2, 2, 4, 12, 12], [2, 2, 6, 6, 6, 10], [2, 2, 6, 6, 8, 8], [2, 2, 6, 8, 14], [2, 2, 6, 10, 12], [2, 2, 8, 8, 12], [2, 2, 8, 10, 10], [2, 2, 14, 14], [2, 4, 4, 4, 4, 4, 4, 6], [2, 4, 4, 4, 4, 4, 10], [2, 4, 4, 4, 4, 6, 8], [2, 4, 4, 4, 4, 14], [2, 4, 4, 4, 6, 6, 6], [2, 4, 4, 4, 6, 12], [2, 4, 4, 4, 8, 10], [2, 4, 4, 6, 6, 10], [2, 4, 4, 6, 8, 8], [2, 4, 4, 8, 14], [2, 4, 4, 10, 12], [2, 4, 6, 6, 6, 8], [2, 4, 6, 6, 14], [2, 4, 6, 8, 12], [2, 4, 6, 10, 10], [2, 4, 8, 8, 10], [2, 4, 12, 14], [2, 6, 6, 6, 6, 6], [2, 6, 6, 6, 12], [2, 6, 6, 8, 10], [2, 6, 8, 8, 8], [2, 6, 10, 14], [2, 6, 12, 12], [2, 8, 8, 14], [2, 8, 10, 12], [2, 10, 10, 10], [4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 8], [4, 4, 4, 4, 4, 6, 6], [4, 4, 4, 4, 4, 12], [4, 4, 4, 4, 6, 10], [4, 4, 4, 4, 8, 8], [4, 4, 4, 6, 6, 8], [4, 4, 4, 6, 14], [4, 4, 4, 8, 12], [4, 4, 4, 10, 10], [4, 4, 6, 6, 6, 6], [4, 4, 6, 6, 12], [4, 4, 6, 8, 10], [4, 4, 8, 8, 8], [4, 4, 10, 14], [4, 4, 12, 12], [4, 6, 6, 6, 10], [4, 6, 6, 8, 8], [4, 6, 8, 14], [4, 6, 10, 12], [4, 8, 8, 12], [4, 8, 10, 10], [4, 14, 14], [6, 6, 6, 6, 8], [6, 6, 6, 14], [6, 6, 8, 12], [6, 6, 10, 10], [6, 8, 8, 10], [6, 12, 14], [8, 8, 8, 8], [8, 10, 14], [8, 12, 12], [10, 10, 12]]\n assert candidate(candidates = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29],target = 30) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 3, 19], [2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 11, 11], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 5, 19], [2, 2, 2, 7, 17], [2, 2, 2, 11, 13], [2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 3, 3, 3, 17], [2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 3, 3, 7, 13], [2, 2, 3, 5, 5, 13], [2, 2, 3, 5, 7, 11], [2, 2, 3, 23], [2, 2, 5, 5, 5, 11], [2, 2, 5, 7, 7, 7], [2, 2, 7, 19], [2, 2, 13, 13], [2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 3, 3, 3, 3, 3, 13], [2, 3, 3, 3, 3, 5, 11], [2, 3, 3, 3, 5, 7, 7], [2, 3, 3, 3, 19], [2, 3, 3, 5, 5, 5, 7], [2, 3, 3, 5, 17], [2, 3, 3, 11, 11], [2, 3, 5, 5, 5, 5, 5], [2, 3, 5, 7, 13], [2, 3, 7, 7, 11], [2, 5, 5, 5, 13], [2, 5, 5, 7, 11], [2, 5, 23], [2, 7, 7, 7, 7], [2, 11, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 5, 19], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [7, 23], [11, 19], [13, 17]]\n assert candidate(candidates = [5, 10, 15, 20],target = 30) == [[5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 10], [5, 5, 5, 15], [5, 5, 10, 10], [5, 5, 20], [5, 10, 15], [10, 10, 10], [10, 20], [15, 15]]\n assert candidate(candidates = [11, 13, 17, 19, 23, 29, 31, 37, 41, 43],target = 97) == [[11, 11, 11, 11, 11, 11, 31], [11, 11, 11, 11, 11, 13, 29], [11, 11, 11, 11, 11, 19, 23], [11, 11, 11, 11, 13, 17, 23], [11, 11, 11, 11, 17, 17, 19], [11, 11, 11, 13, 13, 19, 19], [11, 11, 11, 13, 17, 17, 17], [11, 11, 11, 23, 41], [11, 11, 13, 13, 13, 13, 23], [11, 11, 13, 13, 13, 17, 19], [11, 11, 13, 19, 43], [11, 11, 13, 31, 31], [11, 11, 17, 17, 41], [11, 11, 17, 29, 29], [11, 11, 19, 19, 37], [11, 11, 23, 23, 29], [11, 13, 13, 13, 13, 17, 17], [11, 13, 13, 17, 43], [11, 13, 13, 19, 41], [11, 13, 13, 23, 37], [11, 13, 13, 29, 31], [11, 13, 17, 19, 37], [11, 13, 19, 23, 31], [11, 17, 17, 23, 29], [11, 17, 19, 19, 31], [11, 17, 23, 23, 23], [11, 19, 19, 19, 29], [11, 43, 43], [13, 13, 13, 13, 13, 13, 19], [13, 13, 13, 17, 41], [13, 13, 13, 29, 29], [13, 13, 17, 17, 37], [13, 13, 17, 23, 31], [13, 13, 19, 23, 29], [13, 17, 17, 19, 31], [13, 17, 19, 19, 29], [13, 19, 19, 23, 23], [13, 41, 43], [17, 17, 17, 17, 29], [17, 17, 17, 23, 23], [17, 19, 19, 19, 23], [17, 37, 43], [19, 37, 41], [23, 31, 43], [23, 37, 37], [29, 31, 37]]\n assert candidate(candidates = [2, 3, 5, 7, 11, 13, 17],target = 30) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 11], [2, 2, 2, 2, 2, 2, 2, 2, 7, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 13], [2, 2, 2, 2, 2, 2, 2, 5, 11], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 3, 3, 5, 7], [2, 2, 2, 2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 2, 2, 2, 5, 13], [2, 2, 2, 2, 2, 2, 7, 11], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 3, 3, 3, 11], [2, 2, 2, 2, 2, 3, 3, 7, 7], [2, 2, 2, 2, 2, 3, 5, 5, 7], [2, 2, 2, 2, 2, 3, 17], [2, 2, 2, 2, 2, 5, 5, 5, 5], [2, 2, 2, 2, 2, 7, 13], [2, 2, 2, 2, 3, 3, 3, 3, 3, 7], [2, 2, 2, 2, 3, 3, 3, 3, 5, 5], [2, 2, 2, 2, 3, 3, 3, 13], [2, 2, 2, 2, 3, 3, 5, 11], [2, 2, 2, 2, 3, 5, 7, 7], [2, 2, 2, 2, 5, 5, 5, 7], [2, 2, 2, 2, 5, 17], [2, 2, 2, 2, 11, 11], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 5, 7], [2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 3, 3, 5, 13], [2, 2, 2, 3, 3, 7, 11], [2, 2, 2, 3, 5, 5, 11], [2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 7, 17], [2, 2, 2, 11, 13], [2, 2, 3, 3, 3, 3, 3, 3, 3, 5], [2, 2, 3, 3, 3, 3, 3, 11], [2, 2, 3, 3, 3, 3, 7, 7], [2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 3, 3, 3, 17], [2, 2, 3, 3, 5, 5, 5, 5], [2, 2, 3, 3, 7, 13], [2, 2, 3, 5, 5, 13], [2, 2, 3, 5, 7, 11], [2, 2, 5, 5, 5, 11], [2, 2, 5, 7, 7, 7], [2, 2, 13, 13], [2, 3, 3, 3, 3, 3, 3, 3, 7], [2, 3, 3, 3, 3, 3, 3, 5, 5], [2, 3, 3, 3, 3, 3, 13], [2, 3, 3, 3, 3, 5, 11], [2, 3, 3, 3, 5, 7, 7], [2, 3, 3, 5, 5, 5, 7], [2, 3, 3, 5, 17], [2, 3, 3, 11, 11], [2, 3, 5, 5, 5, 5, 5], [2, 3, 5, 7, 13], [2, 3, 7, 7, 11], [2, 5, 5, 5, 13], [2, 5, 5, 7, 11], [2, 7, 7, 7, 7], [2, 11, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [13, 17]]\n assert candidate(candidates = [1],target = 20) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\n assert candidate(candidates = [2, 6, 10, 14, 18, 22],target = 40) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 14], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 10, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 10], [2, 2, 2, 2, 2, 2, 2, 2, 2, 22], [2, 2, 2, 2, 2, 2, 2, 2, 6, 6, 6, 6], [2, 2, 2, 2, 2, 2, 2, 2, 6, 18], [2, 2, 2, 2, 2, 2, 2, 2, 10, 14], [2, 2, 2, 2, 2, 2, 2, 6, 6, 14], [2, 2, 2, 2, 2, 2, 2, 6, 10, 10], [2, 2, 2, 2, 2, 2, 6, 6, 6, 10], [2, 2, 2, 2, 2, 2, 6, 22], [2, 2, 2, 2, 2, 2, 10, 18], [2, 2, 2, 2, 2, 2, 14, 14], [2, 2, 2, 2, 2, 6, 6, 6, 6, 6], [2, 2, 2, 2, 2, 6, 6, 18], [2, 2, 2, 2, 2, 6, 10, 14], [2, 2, 2, 2, 2, 10, 10, 10], [2, 2, 2, 2, 6, 6, 6, 14], [2, 2, 2, 2, 6, 6, 10, 10], [2, 2, 2, 2, 10, 22], [2, 2, 2, 2, 14, 18], [2, 2, 2, 6, 6, 6, 6, 10], [2, 2, 2, 6, 6, 22], [2, 2, 2, 6, 10, 18], [2, 2, 2, 6, 14, 14], [2, 2, 2, 10, 10, 14], [2, 2, 6, 6, 6, 6, 6, 6], [2, 2, 6, 6, 6, 18], [2, 2, 6, 6, 10, 14], [2, 2, 6, 10, 10, 10], [2, 2, 14, 22], [2, 2, 18, 18], [2, 6, 6, 6, 6, 14], [2, 6, 6, 6, 10, 10], [2, 6, 10, 22], [2, 6, 14, 18], [2, 10, 10, 18], [2, 10, 14, 14], [6, 6, 6, 6, 6, 10], [6, 6, 6, 22], [6, 6, 10, 18], [6, 6, 14, 14], [6, 10, 10, 14], [10, 10, 10, 10], [18, 22]]\n assert candidate(candidates = [10, 20, 30, 40, 50],target = 100) == [[10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 10, 10, 10, 30], [10, 10, 10, 10, 10, 10, 20, 20], [10, 10, 10, 10, 10, 10, 40], [10, 10, 10, 10, 10, 20, 30], [10, 10, 10, 10, 10, 50], [10, 10, 10, 10, 20, 20, 20], [10, 10, 10, 10, 20, 40], [10, 10, 10, 10, 30, 30], [10, 10, 10, 20, 20, 30], [10, 10, 10, 20, 50], [10, 10, 10, 30, 40], [10, 10, 20, 20, 20, 20], [10, 10, 20, 20, 40], [10, 10, 20, 30, 30], [10, 10, 30, 50], [10, 10, 40, 40], [10, 20, 20, 20, 30], [10, 20, 20, 50], [10, 20, 30, 40], [10, 30, 30, 30], [10, 40, 50], [20, 20, 20, 20, 20], [20, 20, 20, 40], [20, 20, 30, 30], [20, 30, 50], [20, 40, 40], [30, 30, 40], [50, 50]]\n assert candidate(candidates = [9, 18, 27, 36, 45],target = 81) == [[9, 9, 9, 9, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 9, 9, 18], [9, 9, 9, 9, 9, 9, 27], [9, 9, 9, 9, 9, 18, 18], [9, 9, 9, 9, 9, 36], [9, 9, 9, 9, 18, 27], [9, 9, 9, 9, 45], [9, 9, 9, 18, 18, 18], [9, 9, 9, 18, 36], [9, 9, 9, 27, 27], [9, 9, 18, 18, 27], [9, 9, 18, 45], [9, 9, 27, 36], [9, 18, 18, 18, 18], [9, 18, 18, 36], [9, 18, 27, 27], [9, 27, 45], [9, 36, 36], [18, 18, 18, 27], [18, 18, 45], [18, 27, 36], [27, 27, 27], [36, 45]]\n assert candidate(candidates = [1, 2, 3, 4, 5],target = 12) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 1, 1, 1, 5], [1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 4], [1, 1, 1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 2, 2, 3], [1, 1, 1, 1, 1, 2, 5], [1, 1, 1, 1, 1, 3, 4], [1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 4], [1, 1, 1, 1, 2, 3, 3], [1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 4, 4], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 5], [1, 1, 1, 2, 3, 4], [1, 1, 1, 3, 3, 3], [1, 1, 1, 4, 5], [1, 1, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 4], [1, 1, 2, 2, 3, 3], [1, 1, 2, 3, 5], [1, 1, 2, 4, 4], [1, 1, 3, 3, 4], [1, 1, 5, 5], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 5], [1, 2, 2, 3, 4], [1, 2, 3, 3, 3], [1, 2, 4, 5], [1, 3, 3, 5], [1, 3, 4, 4], [2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 4], [2, 2, 2, 3, 3], [2, 2, 3, 5], [2, 2, 4, 4], [2, 3, 3, 4], [2, 5, 5], [3, 3, 3, 3], [3, 4, 5], [4, 4, 4]]\n assert candidate(candidates = [7, 14, 21, 28, 35, 42, 49],target = 98) == [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 28], [7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 21], [7, 7, 7, 7, 7, 7, 7, 7, 7, 35], [7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14], [7, 7, 7, 7, 7, 7, 7, 7, 14, 28], [7, 7, 7, 7, 7, 7, 7, 7, 21, 21], [7, 7, 7, 7, 7, 7, 7, 7, 42], [7, 7, 7, 7, 7, 7, 7, 14, 14, 21], [7, 7, 7, 7, 7, 7, 7, 14, 35], [7, 7, 7, 7, 7, 7, 7, 21, 28], [7, 7, 7, 7, 7, 7, 7, 49], [7, 7, 7, 7, 7, 7, 14, 14, 14, 14], [7, 7, 7, 7, 7, 7, 14, 14, 28], [7, 7, 7, 7, 7, 7, 14, 21, 21], [7, 7, 7, 7, 7, 7, 14, 42], [7, 7, 7, 7, 7, 7, 21, 35], [7, 7, 7, 7, 7, 7, 28, 28], [7, 7, 7, 7, 7, 14, 14, 14, 21], [7, 7, 7, 7, 7, 14, 14, 35], [7, 7, 7, 7, 7, 14, 21, 28], [7, 7, 7, 7, 7, 14, 49], [7, 7, 7, 7, 7, 21, 21, 21], [7, 7, 7, 7, 7, 21, 42], [7, 7, 7, 7, 7, 28, 35], [7, 7, 7, 7, 14, 14, 14, 14, 14], [7, 7, 7, 7, 14, 14, 14, 28], [7, 7, 7, 7, 14, 14, 21, 21], [7, 7, 7, 7, 14, 14, 42], [7, 7, 7, 7, 14, 21, 35], [7, 7, 7, 7, 14, 28, 28], [7, 7, 7, 7, 21, 21, 28], [7, 7, 7, 7, 21, 49], [7, 7, 7, 7, 28, 42], [7, 7, 7, 7, 35, 35], [7, 7, 7, 14, 14, 14, 14, 21], [7, 7, 7, 14, 14, 14, 35], [7, 7, 7, 14, 14, 21, 28], [7, 7, 7, 14, 14, 49], [7, 7, 7, 14, 21, 21, 21], [7, 7, 7, 14, 21, 42], [7, 7, 7, 14, 28, 35], [7, 7, 7, 21, 21, 35], [7, 7, 7, 21, 28, 28], [7, 7, 7, 28, 49], [7, 7, 7, 35, 42], [7, 7, 14, 14, 14, 14, 14, 14], [7, 7, 14, 14, 14, 14, 28], [7, 7, 14, 14, 14, 21, 21], [7, 7, 14, 14, 14, 42], [7, 7, 14, 14, 21, 35], [7, 7, 14, 14, 28, 28], [7, 7, 14, 21, 21, 28], [7, 7, 14, 21, 49], [7, 7, 14, 28, 42], [7, 7, 14, 35, 35], [7, 7, 21, 21, 21, 21], [7, 7, 21, 21, 42], [7, 7, 21, 28, 35], [7, 7, 28, 28, 28], [7, 7, 35, 49], [7, 7, 42, 42], [7, 14, 14, 14, 14, 14, 21], [7, 14, 14, 14, 14, 35], [7, 14, 14, 14, 21, 28], [7, 14, 14, 14, 49], [7, 14, 14, 21, 21, 21], [7, 14, 14, 21, 42], [7, 14, 14, 28, 35], [7, 14, 21, 21, 35], [7, 14, 21, 28, 28], [7, 14, 28, 49], [7, 14, 35, 42], [7, 21, 21, 21, 28], [7, 21, 21, 49], [7, 21, 28, 42], [7, 21, 35, 35], [7, 28, 28, 35], [7, 42, 49], [14, 14, 14, 14, 14, 14, 14], [14, 14, 14, 14, 14, 28], [14, 14, 14, 14, 21, 21], [14, 14, 14, 14, 42], [14, 14, 14, 21, 35], [14, 14, 14, 28, 28], [14, 14, 21, 21, 28], [14, 14, 21, 49], [14, 14, 28, 42], [14, 14, 35, 35], [14, 21, 21, 21, 21], [14, 21, 21, 42], [14, 21, 28, 35], [14, 28, 28, 28], [14, 35, 49], [14, 42, 42], [21, 21, 21, 35], [21, 21, 28, 28], [21, 28, 49], [21, 35, 42], [28, 28, 42], [28, 35, 35], [49, 49]]\n assert candidate(candidates = [3, 5, 7, 9, 11, 13, 15, 17, 19],target = 50) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 7], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 17], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 13], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 13], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 7, 11], [3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 9], [3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 11], [3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 7, 9], [3, 3, 3, 3, 3, 3, 3, 3, 5, 7, 7, 7], [3, 3, 3, 3, 3, 3, 3, 3, 7, 19], [3, 3, 3, 3, 3, 3, 3, 3, 9, 17], [3, 3, 3, 3, 3, 3, 3, 3, 11, 15], [3, 3, 3, 3, 3, 3, 3, 3, 13, 13], [3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 9], [3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 7, 7], [3, 3, 3, 3, 3, 3, 3, 5, 5, 19], [3, 3, 3, 3, 3, 3, 3, 5, 7, 17], [3, 3, 3, 3, 3, 3, 3, 5, 9, 15], [3, 3, 3, 3, 3, 3, 3, 5, 11, 13], [3, 3, 3, 3, 3, 3, 3, 7, 7, 15], [3, 3, 3, 3, 3, 3, 3, 7, 9, 13], [3, 3, 3, 3, 3, 3, 3, 7, 11, 11], [3, 3, 3, 3, 3, 3, 3, 9, 9, 11], [3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7], [3, 3, 3, 3, 3, 3, 5, 5, 5, 17], [3, 3, 3, 3, 3, 3, 5, 5, 7, 15], [3, 3, 3, 3, 3, 3, 5, 5, 9, 13], [3, 3, 3, 3, 3, 3, 5, 5, 11, 11], [3, 3, 3, 3, 3, 3, 5, 7, 7, 13], [3, 3, 3, 3, 3, 3, 5, 7, 9, 11], [3, 3, 3, 3, 3, 3, 5, 9, 9, 9], [3, 3, 3, 3, 3, 3, 7, 7, 7, 11], [3, 3, 3, 3, 3, 3, 7, 7, 9, 9], [3, 3, 3, 3, 3, 3, 13, 19], [3, 3, 3, 3, 3, 3, 15, 17], [3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5], [3, 3, 3, 3, 3, 5, 5, 5, 5, 15], [3, 3, 3, 3, 3, 5, 5, 5, 7, 13], [3, 3, 3, 3, 3, 5, 5, 5, 9, 11], [3, 3, 3, 3, 3, 5, 5, 7, 7, 11], [3, 3, 3, 3, 3, 5, 5, 7, 9, 9], [3, 3, 3, 3, 3, 5, 7, 7, 7, 9], [3, 3, 3, 3, 3, 5, 11, 19], [3, 3, 3, 3, 3, 5, 13, 17], [3, 3, 3, 3, 3, 5, 15, 15], [3, 3, 3, 3, 3, 7, 7, 7, 7, 7], [3, 3, 3, 3, 3, 7, 9, 19], [3, 3, 3, 3, 3, 7, 11, 17], [3, 3, 3, 3, 3, 7, 13, 15], [3, 3, 3, 3, 3, 9, 9, 17], [3, 3, 3, 3, 3, 9, 11, 15], [3, 3, 3, 3, 3, 9, 13, 13], [3, 3, 3, 3, 3, 11, 11, 13], [3, 3, 3, 3, 5, 5, 5, 5, 5, 13], [3, 3, 3, 3, 5, 5, 5, 5, 7, 11], [3, 3, 3, 3, 5, 5, 5, 5, 9, 9], [3, 3, 3, 3, 5, 5, 5, 7, 7, 9], [3, 3, 3, 3, 5, 5, 7, 7, 7, 7], [3, 3, 3, 3, 5, 5, 9, 19], [3, 3, 3, 3, 5, 5, 11, 17], [3, 3, 3, 3, 5, 5, 13, 15], [3, 3, 3, 3, 5, 7, 7, 19], [3, 3, 3, 3, 5, 7, 9, 17], [3, 3, 3, 3, 5, 7, 11, 15], [3, 3, 3, 3, 5, 7, 13, 13], [3, 3, 3, 3, 5, 9, 9, 15], [3, 3, 3, 3, 5, 9, 11, 13], [3, 3, 3, 3, 5, 11, 11, 11], [3, 3, 3, 3, 7, 7, 7, 17], [3, 3, 3, 3, 7, 7, 9, 15], [3, 3, 3, 3, 7, 7, 11, 13], [3, 3, 3, 3, 7, 9, 9, 13], [3, 3, 3, 3, 7, 9, 11, 11], [3, 3, 3, 3, 9, 9, 9, 11], [3, 3, 3, 3, 19, 19], [3, 3, 3, 5, 5, 5, 5, 5, 5, 11], [3, 3, 3, 5, 5, 5, 5, 5, 7, 9], [3, 3, 3, 5, 5, 5, 5, 7, 7, 7], [3, 3, 3, 5, 5, 5, 7, 19], [3, 3, 3, 5, 5, 5, 9, 17], [3, 3, 3, 5, 5, 5, 11, 15], [3, 3, 3, 5, 5, 5, 13, 13], [3, 3, 3, 5, 5, 7, 7, 17], [3, 3, 3, 5, 5, 7, 9, 15], [3, 3, 3, 5, 5, 7, 11, 13], [3, 3, 3, 5, 5, 9, 9, 13], [3, 3, 3, 5, 5, 9, 11, 11], [3, 3, 3, 5, 7, 7, 7, 15], [3, 3, 3, 5, 7, 7, 9, 13], [3, 3, 3, 5, 7, 7, 11, 11], [3, 3, 3, 5, 7, 9, 9, 11], [3, 3, 3, 5, 9, 9, 9, 9], [3, 3, 3, 5, 17, 19], [3, 3, 3, 7, 7, 7, 7, 13], [3, 3, 3, 7, 7, 7, 9, 11], [3, 3, 3, 7, 7, 9, 9, 9], [3, 3, 3, 7, 15, 19], [3, 3, 3, 7, 17, 17], [3, 3, 3, 9, 13, 19], [3, 3, 3, 9, 15, 17], [3, 3, 3, 11, 11, 19], [3, 3, 3, 11, 13, 17], [3, 3, 3, 11, 15, 15], [3, 3, 3, 13, 13, 15], [3, 3, 5, 5, 5, 5, 5, 5, 5, 9], [3, 3, 5, 5, 5, 5, 5, 5, 7, 7], [3, 3, 5, 5, 5, 5, 5, 19], [3, 3, 5, 5, 5, 5, 7, 17], [3, 3, 5, 5, 5, 5, 9, 15], [3, 3, 5, 5, 5, 5, 11, 13], [3, 3, 5, 5, 5, 7, 7, 15], [3, 3, 5, 5, 5, 7, 9, 13], [3, 3, 5, 5, 5, 7, 11, 11], [3, 3, 5, 5, 5, 9, 9, 11], [3, 3, 5, 5, 7, 7, 7, 13], [3, 3, 5, 5, 7, 7, 9, 11], [3, 3, 5, 5, 7, 9, 9, 9], [3, 3, 5, 5, 15, 19], [3, 3, 5, 5, 17, 17], [3, 3, 5, 7, 7, 7, 7, 11], [3, 3, 5, 7, 7, 7, 9, 9], [3, 3, 5, 7, 13, 19], [3, 3, 5, 7, 15, 17], [3, 3, 5, 9, 11, 19], [3, 3, 5, 9, 13, 17], [3, 3, 5, 9, 15, 15], [3, 3, 5, 11, 11, 17], [3, 3, 5, 11, 13, 15], [3, 3, 5, 13, 13, 13], [3, 3, 7, 7, 7, 7, 7, 9], [3, 3, 7, 7, 11, 19], [3, 3, 7, 7, 13, 17], [3, 3, 7, 7, 15, 15], [3, 3, 7, 9, 9, 19], [3, 3, 7, 9, 11, 17], [3, 3, 7, 9, 13, 15], [3, 3, 7, 11, 11, 15], [3, 3, 7, 11, 13, 13], [3, 3, 9, 9, 9, 17], [3, 3, 9, 9, 11, 15], [3, 3, 9, 9, 13, 13], [3, 3, 9, 11, 11, 13], [3, 3, 11, 11, 11, 11], [3, 5, 5, 5, 5, 5, 5, 5, 5, 7], [3, 5, 5, 5, 5, 5, 5, 17], [3, 5, 5, 5, 5, 5, 7, 15], [3, 5, 5, 5, 5, 5, 9, 13], [3, 5, 5, 5, 5, 5, 11, 11], [3, 5, 5, 5, 5, 7, 7, 13], [3, 5, 5, 5, 5, 7, 9, 11], [3, 5, 5, 5, 5, 9, 9, 9], [3, 5, 5, 5, 7, 7, 7, 11], [3, 5, 5, 5, 7, 7, 9, 9], [3, 5, 5, 5, 13, 19], [3, 5, 5, 5, 15, 17], [3, 5, 5, 7, 7, 7, 7, 9], [3, 5, 5, 7, 11, 19], [3, 5, 5, 7, 13, 17], [3, 5, 5, 7, 15, 15], [3, 5, 5, 9, 9, 19], [3, 5, 5, 9, 11, 17], [3, 5, 5, 9, 13, 15], [3, 5, 5, 11, 11, 15], [3, 5, 5, 11, 13, 13], [3, 5, 7, 7, 7, 7, 7, 7], [3, 5, 7, 7, 9, 19], [3, 5, 7, 7, 11, 17], [3, 5, 7, 7, 13, 15], [3, 5, 7, 9, 9, 17], [3, 5, 7, 9, 11, 15], [3, 5, 7, 9, 13, 13], [3, 5, 7, 11, 11, 13], [3, 5, 9, 9, 9, 15], [3, 5, 9, 9, 11, 13], [3, 5, 9, 11, 11, 11], [3, 7, 7, 7, 7, 19], [3, 7, 7, 7, 9, 17], [3, 7, 7, 7, 11, 15], [3, 7, 7, 7, 13, 13], [3, 7, 7, 9, 9, 15], [3, 7, 7, 9, 11, 13], [3, 7, 7, 11, 11, 11], [3, 7, 9, 9, 9, 13], [3, 7, 9, 9, 11, 11], [3, 9, 9, 9, 9, 11], [3, 9, 19, 19], [3, 11, 17, 19], [3, 13, 15, 19], [3, 13, 17, 17], [3, 15, 15, 17], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 5, 5, 7, 13], [5, 5, 5, 5, 5, 5, 9, 11], [5, 5, 5, 5, 5, 7, 7, 11], [5, 5, 5, 5, 5, 7, 9, 9], [5, 5, 5, 5, 7, 7, 7, 9], [5, 5, 5, 5, 11, 19], [5, 5, 5, 5, 13, 17], [5, 5, 5, 5, 15, 15], [5, 5, 5, 7, 7, 7, 7, 7], [5, 5, 5, 7, 9, 19], [5, 5, 5, 7, 11, 17], [5, 5, 5, 7, 13, 15], [5, 5, 5, 9, 9, 17], [5, 5, 5, 9, 11, 15], [5, 5, 5, 9, 13, 13], [5, 5, 5, 11, 11, 13], [5, 5, 7, 7, 7, 19], [5, 5, 7, 7, 9, 17], [5, 5, 7, 7, 11, 15], [5, 5, 7, 7, 13, 13], [5, 5, 7, 9, 9, 15], [5, 5, 7, 9, 11, 13], [5, 5, 7, 11, 11, 11], [5, 5, 9, 9, 9, 13], [5, 5, 9, 9, 11, 11], [5, 7, 7, 7, 7, 17], [5, 7, 7, 7, 9, 15], [5, 7, 7, 7, 11, 13], [5, 7, 7, 9, 9, 13], [5, 7, 7, 9, 11, 11], [5, 7, 9, 9, 9, 11], [5, 7, 19, 19], [5, 9, 9, 9, 9, 9], [5, 9, 17, 19], [5, 11, 15, 19], [5, 11, 17, 17], [5, 13, 13, 19], [5, 13, 15, 17], [5, 15, 15, 15], [7, 7, 7, 7, 7, 15], [7, 7, 7, 7, 9, 13], [7, 7, 7, 7, 11, 11], [7, 7, 7, 9, 9, 11], [7, 7, 9, 9, 9, 9], [7, 7, 17, 19], [7, 9, 15, 19], [7, 9, 17, 17], [7, 11, 13, 19], [7, 11, 15, 17], [7, 13, 13, 17], [7, 13, 15, 15], [9, 9, 13, 19], [9, 9, 15, 17], [9, 11, 11, 19], [9, 11, 13, 17], [9, 11, 15, 15], [9, 13, 13, 15], [11, 11, 11, 17], [11, 11, 13, 15], [11, 13, 13, 13]]\n assert candidate(candidates = [2, 3, 5, 7, 11],target = 29) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 11], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 3, 5, 7], [2, 2, 2, 2, 2, 2, 2, 5, 5, 5], [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5], [2, 2, 2, 2, 2, 2, 3, 3, 11], [2, 2, 2, 2, 2, 2, 3, 7, 7], [2, 2, 2, 2, 2, 2, 5, 5, 7], [2, 2, 2, 2, 2, 3, 3, 3, 3, 7], [2, 2, 2, 2, 2, 3, 3, 3, 5, 5], [2, 2, 2, 2, 2, 3, 5, 11], [2, 2, 2, 2, 2, 5, 7, 7], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3, 5, 7], [2, 2, 2, 2, 3, 3, 5, 5, 5], [2, 2, 2, 2, 3, 7, 11], [2, 2, 2, 2, 5, 5, 11], [2, 2, 2, 2, 7, 7, 7], [2, 2, 2, 3, 3, 3, 3, 3, 3, 5], [2, 2, 2, 3, 3, 3, 3, 11], [2, 2, 2, 3, 3, 3, 7, 7], [2, 2, 2, 3, 3, 5, 5, 7], [2, 2, 2, 3, 5, 5, 5, 5], [2, 2, 2, 5, 7, 11], [2, 2, 3, 3, 3, 3, 3, 3, 7], [2, 2, 3, 3, 3, 3, 3, 5, 5], [2, 2, 3, 3, 3, 5, 11], [2, 2, 3, 3, 5, 7, 7], [2, 2, 3, 5, 5, 5, 7], [2, 2, 3, 11, 11], [2, 2, 5, 5, 5, 5, 5], [2, 2, 7, 7, 11], [2, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3, 3, 5, 7], [2, 3, 3, 3, 3, 5, 5, 5], [2, 3, 3, 3, 7, 11], [2, 3, 3, 5, 5, 11], [2, 3, 3, 7, 7, 7], [2, 3, 5, 5, 7, 7], [2, 5, 5, 5, 5, 7], [2, 5, 11, 11], [3, 3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 11], [3, 3, 3, 3, 3, 7, 7], [3, 3, 3, 3, 5, 5, 7], [3, 3, 3, 5, 5, 5, 5], [3, 3, 5, 7, 11], [3, 5, 5, 5, 11], [3, 5, 7, 7, 7], [5, 5, 5, 7, 7], [7, 11, 11]]\n assert candidate(candidates = [6, 12, 18, 24, 30, 36, 42],target = 126) == [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 24, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 30, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 24, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 24, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 30, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 24, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 24, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 12, 30, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 36], [6, 6, 6, 6, 6, 6, 6, 6, 6, 18, 24, 30], [6, 6, 6, 6, 6, 6, 6, 6, 6, 24, 24, 24], [6, 6, 6, 6, 6, 6, 6, 6, 6, 30, 42], [6, 6, 6, 6, 6, 6, 6, 6, 6, 36, 36], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 18], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 30], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 42], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 18, 18], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 36], [6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 24, 30], [6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 18, 30], [6, 6, 6, 6, 6, 6, 6, 6, 12, 18, 24, 24], [6, 6, 6, 6, 6, 6, 6, 6, 12, 24, 42], [6, 6, 6, 6, 6, 6, 6, 6, 12, 30, 36], [6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 18, 24], [6, 6, 6, 6, 6, 6, 6, 6, 18, 18, 42], [6, 6, 6, 6, 6, 6, 6, 6, 18, 24, 36], [6, 6, 6, 6, 6, 6, 6, 6, 18, 30, 30], [6, 6, 6, 6, 6, 6, 6, 6, 24, 24, 30], [6, 6, 6, 6, 6, 6, 6, 6, 36, 42], [6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12], [6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 24], [6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 18, 18], [6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 36], [6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 30], [6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 24, 24], [6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 18, 24], [6, 6, 6, 6, 6, 6, 6, 12, 12, 18, 42], [6, 6, 6, 6, 6, 6, 6, 12, 12, 24, 36], [6, 6, 6, 6, 6, 6, 6, 12, 12, 30, 30], [6, 6, 6, 6, 6, 6, 6, 12, 18, 18, 18, 18], [6, 6, 6, 6, 6, 6, 6, 12, 18, 18, 36], [6, 6, 6, 6, 6, 6, 6, 12, 18, 24, 30], [6, 6, 6, 6, 6, 6, 6, 12, 24, 24, 24], [6, 6, 6, 6, 6, 6, 6, 12, 30, 42], [6, 6, 6, 6, 6, 6, 6, 12, 36, 36], [6, 6, 6, 6, 6, 6, 6, 18, 18, 18, 30], [6, 6, 6, 6, 6, 6, 6, 18, 18, 24, 24], [6, 6, 6, 6, 6, 6, 6, 18, 24, 42], [6, 6, 6, 6, 6, 6, 6, 18, 30, 36], [6, 6, 6, 6, 6, 6, 6, 24, 24, 36], [6, 6, 6, 6, 6, 6, 6, 24, 30, 30], [6, 6, 6, 6, 6, 6, 6, 42, 42], [6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 18], [6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 30], [6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 18, 24], [6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 42], [6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 18, 18], [6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 36], [6, 6, 6, 6, 6, 6, 12, 12, 12, 24, 30], [6, 6, 6, 6, 6, 6, 12, 12, 18, 18, 30], [6, 6, 6, 6, 6, 6, 12, 12, 18, 24, 24], [6, 6, 6, 6, 6, 6, 12, 12, 24, 42], [6, 6, 6, 6, 6, 6, 12, 12, 30, 36], [6, 6, 6, 6, 6, 6, 12, 18, 18, 18, 24], [6, 6, 6, 6, 6, 6, 12, 18, 18, 42], [6, 6, 6, 6, 6, 6, 12, 18, 24, 36], [6, 6, 6, 6, 6, 6, 12, 18, 30, 30], [6, 6, 6, 6, 6, 6, 12, 24, 24, 30], [6, 6, 6, 6, 6, 6, 12, 36, 42], [6, 6, 6, 6, 6, 6, 18, 18, 18, 18, 18], [6, 6, 6, 6, 6, 6, 18, 18, 18, 36], [6, 6, 6, 6, 6, 6, 18, 18, 24, 30], [6, 6, 6, 6, 6, 6, 18, 24, 24, 24], [6, 6, 6, 6, 6, 6, 18, 30, 42], [6, 6, 6, 6, 6, 6, 18, 36, 36], [6, 6, 6, 6, 6, 6, 24, 24, 42], [6, 6, 6, 6, 6, 6, 24, 30, 36], [6, 6, 6, 6, 6, 6, 30, 30, 30], [6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12], [6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 24], [6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 18, 18], [6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 36], [6, 6, 6, 6, 6, 12, 12, 12, 12, 18, 30], [6, 6, 6, 6, 6, 12, 12, 12, 12, 24, 24], [6, 6, 6, 6, 6, 12, 12, 12, 18, 18, 24], [6, 6, 6, 6, 6, 12, 12, 12, 18, 42], [6, 6, 6, 6, 6, 12, 12, 12, 24, 36], [6, 6, 6, 6, 6, 12, 12, 12, 30, 30], [6, 6, 6, 6, 6, 12, 12, 18, 18, 18, 18], [6, 6, 6, 6, 6, 12, 12, 18, 18, 36], [6, 6, 6, 6, 6, 12, 12, 18, 24, 30], [6, 6, 6, 6, 6, 12, 12, 24, 24, 24], [6, 6, 6, 6, 6, 12, 12, 30, 42], [6, 6, 6, 6, 6, 12, 12, 36, 36], [6, 6, 6, 6, 6, 12, 18, 18, 18, 30], [6, 6, 6, 6, 6, 12, 18, 18, 24, 24], [6, 6, 6, 6, 6, 12, 18, 24, 42], [6, 6, 6, 6, 6, 12, 18, 30, 36], [6, 6, 6, 6, 6, 12, 24, 24, 36], [6, 6, 6, 6, 6, 12, 24, 30, 30], [6, 6, 6, 6, 6, 12, 42, 42], [6, 6, 6, 6, 6, 18, 18, 18, 18, 24], [6, 6, 6, 6, 6, 18, 18, 18, 42], [6, 6, 6, 6, 6, 18, 18, 24, 36], [6, 6, 6, 6, 6, 18, 18, 30, 30], [6, 6, 6, 6, 6, 18, 24, 24, 30], [6, 6, 6, 6, 6, 18, 36, 42], [6, 6, 6, 6, 6, 24, 24, 24, 24], [6, 6, 6, 6, 6, 24, 30, 42], [6, 6, 6, 6, 6, 24, 36, 36], [6, 6, 6, 6, 6, 30, 30, 36], [6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 18], [6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 30], [6, 6, 6, 6, 12, 12, 12, 12, 12, 18, 24], [6, 6, 6, 6, 12, 12, 12, 12, 12, 42], [6, 6, 6, 6, 12, 12, 12, 12, 18, 18, 18], [6, 6, 6, 6, 12, 12, 12, 12, 18, 36], [6, 6, 6, 6, 12, 12, 12, 12, 24, 30], [6, 6, 6, 6, 12, 12, 12, 18, 18, 30], [6, 6, 6, 6, 12, 12, 12, 18, 24, 24], [6, 6, 6, 6, 12, 12, 12, 24, 42], [6, 6, 6, 6, 12, 12, 12, 30, 36], [6, 6, 6, 6, 12, 12, 18, 18, 18, 24], [6, 6, 6, 6, 12, 12, 18, 18, 42], [6, 6, 6, 6, 12, 12, 18, 24, 36], [6, 6, 6, 6, 12, 12, 18, 30, 30], [6, 6, 6, 6, 12, 12, 24, 24, 30], [6, 6, 6, 6, 12, 12, 36, 42], [6, 6, 6, 6, 12, 18, 18, 18, 18, 18], [6, 6, 6, 6, 12, 18, 18, 18, 36], [6, 6, 6, 6, 12, 18, 18, 24, 30], [6, 6, 6, 6, 12, 18, 24, 24, 24], [6, 6, 6, 6, 12, 18, 30, 42], [6, 6, 6, 6, 12, 18, 36, 36], [6, 6, 6, 6, 12, 24, 24, 42], [6, 6, 6, 6, 12, 24, 30, 36], [6, 6, 6, 6, 12, 30, 30, 30], [6, 6, 6, 6, 18, 18, 18, 18, 30], [6, 6, 6, 6, 18, 18, 18, 24, 24], [6, 6, 6, 6, 18, 18, 24, 42], [6, 6, 6, 6, 18, 18, 30, 36], [6, 6, 6, 6, 18, 24, 24, 36], [6, 6, 6, 6, 18, 24, 30, 30], [6, 6, 6, 6, 18, 42, 42], [6, 6, 6, 6, 24, 24, 24, 30], [6, 6, 6, 6, 24, 36, 42], [6, 6, 6, 6, 30, 30, 42], [6, 6, 6, 6, 30, 36, 36], [6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12], [6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 24], [6, 6, 6, 12, 12, 12, 12, 12, 12, 18, 18], [6, 6, 6, 12, 12, 12, 12, 12, 12, 36], [6, 6, 6, 12, 12, 12, 12, 12, 18, 30], [6, 6, 6, 12, 12, 12, 12, 12, 24, 24], [6, 6, 6, 12, 12, 12, 12, 18, 18, 24], [6, 6, 6, 12, 12, 12, 12, 18, 42], [6, 6, 6, 12, 12, 12, 12, 24, 36], [6, 6, 6, 12, 12, 12, 12, 30, 30], [6, 6, 6, 12, 12, 12, 18, 18, 18, 18], [6, 6, 6, 12, 12, 12, 18, 18, 36], [6, 6, 6, 12, 12, 12, 18, 24, 30], [6, 6, 6, 12, 12, 12, 24, 24, 24], [6, 6, 6, 12, 12, 12, 30, 42], [6, 6, 6, 12, 12, 12, 36, 36], [6, 6, 6, 12, 12, 18, 18, 18, 30], [6, 6, 6, 12, 12, 18, 18, 24, 24], [6, 6, 6, 12, 12, 18, 24, 42], [6, 6, 6, 12, 12, 18, 30, 36], [6, 6, 6, 12, 12, 24, 24, 36], [6, 6, 6, 12, 12, 24, 30, 30], [6, 6, 6, 12, 12, 42, 42], [6, 6, 6, 12, 18, 18, 18, 18, 24], [6, 6, 6, 12, 18, 18, 18, 42], [6, 6, 6, 12, 18, 18, 24, 36], [6, 6, 6, 12, 18, 18, 30, 30], [6, 6, 6, 12, 18, 24, 24, 30], [6, 6, 6, 12, 18, 36, 42], [6, 6, 6, 12, 24, 24, 24, 24], [6, 6, 6, 12, 24, 30, 42], [6, 6, 6, 12, 24, 36, 36], [6, 6, 6, 12, 30, 30, 36], [6, 6, 6, 18, 18, 18, 18, 18, 18], [6, 6, 6, 18, 18, 18, 18, 36], [6, 6, 6, 18, 18, 18, 24, 30], [6, 6, 6, 18, 18, 24, 24, 24], [6, 6, 6, 18, 18, 30, 42], [6, 6, 6, 18, 18, 36, 36], [6, 6, 6, 18, 24, 24, 42], [6, 6, 6, 18, 24, 30, 36], [6, 6, 6, 18, 30, 30, 30], [6, 6, 6, 24, 24, 24, 36], [6, 6, 6, 24, 24, 30, 30], [6, 6, 6, 24, 42, 42], [6, 6, 6, 30, 36, 42], [6, 6, 6, 36, 36, 36], [6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 18], [6, 6, 12, 12, 12, 12, 12, 12, 12, 30], [6, 6, 12, 12, 12, 12, 12, 12, 18, 24], [6, 6, 12, 12, 12, 12, 12, 12, 42], [6, 6, 12, 12, 12, 12, 12, 18, 18, 18], [6, 6, 12, 12, 12, 12, 12, 18, 36], [6, 6, 12, 12, 12, 12, 12, 24, 30], [6, 6, 12, 12, 12, 12, 18, 18, 30], [6, 6, 12, 12, 12, 12, 18, 24, 24], [6, 6, 12, 12, 12, 12, 24, 42], [6, 6, 12, 12, 12, 12, 30, 36], [6, 6, 12, 12, 12, 18, 18, 18, 24], [6, 6, 12, 12, 12, 18, 18, 42], [6, 6, 12, 12, 12, 18, 24, 36], [6, 6, 12, 12, 12, 18, 30, 30], [6, 6, 12, 12, 12, 24, 24, 30], [6, 6, 12, 12, 12, 36, 42], [6, 6, 12, 12, 18, 18, 18, 18, 18], [6, 6, 12, 12, 18, 18, 18, 36], [6, 6, 12, 12, 18, 18, 24, 30], [6, 6, 12, 12, 18, 24, 24, 24], [6, 6, 12, 12, 18, 30, 42], [6, 6, 12, 12, 18, 36, 36], [6, 6, 12, 12, 24, 24, 42], [6, 6, 12, 12, 24, 30, 36], [6, 6, 12, 12, 30, 30, 30], [6, 6, 12, 18, 18, 18, 18, 30], [6, 6, 12, 18, 18, 18, 24, 24], [6, 6, 12, 18, 18, 24, 42], [6, 6, 12, 18, 18, 30, 36], [6, 6, 12, 18, 24, 24, 36], [6, 6, 12, 18, 24, 30, 30], [6, 6, 12, 18, 42, 42], [6, 6, 12, 24, 24, 24, 30], [6, 6, 12, 24, 36, 42], [6, 6, 12, 30, 30, 42], [6, 6, 12, 30, 36, 36], [6, 6, 18, 18, 18, 18, 18, 24], [6, 6, 18, 18, 18, 18, 42], [6, 6, 18, 18, 18, 24, 36], [6, 6, 18, 18, 18, 30, 30], [6, 6, 18, 18, 24, 24, 30], [6, 6, 18, 18, 36, 42], [6, 6, 18, 24, 24, 24, 24], [6, 6, 18, 24, 30, 42], [6, 6, 18, 24, 36, 36], [6, 6, 18, 30, 30, 36], [6, 6, 24, 24, 24, 42], [6, 6, 24, 24, 30, 36], [6, 6, 24, 30, 30, 30], [6, 6, 30, 42, 42], [6, 6, 36, 36, 42], [6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12], [6, 12, 12, 12, 12, 12, 12, 12, 12, 24], [6, 12, 12, 12, 12, 12, 12, 12, 18, 18], [6, 12, 12, 12, 12, 12, 12, 12, 36], [6, 12, 12, 12, 12, 12, 12, 18, 30], [6, 12, 12, 12, 12, 12, 12, 24, 24], [6, 12, 12, 12, 12, 12, 18, 18, 24], [6, 12, 12, 12, 12, 12, 18, 42], [6, 12, 12, 12, 12, 12, 24, 36], [6, 12, 12, 12, 12, 12, 30, 30], [6, 12, 12, 12, 12, 18, 18, 18, 18], [6, 12, 12, 12, 12, 18, 18, 36], [6, 12, 12, 12, 12, 18, 24, 30], [6, 12, 12, 12, 12, 24, 24, 24], [6, 12, 12, 12, 12, 30, 42], [6, 12, 12, 12, 12, 36, 36], [6, 12, 12, 12, 18, 18, 18, 30], [6, 12, 12, 12, 18, 18, 24, 24], [6, 12, 12, 12, 18, 24, 42], [6, 12, 12, 12, 18, 30, 36], [6, 12, 12, 12, 24, 24, 36], [6, 12, 12, 12, 24, 30, 30], [6, 12, 12, 12, 42, 42], [6, 12, 12, 18, 18, 18, 18, 24], [6, 12, 12, 18, 18, 18, 42], [6, 12, 12, 18, 18, 24, 36], [6, 12, 12, 18, 18, 30, 30], [6, 12, 12, 18, 24, 24, 30], [6, 12, 12, 18, 36, 42], [6, 12, 12, 24, 24, 24, 24], [6, 12, 12, 24, 30, 42], [6, 12, 12, 24, 36, 36], [6, 12, 12, 30, 30, 36], [6, 12, 18, 18, 18, 18, 18, 18], [6, 12, 18, 18, 18, 18, 36], [6, 12, 18, 18, 18, 24, 30], [6, 12, 18, 18, 24, 24, 24], [6, 12, 18, 18, 30, 42], [6, 12, 18, 18, 36, 36], [6, 12, 18, 24, 24, 42], [6, 12, 18, 24, 30, 36], [6, 12, 18, 30, 30, 30], [6, 12, 24, 24, 24, 36], [6, 12, 24, 24, 30, 30], [6, 12, 24, 42, 42], [6, 12, 30, 36, 42], [6, 12, 36, 36, 36], [6, 18, 18, 18, 18, 18, 30], [6, 18, 18, 18, 18, 24, 24], [6, 18, 18, 18, 24, 42], [6, 18, 18, 18, 30, 36], [6, 18, 18, 24, 24, 36], [6, 18, 18, 24, 30, 30], [6, 18, 18, 42, 42], [6, 18, 24, 24, 24, 30], [6, 18, 24, 36, 42], [6, 18, 30, 30, 42], [6, 18, 30, 36, 36], [6, 24, 24, 24, 24, 24], [6, 24, 24, 30, 42], [6, 24, 24, 36, 36], [6, 24, 30, 30, 36], [6, 30, 30, 30, 30], [6, 36, 42, 42], [12, 12, 12, 12, 12, 12, 12, 12, 12, 18], [12, 12, 12, 12, 12, 12, 12, 12, 30], [12, 12, 12, 12, 12, 12, 12, 18, 24], [12, 12, 12, 12, 12, 12, 12, 42], [12, 12, 12, 12, 12, 12, 18, 18, 18], [12, 12, 12, 12, 12, 12, 18, 36], [12, 12, 12, 12, 12, 12, 24, 30], [12, 12, 12, 12, 12, 18, 18, 30], [12, 12, 12, 12, 12, 18, 24, 24], [12, 12, 12, 12, 12, 24, 42], [12, 12, 12, 12, 12, 30, 36], [12, 12, 12, 12, 18, 18, 18, 24], [12, 12, 12, 12, 18, 18, 42], [12, 12, 12, 12, 18, 24, 36], [12, 12, 12, 12, 18, 30, 30], [12, 12, 12, 12, 24, 24, 30], [12, 12, 12, 12, 36, 42], [12, 12, 12, 18, 18, 18, 18, 18], [12, 12, 12, 18, 18, 18, 36], [12, 12, 12, 18, 18, 24, 30], [12, 12, 12, 18, 24, 24, 24], [12, 12, 12, 18, 30, 42], [12, 12, 12, 18, 36, 36], [12, 12, 12, 24, 24, 42], [12, 12, 12, 24, 30, 36], [12, 12, 12, 30, 30, 30], [12, 12, 18, 18, 18, 18, 30], [12, 12, 18, 18, 18, 24, 24], [12, 12, 18, 18, 24, 42], [12, 12, 18, 18, 30, 36], [12, 12, 18, 24, 24, 36], [12, 12, 18, 24, 30, 30], [12, 12, 18, 42, 42], [12, 12, 24, 24, 24, 30], [12, 12, 24, 36, 42], [12, 12, 30, 30, 42], [12, 12, 30, 36, 36], [12, 18, 18, 18, 18, 18, 24], [12, 18, 18, 18, 18, 42], [12, 18, 18, 18, 24, 36], [12, 18, 18, 18, 30, 30], [12, 18, 18, 24, 24, 30], [12, 18, 18, 36, 42], [12, 18, 24, 24, 24, 24], [12, 18, 24, 30, 42], [12, 18, 24, 36, 36], [12, 18, 30, 30, 36], [12, 24, 24, 24, 42], [12, 24, 24, 30, 36], [12, 24, 30, 30, 30], [12, 30, 42, 42], [12, 36, 36, 42], [18, 18, 18, 18, 18, 18, 18], [18, 18, 18, 18, 18, 36], [18, 18, 18, 18, 24, 30], [18, 18, 18, 24, 24, 24], [18, 18, 18, 30, 42], [18, 18, 18, 36, 36], [18, 18, 24, 24, 42], [18, 18, 24, 30, 36], [18, 18, 30, 30, 30], [18, 24, 24, 24, 36], [18, 24, 24, 30, 30], [18, 24, 42, 42], [18, 30, 36, 42], [18, 36, 36, 36], [24, 24, 24, 24, 30], [24, 24, 36, 42], [24, 30, 30, 42], [24, 30, 36, 36], [30, 30, 30, 36], [42, 42, 42]]\n assert candidate(candidates = [2, 18, 34, 50, 66, 82],target = 100) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 34], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 18], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 34], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 18, 18], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 66], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 50], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 34, 34], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 18, 34], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 18, 18, 18], [2, 2, 2, 2, 2, 2, 2, 2, 2, 82], [2, 2, 2, 2, 2, 2, 2, 2, 18, 66], [2, 2, 2, 2, 2, 2, 2, 2, 34, 50], [2, 2, 2, 2, 2, 2, 2, 18, 18, 50], [2, 2, 2, 2, 2, 2, 2, 18, 34, 34], [2, 2, 2, 2, 2, 2, 18, 18, 18, 34], [2, 2, 2, 2, 2, 18, 18, 18, 18, 18], [18, 82], [34, 66], [50, 50]]\n assert candidate(candidates = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 45) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 15], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 12], [3, 3, 3, 3, 3, 3, 3, 3, 3, 9, 9], [3, 3, 3, 3, 3, 3, 3, 3, 3, 18], [3, 3, 3, 3, 3, 3, 3, 3, 6, 6, 9], [3, 3, 3, 3, 3, 3, 3, 3, 6, 15], [3, 3, 3, 3, 3, 3, 3, 3, 9, 12], [3, 3, 3, 3, 3, 3, 3, 3, 21], [3, 3, 3, 3, 3, 3, 3, 6, 6, 6, 6], [3, 3, 3, 3, 3, 3, 3, 6, 6, 12], [3, 3, 3, 3, 3, 3, 3, 6, 9, 9], [3, 3, 3, 3, 3, 3, 3, 6, 18], [3, 3, 3, 3, 3, 3, 3, 9, 15], [3, 3, 3, 3, 3, 3, 3, 12, 12], [3, 3, 3, 3, 3, 3, 3, 24], [3, 3, 3, 3, 3, 3, 6, 6, 6, 9], [3, 3, 3, 3, 3, 3, 6, 6, 15], [3, 3, 3, 3, 3, 3, 6, 9, 12], [3, 3, 3, 3, 3, 3, 6, 21], [3, 3, 3, 3, 3, 3, 9, 9, 9], [3, 3, 3, 3, 3, 3, 9, 18], [3, 3, 3, 3, 3, 3, 12, 15], [3, 3, 3, 3, 3, 3, 27], [3, 3, 3, 3, 3, 6, 6, 6, 6, 6], [3, 3, 3, 3, 3, 6, 6, 6, 12], [3, 3, 3, 3, 3, 6, 6, 9, 9], [3, 3, 3, 3, 3, 6, 6, 18], [3, 3, 3, 3, 3, 6, 9, 15], [3, 3, 3, 3, 3, 6, 12, 12], [3, 3, 3, 3, 3, 6, 24], [3, 3, 3, 3, 3, 9, 9, 12], [3, 3, 3, 3, 3, 9, 21], [3, 3, 3, 3, 3, 12, 18], [3, 3, 3, 3, 3, 15, 15], [3, 3, 3, 3, 3, 30], [3, 3, 3, 3, 6, 6, 6, 6, 9], [3, 3, 3, 3, 6, 6, 6, 15], [3, 3, 3, 3, 6, 6, 9, 12], [3, 3, 3, 3, 6, 6, 21], [3, 3, 3, 3, 6, 9, 9, 9], [3, 3, 3, 3, 6, 9, 18], [3, 3, 3, 3, 6, 12, 15], [3, 3, 3, 3, 6, 27], [3, 3, 3, 3, 9, 9, 15], [3, 3, 3, 3, 9, 12, 12], [3, 3, 3, 3, 9, 24], [3, 3, 3, 3, 12, 21], [3, 3, 3, 3, 15, 18], [3, 3, 3, 6, 6, 6, 6, 6, 6], [3, 3, 3, 6, 6, 6, 6, 12], [3, 3, 3, 6, 6, 6, 9, 9], [3, 3, 3, 6, 6, 6, 18], [3, 3, 3, 6, 6, 9, 15], [3, 3, 3, 6, 6, 12, 12], [3, 3, 3, 6, 6, 24], [3, 3, 3, 6, 9, 9, 12], [3, 3, 3, 6, 9, 21], [3, 3, 3, 6, 12, 18], [3, 3, 3, 6, 15, 15], [3, 3, 3, 6, 30], [3, 3, 3, 9, 9, 9, 9], [3, 3, 3, 9, 9, 18], [3, 3, 3, 9, 12, 15], [3, 3, 3, 9, 27], [3, 3, 3, 12, 12, 12], [3, 3, 3, 12, 24], [3, 3, 3, 15, 21], [3, 3, 3, 18, 18], [3, 3, 6, 6, 6, 6, 6, 9], [3, 3, 6, 6, 6, 6, 15], [3, 3, 6, 6, 6, 9, 12], [3, 3, 6, 6, 6, 21], [3, 3, 6, 6, 9, 9, 9], [3, 3, 6, 6, 9, 18], [3, 3, 6, 6, 12, 15], [3, 3, 6, 6, 27], [3, 3, 6, 9, 9, 15], [3, 3, 6, 9, 12, 12], [3, 3, 6, 9, 24], [3, 3, 6, 12, 21], [3, 3, 6, 15, 18], [3, 3, 9, 9, 9, 12], [3, 3, 9, 9, 21], [3, 3, 9, 12, 18], [3, 3, 9, 15, 15], [3, 3, 9, 30], [3, 3, 12, 12, 15], [3, 3, 12, 27], [3, 3, 15, 24], [3, 3, 18, 21], [3, 6, 6, 6, 6, 6, 6, 6], [3, 6, 6, 6, 6, 6, 12], [3, 6, 6, 6, 6, 9, 9], [3, 6, 6, 6, 6, 18], [3, 6, 6, 6, 9, 15], [3, 6, 6, 6, 12, 12], [3, 6, 6, 6, 24], [3, 6, 6, 9, 9, 12], [3, 6, 6, 9, 21], [3, 6, 6, 12, 18], [3, 6, 6, 15, 15], [3, 6, 6, 30], [3, 6, 9, 9, 9, 9], [3, 6, 9, 9, 18], [3, 6, 9, 12, 15], [3, 6, 9, 27], [3, 6, 12, 12, 12], [3, 6, 12, 24], [3, 6, 15, 21], [3, 6, 18, 18], [3, 9, 9, 9, 15], [3, 9, 9, 12, 12], [3, 9, 9, 24], [3, 9, 12, 21], [3, 9, 15, 18], [3, 12, 12, 18], [3, 12, 15, 15], [3, 12, 30], [3, 15, 27], [3, 18, 24], [3, 21, 21], [6, 6, 6, 6, 6, 6, 9], [6, 6, 6, 6, 6, 15], [6, 6, 6, 6, 9, 12], [6, 6, 6, 6, 21], [6, 6, 6, 9, 9, 9], [6, 6, 6, 9, 18], [6, 6, 6, 12, 15], [6, 6, 6, 27], [6, 6, 9, 9, 15], [6, 6, 9, 12, 12], [6, 6, 9, 24], [6, 6, 12, 21], [6, 6, 15, 18], [6, 9, 9, 9, 12], [6, 9, 9, 21], [6, 9, 12, 18], [6, 9, 15, 15], [6, 9, 30], [6, 12, 12, 15], [6, 12, 27], [6, 15, 24], [6, 18, 21], [9, 9, 9, 9, 9], [9, 9, 9, 18], [9, 9, 12, 15], [9, 9, 27], [9, 12, 12, 12], [9, 12, 24], [9, 15, 21], [9, 18, 18], [12, 12, 21], [12, 15, 18], [15, 15, 15], [15, 30], [18, 27], [21, 24]]\n assert candidate(candidates = [5, 10, 15, 20, 25, 30, 35, 40],target = 80) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 30], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 15], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 15, 20], [5, 5, 5, 5, 5, 5, 5, 5, 5, 35], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 20], [5, 5, 5, 5, 5, 5, 5, 5, 10, 15, 15], [5, 5, 5, 5, 5, 5, 5, 5, 10, 30], [5, 5, 5, 5, 5, 5, 5, 5, 15, 25], [5, 5, 5, 5, 5, 5, 5, 5, 20, 20], [5, 5, 5, 5, 5, 5, 5, 5, 40], [5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 15], [5, 5, 5, 5, 5, 5, 5, 10, 10, 25], [5, 5, 5, 5, 5, 5, 5, 10, 15, 20], [5, 5, 5, 5, 5, 5, 5, 10, 35], [5, 5, 5, 5, 5, 5, 5, 15, 15, 15], [5, 5, 5, 5, 5, 5, 5, 15, 30], [5, 5, 5, 5, 5, 5, 5, 20, 25], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 10, 10, 10, 20], [5, 5, 5, 5, 5, 5, 10, 10, 15, 15], [5, 5, 5, 5, 5, 5, 10, 10, 30], [5, 5, 5, 5, 5, 5, 10, 15, 25], [5, 5, 5, 5, 5, 5, 10, 20, 20], [5, 5, 5, 5, 5, 5, 10, 40], [5, 5, 5, 5, 5, 5, 15, 15, 20], [5, 5, 5, 5, 5, 5, 15, 35], [5, 5, 5, 5, 5, 5, 20, 30], [5, 5, 5, 5, 5, 5, 25, 25], [5, 5, 5, 5, 5, 10, 10, 10, 10, 15], [5, 5, 5, 5, 5, 10, 10, 10, 25], [5, 5, 5, 5, 5, 10, 10, 15, 20], [5, 5, 5, 5, 5, 10, 10, 35], [5, 5, 5, 5, 5, 10, 15, 15, 15], [5, 5, 5, 5, 5, 10, 15, 30], [5, 5, 5, 5, 5, 10, 20, 25], [5, 5, 5, 5, 5, 15, 15, 25], [5, 5, 5, 5, 5, 15, 20, 20], [5, 5, 5, 5, 5, 15, 40], [5, 5, 5, 5, 5, 20, 35], [5, 5, 5, 5, 5, 25, 30], [5, 5, 5, 5, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 10, 10, 10, 10, 20], [5, 5, 5, 5, 10, 10, 10, 15, 15], [5, 5, 5, 5, 10, 10, 10, 30], [5, 5, 5, 5, 10, 10, 15, 25], [5, 5, 5, 5, 10, 10, 20, 20], [5, 5, 5, 5, 10, 10, 40], [5, 5, 5, 5, 10, 15, 15, 20], [5, 5, 5, 5, 10, 15, 35], [5, 5, 5, 5, 10, 20, 30], [5, 5, 5, 5, 10, 25, 25], [5, 5, 5, 5, 15, 15, 15, 15], [5, 5, 5, 5, 15, 15, 30], [5, 5, 5, 5, 15, 20, 25], [5, 5, 5, 5, 20, 20, 20], [5, 5, 5, 5, 20, 40], [5, 5, 5, 5, 25, 35], [5, 5, 5, 5, 30, 30], [5, 5, 5, 10, 10, 10, 10, 10, 15], [5, 5, 5, 10, 10, 10, 10, 25], [5, 5, 5, 10, 10, 10, 15, 20], [5, 5, 5, 10, 10, 10, 35], [5, 5, 5, 10, 10, 15, 15, 15], [5, 5, 5, 10, 10, 15, 30], [5, 5, 5, 10, 10, 20, 25], [5, 5, 5, 10, 15, 15, 25], [5, 5, 5, 10, 15, 20, 20], [5, 5, 5, 10, 15, 40], [5, 5, 5, 10, 20, 35], [5, 5, 5, 10, 25, 30], [5, 5, 5, 15, 15, 15, 20], [5, 5, 5, 15, 15, 35], [5, 5, 5, 15, 20, 30], [5, 5, 5, 15, 25, 25], [5, 5, 5, 20, 20, 25], [5, 5, 5, 25, 40], [5, 5, 5, 30, 35], [5, 5, 10, 10, 10, 10, 10, 10, 10], [5, 5, 10, 10, 10, 10, 10, 20], [5, 5, 10, 10, 10, 10, 15, 15], [5, 5, 10, 10, 10, 10, 30], [5, 5, 10, 10, 10, 15, 25], [5, 5, 10, 10, 10, 20, 20], [5, 5, 10, 10, 10, 40], [5, 5, 10, 10, 15, 15, 20], [5, 5, 10, 10, 15, 35], [5, 5, 10, 10, 20, 30], [5, 5, 10, 10, 25, 25], [5, 5, 10, 15, 15, 15, 15], [5, 5, 10, 15, 15, 30], [5, 5, 10, 15, 20, 25], [5, 5, 10, 20, 20, 20], [5, 5, 10, 20, 40], [5, 5, 10, 25, 35], [5, 5, 10, 30, 30], [5, 5, 15, 15, 15, 25], [5, 5, 15, 15, 20, 20], [5, 5, 15, 15, 40], [5, 5, 15, 20, 35], [5, 5, 15, 25, 30], [5, 5, 20, 20, 30], [5, 5, 20, 25, 25], [5, 5, 30, 40], [5, 5, 35, 35], [5, 10, 10, 10, 10, 10, 10, 15], [5, 10, 10, 10, 10, 10, 25], [5, 10, 10, 10, 10, 15, 20], [5, 10, 10, 10, 10, 35], [5, 10, 10, 10, 15, 15, 15], [5, 10, 10, 10, 15, 30], [5, 10, 10, 10, 20, 25], [5, 10, 10, 15, 15, 25], [5, 10, 10, 15, 20, 20], [5, 10, 10, 15, 40], [5, 10, 10, 20, 35], [5, 10, 10, 25, 30], [5, 10, 15, 15, 15, 20], [5, 10, 15, 15, 35], [5, 10, 15, 20, 30], [5, 10, 15, 25, 25], [5, 10, 20, 20, 25], [5, 10, 25, 40], [5, 10, 30, 35], [5, 15, 15, 15, 15, 15], [5, 15, 15, 15, 30], [5, 15, 15, 20, 25], [5, 15, 20, 20, 20], [5, 15, 20, 40], [5, 15, 25, 35], [5, 15, 30, 30], [5, 20, 20, 35], [5, 20, 25, 30], [5, 25, 25, 25], [5, 35, 40], [10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 20], [10, 10, 10, 10, 10, 15, 15], [10, 10, 10, 10, 10, 30], [10, 10, 10, 10, 15, 25], [10, 10, 10, 10, 20, 20], [10, 10, 10, 10, 40], [10, 10, 10, 15, 15, 20], [10, 10, 10, 15, 35], [10, 10, 10, 20, 30], [10, 10, 10, 25, 25], [10, 10, 15, 15, 15, 15], [10, 10, 15, 15, 30], [10, 10, 15, 20, 25], [10, 10, 20, 20, 20], [10, 10, 20, 40], [10, 10, 25, 35], [10, 10, 30, 30], [10, 15, 15, 15, 25], [10, 15, 15, 20, 20], [10, 15, 15, 40], [10, 15, 20, 35], [10, 15, 25, 30], [10, 20, 20, 30], [10, 20, 25, 25], [10, 30, 40], [10, 35, 35], [15, 15, 15, 15, 20], [15, 15, 15, 35], [15, 15, 20, 30], [15, 15, 25, 25], [15, 20, 20, 25], [15, 25, 40], [15, 30, 35], [20, 20, 20, 20], [20, 20, 40], [20, 25, 35], [20, 30, 30], [25, 25, 30], [40, 40]]\n assert candidate(candidates = [3, 5, 7, 11, 13, 17, 19],target = 30) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 5, 19], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [11, 19], [13, 17]]\n assert candidate(candidates = [8, 16, 32, 64, 128, 256, 512],target = 511) == []\n assert candidate(candidates = [3, 6, 9, 12, 15],target = 100) == []\n assert candidate(candidates = [7, 14, 21, 28, 35, 42],target = 49) == [[7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 14], [7, 7, 7, 7, 21], [7, 7, 7, 14, 14], [7, 7, 7, 28], [7, 7, 14, 21], [7, 7, 35], [7, 14, 14, 14], [7, 14, 28], [7, 21, 21], [7, 42], [14, 14, 21], [14, 35], [21, 28]]\n assert candidate(candidates = [3, 5, 7, 8, 10],target = 25) == [[3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 10], [3, 3, 3, 3, 5, 8], [3, 3, 3, 8, 8], [3, 3, 5, 7, 7], [3, 5, 5, 5, 7], [3, 5, 7, 10], [3, 7, 7, 8], [5, 5, 5, 5, 5], [5, 5, 5, 10], [5, 5, 7, 8], [5, 10, 10], [7, 8, 10]]\n assert candidate(candidates = [3, 5, 7, 11, 13, 17],target = 30) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 5, 7], [3, 3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 13], [3, 3, 3, 3, 7, 11], [3, 3, 3, 5, 5, 11], [3, 3, 3, 7, 7, 7], [3, 3, 5, 5, 7, 7], [3, 3, 7, 17], [3, 3, 11, 13], [3, 5, 5, 5, 5, 7], [3, 5, 5, 17], [3, 5, 11, 11], [3, 7, 7, 13], [5, 5, 5, 5, 5, 5], [5, 5, 7, 13], [5, 7, 7, 11], [13, 17]]\n assert candidate(candidates = [5, 10, 25],target = 100) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 25, 25], [5, 5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 25], [5, 5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 5, 5, 10, 25, 25], [5, 5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 25], [5, 5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 5, 5, 10, 10, 25, 25], [5, 5, 5, 5, 5, 10, 10, 10, 10, 10, 25], [5, 5, 5, 5, 5, 25, 25, 25], [5, 5, 5, 5, 10, 10, 10, 10, 10, 10, 10, 10], [5, 5, 5, 5, 10, 10, 10, 25, 25], [5, 5, 5, 10, 10, 10, 10, 10, 10, 25], [5, 5, 5, 10, 25, 25, 25], [5, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10], [5, 5, 10, 10, 10, 10, 25, 25], [5, 10, 10, 10, 10, 10, 10, 10, 25], [5, 10, 10, 25, 25, 25], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 25, 25], [25, 25, 25, 25]]\n assert candidate(candidates = [13, 11, 7, 5, 3, 2],target = 25) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5], [2, 2, 2, 2, 2, 2, 2, 2, 2, 7], [2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 2, 2, 3, 3, 5], [2, 2, 2, 2, 2, 2, 2, 11], [2, 2, 2, 2, 2, 2, 3, 3, 7], [2, 2, 2, 2, 2, 2, 3, 5, 5], [2, 2, 2, 2, 2, 2, 13], [2, 2, 2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 2, 2, 3, 5, 7], [2, 2, 2, 2, 2, 5, 5, 5], [2, 2, 2, 2, 3, 3, 3, 3, 5], [2, 2, 2, 2, 3, 3, 11], [2, 2, 2, 2, 3, 7, 7], [2, 2, 2, 2, 5, 5, 7], [2, 2, 2, 3, 3, 3, 3, 7], [2, 2, 2, 3, 3, 3, 5, 5], [2, 2, 2, 3, 3, 13], [2, 2, 2, 3, 5, 11], [2, 2, 2, 5, 7, 7], [2, 2, 3, 3, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 5, 7], [2, 2, 3, 3, 5, 5, 5], [2, 2, 3, 5, 13], [2, 2, 3, 7, 11], [2, 2, 5, 5, 11], [2, 2, 7, 7, 7], [2, 3, 3, 3, 3, 3, 3, 5], [2, 3, 3, 3, 3, 11], [2, 3, 3, 3, 7, 7], [2, 3, 3, 5, 5, 7], [2, 3, 5, 5, 5, 5], [2, 3, 7, 13], [2, 5, 5, 13], [2, 5, 7, 11], [3, 3, 3, 3, 3, 3, 7], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 13], [3, 3, 3, 5, 11], [3, 3, 5, 7, 7], [3, 5, 5, 5, 7], [3, 11, 11], [5, 5, 5, 5, 5], [5, 7, 13], [7, 7, 11]]\n assert candidate(candidates = [18, 22, 24, 26, 30],target = 50) == [[24, 26]]\n assert candidate(candidates = [15, 18, 20, 25],target = 50) == [[15, 15, 20], [25, 25]]\n"}, "metadata": {"canonical_parameter_names": ["candidates", "target"], "leetcode_dataset_entry_point": "Solution().combinationSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var combinationSum = function(candidates, target) {", "container": null, "callable": "combinationSum", "parameters": [{"name": "candidates", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 40, "task_id": "combination-sum-ii", "difficulty": "Medium", "problem_description": "Given a collection of candidate numbers (candidates) and a target number (target), find all unique combinations in candidates where the candidate numbers sum to target.\nEach number in candidates may only be used once in the combination.\nNote: The solution set must not contain duplicate combinations.\n \nExample 1:\n\nInput: candidates = [10,1,2,7,6,1,5], target = 8\nOutput: \n[\n[1,1,6],\n[1,2,5],\n[1,7],\n[2,6]\n]\n\nExample 2:\n\nInput: candidates = [2,5,2,1,2], target = 5\nOutput: \n[\n[1,2,2],\n[5]\n]\n\n \nConstraints:\n\n1 <= candidates.length <= 100\n1 <= candidates[i] <= 50\n1 <= target <= 30\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(candidates = [1, 1, 1, 1, 1],target = 3) == [[1, 1, 1]]\n assert candidate(candidates = [2, 5, 2, 1, 2],target = 5) == [[1, 2, 2], [5]]\n assert candidate(candidates = [4, 4, 2, 1, 4, 2, 2, 1, 3],target = 6) == [[1, 1, 2, 2], [1, 1, 4], [1, 2, 3], [2, 2, 2], [2, 4]]\n assert candidate(candidates = [1, 2],target = 4) == []\n assert candidate(candidates = [1, 2, 3, 4, 5],target = 5) == [[1, 4], [2, 3], [5]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5],target = 8) == [[1, 1, 6], [1, 2, 5], [1, 7], [2, 6]]\n assert candidate(candidates = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 25) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\n assert candidate(candidates = [3, 1, 3, 5, 1, 1],target = 8) == [[1, 1, 1, 5], [1, 1, 3, 3], [3, 5]]\n assert candidate(candidates = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 5) == [[1, 1, 1, 1, 1]]\n assert candidate(candidates = [1],target = 1) == [[1]]\n assert candidate(candidates = [1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8],target = 20) == [[1, 1, 2, 2, 2, 3, 3, 6], [1, 1, 2, 2, 2, 3, 4, 5], [1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 2, 2, 2, 4, 8], [1, 1, 2, 2, 2, 5, 7], [1, 1, 2, 2, 2, 6, 6], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 8], [1, 1, 2, 2, 3, 4, 7], [1, 1, 2, 2, 3, 5, 6], [1, 1, 2, 2, 4, 4, 6], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 6, 8], [1, 1, 2, 2, 7, 7], [1, 1, 2, 3, 3, 4, 6], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 5, 8], [1, 1, 2, 3, 6, 7], [1, 1, 2, 4, 4, 4, 4], [1, 1, 2, 4, 4, 8], [1, 1, 2, 4, 5, 7], [1, 1, 2, 4, 6, 6], [1, 1, 2, 5, 5, 6], [1, 1, 2, 8, 8], [1, 1, 3, 3, 4, 4, 4], [1, 1, 3, 3, 4, 8], [1, 1, 3, 3, 5, 7], [1, 1, 3, 3, 6, 6], [1, 1, 3, 4, 4, 7], [1, 1, 3, 4, 5, 6], [1, 1, 3, 5, 5, 5], [1, 1, 3, 7, 8], [1, 1, 4, 4, 4, 6], [1, 1, 4, 4, 5, 5], [1, 1, 4, 6, 8], [1, 1, 4, 7, 7], [1, 1, 5, 5, 8], [1, 1, 5, 6, 7], [1, 1, 6, 6, 6], [1, 2, 2, 2, 3, 3, 7], [1, 2, 2, 2, 3, 4, 6], [1, 2, 2, 2, 3, 5, 5], [1, 2, 2, 2, 4, 4, 5], [1, 2, 2, 2, 5, 8], [1, 2, 2, 2, 6, 7], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 8], [1, 2, 2, 3, 5, 7], [1, 2, 2, 3, 6, 6], [1, 2, 2, 4, 4, 7], [1, 2, 2, 4, 5, 6], [1, 2, 2, 5, 5, 5], [1, 2, 2, 7, 8], [1, 2, 3, 3, 4, 7], [1, 2, 3, 3, 5, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 6, 8], [1, 2, 3, 7, 7], [1, 2, 4, 4, 4, 5], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 5, 5, 7], [1, 2, 5, 6, 6], [1, 3, 3, 4, 4, 5], [1, 3, 3, 5, 8], [1, 3, 3, 6, 7], [1, 3, 4, 4, 4, 4], [1, 3, 4, 4, 8], [1, 3, 4, 5, 7], [1, 3, 4, 6, 6], [1, 3, 5, 5, 6], [1, 3, 8, 8], [1, 4, 4, 4, 7], [1, 4, 4, 5, 6], [1, 4, 5, 5, 5], [1, 4, 7, 8], [1, 5, 6, 8], [1, 5, 7, 7], [1, 6, 6, 7], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 8], [2, 2, 2, 3, 4, 7], [2, 2, 2, 3, 5, 6], [2, 2, 2, 4, 4, 6], [2, 2, 2, 4, 5, 5], [2, 2, 2, 6, 8], [2, 2, 2, 7, 7], [2, 2, 3, 3, 4, 6], [2, 2, 3, 3, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 5, 8], [2, 2, 3, 6, 7], [2, 2, 4, 4, 4, 4], [2, 2, 4, 4, 8], [2, 2, 4, 5, 7], [2, 2, 4, 6, 6], [2, 2, 5, 5, 6], [2, 2, 8, 8], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 8], [2, 3, 3, 5, 7], [2, 3, 3, 6, 6], [2, 3, 4, 4, 7], [2, 3, 4, 5, 6], [2, 3, 5, 5, 5], [2, 3, 7, 8], [2, 4, 4, 4, 6], [2, 4, 4, 5, 5], [2, 4, 6, 8], [2, 4, 7, 7], [2, 5, 5, 8], [2, 5, 6, 7], [2, 6, 6, 6], [3, 3, 4, 4, 6], [3, 3, 4, 5, 5], [3, 3, 6, 8], [3, 3, 7, 7], [3, 4, 4, 4, 5], [3, 4, 5, 8], [3, 4, 6, 7], [3, 5, 5, 7], [3, 5, 6, 6], [4, 4, 4, 8], [4, 4, 5, 7], [4, 4, 6, 6], [4, 5, 5, 6], [4, 8, 8], [5, 5, 5, 5], [5, 7, 8], [6, 6, 8], [6, 7, 7]]\n assert candidate(candidates = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],target = 100) == [[5, 10, 15, 20, 50], [5, 10, 15, 25, 45], [5, 10, 15, 30, 40], [5, 10, 20, 25, 40], [5, 10, 20, 30, 35], [5, 10, 35, 50], [5, 10, 40, 45], [5, 15, 20, 25, 35], [5, 15, 30, 50], [5, 15, 35, 45], [5, 20, 25, 50], [5, 20, 30, 45], [5, 20, 35, 40], [5, 25, 30, 40], [5, 45, 50], [10, 15, 20, 25, 30], [10, 15, 25, 50], [10, 15, 30, 45], [10, 15, 35, 40], [10, 20, 25, 45], [10, 20, 30, 40], [10, 25, 30, 35], [10, 40, 50], [15, 20, 25, 40], [15, 20, 30, 35], [15, 35, 50], [15, 40, 45], [20, 30, 50], [20, 35, 45], [25, 30, 45], [25, 35, 40]]\n assert candidate(candidates = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7],target = 60) == [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5], [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 7, 7], [4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 7, 7], [4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 7], [4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6], [4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 7], [4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6], [4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7], [4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 7], [4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6], [4, 4, 4, 4, 4, 4, 4, 5, 6, 7, 7, 7], [4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 7, 7], [4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6], [4, 4, 4, 4, 4, 4, 5, 5, 5, 7, 7, 7], [4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7], [4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7], [4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6], [4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5], [4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 7, 7], [4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7], [4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6], [4, 4, 4, 4, 4, 5, 7, 7, 7, 7, 7], [4, 4, 4, 4, 4, 6, 6, 7, 7, 7, 7], [4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 7, 7], [4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7], [4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6], [4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 7], [4, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7], [4, 4, 4, 4, 6, 6, 6, 6, 6, 7, 7], [4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7], [4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6], [4, 4, 4, 5, 5, 5, 5, 7, 7, 7, 7], [4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7], [4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7], [4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 7], [4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6], [4, 4, 4, 6, 7, 7, 7, 7, 7, 7], [4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7], [4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6], [4, 4, 5, 5, 5, 5, 5, 6, 7, 7, 7], [4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7], [4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7], [4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6], [4, 4, 5, 5, 7, 7, 7, 7, 7, 7], [4, 4, 5, 6, 6, 7, 7, 7, 7, 7], [4, 4, 6, 6, 6, 6, 7, 7, 7, 7], [4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6], [4, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7], [4, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7], [4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7], [4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6], [4, 5, 5, 5, 6, 7, 7, 7, 7, 7], [4, 5, 5, 6, 6, 6, 7, 7, 7, 7], [4, 5, 6, 6, 6, 6, 6, 7, 7, 7], [4, 6, 6, 6, 6, 6, 6, 6, 7, 7], [4, 7, 7, 7, 7, 7, 7, 7, 7], [5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7], [5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7], [5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6], [5, 5, 5, 5, 5, 7, 7, 7, 7, 7], [5, 5, 5, 5, 6, 6, 7, 7, 7, 7], [5, 5, 5, 6, 6, 6, 6, 7, 7, 7], [5, 5, 6, 6, 6, 6, 6, 6, 7, 7], [5, 6, 6, 6, 6, 6, 6, 6, 6, 7], [5, 6, 7, 7, 7, 7, 7, 7, 7], [6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 7, 7, 7, 7, 7, 7]]\n assert candidate(candidates = [2, 3, 6, 7, 10, 11, 13, 15, 18, 21, 22, 23, 24, 25, 27],target = 50) == [[2, 3, 6, 7, 10, 22], [2, 3, 6, 7, 11, 21], [2, 3, 6, 10, 11, 18], [2, 3, 6, 11, 13, 15], [2, 3, 6, 15, 24], [2, 3, 6, 18, 21], [2, 3, 7, 10, 13, 15], [2, 3, 7, 11, 27], [2, 3, 7, 13, 25], [2, 3, 7, 15, 23], [2, 3, 10, 11, 24], [2, 3, 10, 13, 22], [2, 3, 11, 13, 21], [2, 3, 18, 27], [2, 3, 21, 24], [2, 3, 22, 23], [2, 6, 7, 10, 25], [2, 6, 7, 11, 24], [2, 6, 7, 13, 22], [2, 6, 10, 11, 21], [2, 6, 11, 13, 18], [2, 6, 15, 27], [2, 6, 18, 24], [2, 7, 10, 13, 18], [2, 7, 18, 23], [2, 10, 11, 27], [2, 10, 13, 25], [2, 10, 15, 23], [2, 11, 13, 24], [2, 11, 15, 22], [2, 21, 27], [2, 23, 25], [3, 6, 7, 10, 11, 13], [3, 6, 7, 10, 24], [3, 6, 7, 11, 23], [3, 6, 7, 13, 21], [3, 6, 10, 13, 18], [3, 6, 18, 23], [3, 7, 13, 27], [3, 7, 15, 25], [3, 7, 18, 22], [3, 10, 13, 24], [3, 10, 15, 22], [3, 11, 13, 23], [3, 11, 15, 21], [3, 22, 25], [3, 23, 24], [6, 7, 10, 27], [6, 7, 13, 24], [6, 7, 15, 22], [6, 10, 11, 23], [6, 10, 13, 21], [6, 11, 15, 18], [6, 21, 23], [7, 10, 11, 22], [7, 10, 15, 18], [7, 18, 25], [7, 21, 22], [10, 13, 27], [10, 15, 25], [10, 18, 22], [11, 15, 24], [11, 18, 21], [13, 15, 22], [23, 27]]\n assert candidate(candidates = [10, 20, 30, 40, 50],target = 50) == [[10, 40], [20, 30], [50]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 1, 2],target = 10) == [[1, 1, 1, 2, 5], [1, 1, 1, 7], [1, 1, 2, 6], [1, 2, 2, 5], [1, 2, 7], [2, 2, 6], [10]]\n assert candidate(candidates = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 15) == [[1, 1, 2, 2, 3, 6], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 9], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 8], [1, 1, 2, 4, 7], [1, 1, 2, 5, 6], [1, 1, 3, 3, 7], [1, 1, 3, 4, 6], [1, 1, 3, 5, 5], [1, 1, 3, 10], [1, 1, 4, 4, 5], [1, 1, 4, 9], [1, 1, 5, 8], [1, 1, 6, 7], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 7], [1, 2, 2, 4, 6], [1, 2, 2, 5, 5], [1, 2, 2, 10], [1, 2, 3, 3, 6], [1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 2, 6, 6], [1, 3, 3, 4, 4], [1, 3, 3, 8], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 4, 6], [1, 4, 5, 5], [1, 4, 10], [1, 5, 9], [1, 6, 8], [1, 7, 7], [2, 2, 3, 3, 5], [2, 2, 3, 4, 4], [2, 2, 3, 8], [2, 2, 4, 7], [2, 2, 5, 6], [2, 3, 3, 7], [2, 3, 4, 6], [2, 3, 5, 5], [2, 3, 10], [2, 4, 4, 5], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 3, 4, 5], [3, 3, 9], [3, 4, 8], [3, 5, 7], [3, 6, 6], [4, 4, 7], [4, 5, 6], [5, 10], [6, 9], [7, 8]]\n assert candidate(candidates = [15, 20, 1, 3, 8, 12, 3, 10],target = 33) == [[1, 12, 20], [3, 3, 12, 15], [3, 8, 10, 12], [3, 10, 20], [8, 10, 15]]\n assert candidate(candidates = [3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30],target = 60) == [[3, 3, 6, 6, 9, 9, 12, 12], [3, 3, 6, 6, 9, 9, 24], [3, 3, 6, 6, 9, 12, 21], [3, 3, 6, 6, 9, 15, 18], [3, 3, 6, 6, 12, 12, 18], [3, 3, 6, 6, 12, 15, 15], [3, 3, 6, 6, 12, 30], [3, 3, 6, 6, 15, 27], [3, 3, 6, 6, 18, 24], [3, 3, 6, 6, 21, 21], [3, 3, 6, 9, 9, 12, 18], [3, 3, 6, 9, 9, 15, 15], [3, 3, 6, 9, 9, 30], [3, 3, 6, 9, 12, 12, 15], [3, 3, 6, 9, 12, 27], [3, 3, 6, 9, 15, 24], [3, 3, 6, 9, 18, 21], [3, 3, 6, 12, 12, 24], [3, 3, 6, 12, 15, 21], [3, 3, 6, 12, 18, 18], [3, 3, 6, 15, 15, 18], [3, 3, 6, 18, 30], [3, 3, 6, 21, 27], [3, 3, 6, 24, 24], [3, 3, 9, 9, 12, 24], [3, 3, 9, 9, 15, 21], [3, 3, 9, 9, 18, 18], [3, 3, 9, 12, 12, 21], [3, 3, 9, 12, 15, 18], [3, 3, 9, 15, 30], [3, 3, 9, 18, 27], [3, 3, 9, 21, 24], [3, 3, 12, 12, 15, 15], [3, 3, 12, 12, 30], [3, 3, 12, 15, 27], [3, 3, 12, 18, 24], [3, 3, 12, 21, 21], [3, 3, 15, 15, 24], [3, 3, 15, 18, 21], [3, 3, 24, 30], [3, 3, 27, 27], [3, 6, 6, 9, 9, 12, 15], [3, 6, 6, 9, 9, 27], [3, 6, 6, 9, 12, 24], [3, 6, 6, 9, 15, 21], [3, 6, 6, 9, 18, 18], [3, 6, 6, 12, 12, 21], [3, 6, 6, 12, 15, 18], [3, 6, 6, 15, 30], [3, 6, 6, 18, 27], [3, 6, 6, 21, 24], [3, 6, 9, 9, 12, 21], [3, 6, 9, 9, 15, 18], [3, 6, 9, 12, 12, 18], [3, 6, 9, 12, 15, 15], [3, 6, 9, 12, 30], [3, 6, 9, 15, 27], [3, 6, 9, 18, 24], [3, 6, 9, 21, 21], [3, 6, 12, 12, 27], [3, 6, 12, 15, 24], [3, 6, 12, 18, 21], [3, 6, 15, 15, 21], [3, 6, 15, 18, 18], [3, 6, 21, 30], [3, 6, 24, 27], [3, 9, 9, 12, 12, 15], [3, 9, 9, 12, 27], [3, 9, 9, 15, 24], [3, 9, 9, 18, 21], [3, 9, 12, 12, 24], [3, 9, 12, 15, 21], [3, 9, 12, 18, 18], [3, 9, 15, 15, 18], [3, 9, 18, 30], [3, 9, 21, 27], [3, 9, 24, 24], [3, 12, 12, 15, 18], [3, 12, 15, 30], [3, 12, 18, 27], [3, 12, 21, 24], [3, 15, 15, 27], [3, 15, 18, 24], [3, 15, 21, 21], [3, 18, 18, 21], [3, 27, 30], [6, 6, 9, 9, 12, 18], [6, 6, 9, 9, 15, 15], [6, 6, 9, 9, 30], [6, 6, 9, 12, 12, 15], [6, 6, 9, 12, 27], [6, 6, 9, 15, 24], [6, 6, 9, 18, 21], [6, 6, 12, 12, 24], [6, 6, 12, 15, 21], [6, 6, 12, 18, 18], [6, 6, 15, 15, 18], [6, 6, 18, 30], [6, 6, 21, 27], [6, 6, 24, 24], [6, 9, 9, 12, 24], [6, 9, 9, 15, 21], [6, 9, 9, 18, 18], [6, 9, 12, 12, 21], [6, 9, 12, 15, 18], [6, 9, 15, 30], [6, 9, 18, 27], [6, 9, 21, 24], [6, 12, 12, 15, 15], [6, 12, 12, 30], [6, 12, 15, 27], [6, 12, 18, 24], [6, 12, 21, 21], [6, 15, 15, 24], [6, 15, 18, 21], [6, 24, 30], [6, 27, 27], [9, 9, 12, 12, 18], [9, 9, 12, 15, 15], [9, 9, 12, 30], [9, 9, 15, 27], [9, 9, 18, 24], [9, 9, 21, 21], [9, 12, 12, 27], [9, 12, 15, 24], [9, 12, 18, 21], [9, 15, 15, 21], [9, 15, 18, 18], [9, 21, 30], [9, 24, 27], [12, 12, 15, 21], [12, 12, 18, 18], [12, 15, 15, 18], [12, 18, 30], [12, 21, 27], [12, 24, 24], [15, 15, 30], [15, 18, 27], [15, 21, 24], [18, 18, 24], [18, 21, 21], [30, 30]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 10) == [[5, 5]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 25) == [[1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 15], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 14], [1, 2, 3, 6, 13], [1, 2, 3, 7, 12], [1, 2, 3, 8, 11], [1, 2, 3, 9, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 13], [1, 2, 4, 6, 12], [1, 2, 4, 7, 11], [1, 2, 4, 8, 10], [1, 2, 5, 6, 11], [1, 2, 5, 7, 10], [1, 2, 5, 8, 9], [1, 2, 6, 7, 9], [1, 2, 7, 15], [1, 2, 8, 14], [1, 2, 9, 13], [1, 2, 10, 12], [1, 3, 4, 5, 12], [1, 3, 4, 6, 11], [1, 3, 4, 7, 10], [1, 3, 4, 8, 9], [1, 3, 5, 6, 10], [1, 3, 5, 7, 9], [1, 3, 6, 7, 8], [1, 3, 6, 15], [1, 3, 7, 14], [1, 3, 8, 13], [1, 3, 9, 12], [1, 3, 10, 11], [1, 4, 5, 6, 9], [1, 4, 5, 7, 8], [1, 4, 5, 15], [1, 4, 6, 14], [1, 4, 7, 13], [1, 4, 8, 12], [1, 4, 9, 11], [1, 5, 6, 13], [1, 5, 7, 12], [1, 5, 8, 11], [1, 5, 9, 10], [1, 6, 7, 11], [1, 6, 8, 10], [1, 7, 8, 9], [1, 9, 15], [1, 10, 14], [1, 11, 13], [2, 3, 4, 5, 11], [2, 3, 4, 6, 10], [2, 3, 4, 7, 9], [2, 3, 5, 6, 9], [2, 3, 5, 7, 8], [2, 3, 5, 15], [2, 3, 6, 14], [2, 3, 7, 13], [2, 3, 8, 12], [2, 3, 9, 11], [2, 4, 5, 6, 8], [2, 4, 5, 14], [2, 4, 6, 13], [2, 4, 7, 12], [2, 4, 8, 11], [2, 4, 9, 10], [2, 5, 6, 12], [2, 5, 7, 11], [2, 5, 8, 10], [2, 6, 7, 10], [2, 6, 8, 9], [2, 8, 15], [2, 9, 14], [2, 10, 13], [2, 11, 12], [3, 4, 5, 6, 7], [3, 4, 5, 13], [3, 4, 6, 12], [3, 4, 7, 11], [3, 4, 8, 10], [3, 5, 6, 11], [3, 5, 7, 10], [3, 5, 8, 9], [3, 6, 7, 9], [3, 7, 15], [3, 8, 14], [3, 9, 13], [3, 10, 12], [4, 5, 6, 10], [4, 5, 7, 9], [4, 6, 7, 8], [4, 6, 15], [4, 7, 14], [4, 8, 13], [4, 9, 12], [4, 10, 11], [5, 6, 14], [5, 7, 13], [5, 8, 12], [5, 9, 11], [6, 7, 12], [6, 8, 11], [6, 9, 10], [7, 8, 10], [10, 15], [11, 14], [12, 13]]\n assert candidate(candidates = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],target = 50) == [[2, 4, 6, 8, 10, 20], [2, 4, 6, 8, 12, 18], [2, 4, 6, 8, 14, 16], [2, 4, 6, 8, 30], [2, 4, 6, 10, 12, 16], [2, 4, 6, 10, 28], [2, 4, 6, 12, 26], [2, 4, 6, 14, 24], [2, 4, 6, 16, 22], [2, 4, 6, 18, 20], [2, 4, 8, 10, 12, 14], [2, 4, 8, 10, 26], [2, 4, 8, 12, 24], [2, 4, 8, 14, 22], [2, 4, 8, 16, 20], [2, 4, 10, 12, 22], [2, 4, 10, 14, 20], [2, 4, 10, 16, 18], [2, 4, 12, 14, 18], [2, 4, 14, 30], [2, 4, 16, 28], [2, 4, 18, 26], [2, 4, 20, 24], [2, 6, 8, 10, 24], [2, 6, 8, 12, 22], [2, 6, 8, 14, 20], [2, 6, 8, 16, 18], [2, 6, 10, 12, 20], [2, 6, 10, 14, 18], [2, 6, 12, 14, 16], [2, 6, 12, 30], [2, 6, 14, 28], [2, 6, 16, 26], [2, 6, 18, 24], [2, 6, 20, 22], [2, 8, 10, 12, 18], [2, 8, 10, 14, 16], [2, 8, 10, 30], [2, 8, 12, 28], [2, 8, 14, 26], [2, 8, 16, 24], [2, 8, 18, 22], [2, 10, 12, 26], [2, 10, 14, 24], [2, 10, 16, 22], [2, 10, 18, 20], [2, 12, 14, 22], [2, 12, 16, 20], [2, 14, 16, 18], [2, 18, 30], [2, 20, 28], [2, 22, 26], [4, 6, 8, 10, 22], [4, 6, 8, 12, 20], [4, 6, 8, 14, 18], [4, 6, 10, 12, 18], [4, 6, 10, 14, 16], [4, 6, 10, 30], [4, 6, 12, 28], [4, 6, 14, 26], [4, 6, 16, 24], [4, 6, 18, 22], [4, 8, 10, 12, 16], [4, 8, 10, 28], [4, 8, 12, 26], [4, 8, 14, 24], [4, 8, 16, 22], [4, 8, 18, 20], [4, 10, 12, 24], [4, 10, 14, 22], [4, 10, 16, 20], [4, 12, 14, 20], [4, 12, 16, 18], [4, 16, 30], [4, 18, 28], [4, 20, 26], [4, 22, 24], [6, 8, 10, 12, 14], [6, 8, 10, 26], [6, 8, 12, 24], [6, 8, 14, 22], [6, 8, 16, 20], [6, 10, 12, 22], [6, 10, 14, 20], [6, 10, 16, 18], [6, 12, 14, 18], [6, 14, 30], [6, 16, 28], [6, 18, 26], [6, 20, 24], [8, 10, 12, 20], [8, 10, 14, 18], [8, 12, 14, 16], [8, 12, 30], [8, 14, 28], [8, 16, 26], [8, 18, 24], [8, 20, 22], [10, 12, 28], [10, 14, 26], [10, 16, 24], [10, 18, 22], [12, 14, 24], [12, 16, 22], [12, 18, 20], [14, 16, 20], [20, 30], [22, 28], [24, 26]]\n assert candidate(candidates = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 6) == [[2, 2, 2]]\n assert candidate(candidates = [10, 20, 30, 40, 50],target = 100) == [[10, 20, 30, 40], [10, 40, 50], [20, 30, 50]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],target = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 15], [1, 2, 3, 4, 6, 14], [1, 2, 3, 4, 7, 13], [1, 2, 3, 4, 8, 12], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 20], [1, 2, 3, 5, 6, 13], [1, 2, 3, 5, 7, 12], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 19], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 18], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 17], [1, 2, 3, 8, 16], [1, 2, 3, 9, 15], [1, 2, 3, 10, 14], [1, 2, 3, 11, 13], [1, 2, 3, 24], [1, 2, 4, 5, 6, 12], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 18], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 17], [1, 2, 4, 7, 16], [1, 2, 4, 8, 15], [1, 2, 4, 9, 14], [1, 2, 4, 10, 13], [1, 2, 4, 11, 12], [1, 2, 4, 23], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 16], [1, 2, 5, 7, 15], [1, 2, 5, 8, 14], [1, 2, 5, 9, 13], [1, 2, 5, 10, 12], [1, 2, 5, 22], [1, 2, 6, 7, 14], [1, 2, 6, 8, 13], [1, 2, 6, 9, 12], [1, 2, 6, 10, 11], [1, 2, 6, 21], [1, 2, 7, 8, 12], [1, 2, 7, 9, 11], [1, 2, 7, 20], [1, 2, 8, 9, 10], [1, 2, 8, 19], [1, 2, 9, 18], [1, 2, 10, 17], [1, 2, 11, 16], [1, 2, 12, 15], [1, 2, 13, 14], [1, 2, 27], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 17], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 16], [1, 3, 4, 7, 15], [1, 3, 4, 8, 14], [1, 3, 4, 9, 13], [1, 3, 4, 10, 12], [1, 3, 4, 22], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 15], [1, 3, 5, 7, 14], [1, 3, 5, 8, 13], [1, 3, 5, 9, 12], [1, 3, 5, 10, 11], [1, 3, 5, 21], [1, 3, 6, 7, 13], [1, 3, 6, 8, 12], [1, 3, 6, 9, 11], [1, 3, 6, 20], [1, 3, 7, 8, 11], [1, 3, 7, 9, 10], [1, 3, 7, 19], [1, 3, 8, 18], [1, 3, 9, 17], [1, 3, 10, 16], [1, 3, 11, 15], [1, 3, 12, 14], [1, 3, 26], [1, 4, 5, 6, 14], [1, 4, 5, 7, 13], [1, 4, 5, 8, 12], [1, 4, 5, 9, 11], [1, 4, 5, 20], [1, 4, 6, 7, 12], [1, 4, 6, 8, 11], [1, 4, 6, 9, 10], [1, 4, 6, 19], [1, 4, 7, 8, 10], [1, 4, 7, 18], [1, 4, 8, 17], [1, 4, 9, 16], [1, 4, 10, 15], [1, 4, 11, 14], [1, 4, 12, 13], [1, 4, 25], [1, 5, 6, 7, 11], [1, 5, 6, 8, 10], [1, 5, 6, 18], [1, 5, 7, 8, 9], [1, 5, 7, 17], [1, 5, 8, 16], [1, 5, 9, 15], [1, 5, 10, 14], [1, 5, 11, 13], [1, 5, 24], [1, 6, 7, 16], [1, 6, 8, 15], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 6, 23], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 7, 22], [1, 8, 9, 12], [1, 8, 10, 11], [1, 8, 21], [1, 9, 20], [1, 10, 19], [1, 11, 18], [1, 12, 17], [1, 13, 16], [1, 14, 15], [1, 29], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 16], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 15], [2, 3, 4, 7, 14], [2, 3, 4, 8, 13], [2, 3, 4, 9, 12], [2, 3, 4, 10, 11], [2, 3, 4, 21], [2, 3, 5, 6, 14], [2, 3, 5, 7, 13], [2, 3, 5, 8, 12], [2, 3, 5, 9, 11], [2, 3, 5, 20], [2, 3, 6, 7, 12], [2, 3, 6, 8, 11], [2, 3, 6, 9, 10], [2, 3, 6, 19], [2, 3, 7, 8, 10], [2, 3, 7, 18], [2, 3, 8, 17], [2, 3, 9, 16], [2, 3, 10, 15], [2, 3, 11, 14], [2, 3, 12, 13], [2, 3, 25], [2, 4, 5, 6, 13], [2, 4, 5, 7, 12], [2, 4, 5, 8, 11], [2, 4, 5, 9, 10], [2, 4, 5, 19], [2, 4, 6, 7, 11], [2, 4, 6, 8, 10], [2, 4, 6, 18], [2, 4, 7, 8, 9], [2, 4, 7, 17], [2, 4, 8, 16], [2, 4, 9, 15], [2, 4, 10, 14], [2, 4, 11, 13], [2, 4, 24], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 6, 17], [2, 5, 7, 16], [2, 5, 8, 15], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 5, 23], [2, 6, 7, 15], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 6, 22], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 7, 21], [2, 8, 9, 11], [2, 8, 20], [2, 9, 19], [2, 10, 18], [2, 11, 17], [2, 12, 16], [2, 13, 15], [2, 28], [3, 4, 5, 6, 12], [3, 4, 5, 7, 11], [3, 4, 5, 8, 10], [3, 4, 5, 18], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 6, 17], [3, 4, 7, 16], [3, 4, 8, 15], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 4, 23], [3, 5, 6, 7, 9], [3, 5, 6, 16], [3, 5, 7, 15], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 5, 22], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 6, 21], [3, 7, 8, 12], [3, 7, 9, 11], [3, 7, 20], [3, 8, 9, 10], [3, 8, 19], [3, 9, 18], [3, 10, 17], [3, 11, 16], [3, 12, 15], [3, 13, 14], [3, 27], [4, 5, 6, 7, 8], [4, 5, 6, 15], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 5, 21], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 6, 20], [4, 7, 8, 11], [4, 7, 9, 10], [4, 7, 19], [4, 8, 18], [4, 9, 17], [4, 10, 16], [4, 11, 15], [4, 12, 14], [4, 26], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 6, 19], [5, 7, 8, 10], [5, 7, 18], [5, 8, 17], [5, 9, 16], [5, 10, 15], [5, 11, 14], [5, 12, 13], [5, 25], [6, 7, 8, 9], [6, 7, 17], [6, 8, 16], [6, 9, 15], [6, 10, 14], [6, 11, 13], [6, 24], [7, 8, 15], [7, 9, 14], [7, 10, 13], [7, 11, 12], [7, 23], [8, 9, 13], [8, 10, 12], [8, 22], [9, 10, 11], [9, 21], [10, 20], [11, 19], [12, 18], [13, 17], [14, 16], [30]]\n assert candidate(candidates = [2, 3, 6, 7, 8, 10, 12, 13, 15, 18, 20, 21, 22, 25, 27, 28, 30],target = 30) == [[2, 3, 6, 7, 12], [2, 3, 7, 8, 10], [2, 3, 7, 18], [2, 3, 10, 15], [2, 3, 12, 13], [2, 3, 25], [2, 6, 7, 15], [2, 6, 10, 12], [2, 6, 22], [2, 7, 8, 13], [2, 7, 21], [2, 8, 20], [2, 10, 18], [2, 13, 15], [2, 28], [3, 6, 8, 13], [3, 6, 21], [3, 7, 8, 12], [3, 7, 20], [3, 12, 15], [3, 27], [7, 8, 15], [7, 10, 13], [8, 10, 12], [8, 22], [10, 20], [12, 18], [30]]\n assert candidate(candidates = [20, 16, 12, 15, 25, 30, 10, 2, 5, 3, 1],target = 25) == [[1, 2, 10, 12], [1, 3, 5, 16], [2, 3, 5, 15], [2, 3, 20], [3, 10, 12], [5, 20], [10, 15], [25]]\n assert candidate(candidates = [20, 10, 5, 5, 2, 1, 1],target = 27) == [[1, 1, 5, 20], [2, 5, 20]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 25) == [[5, 5, 5, 5, 5]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9],target = 15) == [[1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 5, 9], [1, 6, 8], [2, 3, 4, 6], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6], [6, 9], [7, 8]]\n assert candidate(candidates = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],target = 27) == [[3, 3, 3, 3, 3, 3, 3, 3, 3]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 28) == [[1, 3, 5, 19], [1, 3, 7, 17], [1, 3, 9, 15], [1, 3, 11, 13], [1, 5, 7, 15], [1, 5, 9, 13], [1, 7, 9, 11], [3, 5, 7, 13], [3, 5, 9, 11], [9, 19], [11, 17], [13, 15]]\n assert candidate(candidates = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],target = 45) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 15) == [[1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 10], [1, 5, 9], [1, 6, 8], [2, 3, 4, 6], [2, 3, 10], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6], [5, 10], [6, 9], [7, 8]]\n assert candidate(candidates = [3, 3, 6, 3, 3, 3],target = 9) == [[3, 3, 3], [3, 6]]\n assert candidate(candidates = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4],target = 20) == [[4, 4, 4, 4, 4]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49],target = 75) == [[1, 3, 5, 7, 9, 11, 39], [1, 3, 5, 7, 9, 13, 37], [1, 3, 5, 7, 9, 15, 35], [1, 3, 5, 7, 9, 17, 33], [1, 3, 5, 7, 9, 19, 31], [1, 3, 5, 7, 9, 21, 29], [1, 3, 5, 7, 9, 23, 27], [1, 3, 5, 7, 11, 13, 35], [1, 3, 5, 7, 11, 15, 33], [1, 3, 5, 7, 11, 17, 31], [1, 3, 5, 7, 11, 19, 29], [1, 3, 5, 7, 11, 21, 27], [1, 3, 5, 7, 11, 23, 25], [1, 3, 5, 7, 13, 15, 31], [1, 3, 5, 7, 13, 17, 29], [1, 3, 5, 7, 13, 19, 27], [1, 3, 5, 7, 13, 21, 25], [1, 3, 5, 7, 15, 17, 27], [1, 3, 5, 7, 15, 19, 25], [1, 3, 5, 7, 15, 21, 23], [1, 3, 5, 7, 17, 19, 23], [1, 3, 5, 9, 11, 13, 33], [1, 3, 5, 9, 11, 15, 31], [1, 3, 5, 9, 11, 17, 29], [1, 3, 5, 9, 11, 19, 27], [1, 3, 5, 9, 11, 21, 25], [1, 3, 5, 9, 13, 15, 29], [1, 3, 5, 9, 13, 17, 27], [1, 3, 5, 9, 13, 19, 25], [1, 3, 5, 9, 13, 21, 23], [1, 3, 5, 9, 15, 17, 25], [1, 3, 5, 9, 15, 19, 23], [1, 3, 5, 9, 17, 19, 21], [1, 3, 5, 11, 13, 15, 27], [1, 3, 5, 11, 13, 17, 25], [1, 3, 5, 11, 13, 19, 23], [1, 3, 5, 11, 15, 17, 23], [1, 3, 5, 11, 15, 19, 21], [1, 3, 5, 13, 15, 17, 21], [1, 3, 5, 17, 49], [1, 3, 5, 19, 47], [1, 3, 5, 21, 45], [1, 3, 5, 23, 43], [1, 3, 5, 25, 41], [1, 3, 5, 27, 39], [1, 3, 5, 29, 37], [1, 3, 5, 31, 35], [1, 3, 7, 9, 11, 13, 31], [1, 3, 7, 9, 11, 15, 29], [1, 3, 7, 9, 11, 17, 27], [1, 3, 7, 9, 11, 19, 25], [1, 3, 7, 9, 11, 21, 23], [1, 3, 7, 9, 13, 15, 27], [1, 3, 7, 9, 13, 17, 25], [1, 3, 7, 9, 13, 19, 23], [1, 3, 7, 9, 15, 17, 23], [1, 3, 7, 9, 15, 19, 21], [1, 3, 7, 11, 13, 15, 25], [1, 3, 7, 11, 13, 17, 23], [1, 3, 7, 11, 13, 19, 21], [1, 3, 7, 11, 15, 17, 21], [1, 3, 7, 13, 15, 17, 19], [1, 3, 7, 15, 49], [1, 3, 7, 17, 47], [1, 3, 7, 19, 45], [1, 3, 7, 21, 43], [1, 3, 7, 23, 41], [1, 3, 7, 25, 39], [1, 3, 7, 27, 37], [1, 3, 7, 29, 35], [1, 3, 7, 31, 33], [1, 3, 9, 11, 13, 15, 23], [1, 3, 9, 11, 13, 17, 21], [1, 3, 9, 11, 15, 17, 19], [1, 3, 9, 13, 49], [1, 3, 9, 15, 47], [1, 3, 9, 17, 45], [1, 3, 9, 19, 43], [1, 3, 9, 21, 41], [1, 3, 9, 23, 39], [1, 3, 9, 25, 37], [1, 3, 9, 27, 35], [1, 3, 9, 29, 33], [1, 3, 11, 13, 47], [1, 3, 11, 15, 45], [1, 3, 11, 17, 43], [1, 3, 11, 19, 41], [1, 3, 11, 21, 39], [1, 3, 11, 23, 37], [1, 3, 11, 25, 35], [1, 3, 11, 27, 33], [1, 3, 11, 29, 31], [1, 3, 13, 15, 43], [1, 3, 13, 17, 41], [1, 3, 13, 19, 39], [1, 3, 13, 21, 37], [1, 3, 13, 23, 35], [1, 3, 13, 25, 33], [1, 3, 13, 27, 31], [1, 3, 15, 17, 39], [1, 3, 15, 19, 37], [1, 3, 15, 21, 35], [1, 3, 15, 23, 33], [1, 3, 15, 25, 31], [1, 3, 15, 27, 29], [1, 3, 17, 19, 35], [1, 3, 17, 21, 33], [1, 3, 17, 23, 31], [1, 3, 17, 25, 29], [1, 3, 19, 21, 31], [1, 3, 19, 23, 29], [1, 3, 19, 25, 27], [1, 3, 21, 23, 27], [1, 5, 7, 9, 11, 13, 29], [1, 5, 7, 9, 11, 15, 27], [1, 5, 7, 9, 11, 17, 25], [1, 5, 7, 9, 11, 19, 23], [1, 5, 7, 9, 13, 15, 25], [1, 5, 7, 9, 13, 17, 23], [1, 5, 7, 9, 13, 19, 21], [1, 5, 7, 9, 15, 17, 21], [1, 5, 7, 11, 13, 15, 23], [1, 5, 7, 11, 13, 17, 21], [1, 5, 7, 11, 15, 17, 19], [1, 5, 7, 13, 49], [1, 5, 7, 15, 47], [1, 5, 7, 17, 45], [1, 5, 7, 19, 43], [1, 5, 7, 21, 41], [1, 5, 7, 23, 39], [1, 5, 7, 25, 37], [1, 5, 7, 27, 35], [1, 5, 7, 29, 33], [1, 5, 9, 11, 13, 15, 21], [1, 5, 9, 11, 13, 17, 19], [1, 5, 9, 11, 49], [1, 5, 9, 13, 47], [1, 5, 9, 15, 45], [1, 5, 9, 17, 43], [1, 5, 9, 19, 41], [1, 5, 9, 21, 39], [1, 5, 9, 23, 37], [1, 5, 9, 25, 35], [1, 5, 9, 27, 33], [1, 5, 9, 29, 31], [1, 5, 11, 13, 45], [1, 5, 11, 15, 43], [1, 5, 11, 17, 41], [1, 5, 11, 19, 39], [1, 5, 11, 21, 37], [1, 5, 11, 23, 35], [1, 5, 11, 25, 33], [1, 5, 11, 27, 31], [1, 5, 13, 15, 41], [1, 5, 13, 17, 39], [1, 5, 13, 19, 37], [1, 5, 13, 21, 35], [1, 5, 13, 23, 33], [1, 5, 13, 25, 31], [1, 5, 13, 27, 29], [1, 5, 15, 17, 37], [1, 5, 15, 19, 35], [1, 5, 15, 21, 33], [1, 5, 15, 23, 31], [1, 5, 15, 25, 29], [1, 5, 17, 19, 33], [1, 5, 17, 21, 31], [1, 5, 17, 23, 29], [1, 5, 17, 25, 27], [1, 5, 19, 21, 29], [1, 5, 19, 23, 27], [1, 5, 21, 23, 25], [1, 7, 9, 11, 13, 15, 19], [1, 7, 9, 11, 47], [1, 7, 9, 13, 45], [1, 7, 9, 15, 43], [1, 7, 9, 17, 41], [1, 7, 9, 19, 39], [1, 7, 9, 21, 37], [1, 7, 9, 23, 35], [1, 7, 9, 25, 33], [1, 7, 9, 27, 31], [1, 7, 11, 13, 43], [1, 7, 11, 15, 41], [1, 7, 11, 17, 39], [1, 7, 11, 19, 37], [1, 7, 11, 21, 35], [1, 7, 11, 23, 33], [1, 7, 11, 25, 31], [1, 7, 11, 27, 29], [1, 7, 13, 15, 39], [1, 7, 13, 17, 37], [1, 7, 13, 19, 35], [1, 7, 13, 21, 33], [1, 7, 13, 23, 31], [1, 7, 13, 25, 29], [1, 7, 15, 17, 35], [1, 7, 15, 19, 33], [1, 7, 15, 21, 31], [1, 7, 15, 23, 29], [1, 7, 15, 25, 27], [1, 7, 17, 19, 31], [1, 7, 17, 21, 29], [1, 7, 17, 23, 27], [1, 7, 19, 21, 27], [1, 7, 19, 23, 25], [1, 9, 11, 13, 41], [1, 9, 11, 15, 39], [1, 9, 11, 17, 37], [1, 9, 11, 19, 35], [1, 9, 11, 21, 33], [1, 9, 11, 23, 31], [1, 9, 11, 25, 29], [1, 9, 13, 15, 37], [1, 9, 13, 17, 35], [1, 9, 13, 19, 33], [1, 9, 13, 21, 31], [1, 9, 13, 23, 29], [1, 9, 13, 25, 27], [1, 9, 15, 17, 33], [1, 9, 15, 19, 31], [1, 9, 15, 21, 29], [1, 9, 15, 23, 27], [1, 9, 17, 19, 29], [1, 9, 17, 21, 27], [1, 9, 17, 23, 25], [1, 9, 19, 21, 25], [1, 11, 13, 15, 35], [1, 11, 13, 17, 33], [1, 11, 13, 19, 31], [1, 11, 13, 21, 29], [1, 11, 13, 23, 27], [1, 11, 15, 17, 31], [1, 11, 15, 19, 29], [1, 11, 15, 21, 27], [1, 11, 15, 23, 25], [1, 11, 17, 19, 27], [1, 11, 17, 21, 25], [1, 11, 19, 21, 23], [1, 13, 15, 17, 29], [1, 13, 15, 19, 27], [1, 13, 15, 21, 25], [1, 13, 17, 19, 25], [1, 13, 17, 21, 23], [1, 15, 17, 19, 23], [1, 25, 49], [1, 27, 47], [1, 29, 45], [1, 31, 43], [1, 33, 41], [1, 35, 39], [3, 5, 7, 9, 11, 13, 27], [3, 5, 7, 9, 11, 15, 25], [3, 5, 7, 9, 11, 17, 23], [3, 5, 7, 9, 11, 19, 21], [3, 5, 7, 9, 13, 15, 23], [3, 5, 7, 9, 13, 17, 21], [3, 5, 7, 9, 15, 17, 19], [3, 5, 7, 11, 13, 15, 21], [3, 5, 7, 11, 13, 17, 19], [3, 5, 7, 11, 49], [3, 5, 7, 13, 47], [3, 5, 7, 15, 45], [3, 5, 7, 17, 43], [3, 5, 7, 19, 41], [3, 5, 7, 21, 39], [3, 5, 7, 23, 37], [3, 5, 7, 25, 35], [3, 5, 7, 27, 33], [3, 5, 7, 29, 31], [3, 5, 9, 11, 13, 15, 19], [3, 5, 9, 11, 47], [3, 5, 9, 13, 45], [3, 5, 9, 15, 43], [3, 5, 9, 17, 41], [3, 5, 9, 19, 39], [3, 5, 9, 21, 37], [3, 5, 9, 23, 35], [3, 5, 9, 25, 33], [3, 5, 9, 27, 31], [3, 5, 11, 13, 43], [3, 5, 11, 15, 41], [3, 5, 11, 17, 39], [3, 5, 11, 19, 37], [3, 5, 11, 21, 35], [3, 5, 11, 23, 33], [3, 5, 11, 25, 31], [3, 5, 11, 27, 29], [3, 5, 13, 15, 39], [3, 5, 13, 17, 37], [3, 5, 13, 19, 35], [3, 5, 13, 21, 33], [3, 5, 13, 23, 31], [3, 5, 13, 25, 29], [3, 5, 15, 17, 35], [3, 5, 15, 19, 33], [3, 5, 15, 21, 31], [3, 5, 15, 23, 29], [3, 5, 15, 25, 27], [3, 5, 17, 19, 31], [3, 5, 17, 21, 29], [3, 5, 17, 23, 27], [3, 5, 19, 21, 27], [3, 5, 19, 23, 25], [3, 7, 9, 11, 13, 15, 17], [3, 7, 9, 11, 45], [3, 7, 9, 13, 43], [3, 7, 9, 15, 41], [3, 7, 9, 17, 39], [3, 7, 9, 19, 37], [3, 7, 9, 21, 35], [3, 7, 9, 23, 33], [3, 7, 9, 25, 31], [3, 7, 9, 27, 29], [3, 7, 11, 13, 41], [3, 7, 11, 15, 39], [3, 7, 11, 17, 37], [3, 7, 11, 19, 35], [3, 7, 11, 21, 33], [3, 7, 11, 23, 31], [3, 7, 11, 25, 29], [3, 7, 13, 15, 37], [3, 7, 13, 17, 35], [3, 7, 13, 19, 33], [3, 7, 13, 21, 31], [3, 7, 13, 23, 29], [3, 7, 13, 25, 27], [3, 7, 15, 17, 33], [3, 7, 15, 19, 31], [3, 7, 15, 21, 29], [3, 7, 15, 23, 27], [3, 7, 17, 19, 29], [3, 7, 17, 21, 27], [3, 7, 17, 23, 25], [3, 7, 19, 21, 25], [3, 9, 11, 13, 39], [3, 9, 11, 15, 37], [3, 9, 11, 17, 35], [3, 9, 11, 19, 33], [3, 9, 11, 21, 31], [3, 9, 11, 23, 29], [3, 9, 11, 25, 27], [3, 9, 13, 15, 35], [3, 9, 13, 17, 33], [3, 9, 13, 19, 31], [3, 9, 13, 21, 29], [3, 9, 13, 23, 27], [3, 9, 15, 17, 31], [3, 9, 15, 19, 29], [3, 9, 15, 21, 27], [3, 9, 15, 23, 25], [3, 9, 17, 19, 27], [3, 9, 17, 21, 25], [3, 9, 19, 21, 23], [3, 11, 13, 15, 33], [3, 11, 13, 17, 31], [3, 11, 13, 19, 29], [3, 11, 13, 21, 27], [3, 11, 13, 23, 25], [3, 11, 15, 17, 29], [3, 11, 15, 19, 27], [3, 11, 15, 21, 25], [3, 11, 17, 19, 25], [3, 11, 17, 21, 23], [3, 13, 15, 17, 27], [3, 13, 15, 19, 25], [3, 13, 15, 21, 23], [3, 13, 17, 19, 23], [3, 15, 17, 19, 21], [3, 23, 49], [3, 25, 47], [3, 27, 45], [3, 29, 43], [3, 31, 41], [3, 33, 39], [3, 35, 37], [5, 7, 9, 11, 43], [5, 7, 9, 13, 41], [5, 7, 9, 15, 39], [5, 7, 9, 17, 37], [5, 7, 9, 19, 35], [5, 7, 9, 21, 33], [5, 7, 9, 23, 31], [5, 7, 9, 25, 29], [5, 7, 11, 13, 39], [5, 7, 11, 15, 37], [5, 7, 11, 17, 35], [5, 7, 11, 19, 33], [5, 7, 11, 21, 31], [5, 7, 11, 23, 29], [5, 7, 11, 25, 27], [5, 7, 13, 15, 35], [5, 7, 13, 17, 33], [5, 7, 13, 19, 31], [5, 7, 13, 21, 29], [5, 7, 13, 23, 27], [5, 7, 15, 17, 31], [5, 7, 15, 19, 29], [5, 7, 15, 21, 27], [5, 7, 15, 23, 25], [5, 7, 17, 19, 27], [5, 7, 17, 21, 25], [5, 7, 19, 21, 23], [5, 9, 11, 13, 37], [5, 9, 11, 15, 35], [5, 9, 11, 17, 33], [5, 9, 11, 19, 31], [5, 9, 11, 21, 29], [5, 9, 11, 23, 27], [5, 9, 13, 15, 33], [5, 9, 13, 17, 31], [5, 9, 13, 19, 29], [5, 9, 13, 21, 27], [5, 9, 13, 23, 25], [5, 9, 15, 17, 29], [5, 9, 15, 19, 27], [5, 9, 15, 21, 25], [5, 9, 17, 19, 25], [5, 9, 17, 21, 23], [5, 11, 13, 15, 31], [5, 11, 13, 17, 29], [5, 11, 13, 19, 27], [5, 11, 13, 21, 25], [5, 11, 15, 17, 27], [5, 11, 15, 19, 25], [5, 11, 15, 21, 23], [5, 11, 17, 19, 23], [5, 13, 15, 17, 25], [5, 13, 15, 19, 23], [5, 13, 17, 19, 21], [5, 21, 49], [5, 23, 47], [5, 25, 45], [5, 27, 43], [5, 29, 41], [5, 31, 39], [5, 33, 37], [7, 9, 11, 13, 35], [7, 9, 11, 15, 33], [7, 9, 11, 17, 31], [7, 9, 11, 19, 29], [7, 9, 11, 21, 27], [7, 9, 11, 23, 25], [7, 9, 13, 15, 31], [7, 9, 13, 17, 29], [7, 9, 13, 19, 27], [7, 9, 13, 21, 25], [7, 9, 15, 17, 27], [7, 9, 15, 19, 25], [7, 9, 15, 21, 23], [7, 9, 17, 19, 23], [7, 11, 13, 15, 29], [7, 11, 13, 17, 27], [7, 11, 13, 19, 25], [7, 11, 13, 21, 23], [7, 11, 15, 17, 25], [7, 11, 15, 19, 23], [7, 11, 17, 19, 21], [7, 13, 15, 17, 23], [7, 13, 15, 19, 21], [7, 19, 49], [7, 21, 47], [7, 23, 45], [7, 25, 43], [7, 27, 41], [7, 29, 39], [7, 31, 37], [7, 33, 35], [9, 11, 13, 15, 27], [9, 11, 13, 17, 25], [9, 11, 13, 19, 23], [9, 11, 15, 17, 23], [9, 11, 15, 19, 21], [9, 13, 15, 17, 21], [9, 17, 49], [9, 19, 47], [9, 21, 45], [9, 23, 43], [9, 25, 41], [9, 27, 39], [9, 29, 37], [9, 31, 35], [11, 13, 15, 17, 19], [11, 15, 49], [11, 17, 47], [11, 19, 45], [11, 21, 43], [11, 23, 41], [11, 25, 39], [11, 27, 37], [11, 29, 35], [11, 31, 33], [13, 15, 47], [13, 17, 45], [13, 19, 43], [13, 21, 41], [13, 23, 39], [13, 25, 37], [13, 27, 35], [13, 29, 33], [15, 17, 43], [15, 19, 41], [15, 21, 39], [15, 23, 37], [15, 25, 35], [15, 27, 33], [15, 29, 31], [17, 19, 39], [17, 21, 37], [17, 23, 35], [17, 25, 33], [17, 27, 31], [19, 21, 35], [19, 23, 33], [19, 25, 31], [19, 27, 29], [21, 23, 31], [21, 25, 29], [23, 25, 27]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 15) == [[5, 5, 5]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 15) == [[5, 5, 5]]\n assert candidate(candidates = [4, 4, 4, 4, 2, 2, 3, 5],target = 10) == [[2, 3, 5], [2, 4, 4]]\n assert candidate(candidates = [9, 7, 3, 8, 1, 4, 2, 1, 5, 8, 7, 9, 4, 1, 2, 5],target = 15) == [[1, 1, 1, 2, 2, 3, 5], [1, 1, 1, 2, 2, 4, 4], [1, 1, 1, 2, 2, 8], [1, 1, 1, 2, 3, 7], [1, 1, 1, 2, 5, 5], [1, 1, 1, 3, 4, 5], [1, 1, 1, 3, 9], [1, 1, 1, 4, 8], [1, 1, 1, 5, 7], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 9], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 8], [1, 1, 2, 4, 7], [1, 1, 3, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 9], [1, 1, 5, 8], [1, 2, 2, 3, 7], [1, 2, 2, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 4, 5, 5], [1, 5, 9], [1, 7, 7], [2, 2, 3, 4, 4], [2, 2, 3, 8], [2, 2, 4, 7], [2, 3, 5, 5], [2, 4, 4, 5], [2, 4, 9], [2, 5, 8], [3, 4, 8], [3, 5, 7], [4, 4, 7], [7, 8]]\n assert candidate(candidates = [2, 3, 6, 7, 8, 10, 11, 13, 15],target = 21) == [[2, 3, 6, 10], [2, 6, 13], [2, 8, 11], [3, 7, 11], [3, 8, 10], [6, 7, 8], [6, 15], [8, 13], [10, 11]]\n assert candidate(candidates = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],target = 56) == [[8, 8, 8, 8, 8, 8, 8]]\n assert candidate(candidates = [1, 3, 2, 5, 4, 7, 6, 9, 8, 10],target = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 6, 8, 10], [1, 2, 3, 7, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 5, 6, 7, 9], [1, 2, 8, 9, 10], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 6, 7, 9], [1, 3, 5, 6, 7, 8], [1, 3, 7, 9, 10], [1, 4, 6, 9, 10], [1, 4, 7, 8, 10], [1, 5, 6, 8, 10], [1, 5, 7, 8, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 6, 7, 8], [2, 3, 6, 9, 10], [2, 3, 7, 8, 10], [2, 4, 5, 9, 10], [2, 4, 6, 8, 10], [2, 4, 7, 8, 9], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [3, 4, 5, 8, 10], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 5, 6, 7, 9], [3, 8, 9, 10], [4, 5, 6, 7, 8], [4, 7, 9, 10], [5, 6, 9, 10], [5, 7, 8, 10], [6, 7, 8, 9]]\n assert candidate(candidates = [10, 15, 20, 25, 30, 35, 40],target = 60) == [[10, 15, 35], [10, 20, 30], [15, 20, 25], [20, 40], [25, 35]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 15], [1, 2, 3, 4, 6, 14], [1, 2, 3, 4, 7, 13], [1, 2, 3, 4, 8, 12], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 20], [1, 2, 3, 5, 6, 13], [1, 2, 3, 5, 7, 12], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 19], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 18], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 17], [1, 2, 3, 8, 16], [1, 2, 3, 9, 15], [1, 2, 3, 10, 14], [1, 2, 3, 11, 13], [1, 2, 4, 5, 6, 12], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 18], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 17], [1, 2, 4, 7, 16], [1, 2, 4, 8, 15], [1, 2, 4, 9, 14], [1, 2, 4, 10, 13], [1, 2, 4, 11, 12], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 16], [1, 2, 5, 7, 15], [1, 2, 5, 8, 14], [1, 2, 5, 9, 13], [1, 2, 5, 10, 12], [1, 2, 6, 7, 14], [1, 2, 6, 8, 13], [1, 2, 6, 9, 12], [1, 2, 6, 10, 11], [1, 2, 7, 8, 12], [1, 2, 7, 9, 11], [1, 2, 7, 20], [1, 2, 8, 9, 10], [1, 2, 8, 19], [1, 2, 9, 18], [1, 2, 10, 17], [1, 2, 11, 16], [1, 2, 12, 15], [1, 2, 13, 14], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 17], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 16], [1, 3, 4, 7, 15], [1, 3, 4, 8, 14], [1, 3, 4, 9, 13], [1, 3, 4, 10, 12], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 15], [1, 3, 5, 7, 14], [1, 3, 5, 8, 13], [1, 3, 5, 9, 12], [1, 3, 5, 10, 11], [1, 3, 6, 7, 13], [1, 3, 6, 8, 12], [1, 3, 6, 9, 11], [1, 3, 6, 20], [1, 3, 7, 8, 11], [1, 3, 7, 9, 10], [1, 3, 7, 19], [1, 3, 8, 18], [1, 3, 9, 17], [1, 3, 10, 16], [1, 3, 11, 15], [1, 3, 12, 14], [1, 4, 5, 6, 14], [1, 4, 5, 7, 13], [1, 4, 5, 8, 12], [1, 4, 5, 9, 11], [1, 4, 5, 20], [1, 4, 6, 7, 12], [1, 4, 6, 8, 11], [1, 4, 6, 9, 10], [1, 4, 6, 19], [1, 4, 7, 8, 10], [1, 4, 7, 18], [1, 4, 8, 17], [1, 4, 9, 16], [1, 4, 10, 15], [1, 4, 11, 14], [1, 4, 12, 13], [1, 5, 6, 7, 11], [1, 5, 6, 8, 10], [1, 5, 6, 18], [1, 5, 7, 8, 9], [1, 5, 7, 17], [1, 5, 8, 16], [1, 5, 9, 15], [1, 5, 10, 14], [1, 5, 11, 13], [1, 6, 7, 16], [1, 6, 8, 15], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 8, 9, 12], [1, 8, 10, 11], [1, 9, 20], [1, 10, 19], [1, 11, 18], [1, 12, 17], [1, 13, 16], [1, 14, 15], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 16], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 15], [2, 3, 4, 7, 14], [2, 3, 4, 8, 13], [2, 3, 4, 9, 12], [2, 3, 4, 10, 11], [2, 3, 5, 6, 14], [2, 3, 5, 7, 13], [2, 3, 5, 8, 12], [2, 3, 5, 9, 11], [2, 3, 5, 20], [2, 3, 6, 7, 12], [2, 3, 6, 8, 11], [2, 3, 6, 9, 10], [2, 3, 6, 19], [2, 3, 7, 8, 10], [2, 3, 7, 18], [2, 3, 8, 17], [2, 3, 9, 16], [2, 3, 10, 15], [2, 3, 11, 14], [2, 3, 12, 13], [2, 4, 5, 6, 13], [2, 4, 5, 7, 12], [2, 4, 5, 8, 11], [2, 4, 5, 9, 10], [2, 4, 5, 19], [2, 4, 6, 7, 11], [2, 4, 6, 8, 10], [2, 4, 6, 18], [2, 4, 7, 8, 9], [2, 4, 7, 17], [2, 4, 8, 16], [2, 4, 9, 15], [2, 4, 10, 14], [2, 4, 11, 13], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 6, 17], [2, 5, 7, 16], [2, 5, 8, 15], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 6, 7, 15], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 8, 9, 11], [2, 8, 20], [2, 9, 19], [2, 10, 18], [2, 11, 17], [2, 12, 16], [2, 13, 15], [3, 4, 5, 6, 12], [3, 4, 5, 7, 11], [3, 4, 5, 8, 10], [3, 4, 5, 18], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 6, 17], [3, 4, 7, 16], [3, 4, 8, 15], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 5, 6, 7, 9], [3, 5, 6, 16], [3, 5, 7, 15], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 7, 8, 12], [3, 7, 9, 11], [3, 7, 20], [3, 8, 9, 10], [3, 8, 19], [3, 9, 18], [3, 10, 17], [3, 11, 16], [3, 12, 15], [3, 13, 14], [4, 5, 6, 7, 8], [4, 5, 6, 15], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 6, 20], [4, 7, 8, 11], [4, 7, 9, 10], [4, 7, 19], [4, 8, 18], [4, 9, 17], [4, 10, 16], [4, 11, 15], [4, 12, 14], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 6, 19], [5, 7, 8, 10], [5, 7, 18], [5, 8, 17], [5, 9, 16], [5, 10, 15], [5, 11, 14], [5, 12, 13], [6, 7, 8, 9], [6, 7, 17], [6, 8, 16], [6, 9, 15], [6, 10, 14], [6, 11, 13], [7, 8, 15], [7, 9, 14], [7, 10, 13], [7, 11, 12], [8, 9, 13], [8, 10, 12], [9, 10, 11], [10, 20], [11, 19], [12, 18], [13, 17], [14, 16]]\n assert candidate(candidates = [2, 3, 6, 7, 1, 5, 8],target = 15) == [[1, 2, 5, 7], [1, 3, 5, 6], [1, 6, 8], [2, 5, 8], [2, 6, 7], [3, 5, 7], [7, 8]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 15) == [[1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 10], [1, 5, 9], [1, 6, 8], [2, 3, 4, 6], [2, 3, 10], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6], [5, 10], [6, 9], [7, 8]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 3, 4, 8, 2, 5, 10, 10],target = 12) == [[1, 1, 2, 2, 6], [1, 1, 2, 3, 5], [1, 1, 2, 8], [1, 1, 3, 7], [1, 1, 4, 6], [1, 1, 5, 5], [1, 1, 10], [1, 2, 2, 3, 4], [1, 2, 2, 7], [1, 2, 3, 6], [1, 2, 4, 5], [1, 3, 8], [1, 4, 7], [1, 5, 6], [2, 2, 3, 5], [2, 2, 8], [2, 3, 7], [2, 4, 6], [2, 5, 5], [2, 10], [3, 4, 5], [4, 8], [5, 7]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 17) == [[1, 2, 3, 4, 7], [1, 2, 3, 5, 6], [1, 2, 4, 10], [1, 2, 5, 9], [1, 2, 6, 8], [1, 3, 4, 9], [1, 3, 5, 8], [1, 3, 6, 7], [1, 4, 5, 7], [1, 6, 10], [1, 7, 9], [2, 3, 4, 8], [2, 3, 5, 7], [2, 4, 5, 6], [2, 5, 10], [2, 6, 9], [2, 7, 8], [3, 4, 10], [3, 5, 9], [3, 6, 8], [4, 5, 8], [4, 6, 7], [7, 10], [8, 9]]\n assert candidate(candidates = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15],target = 30) == [[1, 2, 2, 3, 3, 4, 4, 5, 6], [1, 2, 2, 3, 3, 4, 4, 11], [1, 2, 2, 3, 3, 4, 5, 10], [1, 2, 2, 3, 3, 4, 6, 9], [1, 2, 2, 3, 3, 4, 7, 8], [1, 2, 2, 3, 3, 4, 15], [1, 2, 2, 3, 3, 5, 5, 9], [1, 2, 2, 3, 3, 5, 6, 8], [1, 2, 2, 3, 3, 5, 7, 7], [1, 2, 2, 3, 3, 5, 14], [1, 2, 2, 3, 3, 6, 6, 7], [1, 2, 2, 3, 3, 6, 13], [1, 2, 2, 3, 3, 7, 12], [1, 2, 2, 3, 3, 8, 11], [1, 2, 2, 3, 3, 9, 10], [1, 2, 2, 3, 4, 4, 5, 9], [1, 2, 2, 3, 4, 4, 6, 8], [1, 2, 2, 3, 4, 4, 7, 7], [1, 2, 2, 3, 4, 4, 14], [1, 2, 2, 3, 4, 5, 5, 8], [1, 2, 2, 3, 4, 5, 6, 7], [1, 2, 2, 3, 4, 5, 13], [1, 2, 2, 3, 4, 6, 12], [1, 2, 2, 3, 4, 7, 11], [1, 2, 2, 3, 4, 8, 10], [1, 2, 2, 3, 4, 9, 9], [1, 2, 2, 3, 5, 5, 6, 6], [1, 2, 2, 3, 5, 5, 12], [1, 2, 2, 3, 5, 6, 11], [1, 2, 2, 3, 5, 7, 10], [1, 2, 2, 3, 5, 8, 9], [1, 2, 2, 3, 6, 6, 10], [1, 2, 2, 3, 6, 7, 9], [1, 2, 2, 3, 6, 8, 8], [1, 2, 2, 3, 7, 7, 8], [1, 2, 2, 3, 7, 15], [1, 2, 2, 3, 8, 14], [1, 2, 2, 3, 9, 13], [1, 2, 2, 3, 10, 12], [1, 2, 2, 3, 11, 11], [1, 2, 2, 4, 4, 5, 5, 7], [1, 2, 2, 4, 4, 5, 6, 6], [1, 2, 2, 4, 4, 5, 12], [1, 2, 2, 4, 4, 6, 11], [1, 2, 2, 4, 4, 7, 10], [1, 2, 2, 4, 4, 8, 9], [1, 2, 2, 4, 5, 5, 11], [1, 2, 2, 4, 5, 6, 10], [1, 2, 2, 4, 5, 7, 9], [1, 2, 2, 4, 5, 8, 8], [1, 2, 2, 4, 6, 6, 9], [1, 2, 2, 4, 6, 7, 8], [1, 2, 2, 4, 6, 15], [1, 2, 2, 4, 7, 14], [1, 2, 2, 4, 8, 13], [1, 2, 2, 4, 9, 12], [1, 2, 2, 4, 10, 11], [1, 2, 2, 5, 5, 6, 9], [1, 2, 2, 5, 5, 7, 8], [1, 2, 2, 5, 5, 15], [1, 2, 2, 5, 6, 6, 8], [1, 2, 2, 5, 6, 7, 7], [1, 2, 2, 5, 6, 14], [1, 2, 2, 5, 7, 13], [1, 2, 2, 5, 8, 12], [1, 2, 2, 5, 9, 11], [1, 2, 2, 5, 10, 10], [1, 2, 2, 6, 6, 13], [1, 2, 2, 6, 7, 12], [1, 2, 2, 6, 8, 11], [1, 2, 2, 6, 9, 10], [1, 2, 2, 7, 7, 11], [1, 2, 2, 7, 8, 10], [1, 2, 2, 7, 9, 9], [1, 2, 2, 8, 8, 9], [1, 2, 2, 10, 15], [1, 2, 2, 11, 14], [1, 2, 2, 12, 13], [1, 2, 3, 3, 4, 4, 5, 8], [1, 2, 3, 3, 4, 4, 6, 7], [1, 2, 3, 3, 4, 4, 13], [1, 2, 3, 3, 4, 5, 5, 7], [1, 2, 3, 3, 4, 5, 6, 6], [1, 2, 3, 3, 4, 5, 12], [1, 2, 3, 3, 4, 6, 11], [1, 2, 3, 3, 4, 7, 10], [1, 2, 3, 3, 4, 8, 9], [1, 2, 3, 3, 5, 5, 11], [1, 2, 3, 3, 5, 6, 10], [1, 2, 3, 3, 5, 7, 9], [1, 2, 3, 3, 5, 8, 8], [1, 2, 3, 3, 6, 6, 9], [1, 2, 3, 3, 6, 7, 8], [1, 2, 3, 3, 6, 15], [1, 2, 3, 3, 7, 14], [1, 2, 3, 3, 8, 13], [1, 2, 3, 3, 9, 12], [1, 2, 3, 3, 10, 11], [1, 2, 3, 4, 4, 5, 5, 6], [1, 2, 3, 4, 4, 5, 11], [1, 2, 3, 4, 4, 6, 10], [1, 2, 3, 4, 4, 7, 9], [1, 2, 3, 4, 4, 8, 8], [1, 2, 3, 4, 5, 5, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 15], [1, 2, 3, 4, 6, 6, 8], [1, 2, 3, 4, 6, 7, 7], [1, 2, 3, 4, 6, 14], [1, 2, 3, 4, 7, 13], [1, 2, 3, 4, 8, 12], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 10, 10], [1, 2, 3, 5, 5, 6, 8], [1, 2, 3, 5, 5, 7, 7], [1, 2, 3, 5, 5, 14], [1, 2, 3, 5, 6, 6, 7], [1, 2, 3, 5, 6, 13], [1, 2, 3, 5, 7, 12], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 6, 6, 12], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 9, 9], [1, 2, 3, 7, 7, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 9, 15], [1, 2, 3, 10, 14], [1, 2, 3, 11, 13], [1, 2, 3, 12, 12], [1, 2, 4, 4, 5, 5, 9], [1, 2, 4, 4, 5, 6, 8], [1, 2, 4, 4, 5, 7, 7], [1, 2, 4, 4, 5, 14], [1, 2, 4, 4, 6, 6, 7], [1, 2, 4, 4, 6, 13], [1, 2, 4, 4, 7, 12], [1, 2, 4, 4, 8, 11], [1, 2, 4, 4, 9, 10], [1, 2, 4, 5, 5, 6, 7], [1, 2, 4, 5, 5, 13], [1, 2, 4, 5, 6, 12], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 9, 9], [1, 2, 4, 6, 6, 11], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 7, 7, 9], [1, 2, 4, 7, 8, 8], [1, 2, 4, 8, 15], [1, 2, 4, 9, 14], [1, 2, 4, 10, 13], [1, 2, 4, 11, 12], [1, 2, 5, 5, 6, 11], [1, 2, 5, 5, 7, 10], [1, 2, 5, 5, 8, 9], [1, 2, 5, 6, 6, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 8, 8], [1, 2, 5, 7, 7, 8], [1, 2, 5, 7, 15], [1, 2, 5, 8, 14], [1, 2, 5, 9, 13], [1, 2, 5, 10, 12], [1, 2, 5, 11, 11], [1, 2, 6, 6, 7, 8], [1, 2, 6, 6, 15], [1, 2, 6, 7, 14], [1, 2, 6, 8, 13], [1, 2, 6, 9, 12], [1, 2, 6, 10, 11], [1, 2, 7, 7, 13], [1, 2, 7, 8, 12], [1, 2, 7, 9, 11], [1, 2, 7, 10, 10], [1, 2, 8, 8, 11], [1, 2, 8, 9, 10], [1, 2, 12, 15], [1, 2, 13, 14], [1, 3, 3, 4, 4, 5, 10], [1, 3, 3, 4, 4, 6, 9], [1, 3, 3, 4, 4, 7, 8], [1, 3, 3, 4, 4, 15], [1, 3, 3, 4, 5, 5, 9], [1, 3, 3, 4, 5, 6, 8], [1, 3, 3, 4, 5, 7, 7], [1, 3, 3, 4, 5, 14], [1, 3, 3, 4, 6, 6, 7], [1, 3, 3, 4, 6, 13], [1, 3, 3, 4, 7, 12], [1, 3, 3, 4, 8, 11], [1, 3, 3, 4, 9, 10], [1, 3, 3, 5, 5, 6, 7], [1, 3, 3, 5, 5, 13], [1, 3, 3, 5, 6, 12], [1, 3, 3, 5, 7, 11], [1, 3, 3, 5, 8, 10], [1, 3, 3, 5, 9, 9], [1, 3, 3, 6, 6, 11], [1, 3, 3, 6, 7, 10], [1, 3, 3, 6, 8, 9], [1, 3, 3, 7, 7, 9], [1, 3, 3, 7, 8, 8], [1, 3, 3, 8, 15], [1, 3, 3, 9, 14], [1, 3, 3, 10, 13], [1, 3, 3, 11, 12], [1, 3, 4, 4, 5, 5, 8], [1, 3, 4, 4, 5, 6, 7], [1, 3, 4, 4, 5, 13], [1, 3, 4, 4, 6, 12], [1, 3, 4, 4, 7, 11], [1, 3, 4, 4, 8, 10], [1, 3, 4, 4, 9, 9], [1, 3, 4, 5, 5, 6, 6], [1, 3, 4, 5, 5, 12], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 6, 6, 10], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 8, 8], [1, 3, 4, 7, 7, 8], [1, 3, 4, 7, 15], [1, 3, 4, 8, 14], [1, 3, 4, 9, 13], [1, 3, 4, 10, 12], [1, 3, 4, 11, 11], [1, 3, 5, 5, 6, 10], [1, 3, 5, 5, 7, 9], [1, 3, 5, 5, 8, 8], [1, 3, 5, 6, 6, 9], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 15], [1, 3, 5, 7, 14], [1, 3, 5, 8, 13], [1, 3, 5, 9, 12], [1, 3, 5, 10, 11], [1, 3, 6, 6, 7, 7], [1, 3, 6, 6, 14], [1, 3, 6, 7, 13], [1, 3, 6, 8, 12], [1, 3, 6, 9, 11], [1, 3, 6, 10, 10], [1, 3, 7, 7, 12], [1, 3, 7, 8, 11], [1, 3, 7, 9, 10], [1, 3, 8, 8, 10], [1, 3, 8, 9, 9], [1, 3, 11, 15], [1, 3, 12, 14], [1, 3, 13, 13], [1, 4, 4, 5, 5, 11], [1, 4, 4, 5, 6, 10], [1, 4, 4, 5, 7, 9], [1, 4, 4, 5, 8, 8], [1, 4, 4, 6, 6, 9], [1, 4, 4, 6, 7, 8], [1, 4, 4, 6, 15], [1, 4, 4, 7, 14], [1, 4, 4, 8, 13], [1, 4, 4, 9, 12], [1, 4, 4, 10, 11], [1, 4, 5, 5, 6, 9], [1, 4, 5, 5, 7, 8], [1, 4, 5, 5, 15], [1, 4, 5, 6, 6, 8], [1, 4, 5, 6, 7, 7], [1, 4, 5, 6, 14], [1, 4, 5, 7, 13], [1, 4, 5, 8, 12], [1, 4, 5, 9, 11], [1, 4, 5, 10, 10], [1, 4, 6, 6, 13], [1, 4, 6, 7, 12], [1, 4, 6, 8, 11], [1, 4, 6, 9, 10], [1, 4, 7, 7, 11], [1, 4, 7, 8, 10], [1, 4, 7, 9, 9], [1, 4, 8, 8, 9], [1, 4, 10, 15], [1, 4, 11, 14], [1, 4, 12, 13], [1, 5, 5, 6, 6, 7], [1, 5, 5, 6, 13], [1, 5, 5, 7, 12], [1, 5, 5, 8, 11], [1, 5, 5, 9, 10], [1, 5, 6, 6, 12], [1, 5, 6, 7, 11], [1, 5, 6, 8, 10], [1, 5, 6, 9, 9], [1, 5, 7, 7, 10], [1, 5, 7, 8, 9], [1, 5, 9, 15], [1, 5, 10, 14], [1, 5, 11, 13], [1, 5, 12, 12], [1, 6, 6, 7, 10], [1, 6, 6, 8, 9], [1, 6, 7, 7, 9], [1, 6, 7, 8, 8], [1, 6, 8, 15], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 7, 7, 15], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 7, 11, 11], [1, 8, 8, 13], [1, 8, 9, 12], [1, 8, 10, 11], [1, 9, 9, 11], [1, 9, 10, 10], [1, 14, 15], [2, 2, 3, 3, 4, 4, 5, 7], [2, 2, 3, 3, 4, 4, 6, 6], [2, 2, 3, 3, 4, 4, 12], [2, 2, 3, 3, 4, 5, 5, 6], [2, 2, 3, 3, 4, 5, 11], [2, 2, 3, 3, 4, 6, 10], [2, 2, 3, 3, 4, 7, 9], [2, 2, 3, 3, 4, 8, 8], [2, 2, 3, 3, 5, 5, 10], [2, 2, 3, 3, 5, 6, 9], [2, 2, 3, 3, 5, 7, 8], [2, 2, 3, 3, 5, 15], [2, 2, 3, 3, 6, 6, 8], [2, 2, 3, 3, 6, 7, 7], [2, 2, 3, 3, 6, 14], [2, 2, 3, 3, 7, 13], [2, 2, 3, 3, 8, 12], [2, 2, 3, 3, 9, 11], [2, 2, 3, 3, 10, 10], [2, 2, 3, 4, 4, 5, 10], [2, 2, 3, 4, 4, 6, 9], [2, 2, 3, 4, 4, 7, 8], [2, 2, 3, 4, 4, 15], [2, 2, 3, 4, 5, 5, 9], [2, 2, 3, 4, 5, 6, 8], [2, 2, 3, 4, 5, 7, 7], [2, 2, 3, 4, 5, 14], [2, 2, 3, 4, 6, 6, 7], [2, 2, 3, 4, 6, 13], [2, 2, 3, 4, 7, 12], [2, 2, 3, 4, 8, 11], [2, 2, 3, 4, 9, 10], [2, 2, 3, 5, 5, 6, 7], [2, 2, 3, 5, 5, 13], [2, 2, 3, 5, 6, 12], [2, 2, 3, 5, 7, 11], [2, 2, 3, 5, 8, 10], [2, 2, 3, 5, 9, 9], [2, 2, 3, 6, 6, 11], [2, 2, 3, 6, 7, 10], [2, 2, 3, 6, 8, 9], [2, 2, 3, 7, 7, 9], [2, 2, 3, 7, 8, 8], [2, 2, 3, 8, 15], [2, 2, 3, 9, 14], [2, 2, 3, 10, 13], [2, 2, 3, 11, 12], [2, 2, 4, 4, 5, 5, 8], [2, 2, 4, 4, 5, 6, 7], [2, 2, 4, 4, 5, 13], [2, 2, 4, 4, 6, 12], [2, 2, 4, 4, 7, 11], [2, 2, 4, 4, 8, 10], [2, 2, 4, 4, 9, 9], [2, 2, 4, 5, 5, 6, 6], [2, 2, 4, 5, 5, 12], [2, 2, 4, 5, 6, 11], [2, 2, 4, 5, 7, 10], [2, 2, 4, 5, 8, 9], [2, 2, 4, 6, 6, 10], [2, 2, 4, 6, 7, 9], [2, 2, 4, 6, 8, 8], [2, 2, 4, 7, 7, 8], [2, 2, 4, 7, 15], [2, 2, 4, 8, 14], [2, 2, 4, 9, 13], [2, 2, 4, 10, 12], [2, 2, 4, 11, 11], [2, 2, 5, 5, 6, 10], [2, 2, 5, 5, 7, 9], [2, 2, 5, 5, 8, 8], [2, 2, 5, 6, 6, 9], [2, 2, 5, 6, 7, 8], [2, 2, 5, 6, 15], [2, 2, 5, 7, 14], [2, 2, 5, 8, 13], [2, 2, 5, 9, 12], [2, 2, 5, 10, 11], [2, 2, 6, 6, 7, 7], [2, 2, 6, 6, 14], [2, 2, 6, 7, 13], [2, 2, 6, 8, 12], [2, 2, 6, 9, 11], [2, 2, 6, 10, 10], [2, 2, 7, 7, 12], [2, 2, 7, 8, 11], [2, 2, 7, 9, 10], [2, 2, 8, 8, 10], [2, 2, 8, 9, 9], [2, 2, 11, 15], [2, 2, 12, 14], [2, 2, 13, 13], [2, 3, 3, 4, 4, 5, 9], [2, 3, 3, 4, 4, 6, 8], [2, 3, 3, 4, 4, 7, 7], [2, 3, 3, 4, 4, 14], [2, 3, 3, 4, 5, 5, 8], [2, 3, 3, 4, 5, 6, 7], [2, 3, 3, 4, 5, 13], [2, 3, 3, 4, 6, 12], [2, 3, 3, 4, 7, 11], [2, 3, 3, 4, 8, 10], [2, 3, 3, 4, 9, 9], [2, 3, 3, 5, 5, 6, 6], [2, 3, 3, 5, 5, 12], [2, 3, 3, 5, 6, 11], [2, 3, 3, 5, 7, 10], [2, 3, 3, 5, 8, 9], [2, 3, 3, 6, 6, 10], [2, 3, 3, 6, 7, 9], [2, 3, 3, 6, 8, 8], [2, 3, 3, 7, 7, 8], [2, 3, 3, 7, 15], [2, 3, 3, 8, 14], [2, 3, 3, 9, 13], [2, 3, 3, 10, 12], [2, 3, 3, 11, 11], [2, 3, 4, 4, 5, 5, 7], [2, 3, 4, 4, 5, 6, 6], [2, 3, 4, 4, 5, 12], [2, 3, 4, 4, 6, 11], [2, 3, 4, 4, 7, 10], [2, 3, 4, 4, 8, 9], [2, 3, 4, 5, 5, 11], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 8, 8], [2, 3, 4, 6, 6, 9], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 15], [2, 3, 4, 7, 14], [2, 3, 4, 8, 13], [2, 3, 4, 9, 12], [2, 3, 4, 10, 11], [2, 3, 5, 5, 6, 9], [2, 3, 5, 5, 7, 8], [2, 3, 5, 5, 15], [2, 3, 5, 6, 6, 8], [2, 3, 5, 6, 7, 7], [2, 3, 5, 6, 14], [2, 3, 5, 7, 13], [2, 3, 5, 8, 12], [2, 3, 5, 9, 11], [2, 3, 5, 10, 10], [2, 3, 6, 6, 13], [2, 3, 6, 7, 12], [2, 3, 6, 8, 11], [2, 3, 6, 9, 10], [2, 3, 7, 7, 11], [2, 3, 7, 8, 10], [2, 3, 7, 9, 9], [2, 3, 8, 8, 9], [2, 3, 10, 15], [2, 3, 11, 14], [2, 3, 12, 13], [2, 4, 4, 5, 5, 10], [2, 4, 4, 5, 6, 9], [2, 4, 4, 5, 7, 8], [2, 4, 4, 5, 15], [2, 4, 4, 6, 6, 8], [2, 4, 4, 6, 7, 7], [2, 4, 4, 6, 14], [2, 4, 4, 7, 13], [2, 4, 4, 8, 12], [2, 4, 4, 9, 11], [2, 4, 4, 10, 10], [2, 4, 5, 5, 6, 8], [2, 4, 5, 5, 7, 7], [2, 4, 5, 5, 14], [2, 4, 5, 6, 6, 7], [2, 4, 5, 6, 13], [2, 4, 5, 7, 12], [2, 4, 5, 8, 11], [2, 4, 5, 9, 10], [2, 4, 6, 6, 12], [2, 4, 6, 7, 11], [2, 4, 6, 8, 10], [2, 4, 6, 9, 9], [2, 4, 7, 7, 10], [2, 4, 7, 8, 9], [2, 4, 9, 15], [2, 4, 10, 14], [2, 4, 11, 13], [2, 4, 12, 12], [2, 5, 5, 6, 12], [2, 5, 5, 7, 11], [2, 5, 5, 8, 10], [2, 5, 5, 9, 9], [2, 5, 6, 6, 11], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 7, 7, 9], [2, 5, 7, 8, 8], [2, 5, 8, 15], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 6, 6, 7, 9], [2, 6, 6, 8, 8], [2, 6, 7, 7, 8], [2, 6, 7, 15], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 6, 11, 11], [2, 7, 7, 14], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 8, 8, 12], [2, 8, 9, 11], [2, 8, 10, 10], [2, 9, 9, 10], [2, 13, 15], [2, 14, 14], [3, 3, 4, 4, 5, 5, 6], [3, 3, 4, 4, 5, 11], [3, 3, 4, 4, 6, 10], [3, 3, 4, 4, 7, 9], [3, 3, 4, 4, 8, 8], [3, 3, 4, 5, 5, 10], [3, 3, 4, 5, 6, 9], [3, 3, 4, 5, 7, 8], [3, 3, 4, 5, 15], [3, 3, 4, 6, 6, 8], [3, 3, 4, 6, 7, 7], [3, 3, 4, 6, 14], [3, 3, 4, 7, 13], [3, 3, 4, 8, 12], [3, 3, 4, 9, 11], [3, 3, 4, 10, 10], [3, 3, 5, 5, 6, 8], [3, 3, 5, 5, 7, 7], [3, 3, 5, 5, 14], [3, 3, 5, 6, 6, 7], [3, 3, 5, 6, 13], [3, 3, 5, 7, 12], [3, 3, 5, 8, 11], [3, 3, 5, 9, 10], [3, 3, 6, 6, 12], [3, 3, 6, 7, 11], [3, 3, 6, 8, 10], [3, 3, 6, 9, 9], [3, 3, 7, 7, 10], [3, 3, 7, 8, 9], [3, 3, 9, 15], [3, 3, 10, 14], [3, 3, 11, 13], [3, 3, 12, 12], [3, 4, 4, 5, 5, 9], [3, 4, 4, 5, 6, 8], [3, 4, 4, 5, 7, 7], [3, 4, 4, 5, 14], [3, 4, 4, 6, 6, 7], [3, 4, 4, 6, 13], [3, 4, 4, 7, 12], [3, 4, 4, 8, 11], [3, 4, 4, 9, 10], [3, 4, 5, 5, 6, 7], [3, 4, 5, 5, 13], [3, 4, 5, 6, 12], [3, 4, 5, 7, 11], [3, 4, 5, 8, 10], [3, 4, 5, 9, 9], [3, 4, 6, 6, 11], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 7, 7, 9], [3, 4, 7, 8, 8], [3, 4, 8, 15], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 5, 5, 6, 11], [3, 5, 5, 7, 10], [3, 5, 5, 8, 9], [3, 5, 6, 6, 10], [3, 5, 6, 7, 9], [3, 5, 6, 8, 8], [3, 5, 7, 7, 8], [3, 5, 7, 15], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 5, 11, 11], [3, 6, 6, 7, 8], [3, 6, 6, 15], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 7, 7, 13], [3, 7, 8, 12], [3, 7, 9, 11], [3, 7, 10, 10], [3, 8, 8, 11], [3, 8, 9, 10], [3, 12, 15], [3, 13, 14], [4, 4, 5, 5, 6, 6], [4, 4, 5, 5, 12], [4, 4, 5, 6, 11], [4, 4, 5, 7, 10], [4, 4, 5, 8, 9], [4, 4, 6, 6, 10], [4, 4, 6, 7, 9], [4, 4, 6, 8, 8], [4, 4, 7, 7, 8], [4, 4, 7, 15], [4, 4, 8, 14], [4, 4, 9, 13], [4, 4, 10, 12], [4, 4, 11, 11], [4, 5, 5, 6, 10], [4, 5, 5, 7, 9], [4, 5, 5, 8, 8], [4, 5, 6, 6, 9], [4, 5, 6, 7, 8], [4, 5, 6, 15], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 6, 6, 7, 7], [4, 6, 6, 14], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 6, 10, 10], [4, 7, 7, 12], [4, 7, 8, 11], [4, 7, 9, 10], [4, 8, 8, 10], [4, 8, 9, 9], [4, 11, 15], [4, 12, 14], [4, 13, 13], [5, 5, 6, 6, 8], [5, 5, 6, 7, 7], [5, 5, 6, 14], [5, 5, 7, 13], [5, 5, 8, 12], [5, 5, 9, 11], [5, 5, 10, 10], [5, 6, 6, 13], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 7, 7, 11], [5, 7, 8, 10], [5, 7, 9, 9], [5, 8, 8, 9], [5, 10, 15], [5, 11, 14], [5, 12, 13], [6, 6, 7, 11], [6, 6, 8, 10], [6, 6, 9, 9], [6, 7, 7, 10], [6, 7, 8, 9], [6, 9, 15], [6, 10, 14], [6, 11, 13], [6, 12, 12], [7, 7, 8, 8], [7, 8, 15], [7, 9, 14], [7, 10, 13], [7, 11, 12], [8, 8, 14], [8, 9, 13], [8, 10, 12], [8, 11, 11], [9, 9, 12], [9, 10, 11], [15, 15]]\n assert candidate(candidates = [10, 10, 10, 10, 5, 5, 5, 5, 1, 1, 1, 1],target = 25) == [[5, 5, 5, 10], [5, 10, 10]]\n assert candidate(candidates = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],target = 8) == [[4, 4]]\n assert candidate(candidates = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 10) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 3, 4, 8],target = 15) == [[1, 1, 2, 3, 8], [1, 1, 2, 4, 7], [1, 1, 2, 5, 6], [1, 1, 3, 4, 6], [1, 1, 3, 10], [1, 1, 5, 8], [1, 1, 6, 7], [1, 2, 3, 4, 5], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 10], [1, 6, 8], [2, 3, 4, 6], [2, 3, 10], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6], [5, 10], [7, 8]]\n assert candidate(candidates = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],target = 15) == [[1, 1, 2, 2, 3, 6], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 9], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 8], [1, 1, 2, 4, 7], [1, 1, 2, 5, 6], [1, 1, 3, 3, 7], [1, 1, 3, 4, 6], [1, 1, 3, 5, 5], [1, 1, 3, 10], [1, 1, 4, 4, 5], [1, 1, 4, 9], [1, 1, 5, 8], [1, 1, 6, 7], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 7], [1, 2, 2, 4, 6], [1, 2, 2, 5, 5], [1, 2, 2, 10], [1, 2, 3, 3, 6], [1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 2, 6, 6], [1, 3, 3, 4, 4], [1, 3, 3, 8], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 4, 6], [1, 4, 5, 5], [1, 4, 10], [1, 5, 9], [1, 6, 8], [1, 7, 7], [2, 2, 3, 3, 5], [2, 2, 3, 4, 4], [2, 2, 3, 8], [2, 2, 4, 7], [2, 2, 5, 6], [2, 3, 3, 7], [2, 3, 4, 6], [2, 3, 5, 5], [2, 3, 10], [2, 4, 4, 5], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 3, 4, 5], [3, 3, 9], [3, 4, 8], [3, 5, 7], [3, 6, 6], [4, 4, 7], [4, 5, 6], [5, 10], [6, 9], [7, 8]]\n assert candidate(candidates = [15, 10, 5, 7, 3, 2, 2, 1, 1],target = 18) == [[1, 1, 2, 2, 5, 7], [1, 2, 2, 3, 10], [1, 2, 3, 5, 7], [1, 2, 5, 10], [1, 2, 15], [1, 7, 10], [3, 5, 10], [3, 15]]\n assert candidate(candidates = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 150) == [[10, 20, 30, 40, 50], [10, 20, 30, 90], [10, 20, 40, 80], [10, 20, 50, 70], [10, 30, 40, 70], [10, 30, 50, 60], [10, 40, 100], [10, 50, 90], [10, 60, 80], [20, 30, 40, 60], [20, 30, 100], [20, 40, 90], [20, 50, 80], [20, 60, 70], [30, 40, 80], [30, 50, 70], [40, 50, 60], [50, 100], [60, 90], [70, 80]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 3, 8, 4, 9],target = 10) == [[1, 1, 2, 6], [1, 1, 3, 5], [1, 1, 8], [1, 2, 3, 4], [1, 2, 7], [1, 3, 6], [1, 4, 5], [1, 9], [2, 3, 5], [2, 8], [3, 7], [4, 6], [10]]\n assert candidate(candidates = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 150) == [[10, 20, 30, 40, 50], [10, 20, 30, 90], [10, 20, 40, 80], [10, 20, 50, 70], [10, 30, 40, 70], [10, 30, 50, 60], [10, 40, 100], [10, 50, 90], [10, 60, 80], [20, 30, 40, 60], [20, 30, 100], [20, 40, 90], [20, 50, 80], [20, 60, 70], [30, 40, 80], [30, 50, 70], [40, 50, 60], [50, 100], [60, 90], [70, 80]]\n assert candidate(candidates = [1, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9],target = 10) == [[1, 2, 2, 2, 3], [1, 2, 2, 5], [1, 2, 3, 4], [1, 2, 7], [1, 3, 6], [1, 4, 5], [1, 9], [2, 2, 2, 4], [2, 2, 6], [2, 3, 5], [2, 8], [3, 7], [4, 6]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 25) == [[5, 5, 5, 5, 5]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],target = 45) == [[1, 3, 5, 7, 29], [1, 3, 5, 9, 27], [1, 3, 5, 11, 25], [1, 3, 5, 13, 23], [1, 3, 5, 15, 21], [1, 3, 5, 17, 19], [1, 3, 7, 9, 25], [1, 3, 7, 11, 23], [1, 3, 7, 13, 21], [1, 3, 7, 15, 19], [1, 3, 9, 11, 21], [1, 3, 9, 13, 19], [1, 3, 9, 15, 17], [1, 3, 11, 13, 17], [1, 5, 7, 9, 23], [1, 5, 7, 11, 21], [1, 5, 7, 13, 19], [1, 5, 7, 15, 17], [1, 5, 9, 11, 19], [1, 5, 9, 13, 17], [1, 5, 11, 13, 15], [1, 7, 9, 11, 17], [1, 7, 9, 13, 15], [1, 13, 31], [1, 15, 29], [1, 17, 27], [1, 19, 25], [1, 21, 23], [3, 5, 7, 9, 21], [3, 5, 7, 11, 19], [3, 5, 7, 13, 17], [3, 5, 9, 11, 17], [3, 5, 9, 13, 15], [3, 7, 9, 11, 15], [3, 11, 31], [3, 13, 29], [3, 15, 27], [3, 17, 25], [3, 19, 23], [5, 7, 9, 11, 13], [5, 9, 31], [5, 11, 29], [5, 13, 27], [5, 15, 25], [5, 17, 23], [5, 19, 21], [7, 9, 29], [7, 11, 27], [7, 13, 25], [7, 15, 23], [7, 17, 21], [9, 11, 25], [9, 13, 23], [9, 15, 21], [9, 17, 19], [11, 13, 21], [11, 15, 19], [13, 15, 17]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 25) == [[1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 5, 6, 8], [1, 2, 3, 9, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 8, 10], [1, 2, 5, 7, 10], [1, 2, 5, 8, 9], [1, 2, 6, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 8, 9], [1, 3, 5, 6, 10], [1, 3, 5, 7, 9], [1, 3, 6, 7, 8], [1, 4, 5, 6, 9], [1, 4, 5, 7, 8], [1, 5, 9, 10], [1, 6, 8, 10], [1, 7, 8, 9], [2, 3, 4, 6, 10], [2, 3, 4, 7, 9], [2, 3, 5, 6, 9], [2, 3, 5, 7, 8], [2, 4, 5, 6, 8], [2, 4, 9, 10], [2, 5, 8, 10], [2, 6, 7, 10], [2, 6, 8, 9], [3, 4, 5, 6, 7], [3, 4, 8, 10], [3, 5, 7, 10], [3, 5, 8, 9], [3, 6, 7, 9], [4, 5, 6, 10], [4, 5, 7, 9], [4, 6, 7, 8], [6, 9, 10], [7, 8, 10]]\n assert candidate(candidates = [7, 6, 5, 4, 3, 2, 1],target = 15) == [[1, 2, 3, 4, 5], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [2, 3, 4, 6], [2, 6, 7], [3, 5, 7], [4, 5, 6]]\n assert candidate(candidates = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],target = 10) == [[1, 1, 2, 2, 4], [1, 1, 2, 3, 3], [1, 1, 3, 5], [1, 1, 4, 4], [1, 2, 2, 5], [1, 2, 3, 4], [1, 4, 5], [2, 2, 3, 3], [2, 3, 5], [2, 4, 4], [3, 3, 4], [5, 5]]\n assert candidate(candidates = [1, 3, 2, 5, 4, 2, 2],target = 10) == [[1, 2, 2, 2, 3], [1, 2, 2, 5], [1, 2, 3, 4], [1, 4, 5], [2, 2, 2, 4], [2, 3, 5]]\n assert candidate(candidates = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],target = 20) == [[4, 4, 4, 4, 4]]\n assert candidate(candidates = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 10, 10], [1, 2, 3, 5, 9, 10], [1, 2, 3, 6, 8, 10], [1, 2, 3, 7, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 5, 6, 7, 9], [1, 2, 7, 10, 10], [1, 2, 8, 9, 10], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 6, 7, 9], [1, 3, 5, 6, 7, 8], [1, 3, 6, 10, 10], [1, 3, 7, 9, 10], [1, 4, 5, 10, 10], [1, 4, 6, 9, 10], [1, 4, 7, 8, 10], [1, 5, 6, 8, 10], [1, 5, 7, 8, 9], [1, 9, 10, 10], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 6, 7, 8], [2, 3, 5, 10, 10], [2, 3, 6, 9, 10], [2, 3, 7, 8, 10], [2, 4, 5, 9, 10], [2, 4, 6, 8, 10], [2, 4, 7, 8, 9], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 8, 10, 10], [3, 4, 5, 8, 10], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 5, 6, 7, 9], [3, 7, 10, 10], [3, 8, 9, 10], [4, 5, 6, 7, 8], [4, 6, 10, 10], [4, 7, 9, 10], [5, 6, 9, 10], [5, 7, 8, 10], [6, 7, 8, 9], [10, 10, 10]]\n assert candidate(candidates = [3, 30, 3, 9, 4, 9, 8, 5, 5, 2, 18, 6, 3, 7, 15, 6, 4],target = 49) == [[2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 8], [2, 3, 3, 3, 4, 4, 5, 7, 9, 9], [2, 3, 3, 3, 4, 4, 5, 7, 18], [2, 3, 3, 3, 4, 4, 6, 6, 9, 9], [2, 3, 3, 3, 4, 4, 6, 6, 18], [2, 3, 3, 3, 4, 4, 6, 7, 8, 9], [2, 3, 3, 3, 4, 4, 6, 9, 15], [2, 3, 3, 3, 4, 4, 7, 8, 15], [2, 3, 3, 3, 4, 4, 30], [2, 3, 3, 3, 4, 5, 5, 6, 9, 9], [2, 3, 3, 3, 4, 5, 5, 6, 18], [2, 3, 3, 3, 4, 5, 5, 7, 8, 9], [2, 3, 3, 3, 4, 5, 5, 9, 15], [2, 3, 3, 3, 4, 5, 6, 6, 8, 9], [2, 3, 3, 3, 4, 5, 6, 8, 15], [2, 3, 3, 3, 4, 6, 6, 7, 15], [2, 3, 3, 3, 4, 7, 9, 18], [2, 3, 3, 3, 5, 5, 6, 6, 7, 9], [2, 3, 3, 3, 5, 5, 6, 7, 15], [2, 3, 3, 3, 5, 6, 9, 18], [2, 3, 3, 3, 5, 7, 8, 9, 9], [2, 3, 3, 3, 5, 7, 8, 18], [2, 3, 3, 3, 5, 9, 9, 15], [2, 3, 3, 3, 5, 15, 18], [2, 3, 3, 3, 6, 6, 8, 9, 9], [2, 3, 3, 3, 6, 6, 8, 18], [2, 3, 3, 3, 6, 8, 9, 15], [2, 3, 3, 3, 8, 30], [2, 3, 3, 4, 4, 5, 5, 6, 8, 9], [2, 3, 3, 4, 4, 5, 5, 8, 15], [2, 3, 3, 4, 4, 5, 6, 6, 7, 9], [2, 3, 3, 4, 4, 5, 6, 7, 15], [2, 3, 3, 4, 4, 6, 9, 18], [2, 3, 3, 4, 4, 7, 8, 9, 9], [2, 3, 3, 4, 4, 7, 8, 18], [2, 3, 3, 4, 4, 9, 9, 15], [2, 3, 3, 4, 4, 15, 18], [2, 3, 3, 4, 5, 5, 6, 6, 7, 8], [2, 3, 3, 4, 5, 5, 6, 6, 15], [2, 3, 3, 4, 5, 5, 9, 18], [2, 3, 3, 4, 5, 6, 8, 9, 9], [2, 3, 3, 4, 5, 6, 8, 18], [2, 3, 3, 4, 5, 8, 9, 15], [2, 3, 3, 4, 6, 6, 7, 9, 9], [2, 3, 3, 4, 6, 6, 7, 18], [2, 3, 3, 4, 6, 7, 9, 15], [2, 3, 3, 4, 7, 30], [2, 3, 3, 5, 5, 6, 7, 9, 9], [2, 3, 3, 5, 5, 6, 7, 18], [2, 3, 3, 5, 5, 7, 9, 15], [2, 3, 3, 5, 6, 6, 7, 8, 9], [2, 3, 3, 5, 6, 6, 9, 15], [2, 3, 3, 5, 6, 7, 8, 15], [2, 3, 3, 5, 6, 30], [2, 3, 3, 5, 9, 9, 18], [2, 3, 3, 6, 8, 9, 18], [2, 3, 3, 8, 9, 9, 15], [2, 3, 3, 8, 15, 18], [2, 3, 4, 4, 5, 5, 8, 9, 9], [2, 3, 4, 4, 5, 5, 8, 18], [2, 3, 4, 4, 5, 6, 7, 9, 9], [2, 3, 4, 4, 5, 6, 7, 18], [2, 3, 4, 4, 5, 7, 9, 15], [2, 3, 4, 4, 6, 6, 7, 8, 9], [2, 3, 4, 4, 6, 6, 9, 15], [2, 3, 4, 4, 6, 7, 8, 15], [2, 3, 4, 4, 6, 30], [2, 3, 4, 4, 9, 9, 18], [2, 3, 4, 5, 5, 6, 6, 9, 9], [2, 3, 4, 5, 5, 6, 6, 18], [2, 3, 4, 5, 5, 6, 7, 8, 9], [2, 3, 4, 5, 5, 6, 9, 15], [2, 3, 4, 5, 5, 7, 8, 15], [2, 3, 4, 5, 5, 30], [2, 3, 4, 5, 6, 6, 8, 15], [2, 3, 4, 5, 8, 9, 18], [2, 3, 4, 6, 7, 9, 18], [2, 3, 4, 7, 9, 9, 15], [2, 3, 4, 7, 15, 18], [2, 3, 5, 5, 6, 6, 7, 15], [2, 3, 5, 5, 7, 9, 18], [2, 3, 5, 6, 6, 9, 18], [2, 3, 5, 6, 7, 8, 9, 9], [2, 3, 5, 6, 7, 8, 18], [2, 3, 5, 6, 9, 9, 15], [2, 3, 5, 6, 15, 18], [2, 3, 5, 7, 8, 9, 15], [2, 3, 5, 9, 30], [2, 3, 6, 6, 8, 9, 15], [2, 3, 6, 8, 30], [2, 3, 8, 9, 9, 18], [2, 4, 4, 5, 5, 6, 6, 8, 9], [2, 4, 4, 5, 5, 6, 8, 15], [2, 4, 4, 5, 6, 6, 7, 15], [2, 4, 4, 5, 7, 9, 18], [2, 4, 4, 6, 6, 9, 18], [2, 4, 4, 6, 7, 8, 9, 9], [2, 4, 4, 6, 7, 8, 18], [2, 4, 4, 6, 9, 9, 15], [2, 4, 4, 6, 15, 18], [2, 4, 4, 7, 8, 9, 15], [2, 4, 4, 9, 30], [2, 4, 5, 5, 6, 9, 18], [2, 4, 5, 5, 7, 8, 9, 9], [2, 4, 5, 5, 7, 8, 18], [2, 4, 5, 5, 9, 9, 15], [2, 4, 5, 5, 15, 18], [2, 4, 5, 6, 6, 8, 9, 9], [2, 4, 5, 6, 6, 8, 18], [2, 4, 5, 6, 8, 9, 15], [2, 4, 5, 8, 30], [2, 4, 6, 6, 7, 9, 15], [2, 4, 6, 7, 30], [2, 4, 7, 9, 9, 18], [2, 5, 5, 6, 6, 7, 9, 9], [2, 5, 5, 6, 6, 7, 18], [2, 5, 5, 6, 7, 9, 15], [2, 5, 5, 7, 30], [2, 5, 6, 6, 7, 8, 15], [2, 5, 6, 6, 30], [2, 5, 6, 9, 9, 18], [2, 5, 7, 8, 9, 18], [2, 5, 9, 15, 18], [2, 6, 6, 8, 9, 18], [2, 6, 8, 9, 9, 15], [2, 6, 8, 15, 18], [2, 8, 9, 30], [3, 3, 3, 4, 4, 5, 5, 6, 7, 9], [3, 3, 3, 4, 4, 5, 5, 7, 15], [3, 3, 3, 4, 4, 5, 6, 6, 7, 8], [3, 3, 3, 4, 4, 5, 6, 6, 15], [3, 3, 3, 4, 4, 5, 9, 18], [3, 3, 3, 4, 4, 6, 8, 9, 9], [3, 3, 3, 4, 4, 6, 8, 18], [3, 3, 3, 4, 4, 8, 9, 15], [3, 3, 3, 4, 5, 5, 8, 9, 9], [3, 3, 3, 4, 5, 5, 8, 18], [3, 3, 3, 4, 5, 6, 7, 9, 9], [3, 3, 3, 4, 5, 6, 7, 18], [3, 3, 3, 4, 5, 7, 9, 15], [3, 3, 3, 4, 6, 6, 7, 8, 9], [3, 3, 3, 4, 6, 6, 9, 15], [3, 3, 3, 4, 6, 7, 8, 15], [3, 3, 3, 4, 6, 30], [3, 3, 3, 4, 9, 9, 18], [3, 3, 3, 5, 5, 6, 6, 9, 9], [3, 3, 3, 5, 5, 6, 6, 18], [3, 3, 3, 5, 5, 6, 7, 8, 9], [3, 3, 3, 5, 5, 6, 9, 15], [3, 3, 3, 5, 5, 7, 8, 15], [3, 3, 3, 5, 5, 30], [3, 3, 3, 5, 6, 6, 8, 15], [3, 3, 3, 5, 8, 9, 18], [3, 3, 3, 6, 7, 9, 18], [3, 3, 3, 7, 9, 9, 15], [3, 3, 3, 7, 15, 18], [3, 3, 4, 4, 5, 5, 7, 9, 9], [3, 3, 4, 4, 5, 5, 7, 18], [3, 3, 4, 4, 5, 6, 6, 9, 9], [3, 3, 4, 4, 5, 6, 6, 18], [3, 3, 4, 4, 5, 6, 7, 8, 9], [3, 3, 4, 4, 5, 6, 9, 15], [3, 3, 4, 4, 5, 7, 8, 15], [3, 3, 4, 4, 5, 30], [3, 3, 4, 4, 6, 6, 8, 15], [3, 3, 4, 4, 8, 9, 18], [3, 3, 4, 5, 5, 6, 6, 8, 9], [3, 3, 4, 5, 5, 6, 8, 15], [3, 3, 4, 5, 6, 6, 7, 15], [3, 3, 4, 5, 7, 9, 18], [3, 3, 4, 6, 6, 9, 18], [3, 3, 4, 6, 7, 8, 9, 9], [3, 3, 4, 6, 7, 8, 18], [3, 3, 4, 6, 9, 9, 15], [3, 3, 4, 6, 15, 18], [3, 3, 4, 7, 8, 9, 15], [3, 3, 4, 9, 30], [3, 3, 5, 5, 6, 9, 18], [3, 3, 5, 5, 7, 8, 9, 9], [3, 3, 5, 5, 7, 8, 18], [3, 3, 5, 5, 9, 9, 15], [3, 3, 5, 5, 15, 18], [3, 3, 5, 6, 6, 8, 9, 9], [3, 3, 5, 6, 6, 8, 18], [3, 3, 5, 6, 8, 9, 15], [3, 3, 5, 8, 30], [3, 3, 6, 6, 7, 9, 15], [3, 3, 6, 7, 30], [3, 3, 7, 9, 9, 18], [3, 4, 4, 5, 5, 6, 6, 7, 9], [3, 4, 4, 5, 5, 6, 7, 15], [3, 4, 4, 5, 6, 9, 18], [3, 4, 4, 5, 7, 8, 9, 9], [3, 4, 4, 5, 7, 8, 18], [3, 4, 4, 5, 9, 9, 15], [3, 4, 4, 5, 15, 18], [3, 4, 4, 6, 6, 8, 9, 9], [3, 4, 4, 6, 6, 8, 18], [3, 4, 4, 6, 8, 9, 15], [3, 4, 4, 8, 30], [3, 4, 5, 5, 6, 8, 9, 9], [3, 4, 5, 5, 6, 8, 18], [3, 4, 5, 5, 8, 9, 15], [3, 4, 5, 6, 6, 7, 9, 9], [3, 4, 5, 6, 6, 7, 18], [3, 4, 5, 6, 7, 9, 15], [3, 4, 5, 7, 30], [3, 4, 6, 6, 7, 8, 15], [3, 4, 6, 6, 30], [3, 4, 6, 9, 9, 18], [3, 4, 7, 8, 9, 18], [3, 4, 9, 15, 18], [3, 5, 5, 6, 6, 7, 8, 9], [3, 5, 5, 6, 6, 9, 15], [3, 5, 5, 6, 7, 8, 15], [3, 5, 5, 6, 30], [3, 5, 5, 9, 9, 18], [3, 5, 6, 8, 9, 18], [3, 5, 8, 9, 9, 15], [3, 5, 8, 15, 18], [3, 6, 6, 7, 9, 18], [3, 6, 7, 9, 9, 15], [3, 6, 7, 15, 18], [3, 7, 9, 30], [4, 4, 5, 5, 6, 7, 9, 9], [4, 4, 5, 5, 6, 7, 18], [4, 4, 5, 5, 7, 9, 15], [4, 4, 5, 6, 6, 7, 8, 9], [4, 4, 5, 6, 6, 9, 15], [4, 4, 5, 6, 7, 8, 15], [4, 4, 5, 6, 30], [4, 4, 5, 9, 9, 18], [4, 4, 6, 8, 9, 18], [4, 4, 8, 9, 9, 15], [4, 4, 8, 15, 18], [4, 5, 5, 6, 6, 8, 15], [4, 5, 5, 8, 9, 18], [4, 5, 6, 7, 9, 18], [4, 5, 7, 9, 9, 15], [4, 5, 7, 15, 18], [4, 6, 6, 7, 8, 9, 9], [4, 6, 6, 7, 8, 18], [4, 6, 6, 9, 9, 15], [4, 6, 6, 15, 18], [4, 6, 7, 8, 9, 15], [4, 6, 9, 30], [4, 7, 8, 30], [4, 15, 30], [5, 5, 6, 6, 9, 18], [5, 5, 6, 7, 8, 9, 9], [5, 5, 6, 7, 8, 18], [5, 5, 6, 9, 9, 15], [5, 5, 6, 15, 18], [5, 5, 7, 8, 9, 15], [5, 5, 9, 30], [5, 6, 6, 8, 9, 15], [5, 6, 8, 30], [5, 8, 9, 9, 18], [6, 6, 7, 30], [6, 7, 9, 9, 18], [7, 9, 15, 18]]\n assert candidate(candidates = [5, 10, 15, 20, 25, 30, 35],target = 70) == [[5, 10, 20, 35], [5, 10, 25, 30], [5, 15, 20, 30], [5, 30, 35], [10, 15, 20, 25], [10, 25, 35], [15, 20, 35], [15, 25, 30]]\n assert candidate(candidates = [2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5],target = 11) == [[2, 2, 2, 2, 3], [2, 2, 2, 5], [2, 2, 3, 4], [2, 3, 3, 3], [2, 4, 5], [3, 3, 5], [3, 4, 4]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 3, 4, 2, 3, 1, 5],target = 15) == [[1, 1, 1, 2, 2, 3, 5], [1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 2, 3, 7], [1, 1, 1, 2, 4, 6], [1, 1, 1, 2, 5, 5], [1, 1, 1, 2, 10], [1, 1, 1, 3, 3, 6], [1, 1, 1, 3, 4, 5], [1, 1, 1, 5, 7], [1, 1, 2, 2, 3, 6], [1, 1, 2, 2, 4, 5], [1, 1, 2, 3, 3, 5], [1, 1, 2, 4, 7], [1, 1, 2, 5, 6], [1, 1, 3, 3, 7], [1, 1, 3, 4, 6], [1, 1, 3, 5, 5], [1, 1, 3, 10], [1, 1, 6, 7], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 7], [1, 2, 2, 4, 6], [1, 2, 2, 5, 5], [1, 2, 2, 10], [1, 2, 3, 3, 6], [1, 2, 3, 4, 5], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 5, 5], [1, 4, 10], [2, 2, 3, 3, 5], [2, 2, 4, 7], [2, 2, 5, 6], [2, 3, 3, 7], [2, 3, 4, 6], [2, 3, 5, 5], [2, 3, 10], [2, 6, 7], [3, 3, 4, 5], [3, 5, 7], [4, 5, 6], [5, 10]]\n assert candidate(candidates = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 28) == [[1, 3, 5, 19], [1, 3, 7, 17], [1, 3, 9, 15], [1, 3, 11, 13], [1, 5, 7, 15], [1, 5, 9, 13], [1, 7, 9, 11], [1, 27], [3, 5, 7, 13], [3, 5, 9, 11], [3, 25], [5, 23], [7, 21], [9, 19], [11, 17], [13, 15]]\n assert candidate(candidates = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],target = 15) == [[1, 2, 2, 2, 3, 5], [1, 2, 2, 2, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 5, 5], [1, 2, 3, 4, 5], [1, 2, 4, 4, 4], [1, 3, 3, 3, 5], [1, 3, 3, 4, 4], [1, 4, 5, 5], [2, 2, 2, 3, 3, 3], [2, 2, 2, 4, 5], [2, 2, 3, 3, 5], [2, 2, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 5, 5], [2, 4, 4, 5], [3, 3, 4, 5], [3, 4, 4, 4], [5, 5, 5]]\n assert candidate(candidates = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],target = 20) == [[4, 4, 4, 4, 4]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 20) == [[1, 2, 3, 4, 10], [1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 3, 14], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 4, 13], [1, 2, 5, 12], [1, 2, 6, 11], [1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 4, 5, 7], [1, 3, 4, 12], [1, 3, 5, 11], [1, 3, 6, 10], [1, 3, 7, 9], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 4, 15], [1, 5, 6, 8], [1, 5, 14], [1, 6, 13], [1, 7, 12], [1, 8, 11], [1, 9, 10], [2, 3, 4, 5, 6], [2, 3, 4, 11], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 3, 15], [2, 4, 5, 9], [2, 4, 6, 8], [2, 4, 14], [2, 5, 6, 7], [2, 5, 13], [2, 6, 12], [2, 7, 11], [2, 8, 10], [3, 4, 5, 8], [3, 4, 6, 7], [3, 4, 13], [3, 5, 12], [3, 6, 11], [3, 7, 10], [3, 8, 9], [4, 5, 11], [4, 6, 10], [4, 7, 9], [5, 6, 9], [5, 7, 8], [5, 15], [6, 14], [7, 13], [8, 12], [9, 11]]\n assert candidate(candidates = [10, 20, 30, 40, 50],target = 60) == [[10, 20, 30], [10, 50], [20, 40]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 3, 4, 8],target = 12) == [[1, 1, 2, 3, 5], [1, 1, 2, 8], [1, 1, 3, 7], [1, 1, 4, 6], [1, 1, 10], [1, 2, 3, 6], [1, 2, 4, 5], [1, 3, 8], [1, 4, 7], [1, 5, 6], [2, 3, 7], [2, 4, 6], [2, 10], [3, 4, 5], [4, 8], [5, 7]]\n assert candidate(candidates = [20, 15, 10, 5, 3, 7, 8, 12],target = 25) == [[3, 5, 7, 10], [3, 7, 15], [3, 10, 12], [5, 8, 12], [5, 20], [7, 8, 10], [10, 15]]\n assert candidate(candidates = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22],target = 40) == [[3, 4, 5, 6, 7, 15], [3, 4, 5, 6, 8, 14], [3, 4, 5, 6, 9, 13], [3, 4, 5, 6, 10, 12], [3, 4, 5, 6, 22], [3, 4, 5, 7, 8, 13], [3, 4, 5, 7, 9, 12], [3, 4, 5, 7, 10, 11], [3, 4, 5, 7, 21], [3, 4, 5, 8, 9, 11], [3, 4, 5, 8, 20], [3, 4, 5, 9, 19], [3, 4, 5, 10, 18], [3, 4, 5, 11, 17], [3, 4, 5, 12, 16], [3, 4, 5, 13, 15], [3, 4, 6, 7, 8, 12], [3, 4, 6, 7, 9, 11], [3, 4, 6, 7, 20], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 19], [3, 4, 6, 9, 18], [3, 4, 6, 10, 17], [3, 4, 6, 11, 16], [3, 4, 6, 12, 15], [3, 4, 6, 13, 14], [3, 4, 7, 8, 18], [3, 4, 7, 9, 17], [3, 4, 7, 10, 16], [3, 4, 7, 11, 15], [3, 4, 7, 12, 14], [3, 4, 8, 9, 16], [3, 4, 8, 10, 15], [3, 4, 8, 11, 14], [3, 4, 8, 12, 13], [3, 4, 9, 10, 14], [3, 4, 9, 11, 13], [3, 4, 10, 11, 12], [3, 4, 11, 22], [3, 4, 12, 21], [3, 4, 13, 20], [3, 4, 14, 19], [3, 4, 15, 18], [3, 4, 16, 17], [3, 5, 6, 7, 8, 11], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 19], [3, 5, 6, 8, 18], [3, 5, 6, 9, 17], [3, 5, 6, 10, 16], [3, 5, 6, 11, 15], [3, 5, 6, 12, 14], [3, 5, 7, 8, 17], [3, 5, 7, 9, 16], [3, 5, 7, 10, 15], [3, 5, 7, 11, 14], [3, 5, 7, 12, 13], [3, 5, 8, 9, 15], [3, 5, 8, 10, 14], [3, 5, 8, 11, 13], [3, 5, 9, 10, 13], [3, 5, 9, 11, 12], [3, 5, 10, 22], [3, 5, 11, 21], [3, 5, 12, 20], [3, 5, 13, 19], [3, 5, 14, 18], [3, 5, 15, 17], [3, 6, 7, 8, 16], [3, 6, 7, 9, 15], [3, 6, 7, 10, 14], [3, 6, 7, 11, 13], [3, 6, 8, 9, 14], [3, 6, 8, 10, 13], [3, 6, 8, 11, 12], [3, 6, 9, 10, 12], [3, 6, 9, 22], [3, 6, 10, 21], [3, 6, 11, 20], [3, 6, 12, 19], [3, 6, 13, 18], [3, 6, 14, 17], [3, 6, 15, 16], [3, 7, 8, 9, 13], [3, 7, 8, 10, 12], [3, 7, 8, 22], [3, 7, 9, 10, 11], [3, 7, 9, 21], [3, 7, 10, 20], [3, 7, 11, 19], [3, 7, 12, 18], [3, 7, 13, 17], [3, 7, 14, 16], [3, 8, 9, 20], [3, 8, 10, 19], [3, 8, 11, 18], [3, 8, 12, 17], [3, 8, 13, 16], [3, 8, 14, 15], [3, 9, 10, 18], [3, 9, 11, 17], [3, 9, 12, 16], [3, 9, 13, 15], [3, 10, 11, 16], [3, 10, 12, 15], [3, 10, 13, 14], [3, 11, 12, 14], [3, 15, 22], [3, 16, 21], [3, 17, 20], [3, 18, 19], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 18], [4, 5, 6, 8, 17], [4, 5, 6, 9, 16], [4, 5, 6, 10, 15], [4, 5, 6, 11, 14], [4, 5, 6, 12, 13], [4, 5, 7, 8, 16], [4, 5, 7, 9, 15], [4, 5, 7, 10, 14], [4, 5, 7, 11, 13], [4, 5, 8, 9, 14], [4, 5, 8, 10, 13], [4, 5, 8, 11, 12], [4, 5, 9, 10, 12], [4, 5, 9, 22], [4, 5, 10, 21], [4, 5, 11, 20], [4, 5, 12, 19], [4, 5, 13, 18], [4, 5, 14, 17], [4, 5, 15, 16], [4, 6, 7, 8, 15], [4, 6, 7, 9, 14], [4, 6, 7, 10, 13], [4, 6, 7, 11, 12], [4, 6, 8, 9, 13], [4, 6, 8, 10, 12], [4, 6, 8, 22], [4, 6, 9, 10, 11], [4, 6, 9, 21], [4, 6, 10, 20], [4, 6, 11, 19], [4, 6, 12, 18], [4, 6, 13, 17], [4, 6, 14, 16], [4, 7, 8, 9, 12], [4, 7, 8, 10, 11], [4, 7, 8, 21], [4, 7, 9, 20], [4, 7, 10, 19], [4, 7, 11, 18], [4, 7, 12, 17], [4, 7, 13, 16], [4, 7, 14, 15], [4, 8, 9, 19], [4, 8, 10, 18], [4, 8, 11, 17], [4, 8, 12, 16], [4, 8, 13, 15], [4, 9, 10, 17], [4, 9, 11, 16], [4, 9, 12, 15], [4, 9, 13, 14], [4, 10, 11, 15], [4, 10, 12, 14], [4, 11, 12, 13], [4, 14, 22], [4, 15, 21], [4, 16, 20], [4, 17, 19], [5, 6, 7, 8, 14], [5, 6, 7, 9, 13], [5, 6, 7, 10, 12], [5, 6, 7, 22], [5, 6, 8, 9, 12], [5, 6, 8, 10, 11], [5, 6, 8, 21], [5, 6, 9, 20], [5, 6, 10, 19], [5, 6, 11, 18], [5, 6, 12, 17], [5, 6, 13, 16], [5, 6, 14, 15], [5, 7, 8, 9, 11], [5, 7, 8, 20], [5, 7, 9, 19], [5, 7, 10, 18], [5, 7, 11, 17], [5, 7, 12, 16], [5, 7, 13, 15], [5, 8, 9, 18], [5, 8, 10, 17], [5, 8, 11, 16], [5, 8, 12, 15], [5, 8, 13, 14], [5, 9, 10, 16], [5, 9, 11, 15], [5, 9, 12, 14], [5, 10, 11, 14], [5, 10, 12, 13], [5, 13, 22], [5, 14, 21], [5, 15, 20], [5, 16, 19], [5, 17, 18], [6, 7, 8, 9, 10], [6, 7, 8, 19], [6, 7, 9, 18], [6, 7, 10, 17], [6, 7, 11, 16], [6, 7, 12, 15], [6, 7, 13, 14], [6, 8, 9, 17], [6, 8, 10, 16], [6, 8, 11, 15], [6, 8, 12, 14], [6, 9, 10, 15], [6, 9, 11, 14], [6, 9, 12, 13], [6, 10, 11, 13], [6, 12, 22], [6, 13, 21], [6, 14, 20], [6, 15, 19], [6, 16, 18], [7, 8, 9, 16], [7, 8, 10, 15], [7, 8, 11, 14], [7, 8, 12, 13], [7, 9, 10, 14], [7, 9, 11, 13], [7, 10, 11, 12], [7, 11, 22], [7, 12, 21], [7, 13, 20], [7, 14, 19], [7, 15, 18], [7, 16, 17], [8, 9, 10, 13], [8, 9, 11, 12], [8, 10, 22], [8, 11, 21], [8, 12, 20], [8, 13, 19], [8, 14, 18], [8, 15, 17], [9, 10, 21], [9, 11, 20], [9, 12, 19], [9, 13, 18], [9, 14, 17], [9, 15, 16], [10, 11, 19], [10, 12, 18], [10, 13, 17], [10, 14, 16], [11, 12, 17], [11, 13, 16], [11, 14, 15], [12, 13, 15], [18, 22], [19, 21]]\n assert candidate(candidates = [1, 3, 2, 6, 7, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1],target = 9) == [[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 2, 3], [1, 1, 1, 2, 4], [1, 1, 1, 6], [1, 1, 3, 4], [1, 1, 7], [1, 2, 6], [2, 3, 4], [2, 7], [3, 6]]\n assert candidate(candidates = [10, 20, 30, 40, 50, 60, 70, 80, 90],target = 100) == [[10, 20, 30, 40], [10, 20, 70], [10, 30, 60], [10, 40, 50], [10, 90], [20, 30, 50], [20, 80], [30, 70], [40, 60]]\n assert candidate(candidates = [10, 20, 30, 40, 50],target = 100) == [[10, 20, 30, 40], [10, 40, 50], [20, 30, 50]]\n assert candidate(candidates = [10, 1, 2, 7, 6, 1, 5, 3, 4],target = 10) == [[1, 1, 2, 6], [1, 1, 3, 5], [1, 2, 3, 4], [1, 2, 7], [1, 3, 6], [1, 4, 5], [2, 3, 5], [3, 7], [4, 6], [10]]\n assert candidate(candidates = [30, 20, 10, 5, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 15], [1, 2, 3, 4, 6, 14], [1, 2, 3, 4, 7, 13], [1, 2, 3, 4, 8, 12], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 10, 10], [1, 2, 3, 4, 20], [1, 2, 3, 5, 6, 13], [1, 2, 3, 5, 7, 12], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 9, 15], [1, 2, 3, 10, 14], [1, 2, 3, 11, 13], [1, 2, 4, 5, 6, 12], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 8, 10], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 8, 15], [1, 2, 4, 9, 14], [1, 2, 4, 10, 13], [1, 2, 4, 11, 12], [1, 2, 5, 6, 7, 9], [1, 2, 5, 7, 15], [1, 2, 5, 8, 14], [1, 2, 5, 9, 13], [1, 2, 5, 10, 12], [1, 2, 6, 7, 14], [1, 2, 6, 8, 13], [1, 2, 6, 9, 12], [1, 2, 6, 10, 11], [1, 2, 7, 8, 12], [1, 2, 7, 9, 11], [1, 2, 7, 10, 10], [1, 2, 7, 20], [1, 2, 8, 9, 10], [1, 2, 12, 15], [1, 2, 13, 14], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 6, 7, 9], [1, 3, 4, 7, 15], [1, 3, 4, 8, 14], [1, 3, 4, 9, 13], [1, 3, 4, 10, 12], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 15], [1, 3, 5, 7, 14], [1, 3, 5, 8, 13], [1, 3, 5, 9, 12], [1, 3, 5, 10, 11], [1, 3, 6, 7, 13], [1, 3, 6, 8, 12], [1, 3, 6, 9, 11], [1, 3, 6, 10, 10], [1, 3, 6, 20], [1, 3, 7, 8, 11], [1, 3, 7, 9, 10], [1, 3, 11, 15], [1, 3, 12, 14], [1, 4, 5, 6, 14], [1, 4, 5, 7, 13], [1, 4, 5, 8, 12], [1, 4, 5, 9, 11], [1, 4, 5, 10, 10], [1, 4, 5, 20], [1, 4, 6, 7, 12], [1, 4, 6, 8, 11], [1, 4, 6, 9, 10], [1, 4, 7, 8, 10], [1, 4, 10, 15], [1, 4, 11, 14], [1, 4, 12, 13], [1, 5, 6, 7, 11], [1, 5, 6, 8, 10], [1, 5, 7, 8, 9], [1, 5, 9, 15], [1, 5, 10, 14], [1, 5, 11, 13], [1, 6, 8, 15], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 8, 9, 12], [1, 8, 10, 11], [1, 9, 10, 10], [1, 9, 20], [1, 14, 15], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 15], [2, 3, 4, 7, 14], [2, 3, 4, 8, 13], [2, 3, 4, 9, 12], [2, 3, 4, 10, 11], [2, 3, 5, 6, 14], [2, 3, 5, 7, 13], [2, 3, 5, 8, 12], [2, 3, 5, 9, 11], [2, 3, 5, 10, 10], [2, 3, 5, 20], [2, 3, 6, 7, 12], [2, 3, 6, 8, 11], [2, 3, 6, 9, 10], [2, 3, 7, 8, 10], [2, 3, 10, 15], [2, 3, 11, 14], [2, 3, 12, 13], [2, 4, 5, 6, 13], [2, 4, 5, 7, 12], [2, 4, 5, 8, 11], [2, 4, 5, 9, 10], [2, 4, 6, 7, 11], [2, 4, 6, 8, 10], [2, 4, 7, 8, 9], [2, 4, 9, 15], [2, 4, 10, 14], [2, 4, 11, 13], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 8, 15], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 6, 7, 15], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 8, 9, 11], [2, 8, 10, 10], [2, 8, 20], [2, 13, 15], [3, 4, 5, 6, 12], [3, 4, 5, 7, 11], [3, 4, 5, 8, 10], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 8, 15], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 5, 6, 7, 9], [3, 5, 7, 15], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 7, 8, 12], [3, 7, 9, 11], [3, 7, 10, 10], [3, 7, 20], [3, 8, 9, 10], [3, 12, 15], [3, 13, 14], [4, 5, 6, 7, 8], [4, 5, 6, 15], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 6, 10, 10], [4, 6, 20], [4, 7, 8, 11], [4, 7, 9, 10], [4, 11, 15], [4, 12, 14], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 7, 8, 10], [5, 10, 15], [5, 11, 14], [5, 12, 13], [6, 7, 8, 9], [6, 9, 15], [6, 10, 14], [6, 11, 13], [7, 8, 15], [7, 9, 14], [7, 10, 13], [7, 11, 12], [8, 9, 13], [8, 10, 12], [9, 10, 11], [10, 20], [30]]\n assert candidate(candidates = [1, 3, 2, 5, 4, 7, 6, 9, 8, 10],target = 15) == [[1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 10], [1, 5, 9], [1, 6, 8], [2, 3, 4, 6], [2, 3, 10], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6], [5, 10], [6, 9], [7, 8]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 25) == [[5, 5, 5, 5, 5]]\n assert candidate(candidates = [20, 10, 5, 2, 3, 2, 1, 1],target = 15) == [[1, 1, 3, 10], [1, 2, 2, 10], [2, 3, 10], [5, 10]]\n assert candidate(candidates = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 25) == [[1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 15], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 14], [1, 2, 3, 6, 13], [1, 2, 3, 7, 12], [1, 2, 3, 8, 11], [1, 2, 3, 9, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 13], [1, 2, 4, 6, 12], [1, 2, 4, 7, 11], [1, 2, 4, 8, 10], [1, 2, 5, 6, 11], [1, 2, 5, 7, 10], [1, 2, 5, 8, 9], [1, 2, 6, 7, 9], [1, 2, 7, 15], [1, 2, 8, 14], [1, 2, 9, 13], [1, 2, 10, 12], [1, 3, 4, 5, 12], [1, 3, 4, 6, 11], [1, 3, 4, 7, 10], [1, 3, 4, 8, 9], [1, 3, 5, 6, 10], [1, 3, 5, 7, 9], [1, 3, 6, 7, 8], [1, 3, 6, 15], [1, 3, 7, 14], [1, 3, 8, 13], [1, 3, 9, 12], [1, 3, 10, 11], [1, 4, 5, 6, 9], [1, 4, 5, 7, 8], [1, 4, 5, 15], [1, 4, 6, 14], [1, 4, 7, 13], [1, 4, 8, 12], [1, 4, 9, 11], [1, 5, 6, 13], [1, 5, 7, 12], [1, 5, 8, 11], [1, 5, 9, 10], [1, 6, 7, 11], [1, 6, 8, 10], [1, 7, 8, 9], [1, 9, 15], [1, 10, 14], [1, 11, 13], [2, 3, 4, 5, 11], [2, 3, 4, 6, 10], [2, 3, 4, 7, 9], [2, 3, 5, 6, 9], [2, 3, 5, 7, 8], [2, 3, 5, 15], [2, 3, 6, 14], [2, 3, 7, 13], [2, 3, 8, 12], [2, 3, 9, 11], [2, 4, 5, 6, 8], [2, 4, 5, 14], [2, 4, 6, 13], [2, 4, 7, 12], [2, 4, 8, 11], [2, 4, 9, 10], [2, 5, 6, 12], [2, 5, 7, 11], [2, 5, 8, 10], [2, 6, 7, 10], [2, 6, 8, 9], [2, 8, 15], [2, 9, 14], [2, 10, 13], [2, 11, 12], [3, 4, 5, 6, 7], [3, 4, 5, 13], [3, 4, 6, 12], [3, 4, 7, 11], [3, 4, 8, 10], [3, 5, 6, 11], [3, 5, 7, 10], [3, 5, 8, 9], [3, 6, 7, 9], [3, 7, 15], [3, 8, 14], [3, 9, 13], [3, 10, 12], [4, 5, 6, 10], [4, 5, 7, 9], [4, 6, 7, 8], [4, 6, 15], [4, 7, 14], [4, 8, 13], [4, 9, 12], [4, 10, 11], [5, 6, 14], [5, 7, 13], [5, 8, 12], [5, 9, 11], [6, 7, 12], [6, 8, 11], [6, 9, 10], [7, 8, 10], [10, 15], [11, 14], [12, 13]]\n assert candidate(candidates = [4, 4, 4, 4, 4, 4, 4, 4],target = 16) == [[4, 4, 4, 4]]\n assert candidate(candidates = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 20) == [[1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 9], [1, 2, 2, 3, 4, 8], [1, 2, 2, 3, 5, 7], [1, 2, 2, 3, 6, 6], [1, 2, 2, 4, 4, 7], [1, 2, 2, 4, 5, 6], [1, 2, 2, 5, 10], [1, 2, 2, 6, 9], [1, 2, 2, 7, 8], [1, 2, 3, 3, 4, 7], [1, 2, 3, 3, 5, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 10], [1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 3, 7, 7], [1, 2, 4, 4, 9], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 5, 5, 7], [1, 2, 5, 6, 6], [1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 9], [1, 3, 3, 5, 8], [1, 3, 3, 6, 7], [1, 3, 4, 4, 8], [1, 3, 4, 5, 7], [1, 3, 4, 6, 6], [1, 3, 5, 5, 6], [1, 3, 6, 10], [1, 3, 7, 9], [1, 3, 8, 8], [1, 4, 4, 5, 6], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 5, 9], [1, 5, 6, 8], [1, 5, 7, 7], [1, 6, 6, 7], [1, 9, 10], [2, 2, 3, 3, 4, 6], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 10], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 9], [2, 2, 3, 5, 8], [2, 2, 3, 6, 7], [2, 2, 4, 4, 8], [2, 2, 4, 5, 7], [2, 2, 4, 6, 6], [2, 2, 5, 5, 6], [2, 2, 6, 10], [2, 2, 7, 9], [2, 2, 8, 8], [2, 3, 3, 4, 8], [2, 3, 3, 5, 7], [2, 3, 3, 6, 6], [2, 3, 4, 4, 7], [2, 3, 4, 5, 6], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 4, 5, 5], [2, 4, 4, 10], [2, 4, 5, 9], [2, 4, 6, 8], [2, 4, 7, 7], [2, 5, 5, 8], [2, 5, 6, 7], [2, 8, 10], [2, 9, 9], [3, 3, 4, 4, 6], [3, 3, 4, 5, 5], [3, 3, 4, 10], [3, 3, 5, 9], [3, 3, 6, 8], [3, 3, 7, 7], [3, 4, 4, 9], [3, 4, 5, 8], [3, 4, 6, 7], [3, 5, 5, 7], [3, 5, 6, 6], [3, 7, 10], [3, 8, 9], [4, 4, 5, 7], [4, 4, 6, 6], [4, 5, 5, 6], [4, 6, 10], [4, 7, 9], [4, 8, 8], [5, 5, 10], [5, 6, 9], [5, 7, 8], [6, 6, 8], [6, 7, 7], [10, 10]]\n assert candidate(candidates = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 45) == [[5, 5, 5, 5, 5, 5, 5, 5, 5]]\n assert candidate(candidates = [1, 3, 2, 2, 4, 1, 1, 3, 3, 5, 7, 9, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9],target = 20) == [[1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4], [1, 1, 1, 1, 1, 2, 2, 2, 2, 7], [1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 1, 1, 2, 2, 2, 3, 6], [1, 1, 1, 1, 1, 2, 2, 2, 4, 5], [1, 1, 1, 1, 1, 2, 2, 2, 9], [1, 1, 1, 1, 1, 2, 2, 3, 3, 5], [1, 1, 1, 1, 1, 2, 2, 3, 4, 4], [1, 1, 1, 1, 1, 2, 2, 3, 8], [1, 1, 1, 1, 1, 2, 2, 4, 7], [1, 1, 1, 1, 1, 2, 2, 5, 6], [1, 1, 1, 1, 1, 2, 3, 3, 3, 4], [1, 1, 1, 1, 1, 2, 3, 3, 7], [1, 1, 1, 1, 1, 2, 3, 4, 6], [1, 1, 1, 1, 1, 2, 3, 5, 5], [1, 1, 1, 1, 1, 2, 4, 4, 5], [1, 1, 1, 1, 1, 2, 4, 9], [1, 1, 1, 1, 1, 2, 5, 8], [1, 1, 1, 1, 1, 2, 6, 7], [1, 1, 1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 1, 1, 3, 3, 3, 6], [1, 1, 1, 1, 1, 3, 3, 4, 5], [1, 1, 1, 1, 1, 3, 3, 9], [1, 1, 1, 1, 1, 3, 4, 4, 4], [1, 1, 1, 1, 1, 3, 4, 8], [1, 1, 1, 1, 1, 3, 5, 7], [1, 1, 1, 1, 1, 3, 6, 6], [1, 1, 1, 1, 1, 4, 4, 7], [1, 1, 1, 1, 1, 4, 5, 6], [1, 1, 1, 1, 1, 5, 5, 5], [1, 1, 1, 1, 1, 6, 9], [1, 1, 1, 1, 1, 7, 8], [1, 1, 1, 1, 2, 2, 2, 2, 3, 5], [1, 1, 1, 1, 2, 2, 2, 2, 4, 4], [1, 1, 1, 1, 2, 2, 2, 2, 8], [1, 1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 1, 2, 2, 2, 3, 7], [1, 1, 1, 1, 2, 2, 2, 4, 6], [1, 1, 1, 1, 2, 2, 2, 5, 5], [1, 1, 1, 1, 2, 2, 3, 3, 3, 3], [1, 1, 1, 1, 2, 2, 3, 3, 6], [1, 1, 1, 1, 2, 2, 3, 4, 5], [1, 1, 1, 1, 2, 2, 3, 9], [1, 1, 1, 1, 2, 2, 4, 4, 4], [1, 1, 1, 1, 2, 2, 4, 8], [1, 1, 1, 1, 2, 2, 5, 7], [1, 1, 1, 1, 2, 2, 6, 6], [1, 1, 1, 1, 2, 3, 3, 3, 5], [1, 1, 1, 1, 2, 3, 3, 4, 4], [1, 1, 1, 1, 2, 3, 3, 8], [1, 1, 1, 1, 2, 3, 4, 7], [1, 1, 1, 1, 2, 3, 5, 6], [1, 1, 1, 1, 2, 4, 4, 6], [1, 1, 1, 1, 2, 4, 5, 5], [1, 1, 1, 1, 2, 5, 9], [1, 1, 1, 1, 2, 6, 8], [1, 1, 1, 1, 2, 7, 7], [1, 1, 1, 1, 3, 3, 3, 3, 4], [1, 1, 1, 1, 3, 3, 3, 7], [1, 1, 1, 1, 3, 3, 4, 6], [1, 1, 1, 1, 3, 3, 5, 5], [1, 1, 1, 1, 3, 4, 4, 5], [1, 1, 1, 1, 3, 4, 9], [1, 1, 1, 1, 3, 5, 8], [1, 1, 1, 1, 3, 6, 7], [1, 1, 1, 1, 4, 4, 8], [1, 1, 1, 1, 4, 5, 7], [1, 1, 1, 1, 4, 6, 6], [1, 1, 1, 1, 5, 5, 6], [1, 1, 1, 1, 7, 9], [1, 1, 1, 1, 8, 8], [1, 1, 1, 2, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3, 6], [1, 1, 1, 2, 2, 2, 2, 4, 5], [1, 1, 1, 2, 2, 2, 2, 9], [1, 1, 1, 2, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 8], [1, 1, 1, 2, 2, 2, 4, 7], [1, 1, 1, 2, 2, 2, 5, 6], [1, 1, 1, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 7], [1, 1, 1, 2, 2, 3, 4, 6], [1, 1, 1, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 4, 9], [1, 1, 1, 2, 2, 5, 8], [1, 1, 1, 2, 2, 6, 7], [1, 1, 1, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 3, 3, 3, 6], [1, 1, 1, 2, 3, 3, 4, 5], [1, 1, 1, 2, 3, 3, 9], [1, 1, 1, 2, 3, 4, 4, 4], [1, 1, 1, 2, 3, 4, 8], [1, 1, 1, 2, 3, 5, 7], [1, 1, 1, 2, 3, 6, 6], [1, 1, 1, 2, 4, 4, 7], [1, 1, 1, 2, 4, 5, 6], [1, 1, 1, 2, 5, 5, 5], [1, 1, 1, 2, 6, 9], [1, 1, 1, 2, 7, 8], [1, 1, 1, 3, 3, 3, 3, 5], [1, 1, 1, 3, 3, 3, 4, 4], [1, 1, 1, 3, 3, 3, 8], [1, 1, 1, 3, 3, 4, 7], [1, 1, 1, 3, 3, 5, 6], [1, 1, 1, 3, 4, 4, 6], [1, 1, 1, 3, 4, 5, 5], [1, 1, 1, 3, 5, 9], [1, 1, 1, 3, 6, 8], [1, 1, 1, 3, 7, 7], [1, 1, 1, 4, 4, 4, 5], [1, 1, 1, 4, 4, 9], [1, 1, 1, 4, 5, 8], [1, 1, 1, 4, 6, 7], [1, 1, 1, 5, 5, 7], [1, 1, 1, 5, 6, 6], [1, 1, 1, 8, 9], [1, 1, 2, 2, 2, 2, 3, 3, 4], [1, 1, 2, 2, 2, 2, 3, 7], [1, 1, 2, 2, 2, 2, 4, 6], [1, 1, 2, 2, 2, 2, 5, 5], [1, 1, 2, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3, 6], [1, 1, 2, 2, 2, 3, 4, 5], [1, 1, 2, 2, 2, 3, 9], [1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 2, 2, 2, 4, 8], [1, 1, 2, 2, 2, 5, 7], [1, 1, 2, 2, 2, 6, 6], [1, 1, 2, 2, 3, 3, 3, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 8], [1, 1, 2, 2, 3, 4, 7], [1, 1, 2, 2, 3, 5, 6], [1, 1, 2, 2, 4, 4, 6], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 5, 9], [1, 1, 2, 2, 6, 8], [1, 1, 2, 2, 7, 7], [1, 1, 2, 3, 3, 3, 3, 4], [1, 1, 2, 3, 3, 3, 7], [1, 1, 2, 3, 3, 4, 6], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 9], [1, 1, 2, 3, 5, 8], [1, 1, 2, 3, 6, 7], [1, 1, 2, 4, 4, 8], [1, 1, 2, 4, 5, 7], [1, 1, 2, 4, 6, 6], [1, 1, 2, 5, 5, 6], [1, 1, 2, 7, 9], [1, 1, 2, 8, 8], [1, 1, 3, 3, 3, 3, 6], [1, 1, 3, 3, 3, 4, 5], [1, 1, 3, 3, 3, 9], [1, 1, 3, 3, 4, 4, 4], [1, 1, 3, 3, 4, 8], [1, 1, 3, 3, 5, 7], [1, 1, 3, 3, 6, 6], [1, 1, 3, 4, 4, 7], [1, 1, 3, 4, 5, 6], [1, 1, 3, 5, 5, 5], [1, 1, 3, 6, 9], [1, 1, 3, 7, 8], [1, 1, 4, 4, 4, 6], [1, 1, 4, 4, 5, 5], [1, 1, 4, 5, 9], [1, 1, 4, 6, 8], [1, 1, 4, 7, 7], [1, 1, 5, 5, 8], [1, 1, 5, 6, 7], [1, 1, 9, 9], [1, 2, 2, 2, 2, 3, 3, 5], [1, 2, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 2, 3, 8], [1, 2, 2, 2, 2, 4, 7], [1, 2, 2, 2, 2, 5, 6], [1, 2, 2, 2, 3, 3, 3, 4], [1, 2, 2, 2, 3, 3, 7], [1, 2, 2, 2, 3, 4, 6], [1, 2, 2, 2, 3, 5, 5], [1, 2, 2, 2, 4, 4, 5], [1, 2, 2, 2, 4, 9], [1, 2, 2, 2, 5, 8], [1, 2, 2, 2, 6, 7], [1, 2, 2, 3, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3, 6], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 9], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 8], [1, 2, 2, 3, 5, 7], [1, 2, 2, 3, 6, 6], [1, 2, 2, 4, 4, 7], [1, 2, 2, 4, 5, 6], [1, 2, 2, 5, 5, 5], [1, 2, 2, 6, 9], [1, 2, 2, 7, 8], [1, 2, 3, 3, 3, 3, 5], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 8], [1, 2, 3, 3, 4, 7], [1, 2, 3, 3, 5, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 3, 7, 7], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 9], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 5, 5, 7], [1, 2, 5, 6, 6], [1, 2, 8, 9], [1, 3, 3, 3, 3, 3, 4], [1, 3, 3, 3, 3, 7], [1, 3, 3, 3, 4, 6], [1, 3, 3, 3, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 9], [1, 3, 3, 5, 8], [1, 3, 3, 6, 7], [1, 3, 4, 4, 8], [1, 3, 4, 5, 7], [1, 3, 4, 6, 6], [1, 3, 5, 5, 6], [1, 3, 7, 9], [1, 3, 8, 8], [1, 4, 4, 4, 7], [1, 4, 4, 5, 6], [1, 4, 5, 5, 5], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 5, 9], [1, 5, 6, 8], [1, 5, 7, 7], [1, 6, 6, 7], [2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 6], [2, 2, 2, 2, 3, 4, 5], [2, 2, 2, 2, 3, 9], [2, 2, 2, 2, 4, 4, 4], [2, 2, 2, 2, 4, 8], [2, 2, 2, 2, 5, 7], [2, 2, 2, 2, 6, 6], [2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 8], [2, 2, 2, 3, 4, 7], [2, 2, 2, 3, 5, 6], [2, 2, 2, 4, 4, 6], [2, 2, 2, 4, 5, 5], [2, 2, 2, 5, 9], [2, 2, 2, 6, 8], [2, 2, 2, 7, 7], [2, 2, 3, 3, 3, 3, 4], [2, 2, 3, 3, 3, 7], [2, 2, 3, 3, 4, 6], [2, 2, 3, 3, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 9], [2, 2, 3, 5, 8], [2, 2, 3, 6, 7], [2, 2, 4, 4, 8], [2, 2, 4, 5, 7], [2, 2, 4, 6, 6], [2, 2, 5, 5, 6], [2, 2, 7, 9], [2, 2, 8, 8], [2, 3, 3, 3, 3, 6], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 9], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 8], [2, 3, 3, 5, 7], [2, 3, 3, 6, 6], [2, 3, 4, 4, 7], [2, 3, 4, 5, 6], [2, 3, 5, 5, 5], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 4, 4, 6], [2, 4, 4, 5, 5], [2, 4, 5, 9], [2, 4, 6, 8], [2, 4, 7, 7], [2, 5, 5, 8], [2, 5, 6, 7], [2, 9, 9], [3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 4, 4], [3, 3, 3, 3, 8], [3, 3, 3, 4, 7], [3, 3, 3, 5, 6], [3, 3, 4, 4, 6], [3, 3, 4, 5, 5], [3, 3, 5, 9], [3, 3, 6, 8], [3, 3, 7, 7], [3, 4, 4, 4, 5], [3, 4, 4, 9], [3, 4, 5, 8], [3, 4, 6, 7], [3, 5, 5, 7], [3, 5, 6, 6], [3, 8, 9], [4, 4, 4, 8], [4, 4, 5, 7], [4, 4, 6, 6], [4, 5, 5, 6], [4, 7, 9], [4, 8, 8], [5, 6, 9], [5, 7, 8], [6, 6, 8], [6, 7, 7]]\n assert candidate(candidates = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5],target = 10) == [[1, 2, 2, 5], [1, 2, 3, 4], [1, 3, 3, 3], [1, 4, 5], [2, 2, 3, 3], [2, 3, 5], [2, 4, 4], [3, 3, 4], [5, 5]]\n assert candidate(candidates = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 20) == [[1, 1, 1, 2, 2, 3, 3, 7], [1, 1, 1, 2, 2, 3, 4, 6], [1, 1, 1, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 3, 10], [1, 1, 1, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 4, 9], [1, 1, 1, 2, 2, 5, 8], [1, 1, 1, 2, 2, 6, 7], [1, 1, 1, 2, 3, 3, 4, 5], [1, 1, 1, 2, 3, 3, 9], [1, 1, 1, 2, 3, 4, 8], [1, 1, 1, 2, 3, 5, 7], [1, 1, 1, 2, 3, 6, 6], [1, 1, 1, 2, 4, 4, 7], [1, 1, 1, 2, 4, 5, 6], [1, 1, 1, 2, 5, 10], [1, 1, 1, 2, 6, 9], [1, 1, 1, 2, 7, 8], [1, 1, 1, 3, 3, 4, 7], [1, 1, 1, 3, 3, 5, 6], [1, 1, 1, 3, 4, 4, 6], [1, 1, 1, 3, 4, 5, 5], [1, 1, 1, 3, 4, 10], [1, 1, 1, 3, 5, 9], [1, 1, 1, 3, 6, 8], [1, 1, 1, 3, 7, 7], [1, 1, 1, 4, 4, 9], [1, 1, 1, 4, 5, 8], [1, 1, 1, 4, 6, 7], [1, 1, 1, 5, 5, 7], [1, 1, 1, 5, 6, 6], [1, 1, 1, 7, 10], [1, 1, 1, 8, 9], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 8], [1, 1, 2, 2, 3, 4, 7], [1, 1, 2, 2, 3, 5, 6], [1, 1, 2, 2, 4, 4, 6], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 10], [1, 1, 2, 2, 5, 9], [1, 1, 2, 2, 6, 8], [1, 1, 2, 2, 7, 7], [1, 1, 2, 3, 3, 4, 6], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 10], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 9], [1, 1, 2, 3, 5, 8], [1, 1, 2, 3, 6, 7], [1, 1, 2, 4, 4, 8], [1, 1, 2, 4, 5, 7], [1, 1, 2, 4, 6, 6], [1, 1, 2, 5, 5, 6], [1, 1, 2, 6, 10], [1, 1, 2, 7, 9], [1, 1, 2, 8, 8], [1, 1, 3, 3, 4, 8], [1, 1, 3, 3, 5, 7], [1, 1, 3, 3, 6, 6], [1, 1, 3, 4, 4, 7], [1, 1, 3, 4, 5, 6], [1, 1, 3, 5, 10], [1, 1, 3, 6, 9], [1, 1, 3, 7, 8], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 10], [1, 1, 4, 5, 9], [1, 1, 4, 6, 8], [1, 1, 4, 7, 7], [1, 1, 5, 5, 8], [1, 1, 5, 6, 7], [1, 1, 8, 10], [1, 1, 9, 9], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 9], [1, 2, 2, 3, 4, 8], [1, 2, 2, 3, 5, 7], [1, 2, 2, 3, 6, 6], [1, 2, 2, 4, 4, 7], [1, 2, 2, 4, 5, 6], [1, 2, 2, 5, 10], [1, 2, 2, 6, 9], [1, 2, 2, 7, 8], [1, 2, 3, 3, 4, 7], [1, 2, 3, 3, 5, 6], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 10], [1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 3, 7, 7], [1, 2, 4, 4, 9], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 5, 5, 7], [1, 2, 5, 6, 6], [1, 2, 7, 10], [1, 2, 8, 9], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 9], [1, 3, 3, 5, 8], [1, 3, 3, 6, 7], [1, 3, 4, 4, 8], [1, 3, 4, 5, 7], [1, 3, 4, 6, 6], [1, 3, 5, 5, 6], [1, 3, 6, 10], [1, 3, 7, 9], [1, 3, 8, 8], [1, 4, 4, 5, 6], [1, 4, 5, 10], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 5, 9], [1, 5, 6, 8], [1, 5, 7, 7], [1, 6, 6, 7], [1, 9, 10], [2, 2, 3, 3, 4, 6], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 10], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 9], [2, 2, 3, 5, 8], [2, 2, 3, 6, 7], [2, 2, 4, 4, 8], [2, 2, 4, 5, 7], [2, 2, 4, 6, 6], [2, 2, 5, 5, 6], [2, 2, 6, 10], [2, 2, 7, 9], [2, 2, 8, 8], [2, 3, 3, 4, 8], [2, 3, 3, 5, 7], [2, 3, 3, 6, 6], [2, 3, 4, 4, 7], [2, 3, 4, 5, 6], [2, 3, 5, 10], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 4, 5, 5], [2, 4, 4, 10], [2, 4, 5, 9], [2, 4, 6, 8], [2, 4, 7, 7], [2, 5, 5, 8], [2, 5, 6, 7], [2, 8, 10], [2, 9, 9], [3, 3, 4, 4, 6], [3, 3, 4, 5, 5], [3, 3, 4, 10], [3, 3, 5, 9], [3, 3, 6, 8], [3, 3, 7, 7], [3, 4, 4, 9], [3, 4, 5, 8], [3, 4, 6, 7], [3, 5, 5, 7], [3, 5, 6, 6], [3, 7, 10], [3, 8, 9], [4, 4, 5, 7], [4, 4, 6, 6], [4, 5, 5, 6], [4, 6, 10], [4, 7, 9], [4, 8, 8], [5, 5, 10], [5, 6, 9], [5, 7, 8], [6, 6, 8], [6, 7, 7], [10, 10]]\n assert candidate(candidates = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71],target = 100) == [[2, 3, 5, 7, 11, 13, 17, 19, 23], [2, 3, 5, 7, 11, 13, 59], [2, 3, 5, 7, 11, 19, 53], [2, 3, 5, 7, 11, 29, 43], [2, 3, 5, 7, 11, 31, 41], [2, 3, 5, 7, 13, 17, 53], [2, 3, 5, 7, 13, 23, 47], [2, 3, 5, 7, 13, 29, 41], [2, 3, 5, 7, 17, 19, 47], [2, 3, 5, 7, 17, 23, 43], [2, 3, 5, 7, 17, 29, 37], [2, 3, 5, 7, 19, 23, 41], [2, 3, 5, 7, 23, 29, 31], [2, 3, 5, 11, 13, 19, 47], [2, 3, 5, 11, 13, 23, 43], [2, 3, 5, 11, 13, 29, 37], [2, 3, 5, 11, 17, 19, 43], [2, 3, 5, 11, 19, 23, 37], [2, 3, 5, 11, 19, 29, 31], [2, 3, 5, 13, 17, 19, 41], [2, 3, 5, 13, 17, 23, 37], [2, 3, 5, 13, 17, 29, 31], [2, 3, 5, 17, 19, 23, 31], [2, 3, 5, 19, 71], [2, 3, 5, 23, 67], [2, 3, 5, 29, 61], [2, 3, 5, 31, 59], [2, 3, 5, 37, 53], [2, 3, 5, 43, 47], [2, 3, 7, 11, 13, 17, 47], [2, 3, 7, 11, 13, 23, 41], [2, 3, 7, 11, 17, 19, 41], [2, 3, 7, 11, 17, 23, 37], [2, 3, 7, 11, 17, 29, 31], [2, 3, 7, 17, 19, 23, 29], [2, 3, 7, 17, 71], [2, 3, 7, 29, 59], [2, 3, 7, 41, 47], [2, 3, 11, 13, 17, 23, 31], [2, 3, 11, 13, 19, 23, 29], [2, 3, 11, 13, 71], [2, 3, 11, 17, 67], [2, 3, 11, 23, 61], [2, 3, 11, 31, 53], [2, 3, 11, 37, 47], [2, 3, 11, 41, 43], [2, 3, 13, 23, 59], [2, 3, 13, 29, 53], [2, 3, 17, 19, 59], [2, 3, 17, 31, 47], [2, 3, 17, 37, 41], [2, 3, 19, 23, 53], [2, 3, 19, 29, 47], [2, 3, 23, 29, 43], [2, 3, 23, 31, 41], [2, 5, 7, 11, 13, 19, 43], [2, 5, 7, 13, 17, 19, 37], [2, 5, 7, 13, 19, 23, 31], [2, 5, 7, 19, 67], [2, 5, 11, 13, 17, 23, 29], [2, 5, 11, 23, 59], [2, 5, 11, 29, 53], [2, 5, 13, 19, 61], [2, 5, 13, 37, 43], [2, 5, 17, 23, 53], [2, 5, 17, 29, 47], [2, 5, 19, 31, 43], [2, 5, 23, 29, 41], [2, 7, 11, 13, 17, 19, 31], [2, 7, 11, 13, 67], [2, 7, 11, 19, 61], [2, 7, 11, 37, 43], [2, 7, 13, 17, 61], [2, 7, 13, 19, 59], [2, 7, 13, 31, 47], [2, 7, 13, 37, 41], [2, 7, 17, 31, 43], [2, 7, 19, 29, 43], [2, 7, 19, 31, 41], [2, 7, 23, 31, 37], [2, 11, 13, 31, 43], [2, 11, 17, 23, 47], [2, 11, 17, 29, 41], [2, 11, 19, 31, 37], [2, 13, 17, 31, 37], [2, 13, 19, 23, 43], [2, 13, 19, 29, 37], [2, 31, 67], [2, 37, 61], [3, 5, 7, 11, 13, 61], [3, 5, 7, 11, 31, 43], [3, 5, 7, 13, 19, 53], [3, 5, 7, 13, 29, 43], [3, 5, 7, 13, 31, 41], [3, 5, 7, 17, 31, 37], [3, 5, 7, 19, 23, 43], [3, 5, 7, 19, 29, 37], [3, 5, 11, 13, 31, 37], [3, 5, 11, 17, 23, 41], [3, 5, 13, 17, 19, 43], [3, 5, 13, 19, 23, 37], [3, 5, 13, 19, 29, 31], [3, 5, 31, 61], [3, 7, 11, 13, 19, 47], [3, 7, 11, 13, 23, 43], [3, 7, 11, 13, 29, 37], [3, 7, 11, 17, 19, 43], [3, 7, 11, 19, 23, 37], [3, 7, 11, 19, 29, 31], [3, 7, 13, 17, 19, 41], [3, 7, 13, 17, 23, 37], [3, 7, 13, 17, 29, 31], [3, 7, 17, 19, 23, 31], [3, 7, 19, 71], [3, 7, 23, 67], [3, 7, 29, 61], [3, 7, 31, 59], [3, 7, 37, 53], [3, 7, 43, 47], [3, 11, 13, 17, 19, 37], [3, 11, 13, 19, 23, 31], [3, 11, 19, 67], [3, 13, 17, 67], [3, 13, 23, 61], [3, 13, 31, 53], [3, 13, 37, 47], [3, 13, 41, 43], [3, 17, 19, 61], [3, 17, 37, 43], [3, 19, 31, 47], [3, 19, 37, 41], [3, 23, 31, 43], [3, 29, 31, 37], [5, 7, 11, 13, 17, 47], [5, 7, 11, 13, 23, 41], [5, 7, 11, 17, 19, 41], [5, 7, 11, 17, 23, 37], [5, 7, 11, 17, 29, 31], [5, 7, 17, 19, 23, 29], [5, 7, 17, 71], [5, 7, 29, 59], [5, 7, 41, 47], [5, 11, 13, 17, 23, 31], [5, 11, 13, 19, 23, 29], [5, 11, 13, 71], [5, 11, 17, 67], [5, 11, 23, 61], [5, 11, 31, 53], [5, 11, 37, 47], [5, 11, 41, 43], [5, 13, 23, 59], [5, 13, 29, 53], [5, 17, 19, 59], [5, 17, 31, 47], [5, 17, 37, 41], [5, 19, 23, 53], [5, 19, 29, 47], [5, 23, 29, 43], [5, 23, 31, 41], [7, 11, 13, 17, 23, 29], [7, 11, 23, 59], [7, 11, 29, 53], [7, 13, 19, 61], [7, 13, 37, 43], [7, 17, 23, 53], [7, 17, 29, 47], [7, 19, 31, 43], [7, 23, 29, 41], [11, 13, 17, 59], [11, 13, 23, 53], [11, 13, 29, 47], [11, 17, 19, 53], [11, 17, 29, 43], [11, 17, 31, 41], [11, 19, 23, 47], [11, 19, 29, 41], [11, 23, 29, 37], [13, 17, 23, 47], [13, 17, 29, 41], [13, 19, 31, 37], [17, 19, 23, 41], [17, 23, 29, 31], [29, 71], [41, 59], [47, 53]]\n assert candidate(candidates = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10],target = 30) == [[1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 8], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 7], [1, 1, 1, 2, 2, 2, 3, 3, 3, 6, 6], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 7], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6], [1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 5, 10], [1, 1, 1, 2, 2, 2, 3, 3, 6, 9], [1, 1, 1, 2, 2, 2, 3, 3, 7, 8], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 6], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 10], [1, 1, 1, 2, 2, 2, 3, 4, 5, 9], [1, 1, 1, 2, 2, 2, 3, 4, 6, 8], [1, 1, 1, 2, 2, 2, 3, 4, 7, 7], [1, 1, 1, 2, 2, 2, 3, 5, 5, 8], [1, 1, 1, 2, 2, 2, 3, 5, 6, 7], [1, 1, 1, 2, 2, 2, 3, 6, 6, 6], [1, 1, 1, 2, 2, 2, 3, 8, 10], [1, 1, 1, 2, 2, 2, 3, 9, 9], [1, 1, 1, 2, 2, 2, 4, 4, 4, 9], [1, 1, 1, 2, 2, 2, 4, 4, 5, 8], [1, 1, 1, 2, 2, 2, 4, 4, 6, 7], [1, 1, 1, 2, 2, 2, 4, 5, 5, 7], [1, 1, 1, 2, 2, 2, 4, 5, 6, 6], [1, 1, 1, 2, 2, 2, 4, 7, 10], [1, 1, 1, 2, 2, 2, 4, 8, 9], [1, 1, 1, 2, 2, 2, 5, 5, 5, 6], [1, 1, 1, 2, 2, 2, 5, 6, 10], [1, 1, 1, 2, 2, 2, 5, 7, 9], [1, 1, 1, 2, 2, 2, 5, 8, 8], [1, 1, 1, 2, 2, 2, 6, 6, 9], [1, 1, 1, 2, 2, 2, 6, 7, 8], [1, 1, 1, 2, 2, 2, 7, 7, 7], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 6], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 10], [1, 1, 1, 2, 2, 3, 3, 3, 5, 9], [1, 1, 1, 2, 2, 3, 3, 3, 6, 8], [1, 1, 1, 2, 2, 3, 3, 3, 7, 7], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 9], [1, 1, 1, 2, 2, 3, 3, 4, 5, 8], [1, 1, 1, 2, 2, 3, 3, 4, 6, 7], [1, 1, 1, 2, 2, 3, 3, 5, 5, 7], [1, 1, 1, 2, 2, 3, 3, 5, 6, 6], [1, 1, 1, 2, 2, 3, 3, 7, 10], [1, 1, 1, 2, 2, 3, 3, 8, 9], [1, 1, 1, 2, 2, 3, 4, 4, 4, 8], [1, 1, 1, 2, 2, 3, 4, 4, 5, 7], [1, 1, 1, 2, 2, 3, 4, 4, 6, 6], [1, 1, 1, 2, 2, 3, 4, 5, 5, 6], [1, 1, 1, 2, 2, 3, 4, 6, 10], [1, 1, 1, 2, 2, 3, 4, 7, 9], [1, 1, 1, 2, 2, 3, 4, 8, 8], [1, 1, 1, 2, 2, 3, 5, 5, 10], [1, 1, 1, 2, 2, 3, 5, 6, 9], [1, 1, 1, 2, 2, 3, 5, 7, 8], [1, 1, 1, 2, 2, 3, 6, 6, 8], [1, 1, 1, 2, 2, 3, 6, 7, 7], [1, 1, 1, 2, 2, 3, 10, 10], [1, 1, 1, 2, 2, 4, 4, 4, 5, 6], [1, 1, 1, 2, 2, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 4, 4, 5, 10], [1, 1, 1, 2, 2, 4, 4, 6, 9], [1, 1, 1, 2, 2, 4, 4, 7, 8], [1, 1, 1, 2, 2, 4, 5, 5, 9], [1, 1, 1, 2, 2, 4, 5, 6, 8], [1, 1, 1, 2, 2, 4, 5, 7, 7], [1, 1, 1, 2, 2, 4, 6, 6, 7], [1, 1, 1, 2, 2, 4, 9, 10], [1, 1, 1, 2, 2, 5, 5, 5, 8], [1, 1, 1, 2, 2, 5, 5, 6, 7], [1, 1, 1, 2, 2, 5, 6, 6, 6], [1, 1, 1, 2, 2, 5, 8, 10], [1, 1, 1, 2, 2, 5, 9, 9], [1, 1, 1, 2, 2, 6, 7, 10], [1, 1, 1, 2, 2, 6, 8, 9], [1, 1, 1, 2, 2, 7, 7, 9], [1, 1, 1, 2, 2, 7, 8, 8], [1, 1, 1, 2, 3, 3, 3, 4, 4, 8], [1, 1, 1, 2, 3, 3, 3, 4, 5, 7], [1, 1, 1, 2, 3, 3, 3, 4, 6, 6], [1, 1, 1, 2, 3, 3, 3, 5, 5, 6], [1, 1, 1, 2, 3, 3, 3, 6, 10], [1, 1, 1, 2, 3, 3, 3, 7, 9], [1, 1, 1, 2, 3, 3, 3, 8, 8], [1, 1, 1, 2, 3, 3, 4, 4, 4, 7], [1, 1, 1, 2, 3, 3, 4, 4, 5, 6], [1, 1, 1, 2, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 4, 5, 10], [1, 1, 1, 2, 3, 3, 4, 6, 9], [1, 1, 1, 2, 3, 3, 4, 7, 8], [1, 1, 1, 2, 3, 3, 5, 5, 9], [1, 1, 1, 2, 3, 3, 5, 6, 8], [1, 1, 1, 2, 3, 3, 5, 7, 7], [1, 1, 1, 2, 3, 3, 6, 6, 7], [1, 1, 1, 2, 3, 3, 9, 10], [1, 1, 1, 2, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 3, 4, 4, 4, 10], [1, 1, 1, 2, 3, 4, 4, 5, 9], [1, 1, 1, 2, 3, 4, 4, 6, 8], [1, 1, 1, 2, 3, 4, 4, 7, 7], [1, 1, 1, 2, 3, 4, 5, 5, 8], [1, 1, 1, 2, 3, 4, 5, 6, 7], [1, 1, 1, 2, 3, 4, 6, 6, 6], [1, 1, 1, 2, 3, 4, 8, 10], [1, 1, 1, 2, 3, 4, 9, 9], [1, 1, 1, 2, 3, 5, 5, 5, 7], [1, 1, 1, 2, 3, 5, 5, 6, 6], [1, 1, 1, 2, 3, 5, 7, 10], [1, 1, 1, 2, 3, 5, 8, 9], [1, 1, 1, 2, 3, 6, 6, 10], [1, 1, 1, 2, 3, 6, 7, 9], [1, 1, 1, 2, 3, 6, 8, 8], [1, 1, 1, 2, 3, 7, 7, 8], [1, 1, 1, 2, 4, 4, 4, 5, 8], [1, 1, 1, 2, 4, 4, 4, 6, 7], [1, 1, 1, 2, 4, 4, 5, 5, 7], [1, 1, 1, 2, 4, 4, 5, 6, 6], [1, 1, 1, 2, 4, 4, 7, 10], [1, 1, 1, 2, 4, 4, 8, 9], [1, 1, 1, 2, 4, 5, 5, 5, 6], [1, 1, 1, 2, 4, 5, 6, 10], [1, 1, 1, 2, 4, 5, 7, 9], [1, 1, 1, 2, 4, 5, 8, 8], [1, 1, 1, 2, 4, 6, 6, 9], [1, 1, 1, 2, 4, 6, 7, 8], [1, 1, 1, 2, 4, 7, 7, 7], [1, 1, 1, 2, 5, 5, 5, 10], [1, 1, 1, 2, 5, 5, 6, 9], [1, 1, 1, 2, 5, 5, 7, 8], [1, 1, 1, 2, 5, 6, 6, 8], [1, 1, 1, 2, 5, 6, 7, 7], [1, 1, 1, 2, 5, 10, 10], [1, 1, 1, 2, 6, 6, 6, 7], [1, 1, 1, 2, 6, 9, 10], [1, 1, 1, 2, 7, 8, 10], [1, 1, 1, 2, 7, 9, 9], [1, 1, 1, 2, 8, 8, 9], [1, 1, 1, 3, 3, 3, 4, 4, 4, 6], [1, 1, 1, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 3, 3, 3, 4, 4, 10], [1, 1, 1, 3, 3, 3, 4, 5, 9], [1, 1, 1, 3, 3, 3, 4, 6, 8], [1, 1, 1, 3, 3, 3, 4, 7, 7], [1, 1, 1, 3, 3, 3, 5, 5, 8], [1, 1, 1, 3, 3, 3, 5, 6, 7], [1, 1, 1, 3, 3, 3, 6, 6, 6], [1, 1, 1, 3, 3, 3, 8, 10], [1, 1, 1, 3, 3, 3, 9, 9], [1, 1, 1, 3, 3, 4, 4, 4, 9], [1, 1, 1, 3, 3, 4, 4, 5, 8], [1, 1, 1, 3, 3, 4, 4, 6, 7], [1, 1, 1, 3, 3, 4, 5, 5, 7], [1, 1, 1, 3, 3, 4, 5, 6, 6], [1, 1, 1, 3, 3, 4, 7, 10], [1, 1, 1, 3, 3, 4, 8, 9], [1, 1, 1, 3, 3, 5, 5, 5, 6], [1, 1, 1, 3, 3, 5, 6, 10], [1, 1, 1, 3, 3, 5, 7, 9], [1, 1, 1, 3, 3, 5, 8, 8], [1, 1, 1, 3, 3, 6, 6, 9], [1, 1, 1, 3, 3, 6, 7, 8], [1, 1, 1, 3, 3, 7, 7, 7], [1, 1, 1, 3, 4, 4, 4, 5, 7], [1, 1, 1, 3, 4, 4, 4, 6, 6], [1, 1, 1, 3, 4, 4, 5, 5, 6], [1, 1, 1, 3, 4, 4, 6, 10], [1, 1, 1, 3, 4, 4, 7, 9], [1, 1, 1, 3, 4, 4, 8, 8], [1, 1, 1, 3, 4, 5, 5, 10], [1, 1, 1, 3, 4, 5, 6, 9], [1, 1, 1, 3, 4, 5, 7, 8], [1, 1, 1, 3, 4, 6, 6, 8], [1, 1, 1, 3, 4, 6, 7, 7], [1, 1, 1, 3, 4, 10, 10], [1, 1, 1, 3, 5, 5, 5, 9], [1, 1, 1, 3, 5, 5, 6, 8], [1, 1, 1, 3, 5, 5, 7, 7], [1, 1, 1, 3, 5, 6, 6, 7], [1, 1, 1, 3, 5, 9, 10], [1, 1, 1, 3, 6, 8, 10], [1, 1, 1, 3, 6, 9, 9], [1, 1, 1, 3, 7, 7, 10], [1, 1, 1, 3, 7, 8, 9], [1, 1, 1, 3, 8, 8, 8], [1, 1, 1, 4, 4, 4, 5, 5, 5], [1, 1, 1, 4, 4, 4, 5, 10], [1, 1, 1, 4, 4, 4, 6, 9], [1, 1, 1, 4, 4, 4, 7, 8], [1, 1, 1, 4, 4, 5, 5, 9], [1, 1, 1, 4, 4, 5, 6, 8], [1, 1, 1, 4, 4, 5, 7, 7], [1, 1, 1, 4, 4, 6, 6, 7], [1, 1, 1, 4, 4, 9, 10], [1, 1, 1, 4, 5, 5, 5, 8], [1, 1, 1, 4, 5, 5, 6, 7], [1, 1, 1, 4, 5, 6, 6, 6], [1, 1, 1, 4, 5, 8, 10], [1, 1, 1, 4, 5, 9, 9], [1, 1, 1, 4, 6, 7, 10], [1, 1, 1, 4, 6, 8, 9], [1, 1, 1, 4, 7, 7, 9], [1, 1, 1, 4, 7, 8, 8], [1, 1, 1, 5, 5, 5, 6, 6], [1, 1, 1, 5, 5, 7, 10], [1, 1, 1, 5, 5, 8, 9], [1, 1, 1, 5, 6, 6, 10], [1, 1, 1, 5, 6, 7, 9], [1, 1, 1, 5, 6, 8, 8], [1, 1, 1, 5, 7, 7, 8], [1, 1, 1, 6, 6, 6, 9], [1, 1, 1, 6, 6, 7, 8], [1, 1, 1, 6, 7, 7, 7], [1, 1, 1, 7, 10, 10], [1, 1, 1, 8, 9, 10], [1, 1, 1, 9, 9, 9], [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5], [1, 1, 2, 2, 2, 3, 3, 3, 4, 9], [1, 1, 2, 2, 2, 3, 3, 3, 5, 8], [1, 1, 2, 2, 2, 3, 3, 3, 6, 7], [1, 1, 2, 2, 2, 3, 3, 4, 4, 8], [1, 1, 2, 2, 2, 3, 3, 4, 5, 7], [1, 1, 2, 2, 2, 3, 3, 4, 6, 6], [1, 1, 2, 2, 2, 3, 3, 5, 5, 6], [1, 1, 2, 2, 2, 3, 3, 6, 10], [1, 1, 2, 2, 2, 3, 3, 7, 9], [1, 1, 2, 2, 2, 3, 3, 8, 8], [1, 1, 2, 2, 2, 3, 4, 4, 4, 7], [1, 1, 2, 2, 2, 3, 4, 4, 5, 6], [1, 1, 2, 2, 2, 3, 4, 5, 5, 5], [1, 1, 2, 2, 2, 3, 4, 5, 10], [1, 1, 2, 2, 2, 3, 4, 6, 9], [1, 1, 2, 2, 2, 3, 4, 7, 8], [1, 1, 2, 2, 2, 3, 5, 5, 9], [1, 1, 2, 2, 2, 3, 5, 6, 8], [1, 1, 2, 2, 2, 3, 5, 7, 7], [1, 1, 2, 2, 2, 3, 6, 6, 7], [1, 1, 2, 2, 2, 3, 9, 10], [1, 1, 2, 2, 2, 4, 4, 4, 5, 5], [1, 1, 2, 2, 2, 4, 4, 4, 10], [1, 1, 2, 2, 2, 4, 4, 5, 9], [1, 1, 2, 2, 2, 4, 4, 6, 8], [1, 1, 2, 2, 2, 4, 4, 7, 7], [1, 1, 2, 2, 2, 4, 5, 5, 8], [1, 1, 2, 2, 2, 4, 5, 6, 7], [1, 1, 2, 2, 2, 4, 6, 6, 6], [1, 1, 2, 2, 2, 4, 8, 10], [1, 1, 2, 2, 2, 4, 9, 9], [1, 1, 2, 2, 2, 5, 5, 5, 7], [1, 1, 2, 2, 2, 5, 5, 6, 6], [1, 1, 2, 2, 2, 5, 7, 10], [1, 1, 2, 2, 2, 5, 8, 9], [1, 1, 2, 2, 2, 6, 6, 10], [1, 1, 2, 2, 2, 6, 7, 9], [1, 1, 2, 2, 2, 6, 8, 8], [1, 1, 2, 2, 2, 7, 7, 8], [1, 1, 2, 2, 3, 3, 3, 4, 4, 7], [1, 1, 2, 2, 3, 3, 3, 4, 5, 6], [1, 1, 2, 2, 3, 3, 3, 5, 5, 5], [1, 1, 2, 2, 3, 3, 3, 5, 10], [1, 1, 2, 2, 3, 3, 3, 6, 9], [1, 1, 2, 2, 3, 3, 3, 7, 8], [1, 1, 2, 2, 3, 3, 4, 4, 4, 6], [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 4, 10], [1, 1, 2, 2, 3, 3, 4, 5, 9], [1, 1, 2, 2, 3, 3, 4, 6, 8], [1, 1, 2, 2, 3, 3, 4, 7, 7], [1, 1, 2, 2, 3, 3, 5, 5, 8], [1, 1, 2, 2, 3, 3, 5, 6, 7], [1, 1, 2, 2, 3, 3, 6, 6, 6], [1, 1, 2, 2, 3, 3, 8, 10], [1, 1, 2, 2, 3, 3, 9, 9], [1, 1, 2, 2, 3, 4, 4, 4, 9], [1, 1, 2, 2, 3, 4, 4, 5, 8], [1, 1, 2, 2, 3, 4, 4, 6, 7], [1, 1, 2, 2, 3, 4, 5, 5, 7], [1, 1, 2, 2, 3, 4, 5, 6, 6], [1, 1, 2, 2, 3, 4, 7, 10], [1, 1, 2, 2, 3, 4, 8, 9], [1, 1, 2, 2, 3, 5, 5, 5, 6], [1, 1, 2, 2, 3, 5, 6, 10], [1, 1, 2, 2, 3, 5, 7, 9], [1, 1, 2, 2, 3, 5, 8, 8], [1, 1, 2, 2, 3, 6, 6, 9], [1, 1, 2, 2, 3, 6, 7, 8], [1, 1, 2, 2, 3, 7, 7, 7], [1, 1, 2, 2, 4, 4, 4, 5, 7], [1, 1, 2, 2, 4, 4, 4, 6, 6], [1, 1, 2, 2, 4, 4, 5, 5, 6], [1, 1, 2, 2, 4, 4, 6, 10], [1, 1, 2, 2, 4, 4, 7, 9], [1, 1, 2, 2, 4, 4, 8, 8], [1, 1, 2, 2, 4, 5, 5, 10], [1, 1, 2, 2, 4, 5, 6, 9], [1, 1, 2, 2, 4, 5, 7, 8], [1, 1, 2, 2, 4, 6, 6, 8], [1, 1, 2, 2, 4, 6, 7, 7], [1, 1, 2, 2, 4, 10, 10], [1, 1, 2, 2, 5, 5, 5, 9], [1, 1, 2, 2, 5, 5, 6, 8], [1, 1, 2, 2, 5, 5, 7, 7], [1, 1, 2, 2, 5, 6, 6, 7], [1, 1, 2, 2, 5, 9, 10], [1, 1, 2, 2, 6, 8, 10], [1, 1, 2, 2, 6, 9, 9], [1, 1, 2, 2, 7, 7, 10], [1, 1, 2, 2, 7, 8, 9], [1, 1, 2, 2, 8, 8, 8], [1, 1, 2, 3, 3, 3, 4, 4, 4, 5], [1, 1, 2, 3, 3, 3, 4, 4, 9], [1, 1, 2, 3, 3, 3, 4, 5, 8], [1, 1, 2, 3, 3, 3, 4, 6, 7], [1, 1, 2, 3, 3, 3, 5, 5, 7], [1, 1, 2, 3, 3, 3, 5, 6, 6], [1, 1, 2, 3, 3, 3, 7, 10], [1, 1, 2, 3, 3, 3, 8, 9], [1, 1, 2, 3, 3, 4, 4, 4, 8], [1, 1, 2, 3, 3, 4, 4, 5, 7], [1, 1, 2, 3, 3, 4, 4, 6, 6], [1, 1, 2, 3, 3, 4, 5, 5, 6], [1, 1, 2, 3, 3, 4, 6, 10], [1, 1, 2, 3, 3, 4, 7, 9], [1, 1, 2, 3, 3, 4, 8, 8], [1, 1, 2, 3, 3, 5, 5, 10], [1, 1, 2, 3, 3, 5, 6, 9], [1, 1, 2, 3, 3, 5, 7, 8], [1, 1, 2, 3, 3, 6, 6, 8], [1, 1, 2, 3, 3, 6, 7, 7], [1, 1, 2, 3, 3, 10, 10], [1, 1, 2, 3, 4, 4, 4, 5, 6], [1, 1, 2, 3, 4, 4, 5, 5, 5], [1, 1, 2, 3, 4, 4, 5, 10], [1, 1, 2, 3, 4, 4, 6, 9], [1, 1, 2, 3, 4, 4, 7, 8], [1, 1, 2, 3, 4, 5, 5, 9], [1, 1, 2, 3, 4, 5, 6, 8], [1, 1, 2, 3, 4, 5, 7, 7], [1, 1, 2, 3, 4, 6, 6, 7], [1, 1, 2, 3, 4, 9, 10], [1, 1, 2, 3, 5, 5, 5, 8], [1, 1, 2, 3, 5, 5, 6, 7], [1, 1, 2, 3, 5, 6, 6, 6], [1, 1, 2, 3, 5, 8, 10], [1, 1, 2, 3, 5, 9, 9], [1, 1, 2, 3, 6, 7, 10], [1, 1, 2, 3, 6, 8, 9], [1, 1, 2, 3, 7, 7, 9], [1, 1, 2, 3, 7, 8, 8], [1, 1, 2, 4, 4, 4, 5, 9], [1, 1, 2, 4, 4, 4, 6, 8], [1, 1, 2, 4, 4, 4, 7, 7], [1, 1, 2, 4, 4, 5, 5, 8], [1, 1, 2, 4, 4, 5, 6, 7], [1, 1, 2, 4, 4, 6, 6, 6], [1, 1, 2, 4, 4, 8, 10], [1, 1, 2, 4, 4, 9, 9], [1, 1, 2, 4, 5, 5, 5, 7], [1, 1, 2, 4, 5, 5, 6, 6], [1, 1, 2, 4, 5, 7, 10], [1, 1, 2, 4, 5, 8, 9], [1, 1, 2, 4, 6, 6, 10], [1, 1, 2, 4, 6, 7, 9], [1, 1, 2, 4, 6, 8, 8], [1, 1, 2, 4, 7, 7, 8], [1, 1, 2, 5, 5, 6, 10], [1, 1, 2, 5, 5, 7, 9], [1, 1, 2, 5, 5, 8, 8], [1, 1, 2, 5, 6, 6, 9], [1, 1, 2, 5, 6, 7, 8], [1, 1, 2, 5, 7, 7, 7], [1, 1, 2, 6, 6, 6, 8], [1, 1, 2, 6, 6, 7, 7], [1, 1, 2, 6, 10, 10], [1, 1, 2, 7, 9, 10], [1, 1, 2, 8, 8, 10], [1, 1, 2, 8, 9, 9], [1, 1, 3, 3, 3, 4, 4, 4, 7], [1, 1, 3, 3, 3, 4, 4, 5, 6], [1, 1, 3, 3, 3, 4, 5, 5, 5], [1, 1, 3, 3, 3, 4, 5, 10], [1, 1, 3, 3, 3, 4, 6, 9], [1, 1, 3, 3, 3, 4, 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[2, 2, 2, 3, 4, 5, 6, 6], [2, 2, 2, 3, 4, 7, 10], [2, 2, 2, 3, 4, 8, 9], [2, 2, 2, 3, 5, 5, 5, 6], [2, 2, 2, 3, 5, 6, 10], [2, 2, 2, 3, 5, 7, 9], [2, 2, 2, 3, 5, 8, 8], [2, 2, 2, 3, 6, 6, 9], [2, 2, 2, 3, 6, 7, 8], [2, 2, 2, 3, 7, 7, 7], [2, 2, 2, 4, 4, 4, 5, 7], [2, 2, 2, 4, 4, 4, 6, 6], [2, 2, 2, 4, 4, 5, 5, 6], [2, 2, 2, 4, 4, 6, 10], [2, 2, 2, 4, 4, 7, 9], [2, 2, 2, 4, 4, 8, 8], [2, 2, 2, 4, 5, 5, 10], [2, 2, 2, 4, 5, 6, 9], [2, 2, 2, 4, 5, 7, 8], [2, 2, 2, 4, 6, 6, 8], [2, 2, 2, 4, 6, 7, 7], [2, 2, 2, 4, 10, 10], [2, 2, 2, 5, 5, 5, 9], [2, 2, 2, 5, 5, 6, 8], [2, 2, 2, 5, 5, 7, 7], [2, 2, 2, 5, 6, 6, 7], [2, 2, 2, 5, 9, 10], [2, 2, 2, 6, 8, 10], [2, 2, 2, 6, 9, 9], [2, 2, 2, 7, 7, 10], [2, 2, 2, 7, 8, 9], [2, 2, 2, 8, 8, 8], [2, 2, 3, 3, 3, 4, 4, 4, 5], [2, 2, 3, 3, 3, 4, 4, 9], [2, 2, 3, 3, 3, 4, 5, 8], [2, 2, 3, 3, 3, 4, 6, 7], [2, 2, 3, 3, 3, 5, 5, 7], [2, 2, 3, 3, 3, 5, 6, 6], [2, 2, 3, 3, 3, 7, 10], [2, 2, 3, 3, 3, 8, 9], [2, 2, 3, 3, 4, 4, 4, 8], [2, 2, 3, 3, 4, 4, 5, 7], [2, 2, 3, 3, 4, 4, 6, 6], [2, 2, 3, 3, 4, 5, 5, 6], [2, 2, 3, 3, 4, 6, 10], [2, 2, 3, 3, 4, 7, 9], [2, 2, 3, 3, 4, 8, 8], [2, 2, 3, 3, 5, 5, 10], [2, 2, 3, 3, 5, 6, 9], [2, 2, 3, 3, 5, 7, 8], [2, 2, 3, 3, 6, 6, 8], [2, 2, 3, 3, 6, 7, 7], [2, 2, 3, 3, 10, 10], [2, 2, 3, 4, 4, 4, 5, 6], [2, 2, 3, 4, 4, 5, 5, 5], [2, 2, 3, 4, 4, 5, 10], [2, 2, 3, 4, 4, 6, 9], [2, 2, 3, 4, 4, 7, 8], [2, 2, 3, 4, 5, 5, 9], [2, 2, 3, 4, 5, 6, 8], [2, 2, 3, 4, 5, 7, 7], [2, 2, 3, 4, 6, 6, 7], [2, 2, 3, 4, 9, 10], [2, 2, 3, 5, 5, 5, 8], [2, 2, 3, 5, 5, 6, 7], [2, 2, 3, 5, 6, 6, 6], [2, 2, 3, 5, 8, 10], [2, 2, 3, 5, 9, 9], [2, 2, 3, 6, 7, 10], [2, 2, 3, 6, 8, 9], [2, 2, 3, 7, 7, 9], [2, 2, 3, 7, 8, 8], [2, 2, 4, 4, 4, 5, 9], [2, 2, 4, 4, 4, 6, 8], [2, 2, 4, 4, 4, 7, 7], [2, 2, 4, 4, 5, 5, 8], [2, 2, 4, 4, 5, 6, 7], [2, 2, 4, 4, 6, 6, 6], [2, 2, 4, 4, 8, 10], [2, 2, 4, 4, 9, 9], [2, 2, 4, 5, 5, 5, 7], [2, 2, 4, 5, 5, 6, 6], [2, 2, 4, 5, 7, 10], [2, 2, 4, 5, 8, 9], [2, 2, 4, 6, 6, 10], [2, 2, 4, 6, 7, 9], [2, 2, 4, 6, 8, 8], [2, 2, 4, 7, 7, 8], [2, 2, 5, 5, 6, 10], [2, 2, 5, 5, 7, 9], [2, 2, 5, 5, 8, 8], [2, 2, 5, 6, 6, 9], [2, 2, 5, 6, 7, 8], [2, 2, 5, 7, 7, 7], [2, 2, 6, 6, 6, 8], [2, 2, 6, 6, 7, 7], [2, 2, 6, 10, 10], [2, 2, 7, 9, 10], [2, 2, 8, 8, 10], [2, 2, 8, 9, 9], [2, 3, 3, 3, 4, 4, 4, 7], [2, 3, 3, 3, 4, 4, 5, 6], [2, 3, 3, 3, 4, 5, 5, 5], [2, 3, 3, 3, 4, 5, 10], [2, 3, 3, 3, 4, 6, 9], [2, 3, 3, 3, 4, 7, 8], [2, 3, 3, 3, 5, 5, 9], [2, 3, 3, 3, 5, 6, 8], [2, 3, 3, 3, 5, 7, 7], [2, 3, 3, 3, 6, 6, 7], [2, 3, 3, 3, 9, 10], [2, 3, 3, 4, 4, 4, 5, 5], [2, 3, 3, 4, 4, 4, 10], [2, 3, 3, 4, 4, 5, 9], [2, 3, 3, 4, 4, 6, 8], [2, 3, 3, 4, 4, 7, 7], [2, 3, 3, 4, 5, 5, 8], [2, 3, 3, 4, 5, 6, 7], [2, 3, 3, 4, 6, 6, 6], [2, 3, 3, 4, 8, 10], [2, 3, 3, 4, 9, 9], [2, 3, 3, 5, 5, 5, 7], [2, 3, 3, 5, 5, 6, 6], [2, 3, 3, 5, 7, 10], [2, 3, 3, 5, 8, 9], [2, 3, 3, 6, 6, 10], [2, 3, 3, 6, 7, 9], [2, 3, 3, 6, 8, 8], [2, 3, 3, 7, 7, 8], [2, 3, 4, 4, 4, 5, 8], [2, 3, 4, 4, 4, 6, 7], [2, 3, 4, 4, 5, 5, 7], [2, 3, 4, 4, 5, 6, 6], [2, 3, 4, 4, 7, 10], [2, 3, 4, 4, 8, 9], [2, 3, 4, 5, 5, 5, 6], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 8, 8], [2, 3, 4, 6, 6, 9], [2, 3, 4, 6, 7, 8], [2, 3, 4, 7, 7, 7], [2, 3, 5, 5, 5, 10], [2, 3, 5, 5, 6, 9], [2, 3, 5, 5, 7, 8], [2, 3, 5, 6, 6, 8], [2, 3, 5, 6, 7, 7], [2, 3, 5, 10, 10], [2, 3, 6, 6, 6, 7], [2, 3, 6, 9, 10], [2, 3, 7, 8, 10], [2, 3, 7, 9, 9], [2, 3, 8, 8, 9], [2, 4, 4, 4, 5, 5, 6], [2, 4, 4, 4, 6, 10], [2, 4, 4, 4, 7, 9], [2, 4, 4, 4, 8, 8], [2, 4, 4, 5, 5, 10], [2, 4, 4, 5, 6, 9], [2, 4, 4, 5, 7, 8], [2, 4, 4, 6, 6, 8], [2, 4, 4, 6, 7, 7], [2, 4, 4, 10, 10], [2, 4, 5, 5, 5, 9], [2, 4, 5, 5, 6, 8], [2, 4, 5, 5, 7, 7], [2, 4, 5, 6, 6, 7], [2, 4, 5, 9, 10], [2, 4, 6, 8, 10], [2, 4, 6, 9, 9], [2, 4, 7, 7, 10], [2, 4, 7, 8, 9], [2, 4, 8, 8, 8], [2, 5, 5, 5, 6, 7], [2, 5, 5, 6, 6, 6], [2, 5, 5, 8, 10], [2, 5, 5, 9, 9], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 7, 7, 9], [2, 5, 7, 8, 8], [2, 6, 6, 6, 10], [2, 6, 6, 7, 9], [2, 6, 6, 8, 8], [2, 6, 7, 7, 8], [2, 8, 10, 10], [2, 9, 9, 10], [3, 3, 3, 4, 4, 4, 9], [3, 3, 3, 4, 4, 5, 8], [3, 3, 3, 4, 4, 6, 7], [3, 3, 3, 4, 5, 5, 7], [3, 3, 3, 4, 5, 6, 6], [3, 3, 3, 4, 7, 10], [3, 3, 3, 4, 8, 9], [3, 3, 3, 5, 5, 5, 6], [3, 3, 3, 5, 6, 10], [3, 3, 3, 5, 7, 9], [3, 3, 3, 5, 8, 8], [3, 3, 3, 6, 6, 9], [3, 3, 3, 6, 7, 8], [3, 3, 3, 7, 7, 7], [3, 3, 4, 4, 4, 5, 7], [3, 3, 4, 4, 4, 6, 6], [3, 3, 4, 4, 5, 5, 6], [3, 3, 4, 4, 6, 10], [3, 3, 4, 4, 7, 9], [3, 3, 4, 4, 8, 8], [3, 3, 4, 5, 5, 10], [3, 3, 4, 5, 6, 9], [3, 3, 4, 5, 7, 8], [3, 3, 4, 6, 6, 8], [3, 3, 4, 6, 7, 7], [3, 3, 4, 10, 10], [3, 3, 5, 5, 5, 9], [3, 3, 5, 5, 6, 8], [3, 3, 5, 5, 7, 7], [3, 3, 5, 6, 6, 7], [3, 3, 5, 9, 10], [3, 3, 6, 8, 10], [3, 3, 6, 9, 9], [3, 3, 7, 7, 10], [3, 3, 7, 8, 9], [3, 3, 8, 8, 8], [3, 4, 4, 4, 5, 5, 5], [3, 4, 4, 4, 5, 10], [3, 4, 4, 4, 6, 9], [3, 4, 4, 4, 7, 8], [3, 4, 4, 5, 5, 9], [3, 4, 4, 5, 6, 8], [3, 4, 4, 5, 7, 7], [3, 4, 4, 6, 6, 7], [3, 4, 4, 9, 10], [3, 4, 5, 5, 5, 8], [3, 4, 5, 5, 6, 7], [3, 4, 5, 6, 6, 6], [3, 4, 5, 8, 10], [3, 4, 5, 9, 9], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 7, 7, 9], [3, 4, 7, 8, 8], [3, 5, 5, 5, 6, 6], [3, 5, 5, 7, 10], [3, 5, 5, 8, 9], [3, 5, 6, 6, 10], [3, 5, 6, 7, 9], [3, 5, 6, 8, 8], [3, 5, 7, 7, 8], [3, 6, 6, 6, 9], [3, 6, 6, 7, 8], [3, 6, 7, 7, 7], [3, 7, 10, 10], [3, 8, 9, 10], [3, 9, 9, 9], [4, 4, 4, 5, 5, 8], [4, 4, 4, 5, 6, 7], [4, 4, 4, 6, 6, 6], [4, 4, 4, 8, 10], [4, 4, 4, 9, 9], [4, 4, 5, 5, 5, 7], [4, 4, 5, 5, 6, 6], [4, 4, 5, 7, 10], [4, 4, 5, 8, 9], [4, 4, 6, 6, 10], [4, 4, 6, 7, 9], [4, 4, 6, 8, 8], [4, 4, 7, 7, 8], [4, 5, 5, 6, 10], [4, 5, 5, 7, 9], [4, 5, 5, 8, 8], [4, 5, 6, 6, 9], [4, 5, 6, 7, 8], [4, 5, 7, 7, 7], [4, 6, 6, 6, 8], [4, 6, 6, 7, 7], [4, 6, 10, 10], [4, 7, 9, 10], [4, 8, 8, 10], [4, 8, 9, 9], [5, 5, 5, 6, 9], [5, 5, 5, 7, 8], [5, 5, 6, 6, 8], [5, 5, 6, 7, 7], [5, 5, 10, 10], [5, 6, 6, 6, 7], [5, 6, 9, 10], [5, 7, 8, 10], [5, 7, 9, 9], [5, 8, 8, 9], [6, 6, 8, 10], [6, 6, 9, 9], [6, 7, 7, 10], [6, 7, 8, 9], [6, 8, 8, 8], [7, 7, 7, 9], [7, 7, 8, 8], [10, 10, 10]]\n assert candidate(candidates = [7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 24) == [[1, 2, 3, 4, 14], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 13], [1, 2, 3, 6, 12], [1, 2, 3, 7, 11], [1, 2, 3, 18], [1, 2, 4, 5, 12], [1, 2, 4, 6, 11], [1, 2, 4, 7, 10], [1, 2, 4, 17], [1, 2, 5, 6, 10], [1, 2, 5, 16], [1, 2, 6, 15], [1, 2, 7, 14], [1, 2, 10, 11], [1, 3, 4, 5, 11], [1, 3, 4, 6, 10], [1, 3, 4, 16], [1, 3, 5, 15], [1, 3, 6, 14], [1, 3, 7, 13], [1, 3, 20], [1, 4, 5, 14], [1, 4, 6, 13], [1, 4, 7, 12], [1, 4, 19], [1, 5, 6, 12], [1, 5, 7, 11], [1, 5, 18], [1, 6, 7, 10], [1, 6, 17], [1, 7, 16], [1, 10, 13], [1, 11, 12], [2, 3, 4, 5, 10], [2, 3, 4, 15], [2, 3, 5, 14], [2, 3, 6, 13], [2, 3, 7, 12], [2, 3, 19], [2, 4, 5, 6, 7], [2, 4, 5, 13], [2, 4, 6, 12], [2, 4, 7, 11], [2, 4, 18], [2, 5, 6, 11], [2, 5, 7, 10], [2, 5, 17], [2, 6, 16], [2, 7, 15], [2, 10, 12], [3, 4, 5, 12], [3, 4, 6, 11], [3, 4, 7, 10], [3, 4, 17], [3, 5, 6, 10], [3, 5, 16], [3, 6, 15], [3, 7, 14], [3, 10, 11], [4, 5, 15], [4, 6, 14], [4, 7, 13], [4, 20], [5, 6, 13], [5, 7, 12], [5, 19], [6, 7, 11], [6, 18], [7, 17], [10, 14], [11, 13]]\n assert candidate(candidates = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],target = 15) == [[1, 2, 3, 4, 5], [1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [1, 4, 10], [1, 5, 9], [1, 6, 8], [2, 3, 4, 6], [2, 3, 10], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6], [5, 10], [6, 9], [7, 8]]\n assert candidate(candidates = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],target = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 15], [1, 2, 3, 4, 6, 14], [1, 2, 3, 4, 7, 13], [1, 2, 3, 4, 8, 12], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 20], [1, 2, 3, 5, 6, 13], [1, 2, 3, 5, 7, 12], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 19], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 18], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 17], [1, 2, 3, 8, 16], [1, 2, 3, 9, 15], [1, 2, 3, 10, 14], [1, 2, 3, 11, 13], [1, 2, 3, 24], [1, 2, 4, 5, 6, 12], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 18], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 17], [1, 2, 4, 7, 16], [1, 2, 4, 8, 15], [1, 2, 4, 9, 14], [1, 2, 4, 10, 13], [1, 2, 4, 11, 12], [1, 2, 4, 23], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 16], [1, 2, 5, 7, 15], [1, 2, 5, 8, 14], [1, 2, 5, 9, 13], [1, 2, 5, 10, 12], [1, 2, 5, 22], [1, 2, 6, 7, 14], [1, 2, 6, 8, 13], [1, 2, 6, 9, 12], [1, 2, 6, 10, 11], [1, 2, 6, 21], [1, 2, 7, 8, 12], [1, 2, 7, 9, 11], [1, 2, 7, 20], [1, 2, 8, 9, 10], [1, 2, 8, 19], [1, 2, 9, 18], [1, 2, 10, 17], [1, 2, 11, 16], [1, 2, 12, 15], [1, 2, 13, 14], [1, 2, 27], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 17], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 16], [1, 3, 4, 7, 15], [1, 3, 4, 8, 14], [1, 3, 4, 9, 13], [1, 3, 4, 10, 12], [1, 3, 4, 22], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 15], [1, 3, 5, 7, 14], [1, 3, 5, 8, 13], [1, 3, 5, 9, 12], [1, 3, 5, 10, 11], [1, 3, 5, 21], [1, 3, 6, 7, 13], [1, 3, 6, 8, 12], [1, 3, 6, 9, 11], [1, 3, 6, 20], [1, 3, 7, 8, 11], [1, 3, 7, 9, 10], [1, 3, 7, 19], [1, 3, 8, 18], [1, 3, 9, 17], [1, 3, 10, 16], [1, 3, 11, 15], [1, 3, 12, 14], [1, 3, 26], [1, 4, 5, 6, 14], [1, 4, 5, 7, 13], [1, 4, 5, 8, 12], [1, 4, 5, 9, 11], [1, 4, 5, 20], [1, 4, 6, 7, 12], [1, 4, 6, 8, 11], [1, 4, 6, 9, 10], [1, 4, 6, 19], [1, 4, 7, 8, 10], [1, 4, 7, 18], [1, 4, 8, 17], [1, 4, 9, 16], [1, 4, 10, 15], [1, 4, 11, 14], [1, 4, 12, 13], [1, 4, 25], [1, 5, 6, 7, 11], [1, 5, 6, 8, 10], [1, 5, 6, 18], [1, 5, 7, 8, 9], [1, 5, 7, 17], [1, 5, 8, 16], [1, 5, 9, 15], [1, 5, 10, 14], [1, 5, 11, 13], [1, 5, 24], [1, 6, 7, 16], [1, 6, 8, 15], [1, 6, 9, 14], [1, 6, 10, 13], [1, 6, 11, 12], [1, 6, 23], [1, 7, 8, 14], [1, 7, 9, 13], [1, 7, 10, 12], [1, 7, 22], [1, 8, 9, 12], [1, 8, 10, 11], [1, 8, 21], [1, 9, 20], [1, 10, 19], [1, 11, 18], [1, 12, 17], [1, 13, 16], [1, 14, 15], [1, 29], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 16], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 15], [2, 3, 4, 7, 14], [2, 3, 4, 8, 13], [2, 3, 4, 9, 12], [2, 3, 4, 10, 11], [2, 3, 4, 21], [2, 3, 5, 6, 14], [2, 3, 5, 7, 13], [2, 3, 5, 8, 12], [2, 3, 5, 9, 11], [2, 3, 5, 20], [2, 3, 6, 7, 12], [2, 3, 6, 8, 11], [2, 3, 6, 9, 10], [2, 3, 6, 19], [2, 3, 7, 8, 10], [2, 3, 7, 18], [2, 3, 8, 17], [2, 3, 9, 16], [2, 3, 10, 15], [2, 3, 11, 14], [2, 3, 12, 13], [2, 3, 25], [2, 4, 5, 6, 13], [2, 4, 5, 7, 12], [2, 4, 5, 8, 11], [2, 4, 5, 9, 10], [2, 4, 5, 19], [2, 4, 6, 7, 11], [2, 4, 6, 8, 10], [2, 4, 6, 18], [2, 4, 7, 8, 9], [2, 4, 7, 17], [2, 4, 8, 16], [2, 4, 9, 15], [2, 4, 10, 14], [2, 4, 11, 13], [2, 4, 24], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 6, 17], [2, 5, 7, 16], [2, 5, 8, 15], [2, 5, 9, 14], [2, 5, 10, 13], [2, 5, 11, 12], [2, 5, 23], [2, 6, 7, 15], [2, 6, 8, 14], [2, 6, 9, 13], [2, 6, 10, 12], [2, 6, 22], [2, 7, 8, 13], [2, 7, 9, 12], [2, 7, 10, 11], [2, 7, 21], [2, 8, 9, 11], [2, 8, 20], [2, 9, 19], [2, 10, 18], [2, 11, 17], [2, 12, 16], [2, 13, 15], [2, 28], [3, 4, 5, 6, 12], [3, 4, 5, 7, 11], [3, 4, 5, 8, 10], [3, 4, 5, 18], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 6, 17], [3, 4, 7, 16], [3, 4, 8, 15], [3, 4, 9, 14], [3, 4, 10, 13], [3, 4, 11, 12], [3, 4, 23], [3, 5, 6, 7, 9], [3, 5, 6, 16], [3, 5, 7, 15], [3, 5, 8, 14], [3, 5, 9, 13], [3, 5, 10, 12], [3, 5, 22], [3, 6, 7, 14], [3, 6, 8, 13], [3, 6, 9, 12], [3, 6, 10, 11], [3, 6, 21], [3, 7, 8, 12], [3, 7, 9, 11], [3, 7, 20], [3, 8, 9, 10], [3, 8, 19], [3, 9, 18], [3, 10, 17], [3, 11, 16], [3, 12, 15], [3, 13, 14], [3, 27], [4, 5, 6, 7, 8], [4, 5, 6, 15], [4, 5, 7, 14], [4, 5, 8, 13], [4, 5, 9, 12], [4, 5, 10, 11], [4, 5, 21], [4, 6, 7, 13], [4, 6, 8, 12], [4, 6, 9, 11], [4, 6, 20], [4, 7, 8, 11], [4, 7, 9, 10], [4, 7, 19], [4, 8, 18], [4, 9, 17], [4, 10, 16], [4, 11, 15], [4, 12, 14], [4, 26], [5, 6, 7, 12], [5, 6, 8, 11], [5, 6, 9, 10], [5, 6, 19], [5, 7, 8, 10], [5, 7, 18], [5, 8, 17], [5, 9, 16], [5, 10, 15], [5, 11, 14], [5, 12, 13], [5, 25], [6, 7, 8, 9], [6, 7, 17], [6, 8, 16], [6, 9, 15], [6, 10, 14], [6, 11, 13], [6, 24], [7, 8, 15], [7, 9, 14], [7, 10, 13], [7, 11, 12], [7, 23], [8, 9, 13], [8, 10, 12], [8, 22], [9, 10, 11], [9, 21], [10, 20], [11, 19], [12, 18], [13, 17], [14, 16], [30]]\n assert candidate(candidates = [2, 3, 6, 7, 2, 5, 5, 10],target = 15) == [[2, 2, 5, 6], [2, 3, 5, 5], [2, 3, 10], [2, 6, 7], [3, 5, 7], [5, 10]]\n"}, "metadata": {"canonical_parameter_names": ["candidates", "target"], "leetcode_dataset_entry_point": "Solution().combinationSum2", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var combinationSum2 = function(candidates, target) {", "container": null, "callable": "combinationSum2", "parameters": [{"name": "candidates", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 41, "task_id": "first-missing-positive", "difficulty": "Hard", "problem_description": "Given an unsorted integer array nums. Return the smallest positive integer that is not present in nums.\nYou must implement an algorithm that runs in O(n) time and uses O(1) auxiliary space.\n \nExample 1:\n\nInput: nums = [1,2,0]\nOutput: 3\nExplanation: The numbers in the range [1,2] are all in the array.\n\nExample 2:\n\nInput: nums = [3,4,-1,1]\nOutput: 2\nExplanation: 1 is in the array but 2 is missing.\n\nExample 3:\n\nInput: nums = [7,8,9,11,12]\nOutput: 1\nExplanation: The smallest positive integer 1 is missing.\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-231 <= nums[i] <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1000000, -1000000, 500000]) == 1\n assert candidate(nums = [1000000, -1000000, 1]) == 2\n assert candidate(nums = [1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 2, 2]) == 3\n assert candidate(nums = [2147483647, 1, 2, 0]) == 3\n assert candidate(nums = [-1, -2, -3]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [1]) == 2\n assert candidate(nums = [2]) == 1\n assert candidate(nums = [7, 8, 9, 11, 12]) == 1\n assert candidate(nums = [0, -1, -2]) == 1\n assert candidate(nums = [1, 3, 2]) == 4\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = []) == 1\n assert candidate(nums = [0]) == 1\n assert candidate(nums = [2147483647, -2147483648, 0]) == 1\n assert candidate(nums = [0, -1, -2, -3]) == 1\n assert candidate(nums = [1000000, -1000000, 0]) == 1\n assert candidate(nums = [1, 2, 3]) == 4\n assert candidate(nums = [3, 4, -1, 1]) == 2\n assert candidate(nums = [1000000, 1000001, 1000002]) == 1\n assert candidate(nums = [2, 2]) == 1\n assert candidate(nums = [1, 2, 0]) == 3\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 11\n assert candidate(nums = [7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 1\n assert candidate(nums = [2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1]) == 4\n assert candidate(nums = [-10, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 11\n assert candidate(nums = [3, 4, -1, 1, 2, 5]) == 6\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25]) == 21\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1]) == 11\n assert candidate(nums = [100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, 900000, 1000000]) == 1\n assert candidate(nums = [3, 1, -1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 20\n assert candidate(nums = [2147483647, -2147483648, 0, 1, 2, 3, 4, 5]) == 6\n assert candidate(nums = [5, 3, 5, 2, 3, 3, 9, 0, 123, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 101\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 21\n assert candidate(nums = [1, 2, 0, 4, 6, 3, 8, 5, 7]) == 9\n assert candidate(nums = [2, 3, 1, -1, -2, -3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 21\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, -1, -2, -3, -4, -5]) == 21\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [1, 2, 0, 5, 3, 7, 8, 9, 4, 6]) == 10\n assert candidate(nums = [5, 3, 2, 1, 4, 6, 8, 7, 10, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 41\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0]) == 30\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 11\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 20\n assert candidate(nums = [-10, -20, -30, -40, -50, 100, 200, 300, 400, 500]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]) == 11\n assert candidate(nums = [-5, -4, -3, -2, -1]) == 1\n assert candidate(nums = [100000, 100001, 100002, 100003, 100004, 100005, 100006, 100007, 100008, 100009, 100010, 100011, 100012, 100013, 100014, 100015, 100016, 100017, 100018, 100019]) == 1\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22]) == 21\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 1\n assert candidate(nums = [2, 3, -7, 6, 8, 1, -10, 15]) == 4\n assert candidate(nums = [1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 3\n assert candidate(nums = [0, 2, 2, 1, 3, 5, 4]) == 6\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == 1\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 3\n assert candidate(nums = [3, 4, -1, 1, 5, 2]) == 6\n assert candidate(nums = [3, 2, 1, 5, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 31\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991]) == 1\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1\n assert candidate(nums = [5, 3, 1, 2, 4, 6, 8, 7, 10, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 31\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [100000, 100001, 100002, 100003, 100004, 100005, 100006, 100007, 100008, 100009, 1]) == 2\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 1\n assert candidate(nums = [100000, 100001, 100002, 100003, 100004, 100005, 100006, 100007, 100008, 100009, -1]) == 1\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6]) == 7\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30]) == 22\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 26\n assert candidate(nums = [1000000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]) == 11\n assert candidate(nums = [-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991, -99990, -99989, -99988, -99987, -99986, -99985, -99984, -99983, -99982, -99981]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 41\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 1\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 11\n assert candidate(nums = [5, 3, 4, 1, 2, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 6\n assert candidate(nums = [3, 4, -1, 1, 5, 6, 2]) == 7\n assert candidate(nums = [5, 3, 1, 2, 4, 6, 8, 7, 9, 11, 10, 13, 12, 14, 15, 16, 17, 18, 19, 20]) == 21\n assert candidate(nums = [10000, 10001, 10002, 10003, 10004, 10005, 10006, 10007, 10008, 10009]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 31\n assert candidate(nums = [2147483647, -2147483648, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 10\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 21\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 11\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 4\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 1\n assert candidate(nums = [3, 4, -1, 1, 5, 2, 7, 8, 9, 10]) == 6\n assert candidate(nums = [100, 4, 200, 1, 3, 2]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 16\n assert candidate(nums = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32]) == 31\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [2147483647, -2147483648, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200]) == 1\n assert candidate(nums = [100000, 100001, 100002, 100003, 100004, 100005, 100006, 100007, 100008, 100009, 100010]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, -1, -2, -3]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 21\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 11]) == 10\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 6\n assert candidate(nums = [1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 3\n assert candidate(nums = [5, 3, 1, 4, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 21\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 2\n assert candidate(nums = [1, 2, 0, 0, 0, 0, 0]) == 3\n assert candidate(nums = [3, 5, -2, 1, 4, 2, 3, 6]) == 7\n assert candidate(nums = [1, 2, 0, 4, 5, 6, 7, 8, 9, 10]) == 3\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]) == 20\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 1\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1\n assert candidate(nums = [2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 1\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == 6\n assert candidate(nums = [1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [0, 0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [0, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [1, 1000000, 2, 999999, 3, 999998, 4, 999997, 5, 999996, 6, 999995, 7, 999994, 8, 999993, 9, 999992, 10, 999991, 11, 999990, 12, 999989, 13, 999988, 14, 999987, 15, 999986, 16, 999985, 17, 999984, 18, 999983, 19, 999982, 20, 999981, 21, 999980, 22, 999979, 23, 999978, 24, 999977, 25, 999976, 26, 999975, 27, 999974, 28, 999973, 29, 999972, 30, 999971, 31, 999970, 32, 999969, 33, 999968, 34, 999967, 35, 999966, 36, 999965, 37, 999964, 38, 999963, 39, 999962, 40, 999961, 41, 999960, 42, 999959, 43, 999958, 44, 999957, 45, 999956, 46, 999955, 47, 999954, 48, 999953, 49, 999952, 50, 999951]) == 51\n assert candidate(nums = [3, 5, -7, 1, 2, 4, 6, 8, 9, 10]) == 7\n assert candidate(nums = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [5, 1, 4, 3, 2]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, -1, -2, -3, -4, -5]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, -1, -2, -3, -4, -5]) == 16\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().firstMissingPositive", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var firstMissingPositive = function(nums) {", "container": null, "callable": "firstMissingPositive", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 42, "task_id": "trapping-rain-water", "difficulty": "Hard", "problem_description": "Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.\n \nExample 1:\n\n\nInput: height = [0,1,0,2,1,0,1,3,2,1,2,1]\nOutput: 6\nExplanation: The above elevation map (black section) is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of rain water (blue section) are being trapped.\n\nExample 2:\n\nInput: height = [4,2,0,3,2,5]\nOutput: 9\n\n \nConstraints:\n\nn == height.length\n1 <= n <= 2 * 104\n0 <= height[i] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(height = [3, 1, 2, 1, 4, 3, 2, 1, 5]) == 11\n assert candidate(height = [3, 0, 1, 3, 0, 1, 3]) == 10\n assert candidate(height = [5, 4, 3, 2, 1]) == 0\n assert candidate(height = [1]) == 0\n assert candidate(height = [2, 0, 2]) == 2\n assert candidate(height = [0, 0, 1, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(height = [1, 1, 1, 1, 1, 1]) == 0\n assert candidate(height = [1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 1, 2]) == 12\n assert candidate(height = [1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 1]) == 10\n assert candidate(height = [0, 0, 0, 0, 0]) == 0\n assert candidate(height = [1, 2, 3, 4, 5, 4, 3, 2, 1]) == 0\n assert candidate(height = [0, 0, 0, 0]) == 0\n assert candidate(height = [5, 4, 1, 2]) == 1\n assert candidate(height = [3, 0, 1, 3, 0, 1, 1, 3, 2, 1, 2, 1]) == 13\n assert candidate(height = [4, 2, 0, 3, 2, 5]) == 9\n assert candidate(height = [3, 0, 0, 2, 0, 4]) == 10\n assert candidate(height = [5, 4, 3, 2, 1, 2, 3, 4, 5]) == 16\n assert candidate(height = [1, 0, 2, 0, 1, 0, 3, 1, 0, 1, 2]) == 10\n assert candidate(height = [0, 2, 0, 2, 0]) == 2\n assert candidate(height = [1, 0, 0, 0, 1]) == 3\n assert candidate(height = [3, 0, 1, 3, 0, 1, 2, 1, 2, 1]) == 9\n assert candidate(height = [0, 5, 0, 5, 0]) == 5\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]) == 6\n assert candidate(height = [1, 0, 1, 0, 1]) == 2\n assert candidate(height = [1, 2, 3, 4, 5]) == 0\n assert candidate(height = [2, 1, 0, 2]) == 3\n assert candidate(height = [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == 81\n assert candidate(height = [0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 0]) == 36\n assert candidate(height = [10, 0, 10, 0, 10, 0, 10, 0, 10, 0, 10, 0, 10]) == 60\n assert candidate(height = [6, 4, 2, 0, 3, 2, 0, 3, 1, 4, 5, 3, 2, 7, 5, 3, 0, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1]) == 52\n assert candidate(height = [10, 0, 10, 0, 10, 0, 10, 0, 10]) == 40\n assert candidate(height = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 25\n assert candidate(height = [100, 80, 60, 40, 20, 0, 20, 40, 60, 80, 100]) == 500\n assert candidate(height = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 6\n assert candidate(height = [0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1]) == 12\n assert candidate(height = [10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10]) == 25\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(height = [0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0]) == 50\n assert candidate(height = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 8\n assert candidate(height = [1, 2, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 0, 3, 2, 1, 2, 1, 5]) == 21\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 0, 1]) == 13\n assert candidate(height = [6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6]) == 25\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7]) == 19\n assert candidate(height = [0, 1, 2, 1, 0, 1, 3, 1, 0, 1, 2, 1, 0]) == 8\n assert candidate(height = [10, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == 72\n assert candidate(height = [0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 0]) == 5\n assert candidate(height = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 0, 1, 2, 3, 4, 5]) == 35\n assert candidate(height = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 4, 2, 1, 3, 2, 1, 2, 1]) == 15\n assert candidate(height = [10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 25\n assert candidate(height = [5, 2, 1, 2, 1, 5, 1, 2, 1, 5, 1, 2, 1, 2, 1, 5]) == 43\n assert candidate(height = [2, 1, 0, 1, 2]) == 4\n assert candidate(height = [10, 0, 10, 0, 10, 0, 10]) == 30\n assert candidate(height = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 9\n assert candidate(height = [1, 0, 2, 0, 1, 0, 1, 3, 2, 1, 2, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]) == 42\n assert candidate(height = [2, 8, 5, 5, 5, 9, 8, 9, 2]) == 10\n assert candidate(height = [1, 7, 8, 8, 6, 4, 3, 1, 1, 0, 1, 7, 6, 5, 4, 3, 2, 1, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1]) == 40\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(height = [1, 2, 3, 4, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1]) == 14\n assert candidate(height = [5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0]) == 18\n assert candidate(height = [4, 2, 0, 6, 2, 3, 8, 0, 4, 4, 1, 2, 2, 2, 3, 3, 4, 0, 1, 0, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2]) == 39\n assert candidate(height = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(height = [2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0]) == 18\n assert candidate(height = [1, 2, 3, 0, 1, 2, 0, 1, 2, 0, 1, 2]) == 9\n assert candidate(height = [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 23\n assert candidate(height = [0, 5, 4, 3, 2, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == 37\n assert candidate(height = [2, 1, 0, 1, 2, 1, 0, 1, 2, 1]) == 8\n assert candidate(height = [0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0]) == 4\n assert candidate(height = [1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0]) == 16\n assert candidate(height = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 81\n assert candidate(height = [3, 0, 1, 3, 0, 1, 2, 0, 2]) == 10\n assert candidate(height = [5, 0, 3, 0, 0, 0, 2, 0, 4, 0, 0, 1, 0, 0, 5]) == 55\n assert candidate(height = [3, 0, 3, 0, 3, 0, 3, 0, 3, 0]) == 12\n assert candidate(height = [0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5]) == 50\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 9\n assert candidate(height = [0, 2, 0, 2, 0, 3, 0, 3, 0, 2, 0, 2]) == 11\n assert candidate(height = [3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 2, 0, 1, 0]) == 20\n assert candidate(height = [5, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 5, 1, 2, 1, 2, 1, 5]) == 86\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 0, 1, 2, 1, 0, 2, 1, 0]) == 13\n assert candidate(height = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 4\n assert candidate(height = [0, 1, 2, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 0, 3, 2, 1, 2, 1, 0, 5, 0, 4]) == 28\n assert candidate(height = [0, 2, 0, 2, 0, 3, 0, 3, 0, 4]) == 10\n assert candidate(height = [5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1]) == 30\n assert candidate(height = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 52\n assert candidate(height = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 6\n assert candidate(height = [4, 2, 0, 3, 2, 5, 0, 5, 2, 3, 0, 2, 4, 0, 5]) == 33\n assert candidate(height = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]) == 5\n assert candidate(height = [3, 2, 1, 2, 3]) == 4\n assert candidate(height = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 7\n assert candidate(height = [1, 8, 6, 2, 5, 4, 8, 3, 7, 9, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]) == 35\n assert candidate(height = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 9\n assert candidate(height = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 12\n assert candidate(height = [4, 2, 3, 0, 3, 5, 3, 2, 1, 5, 3, 0, 3, 5, 3, 0, 3, 5, 2, 1]) == 35\n assert candidate(height = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 5\n assert candidate(height = [7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7]) == 36\n assert candidate(height = [3, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 6\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 4, 2, 1, 0, 1, 3]) == 19\n assert candidate(height = [1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1]) == 12\n assert candidate(height = [1, 2, 3, 0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 0, 3]) == 24\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7]) == 49\n assert candidate(height = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 100\n assert candidate(height = [3, 0, 1, 0, 2, 0, 4, 0, 3, 0, 5, 0]) == 21\n assert candidate(height = [5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5]) == 35\n assert candidate(height = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 0, 3, 2, 1, 2, 1]) == 15\n assert candidate(height = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 9\n assert candidate(height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1, 0, 1, 0, 1, 3, 2, 1, 2, 1]) == 22\n assert candidate(height = [2, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2]) == 13\n assert candidate(height = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 6\n assert candidate(height = [5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5]) == 60\n assert candidate(height = [1, 3, 2, 4, 1, 3, 1, 4, 5, 2, 2, 1]) == 8\n assert candidate(height = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]) == 12\n assert candidate(height = [5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5]) == 4\n assert candidate(height = [5, 2, 1, 2, 1, 5]) == 14\n assert candidate(height = [0, 2, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]) == 7\n assert candidate(height = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(height = [2, 0, 2, 0, 2, 0, 2]) == 6\n assert candidate(height = [0, 1, 2, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1]) == 7\n assert candidate(height = [0, 2, 0, 2, 0, 3, 0, 3, 0, 2, 0, 2, 0]) == 11\n assert candidate(height = [5, 5, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 5, 5]) == 36\n assert candidate(height = [3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0]) == 0\n assert candidate(height = [6, 4, 2, 0, 3, 0, 1, 4, 6, 2, 3, 5, 1, 0, 5, 4, 3, 2, 1, 0]) == 42\n assert candidate(height = [5, 0, 3, 0, 0, 5, 0, 0, 2, 4]) == 27\n assert candidate(height = [3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1]) == 16\n assert candidate(height = [5, 5, 1, 7, 1, 1, 5, 2, 7, 6]) == 23\n assert candidate(height = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 9\n assert candidate(height = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n"}, "metadata": {"canonical_parameter_names": ["height"], "leetcode_dataset_entry_point": "Solution().trap", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var trap = function(height) {", "container": null, "callable": "trap", "parameters": [{"name": "height", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 43, "task_id": "multiply-strings", "difficulty": "Medium", "problem_description": "Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.\nNote: You must not use any built-in BigInteger library or convert the inputs to integer directly.\n \nExample 1:\nInput: num1 = \"2\", num2 = \"3\"\nOutput: \"6\"\nExample 2:\nInput: num1 = \"123\", num2 = \"456\"\nOutput: \"56088\"\n\n \nConstraints:\n\n1 <= num1.length, num2.length <= 200\nnum1 and num2 consist of digits only.\nBoth num1 and num2 do not contain any leading zero, except the number 0 itself.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num1 = \"999999999999999999\",num2 = \"888888888888888888\") == \"888888888888888887111111111111111112\"\n assert candidate(num1 = \"0\",num2 = \"12345\") == \"0\"\n assert candidate(num1 = \"2\",num2 = \"3\") == \"6\"\n assert candidate(num1 = \"123456789\",num2 = \"987654321\") == \"121932631112635269\"\n assert candidate(num1 = \"1000\",num2 = \"1000\") == \"1000000\"\n assert candidate(num1 = \"10\",num2 = \"10\") == \"100\"\n assert candidate(num1 = \"0\",num2 = \"123\") == \"0\"\n assert candidate(num1 = \"1\",num2 = \"1\") == \"1\"\n assert candidate(num1 = \"0\",num2 = \"5678\") == \"0\"\n assert candidate(num1 = \"100\",num2 = \"200\") == \"20000\"\n assert candidate(num1 = \"100\",num2 = \"100\") == \"10000\"\n assert candidate(num1 = \"0\",num2 = \"567\") == \"0\"\n assert candidate(num1 = \"999\",num2 = \"999\") == \"998001\"\n assert candidate(num1 = \"1111\",num2 = \"1111\") == \"1234321\"\n assert candidate(num1 = \"123\",num2 = \"456\") == \"56088\"\n assert candidate(num1 = \"987654321\",num2 = \"123456789\") == \"121932631112635269\"\n assert candidate(num1 = \"100000000000000000000\",num2 = \"2\") == \"200000000000000000000\"\n assert candidate(num1 = \"99999999999999999999\",num2 = \"99999999999999999999\") == \"9999999999999999999800000000000000000001\"\n assert candidate(num1 = \"5\",num2 = \"67890\") == \"339450\"\n assert candidate(num1 = \"500000000000000000\",num2 = \"300000000000000000\") == \"150000000000000000000000000000000000\"\n assert candidate(num1 = \"100000000000000000000\",num2 = \"99999999999999999999\") == \"9999999999999999999900000000000000000000\"\n assert candidate(num1 = \"123456789012345678901234567890\",num2 = \"987654321098765432109876543210\") == \"121932631137021795226185032733622923332237463801111263526900\"\n assert candidate(num1 = \"22222222222222222222\",num2 = \"33333333333333333333\") == \"740740740740740740725925925925925925926\"\n assert candidate(num1 = \"19999999999999999999\",num2 = \"2\") == \"39999999999999999998\"\n assert candidate(num1 = \"2718281828459045235360287471352662497757247093699997\",num2 = \"3141592653589793238462643383279502884197169399375105\") == \"8539734222673567065463550869546574495034888535765230304447162480822019507433994115871905265874140374685\"\n assert candidate(num1 = \"9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\",num2 = \"9\") == \"89999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991\"\n assert candidate(num1 = \"123456789\",num2 = \"9876543210987654321\") == \"1219326311248285321112635269\"\n assert candidate(num1 = \"56789012345678901234\",num2 = \"43210987654321098765\") == \"2453909311370219463200426613308794376010\"\n assert candidate(num1 = \"2\",num2 = \"99999999999999999999\") == \"199999999999999999998\"\n assert candidate(num1 = \"1\",num2 = \"20000000000000000000\") == \"20000000000000000000\"\n assert candidate(num1 = \"99\",num2 = \"99\") == \"9801\"\n assert candidate(num1 = \"999999999999999999999999999999999999999999999999999\",num2 = \"888888888888888888888888888888888888888888888888888\") == \"888888888888888888888888888888888888888888888888887111111111111111111111111111111111111111111111111112\"\n assert candidate(num1 = \"1111111111\",num2 = \"11111111111111111111\") == \"12345679011111111110987654321\"\n assert candidate(num1 = \"18446744073709551615\",num2 = \"18446744073709551615\") == \"340282366920938463426481119284349108225\"\n assert candidate(num1 = \"1234567890\",num2 = \"0\") == \"0\"\n assert candidate(num1 = \"9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\",num2 = \"9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\") == \"99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999980000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\"\n assert candidate(num1 = \"10000000000000000000\",num2 = \"10000000000000000000\") == \"100000000000000000000000000000000000000\"\n assert candidate(num1 = \"50000000000000000000\",num2 = \"50000000000000000000\") == \"2500000000000000000000000000000000000000\"\n assert candidate(num1 = \"1234567890123456789012345678901234567890\",num2 = \"9876543210987654321098765432109876543210\") == \"12193263113702179522618503273386678859448712086533622923332237463801111263526900\"\n assert candidate(num1 = \"1000000000000000000000000000000\",num2 = \"2\") == \"2000000000000000000000000000000\"\n assert candidate(num1 = \"11111111111111111111111111111111111111111111111111\",num2 = \"11111111111111111111111111111111111111111111111111\") == \"123456790123456790123456790123456790123456790123454320987654320987654320987654320987654320987654321\"\n assert candidate(num1 = \"0\",num2 = \"0\") == \"0\"\n assert candidate(num1 = \"9\",num2 = \"9\") == \"81\"\n assert candidate(num1 = \"1\",num2 = \"9999999999999999999999999999999999999999999999999\") == \"9999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"99999999999999999999\",num2 = \"1\") == \"99999999999999999999\"\n assert candidate(num1 = \"55555555555555555555\",num2 = \"22222222222222222222\") == \"1234567901234567901209876543209876543210\"\n assert candidate(num1 = \"0\",num2 = \"1234567890\") == \"0\"\n assert candidate(num1 = \"1111111111111111111111111111111111111111111111111111\",num2 = \"2\") == \"2222222222222222222222222222222222222222222222222222\"\n assert candidate(num1 = \"987654321\",num2 = \"1234567890123456789\") == \"1219326311248285321112635269\"\n assert candidate(num1 = \"1234567890\",num2 = \"9876543210\") == \"12193263111263526900\"\n assert candidate(num1 = \"56789012345678901234567890\",num2 = \"98765432109876543210987654\") == \"5608791343414090382626730132663060260783452814830060\"\n assert candidate(num1 = \"9999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"9999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"10000000000000000000000000000000000000000000000000\",num2 = \"10000000000000000000000000000000000000000000000000\") == \"100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"999999999999999999\",num2 = \"999999999999999999\") == \"999999999999999998000000000000000001\"\n assert candidate(num1 = \"55555555555555555555\",num2 = \"55555555555555555555\") == \"3086419753086419753024691358024691358025\"\n assert candidate(num1 = \"1111111111111111111111111111111111111111111111111111\",num2 = \"999999999999999999999999999999999999999999999999999\") == \"1111111111111111111111111111111111111111111111111109888888888888888888888888888888888888888888888888889\"\n assert candidate(num1 = \"5000000000\",num2 = \"5000000000\") == \"25000000000000000000\"\n assert candidate(num1 = \"9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"1234567890123456789\",num2 = \"1234567890123456789\") == \"1524157875323883675019051998750190521\"\n assert candidate(num1 = \"12345678901234567890\",num2 = \"98765432109876543210\") == \"1219326311370217952237463801111263526900\"\n assert candidate(num1 = \"54321098765432109876543210987654321098765432109876543210987654321098765432109876543210\",num2 = \"123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890\") == \"6706308429202743325773485580862669682914799080774333119325718633057400395418222892752948635258986434993786160646167367779295611949397448712086533622923332237463801111263526900\"\n assert candidate(num1 = \"9\",num2 = \"99999999999999999999\") == \"899999999999999999991\"\n assert candidate(num1 = \"271828182845904523536028747135266249775724709369995\",num2 = \"314159265358979323846264338327950288419716939937510\") == \"85397342226735670654635508695465744950348885357650690581833014653136349617576232159238592126769012450\"\n assert candidate(num1 = \"1000000000\",num2 = \"1000000000\") == \"1000000000000000000\"\n assert candidate(num1 = \"1\",num2 = \"1000000000000000000000000000000000000000000000000000\") == \"1000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"9999\",num2 = \"1111\") == \"11108889\"\n assert candidate(num1 = \"1000000000000000000000000000000000000000000000000000\",num2 = \"1000000000000000000000000000000000000000000000000000\") == \"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"98765432109876543210\",num2 = \"12345678901234567890\") == \"1219326311370217952237463801111263526900\"\n assert candidate(num1 = \"200\",num2 = \"300\") == \"60000\"\n assert candidate(num1 = \"9876543210987654321\",num2 = \"9876543210987654321\") == \"97546105798506325256774881877789971041\"\n assert candidate(num1 = \"11111111111111111111\",num2 = \"11111111111111111111\") == \"123456790123456790120987654320987654321\"\n"}, "metadata": {"canonical_parameter_names": ["num1", "num2"], "leetcode_dataset_entry_point": "Solution().multiply", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var multiply = function(num1, num2) {", "container": null, "callable": "multiply", "parameters": [{"name": "num1", "type": "string"}, {"name": "num2", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 44, "task_id": "wildcard-matching", "difficulty": "Hard", "problem_description": "Given an input string (s) and a pattern (p), implement wildcard pattern matching with support for '?' and '*' where:\n\n'?' Matches any single character.\n'*' Matches any sequence of characters (including the empty sequence).\n\nThe matching should cover the entire input string (not partial).\n \nExample 1:\n\nInput: s = \"aa\", p = \"a\"\nOutput: false\nExplanation: \"a\" does not match the entire string \"aa\".\n\nExample 2:\n\nInput: s = \"aa\", p = \"*\"\nOutput: true\nExplanation: '*' matches any sequence.\n\nExample 3:\n\nInput: s = \"cb\", p = \"?a\"\nOutput: false\nExplanation: '?' matches 'c', but the second letter is 'a', which does not match 'b'.\n\n \nConstraints:\n\n0 <= s.length, p.length <= 2000\ns contains only lowercase English letters.\np contains only lowercase English letters, '?' or '*'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcde\",p = \"ab*e\") == True\n assert candidate(s = \"abcde\",p = \"*\") == True\n assert candidate(s = \"mississippi\",p = \"m??*ss*?i*pi\") == False\n assert candidate(s = \"aa\",p = \"a\") == False\n assert candidate(s = \"abcde\",p = \"?bcde\") == True\n assert candidate(s = \"abcde\",p = \"a*b*e\") == True\n assert candidate(s = \"cb\",p = \"?a\") == False\n assert candidate(s = \"abcabczzzde\",p = \"*abc***de*\") == True\n assert candidate(s = \"abcde\",p = \"abc?de\") == False\n assert candidate(s = \"\",p = \"\") == True\n assert candidate(s = \"abcde\",p = \"b*c*d*e*\") == False\n assert candidate(s = \"abcde\",p = \"a?c*e\") == True\n assert candidate(s = \"abefcdgiescdfimde\",p = \"*a*b*ef*cd*ei*de*\") == False\n assert candidate(s = \"abcde\",p = \"*****e\") == True\n assert candidate(s = \"aa\",p = \"*\") == True\n assert candidate(s = \"abcde\",p = \"a*de\") == True\n assert candidate(s = \"adceb\",p = \"*a*b\") == True\n assert candidate(s = \"abcde\",p = \"*****\") == True\n assert candidate(s = \"abcde\",p = \"a*****\") == True\n assert candidate(s = \"acdcb\",p = \"a*c?b\") == False\n assert candidate(s = \"a\",p = \"?\") == True\n assert candidate(s = \"mississippi\",p = \"m*iss*iss*pp*i*pi\") == False\n assert candidate(s = \"abcde\",p = \"a?c?e\") == True\n assert candidate(s = \"abcde\",p = \"a*e?\") == False\n assert candidate(s = \"abcde\",p = \"a*b?e\") == False\n assert candidate(s = \"abcde\",p = \"*b*c*d*e*\") == True\n assert candidate(s = \"abcde\",p = \"a*e\") == True\n assert candidate(s = \"abcde\",p = \"*a*bc*e*\") == True\n assert candidate(s = \"abcde\",p = \"*b*c*d*e\") == True\n assert candidate(s = \"abcde\",p = \"a*b*c*d*e*f\") == False\n assert candidate(s = \"abefcdgiescdfimde\",p = \"ab*ef*cd*ei*de\") == False\n assert candidate(s = \"abcde\",p = \"abc*def\") == False\n assert candidate(s = \"abcde\",p = \"*bcde\") == True\n assert candidate(s = \"abcde\",p = \"abcd*\") == True\n assert candidate(s = \"hoop\",p = \"hoop*\") == True\n assert candidate(s = \"mississippi\",p = \"m??*ss*?si*pp*\") == False\n assert candidate(s = \"aaaa\",p = \"***a\") == True\n assert candidate(s = \"abcde\",p = \"abc??\") == True\n assert candidate(s = \"abcde\",p = \"a*b*c*d*e*\") == True\n assert candidate(s = \"bba\",p = \"?*a**\") == True\n assert candidate(s = \"abcde\",p = \"a*b*c*d*e?\") == False\n assert candidate(s = \"\",p = \"*\") == True\n assert candidate(s = \"abcde\",p = \"abcd?\") == True\n assert candidate(s = \"abcde\",p = \"*a*b*c*d*e*f\") == False\n assert candidate(s = \"a\",p = \"*\") == True\n assert candidate(s = \"\",p = \"?\") == False\n assert candidate(s = \"abcde\",p = \"abc*e\") == True\n assert candidate(s = \"abcde\",p = \"*a*b*c*d*e*\") == True\n assert candidate(s = \"abefcdgiescdfimde\",p = \"ab*ef*cd*de\") == True\n assert candidate(s = \"abefcdgiescdfimde\",p = \"ab*cd?i*de\") == True\n assert candidate(s = \"abcde\",p = \"a*b*c*d*e\") == True\n assert candidate(s = \"abcde\",p = \"abcde\") == True\n assert candidate(s = \"aaaaa\",p = \"a*a*a*a*a\") == True\n assert candidate(s = \"abcdef\",p = \"a*b*c*d*e*f\") == True\n assert candidate(s = \"abcd\",p = \"a*d\") == True\n assert candidate(s = \"xyxzyxytxzyxy\",p = \"x*y*z*x*y*z*x*y*z\") == False\n assert candidate(s = \"xyxxyxyxyx\",p = \"x*yx*yx*yx*yx\") == True\n assert candidate(s = \"abcxyz\",p = \"*xyz\") == True\n assert candidate(s = \"abcabcabc\",p = \"a*bc*a*bc*a*bc*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*c*e*g*i*j\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*bc*de*fgh*i*j\") == True\n assert candidate(s = \"ababababab\",p = \"a*b*a*b*a*b*\") == True\n assert candidate(s = \"xyz\",p = \"*x*y*z*\") == True\n assert candidate(s = \"zxyxzy\",p = \"z*xy*z*\") == True\n assert candidate(s = \"hellohellohello\",p = \"he*lo*he*lo*\") == True\n assert candidate(s = \"xyz\",p = \"*z\") == True\n assert candidate(s = \"xyxzyzyx\",p = \"x*y*x*y*x\") == True\n assert candidate(s = \"ababababa\",p = \"a*b*a*b*a\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*?*c*?*e*?*g*?*i*?*j\") == False\n assert candidate(s = \"abefcdgiescdfimdeeeiad\",p = \"ab*cd?i*de\") == False\n assert candidate(s = \"ababababab\",p = \"a*b*a*b*a*b*a*b*a*b\") == True\n assert candidate(s = \"aabbccdd\",p = \"aab?cc?d*\") == True\n assert candidate(s = \"abc\",p = \"*?*?*\") == True\n assert candidate(s = \"abcdefghij\",p = \"?????????\") == False\n assert candidate(s = \"abcabcabc\",p = \"abc*abc*abc*\") == True\n assert candidate(s = \"abcdefghij\",p = \"*b*d*f*h*\") == True\n assert candidate(s = \"xyzxyzxyz\",p = \"xyz*xyz*xyz\") == True\n assert candidate(s = \"aaaaaa\",p = \"?*?*?*?*?*\") == True\n assert candidate(s = \"abcd\",p = \"?b*d\") == True\n assert candidate(s = \"xxyyzz\",p = \"x*y*z\") == True\n assert candidate(s = \"abcabcabcabcabcabc\",p = \"abcabc*abcabc*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?\") == False\n assert candidate(s = \"abcdabcd\",p = \"ab*cd*ab*cd*\") == True\n assert candidate(s = \"mississippi\",p = \"m??*ss*?\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k*?*l*?\") == False\n assert candidate(s = \"abababab\",p = \"a?b?*b?\") == False\n assert candidate(s = \"mississippi\",p = \"m*is*p*i*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*d*f?j\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k*?*l*\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",p = \"a*b*c*d*e*f*g*h*i*j*k*l*m*n*o*p*q*r*s*t*u*v*w*x*y*z*z*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*?*?*\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*\") == True\n assert candidate(s = \"abcdabcdabcd\",p = \"*a*b*c*d*a*b*c*d*a*b*c*d*\") == True\n assert candidate(s = \"abcabcabc\",p = \"abc*abc*\") == True\n assert candidate(s = \"patternmatching\",p = \"pa*?t*?n*?m*?a*?t*?c*?h*?i*?n*?g\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*?*\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*k*?\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*k?*\") == False\n assert candidate(s = \"abcabcabc\",p = \"*abc*abc*abc*\") == True\n assert candidate(s = \"abcdabcdabcd\",p = \"a*d*d*bc*bc*bc\") == False\n assert candidate(s = \"abcabcabc\",p = \"a*bc*bc*\") == True\n assert candidate(s = \"abcdefghij\",p = \"*a*b*c*d*e*f*g*h*i*j*?*\") == False\n assert candidate(s = \"abcdefghij\",p = \"*?*?*?*?*?*?*?*?\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k*?*\") == False\n assert candidate(s = \"abcdefg\",p = \"a*d?e?*g\") == False\n assert candidate(s = \"abcdefg\",p = \"abc*def*ghi\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k*?\") == False\n assert candidate(s = \"abcdefg\",p = \"a?c*f?g\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j????\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*a*\") == False\n assert candidate(s = \"mississippi\",p = \"m??*ss*?i*\") == True\n assert candidate(s = \"abcabcabc\",p = \"a*b*c*a*b*c*a*b*c\") == True\n assert candidate(s = \"aaaaabbbbbcccc\",p = \"a*b*c*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k*?*l\") == False\n assert candidate(s = \"aabbccddeeff\",p = \"a*b*c*d*e*f*\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",p = \"a*b*c*d*e*f*g*h*i*j*k*l*m*n*o*p*q*r*s*t*u*v*w*x*y*z*z*z*\") == False\n assert candidate(s = \"abcde\",p = \"a*bcd*e\") == True\n assert candidate(s = \"abcdefghij\",p = \"*a*b*c*d*e*f*g*h*i*j*k\") == False\n assert candidate(s = \"abcde\",p = \"a*?c*e\") == True\n assert candidate(s = \"mississippi\",p = \"m??*ss*ip*\") == True\n assert candidate(s = \"xyzxyzxyz\",p = \"*xyzxyzxyz\") == True\n assert candidate(s = \"hello\",p = \"h?ll*\") == True\n assert candidate(s = \"abcdexyz\",p = \"*d*xyz\") == True\n assert candidate(s = \"aaaaabbbbb\",p = \"a*b*\") == True\n assert candidate(s = \"hello\",p = \"he*o\") == True\n assert candidate(s = \"abcdabcd\",p = \"a*b*c*d*\") == True\n assert candidate(s = \"abcdefg\",p = \"a?c*e?g\") == True\n assert candidate(s = \"abxyzz\",p = \"ab*zz\") == True\n assert candidate(s = \"xyzabc\",p = \"*abc\") == True\n assert candidate(s = \"abcabcabc\",p = \"a*?*?*b*c*\") == True\n assert candidate(s = \"xyzzxyzzxyzz\",p = \"*z*z*z\") == True\n assert candidate(s = \"abcxyz\",p = \"abc*xyz\") == True\n assert candidate(s = \"abcdefghij\",p = \"*a????b????c????d????e????f????g????h????i????j*\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*k*\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j?*k?\") == False\n assert candidate(s = \"zazbzczdz\",p = \"z*a*z*b*z*c*z*d*z\") == True\n assert candidate(s = \"abcdefghij\",p = \"*a*b*c*d*e*f*g*h*i*j*\") == True\n assert candidate(s = \"abcdefghij\",p = \"*a*b*c*d*e*f*g*h*i*j\") == True\n assert candidate(s = \"mississippi\",p = \"mi*is*ip*pi\") == True\n assert candidate(s = \"aaaaaa\",p = \"a?a?a?a?a?a\") == False\n assert candidate(s = \"abcdefghij\",p = \"*a*b*c*d*e*f*g*h*i*j*k*?\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*k\") == False\n assert candidate(s = \"xyzzaz\",p = \"*x?z*a*\") == True\n assert candidate(s = \"abcde\",p = \"*abc?e\") == True\n assert candidate(s = \"abcdabcd\",p = \"a*a*a*a*\") == False\n assert candidate(s = \"abc\",p = \"a*c\") == True\n assert candidate(s = \"xyz\",p = \"?yz*\") == True\n assert candidate(s = \"hello_world\",p = \"he*o?wo*rld\") == True\n assert candidate(s = \"abcdefg\",p = \"a*c*e*g\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*d*g*j\") == True\n assert candidate(s = \"abcdexyz\",p = \"a*?d*x*yz\") == True\n assert candidate(s = \"aabbccddeeffgg\",p = \"*b*c*d*e*f*g*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*e*i*\") == True\n assert candidate(s = \"xyxxyxyxyx\",p = \"x*y*x*y*x*y*x\") == True\n assert candidate(s = \"abcd\",p = \"*d\") == True\n assert candidate(s = \"abcdexyz\",p = \"abcd*xyz\") == True\n assert candidate(s = \"mississippi\",p = \"m*iss*ss*ip*\") == True\n assert candidate(s = \"mississippi\",p = \"m??*iss*ippi\") == True\n assert candidate(s = \"abcdefghij\",p = \"*b*d*f*h*j\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j\") == True\n assert candidate(s = \"abc\",p = \"***\") == True\n assert candidate(s = \"aabbccdd\",p = \"a*bb*cc*dd\") == True\n assert candidate(s = \"abcdefghij\",p = \"*\") == True\n assert candidate(s = \"abcde\",p = \"*abcde\") == True\n assert candidate(s = \"aaabbbccc\",p = \"a*bbb*c*\") == True\n assert candidate(s = \"abcde\",p = \"abcde*\") == True\n assert candidate(s = \"xyzabc\",p = \"x*y?*\") == True\n assert candidate(s = \"aabbaabb\",p = \"a*bb*a*bb\") == True\n assert candidate(s = \"abcdedef\",p = \"ab*?de*?\") == True\n assert candidate(s = \"pattern_matching\",p = \"p*a*t*t*e*r_*m*a*t*c*h*i*n*g\") == False\n assert candidate(s = \"worldwide\",p = \"wo*d*i*e\") == True\n assert candidate(s = \"aabbcc\",p = \"a*bb*c*\") == True\n assert candidate(s = \"abcdefg\",p = \"*cde*fg\") == True\n assert candidate(s = \"aabbcc\",p = \"a*b*c*\") == True\n assert candidate(s = \"xyyxxyyxxyy\",p = \"x*y*x*y*x*y*\") == True\n assert candidate(s = \"abcabcabc\",p = \"abc*abc*abc\") == True\n assert candidate(s = \"aabbababab\",p = \"a*b*a*\") == True\n assert candidate(s = \"abcdexyz\",p = \"a*b?c*?d*x?y*z*\") == False\n assert candidate(s = \"abcdefgh\",p = \"a*gh\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*?*k*\") == False\n assert candidate(s = \"zzzzzzzzzz\",p = \"z*z*z*z*z*z*z*z*z*z\") == True\n assert candidate(s = \"abcabcabcabc\",p = \"a*b*c*a*b*c*a*b*c\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*d*f*h*j\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*?\") == False\n assert candidate(s = \"abcdefghij\",p = \"a*b*c*d*e*f*g*h*i*j*?*?\") == False\n assert candidate(s = \"abcdefghij\",p = \"????a*b*c*d*e*f*g*h*i*j\") == False\n assert candidate(s = \"ababab\",p = \"a*b*a*b*\") == True\n assert candidate(s = \"abcabcabc\",p = \"abc*a*bc*a*bc*\") == True\n assert candidate(s = \"abcdefghij\",p = \"*a*b*c*d*e*f*g*h*i*j*j*\") == False\n assert candidate(s = \"abcabcabcabc\",p = \"abc*abc*\") == True\n assert candidate(s = \"abcdefghij\",p = \"*ef*gh*ij\") == True\n assert candidate(s = \"aabbccddeeff\",p = \"a*bb*c*dd*ee*f*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*d*f*h*j*\") == True\n assert candidate(s = \"abcdef\",p = \"*?*?*?*\") == True\n assert candidate(s = \"abcabcabc\",p = \"abcabcabc\") == True\n assert candidate(s = \"abcd\",p = \"*?c*d*\") == True\n assert candidate(s = \"abcdefghij\",p = \"a*d?g*j\") == False\n assert candidate(s = \"abcabcabc\",p = \"*b*a*b*c*a*b*c*\") == True\n assert candidate(s = \"mississippi\",p = \"m??*ss*?si*pp*i*\") == False\n assert candidate(s = \"aabb\",p = \"*b\") == True\n assert candidate(s = \"abcabcabcabc\",p = \"*abcabc*\") == True\n assert candidate(s = \"examplepattern\",p = \"e*ample?attern\") == True\n assert candidate(s = \"nested_matching\",p = \"n*es*t*e*d_*m*a*t*c*h*i*n*g\") == True\n assert candidate(s = \"abcabcabc\",p = \"*a*b*c*a*b*c*a*b*c*\") == True\n assert candidate(s = \"teststring\",p = \"t*st*ng\") == True\n assert candidate(s = \"aabbcc\",p = \"a*a*a*c*c*\") == False\n assert candidate(s = \"abcdef\",p = \"*abc?ef\") == True\n assert candidate(s = \"aaaabaaaab\",p = \"a*a*ba*a*b\") == True\n"}, "metadata": {"canonical_parameter_names": ["s", "p"], "leetcode_dataset_entry_point": "Solution().isMatch", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isMatch = function(s, p) {", "container": null, "callable": "isMatch", "parameters": [{"name": "s", "type": "string"}, {"name": "p", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 45, "task_id": "jump-game-ii", "difficulty": "Medium", "problem_description": "You are given a 0-indexed array of integers nums of length n. You are initially positioned at nums[0].\nEach element nums[i] represents the maximum length of a forward jump from index i. In other words, if you are at nums[i], you can jump to any nums[i + j] where:\n\n0 <= j <= nums[i] and\ni + j < n\n\nReturn the minimum number of jumps to reach nums[n - 1]. The test cases are generated such that you can reach nums[n - 1].\n \nExample 1:\n\nInput: nums = [2,3,1,1,4]\nOutput: 2\nExplanation: The minimum number of jumps to reach the last index is 2. Jump 1 step from index 0 to 1, then 3 steps to the last index.\n\nExample 2:\n\nInput: nums = [2,3,0,1,4]\nOutput: 2\n\n \nConstraints:\n\n1 <= nums.length <= 104\n0 <= nums[i] <= 1000\nIt's guaranteed that you can reach nums[n - 1].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 6, 4, 4, 6, 9, 4, 4, 7, 4, 4, 8, 2, 6, 8, 1, 5, 9, 6, 5, 2, 7, 9, 7, 9, 6, 9, 4, 1, 6, 8, 8, 4, 4, 2, 0, 7, 1, 3, 8, 0, 1, 2, 1, 2, 4, 3, 2, 0, 7, 1, 2, 7, 0, 6, 8, 0, 6, 5, 9, 9, 7, 4, 6, 6, 5, 8, 9, 3, 4, 3, 7, 0, 4, 9, 0, 9, 8, 4, 3, 0, 7, 7, 1, 9, 1, 9, 4, 9, 0, 1, 9, 5, 7, 7, 9, 5, 6, 6, 4, 6, 8, 3, 1, 2, 1, 3, 4, 6, 0, 7, 1, 9, 8, 0, 4, 3, 0, 4, 3, 0, 8, 6, 1, 1, 6, 8, 7, 5, 3, 1, 1, 5, 0, 7, 3, 7, 0, 9, 1, 2, 1, 8, 8, 7, 2, 9, 7, 9, 7, 9, 6, 9, 4, 1, 6, 8, 8, 4, 4, 2, 0, 7, 1, 3, 8, 0, 1, 2, 1, 2, 4, 3, 2, 0, 7, 1, 2, 7, 0, 6, 8, 0, 6, 5, 9, 9, 7, 4, 6, 6, 5, 8, 9, 3, 4, 3, 7, 0, 4, 9, 0, 9, 8, 4, 3, 0, 7, 7, 1, 9]) == 32\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 9\n assert candidate(nums = [2, 3, 0, 1, 4]) == 2\n assert candidate(nums = [5, 6, 4, 4, 6, 9, 4, 4, 7, 4, 4, 8, 2, 6, 8, 1, 5, 9, 6, 5, 2, 7, 9, 7, 9, 6, 9, 4, 1, 6, 8, 8, 4, 4, 2, 0, 3, 8, 5]) == 5\n assert candidate(nums = [0]) == 0\n assert candidate(nums = [5, 6, 4, 4, 6, 9, 4, 4, 7, 4, 4, 8, 2, 6, 8, 1, 5, 9, 6, 5, 2, 7, 9, 7, 9, 6, 9, 4, 1, 6, 8, 8, 4, 4, 2, 0, 1, 1, 2, 6, 5, 5, 0, 1, 2, 2, 9, 1, 4, 9, 5, 8, 0, 1, 9, 4, 5, 0, 8, 0, 3, 4, 6, 6, 1, 5, 8, 5, 9, 6, 2, 6, 1]) == 11\n assert candidate(nums = [1, 2, 3]) == 2\n assert candidate(nums = [1, 1, 1, 1]) == 3\n assert candidate(nums = [2, 3, 1, 1, 4]) == 2\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 0]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 4\n assert candidate(nums = [2, 3, 1, 1, 4, 2, 3, 1, 1, 4, 2, 3, 1, 1, 4, 2, 3, 1, 1, 4]) == 8\n assert candidate(nums = [1, 3, 5, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 4\n assert candidate(nums = [3, 2, 1, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, 0, 4]) == 2\n assert candidate(nums = [5, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 2\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 5\n assert candidate(nums = [9, 4, 2, 1, 0, 2, 0, 1, 0, 0]) == 1\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 4\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 1\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 7\n assert candidate(nums = [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 2\n assert candidate(nums = [1, 3, 5, 3, 1, 2, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 6\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 19\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 4\n assert candidate(nums = [2, 5, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 15\n assert candidate(nums = [2, 0, 1, 0, 1, 1, 1, 1, 1, 1]) == 3\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 19\n assert candidate(nums = [10, 2, 3, 1, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [3, 0, 8, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 11\n assert candidate(nums = [3, 2, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 14\n assert candidate(nums = [1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [100, 20, 10, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [3, 2, 1, 0, 4]) == 2\n assert candidate(nums = [3, 3, 0, 2, 1, 2, 4, 3, 0, 0, 3, 1, 2, 1]) == 5\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 205\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().jump", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var jump = function(nums) {", "container": null, "callable": "jump", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 46, "task_id": "permutations", "difficulty": "Medium", "problem_description": "Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order.\n \nExample 1:\nInput: nums = [1,2,3]\nOutput: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]\nExample 2:\nInput: nums = [0,1]\nOutput: [[0,1],[1,0]]\nExample 3:\nInput: nums = [1]\nOutput: [[1]]\n\n \nConstraints:\n\n1 <= nums.length <= 6\n-10 <= nums[i] <= 10\nAll the integers of nums are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1]) == [[1]]\n assert candidate(nums = [10, -10, 20, 30, 40, 50]) == [[10, -10, 20, 30, 40, 50], [10, -10, 20, 30, 50, 40], [10, -10, 20, 40, 30, 50], [10, -10, 20, 40, 50, 30], [10, -10, 20, 50, 30, 40], [10, -10, 20, 50, 40, 30], [10, -10, 30, 20, 40, 50], [10, -10, 30, 20, 50, 40], [10, -10, 30, 40, 20, 50], [10, -10, 30, 40, 50, 20], [10, -10, 30, 50, 20, 40], [10, -10, 30, 50, 40, 20], [10, -10, 40, 20, 30, 50], [10, -10, 40, 20, 50, 30], [10, -10, 40, 30, 20, 50], [10, -10, 40, 30, 50, 20], [10, -10, 40, 50, 20, 30], [10, -10, 40, 50, 30, 20], [10, -10, 50, 20, 30, 40], [10, -10, 50, 20, 40, 30], [10, -10, 50, 30, 20, 40], [10, -10, 50, 30, 40, 20], [10, -10, 50, 40, 20, 30], [10, -10, 50, 40, 30, 20], [10, 20, -10, 30, 40, 50], [10, 20, -10, 30, 50, 40], [10, 20, -10, 40, 30, 50], [10, 20, -10, 40, 50, 30], [10, 20, -10, 50, 30, 40], [10, 20, -10, 50, 40, 30], [10, 20, 30, -10, 40, 50], [10, 20, 30, -10, 50, 40], [10, 20, 30, 40, -10, 50], [10, 20, 30, 40, 50, -10], [10, 20, 30, 50, -10, 40], [10, 20, 30, 50, 40, -10], [10, 20, 40, -10, 30, 50], [10, 20, 40, -10, 50, 30], [10, 20, 40, 30, -10, 50], [10, 20, 40, 30, 50, -10], [10, 20, 40, 50, -10, 30], [10, 20, 40, 50, 30, -10], [10, 20, 50, -10, 30, 40], [10, 20, 50, -10, 40, 30], [10, 20, 50, 30, -10, 40], [10, 20, 50, 30, 40, -10], [10, 20, 50, 40, -10, 30], [10, 20, 50, 40, 30, -10], [10, 30, -10, 20, 40, 50], [10, 30, -10, 20, 50, 40], [10, 30, -10, 40, 20, 50], [10, 30, -10, 40, 50, 20], [10, 30, -10, 50, 20, 40], [10, 30, -10, 50, 40, 20], [10, 30, 20, -10, 40, 50], [10, 30, 20, -10, 50, 40], [10, 30, 20, 40, -10, 50], [10, 30, 20, 40, 50, -10], [10, 30, 20, 50, -10, 40], [10, 30, 20, 50, 40, -10], [10, 30, 40, -10, 20, 50], [10, 30, 40, -10, 50, 20], [10, 30, 40, 20, -10, 50], [10, 30, 40, 20, 50, -10], [10, 30, 40, 50, -10, 20], [10, 30, 40, 50, 20, -10], [10, 30, 50, -10, 20, 40], [10, 30, 50, -10, 40, 20], [10, 30, 50, 20, -10, 40], [10, 30, 50, 20, 40, -10], [10, 30, 50, 40, -10, 20], [10, 30, 50, 40, 20, -10], [10, 40, -10, 20, 30, 50], [10, 40, -10, 20, 50, 30], [10, 40, -10, 30, 20, 50], [10, 40, -10, 30, 50, 20], [10, 40, -10, 50, 20, 30], [10, 40, -10, 50, 30, 20], [10, 40, 20, -10, 30, 50], [10, 40, 20, -10, 50, 30], [10, 40, 20, 30, -10, 50], [10, 40, 20, 30, 50, -10], [10, 40, 20, 50, -10, 30], [10, 40, 20, 50, 30, -10], [10, 40, 30, -10, 20, 50], [10, 40, 30, -10, 50, 20], [10, 40, 30, 20, -10, 50], [10, 40, 30, 20, 50, -10], [10, 40, 30, 50, -10, 20], [10, 40, 30, 50, 20, -10], [10, 40, 50, -10, 20, 30], [10, 40, 50, -10, 30, 20], [10, 40, 50, 20, -10, 30], [10, 40, 50, 20, 30, -10], [10, 40, 50, 30, -10, 20], [10, 40, 50, 30, 20, -10], [10, 50, -10, 20, 30, 40], [10, 50, -10, 20, 40, 30], [10, 50, -10, 30, 20, 40], [10, 50, -10, 30, 40, 20], [10, 50, -10, 40, 20, 30], [10, 50, -10, 40, 30, 20], [10, 50, 20, -10, 30, 40], [10, 50, 20, -10, 40, 30], [10, 50, 20, 30, -10, 40], [10, 50, 20, 30, 40, -10], [10, 50, 20, 40, -10, 30], [10, 50, 20, 40, 30, -10], [10, 50, 30, -10, 20, 40], [10, 50, 30, -10, 40, 20], [10, 50, 30, 20, -10, 40], [10, 50, 30, 20, 40, -10], [10, 50, 30, 40, -10, 20], [10, 50, 30, 40, 20, -10], [10, 50, 40, -10, 20, 30], [10, 50, 40, -10, 30, 20], [10, 50, 40, 20, -10, 30], [10, 50, 40, 20, 30, -10], [10, 50, 40, 30, -10, 20], [10, 50, 40, 30, 20, -10], [-10, 10, 20, 30, 40, 50], [-10, 10, 20, 30, 50, 40], [-10, 10, 20, 40, 30, 50], [-10, 10, 20, 40, 50, 30], [-10, 10, 20, 50, 30, 40], [-10, 10, 20, 50, 40, 30], [-10, 10, 30, 20, 40, 50], [-10, 10, 30, 20, 50, 40], [-10, 10, 30, 40, 20, 50], [-10, 10, 30, 40, 50, 20], [-10, 10, 30, 50, 20, 40], [-10, 10, 30, 50, 40, 20], [-10, 10, 40, 20, 30, 50], [-10, 10, 40, 20, 50, 30], [-10, 10, 40, 30, 20, 50], [-10, 10, 40, 30, 50, 20], [-10, 10, 40, 50, 20, 30], [-10, 10, 40, 50, 30, 20], [-10, 10, 50, 20, 30, 40], [-10, 10, 50, 20, 40, 30], [-10, 10, 50, 30, 20, 40], [-10, 10, 50, 30, 40, 20], [-10, 10, 50, 40, 20, 30], [-10, 10, 50, 40, 30, 20], [-10, 20, 10, 30, 40, 50], [-10, 20, 10, 30, 50, 40], [-10, 20, 10, 40, 30, 50], [-10, 20, 10, 40, 50, 30], [-10, 20, 10, 50, 30, 40], [-10, 20, 10, 50, 40, 30], [-10, 20, 30, 10, 40, 50], [-10, 20, 30, 10, 50, 40], [-10, 20, 30, 40, 10, 50], [-10, 20, 30, 40, 50, 10], [-10, 20, 30, 50, 10, 40], [-10, 20, 30, 50, 40, 10], [-10, 20, 40, 10, 30, 50], [-10, 20, 40, 10, 50, 30], [-10, 20, 40, 30, 10, 50], [-10, 20, 40, 30, 50, 10], [-10, 20, 40, 50, 10, 30], [-10, 20, 40, 50, 30, 10], [-10, 20, 50, 10, 30, 40], [-10, 20, 50, 10, 40, 30], [-10, 20, 50, 30, 10, 40], [-10, 20, 50, 30, 40, 10], [-10, 20, 50, 40, 10, 30], [-10, 20, 50, 40, 30, 10], [-10, 30, 10, 20, 40, 50], [-10, 30, 10, 20, 50, 40], [-10, 30, 10, 40, 20, 50], [-10, 30, 10, 40, 50, 20], [-10, 30, 10, 50, 20, 40], [-10, 30, 10, 50, 40, 20], [-10, 30, 20, 10, 40, 50], [-10, 30, 20, 10, 50, 40], [-10, 30, 20, 40, 10, 50], [-10, 30, 20, 40, 50, 10], [-10, 30, 20, 50, 10, 40], [-10, 30, 20, 50, 40, 10], [-10, 30, 40, 10, 20, 50], [-10, 30, 40, 10, 50, 20], [-10, 30, 40, 20, 10, 50], [-10, 30, 40, 20, 50, 10], [-10, 30, 40, 50, 10, 20], [-10, 30, 40, 50, 20, 10], [-10, 30, 50, 10, 20, 40], [-10, 30, 50, 10, 40, 20], [-10, 30, 50, 20, 10, 40], [-10, 30, 50, 20, 40, 10], [-10, 30, 50, 40, 10, 20], [-10, 30, 50, 40, 20, 10], [-10, 40, 10, 20, 30, 50], [-10, 40, 10, 20, 50, 30], [-10, 40, 10, 30, 20, 50], [-10, 40, 10, 30, 50, 20], [-10, 40, 10, 50, 20, 30], [-10, 40, 10, 50, 30, 20], [-10, 40, 20, 10, 30, 50], [-10, 40, 20, 10, 50, 30], [-10, 40, 20, 30, 10, 50], [-10, 40, 20, 30, 50, 10], [-10, 40, 20, 50, 10, 30], [-10, 40, 20, 50, 30, 10], [-10, 40, 30, 10, 20, 50], [-10, 40, 30, 10, 50, 20], [-10, 40, 30, 20, 10, 50], [-10, 40, 30, 20, 50, 10], [-10, 40, 30, 50, 10, 20], [-10, 40, 30, 50, 20, 10], [-10, 40, 50, 10, 20, 30], [-10, 40, 50, 10, 30, 20], [-10, 40, 50, 20, 10, 30], [-10, 40, 50, 20, 30, 10], [-10, 40, 50, 30, 10, 20], [-10, 40, 50, 30, 20, 10], [-10, 50, 10, 20, 30, 40], [-10, 50, 10, 20, 40, 30], [-10, 50, 10, 30, 20, 40], [-10, 50, 10, 30, 40, 20], [-10, 50, 10, 40, 20, 30], [-10, 50, 10, 40, 30, 20], [-10, 50, 20, 10, 30, 40], [-10, 50, 20, 10, 40, 30], [-10, 50, 20, 30, 10, 40], [-10, 50, 20, 30, 40, 10], [-10, 50, 20, 40, 10, 30], [-10, 50, 20, 40, 30, 10], [-10, 50, 30, 10, 20, 40], [-10, 50, 30, 10, 40, 20], [-10, 50, 30, 20, 10, 40], [-10, 50, 30, 20, 40, 10], [-10, 50, 30, 40, 10, 20], [-10, 50, 30, 40, 20, 10], [-10, 50, 40, 10, 20, 30], [-10, 50, 40, 10, 30, 20], [-10, 50, 40, 20, 10, 30], [-10, 50, 40, 20, 30, 10], [-10, 50, 40, 30, 10, 20], [-10, 50, 40, 30, 20, 10], [20, 10, -10, 30, 40, 50], [20, 10, -10, 30, 50, 40], [20, 10, -10, 40, 30, 50], [20, 10, -10, 40, 50, 30], [20, 10, -10, 50, 30, 40], [20, 10, -10, 50, 40, 30], [20, 10, 30, -10, 40, 50], [20, 10, 30, -10, 50, 40], [20, 10, 30, 40, -10, 50], [20, 10, 30, 40, 50, -10], [20, 10, 30, 50, -10, 40], [20, 10, 30, 50, 40, -10], [20, 10, 40, -10, 30, 50], [20, 10, 40, -10, 50, 30], [20, 10, 40, 30, -10, 50], [20, 10, 40, 30, 50, -10], [20, 10, 40, 50, -10, 30], [20, 10, 40, 50, 30, -10], [20, 10, 50, -10, 30, 40], [20, 10, 50, -10, 40, 30], [20, 10, 50, 30, -10, 40], [20, 10, 50, 30, 40, -10], [20, 10, 50, 40, -10, 30], [20, 10, 50, 40, 30, -10], [20, -10, 10, 30, 40, 50], [20, -10, 10, 30, 50, 40], [20, -10, 10, 40, 30, 50], [20, -10, 10, 40, 50, 30], [20, -10, 10, 50, 30, 40], [20, -10, 10, 50, 40, 30], [20, -10, 30, 10, 40, 50], [20, -10, 30, 10, 50, 40], [20, -10, 30, 40, 10, 50], [20, -10, 30, 40, 50, 10], [20, -10, 30, 50, 10, 40], [20, -10, 30, 50, 40, 10], [20, -10, 40, 10, 30, 50], [20, -10, 40, 10, 50, 30], [20, -10, 40, 30, 10, 50], [20, -10, 40, 30, 50, 10], [20, -10, 40, 50, 10, 30], [20, -10, 40, 50, 30, 10], [20, -10, 50, 10, 30, 40], [20, -10, 50, 10, 40, 30], [20, -10, 50, 30, 10, 40], [20, -10, 50, 30, 40, 10], [20, -10, 50, 40, 10, 30], [20, -10, 50, 40, 30, 10], [20, 30, 10, -10, 40, 50], [20, 30, 10, -10, 50, 40], [20, 30, 10, 40, -10, 50], [20, 30, 10, 40, 50, -10], [20, 30, 10, 50, -10, 40], [20, 30, 10, 50, 40, -10], [20, 30, -10, 10, 40, 50], [20, 30, -10, 10, 50, 40], [20, 30, -10, 40, 10, 50], [20, 30, -10, 40, 50, 10], [20, 30, -10, 50, 10, 40], [20, 30, -10, 50, 40, 10], [20, 30, 40, 10, -10, 50], [20, 30, 40, 10, 50, -10], [20, 30, 40, -10, 10, 50], [20, 30, 40, -10, 50, 10], [20, 30, 40, 50, 10, -10], [20, 30, 40, 50, -10, 10], [20, 30, 50, 10, -10, 40], [20, 30, 50, 10, 40, -10], [20, 30, 50, -10, 10, 40], [20, 30, 50, -10, 40, 10], [20, 30, 50, 40, 10, -10], [20, 30, 50, 40, -10, 10], [20, 40, 10, -10, 30, 50], [20, 40, 10, -10, 50, 30], [20, 40, 10, 30, -10, 50], [20, 40, 10, 30, 50, -10], [20, 40, 10, 50, -10, 30], [20, 40, 10, 50, 30, -10], [20, 40, -10, 10, 30, 50], [20, 40, -10, 10, 50, 30], [20, 40, -10, 30, 10, 50], [20, 40, -10, 30, 50, 10], [20, 40, -10, 50, 10, 30], [20, 40, -10, 50, 30, 10], [20, 40, 30, 10, -10, 50], [20, 40, 30, 10, 50, -10], [20, 40, 30, -10, 10, 50], [20, 40, 30, -10, 50, 10], [20, 40, 30, 50, 10, -10], [20, 40, 30, 50, -10, 10], [20, 40, 50, 10, -10, 30], [20, 40, 50, 10, 30, -10], [20, 40, 50, -10, 10, 30], [20, 40, 50, -10, 30, 10], [20, 40, 50, 30, 10, -10], [20, 40, 50, 30, -10, 10], [20, 50, 10, -10, 30, 40], [20, 50, 10, -10, 40, 30], [20, 50, 10, 30, -10, 40], [20, 50, 10, 30, 40, -10], [20, 50, 10, 40, -10, 30], [20, 50, 10, 40, 30, -10], [20, 50, -10, 10, 30, 40], [20, 50, -10, 10, 40, 30], [20, 50, -10, 30, 10, 40], [20, 50, -10, 30, 40, 10], [20, 50, -10, 40, 10, 30], [20, 50, -10, 40, 30, 10], [20, 50, 30, 10, -10, 40], [20, 50, 30, 10, 40, -10], [20, 50, 30, -10, 10, 40], [20, 50, 30, -10, 40, 10], [20, 50, 30, 40, 10, -10], [20, 50, 30, 40, -10, 10], [20, 50, 40, 10, -10, 30], [20, 50, 40, 10, 30, -10], [20, 50, 40, -10, 10, 30], [20, 50, 40, -10, 30, 10], [20, 50, 40, 30, 10, -10], [20, 50, 40, 30, -10, 10], [30, 10, -10, 20, 40, 50], [30, 10, -10, 20, 50, 40], [30, 10, -10, 40, 20, 50], [30, 10, -10, 40, 50, 20], [30, 10, -10, 50, 20, 40], [30, 10, -10, 50, 40, 20], [30, 10, 20, -10, 40, 50], [30, 10, 20, -10, 50, 40], [30, 10, 20, 40, -10, 50], [30, 10, 20, 40, 50, -10], [30, 10, 20, 50, -10, 40], [30, 10, 20, 50, 40, -10], [30, 10, 40, -10, 20, 50], [30, 10, 40, -10, 50, 20], [30, 10, 40, 20, -10, 50], [30, 10, 40, 20, 50, -10], [30, 10, 40, 50, -10, 20], [30, 10, 40, 50, 20, -10], [30, 10, 50, -10, 20, 40], [30, 10, 50, -10, 40, 20], [30, 10, 50, 20, -10, 40], [30, 10, 50, 20, 40, -10], [30, 10, 50, 40, -10, 20], [30, 10, 50, 40, 20, -10], [30, -10, 10, 20, 40, 50], [30, -10, 10, 20, 50, 40], [30, -10, 10, 40, 20, 50], [30, -10, 10, 40, 50, 20], [30, -10, 10, 50, 20, 40], [30, -10, 10, 50, 40, 20], [30, -10, 20, 10, 40, 50], [30, -10, 20, 10, 50, 40], [30, -10, 20, 40, 10, 50], [30, -10, 20, 40, 50, 10], [30, -10, 20, 50, 10, 40], [30, -10, 20, 50, 40, 10], [30, -10, 40, 10, 20, 50], [30, -10, 40, 10, 50, 20], [30, -10, 40, 20, 10, 50], [30, -10, 40, 20, 50, 10], [30, -10, 40, 50, 10, 20], [30, -10, 40, 50, 20, 10], [30, -10, 50, 10, 20, 40], [30, -10, 50, 10, 40, 20], [30, -10, 50, 20, 10, 40], [30, -10, 50, 20, 40, 10], [30, -10, 50, 40, 10, 20], [30, -10, 50, 40, 20, 10], [30, 20, 10, -10, 40, 50], [30, 20, 10, -10, 50, 40], [30, 20, 10, 40, -10, 50], [30, 20, 10, 40, 50, -10], [30, 20, 10, 50, -10, 40], [30, 20, 10, 50, 40, -10], [30, 20, -10, 10, 40, 50], [30, 20, -10, 10, 50, 40], [30, 20, -10, 40, 10, 50], [30, 20, -10, 40, 50, 10], [30, 20, -10, 50, 10, 40], [30, 20, -10, 50, 40, 10], [30, 20, 40, 10, -10, 50], [30, 20, 40, 10, 50, -10], [30, 20, 40, -10, 10, 50], [30, 20, 40, -10, 50, 10], [30, 20, 40, 50, 10, -10], [30, 20, 40, 50, -10, 10], [30, 20, 50, 10, -10, 40], [30, 20, 50, 10, 40, -10], [30, 20, 50, -10, 10, 40], [30, 20, 50, -10, 40, 10], [30, 20, 50, 40, 10, -10], [30, 20, 50, 40, -10, 10], [30, 40, 10, -10, 20, 50], [30, 40, 10, -10, 50, 20], [30, 40, 10, 20, -10, 50], [30, 40, 10, 20, 50, -10], [30, 40, 10, 50, -10, 20], [30, 40, 10, 50, 20, -10], [30, 40, -10, 10, 20, 50], [30, 40, -10, 10, 50, 20], [30, 40, -10, 20, 10, 50], [30, 40, -10, 20, 50, 10], [30, 40, -10, 50, 10, 20], [30, 40, -10, 50, 20, 10], [30, 40, 20, 10, -10, 50], [30, 40, 20, 10, 50, -10], [30, 40, 20, -10, 10, 50], [30, 40, 20, -10, 50, 10], [30, 40, 20, 50, 10, -10], [30, 40, 20, 50, -10, 10], [30, 40, 50, 10, -10, 20], [30, 40, 50, 10, 20, -10], [30, 40, 50, -10, 10, 20], [30, 40, 50, -10, 20, 10], [30, 40, 50, 20, 10, -10], [30, 40, 50, 20, -10, 10], [30, 50, 10, -10, 20, 40], [30, 50, 10, -10, 40, 20], [30, 50, 10, 20, -10, 40], [30, 50, 10, 20, 40, -10], [30, 50, 10, 40, -10, 20], [30, 50, 10, 40, 20, -10], [30, 50, -10, 10, 20, 40], [30, 50, -10, 10, 40, 20], [30, 50, -10, 20, 10, 40], [30, 50, -10, 20, 40, 10], [30, 50, -10, 40, 10, 20], [30, 50, -10, 40, 20, 10], [30, 50, 20, 10, -10, 40], [30, 50, 20, 10, 40, -10], [30, 50, 20, -10, 10, 40], [30, 50, 20, -10, 40, 10], [30, 50, 20, 40, 10, -10], [30, 50, 20, 40, -10, 10], [30, 50, 40, 10, -10, 20], [30, 50, 40, 10, 20, -10], [30, 50, 40, -10, 10, 20], [30, 50, 40, -10, 20, 10], [30, 50, 40, 20, 10, -10], [30, 50, 40, 20, -10, 10], [40, 10, -10, 20, 30, 50], [40, 10, -10, 20, 50, 30], [40, 10, -10, 30, 20, 50], [40, 10, -10, 30, 50, 20], [40, 10, -10, 50, 20, 30], [40, 10, -10, 50, 30, 20], [40, 10, 20, -10, 30, 50], [40, 10, 20, -10, 50, 30], [40, 10, 20, 30, -10, 50], [40, 10, 20, 30, 50, -10], [40, 10, 20, 50, -10, 30], [40, 10, 20, 50, 30, -10], [40, 10, 30, -10, 20, 50], [40, 10, 30, -10, 50, 20], [40, 10, 30, 20, -10, 50], [40, 10, 30, 20, 50, -10], [40, 10, 30, 50, -10, 20], [40, 10, 30, 50, 20, -10], [40, 10, 50, -10, 20, 30], [40, 10, 50, -10, 30, 20], [40, 10, 50, 20, -10, 30], [40, 10, 50, 20, 30, -10], [40, 10, 50, 30, -10, 20], [40, 10, 50, 30, 20, -10], [40, -10, 10, 20, 30, 50], [40, -10, 10, 20, 50, 30], [40, -10, 10, 30, 20, 50], [40, -10, 10, 30, 50, 20], [40, -10, 10, 50, 20, 30], [40, -10, 10, 50, 30, 20], [40, -10, 20, 10, 30, 50], [40, -10, 20, 10, 50, 30], [40, -10, 20, 30, 10, 50], [40, -10, 20, 30, 50, 10], [40, -10, 20, 50, 10, 30], [40, -10, 20, 50, 30, 10], [40, -10, 30, 10, 20, 50], [40, -10, 30, 10, 50, 20], [40, -10, 30, 20, 10, 50], [40, -10, 30, 20, 50, 10], [40, -10, 30, 50, 10, 20], [40, -10, 30, 50, 20, 10], [40, -10, 50, 10, 20, 30], [40, -10, 50, 10, 30, 20], [40, -10, 50, 20, 10, 30], [40, -10, 50, 20, 30, 10], [40, -10, 50, 30, 10, 20], [40, -10, 50, 30, 20, 10], [40, 20, 10, -10, 30, 50], [40, 20, 10, -10, 50, 30], [40, 20, 10, 30, -10, 50], [40, 20, 10, 30, 50, -10], [40, 20, 10, 50, -10, 30], [40, 20, 10, 50, 30, -10], [40, 20, -10, 10, 30, 50], [40, 20, -10, 10, 50, 30], [40, 20, -10, 30, 10, 50], [40, 20, -10, 30, 50, 10], [40, 20, -10, 50, 10, 30], [40, 20, -10, 50, 30, 10], [40, 20, 30, 10, -10, 50], [40, 20, 30, 10, 50, -10], [40, 20, 30, -10, 10, 50], [40, 20, 30, -10, 50, 10], [40, 20, 30, 50, 10, -10], [40, 20, 30, 50, -10, 10], [40, 20, 50, 10, -10, 30], [40, 20, 50, 10, 30, -10], [40, 20, 50, -10, 10, 30], [40, 20, 50, -10, 30, 10], [40, 20, 50, 30, 10, -10], [40, 20, 50, 30, -10, 10], [40, 30, 10, -10, 20, 50], [40, 30, 10, -10, 50, 20], [40, 30, 10, 20, -10, 50], [40, 30, 10, 20, 50, -10], [40, 30, 10, 50, -10, 20], [40, 30, 10, 50, 20, -10], [40, 30, -10, 10, 20, 50], [40, 30, -10, 10, 50, 20], [40, 30, -10, 20, 10, 50], [40, 30, -10, 20, 50, 10], [40, 30, -10, 50, 10, 20], [40, 30, -10, 50, 20, 10], [40, 30, 20, 10, -10, 50], [40, 30, 20, 10, 50, -10], [40, 30, 20, -10, 10, 50], [40, 30, 20, -10, 50, 10], [40, 30, 20, 50, 10, -10], [40, 30, 20, 50, -10, 10], [40, 30, 50, 10, -10, 20], [40, 30, 50, 10, 20, -10], [40, 30, 50, -10, 10, 20], [40, 30, 50, -10, 20, 10], [40, 30, 50, 20, 10, -10], [40, 30, 50, 20, -10, 10], [40, 50, 10, -10, 20, 30], [40, 50, 10, -10, 30, 20], [40, 50, 10, 20, -10, 30], [40, 50, 10, 20, 30, -10], [40, 50, 10, 30, -10, 20], [40, 50, 10, 30, 20, -10], [40, 50, -10, 10, 20, 30], [40, 50, -10, 10, 30, 20], [40, 50, -10, 20, 10, 30], [40, 50, -10, 20, 30, 10], [40, 50, -10, 30, 10, 20], [40, 50, -10, 30, 20, 10], [40, 50, 20, 10, -10, 30], [40, 50, 20, 10, 30, -10], [40, 50, 20, -10, 10, 30], [40, 50, 20, -10, 30, 10], [40, 50, 20, 30, 10, -10], [40, 50, 20, 30, -10, 10], [40, 50, 30, 10, -10, 20], [40, 50, 30, 10, 20, -10], [40, 50, 30, -10, 10, 20], [40, 50, 30, -10, 20, 10], [40, 50, 30, 20, 10, -10], [40, 50, 30, 20, -10, 10], [50, 10, -10, 20, 30, 40], [50, 10, -10, 20, 40, 30], [50, 10, -10, 30, 20, 40], [50, 10, -10, 30, 40, 20], [50, 10, -10, 40, 20, 30], [50, 10, -10, 40, 30, 20], [50, 10, 20, -10, 30, 40], [50, 10, 20, -10, 40, 30], [50, 10, 20, 30, -10, 40], [50, 10, 20, 30, 40, -10], [50, 10, 20, 40, -10, 30], [50, 10, 20, 40, 30, -10], [50, 10, 30, -10, 20, 40], [50, 10, 30, -10, 40, 20], [50, 10, 30, 20, -10, 40], [50, 10, 30, 20, 40, -10], [50, 10, 30, 40, -10, 20], [50, 10, 30, 40, 20, -10], [50, 10, 40, -10, 20, 30], [50, 10, 40, -10, 30, 20], [50, 10, 40, 20, -10, 30], [50, 10, 40, 20, 30, -10], [50, 10, 40, 30, -10, 20], [50, 10, 40, 30, 20, -10], [50, -10, 10, 20, 30, 40], [50, -10, 10, 20, 40, 30], [50, -10, 10, 30, 20, 40], [50, -10, 10, 30, 40, 20], [50, -10, 10, 40, 20, 30], [50, -10, 10, 40, 30, 20], [50, -10, 20, 10, 30, 40], [50, -10, 20, 10, 40, 30], [50, -10, 20, 30, 10, 40], [50, -10, 20, 30, 40, 10], [50, -10, 20, 40, 10, 30], [50, -10, 20, 40, 30, 10], [50, -10, 30, 10, 20, 40], [50, -10, 30, 10, 40, 20], [50, -10, 30, 20, 10, 40], [50, -10, 30, 20, 40, 10], [50, -10, 30, 40, 10, 20], [50, -10, 30, 40, 20, 10], [50, -10, 40, 10, 20, 30], [50, -10, 40, 10, 30, 20], [50, -10, 40, 20, 10, 30], [50, -10, 40, 20, 30, 10], [50, -10, 40, 30, 10, 20], [50, -10, 40, 30, 20, 10], [50, 20, 10, -10, 30, 40], [50, 20, 10, -10, 40, 30], [50, 20, 10, 30, -10, 40], [50, 20, 10, 30, 40, -10], [50, 20, 10, 40, -10, 30], [50, 20, 10, 40, 30, -10], [50, 20, -10, 10, 30, 40], [50, 20, -10, 10, 40, 30], [50, 20, -10, 30, 10, 40], [50, 20, -10, 30, 40, 10], [50, 20, -10, 40, 10, 30], [50, 20, -10, 40, 30, 10], [50, 20, 30, 10, -10, 40], [50, 20, 30, 10, 40, -10], [50, 20, 30, -10, 10, 40], [50, 20, 30, -10, 40, 10], [50, 20, 30, 40, 10, -10], [50, 20, 30, 40, -10, 10], [50, 20, 40, 10, -10, 30], [50, 20, 40, 10, 30, -10], [50, 20, 40, -10, 10, 30], [50, 20, 40, -10, 30, 10], [50, 20, 40, 30, 10, -10], [50, 20, 40, 30, -10, 10], [50, 30, 10, -10, 20, 40], [50, 30, 10, -10, 40, 20], [50, 30, 10, 20, -10, 40], [50, 30, 10, 20, 40, -10], [50, 30, 10, 40, -10, 20], [50, 30, 10, 40, 20, -10], [50, 30, -10, 10, 20, 40], [50, 30, -10, 10, 40, 20], [50, 30, -10, 20, 10, 40], [50, 30, -10, 20, 40, 10], [50, 30, -10, 40, 10, 20], [50, 30, -10, 40, 20, 10], [50, 30, 20, 10, -10, 40], [50, 30, 20, 10, 40, -10], [50, 30, 20, -10, 10, 40], [50, 30, 20, -10, 40, 10], [50, 30, 20, 40, 10, -10], [50, 30, 20, 40, -10, 10], [50, 30, 40, 10, -10, 20], [50, 30, 40, 10, 20, -10], [50, 30, 40, -10, 10, 20], [50, 30, 40, -10, 20, 10], [50, 30, 40, 20, 10, -10], [50, 30, 40, 20, -10, 10], [50, 40, 10, -10, 20, 30], [50, 40, 10, -10, 30, 20], [50, 40, 10, 20, -10, 30], [50, 40, 10, 20, 30, -10], [50, 40, 10, 30, -10, 20], [50, 40, 10, 30, 20, -10], [50, 40, -10, 10, 20, 30], [50, 40, -10, 10, 30, 20], [50, 40, -10, 20, 10, 30], [50, 40, -10, 20, 30, 10], [50, 40, -10, 30, 10, 20], [50, 40, -10, 30, 20, 10], [50, 40, 20, 10, -10, 30], [50, 40, 20, 10, 30, -10], [50, 40, 20, -10, 10, 30], [50, 40, 20, -10, 30, 10], [50, 40, 20, 30, 10, -10], [50, 40, 20, 30, -10, 10], [50, 40, 30, 10, -10, 20], [50, 40, 30, 10, 20, -10], [50, 40, 30, -10, 10, 20], [50, 40, 30, -10, 20, 10], [50, 40, 30, 20, 10, -10], [50, 40, 30, 20, -10, 10]]\n assert candidate(nums = [4, 5, 6, 7]) == [[4, 5, 6, 7], [4, 5, 7, 6], [4, 6, 5, 7], [4, 6, 7, 5], [4, 7, 5, 6], [4, 7, 6, 5], [5, 4, 6, 7], [5, 4, 7, 6], [5, 6, 4, 7], [5, 6, 7, 4], [5, 7, 4, 6], [5, 7, 6, 4], [6, 4, 5, 7], [6, 4, 7, 5], [6, 5, 4, 7], [6, 5, 7, 4], [6, 7, 4, 5], [6, 7, 5, 4], [7, 4, 5, 6], [7, 4, 6, 5], [7, 5, 4, 6], [7, 5, 6, 4], [7, 6, 4, 5], [7, 6, 5, 4]]\n assert candidate(nums = [4, 5, 6]) == [[4, 5, 6], [4, 6, 5], [5, 4, 6], [5, 6, 4], [6, 4, 5], [6, 5, 4]]\n assert candidate(nums = [5, 3, 4, 1, 2]) == [[5, 3, 4, 1, 2], [5, 3, 4, 2, 1], [5, 3, 1, 4, 2], [5, 3, 1, 2, 4], [5, 3, 2, 4, 1], [5, 3, 2, 1, 4], [5, 4, 3, 1, 2], [5, 4, 3, 2, 1], [5, 4, 1, 3, 2], [5, 4, 1, 2, 3], [5, 4, 2, 3, 1], [5, 4, 2, 1, 3], [5, 1, 3, 4, 2], [5, 1, 3, 2, 4], [5, 1, 4, 3, 2], [5, 1, 4, 2, 3], [5, 1, 2, 3, 4], [5, 1, 2, 4, 3], [5, 2, 3, 4, 1], [5, 2, 3, 1, 4], [5, 2, 4, 3, 1], [5, 2, 4, 1, 3], [5, 2, 1, 3, 4], [5, 2, 1, 4, 3], [3, 5, 4, 1, 2], [3, 5, 4, 2, 1], [3, 5, 1, 4, 2], [3, 5, 1, 2, 4], [3, 5, 2, 4, 1], [3, 5, 2, 1, 4], [3, 4, 5, 1, 2], [3, 4, 5, 2, 1], [3, 4, 1, 5, 2], [3, 4, 1, 2, 5], [3, 4, 2, 5, 1], [3, 4, 2, 1, 5], [3, 1, 5, 4, 2], [3, 1, 5, 2, 4], [3, 1, 4, 5, 2], [3, 1, 4, 2, 5], [3, 1, 2, 5, 4], [3, 1, 2, 4, 5], [3, 2, 5, 4, 1], [3, 2, 5, 1, 4], [3, 2, 4, 5, 1], [3, 2, 4, 1, 5], [3, 2, 1, 5, 4], [3, 2, 1, 4, 5], [4, 5, 3, 1, 2], [4, 5, 3, 2, 1], [4, 5, 1, 3, 2], [4, 5, 1, 2, 3], [4, 5, 2, 3, 1], [4, 5, 2, 1, 3], [4, 3, 5, 1, 2], [4, 3, 5, 2, 1], [4, 3, 1, 5, 2], [4, 3, 1, 2, 5], [4, 3, 2, 5, 1], [4, 3, 2, 1, 5], [4, 1, 5, 3, 2], [4, 1, 5, 2, 3], [4, 1, 3, 5, 2], [4, 1, 3, 2, 5], [4, 1, 2, 5, 3], [4, 1, 2, 3, 5], [4, 2, 5, 3, 1], [4, 2, 5, 1, 3], [4, 2, 3, 5, 1], [4, 2, 3, 1, 5], [4, 2, 1, 5, 3], [4, 2, 1, 3, 5], [1, 5, 3, 4, 2], [1, 5, 3, 2, 4], [1, 5, 4, 3, 2], [1, 5, 4, 2, 3], [1, 5, 2, 3, 4], [1, 5, 2, 4, 3], [1, 3, 5, 4, 2], [1, 3, 5, 2, 4], [1, 3, 4, 5, 2], [1, 3, 4, 2, 5], [1, 3, 2, 5, 4], [1, 3, 2, 4, 5], [1, 4, 5, 3, 2], [1, 4, 5, 2, 3], [1, 4, 3, 5, 2], [1, 4, 3, 2, 5], [1, 4, 2, 5, 3], [1, 4, 2, 3, 5], [1, 2, 5, 3, 4], [1, 2, 5, 4, 3], [1, 2, 3, 5, 4], [1, 2, 3, 4, 5], [1, 2, 4, 5, 3], [1, 2, 4, 3, 5], [2, 5, 3, 4, 1], [2, 5, 3, 1, 4], [2, 5, 4, 3, 1], [2, 5, 4, 1, 3], [2, 5, 1, 3, 4], [2, 5, 1, 4, 3], [2, 3, 5, 4, 1], [2, 3, 5, 1, 4], [2, 3, 4, 5, 1], [2, 3, 4, 1, 5], [2, 3, 1, 5, 4], [2, 3, 1, 4, 5], [2, 4, 5, 3, 1], [2, 4, 5, 1, 3], [2, 4, 3, 5, 1], [2, 4, 3, 1, 5], [2, 4, 1, 5, 3], [2, 4, 1, 3, 5], [2, 1, 5, 3, 4], [2, 1, 5, 4, 3], [2, 1, 3, 5, 4], [2, 1, 3, 4, 5], [2, 1, 4, 5, 3], [2, 1, 4, 3, 5]]\n assert candidate(nums = [1, 2, 3]) == [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]\n assert candidate(nums = [2, 3, 5, 7, 11, 13]) == [[2, 3, 5, 7, 11, 13], [2, 3, 5, 7, 13, 11], [2, 3, 5, 11, 7, 13], [2, 3, 5, 11, 13, 7], [2, 3, 5, 13, 7, 11], [2, 3, 5, 13, 11, 7], [2, 3, 7, 5, 11, 13], [2, 3, 7, 5, 13, 11], [2, 3, 7, 11, 5, 13], [2, 3, 7, 11, 13, 5], [2, 3, 7, 13, 5, 11], [2, 3, 7, 13, 11, 5], [2, 3, 11, 5, 7, 13], [2, 3, 11, 5, 13, 7], [2, 3, 11, 7, 5, 13], [2, 3, 11, 7, 13, 5], [2, 3, 11, 13, 5, 7], [2, 3, 11, 13, 7, 5], [2, 3, 13, 5, 7, 11], [2, 3, 13, 5, 11, 7], [2, 3, 13, 7, 5, 11], [2, 3, 13, 7, 11, 5], [2, 3, 13, 11, 5, 7], [2, 3, 13, 11, 7, 5], [2, 5, 3, 7, 11, 13], [2, 5, 3, 7, 13, 11], [2, 5, 3, 11, 7, 13], [2, 5, 3, 11, 13, 7], [2, 5, 3, 13, 7, 11], [2, 5, 3, 13, 11, 7], [2, 5, 7, 3, 11, 13], [2, 5, 7, 3, 13, 11], [2, 5, 7, 11, 3, 13], [2, 5, 7, 11, 13, 3], [2, 5, 7, 13, 3, 11], [2, 5, 7, 13, 11, 3], [2, 5, 11, 3, 7, 13], [2, 5, 11, 3, 13, 7], [2, 5, 11, 7, 3, 13], [2, 5, 11, 7, 13, 3], [2, 5, 11, 13, 3, 7], [2, 5, 11, 13, 7, 3], [2, 5, 13, 3, 7, 11], [2, 5, 13, 3, 11, 7], [2, 5, 13, 7, 3, 11], [2, 5, 13, 7, 11, 3], [2, 5, 13, 11, 3, 7], [2, 5, 13, 11, 7, 3], [2, 7, 3, 5, 11, 13], [2, 7, 3, 5, 13, 11], [2, 7, 3, 11, 5, 13], [2, 7, 3, 11, 13, 5], [2, 7, 3, 13, 5, 11], [2, 7, 3, 13, 11, 5], [2, 7, 5, 3, 11, 13], [2, 7, 5, 3, 13, 11], [2, 7, 5, 11, 3, 13], [2, 7, 5, 11, 13, 3], [2, 7, 5, 13, 3, 11], [2, 7, 5, 13, 11, 3], [2, 7, 11, 3, 5, 13], [2, 7, 11, 3, 13, 5], [2, 7, 11, 5, 3, 13], [2, 7, 11, 5, 13, 3], [2, 7, 11, 13, 3, 5], [2, 7, 11, 13, 5, 3], [2, 7, 13, 3, 5, 11], [2, 7, 13, 3, 11, 5], [2, 7, 13, 5, 3, 11], [2, 7, 13, 5, 11, 3], [2, 7, 13, 11, 3, 5], [2, 7, 13, 11, 5, 3], [2, 11, 3, 5, 7, 13], [2, 11, 3, 5, 13, 7], [2, 11, 3, 7, 5, 13], [2, 11, 3, 7, 13, 5], [2, 11, 3, 13, 5, 7], [2, 11, 3, 13, 7, 5], [2, 11, 5, 3, 7, 13], [2, 11, 5, 3, 13, 7], [2, 11, 5, 7, 3, 13], [2, 11, 5, 7, 13, 3], [2, 11, 5, 13, 3, 7], [2, 11, 5, 13, 7, 3], [2, 11, 7, 3, 5, 13], [2, 11, 7, 3, 13, 5], [2, 11, 7, 5, 3, 13], [2, 11, 7, 5, 13, 3], [2, 11, 7, 13, 3, 5], [2, 11, 7, 13, 5, 3], [2, 11, 13, 3, 5, 7], [2, 11, 13, 3, 7, 5], [2, 11, 13, 5, 3, 7], [2, 11, 13, 5, 7, 3], [2, 11, 13, 7, 3, 5], [2, 11, 13, 7, 5, 3], [2, 13, 3, 5, 7, 11], [2, 13, 3, 5, 11, 7], [2, 13, 3, 7, 5, 11], [2, 13, 3, 7, 11, 5], [2, 13, 3, 11, 5, 7], [2, 13, 3, 11, 7, 5], [2, 13, 5, 3, 7, 11], [2, 13, 5, 3, 11, 7], [2, 13, 5, 7, 3, 11], [2, 13, 5, 7, 11, 3], [2, 13, 5, 11, 3, 7], [2, 13, 5, 11, 7, 3], [2, 13, 7, 3, 5, 11], [2, 13, 7, 3, 11, 5], [2, 13, 7, 5, 3, 11], [2, 13, 7, 5, 11, 3], [2, 13, 7, 11, 3, 5], [2, 13, 7, 11, 5, 3], [2, 13, 11, 3, 5, 7], [2, 13, 11, 3, 7, 5], [2, 13, 11, 5, 3, 7], [2, 13, 11, 5, 7, 3], [2, 13, 11, 7, 3, 5], [2, 13, 11, 7, 5, 3], [3, 2, 5, 7, 11, 13], [3, 2, 5, 7, 13, 11], [3, 2, 5, 11, 7, 13], [3, 2, 5, 11, 13, 7], [3, 2, 5, 13, 7, 11], [3, 2, 5, 13, 11, 7], [3, 2, 7, 5, 11, 13], [3, 2, 7, 5, 13, 11], [3, 2, 7, 11, 5, 13], [3, 2, 7, 11, 13, 5], [3, 2, 7, 13, 5, 11], [3, 2, 7, 13, 11, 5], [3, 2, 11, 5, 7, 13], [3, 2, 11, 5, 13, 7], [3, 2, 11, 7, 5, 13], [3, 2, 11, 7, 13, 5], [3, 2, 11, 13, 5, 7], [3, 2, 11, 13, 7, 5], [3, 2, 13, 5, 7, 11], [3, 2, 13, 5, 11, 7], [3, 2, 13, 7, 5, 11], [3, 2, 13, 7, 11, 5], [3, 2, 13, 11, 5, 7], [3, 2, 13, 11, 7, 5], [3, 5, 2, 7, 11, 13], [3, 5, 2, 7, 13, 11], [3, 5, 2, 11, 7, 13], [3, 5, 2, 11, 13, 7], [3, 5, 2, 13, 7, 11], [3, 5, 2, 13, 11, 7], [3, 5, 7, 2, 11, 13], [3, 5, 7, 2, 13, 11], [3, 5, 7, 11, 2, 13], [3, 5, 7, 11, 13, 2], [3, 5, 7, 13, 2, 11], [3, 5, 7, 13, 11, 2], [3, 5, 11, 2, 7, 13], [3, 5, 11, 2, 13, 7], [3, 5, 11, 7, 2, 13], [3, 5, 11, 7, 13, 2], [3, 5, 11, 13, 2, 7], [3, 5, 11, 13, 7, 2], [3, 5, 13, 2, 7, 11], [3, 5, 13, 2, 11, 7], [3, 5, 13, 7, 2, 11], [3, 5, 13, 7, 11, 2], [3, 5, 13, 11, 2, 7], [3, 5, 13, 11, 7, 2], [3, 7, 2, 5, 11, 13], [3, 7, 2, 5, 13, 11], [3, 7, 2, 11, 5, 13], [3, 7, 2, 11, 13, 5], [3, 7, 2, 13, 5, 11], [3, 7, 2, 13, 11, 5], [3, 7, 5, 2, 11, 13], [3, 7, 5, 2, 13, 11], [3, 7, 5, 11, 2, 13], [3, 7, 5, 11, 13, 2], [3, 7, 5, 13, 2, 11], [3, 7, 5, 13, 11, 2], [3, 7, 11, 2, 5, 13], [3, 7, 11, 2, 13, 5], [3, 7, 11, 5, 2, 13], [3, 7, 11, 5, 13, 2], [3, 7, 11, 13, 2, 5], [3, 7, 11, 13, 5, 2], [3, 7, 13, 2, 5, 11], [3, 7, 13, 2, 11, 5], [3, 7, 13, 5, 2, 11], [3, 7, 13, 5, 11, 2], [3, 7, 13, 11, 2, 5], [3, 7, 13, 11, 5, 2], [3, 11, 2, 5, 7, 13], [3, 11, 2, 5, 13, 7], [3, 11, 2, 7, 5, 13], [3, 11, 2, 7, 13, 5], [3, 11, 2, 13, 5, 7], [3, 11, 2, 13, 7, 5], [3, 11, 5, 2, 7, 13], [3, 11, 5, 2, 13, 7], [3, 11, 5, 7, 2, 13], [3, 11, 5, 7, 13, 2], [3, 11, 5, 13, 2, 7], [3, 11, 5, 13, 7, 2], [3, 11, 7, 2, 5, 13], [3, 11, 7, 2, 13, 5], [3, 11, 7, 5, 2, 13], [3, 11, 7, 5, 13, 2], [3, 11, 7, 13, 2, 5], [3, 11, 7, 13, 5, 2], [3, 11, 13, 2, 5, 7], [3, 11, 13, 2, 7, 5], [3, 11, 13, 5, 2, 7], [3, 11, 13, 5, 7, 2], [3, 11, 13, 7, 2, 5], [3, 11, 13, 7, 5, 2], [3, 13, 2, 5, 7, 11], [3, 13, 2, 5, 11, 7], [3, 13, 2, 7, 5, 11], [3, 13, 2, 7, 11, 5], [3, 13, 2, 11, 5, 7], [3, 13, 2, 11, 7, 5], [3, 13, 5, 2, 7, 11], [3, 13, 5, 2, 11, 7], [3, 13, 5, 7, 2, 11], [3, 13, 5, 7, 11, 2], [3, 13, 5, 11, 2, 7], [3, 13, 5, 11, 7, 2], [3, 13, 7, 2, 5, 11], [3, 13, 7, 2, 11, 5], [3, 13, 7, 5, 2, 11], [3, 13, 7, 5, 11, 2], [3, 13, 7, 11, 2, 5], [3, 13, 7, 11, 5, 2], [3, 13, 11, 2, 5, 7], [3, 13, 11, 2, 7, 5], [3, 13, 11, 5, 2, 7], [3, 13, 11, 5, 7, 2], [3, 13, 11, 7, 2, 5], [3, 13, 11, 7, 5, 2], [5, 2, 3, 7, 11, 13], [5, 2, 3, 7, 13, 11], [5, 2, 3, 11, 7, 13], [5, 2, 3, 11, 13, 7], [5, 2, 3, 13, 7, 11], [5, 2, 3, 13, 11, 7], [5, 2, 7, 3, 11, 13], [5, 2, 7, 3, 13, 11], [5, 2, 7, 11, 3, 13], [5, 2, 7, 11, 13, 3], [5, 2, 7, 13, 3, 11], [5, 2, 7, 13, 11, 3], [5, 2, 11, 3, 7, 13], [5, 2, 11, 3, 13, 7], [5, 2, 11, 7, 3, 13], [5, 2, 11, 7, 13, 3], [5, 2, 11, 13, 3, 7], [5, 2, 11, 13, 7, 3], [5, 2, 13, 3, 7, 11], [5, 2, 13, 3, 11, 7], [5, 2, 13, 7, 3, 11], [5, 2, 13, 7, 11, 3], [5, 2, 13, 11, 3, 7], [5, 2, 13, 11, 7, 3], [5, 3, 2, 7, 11, 13], [5, 3, 2, 7, 13, 11], [5, 3, 2, 11, 7, 13], [5, 3, 2, 11, 13, 7], [5, 3, 2, 13, 7, 11], [5, 3, 2, 13, 11, 7], [5, 3, 7, 2, 11, 13], [5, 3, 7, 2, 13, 11], [5, 3, 7, 11, 2, 13], [5, 3, 7, 11, 13, 2], [5, 3, 7, 13, 2, 11], [5, 3, 7, 13, 11, 2], [5, 3, 11, 2, 7, 13], [5, 3, 11, 2, 13, 7], [5, 3, 11, 7, 2, 13], [5, 3, 11, 7, 13, 2], [5, 3, 11, 13, 2, 7], [5, 3, 11, 13, 7, 2], [5, 3, 13, 2, 7, 11], [5, 3, 13, 2, 11, 7], [5, 3, 13, 7, 2, 11], [5, 3, 13, 7, 11, 2], [5, 3, 13, 11, 2, 7], [5, 3, 13, 11, 7, 2], [5, 7, 2, 3, 11, 13], [5, 7, 2, 3, 13, 11], [5, 7, 2, 11, 3, 13], [5, 7, 2, 11, 13, 3], [5, 7, 2, 13, 3, 11], [5, 7, 2, 13, 11, 3], [5, 7, 3, 2, 11, 13], [5, 7, 3, 2, 13, 11], [5, 7, 3, 11, 2, 13], [5, 7, 3, 11, 13, 2], [5, 7, 3, 13, 2, 11], [5, 7, 3, 13, 11, 2], [5, 7, 11, 2, 3, 13], [5, 7, 11, 2, 13, 3], [5, 7, 11, 3, 2, 13], [5, 7, 11, 3, 13, 2], [5, 7, 11, 13, 2, 3], [5, 7, 11, 13, 3, 2], [5, 7, 13, 2, 3, 11], [5, 7, 13, 2, 11, 3], [5, 7, 13, 3, 2, 11], [5, 7, 13, 3, 11, 2], [5, 7, 13, 11, 2, 3], [5, 7, 13, 11, 3, 2], [5, 11, 2, 3, 7, 13], [5, 11, 2, 3, 13, 7], [5, 11, 2, 7, 3, 13], [5, 11, 2, 7, 13, 3], [5, 11, 2, 13, 3, 7], [5, 11, 2, 13, 7, 3], [5, 11, 3, 2, 7, 13], [5, 11, 3, 2, 13, 7], [5, 11, 3, 7, 2, 13], [5, 11, 3, 7, 13, 2], [5, 11, 3, 13, 2, 7], [5, 11, 3, 13, 7, 2], [5, 11, 7, 2, 3, 13], [5, 11, 7, 2, 13, 3], [5, 11, 7, 3, 2, 13], [5, 11, 7, 3, 13, 2], [5, 11, 7, 13, 2, 3], [5, 11, 7, 13, 3, 2], [5, 11, 13, 2, 3, 7], [5, 11, 13, 2, 7, 3], [5, 11, 13, 3, 2, 7], [5, 11, 13, 3, 7, 2], [5, 11, 13, 7, 2, 3], [5, 11, 13, 7, 3, 2], [5, 13, 2, 3, 7, 11], [5, 13, 2, 3, 11, 7], [5, 13, 2, 7, 3, 11], [5, 13, 2, 7, 11, 3], [5, 13, 2, 11, 3, 7], [5, 13, 2, 11, 7, 3], [5, 13, 3, 2, 7, 11], [5, 13, 3, 2, 11, 7], [5, 13, 3, 7, 2, 11], [5, 13, 3, 7, 11, 2], [5, 13, 3, 11, 2, 7], [5, 13, 3, 11, 7, 2], [5, 13, 7, 2, 3, 11], [5, 13, 7, 2, 11, 3], [5, 13, 7, 3, 2, 11], [5, 13, 7, 3, 11, 2], [5, 13, 7, 11, 2, 3], [5, 13, 7, 11, 3, 2], [5, 13, 11, 2, 3, 7], [5, 13, 11, 2, 7, 3], [5, 13, 11, 3, 2, 7], [5, 13, 11, 3, 7, 2], [5, 13, 11, 7, 2, 3], [5, 13, 11, 7, 3, 2], [7, 2, 3, 5, 11, 13], [7, 2, 3, 5, 13, 11], [7, 2, 3, 11, 5, 13], [7, 2, 3, 11, 13, 5], [7, 2, 3, 13, 5, 11], [7, 2, 3, 13, 11, 5], [7, 2, 5, 3, 11, 13], [7, 2, 5, 3, 13, 11], [7, 2, 5, 11, 3, 13], [7, 2, 5, 11, 13, 3], [7, 2, 5, 13, 3, 11], [7, 2, 5, 13, 11, 3], [7, 2, 11, 3, 5, 13], [7, 2, 11, 3, 13, 5], [7, 2, 11, 5, 3, 13], [7, 2, 11, 5, 13, 3], [7, 2, 11, 13, 3, 5], [7, 2, 11, 13, 5, 3], [7, 2, 13, 3, 5, 11], [7, 2, 13, 3, 11, 5], [7, 2, 13, 5, 3, 11], [7, 2, 13, 5, 11, 3], [7, 2, 13, 11, 3, 5], [7, 2, 13, 11, 5, 3], [7, 3, 2, 5, 11, 13], [7, 3, 2, 5, 13, 11], [7, 3, 2, 11, 5, 13], [7, 3, 2, 11, 13, 5], [7, 3, 2, 13, 5, 11], [7, 3, 2, 13, 11, 5], [7, 3, 5, 2, 11, 13], [7, 3, 5, 2, 13, 11], [7, 3, 5, 11, 2, 13], [7, 3, 5, 11, 13, 2], [7, 3, 5, 13, 2, 11], [7, 3, 5, 13, 11, 2], [7, 3, 11, 2, 5, 13], [7, 3, 11, 2, 13, 5], [7, 3, 11, 5, 2, 13], [7, 3, 11, 5, 13, 2], [7, 3, 11, 13, 2, 5], [7, 3, 11, 13, 5, 2], [7, 3, 13, 2, 5, 11], [7, 3, 13, 2, 11, 5], [7, 3, 13, 5, 2, 11], [7, 3, 13, 5, 11, 2], [7, 3, 13, 11, 2, 5], [7, 3, 13, 11, 5, 2], [7, 5, 2, 3, 11, 13], [7, 5, 2, 3, 13, 11], [7, 5, 2, 11, 3, 13], [7, 5, 2, 11, 13, 3], [7, 5, 2, 13, 3, 11], [7, 5, 2, 13, 11, 3], [7, 5, 3, 2, 11, 13], [7, 5, 3, 2, 13, 11], [7, 5, 3, 11, 2, 13], [7, 5, 3, 11, 13, 2], [7, 5, 3, 13, 2, 11], [7, 5, 3, 13, 11, 2], [7, 5, 11, 2, 3, 13], [7, 5, 11, 2, 13, 3], [7, 5, 11, 3, 2, 13], [7, 5, 11, 3, 13, 2], [7, 5, 11, 13, 2, 3], [7, 5, 11, 13, 3, 2], [7, 5, 13, 2, 3, 11], [7, 5, 13, 2, 11, 3], [7, 5, 13, 3, 2, 11], [7, 5, 13, 3, 11, 2], [7, 5, 13, 11, 2, 3], [7, 5, 13, 11, 3, 2], [7, 11, 2, 3, 5, 13], [7, 11, 2, 3, 13, 5], [7, 11, 2, 5, 3, 13], [7, 11, 2, 5, 13, 3], [7, 11, 2, 13, 3, 5], [7, 11, 2, 13, 5, 3], [7, 11, 3, 2, 5, 13], [7, 11, 3, 2, 13, 5], [7, 11, 3, 5, 2, 13], [7, 11, 3, 5, 13, 2], [7, 11, 3, 13, 2, 5], [7, 11, 3, 13, 5, 2], [7, 11, 5, 2, 3, 13], [7, 11, 5, 2, 13, 3], [7, 11, 5, 3, 2, 13], [7, 11, 5, 3, 13, 2], [7, 11, 5, 13, 2, 3], [7, 11, 5, 13, 3, 2], [7, 11, 13, 2, 3, 5], [7, 11, 13, 2, 5, 3], [7, 11, 13, 3, 2, 5], [7, 11, 13, 3, 5, 2], [7, 11, 13, 5, 2, 3], [7, 11, 13, 5, 3, 2], [7, 13, 2, 3, 5, 11], [7, 13, 2, 3, 11, 5], [7, 13, 2, 5, 3, 11], [7, 13, 2, 5, 11, 3], [7, 13, 2, 11, 3, 5], [7, 13, 2, 11, 5, 3], [7, 13, 3, 2, 5, 11], [7, 13, 3, 2, 11, 5], [7, 13, 3, 5, 2, 11], [7, 13, 3, 5, 11, 2], [7, 13, 3, 11, 2, 5], [7, 13, 3, 11, 5, 2], [7, 13, 5, 2, 3, 11], [7, 13, 5, 2, 11, 3], [7, 13, 5, 3, 2, 11], [7, 13, 5, 3, 11, 2], [7, 13, 5, 11, 2, 3], [7, 13, 5, 11, 3, 2], [7, 13, 11, 2, 3, 5], [7, 13, 11, 2, 5, 3], [7, 13, 11, 3, 2, 5], [7, 13, 11, 3, 5, 2], [7, 13, 11, 5, 2, 3], [7, 13, 11, 5, 3, 2], [11, 2, 3, 5, 7, 13], [11, 2, 3, 5, 13, 7], [11, 2, 3, 7, 5, 13], [11, 2, 3, 7, 13, 5], [11, 2, 3, 13, 5, 7], [11, 2, 3, 13, 7, 5], [11, 2, 5, 3, 7, 13], [11, 2, 5, 3, 13, 7], [11, 2, 5, 7, 3, 13], [11, 2, 5, 7, 13, 3], [11, 2, 5, 13, 3, 7], [11, 2, 5, 13, 7, 3], [11, 2, 7, 3, 5, 13], [11, 2, 7, 3, 13, 5], [11, 2, 7, 5, 3, 13], [11, 2, 7, 5, 13, 3], [11, 2, 7, 13, 3, 5], [11, 2, 7, 13, 5, 3], [11, 2, 13, 3, 5, 7], [11, 2, 13, 3, 7, 5], [11, 2, 13, 5, 3, 7], [11, 2, 13, 5, 7, 3], [11, 2, 13, 7, 3, 5], [11, 2, 13, 7, 5, 3], [11, 3, 2, 5, 7, 13], [11, 3, 2, 5, 13, 7], [11, 3, 2, 7, 5, 13], [11, 3, 2, 7, 13, 5], [11, 3, 2, 13, 5, 7], [11, 3, 2, 13, 7, 5], [11, 3, 5, 2, 7, 13], [11, 3, 5, 2, 13, 7], [11, 3, 5, 7, 2, 13], [11, 3, 5, 7, 13, 2], [11, 3, 5, 13, 2, 7], [11, 3, 5, 13, 7, 2], [11, 3, 7, 2, 5, 13], [11, 3, 7, 2, 13, 5], [11, 3, 7, 5, 2, 13], [11, 3, 7, 5, 13, 2], [11, 3, 7, 13, 2, 5], [11, 3, 7, 13, 5, 2], [11, 3, 13, 2, 5, 7], [11, 3, 13, 2, 7, 5], [11, 3, 13, 5, 2, 7], [11, 3, 13, 5, 7, 2], [11, 3, 13, 7, 2, 5], [11, 3, 13, 7, 5, 2], [11, 5, 2, 3, 7, 13], [11, 5, 2, 3, 13, 7], [11, 5, 2, 7, 3, 13], [11, 5, 2, 7, 13, 3], [11, 5, 2, 13, 3, 7], [11, 5, 2, 13, 7, 3], [11, 5, 3, 2, 7, 13], [11, 5, 3, 2, 13, 7], [11, 5, 3, 7, 2, 13], [11, 5, 3, 7, 13, 2], [11, 5, 3, 13, 2, 7], [11, 5, 3, 13, 7, 2], [11, 5, 7, 2, 3, 13], [11, 5, 7, 2, 13, 3], [11, 5, 7, 3, 2, 13], [11, 5, 7, 3, 13, 2], [11, 5, 7, 13, 2, 3], [11, 5, 7, 13, 3, 2], [11, 5, 13, 2, 3, 7], [11, 5, 13, 2, 7, 3], [11, 5, 13, 3, 2, 7], [11, 5, 13, 3, 7, 2], [11, 5, 13, 7, 2, 3], [11, 5, 13, 7, 3, 2], [11, 7, 2, 3, 5, 13], [11, 7, 2, 3, 13, 5], [11, 7, 2, 5, 3, 13], [11, 7, 2, 5, 13, 3], [11, 7, 2, 13, 3, 5], [11, 7, 2, 13, 5, 3], [11, 7, 3, 2, 5, 13], [11, 7, 3, 2, 13, 5], [11, 7, 3, 5, 2, 13], [11, 7, 3, 5, 13, 2], [11, 7, 3, 13, 2, 5], [11, 7, 3, 13, 5, 2], [11, 7, 5, 2, 3, 13], [11, 7, 5, 2, 13, 3], [11, 7, 5, 3, 2, 13], [11, 7, 5, 3, 13, 2], [11, 7, 5, 13, 2, 3], [11, 7, 5, 13, 3, 2], [11, 7, 13, 2, 3, 5], [11, 7, 13, 2, 5, 3], [11, 7, 13, 3, 2, 5], [11, 7, 13, 3, 5, 2], [11, 7, 13, 5, 2, 3], [11, 7, 13, 5, 3, 2], [11, 13, 2, 3, 5, 7], [11, 13, 2, 3, 7, 5], [11, 13, 2, 5, 3, 7], [11, 13, 2, 5, 7, 3], [11, 13, 2, 7, 3, 5], [11, 13, 2, 7, 5, 3], [11, 13, 3, 2, 5, 7], [11, 13, 3, 2, 7, 5], [11, 13, 3, 5, 2, 7], [11, 13, 3, 5, 7, 2], [11, 13, 3, 7, 2, 5], [11, 13, 3, 7, 5, 2], [11, 13, 5, 2, 3, 7], [11, 13, 5, 2, 7, 3], [11, 13, 5, 3, 2, 7], [11, 13, 5, 3, 7, 2], [11, 13, 5, 7, 2, 3], [11, 13, 5, 7, 3, 2], [11, 13, 7, 2, 3, 5], [11, 13, 7, 2, 5, 3], [11, 13, 7, 3, 2, 5], [11, 13, 7, 3, 5, 2], [11, 13, 7, 5, 2, 3], [11, 13, 7, 5, 3, 2], [13, 2, 3, 5, 7, 11], [13, 2, 3, 5, 11, 7], [13, 2, 3, 7, 5, 11], [13, 2, 3, 7, 11, 5], [13, 2, 3, 11, 5, 7], [13, 2, 3, 11, 7, 5], [13, 2, 5, 3, 7, 11], [13, 2, 5, 3, 11, 7], [13, 2, 5, 7, 3, 11], [13, 2, 5, 7, 11, 3], [13, 2, 5, 11, 3, 7], [13, 2, 5, 11, 7, 3], [13, 2, 7, 3, 5, 11], [13, 2, 7, 3, 11, 5], [13, 2, 7, 5, 3, 11], [13, 2, 7, 5, 11, 3], [13, 2, 7, 11, 3, 5], [13, 2, 7, 11, 5, 3], [13, 2, 11, 3, 5, 7], [13, 2, 11, 3, 7, 5], [13, 2, 11, 5, 3, 7], [13, 2, 11, 5, 7, 3], [13, 2, 11, 7, 3, 5], [13, 2, 11, 7, 5, 3], [13, 3, 2, 5, 7, 11], [13, 3, 2, 5, 11, 7], [13, 3, 2, 7, 5, 11], [13, 3, 2, 7, 11, 5], [13, 3, 2, 11, 5, 7], [13, 3, 2, 11, 7, 5], [13, 3, 5, 2, 7, 11], [13, 3, 5, 2, 11, 7], [13, 3, 5, 7, 2, 11], [13, 3, 5, 7, 11, 2], [13, 3, 5, 11, 2, 7], [13, 3, 5, 11, 7, 2], [13, 3, 7, 2, 5, 11], [13, 3, 7, 2, 11, 5], [13, 3, 7, 5, 2, 11], [13, 3, 7, 5, 11, 2], [13, 3, 7, 11, 2, 5], [13, 3, 7, 11, 5, 2], [13, 3, 11, 2, 5, 7], [13, 3, 11, 2, 7, 5], [13, 3, 11, 5, 2, 7], [13, 3, 11, 5, 7, 2], [13, 3, 11, 7, 2, 5], [13, 3, 11, 7, 5, 2], [13, 5, 2, 3, 7, 11], [13, 5, 2, 3, 11, 7], [13, 5, 2, 7, 3, 11], [13, 5, 2, 7, 11, 3], [13, 5, 2, 11, 3, 7], [13, 5, 2, 11, 7, 3], [13, 5, 3, 2, 7, 11], [13, 5, 3, 2, 11, 7], [13, 5, 3, 7, 2, 11], [13, 5, 3, 7, 11, 2], [13, 5, 3, 11, 2, 7], [13, 5, 3, 11, 7, 2], [13, 5, 7, 2, 3, 11], [13, 5, 7, 2, 11, 3], [13, 5, 7, 3, 2, 11], [13, 5, 7, 3, 11, 2], [13, 5, 7, 11, 2, 3], [13, 5, 7, 11, 3, 2], [13, 5, 11, 2, 3, 7], [13, 5, 11, 2, 7, 3], [13, 5, 11, 3, 2, 7], [13, 5, 11, 3, 7, 2], [13, 5, 11, 7, 2, 3], [13, 5, 11, 7, 3, 2], [13, 7, 2, 3, 5, 11], [13, 7, 2, 3, 11, 5], [13, 7, 2, 5, 3, 11], [13, 7, 2, 5, 11, 3], [13, 7, 2, 11, 3, 5], [13, 7, 2, 11, 5, 3], [13, 7, 3, 2, 5, 11], [13, 7, 3, 2, 11, 5], [13, 7, 3, 5, 2, 11], [13, 7, 3, 5, 11, 2], [13, 7, 3, 11, 2, 5], [13, 7, 3, 11, 5, 2], [13, 7, 5, 2, 3, 11], [13, 7, 5, 2, 11, 3], [13, 7, 5, 3, 2, 11], [13, 7, 5, 3, 11, 2], [13, 7, 5, 11, 2, 3], [13, 7, 5, 11, 3, 2], [13, 7, 11, 2, 3, 5], [13, 7, 11, 2, 5, 3], [13, 7, 11, 3, 2, 5], [13, 7, 11, 3, 5, 2], [13, 7, 11, 5, 2, 3], [13, 7, 11, 5, 3, 2], [13, 11, 2, 3, 5, 7], [13, 11, 2, 3, 7, 5], [13, 11, 2, 5, 3, 7], [13, 11, 2, 5, 7, 3], [13, 11, 2, 7, 3, 5], [13, 11, 2, 7, 5, 3], [13, 11, 3, 2, 5, 7], [13, 11, 3, 2, 7, 5], [13, 11, 3, 5, 2, 7], [13, 11, 3, 5, 7, 2], [13, 11, 3, 7, 2, 5], [13, 11, 3, 7, 5, 2], [13, 11, 5, 2, 3, 7], [13, 11, 5, 2, 7, 3], [13, 11, 5, 3, 2, 7], [13, 11, 5, 3, 7, 2], [13, 11, 5, 7, 2, 3], [13, 11, 5, 7, 3, 2], [13, 11, 7, 2, 3, 5], [13, 11, 7, 2, 5, 3], [13, 11, 7, 3, 2, 5], [13, 11, 7, 3, 5, 2], [13, 11, 7, 5, 2, 3], [13, 11, 7, 5, 3, 2]]\n assert candidate(nums = [0, 1]) == [[0, 1], [1, 0]]\n assert candidate(nums = [3, 1, 2]) == [[3, 1, 2], [3, 2, 1], [1, 3, 2], [1, 2, 3], [2, 3, 1], [2, 1, 3]]\n assert candidate(nums = [-1, 2, -3, 4, 5]) == [[-1, 2, -3, 4, 5], [-1, 2, -3, 5, 4], [-1, 2, 4, -3, 5], [-1, 2, 4, 5, -3], [-1, 2, 5, -3, 4], [-1, 2, 5, 4, -3], [-1, -3, 2, 4, 5], [-1, -3, 2, 5, 4], [-1, -3, 4, 2, 5], [-1, -3, 4, 5, 2], [-1, -3, 5, 2, 4], [-1, -3, 5, 4, 2], [-1, 4, 2, -3, 5], [-1, 4, 2, 5, -3], [-1, 4, -3, 2, 5], [-1, 4, -3, 5, 2], [-1, 4, 5, 2, -3], [-1, 4, 5, -3, 2], [-1, 5, 2, -3, 4], [-1, 5, 2, 4, -3], [-1, 5, -3, 2, 4], [-1, 5, -3, 4, 2], [-1, 5, 4, 2, -3], [-1, 5, 4, -3, 2], [2, -1, -3, 4, 5], [2, -1, -3, 5, 4], [2, -1, 4, -3, 5], [2, -1, 4, 5, -3], [2, -1, 5, -3, 4], [2, -1, 5, 4, -3], [2, -3, -1, 4, 5], [2, -3, -1, 5, 4], [2, -3, 4, -1, 5], [2, -3, 4, 5, -1], [2, -3, 5, -1, 4], [2, -3, 5, 4, -1], [2, 4, -1, -3, 5], [2, 4, -1, 5, -3], [2, 4, -3, -1, 5], [2, 4, -3, 5, -1], [2, 4, 5, -1, -3], [2, 4, 5, -3, -1], [2, 5, -1, -3, 4], [2, 5, -1, 4, -3], [2, 5, -3, -1, 4], [2, 5, -3, 4, -1], [2, 5, 4, -1, -3], [2, 5, 4, -3, -1], [-3, -1, 2, 4, 5], [-3, -1, 2, 5, 4], [-3, -1, 4, 2, 5], [-3, -1, 4, 5, 2], [-3, -1, 5, 2, 4], [-3, -1, 5, 4, 2], [-3, 2, -1, 4, 5], [-3, 2, -1, 5, 4], [-3, 2, 4, -1, 5], [-3, 2, 4, 5, -1], [-3, 2, 5, -1, 4], [-3, 2, 5, 4, -1], [-3, 4, -1, 2, 5], [-3, 4, -1, 5, 2], [-3, 4, 2, -1, 5], [-3, 4, 2, 5, -1], [-3, 4, 5, -1, 2], [-3, 4, 5, 2, -1], [-3, 5, -1, 2, 4], [-3, 5, -1, 4, 2], [-3, 5, 2, -1, 4], [-3, 5, 2, 4, -1], [-3, 5, 4, -1, 2], [-3, 5, 4, 2, -1], [4, -1, 2, -3, 5], [4, -1, 2, 5, -3], [4, -1, -3, 2, 5], [4, -1, -3, 5, 2], [4, -1, 5, 2, -3], [4, -1, 5, -3, 2], [4, 2, -1, -3, 5], [4, 2, -1, 5, -3], [4, 2, -3, -1, 5], [4, 2, -3, 5, -1], [4, 2, 5, -1, -3], [4, 2, 5, -3, -1], [4, -3, -1, 2, 5], [4, -3, -1, 5, 2], [4, -3, 2, -1, 5], [4, -3, 2, 5, -1], [4, -3, 5, -1, 2], [4, -3, 5, 2, -1], [4, 5, -1, 2, -3], [4, 5, -1, -3, 2], [4, 5, 2, -1, -3], [4, 5, 2, -3, -1], [4, 5, -3, -1, 2], [4, 5, -3, 2, -1], [5, -1, 2, -3, 4], [5, -1, 2, 4, -3], [5, -1, -3, 2, 4], [5, -1, -3, 4, 2], [5, -1, 4, 2, -3], [5, -1, 4, -3, 2], [5, 2, -1, -3, 4], [5, 2, -1, 4, -3], [5, 2, -3, -1, 4], [5, 2, -3, 4, -1], [5, 2, 4, -1, -3], [5, 2, 4, -3, -1], [5, -3, -1, 2, 4], [5, -3, -1, 4, 2], [5, -3, 2, -1, 4], [5, -3, 2, 4, -1], [5, -3, 4, -1, 2], [5, -3, 4, 2, -1], [5, 4, -1, 2, -3], [5, 4, -1, -3, 2], [5, 4, 2, -1, -3], [5, 4, 2, -3, -1], [5, 4, -3, -1, 2], [5, 4, -3, 2, -1]]\n assert candidate(nums = [-1, 2, -3]) == [[-1, 2, -3], [-1, -3, 2], [2, -1, -3], [2, -3, -1], [-3, -1, 2], [-3, 2, -1]]\n assert candidate(nums = [-1, 0, 1]) == [[-1, 0, 1], [-1, 1, 0], [0, -1, 1], [0, 1, -1], [1, -1, 0], [1, 0, -1]]\n assert candidate(nums = [10, 20, 30, 40]) == [[10, 20, 30, 40], [10, 20, 40, 30], [10, 30, 20, 40], [10, 30, 40, 20], [10, 40, 20, 30], [10, 40, 30, 20], [20, 10, 30, 40], [20, 10, 40, 30], [20, 30, 10, 40], [20, 30, 40, 10], [20, 40, 10, 30], [20, 40, 30, 10], [30, 10, 20, 40], [30, 10, 40, 20], [30, 20, 10, 40], [30, 20, 40, 10], [30, 40, 10, 20], [30, 40, 20, 10], [40, 10, 20, 30], [40, 10, 30, 20], [40, 20, 10, 30], [40, 20, 30, 10], [40, 30, 10, 20], [40, 30, 20, 10]]\n assert candidate(nums = [5, 15, -5, 0, 25]) == [[5, 15, -5, 0, 25], [5, 15, -5, 25, 0], [5, 15, 0, -5, 25], [5, 15, 0, 25, -5], [5, 15, 25, -5, 0], [5, 15, 25, 0, -5], [5, -5, 15, 0, 25], [5, -5, 15, 25, 0], [5, -5, 0, 15, 25], [5, -5, 0, 25, 15], [5, -5, 25, 15, 0], [5, -5, 25, 0, 15], [5, 0, 15, -5, 25], [5, 0, 15, 25, -5], [5, 0, -5, 15, 25], [5, 0, -5, 25, 15], [5, 0, 25, 15, -5], [5, 0, 25, -5, 15], [5, 25, 15, -5, 0], [5, 25, 15, 0, -5], [5, 25, -5, 15, 0], [5, 25, -5, 0, 15], [5, 25, 0, 15, -5], [5, 25, 0, -5, 15], [15, 5, -5, 0, 25], [15, 5, -5, 25, 0], [15, 5, 0, -5, 25], [15, 5, 0, 25, -5], [15, 5, 25, -5, 0], [15, 5, 25, 0, -5], [15, -5, 5, 0, 25], [15, -5, 5, 25, 0], [15, -5, 0, 5, 25], [15, -5, 0, 25, 5], [15, -5, 25, 5, 0], [15, -5, 25, 0, 5], [15, 0, 5, -5, 25], [15, 0, 5, 25, -5], [15, 0, -5, 5, 25], [15, 0, -5, 25, 5], [15, 0, 25, 5, -5], [15, 0, 25, -5, 5], [15, 25, 5, -5, 0], [15, 25, 5, 0, -5], [15, 25, -5, 5, 0], [15, 25, -5, 0, 5], [15, 25, 0, 5, -5], [15, 25, 0, -5, 5], [-5, 5, 15, 0, 25], [-5, 5, 15, 25, 0], [-5, 5, 0, 15, 25], [-5, 5, 0, 25, 15], [-5, 5, 25, 15, 0], [-5, 5, 25, 0, 15], [-5, 15, 5, 0, 25], [-5, 15, 5, 25, 0], [-5, 15, 0, 5, 25], [-5, 15, 0, 25, 5], [-5, 15, 25, 5, 0], [-5, 15, 25, 0, 5], [-5, 0, 5, 15, 25], [-5, 0, 5, 25, 15], [-5, 0, 15, 5, 25], [-5, 0, 15, 25, 5], [-5, 0, 25, 5, 15], [-5, 0, 25, 15, 5], [-5, 25, 5, 15, 0], [-5, 25, 5, 0, 15], [-5, 25, 15, 5, 0], [-5, 25, 15, 0, 5], [-5, 25, 0, 5, 15], [-5, 25, 0, 15, 5], [0, 5, 15, -5, 25], [0, 5, 15, 25, -5], [0, 5, -5, 15, 25], [0, 5, -5, 25, 15], [0, 5, 25, 15, -5], [0, 5, 25, -5, 15], [0, 15, 5, -5, 25], [0, 15, 5, 25, -5], [0, 15, -5, 5, 25], [0, 15, -5, 25, 5], [0, 15, 25, 5, -5], [0, 15, 25, -5, 5], [0, -5, 5, 15, 25], [0, -5, 5, 25, 15], [0, -5, 15, 5, 25], [0, -5, 15, 25, 5], [0, -5, 25, 5, 15], [0, -5, 25, 15, 5], [0, 25, 5, 15, -5], [0, 25, 5, -5, 15], [0, 25, 15, 5, -5], [0, 25, 15, -5, 5], [0, 25, -5, 5, 15], [0, 25, -5, 15, 5], [25, 5, 15, -5, 0], [25, 5, 15, 0, -5], [25, 5, -5, 15, 0], [25, 5, -5, 0, 15], [25, 5, 0, 15, -5], [25, 5, 0, -5, 15], [25, 15, 5, -5, 0], [25, 15, 5, 0, -5], [25, 15, -5, 5, 0], [25, 15, -5, 0, 5], [25, 15, 0, 5, -5], [25, 15, 0, -5, 5], [25, -5, 5, 15, 0], [25, -5, 5, 0, 15], [25, -5, 15, 5, 0], [25, -5, 15, 0, 5], [25, -5, 0, 5, 15], [25, -5, 0, 15, 5], [25, 0, 5, 15, -5], [25, 0, 5, -5, 15], [25, 0, 15, 5, -5], [25, 0, 15, -5, 5], [25, 0, -5, 5, 15], [25, 0, -5, 15, 5]]\n assert candidate(nums = [5, 3, 8, 6]) == [[5, 3, 8, 6], [5, 3, 6, 8], [5, 8, 3, 6], [5, 8, 6, 3], [5, 6, 3, 8], [5, 6, 8, 3], [3, 5, 8, 6], [3, 5, 6, 8], [3, 8, 5, 6], [3, 8, 6, 5], [3, 6, 5, 8], [3, 6, 8, 5], [8, 5, 3, 6], [8, 5, 6, 3], [8, 3, 5, 6], [8, 3, 6, 5], [8, 6, 5, 3], [8, 6, 3, 5], [6, 5, 3, 8], [6, 5, 8, 3], [6, 3, 5, 8], [6, 3, 8, 5], [6, 8, 5, 3], [6, 8, 3, 5]]\n assert candidate(nums = [-7, -8, -9, -10]) == [[-7, -8, -9, -10], [-7, -8, -10, -9], [-7, -9, -8, -10], [-7, -9, -10, -8], [-7, -10, -8, -9], [-7, -10, -9, -8], [-8, -7, -9, -10], [-8, -7, -10, -9], [-8, -9, -7, -10], [-8, -9, -10, -7], [-8, -10, -7, -9], [-8, -10, -9, -7], [-9, -7, -8, -10], [-9, -7, -10, -8], [-9, -8, -7, -10], [-9, -8, -10, -7], [-9, -10, -7, -8], [-9, -10, -8, -7], [-10, -7, -8, -9], [-10, -7, -9, -8], [-10, -8, -7, -9], [-10, -8, -9, -7], [-10, -9, -7, -8], [-10, -9, -8, -7]]\n assert candidate(nums = [-10, -20, -30, -40, -50, -60]) == [[-10, -20, -30, -40, -50, -60], [-10, -20, -30, -40, -60, -50], [-10, -20, -30, -50, -40, -60], [-10, -20, -30, -50, -60, -40], [-10, -20, -30, -60, -40, -50], [-10, -20, -30, -60, -50, -40], [-10, -20, -40, -30, -50, -60], [-10, -20, -40, -30, -60, -50], [-10, -20, -40, -50, -30, -60], [-10, -20, -40, -50, -60, -30], [-10, -20, -40, -60, -30, -50], [-10, -20, -40, -60, -50, -30], [-10, -20, -50, -30, -40, -60], [-10, -20, -50, -30, -60, -40], [-10, -20, -50, -40, -30, -60], [-10, -20, -50, -40, -60, -30], [-10, -20, -50, -60, -30, -40], [-10, -20, -50, -60, -40, -30], [-10, -20, -60, -30, -40, -50], [-10, -20, -60, -30, -50, -40], [-10, -20, -60, -40, -30, -50], [-10, -20, -60, -40, -50, -30], [-10, -20, -60, -50, -30, -40], [-10, -20, -60, -50, -40, -30], [-10, -30, -20, -40, -50, -60], [-10, -30, -20, -40, -60, -50], [-10, -30, -20, -50, -40, -60], [-10, -30, -20, -50, -60, -40], [-10, -30, -20, -60, -40, -50], [-10, -30, -20, -60, -50, -40], [-10, -30, -40, -20, -50, -60], [-10, -30, -40, -20, -60, -50], [-10, -30, -40, -50, -20, -60], [-10, -30, -40, -50, -60, -20], [-10, -30, -40, -60, -20, -50], [-10, -30, -40, -60, -50, -20], [-10, -30, -50, -20, -40, -60], [-10, -30, -50, -20, -60, -40], [-10, -30, -50, -40, -20, -60], [-10, -30, -50, -40, -60, -20], [-10, -30, -50, -60, -20, -40], [-10, -30, -50, -60, -40, -20], [-10, -30, -60, -20, -40, -50], [-10, -30, -60, -20, -50, -40], [-10, -30, -60, -40, -20, -50], [-10, -30, -60, -40, -50, -20], [-10, -30, -60, -50, -20, -40], [-10, -30, -60, -50, -40, -20], [-10, -40, -20, -30, -50, -60], [-10, -40, -20, -30, -60, -50], [-10, -40, -20, -50, -30, -60], [-10, -40, -20, -50, -60, -30], [-10, -40, -20, -60, -30, -50], [-10, -40, -20, -60, -50, -30], [-10, -40, -30, -20, -50, -60], [-10, -40, -30, -20, -60, -50], [-10, -40, -30, -50, -20, -60], [-10, -40, -30, -50, -60, -20], [-10, -40, -30, -60, -20, -50], [-10, -40, -30, -60, -50, -20], [-10, -40, -50, -20, -30, -60], [-10, -40, -50, -20, -60, -30], [-10, -40, -50, -30, -20, -60], [-10, -40, -50, -30, -60, -20], [-10, -40, -50, -60, -20, -30], [-10, -40, -50, -60, -30, -20], [-10, -40, -60, -20, -30, -50], [-10, -40, -60, -20, -50, -30], [-10, -40, -60, -30, -20, -50], [-10, -40, -60, -30, -50, -20], [-10, -40, -60, -50, -20, -30], [-10, -40, -60, -50, -30, -20], [-10, -50, -20, -30, -40, -60], [-10, -50, -20, -30, -60, -40], [-10, -50, -20, -40, -30, -60], [-10, -50, -20, -40, -60, -30], [-10, -50, -20, -60, -30, -40], [-10, -50, -20, -60, -40, -30], [-10, -50, -30, -20, -40, -60], [-10, -50, -30, -20, -60, -40], [-10, -50, -30, -40, -20, -60], [-10, -50, -30, -40, -60, -20], [-10, -50, -30, -60, -20, -40], [-10, -50, -30, -60, -40, -20], [-10, -50, -40, -20, -30, -60], [-10, -50, -40, -20, -60, -30], [-10, -50, -40, -30, -20, -60], [-10, -50, -40, -30, -60, -20], [-10, -50, -40, -60, -20, -30], [-10, -50, -40, -60, -30, -20], [-10, -50, -60, -20, -30, -40], [-10, -50, -60, -20, -40, -30], [-10, -50, -60, -30, -20, -40], [-10, -50, -60, -30, -40, -20], [-10, -50, -60, -40, -20, -30], [-10, -50, -60, -40, -30, -20], [-10, -60, -20, -30, -40, -50], [-10, -60, -20, -30, -50, -40], [-10, -60, -20, -40, -30, -50], [-10, -60, -20, -40, -50, -30], [-10, -60, -20, -50, -30, -40], [-10, -60, -20, -50, -40, -30], [-10, -60, -30, -20, -40, -50], [-10, -60, -30, -20, -50, -40], [-10, -60, -30, -40, -20, -50], [-10, -60, -30, -40, -50, -20], [-10, -60, -30, -50, -20, -40], [-10, -60, -30, -50, -40, -20], [-10, -60, -40, -20, -30, -50], [-10, -60, -40, -20, -50, -30], [-10, -60, -40, -30, -20, -50], [-10, -60, -40, -30, -50, -20], [-10, -60, -40, -50, -20, -30], [-10, -60, -40, -50, -30, -20], [-10, -60, -50, -20, -30, -40], [-10, -60, -50, -20, -40, -30], [-10, -60, -50, -30, -20, -40], [-10, -60, -50, -30, -40, -20], [-10, -60, -50, -40, -20, -30], [-10, -60, -50, -40, -30, -20], [-20, -10, -30, -40, -50, -60], [-20, -10, -30, -40, -60, -50], [-20, -10, -30, -50, -40, -60], [-20, -10, -30, -50, -60, -40], [-20, -10, -30, -60, -40, -50], [-20, -10, -30, -60, -50, -40], [-20, -10, -40, -30, -50, -60], [-20, -10, -40, -30, -60, -50], [-20, -10, -40, -50, -30, -60], [-20, -10, -40, -50, -60, -30], [-20, -10, -40, -60, -30, -50], [-20, -10, -40, -60, -50, -30], [-20, -10, -50, -30, -40, -60], [-20, -10, -50, -30, -60, -40], [-20, -10, -50, -40, -30, -60], [-20, -10, -50, -40, -60, -30], [-20, -10, -50, -60, -30, -40], [-20, -10, -50, -60, -40, -30], [-20, -10, -60, -30, -40, -50], [-20, -10, -60, -30, -50, -40], [-20, -10, -60, -40, -30, -50], [-20, -10, -60, -40, -50, -30], [-20, -10, -60, -50, -30, -40], [-20, -10, -60, -50, -40, -30], [-20, -30, -10, -40, -50, -60], [-20, -30, -10, -40, -60, -50], [-20, -30, -10, -50, -40, -60], [-20, -30, -10, -50, -60, -40], [-20, -30, -10, -60, -40, -50], [-20, -30, -10, -60, -50, -40], [-20, -30, -40, -10, -50, -60], [-20, -30, -40, -10, -60, -50], [-20, -30, -40, -50, -10, -60], [-20, -30, -40, -50, -60, -10], [-20, -30, -40, -60, -10, -50], [-20, -30, -40, -60, -50, -10], [-20, -30, -50, -10, -40, -60], [-20, -30, -50, -10, -60, -40], [-20, -30, -50, -40, -10, -60], [-20, -30, -50, -40, -60, -10], [-20, -30, -50, -60, -10, -40], [-20, -30, -50, -60, -40, -10], [-20, -30, -60, -10, -40, -50], [-20, -30, -60, -10, -50, -40], [-20, -30, -60, -40, -10, -50], [-20, -30, -60, -40, -50, -10], [-20, -30, -60, -50, -10, -40], [-20, -30, -60, -50, -40, -10], [-20, -40, -10, -30, -50, -60], [-20, -40, -10, -30, -60, -50], [-20, -40, -10, -50, -30, -60], [-20, -40, -10, -50, -60, -30], [-20, -40, -10, -60, -30, -50], [-20, -40, -10, -60, -50, -30], [-20, -40, -30, -10, -50, -60], [-20, -40, -30, -10, -60, -50], [-20, -40, -30, -50, -10, -60], [-20, -40, -30, -50, -60, -10], [-20, -40, -30, -60, -10, -50], [-20, -40, -30, -60, -50, -10], [-20, -40, -50, -10, -30, -60], [-20, -40, -50, -10, -60, -30], [-20, -40, -50, -30, -10, -60], [-20, -40, -50, -30, -60, -10], [-20, -40, -50, -60, -10, -30], [-20, -40, -50, -60, -30, -10], [-20, -40, -60, -10, -30, -50], [-20, -40, -60, -10, -50, -30], [-20, -40, -60, -30, -10, -50], [-20, -40, -60, -30, -50, -10], [-20, -40, -60, -50, -10, -30], [-20, -40, -60, -50, -30, -10], [-20, -50, -10, -30, -40, -60], [-20, -50, -10, -30, -60, -40], [-20, -50, -10, -40, -30, -60], [-20, -50, -10, -40, -60, -30], [-20, -50, -10, -60, -30, -40], [-20, -50, -10, -60, -40, -30], [-20, -50, -30, -10, -40, -60], [-20, -50, -30, -10, -60, -40], [-20, -50, -30, -40, -10, -60], [-20, -50, -30, -40, -60, -10], [-20, -50, -30, -60, -10, -40], [-20, -50, -30, -60, -40, -10], [-20, -50, -40, -10, -30, -60], [-20, -50, -40, -10, -60, -30], [-20, -50, -40, -30, -10, -60], [-20, -50, -40, -30, -60, -10], [-20, -50, -40, -60, -10, -30], [-20, -50, -40, -60, -30, -10], [-20, -50, -60, -10, -30, -40], [-20, -50, -60, -10, -40, -30], [-20, -50, -60, -30, -10, -40], [-20, -50, -60, -30, -40, -10], [-20, -50, -60, -40, -10, -30], [-20, -50, -60, -40, -30, -10], [-20, -60, -10, -30, -40, -50], [-20, -60, -10, -30, -50, -40], [-20, -60, -10, -40, -30, -50], [-20, -60, -10, -40, -50, -30], [-20, -60, -10, -50, -30, -40], [-20, -60, -10, -50, -40, -30], [-20, -60, -30, -10, -40, -50], [-20, -60, -30, -10, -50, -40], [-20, -60, -30, -40, -10, -50], [-20, -60, -30, -40, -50, -10], [-20, -60, -30, -50, -10, -40], [-20, -60, -30, -50, -40, -10], [-20, -60, -40, -10, -30, -50], [-20, -60, -40, -10, -50, -30], [-20, -60, -40, -30, -10, -50], [-20, -60, -40, -30, -50, -10], [-20, -60, -40, -50, -10, -30], [-20, -60, -40, -50, -30, -10], [-20, -60, -50, -10, -30, -40], [-20, -60, -50, -10, -40, -30], [-20, -60, -50, -30, -10, -40], [-20, -60, -50, -30, -40, -10], [-20, -60, -50, -40, -10, -30], [-20, -60, -50, -40, -30, -10], [-30, -10, -20, -40, -50, -60], [-30, -10, -20, -40, -60, -50], [-30, -10, -20, -50, -40, -60], [-30, -10, -20, -50, -60, -40], [-30, -10, -20, -60, -40, -50], [-30, -10, -20, -60, -50, -40], [-30, -10, -40, -20, -50, -60], [-30, -10, -40, -20, -60, -50], [-30, -10, -40, -50, -20, -60], [-30, -10, -40, -50, -60, -20], [-30, -10, -40, -60, -20, -50], [-30, -10, -40, -60, -50, -20], [-30, -10, -50, -20, -40, -60], [-30, -10, -50, -20, -60, -40], [-30, -10, -50, -40, -20, -60], [-30, -10, -50, -40, -60, -20], [-30, -10, -50, -60, -20, -40], [-30, -10, -50, -60, -40, -20], [-30, -10, -60, -20, -40, -50], [-30, -10, -60, -20, -50, -40], [-30, -10, -60, -40, -20, -50], [-30, -10, -60, -40, -50, -20], [-30, -10, -60, -50, -20, -40], [-30, -10, -60, -50, -40, -20], [-30, -20, -10, -40, -50, -60], [-30, -20, -10, -40, -60, -50], [-30, -20, -10, -50, -40, -60], [-30, -20, -10, -50, -60, -40], [-30, -20, -10, -60, -40, -50], [-30, -20, -10, -60, -50, -40], [-30, -20, -40, -10, -50, -60], [-30, -20, -40, -10, -60, -50], [-30, -20, -40, -50, -10, -60], [-30, -20, -40, -50, -60, -10], [-30, -20, -40, -60, -10, -50], [-30, -20, -40, -60, 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-50, -40], [-60, -30, -10, -40, -20, -50], [-60, -30, -10, -40, -50, -20], [-60, -30, -10, -50, -20, -40], [-60, -30, -10, -50, -40, -20], [-60, -30, -20, -10, -40, -50], [-60, -30, -20, -10, -50, -40], [-60, -30, -20, -40, -10, -50], [-60, -30, -20, -40, -50, -10], [-60, -30, -20, -50, -10, -40], [-60, -30, -20, -50, -40, -10], [-60, -30, -40, -10, -20, -50], [-60, -30, -40, -10, -50, -20], [-60, -30, -40, -20, -10, -50], [-60, -30, -40, -20, -50, -10], [-60, -30, -40, -50, -10, -20], [-60, -30, -40, -50, -20, -10], [-60, -30, -50, -10, -20, -40], [-60, -30, -50, -10, -40, -20], [-60, -30, -50, -20, -10, -40], [-60, -30, -50, -20, -40, -10], [-60, -30, -50, -40, -10, -20], [-60, -30, -50, -40, -20, -10], [-60, -40, -10, -20, -30, -50], [-60, -40, -10, -20, -50, -30], [-60, -40, -10, -30, -20, -50], [-60, -40, -10, -30, -50, -20], [-60, -40, -10, -50, -20, -30], [-60, -40, -10, -50, -30, -20], [-60, -40, -20, -10, -30, -50], [-60, -40, -20, -10, -50, -30], [-60, -40, -20, -30, -10, -50], [-60, -40, -20, -30, -50, -10], [-60, -40, -20, -50, -10, -30], [-60, -40, -20, -50, -30, -10], [-60, -40, -30, -10, -20, -50], [-60, -40, -30, -10, -50, -20], [-60, -40, -30, -20, -10, -50], [-60, -40, -30, -20, -50, -10], [-60, -40, -30, -50, -10, -20], [-60, -40, -30, -50, -20, -10], [-60, -40, -50, -10, -20, -30], [-60, -40, -50, -10, -30, -20], [-60, -40, -50, -20, -10, -30], [-60, -40, -50, -20, -30, -10], [-60, -40, -50, -30, -10, -20], [-60, -40, -50, -30, -20, -10], [-60, -50, -10, -20, -30, -40], [-60, -50, -10, -20, -40, -30], [-60, -50, -10, -30, -20, -40], [-60, -50, -10, -30, -40, -20], [-60, -50, -10, -40, -20, -30], [-60, -50, -10, -40, -30, -20], [-60, -50, -20, -10, -30, -40], [-60, -50, -20, -10, -40, -30], [-60, -50, -20, -30, -10, -40], [-60, -50, -20, -30, -40, -10], [-60, -50, -20, -40, -10, -30], [-60, -50, -20, -40, -30, -10], [-60, -50, -30, -10, -20, -40], [-60, -50, -30, -10, -40, -20], [-60, -50, -30, -20, -10, -40], [-60, -50, -30, -20, -40, -10], [-60, -50, -30, -40, -10, -20], [-60, -50, -30, -40, -20, -10], [-60, -50, -40, -10, -20, -30], [-60, -50, -40, -10, -30, -20], [-60, -50, -40, -20, -10, -30], [-60, -50, -40, -20, -30, -10], [-60, -50, -40, -30, -10, -20], [-60, -50, -40, -30, -20, -10]]\n assert candidate(nums = [5, 3, 1, 4, 2]) == [[5, 3, 1, 4, 2], [5, 3, 1, 2, 4], [5, 3, 4, 1, 2], [5, 3, 4, 2, 1], [5, 3, 2, 1, 4], [5, 3, 2, 4, 1], [5, 1, 3, 4, 2], [5, 1, 3, 2, 4], [5, 1, 4, 3, 2], [5, 1, 4, 2, 3], [5, 1, 2, 3, 4], [5, 1, 2, 4, 3], [5, 4, 3, 1, 2], [5, 4, 3, 2, 1], [5, 4, 1, 3, 2], [5, 4, 1, 2, 3], [5, 4, 2, 3, 1], [5, 4, 2, 1, 3], [5, 2, 3, 1, 4], [5, 2, 3, 4, 1], [5, 2, 1, 3, 4], [5, 2, 1, 4, 3], [5, 2, 4, 3, 1], [5, 2, 4, 1, 3], [3, 5, 1, 4, 2], [3, 5, 1, 2, 4], [3, 5, 4, 1, 2], [3, 5, 4, 2, 1], [3, 5, 2, 1, 4], [3, 5, 2, 4, 1], [3, 1, 5, 4, 2], [3, 1, 5, 2, 4], [3, 1, 4, 5, 2], [3, 1, 4, 2, 5], [3, 1, 2, 5, 4], [3, 1, 2, 4, 5], [3, 4, 5, 1, 2], [3, 4, 5, 2, 1], [3, 4, 1, 5, 2], [3, 4, 1, 2, 5], [3, 4, 2, 5, 1], [3, 4, 2, 1, 5], [3, 2, 5, 1, 4], [3, 2, 5, 4, 1], [3, 2, 1, 5, 4], [3, 2, 1, 4, 5], [3, 2, 4, 5, 1], [3, 2, 4, 1, 5], [1, 5, 3, 4, 2], [1, 5, 3, 2, 4], [1, 5, 4, 3, 2], [1, 5, 4, 2, 3], [1, 5, 2, 3, 4], [1, 5, 2, 4, 3], [1, 3, 5, 4, 2], [1, 3, 5, 2, 4], [1, 3, 4, 5, 2], [1, 3, 4, 2, 5], [1, 3, 2, 5, 4], [1, 3, 2, 4, 5], [1, 4, 5, 3, 2], [1, 4, 5, 2, 3], [1, 4, 3, 5, 2], [1, 4, 3, 2, 5], [1, 4, 2, 5, 3], [1, 4, 2, 3, 5], [1, 2, 5, 3, 4], [1, 2, 5, 4, 3], [1, 2, 3, 5, 4], [1, 2, 3, 4, 5], [1, 2, 4, 5, 3], [1, 2, 4, 3, 5], [4, 5, 3, 1, 2], [4, 5, 3, 2, 1], [4, 5, 1, 3, 2], [4, 5, 1, 2, 3], [4, 5, 2, 3, 1], [4, 5, 2, 1, 3], [4, 3, 5, 1, 2], [4, 3, 5, 2, 1], [4, 3, 1, 5, 2], [4, 3, 1, 2, 5], [4, 3, 2, 5, 1], [4, 3, 2, 1, 5], [4, 1, 5, 3, 2], [4, 1, 5, 2, 3], [4, 1, 3, 5, 2], [4, 1, 3, 2, 5], [4, 1, 2, 5, 3], [4, 1, 2, 3, 5], [4, 2, 5, 3, 1], [4, 2, 5, 1, 3], [4, 2, 3, 5, 1], [4, 2, 3, 1, 5], [4, 2, 1, 5, 3], [4, 2, 1, 3, 5], [2, 5, 3, 1, 4], [2, 5, 3, 4, 1], [2, 5, 1, 3, 4], [2, 5, 1, 4, 3], [2, 5, 4, 3, 1], [2, 5, 4, 1, 3], [2, 3, 5, 1, 4], [2, 3, 5, 4, 1], [2, 3, 1, 5, 4], [2, 3, 1, 4, 5], [2, 3, 4, 5, 1], [2, 3, 4, 1, 5], [2, 1, 5, 3, 4], [2, 1, 5, 4, 3], [2, 1, 3, 5, 4], [2, 1, 3, 4, 5], [2, 1, 4, 5, 3], [2, 1, 4, 3, 5], [2, 4, 5, 3, 1], [2, 4, 5, 1, 3], [2, 4, 3, 5, 1], [2, 4, 3, 1, 5], [2, 4, 1, 5, 3], [2, 4, 1, 3, 5]]\n assert candidate(nums = [7, 2, 5, 3, 8, 1]) == [[7, 2, 5, 3, 8, 1], [7, 2, 5, 3, 1, 8], [7, 2, 5, 8, 3, 1], [7, 2, 5, 8, 1, 3], [7, 2, 5, 1, 3, 8], [7, 2, 5, 1, 8, 3], [7, 2, 3, 5, 8, 1], [7, 2, 3, 5, 1, 8], [7, 2, 3, 8, 5, 1], [7, 2, 3, 8, 1, 5], [7, 2, 3, 1, 5, 8], [7, 2, 3, 1, 8, 5], [7, 2, 8, 5, 3, 1], [7, 2, 8, 5, 1, 3], [7, 2, 8, 3, 5, 1], [7, 2, 8, 3, 1, 5], [7, 2, 8, 1, 5, 3], [7, 2, 8, 1, 3, 5], [7, 2, 1, 5, 3, 8], [7, 2, 1, 5, 8, 3], [7, 2, 1, 3, 5, 8], [7, 2, 1, 3, 8, 5], [7, 2, 1, 8, 5, 3], [7, 2, 1, 8, 3, 5], [7, 5, 2, 3, 8, 1], [7, 5, 2, 3, 1, 8], [7, 5, 2, 8, 3, 1], [7, 5, 2, 8, 1, 3], [7, 5, 2, 1, 3, 8], [7, 5, 2, 1, 8, 3], [7, 5, 3, 2, 8, 1], [7, 5, 3, 2, 1, 8], [7, 5, 3, 8, 2, 1], [7, 5, 3, 8, 1, 2], [7, 5, 3, 1, 2, 8], [7, 5, 3, 1, 8, 2], [7, 5, 8, 2, 3, 1], [7, 5, 8, 2, 1, 3], [7, 5, 8, 3, 2, 1], [7, 5, 8, 3, 1, 2], [7, 5, 8, 1, 2, 3], [7, 5, 8, 1, 3, 2], [7, 5, 1, 2, 3, 8], [7, 5, 1, 2, 8, 3], [7, 5, 1, 3, 2, 8], [7, 5, 1, 3, 8, 2], [7, 5, 1, 8, 2, 3], [7, 5, 1, 8, 3, 2], [7, 3, 2, 5, 8, 1], [7, 3, 2, 5, 1, 8], [7, 3, 2, 8, 5, 1], [7, 3, 2, 8, 1, 5], [7, 3, 2, 1, 5, 8], [7, 3, 2, 1, 8, 5], [7, 3, 5, 2, 8, 1], [7, 3, 5, 2, 1, 8], [7, 3, 5, 8, 2, 1], [7, 3, 5, 8, 1, 2], [7, 3, 5, 1, 2, 8], [7, 3, 5, 1, 8, 2], [7, 3, 8, 2, 5, 1], [7, 3, 8, 2, 1, 5], [7, 3, 8, 5, 2, 1], [7, 3, 8, 5, 1, 2], [7, 3, 8, 1, 2, 5], [7, 3, 8, 1, 5, 2], [7, 3, 1, 2, 5, 8], [7, 3, 1, 2, 8, 5], [7, 3, 1, 5, 2, 8], [7, 3, 1, 5, 8, 2], [7, 3, 1, 8, 2, 5], [7, 3, 1, 8, 5, 2], [7, 8, 2, 5, 3, 1], [7, 8, 2, 5, 1, 3], [7, 8, 2, 3, 5, 1], [7, 8, 2, 3, 1, 5], [7, 8, 2, 1, 5, 3], [7, 8, 2, 1, 3, 5], [7, 8, 5, 2, 3, 1], [7, 8, 5, 2, 1, 3], [7, 8, 5, 3, 2, 1], [7, 8, 5, 3, 1, 2], [7, 8, 5, 1, 2, 3], [7, 8, 5, 1, 3, 2], [7, 8, 3, 2, 5, 1], [7, 8, 3, 2, 1, 5], [7, 8, 3, 5, 2, 1], [7, 8, 3, 5, 1, 2], [7, 8, 3, 1, 2, 5], [7, 8, 3, 1, 5, 2], [7, 8, 1, 2, 5, 3], [7, 8, 1, 2, 3, 5], [7, 8, 1, 5, 2, 3], [7, 8, 1, 5, 3, 2], [7, 8, 1, 3, 2, 5], [7, 8, 1, 3, 5, 2], [7, 1, 2, 5, 3, 8], [7, 1, 2, 5, 8, 3], [7, 1, 2, 3, 5, 8], [7, 1, 2, 3, 8, 5], [7, 1, 2, 8, 5, 3], [7, 1, 2, 8, 3, 5], [7, 1, 5, 2, 3, 8], [7, 1, 5, 2, 8, 3], [7, 1, 5, 3, 2, 8], [7, 1, 5, 3, 8, 2], [7, 1, 5, 8, 2, 3], [7, 1, 5, 8, 3, 2], [7, 1, 3, 2, 5, 8], [7, 1, 3, 2, 8, 5], [7, 1, 3, 5, 2, 8], [7, 1, 3, 5, 8, 2], [7, 1, 3, 8, 2, 5], [7, 1, 3, 8, 5, 2], [7, 1, 8, 2, 5, 3], [7, 1, 8, 2, 3, 5], [7, 1, 8, 5, 2, 3], [7, 1, 8, 5, 3, 2], [7, 1, 8, 3, 2, 5], [7, 1, 8, 3, 5, 2], [2, 7, 5, 3, 8, 1], [2, 7, 5, 3, 1, 8], [2, 7, 5, 8, 3, 1], [2, 7, 5, 8, 1, 3], [2, 7, 5, 1, 3, 8], [2, 7, 5, 1, 8, 3], [2, 7, 3, 5, 8, 1], [2, 7, 3, 5, 1, 8], [2, 7, 3, 8, 5, 1], [2, 7, 3, 8, 1, 5], [2, 7, 3, 1, 5, 8], [2, 7, 3, 1, 8, 5], [2, 7, 8, 5, 3, 1], [2, 7, 8, 5, 1, 3], [2, 7, 8, 3, 5, 1], [2, 7, 8, 3, 1, 5], [2, 7, 8, 1, 5, 3], [2, 7, 8, 1, 3, 5], [2, 7, 1, 5, 3, 8], [2, 7, 1, 5, 8, 3], [2, 7, 1, 3, 5, 8], [2, 7, 1, 3, 8, 5], [2, 7, 1, 8, 5, 3], [2, 7, 1, 8, 3, 5], [2, 5, 7, 3, 8, 1], [2, 5, 7, 3, 1, 8], [2, 5, 7, 8, 3, 1], [2, 5, 7, 8, 1, 3], [2, 5, 7, 1, 3, 8], [2, 5, 7, 1, 8, 3], [2, 5, 3, 7, 8, 1], [2, 5, 3, 7, 1, 8], [2, 5, 3, 8, 7, 1], [2, 5, 3, 8, 1, 7], [2, 5, 3, 1, 7, 8], [2, 5, 3, 1, 8, 7], [2, 5, 8, 7, 3, 1], [2, 5, 8, 7, 1, 3], [2, 5, 8, 3, 7, 1], [2, 5, 8, 3, 1, 7], [2, 5, 8, 1, 7, 3], [2, 5, 8, 1, 3, 7], [2, 5, 1, 7, 3, 8], [2, 5, 1, 7, 8, 3], [2, 5, 1, 3, 7, 8], [2, 5, 1, 3, 8, 7], [2, 5, 1, 8, 7, 3], [2, 5, 1, 8, 3, 7], [2, 3, 7, 5, 8, 1], [2, 3, 7, 5, 1, 8], [2, 3, 7, 8, 5, 1], [2, 3, 7, 8, 1, 5], [2, 3, 7, 1, 5, 8], [2, 3, 7, 1, 8, 5], [2, 3, 5, 7, 8, 1], [2, 3, 5, 7, 1, 8], [2, 3, 5, 8, 7, 1], [2, 3, 5, 8, 1, 7], [2, 3, 5, 1, 7, 8], [2, 3, 5, 1, 8, 7], [2, 3, 8, 7, 5, 1], [2, 3, 8, 7, 1, 5], [2, 3, 8, 5, 7, 1], [2, 3, 8, 5, 1, 7], [2, 3, 8, 1, 7, 5], [2, 3, 8, 1, 5, 7], [2, 3, 1, 7, 5, 8], [2, 3, 1, 7, 8, 5], [2, 3, 1, 5, 7, 8], [2, 3, 1, 5, 8, 7], [2, 3, 1, 8, 7, 5], [2, 3, 1, 8, 5, 7], [2, 8, 7, 5, 3, 1], [2, 8, 7, 5, 1, 3], [2, 8, 7, 3, 5, 1], [2, 8, 7, 3, 1, 5], [2, 8, 7, 1, 5, 3], [2, 8, 7, 1, 3, 5], [2, 8, 5, 7, 3, 1], [2, 8, 5, 7, 1, 3], [2, 8, 5, 3, 7, 1], [2, 8, 5, 3, 1, 7], [2, 8, 5, 1, 7, 3], [2, 8, 5, 1, 3, 7], [2, 8, 3, 7, 5, 1], [2, 8, 3, 7, 1, 5], [2, 8, 3, 5, 7, 1], [2, 8, 3, 5, 1, 7], [2, 8, 3, 1, 7, 5], [2, 8, 3, 1, 5, 7], [2, 8, 1, 7, 5, 3], [2, 8, 1, 7, 3, 5], [2, 8, 1, 5, 7, 3], [2, 8, 1, 5, 3, 7], [2, 8, 1, 3, 7, 5], [2, 8, 1, 3, 5, 7], [2, 1, 7, 5, 3, 8], [2, 1, 7, 5, 8, 3], [2, 1, 7, 3, 5, 8], [2, 1, 7, 3, 8, 5], [2, 1, 7, 8, 5, 3], [2, 1, 7, 8, 3, 5], [2, 1, 5, 7, 3, 8], [2, 1, 5, 7, 8, 3], [2, 1, 5, 3, 7, 8], [2, 1, 5, 3, 8, 7], [2, 1, 5, 8, 7, 3], [2, 1, 5, 8, 3, 7], [2, 1, 3, 7, 5, 8], [2, 1, 3, 7, 8, 5], [2, 1, 3, 5, 7, 8], [2, 1, 3, 5, 8, 7], [2, 1, 3, 8, 7, 5], [2, 1, 3, 8, 5, 7], [2, 1, 8, 7, 5, 3], [2, 1, 8, 7, 3, 5], [2, 1, 8, 5, 7, 3], [2, 1, 8, 5, 3, 7], [2, 1, 8, 3, 7, 5], [2, 1, 8, 3, 5, 7], [5, 7, 2, 3, 8, 1], [5, 7, 2, 3, 1, 8], [5, 7, 2, 8, 3, 1], [5, 7, 2, 8, 1, 3], [5, 7, 2, 1, 3, 8], [5, 7, 2, 1, 8, 3], [5, 7, 3, 2, 8, 1], [5, 7, 3, 2, 1, 8], [5, 7, 3, 8, 2, 1], [5, 7, 3, 8, 1, 2], [5, 7, 3, 1, 2, 8], [5, 7, 3, 1, 8, 2], [5, 7, 8, 2, 3, 1], [5, 7, 8, 2, 1, 3], [5, 7, 8, 3, 2, 1], [5, 7, 8, 3, 1, 2], [5, 7, 8, 1, 2, 3], [5, 7, 8, 1, 3, 2], [5, 7, 1, 2, 3, 8], [5, 7, 1, 2, 8, 3], [5, 7, 1, 3, 2, 8], [5, 7, 1, 3, 8, 2], [5, 7, 1, 8, 2, 3], [5, 7, 1, 8, 3, 2], [5, 2, 7, 3, 8, 1], [5, 2, 7, 3, 1, 8], [5, 2, 7, 8, 3, 1], [5, 2, 7, 8, 1, 3], [5, 2, 7, 1, 3, 8], [5, 2, 7, 1, 8, 3], [5, 2, 3, 7, 8, 1], [5, 2, 3, 7, 1, 8], [5, 2, 3, 8, 7, 1], [5, 2, 3, 8, 1, 7], [5, 2, 3, 1, 7, 8], [5, 2, 3, 1, 8, 7], [5, 2, 8, 7, 3, 1], [5, 2, 8, 7, 1, 3], [5, 2, 8, 3, 7, 1], [5, 2, 8, 3, 1, 7], [5, 2, 8, 1, 7, 3], [5, 2, 8, 1, 3, 7], [5, 2, 1, 7, 3, 8], [5, 2, 1, 7, 8, 3], [5, 2, 1, 3, 7, 8], [5, 2, 1, 3, 8, 7], [5, 2, 1, 8, 7, 3], [5, 2, 1, 8, 3, 7], [5, 3, 7, 2, 8, 1], [5, 3, 7, 2, 1, 8], [5, 3, 7, 8, 2, 1], [5, 3, 7, 8, 1, 2], [5, 3, 7, 1, 2, 8], [5, 3, 7, 1, 8, 2], [5, 3, 2, 7, 8, 1], [5, 3, 2, 7, 1, 8], [5, 3, 2, 8, 7, 1], [5, 3, 2, 8, 1, 7], [5, 3, 2, 1, 7, 8], [5, 3, 2, 1, 8, 7], [5, 3, 8, 7, 2, 1], [5, 3, 8, 7, 1, 2], [5, 3, 8, 2, 7, 1], [5, 3, 8, 2, 1, 7], [5, 3, 8, 1, 7, 2], [5, 3, 8, 1, 2, 7], [5, 3, 1, 7, 2, 8], [5, 3, 1, 7, 8, 2], [5, 3, 1, 2, 7, 8], [5, 3, 1, 2, 8, 7], [5, 3, 1, 8, 7, 2], [5, 3, 1, 8, 2, 7], [5, 8, 7, 2, 3, 1], [5, 8, 7, 2, 1, 3], [5, 8, 7, 3, 2, 1], [5, 8, 7, 3, 1, 2], [5, 8, 7, 1, 2, 3], [5, 8, 7, 1, 3, 2], [5, 8, 2, 7, 3, 1], [5, 8, 2, 7, 1, 3], [5, 8, 2, 3, 7, 1], [5, 8, 2, 3, 1, 7], [5, 8, 2, 1, 7, 3], [5, 8, 2, 1, 3, 7], [5, 8, 3, 7, 2, 1], [5, 8, 3, 7, 1, 2], [5, 8, 3, 2, 7, 1], [5, 8, 3, 2, 1, 7], [5, 8, 3, 1, 7, 2], [5, 8, 3, 1, 2, 7], [5, 8, 1, 7, 2, 3], [5, 8, 1, 7, 3, 2], [5, 8, 1, 2, 7, 3], [5, 8, 1, 2, 3, 7], [5, 8, 1, 3, 7, 2], [5, 8, 1, 3, 2, 7], [5, 1, 7, 2, 3, 8], [5, 1, 7, 2, 8, 3], [5, 1, 7, 3, 2, 8], [5, 1, 7, 3, 8, 2], [5, 1, 7, 8, 2, 3], [5, 1, 7, 8, 3, 2], [5, 1, 2, 7, 3, 8], [5, 1, 2, 7, 8, 3], [5, 1, 2, 3, 7, 8], [5, 1, 2, 3, 8, 7], [5, 1, 2, 8, 7, 3], [5, 1, 2, 8, 3, 7], [5, 1, 3, 7, 2, 8], [5, 1, 3, 7, 8, 2], [5, 1, 3, 2, 7, 8], [5, 1, 3, 2, 8, 7], [5, 1, 3, 8, 7, 2], [5, 1, 3, 8, 2, 7], [5, 1, 8, 7, 2, 3], [5, 1, 8, 7, 3, 2], [5, 1, 8, 2, 7, 3], [5, 1, 8, 2, 3, 7], [5, 1, 8, 3, 7, 2], [5, 1, 8, 3, 2, 7], [3, 7, 2, 5, 8, 1], [3, 7, 2, 5, 1, 8], [3, 7, 2, 8, 5, 1], [3, 7, 2, 8, 1, 5], [3, 7, 2, 1, 5, 8], [3, 7, 2, 1, 8, 5], [3, 7, 5, 2, 8, 1], [3, 7, 5, 2, 1, 8], [3, 7, 5, 8, 2, 1], [3, 7, 5, 8, 1, 2], [3, 7, 5, 1, 2, 8], [3, 7, 5, 1, 8, 2], [3, 7, 8, 2, 5, 1], [3, 7, 8, 2, 1, 5], [3, 7, 8, 5, 2, 1], [3, 7, 8, 5, 1, 2], [3, 7, 8, 1, 2, 5], [3, 7, 8, 1, 5, 2], [3, 7, 1, 2, 5, 8], [3, 7, 1, 2, 8, 5], [3, 7, 1, 5, 2, 8], [3, 7, 1, 5, 8, 2], [3, 7, 1, 8, 2, 5], [3, 7, 1, 8, 5, 2], [3, 2, 7, 5, 8, 1], [3, 2, 7, 5, 1, 8], [3, 2, 7, 8, 5, 1], [3, 2, 7, 8, 1, 5], [3, 2, 7, 1, 5, 8], [3, 2, 7, 1, 8, 5], [3, 2, 5, 7, 8, 1], [3, 2, 5, 7, 1, 8], [3, 2, 5, 8, 7, 1], [3, 2, 5, 8, 1, 7], [3, 2, 5, 1, 7, 8], [3, 2, 5, 1, 8, 7], [3, 2, 8, 7, 5, 1], [3, 2, 8, 7, 1, 5], [3, 2, 8, 5, 7, 1], [3, 2, 8, 5, 1, 7], [3, 2, 8, 1, 7, 5], [3, 2, 8, 1, 5, 7], [3, 2, 1, 7, 5, 8], [3, 2, 1, 7, 8, 5], [3, 2, 1, 5, 7, 8], [3, 2, 1, 5, 8, 7], [3, 2, 1, 8, 7, 5], [3, 2, 1, 8, 5, 7], [3, 5, 7, 2, 8, 1], [3, 5, 7, 2, 1, 8], [3, 5, 7, 8, 2, 1], [3, 5, 7, 8, 1, 2], [3, 5, 7, 1, 2, 8], [3, 5, 7, 1, 8, 2], [3, 5, 2, 7, 8, 1], [3, 5, 2, 7, 1, 8], [3, 5, 2, 8, 7, 1], [3, 5, 2, 8, 1, 7], [3, 5, 2, 1, 7, 8], [3, 5, 2, 1, 8, 7], [3, 5, 8, 7, 2, 1], [3, 5, 8, 7, 1, 2], [3, 5, 8, 2, 7, 1], [3, 5, 8, 2, 1, 7], [3, 5, 8, 1, 7, 2], [3, 5, 8, 1, 2, 7], [3, 5, 1, 7, 2, 8], [3, 5, 1, 7, 8, 2], [3, 5, 1, 2, 7, 8], [3, 5, 1, 2, 8, 7], [3, 5, 1, 8, 7, 2], [3, 5, 1, 8, 2, 7], [3, 8, 7, 2, 5, 1], [3, 8, 7, 2, 1, 5], [3, 8, 7, 5, 2, 1], [3, 8, 7, 5, 1, 2], [3, 8, 7, 1, 2, 5], [3, 8, 7, 1, 5, 2], [3, 8, 2, 7, 5, 1], [3, 8, 2, 7, 1, 5], [3, 8, 2, 5, 7, 1], [3, 8, 2, 5, 1, 7], [3, 8, 2, 1, 7, 5], [3, 8, 2, 1, 5, 7], [3, 8, 5, 7, 2, 1], [3, 8, 5, 7, 1, 2], [3, 8, 5, 2, 7, 1], [3, 8, 5, 2, 1, 7], [3, 8, 5, 1, 7, 2], [3, 8, 5, 1, 2, 7], [3, 8, 1, 7, 2, 5], [3, 8, 1, 7, 5, 2], [3, 8, 1, 2, 7, 5], [3, 8, 1, 2, 5, 7], [3, 8, 1, 5, 7, 2], [3, 8, 1, 5, 2, 7], [3, 1, 7, 2, 5, 8], [3, 1, 7, 2, 8, 5], [3, 1, 7, 5, 2, 8], [3, 1, 7, 5, 8, 2], [3, 1, 7, 8, 2, 5], [3, 1, 7, 8, 5, 2], [3, 1, 2, 7, 5, 8], [3, 1, 2, 7, 8, 5], [3, 1, 2, 5, 7, 8], [3, 1, 2, 5, 8, 7], [3, 1, 2, 8, 7, 5], [3, 1, 2, 8, 5, 7], [3, 1, 5, 7, 2, 8], [3, 1, 5, 7, 8, 2], [3, 1, 5, 2, 7, 8], [3, 1, 5, 2, 8, 7], [3, 1, 5, 8, 7, 2], [3, 1, 5, 8, 2, 7], [3, 1, 8, 7, 2, 5], [3, 1, 8, 7, 5, 2], [3, 1, 8, 2, 7, 5], [3, 1, 8, 2, 5, 7], [3, 1, 8, 5, 7, 2], [3, 1, 8, 5, 2, 7], [8, 7, 2, 5, 3, 1], [8, 7, 2, 5, 1, 3], [8, 7, 2, 3, 5, 1], [8, 7, 2, 3, 1, 5], [8, 7, 2, 1, 5, 3], [8, 7, 2, 1, 3, 5], [8, 7, 5, 2, 3, 1], [8, 7, 5, 2, 1, 3], [8, 7, 5, 3, 2, 1], [8, 7, 5, 3, 1, 2], [8, 7, 5, 1, 2, 3], [8, 7, 5, 1, 3, 2], [8, 7, 3, 2, 5, 1], [8, 7, 3, 2, 1, 5], [8, 7, 3, 5, 2, 1], [8, 7, 3, 5, 1, 2], [8, 7, 3, 1, 2, 5], [8, 7, 3, 1, 5, 2], [8, 7, 1, 2, 5, 3], [8, 7, 1, 2, 3, 5], [8, 7, 1, 5, 2, 3], [8, 7, 1, 5, 3, 2], [8, 7, 1, 3, 2, 5], [8, 7, 1, 3, 5, 2], [8, 2, 7, 5, 3, 1], [8, 2, 7, 5, 1, 3], [8, 2, 7, 3, 5, 1], [8, 2, 7, 3, 1, 5], [8, 2, 7, 1, 5, 3], [8, 2, 7, 1, 3, 5], [8, 2, 5, 7, 3, 1], [8, 2, 5, 7, 1, 3], [8, 2, 5, 3, 7, 1], [8, 2, 5, 3, 1, 7], [8, 2, 5, 1, 7, 3], [8, 2, 5, 1, 3, 7], [8, 2, 3, 7, 5, 1], [8, 2, 3, 7, 1, 5], [8, 2, 3, 5, 7, 1], [8, 2, 3, 5, 1, 7], [8, 2, 3, 1, 7, 5], [8, 2, 3, 1, 5, 7], [8, 2, 1, 7, 5, 3], [8, 2, 1, 7, 3, 5], [8, 2, 1, 5, 7, 3], [8, 2, 1, 5, 3, 7], [8, 2, 1, 3, 7, 5], [8, 2, 1, 3, 5, 7], [8, 5, 7, 2, 3, 1], [8, 5, 7, 2, 1, 3], [8, 5, 7, 3, 2, 1], [8, 5, 7, 3, 1, 2], [8, 5, 7, 1, 2, 3], [8, 5, 7, 1, 3, 2], [8, 5, 2, 7, 3, 1], [8, 5, 2, 7, 1, 3], [8, 5, 2, 3, 7, 1], [8, 5, 2, 3, 1, 7], [8, 5, 2, 1, 7, 3], [8, 5, 2, 1, 3, 7], [8, 5, 3, 7, 2, 1], [8, 5, 3, 7, 1, 2], [8, 5, 3, 2, 7, 1], [8, 5, 3, 2, 1, 7], [8, 5, 3, 1, 7, 2], [8, 5, 3, 1, 2, 7], [8, 5, 1, 7, 2, 3], [8, 5, 1, 7, 3, 2], [8, 5, 1, 2, 7, 3], [8, 5, 1, 2, 3, 7], [8, 5, 1, 3, 7, 2], [8, 5, 1, 3, 2, 7], [8, 3, 7, 2, 5, 1], [8, 3, 7, 2, 1, 5], [8, 3, 7, 5, 2, 1], [8, 3, 7, 5, 1, 2], [8, 3, 7, 1, 2, 5], [8, 3, 7, 1, 5, 2], [8, 3, 2, 7, 5, 1], [8, 3, 2, 7, 1, 5], [8, 3, 2, 5, 7, 1], [8, 3, 2, 5, 1, 7], [8, 3, 2, 1, 7, 5], [8, 3, 2, 1, 5, 7], [8, 3, 5, 7, 2, 1], [8, 3, 5, 7, 1, 2], [8, 3, 5, 2, 7, 1], [8, 3, 5, 2, 1, 7], [8, 3, 5, 1, 7, 2], [8, 3, 5, 1, 2, 7], [8, 3, 1, 7, 2, 5], [8, 3, 1, 7, 5, 2], [8, 3, 1, 2, 7, 5], [8, 3, 1, 2, 5, 7], [8, 3, 1, 5, 7, 2], [8, 3, 1, 5, 2, 7], [8, 1, 7, 2, 5, 3], [8, 1, 7, 2, 3, 5], [8, 1, 7, 5, 2, 3], [8, 1, 7, 5, 3, 2], [8, 1, 7, 3, 2, 5], [8, 1, 7, 3, 5, 2], [8, 1, 2, 7, 5, 3], [8, 1, 2, 7, 3, 5], [8, 1, 2, 5, 7, 3], [8, 1, 2, 5, 3, 7], [8, 1, 2, 3, 7, 5], [8, 1, 2, 3, 5, 7], [8, 1, 5, 7, 2, 3], [8, 1, 5, 7, 3, 2], [8, 1, 5, 2, 7, 3], [8, 1, 5, 2, 3, 7], [8, 1, 5, 3, 7, 2], [8, 1, 5, 3, 2, 7], [8, 1, 3, 7, 2, 5], [8, 1, 3, 7, 5, 2], [8, 1, 3, 2, 7, 5], [8, 1, 3, 2, 5, 7], [8, 1, 3, 5, 7, 2], [8, 1, 3, 5, 2, 7], [1, 7, 2, 5, 3, 8], [1, 7, 2, 5, 8, 3], [1, 7, 2, 3, 5, 8], [1, 7, 2, 3, 8, 5], [1, 7, 2, 8, 5, 3], [1, 7, 2, 8, 3, 5], [1, 7, 5, 2, 3, 8], [1, 7, 5, 2, 8, 3], [1, 7, 5, 3, 2, 8], [1, 7, 5, 3, 8, 2], [1, 7, 5, 8, 2, 3], [1, 7, 5, 8, 3, 2], [1, 7, 3, 2, 5, 8], [1, 7, 3, 2, 8, 5], [1, 7, 3, 5, 2, 8], [1, 7, 3, 5, 8, 2], [1, 7, 3, 8, 2, 5], [1, 7, 3, 8, 5, 2], [1, 7, 8, 2, 5, 3], [1, 7, 8, 2, 3, 5], [1, 7, 8, 5, 2, 3], [1, 7, 8, 5, 3, 2], [1, 7, 8, 3, 2, 5], [1, 7, 8, 3, 5, 2], [1, 2, 7, 5, 3, 8], [1, 2, 7, 5, 8, 3], [1, 2, 7, 3, 5, 8], [1, 2, 7, 3, 8, 5], [1, 2, 7, 8, 5, 3], [1, 2, 7, 8, 3, 5], [1, 2, 5, 7, 3, 8], [1, 2, 5, 7, 8, 3], [1, 2, 5, 3, 7, 8], [1, 2, 5, 3, 8, 7], [1, 2, 5, 8, 7, 3], [1, 2, 5, 8, 3, 7], [1, 2, 3, 7, 5, 8], [1, 2, 3, 7, 8, 5], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 8, 7], [1, 2, 3, 8, 7, 5], [1, 2, 3, 8, 5, 7], [1, 2, 8, 7, 5, 3], [1, 2, 8, 7, 3, 5], [1, 2, 8, 5, 7, 3], [1, 2, 8, 5, 3, 7], [1, 2, 8, 3, 7, 5], [1, 2, 8, 3, 5, 7], [1, 5, 7, 2, 3, 8], [1, 5, 7, 2, 8, 3], [1, 5, 7, 3, 2, 8], [1, 5, 7, 3, 8, 2], [1, 5, 7, 8, 2, 3], [1, 5, 7, 8, 3, 2], [1, 5, 2, 7, 3, 8], [1, 5, 2, 7, 8, 3], [1, 5, 2, 3, 7, 8], [1, 5, 2, 3, 8, 7], [1, 5, 2, 8, 7, 3], [1, 5, 2, 8, 3, 7], [1, 5, 3, 7, 2, 8], [1, 5, 3, 7, 8, 2], [1, 5, 3, 2, 7, 8], [1, 5, 3, 2, 8, 7], [1, 5, 3, 8, 7, 2], [1, 5, 3, 8, 2, 7], [1, 5, 8, 7, 2, 3], [1, 5, 8, 7, 3, 2], [1, 5, 8, 2, 7, 3], [1, 5, 8, 2, 3, 7], [1, 5, 8, 3, 7, 2], [1, 5, 8, 3, 2, 7], [1, 3, 7, 2, 5, 8], [1, 3, 7, 2, 8, 5], [1, 3, 7, 5, 2, 8], [1, 3, 7, 5, 8, 2], [1, 3, 7, 8, 2, 5], [1, 3, 7, 8, 5, 2], [1, 3, 2, 7, 5, 8], [1, 3, 2, 7, 8, 5], [1, 3, 2, 5, 7, 8], [1, 3, 2, 5, 8, 7], [1, 3, 2, 8, 7, 5], [1, 3, 2, 8, 5, 7], [1, 3, 5, 7, 2, 8], [1, 3, 5, 7, 8, 2], [1, 3, 5, 2, 7, 8], [1, 3, 5, 2, 8, 7], [1, 3, 5, 8, 7, 2], [1, 3, 5, 8, 2, 7], [1, 3, 8, 7, 2, 5], [1, 3, 8, 7, 5, 2], [1, 3, 8, 2, 7, 5], [1, 3, 8, 2, 5, 7], [1, 3, 8, 5, 7, 2], [1, 3, 8, 5, 2, 7], [1, 8, 7, 2, 5, 3], [1, 8, 7, 2, 3, 5], [1, 8, 7, 5, 2, 3], [1, 8, 7, 5, 3, 2], [1, 8, 7, 3, 2, 5], [1, 8, 7, 3, 5, 2], [1, 8, 2, 7, 5, 3], [1, 8, 2, 7, 3, 5], [1, 8, 2, 5, 7, 3], [1, 8, 2, 5, 3, 7], [1, 8, 2, 3, 7, 5], [1, 8, 2, 3, 5, 7], [1, 8, 5, 7, 2, 3], [1, 8, 5, 7, 3, 2], [1, 8, 5, 2, 7, 3], [1, 8, 5, 2, 3, 7], [1, 8, 5, 3, 7, 2], [1, 8, 5, 3, 2, 7], [1, 8, 3, 7, 2, 5], [1, 8, 3, 7, 5, 2], [1, 8, 3, 2, 7, 5], [1, 8, 3, 2, 5, 7], [1, 8, 3, 5, 7, 2], [1, 8, 3, 5, 2, 7]]\n assert candidate(nums = [1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5], [1, 2, 3, 5, 4], [1, 2, 4, 3, 5], [1, 2, 4, 5, 3], [1, 2, 5, 3, 4], [1, 2, 5, 4, 3], [1, 3, 2, 4, 5], [1, 3, 2, 5, 4], [1, 3, 4, 2, 5], [1, 3, 4, 5, 2], [1, 3, 5, 2, 4], [1, 3, 5, 4, 2], [1, 4, 2, 3, 5], [1, 4, 2, 5, 3], [1, 4, 3, 2, 5], [1, 4, 3, 5, 2], [1, 4, 5, 2, 3], [1, 4, 5, 3, 2], [1, 5, 2, 3, 4], [1, 5, 2, 4, 3], [1, 5, 3, 2, 4], [1, 5, 3, 4, 2], [1, 5, 4, 2, 3], [1, 5, 4, 3, 2], [2, 1, 3, 4, 5], [2, 1, 3, 5, 4], [2, 1, 4, 3, 5], [2, 1, 4, 5, 3], [2, 1, 5, 3, 4], [2, 1, 5, 4, 3], [2, 3, 1, 4, 5], [2, 3, 1, 5, 4], [2, 3, 4, 1, 5], [2, 3, 4, 5, 1], [2, 3, 5, 1, 4], [2, 3, 5, 4, 1], [2, 4, 1, 3, 5], [2, 4, 1, 5, 3], [2, 4, 3, 1, 5], [2, 4, 3, 5, 1], [2, 4, 5, 1, 3], [2, 4, 5, 3, 1], [2, 5, 1, 3, 4], [2, 5, 1, 4, 3], [2, 5, 3, 1, 4], [2, 5, 3, 4, 1], [2, 5, 4, 1, 3], [2, 5, 4, 3, 1], [3, 1, 2, 4, 5], [3, 1, 2, 5, 4], [3, 1, 4, 2, 5], [3, 1, 4, 5, 2], [3, 1, 5, 2, 4], [3, 1, 5, 4, 2], [3, 2, 1, 4, 5], [3, 2, 1, 5, 4], [3, 2, 4, 1, 5], [3, 2, 4, 5, 1], [3, 2, 5, 1, 4], [3, 2, 5, 4, 1], [3, 4, 1, 2, 5], [3, 4, 1, 5, 2], [3, 4, 2, 1, 5], [3, 4, 2, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 2, 1], [3, 5, 1, 2, 4], [3, 5, 1, 4, 2], [3, 5, 2, 1, 4], [3, 5, 2, 4, 1], [3, 5, 4, 1, 2], [3, 5, 4, 2, 1], [4, 1, 2, 3, 5], [4, 1, 2, 5, 3], [4, 1, 3, 2, 5], [4, 1, 3, 5, 2], [4, 1, 5, 2, 3], [4, 1, 5, 3, 2], [4, 2, 1, 3, 5], [4, 2, 1, 5, 3], [4, 2, 3, 1, 5], [4, 2, 3, 5, 1], [4, 2, 5, 1, 3], [4, 2, 5, 3, 1], [4, 3, 1, 2, 5], [4, 3, 1, 5, 2], [4, 3, 2, 1, 5], [4, 3, 2, 5, 1], [4, 3, 5, 1, 2], [4, 3, 5, 2, 1], [4, 5, 1, 2, 3], [4, 5, 1, 3, 2], [4, 5, 2, 1, 3], [4, 5, 2, 3, 1], [4, 5, 3, 1, 2], [4, 5, 3, 2, 1], [5, 1, 2, 3, 4], [5, 1, 2, 4, 3], [5, 1, 3, 2, 4], [5, 1, 3, 4, 2], [5, 1, 4, 2, 3], [5, 1, 4, 3, 2], [5, 2, 1, 3, 4], [5, 2, 1, 4, 3], [5, 2, 3, 1, 4], [5, 2, 3, 4, 1], [5, 2, 4, 1, 3], [5, 2, 4, 3, 1], [5, 3, 1, 2, 4], [5, 3, 1, 4, 2], [5, 3, 2, 1, 4], [5, 3, 2, 4, 1], [5, 3, 4, 1, 2], [5, 3, 4, 2, 1], [5, 4, 1, 2, 3], [5, 4, 1, 3, 2], [5, 4, 2, 1, 3], [5, 4, 2, 3, 1], [5, 4, 3, 1, 2], [5, 4, 3, 2, 1]]\n assert candidate(nums = [0, 2, 4, 6, 8, 10]) == [[0, 2, 4, 6, 8, 10], [0, 2, 4, 6, 10, 8], [0, 2, 4, 8, 6, 10], [0, 2, 4, 8, 10, 6], [0, 2, 4, 10, 6, 8], [0, 2, 4, 10, 8, 6], [0, 2, 6, 4, 8, 10], [0, 2, 6, 4, 10, 8], [0, 2, 6, 8, 4, 10], [0, 2, 6, 8, 10, 4], [0, 2, 6, 10, 4, 8], [0, 2, 6, 10, 8, 4], [0, 2, 8, 4, 6, 10], [0, 2, 8, 4, 10, 6], [0, 2, 8, 6, 4, 10], [0, 2, 8, 6, 10, 4], [0, 2, 8, 10, 4, 6], [0, 2, 8, 10, 6, 4], [0, 2, 10, 4, 6, 8], [0, 2, 10, 4, 8, 6], [0, 2, 10, 6, 4, 8], [0, 2, 10, 6, 8, 4], [0, 2, 10, 8, 4, 6], [0, 2, 10, 8, 6, 4], [0, 4, 2, 6, 8, 10], [0, 4, 2, 6, 10, 8], [0, 4, 2, 8, 6, 10], [0, 4, 2, 8, 10, 6], [0, 4, 2, 10, 6, 8], [0, 4, 2, 10, 8, 6], [0, 4, 6, 2, 8, 10], [0, 4, 6, 2, 10, 8], [0, 4, 6, 8, 2, 10], [0, 4, 6, 8, 10, 2], [0, 4, 6, 10, 2, 8], [0, 4, 6, 10, 8, 2], [0, 4, 8, 2, 6, 10], [0, 4, 8, 2, 10, 6], [0, 4, 8, 6, 2, 10], [0, 4, 8, 6, 10, 2], [0, 4, 8, 10, 2, 6], [0, 4, 8, 10, 6, 2], [0, 4, 10, 2, 6, 8], [0, 4, 10, 2, 8, 6], [0, 4, 10, 6, 2, 8], [0, 4, 10, 6, 8, 2], [0, 4, 10, 8, 2, 6], [0, 4, 10, 8, 6, 2], [0, 6, 2, 4, 8, 10], [0, 6, 2, 4, 10, 8], [0, 6, 2, 8, 4, 10], [0, 6, 2, 8, 10, 4], [0, 6, 2, 10, 4, 8], [0, 6, 2, 10, 8, 4], [0, 6, 4, 2, 8, 10], [0, 6, 4, 2, 10, 8], [0, 6, 4, 8, 2, 10], [0, 6, 4, 8, 10, 2], [0, 6, 4, 10, 2, 8], [0, 6, 4, 10, 8, 2], [0, 6, 8, 2, 4, 10], [0, 6, 8, 2, 10, 4], [0, 6, 8, 4, 2, 10], [0, 6, 8, 4, 10, 2], [0, 6, 8, 10, 2, 4], [0, 6, 8, 10, 4, 2], [0, 6, 10, 2, 4, 8], [0, 6, 10, 2, 8, 4], [0, 6, 10, 4, 2, 8], [0, 6, 10, 4, 8, 2], [0, 6, 10, 8, 2, 4], [0, 6, 10, 8, 4, 2], [0, 8, 2, 4, 6, 10], [0, 8, 2, 4, 10, 6], [0, 8, 2, 6, 4, 10], [0, 8, 2, 6, 10, 4], [0, 8, 2, 10, 4, 6], [0, 8, 2, 10, 6, 4], [0, 8, 4, 2, 6, 10], [0, 8, 4, 2, 10, 6], [0, 8, 4, 6, 2, 10], [0, 8, 4, 6, 10, 2], [0, 8, 4, 10, 2, 6], [0, 8, 4, 10, 6, 2], [0, 8, 6, 2, 4, 10], [0, 8, 6, 2, 10, 4], [0, 8, 6, 4, 2, 10], [0, 8, 6, 4, 10, 2], [0, 8, 6, 10, 2, 4], [0, 8, 6, 10, 4, 2], [0, 8, 10, 2, 4, 6], [0, 8, 10, 2, 6, 4], [0, 8, 10, 4, 2, 6], [0, 8, 10, 4, 6, 2], [0, 8, 10, 6, 2, 4], [0, 8, 10, 6, 4, 2], [0, 10, 2, 4, 6, 8], [0, 10, 2, 4, 8, 6], [0, 10, 2, 6, 4, 8], [0, 10, 2, 6, 8, 4], [0, 10, 2, 8, 4, 6], [0, 10, 2, 8, 6, 4], [0, 10, 4, 2, 6, 8], [0, 10, 4, 2, 8, 6], [0, 10, 4, 6, 2, 8], [0, 10, 4, 6, 8, 2], [0, 10, 4, 8, 2, 6], [0, 10, 4, 8, 6, 2], [0, 10, 6, 2, 4, 8], [0, 10, 6, 2, 8, 4], [0, 10, 6, 4, 2, 8], [0, 10, 6, 4, 8, 2], [0, 10, 6, 8, 2, 4], [0, 10, 6, 8, 4, 2], [0, 10, 8, 2, 4, 6], [0, 10, 8, 2, 6, 4], [0, 10, 8, 4, 2, 6], [0, 10, 8, 4, 6, 2], [0, 10, 8, 6, 2, 4], [0, 10, 8, 6, 4, 2], [2, 0, 4, 6, 8, 10], [2, 0, 4, 6, 10, 8], [2, 0, 4, 8, 6, 10], [2, 0, 4, 8, 10, 6], [2, 0, 4, 10, 6, 8], [2, 0, 4, 10, 8, 6], [2, 0, 6, 4, 8, 10], [2, 0, 6, 4, 10, 8], [2, 0, 6, 8, 4, 10], [2, 0, 6, 8, 10, 4], [2, 0, 6, 10, 4, 8], [2, 0, 6, 10, 8, 4], [2, 0, 8, 4, 6, 10], [2, 0, 8, 4, 10, 6], [2, 0, 8, 6, 4, 10], [2, 0, 8, 6, 10, 4], [2, 0, 8, 10, 4, 6], [2, 0, 8, 10, 6, 4], [2, 0, 10, 4, 6, 8], [2, 0, 10, 4, 8, 6], [2, 0, 10, 6, 4, 8], [2, 0, 10, 6, 8, 4], [2, 0, 10, 8, 4, 6], [2, 0, 10, 8, 6, 4], [2, 4, 0, 6, 8, 10], [2, 4, 0, 6, 10, 8], [2, 4, 0, 8, 6, 10], [2, 4, 0, 8, 10, 6], [2, 4, 0, 10, 6, 8], [2, 4, 0, 10, 8, 6], [2, 4, 6, 0, 8, 10], [2, 4, 6, 0, 10, 8], [2, 4, 6, 8, 0, 10], [2, 4, 6, 8, 10, 0], [2, 4, 6, 10, 0, 8], [2, 4, 6, 10, 8, 0], [2, 4, 8, 0, 6, 10], [2, 4, 8, 0, 10, 6], [2, 4, 8, 6, 0, 10], [2, 4, 8, 6, 10, 0], [2, 4, 8, 10, 0, 6], [2, 4, 8, 10, 6, 0], [2, 4, 10, 0, 6, 8], [2, 4, 10, 0, 8, 6], [2, 4, 10, 6, 0, 8], [2, 4, 10, 6, 8, 0], [2, 4, 10, 8, 0, 6], [2, 4, 10, 8, 6, 0], [2, 6, 0, 4, 8, 10], [2, 6, 0, 4, 10, 8], [2, 6, 0, 8, 4, 10], [2, 6, 0, 8, 10, 4], [2, 6, 0, 10, 4, 8], [2, 6, 0, 10, 8, 4], [2, 6, 4, 0, 8, 10], [2, 6, 4, 0, 10, 8], [2, 6, 4, 8, 0, 10], [2, 6, 4, 8, 10, 0], [2, 6, 4, 10, 0, 8], [2, 6, 4, 10, 8, 0], [2, 6, 8, 0, 4, 10], [2, 6, 8, 0, 10, 4], [2, 6, 8, 4, 0, 10], [2, 6, 8, 4, 10, 0], [2, 6, 8, 10, 0, 4], [2, 6, 8, 10, 4, 0], [2, 6, 10, 0, 4, 8], [2, 6, 10, 0, 8, 4], [2, 6, 10, 4, 0, 8], [2, 6, 10, 4, 8, 0], [2, 6, 10, 8, 0, 4], [2, 6, 10, 8, 4, 0], [2, 8, 0, 4, 6, 10], [2, 8, 0, 4, 10, 6], [2, 8, 0, 6, 4, 10], [2, 8, 0, 6, 10, 4], [2, 8, 0, 10, 4, 6], [2, 8, 0, 10, 6, 4], [2, 8, 4, 0, 6, 10], [2, 8, 4, 0, 10, 6], [2, 8, 4, 6, 0, 10], [2, 8, 4, 6, 10, 0], [2, 8, 4, 10, 0, 6], [2, 8, 4, 10, 6, 0], [2, 8, 6, 0, 4, 10], [2, 8, 6, 0, 10, 4], [2, 8, 6, 4, 0, 10], [2, 8, 6, 4, 10, 0], [2, 8, 6, 10, 0, 4], [2, 8, 6, 10, 4, 0], [2, 8, 10, 0, 4, 6], [2, 8, 10, 0, 6, 4], [2, 8, 10, 4, 0, 6], [2, 8, 10, 4, 6, 0], [2, 8, 10, 6, 0, 4], [2, 8, 10, 6, 4, 0], [2, 10, 0, 4, 6, 8], [2, 10, 0, 4, 8, 6], [2, 10, 0, 6, 4, 8], [2, 10, 0, 6, 8, 4], [2, 10, 0, 8, 4, 6], [2, 10, 0, 8, 6, 4], [2, 10, 4, 0, 6, 8], [2, 10, 4, 0, 8, 6], [2, 10, 4, 6, 0, 8], [2, 10, 4, 6, 8, 0], [2, 10, 4, 8, 0, 6], [2, 10, 4, 8, 6, 0], [2, 10, 6, 0, 4, 8], [2, 10, 6, 0, 8, 4], [2, 10, 6, 4, 0, 8], [2, 10, 6, 4, 8, 0], [2, 10, 6, 8, 0, 4], [2, 10, 6, 8, 4, 0], [2, 10, 8, 0, 4, 6], [2, 10, 8, 0, 6, 4], [2, 10, 8, 4, 0, 6], [2, 10, 8, 4, 6, 0], [2, 10, 8, 6, 0, 4], [2, 10, 8, 6, 4, 0], [4, 0, 2, 6, 8, 10], [4, 0, 2, 6, 10, 8], [4, 0, 2, 8, 6, 10], [4, 0, 2, 8, 10, 6], [4, 0, 2, 10, 6, 8], [4, 0, 2, 10, 8, 6], [4, 0, 6, 2, 8, 10], [4, 0, 6, 2, 10, 8], [4, 0, 6, 8, 2, 10], [4, 0, 6, 8, 10, 2], [4, 0, 6, 10, 2, 8], [4, 0, 6, 10, 8, 2], [4, 0, 8, 2, 6, 10], [4, 0, 8, 2, 10, 6], [4, 0, 8, 6, 2, 10], [4, 0, 8, 6, 10, 2], [4, 0, 8, 10, 2, 6], [4, 0, 8, 10, 6, 2], [4, 0, 10, 2, 6, 8], [4, 0, 10, 2, 8, 6], [4, 0, 10, 6, 2, 8], [4, 0, 10, 6, 8, 2], [4, 0, 10, 8, 2, 6], [4, 0, 10, 8, 6, 2], [4, 2, 0, 6, 8, 10], [4, 2, 0, 6, 10, 8], [4, 2, 0, 8, 6, 10], [4, 2, 0, 8, 10, 6], [4, 2, 0, 10, 6, 8], [4, 2, 0, 10, 8, 6], [4, 2, 6, 0, 8, 10], [4, 2, 6, 0, 10, 8], [4, 2, 6, 8, 0, 10], [4, 2, 6, 8, 10, 0], [4, 2, 6, 10, 0, 8], [4, 2, 6, 10, 8, 0], [4, 2, 8, 0, 6, 10], [4, 2, 8, 0, 10, 6], [4, 2, 8, 6, 0, 10], [4, 2, 8, 6, 10, 0], [4, 2, 8, 10, 0, 6], [4, 2, 8, 10, 6, 0], [4, 2, 10, 0, 6, 8], [4, 2, 10, 0, 8, 6], [4, 2, 10, 6, 0, 8], [4, 2, 10, 6, 8, 0], [4, 2, 10, 8, 0, 6], [4, 2, 10, 8, 6, 0], [4, 6, 0, 2, 8, 10], [4, 6, 0, 2, 10, 8], [4, 6, 0, 8, 2, 10], [4, 6, 0, 8, 10, 2], [4, 6, 0, 10, 2, 8], [4, 6, 0, 10, 8, 2], [4, 6, 2, 0, 8, 10], [4, 6, 2, 0, 10, 8], [4, 6, 2, 8, 0, 10], [4, 6, 2, 8, 10, 0], [4, 6, 2, 10, 0, 8], [4, 6, 2, 10, 8, 0], [4, 6, 8, 0, 2, 10], [4, 6, 8, 0, 10, 2], [4, 6, 8, 2, 0, 10], [4, 6, 8, 2, 10, 0], [4, 6, 8, 10, 0, 2], [4, 6, 8, 10, 2, 0], [4, 6, 10, 0, 2, 8], [4, 6, 10, 0, 8, 2], [4, 6, 10, 2, 0, 8], [4, 6, 10, 2, 8, 0], [4, 6, 10, 8, 0, 2], [4, 6, 10, 8, 2, 0], [4, 8, 0, 2, 6, 10], [4, 8, 0, 2, 10, 6], [4, 8, 0, 6, 2, 10], [4, 8, 0, 6, 10, 2], [4, 8, 0, 10, 2, 6], [4, 8, 0, 10, 6, 2], [4, 8, 2, 0, 6, 10], [4, 8, 2, 0, 10, 6], [4, 8, 2, 6, 0, 10], [4, 8, 2, 6, 10, 0], [4, 8, 2, 10, 0, 6], [4, 8, 2, 10, 6, 0], [4, 8, 6, 0, 2, 10], [4, 8, 6, 0, 10, 2], [4, 8, 6, 2, 0, 10], [4, 8, 6, 2, 10, 0], [4, 8, 6, 10, 0, 2], [4, 8, 6, 10, 2, 0], [4, 8, 10, 0, 2, 6], [4, 8, 10, 0, 6, 2], [4, 8, 10, 2, 0, 6], [4, 8, 10, 2, 6, 0], [4, 8, 10, 6, 0, 2], [4, 8, 10, 6, 2, 0], [4, 10, 0, 2, 6, 8], [4, 10, 0, 2, 8, 6], [4, 10, 0, 6, 2, 8], [4, 10, 0, 6, 8, 2], [4, 10, 0, 8, 2, 6], [4, 10, 0, 8, 6, 2], [4, 10, 2, 0, 6, 8], [4, 10, 2, 0, 8, 6], [4, 10, 2, 6, 0, 8], [4, 10, 2, 6, 8, 0], [4, 10, 2, 8, 0, 6], [4, 10, 2, 8, 6, 0], [4, 10, 6, 0, 2, 8], [4, 10, 6, 0, 8, 2], [4, 10, 6, 2, 0, 8], [4, 10, 6, 2, 8, 0], [4, 10, 6, 8, 0, 2], [4, 10, 6, 8, 2, 0], [4, 10, 8, 0, 2, 6], [4, 10, 8, 0, 6, 2], [4, 10, 8, 2, 0, 6], [4, 10, 8, 2, 6, 0], [4, 10, 8, 6, 0, 2], [4, 10, 8, 6, 2, 0], [6, 0, 2, 4, 8, 10], [6, 0, 2, 4, 10, 8], [6, 0, 2, 8, 4, 10], [6, 0, 2, 8, 10, 4], [6, 0, 2, 10, 4, 8], [6, 0, 2, 10, 8, 4], [6, 0, 4, 2, 8, 10], [6, 0, 4, 2, 10, 8], [6, 0, 4, 8, 2, 10], [6, 0, 4, 8, 10, 2], [6, 0, 4, 10, 2, 8], [6, 0, 4, 10, 8, 2], [6, 0, 8, 2, 4, 10], [6, 0, 8, 2, 10, 4], [6, 0, 8, 4, 2, 10], [6, 0, 8, 4, 10, 2], [6, 0, 8, 10, 2, 4], [6, 0, 8, 10, 4, 2], [6, 0, 10, 2, 4, 8], [6, 0, 10, 2, 8, 4], [6, 0, 10, 4, 2, 8], [6, 0, 10, 4, 8, 2], [6, 0, 10, 8, 2, 4], [6, 0, 10, 8, 4, 2], [6, 2, 0, 4, 8, 10], [6, 2, 0, 4, 10, 8], [6, 2, 0, 8, 4, 10], [6, 2, 0, 8, 10, 4], [6, 2, 0, 10, 4, 8], [6, 2, 0, 10, 8, 4], [6, 2, 4, 0, 8, 10], [6, 2, 4, 0, 10, 8], [6, 2, 4, 8, 0, 10], [6, 2, 4, 8, 10, 0], [6, 2, 4, 10, 0, 8], [6, 2, 4, 10, 8, 0], [6, 2, 8, 0, 4, 10], [6, 2, 8, 0, 10, 4], [6, 2, 8, 4, 0, 10], [6, 2, 8, 4, 10, 0], [6, 2, 8, 10, 0, 4], [6, 2, 8, 10, 4, 0], [6, 2, 10, 0, 4, 8], [6, 2, 10, 0, 8, 4], [6, 2, 10, 4, 0, 8], [6, 2, 10, 4, 8, 0], [6, 2, 10, 8, 0, 4], [6, 2, 10, 8, 4, 0], [6, 4, 0, 2, 8, 10], [6, 4, 0, 2, 10, 8], [6, 4, 0, 8, 2, 10], [6, 4, 0, 8, 10, 2], [6, 4, 0, 10, 2, 8], [6, 4, 0, 10, 8, 2], [6, 4, 2, 0, 8, 10], [6, 4, 2, 0, 10, 8], [6, 4, 2, 8, 0, 10], [6, 4, 2, 8, 10, 0], [6, 4, 2, 10, 0, 8], [6, 4, 2, 10, 8, 0], [6, 4, 8, 0, 2, 10], [6, 4, 8, 0, 10, 2], [6, 4, 8, 2, 0, 10], [6, 4, 8, 2, 10, 0], [6, 4, 8, 10, 0, 2], [6, 4, 8, 10, 2, 0], [6, 4, 10, 0, 2, 8], [6, 4, 10, 0, 8, 2], [6, 4, 10, 2, 0, 8], [6, 4, 10, 2, 8, 0], [6, 4, 10, 8, 0, 2], [6, 4, 10, 8, 2, 0], [6, 8, 0, 2, 4, 10], [6, 8, 0, 2, 10, 4], [6, 8, 0, 4, 2, 10], [6, 8, 0, 4, 10, 2], [6, 8, 0, 10, 2, 4], [6, 8, 0, 10, 4, 2], [6, 8, 2, 0, 4, 10], [6, 8, 2, 0, 10, 4], [6, 8, 2, 4, 0, 10], [6, 8, 2, 4, 10, 0], [6, 8, 2, 10, 0, 4], [6, 8, 2, 10, 4, 0], [6, 8, 4, 0, 2, 10], [6, 8, 4, 0, 10, 2], [6, 8, 4, 2, 0, 10], [6, 8, 4, 2, 10, 0], [6, 8, 4, 10, 0, 2], [6, 8, 4, 10, 2, 0], [6, 8, 10, 0, 2, 4], [6, 8, 10, 0, 4, 2], [6, 8, 10, 2, 0, 4], [6, 8, 10, 2, 4, 0], [6, 8, 10, 4, 0, 2], [6, 8, 10, 4, 2, 0], [6, 10, 0, 2, 4, 8], [6, 10, 0, 2, 8, 4], [6, 10, 0, 4, 2, 8], [6, 10, 0, 4, 8, 2], [6, 10, 0, 8, 2, 4], [6, 10, 0, 8, 4, 2], [6, 10, 2, 0, 4, 8], [6, 10, 2, 0, 8, 4], [6, 10, 2, 4, 0, 8], [6, 10, 2, 4, 8, 0], [6, 10, 2, 8, 0, 4], [6, 10, 2, 8, 4, 0], [6, 10, 4, 0, 2, 8], [6, 10, 4, 0, 8, 2], [6, 10, 4, 2, 0, 8], [6, 10, 4, 2, 8, 0], [6, 10, 4, 8, 0, 2], [6, 10, 4, 8, 2, 0], [6, 10, 8, 0, 2, 4], [6, 10, 8, 0, 4, 2], [6, 10, 8, 2, 0, 4], [6, 10, 8, 2, 4, 0], [6, 10, 8, 4, 0, 2], [6, 10, 8, 4, 2, 0], [8, 0, 2, 4, 6, 10], [8, 0, 2, 4, 10, 6], [8, 0, 2, 6, 4, 10], [8, 0, 2, 6, 10, 4], [8, 0, 2, 10, 4, 6], [8, 0, 2, 10, 6, 4], [8, 0, 4, 2, 6, 10], [8, 0, 4, 2, 10, 6], [8, 0, 4, 6, 2, 10], [8, 0, 4, 6, 10, 2], [8, 0, 4, 10, 2, 6], [8, 0, 4, 10, 6, 2], [8, 0, 6, 2, 4, 10], [8, 0, 6, 2, 10, 4], [8, 0, 6, 4, 2, 10], [8, 0, 6, 4, 10, 2], [8, 0, 6, 10, 2, 4], [8, 0, 6, 10, 4, 2], [8, 0, 10, 2, 4, 6], [8, 0, 10, 2, 6, 4], [8, 0, 10, 4, 2, 6], [8, 0, 10, 4, 6, 2], [8, 0, 10, 6, 2, 4], [8, 0, 10, 6, 4, 2], [8, 2, 0, 4, 6, 10], [8, 2, 0, 4, 10, 6], [8, 2, 0, 6, 4, 10], [8, 2, 0, 6, 10, 4], [8, 2, 0, 10, 4, 6], [8, 2, 0, 10, 6, 4], [8, 2, 4, 0, 6, 10], [8, 2, 4, 0, 10, 6], [8, 2, 4, 6, 0, 10], [8, 2, 4, 6, 10, 0], [8, 2, 4, 10, 0, 6], [8, 2, 4, 10, 6, 0], [8, 2, 6, 0, 4, 10], [8, 2, 6, 0, 10, 4], [8, 2, 6, 4, 0, 10], [8, 2, 6, 4, 10, 0], [8, 2, 6, 10, 0, 4], [8, 2, 6, 10, 4, 0], [8, 2, 10, 0, 4, 6], [8, 2, 10, 0, 6, 4], [8, 2, 10, 4, 0, 6], [8, 2, 10, 4, 6, 0], [8, 2, 10, 6, 0, 4], [8, 2, 10, 6, 4, 0], [8, 4, 0, 2, 6, 10], [8, 4, 0, 2, 10, 6], [8, 4, 0, 6, 2, 10], [8, 4, 0, 6, 10, 2], [8, 4, 0, 10, 2, 6], [8, 4, 0, 10, 6, 2], [8, 4, 2, 0, 6, 10], [8, 4, 2, 0, 10, 6], [8, 4, 2, 6, 0, 10], [8, 4, 2, 6, 10, 0], [8, 4, 2, 10, 0, 6], [8, 4, 2, 10, 6, 0], [8, 4, 6, 0, 2, 10], [8, 4, 6, 0, 10, 2], [8, 4, 6, 2, 0, 10], [8, 4, 6, 2, 10, 0], [8, 4, 6, 10, 0, 2], [8, 4, 6, 10, 2, 0], [8, 4, 10, 0, 2, 6], [8, 4, 10, 0, 6, 2], [8, 4, 10, 2, 0, 6], [8, 4, 10, 2, 6, 0], [8, 4, 10, 6, 0, 2], [8, 4, 10, 6, 2, 0], [8, 6, 0, 2, 4, 10], [8, 6, 0, 2, 10, 4], [8, 6, 0, 4, 2, 10], [8, 6, 0, 4, 10, 2], [8, 6, 0, 10, 2, 4], [8, 6, 0, 10, 4, 2], [8, 6, 2, 0, 4, 10], [8, 6, 2, 0, 10, 4], [8, 6, 2, 4, 0, 10], [8, 6, 2, 4, 10, 0], [8, 6, 2, 10, 0, 4], [8, 6, 2, 10, 4, 0], [8, 6, 4, 0, 2, 10], [8, 6, 4, 0, 10, 2], [8, 6, 4, 2, 0, 10], [8, 6, 4, 2, 10, 0], [8, 6, 4, 10, 0, 2], [8, 6, 4, 10, 2, 0], [8, 6, 10, 0, 2, 4], [8, 6, 10, 0, 4, 2], [8, 6, 10, 2, 0, 4], [8, 6, 10, 2, 4, 0], [8, 6, 10, 4, 0, 2], [8, 6, 10, 4, 2, 0], [8, 10, 0, 2, 4, 6], [8, 10, 0, 2, 6, 4], [8, 10, 0, 4, 2, 6], [8, 10, 0, 4, 6, 2], [8, 10, 0, 6, 2, 4], [8, 10, 0, 6, 4, 2], [8, 10, 2, 0, 4, 6], [8, 10, 2, 0, 6, 4], [8, 10, 2, 4, 0, 6], [8, 10, 2, 4, 6, 0], [8, 10, 2, 6, 0, 4], [8, 10, 2, 6, 4, 0], [8, 10, 4, 0, 2, 6], [8, 10, 4, 0, 6, 2], [8, 10, 4, 2, 0, 6], [8, 10, 4, 2, 6, 0], [8, 10, 4, 6, 0, 2], [8, 10, 4, 6, 2, 0], [8, 10, 6, 0, 2, 4], [8, 10, 6, 0, 4, 2], [8, 10, 6, 2, 0, 4], [8, 10, 6, 2, 4, 0], [8, 10, 6, 4, 0, 2], [8, 10, 6, 4, 2, 0], [10, 0, 2, 4, 6, 8], [10, 0, 2, 4, 8, 6], [10, 0, 2, 6, 4, 8], [10, 0, 2, 6, 8, 4], [10, 0, 2, 8, 4, 6], [10, 0, 2, 8, 6, 4], [10, 0, 4, 2, 6, 8], [10, 0, 4, 2, 8, 6], [10, 0, 4, 6, 2, 8], [10, 0, 4, 6, 8, 2], [10, 0, 4, 8, 2, 6], [10, 0, 4, 8, 6, 2], [10, 0, 6, 2, 4, 8], [10, 0, 6, 2, 8, 4], [10, 0, 6, 4, 2, 8], [10, 0, 6, 4, 8, 2], [10, 0, 6, 8, 2, 4], [10, 0, 6, 8, 4, 2], [10, 0, 8, 2, 4, 6], [10, 0, 8, 2, 6, 4], [10, 0, 8, 4, 2, 6], [10, 0, 8, 4, 6, 2], [10, 0, 8, 6, 2, 4], [10, 0, 8, 6, 4, 2], [10, 2, 0, 4, 6, 8], [10, 2, 0, 4, 8, 6], [10, 2, 0, 6, 4, 8], [10, 2, 0, 6, 8, 4], [10, 2, 0, 8, 4, 6], [10, 2, 0, 8, 6, 4], [10, 2, 4, 0, 6, 8], [10, 2, 4, 0, 8, 6], [10, 2, 4, 6, 0, 8], [10, 2, 4, 6, 8, 0], [10, 2, 4, 8, 0, 6], [10, 2, 4, 8, 6, 0], [10, 2, 6, 0, 4, 8], [10, 2, 6, 0, 8, 4], [10, 2, 6, 4, 0, 8], [10, 2, 6, 4, 8, 0], [10, 2, 6, 8, 0, 4], [10, 2, 6, 8, 4, 0], [10, 2, 8, 0, 4, 6], [10, 2, 8, 0, 6, 4], [10, 2, 8, 4, 0, 6], [10, 2, 8, 4, 6, 0], [10, 2, 8, 6, 0, 4], [10, 2, 8, 6, 4, 0], [10, 4, 0, 2, 6, 8], [10, 4, 0, 2, 8, 6], [10, 4, 0, 6, 2, 8], [10, 4, 0, 6, 8, 2], [10, 4, 0, 8, 2, 6], [10, 4, 0, 8, 6, 2], [10, 4, 2, 0, 6, 8], [10, 4, 2, 0, 8, 6], [10, 4, 2, 6, 0, 8], [10, 4, 2, 6, 8, 0], [10, 4, 2, 8, 0, 6], [10, 4, 2, 8, 6, 0], [10, 4, 6, 0, 2, 8], [10, 4, 6, 0, 8, 2], [10, 4, 6, 2, 0, 8], [10, 4, 6, 2, 8, 0], [10, 4, 6, 8, 0, 2], [10, 4, 6, 8, 2, 0], [10, 4, 8, 0, 2, 6], [10, 4, 8, 0, 6, 2], [10, 4, 8, 2, 0, 6], [10, 4, 8, 2, 6, 0], [10, 4, 8, 6, 0, 2], [10, 4, 8, 6, 2, 0], [10, 6, 0, 2, 4, 8], [10, 6, 0, 2, 8, 4], [10, 6, 0, 4, 2, 8], [10, 6, 0, 4, 8, 2], [10, 6, 0, 8, 2, 4], [10, 6, 0, 8, 4, 2], [10, 6, 2, 0, 4, 8], [10, 6, 2, 0, 8, 4], [10, 6, 2, 4, 0, 8], [10, 6, 2, 4, 8, 0], [10, 6, 2, 8, 0, 4], [10, 6, 2, 8, 4, 0], [10, 6, 4, 0, 2, 8], [10, 6, 4, 0, 8, 2], [10, 6, 4, 2, 0, 8], [10, 6, 4, 2, 8, 0], [10, 6, 4, 8, 0, 2], [10, 6, 4, 8, 2, 0], [10, 6, 8, 0, 2, 4], [10, 6, 8, 0, 4, 2], [10, 6, 8, 2, 0, 4], [10, 6, 8, 2, 4, 0], [10, 6, 8, 4, 0, 2], [10, 6, 8, 4, 2, 0], [10, 8, 0, 2, 4, 6], [10, 8, 0, 2, 6, 4], [10, 8, 0, 4, 2, 6], [10, 8, 0, 4, 6, 2], [10, 8, 0, 6, 2, 4], [10, 8, 0, 6, 4, 2], [10, 8, 2, 0, 4, 6], [10, 8, 2, 0, 6, 4], [10, 8, 2, 4, 0, 6], [10, 8, 2, 4, 6, 0], [10, 8, 2, 6, 0, 4], [10, 8, 2, 6, 4, 0], [10, 8, 4, 0, 2, 6], [10, 8, 4, 0, 6, 2], [10, 8, 4, 2, 0, 6], [10, 8, 4, 2, 6, 0], [10, 8, 4, 6, 0, 2], [10, 8, 4, 6, 2, 0], [10, 8, 6, 0, 2, 4], [10, 8, 6, 0, 4, 2], [10, 8, 6, 2, 0, 4], [10, 8, 6, 2, 4, 0], [10, 8, 6, 4, 0, 2], [10, 8, 6, 4, 2, 0]]\n assert candidate(nums = [-5, -3, -1, 1, 3, 5]) == [[-5, -3, -1, 1, 3, 5], [-5, -3, -1, 1, 5, 3], [-5, -3, -1, 3, 1, 5], [-5, -3, -1, 3, 5, 1], [-5, -3, -1, 5, 1, 3], [-5, -3, -1, 5, 3, 1], [-5, -3, 1, -1, 3, 5], [-5, -3, 1, -1, 5, 3], [-5, -3, 1, 3, -1, 5], [-5, -3, 1, 3, 5, -1], [-5, -3, 1, 5, -1, 3], [-5, -3, 1, 5, 3, -1], [-5, -3, 3, -1, 1, 5], [-5, -3, 3, -1, 5, 1], [-5, -3, 3, 1, -1, 5], [-5, -3, 3, 1, 5, -1], [-5, -3, 3, 5, -1, 1], [-5, -3, 3, 5, 1, -1], [-5, -3, 5, -1, 1, 3], [-5, -3, 5, -1, 3, 1], [-5, -3, 5, 1, -1, 3], [-5, -3, 5, 1, 3, -1], [-5, -3, 5, 3, -1, 1], [-5, -3, 5, 3, 1, -1], [-5, -1, -3, 1, 3, 5], [-5, -1, -3, 1, 5, 3], [-5, -1, -3, 3, 1, 5], [-5, -1, -3, 3, 5, 1], [-5, -1, -3, 5, 1, 3], [-5, -1, -3, 5, 3, 1], [-5, -1, 1, -3, 3, 5], [-5, -1, 1, -3, 5, 3], [-5, -1, 1, 3, -3, 5], [-5, -1, 1, 3, 5, -3], [-5, -1, 1, 5, -3, 3], [-5, -1, 1, 5, 3, -3], [-5, -1, 3, -3, 1, 5], [-5, -1, 3, -3, 5, 1], [-5, -1, 3, 1, -3, 5], [-5, -1, 3, 1, 5, -3], [-5, -1, 3, 5, -3, 1], [-5, -1, 3, 5, 1, -3], [-5, -1, 5, -3, 1, 3], [-5, -1, 5, -3, 3, 1], [-5, -1, 5, 1, -3, 3], [-5, -1, 5, 1, 3, -3], [-5, -1, 5, 3, -3, 1], [-5, -1, 5, 3, 1, -3], [-5, 1, -3, -1, 3, 5], [-5, 1, -3, -1, 5, 3], [-5, 1, -3, 3, -1, 5], [-5, 1, -3, 3, 5, -1], [-5, 1, -3, 5, -1, 3], [-5, 1, -3, 5, 3, -1], [-5, 1, -1, -3, 3, 5], [-5, 1, -1, -3, 5, 3], [-5, 1, -1, 3, -3, 5], [-5, 1, -1, 3, 5, -3], [-5, 1, -1, 5, -3, 3], [-5, 1, -1, 5, 3, -3], [-5, 1, 3, -3, -1, 5], [-5, 1, 3, -3, 5, -1], [-5, 1, 3, -1, -3, 5], [-5, 1, 3, -1, 5, -3], [-5, 1, 3, 5, -3, -1], [-5, 1, 3, 5, -1, -3], [-5, 1, 5, -3, -1, 3], [-5, 1, 5, -3, 3, -1], [-5, 1, 5, -1, -3, 3], [-5, 1, 5, -1, 3, -3], [-5, 1, 5, 3, -3, -1], [-5, 1, 5, 3, -1, -3], [-5, 3, -3, -1, 1, 5], [-5, 3, -3, -1, 5, 1], [-5, 3, -3, 1, -1, 5], [-5, 3, -3, 1, 5, -1], [-5, 3, -3, 5, -1, 1], [-5, 3, -3, 5, 1, -1], [-5, 3, -1, -3, 1, 5], [-5, 3, -1, -3, 5, 1], [-5, 3, -1, 1, -3, 5], [-5, 3, -1, 1, 5, -3], [-5, 3, -1, 5, -3, 1], [-5, 3, -1, 5, 1, -3], [-5, 3, 1, -3, -1, 5], [-5, 3, 1, -3, 5, -1], [-5, 3, 1, -1, -3, 5], [-5, 3, 1, -1, 5, -3], [-5, 3, 1, 5, -3, -1], [-5, 3, 1, 5, -1, -3], [-5, 3, 5, -3, -1, 1], [-5, 3, 5, -3, 1, -1], [-5, 3, 5, -1, -3, 1], [-5, 3, 5, -1, 1, -3], [-5, 3, 5, 1, -3, -1], [-5, 3, 5, 1, -1, -3], [-5, 5, -3, -1, 1, 3], [-5, 5, -3, -1, 3, 1], [-5, 5, -3, 1, -1, 3], [-5, 5, -3, 1, 3, -1], [-5, 5, -3, 3, -1, 1], [-5, 5, -3, 3, 1, -1], [-5, 5, -1, -3, 1, 3], [-5, 5, -1, -3, 3, 1], [-5, 5, -1, 1, -3, 3], [-5, 5, -1, 1, 3, -3], [-5, 5, -1, 3, -3, 1], [-5, 5, -1, 3, 1, -3], [-5, 5, 1, -3, -1, 3], [-5, 5, 1, -3, 3, -1], [-5, 5, 1, -1, -3, 3], [-5, 5, 1, -1, 3, -3], [-5, 5, 1, 3, -3, -1], [-5, 5, 1, 3, -1, -3], [-5, 5, 3, -3, -1, 1], [-5, 5, 3, -3, 1, -1], [-5, 5, 3, -1, -3, 1], [-5, 5, 3, -1, 1, -3], [-5, 5, 3, 1, -3, -1], [-5, 5, 3, 1, -1, -3], [-3, -5, -1, 1, 3, 5], [-3, -5, -1, 1, 5, 3], [-3, -5, -1, 3, 1, 5], [-3, -5, -1, 3, 5, 1], [-3, -5, -1, 5, 1, 3], [-3, -5, -1, 5, 3, 1], [-3, -5, 1, -1, 3, 5], [-3, -5, 1, -1, 5, 3], [-3, -5, 1, 3, -1, 5], [-3, -5, 1, 3, 5, -1], [-3, -5, 1, 5, -1, 3], [-3, -5, 1, 5, 3, -1], [-3, -5, 3, -1, 1, 5], [-3, -5, 3, -1, 5, 1], [-3, -5, 3, 1, -1, 5], [-3, -5, 3, 1, 5, -1], [-3, -5, 3, 5, -1, 1], [-3, -5, 3, 5, 1, -1], [-3, -5, 5, -1, 1, 3], [-3, -5, 5, -1, 3, 1], [-3, -5, 5, 1, -1, 3], [-3, -5, 5, 1, 3, -1], [-3, -5, 5, 3, -1, 1], [-3, -5, 5, 3, 1, -1], [-3, -1, -5, 1, 3, 5], [-3, -1, -5, 1, 5, 3], [-3, -1, -5, 3, 1, 5], [-3, -1, -5, 3, 5, 1], [-3, -1, -5, 5, 1, 3], [-3, -1, -5, 5, 3, 1], [-3, -1, 1, -5, 3, 5], [-3, -1, 1, -5, 5, 3], [-3, -1, 1, 3, -5, 5], [-3, -1, 1, 3, 5, -5], [-3, -1, 1, 5, -5, 3], [-3, -1, 1, 5, 3, -5], [-3, -1, 3, -5, 1, 5], [-3, -1, 3, -5, 5, 1], [-3, -1, 3, 1, -5, 5], [-3, -1, 3, 1, 5, -5], [-3, -1, 3, 5, -5, 1], [-3, -1, 3, 5, 1, -5], [-3, -1, 5, -5, 1, 3], [-3, -1, 5, -5, 3, 1], [-3, -1, 5, 1, -5, 3], [-3, -1, 5, 1, 3, -5], [-3, -1, 5, 3, -5, 1], [-3, -1, 5, 3, 1, -5], [-3, 1, -5, -1, 3, 5], [-3, 1, -5, -1, 5, 3], [-3, 1, -5, 3, -1, 5], [-3, 1, -5, 3, 5, -1], [-3, 1, -5, 5, -1, 3], [-3, 1, -5, 5, 3, -1], [-3, 1, -1, -5, 3, 5], [-3, 1, -1, -5, 5, 3], [-3, 1, -1, 3, -5, 5], [-3, 1, -1, 3, 5, -5], [-3, 1, -1, 5, -5, 3], [-3, 1, -1, 5, 3, -5], [-3, 1, 3, -5, -1, 5], [-3, 1, 3, -5, 5, -1], [-3, 1, 3, -1, -5, 5], [-3, 1, 3, -1, 5, -5], [-3, 1, 3, 5, -5, -1], [-3, 1, 3, 5, -1, -5], [-3, 1, 5, -5, -1, 3], [-3, 1, 5, -5, 3, -1], [-3, 1, 5, -1, -5, 3], [-3, 1, 5, -1, 3, -5], [-3, 1, 5, 3, -5, -1], [-3, 1, 5, 3, -1, -5], [-3, 3, -5, -1, 1, 5], [-3, 3, -5, -1, 5, 1], [-3, 3, -5, 1, -1, 5], [-3, 3, -5, 1, 5, -1], [-3, 3, -5, 5, -1, 1], [-3, 3, -5, 5, 1, -1], [-3, 3, -1, -5, 1, 5], [-3, 3, -1, -5, 5, 1], [-3, 3, -1, 1, -5, 5], [-3, 3, -1, 1, 5, -5], [-3, 3, -1, 5, -5, 1], [-3, 3, -1, 5, 1, -5], [-3, 3, 1, -5, -1, 5], [-3, 3, 1, -5, 5, -1], [-3, 3, 1, -1, -5, 5], [-3, 3, 1, -1, 5, -5], [-3, 3, 1, 5, -5, -1], [-3, 3, 1, 5, -1, -5], [-3, 3, 5, -5, -1, 1], [-3, 3, 5, -5, 1, -1], [-3, 3, 5, -1, -5, 1], [-3, 3, 5, -1, 1, -5], [-3, 3, 5, 1, -5, -1], [-3, 3, 5, 1, -1, -5], [-3, 5, -5, -1, 1, 3], [-3, 5, -5, -1, 3, 1], [-3, 5, -5, 1, -1, 3], [-3, 5, -5, 1, 3, -1], [-3, 5, -5, 3, -1, 1], [-3, 5, -5, 3, 1, -1], [-3, 5, -1, -5, 1, 3], [-3, 5, -1, -5, 3, 1], [-3, 5, -1, 1, -5, 3], [-3, 5, -1, 1, 3, -5], [-3, 5, -1, 3, -5, 1], [-3, 5, -1, 3, 1, -5], [-3, 5, 1, -5, -1, 3], [-3, 5, 1, -5, 3, -1], [-3, 5, 1, -1, -5, 3], [-3, 5, 1, -1, 3, -5], [-3, 5, 1, 3, -5, -1], [-3, 5, 1, 3, -1, -5], [-3, 5, 3, -5, -1, 1], [-3, 5, 3, -5, 1, -1], [-3, 5, 3, -1, -5, 1], [-3, 5, 3, -1, 1, -5], [-3, 5, 3, 1, -5, -1], [-3, 5, 3, 1, -1, -5], [-1, -5, -3, 1, 3, 5], [-1, -5, -3, 1, 5, 3], [-1, -5, -3, 3, 1, 5], [-1, -5, -3, 3, 5, 1], [-1, -5, -3, 5, 1, 3], [-1, -5, -3, 5, 3, 1], [-1, -5, 1, -3, 3, 5], [-1, -5, 1, -3, 5, 3], [-1, -5, 1, 3, -3, 5], [-1, -5, 1, 3, 5, -3], [-1, -5, 1, 5, -3, 3], [-1, -5, 1, 5, 3, -3], [-1, -5, 3, -3, 1, 5], [-1, -5, 3, -3, 5, 1], [-1, -5, 3, 1, -3, 5], [-1, -5, 3, 1, 5, -3], [-1, -5, 3, 5, -3, 1], [-1, -5, 3, 5, 1, -3], [-1, -5, 5, -3, 1, 3], [-1, -5, 5, -3, 3, 1], [-1, -5, 5, 1, -3, 3], [-1, -5, 5, 1, 3, -3], [-1, -5, 5, 3, -3, 1], [-1, -5, 5, 3, 1, -3], [-1, -3, -5, 1, 3, 5], [-1, -3, -5, 1, 5, 3], [-1, -3, -5, 3, 1, 5], [-1, -3, -5, 3, 5, 1], [-1, -3, -5, 5, 1, 3], [-1, -3, -5, 5, 3, 1], [-1, -3, 1, -5, 3, 5], [-1, -3, 1, -5, 5, 3], [-1, -3, 1, 3, -5, 5], [-1, -3, 1, 3, 5, -5], [-1, -3, 1, 5, -5, 3], [-1, -3, 1, 5, 3, -5], [-1, -3, 3, -5, 1, 5], [-1, -3, 3, -5, 5, 1], [-1, -3, 3, 1, -5, 5], [-1, -3, 3, 1, 5, -5], [-1, -3, 3, 5, -5, 1], [-1, -3, 3, 5, 1, -5], [-1, -3, 5, -5, 1, 3], [-1, -3, 5, -5, 3, 1], [-1, -3, 5, 1, -5, 3], [-1, -3, 5, 1, 3, -5], [-1, -3, 5, 3, -5, 1], [-1, -3, 5, 3, 1, -5], [-1, 1, -5, -3, 3, 5], [-1, 1, -5, -3, 5, 3], [-1, 1, -5, 3, -3, 5], [-1, 1, -5, 3, 5, -3], [-1, 1, -5, 5, -3, 3], [-1, 1, -5, 5, 3, -3], [-1, 1, -3, -5, 3, 5], [-1, 1, -3, -5, 5, 3], [-1, 1, -3, 3, -5, 5], [-1, 1, -3, 3, 5, -5], [-1, 1, -3, 5, -5, 3], [-1, 1, -3, 5, 3, -5], [-1, 1, 3, -5, -3, 5], [-1, 1, 3, -5, 5, -3], [-1, 1, 3, -3, -5, 5], [-1, 1, 3, -3, 5, -5], [-1, 1, 3, 5, -5, -3], [-1, 1, 3, 5, -3, -5], [-1, 1, 5, -5, -3, 3], [-1, 1, 5, -5, 3, -3], [-1, 1, 5, -3, -5, 3], [-1, 1, 5, -3, 3, -5], [-1, 1, 5, 3, -5, -3], [-1, 1, 5, 3, -3, -5], [-1, 3, -5, -3, 1, 5], [-1, 3, -5, -3, 5, 1], [-1, 3, -5, 1, -3, 5], [-1, 3, -5, 1, 5, -3], [-1, 3, -5, 5, -3, 1], [-1, 3, -5, 5, 1, -3], [-1, 3, -3, -5, 1, 5], [-1, 3, -3, -5, 5, 1], [-1, 3, -3, 1, -5, 5], [-1, 3, -3, 1, 5, -5], [-1, 3, -3, 5, -5, 1], [-1, 3, -3, 5, 1, -5], [-1, 3, 1, -5, -3, 5], [-1, 3, 1, -5, 5, -3], [-1, 3, 1, -3, -5, 5], [-1, 3, 1, -3, 5, -5], [-1, 3, 1, 5, -5, -3], [-1, 3, 1, 5, -3, -5], [-1, 3, 5, -5, -3, 1], [-1, 3, 5, -5, 1, -3], [-1, 3, 5, -3, -5, 1], [-1, 3, 5, -3, 1, -5], [-1, 3, 5, 1, -5, -3], [-1, 3, 5, 1, -3, -5], [-1, 5, -5, -3, 1, 3], [-1, 5, -5, -3, 3, 1], [-1, 5, -5, 1, -3, 3], [-1, 5, -5, 1, 3, -3], [-1, 5, -5, 3, -3, 1], [-1, 5, -5, 3, 1, -3], [-1, 5, -3, -5, 1, 3], [-1, 5, -3, -5, 3, 1], [-1, 5, -3, 1, -5, 3], [-1, 5, -3, 1, 3, -5], [-1, 5, -3, 3, -5, 1], [-1, 5, -3, 3, 1, -5], [-1, 5, 1, -5, -3, 3], [-1, 5, 1, -5, 3, -3], [-1, 5, 1, -3, -5, 3], [-1, 5, 1, -3, 3, -5], [-1, 5, 1, 3, -5, -3], [-1, 5, 1, 3, -3, -5], [-1, 5, 3, -5, -3, 1], [-1, 5, 3, -5, 1, -3], [-1, 5, 3, -3, -5, 1], [-1, 5, 3, -3, 1, -5], [-1, 5, 3, 1, -5, -3], [-1, 5, 3, 1, -3, -5], [1, -5, -3, -1, 3, 5], [1, -5, -3, -1, 5, 3], [1, -5, -3, 3, -1, 5], [1, -5, -3, 3, 5, -1], [1, -5, -3, 5, -1, 3], [1, -5, -3, 5, 3, -1], [1, -5, -1, -3, 3, 5], [1, -5, -1, -3, 5, 3], [1, -5, -1, 3, -3, 5], [1, -5, -1, 3, 5, -3], [1, -5, -1, 5, -3, 3], [1, -5, -1, 5, 3, -3], [1, -5, 3, -3, -1, 5], [1, -5, 3, -3, 5, -1], [1, -5, 3, -1, -3, 5], [1, -5, 3, -1, 5, -3], [1, -5, 3, 5, -3, -1], [1, -5, 3, 5, -1, -3], [1, -5, 5, -3, -1, 3], [1, -5, 5, -3, 3, -1], [1, -5, 5, -1, -3, 3], [1, -5, 5, -1, 3, -3], [1, -5, 5, 3, -3, -1], [1, -5, 5, 3, -1, -3], [1, -3, -5, -1, 3, 5], [1, -3, -5, -1, 5, 3], [1, -3, -5, 3, -1, 5], [1, -3, -5, 3, 5, -1], [1, -3, -5, 5, -1, 3], [1, -3, -5, 5, 3, -1], [1, -3, -1, -5, 3, 5], [1, -3, -1, -5, 5, 3], [1, -3, -1, 3, -5, 5], [1, -3, -1, 3, 5, -5], [1, -3, -1, 5, -5, 3], [1, -3, -1, 5, 3, -5], [1, -3, 3, -5, -1, 5], [1, -3, 3, -5, 5, -1], [1, -3, 3, -1, -5, 5], [1, -3, 3, -1, 5, -5], [1, -3, 3, 5, -5, -1], [1, -3, 3, 5, -1, -5], [1, -3, 5, -5, -1, 3], [1, -3, 5, -5, 3, -1], [1, -3, 5, -1, -5, 3], [1, -3, 5, -1, 3, -5], [1, -3, 5, 3, -5, -1], [1, -3, 5, 3, -1, -5], [1, -1, -5, -3, 3, 5], [1, -1, -5, -3, 5, 3], [1, -1, -5, 3, -3, 5], [1, -1, -5, 3, 5, -3], [1, -1, -5, 5, -3, 3], [1, -1, -5, 5, 3, -3], [1, -1, -3, -5, 3, 5], [1, -1, -3, -5, 5, 3], [1, -1, -3, 3, -5, 5], [1, -1, -3, 3, 5, -5], [1, -1, -3, 5, -5, 3], [1, -1, -3, 5, 3, -5], [1, -1, 3, -5, -3, 5], [1, -1, 3, -5, 5, -3], [1, -1, 3, -3, -5, 5], [1, -1, 3, -3, 5, -5], [1, -1, 3, 5, -5, -3], [1, -1, 3, 5, -3, -5], [1, -1, 5, -5, -3, 3], [1, -1, 5, -5, 3, -3], [1, -1, 5, -3, -5, 3], [1, -1, 5, -3, 3, -5], [1, -1, 5, 3, -5, -3], [1, -1, 5, 3, -3, -5], [1, 3, -5, -3, -1, 5], [1, 3, -5, -3, 5, -1], [1, 3, -5, -1, -3, 5], [1, 3, -5, -1, 5, -3], [1, 3, -5, 5, -3, -1], [1, 3, -5, 5, -1, -3], [1, 3, -3, -5, -1, 5], [1, 3, -3, -5, 5, -1], [1, 3, -3, -1, -5, 5], [1, 3, -3, -1, 5, -5], [1, 3, -3, 5, -5, -1], [1, 3, -3, 5, -1, -5], [1, 3, -1, -5, -3, 5], [1, 3, -1, -5, 5, -3], [1, 3, -1, -3, -5, 5], [1, 3, -1, -3, 5, -5], [1, 3, -1, 5, -5, -3], [1, 3, -1, 5, -3, -5], [1, 3, 5, -5, -3, -1], [1, 3, 5, -5, -1, -3], [1, 3, 5, -3, -5, -1], [1, 3, 5, -3, -1, -5], [1, 3, 5, -1, -5, -3], [1, 3, 5, -1, -3, -5], [1, 5, -5, -3, -1, 3], [1, 5, -5, -3, 3, -1], [1, 5, -5, -1, -3, 3], [1, 5, -5, -1, 3, -3], [1, 5, -5, 3, -3, -1], [1, 5, -5, 3, -1, -3], [1, 5, -3, -5, -1, 3], [1, 5, -3, -5, 3, -1], [1, 5, -3, -1, -5, 3], [1, 5, -3, -1, 3, -5], [1, 5, -3, 3, -5, -1], [1, 5, -3, 3, -1, -5], [1, 5, -1, -5, -3, 3], [1, 5, -1, -5, 3, -3], [1, 5, -1, -3, -5, 3], [1, 5, -1, -3, 3, -5], [1, 5, -1, 3, -5, -3], [1, 5, -1, 3, -3, -5], [1, 5, 3, -5, -3, -1], [1, 5, 3, -5, -1, -3], [1, 5, 3, -3, -5, -1], [1, 5, 3, -3, -1, -5], [1, 5, 3, -1, -5, -3], [1, 5, 3, -1, -3, -5], [3, -5, -3, -1, 1, 5], [3, -5, -3, -1, 5, 1], [3, -5, -3, 1, -1, 5], [3, -5, -3, 1, 5, -1], [3, -5, -3, 5, -1, 1], [3, -5, -3, 5, 1, -1], [3, -5, -1, -3, 1, 5], [3, -5, -1, -3, 5, 1], [3, -5, -1, 1, -3, 5], [3, -5, -1, 1, 5, -3], [3, -5, -1, 5, -3, 1], [3, -5, -1, 5, 1, -3], [3, -5, 1, -3, -1, 5], [3, -5, 1, -3, 5, -1], [3, -5, 1, -1, -3, 5], [3, -5, 1, -1, 5, -3], [3, -5, 1, 5, -3, -1], [3, -5, 1, 5, -1, -3], [3, -5, 5, -3, -1, 1], [3, -5, 5, -3, 1, -1], [3, -5, 5, -1, -3, 1], [3, -5, 5, -1, 1, -3], [3, -5, 5, 1, -3, -1], [3, -5, 5, 1, -1, -3], [3, -3, -5, -1, 1, 5], [3, -3, -5, -1, 5, 1], [3, -3, -5, 1, -1, 5], [3, -3, -5, 1, 5, -1], [3, -3, -5, 5, -1, 1], [3, -3, -5, 5, 1, -1], [3, -3, -1, -5, 1, 5], [3, -3, -1, -5, 5, 1], [3, -3, -1, 1, -5, 5], [3, -3, -1, 1, 5, -5], [3, -3, -1, 5, -5, 1], [3, -3, -1, 5, 1, -5], [3, -3, 1, -5, -1, 5], [3, -3, 1, -5, 5, -1], [3, -3, 1, -1, -5, 5], [3, -3, 1, -1, 5, -5], [3, -3, 1, 5, -5, -1], [3, -3, 1, 5, -1, -5], [3, -3, 5, -5, -1, 1], [3, -3, 5, -5, 1, -1], [3, -3, 5, -1, -5, 1], [3, -3, 5, -1, 1, -5], [3, -3, 5, 1, -5, -1], [3, -3, 5, 1, -1, -5], [3, -1, -5, -3, 1, 5], [3, -1, -5, -3, 5, 1], [3, -1, -5, 1, -3, 5], [3, -1, -5, 1, 5, -3], [3, -1, -5, 5, -3, 1], [3, -1, -5, 5, 1, -3], [3, -1, -3, -5, 1, 5], [3, -1, -3, -5, 5, 1], [3, -1, -3, 1, -5, 5], [3, -1, -3, 1, 5, -5], [3, -1, -3, 5, -5, 1], [3, -1, -3, 5, 1, -5], [3, -1, 1, -5, -3, 5], [3, -1, 1, -5, 5, -3], [3, -1, 1, -3, -5, 5], [3, -1, 1, -3, 5, -5], [3, -1, 1, 5, -5, -3], [3, -1, 1, 5, -3, -5], [3, -1, 5, -5, -3, 1], [3, -1, 5, -5, 1, -3], [3, -1, 5, -3, -5, 1], [3, -1, 5, -3, 1, -5], [3, -1, 5, 1, -5, -3], [3, -1, 5, 1, -3, -5], [3, 1, -5, -3, -1, 5], [3, 1, -5, -3, 5, -1], [3, 1, -5, -1, -3, 5], [3, 1, -5, -1, 5, -3], [3, 1, -5, 5, -3, -1], [3, 1, -5, 5, -1, -3], [3, 1, -3, -5, -1, 5], [3, 1, -3, -5, 5, -1], [3, 1, -3, -1, -5, 5], [3, 1, -3, -1, 5, -5], [3, 1, -3, 5, -5, -1], [3, 1, -3, 5, -1, -5], [3, 1, -1, -5, -3, 5], [3, 1, -1, -5, 5, -3], [3, 1, -1, -3, -5, 5], [3, 1, -1, -3, 5, -5], [3, 1, -1, 5, -5, -3], [3, 1, -1, 5, -3, -5], [3, 1, 5, -5, -3, -1], [3, 1, 5, -5, -1, -3], [3, 1, 5, -3, -5, -1], [3, 1, 5, -3, -1, -5], [3, 1, 5, -1, -5, -3], [3, 1, 5, -1, -3, -5], [3, 5, -5, -3, -1, 1], [3, 5, -5, -3, 1, -1], [3, 5, -5, -1, -3, 1], [3, 5, -5, -1, 1, -3], [3, 5, -5, 1, -3, -1], [3, 5, -5, 1, -1, -3], [3, 5, -3, -5, -1, 1], [3, 5, -3, -5, 1, -1], [3, 5, -3, -1, -5, 1], [3, 5, -3, -1, 1, -5], [3, 5, -3, 1, -5, -1], [3, 5, -3, 1, -1, -5], [3, 5, -1, -5, -3, 1], [3, 5, -1, -5, 1, -3], [3, 5, -1, -3, -5, 1], [3, 5, -1, -3, 1, -5], [3, 5, -1, 1, -5, -3], [3, 5, -1, 1, -3, -5], [3, 5, 1, -5, -3, -1], [3, 5, 1, -5, -1, -3], [3, 5, 1, -3, -5, -1], [3, 5, 1, -3, -1, -5], [3, 5, 1, -1, -5, -3], [3, 5, 1, -1, -3, -5], [5, -5, -3, -1, 1, 3], [5, -5, -3, -1, 3, 1], [5, -5, -3, 1, -1, 3], [5, -5, -3, 1, 3, -1], [5, -5, -3, 3, -1, 1], [5, -5, -3, 3, 1, -1], [5, -5, -1, -3, 1, 3], [5, -5, -1, -3, 3, 1], [5, -5, -1, 1, -3, 3], [5, -5, -1, 1, 3, -3], [5, -5, -1, 3, -3, 1], [5, -5, -1, 3, 1, -3], [5, -5, 1, -3, -1, 3], [5, -5, 1, -3, 3, -1], [5, -5, 1, -1, -3, 3], [5, -5, 1, -1, 3, -3], [5, -5, 1, 3, -3, -1], [5, -5, 1, 3, -1, -3], [5, -5, 3, -3, -1, 1], [5, -5, 3, -3, 1, -1], [5, -5, 3, -1, -3, 1], [5, -5, 3, -1, 1, -3], [5, -5, 3, 1, -3, -1], [5, -5, 3, 1, -1, -3], [5, -3, -5, -1, 1, 3], [5, -3, -5, -1, 3, 1], [5, -3, -5, 1, -1, 3], [5, -3, -5, 1, 3, -1], [5, -3, -5, 3, -1, 1], [5, -3, -5, 3, 1, -1], [5, -3, -1, -5, 1, 3], [5, -3, -1, -5, 3, 1], [5, -3, -1, 1, -5, 3], [5, -3, -1, 1, 3, -5], [5, -3, -1, 3, -5, 1], [5, -3, -1, 3, 1, -5], [5, -3, 1, -5, -1, 3], [5, -3, 1, -5, 3, -1], [5, -3, 1, -1, -5, 3], [5, -3, 1, -1, 3, -5], [5, -3, 1, 3, -5, -1], [5, -3, 1, 3, -1, -5], [5, -3, 3, -5, -1, 1], [5, -3, 3, -5, 1, -1], [5, -3, 3, -1, -5, 1], [5, -3, 3, -1, 1, -5], [5, -3, 3, 1, -5, -1], [5, -3, 3, 1, -1, -5], [5, -1, -5, -3, 1, 3], [5, -1, -5, -3, 3, 1], [5, -1, -5, 1, -3, 3], [5, -1, -5, 1, 3, -3], [5, -1, -5, 3, -3, 1], [5, -1, -5, 3, 1, -3], [5, -1, -3, -5, 1, 3], [5, -1, -3, -5, 3, 1], [5, -1, -3, 1, -5, 3], [5, -1, -3, 1, 3, -5], [5, -1, -3, 3, -5, 1], [5, -1, -3, 3, 1, -5], [5, -1, 1, -5, -3, 3], [5, -1, 1, -5, 3, -3], [5, -1, 1, -3, -5, 3], [5, -1, 1, -3, 3, -5], [5, -1, 1, 3, -5, -3], [5, -1, 1, 3, -3, -5], [5, -1, 3, -5, -3, 1], [5, -1, 3, -5, 1, -3], [5, -1, 3, -3, -5, 1], [5, -1, 3, -3, 1, -5], [5, -1, 3, 1, -5, -3], [5, -1, 3, 1, -3, -5], [5, 1, -5, -3, -1, 3], [5, 1, -5, -3, 3, -1], [5, 1, -5, -1, -3, 3], [5, 1, -5, -1, 3, -3], [5, 1, -5, 3, -3, -1], [5, 1, -5, 3, -1, -3], [5, 1, -3, -5, -1, 3], [5, 1, -3, -5, 3, -1], [5, 1, -3, -1, -5, 3], [5, 1, -3, -1, 3, -5], [5, 1, -3, 3, -5, -1], [5, 1, -3, 3, -1, -5], [5, 1, -1, -5, -3, 3], [5, 1, -1, -5, 3, -3], [5, 1, -1, -3, -5, 3], [5, 1, -1, -3, 3, -5], [5, 1, -1, 3, -5, -3], [5, 1, -1, 3, -3, -5], [5, 1, 3, -5, -3, -1], [5, 1, 3, -5, -1, -3], [5, 1, 3, -3, -5, -1], [5, 1, 3, -3, -1, -5], [5, 1, 3, -1, -5, -3], [5, 1, 3, -1, -3, -5], [5, 3, -5, -3, -1, 1], [5, 3, -5, -3, 1, -1], [5, 3, -5, -1, -3, 1], [5, 3, -5, -1, 1, -3], [5, 3, -5, 1, -3, -1], [5, 3, -5, 1, -1, -3], [5, 3, -3, -5, -1, 1], [5, 3, -3, -5, 1, -1], [5, 3, -3, -1, -5, 1], [5, 3, -3, -1, 1, -5], [5, 3, -3, 1, -5, -1], [5, 3, -3, 1, -1, -5], [5, 3, -1, -5, -3, 1], [5, 3, -1, -5, 1, -3], [5, 3, -1, -3, -5, 1], [5, 3, -1, -3, 1, -5], [5, 3, -1, 1, -5, -3], [5, 3, -1, 1, -3, -5], [5, 3, 1, -5, -3, -1], [5, 3, 1, -5, -1, -3], [5, 3, 1, -3, -5, -1], [5, 3, 1, -3, -1, -5], [5, 3, 1, -1, -5, -3], [5, 3, 1, -1, -3, -5]]\n assert candidate(nums = [-5, 0, 5, 10, -10, 2]) == [[-5, 0, 5, 10, -10, 2], [-5, 0, 5, 10, 2, -10], [-5, 0, 5, -10, 10, 2], [-5, 0, 5, -10, 2, 10], [-5, 0, 5, 2, 10, -10], [-5, 0, 5, 2, -10, 10], [-5, 0, 10, 5, -10, 2], [-5, 0, 10, 5, 2, -10], [-5, 0, 10, -10, 5, 2], [-5, 0, 10, -10, 2, 5], [-5, 0, 10, 2, 5, -10], [-5, 0, 10, 2, -10, 5], [-5, 0, -10, 5, 10, 2], [-5, 0, -10, 5, 2, 10], [-5, 0, -10, 10, 5, 2], [-5, 0, -10, 10, 2, 5], [-5, 0, -10, 2, 5, 10], [-5, 0, -10, 2, 10, 5], [-5, 0, 2, 5, 10, -10], [-5, 0, 2, 5, -10, 10], [-5, 0, 2, 10, 5, -10], [-5, 0, 2, 10, -10, 5], [-5, 0, 2, -10, 5, 10], [-5, 0, 2, -10, 10, 5], [-5, 5, 0, 10, -10, 2], [-5, 5, 0, 10, 2, -10], [-5, 5, 0, -10, 10, 2], [-5, 5, 0, -10, 2, 10], [-5, 5, 0, 2, 10, -10], [-5, 5, 0, 2, -10, 10], [-5, 5, 10, 0, -10, 2], [-5, 5, 10, 0, 2, -10], [-5, 5, 10, -10, 0, 2], [-5, 5, 10, -10, 2, 0], [-5, 5, 10, 2, 0, -10], [-5, 5, 10, 2, -10, 0], [-5, 5, -10, 0, 10, 2], [-5, 5, -10, 0, 2, 10], [-5, 5, -10, 10, 0, 2], [-5, 5, -10, 10, 2, 0], [-5, 5, -10, 2, 0, 10], [-5, 5, -10, 2, 10, 0], [-5, 5, 2, 0, 10, -10], [-5, 5, 2, 0, -10, 10], [-5, 5, 2, 10, 0, -10], [-5, 5, 2, 10, -10, 0], [-5, 5, 2, -10, 0, 10], [-5, 5, 2, -10, 10, 0], [-5, 10, 0, 5, -10, 2], [-5, 10, 0, 5, 2, -10], [-5, 10, 0, -10, 5, 2], [-5, 10, 0, -10, 2, 5], [-5, 10, 0, 2, 5, -10], [-5, 10, 0, 2, -10, 5], [-5, 10, 5, 0, -10, 2], [-5, 10, 5, 0, 2, -10], [-5, 10, 5, -10, 0, 2], [-5, 10, 5, -10, 2, 0], [-5, 10, 5, 2, 0, -10], [-5, 10, 5, 2, -10, 0], [-5, 10, -10, 0, 5, 2], [-5, 10, -10, 0, 2, 5], [-5, 10, -10, 5, 0, 2], [-5, 10, -10, 5, 2, 0], [-5, 10, -10, 2, 0, 5], [-5, 10, -10, 2, 5, 0], [-5, 10, 2, 0, 5, -10], [-5, 10, 2, 0, -10, 5], [-5, 10, 2, 5, 0, -10], [-5, 10, 2, 5, -10, 0], [-5, 10, 2, -10, 0, 5], [-5, 10, 2, -10, 5, 0], [-5, -10, 0, 5, 10, 2], [-5, -10, 0, 5, 2, 10], [-5, -10, 0, 10, 5, 2], [-5, -10, 0, 10, 2, 5], [-5, -10, 0, 2, 5, 10], [-5, -10, 0, 2, 10, 5], [-5, -10, 5, 0, 10, 2], [-5, -10, 5, 0, 2, 10], [-5, -10, 5, 10, 0, 2], [-5, -10, 5, 10, 2, 0], [-5, -10, 5, 2, 0, 10], [-5, -10, 5, 2, 10, 0], [-5, -10, 10, 0, 5, 2], [-5, -10, 10, 0, 2, 5], [-5, -10, 10, 5, 0, 2], [-5, -10, 10, 5, 2, 0], [-5, -10, 10, 2, 0, 5], [-5, -10, 10, 2, 5, 0], [-5, -10, 2, 0, 5, 10], [-5, -10, 2, 0, 10, 5], [-5, -10, 2, 5, 0, 10], [-5, -10, 2, 5, 10, 0], [-5, -10, 2, 10, 0, 5], [-5, -10, 2, 10, 5, 0], [-5, 2, 0, 5, 10, -10], [-5, 2, 0, 5, -10, 10], [-5, 2, 0, 10, 5, -10], [-5, 2, 0, 10, -10, 5], [-5, 2, 0, -10, 5, 10], [-5, 2, 0, -10, 10, 5], [-5, 2, 5, 0, 10, -10], [-5, 2, 5, 0, -10, 10], [-5, 2, 5, 10, 0, -10], [-5, 2, 5, 10, -10, 0], [-5, 2, 5, -10, 0, 10], [-5, 2, 5, -10, 10, 0], [-5, 2, 10, 0, 5, -10], [-5, 2, 10, 0, -10, 5], [-5, 2, 10, 5, 0, -10], [-5, 2, 10, 5, -10, 0], [-5, 2, 10, -10, 0, 5], [-5, 2, 10, -10, 5, 0], [-5, 2, -10, 0, 5, 10], [-5, 2, -10, 0, 10, 5], [-5, 2, -10, 5, 0, 10], [-5, 2, -10, 5, 10, 0], [-5, 2, -10, 10, 0, 5], [-5, 2, -10, 10, 5, 0], [0, -5, 5, 10, -10, 2], [0, -5, 5, 10, 2, -10], [0, -5, 5, -10, 10, 2], [0, -5, 5, -10, 2, 10], [0, -5, 5, 2, 10, -10], [0, -5, 5, 2, -10, 10], [0, -5, 10, 5, -10, 2], [0, -5, 10, 5, 2, -10], [0, -5, 10, -10, 5, 2], [0, -5, 10, -10, 2, 5], [0, -5, 10, 2, 5, -10], [0, -5, 10, 2, -10, 5], [0, -5, -10, 5, 10, 2], [0, -5, -10, 5, 2, 10], [0, -5, -10, 10, 5, 2], [0, -5, -10, 10, 2, 5], [0, -5, -10, 2, 5, 10], [0, -5, -10, 2, 10, 5], [0, -5, 2, 5, 10, -10], [0, -5, 2, 5, -10, 10], [0, -5, 2, 10, 5, -10], [0, -5, 2, 10, -10, 5], [0, -5, 2, -10, 5, 10], [0, -5, 2, -10, 10, 5], [0, 5, -5, 10, -10, 2], [0, 5, -5, 10, 2, -10], [0, 5, -5, -10, 10, 2], [0, 5, -5, -10, 2, 10], [0, 5, -5, 2, 10, -10], [0, 5, -5, 2, -10, 10], [0, 5, 10, -5, -10, 2], [0, 5, 10, -5, 2, -10], [0, 5, 10, -10, -5, 2], [0, 5, 10, -10, 2, -5], [0, 5, 10, 2, -5, -10], [0, 5, 10, 2, -10, -5], [0, 5, -10, -5, 10, 2], [0, 5, -10, -5, 2, 10], [0, 5, -10, 10, -5, 2], [0, 5, -10, 10, 2, -5], [0, 5, -10, 2, -5, 10], [0, 5, -10, 2, 10, -5], [0, 5, 2, -5, 10, -10], [0, 5, 2, -5, -10, 10], [0, 5, 2, 10, -5, -10], [0, 5, 2, 10, -10, -5], [0, 5, 2, -10, -5, 10], [0, 5, 2, -10, 10, -5], [0, 10, -5, 5, -10, 2], [0, 10, -5, 5, 2, -10], [0, 10, -5, -10, 5, 2], [0, 10, -5, -10, 2, 5], [0, 10, -5, 2, 5, -10], [0, 10, -5, 2, -10, 5], [0, 10, 5, -5, -10, 2], [0, 10, 5, -5, 2, -10], [0, 10, 5, -10, -5, 2], [0, 10, 5, -10, 2, -5], [0, 10, 5, 2, -5, -10], [0, 10, 5, 2, -10, -5], [0, 10, -10, -5, 5, 2], [0, 10, -10, -5, 2, 5], [0, 10, -10, 5, -5, 2], [0, 10, -10, 5, 2, -5], [0, 10, -10, 2, -5, 5], [0, 10, -10, 2, 5, -5], [0, 10, 2, -5, 5, -10], [0, 10, 2, -5, -10, 5], [0, 10, 2, 5, -5, -10], [0, 10, 2, 5, -10, -5], [0, 10, 2, -10, -5, 5], [0, 10, 2, -10, 5, -5], [0, -10, -5, 5, 10, 2], [0, -10, -5, 5, 2, 10], [0, -10, -5, 10, 5, 2], [0, -10, -5, 10, 2, 5], [0, -10, -5, 2, 5, 10], [0, -10, -5, 2, 10, 5], [0, -10, 5, -5, 10, 2], [0, -10, 5, -5, 2, 10], [0, -10, 5, 10, -5, 2], [0, -10, 5, 10, 2, -5], [0, -10, 5, 2, -5, 10], [0, -10, 5, 2, 10, -5], [0, -10, 10, -5, 5, 2], [0, -10, 10, -5, 2, 5], [0, -10, 10, 5, -5, 2], [0, -10, 10, 5, 2, -5], [0, -10, 10, 2, -5, 5], [0, -10, 10, 2, 5, -5], [0, -10, 2, -5, 5, 10], [0, -10, 2, -5, 10, 5], [0, -10, 2, 5, -5, 10], [0, -10, 2, 5, 10, -5], [0, -10, 2, 10, -5, 5], [0, -10, 2, 10, 5, -5], [0, 2, -5, 5, 10, -10], [0, 2, -5, 5, -10, 10], [0, 2, -5, 10, 5, -10], [0, 2, -5, 10, -10, 5], [0, 2, -5, -10, 5, 10], [0, 2, -5, -10, 10, 5], [0, 2, 5, -5, 10, -10], [0, 2, 5, -5, -10, 10], [0, 2, 5, 10, -5, -10], [0, 2, 5, 10, -10, -5], [0, 2, 5, -10, -5, 10], [0, 2, 5, -10, 10, -5], [0, 2, 10, -5, 5, -10], [0, 2, 10, -5, -10, 5], [0, 2, 10, 5, -5, -10], [0, 2, 10, 5, -10, -5], [0, 2, 10, -10, -5, 5], [0, 2, 10, -10, 5, -5], [0, 2, -10, -5, 5, 10], [0, 2, -10, -5, 10, 5], [0, 2, -10, 5, -5, 10], [0, 2, -10, 5, 10, -5], [0, 2, -10, 10, -5, 5], [0, 2, -10, 10, 5, -5], [5, -5, 0, 10, -10, 2], [5, -5, 0, 10, 2, -10], [5, -5, 0, -10, 10, 2], [5, -5, 0, -10, 2, 10], [5, -5, 0, 2, 10, -10], [5, -5, 0, 2, -10, 10], [5, -5, 10, 0, -10, 2], [5, -5, 10, 0, 2, -10], [5, -5, 10, -10, 0, 2], [5, -5, 10, -10, 2, 0], [5, -5, 10, 2, 0, -10], [5, -5, 10, 2, -10, 0], [5, -5, -10, 0, 10, 2], [5, -5, -10, 0, 2, 10], [5, -5, -10, 10, 0, 2], [5, -5, -10, 10, 2, 0], [5, -5, -10, 2, 0, 10], [5, -5, -10, 2, 10, 0], [5, -5, 2, 0, 10, -10], [5, -5, 2, 0, -10, 10], [5, -5, 2, 10, 0, -10], [5, -5, 2, 10, -10, 0], [5, -5, 2, -10, 0, 10], [5, -5, 2, -10, 10, 0], [5, 0, -5, 10, -10, 2], [5, 0, -5, 10, 2, -10], [5, 0, -5, -10, 10, 2], [5, 0, -5, -10, 2, 10], [5, 0, -5, 2, 10, -10], [5, 0, -5, 2, -10, 10], [5, 0, 10, -5, -10, 2], [5, 0, 10, -5, 2, -10], [5, 0, 10, -10, -5, 2], [5, 0, 10, -10, 2, -5], [5, 0, 10, 2, -5, -10], [5, 0, 10, 2, -10, -5], [5, 0, -10, -5, 10, 2], [5, 0, -10, -5, 2, 10], [5, 0, -10, 10, -5, 2], [5, 0, -10, 10, 2, -5], [5, 0, -10, 2, -5, 10], [5, 0, -10, 2, 10, -5], [5, 0, 2, -5, 10, -10], [5, 0, 2, -5, -10, 10], [5, 0, 2, 10, -5, -10], [5, 0, 2, 10, -10, -5], [5, 0, 2, -10, -5, 10], [5, 0, 2, -10, 10, -5], [5, 10, -5, 0, -10, 2], [5, 10, -5, 0, 2, -10], [5, 10, -5, -10, 0, 2], [5, 10, -5, -10, 2, 0], [5, 10, -5, 2, 0, -10], [5, 10, -5, 2, -10, 0], [5, 10, 0, -5, -10, 2], [5, 10, 0, -5, 2, -10], [5, 10, 0, -10, -5, 2], [5, 10, 0, -10, 2, -5], [5, 10, 0, 2, -5, -10], [5, 10, 0, 2, -10, -5], [5, 10, -10, -5, 0, 2], [5, 10, -10, -5, 2, 0], [5, 10, -10, 0, -5, 2], [5, 10, -10, 0, 2, -5], [5, 10, -10, 2, -5, 0], [5, 10, -10, 2, 0, -5], [5, 10, 2, -5, 0, -10], [5, 10, 2, -5, -10, 0], [5, 10, 2, 0, -5, -10], [5, 10, 2, 0, -10, -5], [5, 10, 2, -10, -5, 0], [5, 10, 2, -10, 0, -5], [5, -10, -5, 0, 10, 2], [5, -10, -5, 0, 2, 10], [5, -10, -5, 10, 0, 2], [5, -10, -5, 10, 2, 0], [5, -10, -5, 2, 0, 10], [5, -10, -5, 2, 10, 0], [5, -10, 0, -5, 10, 2], [5, -10, 0, -5, 2, 10], [5, -10, 0, 10, -5, 2], [5, -10, 0, 10, 2, -5], [5, -10, 0, 2, -5, 10], [5, -10, 0, 2, 10, -5], [5, -10, 10, -5, 0, 2], [5, -10, 10, -5, 2, 0], [5, -10, 10, 0, -5, 2], [5, -10, 10, 0, 2, -5], [5, -10, 10, 2, -5, 0], [5, -10, 10, 2, 0, -5], [5, -10, 2, -5, 0, 10], [5, -10, 2, -5, 10, 0], [5, -10, 2, 0, -5, 10], [5, -10, 2, 0, 10, -5], [5, -10, 2, 10, -5, 0], [5, -10, 2, 10, 0, -5], [5, 2, -5, 0, 10, -10], [5, 2, -5, 0, -10, 10], [5, 2, -5, 10, 0, -10], [5, 2, -5, 10, -10, 0], [5, 2, -5, -10, 0, 10], [5, 2, -5, -10, 10, 0], [5, 2, 0, -5, 10, -10], [5, 2, 0, -5, -10, 10], [5, 2, 0, 10, -5, -10], [5, 2, 0, 10, -10, -5], [5, 2, 0, -10, -5, 10], [5, 2, 0, -10, 10, -5], [5, 2, 10, -5, 0, -10], [5, 2, 10, -5, -10, 0], [5, 2, 10, 0, -5, -10], [5, 2, 10, 0, -10, -5], [5, 2, 10, -10, -5, 0], [5, 2, 10, -10, 0, -5], [5, 2, -10, -5, 0, 10], [5, 2, -10, -5, 10, 0], [5, 2, -10, 0, -5, 10], [5, 2, -10, 0, 10, -5], [5, 2, -10, 10, -5, 0], [5, 2, -10, 10, 0, -5], [10, -5, 0, 5, -10, 2], [10, -5, 0, 5, 2, -10], [10, -5, 0, -10, 5, 2], [10, -5, 0, -10, 2, 5], [10, -5, 0, 2, 5, -10], [10, -5, 0, 2, -10, 5], [10, -5, 5, 0, -10, 2], [10, -5, 5, 0, 2, -10], [10, -5, 5, -10, 0, 2], [10, -5, 5, -10, 2, 0], [10, -5, 5, 2, 0, -10], [10, -5, 5, 2, -10, 0], [10, -5, -10, 0, 5, 2], [10, -5, -10, 0, 2, 5], [10, -5, -10, 5, 0, 2], [10, -5, -10, 5, 2, 0], [10, -5, -10, 2, 0, 5], [10, -5, -10, 2, 5, 0], [10, -5, 2, 0, 5, -10], [10, -5, 2, 0, -10, 5], [10, -5, 2, 5, 0, -10], [10, -5, 2, 5, -10, 0], [10, -5, 2, -10, 0, 5], [10, -5, 2, -10, 5, 0], [10, 0, -5, 5, -10, 2], [10, 0, -5, 5, 2, -10], [10, 0, -5, -10, 5, 2], [10, 0, -5, -10, 2, 5], [10, 0, -5, 2, 5, -10], [10, 0, -5, 2, -10, 5], [10, 0, 5, -5, -10, 2], [10, 0, 5, -5, 2, -10], [10, 0, 5, -10, -5, 2], [10, 0, 5, -10, 2, -5], [10, 0, 5, 2, -5, -10], [10, 0, 5, 2, -10, -5], [10, 0, -10, -5, 5, 2], [10, 0, -10, -5, 2, 5], [10, 0, -10, 5, -5, 2], [10, 0, -10, 5, 2, -5], [10, 0, -10, 2, -5, 5], [10, 0, -10, 2, 5, -5], [10, 0, 2, -5, 5, -10], [10, 0, 2, -5, -10, 5], [10, 0, 2, 5, -5, -10], [10, 0, 2, 5, -10, -5], [10, 0, 2, -10, -5, 5], [10, 0, 2, -10, 5, -5], [10, 5, -5, 0, -10, 2], [10, 5, -5, 0, 2, -10], [10, 5, -5, -10, 0, 2], [10, 5, -5, -10, 2, 0], [10, 5, -5, 2, 0, -10], [10, 5, -5, 2, -10, 0], [10, 5, 0, -5, -10, 2], [10, 5, 0, -5, 2, -10], [10, 5, 0, -10, -5, 2], [10, 5, 0, -10, 2, -5], [10, 5, 0, 2, -5, -10], [10, 5, 0, 2, -10, -5], [10, 5, -10, -5, 0, 2], [10, 5, -10, -5, 2, 0], [10, 5, -10, 0, -5, 2], [10, 5, -10, 0, 2, -5], [10, 5, -10, 2, -5, 0], [10, 5, -10, 2, 0, -5], [10, 5, 2, -5, 0, -10], [10, 5, 2, -5, -10, 0], [10, 5, 2, 0, -5, -10], [10, 5, 2, 0, -10, -5], [10, 5, 2, -10, -5, 0], [10, 5, 2, -10, 0, -5], [10, -10, -5, 0, 5, 2], [10, -10, -5, 0, 2, 5], [10, -10, -5, 5, 0, 2], [10, -10, -5, 5, 2, 0], [10, -10, -5, 2, 0, 5], [10, -10, -5, 2, 5, 0], [10, -10, 0, -5, 5, 2], [10, -10, 0, -5, 2, 5], [10, -10, 0, 5, -5, 2], [10, -10, 0, 5, 2, -5], [10, -10, 0, 2, -5, 5], [10, -10, 0, 2, 5, -5], [10, -10, 5, -5, 0, 2], [10, -10, 5, -5, 2, 0], [10, -10, 5, 0, -5, 2], [10, -10, 5, 0, 2, -5], [10, -10, 5, 2, -5, 0], [10, -10, 5, 2, 0, -5], [10, -10, 2, -5, 0, 5], [10, -10, 2, -5, 5, 0], [10, -10, 2, 0, -5, 5], [10, -10, 2, 0, 5, -5], [10, -10, 2, 5, -5, 0], [10, -10, 2, 5, 0, -5], [10, 2, -5, 0, 5, -10], [10, 2, -5, 0, -10, 5], [10, 2, -5, 5, 0, -10], [10, 2, -5, 5, -10, 0], [10, 2, -5, -10, 0, 5], [10, 2, -5, -10, 5, 0], [10, 2, 0, -5, 5, -10], [10, 2, 0, -5, -10, 5], [10, 2, 0, 5, -5, -10], [10, 2, 0, 5, -10, -5], [10, 2, 0, -10, -5, 5], [10, 2, 0, -10, 5, -5], [10, 2, 5, -5, 0, -10], [10, 2, 5, -5, -10, 0], [10, 2, 5, 0, -5, -10], [10, 2, 5, 0, -10, -5], [10, 2, 5, -10, -5, 0], [10, 2, 5, -10, 0, -5], [10, 2, -10, -5, 0, 5], [10, 2, -10, -5, 5, 0], [10, 2, -10, 0, -5, 5], [10, 2, -10, 0, 5, -5], [10, 2, -10, 5, -5, 0], [10, 2, -10, 5, 0, -5], [-10, -5, 0, 5, 10, 2], [-10, -5, 0, 5, 2, 10], [-10, -5, 0, 10, 5, 2], [-10, -5, 0, 10, 2, 5], [-10, -5, 0, 2, 5, 10], [-10, -5, 0, 2, 10, 5], [-10, -5, 5, 0, 10, 2], [-10, -5, 5, 0, 2, 10], [-10, -5, 5, 10, 0, 2], [-10, -5, 5, 10, 2, 0], [-10, -5, 5, 2, 0, 10], [-10, -5, 5, 2, 10, 0], [-10, -5, 10, 0, 5, 2], [-10, -5, 10, 0, 2, 5], [-10, -5, 10, 5, 0, 2], [-10, -5, 10, 5, 2, 0], [-10, -5, 10, 2, 0, 5], [-10, -5, 10, 2, 5, 0], [-10, -5, 2, 0, 5, 10], [-10, -5, 2, 0, 10, 5], [-10, -5, 2, 5, 0, 10], [-10, -5, 2, 5, 10, 0], [-10, -5, 2, 10, 0, 5], [-10, -5, 2, 10, 5, 0], [-10, 0, -5, 5, 10, 2], [-10, 0, -5, 5, 2, 10], [-10, 0, -5, 10, 5, 2], [-10, 0, -5, 10, 2, 5], [-10, 0, -5, 2, 5, 10], [-10, 0, -5, 2, 10, 5], [-10, 0, 5, -5, 10, 2], [-10, 0, 5, -5, 2, 10], [-10, 0, 5, 10, -5, 2], [-10, 0, 5, 10, 2, -5], [-10, 0, 5, 2, -5, 10], [-10, 0, 5, 2, 10, -5], [-10, 0, 10, -5, 5, 2], [-10, 0, 10, -5, 2, 5], [-10, 0, 10, 5, -5, 2], [-10, 0, 10, 5, 2, -5], [-10, 0, 10, 2, -5, 5], [-10, 0, 10, 2, 5, -5], [-10, 0, 2, -5, 5, 10], [-10, 0, 2, -5, 10, 5], [-10, 0, 2, 5, -5, 10], [-10, 0, 2, 5, 10, -5], [-10, 0, 2, 10, -5, 5], [-10, 0, 2, 10, 5, -5], [-10, 5, -5, 0, 10, 2], [-10, 5, -5, 0, 2, 10], [-10, 5, -5, 10, 0, 2], [-10, 5, -5, 10, 2, 0], [-10, 5, -5, 2, 0, 10], [-10, 5, -5, 2, 10, 0], [-10, 5, 0, -5, 10, 2], [-10, 5, 0, -5, 2, 10], [-10, 5, 0, 10, -5, 2], [-10, 5, 0, 10, 2, -5], [-10, 5, 0, 2, -5, 10], [-10, 5, 0, 2, 10, -5], [-10, 5, 10, -5, 0, 2], [-10, 5, 10, -5, 2, 0], [-10, 5, 10, 0, -5, 2], [-10, 5, 10, 0, 2, -5], [-10, 5, 10, 2, -5, 0], [-10, 5, 10, 2, 0, -5], [-10, 5, 2, -5, 0, 10], [-10, 5, 2, -5, 10, 0], [-10, 5, 2, 0, -5, 10], [-10, 5, 2, 0, 10, -5], [-10, 5, 2, 10, -5, 0], [-10, 5, 2, 10, 0, -5], [-10, 10, -5, 0, 5, 2], [-10, 10, -5, 0, 2, 5], [-10, 10, -5, 5, 0, 2], [-10, 10, -5, 5, 2, 0], [-10, 10, -5, 2, 0, 5], [-10, 10, -5, 2, 5, 0], [-10, 10, 0, -5, 5, 2], [-10, 10, 0, -5, 2, 5], [-10, 10, 0, 5, -5, 2], [-10, 10, 0, 5, 2, -5], [-10, 10, 0, 2, -5, 5], [-10, 10, 0, 2, 5, -5], [-10, 10, 5, -5, 0, 2], [-10, 10, 5, -5, 2, 0], [-10, 10, 5, 0, -5, 2], [-10, 10, 5, 0, 2, -5], [-10, 10, 5, 2, -5, 0], [-10, 10, 5, 2, 0, -5], [-10, 10, 2, -5, 0, 5], [-10, 10, 2, -5, 5, 0], [-10, 10, 2, 0, -5, 5], [-10, 10, 2, 0, 5, -5], [-10, 10, 2, 5, -5, 0], [-10, 10, 2, 5, 0, -5], [-10, 2, -5, 0, 5, 10], [-10, 2, -5, 0, 10, 5], [-10, 2, -5, 5, 0, 10], [-10, 2, -5, 5, 10, 0], [-10, 2, -5, 10, 0, 5], [-10, 2, -5, 10, 5, 0], [-10, 2, 0, -5, 5, 10], [-10, 2, 0, -5, 10, 5], [-10, 2, 0, 5, -5, 10], [-10, 2, 0, 5, 10, -5], [-10, 2, 0, 10, -5, 5], [-10, 2, 0, 10, 5, -5], [-10, 2, 5, -5, 0, 10], [-10, 2, 5, -5, 10, 0], [-10, 2, 5, 0, -5, 10], [-10, 2, 5, 0, 10, -5], [-10, 2, 5, 10, -5, 0], [-10, 2, 5, 10, 0, -5], [-10, 2, 10, -5, 0, 5], [-10, 2, 10, -5, 5, 0], [-10, 2, 10, 0, -5, 5], [-10, 2, 10, 0, 5, -5], [-10, 2, 10, 5, -5, 0], [-10, 2, 10, 5, 0, -5], [2, -5, 0, 5, 10, -10], [2, -5, 0, 5, -10, 10], [2, -5, 0, 10, 5, -10], [2, -5, 0, 10, -10, 5], [2, -5, 0, -10, 5, 10], [2, -5, 0, -10, 10, 5], [2, -5, 5, 0, 10, -10], [2, -5, 5, 0, -10, 10], [2, -5, 5, 10, 0, -10], [2, -5, 5, 10, -10, 0], [2, -5, 5, -10, 0, 10], [2, -5, 5, -10, 10, 0], [2, -5, 10, 0, 5, -10], [2, -5, 10, 0, -10, 5], [2, -5, 10, 5, 0, -10], [2, -5, 10, 5, -10, 0], [2, -5, 10, -10, 0, 5], [2, -5, 10, -10, 5, 0], [2, -5, -10, 0, 5, 10], [2, -5, -10, 0, 10, 5], [2, -5, -10, 5, 0, 10], [2, -5, -10, 5, 10, 0], [2, -5, -10, 10, 0, 5], [2, -5, -10, 10, 5, 0], [2, 0, -5, 5, 10, -10], [2, 0, -5, 5, -10, 10], [2, 0, -5, 10, 5, -10], [2, 0, -5, 10, -10, 5], [2, 0, -5, -10, 5, 10], [2, 0, -5, -10, 10, 5], [2, 0, 5, -5, 10, -10], [2, 0, 5, -5, -10, 10], [2, 0, 5, 10, -5, -10], [2, 0, 5, 10, -10, -5], [2, 0, 5, -10, -5, 10], [2, 0, 5, -10, 10, -5], [2, 0, 10, -5, 5, -10], [2, 0, 10, -5, -10, 5], [2, 0, 10, 5, -5, -10], [2, 0, 10, 5, -10, -5], [2, 0, 10, -10, -5, 5], [2, 0, 10, -10, 5, -5], [2, 0, -10, -5, 5, 10], [2, 0, -10, -5, 10, 5], [2, 0, -10, 5, -5, 10], [2, 0, -10, 5, 10, -5], [2, 0, -10, 10, -5, 5], [2, 0, -10, 10, 5, -5], [2, 5, -5, 0, 10, -10], [2, 5, -5, 0, -10, 10], [2, 5, -5, 10, 0, -10], [2, 5, -5, 10, -10, 0], [2, 5, -5, -10, 0, 10], [2, 5, -5, -10, 10, 0], [2, 5, 0, -5, 10, -10], [2, 5, 0, -5, -10, 10], [2, 5, 0, 10, -5, -10], [2, 5, 0, 10, -10, -5], [2, 5, 0, -10, -5, 10], [2, 5, 0, -10, 10, -5], [2, 5, 10, -5, 0, -10], [2, 5, 10, -5, -10, 0], [2, 5, 10, 0, -5, -10], [2, 5, 10, 0, -10, -5], [2, 5, 10, -10, -5, 0], [2, 5, 10, -10, 0, -5], [2, 5, -10, -5, 0, 10], [2, 5, -10, -5, 10, 0], [2, 5, -10, 0, -5, 10], [2, 5, -10, 0, 10, -5], [2, 5, -10, 10, -5, 0], [2, 5, -10, 10, 0, -5], [2, 10, -5, 0, 5, -10], [2, 10, -5, 0, -10, 5], [2, 10, -5, 5, 0, -10], [2, 10, -5, 5, -10, 0], [2, 10, -5, -10, 0, 5], [2, 10, -5, -10, 5, 0], [2, 10, 0, -5, 5, -10], [2, 10, 0, -5, -10, 5], [2, 10, 0, 5, -5, -10], [2, 10, 0, 5, -10, -5], [2, 10, 0, -10, -5, 5], [2, 10, 0, -10, 5, -5], [2, 10, 5, -5, 0, -10], [2, 10, 5, -5, -10, 0], [2, 10, 5, 0, -5, -10], [2, 10, 5, 0, -10, -5], [2, 10, 5, -10, -5, 0], [2, 10, 5, -10, 0, -5], [2, 10, -10, -5, 0, 5], [2, 10, -10, -5, 5, 0], [2, 10, -10, 0, -5, 5], [2, 10, -10, 0, 5, -5], [2, 10, -10, 5, -5, 0], [2, 10, -10, 5, 0, -5], [2, -10, -5, 0, 5, 10], [2, -10, -5, 0, 10, 5], [2, -10, -5, 5, 0, 10], [2, -10, -5, 5, 10, 0], [2, -10, -5, 10, 0, 5], [2, -10, -5, 10, 5, 0], [2, -10, 0, -5, 5, 10], [2, -10, 0, -5, 10, 5], [2, -10, 0, 5, -5, 10], [2, -10, 0, 5, 10, -5], [2, -10, 0, 10, -5, 5], [2, -10, 0, 10, 5, -5], [2, -10, 5, -5, 0, 10], [2, -10, 5, -5, 10, 0], [2, -10, 5, 0, -5, 10], [2, -10, 5, 0, 10, -5], [2, -10, 5, 10, -5, 0], [2, -10, 5, 10, 0, -5], [2, -10, 10, -5, 0, 5], [2, -10, 10, -5, 5, 0], [2, -10, 10, 0, -5, 5], [2, -10, 10, 0, 5, -5], [2, -10, 10, 5, -5, 0], [2, -10, 10, 5, 0, -5]]\n assert candidate(nums = [10, 20, 30, 40, 50, 60]) == [[10, 20, 30, 40, 50, 60], [10, 20, 30, 40, 60, 50], [10, 20, 30, 50, 40, 60], [10, 20, 30, 50, 60, 40], [10, 20, 30, 60, 40, 50], [10, 20, 30, 60, 50, 40], [10, 20, 40, 30, 50, 60], [10, 20, 40, 30, 60, 50], [10, 20, 40, 50, 30, 60], [10, 20, 40, 50, 60, 30], [10, 20, 40, 60, 30, 50], [10, 20, 40, 60, 50, 30], [10, 20, 50, 30, 40, 60], [10, 20, 50, 30, 60, 40], [10, 20, 50, 40, 30, 60], [10, 20, 50, 40, 60, 30], [10, 20, 50, 60, 30, 40], [10, 20, 50, 60, 40, 30], [10, 20, 60, 30, 40, 50], [10, 20, 60, 30, 50, 40], [10, 20, 60, 40, 30, 50], [10, 20, 60, 40, 50, 30], [10, 20, 60, 50, 30, 40], [10, 20, 60, 50, 40, 30], [10, 30, 20, 40, 50, 60], [10, 30, 20, 40, 60, 50], [10, 30, 20, 50, 40, 60], [10, 30, 20, 50, 60, 40], [10, 30, 20, 60, 40, 50], [10, 30, 20, 60, 50, 40], [10, 30, 40, 20, 50, 60], [10, 30, 40, 20, 60, 50], [10, 30, 40, 50, 20, 60], [10, 30, 40, 50, 60, 20], [10, 30, 40, 60, 20, 50], [10, 30, 40, 60, 50, 20], [10, 30, 50, 20, 40, 60], [10, 30, 50, 20, 60, 40], [10, 30, 50, 40, 20, 60], [10, 30, 50, 40, 60, 20], [10, 30, 50, 60, 20, 40], [10, 30, 50, 60, 40, 20], [10, 30, 60, 20, 40, 50], [10, 30, 60, 20, 50, 40], [10, 30, 60, 40, 20, 50], [10, 30, 60, 40, 50, 20], [10, 30, 60, 50, 20, 40], [10, 30, 60, 50, 40, 20], [10, 40, 20, 30, 50, 60], [10, 40, 20, 30, 60, 50], [10, 40, 20, 50, 30, 60], [10, 40, 20, 50, 60, 30], [10, 40, 20, 60, 30, 50], [10, 40, 20, 60, 50, 30], [10, 40, 30, 20, 50, 60], [10, 40, 30, 20, 60, 50], [10, 40, 30, 50, 20, 60], [10, 40, 30, 50, 60, 20], [10, 40, 30, 60, 20, 50], [10, 40, 30, 60, 50, 20], [10, 40, 50, 20, 30, 60], [10, 40, 50, 20, 60, 30], [10, 40, 50, 30, 20, 60], [10, 40, 50, 30, 60, 20], [10, 40, 50, 60, 20, 30], [10, 40, 50, 60, 30, 20], [10, 40, 60, 20, 30, 50], [10, 40, 60, 20, 50, 30], [10, 40, 60, 30, 20, 50], [10, 40, 60, 30, 50, 20], [10, 40, 60, 50, 20, 30], [10, 40, 60, 50, 30, 20], [10, 50, 20, 30, 40, 60], [10, 50, 20, 30, 60, 40], [10, 50, 20, 40, 30, 60], [10, 50, 20, 40, 60, 30], [10, 50, 20, 60, 30, 40], [10, 50, 20, 60, 40, 30], [10, 50, 30, 20, 40, 60], [10, 50, 30, 20, 60, 40], [10, 50, 30, 40, 20, 60], [10, 50, 30, 40, 60, 20], [10, 50, 30, 60, 20, 40], [10, 50, 30, 60, 40, 20], [10, 50, 40, 20, 30, 60], [10, 50, 40, 20, 60, 30], [10, 50, 40, 30, 20, 60], [10, 50, 40, 30, 60, 20], [10, 50, 40, 60, 20, 30], [10, 50, 40, 60, 30, 20], [10, 50, 60, 20, 30, 40], [10, 50, 60, 20, 40, 30], [10, 50, 60, 30, 20, 40], [10, 50, 60, 30, 40, 20], [10, 50, 60, 40, 20, 30], [10, 50, 60, 40, 30, 20], [10, 60, 20, 30, 40, 50], [10, 60, 20, 30, 50, 40], [10, 60, 20, 40, 30, 50], [10, 60, 20, 40, 50, 30], [10, 60, 20, 50, 30, 40], [10, 60, 20, 50, 40, 30], [10, 60, 30, 20, 40, 50], [10, 60, 30, 20, 50, 40], [10, 60, 30, 40, 20, 50], [10, 60, 30, 40, 50, 20], [10, 60, 30, 50, 20, 40], [10, 60, 30, 50, 40, 20], [10, 60, 40, 20, 30, 50], [10, 60, 40, 20, 50, 30], [10, 60, 40, 30, 20, 50], [10, 60, 40, 30, 50, 20], [10, 60, 40, 50, 20, 30], [10, 60, 40, 50, 30, 20], [10, 60, 50, 20, 30, 40], [10, 60, 50, 20, 40, 30], [10, 60, 50, 30, 20, 40], [10, 60, 50, 30, 40, 20], [10, 60, 50, 40, 20, 30], [10, 60, 50, 40, 30, 20], [20, 10, 30, 40, 50, 60], [20, 10, 30, 40, 60, 50], [20, 10, 30, 50, 40, 60], [20, 10, 30, 50, 60, 40], [20, 10, 30, 60, 40, 50], [20, 10, 30, 60, 50, 40], [20, 10, 40, 30, 50, 60], [20, 10, 40, 30, 60, 50], [20, 10, 40, 50, 30, 60], [20, 10, 40, 50, 60, 30], [20, 10, 40, 60, 30, 50], [20, 10, 40, 60, 50, 30], [20, 10, 50, 30, 40, 60], [20, 10, 50, 30, 60, 40], [20, 10, 50, 40, 30, 60], [20, 10, 50, 40, 60, 30], [20, 10, 50, 60, 30, 40], [20, 10, 50, 60, 40, 30], [20, 10, 60, 30, 40, 50], [20, 10, 60, 30, 50, 40], [20, 10, 60, 40, 30, 50], [20, 10, 60, 40, 50, 30], [20, 10, 60, 50, 30, 40], [20, 10, 60, 50, 40, 30], [20, 30, 10, 40, 50, 60], [20, 30, 10, 40, 60, 50], [20, 30, 10, 50, 40, 60], [20, 30, 10, 50, 60, 40], [20, 30, 10, 60, 40, 50], [20, 30, 10, 60, 50, 40], [20, 30, 40, 10, 50, 60], [20, 30, 40, 10, 60, 50], [20, 30, 40, 50, 10, 60], [20, 30, 40, 50, 60, 10], [20, 30, 40, 60, 10, 50], [20, 30, 40, 60, 50, 10], [20, 30, 50, 10, 40, 60], [20, 30, 50, 10, 60, 40], [20, 30, 50, 40, 10, 60], [20, 30, 50, 40, 60, 10], [20, 30, 50, 60, 10, 40], [20, 30, 50, 60, 40, 10], [20, 30, 60, 10, 40, 50], [20, 30, 60, 10, 50, 40], [20, 30, 60, 40, 10, 50], [20, 30, 60, 40, 50, 10], [20, 30, 60, 50, 10, 40], [20, 30, 60, 50, 40, 10], [20, 40, 10, 30, 50, 60], [20, 40, 10, 30, 60, 50], [20, 40, 10, 50, 30, 60], [20, 40, 10, 50, 60, 30], [20, 40, 10, 60, 30, 50], [20, 40, 10, 60, 50, 30], [20, 40, 30, 10, 50, 60], [20, 40, 30, 10, 60, 50], [20, 40, 30, 50, 10, 60], [20, 40, 30, 50, 60, 10], [20, 40, 30, 60, 10, 50], [20, 40, 30, 60, 50, 10], [20, 40, 50, 10, 30, 60], [20, 40, 50, 10, 60, 30], [20, 40, 50, 30, 10, 60], [20, 40, 50, 30, 60, 10], [20, 40, 50, 60, 10, 30], [20, 40, 50, 60, 30, 10], [20, 40, 60, 10, 30, 50], [20, 40, 60, 10, 50, 30], [20, 40, 60, 30, 10, 50], [20, 40, 60, 30, 50, 10], [20, 40, 60, 50, 10, 30], [20, 40, 60, 50, 30, 10], [20, 50, 10, 30, 40, 60], [20, 50, 10, 30, 60, 40], [20, 50, 10, 40, 30, 60], [20, 50, 10, 40, 60, 30], [20, 50, 10, 60, 30, 40], [20, 50, 10, 60, 40, 30], [20, 50, 30, 10, 40, 60], [20, 50, 30, 10, 60, 40], [20, 50, 30, 40, 10, 60], [20, 50, 30, 40, 60, 10], [20, 50, 30, 60, 10, 40], [20, 50, 30, 60, 40, 10], [20, 50, 40, 10, 30, 60], [20, 50, 40, 10, 60, 30], [20, 50, 40, 30, 10, 60], [20, 50, 40, 30, 60, 10], [20, 50, 40, 60, 10, 30], [20, 50, 40, 60, 30, 10], [20, 50, 60, 10, 30, 40], [20, 50, 60, 10, 40, 30], [20, 50, 60, 30, 10, 40], [20, 50, 60, 30, 40, 10], [20, 50, 60, 40, 10, 30], [20, 50, 60, 40, 30, 10], [20, 60, 10, 30, 40, 50], [20, 60, 10, 30, 50, 40], [20, 60, 10, 40, 30, 50], [20, 60, 10, 40, 50, 30], [20, 60, 10, 50, 30, 40], [20, 60, 10, 50, 40, 30], [20, 60, 30, 10, 40, 50], [20, 60, 30, 10, 50, 40], [20, 60, 30, 40, 10, 50], [20, 60, 30, 40, 50, 10], [20, 60, 30, 50, 10, 40], [20, 60, 30, 50, 40, 10], [20, 60, 40, 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[30, 20, 10, 50, 60, 40], [30, 20, 10, 60, 40, 50], [30, 20, 10, 60, 50, 40], [30, 20, 40, 10, 50, 60], [30, 20, 40, 10, 60, 50], [30, 20, 40, 50, 10, 60], [30, 20, 40, 50, 60, 10], [30, 20, 40, 60, 10, 50], [30, 20, 40, 60, 50, 10], [30, 20, 50, 10, 40, 60], [30, 20, 50, 10, 60, 40], [30, 20, 50, 40, 10, 60], [30, 20, 50, 40, 60, 10], [30, 20, 50, 60, 10, 40], [30, 20, 50, 60, 40, 10], [30, 20, 60, 10, 40, 50], [30, 20, 60, 10, 50, 40], [30, 20, 60, 40, 10, 50], [30, 20, 60, 40, 50, 10], [30, 20, 60, 50, 10, 40], [30, 20, 60, 50, 40, 10], [30, 40, 10, 20, 50, 60], [30, 40, 10, 20, 60, 50], [30, 40, 10, 50, 20, 60], [30, 40, 10, 50, 60, 20], [30, 40, 10, 60, 20, 50], [30, 40, 10, 60, 50, 20], [30, 40, 20, 10, 50, 60], [30, 40, 20, 10, 60, 50], [30, 40, 20, 50, 10, 60], [30, 40, 20, 50, 60, 10], [30, 40, 20, 60, 10, 50], [30, 40, 20, 60, 50, 10], [30, 40, 50, 10, 20, 60], [30, 40, 50, 10, 60, 20], [30, 40, 50, 20, 10, 60], [30, 40, 50, 20, 60, 10], [30, 40, 50, 60, 10, 20], [30, 40, 50, 60, 20, 10], [30, 40, 60, 10, 20, 50], [30, 40, 60, 10, 50, 20], [30, 40, 60, 20, 10, 50], [30, 40, 60, 20, 50, 10], [30, 40, 60, 50, 10, 20], [30, 40, 60, 50, 20, 10], [30, 50, 10, 20, 40, 60], [30, 50, 10, 20, 60, 40], [30, 50, 10, 40, 20, 60], [30, 50, 10, 40, 60, 20], [30, 50, 10, 60, 20, 40], [30, 50, 10, 60, 40, 20], [30, 50, 20, 10, 40, 60], [30, 50, 20, 10, 60, 40], [30, 50, 20, 40, 10, 60], [30, 50, 20, 40, 60, 10], [30, 50, 20, 60, 10, 40], [30, 50, 20, 60, 40, 10], [30, 50, 40, 10, 20, 60], [30, 50, 40, 10, 60, 20], [30, 50, 40, 20, 10, 60], [30, 50, 40, 20, 60, 10], [30, 50, 40, 60, 10, 20], [30, 50, 40, 60, 20, 10], [30, 50, 60, 10, 20, 40], [30, 50, 60, 10, 40, 20], [30, 50, 60, 20, 10, 40], [30, 50, 60, 20, 40, 10], [30, 50, 60, 40, 10, 20], [30, 50, 60, 40, 20, 10], [30, 60, 10, 20, 40, 50], [30, 60, 10, 20, 50, 40], [30, 60, 10, 40, 20, 50], [30, 60, 10, 40, 50, 20], [30, 60, 10, 50, 20, 40], [30, 60, 10, 50, 40, 20], [30, 60, 20, 10, 40, 50], [30, 60, 20, 10, 50, 40], 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50, 20, 30], [40, 10, 60, 50, 30, 20], [40, 20, 10, 30, 50, 60], [40, 20, 10, 30, 60, 50], [40, 20, 10, 50, 30, 60], [40, 20, 10, 50, 60, 30], [40, 20, 10, 60, 30, 50], [40, 20, 10, 60, 50, 30], [40, 20, 30, 10, 50, 60], [40, 20, 30, 10, 60, 50], [40, 20, 30, 50, 10, 60], [40, 20, 30, 50, 60, 10], [40, 20, 30, 60, 10, 50], [40, 20, 30, 60, 50, 10], [40, 20, 50, 10, 30, 60], [40, 20, 50, 10, 60, 30], [40, 20, 50, 30, 10, 60], [40, 20, 50, 30, 60, 10], [40, 20, 50, 60, 10, 30], [40, 20, 50, 60, 30, 10], [40, 20, 60, 10, 30, 50], [40, 20, 60, 10, 50, 30], [40, 20, 60, 30, 10, 50], [40, 20, 60, 30, 50, 10], [40, 20, 60, 50, 10, 30], [40, 20, 60, 50, 30, 10], [40, 30, 10, 20, 50, 60], [40, 30, 10, 20, 60, 50], [40, 30, 10, 50, 20, 60], [40, 30, 10, 50, 60, 20], [40, 30, 10, 60, 20, 50], [40, 30, 10, 60, 50, 20], [40, 30, 20, 10, 50, 60], [40, 30, 20, 10, 60, 50], [40, 30, 20, 50, 10, 60], [40, 30, 20, 50, 60, 10], [40, 30, 20, 60, 10, 50], [40, 30, 20, 60, 50, 10], [40, 30, 50, 10, 20, 60], [40, 30, 50, 10, 60, 20], [40, 30, 50, 20, 10, 60], [40, 30, 50, 20, 60, 10], [40, 30, 50, 60, 10, 20], [40, 30, 50, 60, 20, 10], [40, 30, 60, 10, 20, 50], [40, 30, 60, 10, 50, 20], [40, 30, 60, 20, 10, 50], [40, 30, 60, 20, 50, 10], [40, 30, 60, 50, 10, 20], [40, 30, 60, 50, 20, 10], [40, 50, 10, 20, 30, 60], [40, 50, 10, 20, 60, 30], [40, 50, 10, 30, 20, 60], [40, 50, 10, 30, 60, 20], [40, 50, 10, 60, 20, 30], [40, 50, 10, 60, 30, 20], [40, 50, 20, 10, 30, 60], [40, 50, 20, 10, 60, 30], [40, 50, 20, 30, 10, 60], [40, 50, 20, 30, 60, 10], [40, 50, 20, 60, 10, 30], [40, 50, 20, 60, 30, 10], [40, 50, 30, 10, 20, 60], [40, 50, 30, 10, 60, 20], [40, 50, 30, 20, 10, 60], [40, 50, 30, 20, 60, 10], [40, 50, 30, 60, 10, 20], [40, 50, 30, 60, 20, 10], [40, 50, 60, 10, 20, 30], [40, 50, 60, 10, 30, 20], [40, 50, 60, 20, 10, 30], [40, 50, 60, 20, 30, 10], [40, 50, 60, 30, 10, 20], [40, 50, 60, 30, 20, 10], [40, 60, 10, 20, 30, 50], [40, 60, 10, 20, 50, 30], [40, 60, 10, 30, 20, 50], [40, 60, 10, 30, 50, 20], [40, 60, 10, 50, 20, 30], [40, 60, 10, 50, 30, 20], [40, 60, 20, 10, 30, 50], [40, 60, 20, 10, 50, 30], [40, 60, 20, 30, 10, 50], [40, 60, 20, 30, 50, 10], [40, 60, 20, 50, 10, 30], [40, 60, 20, 50, 30, 10], [40, 60, 30, 10, 20, 50], [40, 60, 30, 10, 50, 20], [40, 60, 30, 20, 10, 50], [40, 60, 30, 20, 50, 10], [40, 60, 30, 50, 10, 20], [40, 60, 30, 50, 20, 10], [40, 60, 50, 10, 20, 30], [40, 60, 50, 10, 30, 20], [40, 60, 50, 20, 10, 30], [40, 60, 50, 20, 30, 10], [40, 60, 50, 30, 10, 20], [40, 60, 50, 30, 20, 10], [50, 10, 20, 30, 40, 60], [50, 10, 20, 30, 60, 40], [50, 10, 20, 40, 30, 60], [50, 10, 20, 40, 60, 30], [50, 10, 20, 60, 30, 40], [50, 10, 20, 60, 40, 30], [50, 10, 30, 20, 40, 60], [50, 10, 30, 20, 60, 40], [50, 10, 30, 40, 20, 60], [50, 10, 30, 40, 60, 20], [50, 10, 30, 60, 20, 40], [50, 10, 30, 60, 40, 20], [50, 10, 40, 20, 30, 60], [50, 10, 40, 20, 60, 30], [50, 10, 40, 30, 20, 60], [50, 10, 40, 30, 60, 20], [50, 10, 40, 60, 20, 30], [50, 10, 40, 60, 30, 20], [50, 10, 60, 20, 30, 40], [50, 10, 60, 20, 40, 30], [50, 10, 60, 30, 20, 40], [50, 10, 60, 30, 40, 20], [50, 10, 60, 40, 20, 30], [50, 10, 60, 40, 30, 20], [50, 20, 10, 30, 40, 60], [50, 20, 10, 30, 60, 40], [50, 20, 10, 40, 30, 60], [50, 20, 10, 40, 60, 30], [50, 20, 10, 60, 30, 40], [50, 20, 10, 60, 40, 30], [50, 20, 30, 10, 40, 60], [50, 20, 30, 10, 60, 40], [50, 20, 30, 40, 10, 60], [50, 20, 30, 40, 60, 10], [50, 20, 30, 60, 10, 40], [50, 20, 30, 60, 40, 10], [50, 20, 40, 10, 30, 60], [50, 20, 40, 10, 60, 30], [50, 20, 40, 30, 10, 60], [50, 20, 40, 30, 60, 10], [50, 20, 40, 60, 10, 30], [50, 20, 40, 60, 30, 10], [50, 20, 60, 10, 30, 40], [50, 20, 60, 10, 40, 30], [50, 20, 60, 30, 10, 40], [50, 20, 60, 30, 40, 10], [50, 20, 60, 40, 10, 30], [50, 20, 60, 40, 30, 10], [50, 30, 10, 20, 40, 60], [50, 30, 10, 20, 60, 40], [50, 30, 10, 40, 20, 60], [50, 30, 10, 40, 60, 20], [50, 30, 10, 60, 20, 40], [50, 30, 10, 60, 40, 20], [50, 30, 20, 10, 40, 60], [50, 30, 20, 10, 60, 40], [50, 30, 20, 40, 10, 60], [50, 30, 20, 40, 60, 10], [50, 30, 20, 60, 10, 40], [50, 30, 20, 60, 40, 10], [50, 30, 40, 10, 20, 60], [50, 30, 40, 10, 60, 20], [50, 30, 40, 20, 10, 60], [50, 30, 40, 20, 60, 10], [50, 30, 40, 60, 10, 20], [50, 30, 40, 60, 20, 10], [50, 30, 60, 10, 20, 40], [50, 30, 60, 10, 40, 20], [50, 30, 60, 20, 10, 40], [50, 30, 60, 20, 40, 10], [50, 30, 60, 40, 10, 20], [50, 30, 60, 40, 20, 10], [50, 40, 10, 20, 30, 60], [50, 40, 10, 20, 60, 30], [50, 40, 10, 30, 20, 60], [50, 40, 10, 30, 60, 20], [50, 40, 10, 60, 20, 30], [50, 40, 10, 60, 30, 20], [50, 40, 20, 10, 30, 60], [50, 40, 20, 10, 60, 30], [50, 40, 20, 30, 10, 60], [50, 40, 20, 30, 60, 10], [50, 40, 20, 60, 10, 30], [50, 40, 20, 60, 30, 10], [50, 40, 30, 10, 20, 60], [50, 40, 30, 10, 60, 20], [50, 40, 30, 20, 10, 60], [50, 40, 30, 20, 60, 10], [50, 40, 30, 60, 10, 20], [50, 40, 30, 60, 20, 10], [50, 40, 60, 10, 20, 30], [50, 40, 60, 10, 30, 20], [50, 40, 60, 20, 10, 30], [50, 40, 60, 20, 30, 10], [50, 40, 60, 30, 10, 20], [50, 40, 60, 30, 20, 10], [50, 60, 10, 20, 30, 40], [50, 60, 10, 20, 40, 30], [50, 60, 10, 30, 20, 40], [50, 60, 10, 30, 40, 20], [50, 60, 10, 40, 20, 30], [50, 60, 10, 40, 30, 20], [50, 60, 20, 10, 30, 40], [50, 60, 20, 10, 40, 30], [50, 60, 20, 30, 10, 40], [50, 60, 20, 30, 40, 10], [50, 60, 20, 40, 10, 30], [50, 60, 20, 40, 30, 10], [50, 60, 30, 10, 20, 40], [50, 60, 30, 10, 40, 20], [50, 60, 30, 20, 10, 40], [50, 60, 30, 20, 40, 10], [50, 60, 30, 40, 10, 20], [50, 60, 30, 40, 20, 10], [50, 60, 40, 10, 20, 30], [50, 60, 40, 10, 30, 20], [50, 60, 40, 20, 10, 30], [50, 60, 40, 20, 30, 10], [50, 60, 40, 30, 10, 20], [50, 60, 40, 30, 20, 10], [60, 10, 20, 30, 40, 50], [60, 10, 20, 30, 50, 40], [60, 10, 20, 40, 30, 50], [60, 10, 20, 40, 50, 30], [60, 10, 20, 50, 30, 40], [60, 10, 20, 50, 40, 30], [60, 10, 30, 20, 40, 50], [60, 10, 30, 20, 50, 40], [60, 10, 30, 40, 20, 50], [60, 10, 30, 40, 50, 20], [60, 10, 30, 50, 20, 40], [60, 10, 30, 50, 40, 20], [60, 10, 40, 20, 30, 50], [60, 10, 40, 20, 50, 30], [60, 10, 40, 30, 20, 50], [60, 10, 40, 30, 50, 20], [60, 10, 40, 50, 20, 30], [60, 10, 40, 50, 30, 20], [60, 10, 50, 20, 30, 40], [60, 10, 50, 20, 40, 30], [60, 10, 50, 30, 20, 40], [60, 10, 50, 30, 40, 20], [60, 10, 50, 40, 20, 30], [60, 10, 50, 40, 30, 20], [60, 20, 10, 30, 40, 50], [60, 20, 10, 30, 50, 40], [60, 20, 10, 40, 30, 50], [60, 20, 10, 40, 50, 30], [60, 20, 10, 50, 30, 40], [60, 20, 10, 50, 40, 30], [60, 20, 30, 10, 40, 50], [60, 20, 30, 10, 50, 40], [60, 20, 30, 40, 10, 50], [60, 20, 30, 40, 50, 10], [60, 20, 30, 50, 10, 40], [60, 20, 30, 50, 40, 10], [60, 20, 40, 10, 30, 50], [60, 20, 40, 10, 50, 30], [60, 20, 40, 30, 10, 50], [60, 20, 40, 30, 50, 10], [60, 20, 40, 50, 10, 30], [60, 20, 40, 50, 30, 10], [60, 20, 50, 10, 30, 40], [60, 20, 50, 10, 40, 30], [60, 20, 50, 30, 10, 40], [60, 20, 50, 30, 40, 10], [60, 20, 50, 40, 10, 30], [60, 20, 50, 40, 30, 10], [60, 30, 10, 20, 40, 50], [60, 30, 10, 20, 50, 40], [60, 30, 10, 40, 20, 50], [60, 30, 10, 40, 50, 20], [60, 30, 10, 50, 20, 40], [60, 30, 10, 50, 40, 20], [60, 30, 20, 10, 40, 50], [60, 30, 20, 10, 50, 40], [60, 30, 20, 40, 10, 50], [60, 30, 20, 40, 50, 10], [60, 30, 20, 50, 10, 40], [60, 30, 20, 50, 40, 10], [60, 30, 40, 10, 20, 50], [60, 30, 40, 10, 50, 20], [60, 30, 40, 20, 10, 50], [60, 30, 40, 20, 50, 10], [60, 30, 40, 50, 10, 20], [60, 30, 40, 50, 20, 10], [60, 30, 50, 10, 20, 40], [60, 30, 50, 10, 40, 20], [60, 30, 50, 20, 10, 40], [60, 30, 50, 20, 40, 10], [60, 30, 50, 40, 10, 20], [60, 30, 50, 40, 20, 10], [60, 40, 10, 20, 30, 50], [60, 40, 10, 20, 50, 30], [60, 40, 10, 30, 20, 50], [60, 40, 10, 30, 50, 20], [60, 40, 10, 50, 20, 30], [60, 40, 10, 50, 30, 20], [60, 40, 20, 10, 30, 50], [60, 40, 20, 10, 50, 30], [60, 40, 20, 30, 10, 50], [60, 40, 20, 30, 50, 10], [60, 40, 20, 50, 10, 30], [60, 40, 20, 50, 30, 10], [60, 40, 30, 10, 20, 50], [60, 40, 30, 10, 50, 20], [60, 40, 30, 20, 10, 50], [60, 40, 30, 20, 50, 10], [60, 40, 30, 50, 10, 20], [60, 40, 30, 50, 20, 10], [60, 40, 50, 10, 20, 30], [60, 40, 50, 10, 30, 20], [60, 40, 50, 20, 10, 30], [60, 40, 50, 20, 30, 10], [60, 40, 50, 30, 10, 20], [60, 40, 50, 30, 20, 10], [60, 50, 10, 20, 30, 40], [60, 50, 10, 20, 40, 30], [60, 50, 10, 30, 20, 40], [60, 50, 10, 30, 40, 20], [60, 50, 10, 40, 20, 30], [60, 50, 10, 40, 30, 20], [60, 50, 20, 10, 30, 40], [60, 50, 20, 10, 40, 30], [60, 50, 20, 30, 10, 40], [60, 50, 20, 30, 40, 10], [60, 50, 20, 40, 10, 30], [60, 50, 20, 40, 30, 10], [60, 50, 30, 10, 20, 40], [60, 50, 30, 10, 40, 20], [60, 50, 30, 20, 10, 40], [60, 50, 30, 20, 40, 10], [60, 50, 30, 40, 10, 20], [60, 50, 30, 40, 20, 10], [60, 50, 40, 10, 20, 30], [60, 50, 40, 10, 30, 20], [60, 50, 40, 20, 10, 30], [60, 50, 40, 20, 30, 10], [60, 50, 40, 30, 10, 20], [60, 50, 40, 30, 20, 10]]\n assert candidate(nums = [7, 14, 21, 28, 35, 42]) == [[7, 14, 21, 28, 35, 42], [7, 14, 21, 28, 42, 35], [7, 14, 21, 35, 28, 42], [7, 14, 21, 35, 42, 28], [7, 14, 21, 42, 28, 35], [7, 14, 21, 42, 35, 28], [7, 14, 28, 21, 35, 42], [7, 14, 28, 21, 42, 35], [7, 14, 28, 35, 21, 42], [7, 14, 28, 35, 42, 21], [7, 14, 28, 42, 21, 35], [7, 14, 28, 42, 35, 21], [7, 14, 35, 21, 28, 42], [7, 14, 35, 21, 42, 28], [7, 14, 35, 28, 21, 42], [7, 14, 35, 28, 42, 21], [7, 14, 35, 42, 21, 28], [7, 14, 35, 42, 28, 21], [7, 14, 42, 21, 28, 35], [7, 14, 42, 21, 35, 28], [7, 14, 42, 28, 21, 35], [7, 14, 42, 28, 35, 21], [7, 14, 42, 35, 21, 28], [7, 14, 42, 35, 28, 21], [7, 21, 14, 28, 35, 42], [7, 21, 14, 28, 42, 35], [7, 21, 14, 35, 28, 42], [7, 21, 14, 35, 42, 28], [7, 21, 14, 42, 28, 35], [7, 21, 14, 42, 35, 28], [7, 21, 28, 14, 35, 42], [7, 21, 28, 14, 42, 35], [7, 21, 28, 35, 14, 42], [7, 21, 28, 35, 42, 14], [7, 21, 28, 42, 14, 35], [7, 21, 28, 42, 35, 14], [7, 21, 35, 14, 28, 42], [7, 21, 35, 14, 42, 28], [7, 21, 35, 28, 14, 42], [7, 21, 35, 28, 42, 14], [7, 21, 35, 42, 14, 28], [7, 21, 35, 42, 28, 14], [7, 21, 42, 14, 28, 35], [7, 21, 42, 14, 35, 28], [7, 21, 42, 28, 14, 35], [7, 21, 42, 28, 35, 14], [7, 21, 42, 35, 14, 28], [7, 21, 42, 35, 28, 14], [7, 28, 14, 21, 35, 42], [7, 28, 14, 21, 42, 35], [7, 28, 14, 35, 21, 42], [7, 28, 14, 35, 42, 21], [7, 28, 14, 42, 21, 35], [7, 28, 14, 42, 35, 21], [7, 28, 21, 14, 35, 42], [7, 28, 21, 14, 42, 35], [7, 28, 21, 35, 14, 42], [7, 28, 21, 35, 42, 14], [7, 28, 21, 42, 14, 35], [7, 28, 21, 42, 35, 14], [7, 28, 35, 14, 21, 42], [7, 28, 35, 14, 42, 21], [7, 28, 35, 21, 14, 42], [7, 28, 35, 21, 42, 14], [7, 28, 35, 42, 14, 21], [7, 28, 35, 42, 21, 14], [7, 28, 42, 14, 21, 35], [7, 28, 42, 14, 35, 21], [7, 28, 42, 21, 14, 35], [7, 28, 42, 21, 35, 14], [7, 28, 42, 35, 14, 21], [7, 28, 42, 35, 21, 14], [7, 35, 14, 21, 28, 42], [7, 35, 14, 21, 42, 28], [7, 35, 14, 28, 21, 42], [7, 35, 14, 28, 42, 21], [7, 35, 14, 42, 21, 28], [7, 35, 14, 42, 28, 21], [7, 35, 21, 14, 28, 42], [7, 35, 21, 14, 42, 28], [7, 35, 21, 28, 14, 42], [7, 35, 21, 28, 42, 14], [7, 35, 21, 42, 14, 28], [7, 35, 21, 42, 28, 14], [7, 35, 28, 14, 21, 42], [7, 35, 28, 14, 42, 21], [7, 35, 28, 21, 14, 42], [7, 35, 28, 21, 42, 14], [7, 35, 28, 42, 14, 21], [7, 35, 28, 42, 21, 14], [7, 35, 42, 14, 21, 28], [7, 35, 42, 14, 28, 21], [7, 35, 42, 21, 14, 28], [7, 35, 42, 21, 28, 14], [7, 35, 42, 28, 14, 21], [7, 35, 42, 28, 21, 14], [7, 42, 14, 21, 28, 35], [7, 42, 14, 21, 35, 28], [7, 42, 14, 28, 21, 35], [7, 42, 14, 28, 35, 21], [7, 42, 14, 35, 21, 28], [7, 42, 14, 35, 28, 21], [7, 42, 21, 14, 28, 35], [7, 42, 21, 14, 35, 28], [7, 42, 21, 28, 14, 35], [7, 42, 21, 28, 35, 14], [7, 42, 21, 35, 14, 28], [7, 42, 21, 35, 28, 14], [7, 42, 28, 14, 21, 35], [7, 42, 28, 14, 35, 21], [7, 42, 28, 21, 14, 35], [7, 42, 28, 21, 35, 14], [7, 42, 28, 35, 14, 21], [7, 42, 28, 35, 21, 14], [7, 42, 35, 14, 21, 28], [7, 42, 35, 14, 28, 21], [7, 42, 35, 21, 14, 28], [7, 42, 35, 21, 28, 14], [7, 42, 35, 28, 14, 21], [7, 42, 35, 28, 21, 14], [14, 7, 21, 28, 35, 42], [14, 7, 21, 28, 42, 35], [14, 7, 21, 35, 28, 42], [14, 7, 21, 35, 42, 28], [14, 7, 21, 42, 28, 35], [14, 7, 21, 42, 35, 28], [14, 7, 28, 21, 35, 42], [14, 7, 28, 21, 42, 35], [14, 7, 28, 35, 21, 42], [14, 7, 28, 35, 42, 21], [14, 7, 28, 42, 21, 35], [14, 7, 28, 42, 35, 21], [14, 7, 35, 21, 28, 42], [14, 7, 35, 21, 42, 28], [14, 7, 35, 28, 21, 42], [14, 7, 35, 28, 42, 21], [14, 7, 35, 42, 21, 28], [14, 7, 35, 42, 28, 21], [14, 7, 42, 21, 28, 35], [14, 7, 42, 21, 35, 28], [14, 7, 42, 28, 21, 35], [14, 7, 42, 28, 35, 21], [14, 7, 42, 35, 21, 28], [14, 7, 42, 35, 28, 21], [14, 21, 7, 28, 35, 42], [14, 21, 7, 28, 42, 35], [14, 21, 7, 35, 28, 42], [14, 21, 7, 35, 42, 28], [14, 21, 7, 42, 28, 35], [14, 21, 7, 42, 35, 28], [14, 21, 28, 7, 35, 42], [14, 21, 28, 7, 42, 35], [14, 21, 28, 35, 7, 42], [14, 21, 28, 35, 42, 7], [14, 21, 28, 42, 7, 35], [14, 21, 28, 42, 35, 7], [14, 21, 35, 7, 28, 42], [14, 21, 35, 7, 42, 28], [14, 21, 35, 28, 7, 42], [14, 21, 35, 28, 42, 7], [14, 21, 35, 42, 7, 28], [14, 21, 35, 42, 28, 7], [14, 21, 42, 7, 28, 35], [14, 21, 42, 7, 35, 28], [14, 21, 42, 28, 7, 35], [14, 21, 42, 28, 35, 7], [14, 21, 42, 35, 7, 28], [14, 21, 42, 35, 28, 7], [14, 28, 7, 21, 35, 42], [14, 28, 7, 21, 42, 35], [14, 28, 7, 35, 21, 42], [14, 28, 7, 35, 42, 21], [14, 28, 7, 42, 21, 35], [14, 28, 7, 42, 35, 21], [14, 28, 21, 7, 35, 42], [14, 28, 21, 7, 42, 35], [14, 28, 21, 35, 7, 42], [14, 28, 21, 35, 42, 7], [14, 28, 21, 42, 7, 35], [14, 28, 21, 42, 35, 7], [14, 28, 35, 7, 21, 42], [14, 28, 35, 7, 42, 21], [14, 28, 35, 21, 7, 42], [14, 28, 35, 21, 42, 7], [14, 28, 35, 42, 7, 21], [14, 28, 35, 42, 21, 7], [14, 28, 42, 7, 21, 35], [14, 28, 42, 7, 35, 21], [14, 28, 42, 21, 7, 35], [14, 28, 42, 21, 35, 7], [14, 28, 42, 35, 7, 21], [14, 28, 42, 35, 21, 7], [14, 35, 7, 21, 28, 42], [14, 35, 7, 21, 42, 28], [14, 35, 7, 28, 21, 42], [14, 35, 7, 28, 42, 21], [14, 35, 7, 42, 21, 28], [14, 35, 7, 42, 28, 21], [14, 35, 21, 7, 28, 42], [14, 35, 21, 7, 42, 28], [14, 35, 21, 28, 7, 42], [14, 35, 21, 28, 42, 7], [14, 35, 21, 42, 7, 28], [14, 35, 21, 42, 28, 7], [14, 35, 28, 7, 21, 42], [14, 35, 28, 7, 42, 21], [14, 35, 28, 21, 7, 42], [14, 35, 28, 21, 42, 7], [14, 35, 28, 42, 7, 21], [14, 35, 28, 42, 21, 7], [14, 35, 42, 7, 21, 28], [14, 35, 42, 7, 28, 21], [14, 35, 42, 21, 7, 28], [14, 35, 42, 21, 28, 7], [14, 35, 42, 28, 7, 21], [14, 35, 42, 28, 21, 7], [14, 42, 7, 21, 28, 35], [14, 42, 7, 21, 35, 28], [14, 42, 7, 28, 21, 35], [14, 42, 7, 28, 35, 21], [14, 42, 7, 35, 21, 28], [14, 42, 7, 35, 28, 21], [14, 42, 21, 7, 28, 35], [14, 42, 21, 7, 35, 28], [14, 42, 21, 28, 7, 35], [14, 42, 21, 28, 35, 7], [14, 42, 21, 35, 7, 28], [14, 42, 21, 35, 28, 7], [14, 42, 28, 7, 21, 35], [14, 42, 28, 7, 35, 21], [14, 42, 28, 21, 7, 35], [14, 42, 28, 21, 35, 7], [14, 42, 28, 35, 7, 21], [14, 42, 28, 35, 21, 7], [14, 42, 35, 7, 21, 28], [14, 42, 35, 7, 28, 21], [14, 42, 35, 21, 7, 28], [14, 42, 35, 21, 28, 7], [14, 42, 35, 28, 7, 21], [14, 42, 35, 28, 21, 7], [21, 7, 14, 28, 35, 42], [21, 7, 14, 28, 42, 35], [21, 7, 14, 35, 28, 42], [21, 7, 14, 35, 42, 28], [21, 7, 14, 42, 28, 35], [21, 7, 14, 42, 35, 28], [21, 7, 28, 14, 35, 42], [21, 7, 28, 14, 42, 35], [21, 7, 28, 35, 14, 42], [21, 7, 28, 35, 42, 14], [21, 7, 28, 42, 14, 35], [21, 7, 28, 42, 35, 14], [21, 7, 35, 14, 28, 42], [21, 7, 35, 14, 42, 28], [21, 7, 35, 28, 14, 42], [21, 7, 35, 28, 42, 14], [21, 7, 35, 42, 14, 28], [21, 7, 35, 42, 28, 14], [21, 7, 42, 14, 28, 35], [21, 7, 42, 14, 35, 28], [21, 7, 42, 28, 14, 35], [21, 7, 42, 28, 35, 14], [21, 7, 42, 35, 14, 28], [21, 7, 42, 35, 28, 14], [21, 14, 7, 28, 35, 42], [21, 14, 7, 28, 42, 35], [21, 14, 7, 35, 28, 42], [21, 14, 7, 35, 42, 28], [21, 14, 7, 42, 28, 35], [21, 14, 7, 42, 35, 28], [21, 14, 28, 7, 35, 42], [21, 14, 28, 7, 42, 35], [21, 14, 28, 35, 7, 42], [21, 14, 28, 35, 42, 7], [21, 14, 28, 42, 7, 35], [21, 14, 28, 42, 35, 7], [21, 14, 35, 7, 28, 42], [21, 14, 35, 7, 42, 28], [21, 14, 35, 28, 7, 42], [21, 14, 35, 28, 42, 7], [21, 14, 35, 42, 7, 28], [21, 14, 35, 42, 28, 7], [21, 14, 42, 7, 28, 35], [21, 14, 42, 7, 35, 28], [21, 14, 42, 28, 7, 35], [21, 14, 42, 28, 35, 7], [21, 14, 42, 35, 7, 28], [21, 14, 42, 35, 28, 7], [21, 28, 7, 14, 35, 42], [21, 28, 7, 14, 42, 35], [21, 28, 7, 35, 14, 42], [21, 28, 7, 35, 42, 14], [21, 28, 7, 42, 14, 35], [21, 28, 7, 42, 35, 14], [21, 28, 14, 7, 35, 42], [21, 28, 14, 7, 42, 35], [21, 28, 14, 35, 7, 42], [21, 28, 14, 35, 42, 7], [21, 28, 14, 42, 7, 35], [21, 28, 14, 42, 35, 7], [21, 28, 35, 7, 14, 42], [21, 28, 35, 7, 42, 14], [21, 28, 35, 14, 7, 42], [21, 28, 35, 14, 42, 7], [21, 28, 35, 42, 7, 14], [21, 28, 35, 42, 14, 7], [21, 28, 42, 7, 14, 35], [21, 28, 42, 7, 35, 14], [21, 28, 42, 14, 7, 35], [21, 28, 42, 14, 35, 7], [21, 28, 42, 35, 7, 14], [21, 28, 42, 35, 14, 7], [21, 35, 7, 14, 28, 42], [21, 35, 7, 14, 42, 28], [21, 35, 7, 28, 14, 42], [21, 35, 7, 28, 42, 14], [21, 35, 7, 42, 14, 28], [21, 35, 7, 42, 28, 14], [21, 35, 14, 7, 28, 42], [21, 35, 14, 7, 42, 28], [21, 35, 14, 28, 7, 42], [21, 35, 14, 28, 42, 7], [21, 35, 14, 42, 7, 28], [21, 35, 14, 42, 28, 7], [21, 35, 28, 7, 14, 42], [21, 35, 28, 7, 42, 14], [21, 35, 28, 14, 7, 42], [21, 35, 28, 14, 42, 7], [21, 35, 28, 42, 7, 14], [21, 35, 28, 42, 14, 7], [21, 35, 42, 7, 14, 28], [21, 35, 42, 7, 28, 14], [21, 35, 42, 14, 7, 28], [21, 35, 42, 14, 28, 7], [21, 35, 42, 28, 7, 14], [21, 35, 42, 28, 14, 7], [21, 42, 7, 14, 28, 35], [21, 42, 7, 14, 35, 28], [21, 42, 7, 28, 14, 35], [21, 42, 7, 28, 35, 14], [21, 42, 7, 35, 14, 28], [21, 42, 7, 35, 28, 14], [21, 42, 14, 7, 28, 35], [21, 42, 14, 7, 35, 28], [21, 42, 14, 28, 7, 35], [21, 42, 14, 28, 35, 7], [21, 42, 14, 35, 7, 28], [21, 42, 14, 35, 28, 7], [21, 42, 28, 7, 14, 35], [21, 42, 28, 7, 35, 14], [21, 42, 28, 14, 7, 35], [21, 42, 28, 14, 35, 7], [21, 42, 28, 35, 7, 14], [21, 42, 28, 35, 14, 7], [21, 42, 35, 7, 14, 28], [21, 42, 35, 7, 28, 14], [21, 42, 35, 14, 7, 28], [21, 42, 35, 14, 28, 7], [21, 42, 35, 28, 7, 14], [21, 42, 35, 28, 14, 7], [28, 7, 14, 21, 35, 42], [28, 7, 14, 21, 42, 35], [28, 7, 14, 35, 21, 42], [28, 7, 14, 35, 42, 21], [28, 7, 14, 42, 21, 35], [28, 7, 14, 42, 35, 21], [28, 7, 21, 14, 35, 42], [28, 7, 21, 14, 42, 35], [28, 7, 21, 35, 14, 42], [28, 7, 21, 35, 42, 14], [28, 7, 21, 42, 14, 35], [28, 7, 21, 42, 35, 14], [28, 7, 35, 14, 21, 42], [28, 7, 35, 14, 42, 21], [28, 7, 35, 21, 14, 42], [28, 7, 35, 21, 42, 14], [28, 7, 35, 42, 14, 21], [28, 7, 35, 42, 21, 14], [28, 7, 42, 14, 21, 35], [28, 7, 42, 14, 35, 21], [28, 7, 42, 21, 14, 35], [28, 7, 42, 21, 35, 14], [28, 7, 42, 35, 14, 21], [28, 7, 42, 35, 21, 14], [28, 14, 7, 21, 35, 42], [28, 14, 7, 21, 42, 35], [28, 14, 7, 35, 21, 42], [28, 14, 7, 35, 42, 21], [28, 14, 7, 42, 21, 35], [28, 14, 7, 42, 35, 21], [28, 14, 21, 7, 35, 42], [28, 14, 21, 7, 42, 35], [28, 14, 21, 35, 7, 42], [28, 14, 21, 35, 42, 7], [28, 14, 21, 42, 7, 35], [28, 14, 21, 42, 35, 7], [28, 14, 35, 7, 21, 42], [28, 14, 35, 7, 42, 21], [28, 14, 35, 21, 7, 42], [28, 14, 35, 21, 42, 7], [28, 14, 35, 42, 7, 21], [28, 14, 35, 42, 21, 7], [28, 14, 42, 7, 21, 35], [28, 14, 42, 7, 35, 21], [28, 14, 42, 21, 7, 35], [28, 14, 42, 21, 35, 7], [28, 14, 42, 35, 7, 21], [28, 14, 42, 35, 21, 7], [28, 21, 7, 14, 35, 42], [28, 21, 7, 14, 42, 35], [28, 21, 7, 35, 14, 42], [28, 21, 7, 35, 42, 14], [28, 21, 7, 42, 14, 35], [28, 21, 7, 42, 35, 14], [28, 21, 14, 7, 35, 42], [28, 21, 14, 7, 42, 35], [28, 21, 14, 35, 7, 42], [28, 21, 14, 35, 42, 7], [28, 21, 14, 42, 7, 35], [28, 21, 14, 42, 35, 7], [28, 21, 35, 7, 14, 42], [28, 21, 35, 7, 42, 14], [28, 21, 35, 14, 7, 42], [28, 21, 35, 14, 42, 7], [28, 21, 35, 42, 7, 14], [28, 21, 35, 42, 14, 7], [28, 21, 42, 7, 14, 35], [28, 21, 42, 7, 35, 14], [28, 21, 42, 14, 7, 35], [28, 21, 42, 14, 35, 7], [28, 21, 42, 35, 7, 14], [28, 21, 42, 35, 14, 7], [28, 35, 7, 14, 21, 42], [28, 35, 7, 14, 42, 21], [28, 35, 7, 21, 14, 42], [28, 35, 7, 21, 42, 14], [28, 35, 7, 42, 14, 21], [28, 35, 7, 42, 21, 14], [28, 35, 14, 7, 21, 42], [28, 35, 14, 7, 42, 21], [28, 35, 14, 21, 7, 42], [28, 35, 14, 21, 42, 7], [28, 35, 14, 42, 7, 21], [28, 35, 14, 42, 21, 7], [28, 35, 21, 7, 14, 42], [28, 35, 21, 7, 42, 14], [28, 35, 21, 14, 7, 42], [28, 35, 21, 14, 42, 7], [28, 35, 21, 42, 7, 14], [28, 35, 21, 42, 14, 7], [28, 35, 42, 7, 14, 21], [28, 35, 42, 7, 21, 14], [28, 35, 42, 14, 7, 21], [28, 35, 42, 14, 21, 7], [28, 35, 42, 21, 7, 14], [28, 35, 42, 21, 14, 7], [28, 42, 7, 14, 21, 35], [28, 42, 7, 14, 35, 21], [28, 42, 7, 21, 14, 35], [28, 42, 7, 21, 35, 14], [28, 42, 7, 35, 14, 21], [28, 42, 7, 35, 21, 14], [28, 42, 14, 7, 21, 35], [28, 42, 14, 7, 35, 21], [28, 42, 14, 21, 7, 35], [28, 42, 14, 21, 35, 7], [28, 42, 14, 35, 7, 21], [28, 42, 14, 35, 21, 7], [28, 42, 21, 7, 14, 35], [28, 42, 21, 7, 35, 14], [28, 42, 21, 14, 7, 35], [28, 42, 21, 14, 35, 7], [28, 42, 21, 35, 7, 14], [28, 42, 21, 35, 14, 7], [28, 42, 35, 7, 14, 21], [28, 42, 35, 7, 21, 14], [28, 42, 35, 14, 7, 21], [28, 42, 35, 14, 21, 7], [28, 42, 35, 21, 7, 14], [28, 42, 35, 21, 14, 7], [35, 7, 14, 21, 28, 42], [35, 7, 14, 21, 42, 28], [35, 7, 14, 28, 21, 42], [35, 7, 14, 28, 42, 21], [35, 7, 14, 42, 21, 28], [35, 7, 14, 42, 28, 21], [35, 7, 21, 14, 28, 42], [35, 7, 21, 14, 42, 28], [35, 7, 21, 28, 14, 42], [35, 7, 21, 28, 42, 14], [35, 7, 21, 42, 14, 28], [35, 7, 21, 42, 28, 14], [35, 7, 28, 14, 21, 42], [35, 7, 28, 14, 42, 21], [35, 7, 28, 21, 14, 42], [35, 7, 28, 21, 42, 14], [35, 7, 28, 42, 14, 21], [35, 7, 28, 42, 21, 14], [35, 7, 42, 14, 21, 28], [35, 7, 42, 14, 28, 21], [35, 7, 42, 21, 14, 28], [35, 7, 42, 21, 28, 14], [35, 7, 42, 28, 14, 21], [35, 7, 42, 28, 21, 14], [35, 14, 7, 21, 28, 42], [35, 14, 7, 21, 42, 28], [35, 14, 7, 28, 21, 42], [35, 14, 7, 28, 42, 21], [35, 14, 7, 42, 21, 28], [35, 14, 7, 42, 28, 21], [35, 14, 21, 7, 28, 42], [35, 14, 21, 7, 42, 28], [35, 14, 21, 28, 7, 42], [35, 14, 21, 28, 42, 7], [35, 14, 21, 42, 7, 28], [35, 14, 21, 42, 28, 7], [35, 14, 28, 7, 21, 42], [35, 14, 28, 7, 42, 21], [35, 14, 28, 21, 7, 42], [35, 14, 28, 21, 42, 7], [35, 14, 28, 42, 7, 21], [35, 14, 28, 42, 21, 7], [35, 14, 42, 7, 21, 28], [35, 14, 42, 7, 28, 21], [35, 14, 42, 21, 7, 28], [35, 14, 42, 21, 28, 7], [35, 14, 42, 28, 7, 21], [35, 14, 42, 28, 21, 7], [35, 21, 7, 14, 28, 42], [35, 21, 7, 14, 42, 28], [35, 21, 7, 28, 14, 42], [35, 21, 7, 28, 42, 14], [35, 21, 7, 42, 14, 28], [35, 21, 7, 42, 28, 14], [35, 21, 14, 7, 28, 42], [35, 21, 14, 7, 42, 28], [35, 21, 14, 28, 7, 42], [35, 21, 14, 28, 42, 7], [35, 21, 14, 42, 7, 28], [35, 21, 14, 42, 28, 7], [35, 21, 28, 7, 14, 42], [35, 21, 28, 7, 42, 14], [35, 21, 28, 14, 7, 42], [35, 21, 28, 14, 42, 7], [35, 21, 28, 42, 7, 14], [35, 21, 28, 42, 14, 7], [35, 21, 42, 7, 14, 28], [35, 21, 42, 7, 28, 14], [35, 21, 42, 14, 7, 28], [35, 21, 42, 14, 28, 7], [35, 21, 42, 28, 7, 14], [35, 21, 42, 28, 14, 7], [35, 28, 7, 14, 21, 42], [35, 28, 7, 14, 42, 21], [35, 28, 7, 21, 14, 42], [35, 28, 7, 21, 42, 14], [35, 28, 7, 42, 14, 21], [35, 28, 7, 42, 21, 14], [35, 28, 14, 7, 21, 42], [35, 28, 14, 7, 42, 21], [35, 28, 14, 21, 7, 42], [35, 28, 14, 21, 42, 7], [35, 28, 14, 42, 7, 21], [35, 28, 14, 42, 21, 7], [35, 28, 21, 7, 14, 42], [35, 28, 21, 7, 42, 14], [35, 28, 21, 14, 7, 42], [35, 28, 21, 14, 42, 7], [35, 28, 21, 42, 7, 14], [35, 28, 21, 42, 14, 7], [35, 28, 42, 7, 14, 21], [35, 28, 42, 7, 21, 14], [35, 28, 42, 14, 7, 21], [35, 28, 42, 14, 21, 7], [35, 28, 42, 21, 7, 14], [35, 28, 42, 21, 14, 7], [35, 42, 7, 14, 21, 28], [35, 42, 7, 14, 28, 21], [35, 42, 7, 21, 14, 28], [35, 42, 7, 21, 28, 14], [35, 42, 7, 28, 14, 21], [35, 42, 7, 28, 21, 14], [35, 42, 14, 7, 21, 28], [35, 42, 14, 7, 28, 21], [35, 42, 14, 21, 7, 28], [35, 42, 14, 21, 28, 7], [35, 42, 14, 28, 7, 21], [35, 42, 14, 28, 21, 7], [35, 42, 21, 7, 14, 28], [35, 42, 21, 7, 28, 14], [35, 42, 21, 14, 7, 28], [35, 42, 21, 14, 28, 7], [35, 42, 21, 28, 7, 14], [35, 42, 21, 28, 14, 7], [35, 42, 28, 7, 14, 21], [35, 42, 28, 7, 21, 14], [35, 42, 28, 14, 7, 21], [35, 42, 28, 14, 21, 7], [35, 42, 28, 21, 7, 14], [35, 42, 28, 21, 14, 7], [42, 7, 14, 21, 28, 35], [42, 7, 14, 21, 35, 28], [42, 7, 14, 28, 21, 35], [42, 7, 14, 28, 35, 21], [42, 7, 14, 35, 21, 28], [42, 7, 14, 35, 28, 21], [42, 7, 21, 14, 28, 35], [42, 7, 21, 14, 35, 28], [42, 7, 21, 28, 14, 35], [42, 7, 21, 28, 35, 14], [42, 7, 21, 35, 14, 28], [42, 7, 21, 35, 28, 14], [42, 7, 28, 14, 21, 35], [42, 7, 28, 14, 35, 21], [42, 7, 28, 21, 14, 35], [42, 7, 28, 21, 35, 14], [42, 7, 28, 35, 14, 21], [42, 7, 28, 35, 21, 14], [42, 7, 35, 14, 21, 28], [42, 7, 35, 14, 28, 21], [42, 7, 35, 21, 14, 28], [42, 7, 35, 21, 28, 14], [42, 7, 35, 28, 14, 21], [42, 7, 35, 28, 21, 14], [42, 14, 7, 21, 28, 35], [42, 14, 7, 21, 35, 28], [42, 14, 7, 28, 21, 35], [42, 14, 7, 28, 35, 21], [42, 14, 7, 35, 21, 28], [42, 14, 7, 35, 28, 21], [42, 14, 21, 7, 28, 35], [42, 14, 21, 7, 35, 28], [42, 14, 21, 28, 7, 35], [42, 14, 21, 28, 35, 7], [42, 14, 21, 35, 7, 28], [42, 14, 21, 35, 28, 7], [42, 14, 28, 7, 21, 35], [42, 14, 28, 7, 35, 21], [42, 14, 28, 21, 7, 35], [42, 14, 28, 21, 35, 7], [42, 14, 28, 35, 7, 21], [42, 14, 28, 35, 21, 7], [42, 14, 35, 7, 21, 28], [42, 14, 35, 7, 28, 21], [42, 14, 35, 21, 7, 28], [42, 14, 35, 21, 28, 7], [42, 14, 35, 28, 7, 21], [42, 14, 35, 28, 21, 7], [42, 21, 7, 14, 28, 35], [42, 21, 7, 14, 35, 28], [42, 21, 7, 28, 14, 35], [42, 21, 7, 28, 35, 14], [42, 21, 7, 35, 14, 28], [42, 21, 7, 35, 28, 14], [42, 21, 14, 7, 28, 35], [42, 21, 14, 7, 35, 28], [42, 21, 14, 28, 7, 35], [42, 21, 14, 28, 35, 7], [42, 21, 14, 35, 7, 28], [42, 21, 14, 35, 28, 7], [42, 21, 28, 7, 14, 35], [42, 21, 28, 7, 35, 14], [42, 21, 28, 14, 7, 35], [42, 21, 28, 14, 35, 7], [42, 21, 28, 35, 7, 14], [42, 21, 28, 35, 14, 7], [42, 21, 35, 7, 14, 28], [42, 21, 35, 7, 28, 14], [42, 21, 35, 14, 7, 28], [42, 21, 35, 14, 28, 7], [42, 21, 35, 28, 7, 14], [42, 21, 35, 28, 14, 7], [42, 28, 7, 14, 21, 35], [42, 28, 7, 14, 35, 21], [42, 28, 7, 21, 14, 35], [42, 28, 7, 21, 35, 14], [42, 28, 7, 35, 14, 21], [42, 28, 7, 35, 21, 14], [42, 28, 14, 7, 21, 35], [42, 28, 14, 7, 35, 21], [42, 28, 14, 21, 7, 35], [42, 28, 14, 21, 35, 7], [42, 28, 14, 35, 7, 21], [42, 28, 14, 35, 21, 7], [42, 28, 21, 7, 14, 35], [42, 28, 21, 7, 35, 14], [42, 28, 21, 14, 7, 35], [42, 28, 21, 14, 35, 7], [42, 28, 21, 35, 7, 14], [42, 28, 21, 35, 14, 7], [42, 28, 35, 7, 14, 21], [42, 28, 35, 7, 21, 14], [42, 28, 35, 14, 7, 21], [42, 28, 35, 14, 21, 7], [42, 28, 35, 21, 7, 14], [42, 28, 35, 21, 14, 7], [42, 35, 7, 14, 21, 28], [42, 35, 7, 14, 28, 21], [42, 35, 7, 21, 14, 28], [42, 35, 7, 21, 28, 14], [42, 35, 7, 28, 14, 21], [42, 35, 7, 28, 21, 14], [42, 35, 14, 7, 21, 28], [42, 35, 14, 7, 28, 21], [42, 35, 14, 21, 7, 28], [42, 35, 14, 21, 28, 7], [42, 35, 14, 28, 7, 21], [42, 35, 14, 28, 21, 7], [42, 35, 21, 7, 14, 28], [42, 35, 21, 7, 28, 14], [42, 35, 21, 14, 7, 28], [42, 35, 21, 14, 28, 7], [42, 35, 21, 28, 7, 14], [42, 35, 21, 28, 14, 7], [42, 35, 28, 7, 14, 21], [42, 35, 28, 7, 21, 14], [42, 35, 28, 14, 7, 21], [42, 35, 28, 14, 21, 7], [42, 35, 28, 21, 7, 14], [42, 35, 28, 21, 14, 7]]\n assert candidate(nums = [-1, 0, 1, 2, 3, 4]) == [[-1, 0, 1, 2, 3, 4], [-1, 0, 1, 2, 4, 3], [-1, 0, 1, 3, 2, 4], [-1, 0, 1, 3, 4, 2], [-1, 0, 1, 4, 2, 3], [-1, 0, 1, 4, 3, 2], [-1, 0, 2, 1, 3, 4], [-1, 0, 2, 1, 4, 3], [-1, 0, 2, 3, 1, 4], [-1, 0, 2, 3, 4, 1], [-1, 0, 2, 4, 1, 3], [-1, 0, 2, 4, 3, 1], [-1, 0, 3, 1, 2, 4], [-1, 0, 3, 1, 4, 2], [-1, 0, 3, 2, 1, 4], [-1, 0, 3, 2, 4, 1], [-1, 0, 3, 4, 1, 2], [-1, 0, 3, 4, 2, 1], [-1, 0, 4, 1, 2, 3], [-1, 0, 4, 1, 3, 2], [-1, 0, 4, 2, 1, 3], [-1, 0, 4, 2, 3, 1], [-1, 0, 4, 3, 1, 2], [-1, 0, 4, 3, 2, 1], [-1, 1, 0, 2, 3, 4], [-1, 1, 0, 2, 4, 3], [-1, 1, 0, 3, 2, 4], [-1, 1, 0, 3, 4, 2], [-1, 1, 0, 4, 2, 3], [-1, 1, 0, 4, 3, 2], [-1, 1, 2, 0, 3, 4], [-1, 1, 2, 0, 4, 3], [-1, 1, 2, 3, 0, 4], [-1, 1, 2, 3, 4, 0], [-1, 1, 2, 4, 0, 3], [-1, 1, 2, 4, 3, 0], [-1, 1, 3, 0, 2, 4], [-1, 1, 3, 0, 4, 2], [-1, 1, 3, 2, 0, 4], [-1, 1, 3, 2, 4, 0], [-1, 1, 3, 4, 0, 2], [-1, 1, 3, 4, 2, 0], [-1, 1, 4, 0, 2, 3], [-1, 1, 4, 0, 3, 2], [-1, 1, 4, 2, 0, 3], [-1, 1, 4, 2, 3, 0], [-1, 1, 4, 3, 0, 2], [-1, 1, 4, 3, 2, 0], [-1, 2, 0, 1, 3, 4], [-1, 2, 0, 1, 4, 3], [-1, 2, 0, 3, 1, 4], [-1, 2, 0, 3, 4, 1], [-1, 2, 0, 4, 1, 3], [-1, 2, 0, 4, 3, 1], [-1, 2, 1, 0, 3, 4], [-1, 2, 1, 0, 4, 3], [-1, 2, 1, 3, 0, 4], [-1, 2, 1, 3, 4, 0], [-1, 2, 1, 4, 0, 3], [-1, 2, 1, 4, 3, 0], [-1, 2, 3, 0, 1, 4], [-1, 2, 3, 0, 4, 1], [-1, 2, 3, 1, 0, 4], [-1, 2, 3, 1, 4, 0], [-1, 2, 3, 4, 0, 1], [-1, 2, 3, 4, 1, 0], [-1, 2, 4, 0, 1, 3], [-1, 2, 4, 0, 3, 1], [-1, 2, 4, 1, 0, 3], [-1, 2, 4, 1, 3, 0], [-1, 2, 4, 3, 0, 1], [-1, 2, 4, 3, 1, 0], [-1, 3, 0, 1, 2, 4], [-1, 3, 0, 1, 4, 2], [-1, 3, 0, 2, 1, 4], [-1, 3, 0, 2, 4, 1], [-1, 3, 0, 4, 1, 2], [-1, 3, 0, 4, 2, 1], [-1, 3, 1, 0, 2, 4], [-1, 3, 1, 0, 4, 2], [-1, 3, 1, 2, 0, 4], [-1, 3, 1, 2, 4, 0], [-1, 3, 1, 4, 0, 2], [-1, 3, 1, 4, 2, 0], [-1, 3, 2, 0, 1, 4], [-1, 3, 2, 0, 4, 1], [-1, 3, 2, 1, 0, 4], [-1, 3, 2, 1, 4, 0], [-1, 3, 2, 4, 0, 1], [-1, 3, 2, 4, 1, 0], [-1, 3, 4, 0, 1, 2], [-1, 3, 4, 0, 2, 1], [-1, 3, 4, 1, 0, 2], [-1, 3, 4, 1, 2, 0], [-1, 3, 4, 2, 0, 1], [-1, 3, 4, 2, 1, 0], [-1, 4, 0, 1, 2, 3], [-1, 4, 0, 1, 3, 2], [-1, 4, 0, 2, 1, 3], [-1, 4, 0, 2, 3, 1], [-1, 4, 0, 3, 1, 2], [-1, 4, 0, 3, 2, 1], [-1, 4, 1, 0, 2, 3], [-1, 4, 1, 0, 3, 2], [-1, 4, 1, 2, 0, 3], [-1, 4, 1, 2, 3, 0], [-1, 4, 1, 3, 0, 2], [-1, 4, 1, 3, 2, 0], [-1, 4, 2, 0, 1, 3], [-1, 4, 2, 0, 3, 1], [-1, 4, 2, 1, 0, 3], [-1, 4, 2, 1, 3, 0], [-1, 4, 2, 3, 0, 1], [-1, 4, 2, 3, 1, 0], [-1, 4, 3, 0, 1, 2], [-1, 4, 3, 0, 2, 1], [-1, 4, 3, 1, 0, 2], [-1, 4, 3, 1, 2, 0], [-1, 4, 3, 2, 0, 1], [-1, 4, 3, 2, 1, 0], [0, -1, 1, 2, 3, 4], [0, -1, 1, 2, 4, 3], [0, -1, 1, 3, 2, 4], [0, -1, 1, 3, 4, 2], [0, -1, 1, 4, 2, 3], [0, -1, 1, 4, 3, 2], [0, -1, 2, 1, 3, 4], [0, -1, 2, 1, 4, 3], [0, -1, 2, 3, 1, 4], [0, -1, 2, 3, 4, 1], [0, -1, 2, 4, 1, 3], [0, -1, 2, 4, 3, 1], [0, -1, 3, 1, 2, 4], [0, -1, 3, 1, 4, 2], [0, -1, 3, 2, 1, 4], [0, -1, 3, 2, 4, 1], [0, -1, 3, 4, 1, 2], [0, -1, 3, 4, 2, 1], [0, -1, 4, 1, 2, 3], [0, -1, 4, 1, 3, 2], [0, -1, 4, 2, 1, 3], [0, -1, 4, 2, 3, 1], [0, -1, 4, 3, 1, 2], [0, -1, 4, 3, 2, 1], [0, 1, -1, 2, 3, 4], [0, 1, -1, 2, 4, 3], [0, 1, -1, 3, 2, 4], [0, 1, -1, 3, 4, 2], [0, 1, -1, 4, 2, 3], [0, 1, -1, 4, 3, 2], [0, 1, 2, -1, 3, 4], [0, 1, 2, -1, 4, 3], [0, 1, 2, 3, -1, 4], [0, 1, 2, 3, 4, -1], [0, 1, 2, 4, -1, 3], [0, 1, 2, 4, 3, -1], [0, 1, 3, -1, 2, 4], [0, 1, 3, -1, 4, 2], [0, 1, 3, 2, -1, 4], [0, 1, 3, 2, 4, -1], [0, 1, 3, 4, -1, 2], [0, 1, 3, 4, 2, -1], [0, 1, 4, -1, 2, 3], [0, 1, 4, -1, 3, 2], [0, 1, 4, 2, -1, 3], [0, 1, 4, 2, 3, -1], [0, 1, 4, 3, -1, 2], [0, 1, 4, 3, 2, -1], [0, 2, -1, 1, 3, 4], [0, 2, -1, 1, 4, 3], [0, 2, -1, 3, 1, 4], [0, 2, -1, 3, 4, 1], [0, 2, -1, 4, 1, 3], [0, 2, -1, 4, 3, 1], [0, 2, 1, -1, 3, 4], [0, 2, 1, -1, 4, 3], [0, 2, 1, 3, -1, 4], [0, 2, 1, 3, 4, -1], [0, 2, 1, 4, -1, 3], [0, 2, 1, 4, 3, -1], [0, 2, 3, -1, 1, 4], [0, 2, 3, -1, 4, 1], [0, 2, 3, 1, -1, 4], [0, 2, 3, 1, 4, -1], [0, 2, 3, 4, -1, 1], [0, 2, 3, 4, 1, -1], [0, 2, 4, -1, 1, 3], [0, 2, 4, -1, 3, 1], [0, 2, 4, 1, -1, 3], [0, 2, 4, 1, 3, -1], [0, 2, 4, 3, -1, 1], [0, 2, 4, 3, 1, -1], [0, 3, -1, 1, 2, 4], [0, 3, -1, 1, 4, 2], [0, 3, -1, 2, 1, 4], [0, 3, -1, 2, 4, 1], [0, 3, -1, 4, 1, 2], [0, 3, -1, 4, 2, 1], [0, 3, 1, -1, 2, 4], [0, 3, 1, -1, 4, 2], [0, 3, 1, 2, -1, 4], [0, 3, 1, 2, 4, -1], [0, 3, 1, 4, -1, 2], [0, 3, 1, 4, 2, -1], [0, 3, 2, -1, 1, 4], [0, 3, 2, -1, 4, 1], [0, 3, 2, 1, -1, 4], [0, 3, 2, 1, 4, -1], [0, 3, 2, 4, -1, 1], [0, 3, 2, 4, 1, -1], [0, 3, 4, -1, 1, 2], [0, 3, 4, -1, 2, 1], [0, 3, 4, 1, -1, 2], [0, 3, 4, 1, 2, -1], [0, 3, 4, 2, -1, 1], [0, 3, 4, 2, 1, -1], [0, 4, -1, 1, 2, 3], [0, 4, -1, 1, 3, 2], [0, 4, -1, 2, 1, 3], [0, 4, -1, 2, 3, 1], [0, 4, -1, 3, 1, 2], [0, 4, -1, 3, 2, 1], [0, 4, 1, -1, 2, 3], [0, 4, 1, -1, 3, 2], [0, 4, 1, 2, -1, 3], [0, 4, 1, 2, 3, -1], [0, 4, 1, 3, -1, 2], [0, 4, 1, 3, 2, -1], [0, 4, 2, -1, 1, 3], [0, 4, 2, -1, 3, 1], [0, 4, 2, 1, -1, 3], [0, 4, 2, 1, 3, -1], [0, 4, 2, 3, -1, 1], [0, 4, 2, 3, 1, -1], [0, 4, 3, -1, 1, 2], [0, 4, 3, -1, 2, 1], [0, 4, 3, 1, -1, 2], [0, 4, 3, 1, 2, -1], [0, 4, 3, 2, -1, 1], [0, 4, 3, 2, 1, -1], [1, -1, 0, 2, 3, 4], [1, -1, 0, 2, 4, 3], [1, -1, 0, 3, 2, 4], [1, -1, 0, 3, 4, 2], [1, -1, 0, 4, 2, 3], [1, -1, 0, 4, 3, 2], [1, -1, 2, 0, 3, 4], [1, -1, 2, 0, 4, 3], [1, -1, 2, 3, 0, 4], [1, -1, 2, 3, 4, 0], [1, -1, 2, 4, 0, 3], [1, -1, 2, 4, 3, 0], [1, -1, 3, 0, 2, 4], [1, -1, 3, 0, 4, 2], [1, -1, 3, 2, 0, 4], [1, -1, 3, 2, 4, 0], [1, -1, 3, 4, 0, 2], [1, -1, 3, 4, 2, 0], [1, -1, 4, 0, 2, 3], [1, -1, 4, 0, 3, 2], [1, -1, 4, 2, 0, 3], [1, -1, 4, 2, 3, 0], [1, -1, 4, 3, 0, 2], [1, -1, 4, 3, 2, 0], [1, 0, -1, 2, 3, 4], [1, 0, -1, 2, 4, 3], [1, 0, -1, 3, 2, 4], [1, 0, -1, 3, 4, 2], [1, 0, -1, 4, 2, 3], [1, 0, -1, 4, 3, 2], [1, 0, 2, -1, 3, 4], [1, 0, 2, -1, 4, 3], [1, 0, 2, 3, -1, 4], [1, 0, 2, 3, 4, -1], [1, 0, 2, 4, -1, 3], [1, 0, 2, 4, 3, -1], [1, 0, 3, -1, 2, 4], [1, 0, 3, -1, 4, 2], [1, 0, 3, 2, -1, 4], [1, 0, 3, 2, 4, -1], [1, 0, 3, 4, -1, 2], [1, 0, 3, 4, 2, -1], [1, 0, 4, -1, 2, 3], [1, 0, 4, -1, 3, 2], [1, 0, 4, 2, -1, 3], [1, 0, 4, 2, 3, -1], [1, 0, 4, 3, -1, 2], [1, 0, 4, 3, 2, -1], [1, 2, -1, 0, 3, 4], [1, 2, -1, 0, 4, 3], [1, 2, -1, 3, 0, 4], [1, 2, -1, 3, 4, 0], [1, 2, -1, 4, 0, 3], [1, 2, -1, 4, 3, 0], [1, 2, 0, -1, 3, 4], [1, 2, 0, -1, 4, 3], [1, 2, 0, 3, -1, 4], [1, 2, 0, 3, 4, -1], [1, 2, 0, 4, -1, 3], [1, 2, 0, 4, 3, -1], [1, 2, 3, -1, 0, 4], [1, 2, 3, -1, 4, 0], [1, 2, 3, 0, -1, 4], [1, 2, 3, 0, 4, -1], [1, 2, 3, 4, -1, 0], [1, 2, 3, 4, 0, -1], [1, 2, 4, -1, 0, 3], [1, 2, 4, -1, 3, 0], [1, 2, 4, 0, -1, 3], [1, 2, 4, 0, 3, -1], [1, 2, 4, 3, -1, 0], [1, 2, 4, 3, 0, -1], [1, 3, -1, 0, 2, 4], [1, 3, -1, 0, 4, 2], [1, 3, -1, 2, 0, 4], [1, 3, -1, 2, 4, 0], [1, 3, -1, 4, 0, 2], [1, 3, -1, 4, 2, 0], [1, 3, 0, -1, 2, 4], [1, 3, 0, -1, 4, 2], [1, 3, 0, 2, -1, 4], [1, 3, 0, 2, 4, -1], [1, 3, 0, 4, -1, 2], [1, 3, 0, 4, 2, -1], [1, 3, 2, -1, 0, 4], [1, 3, 2, -1, 4, 0], [1, 3, 2, 0, -1, 4], [1, 3, 2, 0, 4, -1], [1, 3, 2, 4, -1, 0], [1, 3, 2, 4, 0, -1], [1, 3, 4, -1, 0, 2], [1, 3, 4, -1, 2, 0], [1, 3, 4, 0, -1, 2], [1, 3, 4, 0, 2, -1], [1, 3, 4, 2, -1, 0], [1, 3, 4, 2, 0, -1], [1, 4, -1, 0, 2, 3], [1, 4, -1, 0, 3, 2], [1, 4, -1, 2, 0, 3], [1, 4, -1, 2, 3, 0], [1, 4, -1, 3, 0, 2], [1, 4, -1, 3, 2, 0], [1, 4, 0, -1, 2, 3], [1, 4, 0, -1, 3, 2], [1, 4, 0, 2, -1, 3], [1, 4, 0, 2, 3, -1], [1, 4, 0, 3, -1, 2], [1, 4, 0, 3, 2, -1], [1, 4, 2, -1, 0, 3], [1, 4, 2, -1, 3, 0], [1, 4, 2, 0, -1, 3], [1, 4, 2, 0, 3, -1], [1, 4, 2, 3, -1, 0], [1, 4, 2, 3, 0, -1], [1, 4, 3, -1, 0, 2], [1, 4, 3, -1, 2, 0], [1, 4, 3, 0, -1, 2], [1, 4, 3, 0, 2, -1], [1, 4, 3, 2, -1, 0], [1, 4, 3, 2, 0, -1], [2, -1, 0, 1, 3, 4], [2, -1, 0, 1, 4, 3], [2, -1, 0, 3, 1, 4], [2, -1, 0, 3, 4, 1], [2, -1, 0, 4, 1, 3], [2, -1, 0, 4, 3, 1], [2, -1, 1, 0, 3, 4], [2, -1, 1, 0, 4, 3], [2, -1, 1, 3, 0, 4], [2, -1, 1, 3, 4, 0], [2, -1, 1, 4, 0, 3], [2, -1, 1, 4, 3, 0], [2, -1, 3, 0, 1, 4], [2, -1, 3, 0, 4, 1], [2, -1, 3, 1, 0, 4], [2, -1, 3, 1, 4, 0], [2, -1, 3, 4, 0, 1], [2, -1, 3, 4, 1, 0], [2, -1, 4, 0, 1, 3], [2, -1, 4, 0, 3, 1], [2, -1, 4, 1, 0, 3], [2, -1, 4, 1, 3, 0], [2, -1, 4, 3, 0, 1], [2, -1, 4, 3, 1, 0], [2, 0, -1, 1, 3, 4], [2, 0, -1, 1, 4, 3], [2, 0, -1, 3, 1, 4], [2, 0, -1, 3, 4, 1], [2, 0, -1, 4, 1, 3], [2, 0, -1, 4, 3, 1], [2, 0, 1, -1, 3, 4], [2, 0, 1, -1, 4, 3], [2, 0, 1, 3, -1, 4], [2, 0, 1, 3, 4, -1], [2, 0, 1, 4, -1, 3], [2, 0, 1, 4, 3, -1], [2, 0, 3, -1, 1, 4], [2, 0, 3, -1, 4, 1], [2, 0, 3, 1, -1, 4], [2, 0, 3, 1, 4, -1], [2, 0, 3, 4, -1, 1], [2, 0, 3, 4, 1, -1], [2, 0, 4, -1, 1, 3], [2, 0, 4, -1, 3, 1], [2, 0, 4, 1, -1, 3], [2, 0, 4, 1, 3, -1], [2, 0, 4, 3, -1, 1], [2, 0, 4, 3, 1, -1], [2, 1, -1, 0, 3, 4], [2, 1, -1, 0, 4, 3], [2, 1, -1, 3, 0, 4], [2, 1, -1, 3, 4, 0], [2, 1, -1, 4, 0, 3], [2, 1, -1, 4, 3, 0], [2, 1, 0, -1, 3, 4], [2, 1, 0, -1, 4, 3], [2, 1, 0, 3, -1, 4], [2, 1, 0, 3, 4, -1], [2, 1, 0, 4, -1, 3], [2, 1, 0, 4, 3, -1], [2, 1, 3, -1, 0, 4], [2, 1, 3, -1, 4, 0], [2, 1, 3, 0, -1, 4], [2, 1, 3, 0, 4, -1], [2, 1, 3, 4, -1, 0], [2, 1, 3, 4, 0, -1], [2, 1, 4, -1, 0, 3], [2, 1, 4, -1, 3, 0], [2, 1, 4, 0, -1, 3], [2, 1, 4, 0, 3, -1], [2, 1, 4, 3, -1, 0], [2, 1, 4, 3, 0, -1], [2, 3, -1, 0, 1, 4], [2, 3, -1, 0, 4, 1], [2, 3, -1, 1, 0, 4], [2, 3, -1, 1, 4, 0], [2, 3, -1, 4, 0, 1], [2, 3, -1, 4, 1, 0], [2, 3, 0, -1, 1, 4], [2, 3, 0, -1, 4, 1], [2, 3, 0, 1, -1, 4], [2, 3, 0, 1, 4, -1], [2, 3, 0, 4, -1, 1], [2, 3, 0, 4, 1, -1], [2, 3, 1, -1, 0, 4], [2, 3, 1, -1, 4, 0], [2, 3, 1, 0, -1, 4], [2, 3, 1, 0, 4, -1], [2, 3, 1, 4, -1, 0], [2, 3, 1, 4, 0, -1], [2, 3, 4, -1, 0, 1], [2, 3, 4, -1, 1, 0], [2, 3, 4, 0, -1, 1], [2, 3, 4, 0, 1, -1], [2, 3, 4, 1, -1, 0], [2, 3, 4, 1, 0, -1], [2, 4, -1, 0, 1, 3], [2, 4, -1, 0, 3, 1], [2, 4, -1, 1, 0, 3], [2, 4, -1, 1, 3, 0], [2, 4, -1, 3, 0, 1], [2, 4, -1, 3, 1, 0], [2, 4, 0, -1, 1, 3], [2, 4, 0, -1, 3, 1], [2, 4, 0, 1, -1, 3], [2, 4, 0, 1, 3, -1], [2, 4, 0, 3, -1, 1], [2, 4, 0, 3, 1, -1], [2, 4, 1, -1, 0, 3], [2, 4, 1, -1, 3, 0], [2, 4, 1, 0, -1, 3], [2, 4, 1, 0, 3, -1], [2, 4, 1, 3, -1, 0], [2, 4, 1, 3, 0, -1], [2, 4, 3, -1, 0, 1], [2, 4, 3, -1, 1, 0], [2, 4, 3, 0, -1, 1], [2, 4, 3, 0, 1, -1], [2, 4, 3, 1, -1, 0], [2, 4, 3, 1, 0, -1], [3, -1, 0, 1, 2, 4], [3, -1, 0, 1, 4, 2], [3, -1, 0, 2, 1, 4], [3, -1, 0, 2, 4, 1], [3, -1, 0, 4, 1, 2], [3, -1, 0, 4, 2, 1], [3, -1, 1, 0, 2, 4], [3, -1, 1, 0, 4, 2], [3, -1, 1, 2, 0, 4], [3, -1, 1, 2, 4, 0], [3, -1, 1, 4, 0, 2], [3, -1, 1, 4, 2, 0], [3, -1, 2, 0, 1, 4], [3, -1, 2, 0, 4, 1], [3, -1, 2, 1, 0, 4], [3, -1, 2, 1, 4, 0], [3, -1, 2, 4, 0, 1], [3, -1, 2, 4, 1, 0], [3, -1, 4, 0, 1, 2], [3, -1, 4, 0, 2, 1], [3, -1, 4, 1, 0, 2], [3, -1, 4, 1, 2, 0], [3, -1, 4, 2, 0, 1], [3, -1, 4, 2, 1, 0], [3, 0, -1, 1, 2, 4], [3, 0, -1, 1, 4, 2], [3, 0, -1, 2, 1, 4], [3, 0, -1, 2, 4, 1], [3, 0, -1, 4, 1, 2], [3, 0, -1, 4, 2, 1], [3, 0, 1, -1, 2, 4], [3, 0, 1, -1, 4, 2], [3, 0, 1, 2, -1, 4], [3, 0, 1, 2, 4, -1], [3, 0, 1, 4, -1, 2], [3, 0, 1, 4, 2, -1], [3, 0, 2, -1, 1, 4], [3, 0, 2, -1, 4, 1], [3, 0, 2, 1, -1, 4], [3, 0, 2, 1, 4, -1], [3, 0, 2, 4, -1, 1], [3, 0, 2, 4, 1, -1], [3, 0, 4, -1, 1, 2], [3, 0, 4, -1, 2, 1], [3, 0, 4, 1, -1, 2], [3, 0, 4, 1, 2, -1], [3, 0, 4, 2, -1, 1], [3, 0, 4, 2, 1, -1], [3, 1, -1, 0, 2, 4], [3, 1, -1, 0, 4, 2], [3, 1, -1, 2, 0, 4], [3, 1, -1, 2, 4, 0], [3, 1, -1, 4, 0, 2], [3, 1, -1, 4, 2, 0], [3, 1, 0, -1, 2, 4], [3, 1, 0, -1, 4, 2], [3, 1, 0, 2, -1, 4], [3, 1, 0, 2, 4, -1], [3, 1, 0, 4, -1, 2], [3, 1, 0, 4, 2, -1], [3, 1, 2, -1, 0, 4], [3, 1, 2, -1, 4, 0], [3, 1, 2, 0, -1, 4], [3, 1, 2, 0, 4, -1], [3, 1, 2, 4, -1, 0], [3, 1, 2, 4, 0, -1], [3, 1, 4, -1, 0, 2], [3, 1, 4, -1, 2, 0], [3, 1, 4, 0, -1, 2], [3, 1, 4, 0, 2, -1], [3, 1, 4, 2, -1, 0], [3, 1, 4, 2, 0, -1], [3, 2, -1, 0, 1, 4], [3, 2, -1, 0, 4, 1], [3, 2, -1, 1, 0, 4], [3, 2, -1, 1, 4, 0], [3, 2, -1, 4, 0, 1], [3, 2, -1, 4, 1, 0], [3, 2, 0, -1, 1, 4], [3, 2, 0, -1, 4, 1], [3, 2, 0, 1, -1, 4], [3, 2, 0, 1, 4, -1], [3, 2, 0, 4, -1, 1], [3, 2, 0, 4, 1, -1], [3, 2, 1, -1, 0, 4], [3, 2, 1, -1, 4, 0], [3, 2, 1, 0, -1, 4], [3, 2, 1, 0, 4, -1], [3, 2, 1, 4, -1, 0], [3, 2, 1, 4, 0, -1], [3, 2, 4, -1, 0, 1], [3, 2, 4, -1, 1, 0], [3, 2, 4, 0, -1, 1], [3, 2, 4, 0, 1, -1], [3, 2, 4, 1, -1, 0], [3, 2, 4, 1, 0, -1], [3, 4, -1, 0, 1, 2], [3, 4, -1, 0, 2, 1], [3, 4, -1, 1, 0, 2], [3, 4, -1, 1, 2, 0], [3, 4, -1, 2, 0, 1], [3, 4, -1, 2, 1, 0], [3, 4, 0, -1, 1, 2], [3, 4, 0, -1, 2, 1], [3, 4, 0, 1, -1, 2], [3, 4, 0, 1, 2, -1], [3, 4, 0, 2, -1, 1], [3, 4, 0, 2, 1, -1], [3, 4, 1, -1, 0, 2], [3, 4, 1, -1, 2, 0], [3, 4, 1, 0, -1, 2], [3, 4, 1, 0, 2, -1], [3, 4, 1, 2, -1, 0], [3, 4, 1, 2, 0, -1], [3, 4, 2, -1, 0, 1], [3, 4, 2, -1, 1, 0], [3, 4, 2, 0, -1, 1], [3, 4, 2, 0, 1, -1], [3, 4, 2, 1, -1, 0], [3, 4, 2, 1, 0, -1], [4, -1, 0, 1, 2, 3], [4, -1, 0, 1, 3, 2], [4, -1, 0, 2, 1, 3], [4, -1, 0, 2, 3, 1], [4, -1, 0, 3, 1, 2], [4, -1, 0, 3, 2, 1], [4, -1, 1, 0, 2, 3], [4, -1, 1, 0, 3, 2], [4, -1, 1, 2, 0, 3], [4, -1, 1, 2, 3, 0], [4, -1, 1, 3, 0, 2], [4, -1, 1, 3, 2, 0], [4, -1, 2, 0, 1, 3], [4, -1, 2, 0, 3, 1], [4, -1, 2, 1, 0, 3], [4, -1, 2, 1, 3, 0], [4, -1, 2, 3, 0, 1], [4, -1, 2, 3, 1, 0], [4, -1, 3, 0, 1, 2], [4, -1, 3, 0, 2, 1], [4, -1, 3, 1, 0, 2], [4, -1, 3, 1, 2, 0], [4, -1, 3, 2, 0, 1], [4, -1, 3, 2, 1, 0], [4, 0, -1, 1, 2, 3], [4, 0, -1, 1, 3, 2], [4, 0, -1, 2, 1, 3], [4, 0, -1, 2, 3, 1], [4, 0, -1, 3, 1, 2], [4, 0, -1, 3, 2, 1], [4, 0, 1, -1, 2, 3], [4, 0, 1, -1, 3, 2], [4, 0, 1, 2, -1, 3], [4, 0, 1, 2, 3, -1], [4, 0, 1, 3, -1, 2], [4, 0, 1, 3, 2, -1], [4, 0, 2, -1, 1, 3], [4, 0, 2, -1, 3, 1], [4, 0, 2, 1, -1, 3], [4, 0, 2, 1, 3, -1], [4, 0, 2, 3, -1, 1], [4, 0, 2, 3, 1, -1], [4, 0, 3, -1, 1, 2], [4, 0, 3, -1, 2, 1], [4, 0, 3, 1, -1, 2], [4, 0, 3, 1, 2, -1], [4, 0, 3, 2, -1, 1], [4, 0, 3, 2, 1, -1], [4, 1, -1, 0, 2, 3], [4, 1, -1, 0, 3, 2], [4, 1, -1, 2, 0, 3], [4, 1, -1, 2, 3, 0], [4, 1, -1, 3, 0, 2], [4, 1, -1, 3, 2, 0], [4, 1, 0, -1, 2, 3], [4, 1, 0, -1, 3, 2], [4, 1, 0, 2, -1, 3], [4, 1, 0, 2, 3, -1], [4, 1, 0, 3, -1, 2], [4, 1, 0, 3, 2, -1], [4, 1, 2, -1, 0, 3], [4, 1, 2, -1, 3, 0], [4, 1, 2, 0, -1, 3], [4, 1, 2, 0, 3, -1], [4, 1, 2, 3, -1, 0], [4, 1, 2, 3, 0, -1], [4, 1, 3, -1, 0, 2], [4, 1, 3, -1, 2, 0], [4, 1, 3, 0, -1, 2], [4, 1, 3, 0, 2, -1], [4, 1, 3, 2, -1, 0], [4, 1, 3, 2, 0, -1], [4, 2, -1, 0, 1, 3], [4, 2, -1, 0, 3, 1], [4, 2, -1, 1, 0, 3], [4, 2, -1, 1, 3, 0], [4, 2, -1, 3, 0, 1], [4, 2, -1, 3, 1, 0], [4, 2, 0, -1, 1, 3], [4, 2, 0, -1, 3, 1], [4, 2, 0, 1, -1, 3], [4, 2, 0, 1, 3, -1], [4, 2, 0, 3, -1, 1], [4, 2, 0, 3, 1, -1], [4, 2, 1, -1, 0, 3], [4, 2, 1, -1, 3, 0], [4, 2, 1, 0, -1, 3], [4, 2, 1, 0, 3, -1], [4, 2, 1, 3, -1, 0], [4, 2, 1, 3, 0, -1], [4, 2, 3, -1, 0, 1], [4, 2, 3, -1, 1, 0], [4, 2, 3, 0, -1, 1], [4, 2, 3, 0, 1, -1], [4, 2, 3, 1, -1, 0], [4, 2, 3, 1, 0, -1], [4, 3, -1, 0, 1, 2], [4, 3, -1, 0, 2, 1], [4, 3, -1, 1, 0, 2], [4, 3, -1, 1, 2, 0], [4, 3, -1, 2, 0, 1], [4, 3, -1, 2, 1, 0], [4, 3, 0, -1, 1, 2], [4, 3, 0, -1, 2, 1], [4, 3, 0, 1, -1, 2], [4, 3, 0, 1, 2, -1], [4, 3, 0, 2, -1, 1], [4, 3, 0, 2, 1, -1], [4, 3, 1, -1, 0, 2], [4, 3, 1, -1, 2, 0], [4, 3, 1, 0, -1, 2], [4, 3, 1, 0, 2, -1], [4, 3, 1, 2, -1, 0], [4, 3, 1, 2, 0, -1], [4, 3, 2, -1, 0, 1], [4, 3, 2, -1, 1, 0], [4, 3, 2, 0, -1, 1], [4, 3, 2, 0, 1, -1], [4, 3, 2, 1, -1, 0], [4, 3, 2, 1, 0, -1]]\n assert candidate(nums = [-5, -3, -8, -6, -1]) == [[-5, -3, -8, -6, -1], [-5, -3, -8, -1, -6], [-5, -3, -6, -8, -1], [-5, -3, -6, -1, -8], [-5, -3, -1, -8, -6], [-5, -3, -1, -6, -8], [-5, -8, -3, -6, -1], [-5, -8, -3, -1, -6], [-5, -8, -6, -3, -1], [-5, -8, -6, -1, -3], [-5, -8, -1, -3, -6], [-5, -8, -1, -6, -3], [-5, -6, -3, -8, -1], [-5, -6, -3, -1, -8], [-5, -6, -8, -3, -1], [-5, -6, -8, -1, -3], [-5, -6, -1, -3, -8], [-5, -6, -1, -8, -3], [-5, -1, -3, -8, -6], [-5, -1, -3, -6, -8], [-5, -1, -8, -3, -6], [-5, -1, -8, -6, -3], [-5, -1, -6, -3, -8], [-5, -1, -6, -8, -3], [-3, -5, -8, -6, -1], [-3, -5, -8, -1, -6], [-3, -5, -6, -8, -1], [-3, -5, -6, -1, -8], [-3, -5, -1, -8, -6], [-3, -5, -1, -6, -8], [-3, -8, -5, -6, -1], [-3, -8, -5, -1, -6], [-3, -8, -6, -5, -1], [-3, -8, -6, -1, -5], [-3, -8, -1, -5, -6], [-3, -8, -1, -6, -5], [-3, -6, -5, -8, -1], [-3, -6, -5, -1, -8], [-3, -6, -8, -5, -1], [-3, -6, -8, -1, -5], [-3, -6, -1, -5, -8], [-3, -6, -1, -8, -5], [-3, -1, -5, -8, -6], [-3, -1, -5, -6, -8], [-3, -1, -8, -5, -6], [-3, -1, -8, -6, -5], [-3, -1, -6, -5, -8], [-3, -1, -6, -8, -5], [-8, -5, -3, -6, -1], [-8, -5, -3, -1, -6], [-8, -5, -6, -3, -1], [-8, -5, -6, -1, -3], [-8, -5, -1, -3, -6], [-8, -5, -1, -6, -3], [-8, -3, -5, -6, -1], [-8, -3, -5, -1, -6], [-8, -3, -6, -5, -1], [-8, -3, -6, -1, -5], [-8, -3, -1, -5, -6], [-8, -3, -1, -6, -5], [-8, -6, -5, -3, -1], [-8, -6, -5, -1, -3], [-8, -6, -3, -5, -1], [-8, -6, -3, -1, -5], [-8, -6, -1, -5, -3], [-8, -6, -1, -3, -5], [-8, -1, -5, -3, -6], [-8, -1, -5, -6, -3], [-8, -1, -3, -5, -6], [-8, -1, -3, -6, -5], [-8, -1, -6, -5, -3], [-8, -1, -6, -3, -5], [-6, -5, -3, -8, -1], [-6, -5, -3, -1, -8], [-6, -5, -8, -3, -1], [-6, -5, -8, -1, -3], [-6, -5, -1, -3, -8], [-6, -5, -1, -8, -3], [-6, -3, -5, -8, -1], [-6, -3, -5, -1, -8], [-6, -3, -8, -5, -1], [-6, -3, -8, -1, -5], [-6, -3, -1, -5, -8], [-6, -3, -1, -8, -5], [-6, -8, -5, -3, -1], [-6, -8, -5, -1, -3], [-6, -8, -3, -5, -1], [-6, -8, -3, -1, -5], [-6, -8, -1, -5, -3], [-6, -8, -1, -3, -5], [-6, -1, -5, -3, -8], [-6, -1, -5, -8, -3], [-6, -1, -3, -5, -8], [-6, -1, -3, -8, -5], [-6, -1, -8, -5, -3], [-6, -1, -8, -3, -5], [-1, -5, -3, -8, -6], [-1, -5, -3, -6, -8], [-1, -5, -8, -3, -6], [-1, -5, -8, -6, -3], [-1, -5, -6, -3, -8], [-1, -5, -6, -8, -3], [-1, -3, -5, -8, -6], [-1, -3, -5, -6, -8], [-1, -3, -8, -5, -6], [-1, -3, -8, -6, -5], [-1, -3, -6, -5, -8], [-1, -3, -6, -8, -5], [-1, -8, -5, -3, -6], [-1, -8, -5, -6, -3], [-1, -8, -3, -5, -6], [-1, -8, -3, -6, -5], [-1, -8, -6, -5, -3], [-1, -8, -6, -3, -5], [-1, -6, -5, -3, -8], [-1, -6, -5, -8, -3], [-1, -6, -3, -5, -8], [-1, -6, -3, -8, -5], [-1, -6, -8, -5, -3], [-1, -6, -8, -3, -5]]\n assert candidate(nums = [-1, -2, -3, -4, -5]) == [[-1, -2, -3, -4, -5], [-1, -2, -3, -5, -4], [-1, -2, -4, -3, -5], [-1, -2, -4, -5, -3], [-1, -2, -5, -3, -4], [-1, -2, -5, -4, -3], [-1, -3, -2, -4, -5], [-1, -3, -2, -5, -4], [-1, -3, -4, -2, -5], [-1, -3, -4, -5, -2], [-1, -3, -5, -2, -4], [-1, -3, -5, -4, -2], [-1, -4, -2, -3, -5], [-1, -4, -2, -5, -3], [-1, -4, -3, -2, -5], [-1, -4, -3, -5, -2], [-1, -4, -5, -2, -3], [-1, -4, -5, -3, -2], [-1, -5, -2, -3, -4], [-1, -5, -2, -4, -3], [-1, -5, -3, -2, -4], [-1, -5, -3, -4, -2], [-1, -5, -4, -2, -3], [-1, -5, -4, -3, -2], [-2, -1, -3, -4, -5], [-2, -1, -3, -5, -4], [-2, -1, -4, -3, -5], [-2, -1, -4, -5, -3], [-2, -1, -5, -3, -4], [-2, -1, -5, -4, -3], [-2, -3, -1, -4, -5], [-2, -3, -1, -5, -4], [-2, -3, -4, -1, -5], [-2, -3, -4, -5, -1], [-2, -3, -5, -1, -4], [-2, -3, -5, -4, -1], [-2, -4, -1, -3, -5], [-2, -4, -1, -5, -3], [-2, -4, -3, -1, -5], [-2, -4, -3, -5, -1], [-2, -4, -5, -1, -3], [-2, -4, -5, -3, -1], [-2, -5, -1, -3, -4], [-2, -5, -1, -4, -3], [-2, -5, -3, -1, -4], [-2, -5, -3, -4, -1], [-2, -5, -4, -1, -3], [-2, -5, -4, -3, -1], [-3, -1, -2, -4, -5], [-3, -1, -2, -5, -4], [-3, -1, -4, -2, -5], [-3, -1, -4, -5, -2], [-3, -1, -5, -2, -4], [-3, -1, -5, -4, -2], [-3, -2, -1, -4, -5], [-3, -2, -1, -5, -4], [-3, -2, -4, -1, -5], [-3, -2, -4, -5, -1], [-3, -2, -5, -1, -4], [-3, -2, -5, -4, -1], [-3, -4, -1, -2, -5], [-3, -4, -1, -5, -2], [-3, -4, -2, -1, -5], [-3, -4, -2, -5, -1], [-3, -4, -5, -1, -2], [-3, -4, -5, -2, -1], [-3, -5, -1, -2, -4], [-3, -5, -1, -4, -2], [-3, -5, -2, -1, -4], [-3, -5, -2, -4, -1], [-3, -5, -4, -1, -2], [-3, -5, -4, -2, -1], [-4, -1, -2, -3, -5], [-4, -1, -2, -5, -3], [-4, -1, -3, -2, -5], [-4, -1, -3, -5, -2], [-4, -1, -5, -2, -3], [-4, -1, -5, -3, -2], [-4, -2, -1, -3, -5], [-4, -2, -1, -5, -3], [-4, -2, -3, -1, -5], [-4, -2, -3, -5, -1], [-4, -2, -5, -1, -3], [-4, -2, -5, -3, -1], [-4, -3, -1, -2, -5], [-4, -3, -1, -5, -2], [-4, -3, -2, -1, -5], [-4, -3, -2, -5, -1], [-4, -3, -5, -1, -2], [-4, -3, -5, -2, -1], [-4, -5, -1, -2, -3], [-4, -5, -1, -3, -2], [-4, -5, -2, -1, -3], [-4, -5, -2, -3, -1], [-4, -5, -3, -1, -2], [-4, -5, -3, -2, -1], [-5, -1, -2, -3, -4], [-5, -1, -2, -4, -3], [-5, -1, -3, -2, -4], [-5, -1, -3, -4, -2], [-5, -1, -4, -2, -3], [-5, -1, -4, -3, -2], [-5, -2, -1, -3, -4], [-5, -2, -1, -4, -3], [-5, -2, -3, -1, -4], [-5, -2, -3, -4, -1], [-5, -2, -4, -1, -3], [-5, -2, -4, -3, -1], [-5, -3, -1, -2, -4], [-5, -3, -1, -4, -2], [-5, -3, -2, -1, -4], [-5, -3, -2, -4, -1], [-5, -3, -4, -1, -2], [-5, -3, -4, -2, -1], [-5, -4, -1, -2, -3], [-5, -4, -1, -3, -2], [-5, -4, -2, -1, -3], [-5, -4, -2, -3, -1], [-5, -4, -3, -1, -2], [-5, -4, -3, -2, -1]]\n assert candidate(nums = [7, 14, 21, 28, 35]) == [[7, 14, 21, 28, 35], [7, 14, 21, 35, 28], [7, 14, 28, 21, 35], [7, 14, 28, 35, 21], [7, 14, 35, 21, 28], [7, 14, 35, 28, 21], [7, 21, 14, 28, 35], [7, 21, 14, 35, 28], [7, 21, 28, 14, 35], [7, 21, 28, 35, 14], [7, 21, 35, 14, 28], [7, 21, 35, 28, 14], [7, 28, 14, 21, 35], [7, 28, 14, 35, 21], [7, 28, 21, 14, 35], [7, 28, 21, 35, 14], [7, 28, 35, 14, 21], [7, 28, 35, 21, 14], [7, 35, 14, 21, 28], [7, 35, 14, 28, 21], [7, 35, 21, 14, 28], [7, 35, 21, 28, 14], [7, 35, 28, 14, 21], [7, 35, 28, 21, 14], [14, 7, 21, 28, 35], [14, 7, 21, 35, 28], [14, 7, 28, 21, 35], [14, 7, 28, 35, 21], [14, 7, 35, 21, 28], [14, 7, 35, 28, 21], [14, 21, 7, 28, 35], [14, 21, 7, 35, 28], [14, 21, 28, 7, 35], [14, 21, 28, 35, 7], [14, 21, 35, 7, 28], [14, 21, 35, 28, 7], [14, 28, 7, 21, 35], [14, 28, 7, 35, 21], [14, 28, 21, 7, 35], [14, 28, 21, 35, 7], [14, 28, 35, 7, 21], [14, 28, 35, 21, 7], [14, 35, 7, 21, 28], [14, 35, 7, 28, 21], [14, 35, 21, 7, 28], [14, 35, 21, 28, 7], [14, 35, 28, 7, 21], [14, 35, 28, 21, 7], [21, 7, 14, 28, 35], [21, 7, 14, 35, 28], [21, 7, 28, 14, 35], [21, 7, 28, 35, 14], [21, 7, 35, 14, 28], [21, 7, 35, 28, 14], [21, 14, 7, 28, 35], [21, 14, 7, 35, 28], [21, 14, 28, 7, 35], [21, 14, 28, 35, 7], [21, 14, 35, 7, 28], [21, 14, 35, 28, 7], [21, 28, 7, 14, 35], [21, 28, 7, 35, 14], [21, 28, 14, 7, 35], [21, 28, 14, 35, 7], [21, 28, 35, 7, 14], [21, 28, 35, 14, 7], [21, 35, 7, 14, 28], [21, 35, 7, 28, 14], [21, 35, 14, 7, 28], [21, 35, 14, 28, 7], [21, 35, 28, 7, 14], [21, 35, 28, 14, 7], [28, 7, 14, 21, 35], [28, 7, 14, 35, 21], [28, 7, 21, 14, 35], [28, 7, 21, 35, 14], [28, 7, 35, 14, 21], [28, 7, 35, 21, 14], [28, 14, 7, 21, 35], [28, 14, 7, 35, 21], [28, 14, 21, 7, 35], [28, 14, 21, 35, 7], [28, 14, 35, 7, 21], [28, 14, 35, 21, 7], [28, 21, 7, 14, 35], [28, 21, 7, 35, 14], [28, 21, 14, 7, 35], [28, 21, 14, 35, 7], [28, 21, 35, 7, 14], [28, 21, 35, 14, 7], [28, 35, 7, 14, 21], [28, 35, 7, 21, 14], [28, 35, 14, 7, 21], [28, 35, 14, 21, 7], [28, 35, 21, 7, 14], [28, 35, 21, 14, 7], [35, 7, 14, 21, 28], [35, 7, 14, 28, 21], [35, 7, 21, 14, 28], [35, 7, 21, 28, 14], [35, 7, 28, 14, 21], [35, 7, 28, 21, 14], [35, 14, 7, 21, 28], [35, 14, 7, 28, 21], [35, 14, 21, 7, 28], [35, 14, 21, 28, 7], [35, 14, 28, 7, 21], [35, 14, 28, 21, 7], [35, 21, 7, 14, 28], [35, 21, 7, 28, 14], [35, 21, 14, 7, 28], [35, 21, 14, 28, 7], [35, 21, 28, 7, 14], [35, 21, 28, 14, 7], [35, 28, 7, 14, 21], [35, 28, 7, 21, 14], [35, 28, 14, 7, 21], [35, 28, 14, 21, 7], [35, 28, 21, 7, 14], [35, 28, 21, 14, 7]]\n assert candidate(nums = [1, 2, 3, 4]) == [[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]]\n assert candidate(nums = [7, 8, 9, 10]) == [[7, 8, 9, 10], [7, 8, 10, 9], [7, 9, 8, 10], [7, 9, 10, 8], [7, 10, 8, 9], [7, 10, 9, 8], [8, 7, 9, 10], [8, 7, 10, 9], [8, 9, 7, 10], [8, 9, 10, 7], [8, 10, 7, 9], [8, 10, 9, 7], [9, 7, 8, 10], [9, 7, 10, 8], [9, 8, 7, 10], [9, 8, 10, 7], [9, 10, 7, 8], [9, 10, 8, 7], [10, 7, 8, 9], [10, 7, 9, 8], [10, 8, 7, 9], [10, 8, 9, 7], [10, 9, 7, 8], [10, 9, 8, 7]]\n assert candidate(nums = [100, 50, 25, 12, 6, 3]) == [[100, 50, 25, 12, 6, 3], [100, 50, 25, 12, 3, 6], [100, 50, 25, 6, 12, 3], [100, 50, 25, 6, 3, 12], [100, 50, 25, 3, 12, 6], [100, 50, 25, 3, 6, 12], [100, 50, 12, 25, 6, 3], [100, 50, 12, 25, 3, 6], [100, 50, 12, 6, 25, 3], [100, 50, 12, 6, 3, 25], [100, 50, 12, 3, 25, 6], [100, 50, 12, 3, 6, 25], [100, 50, 6, 25, 12, 3], [100, 50, 6, 25, 3, 12], [100, 50, 6, 12, 25, 3], [100, 50, 6, 12, 3, 25], [100, 50, 6, 3, 25, 12], [100, 50, 6, 3, 12, 25], [100, 50, 3, 25, 12, 6], [100, 50, 3, 25, 6, 12], [100, 50, 3, 12, 25, 6], [100, 50, 3, 12, 6, 25], [100, 50, 3, 6, 25, 12], [100, 50, 3, 6, 12, 25], [100, 25, 50, 12, 6, 3], [100, 25, 50, 12, 3, 6], [100, 25, 50, 6, 12, 3], [100, 25, 50, 6, 3, 12], [100, 25, 50, 3, 12, 6], [100, 25, 50, 3, 6, 12], [100, 25, 12, 50, 6, 3], [100, 25, 12, 50, 3, 6], [100, 25, 12, 6, 50, 3], [100, 25, 12, 6, 3, 50], [100, 25, 12, 3, 50, 6], [100, 25, 12, 3, 6, 50], [100, 25, 6, 50, 12, 3], [100, 25, 6, 50, 3, 12], [100, 25, 6, 12, 50, 3], [100, 25, 6, 12, 3, 50], [100, 25, 6, 3, 50, 12], [100, 25, 6, 3, 12, 50], [100, 25, 3, 50, 12, 6], [100, 25, 3, 50, 6, 12], [100, 25, 3, 12, 50, 6], [100, 25, 3, 12, 6, 50], [100, 25, 3, 6, 50, 12], [100, 25, 3, 6, 12, 50], [100, 12, 50, 25, 6, 3], [100, 12, 50, 25, 3, 6], [100, 12, 50, 6, 25, 3], [100, 12, 50, 6, 3, 25], [100, 12, 50, 3, 25, 6], [100, 12, 50, 3, 6, 25], [100, 12, 25, 50, 6, 3], [100, 12, 25, 50, 3, 6], [100, 12, 25, 6, 50, 3], [100, 12, 25, 6, 3, 50], [100, 12, 25, 3, 50, 6], [100, 12, 25, 3, 6, 50], [100, 12, 6, 50, 25, 3], [100, 12, 6, 50, 3, 25], [100, 12, 6, 25, 50, 3], [100, 12, 6, 25, 3, 50], [100, 12, 6, 3, 50, 25], [100, 12, 6, 3, 25, 50], [100, 12, 3, 50, 25, 6], [100, 12, 3, 50, 6, 25], [100, 12, 3, 25, 50, 6], [100, 12, 3, 25, 6, 50], [100, 12, 3, 6, 50, 25], [100, 12, 3, 6, 25, 50], [100, 6, 50, 25, 12, 3], [100, 6, 50, 25, 3, 12], [100, 6, 50, 12, 25, 3], [100, 6, 50, 12, 3, 25], [100, 6, 50, 3, 25, 12], [100, 6, 50, 3, 12, 25], [100, 6, 25, 50, 12, 3], [100, 6, 25, 50, 3, 12], [100, 6, 25, 12, 50, 3], [100, 6, 25, 12, 3, 50], [100, 6, 25, 3, 50, 12], [100, 6, 25, 3, 12, 50], [100, 6, 12, 50, 25, 3], [100, 6, 12, 50, 3, 25], [100, 6, 12, 25, 50, 3], [100, 6, 12, 25, 3, 50], [100, 6, 12, 3, 50, 25], [100, 6, 12, 3, 25, 50], [100, 6, 3, 50, 25, 12], [100, 6, 3, 50, 12, 25], [100, 6, 3, 25, 50, 12], [100, 6, 3, 25, 12, 50], [100, 6, 3, 12, 50, 25], [100, 6, 3, 12, 25, 50], [100, 3, 50, 25, 12, 6], [100, 3, 50, 25, 6, 12], [100, 3, 50, 12, 25, 6], [100, 3, 50, 12, 6, 25], [100, 3, 50, 6, 25, 12], [100, 3, 50, 6, 12, 25], [100, 3, 25, 50, 12, 6], [100, 3, 25, 50, 6, 12], [100, 3, 25, 12, 50, 6], [100, 3, 25, 12, 6, 50], [100, 3, 25, 6, 50, 12], [100, 3, 25, 6, 12, 50], [100, 3, 12, 50, 25, 6], [100, 3, 12, 50, 6, 25], [100, 3, 12, 25, 50, 6], [100, 3, 12, 25, 6, 50], [100, 3, 12, 6, 50, 25], [100, 3, 12, 6, 25, 50], [100, 3, 6, 50, 25, 12], [100, 3, 6, 50, 12, 25], [100, 3, 6, 25, 50, 12], [100, 3, 6, 25, 12, 50], [100, 3, 6, 12, 50, 25], [100, 3, 6, 12, 25, 50], [50, 100, 25, 12, 6, 3], [50, 100, 25, 12, 3, 6], [50, 100, 25, 6, 12, 3], [50, 100, 25, 6, 3, 12], [50, 100, 25, 3, 12, 6], [50, 100, 25, 3, 6, 12], [50, 100, 12, 25, 6, 3], [50, 100, 12, 25, 3, 6], [50, 100, 12, 6, 25, 3], [50, 100, 12, 6, 3, 25], [50, 100, 12, 3, 25, 6], [50, 100, 12, 3, 6, 25], [50, 100, 6, 25, 12, 3], [50, 100, 6, 25, 3, 12], [50, 100, 6, 12, 25, 3], [50, 100, 6, 12, 3, 25], [50, 100, 6, 3, 25, 12], [50, 100, 6, 3, 12, 25], [50, 100, 3, 25, 12, 6], [50, 100, 3, 25, 6, 12], [50, 100, 3, 12, 25, 6], [50, 100, 3, 12, 6, 25], [50, 100, 3, 6, 25, 12], [50, 100, 3, 6, 12, 25], [50, 25, 100, 12, 6, 3], [50, 25, 100, 12, 3, 6], [50, 25, 100, 6, 12, 3], [50, 25, 100, 6, 3, 12], [50, 25, 100, 3, 12, 6], [50, 25, 100, 3, 6, 12], [50, 25, 12, 100, 6, 3], [50, 25, 12, 100, 3, 6], [50, 25, 12, 6, 100, 3], [50, 25, 12, 6, 3, 100], [50, 25, 12, 3, 100, 6], [50, 25, 12, 3, 6, 100], [50, 25, 6, 100, 12, 3], [50, 25, 6, 100, 3, 12], [50, 25, 6, 12, 100, 3], [50, 25, 6, 12, 3, 100], [50, 25, 6, 3, 100, 12], [50, 25, 6, 3, 12, 100], [50, 25, 3, 100, 12, 6], [50, 25, 3, 100, 6, 12], [50, 25, 3, 12, 100, 6], [50, 25, 3, 12, 6, 100], [50, 25, 3, 6, 100, 12], [50, 25, 3, 6, 12, 100], 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[3, 100, 25, 12, 50, 6], [3, 100, 25, 12, 6, 50], [3, 100, 25, 6, 50, 12], [3, 100, 25, 6, 12, 50], [3, 100, 12, 50, 25, 6], [3, 100, 12, 50, 6, 25], [3, 100, 12, 25, 50, 6], [3, 100, 12, 25, 6, 50], [3, 100, 12, 6, 50, 25], [3, 100, 12, 6, 25, 50], [3, 100, 6, 50, 25, 12], [3, 100, 6, 50, 12, 25], [3, 100, 6, 25, 50, 12], [3, 100, 6, 25, 12, 50], [3, 100, 6, 12, 50, 25], [3, 100, 6, 12, 25, 50], [3, 50, 100, 25, 12, 6], [3, 50, 100, 25, 6, 12], [3, 50, 100, 12, 25, 6], [3, 50, 100, 12, 6, 25], [3, 50, 100, 6, 25, 12], [3, 50, 100, 6, 12, 25], [3, 50, 25, 100, 12, 6], [3, 50, 25, 100, 6, 12], [3, 50, 25, 12, 100, 6], [3, 50, 25, 12, 6, 100], [3, 50, 25, 6, 100, 12], [3, 50, 25, 6, 12, 100], [3, 50, 12, 100, 25, 6], [3, 50, 12, 100, 6, 25], [3, 50, 12, 25, 100, 6], [3, 50, 12, 25, 6, 100], [3, 50, 12, 6, 100, 25], [3, 50, 12, 6, 25, 100], [3, 50, 6, 100, 25, 12], [3, 50, 6, 100, 12, 25], [3, 50, 6, 25, 100, 12], [3, 50, 6, 25, 12, 100], [3, 50, 6, 12, 100, 25], [3, 50, 6, 12, 25, 100], [3, 25, 100, 50, 12, 6], [3, 25, 100, 50, 6, 12], [3, 25, 100, 12, 50, 6], [3, 25, 100, 12, 6, 50], [3, 25, 100, 6, 50, 12], [3, 25, 100, 6, 12, 50], [3, 25, 50, 100, 12, 6], [3, 25, 50, 100, 6, 12], [3, 25, 50, 12, 100, 6], [3, 25, 50, 12, 6, 100], [3, 25, 50, 6, 100, 12], [3, 25, 50, 6, 12, 100], [3, 25, 12, 100, 50, 6], [3, 25, 12, 100, 6, 50], [3, 25, 12, 50, 100, 6], [3, 25, 12, 50, 6, 100], [3, 25, 12, 6, 100, 50], [3, 25, 12, 6, 50, 100], [3, 25, 6, 100, 50, 12], [3, 25, 6, 100, 12, 50], [3, 25, 6, 50, 100, 12], [3, 25, 6, 50, 12, 100], [3, 25, 6, 12, 100, 50], [3, 25, 6, 12, 50, 100], [3, 12, 100, 50, 25, 6], [3, 12, 100, 50, 6, 25], [3, 12, 100, 25, 50, 6], [3, 12, 100, 25, 6, 50], [3, 12, 100, 6, 50, 25], [3, 12, 100, 6, 25, 50], [3, 12, 50, 100, 25, 6], [3, 12, 50, 100, 6, 25], [3, 12, 50, 25, 100, 6], [3, 12, 50, 25, 6, 100], [3, 12, 50, 6, 100, 25], [3, 12, 50, 6, 25, 100], [3, 12, 25, 100, 50, 6], [3, 12, 25, 100, 6, 50], [3, 12, 25, 50, 100, 6], [3, 12, 25, 50, 6, 100], [3, 12, 25, 6, 100, 50], [3, 12, 25, 6, 50, 100], [3, 12, 6, 100, 50, 25], [3, 12, 6, 100, 25, 50], [3, 12, 6, 50, 100, 25], [3, 12, 6, 50, 25, 100], [3, 12, 6, 25, 100, 50], [3, 12, 6, 25, 50, 100], [3, 6, 100, 50, 25, 12], [3, 6, 100, 50, 12, 25], [3, 6, 100, 25, 50, 12], [3, 6, 100, 25, 12, 50], [3, 6, 100, 12, 50, 25], [3, 6, 100, 12, 25, 50], [3, 6, 50, 100, 25, 12], [3, 6, 50, 100, 12, 25], [3, 6, 50, 25, 100, 12], [3, 6, 50, 25, 12, 100], [3, 6, 50, 12, 100, 25], [3, 6, 50, 12, 25, 100], [3, 6, 25, 100, 50, 12], [3, 6, 25, 100, 12, 50], [3, 6, 25, 50, 100, 12], [3, 6, 25, 50, 12, 100], [3, 6, 25, 12, 100, 50], [3, 6, 25, 12, 50, 100], [3, 6, 12, 100, 50, 25], [3, 6, 12, 100, 25, 50], [3, 6, 12, 50, 100, 25], [3, 6, 12, 50, 25, 100], [3, 6, 12, 25, 100, 50], [3, 6, 12, 25, 50, 100]]\n assert candidate(nums = [1, 3, 5, 7, 9]) == [[1, 3, 5, 7, 9], [1, 3, 5, 9, 7], [1, 3, 7, 5, 9], [1, 3, 7, 9, 5], [1, 3, 9, 5, 7], [1, 3, 9, 7, 5], [1, 5, 3, 7, 9], [1, 5, 3, 9, 7], [1, 5, 7, 3, 9], [1, 5, 7, 9, 3], [1, 5, 9, 3, 7], [1, 5, 9, 7, 3], [1, 7, 3, 5, 9], [1, 7, 3, 9, 5], [1, 7, 5, 3, 9], [1, 7, 5, 9, 3], [1, 7, 9, 3, 5], [1, 7, 9, 5, 3], [1, 9, 3, 5, 7], [1, 9, 3, 7, 5], [1, 9, 5, 3, 7], [1, 9, 5, 7, 3], [1, 9, 7, 3, 5], [1, 9, 7, 5, 3], [3, 1, 5, 7, 9], [3, 1, 5, 9, 7], [3, 1, 7, 5, 9], [3, 1, 7, 9, 5], [3, 1, 9, 5, 7], [3, 1, 9, 7, 5], [3, 5, 1, 7, 9], [3, 5, 1, 9, 7], [3, 5, 7, 1, 9], [3, 5, 7, 9, 1], [3, 5, 9, 1, 7], [3, 5, 9, 7, 1], [3, 7, 1, 5, 9], [3, 7, 1, 9, 5], [3, 7, 5, 1, 9], [3, 7, 5, 9, 1], [3, 7, 9, 1, 5], [3, 7, 9, 5, 1], [3, 9, 1, 5, 7], [3, 9, 1, 7, 5], [3, 9, 5, 1, 7], [3, 9, 5, 7, 1], [3, 9, 7, 1, 5], [3, 9, 7, 5, 1], [5, 1, 3, 7, 9], [5, 1, 3, 9, 7], [5, 1, 7, 3, 9], [5, 1, 7, 9, 3], [5, 1, 9, 3, 7], [5, 1, 9, 7, 3], [5, 3, 1, 7, 9], [5, 3, 1, 9, 7], [5, 3, 7, 1, 9], [5, 3, 7, 9, 1], [5, 3, 9, 1, 7], [5, 3, 9, 7, 1], [5, 7, 1, 3, 9], [5, 7, 1, 9, 3], [5, 7, 3, 1, 9], [5, 7, 3, 9, 1], [5, 7, 9, 1, 3], [5, 7, 9, 3, 1], [5, 9, 1, 3, 7], [5, 9, 1, 7, 3], [5, 9, 3, 1, 7], [5, 9, 3, 7, 1], [5, 9, 7, 1, 3], [5, 9, 7, 3, 1], [7, 1, 3, 5, 9], [7, 1, 3, 9, 5], [7, 1, 5, 3, 9], [7, 1, 5, 9, 3], [7, 1, 9, 3, 5], [7, 1, 9, 5, 3], [7, 3, 1, 5, 9], [7, 3, 1, 9, 5], [7, 3, 5, 1, 9], [7, 3, 5, 9, 1], [7, 3, 9, 1, 5], [7, 3, 9, 5, 1], [7, 5, 1, 3, 9], [7, 5, 1, 9, 3], [7, 5, 3, 1, 9], [7, 5, 3, 9, 1], [7, 5, 9, 1, 3], [7, 5, 9, 3, 1], [7, 9, 1, 3, 5], [7, 9, 1, 5, 3], [7, 9, 3, 1, 5], [7, 9, 3, 5, 1], [7, 9, 5, 1, 3], [7, 9, 5, 3, 1], [9, 1, 3, 5, 7], [9, 1, 3, 7, 5], [9, 1, 5, 3, 7], [9, 1, 5, 7, 3], [9, 1, 7, 3, 5], [9, 1, 7, 5, 3], [9, 3, 1, 5, 7], [9, 3, 1, 7, 5], [9, 3, 5, 1, 7], [9, 3, 5, 7, 1], [9, 3, 7, 1, 5], [9, 3, 7, 5, 1], [9, 5, 1, 3, 7], [9, 5, 1, 7, 3], [9, 5, 3, 1, 7], [9, 5, 3, 7, 1], [9, 5, 7, 1, 3], [9, 5, 7, 3, 1], [9, 7, 1, 3, 5], [9, 7, 1, 5, 3], [9, 7, 3, 1, 5], [9, 7, 3, 5, 1], [9, 7, 5, 1, 3], [9, 7, 5, 3, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6]) == [[1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 6, 5], [1, 2, 3, 5, 4, 6], [1, 2, 3, 5, 6, 4], [1, 2, 3, 6, 4, 5], [1, 2, 3, 6, 5, 4], [1, 2, 4, 3, 5, 6], [1, 2, 4, 3, 6, 5], [1, 2, 4, 5, 3, 6], [1, 2, 4, 5, 6, 3], [1, 2, 4, 6, 3, 5], [1, 2, 4, 6, 5, 3], [1, 2, 5, 3, 4, 6], [1, 2, 5, 3, 6, 4], [1, 2, 5, 4, 3, 6], [1, 2, 5, 4, 6, 3], [1, 2, 5, 6, 3, 4], [1, 2, 5, 6, 4, 3], [1, 2, 6, 3, 4, 5], [1, 2, 6, 3, 5, 4], [1, 2, 6, 4, 3, 5], [1, 2, 6, 4, 5, 3], [1, 2, 6, 5, 3, 4], [1, 2, 6, 5, 4, 3], [1, 3, 2, 4, 5, 6], [1, 3, 2, 4, 6, 5], [1, 3, 2, 5, 4, 6], [1, 3, 2, 5, 6, 4], [1, 3, 2, 6, 4, 5], [1, 3, 2, 6, 5, 4], [1, 3, 4, 2, 5, 6], [1, 3, 4, 2, 6, 5], [1, 3, 4, 5, 2, 6], [1, 3, 4, 5, 6, 2], [1, 3, 4, 6, 2, 5], [1, 3, 4, 6, 5, 2], [1, 3, 5, 2, 4, 6], [1, 3, 5, 2, 6, 4], [1, 3, 5, 4, 2, 6], [1, 3, 5, 4, 6, 2], [1, 3, 5, 6, 2, 4], [1, 3, 5, 6, 4, 2], [1, 3, 6, 2, 4, 5], [1, 3, 6, 2, 5, 4], [1, 3, 6, 4, 2, 5], [1, 3, 6, 4, 5, 2], [1, 3, 6, 5, 2, 4], [1, 3, 6, 5, 4, 2], [1, 4, 2, 3, 5, 6], [1, 4, 2, 3, 6, 5], [1, 4, 2, 5, 3, 6], [1, 4, 2, 5, 6, 3], [1, 4, 2, 6, 3, 5], [1, 4, 2, 6, 5, 3], [1, 4, 3, 2, 5, 6], [1, 4, 3, 2, 6, 5], [1, 4, 3, 5, 2, 6], [1, 4, 3, 5, 6, 2], [1, 4, 3, 6, 2, 5], [1, 4, 3, 6, 5, 2], [1, 4, 5, 2, 3, 6], [1, 4, 5, 2, 6, 3], [1, 4, 5, 3, 2, 6], [1, 4, 5, 3, 6, 2], [1, 4, 5, 6, 2, 3], [1, 4, 5, 6, 3, 2], [1, 4, 6, 2, 3, 5], [1, 4, 6, 2, 5, 3], [1, 4, 6, 3, 2, 5], [1, 4, 6, 3, 5, 2], [1, 4, 6, 5, 2, 3], [1, 4, 6, 5, 3, 2], [1, 5, 2, 3, 4, 6], [1, 5, 2, 3, 6, 4], [1, 5, 2, 4, 3, 6], [1, 5, 2, 4, 6, 3], [1, 5, 2, 6, 3, 4], [1, 5, 2, 6, 4, 3], [1, 5, 3, 2, 4, 6], [1, 5, 3, 2, 6, 4], [1, 5, 3, 4, 2, 6], [1, 5, 3, 4, 6, 2], [1, 5, 3, 6, 2, 4], [1, 5, 3, 6, 4, 2], [1, 5, 4, 2, 3, 6], [1, 5, 4, 2, 6, 3], [1, 5, 4, 3, 2, 6], [1, 5, 4, 3, 6, 2], [1, 5, 4, 6, 2, 3], [1, 5, 4, 6, 3, 2], [1, 5, 6, 2, 3, 4], [1, 5, 6, 2, 4, 3], [1, 5, 6, 3, 2, 4], [1, 5, 6, 3, 4, 2], [1, 5, 6, 4, 2, 3], [1, 5, 6, 4, 3, 2], [1, 6, 2, 3, 4, 5], [1, 6, 2, 3, 5, 4], [1, 6, 2, 4, 3, 5], [1, 6, 2, 4, 5, 3], [1, 6, 2, 5, 3, 4], [1, 6, 2, 5, 4, 3], [1, 6, 3, 2, 4, 5], [1, 6, 3, 2, 5, 4], [1, 6, 3, 4, 2, 5], [1, 6, 3, 4, 5, 2], [1, 6, 3, 5, 2, 4], [1, 6, 3, 5, 4, 2], [1, 6, 4, 2, 3, 5], [1, 6, 4, 2, 5, 3], [1, 6, 4, 3, 2, 5], [1, 6, 4, 3, 5, 2], [1, 6, 4, 5, 2, 3], [1, 6, 4, 5, 3, 2], [1, 6, 5, 2, 3, 4], [1, 6, 5, 2, 4, 3], [1, 6, 5, 3, 2, 4], [1, 6, 5, 3, 4, 2], [1, 6, 5, 4, 2, 3], [1, 6, 5, 4, 3, 2], [2, 1, 3, 4, 5, 6], [2, 1, 3, 4, 6, 5], [2, 1, 3, 5, 4, 6], [2, 1, 3, 5, 6, 4], [2, 1, 3, 6, 4, 5], [2, 1, 3, 6, 5, 4], [2, 1, 4, 3, 5, 6], [2, 1, 4, 3, 6, 5], [2, 1, 4, 5, 3, 6], [2, 1, 4, 5, 6, 3], [2, 1, 4, 6, 3, 5], [2, 1, 4, 6, 5, 3], [2, 1, 5, 3, 4, 6], [2, 1, 5, 3, 6, 4], [2, 1, 5, 4, 3, 6], [2, 1, 5, 4, 6, 3], [2, 1, 5, 6, 3, 4], [2, 1, 5, 6, 4, 3], [2, 1, 6, 3, 4, 5], [2, 1, 6, 3, 5, 4], [2, 1, 6, 4, 3, 5], [2, 1, 6, 4, 5, 3], [2, 1, 6, 5, 3, 4], [2, 1, 6, 5, 4, 3], [2, 3, 1, 4, 5, 6], [2, 3, 1, 4, 6, 5], [2, 3, 1, 5, 4, 6], [2, 3, 1, 5, 6, 4], [2, 3, 1, 6, 4, 5], [2, 3, 1, 6, 5, 4], [2, 3, 4, 1, 5, 6], [2, 3, 4, 1, 6, 5], [2, 3, 4, 5, 1, 6], [2, 3, 4, 5, 6, 1], [2, 3, 4, 6, 1, 5], [2, 3, 4, 6, 5, 1], [2, 3, 5, 1, 4, 6], [2, 3, 5, 1, 6, 4], [2, 3, 5, 4, 1, 6], [2, 3, 5, 4, 6, 1], [2, 3, 5, 6, 1, 4], [2, 3, 5, 6, 4, 1], [2, 3, 6, 1, 4, 5], [2, 3, 6, 1, 5, 4], [2, 3, 6, 4, 1, 5], [2, 3, 6, 4, 5, 1], [2, 3, 6, 5, 1, 4], [2, 3, 6, 5, 4, 1], [2, 4, 1, 3, 5, 6], [2, 4, 1, 3, 6, 5], [2, 4, 1, 5, 3, 6], [2, 4, 1, 5, 6, 3], [2, 4, 1, 6, 3, 5], [2, 4, 1, 6, 5, 3], [2, 4, 3, 1, 5, 6], [2, 4, 3, 1, 6, 5], [2, 4, 3, 5, 1, 6], [2, 4, 3, 5, 6, 1], [2, 4, 3, 6, 1, 5], [2, 4, 3, 6, 5, 1], [2, 4, 5, 1, 3, 6], [2, 4, 5, 1, 6, 3], [2, 4, 5, 3, 1, 6], [2, 4, 5, 3, 6, 1], [2, 4, 5, 6, 1, 3], [2, 4, 5, 6, 3, 1], [2, 4, 6, 1, 3, 5], [2, 4, 6, 1, 5, 3], [2, 4, 6, 3, 1, 5], [2, 4, 6, 3, 5, 1], [2, 4, 6, 5, 1, 3], [2, 4, 6, 5, 3, 1], [2, 5, 1, 3, 4, 6], [2, 5, 1, 3, 6, 4], [2, 5, 1, 4, 3, 6], [2, 5, 1, 4, 6, 3], [2, 5, 1, 6, 3, 4], [2, 5, 1, 6, 4, 3], [2, 5, 3, 1, 4, 6], [2, 5, 3, 1, 6, 4], [2, 5, 3, 4, 1, 6], [2, 5, 3, 4, 6, 1], [2, 5, 3, 6, 1, 4], [2, 5, 3, 6, 4, 1], [2, 5, 4, 1, 3, 6], [2, 5, 4, 1, 6, 3], [2, 5, 4, 3, 1, 6], [2, 5, 4, 3, 6, 1], [2, 5, 4, 6, 1, 3], [2, 5, 4, 6, 3, 1], [2, 5, 6, 1, 3, 4], [2, 5, 6, 1, 4, 3], [2, 5, 6, 3, 1, 4], [2, 5, 6, 3, 4, 1], [2, 5, 6, 4, 1, 3], [2, 5, 6, 4, 3, 1], [2, 6, 1, 3, 4, 5], [2, 6, 1, 3, 5, 4], [2, 6, 1, 4, 3, 5], [2, 6, 1, 4, 5, 3], [2, 6, 1, 5, 3, 4], [2, 6, 1, 5, 4, 3], [2, 6, 3, 1, 4, 5], [2, 6, 3, 1, 5, 4], [2, 6, 3, 4, 1, 5], [2, 6, 3, 4, 5, 1], [2, 6, 3, 5, 1, 4], [2, 6, 3, 5, 4, 1], [2, 6, 4, 1, 3, 5], [2, 6, 4, 1, 5, 3], [2, 6, 4, 3, 1, 5], [2, 6, 4, 3, 5, 1], [2, 6, 4, 5, 1, 3], [2, 6, 4, 5, 3, 1], [2, 6, 5, 1, 3, 4], [2, 6, 5, 1, 4, 3], [2, 6, 5, 3, 1, 4], [2, 6, 5, 3, 4, 1], [2, 6, 5, 4, 1, 3], [2, 6, 5, 4, 3, 1], [3, 1, 2, 4, 5, 6], [3, 1, 2, 4, 6, 5], [3, 1, 2, 5, 4, 6], [3, 1, 2, 5, 6, 4], [3, 1, 2, 6, 4, 5], [3, 1, 2, 6, 5, 4], [3, 1, 4, 2, 5, 6], [3, 1, 4, 2, 6, 5], [3, 1, 4, 5, 2, 6], [3, 1, 4, 5, 6, 2], [3, 1, 4, 6, 2, 5], [3, 1, 4, 6, 5, 2], [3, 1, 5, 2, 4, 6], [3, 1, 5, 2, 6, 4], [3, 1, 5, 4, 2, 6], [3, 1, 5, 4, 6, 2], [3, 1, 5, 6, 2, 4], [3, 1, 5, 6, 4, 2], [3, 1, 6, 2, 4, 5], [3, 1, 6, 2, 5, 4], [3, 1, 6, 4, 2, 5], [3, 1, 6, 4, 5, 2], [3, 1, 6, 5, 2, 4], [3, 1, 6, 5, 4, 2], [3, 2, 1, 4, 5, 6], [3, 2, 1, 4, 6, 5], [3, 2, 1, 5, 4, 6], [3, 2, 1, 5, 6, 4], [3, 2, 1, 6, 4, 5], [3, 2, 1, 6, 5, 4], [3, 2, 4, 1, 5, 6], [3, 2, 4, 1, 6, 5], [3, 2, 4, 5, 1, 6], [3, 2, 4, 5, 6, 1], [3, 2, 4, 6, 1, 5], [3, 2, 4, 6, 5, 1], [3, 2, 5, 1, 4, 6], [3, 2, 5, 1, 6, 4], [3, 2, 5, 4, 1, 6], [3, 2, 5, 4, 6, 1], [3, 2, 5, 6, 1, 4], [3, 2, 5, 6, 4, 1], [3, 2, 6, 1, 4, 5], [3, 2, 6, 1, 5, 4], [3, 2, 6, 4, 1, 5], [3, 2, 6, 4, 5, 1], [3, 2, 6, 5, 1, 4], [3, 2, 6, 5, 4, 1], [3, 4, 1, 2, 5, 6], [3, 4, 1, 2, 6, 5], [3, 4, 1, 5, 2, 6], [3, 4, 1, 5, 6, 2], [3, 4, 1, 6, 2, 5], [3, 4, 1, 6, 5, 2], [3, 4, 2, 1, 5, 6], [3, 4, 2, 1, 6, 5], [3, 4, 2, 5, 1, 6], [3, 4, 2, 5, 6, 1], [3, 4, 2, 6, 1, 5], [3, 4, 2, 6, 5, 1], [3, 4, 5, 1, 2, 6], [3, 4, 5, 1, 6, 2], [3, 4, 5, 2, 1, 6], [3, 4, 5, 2, 6, 1], [3, 4, 5, 6, 1, 2], [3, 4, 5, 6, 2, 1], [3, 4, 6, 1, 2, 5], [3, 4, 6, 1, 5, 2], [3, 4, 6, 2, 1, 5], [3, 4, 6, 2, 5, 1], [3, 4, 6, 5, 1, 2], [3, 4, 6, 5, 2, 1], [3, 5, 1, 2, 4, 6], [3, 5, 1, 2, 6, 4], [3, 5, 1, 4, 2, 6], [3, 5, 1, 4, 6, 2], [3, 5, 1, 6, 2, 4], [3, 5, 1, 6, 4, 2], [3, 5, 2, 1, 4, 6], [3, 5, 2, 1, 6, 4], [3, 5, 2, 4, 1, 6], [3, 5, 2, 4, 6, 1], [3, 5, 2, 6, 1, 4], [3, 5, 2, 6, 4, 1], [3, 5, 4, 1, 2, 6], [3, 5, 4, 1, 6, 2], [3, 5, 4, 2, 1, 6], [3, 5, 4, 2, 6, 1], [3, 5, 4, 6, 1, 2], [3, 5, 4, 6, 2, 1], [3, 5, 6, 1, 2, 4], [3, 5, 6, 1, 4, 2], [3, 5, 6, 2, 1, 4], [3, 5, 6, 2, 4, 1], [3, 5, 6, 4, 1, 2], [3, 5, 6, 4, 2, 1], [3, 6, 1, 2, 4, 5], [3, 6, 1, 2, 5, 4], [3, 6, 1, 4, 2, 5], [3, 6, 1, 4, 5, 2], [3, 6, 1, 5, 2, 4], [3, 6, 1, 5, 4, 2], [3, 6, 2, 1, 4, 5], [3, 6, 2, 1, 5, 4], [3, 6, 2, 4, 1, 5], [3, 6, 2, 4, 5, 1], [3, 6, 2, 5, 1, 4], [3, 6, 2, 5, 4, 1], [3, 6, 4, 1, 2, 5], [3, 6, 4, 1, 5, 2], [3, 6, 4, 2, 1, 5], [3, 6, 4, 2, 5, 1], [3, 6, 4, 5, 1, 2], [3, 6, 4, 5, 2, 1], [3, 6, 5, 1, 2, 4], [3, 6, 5, 1, 4, 2], [3, 6, 5, 2, 1, 4], [3, 6, 5, 2, 4, 1], [3, 6, 5, 4, 1, 2], [3, 6, 5, 4, 2, 1], [4, 1, 2, 3, 5, 6], [4, 1, 2, 3, 6, 5], [4, 1, 2, 5, 3, 6], [4, 1, 2, 5, 6, 3], [4, 1, 2, 6, 3, 5], [4, 1, 2, 6, 5, 3], [4, 1, 3, 2, 5, 6], [4, 1, 3, 2, 6, 5], [4, 1, 3, 5, 2, 6], [4, 1, 3, 5, 6, 2], [4, 1, 3, 6, 2, 5], [4, 1, 3, 6, 5, 2], [4, 1, 5, 2, 3, 6], [4, 1, 5, 2, 6, 3], [4, 1, 5, 3, 2, 6], [4, 1, 5, 3, 6, 2], [4, 1, 5, 6, 2, 3], [4, 1, 5, 6, 3, 2], [4, 1, 6, 2, 3, 5], [4, 1, 6, 2, 5, 3], [4, 1, 6, 3, 2, 5], [4, 1, 6, 3, 5, 2], [4, 1, 6, 5, 2, 3], [4, 1, 6, 5, 3, 2], [4, 2, 1, 3, 5, 6], [4, 2, 1, 3, 6, 5], [4, 2, 1, 5, 3, 6], [4, 2, 1, 5, 6, 3], [4, 2, 1, 6, 3, 5], [4, 2, 1, 6, 5, 3], [4, 2, 3, 1, 5, 6], [4, 2, 3, 1, 6, 5], [4, 2, 3, 5, 1, 6], [4, 2, 3, 5, 6, 1], [4, 2, 3, 6, 1, 5], [4, 2, 3, 6, 5, 1], [4, 2, 5, 1, 3, 6], [4, 2, 5, 1, 6, 3], [4, 2, 5, 3, 1, 6], [4, 2, 5, 3, 6, 1], [4, 2, 5, 6, 1, 3], [4, 2, 5, 6, 3, 1], [4, 2, 6, 1, 3, 5], [4, 2, 6, 1, 5, 3], [4, 2, 6, 3, 1, 5], [4, 2, 6, 3, 5, 1], [4, 2, 6, 5, 1, 3], [4, 2, 6, 5, 3, 1], [4, 3, 1, 2, 5, 6], [4, 3, 1, 2, 6, 5], [4, 3, 1, 5, 2, 6], [4, 3, 1, 5, 6, 2], [4, 3, 1, 6, 2, 5], [4, 3, 1, 6, 5, 2], [4, 3, 2, 1, 5, 6], [4, 3, 2, 1, 6, 5], [4, 3, 2, 5, 1, 6], [4, 3, 2, 5, 6, 1], [4, 3, 2, 6, 1, 5], [4, 3, 2, 6, 5, 1], [4, 3, 5, 1, 2, 6], [4, 3, 5, 1, 6, 2], [4, 3, 5, 2, 1, 6], [4, 3, 5, 2, 6, 1], [4, 3, 5, 6, 1, 2], [4, 3, 5, 6, 2, 1], [4, 3, 6, 1, 2, 5], [4, 3, 6, 1, 5, 2], [4, 3, 6, 2, 1, 5], [4, 3, 6, 2, 5, 1], [4, 3, 6, 5, 1, 2], [4, 3, 6, 5, 2, 1], [4, 5, 1, 2, 3, 6], [4, 5, 1, 2, 6, 3], [4, 5, 1, 3, 2, 6], [4, 5, 1, 3, 6, 2], [4, 5, 1, 6, 2, 3], [4, 5, 1, 6, 3, 2], [4, 5, 2, 1, 3, 6], [4, 5, 2, 1, 6, 3], [4, 5, 2, 3, 1, 6], [4, 5, 2, 3, 6, 1], [4, 5, 2, 6, 1, 3], [4, 5, 2, 6, 3, 1], [4, 5, 3, 1, 2, 6], [4, 5, 3, 1, 6, 2], [4, 5, 3, 2, 1, 6], [4, 5, 3, 2, 6, 1], [4, 5, 3, 6, 1, 2], [4, 5, 3, 6, 2, 1], [4, 5, 6, 1, 2, 3], [4, 5, 6, 1, 3, 2], [4, 5, 6, 2, 1, 3], [4, 5, 6, 2, 3, 1], [4, 5, 6, 3, 1, 2], [4, 5, 6, 3, 2, 1], [4, 6, 1, 2, 3, 5], [4, 6, 1, 2, 5, 3], [4, 6, 1, 3, 2, 5], [4, 6, 1, 3, 5, 2], [4, 6, 1, 5, 2, 3], [4, 6, 1, 5, 3, 2], [4, 6, 2, 1, 3, 5], [4, 6, 2, 1, 5, 3], [4, 6, 2, 3, 1, 5], [4, 6, 2, 3, 5, 1], [4, 6, 2, 5, 1, 3], [4, 6, 2, 5, 3, 1], [4, 6, 3, 1, 2, 5], [4, 6, 3, 1, 5, 2], [4, 6, 3, 2, 1, 5], [4, 6, 3, 2, 5, 1], [4, 6, 3, 5, 1, 2], [4, 6, 3, 5, 2, 1], [4, 6, 5, 1, 2, 3], [4, 6, 5, 1, 3, 2], [4, 6, 5, 2, 1, 3], [4, 6, 5, 2, 3, 1], [4, 6, 5, 3, 1, 2], [4, 6, 5, 3, 2, 1], [5, 1, 2, 3, 4, 6], [5, 1, 2, 3, 6, 4], [5, 1, 2, 4, 3, 6], [5, 1, 2, 4, 6, 3], [5, 1, 2, 6, 3, 4], [5, 1, 2, 6, 4, 3], [5, 1, 3, 2, 4, 6], [5, 1, 3, 2, 6, 4], [5, 1, 3, 4, 2, 6], [5, 1, 3, 4, 6, 2], [5, 1, 3, 6, 2, 4], [5, 1, 3, 6, 4, 2], [5, 1, 4, 2, 3, 6], [5, 1, 4, 2, 6, 3], [5, 1, 4, 3, 2, 6], [5, 1, 4, 3, 6, 2], [5, 1, 4, 6, 2, 3], [5, 1, 4, 6, 3, 2], [5, 1, 6, 2, 3, 4], [5, 1, 6, 2, 4, 3], [5, 1, 6, 3, 2, 4], [5, 1, 6, 3, 4, 2], [5, 1, 6, 4, 2, 3], [5, 1, 6, 4, 3, 2], [5, 2, 1, 3, 4, 6], [5, 2, 1, 3, 6, 4], [5, 2, 1, 4, 3, 6], [5, 2, 1, 4, 6, 3], [5, 2, 1, 6, 3, 4], [5, 2, 1, 6, 4, 3], [5, 2, 3, 1, 4, 6], [5, 2, 3, 1, 6, 4], [5, 2, 3, 4, 1, 6], [5, 2, 3, 4, 6, 1], [5, 2, 3, 6, 1, 4], [5, 2, 3, 6, 4, 1], [5, 2, 4, 1, 3, 6], [5, 2, 4, 1, 6, 3], [5, 2, 4, 3, 1, 6], [5, 2, 4, 3, 6, 1], [5, 2, 4, 6, 1, 3], [5, 2, 4, 6, 3, 1], [5, 2, 6, 1, 3, 4], [5, 2, 6, 1, 4, 3], [5, 2, 6, 3, 1, 4], [5, 2, 6, 3, 4, 1], [5, 2, 6, 4, 1, 3], [5, 2, 6, 4, 3, 1], [5, 3, 1, 2, 4, 6], [5, 3, 1, 2, 6, 4], [5, 3, 1, 4, 2, 6], [5, 3, 1, 4, 6, 2], [5, 3, 1, 6, 2, 4], [5, 3, 1, 6, 4, 2], [5, 3, 2, 1, 4, 6], [5, 3, 2, 1, 6, 4], [5, 3, 2, 4, 1, 6], [5, 3, 2, 4, 6, 1], [5, 3, 2, 6, 1, 4], [5, 3, 2, 6, 4, 1], [5, 3, 4, 1, 2, 6], [5, 3, 4, 1, 6, 2], [5, 3, 4, 2, 1, 6], [5, 3, 4, 2, 6, 1], [5, 3, 4, 6, 1, 2], [5, 3, 4, 6, 2, 1], [5, 3, 6, 1, 2, 4], [5, 3, 6, 1, 4, 2], [5, 3, 6, 2, 1, 4], [5, 3, 6, 2, 4, 1], [5, 3, 6, 4, 1, 2], [5, 3, 6, 4, 2, 1], [5, 4, 1, 2, 3, 6], [5, 4, 1, 2, 6, 3], [5, 4, 1, 3, 2, 6], [5, 4, 1, 3, 6, 2], [5, 4, 1, 6, 2, 3], [5, 4, 1, 6, 3, 2], [5, 4, 2, 1, 3, 6], [5, 4, 2, 1, 6, 3], [5, 4, 2, 3, 1, 6], [5, 4, 2, 3, 6, 1], [5, 4, 2, 6, 1, 3], [5, 4, 2, 6, 3, 1], [5, 4, 3, 1, 2, 6], [5, 4, 3, 1, 6, 2], [5, 4, 3, 2, 1, 6], [5, 4, 3, 2, 6, 1], [5, 4, 3, 6, 1, 2], [5, 4, 3, 6, 2, 1], [5, 4, 6, 1, 2, 3], [5, 4, 6, 1, 3, 2], [5, 4, 6, 2, 1, 3], [5, 4, 6, 2, 3, 1], [5, 4, 6, 3, 1, 2], [5, 4, 6, 3, 2, 1], [5, 6, 1, 2, 3, 4], [5, 6, 1, 2, 4, 3], [5, 6, 1, 3, 2, 4], [5, 6, 1, 3, 4, 2], [5, 6, 1, 4, 2, 3], [5, 6, 1, 4, 3, 2], [5, 6, 2, 1, 3, 4], [5, 6, 2, 1, 4, 3], [5, 6, 2, 3, 1, 4], [5, 6, 2, 3, 4, 1], [5, 6, 2, 4, 1, 3], [5, 6, 2, 4, 3, 1], [5, 6, 3, 1, 2, 4], [5, 6, 3, 1, 4, 2], [5, 6, 3, 2, 1, 4], [5, 6, 3, 2, 4, 1], [5, 6, 3, 4, 1, 2], [5, 6, 3, 4, 2, 1], [5, 6, 4, 1, 2, 3], [5, 6, 4, 1, 3, 2], [5, 6, 4, 2, 1, 3], [5, 6, 4, 2, 3, 1], [5, 6, 4, 3, 1, 2], [5, 6, 4, 3, 2, 1], [6, 1, 2, 3, 4, 5], [6, 1, 2, 3, 5, 4], [6, 1, 2, 4, 3, 5], [6, 1, 2, 4, 5, 3], [6, 1, 2, 5, 3, 4], [6, 1, 2, 5, 4, 3], [6, 1, 3, 2, 4, 5], [6, 1, 3, 2, 5, 4], [6, 1, 3, 4, 2, 5], [6, 1, 3, 4, 5, 2], [6, 1, 3, 5, 2, 4], [6, 1, 3, 5, 4, 2], [6, 1, 4, 2, 3, 5], [6, 1, 4, 2, 5, 3], [6, 1, 4, 3, 2, 5], [6, 1, 4, 3, 5, 2], [6, 1, 4, 5, 2, 3], [6, 1, 4, 5, 3, 2], [6, 1, 5, 2, 3, 4], [6, 1, 5, 2, 4, 3], [6, 1, 5, 3, 2, 4], [6, 1, 5, 3, 4, 2], [6, 1, 5, 4, 2, 3], [6, 1, 5, 4, 3, 2], [6, 2, 1, 3, 4, 5], [6, 2, 1, 3, 5, 4], [6, 2, 1, 4, 3, 5], [6, 2, 1, 4, 5, 3], [6, 2, 1, 5, 3, 4], [6, 2, 1, 5, 4, 3], [6, 2, 3, 1, 4, 5], [6, 2, 3, 1, 5, 4], [6, 2, 3, 4, 1, 5], [6, 2, 3, 4, 5, 1], [6, 2, 3, 5, 1, 4], [6, 2, 3, 5, 4, 1], [6, 2, 4, 1, 3, 5], [6, 2, 4, 1, 5, 3], [6, 2, 4, 3, 1, 5], [6, 2, 4, 3, 5, 1], [6, 2, 4, 5, 1, 3], [6, 2, 4, 5, 3, 1], [6, 2, 5, 1, 3, 4], [6, 2, 5, 1, 4, 3], [6, 2, 5, 3, 1, 4], [6, 2, 5, 3, 4, 1], [6, 2, 5, 4, 1, 3], [6, 2, 5, 4, 3, 1], [6, 3, 1, 2, 4, 5], [6, 3, 1, 2, 5, 4], [6, 3, 1, 4, 2, 5], [6, 3, 1, 4, 5, 2], [6, 3, 1, 5, 2, 4], [6, 3, 1, 5, 4, 2], [6, 3, 2, 1, 4, 5], [6, 3, 2, 1, 5, 4], [6, 3, 2, 4, 1, 5], [6, 3, 2, 4, 5, 1], [6, 3, 2, 5, 1, 4], [6, 3, 2, 5, 4, 1], [6, 3, 4, 1, 2, 5], [6, 3, 4, 1, 5, 2], [6, 3, 4, 2, 1, 5], [6, 3, 4, 2, 5, 1], [6, 3, 4, 5, 1, 2], [6, 3, 4, 5, 2, 1], [6, 3, 5, 1, 2, 4], [6, 3, 5, 1, 4, 2], [6, 3, 5, 2, 1, 4], [6, 3, 5, 2, 4, 1], [6, 3, 5, 4, 1, 2], [6, 3, 5, 4, 2, 1], [6, 4, 1, 2, 3, 5], [6, 4, 1, 2, 5, 3], [6, 4, 1, 3, 2, 5], [6, 4, 1, 3, 5, 2], [6, 4, 1, 5, 2, 3], [6, 4, 1, 5, 3, 2], [6, 4, 2, 1, 3, 5], [6, 4, 2, 1, 5, 3], [6, 4, 2, 3, 1, 5], [6, 4, 2, 3, 5, 1], [6, 4, 2, 5, 1, 3], [6, 4, 2, 5, 3, 1], [6, 4, 3, 1, 2, 5], [6, 4, 3, 1, 5, 2], [6, 4, 3, 2, 1, 5], [6, 4, 3, 2, 5, 1], [6, 4, 3, 5, 1, 2], [6, 4, 3, 5, 2, 1], [6, 4, 5, 1, 2, 3], [6, 4, 5, 1, 3, 2], [6, 4, 5, 2, 1, 3], [6, 4, 5, 2, 3, 1], [6, 4, 5, 3, 1, 2], [6, 4, 5, 3, 2, 1], [6, 5, 1, 2, 3, 4], [6, 5, 1, 2, 4, 3], [6, 5, 1, 3, 2, 4], [6, 5, 1, 3, 4, 2], [6, 5, 1, 4, 2, 3], [6, 5, 1, 4, 3, 2], [6, 5, 2, 1, 3, 4], [6, 5, 2, 1, 4, 3], [6, 5, 2, 3, 1, 4], [6, 5, 2, 3, 4, 1], [6, 5, 2, 4, 1, 3], [6, 5, 2, 4, 3, 1], [6, 5, 3, 1, 2, 4], [6, 5, 3, 1, 4, 2], [6, 5, 3, 2, 1, 4], [6, 5, 3, 2, 4, 1], [6, 5, 3, 4, 1, 2], [6, 5, 3, 4, 2, 1], [6, 5, 4, 1, 2, 3], [6, 5, 4, 1, 3, 2], [6, 5, 4, 2, 1, 3], [6, 5, 4, 2, 3, 1], [6, 5, 4, 3, 1, 2], [6, 5, 4, 3, 2, 1]]\n assert candidate(nums = [-10, 0, 10, 5, -5]) == [[-10, 0, 10, 5, -5], [-10, 0, 10, -5, 5], [-10, 0, 5, 10, -5], [-10, 0, 5, -5, 10], [-10, 0, -5, 10, 5], [-10, 0, -5, 5, 10], [-10, 10, 0, 5, -5], [-10, 10, 0, -5, 5], [-10, 10, 5, 0, -5], [-10, 10, 5, -5, 0], [-10, 10, -5, 0, 5], [-10, 10, -5, 5, 0], [-10, 5, 0, 10, -5], [-10, 5, 0, -5, 10], [-10, 5, 10, 0, -5], [-10, 5, 10, -5, 0], [-10, 5, -5, 0, 10], [-10, 5, -5, 10, 0], [-10, -5, 0, 10, 5], [-10, -5, 0, 5, 10], [-10, -5, 10, 0, 5], [-10, -5, 10, 5, 0], [-10, -5, 5, 0, 10], [-10, -5, 5, 10, 0], [0, -10, 10, 5, -5], [0, -10, 10, -5, 5], [0, -10, 5, 10, -5], [0, -10, 5, -5, 10], [0, -10, -5, 10, 5], [0, -10, -5, 5, 10], [0, 10, -10, 5, -5], [0, 10, -10, -5, 5], [0, 10, 5, -10, -5], [0, 10, 5, -5, -10], [0, 10, -5, -10, 5], [0, 10, -5, 5, -10], [0, 5, -10, 10, -5], [0, 5, -10, -5, 10], [0, 5, 10, -10, -5], [0, 5, 10, -5, -10], [0, 5, -5, -10, 10], [0, 5, -5, 10, -10], [0, -5, -10, 10, 5], [0, -5, -10, 5, 10], [0, -5, 10, -10, 5], [0, -5, 10, 5, -10], [0, -5, 5, -10, 10], [0, -5, 5, 10, -10], [10, -10, 0, 5, -5], [10, -10, 0, -5, 5], [10, -10, 5, 0, -5], [10, -10, 5, -5, 0], [10, -10, -5, 0, 5], [10, -10, -5, 5, 0], [10, 0, -10, 5, -5], [10, 0, -10, -5, 5], [10, 0, 5, -10, -5], [10, 0, 5, -5, -10], [10, 0, -5, -10, 5], [10, 0, -5, 5, -10], [10, 5, -10, 0, -5], [10, 5, -10, -5, 0], [10, 5, 0, -10, -5], [10, 5, 0, -5, -10], [10, 5, -5, -10, 0], [10, 5, -5, 0, -10], [10, -5, -10, 0, 5], [10, -5, -10, 5, 0], [10, -5, 0, -10, 5], [10, -5, 0, 5, -10], [10, -5, 5, -10, 0], [10, -5, 5, 0, -10], [5, -10, 0, 10, -5], [5, -10, 0, -5, 10], [5, -10, 10, 0, -5], [5, -10, 10, -5, 0], [5, -10, -5, 0, 10], [5, -10, -5, 10, 0], [5, 0, -10, 10, -5], [5, 0, -10, -5, 10], [5, 0, 10, -10, -5], [5, 0, 10, -5, -10], [5, 0, -5, -10, 10], [5, 0, -5, 10, -10], [5, 10, -10, 0, -5], [5, 10, -10, -5, 0], [5, 10, 0, -10, -5], [5, 10, 0, -5, -10], [5, 10, -5, -10, 0], [5, 10, -5, 0, -10], [5, -5, -10, 0, 10], [5, -5, -10, 10, 0], [5, -5, 0, -10, 10], [5, -5, 0, 10, -10], [5, -5, 10, -10, 0], [5, -5, 10, 0, -10], [-5, -10, 0, 10, 5], [-5, -10, 0, 5, 10], [-5, -10, 10, 0, 5], [-5, -10, 10, 5, 0], [-5, -10, 5, 0, 10], [-5, -10, 5, 10, 0], [-5, 0, -10, 10, 5], [-5, 0, -10, 5, 10], [-5, 0, 10, -10, 5], [-5, 0, 10, 5, -10], [-5, 0, 5, -10, 10], [-5, 0, 5, 10, -10], [-5, 10, -10, 0, 5], [-5, 10, -10, 5, 0], [-5, 10, 0, -10, 5], [-5, 10, 0, 5, -10], [-5, 10, 5, -10, 0], [-5, 10, 5, 0, -10], [-5, 5, -10, 0, 10], [-5, 5, -10, 10, 0], [-5, 5, 0, -10, 10], [-5, 5, 0, 10, -10], [-5, 5, 10, -10, 0], [-5, 5, 10, 0, -10]]\n assert candidate(nums = [-1, 1, -2, 2, -3, 3]) == [[-1, 1, -2, 2, -3, 3], [-1, 1, -2, 2, 3, -3], [-1, 1, -2, -3, 2, 3], [-1, 1, -2, -3, 3, 2], [-1, 1, -2, 3, 2, -3], [-1, 1, -2, 3, -3, 2], [-1, 1, 2, -2, -3, 3], [-1, 1, 2, -2, 3, -3], [-1, 1, 2, -3, -2, 3], [-1, 1, 2, -3, 3, -2], [-1, 1, 2, 3, -2, -3], [-1, 1, 2, 3, -3, -2], [-1, 1, -3, -2, 2, 3], [-1, 1, -3, -2, 3, 2], [-1, 1, -3, 2, -2, 3], [-1, 1, -3, 2, 3, -2], [-1, 1, -3, 3, -2, 2], [-1, 1, -3, 3, 2, -2], [-1, 1, 3, -2, 2, -3], [-1, 1, 3, -2, -3, 2], [-1, 1, 3, 2, -2, -3], [-1, 1, 3, 2, -3, -2], [-1, 1, 3, -3, -2, 2], [-1, 1, 3, -3, 2, -2], [-1, -2, 1, 2, -3, 3], [-1, -2, 1, 2, 3, -3], [-1, -2, 1, -3, 2, 3], [-1, -2, 1, -3, 3, 2], [-1, -2, 1, 3, 2, -3], [-1, -2, 1, 3, -3, 2], [-1, -2, 2, 1, -3, 3], [-1, -2, 2, 1, 3, -3], [-1, -2, 2, -3, 1, 3], [-1, -2, 2, -3, 3, 1], [-1, -2, 2, 3, 1, -3], [-1, -2, 2, 3, -3, 1], [-1, -2, -3, 1, 2, 3], [-1, -2, -3, 1, 3, 2], [-1, -2, -3, 2, 1, 3], [-1, -2, -3, 2, 3, 1], [-1, -2, -3, 3, 1, 2], [-1, -2, -3, 3, 2, 1], [-1, -2, 3, 1, 2, -3], [-1, -2, 3, 1, -3, 2], [-1, -2, 3, 2, 1, -3], [-1, -2, 3, 2, -3, 1], [-1, -2, 3, -3, 1, 2], [-1, -2, 3, -3, 2, 1], [-1, 2, 1, -2, -3, 3], [-1, 2, 1, -2, 3, -3], [-1, 2, 1, -3, -2, 3], [-1, 2, 1, -3, 3, -2], [-1, 2, 1, 3, -2, -3], [-1, 2, 1, 3, -3, -2], [-1, 2, -2, 1, -3, 3], [-1, 2, -2, 1, 3, -3], [-1, 2, -2, -3, 1, 3], [-1, 2, -2, -3, 3, 1], [-1, 2, -2, 3, 1, -3], [-1, 2, -2, 3, -3, 1], [-1, 2, -3, 1, -2, 3], [-1, 2, -3, 1, 3, -2], [-1, 2, -3, -2, 1, 3], [-1, 2, -3, -2, 3, 1], [-1, 2, -3, 3, 1, -2], [-1, 2, -3, 3, -2, 1], [-1, 2, 3, 1, -2, -3], [-1, 2, 3, 1, -3, -2], [-1, 2, 3, -2, 1, -3], [-1, 2, 3, -2, -3, 1], [-1, 2, 3, -3, 1, -2], [-1, 2, 3, -3, -2, 1], [-1, -3, 1, -2, 2, 3], [-1, -3, 1, -2, 3, 2], [-1, -3, 1, 2, -2, 3], [-1, -3, 1, 2, 3, -2], [-1, -3, 1, 3, -2, 2], [-1, -3, 1, 3, 2, -2], [-1, -3, -2, 1, 2, 3], [-1, -3, -2, 1, 3, 2], [-1, -3, -2, 2, 1, 3], [-1, -3, -2, 2, 3, 1], [-1, -3, -2, 3, 1, 2], [-1, -3, -2, 3, 2, 1], [-1, -3, 2, 1, -2, 3], [-1, -3, 2, 1, 3, -2], [-1, -3, 2, -2, 1, 3], [-1, -3, 2, -2, 3, 1], [-1, -3, 2, 3, 1, -2], [-1, -3, 2, 3, -2, 1], [-1, -3, 3, 1, -2, 2], [-1, -3, 3, 1, 2, -2], [-1, -3, 3, -2, 1, 2], [-1, -3, 3, -2, 2, 1], [-1, -3, 3, 2, 1, -2], [-1, -3, 3, 2, -2, 1], [-1, 3, 1, -2, 2, -3], [-1, 3, 1, -2, -3, 2], [-1, 3, 1, 2, -2, -3], [-1, 3, 1, 2, -3, -2], [-1, 3, 1, -3, -2, 2], [-1, 3, 1, -3, 2, -2], [-1, 3, -2, 1, 2, -3], [-1, 3, -2, 1, -3, 2], [-1, 3, -2, 2, 1, -3], [-1, 3, -2, 2, -3, 1], [-1, 3, -2, -3, 1, 2], [-1, 3, -2, -3, 2, 1], [-1, 3, 2, 1, -2, -3], [-1, 3, 2, 1, -3, -2], [-1, 3, 2, -2, 1, -3], [-1, 3, 2, -2, -3, 1], [-1, 3, 2, -3, 1, -2], [-1, 3, 2, -3, -2, 1], [-1, 3, -3, 1, -2, 2], [-1, 3, -3, 1, 2, -2], [-1, 3, -3, -2, 1, 2], [-1, 3, -3, -2, 2, 1], [-1, 3, -3, 2, 1, -2], [-1, 3, -3, 2, -2, 1], [1, -1, -2, 2, -3, 3], [1, -1, -2, 2, 3, -3], [1, -1, -2, -3, 2, 3], [1, -1, -2, -3, 3, 2], [1, -1, -2, 3, 2, -3], [1, -1, -2, 3, -3, 2], [1, -1, 2, -2, -3, 3], [1, -1, 2, -2, 3, -3], [1, -1, 2, -3, -2, 3], [1, -1, 2, -3, 3, -2], [1, -1, 2, 3, -2, -3], [1, -1, 2, 3, -3, -2], [1, -1, -3, -2, 2, 3], [1, -1, -3, -2, 3, 2], [1, -1, -3, 2, -2, 3], [1, -1, -3, 2, 3, -2], [1, -1, -3, 3, -2, 2], [1, -1, -3, 3, 2, -2], [1, -1, 3, -2, 2, -3], [1, -1, 3, -2, -3, 2], [1, -1, 3, 2, -2, -3], [1, -1, 3, 2, -3, -2], [1, -1, 3, -3, -2, 2], [1, -1, 3, -3, 2, -2], [1, -2, -1, 2, -3, 3], [1, -2, -1, 2, 3, -3], [1, -2, -1, -3, 2, 3], [1, -2, -1, -3, 3, 2], [1, -2, -1, 3, 2, -3], [1, -2, -1, 3, -3, 2], [1, -2, 2, -1, -3, 3], [1, -2, 2, -1, 3, -3], [1, -2, 2, -3, -1, 3], [1, -2, 2, -3, 3, -1], [1, -2, 2, 3, -1, -3], [1, -2, 2, 3, -3, -1], [1, -2, -3, -1, 2, 3], [1, -2, -3, -1, 3, 2], [1, -2, -3, 2, -1, 3], [1, -2, -3, 2, 3, -1], [1, -2, -3, 3, -1, 2], [1, -2, -3, 3, 2, -1], [1, -2, 3, -1, 2, -3], [1, -2, 3, -1, -3, 2], [1, -2, 3, 2, -1, -3], [1, -2, 3, 2, -3, -1], [1, -2, 3, -3, -1, 2], [1, -2, 3, -3, 2, -1], [1, 2, -1, -2, -3, 3], [1, 2, -1, -2, 3, -3], [1, 2, -1, -3, -2, 3], [1, 2, -1, -3, 3, -2], [1, 2, -1, 3, -2, -3], [1, 2, -1, 3, -3, -2], [1, 2, -2, -1, -3, 3], [1, 2, -2, -1, 3, -3], [1, 2, -2, -3, -1, 3], [1, 2, -2, -3, 3, -1], [1, 2, -2, 3, -1, -3], [1, 2, -2, 3, -3, -1], [1, 2, -3, -1, -2, 3], [1, 2, -3, -1, 3, -2], [1, 2, -3, -2, -1, 3], [1, 2, -3, -2, 3, -1], [1, 2, -3, 3, -1, -2], [1, 2, -3, 3, -2, -1], [1, 2, 3, -1, -2, -3], [1, 2, 3, -1, -3, -2], [1, 2, 3, -2, -1, -3], [1, 2, 3, -2, -3, -1], [1, 2, 3, -3, -1, -2], [1, 2, 3, -3, -2, -1], [1, -3, -1, -2, 2, 3], [1, -3, -1, -2, 3, 2], [1, -3, -1, 2, -2, 3], [1, -3, -1, 2, 3, -2], [1, -3, -1, 3, -2, 2], [1, -3, -1, 3, 2, -2], [1, -3, -2, -1, 2, 3], [1, -3, -2, -1, 3, 2], [1, -3, -2, 2, -1, 3], [1, -3, -2, 2, 3, -1], [1, -3, -2, 3, -1, 2], [1, -3, -2, 3, 2, -1], [1, -3, 2, -1, -2, 3], [1, -3, 2, -1, 3, -2], [1, -3, 2, -2, -1, 3], [1, -3, 2, -2, 3, -1], [1, -3, 2, 3, -1, -2], [1, -3, 2, 3, -2, -1], [1, -3, 3, -1, -2, 2], [1, -3, 3, -1, 2, -2], [1, -3, 3, -2, -1, 2], [1, -3, 3, -2, 2, -1], [1, -3, 3, 2, -1, -2], [1, -3, 3, 2, -2, -1], [1, 3, -1, -2, 2, -3], [1, 3, -1, -2, -3, 2], [1, 3, -1, 2, -2, -3], [1, 3, -1, 2, -3, -2], [1, 3, -1, -3, -2, 2], [1, 3, -1, -3, 2, -2], [1, 3, -2, -1, 2, -3], [1, 3, -2, -1, -3, 2], [1, 3, -2, 2, -1, -3], [1, 3, -2, 2, -3, -1], [1, 3, -2, -3, -1, 2], [1, 3, -2, -3, 2, -1], [1, 3, 2, -1, -2, -3], [1, 3, 2, -1, -3, -2], [1, 3, 2, -2, -1, -3], [1, 3, 2, -2, -3, -1], [1, 3, 2, -3, -1, -2], [1, 3, 2, -3, -2, -1], [1, 3, -3, -1, -2, 2], [1, 3, -3, -1, 2, -2], [1, 3, -3, -2, -1, 2], [1, 3, -3, -2, 2, -1], [1, 3, -3, 2, -1, -2], [1, 3, -3, 2, -2, -1], [-2, -1, 1, 2, -3, 3], [-2, -1, 1, 2, 3, -3], [-2, -1, 1, -3, 2, 3], [-2, -1, 1, -3, 3, 2], [-2, -1, 1, 3, 2, -3], [-2, -1, 1, 3, -3, 2], [-2, -1, 2, 1, -3, 3], [-2, -1, 2, 1, 3, -3], [-2, -1, 2, -3, 1, 3], [-2, -1, 2, -3, 3, 1], [-2, -1, 2, 3, 1, -3], [-2, -1, 2, 3, -3, 1], [-2, -1, -3, 1, 2, 3], [-2, -1, -3, 1, 3, 2], [-2, -1, -3, 2, 1, 3], [-2, -1, -3, 2, 3, 1], [-2, -1, -3, 3, 1, 2], [-2, -1, -3, 3, 2, 1], [-2, -1, 3, 1, 2, -3], [-2, -1, 3, 1, -3, 2], [-2, -1, 3, 2, 1, -3], [-2, -1, 3, 2, -3, 1], [-2, -1, 3, -3, 1, 2], [-2, -1, 3, -3, 2, 1], [-2, 1, -1, 2, -3, 3], [-2, 1, -1, 2, 3, -3], [-2, 1, -1, -3, 2, 3], [-2, 1, -1, -3, 3, 2], [-2, 1, -1, 3, 2, -3], [-2, 1, -1, 3, -3, 2], [-2, 1, 2, -1, -3, 3], [-2, 1, 2, -1, 3, -3], [-2, 1, 2, -3, -1, 3], [-2, 1, 2, -3, 3, -1], [-2, 1, 2, 3, -1, -3], [-2, 1, 2, 3, -3, -1], [-2, 1, -3, -1, 2, 3], [-2, 1, -3, -1, 3, 2], [-2, 1, -3, 2, -1, 3], [-2, 1, -3, 2, 3, -1], [-2, 1, -3, 3, -1, 2], [-2, 1, -3, 3, 2, -1], [-2, 1, 3, -1, 2, -3], [-2, 1, 3, -1, -3, 2], [-2, 1, 3, 2, -1, -3], [-2, 1, 3, 2, -3, -1], [-2, 1, 3, -3, -1, 2], [-2, 1, 3, -3, 2, -1], [-2, 2, -1, 1, -3, 3], [-2, 2, -1, 1, 3, -3], [-2, 2, -1, -3, 1, 3], [-2, 2, -1, -3, 3, 1], [-2, 2, -1, 3, 1, -3], [-2, 2, -1, 3, -3, 1], [-2, 2, 1, -1, -3, 3], [-2, 2, 1, -1, 3, -3], [-2, 2, 1, -3, -1, 3], [-2, 2, 1, -3, 3, -1], [-2, 2, 1, 3, -1, -3], [-2, 2, 1, 3, -3, -1], [-2, 2, -3, -1, 1, 3], [-2, 2, -3, -1, 3, 1], [-2, 2, -3, 1, -1, 3], [-2, 2, -3, 1, 3, -1], [-2, 2, -3, 3, -1, 1], [-2, 2, -3, 3, 1, -1], [-2, 2, 3, -1, 1, -3], [-2, 2, 3, -1, -3, 1], [-2, 2, 3, 1, -1, -3], [-2, 2, 3, 1, -3, -1], [-2, 2, 3, -3, -1, 1], [-2, 2, 3, -3, 1, -1], [-2, -3, -1, 1, 2, 3], [-2, -3, -1, 1, 3, 2], [-2, -3, -1, 2, 1, 3], [-2, -3, -1, 2, 3, 1], [-2, -3, -1, 3, 1, 2], [-2, -3, -1, 3, 2, 1], [-2, -3, 1, -1, 2, 3], [-2, -3, 1, -1, 3, 2], [-2, -3, 1, 2, -1, 3], [-2, -3, 1, 2, 3, -1], [-2, -3, 1, 3, -1, 2], [-2, -3, 1, 3, 2, -1], [-2, -3, 2, -1, 1, 3], [-2, -3, 2, -1, 3, 1], [-2, -3, 2, 1, -1, 3], [-2, -3, 2, 1, 3, -1], [-2, -3, 2, 3, -1, 1], [-2, -3, 2, 3, 1, -1], [-2, -3, 3, -1, 1, 2], [-2, -3, 3, -1, 2, 1], [-2, -3, 3, 1, -1, 2], [-2, -3, 3, 1, 2, -1], [-2, -3, 3, 2, -1, 1], [-2, -3, 3, 2, 1, -1], [-2, 3, -1, 1, 2, -3], [-2, 3, -1, 1, -3, 2], [-2, 3, -1, 2, 1, -3], [-2, 3, -1, 2, -3, 1], [-2, 3, -1, -3, 1, 2], [-2, 3, -1, -3, 2, 1], [-2, 3, 1, -1, 2, -3], [-2, 3, 1, -1, -3, 2], [-2, 3, 1, 2, -1, -3], [-2, 3, 1, 2, -3, -1], [-2, 3, 1, -3, -1, 2], [-2, 3, 1, -3, 2, -1], [-2, 3, 2, -1, 1, -3], [-2, 3, 2, -1, -3, 1], [-2, 3, 2, 1, -1, -3], [-2, 3, 2, 1, -3, -1], [-2, 3, 2, -3, -1, 1], [-2, 3, 2, -3, 1, -1], [-2, 3, -3, -1, 1, 2], [-2, 3, -3, -1, 2, 1], [-2, 3, -3, 1, -1, 2], [-2, 3, -3, 1, 2, -1], [-2, 3, -3, 2, -1, 1], [-2, 3, -3, 2, 1, -1], [2, -1, 1, -2, -3, 3], [2, -1, 1, -2, 3, -3], [2, -1, 1, -3, -2, 3], [2, -1, 1, -3, 3, -2], [2, -1, 1, 3, -2, -3], [2, -1, 1, 3, -3, -2], [2, -1, -2, 1, -3, 3], [2, -1, -2, 1, 3, -3], [2, -1, -2, -3, 1, 3], [2, -1, -2, -3, 3, 1], [2, -1, -2, 3, 1, -3], [2, -1, -2, 3, -3, 1], [2, -1, -3, 1, -2, 3], [2, -1, -3, 1, 3, -2], [2, -1, -3, -2, 1, 3], [2, -1, -3, -2, 3, 1], [2, -1, -3, 3, 1, -2], [2, -1, -3, 3, -2, 1], [2, -1, 3, 1, -2, -3], [2, -1, 3, 1, -3, -2], [2, -1, 3, -2, 1, -3], [2, -1, 3, -2, -3, 1], [2, -1, 3, -3, 1, -2], [2, -1, 3, -3, -2, 1], [2, 1, -1, -2, -3, 3], [2, 1, -1, -2, 3, -3], [2, 1, -1, -3, -2, 3], [2, 1, -1, -3, 3, -2], [2, 1, -1, 3, -2, -3], [2, 1, -1, 3, -3, -2], [2, 1, -2, -1, -3, 3], [2, 1, -2, -1, 3, -3], [2, 1, -2, -3, -1, 3], [2, 1, -2, -3, 3, -1], [2, 1, -2, 3, -1, -3], [2, 1, -2, 3, -3, -1], [2, 1, -3, -1, -2, 3], [2, 1, -3, -1, 3, -2], [2, 1, -3, -2, -1, 3], [2, 1, -3, -2, 3, -1], [2, 1, -3, 3, -1, -2], [2, 1, -3, 3, -2, -1], [2, 1, 3, -1, -2, -3], [2, 1, 3, -1, -3, -2], [2, 1, 3, -2, -1, -3], [2, 1, 3, -2, -3, -1], [2, 1, 3, -3, -1, -2], [2, 1, 3, -3, -2, -1], [2, -2, -1, 1, -3, 3], [2, -2, -1, 1, 3, -3], [2, -2, -1, -3, 1, 3], [2, -2, -1, -3, 3, 1], [2, -2, -1, 3, 1, -3], [2, -2, -1, 3, -3, 1], [2, -2, 1, -1, -3, 3], [2, -2, 1, -1, 3, -3], [2, -2, 1, -3, -1, 3], [2, -2, 1, -3, 3, -1], [2, -2, 1, 3, -1, -3], [2, -2, 1, 3, -3, -1], [2, -2, -3, -1, 1, 3], [2, -2, -3, -1, 3, 1], [2, -2, -3, 1, -1, 3], [2, -2, -3, 1, 3, -1], [2, -2, -3, 3, -1, 1], [2, -2, -3, 3, 1, -1], [2, -2, 3, -1, 1, -3], [2, -2, 3, -1, -3, 1], [2, -2, 3, 1, -1, -3], [2, -2, 3, 1, -3, -1], [2, -2, 3, -3, -1, 1], [2, -2, 3, -3, 1, -1], [2, -3, -1, 1, -2, 3], [2, -3, -1, 1, 3, -2], [2, -3, -1, -2, 1, 3], [2, -3, -1, -2, 3, 1], [2, -3, -1, 3, 1, -2], [2, -3, -1, 3, -2, 1], [2, -3, 1, -1, -2, 3], [2, -3, 1, -1, 3, -2], [2, -3, 1, -2, -1, 3], [2, -3, 1, -2, 3, -1], [2, -3, 1, 3, -1, -2], [2, -3, 1, 3, -2, -1], [2, -3, -2, -1, 1, 3], [2, -3, -2, -1, 3, 1], [2, -3, -2, 1, -1, 3], [2, -3, -2, 1, 3, -1], [2, -3, -2, 3, -1, 1], [2, -3, -2, 3, 1, -1], [2, -3, 3, -1, 1, -2], [2, -3, 3, -1, -2, 1], [2, -3, 3, 1, -1, -2], [2, -3, 3, 1, -2, -1], [2, -3, 3, -2, -1, 1], [2, -3, 3, -2, 1, -1], [2, 3, -1, 1, -2, -3], [2, 3, -1, 1, -3, -2], [2, 3, -1, -2, 1, -3], [2, 3, -1, -2, -3, 1], [2, 3, -1, -3, 1, -2], [2, 3, -1, -3, -2, 1], [2, 3, 1, -1, -2, -3], [2, 3, 1, -1, -3, -2], [2, 3, 1, -2, -1, -3], [2, 3, 1, -2, -3, -1], [2, 3, 1, -3, -1, -2], [2, 3, 1, -3, -2, -1], [2, 3, -2, -1, 1, -3], [2, 3, -2, -1, -3, 1], [2, 3, -2, 1, -1, -3], [2, 3, -2, 1, -3, -1], [2, 3, -2, -3, -1, 1], [2, 3, -2, -3, 1, -1], [2, 3, -3, -1, 1, -2], [2, 3, -3, -1, -2, 1], [2, 3, -3, 1, -1, -2], [2, 3, -3, 1, -2, -1], [2, 3, -3, -2, -1, 1], [2, 3, -3, -2, 1, -1], [-3, -1, 1, -2, 2, 3], [-3, -1, 1, -2, 3, 2], [-3, -1, 1, 2, -2, 3], [-3, -1, 1, 2, 3, -2], [-3, -1, 1, 3, -2, 2], [-3, -1, 1, 3, 2, -2], [-3, -1, -2, 1, 2, 3], [-3, -1, -2, 1, 3, 2], [-3, -1, -2, 2, 1, 3], [-3, -1, -2, 2, 3, 1], [-3, -1, -2, 3, 1, 2], [-3, -1, -2, 3, 2, 1], [-3, -1, 2, 1, -2, 3], [-3, -1, 2, 1, 3, -2], [-3, -1, 2, -2, 1, 3], [-3, -1, 2, -2, 3, 1], [-3, -1, 2, 3, 1, -2], [-3, -1, 2, 3, -2, 1], [-3, -1, 3, 1, -2, 2], [-3, -1, 3, 1, 2, -2], [-3, -1, 3, -2, 1, 2], [-3, -1, 3, -2, 2, 1], [-3, -1, 3, 2, 1, -2], [-3, -1, 3, 2, -2, 1], [-3, 1, -1, -2, 2, 3], [-3, 1, -1, -2, 3, 2], [-3, 1, -1, 2, -2, 3], [-3, 1, -1, 2, 3, -2], [-3, 1, -1, 3, -2, 2], [-3, 1, -1, 3, 2, -2], [-3, 1, -2, -1, 2, 3], [-3, 1, -2, -1, 3, 2], [-3, 1, -2, 2, -1, 3], [-3, 1, -2, 2, 3, -1], [-3, 1, -2, 3, -1, 2], [-3, 1, -2, 3, 2, -1], [-3, 1, 2, -1, -2, 3], [-3, 1, 2, -1, 3, -2], [-3, 1, 2, -2, -1, 3], [-3, 1, 2, -2, 3, -1], [-3, 1, 2, 3, -1, -2], [-3, 1, 2, 3, -2, -1], [-3, 1, 3, -1, -2, 2], [-3, 1, 3, -1, 2, -2], [-3, 1, 3, -2, -1, 2], [-3, 1, 3, -2, 2, -1], [-3, 1, 3, 2, -1, -2], [-3, 1, 3, 2, -2, -1], [-3, -2, -1, 1, 2, 3], [-3, -2, -1, 1, 3, 2], [-3, -2, -1, 2, 1, 3], [-3, -2, -1, 2, 3, 1], [-3, -2, -1, 3, 1, 2], [-3, -2, -1, 3, 2, 1], [-3, -2, 1, -1, 2, 3], [-3, -2, 1, -1, 3, 2], [-3, -2, 1, 2, -1, 3], [-3, -2, 1, 2, 3, -1], [-3, -2, 1, 3, -1, 2], [-3, -2, 1, 3, 2, -1], [-3, -2, 2, -1, 1, 3], [-3, -2, 2, -1, 3, 1], [-3, -2, 2, 1, -1, 3], [-3, -2, 2, 1, 3, -1], [-3, -2, 2, 3, -1, 1], [-3, -2, 2, 3, 1, -1], [-3, -2, 3, -1, 1, 2], [-3, -2, 3, -1, 2, 1], [-3, -2, 3, 1, -1, 2], [-3, -2, 3, 1, 2, -1], [-3, -2, 3, 2, -1, 1], [-3, -2, 3, 2, 1, -1], [-3, 2, -1, 1, -2, 3], [-3, 2, -1, 1, 3, -2], [-3, 2, -1, -2, 1, 3], [-3, 2, -1, -2, 3, 1], [-3, 2, -1, 3, 1, -2], [-3, 2, -1, 3, -2, 1], [-3, 2, 1, -1, -2, 3], [-3, 2, 1, -1, 3, -2], [-3, 2, 1, -2, -1, 3], [-3, 2, 1, -2, 3, -1], [-3, 2, 1, 3, -1, -2], [-3, 2, 1, 3, -2, -1], [-3, 2, -2, -1, 1, 3], [-3, 2, -2, -1, 3, 1], [-3, 2, -2, 1, -1, 3], [-3, 2, -2, 1, 3, -1], [-3, 2, -2, 3, -1, 1], [-3, 2, -2, 3, 1, -1], [-3, 2, 3, -1, 1, -2], [-3, 2, 3, -1, -2, 1], [-3, 2, 3, 1, -1, -2], [-3, 2, 3, 1, -2, -1], [-3, 2, 3, -2, -1, 1], [-3, 2, 3, -2, 1, -1], [-3, 3, -1, 1, -2, 2], [-3, 3, -1, 1, 2, -2], [-3, 3, -1, -2, 1, 2], [-3, 3, -1, -2, 2, 1], [-3, 3, -1, 2, 1, -2], [-3, 3, -1, 2, -2, 1], [-3, 3, 1, -1, -2, 2], [-3, 3, 1, -1, 2, -2], [-3, 3, 1, -2, -1, 2], [-3, 3, 1, -2, 2, -1], [-3, 3, 1, 2, -1, -2], [-3, 3, 1, 2, -2, -1], [-3, 3, -2, -1, 1, 2], [-3, 3, -2, -1, 2, 1], [-3, 3, -2, 1, -1, 2], [-3, 3, -2, 1, 2, -1], [-3, 3, -2, 2, -1, 1], [-3, 3, -2, 2, 1, -1], [-3, 3, 2, -1, 1, -2], [-3, 3, 2, -1, -2, 1], [-3, 3, 2, 1, -1, -2], [-3, 3, 2, 1, -2, -1], [-3, 3, 2, -2, -1, 1], [-3, 3, 2, -2, 1, -1], [3, -1, 1, -2, 2, -3], [3, -1, 1, -2, -3, 2], [3, -1, 1, 2, -2, -3], [3, -1, 1, 2, -3, -2], [3, -1, 1, -3, -2, 2], [3, -1, 1, -3, 2, -2], [3, -1, -2, 1, 2, -3], [3, -1, -2, 1, -3, 2], [3, -1, -2, 2, 1, -3], [3, -1, -2, 2, -3, 1], [3, -1, -2, -3, 1, 2], [3, -1, -2, -3, 2, 1], [3, -1, 2, 1, -2, -3], [3, -1, 2, 1, -3, -2], [3, -1, 2, -2, 1, -3], [3, -1, 2, -2, -3, 1], [3, -1, 2, -3, 1, -2], [3, -1, 2, -3, -2, 1], [3, -1, -3, 1, -2, 2], [3, -1, -3, 1, 2, -2], [3, -1, -3, -2, 1, 2], [3, -1, -3, -2, 2, 1], [3, -1, -3, 2, 1, -2], [3, -1, -3, 2, -2, 1], [3, 1, -1, -2, 2, -3], [3, 1, -1, -2, -3, 2], [3, 1, -1, 2, -2, -3], [3, 1, -1, 2, -3, -2], [3, 1, -1, -3, -2, 2], [3, 1, -1, -3, 2, -2], [3, 1, -2, -1, 2, -3], [3, 1, -2, -1, -3, 2], [3, 1, -2, 2, -1, -3], [3, 1, -2, 2, -3, -1], [3, 1, -2, -3, -1, 2], [3, 1, -2, -3, 2, -1], [3, 1, 2, -1, -2, -3], [3, 1, 2, -1, -3, -2], [3, 1, 2, -2, -1, -3], [3, 1, 2, -2, -3, -1], [3, 1, 2, -3, -1, -2], [3, 1, 2, -3, -2, -1], [3, 1, -3, -1, -2, 2], [3, 1, -3, -1, 2, -2], [3, 1, -3, -2, -1, 2], [3, 1, -3, -2, 2, -1], [3, 1, -3, 2, -1, -2], [3, 1, -3, 2, -2, -1], [3, -2, -1, 1, 2, -3], [3, -2, -1, 1, -3, 2], [3, -2, -1, 2, 1, -3], [3, -2, -1, 2, -3, 1], [3, -2, -1, -3, 1, 2], [3, -2, -1, -3, 2, 1], [3, -2, 1, -1, 2, -3], [3, -2, 1, -1, -3, 2], [3, -2, 1, 2, -1, -3], [3, -2, 1, 2, -3, -1], [3, -2, 1, -3, -1, 2], [3, -2, 1, -3, 2, -1], [3, -2, 2, -1, 1, -3], [3, -2, 2, -1, -3, 1], [3, -2, 2, 1, -1, -3], [3, -2, 2, 1, -3, -1], [3, -2, 2, -3, -1, 1], [3, -2, 2, -3, 1, -1], [3, -2, -3, -1, 1, 2], [3, -2, -3, -1, 2, 1], [3, -2, -3, 1, -1, 2], [3, -2, -3, 1, 2, -1], [3, -2, -3, 2, -1, 1], [3, -2, -3, 2, 1, -1], [3, 2, -1, 1, -2, -3], [3, 2, -1, 1, -3, -2], [3, 2, -1, -2, 1, -3], [3, 2, -1, -2, -3, 1], [3, 2, -1, -3, 1, -2], [3, 2, -1, -3, -2, 1], [3, 2, 1, -1, -2, -3], [3, 2, 1, -1, -3, -2], [3, 2, 1, -2, -1, -3], [3, 2, 1, -2, -3, -1], [3, 2, 1, -3, -1, -2], [3, 2, 1, -3, -2, -1], [3, 2, -2, -1, 1, -3], [3, 2, -2, -1, -3, 1], [3, 2, -2, 1, -1, -3], [3, 2, -2, 1, -3, -1], [3, 2, -2, -3, -1, 1], [3, 2, -2, -3, 1, -1], [3, 2, -3, -1, 1, -2], [3, 2, -3, -1, -2, 1], [3, 2, -3, 1, -1, -2], [3, 2, -3, 1, -2, -1], [3, 2, -3, -2, -1, 1], [3, 2, -3, -2, 1, -1], [3, -3, -1, 1, -2, 2], [3, -3, -1, 1, 2, -2], [3, -3, -1, -2, 1, 2], [3, -3, -1, -2, 2, 1], [3, -3, -1, 2, 1, -2], [3, -3, -1, 2, -2, 1], [3, -3, 1, -1, -2, 2], [3, -3, 1, -1, 2, -2], [3, -3, 1, -2, -1, 2], [3, -3, 1, -2, 2, -1], [3, -3, 1, 2, -1, -2], [3, -3, 1, 2, -2, -1], [3, -3, -2, -1, 1, 2], [3, -3, -2, -1, 2, 1], [3, -3, -2, 1, -1, 2], [3, -3, -2, 1, 2, -1], [3, -3, -2, 2, -1, 1], [3, -3, -2, 2, 1, -1], [3, -3, 2, -1, 1, -2], [3, -3, 2, -1, -2, 1], [3, -3, 2, 1, -1, -2], [3, -3, 2, 1, -2, -1], [3, -3, 2, -2, -1, 1], [3, -3, 2, -2, 1, -1]]\n assert candidate(nums = [100, 200, 300, 400, 500, 600]) == [[100, 200, 300, 400, 500, 600], [100, 200, 300, 400, 600, 500], [100, 200, 300, 500, 400, 600], [100, 200, 300, 500, 600, 400], [100, 200, 300, 600, 400, 500], [100, 200, 300, 600, 500, 400], [100, 200, 400, 300, 500, 600], [100, 200, 400, 300, 600, 500], [100, 200, 400, 500, 300, 600], [100, 200, 400, 500, 600, 300], [100, 200, 400, 600, 300, 500], [100, 200, 400, 600, 500, 300], [100, 200, 500, 300, 400, 600], [100, 200, 500, 300, 600, 400], [100, 200, 500, 400, 300, 600], [100, 200, 500, 400, 600, 300], [100, 200, 500, 600, 300, 400], [100, 200, 500, 600, 400, 300], [100, 200, 600, 300, 400, 500], [100, 200, 600, 300, 500, 400], [100, 200, 600, 400, 300, 500], [100, 200, 600, 400, 500, 300], [100, 200, 600, 500, 300, 400], [100, 200, 600, 500, 400, 300], [100, 300, 200, 400, 500, 600], [100, 300, 200, 400, 600, 500], [100, 300, 200, 500, 400, 600], [100, 300, 200, 500, 600, 400], [100, 300, 200, 600, 400, 500], [100, 300, 200, 600, 500, 400], [100, 300, 400, 200, 500, 600], [100, 300, 400, 200, 600, 500], [100, 300, 400, 500, 200, 600], [100, 300, 400, 500, 600, 200], [100, 300, 400, 600, 200, 500], [100, 300, 400, 600, 500, 200], [100, 300, 500, 200, 400, 600], [100, 300, 500, 200, 600, 400], [100, 300, 500, 400, 200, 600], [100, 300, 500, 400, 600, 200], [100, 300, 500, 600, 200, 400], [100, 300, 500, 600, 400, 200], [100, 300, 600, 200, 400, 500], [100, 300, 600, 200, 500, 400], [100, 300, 600, 400, 200, 500], [100, 300, 600, 400, 500, 200], [100, 300, 600, 500, 200, 400], [100, 300, 600, 500, 400, 200], [100, 400, 200, 300, 500, 600], [100, 400, 200, 300, 600, 500], [100, 400, 200, 500, 300, 600], [100, 400, 200, 500, 600, 300], [100, 400, 200, 600, 300, 500], [100, 400, 200, 600, 500, 300], [100, 400, 300, 200, 500, 600], [100, 400, 300, 200, 600, 500], [100, 400, 300, 500, 200, 600], [100, 400, 300, 500, 600, 200], [100, 400, 300, 600, 200, 500], [100, 400, 300, 600, 500, 200], [100, 400, 500, 200, 300, 600], [100, 400, 500, 200, 600, 300], [100, 400, 500, 300, 200, 600], [100, 400, 500, 300, 600, 200], [100, 400, 500, 600, 200, 300], [100, 400, 500, 600, 300, 200], [100, 400, 600, 200, 300, 500], [100, 400, 600, 200, 500, 300], [100, 400, 600, 300, 200, 500], [100, 400, 600, 300, 500, 200], [100, 400, 600, 500, 200, 300], [100, 400, 600, 500, 300, 200], [100, 500, 200, 300, 400, 600], [100, 500, 200, 300, 600, 400], [100, 500, 200, 400, 300, 600], [100, 500, 200, 400, 600, 300], [100, 500, 200, 600, 300, 400], [100, 500, 200, 600, 400, 300], [100, 500, 300, 200, 400, 600], [100, 500, 300, 200, 600, 400], [100, 500, 300, 400, 200, 600], [100, 500, 300, 400, 600, 200], [100, 500, 300, 600, 200, 400], [100, 500, 300, 600, 400, 200], [100, 500, 400, 200, 300, 600], [100, 500, 400, 200, 600, 300], [100, 500, 400, 300, 200, 600], [100, 500, 400, 300, 600, 200], [100, 500, 400, 600, 200, 300], [100, 500, 400, 600, 300, 200], [100, 500, 600, 200, 300, 400], [100, 500, 600, 200, 400, 300], [100, 500, 600, 300, 200, 400], [100, 500, 600, 300, 400, 200], [100, 500, 600, 400, 200, 300], [100, 500, 600, 400, 300, 200], [100, 600, 200, 300, 400, 500], [100, 600, 200, 300, 500, 400], [100, 600, 200, 400, 300, 500], [100, 600, 200, 400, 500, 300], [100, 600, 200, 500, 300, 400], [100, 600, 200, 500, 400, 300], [100, 600, 300, 200, 400, 500], [100, 600, 300, 200, 500, 400], [100, 600, 300, 400, 200, 500], [100, 600, 300, 400, 500, 200], [100, 600, 300, 500, 200, 400], [100, 600, 300, 500, 400, 200], [100, 600, 400, 200, 300, 500], [100, 600, 400, 200, 500, 300], [100, 600, 400, 300, 200, 500], [100, 600, 400, 300, 500, 200], [100, 600, 400, 500, 200, 300], [100, 600, 400, 500, 300, 200], [100, 600, 500, 200, 300, 400], [100, 600, 500, 200, 400, 300], [100, 600, 500, 300, 200, 400], [100, 600, 500, 300, 400, 200], [100, 600, 500, 400, 200, 300], [100, 600, 500, 400, 300, 200], [200, 100, 300, 400, 500, 600], [200, 100, 300, 400, 600, 500], [200, 100, 300, 500, 400, 600], [200, 100, 300, 500, 600, 400], [200, 100, 300, 600, 400, 500], [200, 100, 300, 600, 500, 400], [200, 100, 400, 300, 500, 600], [200, 100, 400, 300, 600, 500], [200, 100, 400, 500, 300, 600], [200, 100, 400, 500, 600, 300], [200, 100, 400, 600, 300, 500], [200, 100, 400, 600, 500, 300], [200, 100, 500, 300, 400, 600], [200, 100, 500, 300, 600, 400], [200, 100, 500, 400, 300, 600], [200, 100, 500, 400, 600, 300], [200, 100, 500, 600, 300, 400], [200, 100, 500, 600, 400, 300], [200, 100, 600, 300, 400, 500], [200, 100, 600, 300, 500, 400], [200, 100, 600, 400, 300, 500], [200, 100, 600, 400, 500, 300], [200, 100, 600, 500, 300, 400], [200, 100, 600, 500, 400, 300], [200, 300, 100, 400, 500, 600], [200, 300, 100, 400, 600, 500], [200, 300, 100, 500, 400, 600], [200, 300, 100, 500, 600, 400], [200, 300, 100, 600, 400, 500], [200, 300, 100, 600, 500, 400], [200, 300, 400, 100, 500, 600], [200, 300, 400, 100, 600, 500], [200, 300, 400, 500, 100, 600], [200, 300, 400, 500, 600, 100], [200, 300, 400, 600, 100, 500], [200, 300, 400, 600, 500, 100], [200, 300, 500, 100, 400, 600], [200, 300, 500, 100, 600, 400], [200, 300, 500, 400, 100, 600], [200, 300, 500, 400, 600, 100], [200, 300, 500, 600, 100, 400], [200, 300, 500, 600, 400, 100], [200, 300, 600, 100, 400, 500], [200, 300, 600, 100, 500, 400], [200, 300, 600, 400, 100, 500], [200, 300, 600, 400, 500, 100], [200, 300, 600, 500, 100, 400], [200, 300, 600, 500, 400, 100], [200, 400, 100, 300, 500, 600], [200, 400, 100, 300, 600, 500], [200, 400, 100, 500, 300, 600], [200, 400, 100, 500, 600, 300], [200, 400, 100, 600, 300, 500], [200, 400, 100, 600, 500, 300], [200, 400, 300, 100, 500, 600], [200, 400, 300, 100, 600, 500], [200, 400, 300, 500, 100, 600], [200, 400, 300, 500, 600, 100], [200, 400, 300, 600, 100, 500], [200, 400, 300, 600, 500, 100], [200, 400, 500, 100, 300, 600], [200, 400, 500, 100, 600, 300], [200, 400, 500, 300, 100, 600], [200, 400, 500, 300, 600, 100], [200, 400, 500, 600, 100, 300], [200, 400, 500, 600, 300, 100], [200, 400, 600, 100, 300, 500], [200, 400, 600, 100, 500, 300], [200, 400, 600, 300, 100, 500], [200, 400, 600, 300, 500, 100], [200, 400, 600, 500, 100, 300], [200, 400, 600, 500, 300, 100], [200, 500, 100, 300, 400, 600], [200, 500, 100, 300, 600, 400], [200, 500, 100, 400, 300, 600], [200, 500, 100, 400, 600, 300], [200, 500, 100, 600, 300, 400], [200, 500, 100, 600, 400, 300], [200, 500, 300, 100, 400, 600], [200, 500, 300, 100, 600, 400], [200, 500, 300, 400, 100, 600], [200, 500, 300, 400, 600, 100], [200, 500, 300, 600, 100, 400], [200, 500, 300, 600, 400, 100], [200, 500, 400, 100, 300, 600], [200, 500, 400, 100, 600, 300], [200, 500, 400, 300, 100, 600], [200, 500, 400, 300, 600, 100], [200, 500, 400, 600, 100, 300], [200, 500, 400, 600, 300, 100], [200, 500, 600, 100, 300, 400], [200, 500, 600, 100, 400, 300], [200, 500, 600, 300, 100, 400], [200, 500, 600, 300, 400, 100], [200, 500, 600, 400, 100, 300], [200, 500, 600, 400, 300, 100], [200, 600, 100, 300, 400, 500], [200, 600, 100, 300, 500, 400], [200, 600, 100, 400, 300, 500], [200, 600, 100, 400, 500, 300], [200, 600, 100, 500, 300, 400], [200, 600, 100, 500, 400, 300], [200, 600, 300, 100, 400, 500], [200, 600, 300, 100, 500, 400], [200, 600, 300, 400, 100, 500], [200, 600, 300, 400, 500, 100], [200, 600, 300, 500, 100, 400], [200, 600, 300, 500, 400, 100], [200, 600, 400, 100, 300, 500], [200, 600, 400, 100, 500, 300], [200, 600, 400, 300, 100, 500], [200, 600, 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100, 300, 500], [600, 200, 400, 100, 500, 300], [600, 200, 400, 300, 100, 500], [600, 200, 400, 300, 500, 100], [600, 200, 400, 500, 100, 300], [600, 200, 400, 500, 300, 100], [600, 200, 500, 100, 300, 400], [600, 200, 500, 100, 400, 300], [600, 200, 500, 300, 100, 400], [600, 200, 500, 300, 400, 100], [600, 200, 500, 400, 100, 300], [600, 200, 500, 400, 300, 100], [600, 300, 100, 200, 400, 500], [600, 300, 100, 200, 500, 400], [600, 300, 100, 400, 200, 500], [600, 300, 100, 400, 500, 200], [600, 300, 100, 500, 200, 400], [600, 300, 100, 500, 400, 200], [600, 300, 200, 100, 400, 500], [600, 300, 200, 100, 500, 400], [600, 300, 200, 400, 100, 500], [600, 300, 200, 400, 500, 100], [600, 300, 200, 500, 100, 400], [600, 300, 200, 500, 400, 100], [600, 300, 400, 100, 200, 500], [600, 300, 400, 100, 500, 200], [600, 300, 400, 200, 100, 500], [600, 300, 400, 200, 500, 100], [600, 300, 400, 500, 100, 200], [600, 300, 400, 500, 200, 100], [600, 300, 500, 100, 200, 400], [600, 300, 500, 100, 400, 200], [600, 300, 500, 200, 100, 400], [600, 300, 500, 200, 400, 100], [600, 300, 500, 400, 100, 200], [600, 300, 500, 400, 200, 100], [600, 400, 100, 200, 300, 500], [600, 400, 100, 200, 500, 300], [600, 400, 100, 300, 200, 500], [600, 400, 100, 300, 500, 200], [600, 400, 100, 500, 200, 300], [600, 400, 100, 500, 300, 200], [600, 400, 200, 100, 300, 500], [600, 400, 200, 100, 500, 300], [600, 400, 200, 300, 100, 500], [600, 400, 200, 300, 500, 100], [600, 400, 200, 500, 100, 300], [600, 400, 200, 500, 300, 100], [600, 400, 300, 100, 200, 500], [600, 400, 300, 100, 500, 200], [600, 400, 300, 200, 100, 500], [600, 400, 300, 200, 500, 100], [600, 400, 300, 500, 100, 200], [600, 400, 300, 500, 200, 100], [600, 400, 500, 100, 200, 300], [600, 400, 500, 100, 300, 200], [600, 400, 500, 200, 100, 300], [600, 400, 500, 200, 300, 100], [600, 400, 500, 300, 100, 200], [600, 400, 500, 300, 200, 100], [600, 500, 100, 200, 300, 400], [600, 500, 100, 200, 400, 300], [600, 500, 100, 300, 200, 400], [600, 500, 100, 300, 400, 200], [600, 500, 100, 400, 200, 300], [600, 500, 100, 400, 300, 200], [600, 500, 200, 100, 300, 400], [600, 500, 200, 100, 400, 300], [600, 500, 200, 300, 100, 400], [600, 500, 200, 300, 400, 100], [600, 500, 200, 400, 100, 300], [600, 500, 200, 400, 300, 100], [600, 500, 300, 100, 200, 400], [600, 500, 300, 100, 400, 200], [600, 500, 300, 200, 100, 400], [600, 500, 300, 200, 400, 100], [600, 500, 300, 400, 100, 200], [600, 500, 300, 400, 200, 100], [600, 500, 400, 100, 200, 300], [600, 500, 400, 100, 300, 200], [600, 500, 400, 200, 100, 300], [600, 500, 400, 200, 300, 100], [600, 500, 400, 300, 100, 200], [600, 500, 400, 300, 200, 100]]\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000]) == [[1, 10, 100, 1000, 10000, 100000], [1, 10, 100, 1000, 100000, 10000], [1, 10, 100, 10000, 1000, 100000], [1, 10, 100, 10000, 100000, 1000], [1, 10, 100, 100000, 1000, 10000], [1, 10, 100, 100000, 10000, 1000], [1, 10, 1000, 100, 10000, 100000], [1, 10, 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100], [100000, 1, 100, 10, 1000, 10000], [100000, 1, 100, 10, 10000, 1000], [100000, 1, 100, 1000, 10, 10000], [100000, 1, 100, 1000, 10000, 10], [100000, 1, 100, 10000, 10, 1000], [100000, 1, 100, 10000, 1000, 10], [100000, 1, 1000, 10, 100, 10000], [100000, 1, 1000, 10, 10000, 100], [100000, 1, 1000, 100, 10, 10000], [100000, 1, 1000, 100, 10000, 10], [100000, 1, 1000, 10000, 10, 100], [100000, 1, 1000, 10000, 100, 10], [100000, 1, 10000, 10, 100, 1000], [100000, 1, 10000, 10, 1000, 100], [100000, 1, 10000, 100, 10, 1000], [100000, 1, 10000, 100, 1000, 10], [100000, 1, 10000, 1000, 10, 100], [100000, 1, 10000, 1000, 100, 10], [100000, 10, 1, 100, 1000, 10000], [100000, 10, 1, 100, 10000, 1000], [100000, 10, 1, 1000, 100, 10000], [100000, 10, 1, 1000, 10000, 100], [100000, 10, 1, 10000, 100, 1000], [100000, 10, 1, 10000, 1000, 100], [100000, 10, 100, 1, 1000, 10000], [100000, 10, 100, 1, 10000, 1000], [100000, 10, 100, 1000, 1, 10000], [100000, 10, 100, 1000, 10000, 1], [100000, 10, 100, 10000, 1, 1000], [100000, 10, 100, 10000, 1000, 1], [100000, 10, 1000, 1, 100, 10000], [100000, 10, 1000, 1, 10000, 100], [100000, 10, 1000, 100, 1, 10000], [100000, 10, 1000, 100, 10000, 1], [100000, 10, 1000, 10000, 1, 100], [100000, 10, 1000, 10000, 100, 1], [100000, 10, 10000, 1, 100, 1000], [100000, 10, 10000, 1, 1000, 100], [100000, 10, 10000, 100, 1, 1000], [100000, 10, 10000, 100, 1000, 1], [100000, 10, 10000, 1000, 1, 100], [100000, 10, 10000, 1000, 100, 1], [100000, 100, 1, 10, 1000, 10000], [100000, 100, 1, 10, 10000, 1000], [100000, 100, 1, 1000, 10, 10000], [100000, 100, 1, 1000, 10000, 10], [100000, 100, 1, 10000, 10, 1000], [100000, 100, 1, 10000, 1000, 10], [100000, 100, 10, 1, 1000, 10000], [100000, 100, 10, 1, 10000, 1000], [100000, 100, 10, 1000, 1, 10000], [100000, 100, 10, 1000, 10000, 1], [100000, 100, 10, 10000, 1, 1000], [100000, 100, 10, 10000, 1000, 1], [100000, 100, 1000, 1, 10, 10000], [100000, 100, 1000, 1, 10000, 10], [100000, 100, 1000, 10, 1, 10000], [100000, 100, 1000, 10, 10000, 1], [100000, 100, 1000, 10000, 1, 10], [100000, 100, 1000, 10000, 10, 1], [100000, 100, 10000, 1, 10, 1000], [100000, 100, 10000, 1, 1000, 10], [100000, 100, 10000, 10, 1, 1000], [100000, 100, 10000, 10, 1000, 1], [100000, 100, 10000, 1000, 1, 10], [100000, 100, 10000, 1000, 10, 1], [100000, 1000, 1, 10, 100, 10000], [100000, 1000, 1, 10, 10000, 100], [100000, 1000, 1, 100, 10, 10000], [100000, 1000, 1, 100, 10000, 10], [100000, 1000, 1, 10000, 10, 100], [100000, 1000, 1, 10000, 100, 10], [100000, 1000, 10, 1, 100, 10000], [100000, 1000, 10, 1, 10000, 100], [100000, 1000, 10, 100, 1, 10000], [100000, 1000, 10, 100, 10000, 1], [100000, 1000, 10, 10000, 1, 100], [100000, 1000, 10, 10000, 100, 1], [100000, 1000, 100, 1, 10, 10000], [100000, 1000, 100, 1, 10000, 10], [100000, 1000, 100, 10, 1, 10000], [100000, 1000, 100, 10, 10000, 1], [100000, 1000, 100, 10000, 1, 10], [100000, 1000, 100, 10000, 10, 1], [100000, 1000, 10000, 1, 10, 100], [100000, 1000, 10000, 1, 100, 10], [100000, 1000, 10000, 10, 1, 100], [100000, 1000, 10000, 10, 100, 1], [100000, 1000, 10000, 100, 1, 10], [100000, 1000, 10000, 100, 10, 1], [100000, 10000, 1, 10, 100, 1000], [100000, 10000, 1, 10, 1000, 100], [100000, 10000, 1, 100, 10, 1000], [100000, 10000, 1, 100, 1000, 10], [100000, 10000, 1, 1000, 10, 100], [100000, 10000, 1, 1000, 100, 10], [100000, 10000, 10, 1, 100, 1000], [100000, 10000, 10, 1, 1000, 100], [100000, 10000, 10, 100, 1, 1000], [100000, 10000, 10, 100, 1000, 1], [100000, 10000, 10, 1000, 1, 100], [100000, 10000, 10, 1000, 100, 1], [100000, 10000, 100, 1, 10, 1000], [100000, 10000, 100, 1, 1000, 10], [100000, 10000, 100, 10, 1, 1000], [100000, 10000, 100, 10, 1000, 1], [100000, 10000, 100, 1000, 1, 10], [100000, 10000, 100, 1000, 10, 1], [100000, 10000, 1000, 1, 10, 100], [100000, 10000, 1000, 1, 100, 10], [100000, 10000, 1000, 10, 1, 100], [100000, 10000, 1000, 10, 100, 1], [100000, 10000, 1000, 100, 1, 10], [100000, 10000, 1000, 100, 10, 1]]\n assert candidate(nums = [2, 4, 6, 8, 10, 12]) == [[2, 4, 6, 8, 10, 12], [2, 4, 6, 8, 12, 10], [2, 4, 6, 10, 8, 12], [2, 4, 6, 10, 12, 8], [2, 4, 6, 12, 8, 10], [2, 4, 6, 12, 10, 8], [2, 4, 8, 6, 10, 12], [2, 4, 8, 6, 12, 10], [2, 4, 8, 10, 6, 12], [2, 4, 8, 10, 12, 6], [2, 4, 8, 12, 6, 10], [2, 4, 8, 12, 10, 6], [2, 4, 10, 6, 8, 12], [2, 4, 10, 6, 12, 8], [2, 4, 10, 8, 6, 12], [2, 4, 10, 8, 12, 6], [2, 4, 10, 12, 6, 8], [2, 4, 10, 12, 8, 6], [2, 4, 12, 6, 8, 10], [2, 4, 12, 6, 10, 8], [2, 4, 12, 8, 6, 10], [2, 4, 12, 8, 10, 6], [2, 4, 12, 10, 6, 8], [2, 4, 12, 10, 8, 6], [2, 6, 4, 8, 10, 12], [2, 6, 4, 8, 12, 10], [2, 6, 4, 10, 8, 12], [2, 6, 4, 10, 12, 8], [2, 6, 4, 12, 8, 10], [2, 6, 4, 12, 10, 8], [2, 6, 8, 4, 10, 12], [2, 6, 8, 4, 12, 10], [2, 6, 8, 10, 4, 12], [2, 6, 8, 10, 12, 4], [2, 6, 8, 12, 4, 10], [2, 6, 8, 12, 10, 4], [2, 6, 10, 4, 8, 12], [2, 6, 10, 4, 12, 8], [2, 6, 10, 8, 4, 12], [2, 6, 10, 8, 12, 4], [2, 6, 10, 12, 4, 8], [2, 6, 10, 12, 8, 4], [2, 6, 12, 4, 8, 10], [2, 6, 12, 4, 10, 8], [2, 6, 12, 8, 4, 10], [2, 6, 12, 8, 10, 4], [2, 6, 12, 10, 4, 8], [2, 6, 12, 10, 8, 4], [2, 8, 4, 6, 10, 12], [2, 8, 4, 6, 12, 10], [2, 8, 4, 10, 6, 12], [2, 8, 4, 10, 12, 6], [2, 8, 4, 12, 6, 10], [2, 8, 4, 12, 10, 6], [2, 8, 6, 4, 10, 12], [2, 8, 6, 4, 12, 10], [2, 8, 6, 10, 4, 12], [2, 8, 6, 10, 12, 4], [2, 8, 6, 12, 4, 10], [2, 8, 6, 12, 10, 4], [2, 8, 10, 4, 6, 12], [2, 8, 10, 4, 12, 6], [2, 8, 10, 6, 4, 12], [2, 8, 10, 6, 12, 4], [2, 8, 10, 12, 4, 6], [2, 8, 10, 12, 6, 4], [2, 8, 12, 4, 6, 10], [2, 8, 12, 4, 10, 6], [2, 8, 12, 6, 4, 10], [2, 8, 12, 6, 10, 4], [2, 8, 12, 10, 4, 6], [2, 8, 12, 10, 6, 4], [2, 10, 4, 6, 8, 12], [2, 10, 4, 6, 12, 8], [2, 10, 4, 8, 6, 12], [2, 10, 4, 8, 12, 6], [2, 10, 4, 12, 6, 8], [2, 10, 4, 12, 8, 6], [2, 10, 6, 4, 8, 12], [2, 10, 6, 4, 12, 8], [2, 10, 6, 8, 4, 12], [2, 10, 6, 8, 12, 4], [2, 10, 6, 12, 4, 8], [2, 10, 6, 12, 8, 4], [2, 10, 8, 4, 6, 12], [2, 10, 8, 4, 12, 6], [2, 10, 8, 6, 4, 12], [2, 10, 8, 6, 12, 4], [2, 10, 8, 12, 4, 6], [2, 10, 8, 12, 6, 4], [2, 10, 12, 4, 6, 8], [2, 10, 12, 4, 8, 6], [2, 10, 12, 6, 4, 8], [2, 10, 12, 6, 8, 4], [2, 10, 12, 8, 4, 6], [2, 10, 12, 8, 6, 4], [2, 12, 4, 6, 8, 10], [2, 12, 4, 6, 10, 8], [2, 12, 4, 8, 6, 10], [2, 12, 4, 8, 10, 6], [2, 12, 4, 10, 6, 8], [2, 12, 4, 10, 8, 6], [2, 12, 6, 4, 8, 10], [2, 12, 6, 4, 10, 8], [2, 12, 6, 8, 4, 10], [2, 12, 6, 8, 10, 4], [2, 12, 6, 10, 4, 8], [2, 12, 6, 10, 8, 4], [2, 12, 8, 4, 6, 10], [2, 12, 8, 4, 10, 6], [2, 12, 8, 6, 4, 10], [2, 12, 8, 6, 10, 4], [2, 12, 8, 10, 4, 6], [2, 12, 8, 10, 6, 4], [2, 12, 10, 4, 6, 8], [2, 12, 10, 4, 8, 6], [2, 12, 10, 6, 4, 8], [2, 12, 10, 6, 8, 4], [2, 12, 10, 8, 4, 6], [2, 12, 10, 8, 6, 4], [4, 2, 6, 8, 10, 12], [4, 2, 6, 8, 12, 10], [4, 2, 6, 10, 8, 12], [4, 2, 6, 10, 12, 8], [4, 2, 6, 12, 8, 10], [4, 2, 6, 12, 10, 8], [4, 2, 8, 6, 10, 12], [4, 2, 8, 6, 12, 10], [4, 2, 8, 10, 6, 12], [4, 2, 8, 10, 12, 6], [4, 2, 8, 12, 6, 10], [4, 2, 8, 12, 10, 6], [4, 2, 10, 6, 8, 12], [4, 2, 10, 6, 12, 8], [4, 2, 10, 8, 6, 12], [4, 2, 10, 8, 12, 6], [4, 2, 10, 12, 6, 8], [4, 2, 10, 12, 8, 6], [4, 2, 12, 6, 8, 10], [4, 2, 12, 6, 10, 8], [4, 2, 12, 8, 6, 10], [4, 2, 12, 8, 10, 6], [4, 2, 12, 10, 6, 8], [4, 2, 12, 10, 8, 6], [4, 6, 2, 8, 10, 12], [4, 6, 2, 8, 12, 10], [4, 6, 2, 10, 8, 12], [4, 6, 2, 10, 12, 8], [4, 6, 2, 12, 8, 10], [4, 6, 2, 12, 10, 8], [4, 6, 8, 2, 10, 12], [4, 6, 8, 2, 12, 10], [4, 6, 8, 10, 2, 12], [4, 6, 8, 10, 12, 2], [4, 6, 8, 12, 2, 10], [4, 6, 8, 12, 10, 2], [4, 6, 10, 2, 8, 12], [4, 6, 10, 2, 12, 8], [4, 6, 10, 8, 2, 12], [4, 6, 10, 8, 12, 2], [4, 6, 10, 12, 2, 8], [4, 6, 10, 12, 8, 2], [4, 6, 12, 2, 8, 10], [4, 6, 12, 2, 10, 8], [4, 6, 12, 8, 2, 10], [4, 6, 12, 8, 10, 2], [4, 6, 12, 10, 2, 8], [4, 6, 12, 10, 8, 2], [4, 8, 2, 6, 10, 12], [4, 8, 2, 6, 12, 10], [4, 8, 2, 10, 6, 12], [4, 8, 2, 10, 12, 6], [4, 8, 2, 12, 6, 10], [4, 8, 2, 12, 10, 6], [4, 8, 6, 2, 10, 12], [4, 8, 6, 2, 12, 10], [4, 8, 6, 10, 2, 12], [4, 8, 6, 10, 12, 2], [4, 8, 6, 12, 2, 10], [4, 8, 6, 12, 10, 2], [4, 8, 10, 2, 6, 12], [4, 8, 10, 2, 12, 6], [4, 8, 10, 6, 2, 12], [4, 8, 10, 6, 12, 2], [4, 8, 10, 12, 2, 6], [4, 8, 10, 12, 6, 2], [4, 8, 12, 2, 6, 10], [4, 8, 12, 2, 10, 6], [4, 8, 12, 6, 2, 10], [4, 8, 12, 6, 10, 2], [4, 8, 12, 10, 2, 6], [4, 8, 12, 10, 6, 2], [4, 10, 2, 6, 8, 12], [4, 10, 2, 6, 12, 8], [4, 10, 2, 8, 6, 12], [4, 10, 2, 8, 12, 6], [4, 10, 2, 12, 6, 8], [4, 10, 2, 12, 8, 6], [4, 10, 6, 2, 8, 12], [4, 10, 6, 2, 12, 8], [4, 10, 6, 8, 2, 12], [4, 10, 6, 8, 12, 2], [4, 10, 6, 12, 2, 8], [4, 10, 6, 12, 8, 2], [4, 10, 8, 2, 6, 12], [4, 10, 8, 2, 12, 6], [4, 10, 8, 6, 2, 12], [4, 10, 8, 6, 12, 2], [4, 10, 8, 12, 2, 6], [4, 10, 8, 12, 6, 2], [4, 10, 12, 2, 6, 8], [4, 10, 12, 2, 8, 6], [4, 10, 12, 6, 2, 8], [4, 10, 12, 6, 8, 2], [4, 10, 12, 8, 2, 6], [4, 10, 12, 8, 6, 2], [4, 12, 2, 6, 8, 10], [4, 12, 2, 6, 10, 8], [4, 12, 2, 8, 6, 10], [4, 12, 2, 8, 10, 6], [4, 12, 2, 10, 6, 8], [4, 12, 2, 10, 8, 6], [4, 12, 6, 2, 8, 10], [4, 12, 6, 2, 10, 8], [4, 12, 6, 8, 2, 10], [4, 12, 6, 8, 10, 2], [4, 12, 6, 10, 2, 8], [4, 12, 6, 10, 8, 2], [4, 12, 8, 2, 6, 10], [4, 12, 8, 2, 10, 6], [4, 12, 8, 6, 2, 10], [4, 12, 8, 6, 10, 2], [4, 12, 8, 10, 2, 6], [4, 12, 8, 10, 6, 2], [4, 12, 10, 2, 6, 8], [4, 12, 10, 2, 8, 6], [4, 12, 10, 6, 2, 8], [4, 12, 10, 6, 8, 2], [4, 12, 10, 8, 2, 6], [4, 12, 10, 8, 6, 2], [6, 2, 4, 8, 10, 12], [6, 2, 4, 8, 12, 10], [6, 2, 4, 10, 8, 12], [6, 2, 4, 10, 12, 8], [6, 2, 4, 12, 8, 10], [6, 2, 4, 12, 10, 8], [6, 2, 8, 4, 10, 12], [6, 2, 8, 4, 12, 10], [6, 2, 8, 10, 4, 12], [6, 2, 8, 10, 12, 4], [6, 2, 8, 12, 4, 10], [6, 2, 8, 12, 10, 4], [6, 2, 10, 4, 8, 12], [6, 2, 10, 4, 12, 8], [6, 2, 10, 8, 4, 12], [6, 2, 10, 8, 12, 4], [6, 2, 10, 12, 4, 8], [6, 2, 10, 12, 8, 4], [6, 2, 12, 4, 8, 10], [6, 2, 12, 4, 10, 8], [6, 2, 12, 8, 4, 10], [6, 2, 12, 8, 10, 4], [6, 2, 12, 10, 4, 8], [6, 2, 12, 10, 8, 4], [6, 4, 2, 8, 10, 12], [6, 4, 2, 8, 12, 10], [6, 4, 2, 10, 8, 12], [6, 4, 2, 10, 12, 8], [6, 4, 2, 12, 8, 10], [6, 4, 2, 12, 10, 8], [6, 4, 8, 2, 10, 12], [6, 4, 8, 2, 12, 10], [6, 4, 8, 10, 2, 12], [6, 4, 8, 10, 12, 2], [6, 4, 8, 12, 2, 10], [6, 4, 8, 12, 10, 2], [6, 4, 10, 2, 8, 12], [6, 4, 10, 2, 12, 8], [6, 4, 10, 8, 2, 12], [6, 4, 10, 8, 12, 2], [6, 4, 10, 12, 2, 8], [6, 4, 10, 12, 8, 2], [6, 4, 12, 2, 8, 10], [6, 4, 12, 2, 10, 8], [6, 4, 12, 8, 2, 10], [6, 4, 12, 8, 10, 2], [6, 4, 12, 10, 2, 8], [6, 4, 12, 10, 8, 2], [6, 8, 2, 4, 10, 12], [6, 8, 2, 4, 12, 10], [6, 8, 2, 10, 4, 12], [6, 8, 2, 10, 12, 4], [6, 8, 2, 12, 4, 10], [6, 8, 2, 12, 10, 4], [6, 8, 4, 2, 10, 12], [6, 8, 4, 2, 12, 10], [6, 8, 4, 10, 2, 12], [6, 8, 4, 10, 12, 2], [6, 8, 4, 12, 2, 10], [6, 8, 4, 12, 10, 2], [6, 8, 10, 2, 4, 12], [6, 8, 10, 2, 12, 4], [6, 8, 10, 4, 2, 12], [6, 8, 10, 4, 12, 2], [6, 8, 10, 12, 2, 4], [6, 8, 10, 12, 4, 2], [6, 8, 12, 2, 4, 10], [6, 8, 12, 2, 10, 4], [6, 8, 12, 4, 2, 10], [6, 8, 12, 4, 10, 2], [6, 8, 12, 10, 2, 4], [6, 8, 12, 10, 4, 2], [6, 10, 2, 4, 8, 12], [6, 10, 2, 4, 12, 8], [6, 10, 2, 8, 4, 12], [6, 10, 2, 8, 12, 4], [6, 10, 2, 12, 4, 8], [6, 10, 2, 12, 8, 4], [6, 10, 4, 2, 8, 12], [6, 10, 4, 2, 12, 8], [6, 10, 4, 8, 2, 12], [6, 10, 4, 8, 12, 2], [6, 10, 4, 12, 2, 8], [6, 10, 4, 12, 8, 2], [6, 10, 8, 2, 4, 12], [6, 10, 8, 2, 12, 4], [6, 10, 8, 4, 2, 12], [6, 10, 8, 4, 12, 2], [6, 10, 8, 12, 2, 4], [6, 10, 8, 12, 4, 2], [6, 10, 12, 2, 4, 8], [6, 10, 12, 2, 8, 4], [6, 10, 12, 4, 2, 8], [6, 10, 12, 4, 8, 2], [6, 10, 12, 8, 2, 4], [6, 10, 12, 8, 4, 2], [6, 12, 2, 4, 8, 10], [6, 12, 2, 4, 10, 8], [6, 12, 2, 8, 4, 10], [6, 12, 2, 8, 10, 4], [6, 12, 2, 10, 4, 8], [6, 12, 2, 10, 8, 4], [6, 12, 4, 2, 8, 10], [6, 12, 4, 2, 10, 8], [6, 12, 4, 8, 2, 10], [6, 12, 4, 8, 10, 2], [6, 12, 4, 10, 2, 8], [6, 12, 4, 10, 8, 2], [6, 12, 8, 2, 4, 10], [6, 12, 8, 2, 10, 4], [6, 12, 8, 4, 2, 10], [6, 12, 8, 4, 10, 2], [6, 12, 8, 10, 2, 4], [6, 12, 8, 10, 4, 2], [6, 12, 10, 2, 4, 8], [6, 12, 10, 2, 8, 4], [6, 12, 10, 4, 2, 8], [6, 12, 10, 4, 8, 2], [6, 12, 10, 8, 2, 4], [6, 12, 10, 8, 4, 2], [8, 2, 4, 6, 10, 12], [8, 2, 4, 6, 12, 10], [8, 2, 4, 10, 6, 12], [8, 2, 4, 10, 12, 6], [8, 2, 4, 12, 6, 10], [8, 2, 4, 12, 10, 6], [8, 2, 6, 4, 10, 12], [8, 2, 6, 4, 12, 10], [8, 2, 6, 10, 4, 12], [8, 2, 6, 10, 12, 4], [8, 2, 6, 12, 4, 10], [8, 2, 6, 12, 10, 4], [8, 2, 10, 4, 6, 12], [8, 2, 10, 4, 12, 6], [8, 2, 10, 6, 4, 12], [8, 2, 10, 6, 12, 4], [8, 2, 10, 12, 4, 6], [8, 2, 10, 12, 6, 4], [8, 2, 12, 4, 6, 10], [8, 2, 12, 4, 10, 6], [8, 2, 12, 6, 4, 10], [8, 2, 12, 6, 10, 4], [8, 2, 12, 10, 4, 6], [8, 2, 12, 10, 6, 4], [8, 4, 2, 6, 10, 12], [8, 4, 2, 6, 12, 10], [8, 4, 2, 10, 6, 12], [8, 4, 2, 10, 12, 6], [8, 4, 2, 12, 6, 10], [8, 4, 2, 12, 10, 6], [8, 4, 6, 2, 10, 12], [8, 4, 6, 2, 12, 10], [8, 4, 6, 10, 2, 12], [8, 4, 6, 10, 12, 2], [8, 4, 6, 12, 2, 10], [8, 4, 6, 12, 10, 2], [8, 4, 10, 2, 6, 12], [8, 4, 10, 2, 12, 6], [8, 4, 10, 6, 2, 12], [8, 4, 10, 6, 12, 2], [8, 4, 10, 12, 2, 6], [8, 4, 10, 12, 6, 2], [8, 4, 12, 2, 6, 10], [8, 4, 12, 2, 10, 6], [8, 4, 12, 6, 2, 10], [8, 4, 12, 6, 10, 2], [8, 4, 12, 10, 2, 6], [8, 4, 12, 10, 6, 2], [8, 6, 2, 4, 10, 12], [8, 6, 2, 4, 12, 10], [8, 6, 2, 10, 4, 12], [8, 6, 2, 10, 12, 4], [8, 6, 2, 12, 4, 10], [8, 6, 2, 12, 10, 4], [8, 6, 4, 2, 10, 12], [8, 6, 4, 2, 12, 10], [8, 6, 4, 10, 2, 12], [8, 6, 4, 10, 12, 2], [8, 6, 4, 12, 2, 10], [8, 6, 4, 12, 10, 2], [8, 6, 10, 2, 4, 12], [8, 6, 10, 2, 12, 4], [8, 6, 10, 4, 2, 12], [8, 6, 10, 4, 12, 2], [8, 6, 10, 12, 2, 4], [8, 6, 10, 12, 4, 2], [8, 6, 12, 2, 4, 10], [8, 6, 12, 2, 10, 4], [8, 6, 12, 4, 2, 10], [8, 6, 12, 4, 10, 2], [8, 6, 12, 10, 2, 4], [8, 6, 12, 10, 4, 2], [8, 10, 2, 4, 6, 12], [8, 10, 2, 4, 12, 6], [8, 10, 2, 6, 4, 12], [8, 10, 2, 6, 12, 4], [8, 10, 2, 12, 4, 6], [8, 10, 2, 12, 6, 4], [8, 10, 4, 2, 6, 12], [8, 10, 4, 2, 12, 6], [8, 10, 4, 6, 2, 12], [8, 10, 4, 6, 12, 2], [8, 10, 4, 12, 2, 6], [8, 10, 4, 12, 6, 2], [8, 10, 6, 2, 4, 12], [8, 10, 6, 2, 12, 4], [8, 10, 6, 4, 2, 12], [8, 10, 6, 4, 12, 2], [8, 10, 6, 12, 2, 4], [8, 10, 6, 12, 4, 2], [8, 10, 12, 2, 4, 6], [8, 10, 12, 2, 6, 4], [8, 10, 12, 4, 2, 6], [8, 10, 12, 4, 6, 2], [8, 10, 12, 6, 2, 4], [8, 10, 12, 6, 4, 2], [8, 12, 2, 4, 6, 10], [8, 12, 2, 4, 10, 6], [8, 12, 2, 6, 4, 10], [8, 12, 2, 6, 10, 4], [8, 12, 2, 10, 4, 6], [8, 12, 2, 10, 6, 4], [8, 12, 4, 2, 6, 10], [8, 12, 4, 2, 10, 6], [8, 12, 4, 6, 2, 10], [8, 12, 4, 6, 10, 2], [8, 12, 4, 10, 2, 6], [8, 12, 4, 10, 6, 2], [8, 12, 6, 2, 4, 10], [8, 12, 6, 2, 10, 4], [8, 12, 6, 4, 2, 10], [8, 12, 6, 4, 10, 2], [8, 12, 6, 10, 2, 4], [8, 12, 6, 10, 4, 2], [8, 12, 10, 2, 4, 6], [8, 12, 10, 2, 6, 4], [8, 12, 10, 4, 2, 6], [8, 12, 10, 4, 6, 2], [8, 12, 10, 6, 2, 4], [8, 12, 10, 6, 4, 2], [10, 2, 4, 6, 8, 12], [10, 2, 4, 6, 12, 8], [10, 2, 4, 8, 6, 12], [10, 2, 4, 8, 12, 6], [10, 2, 4, 12, 6, 8], [10, 2, 4, 12, 8, 6], [10, 2, 6, 4, 8, 12], [10, 2, 6, 4, 12, 8], [10, 2, 6, 8, 4, 12], [10, 2, 6, 8, 12, 4], [10, 2, 6, 12, 4, 8], [10, 2, 6, 12, 8, 4], [10, 2, 8, 4, 6, 12], [10, 2, 8, 4, 12, 6], [10, 2, 8, 6, 4, 12], [10, 2, 8, 6, 12, 4], [10, 2, 8, 12, 4, 6], [10, 2, 8, 12, 6, 4], [10, 2, 12, 4, 6, 8], [10, 2, 12, 4, 8, 6], [10, 2, 12, 6, 4, 8], [10, 2, 12, 6, 8, 4], [10, 2, 12, 8, 4, 6], [10, 2, 12, 8, 6, 4], [10, 4, 2, 6, 8, 12], [10, 4, 2, 6, 12, 8], [10, 4, 2, 8, 6, 12], [10, 4, 2, 8, 12, 6], [10, 4, 2, 12, 6, 8], [10, 4, 2, 12, 8, 6], [10, 4, 6, 2, 8, 12], [10, 4, 6, 2, 12, 8], [10, 4, 6, 8, 2, 12], [10, 4, 6, 8, 12, 2], [10, 4, 6, 12, 2, 8], [10, 4, 6, 12, 8, 2], [10, 4, 8, 2, 6, 12], [10, 4, 8, 2, 12, 6], [10, 4, 8, 6, 2, 12], [10, 4, 8, 6, 12, 2], [10, 4, 8, 12, 2, 6], [10, 4, 8, 12, 6, 2], [10, 4, 12, 2, 6, 8], [10, 4, 12, 2, 8, 6], [10, 4, 12, 6, 2, 8], [10, 4, 12, 6, 8, 2], [10, 4, 12, 8, 2, 6], [10, 4, 12, 8, 6, 2], [10, 6, 2, 4, 8, 12], [10, 6, 2, 4, 12, 8], [10, 6, 2, 8, 4, 12], [10, 6, 2, 8, 12, 4], [10, 6, 2, 12, 4, 8], [10, 6, 2, 12, 8, 4], [10, 6, 4, 2, 8, 12], [10, 6, 4, 2, 12, 8], [10, 6, 4, 8, 2, 12], [10, 6, 4, 8, 12, 2], [10, 6, 4, 12, 2, 8], [10, 6, 4, 12, 8, 2], [10, 6, 8, 2, 4, 12], [10, 6, 8, 2, 12, 4], [10, 6, 8, 4, 2, 12], [10, 6, 8, 4, 12, 2], [10, 6, 8, 12, 2, 4], [10, 6, 8, 12, 4, 2], [10, 6, 12, 2, 4, 8], [10, 6, 12, 2, 8, 4], [10, 6, 12, 4, 2, 8], [10, 6, 12, 4, 8, 2], [10, 6, 12, 8, 2, 4], [10, 6, 12, 8, 4, 2], [10, 8, 2, 4, 6, 12], [10, 8, 2, 4, 12, 6], [10, 8, 2, 6, 4, 12], [10, 8, 2, 6, 12, 4], [10, 8, 2, 12, 4, 6], [10, 8, 2, 12, 6, 4], [10, 8, 4, 2, 6, 12], [10, 8, 4, 2, 12, 6], [10, 8, 4, 6, 2, 12], [10, 8, 4, 6, 12, 2], [10, 8, 4, 12, 2, 6], [10, 8, 4, 12, 6, 2], [10, 8, 6, 2, 4, 12], [10, 8, 6, 2, 12, 4], [10, 8, 6, 4, 2, 12], [10, 8, 6, 4, 12, 2], [10, 8, 6, 12, 2, 4], [10, 8, 6, 12, 4, 2], [10, 8, 12, 2, 4, 6], [10, 8, 12, 2, 6, 4], [10, 8, 12, 4, 2, 6], [10, 8, 12, 4, 6, 2], [10, 8, 12, 6, 2, 4], [10, 8, 12, 6, 4, 2], [10, 12, 2, 4, 6, 8], [10, 12, 2, 4, 8, 6], [10, 12, 2, 6, 4, 8], [10, 12, 2, 6, 8, 4], [10, 12, 2, 8, 4, 6], [10, 12, 2, 8, 6, 4], [10, 12, 4, 2, 6, 8], [10, 12, 4, 2, 8, 6], [10, 12, 4, 6, 2, 8], [10, 12, 4, 6, 8, 2], [10, 12, 4, 8, 2, 6], [10, 12, 4, 8, 6, 2], [10, 12, 6, 2, 4, 8], [10, 12, 6, 2, 8, 4], [10, 12, 6, 4, 2, 8], [10, 12, 6, 4, 8, 2], [10, 12, 6, 8, 2, 4], [10, 12, 6, 8, 4, 2], [10, 12, 8, 2, 4, 6], [10, 12, 8, 2, 6, 4], [10, 12, 8, 4, 2, 6], [10, 12, 8, 4, 6, 2], [10, 12, 8, 6, 2, 4], [10, 12, 8, 6, 4, 2], [12, 2, 4, 6, 8, 10], [12, 2, 4, 6, 10, 8], [12, 2, 4, 8, 6, 10], [12, 2, 4, 8, 10, 6], [12, 2, 4, 10, 6, 8], [12, 2, 4, 10, 8, 6], [12, 2, 6, 4, 8, 10], [12, 2, 6, 4, 10, 8], [12, 2, 6, 8, 4, 10], [12, 2, 6, 8, 10, 4], [12, 2, 6, 10, 4, 8], [12, 2, 6, 10, 8, 4], [12, 2, 8, 4, 6, 10], [12, 2, 8, 4, 10, 6], [12, 2, 8, 6, 4, 10], [12, 2, 8, 6, 10, 4], [12, 2, 8, 10, 4, 6], [12, 2, 8, 10, 6, 4], [12, 2, 10, 4, 6, 8], [12, 2, 10, 4, 8, 6], [12, 2, 10, 6, 4, 8], [12, 2, 10, 6, 8, 4], [12, 2, 10, 8, 4, 6], [12, 2, 10, 8, 6, 4], [12, 4, 2, 6, 8, 10], [12, 4, 2, 6, 10, 8], [12, 4, 2, 8, 6, 10], [12, 4, 2, 8, 10, 6], [12, 4, 2, 10, 6, 8], [12, 4, 2, 10, 8, 6], [12, 4, 6, 2, 8, 10], [12, 4, 6, 2, 10, 8], [12, 4, 6, 8, 2, 10], [12, 4, 6, 8, 10, 2], [12, 4, 6, 10, 2, 8], [12, 4, 6, 10, 8, 2], [12, 4, 8, 2, 6, 10], [12, 4, 8, 2, 10, 6], [12, 4, 8, 6, 2, 10], [12, 4, 8, 6, 10, 2], [12, 4, 8, 10, 2, 6], [12, 4, 8, 10, 6, 2], [12, 4, 10, 2, 6, 8], [12, 4, 10, 2, 8, 6], [12, 4, 10, 6, 2, 8], [12, 4, 10, 6, 8, 2], [12, 4, 10, 8, 2, 6], [12, 4, 10, 8, 6, 2], [12, 6, 2, 4, 8, 10], [12, 6, 2, 4, 10, 8], [12, 6, 2, 8, 4, 10], [12, 6, 2, 8, 10, 4], [12, 6, 2, 10, 4, 8], [12, 6, 2, 10, 8, 4], [12, 6, 4, 2, 8, 10], [12, 6, 4, 2, 10, 8], [12, 6, 4, 8, 2, 10], [12, 6, 4, 8, 10, 2], [12, 6, 4, 10, 2, 8], [12, 6, 4, 10, 8, 2], [12, 6, 8, 2, 4, 10], [12, 6, 8, 2, 10, 4], [12, 6, 8, 4, 2, 10], [12, 6, 8, 4, 10, 2], [12, 6, 8, 10, 2, 4], [12, 6, 8, 10, 4, 2], [12, 6, 10, 2, 4, 8], [12, 6, 10, 2, 8, 4], [12, 6, 10, 4, 2, 8], [12, 6, 10, 4, 8, 2], [12, 6, 10, 8, 2, 4], [12, 6, 10, 8, 4, 2], [12, 8, 2, 4, 6, 10], [12, 8, 2, 4, 10, 6], [12, 8, 2, 6, 4, 10], [12, 8, 2, 6, 10, 4], [12, 8, 2, 10, 4, 6], [12, 8, 2, 10, 6, 4], [12, 8, 4, 2, 6, 10], [12, 8, 4, 2, 10, 6], [12, 8, 4, 6, 2, 10], [12, 8, 4, 6, 10, 2], [12, 8, 4, 10, 2, 6], [12, 8, 4, 10, 6, 2], [12, 8, 6, 2, 4, 10], [12, 8, 6, 2, 10, 4], [12, 8, 6, 4, 2, 10], [12, 8, 6, 4, 10, 2], [12, 8, 6, 10, 2, 4], [12, 8, 6, 10, 4, 2], [12, 8, 10, 2, 4, 6], [12, 8, 10, 2, 6, 4], [12, 8, 10, 4, 2, 6], [12, 8, 10, 4, 6, 2], [12, 8, 10, 6, 2, 4], [12, 8, 10, 6, 4, 2], [12, 10, 2, 4, 6, 8], [12, 10, 2, 4, 8, 6], [12, 10, 2, 6, 4, 8], [12, 10, 2, 6, 8, 4], [12, 10, 2, 8, 4, 6], [12, 10, 2, 8, 6, 4], [12, 10, 4, 2, 6, 8], [12, 10, 4, 2, 8, 6], [12, 10, 4, 6, 2, 8], [12, 10, 4, 6, 8, 2], [12, 10, 4, 8, 2, 6], [12, 10, 4, 8, 6, 2], [12, 10, 6, 2, 4, 8], [12, 10, 6, 2, 8, 4], [12, 10, 6, 4, 2, 8], [12, 10, 6, 4, 8, 2], [12, 10, 6, 8, 2, 4], [12, 10, 6, 8, 4, 2], [12, 10, 8, 2, 4, 6], [12, 10, 8, 2, 6, 4], [12, 10, 8, 4, 2, 6], [12, 10, 8, 4, 6, 2], [12, 10, 8, 6, 2, 4], [12, 10, 8, 6, 4, 2]]\n assert candidate(nums = [1, 2, 3, 0, -1, -2]) == [[1, 2, 3, 0, -1, -2], [1, 2, 3, 0, -2, -1], [1, 2, 3, -1, 0, -2], [1, 2, 3, -1, -2, 0], [1, 2, 3, -2, 0, -1], [1, 2, 3, -2, -1, 0], [1, 2, 0, 3, -1, -2], [1, 2, 0, 3, -2, -1], [1, 2, 0, -1, 3, -2], [1, 2, 0, -1, -2, 3], [1, 2, 0, -2, 3, -1], [1, 2, 0, -2, -1, 3], [1, 2, -1, 3, 0, -2], [1, 2, -1, 3, -2, 0], [1, 2, -1, 0, 3, -2], [1, 2, -1, 0, -2, 3], [1, 2, -1, -2, 3, 0], [1, 2, -1, -2, 0, 3], [1, 2, -2, 3, 0, -1], [1, 2, -2, 3, -1, 0], [1, 2, -2, 0, 3, -1], [1, 2, -2, 0, -1, 3], [1, 2, -2, -1, 3, 0], [1, 2, -2, -1, 0, 3], [1, 3, 2, 0, -1, -2], [1, 3, 2, 0, -2, -1], [1, 3, 2, -1, 0, -2], [1, 3, 2, -1, -2, 0], [1, 3, 2, -2, 0, -1], [1, 3, 2, -2, -1, 0], [1, 3, 0, 2, -1, -2], [1, 3, 0, 2, -2, -1], [1, 3, 0, -1, 2, -2], [1, 3, 0, -1, -2, 2], [1, 3, 0, -2, 2, -1], [1, 3, 0, -2, -1, 2], [1, 3, -1, 2, 0, -2], [1, 3, -1, 2, -2, 0], [1, 3, -1, 0, 2, -2], [1, 3, -1, 0, -2, 2], [1, 3, -1, -2, 2, 0], [1, 3, -1, -2, 0, 2], [1, 3, -2, 2, 0, -1], [1, 3, -2, 2, -1, 0], [1, 3, -2, 0, 2, -1], [1, 3, -2, 0, -1, 2], [1, 3, -2, -1, 2, 0], [1, 3, -2, -1, 0, 2], [1, 0, 2, 3, -1, -2], [1, 0, 2, 3, -2, -1], [1, 0, 2, -1, 3, -2], [1, 0, 2, -1, -2, 3], [1, 0, 2, -2, 3, -1], [1, 0, 2, -2, -1, 3], [1, 0, 3, 2, -1, -2], [1, 0, 3, 2, -2, -1], [1, 0, 3, -1, 2, -2], [1, 0, 3, -1, -2, 2], [1, 0, 3, -2, 2, -1], [1, 0, 3, -2, -1, 2], [1, 0, -1, 2, 3, -2], [1, 0, -1, 2, -2, 3], [1, 0, -1, 3, 2, -2], [1, 0, -1, 3, -2, 2], [1, 0, -1, -2, 2, 3], [1, 0, -1, -2, 3, 2], [1, 0, -2, 2, 3, -1], [1, 0, -2, 2, -1, 3], [1, 0, -2, 3, 2, -1], [1, 0, -2, 3, -1, 2], [1, 0, -2, -1, 2, 3], [1, 0, -2, -1, 3, 2], [1, -1, 2, 3, 0, -2], [1, -1, 2, 3, -2, 0], [1, -1, 2, 0, 3, -2], [1, -1, 2, 0, -2, 3], [1, -1, 2, -2, 3, 0], [1, -1, 2, -2, 0, 3], [1, -1, 3, 2, 0, -2], [1, -1, 3, 2, -2, 0], [1, -1, 3, 0, 2, -2], [1, -1, 3, 0, -2, 2], [1, -1, 3, -2, 2, 0], [1, -1, 3, -2, 0, 2], [1, -1, 0, 2, 3, -2], [1, -1, 0, 2, -2, 3], [1, -1, 0, 3, 2, -2], [1, -1, 0, 3, -2, 2], [1, -1, 0, -2, 2, 3], [1, -1, 0, -2, 3, 2], [1, -1, -2, 2, 3, 0], [1, -1, -2, 2, 0, 3], [1, -1, -2, 3, 2, 0], [1, -1, -2, 3, 0, 2], [1, -1, -2, 0, 2, 3], [1, -1, -2, 0, 3, 2], [1, -2, 2, 3, 0, -1], [1, -2, 2, 3, -1, 0], [1, -2, 2, 0, 3, -1], [1, -2, 2, 0, -1, 3], [1, -2, 2, -1, 3, 0], [1, -2, 2, -1, 0, 3], [1, -2, 3, 2, 0, -1], [1, -2, 3, 2, -1, 0], [1, -2, 3, 0, 2, -1], [1, -2, 3, 0, -1, 2], [1, -2, 3, -1, 2, 0], [1, -2, 3, -1, 0, 2], [1, -2, 0, 2, 3, -1], [1, -2, 0, 2, -1, 3], [1, -2, 0, 3, 2, -1], [1, -2, 0, 3, -1, 2], [1, -2, 0, -1, 2, 3], [1, -2, 0, -1, 3, 2], [1, -2, -1, 2, 3, 0], [1, -2, -1, 2, 0, 3], [1, -2, -1, 3, 2, 0], [1, -2, -1, 3, 0, 2], [1, -2, -1, 0, 2, 3], [1, -2, -1, 0, 3, 2], [2, 1, 3, 0, -1, -2], [2, 1, 3, 0, -2, -1], [2, 1, 3, -1, 0, -2], [2, 1, 3, -1, -2, 0], [2, 1, 3, -2, 0, -1], [2, 1, 3, -2, -1, 0], [2, 1, 0, 3, -1, -2], [2, 1, 0, 3, -2, -1], [2, 1, 0, -1, 3, -2], [2, 1, 0, -1, -2, 3], [2, 1, 0, -2, 3, -1], [2, 1, 0, -2, -1, 3], [2, 1, -1, 3, 0, -2], [2, 1, -1, 3, -2, 0], [2, 1, -1, 0, 3, -2], [2, 1, -1, 0, -2, 3], [2, 1, -1, -2, 3, 0], [2, 1, -1, -2, 0, 3], [2, 1, -2, 3, 0, -1], [2, 1, -2, 3, -1, 0], [2, 1, -2, 0, 3, -1], [2, 1, -2, 0, -1, 3], [2, 1, -2, -1, 3, 0], [2, 1, -2, -1, 0, 3], [2, 3, 1, 0, -1, -2], [2, 3, 1, 0, -2, -1], [2, 3, 1, -1, 0, -2], [2, 3, 1, -1, -2, 0], [2, 3, 1, -2, 0, -1], [2, 3, 1, -2, -1, 0], [2, 3, 0, 1, -1, -2], [2, 3, 0, 1, -2, -1], [2, 3, 0, -1, 1, -2], [2, 3, 0, -1, -2, 1], [2, 3, 0, -2, 1, -1], [2, 3, 0, -2, -1, 1], [2, 3, -1, 1, 0, -2], [2, 3, -1, 1, -2, 0], [2, 3, -1, 0, 1, -2], [2, 3, -1, 0, -2, 1], [2, 3, -1, -2, 1, 0], [2, 3, -1, -2, 0, 1], [2, 3, -2, 1, 0, -1], [2, 3, -2, 1, -1, 0], [2, 3, -2, 0, 1, -1], [2, 3, -2, 0, -1, 1], [2, 3, -2, -1, 1, 0], [2, 3, -2, -1, 0, 1], [2, 0, 1, 3, -1, -2], [2, 0, 1, 3, -2, -1], [2, 0, 1, -1, 3, -2], [2, 0, 1, -1, -2, 3], [2, 0, 1, -2, 3, -1], [2, 0, 1, -2, -1, 3], [2, 0, 3, 1, -1, -2], [2, 0, 3, 1, -2, -1], [2, 0, 3, -1, 1, -2], [2, 0, 3, -1, -2, 1], [2, 0, 3, -2, 1, -1], [2, 0, 3, -2, -1, 1], [2, 0, -1, 1, 3, -2], [2, 0, -1, 1, -2, 3], [2, 0, -1, 3, 1, -2], [2, 0, -1, 3, -2, 1], [2, 0, -1, -2, 1, 3], [2, 0, -1, -2, 3, 1], [2, 0, -2, 1, 3, -1], [2, 0, -2, 1, -1, 3], [2, 0, -2, 3, 1, -1], [2, 0, -2, 3, -1, 1], [2, 0, -2, -1, 1, 3], [2, 0, -2, -1, 3, 1], [2, -1, 1, 3, 0, -2], [2, -1, 1, 3, -2, 0], [2, -1, 1, 0, 3, -2], [2, -1, 1, 0, -2, 3], [2, -1, 1, -2, 3, 0], [2, -1, 1, -2, 0, 3], [2, -1, 3, 1, 0, -2], [2, -1, 3, 1, -2, 0], [2, -1, 3, 0, 1, -2], [2, -1, 3, 0, -2, 1], [2, -1, 3, -2, 1, 0], [2, -1, 3, -2, 0, 1], [2, -1, 0, 1, 3, -2], [2, -1, 0, 1, -2, 3], [2, -1, 0, 3, 1, -2], [2, -1, 0, 3, -2, 1], [2, -1, 0, -2, 1, 3], [2, -1, 0, -2, 3, 1], [2, -1, -2, 1, 3, 0], [2, -1, -2, 1, 0, 3], [2, -1, -2, 3, 1, 0], [2, -1, -2, 3, 0, 1], [2, -1, -2, 0, 1, 3], [2, -1, -2, 0, 3, 1], [2, -2, 1, 3, 0, -1], [2, -2, 1, 3, -1, 0], [2, -2, 1, 0, 3, -1], [2, -2, 1, 0, -1, 3], [2, -2, 1, -1, 3, 0], [2, -2, 1, -1, 0, 3], [2, -2, 3, 1, 0, -1], [2, -2, 3, 1, -1, 0], [2, -2, 3, 0, 1, -1], [2, -2, 3, 0, -1, 1], [2, -2, 3, -1, 1, 0], [2, -2, 3, -1, 0, 1], [2, -2, 0, 1, 3, -1], [2, -2, 0, 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[-1, -2, 3, 0, 2, 1], [-1, -2, 0, 1, 2, 3], [-1, -2, 0, 1, 3, 2], [-1, -2, 0, 2, 1, 3], [-1, -2, 0, 2, 3, 1], [-1, -2, 0, 3, 1, 2], [-1, -2, 0, 3, 2, 1], [-2, 1, 2, 3, 0, -1], [-2, 1, 2, 3, -1, 0], [-2, 1, 2, 0, 3, -1], [-2, 1, 2, 0, -1, 3], [-2, 1, 2, -1, 3, 0], [-2, 1, 2, -1, 0, 3], [-2, 1, 3, 2, 0, -1], [-2, 1, 3, 2, -1, 0], [-2, 1, 3, 0, 2, -1], [-2, 1, 3, 0, -1, 2], [-2, 1, 3, -1, 2, 0], [-2, 1, 3, -1, 0, 2], [-2, 1, 0, 2, 3, -1], [-2, 1, 0, 2, -1, 3], [-2, 1, 0, 3, 2, -1], [-2, 1, 0, 3, -1, 2], [-2, 1, 0, -1, 2, 3], [-2, 1, 0, -1, 3, 2], [-2, 1, -1, 2, 3, 0], [-2, 1, -1, 2, 0, 3], [-2, 1, -1, 3, 2, 0], [-2, 1, -1, 3, 0, 2], [-2, 1, -1, 0, 2, 3], [-2, 1, -1, 0, 3, 2], [-2, 2, 1, 3, 0, -1], [-2, 2, 1, 3, -1, 0], [-2, 2, 1, 0, 3, -1], [-2, 2, 1, 0, -1, 3], [-2, 2, 1, -1, 3, 0], [-2, 2, 1, -1, 0, 3], [-2, 2, 3, 1, 0, -1], [-2, 2, 3, 1, -1, 0], [-2, 2, 3, 0, 1, -1], [-2, 2, 3, 0, -1, 1], [-2, 2, 3, -1, 1, 0], [-2, 2, 3, -1, 0, 1], [-2, 2, 0, 1, 3, -1], [-2, 2, 0, 1, -1, 3], [-2, 2, 0, 3, 1, -1], [-2, 2, 0, 3, -1, 1], [-2, 2, 0, -1, 1, 3], [-2, 2, 0, -1, 3, 1], [-2, 2, -1, 1, 3, 0], [-2, 2, -1, 1, 0, 3], [-2, 2, -1, 3, 1, 0], [-2, 2, -1, 3, 0, 1], [-2, 2, -1, 0, 1, 3], [-2, 2, -1, 0, 3, 1], [-2, 3, 1, 2, 0, -1], [-2, 3, 1, 2, -1, 0], [-2, 3, 1, 0, 2, -1], [-2, 3, 1, 0, -1, 2], [-2, 3, 1, -1, 2, 0], [-2, 3, 1, -1, 0, 2], [-2, 3, 2, 1, 0, -1], [-2, 3, 2, 1, -1, 0], [-2, 3, 2, 0, 1, -1], [-2, 3, 2, 0, -1, 1], [-2, 3, 2, -1, 1, 0], [-2, 3, 2, -1, 0, 1], [-2, 3, 0, 1, 2, -1], [-2, 3, 0, 1, -1, 2], [-2, 3, 0, 2, 1, -1], [-2, 3, 0, 2, -1, 1], [-2, 3, 0, -1, 1, 2], [-2, 3, 0, -1, 2, 1], [-2, 3, -1, 1, 2, 0], [-2, 3, -1, 1, 0, 2], [-2, 3, -1, 2, 1, 0], [-2, 3, -1, 2, 0, 1], [-2, 3, -1, 0, 1, 2], [-2, 3, -1, 0, 2, 1], [-2, 0, 1, 2, 3, -1], [-2, 0, 1, 2, -1, 3], [-2, 0, 1, 3, 2, -1], [-2, 0, 1, 3, -1, 2], [-2, 0, 1, -1, 2, 3], [-2, 0, 1, -1, 3, 2], [-2, 0, 2, 1, 3, -1], [-2, 0, 2, 1, -1, 3], [-2, 0, 2, 3, 1, -1], [-2, 0, 2, 3, -1, 1], [-2, 0, 2, -1, 1, 3], [-2, 0, 2, -1, 3, 1], [-2, 0, 3, 1, 2, -1], [-2, 0, 3, 1, -1, 2], [-2, 0, 3, 2, 1, -1], [-2, 0, 3, 2, -1, 1], [-2, 0, 3, -1, 1, 2], [-2, 0, 3, -1, 2, 1], [-2, 0, -1, 1, 2, 3], [-2, 0, -1, 1, 3, 2], [-2, 0, -1, 2, 1, 3], [-2, 0, -1, 2, 3, 1], [-2, 0, -1, 3, 1, 2], [-2, 0, -1, 3, 2, 1], [-2, -1, 1, 2, 3, 0], [-2, -1, 1, 2, 0, 3], [-2, -1, 1, 3, 2, 0], [-2, -1, 1, 3, 0, 2], [-2, -1, 1, 0, 2, 3], [-2, -1, 1, 0, 3, 2], [-2, -1, 2, 1, 3, 0], [-2, -1, 2, 1, 0, 3], [-2, -1, 2, 3, 1, 0], [-2, -1, 2, 3, 0, 1], [-2, -1, 2, 0, 1, 3], [-2, -1, 2, 0, 3, 1], [-2, -1, 3, 1, 2, 0], [-2, -1, 3, 1, 0, 2], [-2, -1, 3, 2, 1, 0], [-2, -1, 3, 2, 0, 1], [-2, -1, 3, 0, 1, 2], [-2, -1, 3, 0, 2, 1], [-2, -1, 0, 1, 2, 3], [-2, -1, 0, 1, 3, 2], [-2, -1, 0, 2, 1, 3], [-2, -1, 0, 2, 3, 1], [-2, -1, 0, 3, 1, 2], [-2, -1, 0, 3, 2, 1]]\n assert candidate(nums = [-1, 0, 1, 2, 3]) == [[-1, 0, 1, 2, 3], [-1, 0, 1, 3, 2], [-1, 0, 2, 1, 3], [-1, 0, 2, 3, 1], [-1, 0, 3, 1, 2], [-1, 0, 3, 2, 1], [-1, 1, 0, 2, 3], [-1, 1, 0, 3, 2], [-1, 1, 2, 0, 3], [-1, 1, 2, 3, 0], [-1, 1, 3, 0, 2], [-1, 1, 3, 2, 0], [-1, 2, 0, 1, 3], [-1, 2, 0, 3, 1], [-1, 2, 1, 0, 3], [-1, 2, 1, 3, 0], [-1, 2, 3, 0, 1], [-1, 2, 3, 1, 0], [-1, 3, 0, 1, 2], [-1, 3, 0, 2, 1], [-1, 3, 1, 0, 2], [-1, 3, 1, 2, 0], [-1, 3, 2, 0, 1], [-1, 3, 2, 1, 0], [0, -1, 1, 2, 3], [0, -1, 1, 3, 2], [0, -1, 2, 1, 3], [0, -1, 2, 3, 1], [0, -1, 3, 1, 2], [0, -1, 3, 2, 1], [0, 1, -1, 2, 3], [0, 1, -1, 3, 2], [0, 1, 2, -1, 3], [0, 1, 2, 3, -1], [0, 1, 3, -1, 2], [0, 1, 3, 2, -1], [0, 2, -1, 1, 3], [0, 2, -1, 3, 1], [0, 2, 1, -1, 3], [0, 2, 1, 3, -1], [0, 2, 3, -1, 1], [0, 2, 3, 1, -1], [0, 3, -1, 1, 2], [0, 3, -1, 2, 1], [0, 3, 1, -1, 2], [0, 3, 1, 2, -1], [0, 3, 2, -1, 1], [0, 3, 2, 1, -1], [1, -1, 0, 2, 3], [1, -1, 0, 3, 2], [1, -1, 2, 0, 3], [1, -1, 2, 3, 0], [1, -1, 3, 0, 2], [1, -1, 3, 2, 0], [1, 0, -1, 2, 3], [1, 0, -1, 3, 2], [1, 0, 2, -1, 3], [1, 0, 2, 3, -1], [1, 0, 3, -1, 2], [1, 0, 3, 2, -1], [1, 2, -1, 0, 3], [1, 2, -1, 3, 0], [1, 2, 0, -1, 3], [1, 2, 0, 3, -1], [1, 2, 3, -1, 0], [1, 2, 3, 0, -1], [1, 3, -1, 0, 2], [1, 3, -1, 2, 0], [1, 3, 0, -1, 2], [1, 3, 0, 2, -1], [1, 3, 2, -1, 0], [1, 3, 2, 0, -1], [2, -1, 0, 1, 3], [2, -1, 0, 3, 1], [2, -1, 1, 0, 3], [2, -1, 1, 3, 0], [2, -1, 3, 0, 1], [2, -1, 3, 1, 0], [2, 0, -1, 1, 3], [2, 0, -1, 3, 1], [2, 0, 1, -1, 3], [2, 0, 1, 3, -1], [2, 0, 3, -1, 1], [2, 0, 3, 1, -1], [2, 1, -1, 0, 3], [2, 1, -1, 3, 0], [2, 1, 0, -1, 3], [2, 1, 0, 3, -1], [2, 1, 3, -1, 0], [2, 1, 3, 0, -1], [2, 3, -1, 0, 1], [2, 3, -1, 1, 0], [2, 3, 0, -1, 1], [2, 3, 0, 1, -1], [2, 3, 1, -1, 0], [2, 3, 1, 0, -1], [3, -1, 0, 1, 2], [3, -1, 0, 2, 1], [3, -1, 1, 0, 2], [3, -1, 1, 2, 0], [3, -1, 2, 0, 1], [3, -1, 2, 1, 0], [3, 0, -1, 1, 2], [3, 0, -1, 2, 1], [3, 0, 1, -1, 2], [3, 0, 1, 2, -1], [3, 0, 2, -1, 1], [3, 0, 2, 1, -1], [3, 1, -1, 0, 2], [3, 1, -1, 2, 0], [3, 1, 0, -1, 2], [3, 1, 0, 2, -1], [3, 1, 2, -1, 0], [3, 1, 2, 0, -1], [3, 2, -1, 0, 1], [3, 2, -1, 1, 0], [3, 2, 0, -1, 1], [3, 2, 0, 1, -1], [3, 2, 1, -1, 0], [3, 2, 1, 0, -1]]\n assert candidate(nums = [5, 4, 3, 2, 1]) == [[5, 4, 3, 2, 1], [5, 4, 3, 1, 2], [5, 4, 2, 3, 1], [5, 4, 2, 1, 3], [5, 4, 1, 3, 2], [5, 4, 1, 2, 3], [5, 3, 4, 2, 1], [5, 3, 4, 1, 2], [5, 3, 2, 4, 1], [5, 3, 2, 1, 4], [5, 3, 1, 4, 2], [5, 3, 1, 2, 4], [5, 2, 4, 3, 1], [5, 2, 4, 1, 3], [5, 2, 3, 4, 1], [5, 2, 3, 1, 4], [5, 2, 1, 4, 3], [5, 2, 1, 3, 4], [5, 1, 4, 3, 2], [5, 1, 4, 2, 3], [5, 1, 3, 4, 2], [5, 1, 3, 2, 4], [5, 1, 2, 4, 3], [5, 1, 2, 3, 4], [4, 5, 3, 2, 1], [4, 5, 3, 1, 2], [4, 5, 2, 3, 1], [4, 5, 2, 1, 3], [4, 5, 1, 3, 2], [4, 5, 1, 2, 3], [4, 3, 5, 2, 1], [4, 3, 5, 1, 2], [4, 3, 2, 5, 1], [4, 3, 2, 1, 5], [4, 3, 1, 5, 2], [4, 3, 1, 2, 5], [4, 2, 5, 3, 1], [4, 2, 5, 1, 3], [4, 2, 3, 5, 1], [4, 2, 3, 1, 5], [4, 2, 1, 5, 3], [4, 2, 1, 3, 5], [4, 1, 5, 3, 2], [4, 1, 5, 2, 3], [4, 1, 3, 5, 2], [4, 1, 3, 2, 5], [4, 1, 2, 5, 3], [4, 1, 2, 3, 5], [3, 5, 4, 2, 1], [3, 5, 4, 1, 2], [3, 5, 2, 4, 1], [3, 5, 2, 1, 4], [3, 5, 1, 4, 2], [3, 5, 1, 2, 4], [3, 4, 5, 2, 1], [3, 4, 5, 1, 2], [3, 4, 2, 5, 1], [3, 4, 2, 1, 5], [3, 4, 1, 5, 2], [3, 4, 1, 2, 5], [3, 2, 5, 4, 1], [3, 2, 5, 1, 4], [3, 2, 4, 5, 1], [3, 2, 4, 1, 5], [3, 2, 1, 5, 4], [3, 2, 1, 4, 5], [3, 1, 5, 4, 2], [3, 1, 5, 2, 4], [3, 1, 4, 5, 2], [3, 1, 4, 2, 5], [3, 1, 2, 5, 4], [3, 1, 2, 4, 5], [2, 5, 4, 3, 1], [2, 5, 4, 1, 3], [2, 5, 3, 4, 1], [2, 5, 3, 1, 4], [2, 5, 1, 4, 3], [2, 5, 1, 3, 4], [2, 4, 5, 3, 1], [2, 4, 5, 1, 3], [2, 4, 3, 5, 1], [2, 4, 3, 1, 5], [2, 4, 1, 5, 3], [2, 4, 1, 3, 5], [2, 3, 5, 4, 1], [2, 3, 5, 1, 4], [2, 3, 4, 5, 1], [2, 3, 4, 1, 5], [2, 3, 1, 5, 4], [2, 3, 1, 4, 5], [2, 1, 5, 4, 3], [2, 1, 5, 3, 4], [2, 1, 4, 5, 3], [2, 1, 4, 3, 5], [2, 1, 3, 5, 4], [2, 1, 3, 4, 5], [1, 5, 4, 3, 2], [1, 5, 4, 2, 3], [1, 5, 3, 4, 2], [1, 5, 3, 2, 4], [1, 5, 2, 4, 3], [1, 5, 2, 3, 4], [1, 4, 5, 3, 2], [1, 4, 5, 2, 3], [1, 4, 3, 5, 2], [1, 4, 3, 2, 5], [1, 4, 2, 5, 3], [1, 4, 2, 3, 5], [1, 3, 5, 4, 2], [1, 3, 5, 2, 4], [1, 3, 4, 5, 2], [1, 3, 4, 2, 5], [1, 3, 2, 5, 4], [1, 3, 2, 4, 5], [1, 2, 5, 4, 3], [1, 2, 5, 3, 4], [1, 2, 4, 5, 3], [1, 2, 4, 3, 5], [1, 2, 3, 5, 4], [1, 2, 3, 4, 5]]\n assert candidate(nums = [6, 3, -1, 2, 0, -4]) == [[6, 3, -1, 2, 0, -4], [6, 3, -1, 2, -4, 0], [6, 3, -1, 0, 2, -4], [6, 3, -1, 0, -4, 2], [6, 3, -1, -4, 2, 0], [6, 3, -1, -4, 0, 2], [6, 3, 2, -1, 0, -4], [6, 3, 2, -1, -4, 0], [6, 3, 2, 0, -1, -4], [6, 3, 2, 0, -4, -1], [6, 3, 2, -4, -1, 0], [6, 3, 2, -4, 0, -1], [6, 3, 0, -1, 2, -4], [6, 3, 0, -1, -4, 2], [6, 3, 0, 2, -1, -4], [6, 3, 0, 2, -4, -1], [6, 3, 0, -4, -1, 2], [6, 3, 0, -4, 2, -1], [6, 3, -4, -1, 2, 0], [6, 3, -4, -1, 0, 2], [6, 3, -4, 2, -1, 0], [6, 3, -4, 2, 0, -1], [6, 3, -4, 0, -1, 2], [6, 3, -4, 0, 2, -1], [6, -1, 3, 2, 0, -4], [6, -1, 3, 2, -4, 0], [6, -1, 3, 0, 2, -4], [6, -1, 3, 0, -4, 2], [6, -1, 3, -4, 2, 0], [6, -1, 3, -4, 0, 2], [6, -1, 2, 3, 0, -4], [6, -1, 2, 3, -4, 0], [6, -1, 2, 0, 3, -4], [6, -1, 2, 0, -4, 3], [6, -1, 2, -4, 3, 0], [6, -1, 2, -4, 0, 3], [6, -1, 0, 3, 2, -4], [6, -1, 0, 3, -4, 2], [6, -1, 0, 2, 3, -4], [6, -1, 0, 2, -4, 3], [6, -1, 0, -4, 3, 2], [6, -1, 0, -4, 2, 3], [6, -1, -4, 3, 2, 0], [6, -1, -4, 3, 0, 2], [6, -1, -4, 2, 3, 0], [6, -1, -4, 2, 0, 3], [6, -1, -4, 0, 3, 2], [6, -1, -4, 0, 2, 3], [6, 2, 3, -1, 0, -4], [6, 2, 3, -1, -4, 0], [6, 2, 3, 0, -1, -4], [6, 2, 3, 0, -4, -1], [6, 2, 3, -4, -1, 0], [6, 2, 3, -4, 0, -1], [6, 2, -1, 3, 0, -4], [6, 2, -1, 3, -4, 0], [6, 2, -1, 0, 3, -4], [6, 2, -1, 0, -4, 3], [6, 2, -1, -4, 3, 0], [6, 2, -1, -4, 0, 3], [6, 2, 0, 3, -1, -4], [6, 2, 0, 3, -4, -1], [6, 2, 0, -1, 3, -4], [6, 2, 0, -1, -4, 3], [6, 2, 0, -4, 3, -1], [6, 2, 0, -4, -1, 3], [6, 2, -4, 3, -1, 0], [6, 2, -4, 3, 0, -1], [6, 2, -4, -1, 3, 0], [6, 2, -4, -1, 0, 3], [6, 2, -4, 0, 3, -1], [6, 2, -4, 0, -1, 3], [6, 0, 3, -1, 2, -4], [6, 0, 3, -1, -4, 2], [6, 0, 3, 2, -1, -4], [6, 0, 3, 2, -4, -1], [6, 0, 3, -4, -1, 2], [6, 0, 3, -4, 2, -1], [6, 0, -1, 3, 2, -4], [6, 0, -1, 3, -4, 2], [6, 0, -1, 2, 3, -4], [6, 0, -1, 2, -4, 3], [6, 0, -1, -4, 3, 2], [6, 0, -1, -4, 2, 3], [6, 0, 2, 3, -1, -4], [6, 0, 2, 3, -4, -1], [6, 0, 2, -1, 3, -4], [6, 0, 2, -1, -4, 3], [6, 0, 2, -4, 3, -1], [6, 0, 2, -4, -1, 3], [6, 0, -4, 3, -1, 2], [6, 0, -4, 3, 2, -1], [6, 0, -4, -1, 3, 2], [6, 0, -4, -1, 2, 3], [6, 0, -4, 2, 3, -1], [6, 0, -4, 2, -1, 3], [6, -4, 3, -1, 2, 0], [6, -4, 3, -1, 0, 2], [6, -4, 3, 2, -1, 0], [6, -4, 3, 2, 0, -1], [6, -4, 3, 0, -1, 2], [6, -4, 3, 0, 2, -1], [6, -4, -1, 3, 2, 0], [6, -4, -1, 3, 0, 2], [6, -4, -1, 2, 3, 0], [6, -4, -1, 2, 0, 3], [6, -4, -1, 0, 3, 2], [6, -4, -1, 0, 2, 3], [6, -4, 2, 3, -1, 0], [6, -4, 2, 3, 0, -1], [6, -4, 2, -1, 3, 0], [6, -4, 2, -1, 0, 3], [6, -4, 2, 0, 3, -1], [6, -4, 2, 0, -1, 3], [6, -4, 0, 3, -1, 2], [6, -4, 0, 3, 2, -1], [6, -4, 0, -1, 3, 2], [6, -4, 0, -1, 2, 3], [6, -4, 0, 2, 3, -1], [6, -4, 0, 2, -1, 3], [3, 6, -1, 2, 0, -4], [3, 6, -1, 2, -4, 0], [3, 6, -1, 0, 2, -4], [3, 6, -1, 0, -4, 2], [3, 6, -1, -4, 2, 0], [3, 6, -1, -4, 0, 2], [3, 6, 2, -1, 0, -4], [3, 6, 2, -1, -4, 0], [3, 6, 2, 0, -1, -4], [3, 6, 2, 0, -4, -1], [3, 6, 2, -4, -1, 0], [3, 6, 2, -4, 0, -1], [3, 6, 0, -1, 2, -4], [3, 6, 0, -1, -4, 2], [3, 6, 0, 2, -1, -4], [3, 6, 0, 2, -4, -1], [3, 6, 0, -4, -1, 2], [3, 6, 0, -4, 2, -1], [3, 6, -4, -1, 2, 0], [3, 6, -4, -1, 0, 2], [3, 6, -4, 2, -1, 0], [3, 6, -4, 2, 0, -1], [3, 6, -4, 0, -1, 2], [3, 6, -4, 0, 2, -1], [3, -1, 6, 2, 0, -4], [3, -1, 6, 2, -4, 0], [3, -1, 6, 0, 2, -4], [3, -1, 6, 0, -4, 2], [3, -1, 6, -4, 2, 0], [3, -1, 6, -4, 0, 2], [3, -1, 2, 6, 0, -4], [3, -1, 2, 6, -4, 0], [3, -1, 2, 0, 6, -4], [3, -1, 2, 0, -4, 6], [3, -1, 2, -4, 6, 0], [3, -1, 2, -4, 0, 6], [3, -1, 0, 6, 2, -4], [3, -1, 0, 6, -4, 2], [3, -1, 0, 2, 6, -4], [3, -1, 0, 2, -4, 6], [3, -1, 0, -4, 6, 2], [3, -1, 0, -4, 2, 6], [3, -1, -4, 6, 2, 0], [3, -1, -4, 6, 0, 2], [3, -1, -4, 2, 6, 0], [3, -1, -4, 2, 0, 6], [3, -1, -4, 0, 6, 2], [3, -1, -4, 0, 2, 6], [3, 2, 6, -1, 0, -4], [3, 2, 6, -1, -4, 0], [3, 2, 6, 0, -1, -4], [3, 2, 6, 0, -4, -1], [3, 2, 6, -4, -1, 0], [3, 2, 6, -4, 0, -1], [3, 2, -1, 6, 0, -4], [3, 2, -1, 6, -4, 0], [3, 2, -1, 0, 6, -4], [3, 2, -1, 0, -4, 6], [3, 2, -1, -4, 6, 0], [3, 2, -1, -4, 0, 6], [3, 2, 0, 6, -1, -4], [3, 2, 0, 6, -4, -1], [3, 2, 0, -1, 6, -4], [3, 2, 0, -1, -4, 6], [3, 2, 0, -4, 6, -1], [3, 2, 0, -4, -1, 6], [3, 2, -4, 6, -1, 0], [3, 2, -4, 6, 0, -1], [3, 2, -4, -1, 6, 0], [3, 2, -4, -1, 0, 6], [3, 2, -4, 0, 6, -1], [3, 2, -4, 0, -1, 6], [3, 0, 6, -1, 2, -4], [3, 0, 6, -1, -4, 2], [3, 0, 6, 2, -1, -4], [3, 0, 6, 2, -4, -1], [3, 0, 6, -4, -1, 2], [3, 0, 6, -4, 2, -1], [3, 0, -1, 6, 2, -4], [3, 0, -1, 6, -4, 2], [3, 0, -1, 2, 6, -4], [3, 0, -1, 2, -4, 6], [3, 0, -1, -4, 6, 2], [3, 0, -1, -4, 2, 6], [3, 0, 2, 6, -1, -4], [3, 0, 2, 6, -4, -1], [3, 0, 2, -1, 6, -4], [3, 0, 2, -1, -4, 6], [3, 0, 2, -4, 6, -1], [3, 0, 2, -4, -1, 6], [3, 0, -4, 6, -1, 2], [3, 0, -4, 6, 2, -1], [3, 0, -4, -1, 6, 2], [3, 0, -4, -1, 2, 6], [3, 0, -4, 2, 6, -1], [3, 0, -4, 2, -1, 6], [3, -4, 6, -1, 2, 0], [3, -4, 6, -1, 0, 2], [3, -4, 6, 2, -1, 0], [3, -4, 6, 2, 0, -1], [3, -4, 6, 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2, -1], [-4, 3, -1, 6, 2, 0], [-4, 3, -1, 6, 0, 2], [-4, 3, -1, 2, 6, 0], [-4, 3, -1, 2, 0, 6], [-4, 3, -1, 0, 6, 2], [-4, 3, -1, 0, 2, 6], [-4, 3, 2, 6, -1, 0], [-4, 3, 2, 6, 0, -1], [-4, 3, 2, -1, 6, 0], [-4, 3, 2, -1, 0, 6], [-4, 3, 2, 0, 6, -1], [-4, 3, 2, 0, -1, 6], [-4, 3, 0, 6, -1, 2], [-4, 3, 0, 6, 2, -1], [-4, 3, 0, -1, 6, 2], [-4, 3, 0, -1, 2, 6], [-4, 3, 0, 2, 6, -1], [-4, 3, 0, 2, -1, 6], [-4, -1, 6, 3, 2, 0], [-4, -1, 6, 3, 0, 2], [-4, -1, 6, 2, 3, 0], [-4, -1, 6, 2, 0, 3], [-4, -1, 6, 0, 3, 2], [-4, -1, 6, 0, 2, 3], [-4, -1, 3, 6, 2, 0], [-4, -1, 3, 6, 0, 2], [-4, -1, 3, 2, 6, 0], [-4, -1, 3, 2, 0, 6], [-4, -1, 3, 0, 6, 2], [-4, -1, 3, 0, 2, 6], [-4, -1, 2, 6, 3, 0], [-4, -1, 2, 6, 0, 3], [-4, -1, 2, 3, 6, 0], [-4, -1, 2, 3, 0, 6], [-4, -1, 2, 0, 6, 3], [-4, -1, 2, 0, 3, 6], [-4, -1, 0, 6, 3, 2], [-4, -1, 0, 6, 2, 3], [-4, -1, 0, 3, 6, 2], [-4, -1, 0, 3, 2, 6], [-4, -1, 0, 2, 6, 3], [-4, -1, 0, 2, 3, 6], [-4, 2, 6, 3, -1, 0], [-4, 2, 6, 3, 0, -1], [-4, 2, 6, -1, 3, 0], [-4, 2, 6, -1, 0, 3], [-4, 2, 6, 0, 3, -1], [-4, 2, 6, 0, -1, 3], [-4, 2, 3, 6, -1, 0], [-4, 2, 3, 6, 0, -1], [-4, 2, 3, -1, 6, 0], [-4, 2, 3, -1, 0, 6], [-4, 2, 3, 0, 6, -1], [-4, 2, 3, 0, -1, 6], [-4, 2, -1, 6, 3, 0], [-4, 2, -1, 6, 0, 3], [-4, 2, -1, 3, 6, 0], [-4, 2, -1, 3, 0, 6], [-4, 2, -1, 0, 6, 3], [-4, 2, -1, 0, 3, 6], [-4, 2, 0, 6, 3, -1], [-4, 2, 0, 6, -1, 3], [-4, 2, 0, 3, 6, -1], [-4, 2, 0, 3, -1, 6], [-4, 2, 0, -1, 6, 3], [-4, 2, 0, -1, 3, 6], [-4, 0, 6, 3, -1, 2], [-4, 0, 6, 3, 2, -1], [-4, 0, 6, -1, 3, 2], [-4, 0, 6, -1, 2, 3], [-4, 0, 6, 2, 3, -1], [-4, 0, 6, 2, -1, 3], [-4, 0, 3, 6, -1, 2], [-4, 0, 3, 6, 2, -1], [-4, 0, 3, -1, 6, 2], [-4, 0, 3, -1, 2, 6], [-4, 0, 3, 2, 6, -1], [-4, 0, 3, 2, -1, 6], [-4, 0, -1, 6, 3, 2], [-4, 0, -1, 6, 2, 3], [-4, 0, -1, 3, 6, 2], [-4, 0, -1, 3, 2, 6], [-4, 0, -1, 2, 6, 3], [-4, 0, -1, 2, 3, 6], [-4, 0, 2, 6, 3, -1], [-4, 0, 2, 6, -1, 3], [-4, 0, 2, 3, 6, -1], [-4, 0, 2, 3, -1, 6], [-4, 0, 2, -1, 6, 3], [-4, 0, 2, -1, 3, 6]]\n assert candidate(nums = [7, 3, 5, 9, 1, 4]) == [[7, 3, 5, 9, 1, 4], [7, 3, 5, 9, 4, 1], [7, 3, 5, 1, 9, 4], [7, 3, 5, 1, 4, 9], [7, 3, 5, 4, 9, 1], [7, 3, 5, 4, 1, 9], [7, 3, 9, 5, 1, 4], [7, 3, 9, 5, 4, 1], [7, 3, 9, 1, 5, 4], [7, 3, 9, 1, 4, 5], [7, 3, 9, 4, 5, 1], [7, 3, 9, 4, 1, 5], [7, 3, 1, 5, 9, 4], [7, 3, 1, 5, 4, 9], [7, 3, 1, 9, 5, 4], [7, 3, 1, 9, 4, 5], [7, 3, 1, 4, 5, 9], [7, 3, 1, 4, 9, 5], [7, 3, 4, 5, 9, 1], [7, 3, 4, 5, 1, 9], [7, 3, 4, 9, 5, 1], [7, 3, 4, 9, 1, 5], [7, 3, 4, 1, 5, 9], [7, 3, 4, 1, 9, 5], [7, 5, 3, 9, 1, 4], [7, 5, 3, 9, 4, 1], [7, 5, 3, 1, 9, 4], [7, 5, 3, 1, 4, 9], [7, 5, 3, 4, 9, 1], [7, 5, 3, 4, 1, 9], [7, 5, 9, 3, 1, 4], [7, 5, 9, 3, 4, 1], [7, 5, 9, 1, 3, 4], [7, 5, 9, 1, 4, 3], [7, 5, 9, 4, 3, 1], [7, 5, 9, 4, 1, 3], [7, 5, 1, 3, 9, 4], [7, 5, 1, 3, 4, 9], [7, 5, 1, 9, 3, 4], [7, 5, 1, 9, 4, 3], [7, 5, 1, 4, 3, 9], [7, 5, 1, 4, 9, 3], [7, 5, 4, 3, 9, 1], [7, 5, 4, 3, 1, 9], [7, 5, 4, 9, 3, 1], [7, 5, 4, 9, 1, 3], [7, 5, 4, 1, 3, 9], [7, 5, 4, 1, 9, 3], [7, 9, 3, 5, 1, 4], [7, 9, 3, 5, 4, 1], [7, 9, 3, 1, 5, 4], [7, 9, 3, 1, 4, 5], [7, 9, 3, 4, 5, 1], [7, 9, 3, 4, 1, 5], [7, 9, 5, 3, 1, 4], [7, 9, 5, 3, 4, 1], [7, 9, 5, 1, 3, 4], [7, 9, 5, 1, 4, 3], [7, 9, 5, 4, 3, 1], [7, 9, 5, 4, 1, 3], [7, 9, 1, 3, 5, 4], [7, 9, 1, 3, 4, 5], [7, 9, 1, 5, 3, 4], [7, 9, 1, 5, 4, 3], [7, 9, 1, 4, 3, 5], [7, 9, 1, 4, 5, 3], [7, 9, 4, 3, 5, 1], [7, 9, 4, 3, 1, 5], [7, 9, 4, 5, 3, 1], [7, 9, 4, 5, 1, 3], [7, 9, 4, 1, 3, 5], [7, 9, 4, 1, 5, 3], [7, 1, 3, 5, 9, 4], [7, 1, 3, 5, 4, 9], [7, 1, 3, 9, 5, 4], [7, 1, 3, 9, 4, 5], [7, 1, 3, 4, 5, 9], [7, 1, 3, 4, 9, 5], [7, 1, 5, 3, 9, 4], [7, 1, 5, 3, 4, 9], [7, 1, 5, 9, 3, 4], [7, 1, 5, 9, 4, 3], [7, 1, 5, 4, 3, 9], [7, 1, 5, 4, 9, 3], [7, 1, 9, 3, 5, 4], [7, 1, 9, 3, 4, 5], [7, 1, 9, 5, 3, 4], [7, 1, 9, 5, 4, 3], [7, 1, 9, 4, 3, 5], [7, 1, 9, 4, 5, 3], [7, 1, 4, 3, 5, 9], [7, 1, 4, 3, 9, 5], [7, 1, 4, 5, 3, 9], [7, 1, 4, 5, 9, 3], [7, 1, 4, 9, 3, 5], [7, 1, 4, 9, 5, 3], [7, 4, 3, 5, 9, 1], [7, 4, 3, 5, 1, 9], [7, 4, 3, 9, 5, 1], [7, 4, 3, 9, 1, 5], [7, 4, 3, 1, 5, 9], [7, 4, 3, 1, 9, 5], [7, 4, 5, 3, 9, 1], [7, 4, 5, 3, 1, 9], [7, 4, 5, 9, 3, 1], [7, 4, 5, 9, 1, 3], [7, 4, 5, 1, 3, 9], [7, 4, 5, 1, 9, 3], [7, 4, 9, 3, 5, 1], [7, 4, 9, 3, 1, 5], [7, 4, 9, 5, 3, 1], [7, 4, 9, 5, 1, 3], [7, 4, 9, 1, 3, 5], [7, 4, 9, 1, 5, 3], [7, 4, 1, 3, 5, 9], [7, 4, 1, 3, 9, 5], [7, 4, 1, 5, 3, 9], [7, 4, 1, 5, 9, 3], [7, 4, 1, 9, 3, 5], [7, 4, 1, 9, 5, 3], [3, 7, 5, 9, 1, 4], [3, 7, 5, 9, 4, 1], [3, 7, 5, 1, 9, 4], [3, 7, 5, 1, 4, 9], [3, 7, 5, 4, 9, 1], [3, 7, 5, 4, 1, 9], [3, 7, 9, 5, 1, 4], [3, 7, 9, 5, 4, 1], [3, 7, 9, 1, 5, 4], [3, 7, 9, 1, 4, 5], [3, 7, 9, 4, 5, 1], [3, 7, 9, 4, 1, 5], [3, 7, 1, 5, 9, 4], [3, 7, 1, 5, 4, 9], [3, 7, 1, 9, 5, 4], [3, 7, 1, 9, 4, 5], [3, 7, 1, 4, 5, 9], [3, 7, 1, 4, 9, 5], [3, 7, 4, 5, 9, 1], [3, 7, 4, 5, 1, 9], [3, 7, 4, 9, 5, 1], [3, 7, 4, 9, 1, 5], [3, 7, 4, 1, 5, 9], [3, 7, 4, 1, 9, 5], [3, 5, 7, 9, 1, 4], [3, 5, 7, 9, 4, 1], [3, 5, 7, 1, 9, 4], [3, 5, 7, 1, 4, 9], [3, 5, 7, 4, 9, 1], [3, 5, 7, 4, 1, 9], [3, 5, 9, 7, 1, 4], [3, 5, 9, 7, 4, 1], [3, 5, 9, 1, 7, 4], [3, 5, 9, 1, 4, 7], [3, 5, 9, 4, 7, 1], [3, 5, 9, 4, 1, 7], [3, 5, 1, 7, 9, 4], [3, 5, 1, 7, 4, 9], [3, 5, 1, 9, 7, 4], [3, 5, 1, 9, 4, 7], [3, 5, 1, 4, 7, 9], [3, 5, 1, 4, 9, 7], [3, 5, 4, 7, 9, 1], [3, 5, 4, 7, 1, 9], [3, 5, 4, 9, 7, 1], [3, 5, 4, 9, 1, 7], [3, 5, 4, 1, 7, 9], [3, 5, 4, 1, 9, 7], [3, 9, 7, 5, 1, 4], [3, 9, 7, 5, 4, 1], [3, 9, 7, 1, 5, 4], [3, 9, 7, 1, 4, 5], [3, 9, 7, 4, 5, 1], [3, 9, 7, 4, 1, 5], [3, 9, 5, 7, 1, 4], [3, 9, 5, 7, 4, 1], [3, 9, 5, 1, 7, 4], [3, 9, 5, 1, 4, 7], [3, 9, 5, 4, 7, 1], [3, 9, 5, 4, 1, 7], [3, 9, 1, 7, 5, 4], [3, 9, 1, 7, 4, 5], [3, 9, 1, 5, 7, 4], [3, 9, 1, 5, 4, 7], [3, 9, 1, 4, 7, 5], [3, 9, 1, 4, 5, 7], [3, 9, 4, 7, 5, 1], [3, 9, 4, 7, 1, 5], [3, 9, 4, 5, 7, 1], [3, 9, 4, 5, 1, 7], [3, 9, 4, 1, 7, 5], [3, 9, 4, 1, 5, 7], [3, 1, 7, 5, 9, 4], [3, 1, 7, 5, 4, 9], [3, 1, 7, 9, 5, 4], [3, 1, 7, 9, 4, 5], [3, 1, 7, 4, 5, 9], [3, 1, 7, 4, 9, 5], [3, 1, 5, 7, 9, 4], [3, 1, 5, 7, 4, 9], [3, 1, 5, 9, 7, 4], [3, 1, 5, 9, 4, 7], [3, 1, 5, 4, 7, 9], [3, 1, 5, 4, 9, 7], [3, 1, 9, 7, 5, 4], [3, 1, 9, 7, 4, 5], [3, 1, 9, 5, 7, 4], [3, 1, 9, 5, 4, 7], [3, 1, 9, 4, 7, 5], [3, 1, 9, 4, 5, 7], [3, 1, 4, 7, 5, 9], [3, 1, 4, 7, 9, 5], [3, 1, 4, 5, 7, 9], [3, 1, 4, 5, 9, 7], [3, 1, 4, 9, 7, 5], [3, 1, 4, 9, 5, 7], [3, 4, 7, 5, 9, 1], [3, 4, 7, 5, 1, 9], [3, 4, 7, 9, 5, 1], [3, 4, 7, 9, 1, 5], [3, 4, 7, 1, 5, 9], [3, 4, 7, 1, 9, 5], [3, 4, 5, 7, 9, 1], [3, 4, 5, 7, 1, 9], [3, 4, 5, 9, 7, 1], [3, 4, 5, 9, 1, 7], [3, 4, 5, 1, 7, 9], [3, 4, 5, 1, 9, 7], [3, 4, 9, 7, 5, 1], [3, 4, 9, 7, 1, 5], [3, 4, 9, 5, 7, 1], [3, 4, 9, 5, 1, 7], [3, 4, 9, 1, 7, 5], [3, 4, 9, 1, 5, 7], [3, 4, 1, 7, 5, 9], [3, 4, 1, 7, 9, 5], [3, 4, 1, 5, 7, 9], [3, 4, 1, 5, 9, 7], [3, 4, 1, 9, 7, 5], [3, 4, 1, 9, 5, 7], [5, 7, 3, 9, 1, 4], [5, 7, 3, 9, 4, 1], [5, 7, 3, 1, 9, 4], [5, 7, 3, 1, 4, 9], [5, 7, 3, 4, 9, 1], [5, 7, 3, 4, 1, 9], [5, 7, 9, 3, 1, 4], [5, 7, 9, 3, 4, 1], [5, 7, 9, 1, 3, 4], [5, 7, 9, 1, 4, 3], [5, 7, 9, 4, 3, 1], [5, 7, 9, 4, 1, 3], [5, 7, 1, 3, 9, 4], [5, 7, 1, 3, 4, 9], [5, 7, 1, 9, 3, 4], [5, 7, 1, 9, 4, 3], [5, 7, 1, 4, 3, 9], [5, 7, 1, 4, 9, 3], [5, 7, 4, 3, 9, 1], [5, 7, 4, 3, 1, 9], [5, 7, 4, 9, 3, 1], [5, 7, 4, 9, 1, 3], [5, 7, 4, 1, 3, 9], [5, 7, 4, 1, 9, 3], [5, 3, 7, 9, 1, 4], [5, 3, 7, 9, 4, 1], [5, 3, 7, 1, 9, 4], [5, 3, 7, 1, 4, 9], [5, 3, 7, 4, 9, 1], [5, 3, 7, 4, 1, 9], [5, 3, 9, 7, 1, 4], [5, 3, 9, 7, 4, 1], [5, 3, 9, 1, 7, 4], [5, 3, 9, 1, 4, 7], [5, 3, 9, 4, 7, 1], [5, 3, 9, 4, 1, 7], [5, 3, 1, 7, 9, 4], [5, 3, 1, 7, 4, 9], [5, 3, 1, 9, 7, 4], [5, 3, 1, 9, 4, 7], [5, 3, 1, 4, 7, 9], [5, 3, 1, 4, 9, 7], [5, 3, 4, 7, 9, 1], [5, 3, 4, 7, 1, 9], [5, 3, 4, 9, 7, 1], [5, 3, 4, 9, 1, 7], [5, 3, 4, 1, 7, 9], [5, 3, 4, 1, 9, 7], [5, 9, 7, 3, 1, 4], [5, 9, 7, 3, 4, 1], [5, 9, 7, 1, 3, 4], [5, 9, 7, 1, 4, 3], [5, 9, 7, 4, 3, 1], [5, 9, 7, 4, 1, 3], [5, 9, 3, 7, 1, 4], [5, 9, 3, 7, 4, 1], [5, 9, 3, 1, 7, 4], [5, 9, 3, 1, 4, 7], [5, 9, 3, 4, 7, 1], [5, 9, 3, 4, 1, 7], [5, 9, 1, 7, 3, 4], [5, 9, 1, 7, 4, 3], [5, 9, 1, 3, 7, 4], [5, 9, 1, 3, 4, 7], [5, 9, 1, 4, 7, 3], [5, 9, 1, 4, 3, 7], [5, 9, 4, 7, 3, 1], [5, 9, 4, 7, 1, 3], [5, 9, 4, 3, 7, 1], [5, 9, 4, 3, 1, 7], [5, 9, 4, 1, 7, 3], [5, 9, 4, 1, 3, 7], [5, 1, 7, 3, 9, 4], [5, 1, 7, 3, 4, 9], [5, 1, 7, 9, 3, 4], [5, 1, 7, 9, 4, 3], [5, 1, 7, 4, 3, 9], [5, 1, 7, 4, 9, 3], [5, 1, 3, 7, 9, 4], [5, 1, 3, 7, 4, 9], [5, 1, 3, 9, 7, 4], [5, 1, 3, 9, 4, 7], [5, 1, 3, 4, 7, 9], [5, 1, 3, 4, 9, 7], [5, 1, 9, 7, 3, 4], [5, 1, 9, 7, 4, 3], [5, 1, 9, 3, 7, 4], [5, 1, 9, 3, 4, 7], [5, 1, 9, 4, 7, 3], [5, 1, 9, 4, 3, 7], [5, 1, 4, 7, 3, 9], [5, 1, 4, 7, 9, 3], [5, 1, 4, 3, 7, 9], [5, 1, 4, 3, 9, 7], [5, 1, 4, 9, 7, 3], [5, 1, 4, 9, 3, 7], [5, 4, 7, 3, 9, 1], [5, 4, 7, 3, 1, 9], [5, 4, 7, 9, 3, 1], [5, 4, 7, 9, 1, 3], [5, 4, 7, 1, 3, 9], [5, 4, 7, 1, 9, 3], [5, 4, 3, 7, 9, 1], [5, 4, 3, 7, 1, 9], [5, 4, 3, 9, 7, 1], [5, 4, 3, 9, 1, 7], [5, 4, 3, 1, 7, 9], [5, 4, 3, 1, 9, 7], [5, 4, 9, 7, 3, 1], [5, 4, 9, 7, 1, 3], [5, 4, 9, 3, 7, 1], [5, 4, 9, 3, 1, 7], [5, 4, 9, 1, 7, 3], [5, 4, 9, 1, 3, 7], [5, 4, 1, 7, 3, 9], [5, 4, 1, 7, 9, 3], [5, 4, 1, 3, 7, 9], [5, 4, 1, 3, 9, 7], [5, 4, 1, 9, 7, 3], [5, 4, 1, 9, 3, 7], [9, 7, 3, 5, 1, 4], [9, 7, 3, 5, 4, 1], [9, 7, 3, 1, 5, 4], [9, 7, 3, 1, 4, 5], [9, 7, 3, 4, 5, 1], [9, 7, 3, 4, 1, 5], [9, 7, 5, 3, 1, 4], [9, 7, 5, 3, 4, 1], [9, 7, 5, 1, 3, 4], [9, 7, 5, 1, 4, 3], [9, 7, 5, 4, 3, 1], [9, 7, 5, 4, 1, 3], [9, 7, 1, 3, 5, 4], [9, 7, 1, 3, 4, 5], [9, 7, 1, 5, 3, 4], [9, 7, 1, 5, 4, 3], [9, 7, 1, 4, 3, 5], [9, 7, 1, 4, 5, 3], [9, 7, 4, 3, 5, 1], [9, 7, 4, 3, 1, 5], [9, 7, 4, 5, 3, 1], [9, 7, 4, 5, 1, 3], [9, 7, 4, 1, 3, 5], [9, 7, 4, 1, 5, 3], [9, 3, 7, 5, 1, 4], [9, 3, 7, 5, 4, 1], [9, 3, 7, 1, 5, 4], [9, 3, 7, 1, 4, 5], [9, 3, 7, 4, 5, 1], [9, 3, 7, 4, 1, 5], [9, 3, 5, 7, 1, 4], [9, 3, 5, 7, 4, 1], [9, 3, 5, 1, 7, 4], [9, 3, 5, 1, 4, 7], [9, 3, 5, 4, 7, 1], [9, 3, 5, 4, 1, 7], [9, 3, 1, 7, 5, 4], [9, 3, 1, 7, 4, 5], [9, 3, 1, 5, 7, 4], [9, 3, 1, 5, 4, 7], [9, 3, 1, 4, 7, 5], [9, 3, 1, 4, 5, 7], [9, 3, 4, 7, 5, 1], [9, 3, 4, 7, 1, 5], [9, 3, 4, 5, 7, 1], [9, 3, 4, 5, 1, 7], [9, 3, 4, 1, 7, 5], [9, 3, 4, 1, 5, 7], [9, 5, 7, 3, 1, 4], [9, 5, 7, 3, 4, 1], [9, 5, 7, 1, 3, 4], [9, 5, 7, 1, 4, 3], [9, 5, 7, 4, 3, 1], [9, 5, 7, 4, 1, 3], [9, 5, 3, 7, 1, 4], [9, 5, 3, 7, 4, 1], [9, 5, 3, 1, 7, 4], [9, 5, 3, 1, 4, 7], [9, 5, 3, 4, 7, 1], [9, 5, 3, 4, 1, 7], [9, 5, 1, 7, 3, 4], [9, 5, 1, 7, 4, 3], [9, 5, 1, 3, 7, 4], [9, 5, 1, 3, 4, 7], [9, 5, 1, 4, 7, 3], [9, 5, 1, 4, 3, 7], [9, 5, 4, 7, 3, 1], [9, 5, 4, 7, 1, 3], [9, 5, 4, 3, 7, 1], [9, 5, 4, 3, 1, 7], [9, 5, 4, 1, 7, 3], [9, 5, 4, 1, 3, 7], [9, 1, 7, 3, 5, 4], [9, 1, 7, 3, 4, 5], [9, 1, 7, 5, 3, 4], [9, 1, 7, 5, 4, 3], [9, 1, 7, 4, 3, 5], [9, 1, 7, 4, 5, 3], [9, 1, 3, 7, 5, 4], [9, 1, 3, 7, 4, 5], [9, 1, 3, 5, 7, 4], [9, 1, 3, 5, 4, 7], [9, 1, 3, 4, 7, 5], [9, 1, 3, 4, 5, 7], [9, 1, 5, 7, 3, 4], [9, 1, 5, 7, 4, 3], [9, 1, 5, 3, 7, 4], [9, 1, 5, 3, 4, 7], [9, 1, 5, 4, 7, 3], [9, 1, 5, 4, 3, 7], [9, 1, 4, 7, 3, 5], [9, 1, 4, 7, 5, 3], [9, 1, 4, 3, 7, 5], [9, 1, 4, 3, 5, 7], [9, 1, 4, 5, 7, 3], [9, 1, 4, 5, 3, 7], [9, 4, 7, 3, 5, 1], [9, 4, 7, 3, 1, 5], [9, 4, 7, 5, 3, 1], [9, 4, 7, 5, 1, 3], [9, 4, 7, 1, 3, 5], [9, 4, 7, 1, 5, 3], [9, 4, 3, 7, 5, 1], [9, 4, 3, 7, 1, 5], [9, 4, 3, 5, 7, 1], [9, 4, 3, 5, 1, 7], [9, 4, 3, 1, 7, 5], [9, 4, 3, 1, 5, 7], [9, 4, 5, 7, 3, 1], [9, 4, 5, 7, 1, 3], [9, 4, 5, 3, 7, 1], [9, 4, 5, 3, 1, 7], [9, 4, 5, 1, 7, 3], [9, 4, 5, 1, 3, 7], [9, 4, 1, 7, 3, 5], [9, 4, 1, 7, 5, 3], [9, 4, 1, 3, 7, 5], [9, 4, 1, 3, 5, 7], [9, 4, 1, 5, 7, 3], [9, 4, 1, 5, 3, 7], [1, 7, 3, 5, 9, 4], [1, 7, 3, 5, 4, 9], [1, 7, 3, 9, 5, 4], [1, 7, 3, 9, 4, 5], [1, 7, 3, 4, 5, 9], [1, 7, 3, 4, 9, 5], [1, 7, 5, 3, 9, 4], [1, 7, 5, 3, 4, 9], [1, 7, 5, 9, 3, 4], [1, 7, 5, 9, 4, 3], [1, 7, 5, 4, 3, 9], [1, 7, 5, 4, 9, 3], [1, 7, 9, 3, 5, 4], [1, 7, 9, 3, 4, 5], [1, 7, 9, 5, 3, 4], [1, 7, 9, 5, 4, 3], [1, 7, 9, 4, 3, 5], [1, 7, 9, 4, 5, 3], [1, 7, 4, 3, 5, 9], [1, 7, 4, 3, 9, 5], [1, 7, 4, 5, 3, 9], [1, 7, 4, 5, 9, 3], [1, 7, 4, 9, 3, 5], [1, 7, 4, 9, 5, 3], [1, 3, 7, 5, 9, 4], [1, 3, 7, 5, 4, 9], [1, 3, 7, 9, 5, 4], [1, 3, 7, 9, 4, 5], [1, 3, 7, 4, 5, 9], [1, 3, 7, 4, 9, 5], [1, 3, 5, 7, 9, 4], [1, 3, 5, 7, 4, 9], [1, 3, 5, 9, 7, 4], [1, 3, 5, 9, 4, 7], [1, 3, 5, 4, 7, 9], [1, 3, 5, 4, 9, 7], [1, 3, 9, 7, 5, 4], [1, 3, 9, 7, 4, 5], [1, 3, 9, 5, 7, 4], [1, 3, 9, 5, 4, 7], [1, 3, 9, 4, 7, 5], [1, 3, 9, 4, 5, 7], [1, 3, 4, 7, 5, 9], [1, 3, 4, 7, 9, 5], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 9, 7], [1, 3, 4, 9, 7, 5], [1, 3, 4, 9, 5, 7], [1, 5, 7, 3, 9, 4], [1, 5, 7, 3, 4, 9], [1, 5, 7, 9, 3, 4], [1, 5, 7, 9, 4, 3], [1, 5, 7, 4, 3, 9], [1, 5, 7, 4, 9, 3], [1, 5, 3, 7, 9, 4], [1, 5, 3, 7, 4, 9], [1, 5, 3, 9, 7, 4], [1, 5, 3, 9, 4, 7], [1, 5, 3, 4, 7, 9], [1, 5, 3, 4, 9, 7], [1, 5, 9, 7, 3, 4], [1, 5, 9, 7, 4, 3], [1, 5, 9, 3, 7, 4], [1, 5, 9, 3, 4, 7], [1, 5, 9, 4, 7, 3], [1, 5, 9, 4, 3, 7], [1, 5, 4, 7, 3, 9], [1, 5, 4, 7, 9, 3], [1, 5, 4, 3, 7, 9], [1, 5, 4, 3, 9, 7], [1, 5, 4, 9, 7, 3], [1, 5, 4, 9, 3, 7], [1, 9, 7, 3, 5, 4], [1, 9, 7, 3, 4, 5], [1, 9, 7, 5, 3, 4], [1, 9, 7, 5, 4, 3], [1, 9, 7, 4, 3, 5], [1, 9, 7, 4, 5, 3], [1, 9, 3, 7, 5, 4], [1, 9, 3, 7, 4, 5], [1, 9, 3, 5, 7, 4], [1, 9, 3, 5, 4, 7], [1, 9, 3, 4, 7, 5], [1, 9, 3, 4, 5, 7], [1, 9, 5, 7, 3, 4], [1, 9, 5, 7, 4, 3], [1, 9, 5, 3, 7, 4], [1, 9, 5, 3, 4, 7], [1, 9, 5, 4, 7, 3], [1, 9, 5, 4, 3, 7], [1, 9, 4, 7, 3, 5], [1, 9, 4, 7, 5, 3], [1, 9, 4, 3, 7, 5], [1, 9, 4, 3, 5, 7], [1, 9, 4, 5, 7, 3], [1, 9, 4, 5, 3, 7], [1, 4, 7, 3, 5, 9], [1, 4, 7, 3, 9, 5], [1, 4, 7, 5, 3, 9], [1, 4, 7, 5, 9, 3], [1, 4, 7, 9, 3, 5], [1, 4, 7, 9, 5, 3], [1, 4, 3, 7, 5, 9], [1, 4, 3, 7, 9, 5], [1, 4, 3, 5, 7, 9], [1, 4, 3, 5, 9, 7], [1, 4, 3, 9, 7, 5], [1, 4, 3, 9, 5, 7], [1, 4, 5, 7, 3, 9], [1, 4, 5, 7, 9, 3], [1, 4, 5, 3, 7, 9], [1, 4, 5, 3, 9, 7], [1, 4, 5, 9, 7, 3], [1, 4, 5, 9, 3, 7], [1, 4, 9, 7, 3, 5], [1, 4, 9, 7, 5, 3], [1, 4, 9, 3, 7, 5], [1, 4, 9, 3, 5, 7], [1, 4, 9, 5, 7, 3], [1, 4, 9, 5, 3, 7], [4, 7, 3, 5, 9, 1], [4, 7, 3, 5, 1, 9], [4, 7, 3, 9, 5, 1], [4, 7, 3, 9, 1, 5], [4, 7, 3, 1, 5, 9], [4, 7, 3, 1, 9, 5], [4, 7, 5, 3, 9, 1], [4, 7, 5, 3, 1, 9], [4, 7, 5, 9, 3, 1], [4, 7, 5, 9, 1, 3], [4, 7, 5, 1, 3, 9], [4, 7, 5, 1, 9, 3], [4, 7, 9, 3, 5, 1], [4, 7, 9, 3, 1, 5], [4, 7, 9, 5, 3, 1], [4, 7, 9, 5, 1, 3], [4, 7, 9, 1, 3, 5], [4, 7, 9, 1, 5, 3], [4, 7, 1, 3, 5, 9], [4, 7, 1, 3, 9, 5], [4, 7, 1, 5, 3, 9], [4, 7, 1, 5, 9, 3], [4, 7, 1, 9, 3, 5], [4, 7, 1, 9, 5, 3], [4, 3, 7, 5, 9, 1], [4, 3, 7, 5, 1, 9], [4, 3, 7, 9, 5, 1], [4, 3, 7, 9, 1, 5], [4, 3, 7, 1, 5, 9], [4, 3, 7, 1, 9, 5], [4, 3, 5, 7, 9, 1], [4, 3, 5, 7, 1, 9], [4, 3, 5, 9, 7, 1], [4, 3, 5, 9, 1, 7], [4, 3, 5, 1, 7, 9], [4, 3, 5, 1, 9, 7], [4, 3, 9, 7, 5, 1], [4, 3, 9, 7, 1, 5], [4, 3, 9, 5, 7, 1], [4, 3, 9, 5, 1, 7], [4, 3, 9, 1, 7, 5], [4, 3, 9, 1, 5, 7], [4, 3, 1, 7, 5, 9], [4, 3, 1, 7, 9, 5], [4, 3, 1, 5, 7, 9], [4, 3, 1, 5, 9, 7], [4, 3, 1, 9, 7, 5], [4, 3, 1, 9, 5, 7], [4, 5, 7, 3, 9, 1], [4, 5, 7, 3, 1, 9], [4, 5, 7, 9, 3, 1], [4, 5, 7, 9, 1, 3], [4, 5, 7, 1, 3, 9], [4, 5, 7, 1, 9, 3], [4, 5, 3, 7, 9, 1], [4, 5, 3, 7, 1, 9], [4, 5, 3, 9, 7, 1], [4, 5, 3, 9, 1, 7], [4, 5, 3, 1, 7, 9], [4, 5, 3, 1, 9, 7], [4, 5, 9, 7, 3, 1], [4, 5, 9, 7, 1, 3], [4, 5, 9, 3, 7, 1], [4, 5, 9, 3, 1, 7], [4, 5, 9, 1, 7, 3], [4, 5, 9, 1, 3, 7], [4, 5, 1, 7, 3, 9], [4, 5, 1, 7, 9, 3], [4, 5, 1, 3, 7, 9], [4, 5, 1, 3, 9, 7], [4, 5, 1, 9, 7, 3], [4, 5, 1, 9, 3, 7], [4, 9, 7, 3, 5, 1], [4, 9, 7, 3, 1, 5], [4, 9, 7, 5, 3, 1], [4, 9, 7, 5, 1, 3], [4, 9, 7, 1, 3, 5], [4, 9, 7, 1, 5, 3], [4, 9, 3, 7, 5, 1], [4, 9, 3, 7, 1, 5], [4, 9, 3, 5, 7, 1], [4, 9, 3, 5, 1, 7], [4, 9, 3, 1, 7, 5], [4, 9, 3, 1, 5, 7], [4, 9, 5, 7, 3, 1], [4, 9, 5, 7, 1, 3], [4, 9, 5, 3, 7, 1], [4, 9, 5, 3, 1, 7], [4, 9, 5, 1, 7, 3], [4, 9, 5, 1, 3, 7], [4, 9, 1, 7, 3, 5], [4, 9, 1, 7, 5, 3], [4, 9, 1, 3, 7, 5], [4, 9, 1, 3, 5, 7], [4, 9, 1, 5, 7, 3], [4, 9, 1, 5, 3, 7], [4, 1, 7, 3, 5, 9], [4, 1, 7, 3, 9, 5], [4, 1, 7, 5, 3, 9], [4, 1, 7, 5, 9, 3], [4, 1, 7, 9, 3, 5], [4, 1, 7, 9, 5, 3], [4, 1, 3, 7, 5, 9], [4, 1, 3, 7, 9, 5], [4, 1, 3, 5, 7, 9], [4, 1, 3, 5, 9, 7], [4, 1, 3, 9, 7, 5], [4, 1, 3, 9, 5, 7], [4, 1, 5, 7, 3, 9], [4, 1, 5, 7, 9, 3], [4, 1, 5, 3, 7, 9], [4, 1, 5, 3, 9, 7], [4, 1, 5, 9, 7, 3], [4, 1, 5, 9, 3, 7], [4, 1, 9, 7, 3, 5], [4, 1, 9, 7, 5, 3], [4, 1, 9, 3, 7, 5], [4, 1, 9, 3, 5, 7], [4, 1, 9, 5, 7, 3], [4, 1, 9, 5, 3, 7]]\n assert candidate(nums = [0]) == [[0]]\n assert candidate(nums = [-1, 2, -3, 4, -5, 6]) == [[-1, 2, -3, 4, -5, 6], [-1, 2, -3, 4, 6, -5], [-1, 2, -3, -5, 4, 6], [-1, 2, -3, -5, 6, 4], [-1, 2, -3, 6, 4, -5], [-1, 2, -3, 6, -5, 4], [-1, 2, 4, -3, -5, 6], [-1, 2, 4, -3, 6, -5], [-1, 2, 4, -5, -3, 6], [-1, 2, 4, -5, 6, -3], [-1, 2, 4, 6, -3, -5], [-1, 2, 4, 6, -5, -3], [-1, 2, -5, -3, 4, 6], [-1, 2, -5, -3, 6, 4], [-1, 2, -5, 4, -3, 6], [-1, 2, -5, 4, 6, -3], [-1, 2, -5, 6, -3, 4], [-1, 2, -5, 6, 4, -3], [-1, 2, 6, -3, 4, -5], [-1, 2, 6, -3, -5, 4], [-1, 2, 6, 4, -3, -5], [-1, 2, 6, 4, -5, -3], [-1, 2, 6, -5, -3, 4], [-1, 2, 6, -5, 4, -3], [-1, -3, 2, 4, -5, 6], [-1, -3, 2, 4, 6, -5], [-1, -3, 2, -5, 4, 6], [-1, -3, 2, -5, 6, 4], [-1, -3, 2, 6, 4, -5], [-1, -3, 2, 6, -5, 4], [-1, -3, 4, 2, -5, 6], [-1, -3, 4, 2, 6, -5], [-1, -3, 4, -5, 2, 6], [-1, -3, 4, -5, 6, 2], [-1, -3, 4, 6, 2, -5], [-1, -3, 4, 6, -5, 2], [-1, -3, -5, 2, 4, 6], [-1, -3, -5, 2, 6, 4], [-1, -3, -5, 4, 2, 6], [-1, -3, -5, 4, 6, 2], [-1, -3, -5, 6, 2, 4], [-1, -3, -5, 6, 4, 2], [-1, -3, 6, 2, 4, -5], [-1, -3, 6, 2, -5, 4], [-1, -3, 6, 4, 2, -5], [-1, -3, 6, 4, -5, 2], [-1, -3, 6, -5, 2, 4], [-1, -3, 6, -5, 4, 2], [-1, 4, 2, -3, -5, 6], [-1, 4, 2, -3, 6, -5], [-1, 4, 2, -5, -3, 6], [-1, 4, 2, -5, 6, -3], [-1, 4, 2, 6, -3, -5], [-1, 4, 2, 6, -5, -3], [-1, 4, -3, 2, -5, 6], [-1, 4, -3, 2, 6, -5], [-1, 4, -3, -5, 2, 6], [-1, 4, -3, -5, 6, 2], [-1, 4, -3, 6, 2, -5], [-1, 4, -3, 6, -5, 2], [-1, 4, -5, 2, -3, 6], [-1, 4, -5, 2, 6, -3], [-1, 4, -5, -3, 2, 6], [-1, 4, -5, -3, 6, 2], [-1, 4, -5, 6, 2, -3], [-1, 4, -5, 6, -3, 2], [-1, 4, 6, 2, -3, -5], [-1, 4, 6, 2, -5, -3], [-1, 4, 6, -3, 2, -5], [-1, 4, 6, -3, -5, 2], [-1, 4, 6, -5, 2, -3], [-1, 4, 6, -5, -3, 2], [-1, -5, 2, -3, 4, 6], [-1, -5, 2, -3, 6, 4], [-1, -5, 2, 4, -3, 6], [-1, -5, 2, 4, 6, -3], [-1, -5, 2, 6, -3, 4], [-1, -5, 2, 6, 4, -3], [-1, -5, -3, 2, 4, 6], [-1, -5, -3, 2, 6, 4], [-1, -5, -3, 4, 2, 6], [-1, -5, -3, 4, 6, 2], [-1, -5, -3, 6, 2, 4], [-1, -5, -3, 6, 4, 2], [-1, -5, 4, 2, -3, 6], [-1, -5, 4, 2, 6, -3], [-1, -5, 4, -3, 2, 6], [-1, -5, 4, -3, 6, 2], [-1, -5, 4, 6, 2, -3], [-1, -5, 4, 6, -3, 2], [-1, -5, 6, 2, -3, 4], [-1, -5, 6, 2, 4, -3], [-1, -5, 6, -3, 2, 4], [-1, -5, 6, -3, 4, 2], [-1, -5, 6, 4, 2, -3], [-1, -5, 6, 4, -3, 2], [-1, 6, 2, -3, 4, -5], [-1, 6, 2, -3, -5, 4], [-1, 6, 2, 4, -3, -5], [-1, 6, 2, 4, -5, -3], [-1, 6, 2, -5, -3, 4], [-1, 6, 2, -5, 4, -3], [-1, 6, -3, 2, 4, -5], [-1, 6, -3, 2, -5, 4], [-1, 6, -3, 4, 2, -5], [-1, 6, -3, 4, -5, 2], [-1, 6, -3, -5, 2, 4], [-1, 6, 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[6, 2, -1, -5, 4, -3], [6, 2, -3, -1, 4, -5], [6, 2, -3, -1, -5, 4], [6, 2, -3, 4, -1, -5], [6, 2, -3, 4, -5, -1], [6, 2, -3, -5, -1, 4], [6, 2, -3, -5, 4, -1], [6, 2, 4, -1, -3, -5], [6, 2, 4, -1, -5, -3], [6, 2, 4, -3, -1, -5], [6, 2, 4, -3, -5, -1], [6, 2, 4, -5, -1, -3], [6, 2, 4, -5, -3, -1], [6, 2, -5, -1, -3, 4], [6, 2, -5, -1, 4, -3], [6, 2, -5, -3, -1, 4], [6, 2, -5, -3, 4, -1], [6, 2, -5, 4, -1, -3], [6, 2, -5, 4, -3, -1], [6, -3, -1, 2, 4, -5], [6, -3, -1, 2, -5, 4], [6, -3, -1, 4, 2, -5], [6, -3, -1, 4, -5, 2], [6, -3, -1, -5, 2, 4], [6, -3, -1, -5, 4, 2], [6, -3, 2, -1, 4, -5], [6, -3, 2, -1, -5, 4], [6, -3, 2, 4, -1, -5], [6, -3, 2, 4, -5, -1], [6, -3, 2, -5, -1, 4], [6, -3, 2, -5, 4, -1], [6, -3, 4, -1, 2, -5], [6, -3, 4, -1, -5, 2], [6, -3, 4, 2, -1, -5], [6, -3, 4, 2, -5, -1], [6, -3, 4, -5, -1, 2], [6, -3, 4, -5, 2, -1], [6, -3, -5, -1, 2, 4], [6, -3, -5, -1, 4, 2], [6, -3, -5, 2, -1, 4], [6, -3, -5, 2, 4, -1], [6, -3, -5, 4, -1, 2], [6, -3, -5, 4, 2, -1], [6, 4, -1, 2, -3, -5], [6, 4, -1, 2, -5, -3], [6, 4, -1, -3, 2, -5], [6, 4, -1, -3, -5, 2], [6, 4, -1, -5, 2, -3], [6, 4, -1, -5, -3, 2], [6, 4, 2, -1, -3, -5], [6, 4, 2, -1, -5, -3], [6, 4, 2, -3, -1, -5], [6, 4, 2, -3, -5, -1], [6, 4, 2, -5, -1, -3], [6, 4, 2, -5, -3, -1], [6, 4, -3, -1, 2, -5], [6, 4, -3, -1, -5, 2], [6, 4, -3, 2, -1, -5], [6, 4, -3, 2, -5, -1], [6, 4, -3, -5, -1, 2], [6, 4, -3, -5, 2, -1], [6, 4, -5, -1, 2, -3], [6, 4, -5, -1, -3, 2], [6, 4, -5, 2, -1, -3], [6, 4, -5, 2, -3, -1], [6, 4, -5, -3, -1, 2], [6, 4, -5, -3, 2, -1], [6, -5, -1, 2, -3, 4], [6, -5, -1, 2, 4, -3], [6, -5, -1, -3, 2, 4], [6, -5, -1, -3, 4, 2], [6, -5, -1, 4, 2, -3], [6, -5, -1, 4, -3, 2], [6, -5, 2, -1, -3, 4], [6, -5, 2, -1, 4, -3], [6, -5, 2, -3, -1, 4], [6, -5, 2, -3, 4, -1], [6, -5, 2, 4, -1, -3], [6, -5, 2, 4, -3, -1], [6, -5, -3, -1, 2, 4], [6, -5, -3, -1, 4, 2], [6, -5, -3, 2, -1, 4], [6, -5, -3, 2, 4, -1], [6, -5, -3, 4, -1, 2], [6, -5, -3, 4, 2, -1], [6, -5, 4, -1, 2, -3], [6, -5, 4, -1, -3, 2], [6, -5, 4, 2, -1, -3], [6, -5, 4, 2, -3, -1], [6, -5, 4, -3, -1, 2], [6, -5, 4, -3, 2, -1]]\n assert candidate(nums = [10, 20, 30, 40, 50]) == [[10, 20, 30, 40, 50], [10, 20, 30, 50, 40], [10, 20, 40, 30, 50], [10, 20, 40, 50, 30], [10, 20, 50, 30, 40], [10, 20, 50, 40, 30], [10, 30, 20, 40, 50], [10, 30, 20, 50, 40], [10, 30, 40, 20, 50], [10, 30, 40, 50, 20], [10, 30, 50, 20, 40], [10, 30, 50, 40, 20], [10, 40, 20, 30, 50], [10, 40, 20, 50, 30], [10, 40, 30, 20, 50], [10, 40, 30, 50, 20], [10, 40, 50, 20, 30], [10, 40, 50, 30, 20], [10, 50, 20, 30, 40], [10, 50, 20, 40, 30], [10, 50, 30, 20, 40], [10, 50, 30, 40, 20], [10, 50, 40, 20, 30], [10, 50, 40, 30, 20], [20, 10, 30, 40, 50], [20, 10, 30, 50, 40], [20, 10, 40, 30, 50], [20, 10, 40, 50, 30], [20, 10, 50, 30, 40], [20, 10, 50, 40, 30], [20, 30, 10, 40, 50], [20, 30, 10, 50, 40], [20, 30, 40, 10, 50], [20, 30, 40, 50, 10], [20, 30, 50, 10, 40], [20, 30, 50, 40, 10], [20, 40, 10, 30, 50], [20, 40, 10, 50, 30], [20, 40, 30, 10, 50], [20, 40, 30, 50, 10], [20, 40, 50, 10, 30], [20, 40, 50, 30, 10], [20, 50, 10, 30, 40], [20, 50, 10, 40, 30], [20, 50, 30, 10, 40], [20, 50, 30, 40, 10], [20, 50, 40, 10, 30], [20, 50, 40, 30, 10], [30, 10, 20, 40, 50], [30, 10, 20, 50, 40], [30, 10, 40, 20, 50], [30, 10, 40, 50, 20], [30, 10, 50, 20, 40], [30, 10, 50, 40, 20], [30, 20, 10, 40, 50], [30, 20, 10, 50, 40], [30, 20, 40, 10, 50], [30, 20, 40, 50, 10], [30, 20, 50, 10, 40], [30, 20, 50, 40, 10], [30, 40, 10, 20, 50], [30, 40, 10, 50, 20], [30, 40, 20, 10, 50], [30, 40, 20, 50, 10], [30, 40, 50, 10, 20], [30, 40, 50, 20, 10], [30, 50, 10, 20, 40], [30, 50, 10, 40, 20], [30, 50, 20, 10, 40], [30, 50, 20, 40, 10], [30, 50, 40, 10, 20], [30, 50, 40, 20, 10], [40, 10, 20, 30, 50], [40, 10, 20, 50, 30], [40, 10, 30, 20, 50], [40, 10, 30, 50, 20], [40, 10, 50, 20, 30], [40, 10, 50, 30, 20], [40, 20, 10, 30, 50], [40, 20, 10, 50, 30], [40, 20, 30, 10, 50], [40, 20, 30, 50, 10], [40, 20, 50, 10, 30], [40, 20, 50, 30, 10], [40, 30, 10, 20, 50], [40, 30, 10, 50, 20], [40, 30, 20, 10, 50], [40, 30, 20, 50, 10], [40, 30, 50, 10, 20], [40, 30, 50, 20, 10], [40, 50, 10, 20, 30], [40, 50, 10, 30, 20], [40, 50, 20, 10, 30], [40, 50, 20, 30, 10], [40, 50, 30, 10, 20], [40, 50, 30, 20, 10], [50, 10, 20, 30, 40], [50, 10, 20, 40, 30], [50, 10, 30, 20, 40], [50, 10, 30, 40, 20], [50, 10, 40, 20, 30], [50, 10, 40, 30, 20], [50, 20, 10, 30, 40], [50, 20, 10, 40, 30], [50, 20, 30, 10, 40], [50, 20, 30, 40, 10], [50, 20, 40, 10, 30], [50, 20, 40, 30, 10], [50, 30, 10, 20, 40], [50, 30, 10, 40, 20], [50, 30, 20, 10, 40], [50, 30, 20, 40, 10], [50, 30, 40, 10, 20], [50, 30, 40, 20, 10], [50, 40, 10, 20, 30], [50, 40, 10, 30, 20], [50, 40, 20, 10, 30], [50, 40, 20, 30, 10], [50, 40, 30, 10, 20], [50, 40, 30, 20, 10]]\n assert candidate(nums = [11, 22, 33, 44, 55, 66]) == [[11, 22, 33, 44, 55, 66], [11, 22, 33, 44, 66, 55], [11, 22, 33, 55, 44, 66], [11, 22, 33, 55, 66, 44], [11, 22, 33, 66, 44, 55], [11, 22, 33, 66, 55, 44], [11, 22, 44, 33, 55, 66], [11, 22, 44, 33, 66, 55], [11, 22, 44, 55, 33, 66], [11, 22, 44, 55, 66, 33], [11, 22, 44, 66, 33, 55], [11, 22, 44, 66, 55, 33], [11, 22, 55, 33, 44, 66], [11, 22, 55, 33, 66, 44], [11, 22, 55, 44, 33, 66], [11, 22, 55, 44, 66, 33], [11, 22, 55, 66, 33, 44], [11, 22, 55, 66, 44, 33], [11, 22, 66, 33, 44, 55], [11, 22, 66, 33, 55, 44], [11, 22, 66, 44, 33, 55], [11, 22, 66, 44, 55, 33], [11, 22, 66, 55, 33, 44], [11, 22, 66, 55, 44, 33], [11, 33, 22, 44, 55, 66], [11, 33, 22, 44, 66, 55], [11, 33, 22, 55, 44, 66], [11, 33, 22, 55, 66, 44], [11, 33, 22, 66, 44, 55], [11, 33, 22, 66, 55, 44], [11, 33, 44, 22, 55, 66], [11, 33, 44, 22, 66, 55], [11, 33, 44, 55, 22, 66], [11, 33, 44, 55, 66, 22], [11, 33, 44, 66, 22, 55], [11, 33, 44, 66, 55, 22], [11, 33, 55, 22, 44, 66], [11, 33, 55, 22, 66, 44], [11, 33, 55, 44, 22, 66], [11, 33, 55, 44, 66, 22], [11, 33, 55, 66, 22, 44], [11, 33, 55, 66, 44, 22], [11, 33, 66, 22, 44, 55], [11, 33, 66, 22, 55, 44], [11, 33, 66, 44, 22, 55], [11, 33, 66, 44, 55, 22], [11, 33, 66, 55, 22, 44], [11, 33, 66, 55, 44, 22], [11, 44, 22, 33, 55, 66], [11, 44, 22, 33, 66, 55], [11, 44, 22, 55, 33, 66], [11, 44, 22, 55, 66, 33], [11, 44, 22, 66, 33, 55], [11, 44, 22, 66, 55, 33], [11, 44, 33, 22, 55, 66], [11, 44, 33, 22, 66, 55], [11, 44, 33, 55, 22, 66], [11, 44, 33, 55, 66, 22], [11, 44, 33, 66, 22, 55], [11, 44, 33, 66, 55, 22], [11, 44, 55, 22, 33, 66], [11, 44, 55, 22, 66, 33], [11, 44, 55, 33, 22, 66], [11, 44, 55, 33, 66, 22], [11, 44, 55, 66, 22, 33], [11, 44, 55, 66, 33, 22], [11, 44, 66, 22, 33, 55], [11, 44, 66, 22, 55, 33], [11, 44, 66, 33, 22, 55], [11, 44, 66, 33, 55, 22], [11, 44, 66, 55, 22, 33], [11, 44, 66, 55, 33, 22], [11, 55, 22, 33, 44, 66], [11, 55, 22, 33, 66, 44], [11, 55, 22, 44, 33, 66], [11, 55, 22, 44, 66, 33], [11, 55, 22, 66, 33, 44], [11, 55, 22, 66, 44, 33], [11, 55, 33, 22, 44, 66], [11, 55, 33, 22, 66, 44], [11, 55, 33, 44, 22, 66], [11, 55, 33, 44, 66, 22], [11, 55, 33, 66, 22, 44], [11, 55, 33, 66, 44, 22], [11, 55, 44, 22, 33, 66], [11, 55, 44, 22, 66, 33], [11, 55, 44, 33, 22, 66], [11, 55, 44, 33, 66, 22], [11, 55, 44, 66, 22, 33], [11, 55, 44, 66, 33, 22], [11, 55, 66, 22, 33, 44], [11, 55, 66, 22, 44, 33], [11, 55, 66, 33, 22, 44], [11, 55, 66, 33, 44, 22], [11, 55, 66, 44, 22, 33], [11, 55, 66, 44, 33, 22], [11, 66, 22, 33, 44, 55], [11, 66, 22, 33, 55, 44], [11, 66, 22, 44, 33, 55], [11, 66, 22, 44, 55, 33], [11, 66, 22, 55, 33, 44], [11, 66, 22, 55, 44, 33], [11, 66, 33, 22, 44, 55], [11, 66, 33, 22, 55, 44], [11, 66, 33, 44, 22, 55], [11, 66, 33, 44, 55, 22], [11, 66, 33, 55, 22, 44], [11, 66, 33, 55, 44, 22], [11, 66, 44, 22, 33, 55], [11, 66, 44, 22, 55, 33], [11, 66, 44, 33, 22, 55], [11, 66, 44, 33, 55, 22], [11, 66, 44, 55, 22, 33], [11, 66, 44, 55, 33, 22], [11, 66, 55, 22, 33, 44], [11, 66, 55, 22, 44, 33], [11, 66, 55, 33, 22, 44], [11, 66, 55, 33, 44, 22], [11, 66, 55, 44, 22, 33], [11, 66, 55, 44, 33, 22], [22, 11, 33, 44, 55, 66], [22, 11, 33, 44, 66, 55], [22, 11, 33, 55, 44, 66], [22, 11, 33, 55, 66, 44], [22, 11, 33, 66, 44, 55], [22, 11, 33, 66, 55, 44], [22, 11, 44, 33, 55, 66], [22, 11, 44, 33, 66, 55], [22, 11, 44, 55, 33, 66], [22, 11, 44, 55, 66, 33], [22, 11, 44, 66, 33, 55], [22, 11, 44, 66, 55, 33], [22, 11, 55, 33, 44, 66], [22, 11, 55, 33, 66, 44], [22, 11, 55, 44, 33, 66], [22, 11, 55, 44, 66, 33], [22, 11, 55, 66, 33, 44], [22, 11, 55, 66, 44, 33], [22, 11, 66, 33, 44, 55], [22, 11, 66, 33, 55, 44], [22, 11, 66, 44, 33, 55], [22, 11, 66, 44, 55, 33], [22, 11, 66, 55, 33, 44], [22, 11, 66, 55, 44, 33], [22, 33, 11, 44, 55, 66], [22, 33, 11, 44, 66, 55], [22, 33, 11, 55, 44, 66], [22, 33, 11, 55, 66, 44], [22, 33, 11, 66, 44, 55], [22, 33, 11, 66, 55, 44], [22, 33, 44, 11, 55, 66], [22, 33, 44, 11, 66, 55], [22, 33, 44, 55, 11, 66], [22, 33, 44, 55, 66, 11], [22, 33, 44, 66, 11, 55], [22, 33, 44, 66, 55, 11], [22, 33, 55, 11, 44, 66], [22, 33, 55, 11, 66, 44], [22, 33, 55, 44, 11, 66], [22, 33, 55, 44, 66, 11], [22, 33, 55, 66, 11, 44], [22, 33, 55, 66, 44, 11], [22, 33, 66, 11, 44, 55], [22, 33, 66, 11, 55, 44], [22, 33, 66, 44, 11, 55], [22, 33, 66, 44, 55, 11], [22, 33, 66, 55, 11, 44], [22, 33, 66, 55, 44, 11], [22, 44, 11, 33, 55, 66], [22, 44, 11, 33, 66, 55], [22, 44, 11, 55, 33, 66], [22, 44, 11, 55, 66, 33], [22, 44, 11, 66, 33, 55], [22, 44, 11, 66, 55, 33], [22, 44, 33, 11, 55, 66], [22, 44, 33, 11, 66, 55], [22, 44, 33, 55, 11, 66], [22, 44, 33, 55, 66, 11], [22, 44, 33, 66, 11, 55], [22, 44, 33, 66, 55, 11], [22, 44, 55, 11, 33, 66], [22, 44, 55, 11, 66, 33], [22, 44, 55, 33, 11, 66], [22, 44, 55, 33, 66, 11], [22, 44, 55, 66, 11, 33], [22, 44, 55, 66, 33, 11], [22, 44, 66, 11, 33, 55], [22, 44, 66, 11, 55, 33], [22, 44, 66, 33, 11, 55], [22, 44, 66, 33, 55, 11], [22, 44, 66, 55, 11, 33], [22, 44, 66, 55, 33, 11], [22, 55, 11, 33, 44, 66], [22, 55, 11, 33, 66, 44], [22, 55, 11, 44, 33, 66], [22, 55, 11, 44, 66, 33], [22, 55, 11, 66, 33, 44], [22, 55, 11, 66, 44, 33], [22, 55, 33, 11, 44, 66], [22, 55, 33, 11, 66, 44], [22, 55, 33, 44, 11, 66], [22, 55, 33, 44, 66, 11], [22, 55, 33, 66, 11, 44], [22, 55, 33, 66, 44, 11], [22, 55, 44, 11, 33, 66], [22, 55, 44, 11, 66, 33], [22, 55, 44, 33, 11, 66], [22, 55, 44, 33, 66, 11], [22, 55, 44, 66, 11, 33], [22, 55, 44, 66, 33, 11], [22, 55, 66, 11, 33, 44], [22, 55, 66, 11, 44, 33], [22, 55, 66, 33, 11, 44], [22, 55, 66, 33, 44, 11], [22, 55, 66, 44, 11, 33], [22, 55, 66, 44, 33, 11], [22, 66, 11, 33, 44, 55], [22, 66, 11, 33, 55, 44], [22, 66, 11, 44, 33, 55], [22, 66, 11, 44, 55, 33], [22, 66, 11, 55, 33, 44], [22, 66, 11, 55, 44, 33], [22, 66, 33, 11, 44, 55], [22, 66, 33, 11, 55, 44], [22, 66, 33, 44, 11, 55], [22, 66, 33, 44, 55, 11], [22, 66, 33, 55, 11, 44], [22, 66, 33, 55, 44, 11], [22, 66, 44, 11, 33, 55], [22, 66, 44, 11, 55, 33], [22, 66, 44, 33, 11, 55], [22, 66, 44, 33, 55, 11], [22, 66, 44, 55, 11, 33], [22, 66, 44, 55, 33, 11], [22, 66, 55, 11, 33, 44], [22, 66, 55, 11, 44, 33], [22, 66, 55, 33, 11, 44], [22, 66, 55, 33, 44, 11], [22, 66, 55, 44, 11, 33], [22, 66, 55, 44, 33, 11], [33, 11, 22, 44, 55, 66], [33, 11, 22, 44, 66, 55], [33, 11, 22, 55, 44, 66], [33, 11, 22, 55, 66, 44], [33, 11, 22, 66, 44, 55], [33, 11, 22, 66, 55, 44], [33, 11, 44, 22, 55, 66], [33, 11, 44, 22, 66, 55], [33, 11, 44, 55, 22, 66], [33, 11, 44, 55, 66, 22], [33, 11, 44, 66, 22, 55], [33, 11, 44, 66, 55, 22], [33, 11, 55, 22, 44, 66], [33, 11, 55, 22, 66, 44], [33, 11, 55, 44, 22, 66], [33, 11, 55, 44, 66, 22], [33, 11, 55, 66, 22, 44], [33, 11, 55, 66, 44, 22], [33, 11, 66, 22, 44, 55], [33, 11, 66, 22, 55, 44], [33, 11, 66, 44, 22, 55], [33, 11, 66, 44, 55, 22], [33, 11, 66, 55, 22, 44], [33, 11, 66, 55, 44, 22], [33, 22, 11, 44, 55, 66], [33, 22, 11, 44, 66, 55], [33, 22, 11, 55, 44, 66], [33, 22, 11, 55, 66, 44], [33, 22, 11, 66, 44, 55], [33, 22, 11, 66, 55, 44], [33, 22, 44, 11, 55, 66], [33, 22, 44, 11, 66, 55], [33, 22, 44, 55, 11, 66], [33, 22, 44, 55, 66, 11], [33, 22, 44, 66, 11, 55], [33, 22, 44, 66, 55, 11], [33, 22, 55, 11, 44, 66], [33, 22, 55, 11, 66, 44], [33, 22, 55, 44, 11, 66], [33, 22, 55, 44, 66, 11], [33, 22, 55, 66, 11, 44], [33, 22, 55, 66, 44, 11], [33, 22, 66, 11, 44, 55], [33, 22, 66, 11, 55, 44], [33, 22, 66, 44, 11, 55], [33, 22, 66, 44, 55, 11], [33, 22, 66, 55, 11, 44], [33, 22, 66, 55, 44, 11], [33, 44, 11, 22, 55, 66], [33, 44, 11, 22, 66, 55], [33, 44, 11, 55, 22, 66], [33, 44, 11, 55, 66, 22], [33, 44, 11, 66, 22, 55], [33, 44, 11, 66, 55, 22], [33, 44, 22, 11, 55, 66], [33, 44, 22, 11, 66, 55], [33, 44, 22, 55, 11, 66], [33, 44, 22, 55, 66, 11], [33, 44, 22, 66, 11, 55], [33, 44, 22, 66, 55, 11], [33, 44, 55, 11, 22, 66], [33, 44, 55, 11, 66, 22], [33, 44, 55, 22, 11, 66], [33, 44, 55, 22, 66, 11], [33, 44, 55, 66, 11, 22], [33, 44, 55, 66, 22, 11], [33, 44, 66, 11, 22, 55], [33, 44, 66, 11, 55, 22], [33, 44, 66, 22, 11, 55], [33, 44, 66, 22, 55, 11], [33, 44, 66, 55, 11, 22], [33, 44, 66, 55, 22, 11], [33, 55, 11, 22, 44, 66], [33, 55, 11, 22, 66, 44], [33, 55, 11, 44, 22, 66], [33, 55, 11, 44, 66, 22], [33, 55, 11, 66, 22, 44], [33, 55, 11, 66, 44, 22], [33, 55, 22, 11, 44, 66], [33, 55, 22, 11, 66, 44], [33, 55, 22, 44, 11, 66], [33, 55, 22, 44, 66, 11], [33, 55, 22, 66, 11, 44], [33, 55, 22, 66, 44, 11], [33, 55, 44, 11, 22, 66], [33, 55, 44, 11, 66, 22], [33, 55, 44, 22, 11, 66], [33, 55, 44, 22, 66, 11], [33, 55, 44, 66, 11, 22], [33, 55, 44, 66, 22, 11], [33, 55, 66, 11, 22, 44], [33, 55, 66, 11, 44, 22], [33, 55, 66, 22, 11, 44], [33, 55, 66, 22, 44, 11], [33, 55, 66, 44, 11, 22], [33, 55, 66, 44, 22, 11], [33, 66, 11, 22, 44, 55], [33, 66, 11, 22, 55, 44], [33, 66, 11, 44, 22, 55], [33, 66, 11, 44, 55, 22], [33, 66, 11, 55, 22, 44], [33, 66, 11, 55, 44, 22], [33, 66, 22, 11, 44, 55], [33, 66, 22, 11, 55, 44], [33, 66, 22, 44, 11, 55], [33, 66, 22, 44, 55, 11], [33, 66, 22, 55, 11, 44], [33, 66, 22, 55, 44, 11], [33, 66, 44, 11, 22, 55], [33, 66, 44, 11, 55, 22], [33, 66, 44, 22, 11, 55], [33, 66, 44, 22, 55, 11], [33, 66, 44, 55, 11, 22], [33, 66, 44, 55, 22, 11], [33, 66, 55, 11, 22, 44], [33, 66, 55, 11, 44, 22], [33, 66, 55, 22, 11, 44], [33, 66, 55, 22, 44, 11], [33, 66, 55, 44, 11, 22], [33, 66, 55, 44, 22, 11], [44, 11, 22, 33, 55, 66], [44, 11, 22, 33, 66, 55], [44, 11, 22, 55, 33, 66], [44, 11, 22, 55, 66, 33], [44, 11, 22, 66, 33, 55], [44, 11, 22, 66, 55, 33], [44, 11, 33, 22, 55, 66], [44, 11, 33, 22, 66, 55], [44, 11, 33, 55, 22, 66], [44, 11, 33, 55, 66, 22], [44, 11, 33, 66, 22, 55], [44, 11, 33, 66, 55, 22], [44, 11, 55, 22, 33, 66], [44, 11, 55, 22, 66, 33], [44, 11, 55, 33, 22, 66], [44, 11, 55, 33, 66, 22], [44, 11, 55, 66, 22, 33], [44, 11, 55, 66, 33, 22], [44, 11, 66, 22, 33, 55], [44, 11, 66, 22, 55, 33], [44, 11, 66, 33, 22, 55], [44, 11, 66, 33, 55, 22], [44, 11, 66, 55, 22, 33], [44, 11, 66, 55, 33, 22], [44, 22, 11, 33, 55, 66], [44, 22, 11, 33, 66, 55], [44, 22, 11, 55, 33, 66], [44, 22, 11, 55, 66, 33], [44, 22, 11, 66, 33, 55], [44, 22, 11, 66, 55, 33], [44, 22, 33, 11, 55, 66], [44, 22, 33, 11, 66, 55], [44, 22, 33, 55, 11, 66], [44, 22, 33, 55, 66, 11], [44, 22, 33, 66, 11, 55], [44, 22, 33, 66, 55, 11], [44, 22, 55, 11, 33, 66], [44, 22, 55, 11, 66, 33], [44, 22, 55, 33, 11, 66], [44, 22, 55, 33, 66, 11], [44, 22, 55, 66, 11, 33], [44, 22, 55, 66, 33, 11], [44, 22, 66, 11, 33, 55], [44, 22, 66, 11, 55, 33], [44, 22, 66, 33, 11, 55], [44, 22, 66, 33, 55, 11], [44, 22, 66, 55, 11, 33], [44, 22, 66, 55, 33, 11], [44, 33, 11, 22, 55, 66], [44, 33, 11, 22, 66, 55], [44, 33, 11, 55, 22, 66], [44, 33, 11, 55, 66, 22], [44, 33, 11, 66, 22, 55], [44, 33, 11, 66, 55, 22], [44, 33, 22, 11, 55, 66], [44, 33, 22, 11, 66, 55], [44, 33, 22, 55, 11, 66], [44, 33, 22, 55, 66, 11], [44, 33, 22, 66, 11, 55], [44, 33, 22, 66, 55, 11], [44, 33, 55, 11, 22, 66], [44, 33, 55, 11, 66, 22], [44, 33, 55, 22, 11, 66], [44, 33, 55, 22, 66, 11], [44, 33, 55, 66, 11, 22], [44, 33, 55, 66, 22, 11], [44, 33, 66, 11, 22, 55], [44, 33, 66, 11, 55, 22], [44, 33, 66, 22, 11, 55], [44, 33, 66, 22, 55, 11], [44, 33, 66, 55, 11, 22], [44, 33, 66, 55, 22, 11], [44, 55, 11, 22, 33, 66], [44, 55, 11, 22, 66, 33], [44, 55, 11, 33, 22, 66], [44, 55, 11, 33, 66, 22], [44, 55, 11, 66, 22, 33], [44, 55, 11, 66, 33, 22], [44, 55, 22, 11, 33, 66], [44, 55, 22, 11, 66, 33], [44, 55, 22, 33, 11, 66], [44, 55, 22, 33, 66, 11], [44, 55, 22, 66, 11, 33], [44, 55, 22, 66, 33, 11], [44, 55, 33, 11, 22, 66], [44, 55, 33, 11, 66, 22], [44, 55, 33, 22, 11, 66], [44, 55, 33, 22, 66, 11], [44, 55, 33, 66, 11, 22], [44, 55, 33, 66, 22, 11], [44, 55, 66, 11, 22, 33], [44, 55, 66, 11, 33, 22], [44, 55, 66, 22, 11, 33], [44, 55, 66, 22, 33, 11], [44, 55, 66, 33, 11, 22], [44, 55, 66, 33, 22, 11], [44, 66, 11, 22, 33, 55], [44, 66, 11, 22, 55, 33], [44, 66, 11, 33, 22, 55], [44, 66, 11, 33, 55, 22], [44, 66, 11, 55, 22, 33], [44, 66, 11, 55, 33, 22], [44, 66, 22, 11, 33, 55], [44, 66, 22, 11, 55, 33], [44, 66, 22, 33, 11, 55], [44, 66, 22, 33, 55, 11], [44, 66, 22, 55, 11, 33], [44, 66, 22, 55, 33, 11], [44, 66, 33, 11, 22, 55], [44, 66, 33, 11, 55, 22], [44, 66, 33, 22, 11, 55], [44, 66, 33, 22, 55, 11], [44, 66, 33, 55, 11, 22], [44, 66, 33, 55, 22, 11], [44, 66, 55, 11, 22, 33], [44, 66, 55, 11, 33, 22], [44, 66, 55, 22, 11, 33], [44, 66, 55, 22, 33, 11], [44, 66, 55, 33, 11, 22], [44, 66, 55, 33, 22, 11], [55, 11, 22, 33, 44, 66], [55, 11, 22, 33, 66, 44], [55, 11, 22, 44, 33, 66], [55, 11, 22, 44, 66, 33], [55, 11, 22, 66, 33, 44], [55, 11, 22, 66, 44, 33], [55, 11, 33, 22, 44, 66], [55, 11, 33, 22, 66, 44], [55, 11, 33, 44, 22, 66], [55, 11, 33, 44, 66, 22], [55, 11, 33, 66, 22, 44], [55, 11, 33, 66, 44, 22], [55, 11, 44, 22, 33, 66], [55, 11, 44, 22, 66, 33], [55, 11, 44, 33, 22, 66], [55, 11, 44, 33, 66, 22], [55, 11, 44, 66, 22, 33], [55, 11, 44, 66, 33, 22], [55, 11, 66, 22, 33, 44], [55, 11, 66, 22, 44, 33], [55, 11, 66, 33, 22, 44], [55, 11, 66, 33, 44, 22], [55, 11, 66, 44, 22, 33], [55, 11, 66, 44, 33, 22], [55, 22, 11, 33, 44, 66], [55, 22, 11, 33, 66, 44], [55, 22, 11, 44, 33, 66], [55, 22, 11, 44, 66, 33], [55, 22, 11, 66, 33, 44], [55, 22, 11, 66, 44, 33], [55, 22, 33, 11, 44, 66], [55, 22, 33, 11, 66, 44], [55, 22, 33, 44, 11, 66], [55, 22, 33, 44, 66, 11], [55, 22, 33, 66, 11, 44], [55, 22, 33, 66, 44, 11], [55, 22, 44, 11, 33, 66], [55, 22, 44, 11, 66, 33], [55, 22, 44, 33, 11, 66], [55, 22, 44, 33, 66, 11], [55, 22, 44, 66, 11, 33], [55, 22, 44, 66, 33, 11], [55, 22, 66, 11, 33, 44], [55, 22, 66, 11, 44, 33], [55, 22, 66, 33, 11, 44], [55, 22, 66, 33, 44, 11], [55, 22, 66, 44, 11, 33], [55, 22, 66, 44, 33, 11], [55, 33, 11, 22, 44, 66], [55, 33, 11, 22, 66, 44], [55, 33, 11, 44, 22, 66], [55, 33, 11, 44, 66, 22], [55, 33, 11, 66, 22, 44], [55, 33, 11, 66, 44, 22], [55, 33, 22, 11, 44, 66], [55, 33, 22, 11, 66, 44], [55, 33, 22, 44, 11, 66], [55, 33, 22, 44, 66, 11], [55, 33, 22, 66, 11, 44], [55, 33, 22, 66, 44, 11], [55, 33, 44, 11, 22, 66], [55, 33, 44, 11, 66, 22], [55, 33, 44, 22, 11, 66], [55, 33, 44, 22, 66, 11], [55, 33, 44, 66, 11, 22], 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11, 44, 33], [55, 66, 22, 33, 11, 44], [55, 66, 22, 33, 44, 11], [55, 66, 22, 44, 11, 33], [55, 66, 22, 44, 33, 11], [55, 66, 33, 11, 22, 44], [55, 66, 33, 11, 44, 22], [55, 66, 33, 22, 11, 44], [55, 66, 33, 22, 44, 11], [55, 66, 33, 44, 11, 22], [55, 66, 33, 44, 22, 11], [55, 66, 44, 11, 22, 33], [55, 66, 44, 11, 33, 22], [55, 66, 44, 22, 11, 33], [55, 66, 44, 22, 33, 11], [55, 66, 44, 33, 11, 22], [55, 66, 44, 33, 22, 11], [66, 11, 22, 33, 44, 55], [66, 11, 22, 33, 55, 44], [66, 11, 22, 44, 33, 55], [66, 11, 22, 44, 55, 33], [66, 11, 22, 55, 33, 44], [66, 11, 22, 55, 44, 33], [66, 11, 33, 22, 44, 55], [66, 11, 33, 22, 55, 44], [66, 11, 33, 44, 22, 55], [66, 11, 33, 44, 55, 22], [66, 11, 33, 55, 22, 44], [66, 11, 33, 55, 44, 22], [66, 11, 44, 22, 33, 55], [66, 11, 44, 22, 55, 33], [66, 11, 44, 33, 22, 55], [66, 11, 44, 33, 55, 22], [66, 11, 44, 55, 22, 33], [66, 11, 44, 55, 33, 22], [66, 11, 55, 22, 33, 44], [66, 11, 55, 22, 44, 33], [66, 11, 55, 33, 22, 44], [66, 11, 55, 33, 44, 22], [66, 11, 55, 44, 22, 33], [66, 11, 55, 44, 33, 22], [66, 22, 11, 33, 44, 55], [66, 22, 11, 33, 55, 44], [66, 22, 11, 44, 33, 55], [66, 22, 11, 44, 55, 33], [66, 22, 11, 55, 33, 44], [66, 22, 11, 55, 44, 33], [66, 22, 33, 11, 44, 55], [66, 22, 33, 11, 55, 44], [66, 22, 33, 44, 11, 55], [66, 22, 33, 44, 55, 11], [66, 22, 33, 55, 11, 44], [66, 22, 33, 55, 44, 11], [66, 22, 44, 11, 33, 55], [66, 22, 44, 11, 55, 33], [66, 22, 44, 33, 11, 55], [66, 22, 44, 33, 55, 11], [66, 22, 44, 55, 11, 33], [66, 22, 44, 55, 33, 11], [66, 22, 55, 11, 33, 44], [66, 22, 55, 11, 44, 33], [66, 22, 55, 33, 11, 44], [66, 22, 55, 33, 44, 11], [66, 22, 55, 44, 11, 33], [66, 22, 55, 44, 33, 11], [66, 33, 11, 22, 44, 55], [66, 33, 11, 22, 55, 44], [66, 33, 11, 44, 22, 55], [66, 33, 11, 44, 55, 22], [66, 33, 11, 55, 22, 44], [66, 33, 11, 55, 44, 22], [66, 33, 22, 11, 44, 55], [66, 33, 22, 11, 55, 44], [66, 33, 22, 44, 11, 55], [66, 33, 22, 44, 55, 11], [66, 33, 22, 55, 11, 44], [66, 33, 22, 55, 44, 11], [66, 33, 44, 11, 22, 55], [66, 33, 44, 11, 55, 22], [66, 33, 44, 22, 11, 55], [66, 33, 44, 22, 55, 11], [66, 33, 44, 55, 11, 22], [66, 33, 44, 55, 22, 11], [66, 33, 55, 11, 22, 44], [66, 33, 55, 11, 44, 22], [66, 33, 55, 22, 11, 44], [66, 33, 55, 22, 44, 11], [66, 33, 55, 44, 11, 22], [66, 33, 55, 44, 22, 11], [66, 44, 11, 22, 33, 55], [66, 44, 11, 22, 55, 33], [66, 44, 11, 33, 22, 55], [66, 44, 11, 33, 55, 22], [66, 44, 11, 55, 22, 33], [66, 44, 11, 55, 33, 22], [66, 44, 22, 11, 33, 55], [66, 44, 22, 11, 55, 33], [66, 44, 22, 33, 11, 55], [66, 44, 22, 33, 55, 11], [66, 44, 22, 55, 11, 33], [66, 44, 22, 55, 33, 11], [66, 44, 33, 11, 22, 55], [66, 44, 33, 11, 55, 22], [66, 44, 33, 22, 11, 55], [66, 44, 33, 22, 55, 11], [66, 44, 33, 55, 11, 22], [66, 44, 33, 55, 22, 11], [66, 44, 55, 11, 22, 33], [66, 44, 55, 11, 33, 22], [66, 44, 55, 22, 11, 33], [66, 44, 55, 22, 33, 11], [66, 44, 55, 33, 11, 22], [66, 44, 55, 33, 22, 11], [66, 55, 11, 22, 33, 44], [66, 55, 11, 22, 44, 33], [66, 55, 11, 33, 22, 44], [66, 55, 11, 33, 44, 22], [66, 55, 11, 44, 22, 33], [66, 55, 11, 44, 33, 22], [66, 55, 22, 11, 33, 44], [66, 55, 22, 11, 44, 33], [66, 55, 22, 33, 11, 44], [66, 55, 22, 33, 44, 11], [66, 55, 22, 44, 11, 33], [66, 55, 22, 44, 33, 11], [66, 55, 33, 11, 22, 44], [66, 55, 33, 11, 44, 22], [66, 55, 33, 22, 11, 44], [66, 55, 33, 22, 44, 11], [66, 55, 33, 44, 11, 22], [66, 55, 33, 44, 22, 11], [66, 55, 44, 11, 22, 33], [66, 55, 44, 11, 33, 22], [66, 55, 44, 22, 11, 33], [66, 55, 44, 22, 33, 11], [66, 55, 44, 33, 11, 22], [66, 55, 44, 33, 22, 11]]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6]) == [[-1, -2, -3, -4, -5, -6], [-1, -2, -3, -4, -6, -5], [-1, -2, -3, -5, -4, -6], [-1, -2, -3, -5, -6, -4], [-1, -2, -3, -6, -4, -5], [-1, -2, -3, -6, -5, -4], [-1, -2, -4, -3, -5, -6], [-1, -2, -4, -3, -6, -5], [-1, -2, -4, -5, -3, -6], [-1, -2, -4, -5, -6, -3], [-1, -2, -4, -6, -3, -5], [-1, -2, -4, -6, -5, -3], [-1, -2, -5, -3, -4, -6], [-1, -2, -5, -3, -6, -4], [-1, -2, -5, -4, -3, -6], [-1, -2, -5, -4, -6, -3], [-1, -2, -5, -6, -3, -4], [-1, -2, -5, -6, -4, -3], [-1, -2, -6, -3, -4, -5], [-1, -2, -6, -3, -5, -4], [-1, -2, -6, -4, -3, -5], [-1, -2, -6, -4, -5, -3], [-1, -2, -6, -5, -3, -4], [-1, -2, -6, -5, -4, -3], [-1, -3, -2, -4, -5, -6], [-1, -3, -2, -4, -6, -5], [-1, -3, -2, -5, -4, -6], [-1, -3, -2, -5, -6, -4], [-1, -3, -2, -6, -4, -5], [-1, -3, -2, -6, -5, -4], [-1, -3, -4, -2, -5, -6], [-1, -3, -4, -2, -6, -5], [-1, -3, -4, -5, -2, -6], [-1, -3, -4, -5, -6, -2], [-1, -3, -4, -6, -2, -5], [-1, -3, -4, -6, -5, -2], [-1, -3, -5, -2, -4, -6], [-1, -3, -5, -2, -6, -4], [-1, -3, -5, -4, -2, -6], [-1, -3, -5, -4, -6, -2], [-1, -3, -5, -6, -2, -4], [-1, -3, -5, -6, -4, -2], [-1, -3, -6, -2, -4, -5], [-1, -3, -6, -2, -5, -4], [-1, -3, -6, -4, -2, -5], [-1, -3, -6, -4, -5, -2], [-1, -3, -6, -5, -2, -4], [-1, -3, -6, -5, -4, -2], [-1, -4, -2, -3, -5, -6], [-1, -4, -2, -3, -6, -5], [-1, -4, -2, -5, -3, -6], [-1, -4, -2, -5, -6, -3], [-1, -4, -2, -6, -3, -5], [-1, -4, -2, -6, -5, -3], [-1, -4, -3, -2, -5, -6], [-1, -4, -3, -2, -6, -5], [-1, -4, -3, -5, -2, -6], [-1, -4, -3, -5, -6, -2], [-1, -4, -3, -6, -2, -5], [-1, -4, -3, -6, -5, -2], [-1, -4, -5, -2, -3, -6], [-1, -4, -5, -2, -6, -3], [-1, -4, -5, -3, -2, -6], [-1, -4, -5, -3, -6, -2], [-1, -4, -5, -6, -2, -3], [-1, -4, -5, -6, -3, -2], [-1, -4, -6, -2, -3, -5], [-1, -4, -6, -2, -5, -3], [-1, -4, -6, -3, -2, -5], [-1, -4, -6, -3, -5, -2], [-1, -4, -6, -5, -2, -3], [-1, -4, -6, -5, -3, -2], [-1, -5, -2, -3, -4, -6], [-1, -5, -2, -3, -6, -4], [-1, -5, -2, -4, -3, -6], [-1, -5, -2, -4, -6, -3], [-1, -5, -2, -6, -3, -4], [-1, -5, -2, -6, -4, -3], [-1, -5, -3, -2, -4, -6], [-1, -5, -3, -2, -6, -4], [-1, -5, -3, -4, -2, -6], [-1, -5, -3, -4, -6, -2], [-1, -5, -3, -6, -2, -4], [-1, -5, -3, -6, -4, -2], [-1, -5, -4, -2, -3, -6], [-1, -5, -4, -2, -6, -3], [-1, -5, -4, -3, -2, -6], [-1, -5, -4, -3, -6, -2], [-1, -5, -4, -6, -2, -3], [-1, -5, -4, -6, -3, -2], [-1, -5, -6, -2, -3, -4], [-1, -5, -6, -2, -4, -3], [-1, -5, -6, -3, -2, -4], [-1, -5, -6, -3, -4, -2], [-1, -5, -6, -4, -2, -3], [-1, -5, -6, -4, -3, -2], [-1, -6, -2, -3, -4, -5], [-1, -6, -2, -3, -5, -4], [-1, -6, -2, -4, -3, -5], [-1, -6, -2, -4, -5, -3], [-1, -6, -2, -5, -3, -4], [-1, -6, -2, -5, -4, -3], [-1, -6, -3, -2, -4, -5], [-1, -6, -3, -2, -5, -4], [-1, -6, -3, -4, -2, -5], [-1, -6, -3, -4, -5, -2], [-1, -6, -3, -5, -2, -4], [-1, -6, -3, -5, -4, -2], [-1, -6, -4, -2, -3, -5], [-1, -6, -4, -2, -5, -3], [-1, -6, -4, -3, -2, -5], [-1, -6, -4, -3, -5, -2], [-1, -6, -4, -5, -2, -3], [-1, -6, -4, -5, -3, -2], [-1, -6, -5, -2, -3, -4], [-1, -6, -5, -2, -4, -3], [-1, -6, -5, -3, -2, -4], [-1, -6, -5, -3, -4, -2], [-1, -6, -5, -4, -2, -3], [-1, -6, -5, -4, -3, -2], [-2, -1, -3, -4, -5, -6], [-2, -1, -3, -4, -6, -5], [-2, -1, -3, -5, -4, -6], [-2, -1, -3, -5, -6, -4], [-2, -1, -3, -6, -4, -5], [-2, -1, -3, -6, -5, -4], [-2, -1, -4, -3, -5, -6], [-2, -1, -4, -3, -6, -5], [-2, -1, -4, -5, -3, -6], [-2, -1, -4, -5, -6, -3], [-2, -1, -4, -6, -3, -5], [-2, -1, -4, -6, -5, -3], [-2, -1, -5, -3, -4, -6], [-2, -1, -5, -3, -6, -4], [-2, -1, -5, -4, -3, -6], [-2, -1, -5, -4, -6, -3], [-2, -1, -5, -6, -3, -4], [-2, -1, -5, -6, -4, -3], [-2, -1, -6, -3, -4, -5], [-2, -1, -6, -3, -5, -4], [-2, -1, -6, -4, -3, -5], [-2, -1, -6, -4, -5, -3], [-2, -1, -6, -5, -3, -4], [-2, -1, -6, -5, -4, -3], [-2, -3, -1, -4, -5, -6], [-2, -3, -1, -4, -6, -5], [-2, -3, -1, -5, -4, -6], [-2, -3, -1, -5, -6, -4], [-2, -3, -1, -6, -4, -5], [-2, -3, -1, -6, -5, -4], [-2, -3, -4, -1, -5, -6], [-2, -3, -4, -1, -6, -5], [-2, -3, -4, -5, -1, -6], [-2, -3, -4, -5, -6, -1], [-2, -3, -4, -6, -1, -5], [-2, -3, -4, -6, -5, -1], [-2, -3, -5, -1, -4, -6], [-2, -3, -5, -1, -6, -4], [-2, -3, -5, -4, -1, -6], [-2, -3, -5, -4, -6, -1], [-2, -3, -5, -6, -1, -4], [-2, -3, -5, -6, -4, -1], [-2, -3, -6, -1, -4, -5], [-2, -3, -6, -1, -5, -4], [-2, -3, -6, -4, -1, -5], [-2, -3, -6, -4, -5, -1], [-2, -3, -6, -5, -1, -4], [-2, -3, -6, -5, -4, -1], [-2, -4, -1, -3, -5, -6], [-2, -4, -1, -3, -6, -5], [-2, -4, -1, -5, -3, -6], [-2, -4, -1, -5, -6, -3], [-2, -4, -1, -6, -3, -5], [-2, -4, -1, -6, -5, -3], [-2, -4, -3, -1, -5, -6], [-2, -4, -3, -1, -6, -5], [-2, -4, -3, -5, -1, -6], [-2, -4, -3, -5, -6, -1], [-2, -4, -3, -6, -1, -5], [-2, -4, -3, -6, -5, -1], [-2, -4, -5, -1, -3, -6], [-2, -4, -5, -1, -6, -3], [-2, -4, -5, -3, -1, -6], [-2, -4, -5, -3, -6, -1], [-2, -4, -5, -6, -1, -3], [-2, -4, -5, -6, -3, -1], [-2, -4, -6, -1, -3, -5], [-2, -4, -6, -1, -5, -3], [-2, -4, -6, -3, -1, -5], [-2, -4, -6, -3, -5, -1], [-2, -4, -6, -5, -1, -3], [-2, -4, -6, -5, -3, -1], [-2, -5, -1, -3, -4, -6], [-2, -5, -1, -3, -6, -4], [-2, -5, -1, -4, -3, -6], [-2, -5, -1, -4, -6, -3], [-2, -5, -1, -6, -3, -4], [-2, -5, -1, -6, -4, -3], [-2, -5, -3, -1, -4, -6], [-2, -5, -3, -1, -6, -4], [-2, -5, -3, -4, -1, -6], [-2, -5, -3, -4, -6, -1], [-2, -5, -3, -6, -1, -4], [-2, -5, -3, -6, -4, -1], [-2, -5, -4, -1, -3, -6], [-2, -5, -4, -1, -6, -3], [-2, -5, -4, -3, -1, -6], [-2, -5, -4, -3, -6, -1], [-2, -5, -4, -6, -1, -3], [-2, -5, -4, -6, -3, -1], [-2, -5, -6, -1, -3, -4], [-2, -5, -6, -1, -4, -3], [-2, -5, -6, -3, -1, -4], [-2, -5, -6, -3, -4, -1], [-2, -5, -6, -4, -1, -3], [-2, -5, -6, -4, -3, -1], [-2, -6, -1, -3, -4, -5], [-2, -6, -1, -3, -5, -4], [-2, -6, -1, -4, -3, -5], [-2, -6, -1, -4, -5, -3], [-2, -6, -1, -5, -3, -4], [-2, -6, -1, -5, -4, -3], [-2, -6, -3, -1, -4, -5], [-2, -6, -3, -1, -5, -4], [-2, -6, -3, -4, -1, -5], [-2, -6, -3, -4, -5, -1], [-2, -6, -3, -5, -1, -4], [-2, -6, -3, -5, -4, -1], [-2, -6, -4, -1, -3, -5], [-2, -6, -4, -1, -5, -3], [-2, -6, -4, -3, -1, -5], [-2, -6, -4, -3, -5, -1], [-2, -6, -4, -5, -1, -3], [-2, -6, -4, -5, -3, -1], [-2, -6, -5, -1, -3, -4], [-2, -6, -5, -1, -4, -3], [-2, -6, -5, -3, -1, -4], [-2, -6, -5, -3, -4, -1], [-2, -6, -5, -4, -1, -3], [-2, -6, -5, -4, -3, -1], [-3, -1, -2, -4, -5, -6], [-3, -1, -2, -4, -6, -5], [-3, -1, -2, -5, -4, -6], [-3, -1, -2, -5, -6, -4], [-3, -1, -2, -6, -4, -5], [-3, -1, -2, -6, -5, -4], [-3, -1, -4, -2, -5, -6], [-3, -1, -4, -2, -6, -5], [-3, -1, -4, -5, -2, -6], [-3, -1, -4, -5, -6, -2], [-3, -1, -4, -6, -2, -5], [-3, -1, -4, -6, -5, -2], [-3, -1, -5, -2, -4, -6], [-3, -1, -5, -2, -6, -4], [-3, -1, -5, -4, -2, -6], [-3, -1, -5, -4, -6, -2], [-3, -1, -5, -6, -2, -4], [-3, -1, -5, -6, -4, -2], [-3, -1, -6, -2, -4, -5], [-3, -1, -6, -2, -5, -4], [-3, -1, -6, -4, -2, -5], [-3, -1, -6, -4, -5, -2], [-3, -1, -6, -5, -2, -4], [-3, -1, -6, -5, -4, -2], [-3, -2, -1, -4, -5, -6], [-3, -2, -1, -4, -6, -5], [-3, -2, -1, -5, -4, -6], [-3, -2, -1, -5, -6, -4], [-3, -2, -1, -6, -4, -5], [-3, -2, -1, -6, -5, -4], [-3, -2, -4, -1, -5, -6], [-3, -2, -4, -1, -6, -5], [-3, -2, -4, -5, -1, -6], [-3, -2, -4, -5, -6, -1], [-3, -2, -4, -6, -1, -5], [-3, -2, -4, -6, -5, -1], [-3, -2, -5, -1, -4, -6], [-3, -2, -5, -1, -6, -4], [-3, -2, -5, -4, -1, -6], [-3, -2, -5, -4, -6, -1], [-3, -2, -5, -6, -1, -4], [-3, -2, -5, -6, -4, -1], [-3, -2, -6, -1, -4, -5], [-3, -2, -6, -1, -5, -4], [-3, -2, -6, -4, -1, -5], [-3, -2, -6, -4, -5, -1], [-3, -2, -6, -5, -1, -4], [-3, -2, -6, -5, -4, -1], [-3, -4, -1, -2, -5, -6], [-3, -4, -1, -2, -6, -5], [-3, -4, -1, -5, -2, -6], [-3, -4, -1, -5, -6, -2], [-3, -4, -1, -6, -2, -5], [-3, -4, -1, -6, -5, -2], [-3, -4, -2, -1, -5, -6], [-3, -4, -2, -1, -6, -5], [-3, -4, -2, -5, -1, -6], [-3, -4, -2, -5, -6, -1], [-3, -4, -2, -6, -1, -5], [-3, -4, -2, -6, -5, -1], [-3, -4, -5, -1, -2, -6], [-3, -4, -5, -1, -6, -2], [-3, -4, -5, -2, -1, -6], [-3, -4, -5, -2, -6, -1], [-3, -4, -5, -6, -1, -2], [-3, -4, -5, -6, -2, -1], [-3, -4, -6, -1, -2, -5], [-3, -4, -6, -1, -5, -2], [-3, -4, -6, -2, -1, -5], [-3, -4, -6, -2, -5, -1], [-3, -4, -6, -5, -1, -2], [-3, -4, -6, -5, -2, -1], [-3, -5, -1, -2, -4, -6], [-3, -5, -1, -2, -6, -4], [-3, -5, -1, -4, -2, -6], [-3, -5, -1, -4, -6, -2], [-3, -5, -1, -6, -2, -4], [-3, -5, -1, -6, -4, -2], [-3, -5, -2, -1, -4, -6], [-3, -5, -2, -1, -6, -4], [-3, -5, -2, -4, -1, -6], [-3, -5, -2, -4, -6, -1], [-3, -5, -2, -6, -1, -4], 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-2, -4, -1], [-6, -3, -5, -4, -1, -2], [-6, -3, -5, -4, -2, -1], [-6, -4, -1, -2, -3, -5], [-6, -4, -1, -2, -5, -3], [-6, -4, -1, -3, -2, -5], [-6, -4, -1, -3, -5, -2], [-6, -4, -1, -5, -2, -3], [-6, -4, -1, -5, -3, -2], [-6, -4, -2, -1, -3, -5], [-6, -4, -2, -1, -5, -3], [-6, -4, -2, -3, -1, -5], [-6, -4, -2, -3, -5, -1], [-6, -4, -2, -5, -1, -3], [-6, -4, -2, -5, -3, -1], [-6, -4, -3, -1, -2, -5], [-6, -4, -3, -1, -5, -2], [-6, -4, -3, -2, -1, -5], [-6, -4, -3, -2, -5, -1], [-6, -4, -3, -5, -1, -2], [-6, -4, -3, -5, -2, -1], [-6, -4, -5, -1, -2, -3], [-6, -4, -5, -1, -3, -2], [-6, -4, -5, -2, -1, -3], [-6, -4, -5, -2, -3, -1], [-6, -4, -5, -3, -1, -2], [-6, -4, -5, -3, -2, -1], [-6, -5, -1, -2, -3, -4], [-6, -5, -1, -2, -4, -3], [-6, -5, -1, -3, -2, -4], [-6, -5, -1, -3, -4, -2], [-6, -5, -1, -4, -2, -3], [-6, -5, -1, -4, -3, -2], [-6, -5, -2, -1, -3, -4], [-6, -5, -2, -1, -4, -3], [-6, -5, -2, -3, -1, -4], [-6, -5, -2, -3, -4, -1], [-6, -5, -2, -4, -1, -3], [-6, -5, -2, -4, -3, -1], [-6, -5, -3, -1, -2, -4], [-6, -5, -3, -1, -4, -2], [-6, -5, -3, -2, -1, -4], [-6, -5, -3, -2, -4, -1], [-6, -5, -3, -4, -1, -2], [-6, -5, -3, -4, -2, -1], [-6, -5, -4, -1, -2, -3], [-6, -5, -4, -1, -3, -2], [-6, -5, -4, -2, -1, -3], [-6, -5, -4, -2, -3, -1], [-6, -5, -4, -3, -1, -2], [-6, -5, -4, -3, -2, -1]]\n assert candidate(nums = [-6, -4, -2, 0, 2, 4]) == [[-6, -4, -2, 0, 2, 4], [-6, -4, -2, 0, 4, 2], [-6, -4, -2, 2, 0, 4], [-6, -4, -2, 2, 4, 0], [-6, -4, -2, 4, 0, 2], [-6, -4, -2, 4, 2, 0], [-6, -4, 0, -2, 2, 4], [-6, -4, 0, -2, 4, 2], [-6, -4, 0, 2, -2, 4], [-6, -4, 0, 2, 4, -2], [-6, -4, 0, 4, -2, 2], [-6, -4, 0, 4, 2, -2], [-6, -4, 2, -2, 0, 4], [-6, -4, 2, -2, 4, 0], [-6, -4, 2, 0, -2, 4], [-6, -4, 2, 0, 4, -2], [-6, -4, 2, 4, -2, 0], [-6, -4, 2, 4, 0, -2], [-6, -4, 4, -2, 0, 2], [-6, -4, 4, -2, 2, 0], [-6, -4, 4, 0, -2, 2], [-6, -4, 4, 0, 2, -2], [-6, -4, 4, 2, -2, 0], [-6, -4, 4, 2, 0, -2], [-6, -2, -4, 0, 2, 4], [-6, -2, -4, 0, 4, 2], [-6, -2, -4, 2, 0, 4], [-6, -2, -4, 2, 4, 0], [-6, -2, -4, 4, 0, 2], [-6, -2, -4, 4, 2, 0], [-6, -2, 0, -4, 2, 4], [-6, -2, 0, -4, 4, 2], [-6, -2, 0, 2, -4, 4], [-6, -2, 0, 2, 4, -4], [-6, -2, 0, 4, -4, 2], [-6, -2, 0, 4, 2, -4], [-6, -2, 2, -4, 0, 4], [-6, -2, 2, -4, 4, 0], [-6, -2, 2, 0, -4, 4], [-6, -2, 2, 0, 4, -4], [-6, -2, 2, 4, -4, 0], [-6, -2, 2, 4, 0, -4], [-6, -2, 4, -4, 0, 2], [-6, -2, 4, -4, 2, 0], [-6, -2, 4, 0, -4, 2], [-6, -2, 4, 0, 2, -4], [-6, -2, 4, 2, -4, 0], [-6, -2, 4, 2, 0, -4], [-6, 0, -4, -2, 2, 4], [-6, 0, -4, -2, 4, 2], [-6, 0, -4, 2, -2, 4], [-6, 0, -4, 2, 4, -2], [-6, 0, -4, 4, -2, 2], [-6, 0, -4, 4, 2, -2], [-6, 0, -2, -4, 2, 4], [-6, 0, -2, -4, 4, 2], [-6, 0, -2, 2, -4, 4], [-6, 0, -2, 2, 4, -4], [-6, 0, -2, 4, -4, 2], [-6, 0, -2, 4, 2, -4], [-6, 0, 2, -4, -2, 4], [-6, 0, 2, -4, 4, -2], [-6, 0, 2, -2, -4, 4], [-6, 0, 2, -2, 4, -4], [-6, 0, 2, 4, -4, -2], [-6, 0, 2, 4, -2, -4], [-6, 0, 4, -4, -2, 2], [-6, 0, 4, -4, 2, -2], [-6, 0, 4, -2, -4, 2], [-6, 0, 4, -2, 2, -4], [-6, 0, 4, 2, -4, -2], [-6, 0, 4, 2, -2, -4], [-6, 2, -4, -2, 0, 4], [-6, 2, -4, -2, 4, 0], [-6, 2, -4, 0, -2, 4], [-6, 2, -4, 0, 4, -2], [-6, 2, -4, 4, -2, 0], [-6, 2, -4, 4, 0, -2], [-6, 2, -2, -4, 0, 4], [-6, 2, -2, -4, 4, 0], [-6, 2, -2, 0, -4, 4], [-6, 2, -2, 0, 4, -4], [-6, 2, -2, 4, -4, 0], [-6, 2, -2, 4, 0, -4], [-6, 2, 0, -4, -2, 4], [-6, 2, 0, -4, 4, -2], [-6, 2, 0, -2, -4, 4], [-6, 2, 0, -2, 4, -4], [-6, 2, 0, 4, -4, -2], [-6, 2, 0, 4, -2, -4], [-6, 2, 4, -4, -2, 0], [-6, 2, 4, -4, 0, -2], [-6, 2, 4, -2, -4, 0], [-6, 2, 4, -2, 0, -4], [-6, 2, 4, 0, -4, -2], [-6, 2, 4, 0, -2, -4], [-6, 4, -4, -2, 0, 2], [-6, 4, -4, -2, 2, 0], [-6, 4, -4, 0, -2, 2], [-6, 4, -4, 0, 2, -2], [-6, 4, -4, 2, -2, 0], [-6, 4, -4, 2, 0, -2], [-6, 4, -2, -4, 0, 2], [-6, 4, -2, -4, 2, 0], [-6, 4, -2, 0, -4, 2], [-6, 4, -2, 0, 2, -4], [-6, 4, -2, 2, -4, 0], [-6, 4, -2, 2, 0, -4], [-6, 4, 0, -4, -2, 2], [-6, 4, 0, -4, 2, -2], [-6, 4, 0, -2, -4, 2], [-6, 4, 0, -2, 2, -4], [-6, 4, 0, 2, -4, -2], [-6, 4, 0, 2, -2, -4], [-6, 4, 2, -4, -2, 0], [-6, 4, 2, -4, 0, -2], [-6, 4, 2, -2, -4, 0], [-6, 4, 2, -2, 0, -4], [-6, 4, 2, 0, -4, -2], [-6, 4, 2, 0, -2, -4], [-4, -6, -2, 0, 2, 4], [-4, -6, -2, 0, 4, 2], [-4, -6, -2, 2, 0, 4], [-4, -6, -2, 2, 4, 0], [-4, -6, -2, 4, 0, 2], [-4, -6, -2, 4, 2, 0], [-4, -6, 0, -2, 2, 4], [-4, -6, 0, -2, 4, 2], [-4, -6, 0, 2, -2, 4], [-4, -6, 0, 2, 4, -2], [-4, -6, 0, 4, -2, 2], [-4, -6, 0, 4, 2, -2], [-4, -6, 2, -2, 0, 4], [-4, -6, 2, -2, 4, 0], [-4, -6, 2, 0, -2, 4], [-4, -6, 2, 0, 4, -2], [-4, -6, 2, 4, -2, 0], [-4, -6, 2, 4, 0, -2], [-4, -6, 4, -2, 0, 2], [-4, -6, 4, -2, 2, 0], [-4, -6, 4, 0, -2, 2], [-4, -6, 4, 0, 2, -2], [-4, -6, 4, 2, -2, 0], [-4, -6, 4, 2, 0, -2], [-4, -2, -6, 0, 2, 4], [-4, -2, -6, 0, 4, 2], [-4, -2, -6, 2, 0, 4], [-4, -2, -6, 2, 4, 0], [-4, -2, -6, 4, 0, 2], [-4, -2, -6, 4, 2, 0], [-4, -2, 0, -6, 2, 4], [-4, -2, 0, -6, 4, 2], [-4, -2, 0, 2, -6, 4], [-4, -2, 0, 2, 4, -6], [-4, -2, 0, 4, -6, 2], [-4, -2, 0, 4, 2, -6], [-4, -2, 2, -6, 0, 4], [-4, -2, 2, -6, 4, 0], [-4, -2, 2, 0, -6, 4], [-4, -2, 2, 0, 4, -6], [-4, -2, 2, 4, -6, 0], [-4, -2, 2, 4, 0, -6], [-4, -2, 4, -6, 0, 2], [-4, -2, 4, -6, 2, 0], [-4, -2, 4, 0, -6, 2], [-4, -2, 4, 0, 2, -6], [-4, -2, 4, 2, -6, 0], [-4, -2, 4, 2, 0, -6], [-4, 0, -6, -2, 2, 4], [-4, 0, -6, -2, 4, 2], [-4, 0, -6, 2, -2, 4], [-4, 0, -6, 2, 4, -2], [-4, 0, -6, 4, -2, 2], [-4, 0, -6, 4, 2, -2], [-4, 0, -2, -6, 2, 4], [-4, 0, -2, -6, 4, 2], [-4, 0, -2, 2, -6, 4], [-4, 0, -2, 2, 4, -6], [-4, 0, -2, 4, -6, 2], [-4, 0, -2, 4, 2, -6], [-4, 0, 2, -6, -2, 4], [-4, 0, 2, -6, 4, -2], [-4, 0, 2, -2, -6, 4], [-4, 0, 2, -2, 4, -6], [-4, 0, 2, 4, -6, -2], [-4, 0, 2, 4, -2, -6], [-4, 0, 4, -6, -2, 2], [-4, 0, 4, -6, 2, -2], [-4, 0, 4, -2, -6, 2], [-4, 0, 4, -2, 2, -6], [-4, 0, 4, 2, -6, -2], [-4, 0, 4, 2, -2, -6], [-4, 2, -6, -2, 0, 4], [-4, 2, -6, -2, 4, 0], [-4, 2, -6, 0, -2, 4], [-4, 2, -6, 0, 4, -2], [-4, 2, -6, 4, -2, 0], [-4, 2, -6, 4, 0, -2], [-4, 2, -2, -6, 0, 4], [-4, 2, -2, -6, 4, 0], [-4, 2, -2, 0, -6, 4], [-4, 2, -2, 0, 4, -6], [-4, 2, -2, 4, -6, 0], [-4, 2, -2, 4, 0, -6], [-4, 2, 0, -6, -2, 4], [-4, 2, 0, -6, 4, -2], [-4, 2, 0, -2, -6, 4], [-4, 2, 0, -2, 4, -6], [-4, 2, 0, 4, -6, -2], [-4, 2, 0, 4, -2, -6], [-4, 2, 4, -6, -2, 0], [-4, 2, 4, -6, 0, -2], [-4, 2, 4, -2, -6, 0], [-4, 2, 4, -2, 0, -6], [-4, 2, 4, 0, -6, -2], [-4, 2, 4, 0, -2, -6], [-4, 4, -6, -2, 0, 2], [-4, 4, -6, -2, 2, 0], [-4, 4, -6, 0, -2, 2], [-4, 4, -6, 0, 2, -2], [-4, 4, -6, 2, -2, 0], [-4, 4, -6, 2, 0, -2], [-4, 4, -2, -6, 0, 2], [-4, 4, -2, -6, 2, 0], [-4, 4, -2, 0, -6, 2], [-4, 4, -2, 0, 2, -6], [-4, 4, -2, 2, -6, 0], [-4, 4, -2, 2, 0, -6], [-4, 4, 0, -6, -2, 2], [-4, 4, 0, -6, 2, -2], [-4, 4, 0, -2, -6, 2], [-4, 4, 0, -2, 2, -6], [-4, 4, 0, 2, -6, -2], [-4, 4, 0, 2, -2, -6], [-4, 4, 2, -6, -2, 0], [-4, 4, 2, -6, 0, -2], [-4, 4, 2, -2, -6, 0], [-4, 4, 2, -2, 0, -6], [-4, 4, 2, 0, -6, -2], [-4, 4, 2, 0, -2, -6], [-2, -6, -4, 0, 2, 4], [-2, -6, -4, 0, 4, 2], [-2, -6, -4, 2, 0, 4], [-2, -6, -4, 2, 4, 0], [-2, -6, -4, 4, 0, 2], [-2, -6, -4, 4, 2, 0], [-2, -6, 0, -4, 2, 4], [-2, -6, 0, -4, 4, 2], [-2, -6, 0, 2, -4, 4], [-2, -6, 0, 2, 4, -4], [-2, -6, 0, 4, -4, 2], [-2, -6, 0, 4, 2, -4], [-2, -6, 2, -4, 0, 4], [-2, -6, 2, -4, 4, 0], [-2, -6, 2, 0, -4, 4], [-2, -6, 2, 0, 4, -4], [-2, -6, 2, 4, -4, 0], [-2, -6, 2, 4, 0, -4], [-2, -6, 4, -4, 0, 2], [-2, -6, 4, -4, 2, 0], [-2, -6, 4, 0, -4, 2], [-2, -6, 4, 0, 2, -4], [-2, -6, 4, 2, -4, 0], [-2, -6, 4, 2, 0, -4], [-2, -4, -6, 0, 2, 4], [-2, -4, -6, 0, 4, 2], [-2, -4, -6, 2, 0, 4], [-2, -4, -6, 2, 4, 0], [-2, -4, -6, 4, 0, 2], [-2, -4, -6, 4, 2, 0], [-2, -4, 0, -6, 2, 4], [-2, -4, 0, -6, 4, 2], [-2, -4, 0, 2, -6, 4], [-2, -4, 0, 2, 4, -6], [-2, -4, 0, 4, -6, 2], [-2, -4, 0, 4, 2, -6], [-2, -4, 2, -6, 0, 4], [-2, -4, 2, -6, 4, 0], [-2, -4, 2, 0, -6, 4], [-2, -4, 2, 0, 4, -6], [-2, -4, 2, 4, -6, 0], [-2, -4, 2, 4, 0, -6], [-2, -4, 4, -6, 0, 2], [-2, -4, 4, -6, 2, 0], [-2, -4, 4, 0, -6, 2], [-2, -4, 4, 0, 2, -6], [-2, -4, 4, 2, -6, 0], [-2, -4, 4, 2, 0, -6], [-2, 0, -6, -4, 2, 4], [-2, 0, -6, -4, 4, 2], [-2, 0, -6, 2, -4, 4], [-2, 0, -6, 2, 4, -4], [-2, 0, -6, 4, -4, 2], [-2, 0, -6, 4, 2, -4], [-2, 0, -4, -6, 2, 4], [-2, 0, -4, -6, 4, 2], [-2, 0, -4, 2, -6, 4], [-2, 0, -4, 2, 4, -6], [-2, 0, -4, 4, -6, 2], [-2, 0, -4, 4, 2, -6], [-2, 0, 2, -6, -4, 4], [-2, 0, 2, -6, 4, -4], [-2, 0, 2, -4, -6, 4], [-2, 0, 2, -4, 4, -6], [-2, 0, 2, 4, -6, -4], [-2, 0, 2, 4, -4, -6], [-2, 0, 4, -6, -4, 2], [-2, 0, 4, -6, 2, -4], [-2, 0, 4, -4, -6, 2], [-2, 0, 4, -4, 2, -6], [-2, 0, 4, 2, -6, -4], [-2, 0, 4, 2, -4, -6], [-2, 2, -6, -4, 0, 4], [-2, 2, -6, -4, 4, 0], [-2, 2, -6, 0, -4, 4], [-2, 2, -6, 0, 4, -4], [-2, 2, -6, 4, -4, 0], [-2, 2, -6, 4, 0, -4], [-2, 2, -4, -6, 0, 4], [-2, 2, -4, -6, 4, 0], [-2, 2, -4, 0, -6, 4], [-2, 2, -4, 0, 4, -6], [-2, 2, -4, 4, -6, 0], [-2, 2, -4, 4, 0, -6], [-2, 2, 0, -6, -4, 4], [-2, 2, 0, -6, 4, -4], [-2, 2, 0, -4, -6, 4], [-2, 2, 0, -4, 4, -6], [-2, 2, 0, 4, -6, -4], [-2, 2, 0, 4, -4, -6], [-2, 2, 4, -6, -4, 0], [-2, 2, 4, -6, 0, -4], [-2, 2, 4, -4, -6, 0], [-2, 2, 4, -4, 0, -6], [-2, 2, 4, 0, -6, -4], [-2, 2, 4, 0, -4, -6], [-2, 4, -6, -4, 0, 2], [-2, 4, -6, -4, 2, 0], [-2, 4, -6, 0, -4, 2], [-2, 4, -6, 0, 2, -4], [-2, 4, -6, 2, -4, 0], [-2, 4, -6, 2, 0, -4], [-2, 4, -4, -6, 0, 2], [-2, 4, -4, -6, 2, 0], [-2, 4, -4, 0, -6, 2], [-2, 4, -4, 0, 2, -6], [-2, 4, -4, 2, -6, 0], [-2, 4, -4, 2, 0, -6], [-2, 4, 0, -6, -4, 2], [-2, 4, 0, -6, 2, -4], [-2, 4, 0, -4, -6, 2], [-2, 4, 0, -4, 2, -6], [-2, 4, 0, 2, -6, -4], [-2, 4, 0, 2, -4, -6], [-2, 4, 2, -6, -4, 0], [-2, 4, 2, -6, 0, -4], [-2, 4, 2, -4, -6, 0], [-2, 4, 2, -4, 0, -6], [-2, 4, 2, 0, -6, -4], [-2, 4, 2, 0, -4, -6], [0, -6, -4, -2, 2, 4], [0, -6, -4, -2, 4, 2], [0, -6, -4, 2, -2, 4], [0, -6, -4, 2, 4, -2], [0, -6, -4, 4, -2, 2], [0, -6, -4, 4, 2, -2], [0, -6, -2, -4, 2, 4], [0, -6, -2, -4, 4, 2], [0, -6, -2, 2, -4, 4], [0, -6, -2, 2, 4, -4], [0, -6, -2, 4, -4, 2], [0, -6, -2, 4, 2, -4], [0, -6, 2, -4, -2, 4], [0, -6, 2, -4, 4, -2], [0, -6, 2, -2, -4, 4], [0, -6, 2, -2, 4, -4], [0, -6, 2, 4, -4, -2], [0, -6, 2, 4, -2, -4], [0, -6, 4, -4, -2, 2], [0, -6, 4, -4, 2, -2], [0, -6, 4, -2, -4, 2], [0, -6, 4, -2, 2, -4], [0, -6, 4, 2, -4, -2], [0, -6, 4, 2, -2, -4], [0, -4, -6, -2, 2, 4], [0, -4, -6, -2, 4, 2], [0, -4, -6, 2, -2, 4], [0, -4, -6, 2, 4, -2], [0, -4, -6, 4, -2, 2], [0, -4, -6, 4, 2, -2], [0, -4, -2, -6, 2, 4], [0, -4, -2, -6, 4, 2], [0, -4, -2, 2, -6, 4], [0, -4, -2, 2, 4, -6], [0, -4, -2, 4, -6, 2], [0, -4, -2, 4, 2, -6], [0, -4, 2, -6, -2, 4], [0, -4, 2, -6, 4, -2], [0, -4, 2, -2, -6, 4], [0, -4, 2, -2, 4, -6], [0, -4, 2, 4, -6, -2], [0, -4, 2, 4, -2, -6], [0, -4, 4, -6, -2, 2], [0, -4, 4, -6, 2, -2], [0, -4, 4, -2, -6, 2], [0, -4, 4, -2, 2, -6], [0, -4, 4, 2, -6, -2], [0, -4, 4, 2, -2, -6], [0, -2, -6, -4, 2, 4], [0, -2, -6, -4, 4, 2], [0, -2, -6, 2, -4, 4], [0, -2, -6, 2, 4, -4], [0, -2, -6, 4, -4, 2], [0, -2, -6, 4, 2, -4], [0, -2, -4, -6, 2, 4], [0, -2, -4, -6, 4, 2], [0, -2, -4, 2, -6, 4], [0, -2, -4, 2, 4, -6], [0, -2, -4, 4, -6, 2], [0, -2, -4, 4, 2, -6], [0, -2, 2, -6, -4, 4], [0, -2, 2, -6, 4, -4], [0, -2, 2, -4, -6, 4], [0, -2, 2, -4, 4, -6], [0, -2, 2, 4, -6, -4], [0, -2, 2, 4, -4, -6], [0, -2, 4, -6, -4, 2], [0, -2, 4, -6, 2, -4], [0, -2, 4, -4, -6, 2], [0, -2, 4, -4, 2, -6], [0, -2, 4, 2, -6, -4], [0, -2, 4, 2, -4, -6], [0, 2, -6, -4, -2, 4], [0, 2, -6, -4, 4, -2], [0, 2, -6, -2, -4, 4], [0, 2, -6, -2, 4, -4], [0, 2, -6, 4, -4, -2], [0, 2, -6, 4, -2, -4], [0, 2, -4, -6, -2, 4], [0, 2, -4, -6, 4, -2], [0, 2, -4, -2, -6, 4], [0, 2, -4, -2, 4, -6], [0, 2, -4, 4, -6, -2], [0, 2, -4, 4, -2, -6], [0, 2, -2, -6, -4, 4], [0, 2, -2, -6, 4, -4], [0, 2, -2, -4, -6, 4], [0, 2, -2, -4, 4, -6], [0, 2, -2, 4, -6, -4], [0, 2, -2, 4, -4, -6], [0, 2, 4, -6, -4, -2], [0, 2, 4, -6, -2, -4], [0, 2, 4, -4, -6, -2], [0, 2, 4, -4, -2, -6], [0, 2, 4, -2, -6, -4], [0, 2, 4, -2, -4, -6], [0, 4, -6, -4, -2, 2], [0, 4, -6, -4, 2, -2], [0, 4, -6, -2, -4, 2], [0, 4, -6, -2, 2, -4], [0, 4, -6, 2, -4, -2], [0, 4, -6, 2, -2, -4], [0, 4, -4, -6, -2, 2], [0, 4, -4, -6, 2, -2], [0, 4, -4, -2, -6, 2], [0, 4, -4, -2, 2, -6], [0, 4, -4, 2, -6, -2], [0, 4, -4, 2, -2, -6], [0, 4, -2, -6, -4, 2], [0, 4, -2, -6, 2, -4], [0, 4, -2, -4, -6, 2], [0, 4, -2, -4, 2, -6], [0, 4, -2, 2, -6, -4], [0, 4, -2, 2, -4, -6], [0, 4, 2, -6, -4, -2], [0, 4, 2, -6, -2, -4], [0, 4, 2, -4, -6, -2], [0, 4, 2, -4, -2, -6], [0, 4, 2, -2, -6, -4], [0, 4, 2, -2, -4, -6], [2, -6, -4, -2, 0, 4], [2, -6, -4, -2, 4, 0], [2, -6, -4, 0, -2, 4], [2, -6, -4, 0, 4, -2], [2, -6, -4, 4, -2, 0], [2, -6, -4, 4, 0, -2], [2, -6, -2, -4, 0, 4], [2, -6, -2, -4, 4, 0], [2, -6, -2, 0, -4, 4], [2, -6, -2, 0, 4, -4], [2, -6, -2, 4, -4, 0], [2, -6, -2, 4, 0, -4], [2, -6, 0, -4, -2, 4], [2, -6, 0, -4, 4, -2], [2, -6, 0, -2, -4, 4], [2, -6, 0, -2, 4, -4], [2, -6, 0, 4, -4, -2], [2, -6, 0, 4, -2, -4], [2, -6, 4, -4, -2, 0], [2, -6, 4, -4, 0, -2], [2, -6, 4, -2, -4, 0], [2, -6, 4, -2, 0, -4], [2, -6, 4, 0, -4, -2], [2, -6, 4, 0, -2, -4], [2, -4, -6, -2, 0, 4], [2, -4, -6, -2, 4, 0], [2, -4, -6, 0, -2, 4], [2, -4, -6, 0, 4, -2], [2, -4, -6, 4, -2, 0], [2, -4, -6, 4, 0, -2], [2, -4, -2, -6, 0, 4], [2, -4, -2, -6, 4, 0], [2, -4, -2, 0, -6, 4], [2, -4, -2, 0, 4, -6], [2, -4, -2, 4, -6, 0], [2, -4, -2, 4, 0, -6], [2, -4, 0, -6, -2, 4], [2, -4, 0, -6, 4, -2], [2, -4, 0, -2, -6, 4], [2, -4, 0, -2, 4, -6], [2, -4, 0, 4, -6, -2], [2, -4, 0, 4, -2, -6], [2, -4, 4, -6, -2, 0], [2, -4, 4, -6, 0, -2], [2, -4, 4, -2, -6, 0], [2, -4, 4, -2, 0, -6], [2, -4, 4, 0, -6, -2], [2, -4, 4, 0, -2, -6], [2, -2, -6, -4, 0, 4], [2, -2, -6, -4, 4, 0], [2, -2, -6, 0, -4, 4], [2, -2, -6, 0, 4, -4], [2, -2, -6, 4, -4, 0], [2, -2, -6, 4, 0, -4], [2, -2, -4, -6, 0, 4], [2, -2, -4, -6, 4, 0], [2, -2, -4, 0, -6, 4], [2, -2, -4, 0, 4, -6], [2, -2, -4, 4, -6, 0], [2, -2, -4, 4, 0, -6], [2, -2, 0, -6, -4, 4], [2, -2, 0, -6, 4, -4], [2, -2, 0, -4, -6, 4], [2, -2, 0, -4, 4, -6], [2, -2, 0, 4, -6, -4], [2, -2, 0, 4, -4, -6], [2, -2, 4, -6, -4, 0], [2, -2, 4, -6, 0, -4], [2, -2, 4, -4, -6, 0], [2, -2, 4, -4, 0, -6], [2, -2, 4, 0, -6, -4], [2, -2, 4, 0, -4, -6], [2, 0, -6, -4, -2, 4], [2, 0, -6, -4, 4, -2], [2, 0, -6, -2, -4, 4], [2, 0, -6, -2, 4, -4], [2, 0, -6, 4, -4, -2], [2, 0, -6, 4, -2, -4], [2, 0, -4, -6, -2, 4], [2, 0, -4, -6, 4, -2], [2, 0, -4, -2, -6, 4], [2, 0, -4, -2, 4, -6], [2, 0, -4, 4, -6, -2], [2, 0, -4, 4, -2, -6], [2, 0, -2, -6, -4, 4], [2, 0, -2, -6, 4, -4], [2, 0, -2, -4, -6, 4], [2, 0, -2, -4, 4, -6], [2, 0, -2, 4, -6, -4], [2, 0, -2, 4, -4, -6], [2, 0, 4, -6, -4, -2], [2, 0, 4, -6, -2, -4], [2, 0, 4, -4, -6, -2], [2, 0, 4, -4, -2, -6], [2, 0, 4, -2, -6, -4], [2, 0, 4, -2, -4, -6], [2, 4, -6, -4, -2, 0], [2, 4, -6, -4, 0, -2], [2, 4, -6, -2, -4, 0], [2, 4, -6, -2, 0, -4], [2, 4, -6, 0, -4, -2], [2, 4, -6, 0, -2, -4], [2, 4, -4, -6, -2, 0], [2, 4, -4, -6, 0, -2], [2, 4, -4, -2, -6, 0], [2, 4, -4, -2, 0, -6], [2, 4, -4, 0, -6, -2], [2, 4, -4, 0, -2, -6], [2, 4, -2, -6, -4, 0], [2, 4, -2, -6, 0, -4], [2, 4, -2, -4, -6, 0], [2, 4, -2, -4, 0, -6], [2, 4, -2, 0, -6, -4], [2, 4, -2, 0, -4, -6], [2, 4, 0, -6, -4, -2], [2, 4, 0, -6, -2, -4], [2, 4, 0, -4, -6, -2], [2, 4, 0, -4, -2, -6], [2, 4, 0, -2, -6, -4], [2, 4, 0, -2, -4, -6], [4, -6, -4, -2, 0, 2], [4, -6, -4, -2, 2, 0], [4, -6, -4, 0, -2, 2], [4, -6, -4, 0, 2, -2], [4, -6, -4, 2, -2, 0], [4, -6, -4, 2, 0, -2], [4, -6, -2, -4, 0, 2], [4, -6, -2, -4, 2, 0], [4, -6, -2, 0, -4, 2], [4, -6, -2, 0, 2, -4], [4, -6, -2, 2, -4, 0], [4, -6, -2, 2, 0, -4], [4, -6, 0, -4, -2, 2], [4, -6, 0, -4, 2, -2], [4, -6, 0, -2, -4, 2], [4, -6, 0, -2, 2, -4], [4, -6, 0, 2, -4, -2], [4, -6, 0, 2, -2, -4], [4, -6, 2, -4, -2, 0], [4, -6, 2, -4, 0, -2], [4, -6, 2, -2, -4, 0], [4, -6, 2, -2, 0, -4], [4, -6, 2, 0, -4, -2], [4, -6, 2, 0, -2, -4], [4, -4, -6, -2, 0, 2], [4, -4, -6, -2, 2, 0], [4, -4, -6, 0, -2, 2], [4, -4, -6, 0, 2, -2], [4, -4, -6, 2, -2, 0], [4, -4, -6, 2, 0, -2], [4, -4, -2, -6, 0, 2], [4, -4, -2, -6, 2, 0], [4, -4, -2, 0, -6, 2], [4, -4, -2, 0, 2, -6], [4, -4, -2, 2, -6, 0], [4, -4, -2, 2, 0, -6], [4, -4, 0, -6, -2, 2], [4, -4, 0, -6, 2, -2], [4, -4, 0, -2, -6, 2], [4, -4, 0, -2, 2, -6], [4, -4, 0, 2, -6, -2], [4, -4, 0, 2, -2, -6], [4, -4, 2, -6, -2, 0], [4, -4, 2, -6, 0, -2], [4, -4, 2, -2, -6, 0], [4, -4, 2, -2, 0, -6], [4, -4, 2, 0, -6, -2], [4, -4, 2, 0, -2, -6], [4, -2, -6, -4, 0, 2], [4, -2, -6, -4, 2, 0], [4, -2, -6, 0, -4, 2], [4, -2, -6, 0, 2, -4], [4, -2, -6, 2, -4, 0], [4, -2, -6, 2, 0, -4], [4, -2, -4, -6, 0, 2], [4, -2, -4, -6, 2, 0], [4, -2, -4, 0, -6, 2], [4, -2, -4, 0, 2, -6], [4, -2, -4, 2, -6, 0], [4, -2, -4, 2, 0, -6], [4, -2, 0, -6, -4, 2], [4, -2, 0, -6, 2, -4], [4, -2, 0, -4, -6, 2], [4, -2, 0, -4, 2, -6], [4, -2, 0, 2, -6, -4], [4, -2, 0, 2, -4, -6], [4, -2, 2, -6, -4, 0], [4, -2, 2, -6, 0, -4], [4, -2, 2, -4, -6, 0], [4, -2, 2, -4, 0, -6], [4, -2, 2, 0, -6, -4], [4, -2, 2, 0, -4, -6], [4, 0, -6, -4, -2, 2], [4, 0, -6, -4, 2, -2], [4, 0, -6, -2, -4, 2], [4, 0, -6, -2, 2, -4], [4, 0, -6, 2, -4, -2], [4, 0, -6, 2, -2, -4], [4, 0, -4, -6, -2, 2], [4, 0, -4, -6, 2, -2], [4, 0, -4, -2, -6, 2], [4, 0, -4, -2, 2, -6], [4, 0, -4, 2, -6, -2], [4, 0, -4, 2, -2, -6], [4, 0, -2, -6, -4, 2], [4, 0, -2, -6, 2, -4], [4, 0, -2, -4, -6, 2], [4, 0, -2, -4, 2, -6], [4, 0, -2, 2, -6, -4], [4, 0, -2, 2, -4, -6], [4, 0, 2, -6, -4, -2], [4, 0, 2, -6, -2, -4], [4, 0, 2, -4, -6, -2], [4, 0, 2, -4, -2, -6], [4, 0, 2, -2, -6, -4], [4, 0, 2, -2, -4, -6], [4, 2, -6, -4, -2, 0], [4, 2, -6, -4, 0, -2], [4, 2, -6, -2, -4, 0], [4, 2, -6, -2, 0, -4], [4, 2, -6, 0, -4, -2], [4, 2, -6, 0, -2, -4], [4, 2, -4, -6, -2, 0], [4, 2, -4, -6, 0, -2], [4, 2, -4, -2, -6, 0], [4, 2, -4, -2, 0, -6], [4, 2, -4, 0, -6, -2], [4, 2, -4, 0, -2, -6], [4, 2, -2, -6, -4, 0], [4, 2, -2, -6, 0, -4], [4, 2, -2, -4, -6, 0], [4, 2, -2, -4, 0, -6], [4, 2, -2, 0, -6, -4], [4, 2, -2, 0, -4, -6], [4, 2, 0, -6, -4, -2], [4, 2, 0, -6, -2, -4], [4, 2, 0, -4, -6, -2], [4, 2, 0, -4, -2, -6], [4, 2, 0, -2, -6, -4], [4, 2, 0, -2, -4, -6]]\n assert candidate(nums = [0, 1, -1, 2, -2, 3]) == [[0, 1, -1, 2, -2, 3], [0, 1, -1, 2, 3, -2], [0, 1, -1, -2, 2, 3], [0, 1, -1, -2, 3, 2], [0, 1, -1, 3, 2, -2], [0, 1, -1, 3, -2, 2], [0, 1, 2, -1, -2, 3], [0, 1, 2, -1, 3, -2], [0, 1, 2, -2, -1, 3], [0, 1, 2, -2, 3, -1], [0, 1, 2, 3, -1, -2], [0, 1, 2, 3, -2, -1], [0, 1, -2, -1, 2, 3], [0, 1, -2, -1, 3, 2], [0, 1, -2, 2, -1, 3], [0, 1, -2, 2, 3, -1], [0, 1, -2, 3, -1, 2], [0, 1, -2, 3, 2, -1], [0, 1, 3, -1, 2, -2], [0, 1, 3, -1, -2, 2], [0, 1, 3, 2, -1, -2], [0, 1, 3, 2, -2, -1], [0, 1, 3, -2, -1, 2], [0, 1, 3, -2, 2, -1], [0, -1, 1, 2, -2, 3], [0, -1, 1, 2, 3, -2], [0, -1, 1, -2, 2, 3], [0, -1, 1, -2, 3, 2], [0, -1, 1, 3, 2, -2], [0, -1, 1, 3, -2, 2], [0, -1, 2, 1, -2, 3], [0, -1, 2, 1, 3, -2], [0, -1, 2, -2, 1, 3], [0, -1, 2, -2, 3, 1], [0, -1, 2, 3, 1, -2], [0, -1, 2, 3, -2, 1], [0, -1, -2, 1, 2, 3], [0, -1, -2, 1, 3, 2], [0, -1, -2, 2, 1, 3], [0, -1, -2, 2, 3, 1], [0, -1, -2, 3, 1, 2], [0, -1, -2, 3, 2, 1], [0, -1, 3, 1, 2, -2], [0, -1, 3, 1, -2, 2], [0, -1, 3, 2, 1, -2], [0, -1, 3, 2, -2, 1], [0, -1, 3, -2, 1, 2], [0, -1, 3, -2, 2, 1], [0, 2, 1, -1, -2, 3], [0, 2, 1, -1, 3, -2], [0, 2, 1, -2, -1, 3], [0, 2, 1, -2, 3, -1], [0, 2, 1, 3, -1, -2], [0, 2, 1, 3, -2, -1], [0, 2, -1, 1, -2, 3], [0, 2, -1, 1, 3, -2], [0, 2, -1, -2, 1, 3], [0, 2, -1, -2, 3, 1], [0, 2, -1, 3, 1, -2], [0, 2, -1, 3, -2, 1], [0, 2, -2, 1, -1, 3], [0, 2, -2, 1, 3, -1], [0, 2, -2, -1, 1, 3], [0, 2, -2, -1, 3, 1], [0, 2, -2, 3, 1, -1], [0, 2, -2, 3, -1, 1], [0, 2, 3, 1, -1, -2], [0, 2, 3, 1, -2, -1], [0, 2, 3, -1, 1, -2], [0, 2, 3, -1, -2, 1], [0, 2, 3, -2, 1, -1], [0, 2, 3, -2, -1, 1], [0, -2, 1, -1, 2, 3], [0, -2, 1, -1, 3, 2], [0, -2, 1, 2, -1, 3], [0, -2, 1, 2, 3, -1], [0, -2, 1, 3, -1, 2], [0, -2, 1, 3, 2, -1], [0, -2, -1, 1, 2, 3], [0, -2, -1, 1, 3, 2], [0, -2, -1, 2, 1, 3], [0, -2, -1, 2, 3, 1], [0, -2, -1, 3, 1, 2], [0, -2, -1, 3, 2, 1], [0, -2, 2, 1, -1, 3], [0, -2, 2, 1, 3, -1], [0, -2, 2, -1, 1, 3], [0, -2, 2, -1, 3, 1], [0, -2, 2, 3, 1, -1], [0, -2, 2, 3, -1, 1], [0, -2, 3, 1, -1, 2], [0, -2, 3, 1, 2, -1], [0, -2, 3, -1, 1, 2], [0, -2, 3, -1, 2, 1], [0, -2, 3, 2, 1, -1], [0, -2, 3, 2, -1, 1], [0, 3, 1, -1, 2, -2], [0, 3, 1, -1, -2, 2], [0, 3, 1, 2, -1, -2], [0, 3, 1, 2, -2, -1], [0, 3, 1, -2, -1, 2], [0, 3, 1, -2, 2, -1], [0, 3, -1, 1, 2, -2], [0, 3, -1, 1, -2, 2], [0, 3, -1, 2, 1, -2], [0, 3, -1, 2, -2, 1], [0, 3, -1, -2, 1, 2], [0, 3, -1, -2, 2, 1], [0, 3, 2, 1, -1, -2], [0, 3, 2, 1, -2, -1], [0, 3, 2, -1, 1, -2], [0, 3, 2, -1, -2, 1], [0, 3, 2, -2, 1, -1], [0, 3, 2, -2, -1, 1], [0, 3, -2, 1, -1, 2], [0, 3, -2, 1, 2, -1], [0, 3, -2, -1, 1, 2], [0, 3, -2, -1, 2, 1], [0, 3, -2, 2, 1, -1], [0, 3, -2, 2, -1, 1], [1, 0, -1, 2, -2, 3], [1, 0, -1, 2, 3, -2], [1, 0, -1, -2, 2, 3], [1, 0, -1, -2, 3, 2], [1, 0, -1, 3, 2, -2], [1, 0, -1, 3, -2, 2], [1, 0, 2, -1, -2, 3], [1, 0, 2, -1, 3, -2], [1, 0, 2, -2, -1, 3], [1, 0, 2, -2, 3, -1], [1, 0, 2, 3, -1, -2], [1, 0, 2, 3, -2, -1], [1, 0, -2, -1, 2, 3], [1, 0, -2, -1, 3, 2], [1, 0, -2, 2, -1, 3], [1, 0, -2, 2, 3, -1], [1, 0, -2, 3, -1, 2], [1, 0, -2, 3, 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[-2, 0, 3, -1, 2, 1], [-2, 0, 3, 2, 1, -1], [-2, 0, 3, 2, -1, 1], [-2, 1, 0, -1, 2, 3], [-2, 1, 0, -1, 3, 2], [-2, 1, 0, 2, -1, 3], [-2, 1, 0, 2, 3, -1], [-2, 1, 0, 3, -1, 2], [-2, 1, 0, 3, 2, -1], [-2, 1, -1, 0, 2, 3], [-2, 1, -1, 0, 3, 2], [-2, 1, -1, 2, 0, 3], [-2, 1, -1, 2, 3, 0], [-2, 1, -1, 3, 0, 2], [-2, 1, -1, 3, 2, 0], [-2, 1, 2, 0, -1, 3], [-2, 1, 2, 0, 3, -1], [-2, 1, 2, -1, 0, 3], [-2, 1, 2, -1, 3, 0], [-2, 1, 2, 3, 0, -1], [-2, 1, 2, 3, -1, 0], [-2, 1, 3, 0, -1, 2], [-2, 1, 3, 0, 2, -1], [-2, 1, 3, -1, 0, 2], [-2, 1, 3, -1, 2, 0], [-2, 1, 3, 2, 0, -1], [-2, 1, 3, 2, -1, 0], [-2, -1, 0, 1, 2, 3], [-2, -1, 0, 1, 3, 2], [-2, -1, 0, 2, 1, 3], [-2, -1, 0, 2, 3, 1], [-2, -1, 0, 3, 1, 2], [-2, -1, 0, 3, 2, 1], [-2, -1, 1, 0, 2, 3], [-2, -1, 1, 0, 3, 2], [-2, -1, 1, 2, 0, 3], [-2, -1, 1, 2, 3, 0], [-2, -1, 1, 3, 0, 2], [-2, -1, 1, 3, 2, 0], [-2, -1, 2, 0, 1, 3], [-2, -1, 2, 0, 3, 1], [-2, -1, 2, 1, 0, 3], [-2, -1, 2, 1, 3, 0], [-2, -1, 2, 3, 0, 1], [-2, -1, 2, 3, 1, 0], [-2, -1, 3, 0, 1, 2], [-2, -1, 3, 0, 2, 1], [-2, -1, 3, 1, 0, 2], [-2, -1, 3, 1, 2, 0], [-2, -1, 3, 2, 0, 1], [-2, -1, 3, 2, 1, 0], [-2, 2, 0, 1, -1, 3], [-2, 2, 0, 1, 3, -1], [-2, 2, 0, -1, 1, 3], [-2, 2, 0, -1, 3, 1], [-2, 2, 0, 3, 1, -1], [-2, 2, 0, 3, -1, 1], [-2, 2, 1, 0, -1, 3], [-2, 2, 1, 0, 3, -1], [-2, 2, 1, -1, 0, 3], [-2, 2, 1, -1, 3, 0], [-2, 2, 1, 3, 0, -1], [-2, 2, 1, 3, -1, 0], [-2, 2, -1, 0, 1, 3], [-2, 2, -1, 0, 3, 1], [-2, 2, -1, 1, 0, 3], [-2, 2, -1, 1, 3, 0], [-2, 2, -1, 3, 0, 1], [-2, 2, -1, 3, 1, 0], [-2, 2, 3, 0, 1, -1], [-2, 2, 3, 0, -1, 1], [-2, 2, 3, 1, 0, -1], [-2, 2, 3, 1, -1, 0], [-2, 2, 3, -1, 0, 1], [-2, 2, 3, -1, 1, 0], [-2, 3, 0, 1, -1, 2], [-2, 3, 0, 1, 2, -1], [-2, 3, 0, -1, 1, 2], [-2, 3, 0, -1, 2, 1], [-2, 3, 0, 2, 1, -1], [-2, 3, 0, 2, -1, 1], [-2, 3, 1, 0, -1, 2], [-2, 3, 1, 0, 2, -1], [-2, 3, 1, -1, 0, 2], [-2, 3, 1, -1, 2, 0], [-2, 3, 1, 2, 0, -1], [-2, 3, 1, 2, -1, 0], [-2, 3, -1, 0, 1, 2], [-2, 3, -1, 0, 2, 1], [-2, 3, -1, 1, 0, 2], [-2, 3, -1, 1, 2, 0], [-2, 3, -1, 2, 0, 1], [-2, 3, -1, 2, 1, 0], [-2, 3, 2, 0, 1, -1], [-2, 3, 2, 0, -1, 1], [-2, 3, 2, 1, 0, -1], [-2, 3, 2, 1, -1, 0], [-2, 3, 2, -1, 0, 1], [-2, 3, 2, -1, 1, 0], [3, 0, 1, -1, 2, -2], [3, 0, 1, -1, -2, 2], [3, 0, 1, 2, -1, -2], [3, 0, 1, 2, -2, -1], [3, 0, 1, -2, -1, 2], [3, 0, 1, -2, 2, -1], [3, 0, -1, 1, 2, -2], [3, 0, -1, 1, -2, 2], [3, 0, -1, 2, 1, -2], [3, 0, -1, 2, -2, 1], [3, 0, -1, -2, 1, 2], [3, 0, -1, -2, 2, 1], [3, 0, 2, 1, -1, -2], [3, 0, 2, 1, -2, -1], [3, 0, 2, -1, 1, -2], [3, 0, 2, -1, -2, 1], [3, 0, 2, -2, 1, -1], [3, 0, 2, -2, -1, 1], [3, 0, -2, 1, -1, 2], [3, 0, -2, 1, 2, -1], [3, 0, -2, -1, 1, 2], [3, 0, -2, -1, 2, 1], [3, 0, -2, 2, 1, -1], [3, 0, -2, 2, -1, 1], [3, 1, 0, -1, 2, -2], [3, 1, 0, -1, -2, 2], [3, 1, 0, 2, -1, -2], [3, 1, 0, 2, -2, -1], [3, 1, 0, -2, -1, 2], [3, 1, 0, -2, 2, -1], [3, 1, -1, 0, 2, -2], [3, 1, -1, 0, -2, 2], [3, 1, -1, 2, 0, -2], [3, 1, -1, 2, -2, 0], [3, 1, -1, -2, 0, 2], [3, 1, -1, -2, 2, 0], [3, 1, 2, 0, -1, -2], [3, 1, 2, 0, -2, -1], [3, 1, 2, -1, 0, -2], [3, 1, 2, -1, -2, 0], [3, 1, 2, -2, 0, -1], [3, 1, 2, -2, -1, 0], [3, 1, -2, 0, -1, 2], [3, 1, -2, 0, 2, -1], [3, 1, -2, -1, 0, 2], [3, 1, -2, -1, 2, 0], [3, 1, -2, 2, 0, -1], [3, 1, -2, 2, -1, 0], [3, -1, 0, 1, 2, -2], [3, -1, 0, 1, -2, 2], [3, -1, 0, 2, 1, -2], [3, -1, 0, 2, -2, 1], [3, -1, 0, -2, 1, 2], [3, -1, 0, -2, 2, 1], [3, -1, 1, 0, 2, -2], [3, -1, 1, 0, -2, 2], [3, -1, 1, 2, 0, -2], [3, -1, 1, 2, -2, 0], [3, -1, 1, -2, 0, 2], [3, -1, 1, -2, 2, 0], [3, -1, 2, 0, 1, -2], [3, -1, 2, 0, -2, 1], [3, -1, 2, 1, 0, -2], [3, -1, 2, 1, -2, 0], [3, -1, 2, -2, 0, 1], [3, -1, 2, -2, 1, 0], [3, -1, -2, 0, 1, 2], [3, -1, -2, 0, 2, 1], [3, -1, -2, 1, 0, 2], [3, -1, -2, 1, 2, 0], [3, -1, -2, 2, 0, 1], [3, -1, -2, 2, 1, 0], [3, 2, 0, 1, -1, -2], [3, 2, 0, 1, -2, -1], [3, 2, 0, -1, 1, -2], [3, 2, 0, -1, -2, 1], [3, 2, 0, -2, 1, -1], [3, 2, 0, -2, -1, 1], [3, 2, 1, 0, -1, -2], [3, 2, 1, 0, -2, -1], [3, 2, 1, -1, 0, -2], [3, 2, 1, -1, -2, 0], [3, 2, 1, -2, 0, -1], [3, 2, 1, -2, -1, 0], [3, 2, -1, 0, 1, -2], [3, 2, -1, 0, -2, 1], [3, 2, -1, 1, 0, -2], [3, 2, -1, 1, -2, 0], [3, 2, -1, -2, 0, 1], [3, 2, -1, -2, 1, 0], [3, 2, -2, 0, 1, -1], [3, 2, -2, 0, -1, 1], [3, 2, -2, 1, 0, -1], [3, 2, -2, 1, -1, 0], [3, 2, -2, -1, 0, 1], [3, 2, -2, -1, 1, 0], [3, -2, 0, 1, -1, 2], [3, -2, 0, 1, 2, -1], [3, -2, 0, -1, 1, 2], [3, -2, 0, -1, 2, 1], [3, -2, 0, 2, 1, -1], [3, -2, 0, 2, -1, 1], [3, -2, 1, 0, -1, 2], [3, -2, 1, 0, 2, -1], [3, -2, 1, -1, 0, 2], [3, -2, 1, -1, 2, 0], [3, -2, 1, 2, 0, -1], [3, -2, 1, 2, -1, 0], [3, -2, -1, 0, 1, 2], [3, -2, -1, 0, 2, 1], [3, -2, -1, 1, 0, 2], [3, -2, -1, 1, 2, 0], [3, -2, -1, 2, 0, 1], [3, -2, -1, 2, 1, 0], [3, -2, 2, 0, 1, -1], [3, -2, 2, 0, -1, 1], [3, -2, 2, 1, 0, -1], [3, -2, 2, 1, -1, 0], [3, -2, 2, -1, 0, 1], [3, -2, 2, -1, 1, 0]]\n assert candidate(nums = [1, 2, 3, 4, 5, -1]) == [[1, 2, 3, 4, 5, -1], [1, 2, 3, 4, -1, 5], [1, 2, 3, 5, 4, -1], [1, 2, 3, 5, -1, 4], [1, 2, 3, -1, 4, 5], [1, 2, 3, -1, 5, 4], [1, 2, 4, 3, 5, -1], [1, 2, 4, 3, -1, 5], [1, 2, 4, 5, 3, -1], [1, 2, 4, 5, -1, 3], [1, 2, 4, -1, 3, 5], [1, 2, 4, -1, 5, 3], [1, 2, 5, 3, 4, -1], [1, 2, 5, 3, -1, 4], [1, 2, 5, 4, 3, -1], [1, 2, 5, 4, -1, 3], [1, 2, 5, -1, 3, 4], [1, 2, 5, -1, 4, 3], [1, 2, -1, 3, 4, 5], [1, 2, -1, 3, 5, 4], [1, 2, -1, 4, 3, 5], [1, 2, -1, 4, 5, 3], [1, 2, -1, 5, 3, 4], [1, 2, -1, 5, 4, 3], [1, 3, 2, 4, 5, -1], [1, 3, 2, 4, -1, 5], [1, 3, 2, 5, 4, -1], [1, 3, 2, 5, -1, 4], [1, 3, 2, -1, 4, 5], [1, 3, 2, -1, 5, 4], [1, 3, 4, 2, 5, -1], [1, 3, 4, 2, -1, 5], [1, 3, 4, 5, 2, -1], [1, 3, 4, 5, -1, 2], [1, 3, 4, -1, 2, 5], [1, 3, 4, -1, 5, 2], [1, 3, 5, 2, 4, -1], [1, 3, 5, 2, -1, 4], [1, 3, 5, 4, 2, -1], [1, 3, 5, 4, -1, 2], [1, 3, 5, -1, 2, 4], [1, 3, 5, -1, 4, 2], [1, 3, -1, 2, 4, 5], [1, 3, -1, 2, 5, 4], [1, 3, -1, 4, 2, 5], [1, 3, -1, 4, 5, 2], [1, 3, -1, 5, 2, 4], [1, 3, -1, 5, 4, 2], [1, 4, 2, 3, 5, -1], [1, 4, 2, 3, -1, 5], [1, 4, 2, 5, 3, -1], [1, 4, 2, 5, -1, 3], [1, 4, 2, -1, 3, 5], [1, 4, 2, -1, 5, 3], [1, 4, 3, 2, 5, -1], [1, 4, 3, 2, -1, 5], [1, 4, 3, 5, 2, -1], [1, 4, 3, 5, -1, 2], [1, 4, 3, -1, 2, 5], [1, 4, 3, -1, 5, 2], [1, 4, 5, 2, 3, -1], [1, 4, 5, 2, -1, 3], [1, 4, 5, 3, 2, -1], [1, 4, 5, 3, -1, 2], [1, 4, 5, -1, 2, 3], [1, 4, 5, -1, 3, 2], [1, 4, -1, 2, 3, 5], [1, 4, -1, 2, 5, 3], [1, 4, -1, 3, 2, 5], [1, 4, -1, 3, 5, 2], [1, 4, -1, 5, 2, 3], [1, 4, -1, 5, 3, 2], [1, 5, 2, 3, 4, -1], [1, 5, 2, 3, -1, 4], [1, 5, 2, 4, 3, -1], [1, 5, 2, 4, -1, 3], [1, 5, 2, -1, 3, 4], [1, 5, 2, -1, 4, 3], [1, 5, 3, 2, 4, -1], [1, 5, 3, 2, -1, 4], [1, 5, 3, 4, 2, -1], [1, 5, 3, 4, -1, 2], [1, 5, 3, -1, 2, 4], [1, 5, 3, -1, 4, 2], [1, 5, 4, 2, 3, -1], [1, 5, 4, 2, -1, 3], [1, 5, 4, 3, 2, -1], [1, 5, 4, 3, -1, 2], [1, 5, 4, -1, 2, 3], [1, 5, 4, -1, 3, 2], [1, 5, -1, 2, 3, 4], [1, 5, -1, 2, 4, 3], [1, 5, -1, 3, 2, 4], [1, 5, -1, 3, 4, 2], [1, 5, -1, 4, 2, 3], [1, 5, -1, 4, 3, 2], [1, -1, 2, 3, 4, 5], [1, -1, 2, 3, 5, 4], [1, -1, 2, 4, 3, 5], [1, -1, 2, 4, 5, 3], [1, -1, 2, 5, 3, 4], [1, -1, 2, 5, 4, 3], [1, -1, 3, 2, 4, 5], [1, -1, 3, 2, 5, 4], [1, -1, 3, 4, 2, 5], [1, -1, 3, 4, 5, 2], [1, -1, 3, 5, 2, 4], [1, -1, 3, 5, 4, 2], [1, -1, 4, 2, 3, 5], [1, -1, 4, 2, 5, 3], [1, -1, 4, 3, 2, 5], [1, -1, 4, 3, 5, 2], [1, -1, 4, 5, 2, 3], [1, -1, 4, 5, 3, 2], [1, -1, 5, 2, 3, 4], [1, -1, 5, 2, 4, 3], [1, -1, 5, 3, 2, 4], [1, -1, 5, 3, 4, 2], [1, -1, 5, 4, 2, 3], [1, -1, 5, 4, 3, 2], [2, 1, 3, 4, 5, -1], [2, 1, 3, 4, -1, 5], [2, 1, 3, 5, 4, -1], [2, 1, 3, 5, -1, 4], [2, 1, 3, -1, 4, 5], [2, 1, 3, -1, 5, 4], [2, 1, 4, 3, 5, -1], [2, 1, 4, 3, -1, 5], [2, 1, 4, 5, 3, -1], [2, 1, 4, 5, -1, 3], [2, 1, 4, -1, 3, 5], [2, 1, 4, -1, 5, 3], [2, 1, 5, 3, 4, -1], [2, 1, 5, 3, -1, 4], [2, 1, 5, 4, 3, -1], [2, 1, 5, 4, -1, 3], [2, 1, 5, -1, 3, 4], [2, 1, 5, -1, 4, 3], [2, 1, -1, 3, 4, 5], [2, 1, -1, 3, 5, 4], [2, 1, -1, 4, 3, 5], [2, 1, -1, 4, 5, 3], [2, 1, -1, 5, 3, 4], [2, 1, -1, 5, 4, 3], [2, 3, 1, 4, 5, -1], [2, 3, 1, 4, -1, 5], [2, 3, 1, 5, 4, -1], [2, 3, 1, 5, -1, 4], [2, 3, 1, -1, 4, 5], [2, 3, 1, -1, 5, 4], [2, 3, 4, 1, 5, -1], [2, 3, 4, 1, -1, 5], [2, 3, 4, 5, 1, -1], [2, 3, 4, 5, -1, 1], [2, 3, 4, -1, 1, 5], [2, 3, 4, -1, 5, 1], [2, 3, 5, 1, 4, -1], [2, 3, 5, 1, -1, 4], [2, 3, 5, 4, 1, -1], [2, 3, 5, 4, -1, 1], [2, 3, 5, -1, 1, 4], [2, 3, 5, -1, 4, 1], [2, 3, -1, 1, 4, 5], [2, 3, -1, 1, 5, 4], [2, 3, -1, 4, 1, 5], [2, 3, -1, 4, 5, 1], [2, 3, -1, 5, 1, 4], [2, 3, -1, 5, 4, 1], [2, 4, 1, 3, 5, -1], [2, 4, 1, 3, -1, 5], [2, 4, 1, 5, 3, -1], [2, 4, 1, 5, -1, 3], [2, 4, 1, -1, 3, 5], [2, 4, 1, -1, 5, 3], [2, 4, 3, 1, 5, -1], [2, 4, 3, 1, -1, 5], [2, 4, 3, 5, 1, -1], [2, 4, 3, 5, -1, 1], [2, 4, 3, -1, 1, 5], [2, 4, 3, -1, 5, 1], [2, 4, 5, 1, 3, -1], [2, 4, 5, 1, -1, 3], [2, 4, 5, 3, 1, -1], [2, 4, 5, 3, -1, 1], [2, 4, 5, -1, 1, 3], [2, 4, 5, -1, 3, 1], [2, 4, -1, 1, 3, 5], [2, 4, -1, 1, 5, 3], [2, 4, -1, 3, 1, 5], [2, 4, -1, 3, 5, 1], [2, 4, -1, 5, 1, 3], [2, 4, -1, 5, 3, 1], [2, 5, 1, 3, 4, -1], [2, 5, 1, 3, -1, 4], [2, 5, 1, 4, 3, -1], [2, 5, 1, 4, -1, 3], [2, 5, 1, -1, 3, 4], [2, 5, 1, -1, 4, 3], [2, 5, 3, 1, 4, -1], [2, 5, 3, 1, -1, 4], [2, 5, 3, 4, 1, -1], [2, 5, 3, 4, -1, 1], [2, 5, 3, -1, 1, 4], [2, 5, 3, -1, 4, 1], [2, 5, 4, 1, 3, -1], [2, 5, 4, 1, -1, 3], [2, 5, 4, 3, 1, -1], [2, 5, 4, 3, -1, 1], [2, 5, 4, -1, 1, 3], [2, 5, 4, -1, 3, 1], [2, 5, -1, 1, 3, 4], [2, 5, -1, 1, 4, 3], [2, 5, -1, 3, 1, 4], [2, 5, -1, 3, 4, 1], [2, 5, -1, 4, 1, 3], [2, 5, -1, 4, 3, 1], [2, -1, 1, 3, 4, 5], [2, -1, 1, 3, 5, 4], [2, -1, 1, 4, 3, 5], [2, -1, 1, 4, 5, 3], [2, -1, 1, 5, 3, 4], [2, -1, 1, 5, 4, 3], [2, -1, 3, 1, 4, 5], [2, -1, 3, 1, 5, 4], [2, -1, 3, 4, 1, 5], [2, -1, 3, 4, 5, 1], [2, -1, 3, 5, 1, 4], [2, -1, 3, 5, 4, 1], [2, -1, 4, 1, 3, 5], [2, -1, 4, 1, 5, 3], [2, -1, 4, 3, 1, 5], [2, -1, 4, 3, 5, 1], [2, -1, 4, 5, 1, 3], [2, -1, 4, 5, 3, 1], [2, -1, 5, 1, 3, 4], [2, -1, 5, 1, 4, 3], [2, -1, 5, 3, 1, 4], [2, -1, 5, 3, 4, 1], [2, -1, 5, 4, 1, 3], [2, -1, 5, 4, 3, 1], [3, 1, 2, 4, 5, -1], [3, 1, 2, 4, -1, 5], [3, 1, 2, 5, 4, -1], [3, 1, 2, 5, -1, 4], [3, 1, 2, -1, 4, 5], [3, 1, 2, -1, 5, 4], [3, 1, 4, 2, 5, -1], [3, 1, 4, 2, -1, 5], [3, 1, 4, 5, 2, -1], [3, 1, 4, 5, -1, 2], [3, 1, 4, -1, 2, 5], [3, 1, 4, -1, 5, 2], [3, 1, 5, 2, 4, -1], [3, 1, 5, 2, -1, 4], [3, 1, 5, 4, 2, -1], [3, 1, 5, 4, -1, 2], [3, 1, 5, -1, 2, 4], [3, 1, 5, -1, 4, 2], [3, 1, -1, 2, 4, 5], [3, 1, -1, 2, 5, 4], [3, 1, -1, 4, 2, 5], [3, 1, -1, 4, 5, 2], [3, 1, -1, 5, 2, 4], [3, 1, -1, 5, 4, 2], [3, 2, 1, 4, 5, -1], [3, 2, 1, 4, -1, 5], [3, 2, 1, 5, 4, -1], [3, 2, 1, 5, -1, 4], [3, 2, 1, -1, 4, 5], [3, 2, 1, -1, 5, 4], [3, 2, 4, 1, 5, -1], [3, 2, 4, 1, -1, 5], [3, 2, 4, 5, 1, -1], [3, 2, 4, 5, -1, 1], [3, 2, 4, -1, 1, 5], [3, 2, 4, -1, 5, 1], [3, 2, 5, 1, 4, -1], [3, 2, 5, 1, -1, 4], [3, 2, 5, 4, 1, -1], [3, 2, 5, 4, -1, 1], [3, 2, 5, -1, 1, 4], [3, 2, 5, -1, 4, 1], [3, 2, -1, 1, 4, 5], [3, 2, -1, 1, 5, 4], [3, 2, -1, 4, 1, 5], [3, 2, -1, 4, 5, 1], [3, 2, -1, 5, 1, 4], [3, 2, -1, 5, 4, 1], [3, 4, 1, 2, 5, -1], [3, 4, 1, 2, -1, 5], [3, 4, 1, 5, 2, -1], [3, 4, 1, 5, -1, 2], [3, 4, 1, -1, 2, 5], [3, 4, 1, -1, 5, 2], [3, 4, 2, 1, 5, -1], [3, 4, 2, 1, -1, 5], [3, 4, 2, 5, 1, -1], [3, 4, 2, 5, -1, 1], [3, 4, 2, -1, 1, 5], [3, 4, 2, -1, 5, 1], [3, 4, 5, 1, 2, -1], [3, 4, 5, 1, -1, 2], [3, 4, 5, 2, 1, -1], [3, 4, 5, 2, -1, 1], [3, 4, 5, -1, 1, 2], [3, 4, 5, -1, 2, 1], [3, 4, -1, 1, 2, 5], [3, 4, -1, 1, 5, 2], [3, 4, -1, 2, 1, 5], [3, 4, -1, 2, 5, 1], [3, 4, -1, 5, 1, 2], [3, 4, -1, 5, 2, 1], [3, 5, 1, 2, 4, -1], [3, 5, 1, 2, -1, 4], [3, 5, 1, 4, 2, -1], [3, 5, 1, 4, -1, 2], [3, 5, 1, -1, 2, 4], [3, 5, 1, -1, 4, 2], [3, 5, 2, 1, 4, -1], [3, 5, 2, 1, -1, 4], [3, 5, 2, 4, 1, -1], [3, 5, 2, 4, -1, 1], [3, 5, 2, -1, 1, 4], [3, 5, 2, -1, 4, 1], [3, 5, 4, 1, 2, -1], [3, 5, 4, 1, -1, 2], [3, 5, 4, 2, 1, -1], [3, 5, 4, 2, -1, 1], [3, 5, 4, -1, 1, 2], [3, 5, 4, -1, 2, 1], [3, 5, -1, 1, 2, 4], [3, 5, -1, 1, 4, 2], [3, 5, -1, 2, 1, 4], [3, 5, -1, 2, 4, 1], [3, 5, -1, 4, 1, 2], [3, 5, -1, 4, 2, 1], [3, -1, 1, 2, 4, 5], [3, -1, 1, 2, 5, 4], [3, -1, 1, 4, 2, 5], [3, -1, 1, 4, 5, 2], [3, -1, 1, 5, 2, 4], [3, -1, 1, 5, 4, 2], [3, -1, 2, 1, 4, 5], [3, -1, 2, 1, 5, 4], [3, -1, 2, 4, 1, 5], [3, -1, 2, 4, 5, 1], [3, -1, 2, 5, 1, 4], [3, -1, 2, 5, 4, 1], [3, -1, 4, 1, 2, 5], [3, -1, 4, 1, 5, 2], [3, -1, 4, 2, 1, 5], [3, -1, 4, 2, 5, 1], [3, -1, 4, 5, 1, 2], [3, -1, 4, 5, 2, 1], [3, -1, 5, 1, 2, 4], [3, -1, 5, 1, 4, 2], [3, -1, 5, 2, 1, 4], [3, -1, 5, 2, 4, 1], [3, -1, 5, 4, 1, 2], [3, -1, 5, 4, 2, 1], [4, 1, 2, 3, 5, -1], [4, 1, 2, 3, -1, 5], [4, 1, 2, 5, 3, -1], [4, 1, 2, 5, -1, 3], [4, 1, 2, -1, 3, 5], [4, 1, 2, -1, 5, 3], [4, 1, 3, 2, 5, -1], [4, 1, 3, 2, -1, 5], [4, 1, 3, 5, 2, -1], [4, 1, 3, 5, -1, 2], [4, 1, 3, -1, 2, 5], [4, 1, 3, -1, 5, 2], [4, 1, 5, 2, 3, -1], [4, 1, 5, 2, -1, 3], [4, 1, 5, 3, 2, -1], [4, 1, 5, 3, -1, 2], [4, 1, 5, -1, 2, 3], [4, 1, 5, -1, 3, 2], [4, 1, -1, 2, 3, 5], [4, 1, -1, 2, 5, 3], [4, 1, -1, 3, 2, 5], [4, 1, -1, 3, 5, 2], [4, 1, -1, 5, 2, 3], [4, 1, -1, 5, 3, 2], [4, 2, 1, 3, 5, -1], [4, 2, 1, 3, -1, 5], [4, 2, 1, 5, 3, -1], [4, 2, 1, 5, -1, 3], [4, 2, 1, -1, 3, 5], [4, 2, 1, -1, 5, 3], [4, 2, 3, 1, 5, -1], [4, 2, 3, 1, -1, 5], [4, 2, 3, 5, 1, -1], [4, 2, 3, 5, -1, 1], [4, 2, 3, -1, 1, 5], [4, 2, 3, -1, 5, 1], [4, 2, 5, 1, 3, -1], [4, 2, 5, 1, -1, 3], [4, 2, 5, 3, 1, -1], [4, 2, 5, 3, -1, 1], [4, 2, 5, -1, 1, 3], [4, 2, 5, -1, 3, 1], [4, 2, -1, 1, 3, 5], [4, 2, -1, 1, 5, 3], [4, 2, -1, 3, 1, 5], [4, 2, -1, 3, 5, 1], [4, 2, -1, 5, 1, 3], [4, 2, -1, 5, 3, 1], [4, 3, 1, 2, 5, -1], [4, 3, 1, 2, -1, 5], [4, 3, 1, 5, 2, -1], [4, 3, 1, 5, -1, 2], [4, 3, 1, -1, 2, 5], [4, 3, 1, -1, 5, 2], [4, 3, 2, 1, 5, -1], [4, 3, 2, 1, -1, 5], [4, 3, 2, 5, 1, -1], [4, 3, 2, 5, -1, 1], [4, 3, 2, -1, 1, 5], [4, 3, 2, -1, 5, 1], [4, 3, 5, 1, 2, -1], [4, 3, 5, 1, -1, 2], [4, 3, 5, 2, 1, -1], [4, 3, 5, 2, -1, 1], [4, 3, 5, -1, 1, 2], [4, 3, 5, -1, 2, 1], [4, 3, -1, 1, 2, 5], [4, 3, -1, 1, 5, 2], [4, 3, -1, 2, 1, 5], [4, 3, -1, 2, 5, 1], [4, 3, -1, 5, 1, 2], [4, 3, -1, 5, 2, 1], [4, 5, 1, 2, 3, -1], [4, 5, 1, 2, -1, 3], [4, 5, 1, 3, 2, -1], [4, 5, 1, 3, -1, 2], [4, 5, 1, -1, 2, 3], [4, 5, 1, -1, 3, 2], [4, 5, 2, 1, 3, -1], [4, 5, 2, 1, -1, 3], [4, 5, 2, 3, 1, -1], [4, 5, 2, 3, -1, 1], [4, 5, 2, -1, 1, 3], [4, 5, 2, -1, 3, 1], [4, 5, 3, 1, 2, -1], [4, 5, 3, 1, -1, 2], [4, 5, 3, 2, 1, -1], [4, 5, 3, 2, -1, 1], [4, 5, 3, -1, 1, 2], [4, 5, 3, -1, 2, 1], [4, 5, -1, 1, 2, 3], [4, 5, -1, 1, 3, 2], [4, 5, -1, 2, 1, 3], [4, 5, -1, 2, 3, 1], [4, 5, -1, 3, 1, 2], [4, 5, -1, 3, 2, 1], [4, -1, 1, 2, 3, 5], [4, -1, 1, 2, 5, 3], [4, -1, 1, 3, 2, 5], [4, -1, 1, 3, 5, 2], [4, -1, 1, 5, 2, 3], [4, -1, 1, 5, 3, 2], [4, -1, 2, 1, 3, 5], [4, -1, 2, 1, 5, 3], [4, -1, 2, 3, 1, 5], [4, -1, 2, 3, 5, 1], [4, -1, 2, 5, 1, 3], [4, -1, 2, 5, 3, 1], [4, -1, 3, 1, 2, 5], [4, -1, 3, 1, 5, 2], [4, -1, 3, 2, 1, 5], [4, -1, 3, 2, 5, 1], [4, -1, 3, 5, 1, 2], [4, -1, 3, 5, 2, 1], [4, -1, 5, 1, 2, 3], [4, -1, 5, 1, 3, 2], [4, -1, 5, 2, 1, 3], [4, -1, 5, 2, 3, 1], [4, -1, 5, 3, 1, 2], [4, -1, 5, 3, 2, 1], [5, 1, 2, 3, 4, -1], [5, 1, 2, 3, -1, 4], [5, 1, 2, 4, 3, -1], [5, 1, 2, 4, -1, 3], [5, 1, 2, -1, 3, 4], [5, 1, 2, -1, 4, 3], [5, 1, 3, 2, 4, -1], [5, 1, 3, 2, -1, 4], [5, 1, 3, 4, 2, -1], [5, 1, 3, 4, -1, 2], [5, 1, 3, -1, 2, 4], [5, 1, 3, -1, 4, 2], [5, 1, 4, 2, 3, -1], [5, 1, 4, 2, -1, 3], [5, 1, 4, 3, 2, -1], [5, 1, 4, 3, -1, 2], [5, 1, 4, -1, 2, 3], [5, 1, 4, -1, 3, 2], [5, 1, -1, 2, 3, 4], [5, 1, -1, 2, 4, 3], [5, 1, -1, 3, 2, 4], [5, 1, -1, 3, 4, 2], [5, 1, -1, 4, 2, 3], [5, 1, -1, 4, 3, 2], [5, 2, 1, 3, 4, -1], [5, 2, 1, 3, -1, 4], [5, 2, 1, 4, 3, -1], [5, 2, 1, 4, -1, 3], [5, 2, 1, -1, 3, 4], [5, 2, 1, -1, 4, 3], [5, 2, 3, 1, 4, -1], [5, 2, 3, 1, -1, 4], [5, 2, 3, 4, 1, -1], [5, 2, 3, 4, -1, 1], [5, 2, 3, -1, 1, 4], [5, 2, 3, -1, 4, 1], [5, 2, 4, 1, 3, -1], [5, 2, 4, 1, -1, 3], [5, 2, 4, 3, 1, -1], [5, 2, 4, 3, -1, 1], [5, 2, 4, -1, 1, 3], [5, 2, 4, -1, 3, 1], [5, 2, -1, 1, 3, 4], [5, 2, -1, 1, 4, 3], [5, 2, -1, 3, 1, 4], [5, 2, -1, 3, 4, 1], [5, 2, -1, 4, 1, 3], [5, 2, -1, 4, 3, 1], [5, 3, 1, 2, 4, -1], [5, 3, 1, 2, -1, 4], [5, 3, 1, 4, 2, -1], [5, 3, 1, 4, -1, 2], [5, 3, 1, -1, 2, 4], [5, 3, 1, -1, 4, 2], [5, 3, 2, 1, 4, -1], [5, 3, 2, 1, -1, 4], [5, 3, 2, 4, 1, -1], [5, 3, 2, 4, -1, 1], [5, 3, 2, -1, 1, 4], [5, 3, 2, -1, 4, 1], [5, 3, 4, 1, 2, -1], [5, 3, 4, 1, -1, 2], [5, 3, 4, 2, 1, -1], [5, 3, 4, 2, -1, 1], [5, 3, 4, -1, 1, 2], [5, 3, 4, -1, 2, 1], [5, 3, -1, 1, 2, 4], [5, 3, -1, 1, 4, 2], [5, 3, -1, 2, 1, 4], [5, 3, -1, 2, 4, 1], [5, 3, -1, 4, 1, 2], [5, 3, -1, 4, 2, 1], [5, 4, 1, 2, 3, -1], [5, 4, 1, 2, -1, 3], [5, 4, 1, 3, 2, -1], [5, 4, 1, 3, -1, 2], [5, 4, 1, -1, 2, 3], [5, 4, 1, -1, 3, 2], [5, 4, 2, 1, 3, -1], [5, 4, 2, 1, -1, 3], [5, 4, 2, 3, 1, -1], [5, 4, 2, 3, -1, 1], [5, 4, 2, -1, 1, 3], [5, 4, 2, -1, 3, 1], [5, 4, 3, 1, 2, -1], [5, 4, 3, 1, -1, 2], [5, 4, 3, 2, 1, -1], [5, 4, 3, 2, -1, 1], [5, 4, 3, -1, 1, 2], [5, 4, 3, -1, 2, 1], [5, 4, -1, 1, 2, 3], [5, 4, -1, 1, 3, 2], [5, 4, -1, 2, 1, 3], [5, 4, -1, 2, 3, 1], [5, 4, -1, 3, 1, 2], [5, 4, -1, 3, 2, 1], [5, -1, 1, 2, 3, 4], [5, -1, 1, 2, 4, 3], [5, -1, 1, 3, 2, 4], [5, -1, 1, 3, 4, 2], [5, -1, 1, 4, 2, 3], [5, -1, 1, 4, 3, 2], [5, -1, 2, 1, 3, 4], [5, -1, 2, 1, 4, 3], [5, -1, 2, 3, 1, 4], [5, -1, 2, 3, 4, 1], [5, -1, 2, 4, 1, 3], [5, -1, 2, 4, 3, 1], [5, -1, 3, 1, 2, 4], [5, -1, 3, 1, 4, 2], [5, -1, 3, 2, 1, 4], [5, -1, 3, 2, 4, 1], [5, -1, 3, 4, 1, 2], [5, -1, 3, 4, 2, 1], [5, -1, 4, 1, 2, 3], [5, -1, 4, 1, 3, 2], [5, -1, 4, 2, 1, 3], [5, -1, 4, 2, 3, 1], [5, -1, 4, 3, 1, 2], [5, -1, 4, 3, 2, 1], [-1, 1, 2, 3, 4, 5], [-1, 1, 2, 3, 5, 4], [-1, 1, 2, 4, 3, 5], [-1, 1, 2, 4, 5, 3], [-1, 1, 2, 5, 3, 4], [-1, 1, 2, 5, 4, 3], [-1, 1, 3, 2, 4, 5], [-1, 1, 3, 2, 5, 4], [-1, 1, 3, 4, 2, 5], [-1, 1, 3, 4, 5, 2], [-1, 1, 3, 5, 2, 4], [-1, 1, 3, 5, 4, 2], [-1, 1, 4, 2, 3, 5], [-1, 1, 4, 2, 5, 3], [-1, 1, 4, 3, 2, 5], [-1, 1, 4, 3, 5, 2], [-1, 1, 4, 5, 2, 3], [-1, 1, 4, 5, 3, 2], [-1, 1, 5, 2, 3, 4], [-1, 1, 5, 2, 4, 3], [-1, 1, 5, 3, 2, 4], [-1, 1, 5, 3, 4, 2], [-1, 1, 5, 4, 2, 3], [-1, 1, 5, 4, 3, 2], [-1, 2, 1, 3, 4, 5], [-1, 2, 1, 3, 5, 4], [-1, 2, 1, 4, 3, 5], [-1, 2, 1, 4, 5, 3], [-1, 2, 1, 5, 3, 4], [-1, 2, 1, 5, 4, 3], [-1, 2, 3, 1, 4, 5], [-1, 2, 3, 1, 5, 4], [-1, 2, 3, 4, 1, 5], [-1, 2, 3, 4, 5, 1], [-1, 2, 3, 5, 1, 4], [-1, 2, 3, 5, 4, 1], [-1, 2, 4, 1, 3, 5], [-1, 2, 4, 1, 5, 3], [-1, 2, 4, 3, 1, 5], [-1, 2, 4, 3, 5, 1], [-1, 2, 4, 5, 1, 3], [-1, 2, 4, 5, 3, 1], [-1, 2, 5, 1, 3, 4], [-1, 2, 5, 1, 4, 3], [-1, 2, 5, 3, 1, 4], [-1, 2, 5, 3, 4, 1], [-1, 2, 5, 4, 1, 3], [-1, 2, 5, 4, 3, 1], [-1, 3, 1, 2, 4, 5], [-1, 3, 1, 2, 5, 4], [-1, 3, 1, 4, 2, 5], [-1, 3, 1, 4, 5, 2], [-1, 3, 1, 5, 2, 4], [-1, 3, 1, 5, 4, 2], [-1, 3, 2, 1, 4, 5], [-1, 3, 2, 1, 5, 4], [-1, 3, 2, 4, 1, 5], [-1, 3, 2, 4, 5, 1], [-1, 3, 2, 5, 1, 4], [-1, 3, 2, 5, 4, 1], [-1, 3, 4, 1, 2, 5], [-1, 3, 4, 1, 5, 2], [-1, 3, 4, 2, 1, 5], [-1, 3, 4, 2, 5, 1], [-1, 3, 4, 5, 1, 2], [-1, 3, 4, 5, 2, 1], [-1, 3, 5, 1, 2, 4], [-1, 3, 5, 1, 4, 2], [-1, 3, 5, 2, 1, 4], [-1, 3, 5, 2, 4, 1], [-1, 3, 5, 4, 1, 2], [-1, 3, 5, 4, 2, 1], [-1, 4, 1, 2, 3, 5], [-1, 4, 1, 2, 5, 3], [-1, 4, 1, 3, 2, 5], [-1, 4, 1, 3, 5, 2], [-1, 4, 1, 5, 2, 3], [-1, 4, 1, 5, 3, 2], [-1, 4, 2, 1, 3, 5], [-1, 4, 2, 1, 5, 3], [-1, 4, 2, 3, 1, 5], [-1, 4, 2, 3, 5, 1], [-1, 4, 2, 5, 1, 3], [-1, 4, 2, 5, 3, 1], [-1, 4, 3, 1, 2, 5], [-1, 4, 3, 1, 5, 2], [-1, 4, 3, 2, 1, 5], [-1, 4, 3, 2, 5, 1], [-1, 4, 3, 5, 1, 2], [-1, 4, 3, 5, 2, 1], [-1, 4, 5, 1, 2, 3], [-1, 4, 5, 1, 3, 2], [-1, 4, 5, 2, 1, 3], [-1, 4, 5, 2, 3, 1], [-1, 4, 5, 3, 1, 2], [-1, 4, 5, 3, 2, 1], [-1, 5, 1, 2, 3, 4], [-1, 5, 1, 2, 4, 3], [-1, 5, 1, 3, 2, 4], [-1, 5, 1, 3, 4, 2], [-1, 5, 1, 4, 2, 3], [-1, 5, 1, 4, 3, 2], [-1, 5, 2, 1, 3, 4], [-1, 5, 2, 1, 4, 3], [-1, 5, 2, 3, 1, 4], [-1, 5, 2, 3, 4, 1], [-1, 5, 2, 4, 1, 3], [-1, 5, 2, 4, 3, 1], [-1, 5, 3, 1, 2, 4], [-1, 5, 3, 1, 4, 2], [-1, 5, 3, 2, 1, 4], [-1, 5, 3, 2, 4, 1], [-1, 5, 3, 4, 1, 2], [-1, 5, 3, 4, 2, 1], [-1, 5, 4, 1, 2, 3], [-1, 5, 4, 1, 3, 2], [-1, 5, 4, 2, 1, 3], [-1, 5, 4, 2, 3, 1], [-1, 5, 4, 3, 1, 2], [-1, 5, 4, 3, 2, 1]]\n assert candidate(nums = [5, 1, 4, 2, 3]) == [[5, 1, 4, 2, 3], [5, 1, 4, 3, 2], [5, 1, 2, 4, 3], [5, 1, 2, 3, 4], [5, 1, 3, 4, 2], [5, 1, 3, 2, 4], [5, 4, 1, 2, 3], [5, 4, 1, 3, 2], [5, 4, 2, 1, 3], [5, 4, 2, 3, 1], [5, 4, 3, 1, 2], [5, 4, 3, 2, 1], [5, 2, 1, 4, 3], [5, 2, 1, 3, 4], [5, 2, 4, 1, 3], [5, 2, 4, 3, 1], [5, 2, 3, 1, 4], [5, 2, 3, 4, 1], [5, 3, 1, 4, 2], [5, 3, 1, 2, 4], [5, 3, 4, 1, 2], [5, 3, 4, 2, 1], [5, 3, 2, 1, 4], [5, 3, 2, 4, 1], [1, 5, 4, 2, 3], [1, 5, 4, 3, 2], [1, 5, 2, 4, 3], [1, 5, 2, 3, 4], [1, 5, 3, 4, 2], [1, 5, 3, 2, 4], [1, 4, 5, 2, 3], [1, 4, 5, 3, 2], [1, 4, 2, 5, 3], [1, 4, 2, 3, 5], [1, 4, 3, 5, 2], [1, 4, 3, 2, 5], [1, 2, 5, 4, 3], [1, 2, 5, 3, 4], [1, 2, 4, 5, 3], [1, 2, 4, 3, 5], [1, 2, 3, 5, 4], [1, 2, 3, 4, 5], [1, 3, 5, 4, 2], [1, 3, 5, 2, 4], [1, 3, 4, 5, 2], [1, 3, 4, 2, 5], [1, 3, 2, 5, 4], [1, 3, 2, 4, 5], [4, 5, 1, 2, 3], [4, 5, 1, 3, 2], [4, 5, 2, 1, 3], [4, 5, 2, 3, 1], [4, 5, 3, 1, 2], [4, 5, 3, 2, 1], [4, 1, 5, 2, 3], [4, 1, 5, 3, 2], [4, 1, 2, 5, 3], [4, 1, 2, 3, 5], [4, 1, 3, 5, 2], [4, 1, 3, 2, 5], [4, 2, 5, 1, 3], [4, 2, 5, 3, 1], [4, 2, 1, 5, 3], [4, 2, 1, 3, 5], [4, 2, 3, 5, 1], [4, 2, 3, 1, 5], [4, 3, 5, 1, 2], [4, 3, 5, 2, 1], [4, 3, 1, 5, 2], [4, 3, 1, 2, 5], [4, 3, 2, 5, 1], [4, 3, 2, 1, 5], [2, 5, 1, 4, 3], [2, 5, 1, 3, 4], [2, 5, 4, 1, 3], [2, 5, 4, 3, 1], [2, 5, 3, 1, 4], [2, 5, 3, 4, 1], [2, 1, 5, 4, 3], [2, 1, 5, 3, 4], [2, 1, 4, 5, 3], [2, 1, 4, 3, 5], [2, 1, 3, 5, 4], [2, 1, 3, 4, 5], [2, 4, 5, 1, 3], [2, 4, 5, 3, 1], [2, 4, 1, 5, 3], [2, 4, 1, 3, 5], [2, 4, 3, 5, 1], [2, 4, 3, 1, 5], [2, 3, 5, 1, 4], [2, 3, 5, 4, 1], [2, 3, 1, 5, 4], [2, 3, 1, 4, 5], [2, 3, 4, 5, 1], [2, 3, 4, 1, 5], [3, 5, 1, 4, 2], [3, 5, 1, 2, 4], [3, 5, 4, 1, 2], [3, 5, 4, 2, 1], [3, 5, 2, 1, 4], [3, 5, 2, 4, 1], [3, 1, 5, 4, 2], [3, 1, 5, 2, 4], [3, 1, 4, 5, 2], [3, 1, 4, 2, 5], [3, 1, 2, 5, 4], [3, 1, 2, 4, 5], [3, 4, 5, 1, 2], [3, 4, 5, 2, 1], [3, 4, 1, 5, 2], [3, 4, 1, 2, 5], [3, 4, 2, 5, 1], [3, 4, 2, 1, 5], [3, 2, 5, 1, 4], [3, 2, 5, 4, 1], [3, 2, 1, 5, 4], [3, 2, 1, 4, 5], [3, 2, 4, 5, 1], [3, 2, 4, 1, 5]]\n assert candidate(nums = [1, -1, 2, -2, 3, -3]) == [[1, -1, 2, -2, 3, -3], [1, -1, 2, -2, -3, 3], [1, -1, 2, 3, -2, -3], [1, -1, 2, 3, -3, -2], [1, -1, 2, -3, -2, 3], [1, -1, 2, -3, 3, -2], [1, -1, -2, 2, 3, -3], [1, -1, -2, 2, -3, 3], [1, -1, -2, 3, 2, -3], [1, -1, -2, 3, -3, 2], [1, -1, -2, -3, 2, 3], [1, -1, -2, -3, 3, 2], [1, -1, 3, 2, -2, -3], [1, -1, 3, 2, -3, -2], [1, -1, 3, -2, 2, -3], [1, -1, 3, -2, -3, 2], [1, -1, 3, -3, 2, -2], [1, -1, 3, -3, -2, 2], [1, -1, -3, 2, -2, 3], [1, -1, -3, 2, 3, -2], [1, -1, -3, -2, 2, 3], [1, -1, -3, -2, 3, 2], [1, -1, -3, 3, 2, -2], [1, -1, -3, 3, -2, 2], [1, 2, -1, -2, 3, -3], [1, 2, -1, -2, -3, 3], [1, 2, -1, 3, -2, -3], [1, 2, -1, 3, -3, -2], [1, 2, -1, -3, -2, 3], [1, 2, -1, -3, 3, -2], [1, 2, -2, -1, 3, -3], [1, 2, -2, -1, -3, 3], [1, 2, -2, 3, -1, -3], [1, 2, -2, 3, -3, -1], [1, 2, -2, -3, -1, 3], [1, 2, -2, -3, 3, -1], [1, 2, 3, -1, -2, -3], [1, 2, 3, -1, -3, -2], [1, 2, 3, -2, -1, -3], [1, 2, 3, -2, -3, -1], [1, 2, 3, -3, -1, -2], [1, 2, 3, -3, -2, -1], [1, 2, -3, -1, -2, 3], [1, 2, -3, -1, 3, -2], [1, 2, -3, -2, -1, 3], [1, 2, -3, -2, 3, -1], [1, 2, -3, 3, -1, -2], [1, 2, -3, 3, -2, -1], [1, -2, -1, 2, 3, -3], [1, -2, -1, 2, -3, 3], [1, -2, -1, 3, 2, -3], [1, -2, -1, 3, -3, 2], [1, -2, -1, -3, 2, 3], [1, -2, -1, -3, 3, 2], [1, -2, 2, -1, 3, -3], [1, -2, 2, -1, -3, 3], [1, -2, 2, 3, -1, -3], [1, -2, 2, 3, -3, -1], [1, -2, 2, -3, -1, 3], [1, -2, 2, -3, 3, -1], [1, -2, 3, -1, 2, -3], [1, -2, 3, -1, -3, 2], [1, -2, 3, 2, -1, -3], [1, -2, 3, 2, -3, -1], [1, -2, 3, -3, -1, 2], [1, -2, 3, -3, 2, -1], [1, -2, -3, -1, 2, 3], [1, -2, -3, -1, 3, 2], [1, -2, -3, 2, -1, 3], [1, -2, -3, 2, 3, -1], [1, -2, -3, 3, -1, 2], [1, -2, -3, 3, 2, -1], [1, 3, -1, 2, -2, -3], [1, 3, -1, 2, -3, -2], [1, 3, -1, -2, 2, -3], [1, 3, -1, -2, -3, 2], [1, 3, -1, -3, 2, -2], [1, 3, -1, -3, -2, 2], [1, 3, 2, -1, -2, -3], [1, 3, 2, -1, -3, -2], [1, 3, 2, -2, -1, -3], [1, 3, 2, -2, -3, -1], [1, 3, 2, -3, -1, -2], [1, 3, 2, -3, -2, -1], [1, 3, -2, -1, 2, -3], [1, 3, -2, -1, -3, 2], [1, 3, -2, 2, -1, -3], [1, 3, -2, 2, -3, -1], [1, 3, -2, -3, -1, 2], [1, 3, -2, -3, 2, -1], [1, 3, -3, -1, 2, -2], [1, 3, -3, -1, -2, 2], [1, 3, -3, 2, -1, -2], [1, 3, -3, 2, -2, -1], [1, 3, -3, -2, -1, 2], [1, 3, -3, -2, 2, -1], [1, -3, -1, 2, -2, 3], [1, -3, -1, 2, 3, -2], [1, -3, -1, -2, 2, 3], [1, -3, -1, -2, 3, 2], [1, -3, -1, 3, 2, -2], [1, -3, -1, 3, -2, 2], [1, -3, 2, -1, -2, 3], [1, -3, 2, -1, 3, -2], [1, -3, 2, -2, -1, 3], [1, -3, 2, -2, 3, -1], [1, -3, 2, 3, -1, -2], [1, -3, 2, 3, -2, -1], [1, -3, -2, -1, 2, 3], [1, -3, -2, -1, 3, 2], [1, -3, -2, 2, -1, 3], [1, -3, -2, 2, 3, -1], [1, -3, -2, 3, -1, 2], [1, -3, -2, 3, 2, -1], [1, -3, 3, -1, 2, -2], [1, -3, 3, -1, -2, 2], [1, -3, 3, 2, -1, -2], [1, -3, 3, 2, -2, -1], [1, -3, 3, -2, -1, 2], [1, -3, 3, -2, 2, -1], [-1, 1, 2, -2, 3, -3], [-1, 1, 2, -2, -3, 3], [-1, 1, 2, 3, -2, -3], [-1, 1, 2, 3, -3, -2], [-1, 1, 2, -3, -2, 3], [-1, 1, 2, -3, 3, -2], [-1, 1, -2, 2, 3, -3], [-1, 1, -2, 2, -3, 3], [-1, 1, -2, 3, 2, -3], [-1, 1, -2, 3, -3, 2], [-1, 1, -2, -3, 2, 3], [-1, 1, -2, -3, 3, 2], [-1, 1, 3, 2, -2, -3], [-1, 1, 3, 2, -3, -2], [-1, 1, 3, -2, 2, -3], [-1, 1, 3, -2, -3, 2], [-1, 1, 3, -3, 2, -2], [-1, 1, 3, -3, -2, 2], [-1, 1, -3, 2, -2, 3], [-1, 1, -3, 2, 3, -2], [-1, 1, -3, -2, 2, 3], [-1, 1, -3, -2, 3, 2], [-1, 1, -3, 3, 2, -2], [-1, 1, -3, 3, -2, 2], [-1, 2, 1, -2, 3, -3], [-1, 2, 1, -2, -3, 3], [-1, 2, 1, 3, -2, -3], [-1, 2, 1, 3, -3, -2], [-1, 2, 1, -3, -2, 3], [-1, 2, 1, -3, 3, -2], [-1, 2, -2, 1, 3, -3], [-1, 2, -2, 1, -3, 3], [-1, 2, -2, 3, 1, -3], [-1, 2, -2, 3, -3, 1], [-1, 2, -2, -3, 1, 3], [-1, 2, -2, -3, 3, 1], [-1, 2, 3, 1, -2, -3], [-1, 2, 3, 1, -3, -2], [-1, 2, 3, -2, 1, -3], [-1, 2, 3, -2, -3, 1], [-1, 2, 3, -3, 1, -2], [-1, 2, 3, -3, -2, 1], [-1, 2, -3, 1, -2, 3], [-1, 2, -3, 1, 3, -2], [-1, 2, -3, -2, 1, 3], [-1, 2, -3, -2, 3, 1], [-1, 2, -3, 3, 1, -2], [-1, 2, -3, 3, -2, 1], [-1, -2, 1, 2, 3, -3], [-1, -2, 1, 2, -3, 3], [-1, -2, 1, 3, 2, -3], [-1, -2, 1, 3, -3, 2], [-1, -2, 1, -3, 2, 3], [-1, -2, 1, -3, 3, 2], [-1, -2, 2, 1, 3, -3], [-1, -2, 2, 1, -3, 3], [-1, -2, 2, 3, 1, -3], [-1, -2, 2, 3, -3, 1], [-1, -2, 2, -3, 1, 3], [-1, -2, 2, -3, 3, 1], [-1, -2, 3, 1, 2, -3], [-1, -2, 3, 1, -3, 2], [-1, -2, 3, 2, 1, -3], [-1, -2, 3, 2, -3, 1], [-1, -2, 3, -3, 1, 2], [-1, -2, 3, -3, 2, 1], [-1, -2, -3, 1, 2, 3], [-1, -2, -3, 1, 3, 2], [-1, -2, -3, 2, 1, 3], [-1, -2, -3, 2, 3, 1], [-1, -2, -3, 3, 1, 2], [-1, -2, -3, 3, 2, 1], [-1, 3, 1, 2, -2, -3], [-1, 3, 1, 2, -3, -2], [-1, 3, 1, -2, 2, -3], [-1, 3, 1, -2, -3, 2], [-1, 3, 1, -3, 2, -2], [-1, 3, 1, -3, -2, 2], [-1, 3, 2, 1, -2, -3], [-1, 3, 2, 1, -3, -2], [-1, 3, 2, -2, 1, -3], [-1, 3, 2, -2, -3, 1], [-1, 3, 2, -3, 1, -2], [-1, 3, 2, -3, -2, 1], [-1, 3, -2, 1, 2, -3], [-1, 3, -2, 1, -3, 2], [-1, 3, -2, 2, 1, -3], [-1, 3, -2, 2, -3, 1], [-1, 3, -2, -3, 1, 2], [-1, 3, -2, -3, 2, 1], [-1, 3, -3, 1, 2, -2], [-1, 3, -3, 1, -2, 2], [-1, 3, -3, 2, 1, -2], [-1, 3, -3, 2, -2, 1], [-1, 3, -3, -2, 1, 2], [-1, 3, -3, -2, 2, 1], [-1, -3, 1, 2, -2, 3], [-1, -3, 1, 2, 3, -2], [-1, -3, 1, -2, 2, 3], [-1, -3, 1, -2, 3, 2], [-1, -3, 1, 3, 2, -2], [-1, -3, 1, 3, -2, 2], [-1, -3, 2, 1, -2, 3], [-1, -3, 2, 1, 3, -2], [-1, -3, 2, -2, 1, 3], [-1, -3, 2, -2, 3, 1], [-1, -3, 2, 3, 1, -2], [-1, -3, 2, 3, -2, 1], [-1, -3, -2, 1, 2, 3], [-1, -3, -2, 1, 3, 2], [-1, -3, -2, 2, 1, 3], [-1, -3, -2, 2, 3, 1], [-1, -3, -2, 3, 1, 2], [-1, -3, -2, 3, 2, 1], [-1, -3, 3, 1, 2, -2], [-1, -3, 3, 1, -2, 2], [-1, -3, 3, 2, 1, -2], [-1, -3, 3, 2, -2, 1], [-1, -3, 3, -2, 1, 2], [-1, -3, 3, -2, 2, 1], [2, 1, -1, -2, 3, -3], [2, 1, -1, -2, -3, 3], [2, 1, -1, 3, -2, -3], [2, 1, -1, 3, -3, -2], [2, 1, -1, -3, -2, 3], [2, 1, -1, -3, 3, -2], [2, 1, -2, -1, 3, -3], [2, 1, -2, -1, -3, 3], [2, 1, -2, 3, -1, -3], [2, 1, -2, 3, -3, -1], [2, 1, -2, -3, -1, 3], [2, 1, -2, -3, 3, -1], [2, 1, 3, -1, -2, -3], [2, 1, 3, -1, -3, -2], [2, 1, 3, -2, -1, -3], [2, 1, 3, -2, -3, -1], [2, 1, 3, -3, -1, -2], [2, 1, 3, -3, -2, -1], [2, 1, -3, -1, -2, 3], [2, 1, -3, -1, 3, -2], [2, 1, -3, -2, -1, 3], [2, 1, -3, -2, 3, -1], [2, 1, -3, 3, -1, -2], [2, 1, -3, 3, -2, -1], [2, -1, 1, -2, 3, -3], [2, -1, 1, -2, -3, 3], [2, -1, 1, 3, -2, -3], [2, -1, 1, 3, -3, -2], [2, -1, 1, -3, -2, 3], [2, -1, 1, -3, 3, -2], [2, -1, -2, 1, 3, -3], [2, -1, -2, 1, -3, 3], [2, -1, -2, 3, 1, -3], [2, -1, -2, 3, -3, 1], [2, -1, -2, -3, 1, 3], [2, -1, -2, -3, 3, 1], [2, -1, 3, 1, -2, -3], [2, -1, 3, 1, -3, -2], [2, -1, 3, -2, 1, -3], [2, -1, 3, -2, -3, 1], [2, -1, 3, -3, 1, -2], [2, -1, 3, -3, -2, 1], [2, -1, -3, 1, -2, 3], [2, -1, -3, 1, 3, -2], [2, -1, -3, -2, 1, 3], [2, -1, -3, -2, 3, 1], [2, -1, -3, 3, 1, -2], [2, -1, -3, 3, -2, 1], [2, -2, 1, -1, 3, -3], [2, -2, 1, -1, -3, 3], [2, -2, 1, 3, -1, -3], [2, -2, 1, 3, -3, -1], [2, -2, 1, -3, -1, 3], [2, -2, 1, -3, 3, -1], [2, -2, -1, 1, 3, -3], [2, -2, -1, 1, -3, 3], [2, -2, -1, 3, 1, -3], [2, -2, -1, 3, -3, 1], [2, -2, -1, -3, 1, 3], [2, -2, -1, -3, 3, 1], [2, -2, 3, 1, -1, -3], [2, -2, 3, 1, -3, -1], [2, -2, 3, -1, 1, -3], [2, -2, 3, -1, -3, 1], [2, -2, 3, -3, 1, -1], [2, -2, 3, -3, -1, 1], [2, -2, -3, 1, -1, 3], [2, -2, -3, 1, 3, -1], [2, -2, -3, -1, 1, 3], [2, -2, -3, -1, 3, 1], [2, -2, -3, 3, 1, -1], [2, -2, -3, 3, -1, 1], [2, 3, 1, -1, -2, -3], [2, 3, 1, -1, -3, -2], [2, 3, 1, -2, -1, -3], [2, 3, 1, -2, -3, -1], [2, 3, 1, -3, -1, -2], [2, 3, 1, -3, -2, -1], [2, 3, -1, 1, -2, -3], [2, 3, -1, 1, -3, -2], [2, 3, -1, -2, 1, -3], [2, 3, -1, -2, -3, 1], [2, 3, -1, -3, 1, -2], [2, 3, -1, -3, -2, 1], [2, 3, -2, 1, -1, -3], [2, 3, -2, 1, -3, -1], [2, 3, -2, -1, 1, -3], [2, 3, -2, -1, -3, 1], [2, 3, -2, -3, 1, -1], [2, 3, -2, -3, -1, 1], [2, 3, -3, 1, -1, -2], [2, 3, -3, 1, -2, -1], [2, 3, -3, -1, 1, -2], [2, 3, -3, -1, -2, 1], [2, 3, -3, -2, 1, -1], [2, 3, -3, -2, -1, 1], [2, -3, 1, -1, -2, 3], [2, -3, 1, -1, 3, -2], [2, -3, 1, -2, -1, 3], [2, -3, 1, -2, 3, -1], [2, -3, 1, 3, -1, -2], [2, -3, 1, 3, -2, -1], [2, -3, -1, 1, -2, 3], [2, -3, -1, 1, 3, -2], [2, -3, -1, -2, 1, 3], [2, -3, -1, -2, 3, 1], [2, -3, -1, 3, 1, -2], [2, -3, -1, 3, -2, 1], [2, -3, -2, 1, -1, 3], [2, -3, -2, 1, 3, -1], [2, -3, -2, -1, 1, 3], [2, -3, -2, -1, 3, 1], [2, -3, -2, 3, 1, -1], [2, -3, -2, 3, -1, 1], [2, -3, 3, 1, -1, -2], [2, -3, 3, 1, -2, -1], [2, -3, 3, -1, 1, -2], [2, -3, 3, -1, -2, 1], [2, -3, 3, -2, 1, -1], [2, -3, 3, -2, -1, 1], [-2, 1, -1, 2, 3, -3], [-2, 1, -1, 2, -3, 3], [-2, 1, -1, 3, 2, -3], [-2, 1, -1, 3, -3, 2], [-2, 1, -1, -3, 2, 3], [-2, 1, -1, -3, 3, 2], [-2, 1, 2, -1, 3, -3], [-2, 1, 2, -1, -3, 3], [-2, 1, 2, 3, -1, -3], [-2, 1, 2, 3, -3, -1], [-2, 1, 2, -3, -1, 3], [-2, 1, 2, -3, 3, -1], [-2, 1, 3, -1, 2, -3], [-2, 1, 3, -1, -3, 2], [-2, 1, 3, 2, -1, -3], [-2, 1, 3, 2, -3, -1], [-2, 1, 3, -3, -1, 2], [-2, 1, 3, -3, 2, -1], [-2, 1, -3, -1, 2, 3], [-2, 1, -3, -1, 3, 2], [-2, 1, -3, 2, -1, 3], [-2, 1, -3, 2, 3, -1], [-2, 1, -3, 3, -1, 2], [-2, 1, -3, 3, 2, -1], [-2, -1, 1, 2, 3, -3], [-2, -1, 1, 2, -3, 3], [-2, -1, 1, 3, 2, -3], [-2, -1, 1, 3, -3, 2], [-2, -1, 1, -3, 2, 3], [-2, -1, 1, -3, 3, 2], [-2, -1, 2, 1, 3, -3], [-2, -1, 2, 1, -3, 3], [-2, -1, 2, 3, 1, -3], [-2, -1, 2, 3, -3, 1], [-2, -1, 2, -3, 1, 3], [-2, -1, 2, -3, 3, 1], [-2, -1, 3, 1, 2, -3], [-2, -1, 3, 1, -3, 2], [-2, -1, 3, 2, 1, -3], [-2, -1, 3, 2, -3, 1], [-2, -1, 3, -3, 1, 2], [-2, -1, 3, -3, 2, 1], [-2, -1, -3, 1, 2, 3], [-2, -1, -3, 1, 3, 2], [-2, -1, -3, 2, 1, 3], [-2, -1, -3, 2, 3, 1], [-2, -1, -3, 3, 1, 2], [-2, -1, -3, 3, 2, 1], [-2, 2, 1, -1, 3, -3], [-2, 2, 1, -1, -3, 3], [-2, 2, 1, 3, -1, -3], [-2, 2, 1, 3, -3, -1], [-2, 2, 1, -3, -1, 3], [-2, 2, 1, -3, 3, -1], [-2, 2, -1, 1, 3, -3], [-2, 2, -1, 1, -3, 3], [-2, 2, -1, 3, 1, -3], [-2, 2, -1, 3, -3, 1], [-2, 2, -1, -3, 1, 3], [-2, 2, -1, -3, 3, 1], [-2, 2, 3, 1, -1, -3], [-2, 2, 3, 1, -3, -1], [-2, 2, 3, -1, 1, -3], [-2, 2, 3, -1, -3, 1], [-2, 2, 3, -3, 1, -1], [-2, 2, 3, -3, -1, 1], [-2, 2, -3, 1, -1, 3], [-2, 2, -3, 1, 3, -1], [-2, 2, -3, -1, 1, 3], [-2, 2, -3, -1, 3, 1], [-2, 2, -3, 3, 1, -1], [-2, 2, -3, 3, -1, 1], [-2, 3, 1, -1, 2, -3], [-2, 3, 1, -1, -3, 2], [-2, 3, 1, 2, -1, -3], [-2, 3, 1, 2, -3, -1], [-2, 3, 1, -3, -1, 2], [-2, 3, 1, -3, 2, -1], [-2, 3, -1, 1, 2, -3], [-2, 3, -1, 1, -3, 2], [-2, 3, -1, 2, 1, -3], [-2, 3, -1, 2, -3, 1], [-2, 3, -1, -3, 1, 2], [-2, 3, -1, -3, 2, 1], [-2, 3, 2, 1, -1, -3], [-2, 3, 2, 1, -3, -1], [-2, 3, 2, -1, 1, -3], [-2, 3, 2, -1, -3, 1], [-2, 3, 2, -3, 1, -1], [-2, 3, 2, -3, -1, 1], [-2, 3, -3, 1, -1, 2], [-2, 3, -3, 1, 2, -1], [-2, 3, -3, -1, 1, 2], [-2, 3, -3, -1, 2, 1], [-2, 3, -3, 2, 1, -1], [-2, 3, -3, 2, -1, 1], [-2, -3, 1, -1, 2, 3], [-2, -3, 1, -1, 3, 2], [-2, -3, 1, 2, -1, 3], [-2, -3, 1, 2, 3, -1], [-2, -3, 1, 3, -1, 2], [-2, -3, 1, 3, 2, -1], [-2, -3, -1, 1, 2, 3], [-2, -3, -1, 1, 3, 2], [-2, -3, -1, 2, 1, 3], [-2, -3, -1, 2, 3, 1], [-2, -3, -1, 3, 1, 2], [-2, -3, -1, 3, 2, 1], [-2, -3, 2, 1, -1, 3], [-2, -3, 2, 1, 3, -1], [-2, -3, 2, -1, 1, 3], [-2, -3, 2, -1, 3, 1], [-2, -3, 2, 3, 1, -1], [-2, -3, 2, 3, -1, 1], [-2, -3, 3, 1, -1, 2], [-2, -3, 3, 1, 2, -1], [-2, -3, 3, -1, 1, 2], [-2, -3, 3, -1, 2, 1], [-2, -3, 3, 2, 1, -1], [-2, -3, 3, 2, -1, 1], [3, 1, -1, 2, -2, -3], [3, 1, -1, 2, -3, -2], [3, 1, -1, -2, 2, -3], [3, 1, -1, -2, -3, 2], [3, 1, -1, -3, 2, -2], [3, 1, -1, -3, -2, 2], [3, 1, 2, -1, -2, -3], [3, 1, 2, -1, -3, -2], [3, 1, 2, -2, -1, -3], [3, 1, 2, -2, -3, -1], [3, 1, 2, -3, -1, -2], [3, 1, 2, -3, -2, -1], [3, 1, -2, -1, 2, -3], [3, 1, -2, -1, -3, 2], [3, 1, -2, 2, -1, -3], [3, 1, -2, 2, -3, -1], [3, 1, -2, -3, -1, 2], [3, 1, -2, -3, 2, -1], [3, 1, -3, -1, 2, -2], [3, 1, -3, -1, -2, 2], [3, 1, -3, 2, -1, -2], [3, 1, -3, 2, -2, -1], [3, 1, -3, -2, -1, 2], [3, 1, -3, -2, 2, -1], [3, -1, 1, 2, -2, -3], [3, -1, 1, 2, -3, -2], [3, -1, 1, -2, 2, -3], [3, -1, 1, -2, -3, 2], [3, -1, 1, -3, 2, -2], [3, -1, 1, -3, -2, 2], [3, -1, 2, 1, -2, -3], [3, -1, 2, 1, -3, -2], [3, -1, 2, -2, 1, -3], [3, -1, 2, -2, -3, 1], [3, -1, 2, -3, 1, -2], [3, -1, 2, -3, -2, 1], [3, -1, -2, 1, 2, -3], [3, -1, -2, 1, -3, 2], [3, -1, -2, 2, 1, -3], [3, -1, -2, 2, -3, 1], [3, -1, -2, -3, 1, 2], [3, -1, -2, -3, 2, 1], [3, -1, -3, 1, 2, -2], [3, -1, -3, 1, -2, 2], [3, -1, -3, 2, 1, -2], [3, -1, -3, 2, -2, 1], [3, -1, -3, -2, 1, 2], [3, -1, -3, -2, 2, 1], [3, 2, 1, -1, -2, -3], [3, 2, 1, -1, -3, -2], [3, 2, 1, -2, -1, -3], [3, 2, 1, -2, -3, -1], [3, 2, 1, -3, -1, -2], [3, 2, 1, -3, -2, -1], [3, 2, -1, 1, -2, -3], [3, 2, -1, 1, -3, -2], [3, 2, -1, -2, 1, -3], [3, 2, -1, -2, -3, 1], [3, 2, -1, -3, 1, -2], [3, 2, -1, -3, -2, 1], [3, 2, -2, 1, -1, -3], [3, 2, -2, 1, -3, -1], [3, 2, -2, -1, 1, -3], [3, 2, -2, -1, -3, 1], [3, 2, -2, -3, 1, -1], [3, 2, -2, -3, -1, 1], [3, 2, -3, 1, -1, -2], [3, 2, -3, 1, -2, -1], [3, 2, -3, -1, 1, -2], [3, 2, -3, -1, -2, 1], [3, 2, -3, -2, 1, -1], [3, 2, -3, -2, -1, 1], [3, -2, 1, -1, 2, -3], [3, -2, 1, -1, -3, 2], [3, -2, 1, 2, -1, -3], [3, -2, 1, 2, -3, -1], [3, -2, 1, -3, -1, 2], [3, -2, 1, -3, 2, -1], [3, -2, -1, 1, 2, -3], [3, -2, -1, 1, -3, 2], [3, -2, -1, 2, 1, -3], [3, -2, -1, 2, -3, 1], [3, -2, -1, -3, 1, 2], [3, -2, -1, -3, 2, 1], [3, -2, 2, 1, -1, -3], [3, -2, 2, 1, -3, -1], [3, -2, 2, -1, 1, -3], [3, -2, 2, -1, -3, 1], [3, -2, 2, -3, 1, -1], [3, -2, 2, -3, -1, 1], [3, -2, -3, 1, -1, 2], [3, -2, -3, 1, 2, -1], [3, -2, -3, -1, 1, 2], [3, -2, -3, -1, 2, 1], [3, -2, -3, 2, 1, -1], [3, -2, -3, 2, -1, 1], [3, -3, 1, -1, 2, -2], [3, -3, 1, -1, -2, 2], [3, -3, 1, 2, -1, -2], [3, -3, 1, 2, -2, -1], [3, -3, 1, -2, -1, 2], [3, -3, 1, -2, 2, -1], [3, -3, -1, 1, 2, -2], [3, -3, -1, 1, -2, 2], [3, -3, -1, 2, 1, -2], [3, -3, -1, 2, -2, 1], [3, -3, -1, -2, 1, 2], [3, -3, -1, -2, 2, 1], [3, -3, 2, 1, -1, -2], [3, -3, 2, 1, -2, -1], [3, -3, 2, -1, 1, -2], [3, -3, 2, -1, -2, 1], [3, -3, 2, -2, 1, -1], [3, -3, 2, -2, -1, 1], [3, -3, -2, 1, -1, 2], [3, -3, -2, 1, 2, -1], [3, -3, -2, -1, 1, 2], [3, -3, -2, -1, 2, 1], [3, -3, -2, 2, 1, -1], [3, -3, -2, 2, -1, 1], [-3, 1, -1, 2, -2, 3], [-3, 1, -1, 2, 3, -2], [-3, 1, -1, -2, 2, 3], [-3, 1, -1, -2, 3, 2], [-3, 1, -1, 3, 2, -2], [-3, 1, -1, 3, -2, 2], [-3, 1, 2, -1, -2, 3], [-3, 1, 2, -1, 3, -2], [-3, 1, 2, -2, -1, 3], [-3, 1, 2, -2, 3, -1], [-3, 1, 2, 3, -1, -2], [-3, 1, 2, 3, -2, -1], [-3, 1, -2, -1, 2, 3], [-3, 1, -2, -1, 3, 2], [-3, 1, -2, 2, -1, 3], [-3, 1, -2, 2, 3, -1], [-3, 1, -2, 3, -1, 2], [-3, 1, -2, 3, 2, -1], [-3, 1, 3, -1, 2, -2], [-3, 1, 3, -1, -2, 2], [-3, 1, 3, 2, -1, -2], [-3, 1, 3, 2, -2, -1], [-3, 1, 3, -2, -1, 2], [-3, 1, 3, -2, 2, -1], [-3, -1, 1, 2, -2, 3], [-3, -1, 1, 2, 3, -2], [-3, -1, 1, -2, 2, 3], [-3, -1, 1, -2, 3, 2], [-3, -1, 1, 3, 2, -2], [-3, -1, 1, 3, -2, 2], [-3, -1, 2, 1, -2, 3], [-3, -1, 2, 1, 3, -2], [-3, -1, 2, -2, 1, 3], [-3, -1, 2, -2, 3, 1], [-3, -1, 2, 3, 1, -2], [-3, -1, 2, 3, -2, 1], [-3, -1, -2, 1, 2, 3], [-3, -1, -2, 1, 3, 2], [-3, -1, -2, 2, 1, 3], [-3, -1, -2, 2, 3, 1], [-3, -1, -2, 3, 1, 2], [-3, -1, -2, 3, 2, 1], [-3, -1, 3, 1, 2, -2], [-3, -1, 3, 1, -2, 2], [-3, -1, 3, 2, 1, -2], [-3, -1, 3, 2, -2, 1], [-3, -1, 3, -2, 1, 2], [-3, -1, 3, -2, 2, 1], [-3, 2, 1, -1, -2, 3], [-3, 2, 1, -1, 3, -2], [-3, 2, 1, -2, -1, 3], [-3, 2, 1, -2, 3, -1], [-3, 2, 1, 3, -1, -2], [-3, 2, 1, 3, -2, -1], [-3, 2, -1, 1, -2, 3], [-3, 2, -1, 1, 3, -2], [-3, 2, -1, -2, 1, 3], [-3, 2, -1, -2, 3, 1], [-3, 2, -1, 3, 1, -2], [-3, 2, -1, 3, -2, 1], [-3, 2, -2, 1, -1, 3], [-3, 2, -2, 1, 3, -1], [-3, 2, -2, -1, 1, 3], [-3, 2, -2, -1, 3, 1], [-3, 2, -2, 3, 1, -1], [-3, 2, -2, 3, -1, 1], [-3, 2, 3, 1, -1, -2], [-3, 2, 3, 1, -2, -1], [-3, 2, 3, -1, 1, -2], [-3, 2, 3, -1, -2, 1], [-3, 2, 3, -2, 1, -1], [-3, 2, 3, -2, -1, 1], [-3, -2, 1, -1, 2, 3], [-3, -2, 1, -1, 3, 2], [-3, -2, 1, 2, -1, 3], [-3, -2, 1, 2, 3, -1], [-3, -2, 1, 3, -1, 2], [-3, -2, 1, 3, 2, -1], [-3, -2, -1, 1, 2, 3], [-3, -2, -1, 1, 3, 2], [-3, -2, -1, 2, 1, 3], [-3, -2, -1, 2, 3, 1], [-3, -2, -1, 3, 1, 2], [-3, -2, -1, 3, 2, 1], [-3, -2, 2, 1, -1, 3], [-3, -2, 2, 1, 3, -1], [-3, -2, 2, -1, 1, 3], [-3, -2, 2, -1, 3, 1], [-3, -2, 2, 3, 1, -1], [-3, -2, 2, 3, -1, 1], [-3, -2, 3, 1, -1, 2], [-3, -2, 3, 1, 2, -1], [-3, -2, 3, -1, 1, 2], [-3, -2, 3, -1, 2, 1], [-3, -2, 3, 2, 1, -1], [-3, -2, 3, 2, -1, 1], [-3, 3, 1, -1, 2, -2], [-3, 3, 1, -1, -2, 2], [-3, 3, 1, 2, -1, -2], [-3, 3, 1, 2, -2, -1], [-3, 3, 1, -2, -1, 2], [-3, 3, 1, -2, 2, -1], [-3, 3, -1, 1, 2, -2], [-3, 3, -1, 1, -2, 2], [-3, 3, -1, 2, 1, -2], [-3, 3, -1, 2, -2, 1], [-3, 3, -1, -2, 1, 2], [-3, 3, -1, -2, 2, 1], [-3, 3, 2, 1, -1, -2], [-3, 3, 2, 1, -2, -1], [-3, 3, 2, -1, 1, -2], [-3, 3, 2, -1, -2, 1], [-3, 3, 2, -2, 1, -1], [-3, 3, 2, -2, -1, 1], [-3, 3, -2, 1, -1, 2], [-3, 3, -2, 1, 2, -1], [-3, 3, -2, -1, 1, 2], [-3, 3, -2, -1, 2, 1], [-3, 3, -2, 2, 1, -1], [-3, 3, -2, 2, -1, 1]]\n assert candidate(nums = [-5, -4, -3, -2, -1]) == [[-5, -4, -3, -2, -1], [-5, -4, -3, -1, -2], [-5, -4, -2, -3, -1], [-5, -4, -2, -1, -3], [-5, -4, -1, -3, -2], [-5, -4, -1, -2, -3], [-5, -3, -4, -2, -1], [-5, -3, -4, -1, -2], [-5, -3, -2, -4, -1], [-5, -3, -2, -1, -4], [-5, -3, -1, -4, -2], [-5, -3, -1, -2, -4], [-5, -2, -4, -3, -1], [-5, -2, -4, -1, -3], [-5, -2, -3, -4, -1], [-5, -2, -3, -1, -4], [-5, -2, -1, -4, -3], [-5, -2, -1, -3, -4], [-5, -1, -4, -3, -2], [-5, -1, -4, -2, -3], [-5, -1, -3, -4, -2], [-5, -1, -3, -2, -4], [-5, -1, -2, -4, -3], [-5, -1, -2, -3, -4], [-4, -5, -3, -2, -1], [-4, -5, -3, -1, -2], [-4, -5, -2, -3, -1], [-4, -5, -2, -1, -3], [-4, -5, -1, -3, -2], [-4, -5, -1, -2, -3], [-4, -3, -5, -2, -1], [-4, -3, -5, -1, -2], [-4, -3, -2, -5, -1], [-4, -3, -2, -1, -5], [-4, -3, -1, -5, -2], [-4, -3, -1, -2, -5], [-4, -2, -5, -3, -1], [-4, -2, -5, -1, -3], [-4, -2, -3, -5, -1], [-4, -2, -3, -1, -5], [-4, -2, -1, -5, -3], [-4, -2, -1, -3, -5], [-4, -1, -5, -3, -2], [-4, -1, -5, -2, -3], [-4, -1, -3, -5, -2], [-4, -1, -3, -2, -5], [-4, -1, -2, -5, -3], [-4, -1, -2, -3, -5], [-3, -5, -4, -2, -1], [-3, -5, -4, -1, -2], [-3, -5, -2, -4, -1], [-3, -5, -2, -1, -4], [-3, -5, -1, -4, -2], [-3, -5, -1, -2, -4], [-3, -4, -5, -2, -1], [-3, -4, -5, -1, -2], [-3, -4, -2, -5, -1], [-3, -4, -2, -1, -5], [-3, -4, -1, -5, -2], [-3, -4, -1, -2, -5], [-3, -2, -5, -4, -1], [-3, -2, -5, -1, -4], [-3, -2, -4, -5, -1], [-3, -2, -4, -1, -5], [-3, -2, -1, -5, -4], [-3, -2, -1, -4, -5], [-3, -1, -5, -4, -2], [-3, -1, -5, -2, -4], [-3, -1, -4, -5, -2], [-3, -1, -4, -2, -5], [-3, -1, -2, -5, -4], [-3, -1, -2, -4, -5], [-2, -5, -4, -3, -1], [-2, -5, -4, -1, -3], [-2, -5, -3, -4, -1], [-2, -5, -3, -1, -4], [-2, -5, -1, -4, -3], [-2, -5, -1, -3, -4], [-2, -4, -5, -3, -1], [-2, -4, -5, -1, -3], [-2, -4, -3, -5, -1], [-2, -4, -3, -1, -5], [-2, -4, -1, -5, -3], [-2, -4, -1, -3, -5], [-2, -3, -5, -4, -1], [-2, -3, -5, -1, -4], [-2, -3, -4, -5, -1], [-2, -3, -4, -1, -5], [-2, -3, -1, -5, -4], [-2, -3, -1, -4, -5], [-2, -1, -5, -4, -3], [-2, -1, -5, -3, -4], [-2, -1, -4, -5, -3], [-2, -1, -4, -3, -5], [-2, -1, -3, -5, -4], [-2, -1, -3, -4, -5], [-1, -5, -4, -3, -2], [-1, -5, -4, -2, -3], [-1, -5, -3, -4, -2], [-1, -5, -3, -2, -4], [-1, -5, -2, -4, -3], [-1, -5, -2, -3, -4], [-1, -4, -5, -3, -2], [-1, -4, -5, -2, -3], [-1, -4, -3, -5, -2], [-1, -4, -3, -2, -5], [-1, -4, -2, -5, -3], [-1, -4, -2, -3, -5], [-1, -3, -5, -4, -2], [-1, -3, -5, -2, -4], [-1, -3, -4, -5, -2], [-1, -3, -4, -2, -5], [-1, -3, -2, -5, -4], [-1, -3, -2, -4, -5], [-1, -2, -5, -4, -3], [-1, -2, -5, -3, -4], [-1, -2, -4, -5, -3], [-1, -2, -4, -3, -5], [-1, -2, -3, -5, -4], [-1, -2, -3, -4, -5]]\n assert candidate(nums = [-5, -3, -1, -4, -2]) == [[-5, -3, -1, -4, -2], [-5, -3, -1, -2, -4], [-5, -3, -4, -1, -2], [-5, -3, -4, -2, -1], [-5, -3, -2, -1, -4], [-5, -3, -2, -4, -1], [-5, -1, -3, -4, -2], [-5, -1, -3, -2, -4], [-5, -1, -4, -3, -2], [-5, -1, -4, -2, -3], [-5, -1, -2, -3, -4], [-5, -1, -2, -4, -3], [-5, -4, -3, -1, -2], [-5, -4, -3, -2, -1], [-5, -4, -1, -3, -2], [-5, -4, -1, -2, -3], [-5, -4, -2, -3, -1], [-5, -4, -2, -1, -3], [-5, -2, -3, -1, -4], [-5, -2, -3, -4, -1], [-5, -2, -1, -3, -4], [-5, -2, -1, -4, -3], [-5, -2, -4, -3, -1], [-5, -2, -4, -1, -3], [-3, -5, -1, -4, -2], [-3, -5, -1, -2, -4], [-3, -5, -4, -1, -2], [-3, -5, -4, -2, -1], [-3, -5, -2, -1, -4], [-3, -5, -2, -4, -1], [-3, -1, -5, -4, -2], [-3, -1, -5, -2, -4], [-3, -1, -4, -5, -2], [-3, -1, -4, -2, -5], [-3, -1, -2, -5, -4], [-3, -1, -2, -4, -5], [-3, -4, -5, -1, -2], [-3, -4, -5, -2, -1], [-3, -4, -1, -5, -2], [-3, -4, -1, -2, -5], [-3, -4, -2, -5, -1], [-3, -4, -2, -1, -5], [-3, -2, -5, -1, -4], [-3, -2, -5, -4, -1], [-3, -2, -1, -5, -4], [-3, -2, -1, -4, -5], [-3, -2, -4, -5, -1], [-3, -2, -4, -1, -5], [-1, -5, -3, -4, -2], [-1, -5, -3, -2, -4], [-1, -5, -4, -3, -2], [-1, -5, -4, -2, -3], [-1, -5, -2, -3, -4], [-1, -5, -2, -4, -3], [-1, -3, -5, -4, -2], [-1, -3, -5, -2, -4], [-1, -3, -4, -5, -2], [-1, -3, -4, -2, -5], [-1, -3, -2, -5, -4], [-1, -3, -2, -4, -5], [-1, -4, -5, -3, -2], [-1, -4, -5, -2, -3], [-1, -4, -3, -5, -2], [-1, -4, -3, -2, -5], [-1, -4, -2, -5, -3], [-1, -4, -2, -3, -5], [-1, -2, -5, -3, -4], [-1, -2, -5, -4, -3], [-1, -2, -3, -5, -4], [-1, -2, -3, -4, -5], [-1, -2, -4, -5, -3], [-1, -2, -4, -3, -5], [-4, -5, -3, -1, -2], [-4, -5, -3, -2, -1], [-4, -5, -1, -3, -2], [-4, -5, -1, -2, -3], [-4, -5, -2, -3, -1], [-4, -5, -2, -1, -3], [-4, -3, -5, -1, -2], [-4, -3, -5, -2, -1], [-4, -3, -1, -5, -2], [-4, -3, -1, -2, -5], [-4, -3, -2, -5, -1], [-4, -3, -2, -1, -5], [-4, -1, -5, -3, -2], [-4, -1, -5, -2, -3], [-4, -1, -3, -5, -2], [-4, -1, -3, -2, -5], [-4, -1, -2, -5, -3], [-4, -1, -2, -3, -5], [-4, -2, -5, -3, -1], [-4, -2, -5, -1, -3], [-4, -2, -3, -5, -1], [-4, -2, -3, -1, -5], [-4, -2, -1, -5, -3], [-4, -2, -1, -3, -5], [-2, -5, -3, -1, -4], [-2, -5, -3, -4, -1], [-2, -5, -1, -3, -4], [-2, -5, -1, -4, -3], [-2, -5, -4, -3, -1], [-2, -5, -4, -1, -3], [-2, -3, -5, -1, -4], [-2, -3, -5, -4, -1], [-2, -3, -1, -5, -4], [-2, -3, -1, -4, -5], [-2, -3, -4, -5, -1], [-2, -3, -4, -1, -5], [-2, -1, -5, -3, -4], [-2, -1, -5, -4, -3], [-2, -1, -3, -5, -4], [-2, -1, -3, -4, -5], [-2, -1, -4, -5, -3], [-2, -1, -4, -3, -5], [-2, -4, -5, -3, -1], [-2, -4, -5, -1, -3], [-2, -4, -3, -5, -1], [-2, -4, -3, -1, -5], [-2, -4, -1, -5, -3], [-2, -4, -1, -3, -5]]\n assert candidate(nums = [100, 200, 300, -100, -200, -300]) == [[100, 200, 300, -100, -200, -300], [100, 200, 300, -100, -300, -200], [100, 200, 300, -200, -100, -300], [100, 200, 300, -200, -300, -100], [100, 200, 300, -300, -100, -200], [100, 200, 300, -300, -200, -100], [100, 200, -100, 300, -200, -300], [100, 200, -100, 300, -300, -200], [100, 200, -100, -200, 300, -300], [100, 200, -100, -200, -300, 300], [100, 200, -100, -300, 300, -200], [100, 200, -100, -300, -200, 300], [100, 200, -200, 300, -100, -300], [100, 200, -200, 300, -300, -100], [100, 200, -200, -100, 300, -300], [100, 200, -200, -100, -300, 300], [100, 200, -200, -300, 300, -100], [100, 200, -200, -300, -100, 300], [100, 200, -300, 300, -100, -200], [100, 200, -300, 300, -200, -100], [100, 200, -300, -100, 300, -200], [100, 200, -300, -100, -200, 300], [100, 200, -300, -200, 300, -100], [100, 200, -300, -200, -100, 300], [100, 300, 200, -100, -200, -300], [100, 300, 200, -100, -300, -200], [100, 300, 200, -200, -100, -300], [100, 300, 200, -200, -300, -100], [100, 300, 200, -300, -100, -200], [100, 300, 200, -300, -200, -100], [100, 300, -100, 200, -200, -300], [100, 300, -100, 200, -300, -200], [100, 300, -100, -200, 200, -300], [100, 300, -100, -200, -300, 200], [100, 300, -100, -300, 200, -200], [100, 300, -100, -300, -200, 200], [100, 300, -200, 200, -100, -300], [100, 300, -200, 200, -300, -100], [100, 300, -200, -100, 200, -300], [100, 300, -200, -100, -300, 200], [100, 300, -200, -300, 200, -100], [100, 300, -200, -300, -100, 200], [100, 300, -300, 200, -100, -200], [100, 300, -300, 200, -200, -100], [100, 300, -300, -100, 200, -200], [100, 300, -300, -100, -200, 200], [100, 300, -300, -200, 200, -100], [100, 300, -300, -200, -100, 200], [100, -100, 200, 300, -200, -300], [100, -100, 200, 300, -300, -200], [100, -100, 200, -200, 300, -300], [100, -100, 200, -200, -300, 300], [100, -100, 200, -300, 300, -200], [100, -100, 200, -300, -200, 300], [100, -100, 300, 200, -200, -300], [100, -100, 300, 200, -300, -200], [100, -100, 300, -200, 200, -300], [100, -100, 300, -200, -300, 200], [100, -100, 300, -300, 200, -200], [100, -100, 300, -300, -200, 200], [100, -100, -200, 200, 300, -300], [100, -100, -200, 200, -300, 300], [100, -100, -200, 300, 200, -300], [100, -100, -200, 300, -300, 200], [100, -100, -200, -300, 200, 300], [100, -100, -200, -300, 300, 200], [100, -100, -300, 200, 300, -200], [100, -100, -300, 200, -200, 300], [100, -100, -300, 300, 200, -200], [100, -100, -300, 300, -200, 200], [100, -100, -300, -200, 200, 300], [100, -100, -300, -200, 300, 200], [100, -200, 200, 300, -100, -300], [100, -200, 200, 300, -300, -100], [100, -200, 200, -100, 300, -300], [100, -200, 200, -100, -300, 300], [100, -200, 200, -300, 300, -100], [100, -200, 200, -300, -100, 300], [100, -200, 300, 200, -100, -300], [100, -200, 300, 200, -300, -100], [100, -200, 300, -100, 200, -300], [100, -200, 300, -100, -300, 200], [100, -200, 300, -300, 200, -100], [100, -200, 300, -300, -100, 200], [100, -200, -100, 200, 300, -300], [100, -200, -100, 200, -300, 300], [100, -200, -100, 300, 200, -300], [100, -200, -100, 300, -300, 200], [100, -200, -100, -300, 200, 300], [100, -200, -100, -300, 300, 200], [100, -200, -300, 200, 300, -100], [100, -200, -300, 200, -100, 300], [100, -200, -300, 300, 200, -100], [100, -200, -300, 300, -100, 200], [100, -200, -300, -100, 200, 300], [100, -200, -300, -100, 300, 200], [100, -300, 200, 300, -100, -200], [100, -300, 200, 300, -200, -100], [100, -300, 200, -100, 300, -200], [100, -300, 200, -100, -200, 300], [100, -300, 200, -200, 300, -100], [100, -300, 200, -200, -100, 300], [100, -300, 300, 200, -100, -200], [100, -300, 300, 200, -200, -100], [100, -300, 300, -100, 200, -200], [100, -300, 300, -100, -200, 200], [100, -300, 300, -200, 200, -100], [100, -300, 300, -200, -100, 200], [100, -300, -100, 200, 300, -200], [100, -300, -100, 200, -200, 300], [100, -300, -100, 300, 200, -200], [100, -300, -100, 300, -200, 200], [100, -300, -100, -200, 200, 300], [100, -300, -100, -200, 300, 200], [100, -300, -200, 200, 300, -100], [100, -300, -200, 200, -100, 300], [100, -300, -200, 300, 200, -100], [100, -300, -200, 300, -100, 200], [100, -300, -200, -100, 200, 300], [100, -300, -200, -100, 300, 200], [200, 100, 300, -100, -200, -300], [200, 100, 300, -100, -300, -200], [200, 100, 300, -200, -100, -300], [200, 100, 300, -200, -300, -100], [200, 100, 300, -300, -100, -200], [200, 100, 300, -300, -200, -100], [200, 100, -100, 300, -200, -300], [200, 100, -100, 300, -300, -200], [200, 100, -100, -200, 300, -300], [200, 100, -100, -200, -300, 300], [200, 100, -100, -300, 300, -200], [200, 100, -100, -300, -200, 300], [200, 100, -200, 300, -100, -300], [200, 100, -200, 300, -300, -100], [200, 100, -200, -100, 300, -300], [200, 100, -200, -100, -300, 300], [200, 100, -200, -300, 300, -100], [200, 100, -200, -300, -100, 300], [200, 100, -300, 300, -100, -200], [200, 100, -300, 300, -200, -100], [200, 100, -300, -100, 300, -200], [200, 100, -300, -100, -200, 300], [200, 100, -300, -200, 300, -100], [200, 100, -300, -200, -100, 300], [200, 300, 100, -100, -200, -300], [200, 300, 100, -100, -300, -200], [200, 300, 100, -200, -100, -300], [200, 300, 100, -200, -300, -100], [200, 300, 100, -300, -100, -200], [200, 300, 100, -300, -200, -100], [200, 300, -100, 100, -200, -300], [200, 300, -100, 100, -300, -200], [200, 300, -100, -200, 100, -300], [200, 300, -100, -200, -300, 100], [200, 300, -100, -300, 100, -200], [200, 300, -100, -300, -200, 100], [200, 300, -200, 100, -100, -300], [200, 300, -200, 100, -300, -100], [200, 300, -200, -100, 100, -300], [200, 300, -200, -100, -300, 100], [200, 300, -200, -300, 100, -100], [200, 300, -200, -300, -100, 100], [200, 300, -300, 100, -100, -200], [200, 300, -300, 100, -200, -100], [200, 300, -300, -100, 100, -200], [200, 300, -300, -100, -200, 100], [200, 300, -300, -200, 100, -100], [200, 300, -300, -200, -100, 100], [200, -100, 100, 300, -200, -300], [200, -100, 100, 300, -300, -200], [200, -100, 100, -200, 300, -300], [200, -100, 100, -200, -300, 300], [200, -100, 100, -300, 300, -200], [200, -100, 100, -300, -200, 300], [200, -100, 300, 100, -200, -300], [200, -100, 300, 100, -300, -200], [200, -100, 300, -200, 100, -300], [200, -100, 300, -200, -300, 100], [200, -100, 300, -300, 100, -200], [200, -100, 300, -300, -200, 100], [200, -100, -200, 100, 300, -300], [200, -100, -200, 100, -300, 300], [200, -100, -200, 300, 100, -300], [200, -100, -200, 300, -300, 100], [200, -100, -200, -300, 100, 300], [200, -100, -200, -300, 300, 100], [200, -100, -300, 100, 300, -200], [200, -100, -300, 100, -200, 300], [200, -100, -300, 300, 100, -200], [200, -100, -300, 300, -200, 100], [200, -100, -300, -200, 100, 300], [200, -100, -300, -200, 300, 100], [200, -200, 100, 300, -100, -300], [200, -200, 100, 300, -300, -100], [200, -200, 100, -100, 300, -300], [200, -200, 100, -100, -300, 300], [200, -200, 100, -300, 300, -100], [200, -200, 100, -300, -100, 300], [200, -200, 300, 100, -100, -300], [200, -200, 300, 100, -300, -100], [200, -200, 300, -100, 100, -300], [200, -200, 300, -100, -300, 100], [200, -200, 300, -300, 100, -100], [200, -200, 300, -300, -100, 100], [200, -200, -100, 100, 300, -300], [200, -200, -100, 100, -300, 300], [200, -200, -100, 300, 100, -300], [200, -200, -100, 300, -300, 100], [200, -200, -100, -300, 100, 300], [200, -200, -100, -300, 300, 100], [200, -200, -300, 100, 300, -100], [200, -200, -300, 100, -100, 300], [200, -200, -300, 300, 100, -100], [200, -200, -300, 300, -100, 100], [200, -200, -300, -100, 100, 300], [200, -200, -300, -100, 300, 100], [200, -300, 100, 300, -100, -200], [200, -300, 100, 300, -200, -100], [200, -300, 100, -100, 300, -200], [200, -300, 100, -100, -200, 300], [200, -300, 100, -200, 300, -100], [200, -300, 100, -200, -100, 300], [200, -300, 300, 100, -100, -200], [200, -300, 300, 100, -200, -100], [200, -300, 300, -100, 100, -200], [200, -300, 300, -100, -200, 100], [200, -300, 300, -200, 100, -100], [200, -300, 300, -200, -100, 100], [200, -300, -100, 100, 300, -200], [200, -300, -100, 100, -200, 300], [200, -300, -100, 300, 100, -200], [200, -300, -100, 300, -200, 100], [200, -300, -100, -200, 100, 300], [200, -300, -100, -200, 300, 100], [200, -300, -200, 100, 300, -100], [200, -300, -200, 100, -100, 300], [200, -300, -200, 300, 100, -100], [200, -300, -200, 300, -100, 100], [200, -300, -200, -100, 100, 300], [200, -300, -200, -100, 300, 100], [300, 100, 200, -100, -200, -300], [300, 100, 200, -100, -300, -200], [300, 100, 200, -200, -100, -300], [300, 100, 200, -200, -300, -100], [300, 100, 200, -300, -100, -200], [300, 100, 200, -300, -200, -100], [300, 100, -100, 200, -200, -300], [300, 100, -100, 200, -300, -200], [300, 100, -100, -200, 200, -300], [300, 100, -100, -200, -300, 200], [300, 100, -100, -300, 200, -200], [300, 100, -100, -300, -200, 200], [300, 100, -200, 200, -100, -300], [300, 100, -200, 200, -300, -100], [300, 100, -200, -100, 200, -300], [300, 100, -200, -100, -300, 200], [300, 100, -200, -300, 200, -100], [300, 100, -200, -300, -100, 200], [300, 100, -300, 200, -100, -200], [300, 100, -300, 200, -200, -100], [300, 100, -300, -100, 200, -200], [300, 100, -300, -100, -200, 200], [300, 100, -300, -200, 200, -100], [300, 100, -300, -200, -100, 200], [300, 200, 100, -100, -200, -300], [300, 200, 100, -100, -300, -200], [300, 200, 100, -200, -100, -300], [300, 200, 100, -200, -300, -100], [300, 200, 100, -300, -100, -200], [300, 200, 100, -300, -200, -100], [300, 200, -100, 100, -200, -300], [300, 200, -100, 100, -300, -200], [300, 200, -100, -200, 100, -300], [300, 200, -100, -200, -300, 100], [300, 200, -100, -300, 100, -200], [300, 200, -100, -300, -200, 100], [300, 200, -200, 100, -100, -300], [300, 200, -200, 100, -300, -100], [300, 200, -200, -100, 100, -300], [300, 200, -200, -100, -300, 100], [300, 200, -200, -300, 100, -100], [300, 200, -200, -300, -100, 100], [300, 200, -300, 100, -100, -200], [300, 200, -300, 100, -200, -100], [300, 200, -300, -100, 100, -200], [300, 200, -300, -100, -200, 100], [300, 200, -300, -200, 100, -100], [300, 200, -300, -200, -100, 100], [300, -100, 100, 200, -200, -300], [300, -100, 100, 200, -300, -200], [300, -100, 100, -200, 200, -300], [300, -100, 100, -200, -300, 200], [300, -100, 100, -300, 200, -200], [300, -100, 100, -300, -200, 200], [300, -100, 200, 100, -200, -300], [300, -100, 200, 100, -300, -200], [300, -100, 200, -200, 100, -300], [300, -100, 200, -200, -300, 100], [300, -100, 200, -300, 100, -200], [300, -100, 200, -300, -200, 100], [300, -100, -200, 100, 200, -300], [300, -100, -200, 100, -300, 200], [300, -100, -200, 200, 100, -300], [300, -100, -200, 200, -300, 100], [300, -100, -200, -300, 100, 200], [300, -100, -200, -300, 200, 100], [300, -100, -300, 100, 200, -200], [300, -100, -300, 100, -200, 200], [300, -100, -300, 200, 100, -200], [300, -100, -300, 200, -200, 100], [300, -100, -300, -200, 100, 200], [300, -100, -300, -200, 200, 100], [300, -200, 100, 200, -100, -300], [300, -200, 100, 200, -300, -100], [300, -200, 100, -100, 200, -300], [300, -200, 100, -100, -300, 200], [300, -200, 100, -300, 200, -100], [300, -200, 100, -300, -100, 200], [300, -200, 200, 100, -100, -300], [300, -200, 200, 100, -300, -100], [300, -200, 200, -100, 100, -300], [300, -200, 200, -100, -300, 100], [300, -200, 200, -300, 100, -100], [300, -200, 200, -300, -100, 100], [300, -200, -100, 100, 200, -300], [300, -200, -100, 100, -300, 200], [300, -200, -100, 200, 100, -300], [300, -200, -100, 200, -300, 100], [300, -200, -100, -300, 100, 200], [300, -200, -100, -300, 200, 100], [300, -200, -300, 100, 200, -100], [300, -200, -300, 100, -100, 200], [300, -200, -300, 200, 100, -100], [300, -200, -300, 200, -100, 100], [300, -200, -300, -100, 100, 200], [300, -200, -300, -100, 200, 100], [300, -300, 100, 200, -100, -200], [300, -300, 100, 200, -200, -100], [300, -300, 100, -100, 200, -200], [300, -300, 100, -100, -200, 200], [300, -300, 100, -200, 200, -100], [300, -300, 100, -200, -100, 200], [300, -300, 200, 100, -100, -200], [300, -300, 200, 100, -200, -100], [300, -300, 200, -100, 100, -200], [300, -300, 200, -100, -200, 100], [300, -300, 200, -200, 100, -100], [300, -300, 200, -200, -100, 100], [300, -300, -100, 100, 200, -200], [300, -300, -100, 100, -200, 200], [300, -300, -100, 200, 100, -200], [300, -300, -100, 200, -200, 100], [300, -300, -100, -200, 100, 200], [300, -300, -100, -200, 200, 100], [300, -300, -200, 100, 200, -100], [300, -300, -200, 100, -100, 200], [300, -300, -200, 200, 100, -100], [300, -300, -200, 200, -100, 100], [300, -300, -200, -100, 100, 200], [300, -300, -200, -100, 200, 100], [-100, 100, 200, 300, -200, -300], [-100, 100, 200, 300, -300, -200], [-100, 100, 200, -200, 300, -300], [-100, 100, 200, -200, -300, 300], [-100, 100, 200, -300, 300, -200], [-100, 100, 200, -300, -200, 300], [-100, 100, 300, 200, -200, -300], [-100, 100, 300, 200, -300, -200], [-100, 100, 300, -200, 200, -300], [-100, 100, 300, -200, -300, 200], [-100, 100, 300, -300, 200, -200], [-100, 100, 300, -300, -200, 200], [-100, 100, -200, 200, 300, -300], [-100, 100, -200, 200, -300, 300], [-100, 100, -200, 300, 200, -300], [-100, 100, -200, 300, -300, 200], [-100, 100, -200, -300, 200, 300], [-100, 100, -200, -300, 300, 200], [-100, 100, -300, 200, 300, -200], [-100, 100, -300, 200, -200, 300], [-100, 100, -300, 300, 200, -200], [-100, 100, -300, 300, -200, 200], [-100, 100, -300, -200, 200, 300], [-100, 100, -300, -200, 300, 200], [-100, 200, 100, 300, -200, -300], [-100, 200, 100, 300, -300, -200], [-100, 200, 100, -200, 300, -300], [-100, 200, 100, -200, -300, 300], [-100, 200, 100, -300, 300, -200], [-100, 200, 100, -300, -200, 300], [-100, 200, 300, 100, -200, -300], [-100, 200, 300, 100, -300, -200], [-100, 200, 300, -200, 100, -300], [-100, 200, 300, -200, -300, 100], [-100, 200, 300, -300, 100, -200], [-100, 200, 300, -300, -200, 100], [-100, 200, -200, 100, 300, -300], [-100, 200, -200, 100, -300, 300], [-100, 200, -200, 300, 100, -300], [-100, 200, -200, 300, -300, 100], [-100, 200, -200, -300, 100, 300], [-100, 200, -200, -300, 300, 100], [-100, 200, -300, 100, 300, -200], [-100, 200, -300, 100, -200, 300], [-100, 200, -300, 300, 100, -200], [-100, 200, -300, 300, -200, 100], [-100, 200, -300, -200, 100, 300], [-100, 200, -300, -200, 300, 100], [-100, 300, 100, 200, -200, -300], [-100, 300, 100, 200, -300, -200], [-100, 300, 100, -200, 200, -300], [-100, 300, 100, -200, -300, 200], [-100, 300, 100, -300, 200, -200], [-100, 300, 100, -300, -200, 200], [-100, 300, 200, 100, -200, -300], [-100, 300, 200, 100, -300, -200], [-100, 300, 200, -200, 100, -300], [-100, 300, 200, -200, -300, 100], [-100, 300, 200, -300, 100, -200], [-100, 300, 200, -300, -200, 100], [-100, 300, -200, 100, 200, -300], [-100, 300, -200, 100, -300, 200], [-100, 300, -200, 200, 100, -300], [-100, 300, -200, 200, -300, 100], [-100, 300, -200, -300, 100, 200], [-100, 300, -200, -300, 200, 100], [-100, 300, -300, 100, 200, -200], [-100, 300, -300, 100, -200, 200], [-100, 300, -300, 200, 100, -200], [-100, 300, -300, 200, -200, 100], [-100, 300, -300, -200, 100, 200], [-100, 300, -300, -200, 200, 100], [-100, -200, 100, 200, 300, -300], [-100, -200, 100, 200, -300, 300], [-100, -200, 100, 300, 200, -300], [-100, -200, 100, 300, -300, 200], [-100, -200, 100, -300, 200, 300], [-100, -200, 100, -300, 300, 200], [-100, -200, 200, 100, 300, -300], [-100, -200, 200, 100, -300, 300], [-100, -200, 200, 300, 100, -300], [-100, -200, 200, 300, -300, 100], [-100, -200, 200, -300, 100, 300], [-100, -200, 200, -300, 300, 100], [-100, -200, 300, 100, 200, -300], [-100, -200, 300, 100, -300, 200], [-100, -200, 300, 200, 100, -300], [-100, -200, 300, 200, -300, 100], [-100, -200, 300, -300, 100, 200], [-100, -200, 300, -300, 200, 100], [-100, -200, -300, 100, 200, 300], [-100, -200, -300, 100, 300, 200], [-100, -200, -300, 200, 100, 300], [-100, -200, -300, 200, 300, 100], [-100, -200, -300, 300, 100, 200], [-100, -200, -300, 300, 200, 100], [-100, -300, 100, 200, 300, -200], [-100, -300, 100, 200, -200, 300], [-100, -300, 100, 300, 200, -200], [-100, -300, 100, 300, -200, 200], [-100, -300, 100, -200, 200, 300], [-100, -300, 100, -200, 300, 200], [-100, -300, 200, 100, 300, -200], [-100, -300, 200, 100, -200, 300], [-100, -300, 200, 300, 100, -200], [-100, -300, 200, 300, -200, 100], [-100, -300, 200, -200, 100, 300], [-100, -300, 200, -200, 300, 100], [-100, -300, 300, 100, 200, -200], [-100, -300, 300, 100, -200, 200], [-100, -300, 300, 200, 100, -200], [-100, -300, 300, 200, -200, 100], [-100, -300, 300, -200, 100, 200], [-100, -300, 300, -200, 200, 100], [-100, -300, -200, 100, 200, 300], [-100, -300, -200, 100, 300, 200], [-100, -300, -200, 200, 100, 300], [-100, -300, -200, 200, 300, 100], [-100, -300, -200, 300, 100, 200], [-100, -300, -200, 300, 200, 100], [-200, 100, 200, 300, -100, -300], [-200, 100, 200, 300, -300, -100], [-200, 100, 200, -100, 300, -300], [-200, 100, 200, -100, -300, 300], [-200, 100, 200, -300, 300, -100], [-200, 100, 200, -300, -100, 300], [-200, 100, 300, 200, -100, -300], [-200, 100, 300, 200, -300, -100], [-200, 100, 300, -100, 200, -300], [-200, 100, 300, -100, -300, 200], [-200, 100, 300, -300, 200, -100], [-200, 100, 300, -300, -100, 200], [-200, 100, -100, 200, 300, -300], [-200, 100, -100, 200, -300, 300], [-200, 100, -100, 300, 200, -300], [-200, 100, -100, 300, -300, 200], [-200, 100, -100, -300, 200, 300], [-200, 100, -100, -300, 300, 200], [-200, 100, -300, 200, 300, -100], [-200, 100, -300, 200, -100, 300], [-200, 100, -300, 300, 200, -100], [-200, 100, -300, 300, -100, 200], [-200, 100, -300, -100, 200, 300], [-200, 100, -300, -100, 300, 200], [-200, 200, 100, 300, -100, -300], [-200, 200, 100, 300, -300, -100], [-200, 200, 100, -100, 300, -300], [-200, 200, 100, -100, -300, 300], [-200, 200, 100, -300, 300, -100], [-200, 200, 100, -300, -100, 300], [-200, 200, 300, 100, -100, -300], [-200, 200, 300, 100, -300, -100], [-200, 200, 300, -100, 100, -300], [-200, 200, 300, -100, -300, 100], [-200, 200, 300, -300, 100, -100], [-200, 200, 300, -300, -100, 100], [-200, 200, -100, 100, 300, -300], [-200, 200, -100, 100, -300, 300], [-200, 200, -100, 300, 100, -300], [-200, 200, -100, 300, -300, 100], [-200, 200, -100, -300, 100, 300], [-200, 200, -100, -300, 300, 100], [-200, 200, -300, 100, 300, -100], [-200, 200, -300, 100, -100, 300], [-200, 200, -300, 300, 100, -100], [-200, 200, -300, 300, -100, 100], [-200, 200, -300, -100, 100, 300], [-200, 200, -300, -100, 300, 100], [-200, 300, 100, 200, -100, -300], [-200, 300, 100, 200, -300, -100], [-200, 300, 100, -100, 200, -300], [-200, 300, 100, -100, -300, 200], [-200, 300, 100, -300, 200, -100], [-200, 300, 100, -300, -100, 200], [-200, 300, 200, 100, -100, -300], [-200, 300, 200, 100, -300, -100], [-200, 300, 200, -100, 100, -300], [-200, 300, 200, -100, -300, 100], [-200, 300, 200, -300, 100, -100], [-200, 300, 200, -300, -100, 100], [-200, 300, -100, 100, 200, -300], [-200, 300, -100, 100, -300, 200], [-200, 300, -100, 200, 100, -300], [-200, 300, -100, 200, -300, 100], [-200, 300, -100, -300, 100, 200], [-200, 300, -100, -300, 200, 100], [-200, 300, -300, 100, 200, -100], [-200, 300, -300, 100, -100, 200], [-200, 300, -300, 200, 100, -100], [-200, 300, -300, 200, -100, 100], [-200, 300, -300, -100, 100, 200], [-200, 300, -300, -100, 200, 100], [-200, -100, 100, 200, 300, -300], [-200, -100, 100, 200, -300, 300], [-200, -100, 100, 300, 200, -300], [-200, -100, 100, 300, -300, 200], [-200, -100, 100, -300, 200, 300], [-200, -100, 100, -300, 300, 200], [-200, -100, 200, 100, 300, -300], [-200, -100, 200, 100, -300, 300], [-200, -100, 200, 300, 100, -300], [-200, -100, 200, 300, -300, 100], [-200, -100, 200, -300, 100, 300], [-200, -100, 200, -300, 300, 100], [-200, -100, 300, 100, 200, -300], [-200, -100, 300, 100, -300, 200], [-200, -100, 300, 200, 100, -300], [-200, -100, 300, 200, -300, 100], [-200, -100, 300, -300, 100, 200], [-200, -100, 300, -300, 200, 100], [-200, -100, -300, 100, 200, 300], [-200, -100, -300, 100, 300, 200], [-200, -100, -300, 200, 100, 300], [-200, -100, -300, 200, 300, 100], [-200, -100, -300, 300, 100, 200], [-200, -100, -300, 300, 200, 100], [-200, -300, 100, 200, 300, -100], [-200, -300, 100, 200, -100, 300], [-200, -300, 100, 300, 200, -100], [-200, -300, 100, 300, -100, 200], [-200, -300, 100, -100, 200, 300], [-200, -300, 100, -100, 300, 200], [-200, -300, 200, 100, 300, -100], [-200, -300, 200, 100, -100, 300], [-200, -300, 200, 300, 100, -100], [-200, -300, 200, 300, -100, 100], [-200, -300, 200, -100, 100, 300], [-200, -300, 200, -100, 300, 100], [-200, -300, 300, 100, 200, -100], [-200, -300, 300, 100, -100, 200], [-200, -300, 300, 200, 100, -100], [-200, -300, 300, 200, -100, 100], [-200, -300, 300, -100, 100, 200], [-200, -300, 300, -100, 200, 100], [-200, -300, -100, 100, 200, 300], [-200, -300, -100, 100, 300, 200], [-200, -300, -100, 200, 100, 300], [-200, -300, -100, 200, 300, 100], [-200, -300, -100, 300, 100, 200], [-200, -300, -100, 300, 200, 100], [-300, 100, 200, 300, -100, -200], [-300, 100, 200, 300, -200, -100], [-300, 100, 200, -100, 300, -200], [-300, 100, 200, -100, -200, 300], [-300, 100, 200, -200, 300, -100], [-300, 100, 200, -200, -100, 300], [-300, 100, 300, 200, -100, -200], [-300, 100, 300, 200, -200, -100], [-300, 100, 300, -100, 200, -200], [-300, 100, 300, -100, -200, 200], [-300, 100, 300, -200, 200, -100], [-300, 100, 300, -200, -100, 200], [-300, 100, -100, 200, 300, -200], [-300, 100, -100, 200, -200, 300], [-300, 100, -100, 300, 200, -200], [-300, 100, -100, 300, -200, 200], [-300, 100, -100, -200, 200, 300], [-300, 100, -100, -200, 300, 200], [-300, 100, -200, 200, 300, -100], [-300, 100, -200, 200, -100, 300], [-300, 100, -200, 300, 200, -100], [-300, 100, -200, 300, -100, 200], [-300, 100, -200, -100, 200, 300], [-300, 100, -200, -100, 300, 200], [-300, 200, 100, 300, -100, -200], [-300, 200, 100, 300, -200, -100], [-300, 200, 100, -100, 300, -200], [-300, 200, 100, -100, -200, 300], [-300, 200, 100, -200, 300, -100], [-300, 200, 100, -200, -100, 300], [-300, 200, 300, 100, -100, -200], [-300, 200, 300, 100, -200, -100], [-300, 200, 300, -100, 100, -200], [-300, 200, 300, -100, -200, 100], [-300, 200, 300, -200, 100, -100], [-300, 200, 300, -200, -100, 100], [-300, 200, -100, 100, 300, -200], [-300, 200, -100, 100, -200, 300], [-300, 200, -100, 300, 100, -200], [-300, 200, -100, 300, -200, 100], [-300, 200, -100, -200, 100, 300], [-300, 200, -100, -200, 300, 100], [-300, 200, -200, 100, 300, -100], [-300, 200, -200, 100, -100, 300], [-300, 200, -200, 300, 100, -100], [-300, 200, -200, 300, -100, 100], [-300, 200, -200, -100, 100, 300], [-300, 200, -200, -100, 300, 100], [-300, 300, 100, 200, -100, -200], [-300, 300, 100, 200, -200, -100], [-300, 300, 100, -100, 200, -200], [-300, 300, 100, -100, -200, 200], [-300, 300, 100, -200, 200, -100], [-300, 300, 100, -200, -100, 200], [-300, 300, 200, 100, -100, -200], [-300, 300, 200, 100, -200, -100], [-300, 300, 200, -100, 100, -200], [-300, 300, 200, -100, -200, 100], [-300, 300, 200, -200, 100, -100], [-300, 300, 200, -200, -100, 100], [-300, 300, -100, 100, 200, -200], [-300, 300, -100, 100, -200, 200], [-300, 300, -100, 200, 100, -200], [-300, 300, -100, 200, -200, 100], [-300, 300, -100, -200, 100, 200], [-300, 300, -100, -200, 200, 100], [-300, 300, -200, 100, 200, -100], [-300, 300, -200, 100, -100, 200], [-300, 300, -200, 200, 100, -100], [-300, 300, -200, 200, -100, 100], [-300, 300, -200, -100, 100, 200], [-300, 300, -200, -100, 200, 100], [-300, -100, 100, 200, 300, -200], [-300, -100, 100, 200, -200, 300], [-300, -100, 100, 300, 200, -200], [-300, -100, 100, 300, -200, 200], [-300, -100, 100, -200, 200, 300], [-300, -100, 100, -200, 300, 200], [-300, -100, 200, 100, 300, -200], [-300, -100, 200, 100, -200, 300], [-300, -100, 200, 300, 100, -200], [-300, -100, 200, 300, -200, 100], [-300, -100, 200, -200, 100, 300], [-300, -100, 200, -200, 300, 100], [-300, -100, 300, 100, 200, -200], [-300, -100, 300, 100, -200, 200], [-300, -100, 300, 200, 100, -200], [-300, -100, 300, 200, -200, 100], [-300, -100, 300, -200, 100, 200], [-300, -100, 300, -200, 200, 100], [-300, -100, -200, 100, 200, 300], [-300, -100, -200, 100, 300, 200], [-300, -100, -200, 200, 100, 300], [-300, -100, -200, 200, 300, 100], [-300, -100, -200, 300, 100, 200], [-300, -100, -200, 300, 200, 100], [-300, -200, 100, 200, 300, -100], [-300, -200, 100, 200, -100, 300], [-300, -200, 100, 300, 200, -100], [-300, -200, 100, 300, -100, 200], [-300, -200, 100, -100, 200, 300], [-300, -200, 100, -100, 300, 200], [-300, -200, 200, 100, 300, -100], [-300, -200, 200, 100, -100, 300], [-300, -200, 200, 300, 100, -100], [-300, -200, 200, 300, -100, 100], [-300, -200, 200, -100, 100, 300], [-300, -200, 200, -100, 300, 100], [-300, -200, 300, 100, 200, -100], [-300, -200, 300, 100, -100, 200], [-300, -200, 300, 200, 100, -100], [-300, -200, 300, 200, -100, 100], [-300, -200, 300, -100, 100, 200], [-300, -200, 300, -100, 200, 100], [-300, -200, -100, 100, 200, 300], [-300, -200, -100, 100, 300, 200], [-300, -200, -100, 200, 100, 300], [-300, -200, -100, 200, 300, 100], [-300, -200, -100, 300, 100, 200], [-300, -200, -100, 300, 200, 100]]\n assert candidate(nums = [-5, 0, 5, 10]) == [[-5, 0, 5, 10], [-5, 0, 10, 5], [-5, 5, 0, 10], [-5, 5, 10, 0], [-5, 10, 0, 5], [-5, 10, 5, 0], [0, -5, 5, 10], [0, -5, 10, 5], [0, 5, -5, 10], [0, 5, 10, -5], [0, 10, -5, 5], [0, 10, 5, -5], [5, -5, 0, 10], [5, -5, 10, 0], [5, 0, -5, 10], [5, 0, 10, -5], [5, 10, -5, 0], [5, 10, 0, -5], [10, -5, 0, 5], [10, -5, 5, 0], [10, 0, -5, 5], [10, 0, 5, -5], [10, 5, -5, 0], [10, 5, 0, -5]]\n assert candidate(nums = [-1, 0, 1]) == [[-1, 0, 1], [-1, 1, 0], [0, -1, 1], [0, 1, -1], [1, -1, 0], [1, 0, -1]]\n assert candidate(nums = [6, 5, 4, 3, 2, 1]) == [[6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 1, 2], [6, 5, 4, 2, 3, 1], [6, 5, 4, 2, 1, 3], [6, 5, 4, 1, 3, 2], [6, 5, 4, 1, 2, 3], [6, 5, 3, 4, 2, 1], [6, 5, 3, 4, 1, 2], [6, 5, 3, 2, 4, 1], [6, 5, 3, 2, 1, 4], [6, 5, 3, 1, 4, 2], [6, 5, 3, 1, 2, 4], [6, 5, 2, 4, 3, 1], [6, 5, 2, 4, 1, 3], [6, 5, 2, 3, 4, 1], [6, 5, 2, 3, 1, 4], [6, 5, 2, 1, 4, 3], [6, 5, 2, 1, 3, 4], [6, 5, 1, 4, 3, 2], [6, 5, 1, 4, 2, 3], [6, 5, 1, 3, 4, 2], [6, 5, 1, 3, 2, 4], [6, 5, 1, 2, 4, 3], [6, 5, 1, 2, 3, 4], [6, 4, 5, 3, 2, 1], [6, 4, 5, 3, 1, 2], [6, 4, 5, 2, 3, 1], [6, 4, 5, 2, 1, 3], [6, 4, 5, 1, 3, 2], [6, 4, 5, 1, 2, 3], [6, 4, 3, 5, 2, 1], [6, 4, 3, 5, 1, 2], [6, 4, 3, 2, 5, 1], [6, 4, 3, 2, 1, 5], [6, 4, 3, 1, 5, 2], [6, 4, 3, 1, 2, 5], [6, 4, 2, 5, 3, 1], [6, 4, 2, 5, 1, 3], [6, 4, 2, 3, 5, 1], [6, 4, 2, 3, 1, 5], [6, 4, 2, 1, 5, 3], [6, 4, 2, 1, 3, 5], [6, 4, 1, 5, 3, 2], [6, 4, 1, 5, 2, 3], [6, 4, 1, 3, 5, 2], [6, 4, 1, 3, 2, 5], [6, 4, 1, 2, 5, 3], [6, 4, 1, 2, 3, 5], [6, 3, 5, 4, 2, 1], [6, 3, 5, 4, 1, 2], [6, 3, 5, 2, 4, 1], [6, 3, 5, 2, 1, 4], [6, 3, 5, 1, 4, 2], [6, 3, 5, 1, 2, 4], [6, 3, 4, 5, 2, 1], [6, 3, 4, 5, 1, 2], [6, 3, 4, 2, 5, 1], [6, 3, 4, 2, 1, 5], [6, 3, 4, 1, 5, 2], [6, 3, 4, 1, 2, 5], [6, 3, 2, 5, 4, 1], [6, 3, 2, 5, 1, 4], [6, 3, 2, 4, 5, 1], [6, 3, 2, 4, 1, 5], [6, 3, 2, 1, 5, 4], [6, 3, 2, 1, 4, 5], [6, 3, 1, 5, 4, 2], [6, 3, 1, 5, 2, 4], [6, 3, 1, 4, 5, 2], [6, 3, 1, 4, 2, 5], [6, 3, 1, 2, 5, 4], [6, 3, 1, 2, 4, 5], [6, 2, 5, 4, 3, 1], [6, 2, 5, 4, 1, 3], [6, 2, 5, 3, 4, 1], [6, 2, 5, 3, 1, 4], [6, 2, 5, 1, 4, 3], [6, 2, 5, 1, 3, 4], [6, 2, 4, 5, 3, 1], [6, 2, 4, 5, 1, 3], [6, 2, 4, 3, 5, 1], [6, 2, 4, 3, 1, 5], [6, 2, 4, 1, 5, 3], [6, 2, 4, 1, 3, 5], [6, 2, 3, 5, 4, 1], [6, 2, 3, 5, 1, 4], [6, 2, 3, 4, 5, 1], [6, 2, 3, 4, 1, 5], [6, 2, 3, 1, 5, 4], [6, 2, 3, 1, 4, 5], [6, 2, 1, 5, 4, 3], [6, 2, 1, 5, 3, 4], [6, 2, 1, 4, 5, 3], [6, 2, 1, 4, 3, 5], [6, 2, 1, 3, 5, 4], [6, 2, 1, 3, 4, 5], [6, 1, 5, 4, 3, 2], [6, 1, 5, 4, 2, 3], [6, 1, 5, 3, 4, 2], [6, 1, 5, 3, 2, 4], [6, 1, 5, 2, 4, 3], [6, 1, 5, 2, 3, 4], [6, 1, 4, 5, 3, 2], [6, 1, 4, 5, 2, 3], [6, 1, 4, 3, 5, 2], [6, 1, 4, 3, 2, 5], [6, 1, 4, 2, 5, 3], [6, 1, 4, 2, 3, 5], [6, 1, 3, 5, 4, 2], [6, 1, 3, 5, 2, 4], [6, 1, 3, 4, 5, 2], [6, 1, 3, 4, 2, 5], [6, 1, 3, 2, 5, 4], [6, 1, 3, 2, 4, 5], [6, 1, 2, 5, 4, 3], [6, 1, 2, 5, 3, 4], [6, 1, 2, 4, 5, 3], [6, 1, 2, 4, 3, 5], [6, 1, 2, 3, 5, 4], [6, 1, 2, 3, 4, 5], [5, 6, 4, 3, 2, 1], [5, 6, 4, 3, 1, 2], [5, 6, 4, 2, 3, 1], [5, 6, 4, 2, 1, 3], [5, 6, 4, 1, 3, 2], [5, 6, 4, 1, 2, 3], [5, 6, 3, 4, 2, 1], [5, 6, 3, 4, 1, 2], [5, 6, 3, 2, 4, 1], [5, 6, 3, 2, 1, 4], [5, 6, 3, 1, 4, 2], [5, 6, 3, 1, 2, 4], [5, 6, 2, 4, 3, 1], [5, 6, 2, 4, 1, 3], [5, 6, 2, 3, 4, 1], [5, 6, 2, 3, 1, 4], [5, 6, 2, 1, 4, 3], [5, 6, 2, 1, 3, 4], [5, 6, 1, 4, 3, 2], [5, 6, 1, 4, 2, 3], [5, 6, 1, 3, 4, 2], [5, 6, 1, 3, 2, 4], [5, 6, 1, 2, 4, 3], [5, 6, 1, 2, 3, 4], [5, 4, 6, 3, 2, 1], [5, 4, 6, 3, 1, 2], [5, 4, 6, 2, 3, 1], [5, 4, 6, 2, 1, 3], [5, 4, 6, 1, 3, 2], [5, 4, 6, 1, 2, 3], [5, 4, 3, 6, 2, 1], [5, 4, 3, 6, 1, 2], [5, 4, 3, 2, 6, 1], [5, 4, 3, 2, 1, 6], [5, 4, 3, 1, 6, 2], [5, 4, 3, 1, 2, 6], [5, 4, 2, 6, 3, 1], [5, 4, 2, 6, 1, 3], [5, 4, 2, 3, 6, 1], [5, 4, 2, 3, 1, 6], [5, 4, 2, 1, 6, 3], [5, 4, 2, 1, 3, 6], [5, 4, 1, 6, 3, 2], [5, 4, 1, 6, 2, 3], [5, 4, 1, 3, 6, 2], [5, 4, 1, 3, 2, 6], [5, 4, 1, 2, 6, 3], [5, 4, 1, 2, 3, 6], [5, 3, 6, 4, 2, 1], [5, 3, 6, 4, 1, 2], [5, 3, 6, 2, 4, 1], [5, 3, 6, 2, 1, 4], [5, 3, 6, 1, 4, 2], [5, 3, 6, 1, 2, 4], [5, 3, 4, 6, 2, 1], [5, 3, 4, 6, 1, 2], [5, 3, 4, 2, 6, 1], [5, 3, 4, 2, 1, 6], [5, 3, 4, 1, 6, 2], [5, 3, 4, 1, 2, 6], [5, 3, 2, 6, 4, 1], [5, 3, 2, 6, 1, 4], [5, 3, 2, 4, 6, 1], [5, 3, 2, 4, 1, 6], [5, 3, 2, 1, 6, 4], [5, 3, 2, 1, 4, 6], [5, 3, 1, 6, 4, 2], [5, 3, 1, 6, 2, 4], [5, 3, 1, 4, 6, 2], [5, 3, 1, 4, 2, 6], [5, 3, 1, 2, 6, 4], [5, 3, 1, 2, 4, 6], [5, 2, 6, 4, 3, 1], [5, 2, 6, 4, 1, 3], [5, 2, 6, 3, 4, 1], [5, 2, 6, 3, 1, 4], [5, 2, 6, 1, 4, 3], [5, 2, 6, 1, 3, 4], [5, 2, 4, 6, 3, 1], [5, 2, 4, 6, 1, 3], [5, 2, 4, 3, 6, 1], [5, 2, 4, 3, 1, 6], [5, 2, 4, 1, 6, 3], [5, 2, 4, 1, 3, 6], [5, 2, 3, 6, 4, 1], [5, 2, 3, 6, 1, 4], [5, 2, 3, 4, 6, 1], [5, 2, 3, 4, 1, 6], [5, 2, 3, 1, 6, 4], [5, 2, 3, 1, 4, 6], [5, 2, 1, 6, 4, 3], [5, 2, 1, 6, 3, 4], [5, 2, 1, 4, 6, 3], [5, 2, 1, 4, 3, 6], [5, 2, 1, 3, 6, 4], [5, 2, 1, 3, 4, 6], [5, 1, 6, 4, 3, 2], [5, 1, 6, 4, 2, 3], [5, 1, 6, 3, 4, 2], [5, 1, 6, 3, 2, 4], [5, 1, 6, 2, 4, 3], [5, 1, 6, 2, 3, 4], [5, 1, 4, 6, 3, 2], [5, 1, 4, 6, 2, 3], [5, 1, 4, 3, 6, 2], [5, 1, 4, 3, 2, 6], [5, 1, 4, 2, 6, 3], [5, 1, 4, 2, 3, 6], [5, 1, 3, 6, 4, 2], [5, 1, 3, 6, 2, 4], [5, 1, 3, 4, 6, 2], [5, 1, 3, 4, 2, 6], [5, 1, 3, 2, 6, 4], [5, 1, 3, 2, 4, 6], [5, 1, 2, 6, 4, 3], [5, 1, 2, 6, 3, 4], [5, 1, 2, 4, 6, 3], [5, 1, 2, 4, 3, 6], [5, 1, 2, 3, 6, 4], [5, 1, 2, 3, 4, 6], [4, 6, 5, 3, 2, 1], [4, 6, 5, 3, 1, 2], [4, 6, 5, 2, 3, 1], [4, 6, 5, 2, 1, 3], [4, 6, 5, 1, 3, 2], [4, 6, 5, 1, 2, 3], [4, 6, 3, 5, 2, 1], [4, 6, 3, 5, 1, 2], [4, 6, 3, 2, 5, 1], [4, 6, 3, 2, 1, 5], [4, 6, 3, 1, 5, 2], [4, 6, 3, 1, 2, 5], [4, 6, 2, 5, 3, 1], [4, 6, 2, 5, 1, 3], [4, 6, 2, 3, 5, 1], [4, 6, 2, 3, 1, 5], [4, 6, 2, 1, 5, 3], [4, 6, 2, 1, 3, 5], [4, 6, 1, 5, 3, 2], [4, 6, 1, 5, 2, 3], [4, 6, 1, 3, 5, 2], [4, 6, 1, 3, 2, 5], [4, 6, 1, 2, 5, 3], [4, 6, 1, 2, 3, 5], [4, 5, 6, 3, 2, 1], [4, 5, 6, 3, 1, 2], [4, 5, 6, 2, 3, 1], [4, 5, 6, 2, 1, 3], [4, 5, 6, 1, 3, 2], [4, 5, 6, 1, 2, 3], [4, 5, 3, 6, 2, 1], [4, 5, 3, 6, 1, 2], [4, 5, 3, 2, 6, 1], [4, 5, 3, 2, 1, 6], [4, 5, 3, 1, 6, 2], [4, 5, 3, 1, 2, 6], [4, 5, 2, 6, 3, 1], [4, 5, 2, 6, 1, 3], [4, 5, 2, 3, 6, 1], [4, 5, 2, 3, 1, 6], [4, 5, 2, 1, 6, 3], [4, 5, 2, 1, 3, 6], [4, 5, 1, 6, 3, 2], [4, 5, 1, 6, 2, 3], [4, 5, 1, 3, 6, 2], [4, 5, 1, 3, 2, 6], [4, 5, 1, 2, 6, 3], [4, 5, 1, 2, 3, 6], [4, 3, 6, 5, 2, 1], [4, 3, 6, 5, 1, 2], [4, 3, 6, 2, 5, 1], [4, 3, 6, 2, 1, 5], [4, 3, 6, 1, 5, 2], [4, 3, 6, 1, 2, 5], [4, 3, 5, 6, 2, 1], [4, 3, 5, 6, 1, 2], [4, 3, 5, 2, 6, 1], [4, 3, 5, 2, 1, 6], [4, 3, 5, 1, 6, 2], [4, 3, 5, 1, 2, 6], [4, 3, 2, 6, 5, 1], [4, 3, 2, 6, 1, 5], [4, 3, 2, 5, 6, 1], [4, 3, 2, 5, 1, 6], [4, 3, 2, 1, 6, 5], [4, 3, 2, 1, 5, 6], [4, 3, 1, 6, 5, 2], [4, 3, 1, 6, 2, 5], [4, 3, 1, 5, 6, 2], [4, 3, 1, 5, 2, 6], [4, 3, 1, 2, 6, 5], [4, 3, 1, 2, 5, 6], [4, 2, 6, 5, 3, 1], [4, 2, 6, 5, 1, 3], [4, 2, 6, 3, 5, 1], [4, 2, 6, 3, 1, 5], [4, 2, 6, 1, 5, 3], [4, 2, 6, 1, 3, 5], [4, 2, 5, 6, 3, 1], [4, 2, 5, 6, 1, 3], [4, 2, 5, 3, 6, 1], [4, 2, 5, 3, 1, 6], [4, 2, 5, 1, 6, 3], [4, 2, 5, 1, 3, 6], [4, 2, 3, 6, 5, 1], [4, 2, 3, 6, 1, 5], [4, 2, 3, 5, 6, 1], [4, 2, 3, 5, 1, 6], [4, 2, 3, 1, 6, 5], [4, 2, 3, 1, 5, 6], [4, 2, 1, 6, 5, 3], [4, 2, 1, 6, 3, 5], [4, 2, 1, 5, 6, 3], [4, 2, 1, 5, 3, 6], [4, 2, 1, 3, 6, 5], [4, 2, 1, 3, 5, 6], [4, 1, 6, 5, 3, 2], [4, 1, 6, 5, 2, 3], [4, 1, 6, 3, 5, 2], [4, 1, 6, 3, 2, 5], [4, 1, 6, 2, 5, 3], [4, 1, 6, 2, 3, 5], [4, 1, 5, 6, 3, 2], [4, 1, 5, 6, 2, 3], [4, 1, 5, 3, 6, 2], [4, 1, 5, 3, 2, 6], [4, 1, 5, 2, 6, 3], [4, 1, 5, 2, 3, 6], [4, 1, 3, 6, 5, 2], [4, 1, 3, 6, 2, 5], [4, 1, 3, 5, 6, 2], [4, 1, 3, 5, 2, 6], [4, 1, 3, 2, 6, 5], [4, 1, 3, 2, 5, 6], [4, 1, 2, 6, 5, 3], [4, 1, 2, 6, 3, 5], [4, 1, 2, 5, 6, 3], [4, 1, 2, 5, 3, 6], [4, 1, 2, 3, 6, 5], [4, 1, 2, 3, 5, 6], [3, 6, 5, 4, 2, 1], [3, 6, 5, 4, 1, 2], [3, 6, 5, 2, 4, 1], [3, 6, 5, 2, 1, 4], [3, 6, 5, 1, 4, 2], [3, 6, 5, 1, 2, 4], [3, 6, 4, 5, 2, 1], [3, 6, 4, 5, 1, 2], [3, 6, 4, 2, 5, 1], [3, 6, 4, 2, 1, 5], [3, 6, 4, 1, 5, 2], [3, 6, 4, 1, 2, 5], [3, 6, 2, 5, 4, 1], [3, 6, 2, 5, 1, 4], [3, 6, 2, 4, 5, 1], [3, 6, 2, 4, 1, 5], [3, 6, 2, 1, 5, 4], [3, 6, 2, 1, 4, 5], [3, 6, 1, 5, 4, 2], [3, 6, 1, 5, 2, 4], [3, 6, 1, 4, 5, 2], [3, 6, 1, 4, 2, 5], [3, 6, 1, 2, 5, 4], [3, 6, 1, 2, 4, 5], [3, 5, 6, 4, 2, 1], [3, 5, 6, 4, 1, 2], [3, 5, 6, 2, 4, 1], [3, 5, 6, 2, 1, 4], [3, 5, 6, 1, 4, 2], [3, 5, 6, 1, 2, 4], [3, 5, 4, 6, 2, 1], [3, 5, 4, 6, 1, 2], [3, 5, 4, 2, 6, 1], [3, 5, 4, 2, 1, 6], [3, 5, 4, 1, 6, 2], [3, 5, 4, 1, 2, 6], [3, 5, 2, 6, 4, 1], [3, 5, 2, 6, 1, 4], [3, 5, 2, 4, 6, 1], [3, 5, 2, 4, 1, 6], [3, 5, 2, 1, 6, 4], [3, 5, 2, 1, 4, 6], [3, 5, 1, 6, 4, 2], [3, 5, 1, 6, 2, 4], [3, 5, 1, 4, 6, 2], [3, 5, 1, 4, 2, 6], [3, 5, 1, 2, 6, 4], [3, 5, 1, 2, 4, 6], [3, 4, 6, 5, 2, 1], [3, 4, 6, 5, 1, 2], [3, 4, 6, 2, 5, 1], [3, 4, 6, 2, 1, 5], [3, 4, 6, 1, 5, 2], [3, 4, 6, 1, 2, 5], [3, 4, 5, 6, 2, 1], [3, 4, 5, 6, 1, 2], [3, 4, 5, 2, 6, 1], [3, 4, 5, 2, 1, 6], [3, 4, 5, 1, 6, 2], [3, 4, 5, 1, 2, 6], [3, 4, 2, 6, 5, 1], [3, 4, 2, 6, 1, 5], [3, 4, 2, 5, 6, 1], [3, 4, 2, 5, 1, 6], [3, 4, 2, 1, 6, 5], [3, 4, 2, 1, 5, 6], [3, 4, 1, 6, 5, 2], [3, 4, 1, 6, 2, 5], [3, 4, 1, 5, 6, 2], [3, 4, 1, 5, 2, 6], [3, 4, 1, 2, 6, 5], [3, 4, 1, 2, 5, 6], [3, 2, 6, 5, 4, 1], [3, 2, 6, 5, 1, 4], [3, 2, 6, 4, 5, 1], [3, 2, 6, 4, 1, 5], [3, 2, 6, 1, 5, 4], [3, 2, 6, 1, 4, 5], [3, 2, 5, 6, 4, 1], [3, 2, 5, 6, 1, 4], [3, 2, 5, 4, 6, 1], [3, 2, 5, 4, 1, 6], [3, 2, 5, 1, 6, 4], [3, 2, 5, 1, 4, 6], [3, 2, 4, 6, 5, 1], [3, 2, 4, 6, 1, 5], [3, 2, 4, 5, 6, 1], [3, 2, 4, 5, 1, 6], [3, 2, 4, 1, 6, 5], [3, 2, 4, 1, 5, 6], [3, 2, 1, 6, 5, 4], [3, 2, 1, 6, 4, 5], [3, 2, 1, 5, 6, 4], [3, 2, 1, 5, 4, 6], [3, 2, 1, 4, 6, 5], [3, 2, 1, 4, 5, 6], [3, 1, 6, 5, 4, 2], [3, 1, 6, 5, 2, 4], [3, 1, 6, 4, 5, 2], [3, 1, 6, 4, 2, 5], [3, 1, 6, 2, 5, 4], [3, 1, 6, 2, 4, 5], [3, 1, 5, 6, 4, 2], [3, 1, 5, 6, 2, 4], [3, 1, 5, 4, 6, 2], [3, 1, 5, 4, 2, 6], [3, 1, 5, 2, 6, 4], [3, 1, 5, 2, 4, 6], [3, 1, 4, 6, 5, 2], [3, 1, 4, 6, 2, 5], [3, 1, 4, 5, 6, 2], [3, 1, 4, 5, 2, 6], [3, 1, 4, 2, 6, 5], [3, 1, 4, 2, 5, 6], [3, 1, 2, 6, 5, 4], [3, 1, 2, 6, 4, 5], [3, 1, 2, 5, 6, 4], [3, 1, 2, 5, 4, 6], [3, 1, 2, 4, 6, 5], [3, 1, 2, 4, 5, 6], [2, 6, 5, 4, 3, 1], [2, 6, 5, 4, 1, 3], [2, 6, 5, 3, 4, 1], [2, 6, 5, 3, 1, 4], [2, 6, 5, 1, 4, 3], [2, 6, 5, 1, 3, 4], [2, 6, 4, 5, 3, 1], [2, 6, 4, 5, 1, 3], [2, 6, 4, 3, 5, 1], [2, 6, 4, 3, 1, 5], [2, 6, 4, 1, 5, 3], [2, 6, 4, 1, 3, 5], [2, 6, 3, 5, 4, 1], [2, 6, 3, 5, 1, 4], [2, 6, 3, 4, 5, 1], [2, 6, 3, 4, 1, 5], [2, 6, 3, 1, 5, 4], [2, 6, 3, 1, 4, 5], [2, 6, 1, 5, 4, 3], [2, 6, 1, 5, 3, 4], [2, 6, 1, 4, 5, 3], [2, 6, 1, 4, 3, 5], [2, 6, 1, 3, 5, 4], [2, 6, 1, 3, 4, 5], [2, 5, 6, 4, 3, 1], [2, 5, 6, 4, 1, 3], [2, 5, 6, 3, 4, 1], [2, 5, 6, 3, 1, 4], [2, 5, 6, 1, 4, 3], [2, 5, 6, 1, 3, 4], [2, 5, 4, 6, 3, 1], [2, 5, 4, 6, 1, 3], [2, 5, 4, 3, 6, 1], [2, 5, 4, 3, 1, 6], [2, 5, 4, 1, 6, 3], [2, 5, 4, 1, 3, 6], [2, 5, 3, 6, 4, 1], [2, 5, 3, 6, 1, 4], [2, 5, 3, 4, 6, 1], [2, 5, 3, 4, 1, 6], [2, 5, 3, 1, 6, 4], [2, 5, 3, 1, 4, 6], [2, 5, 1, 6, 4, 3], [2, 5, 1, 6, 3, 4], [2, 5, 1, 4, 6, 3], [2, 5, 1, 4, 3, 6], [2, 5, 1, 3, 6, 4], [2, 5, 1, 3, 4, 6], [2, 4, 6, 5, 3, 1], [2, 4, 6, 5, 1, 3], [2, 4, 6, 3, 5, 1], [2, 4, 6, 3, 1, 5], [2, 4, 6, 1, 5, 3], [2, 4, 6, 1, 3, 5], [2, 4, 5, 6, 3, 1], [2, 4, 5, 6, 1, 3], [2, 4, 5, 3, 6, 1], [2, 4, 5, 3, 1, 6], [2, 4, 5, 1, 6, 3], [2, 4, 5, 1, 3, 6], [2, 4, 3, 6, 5, 1], [2, 4, 3, 6, 1, 5], [2, 4, 3, 5, 6, 1], [2, 4, 3, 5, 1, 6], [2, 4, 3, 1, 6, 5], [2, 4, 3, 1, 5, 6], [2, 4, 1, 6, 5, 3], [2, 4, 1, 6, 3, 5], [2, 4, 1, 5, 6, 3], [2, 4, 1, 5, 3, 6], [2, 4, 1, 3, 6, 5], [2, 4, 1, 3, 5, 6], [2, 3, 6, 5, 4, 1], [2, 3, 6, 5, 1, 4], [2, 3, 6, 4, 5, 1], [2, 3, 6, 4, 1, 5], [2, 3, 6, 1, 5, 4], [2, 3, 6, 1, 4, 5], [2, 3, 5, 6, 4, 1], [2, 3, 5, 6, 1, 4], [2, 3, 5, 4, 6, 1], [2, 3, 5, 4, 1, 6], [2, 3, 5, 1, 6, 4], [2, 3, 5, 1, 4, 6], [2, 3, 4, 6, 5, 1], [2, 3, 4, 6, 1, 5], [2, 3, 4, 5, 6, 1], [2, 3, 4, 5, 1, 6], [2, 3, 4, 1, 6, 5], [2, 3, 4, 1, 5, 6], [2, 3, 1, 6, 5, 4], [2, 3, 1, 6, 4, 5], [2, 3, 1, 5, 6, 4], [2, 3, 1, 5, 4, 6], [2, 3, 1, 4, 6, 5], [2, 3, 1, 4, 5, 6], [2, 1, 6, 5, 4, 3], [2, 1, 6, 5, 3, 4], [2, 1, 6, 4, 5, 3], [2, 1, 6, 4, 3, 5], [2, 1, 6, 3, 5, 4], [2, 1, 6, 3, 4, 5], [2, 1, 5, 6, 4, 3], [2, 1, 5, 6, 3, 4], [2, 1, 5, 4, 6, 3], [2, 1, 5, 4, 3, 6], [2, 1, 5, 3, 6, 4], [2, 1, 5, 3, 4, 6], [2, 1, 4, 6, 5, 3], [2, 1, 4, 6, 3, 5], [2, 1, 4, 5, 6, 3], [2, 1, 4, 5, 3, 6], [2, 1, 4, 3, 6, 5], [2, 1, 4, 3, 5, 6], [2, 1, 3, 6, 5, 4], [2, 1, 3, 6, 4, 5], [2, 1, 3, 5, 6, 4], [2, 1, 3, 5, 4, 6], [2, 1, 3, 4, 6, 5], [2, 1, 3, 4, 5, 6], [1, 6, 5, 4, 3, 2], [1, 6, 5, 4, 2, 3], [1, 6, 5, 3, 4, 2], [1, 6, 5, 3, 2, 4], [1, 6, 5, 2, 4, 3], [1, 6, 5, 2, 3, 4], [1, 6, 4, 5, 3, 2], [1, 6, 4, 5, 2, 3], [1, 6, 4, 3, 5, 2], [1, 6, 4, 3, 2, 5], [1, 6, 4, 2, 5, 3], [1, 6, 4, 2, 3, 5], [1, 6, 3, 5, 4, 2], [1, 6, 3, 5, 2, 4], [1, 6, 3, 4, 5, 2], [1, 6, 3, 4, 2, 5], [1, 6, 3, 2, 5, 4], [1, 6, 3, 2, 4, 5], [1, 6, 2, 5, 4, 3], [1, 6, 2, 5, 3, 4], [1, 6, 2, 4, 5, 3], [1, 6, 2, 4, 3, 5], [1, 6, 2, 3, 5, 4], [1, 6, 2, 3, 4, 5], [1, 5, 6, 4, 3, 2], [1, 5, 6, 4, 2, 3], [1, 5, 6, 3, 4, 2], [1, 5, 6, 3, 2, 4], [1, 5, 6, 2, 4, 3], [1, 5, 6, 2, 3, 4], [1, 5, 4, 6, 3, 2], [1, 5, 4, 6, 2, 3], [1, 5, 4, 3, 6, 2], [1, 5, 4, 3, 2, 6], [1, 5, 4, 2, 6, 3], [1, 5, 4, 2, 3, 6], [1, 5, 3, 6, 4, 2], [1, 5, 3, 6, 2, 4], [1, 5, 3, 4, 6, 2], [1, 5, 3, 4, 2, 6], [1, 5, 3, 2, 6, 4], [1, 5, 3, 2, 4, 6], [1, 5, 2, 6, 4, 3], [1, 5, 2, 6, 3, 4], [1, 5, 2, 4, 6, 3], [1, 5, 2, 4, 3, 6], [1, 5, 2, 3, 6, 4], [1, 5, 2, 3, 4, 6], [1, 4, 6, 5, 3, 2], [1, 4, 6, 5, 2, 3], [1, 4, 6, 3, 5, 2], [1, 4, 6, 3, 2, 5], [1, 4, 6, 2, 5, 3], [1, 4, 6, 2, 3, 5], [1, 4, 5, 6, 3, 2], [1, 4, 5, 6, 2, 3], [1, 4, 5, 3, 6, 2], [1, 4, 5, 3, 2, 6], [1, 4, 5, 2, 6, 3], [1, 4, 5, 2, 3, 6], [1, 4, 3, 6, 5, 2], [1, 4, 3, 6, 2, 5], [1, 4, 3, 5, 6, 2], [1, 4, 3, 5, 2, 6], [1, 4, 3, 2, 6, 5], [1, 4, 3, 2, 5, 6], [1, 4, 2, 6, 5, 3], [1, 4, 2, 6, 3, 5], [1, 4, 2, 5, 6, 3], [1, 4, 2, 5, 3, 6], [1, 4, 2, 3, 6, 5], [1, 4, 2, 3, 5, 6], [1, 3, 6, 5, 4, 2], [1, 3, 6, 5, 2, 4], [1, 3, 6, 4, 5, 2], [1, 3, 6, 4, 2, 5], [1, 3, 6, 2, 5, 4], [1, 3, 6, 2, 4, 5], [1, 3, 5, 6, 4, 2], [1, 3, 5, 6, 2, 4], [1, 3, 5, 4, 6, 2], [1, 3, 5, 4, 2, 6], [1, 3, 5, 2, 6, 4], [1, 3, 5, 2, 4, 6], [1, 3, 4, 6, 5, 2], [1, 3, 4, 6, 2, 5], [1, 3, 4, 5, 6, 2], [1, 3, 4, 5, 2, 6], [1, 3, 4, 2, 6, 5], [1, 3, 4, 2, 5, 6], [1, 3, 2, 6, 5, 4], [1, 3, 2, 6, 4, 5], [1, 3, 2, 5, 6, 4], [1, 3, 2, 5, 4, 6], [1, 3, 2, 4, 6, 5], [1, 3, 2, 4, 5, 6], [1, 2, 6, 5, 4, 3], [1, 2, 6, 5, 3, 4], [1, 2, 6, 4, 5, 3], [1, 2, 6, 4, 3, 5], [1, 2, 6, 3, 5, 4], [1, 2, 6, 3, 4, 5], [1, 2, 5, 6, 4, 3], [1, 2, 5, 6, 3, 4], [1, 2, 5, 4, 6, 3], [1, 2, 5, 4, 3, 6], [1, 2, 5, 3, 6, 4], [1, 2, 5, 3, 4, 6], [1, 2, 4, 6, 5, 3], [1, 2, 4, 6, 3, 5], [1, 2, 4, 5, 6, 3], [1, 2, 4, 5, 3, 6], [1, 2, 4, 3, 6, 5], [1, 2, 4, 3, 5, 6], [1, 2, 3, 6, 5, 4], [1, 2, 3, 6, 4, 5], [1, 2, 3, 5, 6, 4], [1, 2, 3, 5, 4, 6], [1, 2, 3, 4, 6, 5], [1, 2, 3, 4, 5, 6]]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().permute", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var permute = function(nums) {", "container": null, "callable": "permute", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 47, "task_id": "permutations-ii", "difficulty": "Medium", "problem_description": "Given a collection of numbers, nums, that might contain duplicates, return all possible unique permutations in any order.\n \nExample 1:\n\nInput: nums = [1,1,2]\nOutput:\n[[1,1,2],\n [1,2,1],\n [2,1,1]]\n\nExample 2:\n\nInput: nums = [1,2,3]\nOutput: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]\n\n \nConstraints:\n\n1 <= nums.length <= 8\n-10 <= nums[i] <= 10\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 1, 0, 0, 9]) == [[0, 0, 0, 1, 9], [0, 0, 0, 9, 1], [0, 0, 1, 0, 9], [0, 0, 1, 9, 0], [0, 0, 9, 0, 1], [0, 0, 9, 1, 0], [0, 1, 0, 0, 9], [0, 1, 0, 9, 0], [0, 1, 9, 0, 0], [0, 9, 0, 0, 1], [0, 9, 0, 1, 0], [0, 9, 1, 0, 0], [1, 0, 0, 0, 9], [1, 0, 0, 9, 0], [1, 0, 9, 0, 0], [1, 9, 0, 0, 0], [9, 0, 0, 0, 1], [9, 0, 0, 1, 0], [9, 0, 1, 0, 0], [9, 1, 0, 0, 0]]\n assert candidate(nums = [1, 1, 1, 1]) == [[1, 1, 1, 1]]\n assert candidate(nums = [1, 1, 1]) == [[1, 1, 1]]\n assert candidate(nums = [-1, 2, -1, 2]) == [[-1, -1, 2, 2], [-1, 2, -1, 2], [-1, 2, 2, -1], [2, -1, -1, 2], [2, -1, 2, -1], [2, 2, -1, -1]]\n assert candidate(nums = [3, 3, 0, 3]) == [[0, 3, 3, 3], [3, 0, 3, 3], [3, 3, 0, 3], [3, 3, 3, 0]]\n assert candidate(nums = [0, 1, 0, 0, 1]) == [[0, 0, 0, 1, 1], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 1, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 1, 0], [1, 0, 1, 0, 0], [1, 1, 0, 0, 0]]\n assert candidate(nums = [1]) == [[1]]\n assert candidate(nums = [4, 4, 4]) == [[4, 4, 4]]\n assert candidate(nums = [1, 2, 2]) == [[1, 2, 2], [2, 1, 2], [2, 2, 1]]\n assert candidate(nums = [1, 1, 1, 2]) == [[1, 1, 1, 2], [1, 1, 2, 1], [1, 2, 1, 1], [2, 1, 1, 1]]\n assert candidate(nums = [1, 1, 2]) == [[1, 1, 2], [1, 2, 1], [2, 1, 1]]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7]) == [[7, 7, 7, 7, 7, 7, 7, 7]]\n assert candidate(nums = [1, -1, 1, 1]) == [[-1, 1, 1, 1], [1, -1, 1, 1], [1, 1, -1, 1], [1, 1, 1, -1]]\n assert candidate(nums = [2, 2, 2, 1, 1]) == [[1, 1, 2, 2, 2], [1, 2, 1, 2, 2], [1, 2, 2, 1, 2], [1, 2, 2, 2, 1], [2, 1, 1, 2, 2], [2, 1, 2, 1, 2], [2, 1, 2, 2, 1], [2, 2, 1, 1, 2], [2, 2, 1, 2, 1], [2, 2, 2, 1, 1]]\n assert candidate(nums = [0, 1, 0, 0, 9, 6]) == [[0, 0, 0, 1, 6, 9], [0, 0, 0, 1, 9, 6], [0, 0, 0, 6, 1, 9], [0, 0, 0, 6, 9, 1], [0, 0, 0, 9, 1, 6], [0, 0, 0, 9, 6, 1], [0, 0, 1, 0, 6, 9], [0, 0, 1, 0, 9, 6], [0, 0, 1, 6, 0, 9], [0, 0, 1, 6, 9, 0], [0, 0, 1, 9, 0, 6], [0, 0, 1, 9, 6, 0], [0, 0, 6, 0, 1, 9], [0, 0, 6, 0, 9, 1], [0, 0, 6, 1, 0, 9], [0, 0, 6, 1, 9, 0], [0, 0, 6, 9, 0, 1], [0, 0, 6, 9, 1, 0], [0, 0, 9, 0, 1, 6], [0, 0, 9, 0, 6, 1], [0, 0, 9, 1, 0, 6], [0, 0, 9, 1, 6, 0], [0, 0, 9, 6, 0, 1], [0, 0, 9, 6, 1, 0], [0, 1, 0, 0, 6, 9], [0, 1, 0, 0, 9, 6], [0, 1, 0, 6, 0, 9], [0, 1, 0, 6, 9, 0], [0, 1, 0, 9, 0, 6], [0, 1, 0, 9, 6, 0], [0, 1, 6, 0, 0, 9], [0, 1, 6, 0, 9, 0], [0, 1, 6, 9, 0, 0], [0, 1, 9, 0, 0, 6], [0, 1, 9, 0, 6, 0], [0, 1, 9, 6, 0, 0], [0, 6, 0, 0, 1, 9], [0, 6, 0, 0, 9, 1], [0, 6, 0, 1, 0, 9], [0, 6, 0, 1, 9, 0], [0, 6, 0, 9, 0, 1], [0, 6, 0, 9, 1, 0], [0, 6, 1, 0, 0, 9], [0, 6, 1, 0, 9, 0], [0, 6, 1, 9, 0, 0], [0, 6, 9, 0, 0, 1], [0, 6, 9, 0, 1, 0], [0, 6, 9, 1, 0, 0], [0, 9, 0, 0, 1, 6], [0, 9, 0, 0, 6, 1], [0, 9, 0, 1, 0, 6], [0, 9, 0, 1, 6, 0], [0, 9, 0, 6, 0, 1], [0, 9, 0, 6, 1, 0], [0, 9, 1, 0, 0, 6], [0, 9, 1, 0, 6, 0], [0, 9, 1, 6, 0, 0], [0, 9, 6, 0, 0, 1], [0, 9, 6, 0, 1, 0], [0, 9, 6, 1, 0, 0], [1, 0, 0, 0, 6, 9], [1, 0, 0, 0, 9, 6], [1, 0, 0, 6, 0, 9], [1, 0, 0, 6, 9, 0], [1, 0, 0, 9, 0, 6], [1, 0, 0, 9, 6, 0], [1, 0, 6, 0, 0, 9], [1, 0, 6, 0, 9, 0], [1, 0, 6, 9, 0, 0], [1, 0, 9, 0, 0, 6], [1, 0, 9, 0, 6, 0], [1, 0, 9, 6, 0, 0], [1, 6, 0, 0, 0, 9], [1, 6, 0, 0, 9, 0], [1, 6, 0, 9, 0, 0], [1, 6, 9, 0, 0, 0], [1, 9, 0, 0, 0, 6], [1, 9, 0, 0, 6, 0], [1, 9, 0, 6, 0, 0], [1, 9, 6, 0, 0, 0], [6, 0, 0, 0, 1, 9], [6, 0, 0, 0, 9, 1], [6, 0, 0, 1, 0, 9], [6, 0, 0, 1, 9, 0], [6, 0, 0, 9, 0, 1], [6, 0, 0, 9, 1, 0], [6, 0, 1, 0, 0, 9], [6, 0, 1, 0, 9, 0], [6, 0, 1, 9, 0, 0], [6, 0, 9, 0, 0, 1], [6, 0, 9, 0, 1, 0], [6, 0, 9, 1, 0, 0], [6, 1, 0, 0, 0, 9], [6, 1, 0, 0, 9, 0], [6, 1, 0, 9, 0, 0], [6, 1, 9, 0, 0, 0], [6, 9, 0, 0, 0, 1], [6, 9, 0, 0, 1, 0], [6, 9, 0, 1, 0, 0], [6, 9, 1, 0, 0, 0], [9, 0, 0, 0, 1, 6], [9, 0, 0, 0, 6, 1], [9, 0, 0, 1, 0, 6], [9, 0, 0, 1, 6, 0], [9, 0, 0, 6, 0, 1], [9, 0, 0, 6, 1, 0], [9, 0, 1, 0, 0, 6], [9, 0, 1, 0, 6, 0], [9, 0, 1, 6, 0, 0], [9, 0, 6, 0, 0, 1], [9, 0, 6, 0, 1, 0], [9, 0, 6, 1, 0, 0], [9, 1, 0, 0, 0, 6], [9, 1, 0, 0, 6, 0], [9, 1, 0, 6, 0, 0], [9, 1, 6, 0, 0, 0], [9, 6, 0, 0, 0, 1], [9, 6, 0, 0, 1, 0], [9, 6, 0, 1, 0, 0], [9, 6, 1, 0, 0, 0]]\n assert candidate(nums = [0, 1, 0, 0, 9, 6, 7]) == [[0, 0, 0, 1, 6, 7, 9], [0, 0, 0, 1, 6, 9, 7], [0, 0, 0, 1, 7, 6, 9], [0, 0, 0, 1, 7, 9, 6], [0, 0, 0, 1, 9, 6, 7], [0, 0, 0, 1, 9, 7, 6], [0, 0, 0, 6, 1, 7, 9], [0, 0, 0, 6, 1, 9, 7], [0, 0, 0, 6, 7, 1, 9], [0, 0, 0, 6, 7, 9, 1], [0, 0, 0, 6, 9, 1, 7], [0, 0, 0, 6, 9, 7, 1], [0, 0, 0, 7, 1, 6, 9], [0, 0, 0, 7, 1, 9, 6], [0, 0, 0, 7, 6, 1, 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0], [6, 0, 9, 7, 0, 0, 1], [6, 0, 9, 7, 0, 1, 0], [6, 0, 9, 7, 1, 0, 0], [6, 1, 0, 0, 0, 7, 9], [6, 1, 0, 0, 0, 9, 7], [6, 1, 0, 0, 7, 0, 9], [6, 1, 0, 0, 7, 9, 0], [6, 1, 0, 0, 9, 0, 7], [6, 1, 0, 0, 9, 7, 0], [6, 1, 0, 7, 0, 0, 9], [6, 1, 0, 7, 0, 9, 0], [6, 1, 0, 7, 9, 0, 0], [6, 1, 0, 9, 0, 0, 7], [6, 1, 0, 9, 0, 7, 0], [6, 1, 0, 9, 7, 0, 0], [6, 1, 7, 0, 0, 0, 9], [6, 1, 7, 0, 0, 9, 0], [6, 1, 7, 0, 9, 0, 0], [6, 1, 7, 9, 0, 0, 0], [6, 1, 9, 0, 0, 0, 7], [6, 1, 9, 0, 0, 7, 0], [6, 1, 9, 0, 7, 0, 0], [6, 1, 9, 7, 0, 0, 0], [6, 7, 0, 0, 0, 1, 9], [6, 7, 0, 0, 0, 9, 1], [6, 7, 0, 0, 1, 0, 9], [6, 7, 0, 0, 1, 9, 0], [6, 7, 0, 0, 9, 0, 1], [6, 7, 0, 0, 9, 1, 0], [6, 7, 0, 1, 0, 0, 9], [6, 7, 0, 1, 0, 9, 0], [6, 7, 0, 1, 9, 0, 0], [6, 7, 0, 9, 0, 0, 1], [6, 7, 0, 9, 0, 1, 0], [6, 7, 0, 9, 1, 0, 0], [6, 7, 1, 0, 0, 0, 9], [6, 7, 1, 0, 0, 9, 0], [6, 7, 1, 0, 9, 0, 0], [6, 7, 1, 9, 0, 0, 0], [6, 7, 9, 0, 0, 0, 1], [6, 7, 9, 0, 0, 1, 0], [6, 7, 9, 0, 1, 0, 0], [6, 7, 9, 1, 0, 0, 0], [6, 9, 0, 0, 0, 1, 7], [6, 9, 0, 0, 0, 7, 1], [6, 9, 0, 0, 1, 0, 7], [6, 9, 0, 0, 1, 7, 0], [6, 9, 0, 0, 7, 0, 1], [6, 9, 0, 0, 7, 1, 0], [6, 9, 0, 1, 0, 0, 7], [6, 9, 0, 1, 0, 7, 0], [6, 9, 0, 1, 7, 0, 0], [6, 9, 0, 7, 0, 0, 1], [6, 9, 0, 7, 0, 1, 0], [6, 9, 0, 7, 1, 0, 0], [6, 9, 1, 0, 0, 0, 7], [6, 9, 1, 0, 0, 7, 0], [6, 9, 1, 0, 7, 0, 0], [6, 9, 1, 7, 0, 0, 0], [6, 9, 7, 0, 0, 0, 1], [6, 9, 7, 0, 0, 1, 0], [6, 9, 7, 0, 1, 0, 0], [6, 9, 7, 1, 0, 0, 0], [7, 0, 0, 0, 1, 6, 9], [7, 0, 0, 0, 1, 9, 6], [7, 0, 0, 0, 6, 1, 9], [7, 0, 0, 0, 6, 9, 1], [7, 0, 0, 0, 9, 1, 6], [7, 0, 0, 0, 9, 6, 1], [7, 0, 0, 1, 0, 6, 9], [7, 0, 0, 1, 0, 9, 6], [7, 0, 0, 1, 6, 0, 9], [7, 0, 0, 1, 6, 9, 0], [7, 0, 0, 1, 9, 0, 6], [7, 0, 0, 1, 9, 6, 0], [7, 0, 0, 6, 0, 1, 9], [7, 0, 0, 6, 0, 9, 1], [7, 0, 0, 6, 1, 0, 9], [7, 0, 0, 6, 1, 9, 0], [7, 0, 0, 6, 9, 0, 1], [7, 0, 0, 6, 9, 1, 0], [7, 0, 0, 9, 0, 1, 6], [7, 0, 0, 9, 0, 6, 1], [7, 0, 0, 9, 1, 0, 6], [7, 0, 0, 9, 1, 6, 0], [7, 0, 0, 9, 6, 0, 1], [7, 0, 0, 9, 6, 1, 0], [7, 0, 1, 0, 0, 6, 9], [7, 0, 1, 0, 0, 9, 6], [7, 0, 1, 0, 6, 0, 9], [7, 0, 1, 0, 6, 9, 0], [7, 0, 1, 0, 9, 0, 6], [7, 0, 1, 0, 9, 6, 0], [7, 0, 1, 6, 0, 0, 9], [7, 0, 1, 6, 0, 9, 0], [7, 0, 1, 6, 9, 0, 0], [7, 0, 1, 9, 0, 0, 6], [7, 0, 1, 9, 0, 6, 0], [7, 0, 1, 9, 6, 0, 0], [7, 0, 6, 0, 0, 1, 9], [7, 0, 6, 0, 0, 9, 1], [7, 0, 6, 0, 1, 0, 9], [7, 0, 6, 0, 1, 9, 0], [7, 0, 6, 0, 9, 0, 1], [7, 0, 6, 0, 9, 1, 0], [7, 0, 6, 1, 0, 0, 9], [7, 0, 6, 1, 0, 9, 0], [7, 0, 6, 1, 9, 0, 0], [7, 0, 6, 9, 0, 0, 1], [7, 0, 6, 9, 0, 1, 0], [7, 0, 6, 9, 1, 0, 0], [7, 0, 9, 0, 0, 1, 6], [7, 0, 9, 0, 0, 6, 1], [7, 0, 9, 0, 1, 0, 6], [7, 0, 9, 0, 1, 6, 0], [7, 0, 9, 0, 6, 0, 1], [7, 0, 9, 0, 6, 1, 0], [7, 0, 9, 1, 0, 0, 6], [7, 0, 9, 1, 0, 6, 0], [7, 0, 9, 1, 6, 0, 0], [7, 0, 9, 6, 0, 0, 1], [7, 0, 9, 6, 0, 1, 0], [7, 0, 9, 6, 1, 0, 0], [7, 1, 0, 0, 0, 6, 9], [7, 1, 0, 0, 0, 9, 6], [7, 1, 0, 0, 6, 0, 9], [7, 1, 0, 0, 6, 9, 0], [7, 1, 0, 0, 9, 0, 6], [7, 1, 0, 0, 9, 6, 0], [7, 1, 0, 6, 0, 0, 9], [7, 1, 0, 6, 0, 9, 0], [7, 1, 0, 6, 9, 0, 0], [7, 1, 0, 9, 0, 0, 6], [7, 1, 0, 9, 0, 6, 0], [7, 1, 0, 9, 6, 0, 0], [7, 1, 6, 0, 0, 0, 9], [7, 1, 6, 0, 0, 9, 0], [7, 1, 6, 0, 9, 0, 0], [7, 1, 6, 9, 0, 0, 0], [7, 1, 9, 0, 0, 0, 6], [7, 1, 9, 0, 0, 6, 0], [7, 1, 9, 0, 6, 0, 0], [7, 1, 9, 6, 0, 0, 0], [7, 6, 0, 0, 0, 1, 9], [7, 6, 0, 0, 0, 9, 1], [7, 6, 0, 0, 1, 0, 9], [7, 6, 0, 0, 1, 9, 0], [7, 6, 0, 0, 9, 0, 1], [7, 6, 0, 0, 9, 1, 0], [7, 6, 0, 1, 0, 0, 9], [7, 6, 0, 1, 0, 9, 0], [7, 6, 0, 1, 9, 0, 0], [7, 6, 0, 9, 0, 0, 1], [7, 6, 0, 9, 0, 1, 0], [7, 6, 0, 9, 1, 0, 0], [7, 6, 1, 0, 0, 0, 9], [7, 6, 1, 0, 0, 9, 0], [7, 6, 1, 0, 9, 0, 0], [7, 6, 1, 9, 0, 0, 0], [7, 6, 9, 0, 0, 0, 1], [7, 6, 9, 0, 0, 1, 0], [7, 6, 9, 0, 1, 0, 0], [7, 6, 9, 1, 0, 0, 0], [7, 9, 0, 0, 0, 1, 6], [7, 9, 0, 0, 0, 6, 1], [7, 9, 0, 0, 1, 0, 6], [7, 9, 0, 0, 1, 6, 0], [7, 9, 0, 0, 6, 0, 1], [7, 9, 0, 0, 6, 1, 0], [7, 9, 0, 1, 0, 0, 6], [7, 9, 0, 1, 0, 6, 0], [7, 9, 0, 1, 6, 0, 0], [7, 9, 0, 6, 0, 0, 1], [7, 9, 0, 6, 0, 1, 0], [7, 9, 0, 6, 1, 0, 0], [7, 9, 1, 0, 0, 0, 6], [7, 9, 1, 0, 0, 6, 0], [7, 9, 1, 0, 6, 0, 0], [7, 9, 1, 6, 0, 0, 0], [7, 9, 6, 0, 0, 0, 1], [7, 9, 6, 0, 0, 1, 0], [7, 9, 6, 0, 1, 0, 0], [7, 9, 6, 1, 0, 0, 0], [9, 0, 0, 0, 1, 6, 7], [9, 0, 0, 0, 1, 7, 6], [9, 0, 0, 0, 6, 1, 7], [9, 0, 0, 0, 6, 7, 1], [9, 0, 0, 0, 7, 1, 6], [9, 0, 0, 0, 7, 6, 1], [9, 0, 0, 1, 0, 6, 7], [9, 0, 0, 1, 0, 7, 6], [9, 0, 0, 1, 6, 0, 7], [9, 0, 0, 1, 6, 7, 0], [9, 0, 0, 1, 7, 0, 6], [9, 0, 0, 1, 7, 6, 0], [9, 0, 0, 6, 0, 1, 7], [9, 0, 0, 6, 0, 7, 1], [9, 0, 0, 6, 1, 0, 7], [9, 0, 0, 6, 1, 7, 0], [9, 0, 0, 6, 7, 0, 1], [9, 0, 0, 6, 7, 1, 0], [9, 0, 0, 7, 0, 1, 6], [9, 0, 0, 7, 0, 6, 1], [9, 0, 0, 7, 1, 0, 6], [9, 0, 0, 7, 1, 6, 0], [9, 0, 0, 7, 6, 0, 1], [9, 0, 0, 7, 6, 1, 0], [9, 0, 1, 0, 0, 6, 7], [9, 0, 1, 0, 0, 7, 6], [9, 0, 1, 0, 6, 0, 7], [9, 0, 1, 0, 6, 7, 0], [9, 0, 1, 0, 7, 0, 6], [9, 0, 1, 0, 7, 6, 0], [9, 0, 1, 6, 0, 0, 7], [9, 0, 1, 6, 0, 7, 0], [9, 0, 1, 6, 7, 0, 0], [9, 0, 1, 7, 0, 0, 6], [9, 0, 1, 7, 0, 6, 0], [9, 0, 1, 7, 6, 0, 0], [9, 0, 6, 0, 0, 1, 7], [9, 0, 6, 0, 0, 7, 1], [9, 0, 6, 0, 1, 0, 7], [9, 0, 6, 0, 1, 7, 0], [9, 0, 6, 0, 7, 0, 1], [9, 0, 6, 0, 7, 1, 0], [9, 0, 6, 1, 0, 0, 7], [9, 0, 6, 1, 0, 7, 0], [9, 0, 6, 1, 7, 0, 0], [9, 0, 6, 7, 0, 0, 1], [9, 0, 6, 7, 0, 1, 0], [9, 0, 6, 7, 1, 0, 0], [9, 0, 7, 0, 0, 1, 6], [9, 0, 7, 0, 0, 6, 1], [9, 0, 7, 0, 1, 0, 6], [9, 0, 7, 0, 1, 6, 0], [9, 0, 7, 0, 6, 0, 1], [9, 0, 7, 0, 6, 1, 0], [9, 0, 7, 1, 0, 0, 6], [9, 0, 7, 1, 0, 6, 0], [9, 0, 7, 1, 6, 0, 0], [9, 0, 7, 6, 0, 0, 1], [9, 0, 7, 6, 0, 1, 0], [9, 0, 7, 6, 1, 0, 0], [9, 1, 0, 0, 0, 6, 7], [9, 1, 0, 0, 0, 7, 6], [9, 1, 0, 0, 6, 0, 7], [9, 1, 0, 0, 6, 7, 0], [9, 1, 0, 0, 7, 0, 6], [9, 1, 0, 0, 7, 6, 0], [9, 1, 0, 6, 0, 0, 7], [9, 1, 0, 6, 0, 7, 0], [9, 1, 0, 6, 7, 0, 0], [9, 1, 0, 7, 0, 0, 6], [9, 1, 0, 7, 0, 6, 0], [9, 1, 0, 7, 6, 0, 0], [9, 1, 6, 0, 0, 0, 7], [9, 1, 6, 0, 0, 7, 0], [9, 1, 6, 0, 7, 0, 0], [9, 1, 6, 7, 0, 0, 0], [9, 1, 7, 0, 0, 0, 6], [9, 1, 7, 0, 0, 6, 0], [9, 1, 7, 0, 6, 0, 0], [9, 1, 7, 6, 0, 0, 0], [9, 6, 0, 0, 0, 1, 7], [9, 6, 0, 0, 0, 7, 1], [9, 6, 0, 0, 1, 0, 7], [9, 6, 0, 0, 1, 7, 0], [9, 6, 0, 0, 7, 0, 1], [9, 6, 0, 0, 7, 1, 0], [9, 6, 0, 1, 0, 0, 7], [9, 6, 0, 1, 0, 7, 0], [9, 6, 0, 1, 7, 0, 0], [9, 6, 0, 7, 0, 0, 1], [9, 6, 0, 7, 0, 1, 0], [9, 6, 0, 7, 1, 0, 0], [9, 6, 1, 0, 0, 0, 7], [9, 6, 1, 0, 0, 7, 0], [9, 6, 1, 0, 7, 0, 0], [9, 6, 1, 7, 0, 0, 0], [9, 6, 7, 0, 0, 0, 1], [9, 6, 7, 0, 0, 1, 0], [9, 6, 7, 0, 1, 0, 0], [9, 6, 7, 1, 0, 0, 0], [9, 7, 0, 0, 0, 1, 6], [9, 7, 0, 0, 0, 6, 1], [9, 7, 0, 0, 1, 0, 6], [9, 7, 0, 0, 1, 6, 0], [9, 7, 0, 0, 6, 0, 1], [9, 7, 0, 0, 6, 1, 0], [9, 7, 0, 1, 0, 0, 6], [9, 7, 0, 1, 0, 6, 0], [9, 7, 0, 1, 6, 0, 0], [9, 7, 0, 6, 0, 0, 1], [9, 7, 0, 6, 0, 1, 0], [9, 7, 0, 6, 1, 0, 0], [9, 7, 1, 0, 0, 0, 6], [9, 7, 1, 0, 0, 6, 0], [9, 7, 1, 0, 6, 0, 0], [9, 7, 1, 6, 0, 0, 0], [9, 7, 6, 0, 0, 0, 1], [9, 7, 6, 0, 0, 1, 0], [9, 7, 6, 0, 1, 0, 0], [9, 7, 6, 1, 0, 0, 0]]\n assert candidate(nums = [1, 2, 3]) == [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]\n assert candidate(nums = [-1, 0, 1]) == [[-1, 0, 1], [-1, 1, 0], [0, -1, 1], [0, 1, -1], [1, -1, 0], [1, 0, -1]]\n assert candidate(nums = [0, 1, 1]) == [[0, 1, 1], [1, 0, 1], [1, 1, 0]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0, 0, 0, 0]]\n assert candidate(nums = [1, 1, 2, 2]) == [[1, 1, 2, 2], [1, 2, 1, 2], [1, 2, 2, 1], [2, 1, 1, 2], [2, 1, 2, 1], [2, 2, 1, 1]]\n assert candidate(nums = [1, 2, 3, 3, 4, 4, 5]) == [[1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 5, 4], [1, 2, 3, 3, 5, 4, 4], [1, 2, 3, 4, 3, 4, 5], [1, 2, 3, 4, 3, 5, 4], [1, 2, 3, 4, 4, 3, 5], [1, 2, 3, 4, 4, 5, 3], [1, 2, 3, 4, 5, 3, 4], [1, 2, 3, 4, 5, 4, 3], [1, 2, 3, 5, 3, 4, 4], [1, 2, 3, 5, 4, 3, 4], [1, 2, 3, 5, 4, 4, 3], [1, 2, 4, 3, 3, 4, 5], [1, 2, 4, 3, 3, 5, 4], [1, 2, 4, 3, 4, 3, 5], [1, 2, 4, 3, 4, 5, 3], [1, 2, 4, 3, 5, 3, 4], [1, 2, 4, 3, 5, 4, 3], [1, 2, 4, 4, 3, 3, 5], [1, 2, 4, 4, 3, 5, 3], [1, 2, 4, 4, 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1], [4, 3, 4, 5, 3, 1, 2], [4, 3, 4, 5, 3, 2, 1], [4, 3, 5, 1, 2, 3, 4], [4, 3, 5, 1, 2, 4, 3], [4, 3, 5, 1, 3, 2, 4], [4, 3, 5, 1, 3, 4, 2], [4, 3, 5, 1, 4, 2, 3], [4, 3, 5, 1, 4, 3, 2], [4, 3, 5, 2, 1, 3, 4], [4, 3, 5, 2, 1, 4, 3], [4, 3, 5, 2, 3, 1, 4], [4, 3, 5, 2, 3, 4, 1], [4, 3, 5, 2, 4, 1, 3], [4, 3, 5, 2, 4, 3, 1], [4, 3, 5, 3, 1, 2, 4], [4, 3, 5, 3, 1, 4, 2], [4, 3, 5, 3, 2, 1, 4], [4, 3, 5, 3, 2, 4, 1], [4, 3, 5, 3, 4, 1, 2], [4, 3, 5, 3, 4, 2, 1], [4, 3, 5, 4, 1, 2, 3], [4, 3, 5, 4, 1, 3, 2], [4, 3, 5, 4, 2, 1, 3], [4, 3, 5, 4, 2, 3, 1], [4, 3, 5, 4, 3, 1, 2], [4, 3, 5, 4, 3, 2, 1], [4, 4, 1, 2, 3, 3, 5], [4, 4, 1, 2, 3, 5, 3], [4, 4, 1, 2, 5, 3, 3], [4, 4, 1, 3, 2, 3, 5], [4, 4, 1, 3, 2, 5, 3], [4, 4, 1, 3, 3, 2, 5], [4, 4, 1, 3, 3, 5, 2], [4, 4, 1, 3, 5, 2, 3], [4, 4, 1, 3, 5, 3, 2], [4, 4, 1, 5, 2, 3, 3], [4, 4, 1, 5, 3, 2, 3], [4, 4, 1, 5, 3, 3, 2], [4, 4, 2, 1, 3, 3, 5], [4, 4, 2, 1, 3, 5, 3], [4, 4, 2, 1, 5, 3, 3], [4, 4, 2, 3, 1, 3, 5], [4, 4, 2, 3, 1, 5, 3], [4, 4, 2, 3, 3, 1, 5], [4, 4, 2, 3, 3, 5, 1], [4, 4, 2, 3, 5, 1, 3], [4, 4, 2, 3, 5, 3, 1], [4, 4, 2, 5, 1, 3, 3], [4, 4, 2, 5, 3, 1, 3], [4, 4, 2, 5, 3, 3, 1], [4, 4, 3, 1, 2, 3, 5], [4, 4, 3, 1, 2, 5, 3], [4, 4, 3, 1, 3, 2, 5], [4, 4, 3, 1, 3, 5, 2], [4, 4, 3, 1, 5, 2, 3], [4, 4, 3, 1, 5, 3, 2], [4, 4, 3, 2, 1, 3, 5], [4, 4, 3, 2, 1, 5, 3], [4, 4, 3, 2, 3, 1, 5], [4, 4, 3, 2, 3, 5, 1], [4, 4, 3, 2, 5, 1, 3], [4, 4, 3, 2, 5, 3, 1], [4, 4, 3, 3, 1, 2, 5], [4, 4, 3, 3, 1, 5, 2], [4, 4, 3, 3, 2, 1, 5], [4, 4, 3, 3, 2, 5, 1], [4, 4, 3, 3, 5, 1, 2], [4, 4, 3, 3, 5, 2, 1], [4, 4, 3, 5, 1, 2, 3], [4, 4, 3, 5, 1, 3, 2], [4, 4, 3, 5, 2, 1, 3], [4, 4, 3, 5, 2, 3, 1], [4, 4, 3, 5, 3, 1, 2], [4, 4, 3, 5, 3, 2, 1], [4, 4, 5, 1, 2, 3, 3], [4, 4, 5, 1, 3, 2, 3], [4, 4, 5, 1, 3, 3, 2], [4, 4, 5, 2, 1, 3, 3], [4, 4, 5, 2, 3, 1, 3], [4, 4, 5, 2, 3, 3, 1], [4, 4, 5, 3, 1, 2, 3], [4, 4, 5, 3, 1, 3, 2], [4, 4, 5, 3, 2, 1, 3], [4, 4, 5, 3, 2, 3, 1], [4, 4, 5, 3, 3, 1, 2], [4, 4, 5, 3, 3, 2, 1], [4, 5, 1, 2, 3, 3, 4], [4, 5, 1, 2, 3, 4, 3], [4, 5, 1, 2, 4, 3, 3], [4, 5, 1, 3, 2, 3, 4], [4, 5, 1, 3, 2, 4, 3], [4, 5, 1, 3, 3, 2, 4], [4, 5, 1, 3, 3, 4, 2], [4, 5, 1, 3, 4, 2, 3], [4, 5, 1, 3, 4, 3, 2], [4, 5, 1, 4, 2, 3, 3], [4, 5, 1, 4, 3, 2, 3], [4, 5, 1, 4, 3, 3, 2], [4, 5, 2, 1, 3, 3, 4], [4, 5, 2, 1, 3, 4, 3], [4, 5, 2, 1, 4, 3, 3], [4, 5, 2, 3, 1, 3, 4], [4, 5, 2, 3, 1, 4, 3], [4, 5, 2, 3, 3, 1, 4], [4, 5, 2, 3, 3, 4, 1], [4, 5, 2, 3, 4, 1, 3], [4, 5, 2, 3, 4, 3, 1], [4, 5, 2, 4, 1, 3, 3], [4, 5, 2, 4, 3, 1, 3], [4, 5, 2, 4, 3, 3, 1], [4, 5, 3, 1, 2, 3, 4], [4, 5, 3, 1, 2, 4, 3], [4, 5, 3, 1, 3, 2, 4], [4, 5, 3, 1, 3, 4, 2], [4, 5, 3, 1, 4, 2, 3], [4, 5, 3, 1, 4, 3, 2], [4, 5, 3, 2, 1, 3, 4], [4, 5, 3, 2, 1, 4, 3], [4, 5, 3, 2, 3, 1, 4], [4, 5, 3, 2, 3, 4, 1], [4, 5, 3, 2, 4, 1, 3], [4, 5, 3, 2, 4, 3, 1], [4, 5, 3, 3, 1, 2, 4], [4, 5, 3, 3, 1, 4, 2], [4, 5, 3, 3, 2, 1, 4], [4, 5, 3, 3, 2, 4, 1], [4, 5, 3, 3, 4, 1, 2], [4, 5, 3, 3, 4, 2, 1], [4, 5, 3, 4, 1, 2, 3], [4, 5, 3, 4, 1, 3, 2], [4, 5, 3, 4, 2, 1, 3], [4, 5, 3, 4, 2, 3, 1], [4, 5, 3, 4, 3, 1, 2], [4, 5, 3, 4, 3, 2, 1], [4, 5, 4, 1, 2, 3, 3], [4, 5, 4, 1, 3, 2, 3], [4, 5, 4, 1, 3, 3, 2], [4, 5, 4, 2, 1, 3, 3], [4, 5, 4, 2, 3, 1, 3], [4, 5, 4, 2, 3, 3, 1], [4, 5, 4, 3, 1, 2, 3], [4, 5, 4, 3, 1, 3, 2], [4, 5, 4, 3, 2, 1, 3], [4, 5, 4, 3, 2, 3, 1], [4, 5, 4, 3, 3, 1, 2], [4, 5, 4, 3, 3, 2, 1], [5, 1, 2, 3, 3, 4, 4], [5, 1, 2, 3, 4, 3, 4], [5, 1, 2, 3, 4, 4, 3], [5, 1, 2, 4, 3, 3, 4], [5, 1, 2, 4, 3, 4, 3], [5, 1, 2, 4, 4, 3, 3], [5, 1, 3, 2, 3, 4, 4], [5, 1, 3, 2, 4, 3, 4], [5, 1, 3, 2, 4, 4, 3], [5, 1, 3, 3, 2, 4, 4], [5, 1, 3, 3, 4, 2, 4], [5, 1, 3, 3, 4, 4, 2], [5, 1, 3, 4, 2, 3, 4], [5, 1, 3, 4, 2, 4, 3], [5, 1, 3, 4, 3, 2, 4], [5, 1, 3, 4, 3, 4, 2], [5, 1, 3, 4, 4, 2, 3], [5, 1, 3, 4, 4, 3, 2], [5, 1, 4, 2, 3, 3, 4], [5, 1, 4, 2, 3, 4, 3], [5, 1, 4, 2, 4, 3, 3], [5, 1, 4, 3, 2, 3, 4], [5, 1, 4, 3, 2, 4, 3], [5, 1, 4, 3, 3, 2, 4], [5, 1, 4, 3, 3, 4, 2], [5, 1, 4, 3, 4, 2, 3], [5, 1, 4, 3, 4, 3, 2], [5, 1, 4, 4, 2, 3, 3], [5, 1, 4, 4, 3, 2, 3], [5, 1, 4, 4, 3, 3, 2], [5, 2, 1, 3, 3, 4, 4], [5, 2, 1, 3, 4, 3, 4], [5, 2, 1, 3, 4, 4, 3], [5, 2, 1, 4, 3, 3, 4], [5, 2, 1, 4, 3, 4, 3], [5, 2, 1, 4, 4, 3, 3], [5, 2, 3, 1, 3, 4, 4], [5, 2, 3, 1, 4, 3, 4], [5, 2, 3, 1, 4, 4, 3], [5, 2, 3, 3, 1, 4, 4], [5, 2, 3, 3, 4, 1, 4], [5, 2, 3, 3, 4, 4, 1], [5, 2, 3, 4, 1, 3, 4], [5, 2, 3, 4, 1, 4, 3], [5, 2, 3, 4, 3, 1, 4], [5, 2, 3, 4, 3, 4, 1], [5, 2, 3, 4, 4, 1, 3], [5, 2, 3, 4, 4, 3, 1], [5, 2, 4, 1, 3, 3, 4], [5, 2, 4, 1, 3, 4, 3], [5, 2, 4, 1, 4, 3, 3], [5, 2, 4, 3, 1, 3, 4], [5, 2, 4, 3, 1, 4, 3], [5, 2, 4, 3, 3, 1, 4], [5, 2, 4, 3, 3, 4, 1], [5, 2, 4, 3, 4, 1, 3], [5, 2, 4, 3, 4, 3, 1], [5, 2, 4, 4, 1, 3, 3], [5, 2, 4, 4, 3, 1, 3], [5, 2, 4, 4, 3, 3, 1], [5, 3, 1, 2, 3, 4, 4], [5, 3, 1, 2, 4, 3, 4], [5, 3, 1, 2, 4, 4, 3], [5, 3, 1, 3, 2, 4, 4], [5, 3, 1, 3, 4, 2, 4], [5, 3, 1, 3, 4, 4, 2], [5, 3, 1, 4, 2, 3, 4], [5, 3, 1, 4, 2, 4, 3], [5, 3, 1, 4, 3, 2, 4], [5, 3, 1, 4, 3, 4, 2], [5, 3, 1, 4, 4, 2, 3], [5, 3, 1, 4, 4, 3, 2], [5, 3, 2, 1, 3, 4, 4], [5, 3, 2, 1, 4, 3, 4], [5, 3, 2, 1, 4, 4, 3], [5, 3, 2, 3, 1, 4, 4], [5, 3, 2, 3, 4, 1, 4], [5, 3, 2, 3, 4, 4, 1], [5, 3, 2, 4, 1, 3, 4], [5, 3, 2, 4, 1, 4, 3], [5, 3, 2, 4, 3, 1, 4], [5, 3, 2, 4, 3, 4, 1], [5, 3, 2, 4, 4, 1, 3], [5, 3, 2, 4, 4, 3, 1], [5, 3, 3, 1, 2, 4, 4], [5, 3, 3, 1, 4, 2, 4], [5, 3, 3, 1, 4, 4, 2], [5, 3, 3, 2, 1, 4, 4], [5, 3, 3, 2, 4, 1, 4], [5, 3, 3, 2, 4, 4, 1], [5, 3, 3, 4, 1, 2, 4], [5, 3, 3, 4, 1, 4, 2], [5, 3, 3, 4, 2, 1, 4], [5, 3, 3, 4, 2, 4, 1], [5, 3, 3, 4, 4, 1, 2], [5, 3, 3, 4, 4, 2, 1], [5, 3, 4, 1, 2, 3, 4], [5, 3, 4, 1, 2, 4, 3], [5, 3, 4, 1, 3, 2, 4], [5, 3, 4, 1, 3, 4, 2], [5, 3, 4, 1, 4, 2, 3], [5, 3, 4, 1, 4, 3, 2], [5, 3, 4, 2, 1, 3, 4], [5, 3, 4, 2, 1, 4, 3], [5, 3, 4, 2, 3, 1, 4], [5, 3, 4, 2, 3, 4, 1], [5, 3, 4, 2, 4, 1, 3], [5, 3, 4, 2, 4, 3, 1], [5, 3, 4, 3, 1, 2, 4], [5, 3, 4, 3, 1, 4, 2], [5, 3, 4, 3, 2, 1, 4], [5, 3, 4, 3, 2, 4, 1], [5, 3, 4, 3, 4, 1, 2], [5, 3, 4, 3, 4, 2, 1], [5, 3, 4, 4, 1, 2, 3], [5, 3, 4, 4, 1, 3, 2], [5, 3, 4, 4, 2, 1, 3], [5, 3, 4, 4, 2, 3, 1], [5, 3, 4, 4, 3, 1, 2], [5, 3, 4, 4, 3, 2, 1], [5, 4, 1, 2, 3, 3, 4], [5, 4, 1, 2, 3, 4, 3], [5, 4, 1, 2, 4, 3, 3], [5, 4, 1, 3, 2, 3, 4], [5, 4, 1, 3, 2, 4, 3], [5, 4, 1, 3, 3, 2, 4], [5, 4, 1, 3, 3, 4, 2], [5, 4, 1, 3, 4, 2, 3], [5, 4, 1, 3, 4, 3, 2], [5, 4, 1, 4, 2, 3, 3], [5, 4, 1, 4, 3, 2, 3], [5, 4, 1, 4, 3, 3, 2], [5, 4, 2, 1, 3, 3, 4], [5, 4, 2, 1, 3, 4, 3], [5, 4, 2, 1, 4, 3, 3], [5, 4, 2, 3, 1, 3, 4], [5, 4, 2, 3, 1, 4, 3], [5, 4, 2, 3, 3, 1, 4], [5, 4, 2, 3, 3, 4, 1], [5, 4, 2, 3, 4, 1, 3], [5, 4, 2, 3, 4, 3, 1], [5, 4, 2, 4, 1, 3, 3], [5, 4, 2, 4, 3, 1, 3], [5, 4, 2, 4, 3, 3, 1], [5, 4, 3, 1, 2, 3, 4], [5, 4, 3, 1, 2, 4, 3], [5, 4, 3, 1, 3, 2, 4], [5, 4, 3, 1, 3, 4, 2], [5, 4, 3, 1, 4, 2, 3], [5, 4, 3, 1, 4, 3, 2], [5, 4, 3, 2, 1, 3, 4], [5, 4, 3, 2, 1, 4, 3], [5, 4, 3, 2, 3, 1, 4], [5, 4, 3, 2, 3, 4, 1], [5, 4, 3, 2, 4, 1, 3], [5, 4, 3, 2, 4, 3, 1], [5, 4, 3, 3, 1, 2, 4], [5, 4, 3, 3, 1, 4, 2], [5, 4, 3, 3, 2, 1, 4], [5, 4, 3, 3, 2, 4, 1], [5, 4, 3, 3, 4, 1, 2], [5, 4, 3, 3, 4, 2, 1], [5, 4, 3, 4, 1, 2, 3], [5, 4, 3, 4, 1, 3, 2], [5, 4, 3, 4, 2, 1, 3], [5, 4, 3, 4, 2, 3, 1], [5, 4, 3, 4, 3, 1, 2], [5, 4, 3, 4, 3, 2, 1], [5, 4, 4, 1, 2, 3, 3], [5, 4, 4, 1, 3, 2, 3], [5, 4, 4, 1, 3, 3, 2], [5, 4, 4, 2, 1, 3, 3], [5, 4, 4, 2, 3, 1, 3], [5, 4, 4, 2, 3, 3, 1], [5, 4, 4, 3, 1, 2, 3], [5, 4, 4, 3, 1, 3, 2], [5, 4, 4, 3, 2, 1, 3], [5, 4, 4, 3, 2, 3, 1], [5, 4, 4, 3, 3, 1, 2], [5, 4, 4, 3, 3, 2, 1]]\n assert candidate(nums = [1, 2, 3, 4]) == [[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10]) == [[10, 10, 10, 10, 10, 10, 10, 10]]\n assert candidate(nums = [6, 6, 6, 6, 6, 6, 6]) == [[6, 6, 6, 6, 6, 6, 6]]\n assert candidate(nums = [1, 2, 2, 3, 3, 3]) == [[1, 2, 2, 3, 3, 3], [1, 2, 3, 2, 3, 3], [1, 2, 3, 3, 2, 3], [1, 2, 3, 3, 3, 2], [1, 3, 2, 2, 3, 3], [1, 3, 2, 3, 2, 3], [1, 3, 2, 3, 3, 2], [1, 3, 3, 2, 2, 3], [1, 3, 3, 2, 3, 2], [1, 3, 3, 3, 2, 2], [2, 1, 2, 3, 3, 3], [2, 1, 3, 2, 3, 3], [2, 1, 3, 3, 2, 3], [2, 1, 3, 3, 3, 2], [2, 2, 1, 3, 3, 3], [2, 2, 3, 1, 3, 3], [2, 2, 3, 3, 1, 3], [2, 2, 3, 3, 3, 1], [2, 3, 1, 2, 3, 3], [2, 3, 1, 3, 2, 3], [2, 3, 1, 3, 3, 2], [2, 3, 2, 1, 3, 3], [2, 3, 2, 3, 1, 3], [2, 3, 2, 3, 3, 1], [2, 3, 3, 1, 2, 3], [2, 3, 3, 1, 3, 2], [2, 3, 3, 2, 1, 3], [2, 3, 3, 2, 3, 1], [2, 3, 3, 3, 1, 2], [2, 3, 3, 3, 2, 1], [3, 1, 2, 2, 3, 3], [3, 1, 2, 3, 2, 3], [3, 1, 2, 3, 3, 2], [3, 1, 3, 2, 2, 3], [3, 1, 3, 2, 3, 2], [3, 1, 3, 3, 2, 2], [3, 2, 1, 2, 3, 3], [3, 2, 1, 3, 2, 3], [3, 2, 1, 3, 3, 2], [3, 2, 2, 1, 3, 3], [3, 2, 2, 3, 1, 3], [3, 2, 2, 3, 3, 1], [3, 2, 3, 1, 2, 3], [3, 2, 3, 1, 3, 2], [3, 2, 3, 2, 1, 3], [3, 2, 3, 2, 3, 1], [3, 2, 3, 3, 1, 2], [3, 2, 3, 3, 2, 1], [3, 3, 1, 2, 2, 3], [3, 3, 1, 2, 3, 2], [3, 3, 1, 3, 2, 2], [3, 3, 2, 1, 2, 3], [3, 3, 2, 1, 3, 2], [3, 3, 2, 2, 1, 3], [3, 3, 2, 2, 3, 1], [3, 3, 2, 3, 1, 2], [3, 3, 2, 3, 2, 1], [3, 3, 3, 1, 2, 2], [3, 3, 3, 2, 1, 2], [3, 3, 3, 2, 2, 1]]\n assert candidate(nums = [6, 6, 6, 6, 6, 6, 6, 6]) == [[6, 6, 6, 6, 6, 6, 6, 6]]\n assert candidate(nums = [1, 2, 2, 3, 4]) == [[1, 2, 2, 3, 4], [1, 2, 2, 4, 3], [1, 2, 3, 2, 4], [1, 2, 3, 4, 2], [1, 2, 4, 2, 3], [1, 2, 4, 3, 2], [1, 3, 2, 2, 4], [1, 3, 2, 4, 2], [1, 3, 4, 2, 2], [1, 4, 2, 2, 3], [1, 4, 2, 3, 2], [1, 4, 3, 2, 2], [2, 1, 2, 3, 4], [2, 1, 2, 4, 3], [2, 1, 3, 2, 4], [2, 1, 3, 4, 2], [2, 1, 4, 2, 3], [2, 1, 4, 3, 2], [2, 2, 1, 3, 4], [2, 2, 1, 4, 3], [2, 2, 3, 1, 4], [2, 2, 3, 4, 1], [2, 2, 4, 1, 3], [2, 2, 4, 3, 1], [2, 3, 1, 2, 4], [2, 3, 1, 4, 2], [2, 3, 2, 1, 4], [2, 3, 2, 4, 1], [2, 3, 4, 1, 2], [2, 3, 4, 2, 1], [2, 4, 1, 2, 3], [2, 4, 1, 3, 2], [2, 4, 2, 1, 3], [2, 4, 2, 3, 1], [2, 4, 3, 1, 2], [2, 4, 3, 2, 1], [3, 1, 2, 2, 4], [3, 1, 2, 4, 2], [3, 1, 4, 2, 2], [3, 2, 1, 2, 4], [3, 2, 1, 4, 2], [3, 2, 2, 1, 4], [3, 2, 2, 4, 1], [3, 2, 4, 1, 2], [3, 2, 4, 2, 1], [3, 4, 1, 2, 2], [3, 4, 2, 1, 2], [3, 4, 2, 2, 1], [4, 1, 2, 2, 3], [4, 1, 2, 3, 2], [4, 1, 3, 2, 2], [4, 2, 1, 2, 3], [4, 2, 1, 3, 2], [4, 2, 2, 1, 3], [4, 2, 2, 3, 1], [4, 2, 3, 1, 2], [4, 2, 3, 2, 1], [4, 3, 1, 2, 2], [4, 3, 2, 1, 2], [4, 3, 2, 2, 1]]\n assert candidate(nums = [10, -10, 0, 10, -10]) == [[-10, -10, 0, 10, 10], [-10, -10, 10, 0, 10], [-10, -10, 10, 10, 0], [-10, 0, -10, 10, 10], [-10, 0, 10, -10, 10], [-10, 0, 10, 10, -10], [-10, 10, -10, 0, 10], [-10, 10, -10, 10, 0], [-10, 10, 0, -10, 10], [-10, 10, 0, 10, -10], [-10, 10, 10, -10, 0], [-10, 10, 10, 0, -10], [0, -10, -10, 10, 10], [0, -10, 10, -10, 10], [0, -10, 10, 10, -10], [0, 10, -10, -10, 10], [0, 10, -10, 10, -10], [0, 10, 10, -10, -10], [10, -10, -10, 0, 10], [10, -10, -10, 10, 0], [10, -10, 0, -10, 10], [10, -10, 0, 10, -10], [10, -10, 10, -10, 0], [10, -10, 10, 0, -10], [10, 0, -10, -10, 10], [10, 0, -10, 10, -10], [10, 0, 10, -10, -10], [10, 10, -10, -10, 0], [10, 10, -10, 0, -10], [10, 10, 0, -10, -10]]\n assert candidate(nums = [8, 8, 8, 8, 8, 8, 8, 8]) == [[8, 8, 8, 8, 8, 8, 8, 8]]\n assert candidate(nums = [0, 1, 0, 1, 0, 1]) == [[0, 0, 0, 1, 1, 1], [0, 0, 1, 0, 1, 1], [0, 0, 1, 1, 0, 1], [0, 0, 1, 1, 1, 0], [0, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 1, 0], [0, 1, 1, 0, 0, 1], [0, 1, 1, 0, 1, 0], [0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 1, 1], [1, 0, 0, 1, 0, 1], [1, 0, 0, 1, 1, 0], [1, 0, 1, 0, 0, 1], [1, 0, 1, 0, 1, 0], [1, 0, 1, 1, 0, 0], [1, 1, 0, 0, 0, 1], [1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0]]\n assert candidate(nums = [4, 4, 4, 4, 4]) == [[4, 4, 4, 4, 4]]\n assert candidate(nums = [0, 1, 0, 1, 0]) == [[0, 0, 0, 1, 1], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 1, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 1, 0], [1, 0, 1, 0, 0], [1, 1, 0, 0, 0]]\n assert candidate(nums = [1, 1, 2, 2, 3, 3]) == [[1, 1, 2, 2, 3, 3], [1, 1, 2, 3, 2, 3], [1, 1, 2, 3, 3, 2], [1, 1, 3, 2, 2, 3], [1, 1, 3, 2, 3, 2], [1, 1, 3, 3, 2, 2], [1, 2, 1, 2, 3, 3], [1, 2, 1, 3, 2, 3], [1, 2, 1, 3, 3, 2], [1, 2, 2, 1, 3, 3], [1, 2, 2, 3, 1, 3], [1, 2, 2, 3, 3, 1], [1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 3, 2], [1, 2, 3, 2, 1, 3], [1, 2, 3, 2, 3, 1], [1, 2, 3, 3, 1, 2], [1, 2, 3, 3, 2, 1], [1, 3, 1, 2, 2, 3], [1, 3, 1, 2, 3, 2], [1, 3, 1, 3, 2, 2], [1, 3, 2, 1, 2, 3], [1, 3, 2, 1, 3, 2], [1, 3, 2, 2, 1, 3], [1, 3, 2, 2, 3, 1], [1, 3, 2, 3, 1, 2], [1, 3, 2, 3, 2, 1], [1, 3, 3, 1, 2, 2], [1, 3, 3, 2, 1, 2], [1, 3, 3, 2, 2, 1], [2, 1, 1, 2, 3, 3], [2, 1, 1, 3, 2, 3], [2, 1, 1, 3, 3, 2], [2, 1, 2, 1, 3, 3], [2, 1, 2, 3, 1, 3], [2, 1, 2, 3, 3, 1], [2, 1, 3, 1, 2, 3], [2, 1, 3, 1, 3, 2], [2, 1, 3, 2, 1, 3], [2, 1, 3, 2, 3, 1], [2, 1, 3, 3, 1, 2], [2, 1, 3, 3, 2, 1], [2, 2, 1, 1, 3, 3], [2, 2, 1, 3, 1, 3], [2, 2, 1, 3, 3, 1], [2, 2, 3, 1, 1, 3], [2, 2, 3, 1, 3, 1], [2, 2, 3, 3, 1, 1], [2, 3, 1, 1, 2, 3], [2, 3, 1, 1, 3, 2], [2, 3, 1, 2, 1, 3], [2, 3, 1, 2, 3, 1], [2, 3, 1, 3, 1, 2], [2, 3, 1, 3, 2, 1], [2, 3, 2, 1, 1, 3], [2, 3, 2, 1, 3, 1], [2, 3, 2, 3, 1, 1], [2, 3, 3, 1, 1, 2], [2, 3, 3, 1, 2, 1], [2, 3, 3, 2, 1, 1], [3, 1, 1, 2, 2, 3], [3, 1, 1, 2, 3, 2], [3, 1, 1, 3, 2, 2], [3, 1, 2, 1, 2, 3], [3, 1, 2, 1, 3, 2], [3, 1, 2, 2, 1, 3], [3, 1, 2, 2, 3, 1], [3, 1, 2, 3, 1, 2], [3, 1, 2, 3, 2, 1], [3, 1, 3, 1, 2, 2], [3, 1, 3, 2, 1, 2], [3, 1, 3, 2, 2, 1], [3, 2, 1, 1, 2, 3], [3, 2, 1, 1, 3, 2], [3, 2, 1, 2, 1, 3], [3, 2, 1, 2, 3, 1], [3, 2, 1, 3, 1, 2], [3, 2, 1, 3, 2, 1], [3, 2, 2, 1, 1, 3], [3, 2, 2, 1, 3, 1], [3, 2, 2, 3, 1, 1], [3, 2, 3, 1, 1, 2], [3, 2, 3, 1, 2, 1], [3, 2, 3, 2, 1, 1], [3, 3, 1, 1, 2, 2], [3, 3, 1, 2, 1, 2], [3, 3, 1, 2, 2, 1], [3, 3, 2, 1, 1, 2], [3, 3, 2, 1, 2, 1], [3, 3, 2, 2, 1, 1]]\n assert candidate(nums = [-10, 10, -10, 10, -10, 10, -10, 10]) == [[-10, -10, -10, -10, 10, 10, 10, 10], [-10, -10, -10, 10, -10, 10, 10, 10], [-10, -10, -10, 10, 10, -10, 10, 10], [-10, -10, -10, 10, 10, 10, -10, 10], [-10, -10, -10, 10, 10, 10, 10, -10], [-10, -10, 10, -10, -10, 10, 10, 10], [-10, -10, 10, -10, 10, -10, 10, 10], [-10, -10, 10, -10, 10, 10, -10, 10], [-10, -10, 10, -10, 10, 10, 10, -10], [-10, -10, 10, 10, -10, -10, 10, 10], [-10, -10, 10, 10, -10, 10, -10, 10], [-10, -10, 10, 10, -10, 10, 10, -10], [-10, -10, 10, 10, 10, -10, -10, 10], [-10, -10, 10, 10, 10, -10, 10, -10], [-10, -10, 10, 10, 10, 10, -10, -10], [-10, 10, -10, -10, -10, 10, 10, 10], [-10, 10, -10, -10, 10, -10, 10, 10], [-10, 10, -10, -10, 10, 10, -10, 10], [-10, 10, -10, -10, 10, 10, 10, -10], [-10, 10, -10, 10, -10, -10, 10, 10], [-10, 10, -10, 10, -10, 10, -10, 10], [-10, 10, -10, 10, -10, 10, 10, -10], [-10, 10, -10, 10, 10, -10, -10, 10], [-10, 10, -10, 10, 10, -10, 10, -10], [-10, 10, -10, 10, 10, 10, -10, -10], [-10, 10, 10, -10, -10, -10, 10, 10], [-10, 10, 10, -10, -10, 10, -10, 10], [-10, 10, 10, -10, -10, 10, 10, -10], [-10, 10, 10, -10, 10, -10, -10, 10], [-10, 10, 10, -10, 10, -10, 10, -10], [-10, 10, 10, -10, 10, 10, -10, -10], [-10, 10, 10, 10, -10, -10, -10, 10], [-10, 10, 10, 10, -10, -10, 10, -10], [-10, 10, 10, 10, -10, 10, -10, -10], [-10, 10, 10, 10, 10, -10, -10, -10], [10, -10, -10, -10, -10, 10, 10, 10], [10, -10, -10, -10, 10, -10, 10, 10], [10, -10, -10, -10, 10, 10, -10, 10], [10, -10, -10, -10, 10, 10, 10, -10], [10, -10, -10, 10, -10, -10, 10, 10], [10, -10, -10, 10, -10, 10, -10, 10], [10, -10, -10, 10, -10, 10, 10, -10], [10, -10, -10, 10, 10, -10, -10, 10], [10, -10, -10, 10, 10, -10, 10, -10], [10, -10, -10, 10, 10, 10, -10, -10], [10, -10, 10, -10, -10, -10, 10, 10], [10, -10, 10, -10, -10, 10, -10, 10], [10, -10, 10, -10, -10, 10, 10, -10], [10, -10, 10, -10, 10, -10, -10, 10], [10, -10, 10, -10, 10, -10, 10, -10], [10, -10, 10, -10, 10, 10, -10, -10], [10, -10, 10, 10, -10, -10, -10, 10], [10, -10, 10, 10, -10, -10, 10, -10], [10, -10, 10, 10, -10, 10, -10, -10], [10, -10, 10, 10, 10, -10, -10, -10], [10, 10, -10, -10, -10, -10, 10, 10], [10, 10, -10, -10, -10, 10, -10, 10], [10, 10, -10, -10, -10, 10, 10, -10], [10, 10, -10, -10, 10, -10, -10, 10], [10, 10, -10, -10, 10, -10, 10, -10], [10, 10, -10, -10, 10, 10, -10, -10], [10, 10, -10, 10, -10, -10, -10, 10], [10, 10, -10, 10, -10, -10, 10, -10], [10, 10, -10, 10, -10, 10, -10, -10], [10, 10, -10, 10, 10, -10, -10, -10], [10, 10, 10, -10, -10, -10, -10, 10], [10, 10, 10, -10, -10, -10, 10, -10], [10, 10, 10, -10, -10, 10, -10, -10], [10, 10, 10, -10, 10, -10, -10, -10], [10, 10, 10, 10, -10, -10, -10, -10]]\n assert candidate(nums = [7, 0, 7, 0, 7, 0]) == [[0, 0, 0, 7, 7, 7], [0, 0, 7, 0, 7, 7], [0, 0, 7, 7, 0, 7], [0, 0, 7, 7, 7, 0], [0, 7, 0, 0, 7, 7], [0, 7, 0, 7, 0, 7], [0, 7, 0, 7, 7, 0], [0, 7, 7, 0, 0, 7], [0, 7, 7, 0, 7, 0], [0, 7, 7, 7, 0, 0], [7, 0, 0, 0, 7, 7], [7, 0, 0, 7, 0, 7], [7, 0, 0, 7, 7, 0], [7, 0, 7, 0, 0, 7], [7, 0, 7, 0, 7, 0], [7, 0, 7, 7, 0, 0], [7, 7, 0, 0, 0, 7], [7, 7, 0, 0, 7, 0], [7, 7, 0, 7, 0, 0], [7, 7, 7, 0, 0, 0]]\n assert candidate(nums = [5, 5, 5, 5]) == [[5, 5, 5, 5]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6]) == [[1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 6, 5], [1, 2, 3, 5, 4, 6], [1, 2, 3, 5, 6, 4], [1, 2, 3, 6, 4, 5], [1, 2, 3, 6, 5, 4], [1, 2, 4, 3, 5, 6], [1, 2, 4, 3, 6, 5], [1, 2, 4, 5, 3, 6], [1, 2, 4, 5, 6, 3], [1, 2, 4, 6, 3, 5], [1, 2, 4, 6, 5, 3], [1, 2, 5, 3, 4, 6], [1, 2, 5, 3, 6, 4], [1, 2, 5, 4, 3, 6], [1, 2, 5, 4, 6, 3], [1, 2, 5, 6, 3, 4], [1, 2, 5, 6, 4, 3], [1, 2, 6, 3, 4, 5], [1, 2, 6, 3, 5, 4], [1, 2, 6, 4, 3, 5], [1, 2, 6, 4, 5, 3], [1, 2, 6, 5, 3, 4], [1, 2, 6, 5, 4, 3], [1, 3, 2, 4, 5, 6], [1, 3, 2, 4, 6, 5], [1, 3, 2, 5, 4, 6], [1, 3, 2, 5, 6, 4], [1, 3, 2, 6, 4, 5], [1, 3, 2, 6, 5, 4], [1, 3, 4, 2, 5, 6], [1, 3, 4, 2, 6, 5], [1, 3, 4, 5, 2, 6], [1, 3, 4, 5, 6, 2], [1, 3, 4, 6, 2, 5], [1, 3, 4, 6, 5, 2], [1, 3, 5, 2, 4, 6], [1, 3, 5, 2, 6, 4], [1, 3, 5, 4, 2, 6], [1, 3, 5, 4, 6, 2], [1, 3, 5, 6, 2, 4], [1, 3, 5, 6, 4, 2], [1, 3, 6, 2, 4, 5], [1, 3, 6, 2, 5, 4], [1, 3, 6, 4, 2, 5], [1, 3, 6, 4, 5, 2], [1, 3, 6, 5, 2, 4], [1, 3, 6, 5, 4, 2], [1, 4, 2, 3, 5, 6], [1, 4, 2, 3, 6, 5], [1, 4, 2, 5, 3, 6], [1, 4, 2, 5, 6, 3], [1, 4, 2, 6, 3, 5], [1, 4, 2, 6, 5, 3], [1, 4, 3, 2, 5, 6], [1, 4, 3, 2, 6, 5], [1, 4, 3, 5, 2, 6], [1, 4, 3, 5, 6, 2], [1, 4, 3, 6, 2, 5], [1, 4, 3, 6, 5, 2], [1, 4, 5, 2, 3, 6], [1, 4, 5, 2, 6, 3], [1, 4, 5, 3, 2, 6], [1, 4, 5, 3, 6, 2], [1, 4, 5, 6, 2, 3], [1, 4, 5, 6, 3, 2], [1, 4, 6, 2, 3, 5], [1, 4, 6, 2, 5, 3], [1, 4, 6, 3, 2, 5], [1, 4, 6, 3, 5, 2], [1, 4, 6, 5, 2, 3], [1, 4, 6, 5, 3, 2], [1, 5, 2, 3, 4, 6], [1, 5, 2, 3, 6, 4], [1, 5, 2, 4, 3, 6], [1, 5, 2, 4, 6, 3], [1, 5, 2, 6, 3, 4], [1, 5, 2, 6, 4, 3], [1, 5, 3, 2, 4, 6], [1, 5, 3, 2, 6, 4], [1, 5, 3, 4, 2, 6], [1, 5, 3, 4, 6, 2], [1, 5, 3, 6, 2, 4], [1, 5, 3, 6, 4, 2], [1, 5, 4, 2, 3, 6], [1, 5, 4, 2, 6, 3], [1, 5, 4, 3, 2, 6], [1, 5, 4, 3, 6, 2], [1, 5, 4, 6, 2, 3], [1, 5, 4, 6, 3, 2], [1, 5, 6, 2, 3, 4], [1, 5, 6, 2, 4, 3], [1, 5, 6, 3, 2, 4], [1, 5, 6, 3, 4, 2], [1, 5, 6, 4, 2, 3], [1, 5, 6, 4, 3, 2], [1, 6, 2, 3, 4, 5], [1, 6, 2, 3, 5, 4], [1, 6, 2, 4, 3, 5], [1, 6, 2, 4, 5, 3], [1, 6, 2, 5, 3, 4], [1, 6, 2, 5, 4, 3], [1, 6, 3, 2, 4, 5], [1, 6, 3, 2, 5, 4], [1, 6, 3, 4, 2, 5], [1, 6, 3, 4, 5, 2], [1, 6, 3, 5, 2, 4], [1, 6, 3, 5, 4, 2], [1, 6, 4, 2, 3, 5], [1, 6, 4, 2, 5, 3], [1, 6, 4, 3, 2, 5], [1, 6, 4, 3, 5, 2], [1, 6, 4, 5, 2, 3], [1, 6, 4, 5, 3, 2], [1, 6, 5, 2, 3, 4], [1, 6, 5, 2, 4, 3], [1, 6, 5, 3, 2, 4], [1, 6, 5, 3, 4, 2], [1, 6, 5, 4, 2, 3], [1, 6, 5, 4, 3, 2], [2, 1, 3, 4, 5, 6], [2, 1, 3, 4, 6, 5], [2, 1, 3, 5, 4, 6], [2, 1, 3, 5, 6, 4], [2, 1, 3, 6, 4, 5], [2, 1, 3, 6, 5, 4], [2, 1, 4, 3, 5, 6], [2, 1, 4, 3, 6, 5], [2, 1, 4, 5, 3, 6], [2, 1, 4, 5, 6, 3], [2, 1, 4, 6, 3, 5], [2, 1, 4, 6, 5, 3], [2, 1, 5, 3, 4, 6], [2, 1, 5, 3, 6, 4], [2, 1, 5, 4, 3, 6], [2, 1, 5, 4, 6, 3], [2, 1, 5, 6, 3, 4], [2, 1, 5, 6, 4, 3], [2, 1, 6, 3, 4, 5], [2, 1, 6, 3, 5, 4], [2, 1, 6, 4, 3, 5], [2, 1, 6, 4, 5, 3], [2, 1, 6, 5, 3, 4], [2, 1, 6, 5, 4, 3], [2, 3, 1, 4, 5, 6], [2, 3, 1, 4, 6, 5], [2, 3, 1, 5, 4, 6], [2, 3, 1, 5, 6, 4], [2, 3, 1, 6, 4, 5], [2, 3, 1, 6, 5, 4], [2, 3, 4, 1, 5, 6], [2, 3, 4, 1, 6, 5], [2, 3, 4, 5, 1, 6], [2, 3, 4, 5, 6, 1], [2, 3, 4, 6, 1, 5], [2, 3, 4, 6, 5, 1], [2, 3, 5, 1, 4, 6], [2, 3, 5, 1, 6, 4], [2, 3, 5, 4, 1, 6], [2, 3, 5, 4, 6, 1], [2, 3, 5, 6, 1, 4], [2, 3, 5, 6, 4, 1], [2, 3, 6, 1, 4, 5], [2, 3, 6, 1, 5, 4], [2, 3, 6, 4, 1, 5], [2, 3, 6, 4, 5, 1], [2, 3, 6, 5, 1, 4], [2, 3, 6, 5, 4, 1], [2, 4, 1, 3, 5, 6], [2, 4, 1, 3, 6, 5], [2, 4, 1, 5, 3, 6], [2, 4, 1, 5, 6, 3], [2, 4, 1, 6, 3, 5], [2, 4, 1, 6, 5, 3], [2, 4, 3, 1, 5, 6], [2, 4, 3, 1, 6, 5], [2, 4, 3, 5, 1, 6], [2, 4, 3, 5, 6, 1], [2, 4, 3, 6, 1, 5], [2, 4, 3, 6, 5, 1], [2, 4, 5, 1, 3, 6], [2, 4, 5, 1, 6, 3], [2, 4, 5, 3, 1, 6], [2, 4, 5, 3, 6, 1], [2, 4, 5, 6, 1, 3], [2, 4, 5, 6, 3, 1], [2, 4, 6, 1, 3, 5], [2, 4, 6, 1, 5, 3], [2, 4, 6, 3, 1, 5], [2, 4, 6, 3, 5, 1], [2, 4, 6, 5, 1, 3], [2, 4, 6, 5, 3, 1], [2, 5, 1, 3, 4, 6], [2, 5, 1, 3, 6, 4], [2, 5, 1, 4, 3, 6], [2, 5, 1, 4, 6, 3], [2, 5, 1, 6, 3, 4], [2, 5, 1, 6, 4, 3], [2, 5, 3, 1, 4, 6], [2, 5, 3, 1, 6, 4], [2, 5, 3, 4, 1, 6], [2, 5, 3, 4, 6, 1], [2, 5, 3, 6, 1, 4], [2, 5, 3, 6, 4, 1], [2, 5, 4, 1, 3, 6], [2, 5, 4, 1, 6, 3], [2, 5, 4, 3, 1, 6], [2, 5, 4, 3, 6, 1], [2, 5, 4, 6, 1, 3], [2, 5, 4, 6, 3, 1], [2, 5, 6, 1, 3, 4], [2, 5, 6, 1, 4, 3], [2, 5, 6, 3, 1, 4], [2, 5, 6, 3, 4, 1], [2, 5, 6, 4, 1, 3], [2, 5, 6, 4, 3, 1], [2, 6, 1, 3, 4, 5], [2, 6, 1, 3, 5, 4], [2, 6, 1, 4, 3, 5], [2, 6, 1, 4, 5, 3], [2, 6, 1, 5, 3, 4], [2, 6, 1, 5, 4, 3], [2, 6, 3, 1, 4, 5], [2, 6, 3, 1, 5, 4], [2, 6, 3, 4, 1, 5], [2, 6, 3, 4, 5, 1], [2, 6, 3, 5, 1, 4], [2, 6, 3, 5, 4, 1], [2, 6, 4, 1, 3, 5], [2, 6, 4, 1, 5, 3], [2, 6, 4, 3, 1, 5], [2, 6, 4, 3, 5, 1], [2, 6, 4, 5, 1, 3], [2, 6, 4, 5, 3, 1], [2, 6, 5, 1, 3, 4], [2, 6, 5, 1, 4, 3], [2, 6, 5, 3, 1, 4], [2, 6, 5, 3, 4, 1], [2, 6, 5, 4, 1, 3], [2, 6, 5, 4, 3, 1], [3, 1, 2, 4, 5, 6], [3, 1, 2, 4, 6, 5], [3, 1, 2, 5, 4, 6], [3, 1, 2, 5, 6, 4], [3, 1, 2, 6, 4, 5], [3, 1, 2, 6, 5, 4], [3, 1, 4, 2, 5, 6], [3, 1, 4, 2, 6, 5], [3, 1, 4, 5, 2, 6], [3, 1, 4, 5, 6, 2], [3, 1, 4, 6, 2, 5], [3, 1, 4, 6, 5, 2], [3, 1, 5, 2, 4, 6], [3, 1, 5, 2, 6, 4], [3, 1, 5, 4, 2, 6], [3, 1, 5, 4, 6, 2], [3, 1, 5, 6, 2, 4], [3, 1, 5, 6, 4, 2], [3, 1, 6, 2, 4, 5], [3, 1, 6, 2, 5, 4], [3, 1, 6, 4, 2, 5], [3, 1, 6, 4, 5, 2], [3, 1, 6, 5, 2, 4], [3, 1, 6, 5, 4, 2], [3, 2, 1, 4, 5, 6], [3, 2, 1, 4, 6, 5], [3, 2, 1, 5, 4, 6], [3, 2, 1, 5, 6, 4], [3, 2, 1, 6, 4, 5], [3, 2, 1, 6, 5, 4], [3, 2, 4, 1, 5, 6], [3, 2, 4, 1, 6, 5], [3, 2, 4, 5, 1, 6], [3, 2, 4, 5, 6, 1], [3, 2, 4, 6, 1, 5], [3, 2, 4, 6, 5, 1], [3, 2, 5, 1, 4, 6], [3, 2, 5, 1, 6, 4], [3, 2, 5, 4, 1, 6], [3, 2, 5, 4, 6, 1], [3, 2, 5, 6, 1, 4], [3, 2, 5, 6, 4, 1], [3, 2, 6, 1, 4, 5], [3, 2, 6, 1, 5, 4], [3, 2, 6, 4, 1, 5], [3, 2, 6, 4, 5, 1], [3, 2, 6, 5, 1, 4], [3, 2, 6, 5, 4, 1], [3, 4, 1, 2, 5, 6], [3, 4, 1, 2, 6, 5], [3, 4, 1, 5, 2, 6], [3, 4, 1, 5, 6, 2], [3, 4, 1, 6, 2, 5], [3, 4, 1, 6, 5, 2], [3, 4, 2, 1, 5, 6], [3, 4, 2, 1, 6, 5], [3, 4, 2, 5, 1, 6], [3, 4, 2, 5, 6, 1], [3, 4, 2, 6, 1, 5], [3, 4, 2, 6, 5, 1], [3, 4, 5, 1, 2, 6], [3, 4, 5, 1, 6, 2], [3, 4, 5, 2, 1, 6], [3, 4, 5, 2, 6, 1], [3, 4, 5, 6, 1, 2], [3, 4, 5, 6, 2, 1], [3, 4, 6, 1, 2, 5], [3, 4, 6, 1, 5, 2], [3, 4, 6, 2, 1, 5], [3, 4, 6, 2, 5, 1], [3, 4, 6, 5, 1, 2], [3, 4, 6, 5, 2, 1], [3, 5, 1, 2, 4, 6], [3, 5, 1, 2, 6, 4], [3, 5, 1, 4, 2, 6], [3, 5, 1, 4, 6, 2], [3, 5, 1, 6, 2, 4], [3, 5, 1, 6, 4, 2], [3, 5, 2, 1, 4, 6], [3, 5, 2, 1, 6, 4], [3, 5, 2, 4, 1, 6], [3, 5, 2, 4, 6, 1], [3, 5, 2, 6, 1, 4], [3, 5, 2, 6, 4, 1], [3, 5, 4, 1, 2, 6], [3, 5, 4, 1, 6, 2], [3, 5, 4, 2, 1, 6], [3, 5, 4, 2, 6, 1], [3, 5, 4, 6, 1, 2], [3, 5, 4, 6, 2, 1], [3, 5, 6, 1, 2, 4], [3, 5, 6, 1, 4, 2], [3, 5, 6, 2, 1, 4], [3, 5, 6, 2, 4, 1], [3, 5, 6, 4, 1, 2], [3, 5, 6, 4, 2, 1], [3, 6, 1, 2, 4, 5], [3, 6, 1, 2, 5, 4], [3, 6, 1, 4, 2, 5], [3, 6, 1, 4, 5, 2], [3, 6, 1, 5, 2, 4], [3, 6, 1, 5, 4, 2], [3, 6, 2, 1, 4, 5], [3, 6, 2, 1, 5, 4], [3, 6, 2, 4, 1, 5], [3, 6, 2, 4, 5, 1], [3, 6, 2, 5, 1, 4], [3, 6, 2, 5, 4, 1], [3, 6, 4, 1, 2, 5], [3, 6, 4, 1, 5, 2], [3, 6, 4, 2, 1, 5], [3, 6, 4, 2, 5, 1], [3, 6, 4, 5, 1, 2], [3, 6, 4, 5, 2, 1], [3, 6, 5, 1, 2, 4], [3, 6, 5, 1, 4, 2], [3, 6, 5, 2, 1, 4], [3, 6, 5, 2, 4, 1], [3, 6, 5, 4, 1, 2], [3, 6, 5, 4, 2, 1], [4, 1, 2, 3, 5, 6], [4, 1, 2, 3, 6, 5], [4, 1, 2, 5, 3, 6], [4, 1, 2, 5, 6, 3], [4, 1, 2, 6, 3, 5], [4, 1, 2, 6, 5, 3], [4, 1, 3, 2, 5, 6], [4, 1, 3, 2, 6, 5], [4, 1, 3, 5, 2, 6], [4, 1, 3, 5, 6, 2], [4, 1, 3, 6, 2, 5], [4, 1, 3, 6, 5, 2], [4, 1, 5, 2, 3, 6], [4, 1, 5, 2, 6, 3], [4, 1, 5, 3, 2, 6], [4, 1, 5, 3, 6, 2], [4, 1, 5, 6, 2, 3], [4, 1, 5, 6, 3, 2], [4, 1, 6, 2, 3, 5], [4, 1, 6, 2, 5, 3], [4, 1, 6, 3, 2, 5], [4, 1, 6, 3, 5, 2], [4, 1, 6, 5, 2, 3], [4, 1, 6, 5, 3, 2], [4, 2, 1, 3, 5, 6], [4, 2, 1, 3, 6, 5], [4, 2, 1, 5, 3, 6], [4, 2, 1, 5, 6, 3], [4, 2, 1, 6, 3, 5], [4, 2, 1, 6, 5, 3], [4, 2, 3, 1, 5, 6], [4, 2, 3, 1, 6, 5], [4, 2, 3, 5, 1, 6], [4, 2, 3, 5, 6, 1], [4, 2, 3, 6, 1, 5], [4, 2, 3, 6, 5, 1], [4, 2, 5, 1, 3, 6], [4, 2, 5, 1, 6, 3], [4, 2, 5, 3, 1, 6], [4, 2, 5, 3, 6, 1], [4, 2, 5, 6, 1, 3], [4, 2, 5, 6, 3, 1], [4, 2, 6, 1, 3, 5], [4, 2, 6, 1, 5, 3], [4, 2, 6, 3, 1, 5], [4, 2, 6, 3, 5, 1], [4, 2, 6, 5, 1, 3], [4, 2, 6, 5, 3, 1], [4, 3, 1, 2, 5, 6], [4, 3, 1, 2, 6, 5], [4, 3, 1, 5, 2, 6], [4, 3, 1, 5, 6, 2], [4, 3, 1, 6, 2, 5], [4, 3, 1, 6, 5, 2], [4, 3, 2, 1, 5, 6], [4, 3, 2, 1, 6, 5], [4, 3, 2, 5, 1, 6], [4, 3, 2, 5, 6, 1], [4, 3, 2, 6, 1, 5], [4, 3, 2, 6, 5, 1], [4, 3, 5, 1, 2, 6], [4, 3, 5, 1, 6, 2], [4, 3, 5, 2, 1, 6], [4, 3, 5, 2, 6, 1], [4, 3, 5, 6, 1, 2], [4, 3, 5, 6, 2, 1], [4, 3, 6, 1, 2, 5], [4, 3, 6, 1, 5, 2], [4, 3, 6, 2, 1, 5], [4, 3, 6, 2, 5, 1], [4, 3, 6, 5, 1, 2], [4, 3, 6, 5, 2, 1], [4, 5, 1, 2, 3, 6], [4, 5, 1, 2, 6, 3], [4, 5, 1, 3, 2, 6], [4, 5, 1, 3, 6, 2], [4, 5, 1, 6, 2, 3], [4, 5, 1, 6, 3, 2], [4, 5, 2, 1, 3, 6], [4, 5, 2, 1, 6, 3], [4, 5, 2, 3, 1, 6], [4, 5, 2, 3, 6, 1], [4, 5, 2, 6, 1, 3], [4, 5, 2, 6, 3, 1], [4, 5, 3, 1, 2, 6], [4, 5, 3, 1, 6, 2], [4, 5, 3, 2, 1, 6], [4, 5, 3, 2, 6, 1], [4, 5, 3, 6, 1, 2], [4, 5, 3, 6, 2, 1], [4, 5, 6, 1, 2, 3], [4, 5, 6, 1, 3, 2], [4, 5, 6, 2, 1, 3], [4, 5, 6, 2, 3, 1], [4, 5, 6, 3, 1, 2], [4, 5, 6, 3, 2, 1], [4, 6, 1, 2, 3, 5], [4, 6, 1, 2, 5, 3], [4, 6, 1, 3, 2, 5], [4, 6, 1, 3, 5, 2], [4, 6, 1, 5, 2, 3], [4, 6, 1, 5, 3, 2], [4, 6, 2, 1, 3, 5], [4, 6, 2, 1, 5, 3], [4, 6, 2, 3, 1, 5], [4, 6, 2, 3, 5, 1], [4, 6, 2, 5, 1, 3], [4, 6, 2, 5, 3, 1], [4, 6, 3, 1, 2, 5], [4, 6, 3, 1, 5, 2], [4, 6, 3, 2, 1, 5], [4, 6, 3, 2, 5, 1], [4, 6, 3, 5, 1, 2], [4, 6, 3, 5, 2, 1], [4, 6, 5, 1, 2, 3], [4, 6, 5, 1, 3, 2], [4, 6, 5, 2, 1, 3], [4, 6, 5, 2, 3, 1], [4, 6, 5, 3, 1, 2], [4, 6, 5, 3, 2, 1], [5, 1, 2, 3, 4, 6], [5, 1, 2, 3, 6, 4], [5, 1, 2, 4, 3, 6], [5, 1, 2, 4, 6, 3], [5, 1, 2, 6, 3, 4], [5, 1, 2, 6, 4, 3], [5, 1, 3, 2, 4, 6], [5, 1, 3, 2, 6, 4], [5, 1, 3, 4, 2, 6], [5, 1, 3, 4, 6, 2], [5, 1, 3, 6, 2, 4], [5, 1, 3, 6, 4, 2], [5, 1, 4, 2, 3, 6], [5, 1, 4, 2, 6, 3], [5, 1, 4, 3, 2, 6], [5, 1, 4, 3, 6, 2], [5, 1, 4, 6, 2, 3], [5, 1, 4, 6, 3, 2], [5, 1, 6, 2, 3, 4], [5, 1, 6, 2, 4, 3], [5, 1, 6, 3, 2, 4], [5, 1, 6, 3, 4, 2], [5, 1, 6, 4, 2, 3], [5, 1, 6, 4, 3, 2], [5, 2, 1, 3, 4, 6], [5, 2, 1, 3, 6, 4], [5, 2, 1, 4, 3, 6], [5, 2, 1, 4, 6, 3], [5, 2, 1, 6, 3, 4], [5, 2, 1, 6, 4, 3], [5, 2, 3, 1, 4, 6], [5, 2, 3, 1, 6, 4], [5, 2, 3, 4, 1, 6], [5, 2, 3, 4, 6, 1], [5, 2, 3, 6, 1, 4], [5, 2, 3, 6, 4, 1], [5, 2, 4, 1, 3, 6], [5, 2, 4, 1, 6, 3], [5, 2, 4, 3, 1, 6], [5, 2, 4, 3, 6, 1], [5, 2, 4, 6, 1, 3], [5, 2, 4, 6, 3, 1], [5, 2, 6, 1, 3, 4], [5, 2, 6, 1, 4, 3], [5, 2, 6, 3, 1, 4], [5, 2, 6, 3, 4, 1], [5, 2, 6, 4, 1, 3], [5, 2, 6, 4, 3, 1], [5, 3, 1, 2, 4, 6], [5, 3, 1, 2, 6, 4], [5, 3, 1, 4, 2, 6], [5, 3, 1, 4, 6, 2], [5, 3, 1, 6, 2, 4], [5, 3, 1, 6, 4, 2], [5, 3, 2, 1, 4, 6], [5, 3, 2, 1, 6, 4], [5, 3, 2, 4, 1, 6], [5, 3, 2, 4, 6, 1], [5, 3, 2, 6, 1, 4], [5, 3, 2, 6, 4, 1], [5, 3, 4, 1, 2, 6], [5, 3, 4, 1, 6, 2], [5, 3, 4, 2, 1, 6], [5, 3, 4, 2, 6, 1], [5, 3, 4, 6, 1, 2], [5, 3, 4, 6, 2, 1], [5, 3, 6, 1, 2, 4], [5, 3, 6, 1, 4, 2], [5, 3, 6, 2, 1, 4], [5, 3, 6, 2, 4, 1], [5, 3, 6, 4, 1, 2], [5, 3, 6, 4, 2, 1], [5, 4, 1, 2, 3, 6], [5, 4, 1, 2, 6, 3], [5, 4, 1, 3, 2, 6], [5, 4, 1, 3, 6, 2], [5, 4, 1, 6, 2, 3], [5, 4, 1, 6, 3, 2], [5, 4, 2, 1, 3, 6], [5, 4, 2, 1, 6, 3], [5, 4, 2, 3, 1, 6], [5, 4, 2, 3, 6, 1], [5, 4, 2, 6, 1, 3], [5, 4, 2, 6, 3, 1], [5, 4, 3, 1, 2, 6], [5, 4, 3, 1, 6, 2], [5, 4, 3, 2, 1, 6], [5, 4, 3, 2, 6, 1], [5, 4, 3, 6, 1, 2], [5, 4, 3, 6, 2, 1], [5, 4, 6, 1, 2, 3], [5, 4, 6, 1, 3, 2], [5, 4, 6, 2, 1, 3], [5, 4, 6, 2, 3, 1], [5, 4, 6, 3, 1, 2], [5, 4, 6, 3, 2, 1], [5, 6, 1, 2, 3, 4], [5, 6, 1, 2, 4, 3], [5, 6, 1, 3, 2, 4], [5, 6, 1, 3, 4, 2], [5, 6, 1, 4, 2, 3], [5, 6, 1, 4, 3, 2], [5, 6, 2, 1, 3, 4], [5, 6, 2, 1, 4, 3], [5, 6, 2, 3, 1, 4], [5, 6, 2, 3, 4, 1], [5, 6, 2, 4, 1, 3], [5, 6, 2, 4, 3, 1], [5, 6, 3, 1, 2, 4], [5, 6, 3, 1, 4, 2], [5, 6, 3, 2, 1, 4], [5, 6, 3, 2, 4, 1], [5, 6, 3, 4, 1, 2], [5, 6, 3, 4, 2, 1], [5, 6, 4, 1, 2, 3], [5, 6, 4, 1, 3, 2], [5, 6, 4, 2, 1, 3], [5, 6, 4, 2, 3, 1], [5, 6, 4, 3, 1, 2], [5, 6, 4, 3, 2, 1], [6, 1, 2, 3, 4, 5], [6, 1, 2, 3, 5, 4], [6, 1, 2, 4, 3, 5], [6, 1, 2, 4, 5, 3], [6, 1, 2, 5, 3, 4], [6, 1, 2, 5, 4, 3], [6, 1, 3, 2, 4, 5], [6, 1, 3, 2, 5, 4], [6, 1, 3, 4, 2, 5], [6, 1, 3, 4, 5, 2], [6, 1, 3, 5, 2, 4], [6, 1, 3, 5, 4, 2], [6, 1, 4, 2, 3, 5], [6, 1, 4, 2, 5, 3], [6, 1, 4, 3, 2, 5], [6, 1, 4, 3, 5, 2], [6, 1, 4, 5, 2, 3], [6, 1, 4, 5, 3, 2], [6, 1, 5, 2, 3, 4], [6, 1, 5, 2, 4, 3], [6, 1, 5, 3, 2, 4], [6, 1, 5, 3, 4, 2], [6, 1, 5, 4, 2, 3], [6, 1, 5, 4, 3, 2], [6, 2, 1, 3, 4, 5], [6, 2, 1, 3, 5, 4], [6, 2, 1, 4, 3, 5], [6, 2, 1, 4, 5, 3], [6, 2, 1, 5, 3, 4], [6, 2, 1, 5, 4, 3], [6, 2, 3, 1, 4, 5], [6, 2, 3, 1, 5, 4], [6, 2, 3, 4, 1, 5], [6, 2, 3, 4, 5, 1], [6, 2, 3, 5, 1, 4], [6, 2, 3, 5, 4, 1], [6, 2, 4, 1, 3, 5], [6, 2, 4, 1, 5, 3], [6, 2, 4, 3, 1, 5], [6, 2, 4, 3, 5, 1], [6, 2, 4, 5, 1, 3], [6, 2, 4, 5, 3, 1], [6, 2, 5, 1, 3, 4], [6, 2, 5, 1, 4, 3], [6, 2, 5, 3, 1, 4], [6, 2, 5, 3, 4, 1], [6, 2, 5, 4, 1, 3], [6, 2, 5, 4, 3, 1], [6, 3, 1, 2, 4, 5], [6, 3, 1, 2, 5, 4], [6, 3, 1, 4, 2, 5], [6, 3, 1, 4, 5, 2], [6, 3, 1, 5, 2, 4], [6, 3, 1, 5, 4, 2], [6, 3, 2, 1, 4, 5], [6, 3, 2, 1, 5, 4], [6, 3, 2, 4, 1, 5], [6, 3, 2, 4, 5, 1], [6, 3, 2, 5, 1, 4], [6, 3, 2, 5, 4, 1], [6, 3, 4, 1, 2, 5], [6, 3, 4, 1, 5, 2], [6, 3, 4, 2, 1, 5], [6, 3, 4, 2, 5, 1], [6, 3, 4, 5, 1, 2], [6, 3, 4, 5, 2, 1], [6, 3, 5, 1, 2, 4], [6, 3, 5, 1, 4, 2], [6, 3, 5, 2, 1, 4], [6, 3, 5, 2, 4, 1], [6, 3, 5, 4, 1, 2], [6, 3, 5, 4, 2, 1], [6, 4, 1, 2, 3, 5], [6, 4, 1, 2, 5, 3], [6, 4, 1, 3, 2, 5], [6, 4, 1, 3, 5, 2], [6, 4, 1, 5, 2, 3], [6, 4, 1, 5, 3, 2], [6, 4, 2, 1, 3, 5], [6, 4, 2, 1, 5, 3], [6, 4, 2, 3, 1, 5], [6, 4, 2, 3, 5, 1], [6, 4, 2, 5, 1, 3], [6, 4, 2, 5, 3, 1], [6, 4, 3, 1, 2, 5], [6, 4, 3, 1, 5, 2], [6, 4, 3, 2, 1, 5], [6, 4, 3, 2, 5, 1], [6, 4, 3, 5, 1, 2], [6, 4, 3, 5, 2, 1], [6, 4, 5, 1, 2, 3], [6, 4, 5, 1, 3, 2], [6, 4, 5, 2, 1, 3], [6, 4, 5, 2, 3, 1], [6, 4, 5, 3, 1, 2], [6, 4, 5, 3, 2, 1], [6, 5, 1, 2, 3, 4], [6, 5, 1, 2, 4, 3], [6, 5, 1, 3, 2, 4], [6, 5, 1, 3, 4, 2], [6, 5, 1, 4, 2, 3], [6, 5, 1, 4, 3, 2], [6, 5, 2, 1, 3, 4], [6, 5, 2, 1, 4, 3], [6, 5, 2, 3, 1, 4], [6, 5, 2, 3, 4, 1], [6, 5, 2, 4, 1, 3], [6, 5, 2, 4, 3, 1], [6, 5, 3, 1, 2, 4], [6, 5, 3, 1, 4, 2], [6, 5, 3, 2, 1, 4], [6, 5, 3, 2, 4, 1], [6, 5, 3, 4, 1, 2], [6, 5, 3, 4, 2, 1], [6, 5, 4, 1, 2, 3], [6, 5, 4, 1, 3, 2], [6, 5, 4, 2, 1, 3], [6, 5, 4, 2, 3, 1], [6, 5, 4, 3, 1, 2], [6, 5, 4, 3, 2, 1]]\n assert candidate(nums = [-1, -1, 2, 2, -1]) == [[-1, -1, -1, 2, 2], [-1, -1, 2, -1, 2], [-1, -1, 2, 2, -1], [-1, 2, -1, -1, 2], [-1, 2, -1, 2, -1], [-1, 2, 2, -1, -1], [2, -1, -1, -1, 2], [2, -1, -1, 2, -1], [2, -1, 2, -1, -1], [2, 2, -1, -1, -1]]\n assert candidate(nums = [4, 4, 4, 4]) == [[4, 4, 4, 4]]\n assert candidate(nums = [5, 1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5, 5], [1, 2, 3, 5, 4, 5], [1, 2, 3, 5, 5, 4], [1, 2, 4, 3, 5, 5], [1, 2, 4, 5, 3, 5], [1, 2, 4, 5, 5, 3], [1, 2, 5, 3, 4, 5], [1, 2, 5, 3, 5, 4], [1, 2, 5, 4, 3, 5], [1, 2, 5, 4, 5, 3], [1, 2, 5, 5, 3, 4], [1, 2, 5, 5, 4, 3], [1, 3, 2, 4, 5, 5], [1, 3, 2, 5, 4, 5], [1, 3, 2, 5, 5, 4], [1, 3, 4, 2, 5, 5], [1, 3, 4, 5, 2, 5], [1, 3, 4, 5, 5, 2], [1, 3, 5, 2, 4, 5], [1, 3, 5, 2, 5, 4], [1, 3, 5, 4, 2, 5], [1, 3, 5, 4, 5, 2], [1, 3, 5, 5, 2, 4], [1, 3, 5, 5, 4, 2], [1, 4, 2, 3, 5, 5], [1, 4, 2, 5, 3, 5], [1, 4, 2, 5, 5, 3], [1, 4, 3, 2, 5, 5], [1, 4, 3, 5, 2, 5], [1, 4, 3, 5, 5, 2], [1, 4, 5, 2, 3, 5], [1, 4, 5, 2, 5, 3], [1, 4, 5, 3, 2, 5], [1, 4, 5, 3, 5, 2], [1, 4, 5, 5, 2, 3], [1, 4, 5, 5, 3, 2], [1, 5, 2, 3, 4, 5], [1, 5, 2, 3, 5, 4], [1, 5, 2, 4, 3, 5], [1, 5, 2, 4, 5, 3], [1, 5, 2, 5, 3, 4], [1, 5, 2, 5, 4, 3], [1, 5, 3, 2, 4, 5], [1, 5, 3, 2, 5, 4], [1, 5, 3, 4, 2, 5], [1, 5, 3, 4, 5, 2], [1, 5, 3, 5, 2, 4], [1, 5, 3, 5, 4, 2], [1, 5, 4, 2, 3, 5], [1, 5, 4, 2, 5, 3], [1, 5, 4, 3, 2, 5], [1, 5, 4, 3, 5, 2], [1, 5, 4, 5, 2, 3], [1, 5, 4, 5, 3, 2], [1, 5, 5, 2, 3, 4], [1, 5, 5, 2, 4, 3], [1, 5, 5, 3, 2, 4], [1, 5, 5, 3, 4, 2], [1, 5, 5, 4, 2, 3], [1, 5, 5, 4, 3, 2], [2, 1, 3, 4, 5, 5], [2, 1, 3, 5, 4, 5], [2, 1, 3, 5, 5, 4], [2, 1, 4, 3, 5, 5], [2, 1, 4, 5, 3, 5], [2, 1, 4, 5, 5, 3], [2, 1, 5, 3, 4, 5], [2, 1, 5, 3, 5, 4], [2, 1, 5, 4, 3, 5], [2, 1, 5, 4, 5, 3], [2, 1, 5, 5, 3, 4], [2, 1, 5, 5, 4, 3], [2, 3, 1, 4, 5, 5], [2, 3, 1, 5, 4, 5], [2, 3, 1, 5, 5, 4], [2, 3, 4, 1, 5, 5], [2, 3, 4, 5, 1, 5], [2, 3, 4, 5, 5, 1], [2, 3, 5, 1, 4, 5], [2, 3, 5, 1, 5, 4], [2, 3, 5, 4, 1, 5], [2, 3, 5, 4, 5, 1], [2, 3, 5, 5, 1, 4], [2, 3, 5, 5, 4, 1], [2, 4, 1, 3, 5, 5], [2, 4, 1, 5, 3, 5], [2, 4, 1, 5, 5, 3], [2, 4, 3, 1, 5, 5], [2, 4, 3, 5, 1, 5], [2, 4, 3, 5, 5, 1], [2, 4, 5, 1, 3, 5], [2, 4, 5, 1, 5, 3], [2, 4, 5, 3, 1, 5], [2, 4, 5, 3, 5, 1], [2, 4, 5, 5, 1, 3], [2, 4, 5, 5, 3, 1], [2, 5, 1, 3, 4, 5], [2, 5, 1, 3, 5, 4], [2, 5, 1, 4, 3, 5], [2, 5, 1, 4, 5, 3], [2, 5, 1, 5, 3, 4], [2, 5, 1, 5, 4, 3], [2, 5, 3, 1, 4, 5], [2, 5, 3, 1, 5, 4], [2, 5, 3, 4, 1, 5], [2, 5, 3, 4, 5, 1], [2, 5, 3, 5, 1, 4], [2, 5, 3, 5, 4, 1], [2, 5, 4, 1, 3, 5], [2, 5, 4, 1, 5, 3], [2, 5, 4, 3, 1, 5], [2, 5, 4, 3, 5, 1], [2, 5, 4, 5, 1, 3], [2, 5, 4, 5, 3, 1], [2, 5, 5, 1, 3, 4], [2, 5, 5, 1, 4, 3], [2, 5, 5, 3, 1, 4], [2, 5, 5, 3, 4, 1], [2, 5, 5, 4, 1, 3], [2, 5, 5, 4, 3, 1], [3, 1, 2, 4, 5, 5], [3, 1, 2, 5, 4, 5], [3, 1, 2, 5, 5, 4], [3, 1, 4, 2, 5, 5], [3, 1, 4, 5, 2, 5], [3, 1, 4, 5, 5, 2], [3, 1, 5, 2, 4, 5], [3, 1, 5, 2, 5, 4], [3, 1, 5, 4, 2, 5], [3, 1, 5, 4, 5, 2], [3, 1, 5, 5, 2, 4], [3, 1, 5, 5, 4, 2], [3, 2, 1, 4, 5, 5], [3, 2, 1, 5, 4, 5], [3, 2, 1, 5, 5, 4], [3, 2, 4, 1, 5, 5], [3, 2, 4, 5, 1, 5], [3, 2, 4, 5, 5, 1], [3, 2, 5, 1, 4, 5], [3, 2, 5, 1, 5, 4], [3, 2, 5, 4, 1, 5], [3, 2, 5, 4, 5, 1], [3, 2, 5, 5, 1, 4], [3, 2, 5, 5, 4, 1], [3, 4, 1, 2, 5, 5], [3, 4, 1, 5, 2, 5], [3, 4, 1, 5, 5, 2], [3, 4, 2, 1, 5, 5], [3, 4, 2, 5, 1, 5], [3, 4, 2, 5, 5, 1], [3, 4, 5, 1, 2, 5], [3, 4, 5, 1, 5, 2], [3, 4, 5, 2, 1, 5], [3, 4, 5, 2, 5, 1], [3, 4, 5, 5, 1, 2], [3, 4, 5, 5, 2, 1], [3, 5, 1, 2, 4, 5], [3, 5, 1, 2, 5, 4], [3, 5, 1, 4, 2, 5], [3, 5, 1, 4, 5, 2], [3, 5, 1, 5, 2, 4], [3, 5, 1, 5, 4, 2], [3, 5, 2, 1, 4, 5], [3, 5, 2, 1, 5, 4], [3, 5, 2, 4, 1, 5], [3, 5, 2, 4, 5, 1], [3, 5, 2, 5, 1, 4], [3, 5, 2, 5, 4, 1], [3, 5, 4, 1, 2, 5], [3, 5, 4, 1, 5, 2], [3, 5, 4, 2, 1, 5], [3, 5, 4, 2, 5, 1], [3, 5, 4, 5, 1, 2], [3, 5, 4, 5, 2, 1], [3, 5, 5, 1, 2, 4], [3, 5, 5, 1, 4, 2], [3, 5, 5, 2, 1, 4], [3, 5, 5, 2, 4, 1], [3, 5, 5, 4, 1, 2], [3, 5, 5, 4, 2, 1], [4, 1, 2, 3, 5, 5], [4, 1, 2, 5, 3, 5], [4, 1, 2, 5, 5, 3], [4, 1, 3, 2, 5, 5], [4, 1, 3, 5, 2, 5], [4, 1, 3, 5, 5, 2], [4, 1, 5, 2, 3, 5], [4, 1, 5, 2, 5, 3], [4, 1, 5, 3, 2, 5], [4, 1, 5, 3, 5, 2], [4, 1, 5, 5, 2, 3], [4, 1, 5, 5, 3, 2], [4, 2, 1, 3, 5, 5], [4, 2, 1, 5, 3, 5], [4, 2, 1, 5, 5, 3], [4, 2, 3, 1, 5, 5], [4, 2, 3, 5, 1, 5], [4, 2, 3, 5, 5, 1], [4, 2, 5, 1, 3, 5], [4, 2, 5, 1, 5, 3], [4, 2, 5, 3, 1, 5], [4, 2, 5, 3, 5, 1], [4, 2, 5, 5, 1, 3], [4, 2, 5, 5, 3, 1], [4, 3, 1, 2, 5, 5], [4, 3, 1, 5, 2, 5], [4, 3, 1, 5, 5, 2], [4, 3, 2, 1, 5, 5], [4, 3, 2, 5, 1, 5], [4, 3, 2, 5, 5, 1], [4, 3, 5, 1, 2, 5], [4, 3, 5, 1, 5, 2], [4, 3, 5, 2, 1, 5], [4, 3, 5, 2, 5, 1], [4, 3, 5, 5, 1, 2], [4, 3, 5, 5, 2, 1], [4, 5, 1, 2, 3, 5], [4, 5, 1, 2, 5, 3], [4, 5, 1, 3, 2, 5], [4, 5, 1, 3, 5, 2], [4, 5, 1, 5, 2, 3], [4, 5, 1, 5, 3, 2], [4, 5, 2, 1, 3, 5], [4, 5, 2, 1, 5, 3], [4, 5, 2, 3, 1, 5], [4, 5, 2, 3, 5, 1], [4, 5, 2, 5, 1, 3], [4, 5, 2, 5, 3, 1], [4, 5, 3, 1, 2, 5], [4, 5, 3, 1, 5, 2], [4, 5, 3, 2, 1, 5], [4, 5, 3, 2, 5, 1], [4, 5, 3, 5, 1, 2], [4, 5, 3, 5, 2, 1], [4, 5, 5, 1, 2, 3], [4, 5, 5, 1, 3, 2], [4, 5, 5, 2, 1, 3], [4, 5, 5, 2, 3, 1], [4, 5, 5, 3, 1, 2], [4, 5, 5, 3, 2, 1], [5, 1, 2, 3, 4, 5], [5, 1, 2, 3, 5, 4], [5, 1, 2, 4, 3, 5], [5, 1, 2, 4, 5, 3], [5, 1, 2, 5, 3, 4], [5, 1, 2, 5, 4, 3], [5, 1, 3, 2, 4, 5], [5, 1, 3, 2, 5, 4], [5, 1, 3, 4, 2, 5], [5, 1, 3, 4, 5, 2], [5, 1, 3, 5, 2, 4], [5, 1, 3, 5, 4, 2], [5, 1, 4, 2, 3, 5], [5, 1, 4, 2, 5, 3], [5, 1, 4, 3, 2, 5], [5, 1, 4, 3, 5, 2], [5, 1, 4, 5, 2, 3], [5, 1, 4, 5, 3, 2], [5, 1, 5, 2, 3, 4], [5, 1, 5, 2, 4, 3], [5, 1, 5, 3, 2, 4], [5, 1, 5, 3, 4, 2], [5, 1, 5, 4, 2, 3], [5, 1, 5, 4, 3, 2], [5, 2, 1, 3, 4, 5], [5, 2, 1, 3, 5, 4], [5, 2, 1, 4, 3, 5], [5, 2, 1, 4, 5, 3], [5, 2, 1, 5, 3, 4], [5, 2, 1, 5, 4, 3], [5, 2, 3, 1, 4, 5], [5, 2, 3, 1, 5, 4], [5, 2, 3, 4, 1, 5], [5, 2, 3, 4, 5, 1], [5, 2, 3, 5, 1, 4], [5, 2, 3, 5, 4, 1], [5, 2, 4, 1, 3, 5], [5, 2, 4, 1, 5, 3], [5, 2, 4, 3, 1, 5], [5, 2, 4, 3, 5, 1], [5, 2, 4, 5, 1, 3], [5, 2, 4, 5, 3, 1], [5, 2, 5, 1, 3, 4], [5, 2, 5, 1, 4, 3], [5, 2, 5, 3, 1, 4], [5, 2, 5, 3, 4, 1], [5, 2, 5, 4, 1, 3], [5, 2, 5, 4, 3, 1], [5, 3, 1, 2, 4, 5], [5, 3, 1, 2, 5, 4], [5, 3, 1, 4, 2, 5], [5, 3, 1, 4, 5, 2], [5, 3, 1, 5, 2, 4], [5, 3, 1, 5, 4, 2], [5, 3, 2, 1, 4, 5], [5, 3, 2, 1, 5, 4], [5, 3, 2, 4, 1, 5], [5, 3, 2, 4, 5, 1], [5, 3, 2, 5, 1, 4], [5, 3, 2, 5, 4, 1], [5, 3, 4, 1, 2, 5], [5, 3, 4, 1, 5, 2], [5, 3, 4, 2, 1, 5], [5, 3, 4, 2, 5, 1], [5, 3, 4, 5, 1, 2], [5, 3, 4, 5, 2, 1], [5, 3, 5, 1, 2, 4], [5, 3, 5, 1, 4, 2], [5, 3, 5, 2, 1, 4], [5, 3, 5, 2, 4, 1], [5, 3, 5, 4, 1, 2], [5, 3, 5, 4, 2, 1], [5, 4, 1, 2, 3, 5], [5, 4, 1, 2, 5, 3], [5, 4, 1, 3, 2, 5], [5, 4, 1, 3, 5, 2], [5, 4, 1, 5, 2, 3], [5, 4, 1, 5, 3, 2], [5, 4, 2, 1, 3, 5], [5, 4, 2, 1, 5, 3], [5, 4, 2, 3, 1, 5], [5, 4, 2, 3, 5, 1], [5, 4, 2, 5, 1, 3], [5, 4, 2, 5, 3, 1], [5, 4, 3, 1, 2, 5], [5, 4, 3, 1, 5, 2], [5, 4, 3, 2, 1, 5], [5, 4, 3, 2, 5, 1], [5, 4, 3, 5, 1, 2], [5, 4, 3, 5, 2, 1], [5, 4, 5, 1, 2, 3], [5, 4, 5, 1, 3, 2], [5, 4, 5, 2, 1, 3], [5, 4, 5, 2, 3, 1], [5, 4, 5, 3, 1, 2], [5, 4, 5, 3, 2, 1], [5, 5, 1, 2, 3, 4], [5, 5, 1, 2, 4, 3], [5, 5, 1, 3, 2, 4], [5, 5, 1, 3, 4, 2], [5, 5, 1, 4, 2, 3], [5, 5, 1, 4, 3, 2], [5, 5, 2, 1, 3, 4], [5, 5, 2, 1, 4, 3], [5, 5, 2, 3, 1, 4], [5, 5, 2, 3, 4, 1], [5, 5, 2, 4, 1, 3], [5, 5, 2, 4, 3, 1], [5, 5, 3, 1, 2, 4], [5, 5, 3, 1, 4, 2], [5, 5, 3, 2, 1, 4], [5, 5, 3, 2, 4, 1], [5, 5, 3, 4, 1, 2], [5, 5, 3, 4, 2, 1], [5, 5, 4, 1, 2, 3], [5, 5, 4, 1, 3, 2], [5, 5, 4, 2, 1, 3], [5, 5, 4, 2, 3, 1], [5, 5, 4, 3, 1, 2], [5, 5, 4, 3, 2, 1]]\n assert candidate(nums = [5, 4, 3, 2, 1, 0]) == [[0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 5, 4], [0, 1, 2, 4, 3, 5], [0, 1, 2, 4, 5, 3], [0, 1, 2, 5, 3, 4], [0, 1, 2, 5, 4, 3], [0, 1, 3, 2, 4, 5], [0, 1, 3, 2, 5, 4], [0, 1, 3, 4, 2, 5], [0, 1, 3, 4, 5, 2], [0, 1, 3, 5, 2, 4], [0, 1, 3, 5, 4, 2], [0, 1, 4, 2, 3, 5], [0, 1, 4, 2, 5, 3], [0, 1, 4, 3, 2, 5], [0, 1, 4, 3, 5, 2], [0, 1, 4, 5, 2, 3], [0, 1, 4, 5, 3, 2], [0, 1, 5, 2, 3, 4], [0, 1, 5, 2, 4, 3], [0, 1, 5, 3, 2, 4], [0, 1, 5, 3, 4, 2], [0, 1, 5, 4, 2, 3], [0, 1, 5, 4, 3, 2], [0, 2, 1, 3, 4, 5], [0, 2, 1, 3, 5, 4], [0, 2, 1, 4, 3, 5], [0, 2, 1, 4, 5, 3], [0, 2, 1, 5, 3, 4], [0, 2, 1, 5, 4, 3], [0, 2, 3, 1, 4, 5], [0, 2, 3, 1, 5, 4], [0, 2, 3, 4, 1, 5], [0, 2, 3, 4, 5, 1], [0, 2, 3, 5, 1, 4], [0, 2, 3, 5, 4, 1], [0, 2, 4, 1, 3, 5], [0, 2, 4, 1, 5, 3], [0, 2, 4, 3, 1, 5], [0, 2, 4, 3, 5, 1], [0, 2, 4, 5, 1, 3], [0, 2, 4, 5, 3, 1], [0, 2, 5, 1, 3, 4], [0, 2, 5, 1, 4, 3], [0, 2, 5, 3, 1, 4], [0, 2, 5, 3, 4, 1], [0, 2, 5, 4, 1, 3], [0, 2, 5, 4, 3, 1], [0, 3, 1, 2, 4, 5], [0, 3, 1, 2, 5, 4], [0, 3, 1, 4, 2, 5], [0, 3, 1, 4, 5, 2], [0, 3, 1, 5, 2, 4], [0, 3, 1, 5, 4, 2], [0, 3, 2, 1, 4, 5], [0, 3, 2, 1, 5, 4], [0, 3, 2, 4, 1, 5], [0, 3, 2, 4, 5, 1], [0, 3, 2, 5, 1, 4], [0, 3, 2, 5, 4, 1], [0, 3, 4, 1, 2, 5], [0, 3, 4, 1, 5, 2], [0, 3, 4, 2, 1, 5], [0, 3, 4, 2, 5, 1], [0, 3, 4, 5, 1, 2], [0, 3, 4, 5, 2, 1], [0, 3, 5, 1, 2, 4], [0, 3, 5, 1, 4, 2], [0, 3, 5, 2, 1, 4], [0, 3, 5, 2, 4, 1], [0, 3, 5, 4, 1, 2], [0, 3, 5, 4, 2, 1], [0, 4, 1, 2, 3, 5], [0, 4, 1, 2, 5, 3], [0, 4, 1, 3, 2, 5], [0, 4, 1, 3, 5, 2], [0, 4, 1, 5, 2, 3], [0, 4, 1, 5, 3, 2], [0, 4, 2, 1, 3, 5], [0, 4, 2, 1, 5, 3], [0, 4, 2, 3, 1, 5], [0, 4, 2, 3, 5, 1], [0, 4, 2, 5, 1, 3], [0, 4, 2, 5, 3, 1], [0, 4, 3, 1, 2, 5], [0, 4, 3, 1, 5, 2], [0, 4, 3, 2, 1, 5], [0, 4, 3, 2, 5, 1], [0, 4, 3, 5, 1, 2], [0, 4, 3, 5, 2, 1], [0, 4, 5, 1, 2, 3], [0, 4, 5, 1, 3, 2], [0, 4, 5, 2, 1, 3], [0, 4, 5, 2, 3, 1], [0, 4, 5, 3, 1, 2], [0, 4, 5, 3, 2, 1], [0, 5, 1, 2, 3, 4], [0, 5, 1, 2, 4, 3], [0, 5, 1, 3, 2, 4], [0, 5, 1, 3, 4, 2], [0, 5, 1, 4, 2, 3], [0, 5, 1, 4, 3, 2], [0, 5, 2, 1, 3, 4], [0, 5, 2, 1, 4, 3], [0, 5, 2, 3, 1, 4], [0, 5, 2, 3, 4, 1], [0, 5, 2, 4, 1, 3], [0, 5, 2, 4, 3, 1], [0, 5, 3, 1, 2, 4], [0, 5, 3, 1, 4, 2], [0, 5, 3, 2, 1, 4], [0, 5, 3, 2, 4, 1], [0, 5, 3, 4, 1, 2], [0, 5, 3, 4, 2, 1], [0, 5, 4, 1, 2, 3], [0, 5, 4, 1, 3, 2], [0, 5, 4, 2, 1, 3], [0, 5, 4, 2, 3, 1], [0, 5, 4, 3, 1, 2], [0, 5, 4, 3, 2, 1], [1, 0, 2, 3, 4, 5], [1, 0, 2, 3, 5, 4], [1, 0, 2, 4, 3, 5], [1, 0, 2, 4, 5, 3], [1, 0, 2, 5, 3, 4], [1, 0, 2, 5, 4, 3], [1, 0, 3, 2, 4, 5], [1, 0, 3, 2, 5, 4], [1, 0, 3, 4, 2, 5], [1, 0, 3, 4, 5, 2], [1, 0, 3, 5, 2, 4], [1, 0, 3, 5, 4, 2], [1, 0, 4, 2, 3, 5], [1, 0, 4, 2, 5, 3], [1, 0, 4, 3, 2, 5], [1, 0, 4, 3, 5, 2], [1, 0, 4, 5, 2, 3], [1, 0, 4, 5, 3, 2], [1, 0, 5, 2, 3, 4], [1, 0, 5, 2, 4, 3], [1, 0, 5, 3, 2, 4], [1, 0, 5, 3, 4, 2], [1, 0, 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3, 1, 0, 5], [4, 2, 3, 1, 5, 0], [4, 2, 3, 5, 0, 1], [4, 2, 3, 5, 1, 0], [4, 2, 5, 0, 1, 3], [4, 2, 5, 0, 3, 1], [4, 2, 5, 1, 0, 3], [4, 2, 5, 1, 3, 0], [4, 2, 5, 3, 0, 1], [4, 2, 5, 3, 1, 0], [4, 3, 0, 1, 2, 5], [4, 3, 0, 1, 5, 2], [4, 3, 0, 2, 1, 5], [4, 3, 0, 2, 5, 1], [4, 3, 0, 5, 1, 2], [4, 3, 0, 5, 2, 1], [4, 3, 1, 0, 2, 5], [4, 3, 1, 0, 5, 2], [4, 3, 1, 2, 0, 5], [4, 3, 1, 2, 5, 0], [4, 3, 1, 5, 0, 2], [4, 3, 1, 5, 2, 0], [4, 3, 2, 0, 1, 5], [4, 3, 2, 0, 5, 1], [4, 3, 2, 1, 0, 5], [4, 3, 2, 1, 5, 0], [4, 3, 2, 5, 0, 1], [4, 3, 2, 5, 1, 0], [4, 3, 5, 0, 1, 2], [4, 3, 5, 0, 2, 1], [4, 3, 5, 1, 0, 2], [4, 3, 5, 1, 2, 0], [4, 3, 5, 2, 0, 1], [4, 3, 5, 2, 1, 0], [4, 5, 0, 1, 2, 3], [4, 5, 0, 1, 3, 2], [4, 5, 0, 2, 1, 3], [4, 5, 0, 2, 3, 1], [4, 5, 0, 3, 1, 2], [4, 5, 0, 3, 2, 1], [4, 5, 1, 0, 2, 3], [4, 5, 1, 0, 3, 2], [4, 5, 1, 2, 0, 3], [4, 5, 1, 2, 3, 0], [4, 5, 1, 3, 0, 2], [4, 5, 1, 3, 2, 0], [4, 5, 2, 0, 1, 3], [4, 5, 2, 0, 3, 1], [4, 5, 2, 1, 0, 3], [4, 5, 2, 1, 3, 0], [4, 5, 2, 3, 0, 1], [4, 5, 2, 3, 1, 0], [4, 5, 3, 0, 1, 2], [4, 5, 3, 0, 2, 1], [4, 5, 3, 1, 0, 2], [4, 5, 3, 1, 2, 0], [4, 5, 3, 2, 0, 1], [4, 5, 3, 2, 1, 0], [5, 0, 1, 2, 3, 4], [5, 0, 1, 2, 4, 3], [5, 0, 1, 3, 2, 4], [5, 0, 1, 3, 4, 2], [5, 0, 1, 4, 2, 3], [5, 0, 1, 4, 3, 2], [5, 0, 2, 1, 3, 4], [5, 0, 2, 1, 4, 3], [5, 0, 2, 3, 1, 4], [5, 0, 2, 3, 4, 1], [5, 0, 2, 4, 1, 3], [5, 0, 2, 4, 3, 1], [5, 0, 3, 1, 2, 4], [5, 0, 3, 1, 4, 2], [5, 0, 3, 2, 1, 4], [5, 0, 3, 2, 4, 1], [5, 0, 3, 4, 1, 2], [5, 0, 3, 4, 2, 1], [5, 0, 4, 1, 2, 3], [5, 0, 4, 1, 3, 2], [5, 0, 4, 2, 1, 3], [5, 0, 4, 2, 3, 1], [5, 0, 4, 3, 1, 2], [5, 0, 4, 3, 2, 1], [5, 1, 0, 2, 3, 4], [5, 1, 0, 2, 4, 3], [5, 1, 0, 3, 2, 4], [5, 1, 0, 3, 4, 2], [5, 1, 0, 4, 2, 3], [5, 1, 0, 4, 3, 2], [5, 1, 2, 0, 3, 4], [5, 1, 2, 0, 4, 3], [5, 1, 2, 3, 0, 4], [5, 1, 2, 3, 4, 0], [5, 1, 2, 4, 0, 3], [5, 1, 2, 4, 3, 0], [5, 1, 3, 0, 2, 4], [5, 1, 3, 0, 4, 2], [5, 1, 3, 2, 0, 4], [5, 1, 3, 2, 4, 0], [5, 1, 3, 4, 0, 2], [5, 1, 3, 4, 2, 0], [5, 1, 4, 0, 2, 3], [5, 1, 4, 0, 3, 2], [5, 1, 4, 2, 0, 3], [5, 1, 4, 2, 3, 0], [5, 1, 4, 3, 0, 2], [5, 1, 4, 3, 2, 0], [5, 2, 0, 1, 3, 4], [5, 2, 0, 1, 4, 3], [5, 2, 0, 3, 1, 4], [5, 2, 0, 3, 4, 1], [5, 2, 0, 4, 1, 3], [5, 2, 0, 4, 3, 1], [5, 2, 1, 0, 3, 4], [5, 2, 1, 0, 4, 3], [5, 2, 1, 3, 0, 4], [5, 2, 1, 3, 4, 0], [5, 2, 1, 4, 0, 3], [5, 2, 1, 4, 3, 0], [5, 2, 3, 0, 1, 4], [5, 2, 3, 0, 4, 1], [5, 2, 3, 1, 0, 4], [5, 2, 3, 1, 4, 0], [5, 2, 3, 4, 0, 1], [5, 2, 3, 4, 1, 0], [5, 2, 4, 0, 1, 3], [5, 2, 4, 0, 3, 1], [5, 2, 4, 1, 0, 3], [5, 2, 4, 1, 3, 0], [5, 2, 4, 3, 0, 1], [5, 2, 4, 3, 1, 0], [5, 3, 0, 1, 2, 4], [5, 3, 0, 1, 4, 2], [5, 3, 0, 2, 1, 4], [5, 3, 0, 2, 4, 1], [5, 3, 0, 4, 1, 2], [5, 3, 0, 4, 2, 1], [5, 3, 1, 0, 2, 4], [5, 3, 1, 0, 4, 2], [5, 3, 1, 2, 0, 4], [5, 3, 1, 2, 4, 0], [5, 3, 1, 4, 0, 2], [5, 3, 1, 4, 2, 0], [5, 3, 2, 0, 1, 4], [5, 3, 2, 0, 4, 1], [5, 3, 2, 1, 0, 4], [5, 3, 2, 1, 4, 0], [5, 3, 2, 4, 0, 1], [5, 3, 2, 4, 1, 0], [5, 3, 4, 0, 1, 2], [5, 3, 4, 0, 2, 1], [5, 3, 4, 1, 0, 2], [5, 3, 4, 1, 2, 0], [5, 3, 4, 2, 0, 1], [5, 3, 4, 2, 1, 0], [5, 4, 0, 1, 2, 3], [5, 4, 0, 1, 3, 2], [5, 4, 0, 2, 1, 3], [5, 4, 0, 2, 3, 1], [5, 4, 0, 3, 1, 2], [5, 4, 0, 3, 2, 1], [5, 4, 1, 0, 2, 3], [5, 4, 1, 0, 3, 2], [5, 4, 1, 2, 0, 3], [5, 4, 1, 2, 3, 0], [5, 4, 1, 3, 0, 2], [5, 4, 1, 3, 2, 0], [5, 4, 2, 0, 1, 3], [5, 4, 2, 0, 3, 1], [5, 4, 2, 1, 0, 3], [5, 4, 2, 1, 3, 0], [5, 4, 2, 3, 0, 1], [5, 4, 2, 3, 1, 0], [5, 4, 3, 0, 1, 2], [5, 4, 3, 0, 2, 1], [5, 4, 3, 1, 0, 2], [5, 4, 3, 1, 2, 0], [5, 4, 3, 2, 0, 1], [5, 4, 3, 2, 1, 0]]\n assert candidate(nums = [7, 8, 9, 7, 8, 9]) == [[7, 7, 8, 8, 9, 9], [7, 7, 8, 9, 8, 9], [7, 7, 8, 9, 9, 8], [7, 7, 9, 8, 8, 9], [7, 7, 9, 8, 9, 8], [7, 7, 9, 9, 8, 8], [7, 8, 7, 8, 9, 9], [7, 8, 7, 9, 8, 9], [7, 8, 7, 9, 9, 8], [7, 8, 8, 7, 9, 9], [7, 8, 8, 9, 7, 9], [7, 8, 8, 9, 9, 7], [7, 8, 9, 7, 8, 9], [7, 8, 9, 7, 9, 8], [7, 8, 9, 8, 7, 9], [7, 8, 9, 8, 9, 7], [7, 8, 9, 9, 7, 8], [7, 8, 9, 9, 8, 7], [7, 9, 7, 8, 8, 9], [7, 9, 7, 8, 9, 8], [7, 9, 7, 9, 8, 8], [7, 9, 8, 7, 8, 9], [7, 9, 8, 7, 9, 8], [7, 9, 8, 8, 7, 9], [7, 9, 8, 8, 9, 7], [7, 9, 8, 9, 7, 8], [7, 9, 8, 9, 8, 7], [7, 9, 9, 7, 8, 8], [7, 9, 9, 8, 7, 8], [7, 9, 9, 8, 8, 7], [8, 7, 7, 8, 9, 9], [8, 7, 7, 9, 8, 9], [8, 7, 7, 9, 9, 8], [8, 7, 8, 7, 9, 9], [8, 7, 8, 9, 7, 9], [8, 7, 8, 9, 9, 7], [8, 7, 9, 7, 8, 9], [8, 7, 9, 7, 9, 8], [8, 7, 9, 8, 7, 9], [8, 7, 9, 8, 9, 7], [8, 7, 9, 9, 7, 8], [8, 7, 9, 9, 8, 7], [8, 8, 7, 7, 9, 9], [8, 8, 7, 9, 7, 9], [8, 8, 7, 9, 9, 7], [8, 8, 9, 7, 7, 9], [8, 8, 9, 7, 9, 7], [8, 8, 9, 9, 7, 7], [8, 9, 7, 7, 8, 9], [8, 9, 7, 7, 9, 8], [8, 9, 7, 8, 7, 9], [8, 9, 7, 8, 9, 7], [8, 9, 7, 9, 7, 8], [8, 9, 7, 9, 8, 7], [8, 9, 8, 7, 7, 9], [8, 9, 8, 7, 9, 7], [8, 9, 8, 9, 7, 7], [8, 9, 9, 7, 7, 8], [8, 9, 9, 7, 8, 7], [8, 9, 9, 8, 7, 7], [9, 7, 7, 8, 8, 9], [9, 7, 7, 8, 9, 8], [9, 7, 7, 9, 8, 8], [9, 7, 8, 7, 8, 9], [9, 7, 8, 7, 9, 8], [9, 7, 8, 8, 7, 9], [9, 7, 8, 8, 9, 7], [9, 7, 8, 9, 7, 8], [9, 7, 8, 9, 8, 7], [9, 7, 9, 7, 8, 8], [9, 7, 9, 8, 7, 8], [9, 7, 9, 8, 8, 7], [9, 8, 7, 7, 8, 9], [9, 8, 7, 7, 9, 8], [9, 8, 7, 8, 7, 9], [9, 8, 7, 8, 9, 7], [9, 8, 7, 9, 7, 8], [9, 8, 7, 9, 8, 7], [9, 8, 8, 7, 7, 9], [9, 8, 8, 7, 9, 7], [9, 8, 8, 9, 7, 7], [9, 8, 9, 7, 7, 8], [9, 8, 9, 7, 8, 7], [9, 8, 9, 8, 7, 7], [9, 9, 7, 7, 8, 8], [9, 9, 7, 8, 7, 8], [9, 9, 7, 8, 8, 7], [9, 9, 8, 7, 7, 8], [9, 9, 8, 7, 8, 7], [9, 9, 8, 8, 7, 7]]\n assert candidate(nums = [10, -10, 0, 10, -10]) == [[-10, -10, 0, 10, 10], [-10, -10, 10, 0, 10], [-10, -10, 10, 10, 0], [-10, 0, -10, 10, 10], [-10, 0, 10, -10, 10], [-10, 0, 10, 10, -10], [-10, 10, -10, 0, 10], [-10, 10, -10, 10, 0], [-10, 10, 0, -10, 10], [-10, 10, 0, 10, -10], [-10, 10, 10, -10, 0], [-10, 10, 10, 0, -10], [0, -10, -10, 10, 10], [0, -10, 10, -10, 10], [0, -10, 10, 10, -10], [0, 10, -10, -10, 10], [0, 10, -10, 10, -10], [0, 10, 10, -10, -10], [10, -10, -10, 0, 10], [10, -10, -10, 10, 0], [10, -10, 0, -10, 10], [10, -10, 0, 10, -10], [10, -10, 10, -10, 0], [10, -10, 10, 0, -10], [10, 0, -10, -10, 10], [10, 0, -10, 10, -10], [10, 0, 10, -10, -10], [10, 10, -10, -10, 0], [10, 10, -10, 0, -10], [10, 10, 0, -10, -10]]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5]) == [[2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 5, 4], [2, 2, 3, 3, 5, 4, 4], [2, 2, 3, 4, 3, 4, 5], [2, 2, 3, 4, 3, 5, 4], [2, 2, 3, 4, 4, 3, 5], [2, 2, 3, 4, 4, 5, 3], [2, 2, 3, 4, 5, 3, 4], [2, 2, 3, 4, 5, 4, 3], [2, 2, 3, 5, 3, 4, 4], [2, 2, 3, 5, 4, 3, 4], [2, 2, 3, 5, 4, 4, 3], [2, 2, 4, 3, 3, 4, 5], [2, 2, 4, 3, 3, 5, 4], [2, 2, 4, 3, 4, 3, 5], [2, 2, 4, 3, 4, 5, 3], [2, 2, 4, 3, 5, 3, 4], [2, 2, 4, 3, 5, 4, 3], [2, 2, 4, 4, 3, 3, 5], [2, 2, 4, 4, 3, 5, 3], [2, 2, 4, 4, 5, 3, 3], [2, 2, 4, 5, 3, 3, 4], [2, 2, 4, 5, 3, 4, 3], [2, 2, 4, 5, 4, 3, 3], [2, 2, 5, 3, 3, 4, 4], [2, 2, 5, 3, 4, 3, 4], [2, 2, 5, 3, 4, 4, 3], [2, 2, 5, 4, 3, 3, 4], [2, 2, 5, 4, 3, 4, 3], [2, 2, 5, 4, 4, 3, 3], [2, 3, 2, 3, 4, 4, 5], [2, 3, 2, 3, 4, 5, 4], [2, 3, 2, 3, 5, 4, 4], [2, 3, 2, 4, 3, 4, 5], [2, 3, 2, 4, 3, 5, 4], [2, 3, 2, 4, 4, 3, 5], [2, 3, 2, 4, 4, 5, 3], [2, 3, 2, 4, 5, 3, 4], [2, 3, 2, 4, 5, 4, 3], [2, 3, 2, 5, 3, 4, 4], [2, 3, 2, 5, 4, 3, 4], [2, 3, 2, 5, 4, 4, 3], [2, 3, 3, 2, 4, 4, 5], [2, 3, 3, 2, 4, 5, 4], [2, 3, 3, 2, 5, 4, 4], [2, 3, 3, 4, 2, 4, 5], [2, 3, 3, 4, 2, 5, 4], [2, 3, 3, 4, 4, 2, 5], [2, 3, 3, 4, 4, 5, 2], [2, 3, 3, 4, 5, 2, 4], [2, 3, 3, 4, 5, 4, 2], [2, 3, 3, 5, 2, 4, 4], [2, 3, 3, 5, 4, 2, 4], [2, 3, 3, 5, 4, 4, 2], [2, 3, 4, 2, 3, 4, 5], [2, 3, 4, 2, 3, 5, 4], [2, 3, 4, 2, 4, 3, 5], [2, 3, 4, 2, 4, 5, 3], [2, 3, 4, 2, 5, 3, 4], [2, 3, 4, 2, 5, 4, 3], [2, 3, 4, 3, 2, 4, 5], [2, 3, 4, 3, 2, 5, 4], [2, 3, 4, 3, 4, 2, 5], [2, 3, 4, 3, 4, 5, 2], [2, 3, 4, 3, 5, 2, 4], [2, 3, 4, 3, 5, 4, 2], [2, 3, 4, 4, 2, 3, 5], [2, 3, 4, 4, 2, 5, 3], [2, 3, 4, 4, 3, 2, 5], [2, 3, 4, 4, 3, 5, 2], [2, 3, 4, 4, 5, 2, 3], [2, 3, 4, 4, 5, 3, 2], [2, 3, 4, 5, 2, 3, 4], [2, 3, 4, 5, 2, 4, 3], [2, 3, 4, 5, 3, 2, 4], [2, 3, 4, 5, 3, 4, 2], [2, 3, 4, 5, 4, 2, 3], [2, 3, 4, 5, 4, 3, 2], [2, 3, 5, 2, 3, 4, 4], [2, 3, 5, 2, 4, 3, 4], [2, 3, 5, 2, 4, 4, 3], [2, 3, 5, 3, 2, 4, 4], [2, 3, 5, 3, 4, 2, 4], [2, 3, 5, 3, 4, 4, 2], [2, 3, 5, 4, 2, 3, 4], [2, 3, 5, 4, 2, 4, 3], [2, 3, 5, 4, 3, 2, 4], [2, 3, 5, 4, 3, 4, 2], [2, 3, 5, 4, 4, 2, 3], [2, 3, 5, 4, 4, 3, 2], [2, 4, 2, 3, 3, 4, 5], [2, 4, 2, 3, 3, 5, 4], [2, 4, 2, 3, 4, 3, 5], [2, 4, 2, 3, 4, 5, 3], [2, 4, 2, 3, 5, 3, 4], [2, 4, 2, 3, 5, 4, 3], [2, 4, 2, 4, 3, 3, 5], [2, 4, 2, 4, 3, 5, 3], [2, 4, 2, 4, 5, 3, 3], [2, 4, 2, 5, 3, 3, 4], [2, 4, 2, 5, 3, 4, 3], [2, 4, 2, 5, 4, 3, 3], [2, 4, 3, 2, 3, 4, 5], [2, 4, 3, 2, 3, 5, 4], [2, 4, 3, 2, 4, 3, 5], [2, 4, 3, 2, 4, 5, 3], [2, 4, 3, 2, 5, 3, 4], [2, 4, 3, 2, 5, 4, 3], [2, 4, 3, 3, 2, 4, 5], [2, 4, 3, 3, 2, 5, 4], [2, 4, 3, 3, 4, 2, 5], [2, 4, 3, 3, 4, 5, 2], [2, 4, 3, 3, 5, 2, 4], [2, 4, 3, 3, 5, 4, 2], [2, 4, 3, 4, 2, 3, 5], [2, 4, 3, 4, 2, 5, 3], [2, 4, 3, 4, 3, 2, 5], [2, 4, 3, 4, 3, 5, 2], [2, 4, 3, 4, 5, 2, 3], [2, 4, 3, 4, 5, 3, 2], [2, 4, 3, 5, 2, 3, 4], [2, 4, 3, 5, 2, 4, 3], [2, 4, 3, 5, 3, 2, 4], [2, 4, 3, 5, 3, 4, 2], [2, 4, 3, 5, 4, 2, 3], [2, 4, 3, 5, 4, 3, 2], [2, 4, 4, 2, 3, 3, 5], [2, 4, 4, 2, 3, 5, 3], [2, 4, 4, 2, 5, 3, 3], [2, 4, 4, 3, 2, 3, 5], [2, 4, 4, 3, 2, 5, 3], [2, 4, 4, 3, 3, 2, 5], [2, 4, 4, 3, 3, 5, 2], [2, 4, 4, 3, 5, 2, 3], [2, 4, 4, 3, 5, 3, 2], [2, 4, 4, 5, 2, 3, 3], [2, 4, 4, 5, 3, 2, 3], [2, 4, 4, 5, 3, 3, 2], [2, 4, 5, 2, 3, 3, 4], [2, 4, 5, 2, 3, 4, 3], [2, 4, 5, 2, 4, 3, 3], [2, 4, 5, 3, 2, 3, 4], [2, 4, 5, 3, 2, 4, 3], [2, 4, 5, 3, 3, 2, 4], [2, 4, 5, 3, 3, 4, 2], [2, 4, 5, 3, 4, 2, 3], [2, 4, 5, 3, 4, 3, 2], [2, 4, 5, 4, 2, 3, 3], [2, 4, 5, 4, 3, 2, 3], [2, 4, 5, 4, 3, 3, 2], [2, 5, 2, 3, 3, 4, 4], [2, 5, 2, 3, 4, 3, 4], [2, 5, 2, 3, 4, 4, 3], [2, 5, 2, 4, 3, 3, 4], [2, 5, 2, 4, 3, 4, 3], [2, 5, 2, 4, 4, 3, 3], [2, 5, 3, 2, 3, 4, 4], [2, 5, 3, 2, 4, 3, 4], [2, 5, 3, 2, 4, 4, 3], [2, 5, 3, 3, 2, 4, 4], [2, 5, 3, 3, 4, 2, 4], [2, 5, 3, 3, 4, 4, 2], [2, 5, 3, 4, 2, 3, 4], [2, 5, 3, 4, 2, 4, 3], [2, 5, 3, 4, 3, 2, 4], [2, 5, 3, 4, 3, 4, 2], [2, 5, 3, 4, 4, 2, 3], [2, 5, 3, 4, 4, 3, 2], [2, 5, 4, 2, 3, 3, 4], [2, 5, 4, 2, 3, 4, 3], [2, 5, 4, 2, 4, 3, 3], [2, 5, 4, 3, 2, 3, 4], [2, 5, 4, 3, 2, 4, 3], [2, 5, 4, 3, 3, 2, 4], [2, 5, 4, 3, 3, 4, 2], [2, 5, 4, 3, 4, 2, 3], [2, 5, 4, 3, 4, 3, 2], [2, 5, 4, 4, 2, 3, 3], [2, 5, 4, 4, 3, 2, 3], [2, 5, 4, 4, 3, 3, 2], [3, 2, 2, 3, 4, 4, 5], [3, 2, 2, 3, 4, 5, 4], [3, 2, 2, 3, 5, 4, 4], [3, 2, 2, 4, 3, 4, 5], [3, 2, 2, 4, 3, 5, 4], [3, 2, 2, 4, 4, 3, 5], [3, 2, 2, 4, 4, 5, 3], [3, 2, 2, 4, 5, 3, 4], [3, 2, 2, 4, 5, 4, 3], [3, 2, 2, 5, 3, 4, 4], [3, 2, 2, 5, 4, 3, 4], [3, 2, 2, 5, 4, 4, 3], [3, 2, 3, 2, 4, 4, 5], [3, 2, 3, 2, 4, 5, 4], [3, 2, 3, 2, 5, 4, 4], [3, 2, 3, 4, 2, 4, 5], [3, 2, 3, 4, 2, 5, 4], [3, 2, 3, 4, 4, 2, 5], [3, 2, 3, 4, 4, 5, 2], [3, 2, 3, 4, 5, 2, 4], [3, 2, 3, 4, 5, 4, 2], [3, 2, 3, 5, 2, 4, 4], [3, 2, 3, 5, 4, 2, 4], [3, 2, 3, 5, 4, 4, 2], [3, 2, 4, 2, 3, 4, 5], [3, 2, 4, 2, 3, 5, 4], [3, 2, 4, 2, 4, 3, 5], [3, 2, 4, 2, 4, 5, 3], [3, 2, 4, 2, 5, 3, 4], [3, 2, 4, 2, 5, 4, 3], [3, 2, 4, 3, 2, 4, 5], [3, 2, 4, 3, 2, 5, 4], [3, 2, 4, 3, 4, 2, 5], [3, 2, 4, 3, 4, 5, 2], [3, 2, 4, 3, 5, 2, 4], [3, 2, 4, 3, 5, 4, 2], [3, 2, 4, 4, 2, 3, 5], [3, 2, 4, 4, 2, 5, 3], [3, 2, 4, 4, 3, 2, 5], [3, 2, 4, 4, 3, 5, 2], [3, 2, 4, 4, 5, 2, 3], [3, 2, 4, 4, 5, 3, 2], [3, 2, 4, 5, 2, 3, 4], [3, 2, 4, 5, 2, 4, 3], [3, 2, 4, 5, 3, 2, 4], [3, 2, 4, 5, 3, 4, 2], [3, 2, 4, 5, 4, 2, 3], [3, 2, 4, 5, 4, 3, 2], [3, 2, 5, 2, 3, 4, 4], [3, 2, 5, 2, 4, 3, 4], [3, 2, 5, 2, 4, 4, 3], [3, 2, 5, 3, 2, 4, 4], [3, 2, 5, 3, 4, 2, 4], [3, 2, 5, 3, 4, 4, 2], [3, 2, 5, 4, 2, 3, 4], [3, 2, 5, 4, 2, 4, 3], [3, 2, 5, 4, 3, 2, 4], [3, 2, 5, 4, 3, 4, 2], [3, 2, 5, 4, 4, 2, 3], [3, 2, 5, 4, 4, 3, 2], [3, 3, 2, 2, 4, 4, 5], [3, 3, 2, 2, 4, 5, 4], [3, 3, 2, 2, 5, 4, 4], [3, 3, 2, 4, 2, 4, 5], [3, 3, 2, 4, 2, 5, 4], [3, 3, 2, 4, 4, 2, 5], [3, 3, 2, 4, 4, 5, 2], [3, 3, 2, 4, 5, 2, 4], [3, 3, 2, 4, 5, 4, 2], [3, 3, 2, 5, 2, 4, 4], [3, 3, 2, 5, 4, 2, 4], [3, 3, 2, 5, 4, 4, 2], [3, 3, 4, 2, 2, 4, 5], [3, 3, 4, 2, 2, 5, 4], [3, 3, 4, 2, 4, 2, 5], [3, 3, 4, 2, 4, 5, 2], [3, 3, 4, 2, 5, 2, 4], [3, 3, 4, 2, 5, 4, 2], [3, 3, 4, 4, 2, 2, 5], [3, 3, 4, 4, 2, 5, 2], [3, 3, 4, 4, 5, 2, 2], [3, 3, 4, 5, 2, 2, 4], [3, 3, 4, 5, 2, 4, 2], [3, 3, 4, 5, 4, 2, 2], [3, 3, 5, 2, 2, 4, 4], [3, 3, 5, 2, 4, 2, 4], [3, 3, 5, 2, 4, 4, 2], [3, 3, 5, 4, 2, 2, 4], [3, 3, 5, 4, 2, 4, 2], [3, 3, 5, 4, 4, 2, 2], [3, 4, 2, 2, 3, 4, 5], [3, 4, 2, 2, 3, 5, 4], [3, 4, 2, 2, 4, 3, 5], [3, 4, 2, 2, 4, 5, 3], [3, 4, 2, 2, 5, 3, 4], [3, 4, 2, 2, 5, 4, 3], [3, 4, 2, 3, 2, 4, 5], [3, 4, 2, 3, 2, 5, 4], [3, 4, 2, 3, 4, 2, 5], [3, 4, 2, 3, 4, 5, 2], [3, 4, 2, 3, 5, 2, 4], [3, 4, 2, 3, 5, 4, 2], [3, 4, 2, 4, 2, 3, 5], [3, 4, 2, 4, 2, 5, 3], [3, 4, 2, 4, 3, 2, 5], [3, 4, 2, 4, 3, 5, 2], [3, 4, 2, 4, 5, 2, 3], [3, 4, 2, 4, 5, 3, 2], [3, 4, 2, 5, 2, 3, 4], [3, 4, 2, 5, 2, 4, 3], [3, 4, 2, 5, 3, 2, 4], [3, 4, 2, 5, 3, 4, 2], [3, 4, 2, 5, 4, 2, 3], [3, 4, 2, 5, 4, 3, 2], [3, 4, 3, 2, 2, 4, 5], [3, 4, 3, 2, 2, 5, 4], [3, 4, 3, 2, 4, 2, 5], [3, 4, 3, 2, 4, 5, 2], [3, 4, 3, 2, 5, 2, 4], [3, 4, 3, 2, 5, 4, 2], [3, 4, 3, 4, 2, 2, 5], [3, 4, 3, 4, 2, 5, 2], [3, 4, 3, 4, 5, 2, 2], [3, 4, 3, 5, 2, 2, 4], [3, 4, 3, 5, 2, 4, 2], [3, 4, 3, 5, 4, 2, 2], [3, 4, 4, 2, 2, 3, 5], [3, 4, 4, 2, 2, 5, 3], [3, 4, 4, 2, 3, 2, 5], [3, 4, 4, 2, 3, 5, 2], [3, 4, 4, 2, 5, 2, 3], [3, 4, 4, 2, 5, 3, 2], [3, 4, 4, 3, 2, 2, 5], [3, 4, 4, 3, 2, 5, 2], [3, 4, 4, 3, 5, 2, 2], [3, 4, 4, 5, 2, 2, 3], [3, 4, 4, 5, 2, 3, 2], [3, 4, 4, 5, 3, 2, 2], [3, 4, 5, 2, 2, 3, 4], [3, 4, 5, 2, 2, 4, 3], [3, 4, 5, 2, 3, 2, 4], [3, 4, 5, 2, 3, 4, 2], [3, 4, 5, 2, 4, 2, 3], [3, 4, 5, 2, 4, 3, 2], [3, 4, 5, 3, 2, 2, 4], [3, 4, 5, 3, 2, 4, 2], [3, 4, 5, 3, 4, 2, 2], [3, 4, 5, 4, 2, 2, 3], [3, 4, 5, 4, 2, 3, 2], [3, 4, 5, 4, 3, 2, 2], [3, 5, 2, 2, 3, 4, 4], [3, 5, 2, 2, 4, 3, 4], [3, 5, 2, 2, 4, 4, 3], [3, 5, 2, 3, 2, 4, 4], [3, 5, 2, 3, 4, 2, 4], [3, 5, 2, 3, 4, 4, 2], [3, 5, 2, 4, 2, 3, 4], [3, 5, 2, 4, 2, 4, 3], [3, 5, 2, 4, 3, 2, 4], [3, 5, 2, 4, 3, 4, 2], [3, 5, 2, 4, 4, 2, 3], [3, 5, 2, 4, 4, 3, 2], [3, 5, 3, 2, 2, 4, 4], [3, 5, 3, 2, 4, 2, 4], [3, 5, 3, 2, 4, 4, 2], [3, 5, 3, 4, 2, 2, 4], [3, 5, 3, 4, 2, 4, 2], [3, 5, 3, 4, 4, 2, 2], [3, 5, 4, 2, 2, 3, 4], [3, 5, 4, 2, 2, 4, 3], [3, 5, 4, 2, 3, 2, 4], [3, 5, 4, 2, 3, 4, 2], [3, 5, 4, 2, 4, 2, 3], [3, 5, 4, 2, 4, 3, 2], [3, 5, 4, 3, 2, 2, 4], [3, 5, 4, 3, 2, 4, 2], [3, 5, 4, 3, 4, 2, 2], [3, 5, 4, 4, 2, 2, 3], [3, 5, 4, 4, 2, 3, 2], [3, 5, 4, 4, 3, 2, 2], [4, 2, 2, 3, 3, 4, 5], [4, 2, 2, 3, 3, 5, 4], [4, 2, 2, 3, 4, 3, 5], [4, 2, 2, 3, 4, 5, 3], [4, 2, 2, 3, 5, 3, 4], [4, 2, 2, 3, 5, 4, 3], [4, 2, 2, 4, 3, 3, 5], [4, 2, 2, 4, 3, 5, 3], [4, 2, 2, 4, 5, 3, 3], [4, 2, 2, 5, 3, 3, 4], [4, 2, 2, 5, 3, 4, 3], [4, 2, 2, 5, 4, 3, 3], [4, 2, 3, 2, 3, 4, 5], [4, 2, 3, 2, 3, 5, 4], [4, 2, 3, 2, 4, 3, 5], [4, 2, 3, 2, 4, 5, 3], [4, 2, 3, 2, 5, 3, 4], [4, 2, 3, 2, 5, 4, 3], [4, 2, 3, 3, 2, 4, 5], [4, 2, 3, 3, 2, 5, 4], [4, 2, 3, 3, 4, 2, 5], [4, 2, 3, 3, 4, 5, 2], [4, 2, 3, 3, 5, 2, 4], [4, 2, 3, 3, 5, 4, 2], [4, 2, 3, 4, 2, 3, 5], [4, 2, 3, 4, 2, 5, 3], [4, 2, 3, 4, 3, 2, 5], [4, 2, 3, 4, 3, 5, 2], [4, 2, 3, 4, 5, 2, 3], [4, 2, 3, 4, 5, 3, 2], [4, 2, 3, 5, 2, 3, 4], [4, 2, 3, 5, 2, 4, 3], [4, 2, 3, 5, 3, 2, 4], [4, 2, 3, 5, 3, 4, 2], [4, 2, 3, 5, 4, 2, 3], [4, 2, 3, 5, 4, 3, 2], [4, 2, 4, 2, 3, 3, 5], [4, 2, 4, 2, 3, 5, 3], [4, 2, 4, 2, 5, 3, 3], [4, 2, 4, 3, 2, 3, 5], [4, 2, 4, 3, 2, 5, 3], [4, 2, 4, 3, 3, 2, 5], [4, 2, 4, 3, 3, 5, 2], [4, 2, 4, 3, 5, 2, 3], [4, 2, 4, 3, 5, 3, 2], [4, 2, 4, 5, 2, 3, 3], [4, 2, 4, 5, 3, 2, 3], [4, 2, 4, 5, 3, 3, 2], [4, 2, 5, 2, 3, 3, 4], [4, 2, 5, 2, 3, 4, 3], [4, 2, 5, 2, 4, 3, 3], [4, 2, 5, 3, 2, 3, 4], [4, 2, 5, 3, 2, 4, 3], [4, 2, 5, 3, 3, 2, 4], [4, 2, 5, 3, 3, 4, 2], [4, 2, 5, 3, 4, 2, 3], [4, 2, 5, 3, 4, 3, 2], [4, 2, 5, 4, 2, 3, 3], [4, 2, 5, 4, 3, 2, 3], [4, 2, 5, 4, 3, 3, 2], [4, 3, 2, 2, 3, 4, 5], [4, 3, 2, 2, 3, 5, 4], [4, 3, 2, 2, 4, 3, 5], [4, 3, 2, 2, 4, 5, 3], [4, 3, 2, 2, 5, 3, 4], [4, 3, 2, 2, 5, 4, 3], [4, 3, 2, 3, 2, 4, 5], [4, 3, 2, 3, 2, 5, 4], [4, 3, 2, 3, 4, 2, 5], [4, 3, 2, 3, 4, 5, 2], [4, 3, 2, 3, 5, 2, 4], [4, 3, 2, 3, 5, 4, 2], [4, 3, 2, 4, 2, 3, 5], [4, 3, 2, 4, 2, 5, 3], [4, 3, 2, 4, 3, 2, 5], [4, 3, 2, 4, 3, 5, 2], [4, 3, 2, 4, 5, 2, 3], [4, 3, 2, 4, 5, 3, 2], [4, 3, 2, 5, 2, 3, 4], [4, 3, 2, 5, 2, 4, 3], [4, 3, 2, 5, 3, 2, 4], [4, 3, 2, 5, 3, 4, 2], [4, 3, 2, 5, 4, 2, 3], [4, 3, 2, 5, 4, 3, 2], [4, 3, 3, 2, 2, 4, 5], [4, 3, 3, 2, 2, 5, 4], [4, 3, 3, 2, 4, 2, 5], [4, 3, 3, 2, 4, 5, 2], [4, 3, 3, 2, 5, 2, 4], [4, 3, 3, 2, 5, 4, 2], [4, 3, 3, 4, 2, 2, 5], [4, 3, 3, 4, 2, 5, 2], [4, 3, 3, 4, 5, 2, 2], [4, 3, 3, 5, 2, 2, 4], [4, 3, 3, 5, 2, 4, 2], [4, 3, 3, 5, 4, 2, 2], [4, 3, 4, 2, 2, 3, 5], [4, 3, 4, 2, 2, 5, 3], [4, 3, 4, 2, 3, 2, 5], [4, 3, 4, 2, 3, 5, 2], [4, 3, 4, 2, 5, 2, 3], [4, 3, 4, 2, 5, 3, 2], [4, 3, 4, 3, 2, 2, 5], [4, 3, 4, 3, 2, 5, 2], [4, 3, 4, 3, 5, 2, 2], [4, 3, 4, 5, 2, 2, 3], [4, 3, 4, 5, 2, 3, 2], [4, 3, 4, 5, 3, 2, 2], [4, 3, 5, 2, 2, 3, 4], [4, 3, 5, 2, 2, 4, 3], [4, 3, 5, 2, 3, 2, 4], [4, 3, 5, 2, 3, 4, 2], [4, 3, 5, 2, 4, 2, 3], [4, 3, 5, 2, 4, 3, 2], [4, 3, 5, 3, 2, 2, 4], [4, 3, 5, 3, 2, 4, 2], [4, 3, 5, 3, 4, 2, 2], [4, 3, 5, 4, 2, 2, 3], [4, 3, 5, 4, 2, 3, 2], [4, 3, 5, 4, 3, 2, 2], [4, 4, 2, 2, 3, 3, 5], [4, 4, 2, 2, 3, 5, 3], [4, 4, 2, 2, 5, 3, 3], [4, 4, 2, 3, 2, 3, 5], [4, 4, 2, 3, 2, 5, 3], [4, 4, 2, 3, 3, 2, 5], [4, 4, 2, 3, 3, 5, 2], [4, 4, 2, 3, 5, 2, 3], [4, 4, 2, 3, 5, 3, 2], [4, 4, 2, 5, 2, 3, 3], [4, 4, 2, 5, 3, 2, 3], [4, 4, 2, 5, 3, 3, 2], [4, 4, 3, 2, 2, 3, 5], [4, 4, 3, 2, 2, 5, 3], [4, 4, 3, 2, 3, 2, 5], [4, 4, 3, 2, 3, 5, 2], [4, 4, 3, 2, 5, 2, 3], [4, 4, 3, 2, 5, 3, 2], [4, 4, 3, 3, 2, 2, 5], [4, 4, 3, 3, 2, 5, 2], [4, 4, 3, 3, 5, 2, 2], [4, 4, 3, 5, 2, 2, 3], [4, 4, 3, 5, 2, 3, 2], [4, 4, 3, 5, 3, 2, 2], [4, 4, 5, 2, 2, 3, 3], [4, 4, 5, 2, 3, 2, 3], [4, 4, 5, 2, 3, 3, 2], [4, 4, 5, 3, 2, 2, 3], [4, 4, 5, 3, 2, 3, 2], [4, 4, 5, 3, 3, 2, 2], [4, 5, 2, 2, 3, 3, 4], [4, 5, 2, 2, 3, 4, 3], [4, 5, 2, 2, 4, 3, 3], [4, 5, 2, 3, 2, 3, 4], [4, 5, 2, 3, 2, 4, 3], [4, 5, 2, 3, 3, 2, 4], [4, 5, 2, 3, 3, 4, 2], [4, 5, 2, 3, 4, 2, 3], [4, 5, 2, 3, 4, 3, 2], [4, 5, 2, 4, 2, 3, 3], [4, 5, 2, 4, 3, 2, 3], [4, 5, 2, 4, 3, 3, 2], [4, 5, 3, 2, 2, 3, 4], [4, 5, 3, 2, 2, 4, 3], [4, 5, 3, 2, 3, 2, 4], [4, 5, 3, 2, 3, 4, 2], [4, 5, 3, 2, 4, 2, 3], [4, 5, 3, 2, 4, 3, 2], [4, 5, 3, 3, 2, 2, 4], [4, 5, 3, 3, 2, 4, 2], [4, 5, 3, 3, 4, 2, 2], [4, 5, 3, 4, 2, 2, 3], [4, 5, 3, 4, 2, 3, 2], [4, 5, 3, 4, 3, 2, 2], [4, 5, 4, 2, 2, 3, 3], [4, 5, 4, 2, 3, 2, 3], [4, 5, 4, 2, 3, 3, 2], [4, 5, 4, 3, 2, 2, 3], [4, 5, 4, 3, 2, 3, 2], [4, 5, 4, 3, 3, 2, 2], [5, 2, 2, 3, 3, 4, 4], [5, 2, 2, 3, 4, 3, 4], [5, 2, 2, 3, 4, 4, 3], [5, 2, 2, 4, 3, 3, 4], [5, 2, 2, 4, 3, 4, 3], [5, 2, 2, 4, 4, 3, 3], [5, 2, 3, 2, 3, 4, 4], [5, 2, 3, 2, 4, 3, 4], [5, 2, 3, 2, 4, 4, 3], [5, 2, 3, 3, 2, 4, 4], [5, 2, 3, 3, 4, 2, 4], [5, 2, 3, 3, 4, 4, 2], [5, 2, 3, 4, 2, 3, 4], [5, 2, 3, 4, 2, 4, 3], [5, 2, 3, 4, 3, 2, 4], [5, 2, 3, 4, 3, 4, 2], [5, 2, 3, 4, 4, 2, 3], [5, 2, 3, 4, 4, 3, 2], [5, 2, 4, 2, 3, 3, 4], [5, 2, 4, 2, 3, 4, 3], [5, 2, 4, 2, 4, 3, 3], [5, 2, 4, 3, 2, 3, 4], [5, 2, 4, 3, 2, 4, 3], [5, 2, 4, 3, 3, 2, 4], [5, 2, 4, 3, 3, 4, 2], [5, 2, 4, 3, 4, 2, 3], [5, 2, 4, 3, 4, 3, 2], [5, 2, 4, 4, 2, 3, 3], [5, 2, 4, 4, 3, 2, 3], [5, 2, 4, 4, 3, 3, 2], [5, 3, 2, 2, 3, 4, 4], [5, 3, 2, 2, 4, 3, 4], [5, 3, 2, 2, 4, 4, 3], [5, 3, 2, 3, 2, 4, 4], [5, 3, 2, 3, 4, 2, 4], [5, 3, 2, 3, 4, 4, 2], [5, 3, 2, 4, 2, 3, 4], [5, 3, 2, 4, 2, 4, 3], [5, 3, 2, 4, 3, 2, 4], [5, 3, 2, 4, 3, 4, 2], [5, 3, 2, 4, 4, 2, 3], [5, 3, 2, 4, 4, 3, 2], [5, 3, 3, 2, 2, 4, 4], [5, 3, 3, 2, 4, 2, 4], [5, 3, 3, 2, 4, 4, 2], [5, 3, 3, 4, 2, 2, 4], [5, 3, 3, 4, 2, 4, 2], [5, 3, 3, 4, 4, 2, 2], [5, 3, 4, 2, 2, 3, 4], [5, 3, 4, 2, 2, 4, 3], [5, 3, 4, 2, 3, 2, 4], [5, 3, 4, 2, 3, 4, 2], [5, 3, 4, 2, 4, 2, 3], [5, 3, 4, 2, 4, 3, 2], [5, 3, 4, 3, 2, 2, 4], [5, 3, 4, 3, 2, 4, 2], [5, 3, 4, 3, 4, 2, 2], [5, 3, 4, 4, 2, 2, 3], [5, 3, 4, 4, 2, 3, 2], [5, 3, 4, 4, 3, 2, 2], [5, 4, 2, 2, 3, 3, 4], [5, 4, 2, 2, 3, 4, 3], [5, 4, 2, 2, 4, 3, 3], [5, 4, 2, 3, 2, 3, 4], [5, 4, 2, 3, 2, 4, 3], [5, 4, 2, 3, 3, 2, 4], [5, 4, 2, 3, 3, 4, 2], [5, 4, 2, 3, 4, 2, 3], [5, 4, 2, 3, 4, 3, 2], [5, 4, 2, 4, 2, 3, 3], [5, 4, 2, 4, 3, 2, 3], [5, 4, 2, 4, 3, 3, 2], [5, 4, 3, 2, 2, 3, 4], [5, 4, 3, 2, 2, 4, 3], [5, 4, 3, 2, 3, 2, 4], [5, 4, 3, 2, 3, 4, 2], [5, 4, 3, 2, 4, 2, 3], [5, 4, 3, 2, 4, 3, 2], [5, 4, 3, 3, 2, 2, 4], [5, 4, 3, 3, 2, 4, 2], [5, 4, 3, 3, 4, 2, 2], [5, 4, 3, 4, 2, 2, 3], [5, 4, 3, 4, 2, 3, 2], [5, 4, 3, 4, 3, 2, 2], [5, 4, 4, 2, 2, 3, 3], [5, 4, 4, 2, 3, 2, 3], [5, 4, 4, 2, 3, 3, 2], [5, 4, 4, 3, 2, 2, 3], [5, 4, 4, 3, 2, 3, 2], [5, 4, 4, 3, 3, 2, 2]]\n assert candidate(nums = [4, 4, 4, 4]) == [[4, 4, 4, 4]]\n assert candidate(nums = [0, -1, 1, -2, 2]) == [[-2, -1, 0, 1, 2], [-2, -1, 0, 2, 1], [-2, -1, 1, 0, 2], [-2, -1, 1, 2, 0], [-2, -1, 2, 0, 1], [-2, -1, 2, 1, 0], [-2, 0, -1, 1, 2], [-2, 0, -1, 2, 1], [-2, 0, 1, -1, 2], [-2, 0, 1, 2, -1], [-2, 0, 2, -1, 1], [-2, 0, 2, 1, -1], [-2, 1, -1, 0, 2], [-2, 1, -1, 2, 0], [-2, 1, 0, -1, 2], [-2, 1, 0, 2, -1], [-2, 1, 2, -1, 0], [-2, 1, 2, 0, -1], [-2, 2, -1, 0, 1], [-2, 2, -1, 1, 0], [-2, 2, 0, -1, 1], [-2, 2, 0, 1, -1], [-2, 2, 1, -1, 0], [-2, 2, 1, 0, -1], [-1, -2, 0, 1, 2], [-1, -2, 0, 2, 1], [-1, -2, 1, 0, 2], [-1, -2, 1, 2, 0], [-1, -2, 2, 0, 1], [-1, -2, 2, 1, 0], [-1, 0, -2, 1, 2], [-1, 0, -2, 2, 1], [-1, 0, 1, -2, 2], [-1, 0, 1, 2, -2], [-1, 0, 2, -2, 1], [-1, 0, 2, 1, -2], [-1, 1, -2, 0, 2], [-1, 1, -2, 2, 0], [-1, 1, 0, -2, 2], [-1, 1, 0, 2, -2], [-1, 1, 2, -2, 0], [-1, 1, 2, 0, -2], [-1, 2, -2, 0, 1], [-1, 2, -2, 1, 0], [-1, 2, 0, -2, 1], [-1, 2, 0, 1, -2], [-1, 2, 1, -2, 0], [-1, 2, 1, 0, -2], [0, -2, -1, 1, 2], [0, -2, -1, 2, 1], [0, -2, 1, -1, 2], [0, -2, 1, 2, -1], [0, -2, 2, -1, 1], [0, -2, 2, 1, -1], [0, -1, -2, 1, 2], [0, -1, -2, 2, 1], [0, -1, 1, -2, 2], [0, -1, 1, 2, -2], [0, -1, 2, -2, 1], [0, -1, 2, 1, -2], [0, 1, -2, -1, 2], [0, 1, -2, 2, -1], [0, 1, -1, -2, 2], [0, 1, -1, 2, -2], [0, 1, 2, -2, -1], [0, 1, 2, -1, -2], [0, 2, -2, -1, 1], [0, 2, -2, 1, -1], [0, 2, -1, -2, 1], [0, 2, -1, 1, -2], [0, 2, 1, -2, -1], [0, 2, 1, -1, -2], [1, -2, -1, 0, 2], [1, -2, -1, 2, 0], [1, -2, 0, -1, 2], [1, -2, 0, 2, -1], [1, -2, 2, -1, 0], [1, -2, 2, 0, -1], [1, -1, -2, 0, 2], [1, -1, -2, 2, 0], [1, -1, 0, -2, 2], [1, -1, 0, 2, -2], [1, -1, 2, -2, 0], [1, -1, 2, 0, -2], [1, 0, -2, -1, 2], [1, 0, -2, 2, -1], [1, 0, -1, -2, 2], [1, 0, -1, 2, -2], [1, 0, 2, -2, -1], [1, 0, 2, -1, -2], [1, 2, -2, -1, 0], [1, 2, -2, 0, -1], [1, 2, -1, -2, 0], [1, 2, -1, 0, -2], [1, 2, 0, -2, -1], [1, 2, 0, -1, -2], [2, -2, -1, 0, 1], [2, -2, -1, 1, 0], [2, -2, 0, -1, 1], [2, -2, 0, 1, -1], [2, -2, 1, -1, 0], [2, -2, 1, 0, -1], [2, -1, -2, 0, 1], [2, -1, -2, 1, 0], [2, -1, 0, -2, 1], [2, -1, 0, 1, -2], [2, -1, 1, -2, 0], [2, -1, 1, 0, -2], [2, 0, -2, -1, 1], [2, 0, -2, 1, -1], [2, 0, -1, -2, 1], [2, 0, -1, 1, -2], [2, 0, 1, -2, -1], [2, 0, 1, -1, -2], [2, 1, -2, -1, 0], [2, 1, -2, 0, -1], [2, 1, -1, -2, 0], [2, 1, -1, 0, -2], [2, 1, 0, -2, -1], [2, 1, 0, -1, -2]]\n assert candidate(nums = [5, 5, 6, 7, 7]) == [[5, 5, 6, 7, 7], [5, 5, 7, 6, 7], [5, 5, 7, 7, 6], [5, 6, 5, 7, 7], [5, 6, 7, 5, 7], [5, 6, 7, 7, 5], [5, 7, 5, 6, 7], [5, 7, 5, 7, 6], [5, 7, 6, 5, 7], [5, 7, 6, 7, 5], [5, 7, 7, 5, 6], [5, 7, 7, 6, 5], [6, 5, 5, 7, 7], [6, 5, 7, 5, 7], [6, 5, 7, 7, 5], [6, 7, 5, 5, 7], [6, 7, 5, 7, 5], [6, 7, 7, 5, 5], [7, 5, 5, 6, 7], [7, 5, 5, 7, 6], [7, 5, 6, 5, 7], [7, 5, 6, 7, 5], [7, 5, 7, 5, 6], [7, 5, 7, 6, 5], [7, 6, 5, 5, 7], [7, 6, 5, 7, 5], [7, 6, 7, 5, 5], [7, 7, 5, 5, 6], [7, 7, 5, 6, 5], [7, 7, 6, 5, 5]]\n assert candidate(nums = [5, 5, 6, 7, 8]) == [[5, 5, 6, 7, 8], [5, 5, 6, 8, 7], [5, 5, 7, 6, 8], [5, 5, 7, 8, 6], [5, 5, 8, 6, 7], [5, 5, 8, 7, 6], [5, 6, 5, 7, 8], [5, 6, 5, 8, 7], [5, 6, 7, 5, 8], [5, 6, 7, 8, 5], [5, 6, 8, 5, 7], [5, 6, 8, 7, 5], [5, 7, 5, 6, 8], [5, 7, 5, 8, 6], [5, 7, 6, 5, 8], [5, 7, 6, 8, 5], [5, 7, 8, 5, 6], [5, 7, 8, 6, 5], [5, 8, 5, 6, 7], [5, 8, 5, 7, 6], [5, 8, 6, 5, 7], [5, 8, 6, 7, 5], [5, 8, 7, 5, 6], [5, 8, 7, 6, 5], [6, 5, 5, 7, 8], [6, 5, 5, 8, 7], [6, 5, 7, 5, 8], [6, 5, 7, 8, 5], [6, 5, 8, 5, 7], [6, 5, 8, 7, 5], [6, 7, 5, 5, 8], [6, 7, 5, 8, 5], [6, 7, 8, 5, 5], [6, 8, 5, 5, 7], [6, 8, 5, 7, 5], [6, 8, 7, 5, 5], [7, 5, 5, 6, 8], [7, 5, 5, 8, 6], [7, 5, 6, 5, 8], [7, 5, 6, 8, 5], [7, 5, 8, 5, 6], [7, 5, 8, 6, 5], [7, 6, 5, 5, 8], [7, 6, 5, 8, 5], [7, 6, 8, 5, 5], [7, 8, 5, 5, 6], [7, 8, 5, 6, 5], [7, 8, 6, 5, 5], [8, 5, 5, 6, 7], [8, 5, 5, 7, 6], [8, 5, 6, 5, 7], [8, 5, 6, 7, 5], [8, 5, 7, 5, 6], [8, 5, 7, 6, 5], [8, 6, 5, 5, 7], [8, 6, 5, 7, 5], [8, 6, 7, 5, 5], [8, 7, 5, 5, 6], [8, 7, 5, 6, 5], [8, 7, 6, 5, 5]]\n assert candidate(nums = [8, 8, 8, 8, 8, 8, 8, 8]) == [[8, 8, 8, 8, 8, 8, 8, 8]]\n assert candidate(nums = [0, -1, 1, 0, -1]) == [[-1, -1, 0, 0, 1], [-1, -1, 0, 1, 0], [-1, -1, 1, 0, 0], [-1, 0, -1, 0, 1], [-1, 0, -1, 1, 0], [-1, 0, 0, -1, 1], [-1, 0, 0, 1, -1], [-1, 0, 1, -1, 0], [-1, 0, 1, 0, -1], [-1, 1, -1, 0, 0], [-1, 1, 0, -1, 0], [-1, 1, 0, 0, -1], [0, -1, -1, 0, 1], [0, -1, -1, 1, 0], [0, -1, 0, -1, 1], [0, -1, 0, 1, -1], [0, -1, 1, -1, 0], [0, -1, 1, 0, -1], [0, 0, -1, -1, 1], [0, 0, -1, 1, -1], [0, 0, 1, -1, -1], [0, 1, -1, -1, 0], [0, 1, -1, 0, -1], [0, 1, 0, -1, -1], [1, -1, -1, 0, 0], [1, -1, 0, -1, 0], [1, -1, 0, 0, -1], [1, 0, -1, -1, 0], [1, 0, -1, 0, -1], [1, 0, 0, -1, -1]]\n assert candidate(nums = [-5, -5, -5, -5, -5]) == [[-5, -5, -5, -5, -5]]\n assert candidate(nums = [7, 3, 3, 7, 3, 3, 7]) == [[3, 3, 3, 3, 7, 7, 7], [3, 3, 3, 7, 3, 7, 7], [3, 3, 3, 7, 7, 3, 7], [3, 3, 3, 7, 7, 7, 3], [3, 3, 7, 3, 3, 7, 7], [3, 3, 7, 3, 7, 3, 7], [3, 3, 7, 3, 7, 7, 3], [3, 3, 7, 7, 3, 3, 7], [3, 3, 7, 7, 3, 7, 3], [3, 3, 7, 7, 7, 3, 3], [3, 7, 3, 3, 3, 7, 7], [3, 7, 3, 3, 7, 3, 7], [3, 7, 3, 3, 7, 7, 3], [3, 7, 3, 7, 3, 3, 7], [3, 7, 3, 7, 3, 7, 3], [3, 7, 3, 7, 7, 3, 3], [3, 7, 7, 3, 3, 3, 7], [3, 7, 7, 3, 3, 7, 3], [3, 7, 7, 3, 7, 3, 3], [3, 7, 7, 7, 3, 3, 3], [7, 3, 3, 3, 3, 7, 7], [7, 3, 3, 3, 7, 3, 7], [7, 3, 3, 3, 7, 7, 3], [7, 3, 3, 7, 3, 3, 7], [7, 3, 3, 7, 3, 7, 3], [7, 3, 3, 7, 7, 3, 3], [7, 3, 7, 3, 3, 3, 7], [7, 3, 7, 3, 3, 7, 3], [7, 3, 7, 3, 7, 3, 3], [7, 3, 7, 7, 3, 3, 3], [7, 7, 3, 3, 3, 3, 7], [7, 7, 3, 3, 3, 7, 3], [7, 7, 3, 3, 7, 3, 3], [7, 7, 3, 7, 3, 3, 3], [7, 7, 7, 3, 3, 3, 3]]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1]) == [[1, 1, 1, 1, 1, 1, 1, 1]]\n assert candidate(nums = [0, 1, -1, 0, 1, -1]) == [[-1, -1, 0, 0, 1, 1], [-1, -1, 0, 1, 0, 1], [-1, -1, 0, 1, 1, 0], [-1, -1, 1, 0, 0, 1], [-1, -1, 1, 0, 1, 0], [-1, -1, 1, 1, 0, 0], [-1, 0, -1, 0, 1, 1], [-1, 0, -1, 1, 0, 1], [-1, 0, -1, 1, 1, 0], [-1, 0, 0, -1, 1, 1], [-1, 0, 0, 1, -1, 1], [-1, 0, 0, 1, 1, -1], [-1, 0, 1, -1, 0, 1], [-1, 0, 1, -1, 1, 0], [-1, 0, 1, 0, -1, 1], [-1, 0, 1, 0, 1, -1], [-1, 0, 1, 1, -1, 0], [-1, 0, 1, 1, 0, -1], [-1, 1, -1, 0, 0, 1], [-1, 1, -1, 0, 1, 0], [-1, 1, -1, 1, 0, 0], [-1, 1, 0, -1, 0, 1], [-1, 1, 0, -1, 1, 0], [-1, 1, 0, 0, -1, 1], [-1, 1, 0, 0, 1, -1], [-1, 1, 0, 1, -1, 0], [-1, 1, 0, 1, 0, -1], [-1, 1, 1, -1, 0, 0], [-1, 1, 1, 0, -1, 0], [-1, 1, 1, 0, 0, -1], [0, -1, -1, 0, 1, 1], [0, -1, -1, 1, 0, 1], [0, -1, -1, 1, 1, 0], [0, -1, 0, -1, 1, 1], [0, -1, 0, 1, -1, 1], [0, -1, 0, 1, 1, -1], [0, -1, 1, -1, 0, 1], [0, -1, 1, -1, 1, 0], [0, -1, 1, 0, -1, 1], [0, -1, 1, 0, 1, -1], [0, -1, 1, 1, -1, 0], [0, -1, 1, 1, 0, -1], [0, 0, -1, -1, 1, 1], [0, 0, -1, 1, -1, 1], [0, 0, -1, 1, 1, -1], [0, 0, 1, -1, -1, 1], [0, 0, 1, -1, 1, -1], [0, 0, 1, 1, -1, -1], [0, 1, -1, -1, 0, 1], [0, 1, -1, -1, 1, 0], [0, 1, -1, 0, -1, 1], [0, 1, -1, 0, 1, -1], [0, 1, -1, 1, -1, 0], [0, 1, -1, 1, 0, -1], [0, 1, 0, -1, -1, 1], [0, 1, 0, -1, 1, -1], [0, 1, 0, 1, -1, -1], [0, 1, 1, -1, -1, 0], [0, 1, 1, -1, 0, -1], [0, 1, 1, 0, -1, -1], [1, -1, -1, 0, 0, 1], [1, -1, -1, 0, 1, 0], [1, -1, -1, 1, 0, 0], [1, -1, 0, -1, 0, 1], [1, -1, 0, -1, 1, 0], [1, -1, 0, 0, -1, 1], [1, -1, 0, 0, 1, -1], [1, -1, 0, 1, -1, 0], [1, -1, 0, 1, 0, -1], [1, -1, 1, -1, 0, 0], [1, -1, 1, 0, -1, 0], [1, -1, 1, 0, 0, -1], [1, 0, -1, -1, 0, 1], [1, 0, -1, -1, 1, 0], [1, 0, -1, 0, -1, 1], [1, 0, -1, 0, 1, -1], [1, 0, -1, 1, -1, 0], [1, 0, -1, 1, 0, -1], [1, 0, 0, -1, -1, 1], [1, 0, 0, -1, 1, -1], [1, 0, 0, 1, -1, -1], [1, 0, 1, -1, -1, 0], [1, 0, 1, -1, 0, -1], [1, 0, 1, 0, -1, -1], [1, 1, -1, -1, 0, 0], [1, 1, -1, 0, -1, 0], [1, 1, -1, 0, 0, -1], [1, 1, 0, -1, -1, 0], [1, 1, 0, -1, 0, -1], [1, 1, 0, 0, -1, -1]]\n assert candidate(nums = [10, 20, 10, 20, 30, 30, 30]) == [[10, 10, 20, 20, 30, 30, 30], [10, 10, 20, 30, 20, 30, 30], [10, 10, 20, 30, 30, 20, 30], [10, 10, 20, 30, 30, 30, 20], [10, 10, 30, 20, 20, 30, 30], [10, 10, 30, 20, 30, 20, 30], [10, 10, 30, 20, 30, 30, 20], [10, 10, 30, 30, 20, 20, 30], [10, 10, 30, 30, 20, 30, 20], [10, 10, 30, 30, 30, 20, 20], [10, 20, 10, 20, 30, 30, 30], [10, 20, 10, 30, 20, 30, 30], [10, 20, 10, 30, 30, 20, 30], [10, 20, 10, 30, 30, 30, 20], [10, 20, 20, 10, 30, 30, 30], [10, 20, 20, 30, 10, 30, 30], [10, 20, 20, 30, 30, 10, 30], [10, 20, 20, 30, 30, 30, 10], [10, 20, 30, 10, 20, 30, 30], [10, 20, 30, 10, 30, 20, 30], [10, 20, 30, 10, 30, 30, 20], [10, 20, 30, 20, 10, 30, 30], [10, 20, 30, 20, 30, 10, 30], [10, 20, 30, 20, 30, 30, 10], [10, 20, 30, 30, 10, 20, 30], [10, 20, 30, 30, 10, 30, 20], [10, 20, 30, 30, 20, 10, 30], [10, 20, 30, 30, 20, 30, 10], [10, 20, 30, 30, 30, 10, 20], [10, 20, 30, 30, 30, 20, 10], [10, 30, 10, 20, 20, 30, 30], [10, 30, 10, 20, 30, 20, 30], [10, 30, 10, 20, 30, 30, 20], [10, 30, 10, 30, 20, 20, 30], [10, 30, 10, 30, 20, 30, 20], [10, 30, 10, 30, 30, 20, 20], [10, 30, 20, 10, 20, 30, 30], [10, 30, 20, 10, 30, 20, 30], [10, 30, 20, 10, 30, 30, 20], [10, 30, 20, 20, 10, 30, 30], [10, 30, 20, 20, 30, 10, 30], [10, 30, 20, 20, 30, 30, 10], [10, 30, 20, 30, 10, 20, 30], [10, 30, 20, 30, 10, 30, 20], [10, 30, 20, 30, 20, 10, 30], [10, 30, 20, 30, 20, 30, 10], [10, 30, 20, 30, 30, 10, 20], [10, 30, 20, 30, 30, 20, 10], [10, 30, 30, 10, 20, 20, 30], [10, 30, 30, 10, 20, 30, 20], [10, 30, 30, 10, 30, 20, 20], [10, 30, 30, 20, 10, 20, 30], [10, 30, 30, 20, 10, 30, 20], [10, 30, 30, 20, 20, 10, 30], [10, 30, 30, 20, 20, 30, 10], [10, 30, 30, 20, 30, 10, 20], [10, 30, 30, 20, 30, 20, 10], [10, 30, 30, 30, 10, 20, 20], [10, 30, 30, 30, 20, 10, 20], [10, 30, 30, 30, 20, 20, 10], [20, 10, 10, 20, 30, 30, 30], [20, 10, 10, 30, 20, 30, 30], [20, 10, 10, 30, 30, 20, 30], [20, 10, 10, 30, 30, 30, 20], [20, 10, 20, 10, 30, 30, 30], [20, 10, 20, 30, 10, 30, 30], [20, 10, 20, 30, 30, 10, 30], [20, 10, 20, 30, 30, 30, 10], [20, 10, 30, 10, 20, 30, 30], [20, 10, 30, 10, 30, 20, 30], [20, 10, 30, 10, 30, 30, 20], [20, 10, 30, 20, 10, 30, 30], [20, 10, 30, 20, 30, 10, 30], [20, 10, 30, 20, 30, 30, 10], [20, 10, 30, 30, 10, 20, 30], [20, 10, 30, 30, 10, 30, 20], [20, 10, 30, 30, 20, 10, 30], [20, 10, 30, 30, 20, 30, 10], [20, 10, 30, 30, 30, 10, 20], [20, 10, 30, 30, 30, 20, 10], [20, 20, 10, 10, 30, 30, 30], [20, 20, 10, 30, 10, 30, 30], [20, 20, 10, 30, 30, 10, 30], [20, 20, 10, 30, 30, 30, 10], [20, 20, 30, 10, 10, 30, 30], [20, 20, 30, 10, 30, 10, 30], [20, 20, 30, 10, 30, 30, 10], [20, 20, 30, 30, 10, 10, 30], [20, 20, 30, 30, 10, 30, 10], [20, 20, 30, 30, 30, 10, 10], [20, 30, 10, 10, 20, 30, 30], [20, 30, 10, 10, 30, 20, 30], [20, 30, 10, 10, 30, 30, 20], [20, 30, 10, 20, 10, 30, 30], [20, 30, 10, 20, 30, 10, 30], [20, 30, 10, 20, 30, 30, 10], [20, 30, 10, 30, 10, 20, 30], [20, 30, 10, 30, 10, 30, 20], [20, 30, 10, 30, 20, 10, 30], [20, 30, 10, 30, 20, 30, 10], [20, 30, 10, 30, 30, 10, 20], [20, 30, 10, 30, 30, 20, 10], [20, 30, 20, 10, 10, 30, 30], [20, 30, 20, 10, 30, 10, 30], [20, 30, 20, 10, 30, 30, 10], [20, 30, 20, 30, 10, 10, 30], [20, 30, 20, 30, 10, 30, 10], [20, 30, 20, 30, 30, 10, 10], [20, 30, 30, 10, 10, 20, 30], [20, 30, 30, 10, 10, 30, 20], [20, 30, 30, 10, 20, 10, 30], [20, 30, 30, 10, 20, 30, 10], [20, 30, 30, 10, 30, 10, 20], [20, 30, 30, 10, 30, 20, 10], [20, 30, 30, 20, 10, 10, 30], [20, 30, 30, 20, 10, 30, 10], [20, 30, 30, 20, 30, 10, 10], [20, 30, 30, 30, 10, 10, 20], [20, 30, 30, 30, 10, 20, 10], [20, 30, 30, 30, 20, 10, 10], [30, 10, 10, 20, 20, 30, 30], [30, 10, 10, 20, 30, 20, 30], [30, 10, 10, 20, 30, 30, 20], [30, 10, 10, 30, 20, 20, 30], [30, 10, 10, 30, 20, 30, 20], [30, 10, 10, 30, 30, 20, 20], [30, 10, 20, 10, 20, 30, 30], [30, 10, 20, 10, 30, 20, 30], [30, 10, 20, 10, 30, 30, 20], [30, 10, 20, 20, 10, 30, 30], [30, 10, 20, 20, 30, 10, 30], [30, 10, 20, 20, 30, 30, 10], [30, 10, 20, 30, 10, 20, 30], [30, 10, 20, 30, 10, 30, 20], [30, 10, 20, 30, 20, 10, 30], [30, 10, 20, 30, 20, 30, 10], [30, 10, 20, 30, 30, 10, 20], [30, 10, 20, 30, 30, 20, 10], [30, 10, 30, 10, 20, 20, 30], [30, 10, 30, 10, 20, 30, 20], [30, 10, 30, 10, 30, 20, 20], [30, 10, 30, 20, 10, 20, 30], [30, 10, 30, 20, 10, 30, 20], [30, 10, 30, 20, 20, 10, 30], [30, 10, 30, 20, 20, 30, 10], [30, 10, 30, 20, 30, 10, 20], [30, 10, 30, 20, 30, 20, 10], [30, 10, 30, 30, 10, 20, 20], [30, 10, 30, 30, 20, 10, 20], [30, 10, 30, 30, 20, 20, 10], [30, 20, 10, 10, 20, 30, 30], [30, 20, 10, 10, 30, 20, 30], [30, 20, 10, 10, 30, 30, 20], [30, 20, 10, 20, 10, 30, 30], [30, 20, 10, 20, 30, 10, 30], [30, 20, 10, 20, 30, 30, 10], [30, 20, 10, 30, 10, 20, 30], [30, 20, 10, 30, 10, 30, 20], [30, 20, 10, 30, 20, 10, 30], [30, 20, 10, 30, 20, 30, 10], [30, 20, 10, 30, 30, 10, 20], [30, 20, 10, 30, 30, 20, 10], [30, 20, 20, 10, 10, 30, 30], [30, 20, 20, 10, 30, 10, 30], [30, 20, 20, 10, 30, 30, 10], [30, 20, 20, 30, 10, 10, 30], [30, 20, 20, 30, 10, 30, 10], [30, 20, 20, 30, 30, 10, 10], [30, 20, 30, 10, 10, 20, 30], [30, 20, 30, 10, 10, 30, 20], [30, 20, 30, 10, 20, 10, 30], [30, 20, 30, 10, 20, 30, 10], [30, 20, 30, 10, 30, 10, 20], [30, 20, 30, 10, 30, 20, 10], [30, 20, 30, 20, 10, 10, 30], [30, 20, 30, 20, 10, 30, 10], [30, 20, 30, 20, 30, 10, 10], [30, 20, 30, 30, 10, 10, 20], [30, 20, 30, 30, 10, 20, 10], [30, 20, 30, 30, 20, 10, 10], [30, 30, 10, 10, 20, 20, 30], [30, 30, 10, 10, 20, 30, 20], [30, 30, 10, 10, 30, 20, 20], [30, 30, 10, 20, 10, 20, 30], [30, 30, 10, 20, 10, 30, 20], [30, 30, 10, 20, 20, 10, 30], [30, 30, 10, 20, 20, 30, 10], [30, 30, 10, 20, 30, 10, 20], [30, 30, 10, 20, 30, 20, 10], [30, 30, 10, 30, 10, 20, 20], [30, 30, 10, 30, 20, 10, 20], [30, 30, 10, 30, 20, 20, 10], [30, 30, 20, 10, 10, 20, 30], [30, 30, 20, 10, 10, 30, 20], [30, 30, 20, 10, 20, 10, 30], [30, 30, 20, 10, 20, 30, 10], [30, 30, 20, 10, 30, 10, 20], [30, 30, 20, 10, 30, 20, 10], [30, 30, 20, 20, 10, 10, 30], [30, 30, 20, 20, 10, 30, 10], [30, 30, 20, 20, 30, 10, 10], [30, 30, 20, 30, 10, 10, 20], [30, 30, 20, 30, 10, 20, 10], [30, 30, 20, 30, 20, 10, 10], [30, 30, 30, 10, 10, 20, 20], [30, 30, 30, 10, 20, 10, 20], [30, 30, 30, 10, 20, 20, 10], [30, 30, 30, 20, 10, 10, 20], [30, 30, 30, 20, 10, 20, 10], [30, 30, 30, 20, 20, 10, 10]]\n assert candidate(nums = [-1, -2, -3, -2, -1]) == [[-3, -2, -2, -1, -1], [-3, -2, -1, -2, -1], [-3, -2, -1, -1, -2], [-3, -1, -2, -2, -1], [-3, -1, -2, -1, -2], [-3, -1, -1, -2, -2], [-2, -3, -2, -1, -1], [-2, -3, -1, -2, -1], [-2, -3, -1, -1, -2], [-2, -2, -3, -1, -1], [-2, -2, -1, -3, -1], [-2, -2, -1, -1, -3], [-2, -1, -3, -2, -1], [-2, -1, -3, -1, -2], [-2, -1, -2, -3, -1], [-2, -1, -2, -1, -3], [-2, -1, -1, -3, -2], [-2, -1, -1, -2, -3], [-1, -3, -2, -2, -1], [-1, -3, -2, -1, -2], [-1, -3, -1, -2, -2], [-1, -2, -3, -2, -1], [-1, -2, -3, -1, -2], [-1, -2, -2, -3, -1], [-1, -2, -2, -1, -3], [-1, -2, -1, -3, -2], [-1, -2, -1, -2, -3], [-1, -1, -3, -2, -2], [-1, -1, -2, -3, -2], [-1, -1, -2, -2, -3]]\n assert candidate(nums = [7, 1, 1, 2, 2, 3, 3]) == [[1, 1, 2, 2, 3, 3, 7], [1, 1, 2, 2, 3, 7, 3], [1, 1, 2, 2, 7, 3, 3], [1, 1, 2, 3, 2, 3, 7], [1, 1, 2, 3, 2, 7, 3], [1, 1, 2, 3, 3, 2, 7], [1, 1, 2, 3, 3, 7, 2], [1, 1, 2, 3, 7, 2, 3], [1, 1, 2, 3, 7, 3, 2], [1, 1, 2, 7, 2, 3, 3], [1, 1, 2, 7, 3, 2, 3], [1, 1, 2, 7, 3, 3, 2], [1, 1, 3, 2, 2, 3, 7], [1, 1, 3, 2, 2, 7, 3], [1, 1, 3, 2, 3, 2, 7], [1, 1, 3, 2, 3, 7, 2], [1, 1, 3, 2, 7, 2, 3], [1, 1, 3, 2, 7, 3, 2], [1, 1, 3, 3, 2, 2, 7], [1, 1, 3, 3, 2, 7, 2], [1, 1, 3, 3, 7, 2, 2], [1, 1, 3, 7, 2, 2, 3], [1, 1, 3, 7, 2, 3, 2], [1, 1, 3, 7, 3, 2, 2], [1, 1, 7, 2, 2, 3, 3], [1, 1, 7, 2, 3, 2, 3], [1, 1, 7, 2, 3, 3, 2], [1, 1, 7, 3, 2, 2, 3], [1, 1, 7, 3, 2, 3, 2], [1, 1, 7, 3, 3, 2, 2], [1, 2, 1, 2, 3, 3, 7], [1, 2, 1, 2, 3, 7, 3], [1, 2, 1, 2, 7, 3, 3], [1, 2, 1, 3, 2, 3, 7], [1, 2, 1, 3, 2, 7, 3], [1, 2, 1, 3, 3, 2, 7], [1, 2, 1, 3, 3, 7, 2], [1, 2, 1, 3, 7, 2, 3], [1, 2, 1, 3, 7, 3, 2], [1, 2, 1, 7, 2, 3, 3], [1, 2, 1, 7, 3, 2, 3], [1, 2, 1, 7, 3, 3, 2], [1, 2, 2, 1, 3, 3, 7], [1, 2, 2, 1, 3, 7, 3], [1, 2, 2, 1, 7, 3, 3], [1, 2, 2, 3, 1, 3, 7], [1, 2, 2, 3, 1, 7, 3], [1, 2, 2, 3, 3, 1, 7], [1, 2, 2, 3, 3, 7, 1], [1, 2, 2, 3, 7, 1, 3], [1, 2, 2, 3, 7, 3, 1], [1, 2, 2, 7, 1, 3, 3], [1, 2, 2, 7, 3, 1, 3], [1, 2, 2, 7, 3, 3, 1], [1, 2, 3, 1, 2, 3, 7], [1, 2, 3, 1, 2, 7, 3], [1, 2, 3, 1, 3, 2, 7], [1, 2, 3, 1, 3, 7, 2], [1, 2, 3, 1, 7, 2, 3], [1, 2, 3, 1, 7, 3, 2], [1, 2, 3, 2, 1, 3, 7], [1, 2, 3, 2, 1, 7, 3], [1, 2, 3, 2, 3, 1, 7], [1, 2, 3, 2, 3, 7, 1], [1, 2, 3, 2, 7, 1, 3], [1, 2, 3, 2, 7, 3, 1], [1, 2, 3, 3, 1, 2, 7], [1, 2, 3, 3, 1, 7, 2], [1, 2, 3, 3, 2, 1, 7], [1, 2, 3, 3, 2, 7, 1], [1, 2, 3, 3, 7, 1, 2], [1, 2, 3, 3, 7, 2, 1], [1, 2, 3, 7, 1, 2, 3], [1, 2, 3, 7, 1, 3, 2], [1, 2, 3, 7, 2, 1, 3], [1, 2, 3, 7, 2, 3, 1], [1, 2, 3, 7, 3, 1, 2], [1, 2, 3, 7, 3, 2, 1], [1, 2, 7, 1, 2, 3, 3], [1, 2, 7, 1, 3, 2, 3], [1, 2, 7, 1, 3, 3, 2], [1, 2, 7, 2, 1, 3, 3], [1, 2, 7, 2, 3, 1, 3], [1, 2, 7, 2, 3, 3, 1], [1, 2, 7, 3, 1, 2, 3], [1, 2, 7, 3, 1, 3, 2], [1, 2, 7, 3, 2, 1, 3], [1, 2, 7, 3, 2, 3, 1], [1, 2, 7, 3, 3, 1, 2], [1, 2, 7, 3, 3, 2, 1], [1, 3, 1, 2, 2, 3, 7], [1, 3, 1, 2, 2, 7, 3], [1, 3, 1, 2, 3, 2, 7], [1, 3, 1, 2, 3, 7, 2], [1, 3, 1, 2, 7, 2, 3], [1, 3, 1, 2, 7, 3, 2], [1, 3, 1, 3, 2, 2, 7], [1, 3, 1, 3, 2, 7, 2], [1, 3, 1, 3, 7, 2, 2], [1, 3, 1, 7, 2, 2, 3], [1, 3, 1, 7, 2, 3, 2], [1, 3, 1, 7, 3, 2, 2], [1, 3, 2, 1, 2, 3, 7], [1, 3, 2, 1, 2, 7, 3], [1, 3, 2, 1, 3, 2, 7], [1, 3, 2, 1, 3, 7, 2], [1, 3, 2, 1, 7, 2, 3], [1, 3, 2, 1, 7, 3, 2], [1, 3, 2, 2, 1, 3, 7], [1, 3, 2, 2, 1, 7, 3], [1, 3, 2, 2, 3, 1, 7], [1, 3, 2, 2, 3, 7, 1], [1, 3, 2, 2, 7, 1, 3], [1, 3, 2, 2, 7, 3, 1], [1, 3, 2, 3, 1, 2, 7], [1, 3, 2, 3, 1, 7, 2], [1, 3, 2, 3, 2, 1, 7], [1, 3, 2, 3, 2, 7, 1], [1, 3, 2, 3, 7, 1, 2], [1, 3, 2, 3, 7, 2, 1], [1, 3, 2, 7, 1, 2, 3], [1, 3, 2, 7, 1, 3, 2], [1, 3, 2, 7, 2, 1, 3], [1, 3, 2, 7, 2, 3, 1], [1, 3, 2, 7, 3, 1, 2], [1, 3, 2, 7, 3, 2, 1], [1, 3, 3, 1, 2, 2, 7], [1, 3, 3, 1, 2, 7, 2], [1, 3, 3, 1, 7, 2, 2], [1, 3, 3, 2, 1, 2, 7], [1, 3, 3, 2, 1, 7, 2], [1, 3, 3, 2, 2, 1, 7], [1, 3, 3, 2, 2, 7, 1], [1, 3, 3, 2, 7, 1, 2], [1, 3, 3, 2, 7, 2, 1], [1, 3, 3, 7, 1, 2, 2], [1, 3, 3, 7, 2, 1, 2], [1, 3, 3, 7, 2, 2, 1], [1, 3, 7, 1, 2, 2, 3], [1, 3, 7, 1, 2, 3, 2], [1, 3, 7, 1, 3, 2, 2], [1, 3, 7, 2, 1, 2, 3], [1, 3, 7, 2, 1, 3, 2], [1, 3, 7, 2, 2, 1, 3], [1, 3, 7, 2, 2, 3, 1], [1, 3, 7, 2, 3, 1, 2], [1, 3, 7, 2, 3, 2, 1], [1, 3, 7, 3, 1, 2, 2], [1, 3, 7, 3, 2, 1, 2], [1, 3, 7, 3, 2, 2, 1], [1, 7, 1, 2, 2, 3, 3], [1, 7, 1, 2, 3, 2, 3], [1, 7, 1, 2, 3, 3, 2], [1, 7, 1, 3, 2, 2, 3], [1, 7, 1, 3, 2, 3, 2], [1, 7, 1, 3, 3, 2, 2], [1, 7, 2, 1, 2, 3, 3], [1, 7, 2, 1, 3, 2, 3], [1, 7, 2, 1, 3, 3, 2], [1, 7, 2, 2, 1, 3, 3], [1, 7, 2, 2, 3, 1, 3], [1, 7, 2, 2, 3, 3, 1], [1, 7, 2, 3, 1, 2, 3], [1, 7, 2, 3, 1, 3, 2], [1, 7, 2, 3, 2, 1, 3], [1, 7, 2, 3, 2, 3, 1], [1, 7, 2, 3, 3, 1, 2], [1, 7, 2, 3, 3, 2, 1], [1, 7, 3, 1, 2, 2, 3], [1, 7, 3, 1, 2, 3, 2], [1, 7, 3, 1, 3, 2, 2], [1, 7, 3, 2, 1, 2, 3], [1, 7, 3, 2, 1, 3, 2], [1, 7, 3, 2, 2, 1, 3], [1, 7, 3, 2, 2, 3, 1], [1, 7, 3, 2, 3, 1, 2], [1, 7, 3, 2, 3, 2, 1], [1, 7, 3, 3, 1, 2, 2], [1, 7, 3, 3, 2, 1, 2], [1, 7, 3, 3, 2, 2, 1], [2, 1, 1, 2, 3, 3, 7], [2, 1, 1, 2, 3, 7, 3], [2, 1, 1, 2, 7, 3, 3], [2, 1, 1, 3, 2, 3, 7], [2, 1, 1, 3, 2, 7, 3], [2, 1, 1, 3, 3, 2, 7], [2, 1, 1, 3, 3, 7, 2], [2, 1, 1, 3, 7, 2, 3], [2, 1, 1, 3, 7, 3, 2], [2, 1, 1, 7, 2, 3, 3], [2, 1, 1, 7, 3, 2, 3], [2, 1, 1, 7, 3, 3, 2], [2, 1, 2, 1, 3, 3, 7], [2, 1, 2, 1, 3, 7, 3], [2, 1, 2, 1, 7, 3, 3], [2, 1, 2, 3, 1, 3, 7], [2, 1, 2, 3, 1, 7, 3], [2, 1, 2, 3, 3, 1, 7], [2, 1, 2, 3, 3, 7, 1], [2, 1, 2, 3, 7, 1, 3], [2, 1, 2, 3, 7, 3, 1], [2, 1, 2, 7, 1, 3, 3], [2, 1, 2, 7, 3, 1, 3], [2, 1, 2, 7, 3, 3, 1], [2, 1, 3, 1, 2, 3, 7], [2, 1, 3, 1, 2, 7, 3], [2, 1, 3, 1, 3, 2, 7], [2, 1, 3, 1, 3, 7, 2], [2, 1, 3, 1, 7, 2, 3], [2, 1, 3, 1, 7, 3, 2], [2, 1, 3, 2, 1, 3, 7], [2, 1, 3, 2, 1, 7, 3], [2, 1, 3, 2, 3, 1, 7], [2, 1, 3, 2, 3, 7, 1], [2, 1, 3, 2, 7, 1, 3], [2, 1, 3, 2, 7, 3, 1], [2, 1, 3, 3, 1, 2, 7], [2, 1, 3, 3, 1, 7, 2], [2, 1, 3, 3, 2, 1, 7], [2, 1, 3, 3, 2, 7, 1], [2, 1, 3, 3, 7, 1, 2], [2, 1, 3, 3, 7, 2, 1], [2, 1, 3, 7, 1, 2, 3], [2, 1, 3, 7, 1, 3, 2], [2, 1, 3, 7, 2, 1, 3], [2, 1, 3, 7, 2, 3, 1], [2, 1, 3, 7, 3, 1, 2], [2, 1, 3, 7, 3, 2, 1], [2, 1, 7, 1, 2, 3, 3], [2, 1, 7, 1, 3, 2, 3], [2, 1, 7, 1, 3, 3, 2], [2, 1, 7, 2, 1, 3, 3], [2, 1, 7, 2, 3, 1, 3], [2, 1, 7, 2, 3, 3, 1], [2, 1, 7, 3, 1, 2, 3], [2, 1, 7, 3, 1, 3, 2], [2, 1, 7, 3, 2, 1, 3], [2, 1, 7, 3, 2, 3, 1], [2, 1, 7, 3, 3, 1, 2], [2, 1, 7, 3, 3, 2, 1], [2, 2, 1, 1, 3, 3, 7], [2, 2, 1, 1, 3, 7, 3], [2, 2, 1, 1, 7, 3, 3], [2, 2, 1, 3, 1, 3, 7], [2, 2, 1, 3, 1, 7, 3], [2, 2, 1, 3, 3, 1, 7], [2, 2, 1, 3, 3, 7, 1], [2, 2, 1, 3, 7, 1, 3], [2, 2, 1, 3, 7, 3, 1], [2, 2, 1, 7, 1, 3, 3], [2, 2, 1, 7, 3, 1, 3], [2, 2, 1, 7, 3, 3, 1], [2, 2, 3, 1, 1, 3, 7], [2, 2, 3, 1, 1, 7, 3], [2, 2, 3, 1, 3, 1, 7], [2, 2, 3, 1, 3, 7, 1], [2, 2, 3, 1, 7, 1, 3], [2, 2, 3, 1, 7, 3, 1], [2, 2, 3, 3, 1, 1, 7], [2, 2, 3, 3, 1, 7, 1], [2, 2, 3, 3, 7, 1, 1], [2, 2, 3, 7, 1, 1, 3], [2, 2, 3, 7, 1, 3, 1], [2, 2, 3, 7, 3, 1, 1], [2, 2, 7, 1, 1, 3, 3], [2, 2, 7, 1, 3, 1, 3], [2, 2, 7, 1, 3, 3, 1], [2, 2, 7, 3, 1, 1, 3], [2, 2, 7, 3, 1, 3, 1], [2, 2, 7, 3, 3, 1, 1], [2, 3, 1, 1, 2, 3, 7], [2, 3, 1, 1, 2, 7, 3], [2, 3, 1, 1, 3, 2, 7], [2, 3, 1, 1, 3, 7, 2], [2, 3, 1, 1, 7, 2, 3], [2, 3, 1, 1, 7, 3, 2], [2, 3, 1, 2, 1, 3, 7], [2, 3, 1, 2, 1, 7, 3], [2, 3, 1, 2, 3, 1, 7], [2, 3, 1, 2, 3, 7, 1], [2, 3, 1, 2, 7, 1, 3], [2, 3, 1, 2, 7, 3, 1], [2, 3, 1, 3, 1, 2, 7], [2, 3, 1, 3, 1, 7, 2], [2, 3, 1, 3, 2, 1, 7], [2, 3, 1, 3, 2, 7, 1], [2, 3, 1, 3, 7, 1, 2], [2, 3, 1, 3, 7, 2, 1], [2, 3, 1, 7, 1, 2, 3], [2, 3, 1, 7, 1, 3, 2], [2, 3, 1, 7, 2, 1, 3], [2, 3, 1, 7, 2, 3, 1], [2, 3, 1, 7, 3, 1, 2], [2, 3, 1, 7, 3, 2, 1], [2, 3, 2, 1, 1, 3, 7], [2, 3, 2, 1, 1, 7, 3], [2, 3, 2, 1, 3, 1, 7], [2, 3, 2, 1, 3, 7, 1], [2, 3, 2, 1, 7, 1, 3], [2, 3, 2, 1, 7, 3, 1], [2, 3, 2, 3, 1, 1, 7], [2, 3, 2, 3, 1, 7, 1], [2, 3, 2, 3, 7, 1, 1], [2, 3, 2, 7, 1, 1, 3], [2, 3, 2, 7, 1, 3, 1], [2, 3, 2, 7, 3, 1, 1], [2, 3, 3, 1, 1, 2, 7], [2, 3, 3, 1, 1, 7, 2], [2, 3, 3, 1, 2, 1, 7], [2, 3, 3, 1, 2, 7, 1], [2, 3, 3, 1, 7, 1, 2], [2, 3, 3, 1, 7, 2, 1], [2, 3, 3, 2, 1, 1, 7], [2, 3, 3, 2, 1, 7, 1], [2, 3, 3, 2, 7, 1, 1], [2, 3, 3, 7, 1, 1, 2], [2, 3, 3, 7, 1, 2, 1], [2, 3, 3, 7, 2, 1, 1], [2, 3, 7, 1, 1, 2, 3], [2, 3, 7, 1, 1, 3, 2], [2, 3, 7, 1, 2, 1, 3], [2, 3, 7, 1, 2, 3, 1], [2, 3, 7, 1, 3, 1, 2], [2, 3, 7, 1, 3, 2, 1], [2, 3, 7, 2, 1, 1, 3], [2, 3, 7, 2, 1, 3, 1], [2, 3, 7, 2, 3, 1, 1], [2, 3, 7, 3, 1, 1, 2], [2, 3, 7, 3, 1, 2, 1], [2, 3, 7, 3, 2, 1, 1], [2, 7, 1, 1, 2, 3, 3], [2, 7, 1, 1, 3, 2, 3], [2, 7, 1, 1, 3, 3, 2], [2, 7, 1, 2, 1, 3, 3], [2, 7, 1, 2, 3, 1, 3], [2, 7, 1, 2, 3, 3, 1], [2, 7, 1, 3, 1, 2, 3], [2, 7, 1, 3, 1, 3, 2], [2, 7, 1, 3, 2, 1, 3], [2, 7, 1, 3, 2, 3, 1], [2, 7, 1, 3, 3, 1, 2], [2, 7, 1, 3, 3, 2, 1], [2, 7, 2, 1, 1, 3, 3], [2, 7, 2, 1, 3, 1, 3], [2, 7, 2, 1, 3, 3, 1], [2, 7, 2, 3, 1, 1, 3], [2, 7, 2, 3, 1, 3, 1], [2, 7, 2, 3, 3, 1, 1], [2, 7, 3, 1, 1, 2, 3], [2, 7, 3, 1, 1, 3, 2], [2, 7, 3, 1, 2, 1, 3], [2, 7, 3, 1, 2, 3, 1], [2, 7, 3, 1, 3, 1, 2], [2, 7, 3, 1, 3, 2, 1], [2, 7, 3, 2, 1, 1, 3], [2, 7, 3, 2, 1, 3, 1], [2, 7, 3, 2, 3, 1, 1], [2, 7, 3, 3, 1, 1, 2], [2, 7, 3, 3, 1, 2, 1], [2, 7, 3, 3, 2, 1, 1], [3, 1, 1, 2, 2, 3, 7], [3, 1, 1, 2, 2, 7, 3], [3, 1, 1, 2, 3, 2, 7], [3, 1, 1, 2, 3, 7, 2], [3, 1, 1, 2, 7, 2, 3], [3, 1, 1, 2, 7, 3, 2], [3, 1, 1, 3, 2, 2, 7], [3, 1, 1, 3, 2, 7, 2], [3, 1, 1, 3, 7, 2, 2], [3, 1, 1, 7, 2, 2, 3], [3, 1, 1, 7, 2, 3, 2], [3, 1, 1, 7, 3, 2, 2], [3, 1, 2, 1, 2, 3, 7], [3, 1, 2, 1, 2, 7, 3], [3, 1, 2, 1, 3, 2, 7], [3, 1, 2, 1, 3, 7, 2], [3, 1, 2, 1, 7, 2, 3], [3, 1, 2, 1, 7, 3, 2], [3, 1, 2, 2, 1, 3, 7], [3, 1, 2, 2, 1, 7, 3], [3, 1, 2, 2, 3, 1, 7], [3, 1, 2, 2, 3, 7, 1], [3, 1, 2, 2, 7, 1, 3], [3, 1, 2, 2, 7, 3, 1], [3, 1, 2, 3, 1, 2, 7], [3, 1, 2, 3, 1, 7, 2], [3, 1, 2, 3, 2, 1, 7], [3, 1, 2, 3, 2, 7, 1], [3, 1, 2, 3, 7, 1, 2], [3, 1, 2, 3, 7, 2, 1], [3, 1, 2, 7, 1, 2, 3], [3, 1, 2, 7, 1, 3, 2], [3, 1, 2, 7, 2, 1, 3], [3, 1, 2, 7, 2, 3, 1], [3, 1, 2, 7, 3, 1, 2], [3, 1, 2, 7, 3, 2, 1], [3, 1, 3, 1, 2, 2, 7], [3, 1, 3, 1, 2, 7, 2], [3, 1, 3, 1, 7, 2, 2], [3, 1, 3, 2, 1, 2, 7], [3, 1, 3, 2, 1, 7, 2], [3, 1, 3, 2, 2, 1, 7], [3, 1, 3, 2, 2, 7, 1], [3, 1, 3, 2, 7, 1, 2], [3, 1, 3, 2, 7, 2, 1], [3, 1, 3, 7, 1, 2, 2], [3, 1, 3, 7, 2, 1, 2], [3, 1, 3, 7, 2, 2, 1], [3, 1, 7, 1, 2, 2, 3], [3, 1, 7, 1, 2, 3, 2], [3, 1, 7, 1, 3, 2, 2], [3, 1, 7, 2, 1, 2, 3], [3, 1, 7, 2, 1, 3, 2], [3, 1, 7, 2, 2, 1, 3], [3, 1, 7, 2, 2, 3, 1], [3, 1, 7, 2, 3, 1, 2], [3, 1, 7, 2, 3, 2, 1], [3, 1, 7, 3, 1, 2, 2], [3, 1, 7, 3, 2, 1, 2], [3, 1, 7, 3, 2, 2, 1], [3, 2, 1, 1, 2, 3, 7], [3, 2, 1, 1, 2, 7, 3], [3, 2, 1, 1, 3, 2, 7], [3, 2, 1, 1, 3, 7, 2], [3, 2, 1, 1, 7, 2, 3], [3, 2, 1, 1, 7, 3, 2], [3, 2, 1, 2, 1, 3, 7], [3, 2, 1, 2, 1, 7, 3], [3, 2, 1, 2, 3, 1, 7], [3, 2, 1, 2, 3, 7, 1], [3, 2, 1, 2, 7, 1, 3], [3, 2, 1, 2, 7, 3, 1], [3, 2, 1, 3, 1, 2, 7], [3, 2, 1, 3, 1, 7, 2], [3, 2, 1, 3, 2, 1, 7], [3, 2, 1, 3, 2, 7, 1], [3, 2, 1, 3, 7, 1, 2], [3, 2, 1, 3, 7, 2, 1], [3, 2, 1, 7, 1, 2, 3], [3, 2, 1, 7, 1, 3, 2], [3, 2, 1, 7, 2, 1, 3], [3, 2, 1, 7, 2, 3, 1], [3, 2, 1, 7, 3, 1, 2], [3, 2, 1, 7, 3, 2, 1], [3, 2, 2, 1, 1, 3, 7], [3, 2, 2, 1, 1, 7, 3], [3, 2, 2, 1, 3, 1, 7], [3, 2, 2, 1, 3, 7, 1], [3, 2, 2, 1, 7, 1, 3], [3, 2, 2, 1, 7, 3, 1], [3, 2, 2, 3, 1, 1, 7], [3, 2, 2, 3, 1, 7, 1], [3, 2, 2, 3, 7, 1, 1], [3, 2, 2, 7, 1, 1, 3], [3, 2, 2, 7, 1, 3, 1], [3, 2, 2, 7, 3, 1, 1], [3, 2, 3, 1, 1, 2, 7], [3, 2, 3, 1, 1, 7, 2], [3, 2, 3, 1, 2, 1, 7], [3, 2, 3, 1, 2, 7, 1], [3, 2, 3, 1, 7, 1, 2], [3, 2, 3, 1, 7, 2, 1], [3, 2, 3, 2, 1, 1, 7], [3, 2, 3, 2, 1, 7, 1], [3, 2, 3, 2, 7, 1, 1], [3, 2, 3, 7, 1, 1, 2], [3, 2, 3, 7, 1, 2, 1], [3, 2, 3, 7, 2, 1, 1], [3, 2, 7, 1, 1, 2, 3], [3, 2, 7, 1, 1, 3, 2], [3, 2, 7, 1, 2, 1, 3], [3, 2, 7, 1, 2, 3, 1], [3, 2, 7, 1, 3, 1, 2], [3, 2, 7, 1, 3, 2, 1], [3, 2, 7, 2, 1, 1, 3], [3, 2, 7, 2, 1, 3, 1], [3, 2, 7, 2, 3, 1, 1], [3, 2, 7, 3, 1, 1, 2], [3, 2, 7, 3, 1, 2, 1], [3, 2, 7, 3, 2, 1, 1], [3, 3, 1, 1, 2, 2, 7], [3, 3, 1, 1, 2, 7, 2], [3, 3, 1, 1, 7, 2, 2], [3, 3, 1, 2, 1, 2, 7], [3, 3, 1, 2, 1, 7, 2], [3, 3, 1, 2, 2, 1, 7], [3, 3, 1, 2, 2, 7, 1], [3, 3, 1, 2, 7, 1, 2], [3, 3, 1, 2, 7, 2, 1], [3, 3, 1, 7, 1, 2, 2], [3, 3, 1, 7, 2, 1, 2], [3, 3, 1, 7, 2, 2, 1], [3, 3, 2, 1, 1, 2, 7], [3, 3, 2, 1, 1, 7, 2], [3, 3, 2, 1, 2, 1, 7], [3, 3, 2, 1, 2, 7, 1], [3, 3, 2, 1, 7, 1, 2], [3, 3, 2, 1, 7, 2, 1], [3, 3, 2, 2, 1, 1, 7], [3, 3, 2, 2, 1, 7, 1], [3, 3, 2, 2, 7, 1, 1], [3, 3, 2, 7, 1, 1, 2], [3, 3, 2, 7, 1, 2, 1], [3, 3, 2, 7, 2, 1, 1], [3, 3, 7, 1, 1, 2, 2], [3, 3, 7, 1, 2, 1, 2], [3, 3, 7, 1, 2, 2, 1], [3, 3, 7, 2, 1, 1, 2], [3, 3, 7, 2, 1, 2, 1], [3, 3, 7, 2, 2, 1, 1], [3, 7, 1, 1, 2, 2, 3], [3, 7, 1, 1, 2, 3, 2], [3, 7, 1, 1, 3, 2, 2], [3, 7, 1, 2, 1, 2, 3], [3, 7, 1, 2, 1, 3, 2], [3, 7, 1, 2, 2, 1, 3], [3, 7, 1, 2, 2, 3, 1], [3, 7, 1, 2, 3, 1, 2], [3, 7, 1, 2, 3, 2, 1], [3, 7, 1, 3, 1, 2, 2], [3, 7, 1, 3, 2, 1, 2], [3, 7, 1, 3, 2, 2, 1], [3, 7, 2, 1, 1, 2, 3], [3, 7, 2, 1, 1, 3, 2], [3, 7, 2, 1, 2, 1, 3], [3, 7, 2, 1, 2, 3, 1], [3, 7, 2, 1, 3, 1, 2], [3, 7, 2, 1, 3, 2, 1], [3, 7, 2, 2, 1, 1, 3], [3, 7, 2, 2, 1, 3, 1], [3, 7, 2, 2, 3, 1, 1], [3, 7, 2, 3, 1, 1, 2], [3, 7, 2, 3, 1, 2, 1], [3, 7, 2, 3, 2, 1, 1], [3, 7, 3, 1, 1, 2, 2], [3, 7, 3, 1, 2, 1, 2], [3, 7, 3, 1, 2, 2, 1], [3, 7, 3, 2, 1, 1, 2], [3, 7, 3, 2, 1, 2, 1], [3, 7, 3, 2, 2, 1, 1], [7, 1, 1, 2, 2, 3, 3], [7, 1, 1, 2, 3, 2, 3], [7, 1, 1, 2, 3, 3, 2], [7, 1, 1, 3, 2, 2, 3], [7, 1, 1, 3, 2, 3, 2], [7, 1, 1, 3, 3, 2, 2], [7, 1, 2, 1, 2, 3, 3], [7, 1, 2, 1, 3, 2, 3], [7, 1, 2, 1, 3, 3, 2], [7, 1, 2, 2, 1, 3, 3], [7, 1, 2, 2, 3, 1, 3], [7, 1, 2, 2, 3, 3, 1], [7, 1, 2, 3, 1, 2, 3], [7, 1, 2, 3, 1, 3, 2], [7, 1, 2, 3, 2, 1, 3], [7, 1, 2, 3, 2, 3, 1], [7, 1, 2, 3, 3, 1, 2], [7, 1, 2, 3, 3, 2, 1], [7, 1, 3, 1, 2, 2, 3], [7, 1, 3, 1, 2, 3, 2], [7, 1, 3, 1, 3, 2, 2], [7, 1, 3, 2, 1, 2, 3], [7, 1, 3, 2, 1, 3, 2], [7, 1, 3, 2, 2, 1, 3], [7, 1, 3, 2, 2, 3, 1], [7, 1, 3, 2, 3, 1, 2], [7, 1, 3, 2, 3, 2, 1], [7, 1, 3, 3, 1, 2, 2], [7, 1, 3, 3, 2, 1, 2], [7, 1, 3, 3, 2, 2, 1], [7, 2, 1, 1, 2, 3, 3], [7, 2, 1, 1, 3, 2, 3], [7, 2, 1, 1, 3, 3, 2], [7, 2, 1, 2, 1, 3, 3], [7, 2, 1, 2, 3, 1, 3], [7, 2, 1, 2, 3, 3, 1], [7, 2, 1, 3, 1, 2, 3], [7, 2, 1, 3, 1, 3, 2], [7, 2, 1, 3, 2, 1, 3], [7, 2, 1, 3, 2, 3, 1], [7, 2, 1, 3, 3, 1, 2], [7, 2, 1, 3, 3, 2, 1], [7, 2, 2, 1, 1, 3, 3], [7, 2, 2, 1, 3, 1, 3], [7, 2, 2, 1, 3, 3, 1], [7, 2, 2, 3, 1, 1, 3], [7, 2, 2, 3, 1, 3, 1], [7, 2, 2, 3, 3, 1, 1], [7, 2, 3, 1, 1, 2, 3], [7, 2, 3, 1, 1, 3, 2], [7, 2, 3, 1, 2, 1, 3], [7, 2, 3, 1, 2, 3, 1], [7, 2, 3, 1, 3, 1, 2], [7, 2, 3, 1, 3, 2, 1], [7, 2, 3, 2, 1, 1, 3], [7, 2, 3, 2, 1, 3, 1], [7, 2, 3, 2, 3, 1, 1], [7, 2, 3, 3, 1, 1, 2], [7, 2, 3, 3, 1, 2, 1], [7, 2, 3, 3, 2, 1, 1], [7, 3, 1, 1, 2, 2, 3], [7, 3, 1, 1, 2, 3, 2], [7, 3, 1, 1, 3, 2, 2], [7, 3, 1, 2, 1, 2, 3], [7, 3, 1, 2, 1, 3, 2], [7, 3, 1, 2, 2, 1, 3], [7, 3, 1, 2, 2, 3, 1], [7, 3, 1, 2, 3, 1, 2], [7, 3, 1, 2, 3, 2, 1], [7, 3, 1, 3, 1, 2, 2], [7, 3, 1, 3, 2, 1, 2], [7, 3, 1, 3, 2, 2, 1], [7, 3, 2, 1, 1, 2, 3], [7, 3, 2, 1, 1, 3, 2], [7, 3, 2, 1, 2, 1, 3], [7, 3, 2, 1, 2, 3, 1], [7, 3, 2, 1, 3, 1, 2], [7, 3, 2, 1, 3, 2, 1], [7, 3, 2, 2, 1, 1, 3], [7, 3, 2, 2, 1, 3, 1], [7, 3, 2, 2, 3, 1, 1], [7, 3, 2, 3, 1, 1, 2], [7, 3, 2, 3, 1, 2, 1], [7, 3, 2, 3, 2, 1, 1], [7, 3, 3, 1, 1, 2, 2], [7, 3, 3, 1, 2, 1, 2], [7, 3, 3, 1, 2, 2, 1], [7, 3, 3, 2, 1, 1, 2], [7, 3, 3, 2, 1, 2, 1], [7, 3, 3, 2, 2, 1, 1]]\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2]) == [[1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 2, 1, 2, 2, 2], [1, 1, 1, 2, 2, 1, 2, 2], [1, 1, 1, 2, 2, 2, 1, 2], [1, 1, 1, 2, 2, 2, 2, 1], [1, 1, 2, 1, 1, 2, 2, 2], [1, 1, 2, 1, 2, 1, 2, 2], [1, 1, 2, 1, 2, 2, 1, 2], [1, 1, 2, 1, 2, 2, 2, 1], [1, 1, 2, 2, 1, 1, 2, 2], [1, 1, 2, 2, 1, 2, 1, 2], [1, 1, 2, 2, 1, 2, 2, 1], [1, 1, 2, 2, 2, 1, 1, 2], [1, 1, 2, 2, 2, 1, 2, 1], [1, 1, 2, 2, 2, 2, 1, 1], [1, 2, 1, 1, 1, 2, 2, 2], [1, 2, 1, 1, 2, 1, 2, 2], [1, 2, 1, 1, 2, 2, 1, 2], [1, 2, 1, 1, 2, 2, 2, 1], [1, 2, 1, 2, 1, 1, 2, 2], [1, 2, 1, 2, 1, 2, 1, 2], [1, 2, 1, 2, 1, 2, 2, 1], [1, 2, 1, 2, 2, 1, 1, 2], [1, 2, 1, 2, 2, 1, 2, 1], [1, 2, 1, 2, 2, 2, 1, 1], [1, 2, 2, 1, 1, 1, 2, 2], [1, 2, 2, 1, 1, 2, 1, 2], [1, 2, 2, 1, 1, 2, 2, 1], [1, 2, 2, 1, 2, 1, 1, 2], [1, 2, 2, 1, 2, 1, 2, 1], [1, 2, 2, 1, 2, 2, 1, 1], [1, 2, 2, 2, 1, 1, 1, 2], [1, 2, 2, 2, 1, 1, 2, 1], [1, 2, 2, 2, 1, 2, 1, 1], [1, 2, 2, 2, 2, 1, 1, 1], [2, 1, 1, 1, 1, 2, 2, 2], [2, 1, 1, 1, 2, 1, 2, 2], [2, 1, 1, 1, 2, 2, 1, 2], [2, 1, 1, 1, 2, 2, 2, 1], [2, 1, 1, 2, 1, 1, 2, 2], [2, 1, 1, 2, 1, 2, 1, 2], [2, 1, 1, 2, 1, 2, 2, 1], [2, 1, 1, 2, 2, 1, 1, 2], [2, 1, 1, 2, 2, 1, 2, 1], [2, 1, 1, 2, 2, 2, 1, 1], [2, 1, 2, 1, 1, 1, 2, 2], [2, 1, 2, 1, 1, 2, 1, 2], [2, 1, 2, 1, 1, 2, 2, 1], [2, 1, 2, 1, 2, 1, 1, 2], [2, 1, 2, 1, 2, 1, 2, 1], [2, 1, 2, 1, 2, 2, 1, 1], [2, 1, 2, 2, 1, 1, 1, 2], [2, 1, 2, 2, 1, 1, 2, 1], [2, 1, 2, 2, 1, 2, 1, 1], [2, 1, 2, 2, 2, 1, 1, 1], [2, 2, 1, 1, 1, 1, 2, 2], [2, 2, 1, 1, 1, 2, 1, 2], [2, 2, 1, 1, 1, 2, 2, 1], [2, 2, 1, 1, 2, 1, 1, 2], [2, 2, 1, 1, 2, 1, 2, 1], [2, 2, 1, 1, 2, 2, 1, 1], [2, 2, 1, 2, 1, 1, 1, 2], [2, 2, 1, 2, 1, 1, 2, 1], [2, 2, 1, 2, 1, 2, 1, 1], [2, 2, 1, 2, 2, 1, 1, 1], [2, 2, 2, 1, 1, 1, 1, 2], [2, 2, 2, 1, 1, 1, 2, 1], [2, 2, 2, 1, 1, 2, 1, 1], [2, 2, 2, 1, 2, 1, 1, 1], [2, 2, 2, 2, 1, 1, 1, 1]]\n assert candidate(nums = [1, 1, 1, 2, 2]) == [[1, 1, 1, 2, 2], [1, 1, 2, 1, 2], [1, 1, 2, 2, 1], [1, 2, 1, 1, 2], [1, 2, 1, 2, 1], [1, 2, 2, 1, 1], [2, 1, 1, 1, 2], [2, 1, 1, 2, 1], [2, 1, 2, 1, 1], [2, 2, 1, 1, 1]]\n assert candidate(nums = [1, 1, 1, 2, 2, 3]) == [[1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 3, 2], [1, 1, 1, 3, 2, 2], [1, 1, 2, 1, 2, 3], [1, 1, 2, 1, 3, 2], [1, 1, 2, 2, 1, 3], [1, 1, 2, 2, 3, 1], [1, 1, 2, 3, 1, 2], [1, 1, 2, 3, 2, 1], [1, 1, 3, 1, 2, 2], [1, 1, 3, 2, 1, 2], [1, 1, 3, 2, 2, 1], [1, 2, 1, 1, 2, 3], [1, 2, 1, 1, 3, 2], [1, 2, 1, 2, 1, 3], [1, 2, 1, 2, 3, 1], [1, 2, 1, 3, 1, 2], [1, 2, 1, 3, 2, 1], [1, 2, 2, 1, 1, 3], [1, 2, 2, 1, 3, 1], [1, 2, 2, 3, 1, 1], [1, 2, 3, 1, 1, 2], [1, 2, 3, 1, 2, 1], [1, 2, 3, 2, 1, 1], [1, 3, 1, 1, 2, 2], [1, 3, 1, 2, 1, 2], [1, 3, 1, 2, 2, 1], [1, 3, 2, 1, 1, 2], [1, 3, 2, 1, 2, 1], [1, 3, 2, 2, 1, 1], [2, 1, 1, 1, 2, 3], [2, 1, 1, 1, 3, 2], [2, 1, 1, 2, 1, 3], [2, 1, 1, 2, 3, 1], [2, 1, 1, 3, 1, 2], [2, 1, 1, 3, 2, 1], [2, 1, 2, 1, 1, 3], [2, 1, 2, 1, 3, 1], [2, 1, 2, 3, 1, 1], [2, 1, 3, 1, 1, 2], [2, 1, 3, 1, 2, 1], [2, 1, 3, 2, 1, 1], [2, 2, 1, 1, 1, 3], [2, 2, 1, 1, 3, 1], [2, 2, 1, 3, 1, 1], [2, 2, 3, 1, 1, 1], [2, 3, 1, 1, 1, 2], [2, 3, 1, 1, 2, 1], [2, 3, 1, 2, 1, 1], [2, 3, 2, 1, 1, 1], [3, 1, 1, 1, 2, 2], [3, 1, 1, 2, 1, 2], [3, 1, 1, 2, 2, 1], [3, 1, 2, 1, 1, 2], [3, 1, 2, 1, 2, 1], [3, 1, 2, 2, 1, 1], [3, 2, 1, 1, 1, 2], [3, 2, 1, 1, 2, 1], [3, 2, 1, 2, 1, 1], [3, 2, 2, 1, 1, 1]]\n assert candidate(nums = [10, -10, 0, 5, -5, 5]) == [[-10, -5, 0, 5, 5, 10], [-10, -5, 0, 5, 10, 5], [-10, -5, 0, 10, 5, 5], [-10, -5, 5, 0, 5, 10], [-10, -5, 5, 0, 10, 5], [-10, -5, 5, 5, 0, 10], [-10, -5, 5, 5, 10, 0], [-10, -5, 5, 10, 0, 5], [-10, -5, 5, 10, 5, 0], [-10, -5, 10, 0, 5, 5], [-10, -5, 10, 5, 0, 5], [-10, -5, 10, 5, 5, 0], [-10, 0, -5, 5, 5, 10], [-10, 0, -5, 5, 10, 5], [-10, 0, -5, 10, 5, 5], [-10, 0, 5, -5, 5, 10], [-10, 0, 5, -5, 10, 5], [-10, 0, 5, 5, -5, 10], [-10, 0, 5, 5, 10, -5], [-10, 0, 5, 10, -5, 5], [-10, 0, 5, 10, 5, -5], [-10, 0, 10, -5, 5, 5], [-10, 0, 10, 5, -5, 5], [-10, 0, 10, 5, 5, -5], [-10, 5, -5, 0, 5, 10], [-10, 5, -5, 0, 10, 5], [-10, 5, -5, 5, 0, 10], [-10, 5, -5, 5, 10, 0], [-10, 5, -5, 10, 0, 5], [-10, 5, -5, 10, 5, 0], [-10, 5, 0, -5, 5, 10], [-10, 5, 0, -5, 10, 5], [-10, 5, 0, 5, -5, 10], [-10, 5, 0, 5, 10, -5], [-10, 5, 0, 10, -5, 5], [-10, 5, 0, 10, 5, -5], [-10, 5, 5, -5, 0, 10], [-10, 5, 5, -5, 10, 0], [-10, 5, 5, 0, -5, 10], [-10, 5, 5, 0, 10, -5], [-10, 5, 5, 10, -5, 0], [-10, 5, 5, 10, 0, -5], [-10, 5, 10, -5, 0, 5], [-10, 5, 10, -5, 5, 0], [-10, 5, 10, 0, -5, 5], [-10, 5, 10, 0, 5, -5], [-10, 5, 10, 5, -5, 0], [-10, 5, 10, 5, 0, -5], [-10, 10, -5, 0, 5, 5], [-10, 10, -5, 5, 0, 5], [-10, 10, -5, 5, 5, 0], [-10, 10, 0, -5, 5, 5], [-10, 10, 0, 5, -5, 5], [-10, 10, 0, 5, 5, -5], [-10, 10, 5, -5, 0, 5], [-10, 10, 5, -5, 5, 0], [-10, 10, 5, 0, -5, 5], [-10, 10, 5, 0, 5, -5], [-10, 10, 5, 5, -5, 0], [-10, 10, 5, 5, 0, -5], [-5, -10, 0, 5, 5, 10], [-5, -10, 0, 5, 10, 5], [-5, -10, 0, 10, 5, 5], [-5, -10, 5, 0, 5, 10], [-5, -10, 5, 0, 10, 5], [-5, -10, 5, 5, 0, 10], [-5, -10, 5, 5, 10, 0], [-5, -10, 5, 10, 0, 5], [-5, -10, 5, 10, 5, 0], [-5, -10, 10, 0, 5, 5], [-5, -10, 10, 5, 0, 5], [-5, -10, 10, 5, 5, 0], [-5, 0, -10, 5, 5, 10], [-5, 0, -10, 5, 10, 5], [-5, 0, -10, 10, 5, 5], [-5, 0, 5, -10, 5, 10], [-5, 0, 5, -10, 10, 5], [-5, 0, 5, 5, -10, 10], [-5, 0, 5, 5, 10, -10], [-5, 0, 5, 10, -10, 5], [-5, 0, 5, 10, 5, -10], [-5, 0, 10, -10, 5, 5], [-5, 0, 10, 5, -10, 5], [-5, 0, 10, 5, 5, -10], [-5, 5, -10, 0, 5, 10], [-5, 5, -10, 0, 10, 5], [-5, 5, -10, 5, 0, 10], [-5, 5, -10, 5, 10, 0], [-5, 5, -10, 10, 0, 5], [-5, 5, -10, 10, 5, 0], [-5, 5, 0, -10, 5, 10], [-5, 5, 0, -10, 10, 5], [-5, 5, 0, 5, -10, 10], [-5, 5, 0, 5, 10, -10], [-5, 5, 0, 10, -10, 5], [-5, 5, 0, 10, 5, -10], [-5, 5, 5, -10, 0, 10], [-5, 5, 5, -10, 10, 0], [-5, 5, 5, 0, -10, 10], [-5, 5, 5, 0, 10, -10], [-5, 5, 5, 10, -10, 0], [-5, 5, 5, 10, 0, -10], [-5, 5, 10, -10, 0, 5], [-5, 5, 10, -10, 5, 0], [-5, 5, 10, 0, -10, 5], [-5, 5, 10, 0, 5, -10], [-5, 5, 10, 5, -10, 0], [-5, 5, 10, 5, 0, -10], [-5, 10, -10, 0, 5, 5], [-5, 10, -10, 5, 0, 5], [-5, 10, -10, 5, 5, 0], [-5, 10, 0, -10, 5, 5], [-5, 10, 0, 5, -10, 5], [-5, 10, 0, 5, 5, -10], [-5, 10, 5, -10, 0, 5], [-5, 10, 5, -10, 5, 0], [-5, 10, 5, 0, -10, 5], [-5, 10, 5, 0, 5, -10], [-5, 10, 5, 5, -10, 0], [-5, 10, 5, 5, 0, -10], [0, -10, -5, 5, 5, 10], [0, -10, -5, 5, 10, 5], [0, -10, -5, 10, 5, 5], [0, -10, 5, -5, 5, 10], [0, -10, 5, -5, 10, 5], [0, -10, 5, 5, -5, 10], [0, -10, 5, 5, 10, -5], [0, -10, 5, 10, -5, 5], [0, -10, 5, 10, 5, -5], [0, -10, 10, -5, 5, 5], [0, -10, 10, 5, -5, 5], [0, -10, 10, 5, 5, -5], [0, -5, -10, 5, 5, 10], [0, -5, -10, 5, 10, 5], [0, -5, -10, 10, 5, 5], [0, -5, 5, -10, 5, 10], [0, -5, 5, -10, 10, 5], [0, -5, 5, 5, -10, 10], [0, -5, 5, 5, 10, -10], [0, -5, 5, 10, -10, 5], [0, -5, 5, 10, 5, -10], [0, -5, 10, -10, 5, 5], [0, -5, 10, 5, -10, 5], [0, -5, 10, 5, 5, -10], [0, 5, -10, -5, 5, 10], [0, 5, -10, -5, 10, 5], [0, 5, -10, 5, -5, 10], [0, 5, -10, 5, 10, -5], [0, 5, -10, 10, -5, 5], [0, 5, -10, 10, 5, -5], [0, 5, -5, -10, 5, 10], [0, 5, -5, -10, 10, 5], [0, 5, -5, 5, -10, 10], [0, 5, -5, 5, 10, -10], [0, 5, -5, 10, -10, 5], [0, 5, -5, 10, 5, -10], [0, 5, 5, -10, -5, 10], [0, 5, 5, -10, 10, -5], [0, 5, 5, -5, -10, 10], [0, 5, 5, -5, 10, -10], [0, 5, 5, 10, -10, -5], [0, 5, 5, 10, -5, -10], [0, 5, 10, -10, -5, 5], [0, 5, 10, -10, 5, -5], [0, 5, 10, -5, -10, 5], [0, 5, 10, -5, 5, -10], [0, 5, 10, 5, -10, -5], [0, 5, 10, 5, -5, -10], [0, 10, -10, -5, 5, 5], [0, 10, -10, 5, -5, 5], [0, 10, -10, 5, 5, -5], [0, 10, -5, -10, 5, 5], [0, 10, -5, 5, -10, 5], [0, 10, -5, 5, 5, -10], [0, 10, 5, -10, -5, 5], [0, 10, 5, -10, 5, -5], [0, 10, 5, -5, -10, 5], [0, 10, 5, -5, 5, -10], [0, 10, 5, 5, -10, -5], [0, 10, 5, 5, -5, -10], [5, -10, -5, 0, 5, 10], [5, -10, -5, 0, 10, 5], [5, -10, -5, 5, 0, 10], [5, -10, -5, 5, 10, 0], [5, -10, -5, 10, 0, 5], [5, -10, -5, 10, 5, 0], [5, -10, 0, -5, 5, 10], [5, -10, 0, -5, 10, 5], [5, -10, 0, 5, -5, 10], [5, -10, 0, 5, 10, -5], [5, -10, 0, 10, -5, 5], [5, -10, 0, 10, 5, -5], [5, -10, 5, -5, 0, 10], [5, -10, 5, -5, 10, 0], [5, -10, 5, 0, -5, 10], [5, -10, 5, 0, 10, -5], [5, -10, 5, 10, -5, 0], [5, -10, 5, 10, 0, -5], [5, -10, 10, -5, 0, 5], [5, -10, 10, -5, 5, 0], [5, -10, 10, 0, -5, 5], [5, -10, 10, 0, 5, -5], [5, -10, 10, 5, -5, 0], [5, -10, 10, 5, 0, -5], [5, -5, -10, 0, 5, 10], [5, -5, -10, 0, 10, 5], [5, -5, -10, 5, 0, 10], [5, -5, -10, 5, 10, 0], [5, -5, -10, 10, 0, 5], [5, -5, -10, 10, 5, 0], [5, -5, 0, -10, 5, 10], [5, -5, 0, -10, 10, 5], [5, -5, 0, 5, -10, 10], [5, -5, 0, 5, 10, -10], [5, -5, 0, 10, -10, 5], [5, -5, 0, 10, 5, -10], [5, -5, 5, -10, 0, 10], [5, -5, 5, -10, 10, 0], [5, -5, 5, 0, -10, 10], [5, -5, 5, 0, 10, -10], [5, -5, 5, 10, -10, 0], [5, -5, 5, 10, 0, -10], [5, -5, 10, -10, 0, 5], [5, -5, 10, -10, 5, 0], [5, -5, 10, 0, -10, 5], [5, -5, 10, 0, 5, -10], [5, -5, 10, 5, -10, 0], [5, -5, 10, 5, 0, -10], [5, 0, -10, -5, 5, 10], [5, 0, -10, -5, 10, 5], [5, 0, -10, 5, -5, 10], [5, 0, -10, 5, 10, -5], [5, 0, -10, 10, -5, 5], [5, 0, -10, 10, 5, -5], [5, 0, -5, -10, 5, 10], [5, 0, -5, -10, 10, 5], [5, 0, -5, 5, -10, 10], [5, 0, -5, 5, 10, -10], [5, 0, -5, 10, -10, 5], [5, 0, -5, 10, 5, -10], [5, 0, 5, -10, -5, 10], [5, 0, 5, -10, 10, -5], [5, 0, 5, -5, -10, 10], [5, 0, 5, -5, 10, -10], [5, 0, 5, 10, -10, -5], [5, 0, 5, 10, -5, -10], [5, 0, 10, -10, -5, 5], [5, 0, 10, -10, 5, -5], [5, 0, 10, -5, -10, 5], [5, 0, 10, -5, 5, -10], [5, 0, 10, 5, -10, -5], [5, 0, 10, 5, -5, -10], [5, 5, -10, -5, 0, 10], [5, 5, -10, -5, 10, 0], [5, 5, -10, 0, -5, 10], [5, 5, -10, 0, 10, -5], [5, 5, -10, 10, -5, 0], [5, 5, -10, 10, 0, -5], [5, 5, -5, -10, 0, 10], [5, 5, -5, -10, 10, 0], [5, 5, -5, 0, -10, 10], [5, 5, -5, 0, 10, -10], [5, 5, -5, 10, -10, 0], [5, 5, -5, 10, 0, -10], [5, 5, 0, -10, -5, 10], [5, 5, 0, -10, 10, -5], [5, 5, 0, -5, -10, 10], [5, 5, 0, -5, 10, -10], [5, 5, 0, 10, -10, -5], [5, 5, 0, 10, -5, -10], [5, 5, 10, -10, -5, 0], [5, 5, 10, -10, 0, -5], [5, 5, 10, -5, -10, 0], [5, 5, 10, -5, 0, -10], [5, 5, 10, 0, -10, -5], [5, 5, 10, 0, -5, -10], [5, 10, -10, -5, 0, 5], [5, 10, -10, -5, 5, 0], [5, 10, -10, 0, -5, 5], [5, 10, -10, 0, 5, -5], [5, 10, -10, 5, -5, 0], [5, 10, -10, 5, 0, -5], [5, 10, -5, -10, 0, 5], [5, 10, -5, -10, 5, 0], [5, 10, -5, 0, -10, 5], [5, 10, -5, 0, 5, -10], [5, 10, -5, 5, -10, 0], [5, 10, -5, 5, 0, -10], [5, 10, 0, -10, -5, 5], [5, 10, 0, -10, 5, -5], [5, 10, 0, -5, -10, 5], [5, 10, 0, -5, 5, -10], [5, 10, 0, 5, -10, -5], [5, 10, 0, 5, -5, -10], [5, 10, 5, -10, -5, 0], [5, 10, 5, -10, 0, -5], [5, 10, 5, -5, -10, 0], [5, 10, 5, -5, 0, -10], [5, 10, 5, 0, -10, -5], [5, 10, 5, 0, -5, -10], [10, -10, -5, 0, 5, 5], [10, -10, -5, 5, 0, 5], [10, -10, -5, 5, 5, 0], [10, -10, 0, -5, 5, 5], [10, -10, 0, 5, -5, 5], [10, -10, 0, 5, 5, -5], [10, -10, 5, -5, 0, 5], [10, -10, 5, -5, 5, 0], [10, -10, 5, 0, -5, 5], [10, -10, 5, 0, 5, -5], [10, -10, 5, 5, -5, 0], [10, -10, 5, 5, 0, -5], [10, -5, -10, 0, 5, 5], [10, -5, -10, 5, 0, 5], [10, -5, -10, 5, 5, 0], [10, -5, 0, -10, 5, 5], [10, -5, 0, 5, -10, 5], [10, -5, 0, 5, 5, -10], [10, -5, 5, -10, 0, 5], [10, -5, 5, -10, 5, 0], [10, -5, 5, 0, -10, 5], [10, -5, 5, 0, 5, -10], [10, -5, 5, 5, -10, 0], [10, -5, 5, 5, 0, -10], [10, 0, -10, -5, 5, 5], [10, 0, -10, 5, -5, 5], [10, 0, -10, 5, 5, -5], [10, 0, -5, -10, 5, 5], [10, 0, -5, 5, -10, 5], [10, 0, -5, 5, 5, -10], [10, 0, 5, -10, -5, 5], [10, 0, 5, -10, 5, -5], [10, 0, 5, -5, -10, 5], [10, 0, 5, -5, 5, -10], [10, 0, 5, 5, -10, -5], [10, 0, 5, 5, -5, -10], [10, 5, -10, -5, 0, 5], [10, 5, -10, -5, 5, 0], [10, 5, -10, 0, -5, 5], [10, 5, -10, 0, 5, -5], [10, 5, -10, 5, -5, 0], [10, 5, -10, 5, 0, -5], [10, 5, -5, -10, 0, 5], [10, 5, -5, -10, 5, 0], [10, 5, -5, 0, -10, 5], [10, 5, -5, 0, 5, -10], [10, 5, -5, 5, -10, 0], [10, 5, -5, 5, 0, -10], [10, 5, 0, -10, -5, 5], [10, 5, 0, -10, 5, -5], [10, 5, 0, -5, -10, 5], [10, 5, 0, -5, 5, -10], [10, 5, 0, 5, -10, -5], [10, 5, 0, 5, -5, -10], [10, 5, 5, -10, -5, 0], [10, 5, 5, -10, 0, -5], [10, 5, 5, -5, -10, 0], [10, 5, 5, -5, 0, -10], [10, 5, 5, 0, -10, -5], [10, 5, 5, 0, -5, -10]]\n assert candidate(nums = [1, 2, 3, 4]) == [[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]]\n assert candidate(nums = [5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5]]\n assert candidate(nums = [1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5], [1, 2, 3, 5, 4], [1, 2, 4, 3, 5], [1, 2, 4, 5, 3], [1, 2, 5, 3, 4], [1, 2, 5, 4, 3], [1, 3, 2, 4, 5], [1, 3, 2, 5, 4], [1, 3, 4, 2, 5], [1, 3, 4, 5, 2], [1, 3, 5, 2, 4], [1, 3, 5, 4, 2], [1, 4, 2, 3, 5], [1, 4, 2, 5, 3], [1, 4, 3, 2, 5], [1, 4, 3, 5, 2], [1, 4, 5, 2, 3], [1, 4, 5, 3, 2], [1, 5, 2, 3, 4], [1, 5, 2, 4, 3], [1, 5, 3, 2, 4], [1, 5, 3, 4, 2], [1, 5, 4, 2, 3], [1, 5, 4, 3, 2], [2, 1, 3, 4, 5], [2, 1, 3, 5, 4], [2, 1, 4, 3, 5], [2, 1, 4, 5, 3], [2, 1, 5, 3, 4], [2, 1, 5, 4, 3], [2, 3, 1, 4, 5], [2, 3, 1, 5, 4], [2, 3, 4, 1, 5], [2, 3, 4, 5, 1], [2, 3, 5, 1, 4], [2, 3, 5, 4, 1], [2, 4, 1, 3, 5], [2, 4, 1, 5, 3], [2, 4, 3, 1, 5], [2, 4, 3, 5, 1], [2, 4, 5, 1, 3], [2, 4, 5, 3, 1], [2, 5, 1, 3, 4], [2, 5, 1, 4, 3], [2, 5, 3, 1, 4], [2, 5, 3, 4, 1], [2, 5, 4, 1, 3], [2, 5, 4, 3, 1], [3, 1, 2, 4, 5], [3, 1, 2, 5, 4], [3, 1, 4, 2, 5], [3, 1, 4, 5, 2], [3, 1, 5, 2, 4], [3, 1, 5, 4, 2], [3, 2, 1, 4, 5], [3, 2, 1, 5, 4], [3, 2, 4, 1, 5], [3, 2, 4, 5, 1], [3, 2, 5, 1, 4], [3, 2, 5, 4, 1], [3, 4, 1, 2, 5], [3, 4, 1, 5, 2], [3, 4, 2, 1, 5], [3, 4, 2, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 2, 1], [3, 5, 1, 2, 4], [3, 5, 1, 4, 2], [3, 5, 2, 1, 4], [3, 5, 2, 4, 1], [3, 5, 4, 1, 2], [3, 5, 4, 2, 1], [4, 1, 2, 3, 5], [4, 1, 2, 5, 3], [4, 1, 3, 2, 5], [4, 1, 3, 5, 2], [4, 1, 5, 2, 3], [4, 1, 5, 3, 2], [4, 2, 1, 3, 5], [4, 2, 1, 5, 3], [4, 2, 3, 1, 5], [4, 2, 3, 5, 1], [4, 2, 5, 1, 3], [4, 2, 5, 3, 1], [4, 3, 1, 2, 5], [4, 3, 1, 5, 2], [4, 3, 2, 1, 5], [4, 3, 2, 5, 1], [4, 3, 5, 1, 2], [4, 3, 5, 2, 1], [4, 5, 1, 2, 3], [4, 5, 1, 3, 2], [4, 5, 2, 1, 3], [4, 5, 2, 3, 1], [4, 5, 3, 1, 2], [4, 5, 3, 2, 1], [5, 1, 2, 3, 4], [5, 1, 2, 4, 3], [5, 1, 3, 2, 4], [5, 1, 3, 4, 2], [5, 1, 4, 2, 3], [5, 1, 4, 3, 2], [5, 2, 1, 3, 4], [5, 2, 1, 4, 3], [5, 2, 3, 1, 4], [5, 2, 3, 4, 1], [5, 2, 4, 1, 3], [5, 2, 4, 3, 1], [5, 3, 1, 2, 4], [5, 3, 1, 4, 2], [5, 3, 2, 1, 4], [5, 3, 2, 4, 1], [5, 3, 4, 1, 2], [5, 3, 4, 2, 1], [5, 4, 1, 2, 3], [5, 4, 1, 3, 2], [5, 4, 2, 1, 3], [5, 4, 2, 3, 1], [5, 4, 3, 1, 2], [5, 4, 3, 2, 1]]\n assert candidate(nums = [-10, 10, -10, 10, 0, 0]) == [[-10, -10, 0, 0, 10, 10], [-10, -10, 0, 10, 0, 10], [-10, -10, 0, 10, 10, 0], [-10, -10, 10, 0, 0, 10], [-10, -10, 10, 0, 10, 0], [-10, -10, 10, 10, 0, 0], [-10, 0, -10, 0, 10, 10], [-10, 0, -10, 10, 0, 10], [-10, 0, -10, 10, 10, 0], [-10, 0, 0, -10, 10, 10], [-10, 0, 0, 10, -10, 10], [-10, 0, 0, 10, 10, -10], [-10, 0, 10, -10, 0, 10], [-10, 0, 10, -10, 10, 0], [-10, 0, 10, 0, -10, 10], [-10, 0, 10, 0, 10, -10], [-10, 0, 10, 10, -10, 0], [-10, 0, 10, 10, 0, -10], [-10, 10, -10, 0, 0, 10], [-10, 10, -10, 0, 10, 0], [-10, 10, -10, 10, 0, 0], [-10, 10, 0, -10, 0, 10], [-10, 10, 0, -10, 10, 0], [-10, 10, 0, 0, -10, 10], [-10, 10, 0, 0, 10, -10], [-10, 10, 0, 10, -10, 0], [-10, 10, 0, 10, 0, -10], [-10, 10, 10, -10, 0, 0], [-10, 10, 10, 0, -10, 0], [-10, 10, 10, 0, 0, -10], [0, -10, -10, 0, 10, 10], [0, -10, -10, 10, 0, 10], [0, -10, -10, 10, 10, 0], [0, -10, 0, -10, 10, 10], [0, -10, 0, 10, -10, 10], [0, -10, 0, 10, 10, -10], [0, -10, 10, -10, 0, 10], [0, -10, 10, -10, 10, 0], [0, -10, 10, 0, -10, 10], [0, -10, 10, 0, 10, -10], [0, -10, 10, 10, -10, 0], [0, -10, 10, 10, 0, -10], [0, 0, -10, -10, 10, 10], [0, 0, -10, 10, -10, 10], [0, 0, -10, 10, 10, -10], [0, 0, 10, -10, -10, 10], [0, 0, 10, -10, 10, -10], [0, 0, 10, 10, -10, -10], [0, 10, -10, -10, 0, 10], [0, 10, -10, -10, 10, 0], [0, 10, -10, 0, -10, 10], [0, 10, -10, 0, 10, -10], [0, 10, -10, 10, -10, 0], [0, 10, -10, 10, 0, -10], [0, 10, 0, -10, -10, 10], [0, 10, 0, -10, 10, -10], [0, 10, 0, 10, -10, -10], [0, 10, 10, -10, -10, 0], [0, 10, 10, -10, 0, -10], [0, 10, 10, 0, -10, -10], [10, -10, -10, 0, 0, 10], [10, -10, -10, 0, 10, 0], [10, -10, -10, 10, 0, 0], [10, -10, 0, -10, 0, 10], [10, -10, 0, -10, 10, 0], [10, -10, 0, 0, -10, 10], [10, -10, 0, 0, 10, -10], [10, -10, 0, 10, -10, 0], [10, -10, 0, 10, 0, -10], [10, -10, 10, -10, 0, 0], [10, -10, 10, 0, -10, 0], [10, -10, 10, 0, 0, -10], [10, 0, -10, -10, 0, 10], [10, 0, -10, -10, 10, 0], [10, 0, -10, 0, -10, 10], [10, 0, -10, 0, 10, -10], [10, 0, -10, 10, -10, 0], [10, 0, -10, 10, 0, -10], [10, 0, 0, -10, -10, 10], [10, 0, 0, -10, 10, -10], [10, 0, 0, 10, -10, -10], [10, 0, 10, -10, -10, 0], [10, 0, 10, -10, 0, -10], [10, 0, 10, 0, -10, -10], [10, 10, -10, -10, 0, 0], [10, 10, -10, 0, -10, 0], [10, 10, -10, 0, 0, -10], [10, 10, 0, -10, -10, 0], [10, 10, 0, -10, 0, -10], [10, 10, 0, 0, -10, -10]]\n assert candidate(nums = [0, -1, 1, -1, 0]) == [[-1, -1, 0, 0, 1], [-1, -1, 0, 1, 0], [-1, -1, 1, 0, 0], [-1, 0, -1, 0, 1], [-1, 0, -1, 1, 0], [-1, 0, 0, -1, 1], [-1, 0, 0, 1, -1], [-1, 0, 1, -1, 0], [-1, 0, 1, 0, -1], [-1, 1, -1, 0, 0], [-1, 1, 0, -1, 0], [-1, 1, 0, 0, -1], [0, -1, -1, 0, 1], [0, -1, -1, 1, 0], [0, -1, 0, -1, 1], [0, -1, 0, 1, -1], [0, -1, 1, -1, 0], [0, -1, 1, 0, -1], [0, 0, -1, -1, 1], [0, 0, -1, 1, -1], [0, 0, 1, -1, -1], [0, 1, -1, -1, 0], [0, 1, -1, 0, -1], [0, 1, 0, -1, -1], [1, -1, -1, 0, 0], [1, -1, 0, -1, 0], [1, -1, 0, 0, -1], [1, 0, -1, -1, 0], [1, 0, -1, 0, -1], [1, 0, 0, -1, -1]]\n assert candidate(nums = [10, -10, 10, -10, 10]) == [[-10, -10, 10, 10, 10], [-10, 10, -10, 10, 10], [-10, 10, 10, -10, 10], [-10, 10, 10, 10, -10], [10, -10, -10, 10, 10], [10, -10, 10, -10, 10], [10, -10, 10, 10, -10], [10, 10, -10, -10, 10], [10, 10, -10, 10, -10], [10, 10, 10, -10, -10]]\n assert candidate(nums = [5, 5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5, 5]]\n assert candidate(nums = [4, 4, 4, 1, 4]) == [[1, 4, 4, 4, 4], [4, 1, 4, 4, 4], [4, 4, 1, 4, 4], [4, 4, 4, 1, 4], [4, 4, 4, 4, 1]]\n assert candidate(nums = [-1, 0, 1, -1, 0, 1]) == [[-1, -1, 0, 0, 1, 1], [-1, -1, 0, 1, 0, 1], [-1, -1, 0, 1, 1, 0], [-1, -1, 1, 0, 0, 1], [-1, -1, 1, 0, 1, 0], [-1, -1, 1, 1, 0, 0], [-1, 0, -1, 0, 1, 1], [-1, 0, -1, 1, 0, 1], [-1, 0, -1, 1, 1, 0], [-1, 0, 0, -1, 1, 1], [-1, 0, 0, 1, -1, 1], [-1, 0, 0, 1, 1, -1], [-1, 0, 1, -1, 0, 1], [-1, 0, 1, -1, 1, 0], [-1, 0, 1, 0, -1, 1], [-1, 0, 1, 0, 1, -1], [-1, 0, 1, 1, -1, 0], [-1, 0, 1, 1, 0, -1], [-1, 1, -1, 0, 0, 1], [-1, 1, -1, 0, 1, 0], [-1, 1, -1, 1, 0, 0], [-1, 1, 0, -1, 0, 1], [-1, 1, 0, -1, 1, 0], [-1, 1, 0, 0, -1, 1], [-1, 1, 0, 0, 1, -1], [-1, 1, 0, 1, -1, 0], [-1, 1, 0, 1, 0, -1], [-1, 1, 1, -1, 0, 0], [-1, 1, 1, 0, -1, 0], [-1, 1, 1, 0, 0, -1], [0, -1, -1, 0, 1, 1], [0, -1, -1, 1, 0, 1], [0, -1, -1, 1, 1, 0], [0, -1, 0, -1, 1, 1], [0, -1, 0, 1, -1, 1], [0, -1, 0, 1, 1, -1], [0, -1, 1, -1, 0, 1], [0, -1, 1, -1, 1, 0], [0, -1, 1, 0, -1, 1], [0, -1, 1, 0, 1, -1], [0, -1, 1, 1, -1, 0], [0, -1, 1, 1, 0, -1], [0, 0, -1, -1, 1, 1], [0, 0, -1, 1, -1, 1], [0, 0, -1, 1, 1, -1], [0, 0, 1, -1, -1, 1], [0, 0, 1, -1, 1, -1], [0, 0, 1, 1, -1, -1], [0, 1, -1, -1, 0, 1], [0, 1, -1, -1, 1, 0], [0, 1, -1, 0, -1, 1], [0, 1, -1, 0, 1, -1], [0, 1, -1, 1, -1, 0], [0, 1, -1, 1, 0, -1], [0, 1, 0, -1, -1, 1], [0, 1, 0, -1, 1, -1], [0, 1, 0, 1, -1, -1], [0, 1, 1, -1, -1, 0], [0, 1, 1, -1, 0, -1], [0, 1, 1, 0, -1, -1], [1, -1, -1, 0, 0, 1], [1, -1, -1, 0, 1, 0], [1, -1, -1, 1, 0, 0], [1, -1, 0, -1, 0, 1], [1, -1, 0, -1, 1, 0], [1, -1, 0, 0, -1, 1], [1, -1, 0, 0, 1, -1], [1, -1, 0, 1, -1, 0], [1, -1, 0, 1, 0, -1], [1, -1, 1, -1, 0, 0], [1, -1, 1, 0, -1, 0], [1, -1, 1, 0, 0, -1], [1, 0, -1, -1, 0, 1], [1, 0, -1, -1, 1, 0], [1, 0, -1, 0, -1, 1], [1, 0, -1, 0, 1, -1], [1, 0, -1, 1, -1, 0], [1, 0, -1, 1, 0, -1], [1, 0, 0, -1, -1, 1], [1, 0, 0, -1, 1, -1], [1, 0, 0, 1, -1, -1], [1, 0, 1, -1, -1, 0], [1, 0, 1, -1, 0, -1], [1, 0, 1, 0, -1, -1], [1, 1, -1, -1, 0, 0], [1, 1, -1, 0, -1, 0], [1, 1, -1, 0, 0, -1], [1, 1, 0, -1, -1, 0], [1, 1, 0, -1, 0, -1], [1, 1, 0, 0, -1, -1]]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5, 5, 5]]\n assert candidate(nums = [1, 1, 2, 2, 3, 3]) == [[1, 1, 2, 2, 3, 3], [1, 1, 2, 3, 2, 3], [1, 1, 2, 3, 3, 2], [1, 1, 3, 2, 2, 3], [1, 1, 3, 2, 3, 2], [1, 1, 3, 3, 2, 2], [1, 2, 1, 2, 3, 3], [1, 2, 1, 3, 2, 3], [1, 2, 1, 3, 3, 2], [1, 2, 2, 1, 3, 3], [1, 2, 2, 3, 1, 3], [1, 2, 2, 3, 3, 1], [1, 2, 3, 1, 2, 3], [1, 2, 3, 1, 3, 2], [1, 2, 3, 2, 1, 3], [1, 2, 3, 2, 3, 1], [1, 2, 3, 3, 1, 2], [1, 2, 3, 3, 2, 1], [1, 3, 1, 2, 2, 3], [1, 3, 1, 2, 3, 2], [1, 3, 1, 3, 2, 2], [1, 3, 2, 1, 2, 3], [1, 3, 2, 1, 3, 2], [1, 3, 2, 2, 1, 3], [1, 3, 2, 2, 3, 1], [1, 3, 2, 3, 1, 2], [1, 3, 2, 3, 2, 1], [1, 3, 3, 1, 2, 2], [1, 3, 3, 2, 1, 2], [1, 3, 3, 2, 2, 1], [2, 1, 1, 2, 3, 3], [2, 1, 1, 3, 2, 3], [2, 1, 1, 3, 3, 2], [2, 1, 2, 1, 3, 3], [2, 1, 2, 3, 1, 3], [2, 1, 2, 3, 3, 1], [2, 1, 3, 1, 2, 3], [2, 1, 3, 1, 3, 2], [2, 1, 3, 2, 1, 3], [2, 1, 3, 2, 3, 1], [2, 1, 3, 3, 1, 2], [2, 1, 3, 3, 2, 1], [2, 2, 1, 1, 3, 3], [2, 2, 1, 3, 1, 3], [2, 2, 1, 3, 3, 1], [2, 2, 3, 1, 1, 3], [2, 2, 3, 1, 3, 1], [2, 2, 3, 3, 1, 1], [2, 3, 1, 1, 2, 3], [2, 3, 1, 1, 3, 2], [2, 3, 1, 2, 1, 3], [2, 3, 1, 2, 3, 1], [2, 3, 1, 3, 1, 2], [2, 3, 1, 3, 2, 1], [2, 3, 2, 1, 1, 3], [2, 3, 2, 1, 3, 1], [2, 3, 2, 3, 1, 1], [2, 3, 3, 1, 1, 2], [2, 3, 3, 1, 2, 1], [2, 3, 3, 2, 1, 1], [3, 1, 1, 2, 2, 3], [3, 1, 1, 2, 3, 2], [3, 1, 1, 3, 2, 2], [3, 1, 2, 1, 2, 3], [3, 1, 2, 1, 3, 2], [3, 1, 2, 2, 1, 3], [3, 1, 2, 2, 3, 1], [3, 1, 2, 3, 1, 2], [3, 1, 2, 3, 2, 1], [3, 1, 3, 1, 2, 2], [3, 1, 3, 2, 1, 2], [3, 1, 3, 2, 2, 1], [3, 2, 1, 1, 2, 3], [3, 2, 1, 1, 3, 2], [3, 2, 1, 2, 1, 3], [3, 2, 1, 2, 3, 1], [3, 2, 1, 3, 1, 2], [3, 2, 1, 3, 2, 1], [3, 2, 2, 1, 1, 3], [3, 2, 2, 1, 3, 1], [3, 2, 2, 3, 1, 1], [3, 2, 3, 1, 1, 2], [3, 2, 3, 1, 2, 1], [3, 2, 3, 2, 1, 1], [3, 3, 1, 1, 2, 2], [3, 3, 1, 2, 1, 2], [3, 3, 1, 2, 2, 1], [3, 3, 2, 1, 1, 2], [3, 3, 2, 1, 2, 1], [3, 3, 2, 2, 1, 1]]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().permuteUnique", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var permuteUnique = function(nums) {", "container": null, "callable": "permuteUnique", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 49, "task_id": "group-anagrams", "difficulty": "Medium", "problem_description": "Given an array of strings strs, group the anagrams together. You can return the answer in any order.\n \nExample 1:\n\nInput: strs = [\"eat\",\"tea\",\"tan\",\"ate\",\"nat\",\"bat\"]\nOutput: [[\"bat\"],[\"nat\",\"tan\"],[\"ate\",\"eat\",\"tea\"]]\nExplanation:\n\nThere is no string in strs that can be rearranged to form \"bat\".\nThe strings \"nat\" and \"tan\" are anagrams as they can be rearranged to form each other.\nThe strings \"ate\", \"eat\", and \"tea\" are anagrams as they can be rearranged to form each other.\n\n\nExample 2:\n\nInput: strs = [\"\"]\nOutput: [[\"\"]]\n\nExample 3:\n\nInput: strs = [\"a\"]\nOutput: [[\"a\"]]\n\n \nConstraints:\n\n1 <= strs.length <= 104\n0 <= strs[i].length <= 100\nstrs[i] consists of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(strs = ['a', 'b', 'c', 'd', 'e']) == [['a'], ['b'], ['c'], ['d'], ['e']]\n assert candidate(strs = ['abc', 'bca', 'cab', 'xyz', 'zyx', 'yxz']) == [['abc', 'bca', 'cab'], ['xyz', 'zyx', 'yxz']]\n assert candidate(strs = ['abc', 'def', 'ghi', 'jkl']) == [['abc'], ['def'], ['ghi'], ['jkl']]\n assert candidate(strs = ['abc', 'acb', 'bac', 'bca', 'cab', 'cba']) == [['abc', 'acb', 'bac', 'bca', 'cab', 'cba']]\n assert candidate(strs = ['eat', 'tea', 'tan', 'ate', 'nat', 'bat']) == [['eat', 'tea', 'ate'], ['tan', 'nat'], ['bat']]\n assert candidate(strs = ['listen', 'silent', 'enlist']) == [['listen', 'silent', 'enlist']]\n assert candidate(strs = ['a']) == [['a']]\n assert candidate(strs = ['aabb', 'bbaa', 'abab', 'baab', 'baba', 'abba', 'aaaa', 'bbbb']) == [['aabb', 'bbaa', 'abab', 'baab', 'baba', 'abba'], ['aaaa'], ['bbbb']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'rat', 'tar', 'art']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['rat', 'tar', 'art']]\n assert candidate(strs = ['abc', 'bac', 'cab', 'bca', 'acb', 'cba']) == [['abc', 'bac', 'cab', 'bca', 'acb', 'cba']]\n assert candidate(strs = ['dormitory', 'dirtyroom', 'conversation', 'voicesranton', 'listen', 'silent']) == [['dormitory', 'dirtyroom'], ['conversation', 'voicesranton'], ['listen', 'silent']]\n assert candidate(strs = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']) == [['a'], ['b'], ['c'], ['d'], ['e'], ['f'], ['g'], ['h'], ['i'], ['j']]\n assert candidate(strs = ['hello', 'world', 'hold', 'olelh', 'dlrow', 'owrld']) == [['hello', 'olelh'], ['world', 'dlrow', 'owrld'], ['hold']]\n assert candidate(strs = ['dormitory', 'dirtyroom', 'conversation', 'voicesranton', 'schoolmaster', 'theclassroom']) == [['dormitory', 'dirtyroom'], ['conversation', 'voicesranton'], ['schoolmaster', 'theclassroom']]\n assert candidate(strs = ['hello', 'bello', 'olelh', 'world', 'dlrow', 'dlorw', 'droll']) == [['hello', 'olelh'], ['bello'], ['world', 'dlrow', 'dlorw'], ['droll']]\n assert candidate(strs = ['']) == [['']]\n assert candidate(strs = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'cba', 'bca', 'bac', 'acb', 'cab', 'abc']) == [['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba'], ['cba', 'bca', 'bac', 'acb', 'cab', 'abc']]\n assert candidate(strs = ['abc', 'abcd', 'abdc', 'bacd', 'badc', 'cabd', 'cadb', 'dcba', 'dcab', 'abcd', 'abdc', 'bacd', 'badc', 'cabd', 'cadb', 'dcba', 'dcab', 'abcd', 'abdc', 'bacd', 'badc', 'cabd', 'cadb', 'dcba', 'dcab']) == [['abc'], ['abcd', 'abdc', 'bacd', 'badc', 'cabd', 'cadb', 'dcba', 'dcab', 'abcd', 'abdc', 'bacd', 'badc', 'cabd', 'cadb', 'dcba', 'dcab', 'abcd', 'abdc', 'bacd', 'badc', 'cabd', 'cadb', 'dcba', 'dcab']]\n assert candidate(strs = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuvwxyzabcdefghijkl', 'qrstuvwxyzaabcdefghijklmnop', 'hgfedcbazyxwvutsrqponmlkjijklmnopqrstuvwxyzabcde']) == [['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuvwxyzabcdefghijkl'], ['qrstuvwxyzaabcdefghijklmnop'], ['hgfedcbazyxwvutsrqponmlkjijklmnopqrstuvwxyzabcde']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'child', 'brink', 'drink', 'crimp', 'crimp', 'stick', 'smirk', 'smirk', 'smith', 'tinsy', 'stint']) == [['dusty', 'study'], ['night', 'thing'], ['child'], ['brink'], ['drink'], ['crimp', 'crimp'], ['stick'], ['smirk', 'smirk'], ['smith'], ['tinsy'], ['stint']]\n assert candidate(strs = ['aabb', 'abab', 'baba', 'baab', 'abba', 'bbaa', 'aabb', 'abab', 'baba', 'baab', 'abba', 'bbaa']) == [['aabb', 'abab', 'baba', 'baab', 'abba', 'bbaa', 'aabb', 'abab', 'baba', 'baab', 'abba', 'bbaa']]\n assert candidate(strs = ['apple', 'pepal', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe', 'appel', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe']) == [['apple', 'pepal', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe', 'appel', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe', 'ppale', 'pplea', 'ppela', 'elppa', 'ppael', 'palpe']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'delta', 'tigon', 'state', 'taste', 'date', 'rated']) == [['dusty', 'study'], ['night', 'thing'], ['delta'], ['tigon'], ['state', 'taste'], ['date'], ['rated']]\n assert candidate(strs = ['aabbcc', 'abcabc', 'baccab', 'acbbac', 'cabbaa', 'aabbcc', 'abcabc']) == [['aabbcc', 'abcabc', 'baccab', 'acbbac', 'aabbcc', 'abcabc'], ['cabbaa']]\n assert candidate(strs = ['rat', 'car', 'tar', 'arc', 'cat', 'tac', 'act', 'rat', 'car', 'tar', 'arc', 'cat', 'tac', 'act']) == [['rat', 'tar', 'rat', 'tar'], ['car', 'arc', 'car', 'arc'], ['cat', 'tac', 'act', 'cat', 'tac', 'act']]\n assert candidate(strs = ['aabbcc', 'abcabc', 'bcaabc', 'cababc', 'aabbcc', 'ccbaab', 'abcabc', 'baccab', 'bacabc', 'cababc', 'abcabc']) == [['aabbcc', 'abcabc', 'bcaabc', 'cababc', 'aabbcc', 'ccbaab', 'abcabc', 'baccab', 'bacabc', 'cababc', 'abcabc']]\n assert candidate(strs = ['aabb', 'abab', 'bbaa', 'abba', 'baab', 'aaba', 'baba', 'bbba', 'baaa', 'aaaa', 'bbbb']) == [['aabb', 'abab', 'bbaa', 'abba', 'baab', 'baba'], ['aaba', 'baaa'], ['bbba'], ['aaaa'], ['bbbb']]\n assert candidate(strs = ['ab', 'ba', 'ac', 'ca', 'ad', 'da', 'bc', 'cb', 'ef', 'fe', 'gh', 'hg', 'ij', 'ji', 'kl', 'lk', 'mnop', 'nopm', 'opmn', 'pmno', 'qrst', 'srqt', 'tqrs', 'qrst', 'stqr', 'qrstuv', 'rstquv', 'tsrquv', 'uvqrst', 'vqrstu', 'wxyz', 'xyzw', 'yzwx', 'zwxy']) == [['ab', 'ba'], ['ac', 'ca'], ['ad', 'da'], ['bc', 'cb'], ['ef', 'fe'], ['gh', 'hg'], ['ij', 'ji'], ['kl', 'lk'], ['mnop', 'nopm', 'opmn', 'pmno'], ['qrst', 'srqt', 'tqrs', 'qrst', 'stqr'], ['qrstuv', 'rstquv', 'tsrquv', 'uvqrst', 'vqrstu'], ['wxyz', 'xyzw', 'yzwx', 'zwxy']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'rat', 'tar', 'art', 'arc', 'car', 'arc']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['rat', 'tar', 'art'], ['arc', 'car', 'arc']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'abc', 'cab', 'bac', 'bca', 'acb', 'cba']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['abc', 'cab', 'bac', 'bca', 'acb', 'cba']]\n assert candidate(strs = ['zzzz', 'zazaz', 'zzzzz', 'zz', 'z', 'za', 'az', 'zzzz', 'zazaz', 'zzzzz', 'zz', 'z', 'za', 'az']) == [['zzzz', 'zzzz'], ['zazaz', 'zazaz'], ['zzzzz', 'zzzzz'], ['zz', 'zz'], ['z', 'z'], ['za', 'az', 'za', 'az']]\n assert candidate(strs = ['aabb', 'bbaa', 'abab', 'abba', 'baab', 'baba', 'aaaa', 'bbbb', 'aabbcc', 'ccbaab', 'aabbc', 'abbac', 'abc', 'acb', 'bac', 'bca', 'cab', 'cba', 'zzz', 'zzzz', 'zzzzz']) == [['aabb', 'bbaa', 'abab', 'abba', 'baab', 'baba'], ['aaaa'], ['bbbb'], ['aabbcc', 'ccbaab'], ['aabbc', 'abbac'], ['abc', 'acb', 'bac', 'bca', 'cab', 'cba'], ['zzz'], ['zzzz'], ['zzzzz']]\n assert candidate(strs = ['aabbcc', 'abcabc', 'bcaabc', 'cababc', 'aabbcc', 'ccbaab', 'abcabc', 'baccab', 'bacabc', 'cababc', 'abcabc', 'xyz', 'zyx', 'yzx', 'zyx', 'xyz', 'yzx', 'zyx', 'xyz', 'zyx', 'yzx', 'zyx', 'xyz', 'yzx', 'zyx', 'xyz', 'zyx', 'yzx', 'zyx', 'xyz', 'yzx', 'zyx', 'xyz']) == [['aabbcc', 'abcabc', 'bcaabc', 'cababc', 'aabbcc', 'ccbaab', 'abcabc', 'baccab', 'bacabc', 'cababc', 'abcabc'], ['xyz', 'zyx', 'yzx', 'zyx', 'xyz', 'yzx', 'zyx', 'xyz', 'zyx', 'yzx', 'zyx', 'xyz', 'yzx', 'zyx', 'xyz', 'zyx', 'yzx', 'zyx', 'xyz', 'yzx', 'zyx', 'xyz']]\n assert candidate(strs = ['python', 'typhon', 'hypton', 'pythno', 'ypthon', 'thypno', 'hypnot', 'hypnotize', 'notphyno', 'nothpyin', ' hypnot', 'hypnotic', 'hypnothize', 'hypnothise', 'notthpyin', 'pythonic', 'typhonian', 'pythongod', 'hypno', 'hypnosis', 'hypnotherapy', 'hypnagogia', 'hypnoid']) == [['python', 'typhon', 'hypton', 'pythno', 'ypthon', 'thypno', 'hypnot'], ['hypnotize'], ['notphyno'], ['nothpyin'], [' hypnot'], ['hypnotic', 'pythonic'], ['hypnothize'], ['hypnothise'], ['notthpyin'], ['typhonian'], ['pythongod'], ['hypno'], ['hypnosis'], ['hypnotherapy'], ['hypnagogia'], ['hypnoid']]\n assert candidate(strs = ['abcde', 'edcba', 'bcdea', 'decba', 'bacde', 'cabde', 'eabcd', 'acbde', 'dbcea', 'adbce']) == [['abcde', 'edcba', 'bcdea', 'decba', 'bacde', 'cabde', 'eabcd', 'acbde', 'dbcea', 'adbce']]\n assert candidate(strs = ['abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed']) == [['abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed', 'abcde', 'edcba', 'bcdea', 'decba', 'edbac', 'acbed']]\n assert candidate(strs = ['abcd', 'dcba', 'adbc', 'cbad', 'abcd', 'bcda', 'abcd', 'dcba', 'adbc', 'cbad', 'abcd', 'bcda', 'abcd', 'dcba', 'adbc', 'cbad', 'abcd', 'bcda', 'abcd', 'dcba']) == [['abcd', 'dcba', 'adbc', 'cbad', 'abcd', 'bcda', 'abcd', 'dcba', 'adbc', 'cbad', 'abcd', 'bcda', 'abcd', 'dcba', 'adbc', 'cbad', 'abcd', 'bcda', 'abcd', 'dcba']]\n assert candidate(strs = ['abcd', 'dcba', 'cabd', 'badc', 'dacb', 'cdab', 'bcad', 'bcda', 'acbd', 'cadb', 'acdb', 'abdc']) == [['abcd', 'dcba', 'cabd', 'badc', 'dacb', 'cdab', 'bcad', 'bcda', 'acbd', 'cadb', 'acdb', 'abdc']]\n assert candidate(strs = ['dormitory', 'dirtyroom', 'listen', 'silent', 'enlist', 'google', 'gooegl', 'abc', 'cab', 'bac', 'bca', 'acb', 'cba', 'zzz', 'zzzz', 'zzzzz', 'zzzzzz']) == [['dormitory', 'dirtyroom'], ['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['abc', 'cab', 'bac', 'bca', 'acb', 'cba'], ['zzz'], ['zzzz'], ['zzzzz'], ['zzzzzz']]\n assert candidate(strs = ['abcd', 'dcba', 'abcd', 'cdab', 'bdac', 'cabd', 'bacd', 'abcd', 'dcba', 'abcd']) == [['abcd', 'dcba', 'abcd', 'cdab', 'bdac', 'cabd', 'bacd', 'abcd', 'dcba', 'abcd']]\n assert candidate(strs = ['aabb', 'abab', 'bbaa', 'abba', 'aaaa', 'aaab', 'baaa', 'baba', 'abba', 'aabb', 'abab', 'bbaa', 'aaaa']) == [['aabb', 'abab', 'bbaa', 'abba', 'baba', 'abba', 'aabb', 'abab', 'bbaa'], ['aaaa', 'aaaa'], ['aaab', 'baaa']]\n assert candidate(strs = ['abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb', 'abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb', 'abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb', 'abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb']) == [['abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb', 'abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb', 'abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb', 'abcd', 'dcba', 'adcb', 'cbad', 'bdac', 'cabd', 'bacd', 'acbd', 'dbca', 'bcad', 'cadb']]\n assert candidate(strs = ['anagram', 'nagaram', 'margana', 'anagrama', 'anagram', 'anagram', 'granama', 'nagaramm']) == [['anagram', 'nagaram', 'margana', 'anagram', 'anagram', 'granama'], ['anagrama'], ['nagaramm']]\n assert candidate(strs = ['aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc', 'aaa', 'bbb', 'ccc']) == [['aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa', 'aaa'], ['bbb', 'bbb', 'bbb', 'bbb', 'bbb', 'bbb', 'bbb', 'bbb'], ['ccc', 'ccc', 'ccc', 'ccc', 'ccc', 'ccc', 'ccc', 'ccc']]\n assert candidate(strs = ['aabb', 'bbaa', 'abab', 'baba', 'abba', 'baab', 'abc', 'bac', 'bca', 'acb', 'cba', 'zzz', 'zzzz', 'zzzzz', 'zzzzzz', 'zzzzzzz', 'zzzzzzzz', 'zzzzzzzzz']) == [['aabb', 'bbaa', 'abab', 'baba', 'abba', 'baab'], ['abc', 'bac', 'bca', 'acb', 'cba'], ['zzz'], ['zzzz'], ['zzzzz'], ['zzzzzz'], ['zzzzzzz'], ['zzzzzzzz'], ['zzzzzzzzz']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'gnhit', 'inthe', 'night', 'thing', 'night', 'thing', 'night']) == [['dusty', 'study'], ['night', 'thing', 'gnhit', 'night', 'thing', 'night', 'thing', 'night'], ['inthe']]\n assert candidate(strs = ['aabbcc', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac']) == [['aabbcc', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac', 'abcabc', 'bcaacb', 'cababc', 'bcacab', 'bacbac', 'aabbcc', 'aabbcc', 'aabcbc', 'bcaabc', 'abacbc', 'babcac']]\n assert candidate(strs = ['aabbcc', 'abcabc', 'bcaabc', 'cababc', 'abccba', 'acbbac', 'baccab', 'bcacab', 'bacbac', 'acbacb', 'bacbac', 'bacbac', 'bacbac', 'bacbac', 'bacbac']) == [['aabbcc', 'abcabc', 'bcaabc', 'cababc', 'abccba', 'acbbac', 'baccab', 'bcacab', 'bacbac', 'acbacb', 'bacbac', 'bacbac', 'bacbac', 'bacbac', 'bacbac']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'eight', 'gnite', 'inthe', 'front', 'trofn', 'gnhet', 'gfno', 'gnfoe', 'thingo', 'niothg', 'ightn']) == [['dusty', 'study'], ['night', 'thing', 'ightn'], ['eight'], ['gnite'], ['inthe'], ['front', 'trofn'], ['gnhet'], ['gfno'], ['gnfoe'], ['thingo', 'niothg']]\n assert candidate(strs = ['rat', 'car', 'tar', 'arc', 'arc', 'rta', 'cat', 'tac', 'act', 'cta', 'tca', 'atc']) == [['rat', 'tar', 'rta'], ['car', 'arc', 'arc'], ['cat', 'tac', 'act', 'cta', 'tca', 'atc']]\n assert candidate(strs = ['abcde', 'edcba', 'fghij', 'jihgf', 'mnopq', 'qponm', 'rstuv', 'vutsr', 'wxyz', 'zyxw', 'aaaaa', 'bbbbb', 'ccccc', 'ddddd', 'eeeee', 'zzzzz']) == [['abcde', 'edcba'], ['fghij', 'jihgf'], ['mnopq', 'qponm'], ['rstuv', 'vutsr'], ['wxyz', 'zyxw'], ['aaaaa'], ['bbbbb'], ['ccccc'], ['ddddd'], ['eeeee'], ['zzzzz']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'inlets', 'banana', 'anabna', 'xyz', 'zyx']) == [['listen', 'silent', 'enlist', 'inlets'], ['google', 'gooegl'], ['banana', 'anabna'], ['xyz', 'zyx']]\n assert candidate(strs = ['abcd', 'dcba', 'abcd', 'abcd', 'dcba', 'abcd', 'dcba', 'abcd', 'abcd']) == [['abcd', 'dcba', 'abcd', 'abcd', 'dcba', 'abcd', 'dcba', 'abcd', 'abcd']]\n assert candidate(strs = ['zzzz', 'zzz', 'zz', 'z', 'aaaa', 'aaa', 'aa', 'a', 'bbbb', 'bbb', 'bb', 'b', 'cccc', 'ccc', 'cc', 'c', 'dddd', 'ddd', 'dd', 'd', 'eeee', 'eee', 'ee', 'e']) == [['zzzz'], ['zzz'], ['zz'], ['z'], ['aaaa'], ['aaa'], ['aa'], ['a'], ['bbbb'], ['bbb'], ['bb'], ['b'], ['cccc'], ['ccc'], ['cc'], ['c'], ['dddd'], ['ddd'], ['dd'], ['d'], ['eeee'], ['eee'], ['ee'], ['e']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'rat', 'tar', 'art', 'elbow', 'below']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['rat', 'tar', 'art'], ['elbow', 'below']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'abc', 'cab', 'bac']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['abc', 'cab', 'bac']]\n assert candidate(strs = ['xyz', 'zyx', 'yxz', 'xzy', 'zyx', 'yzy', 'xyx', 'xxy', 'xyy', 'yxx', 'yyx', 'yyy', 'xxx']) == [['xyz', 'zyx', 'yxz', 'xzy', 'zyx'], ['yzy'], ['xyx', 'xxy', 'yxx'], ['xyy', 'yyx'], ['yyy'], ['xxx']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'enlist', 'google', 'gogole', 'inlets', 'abc', 'cba', 'bac', 'zyx', 'xyz', 'xyzzyx', 'zyxzyx']) == [['dusty', 'study'], ['night', 'thing'], ['enlist', 'inlets'], ['google', 'gogole'], ['abc', 'cba', 'bac'], ['zyx', 'xyz'], ['xyzzyx', 'zyxzyx']]\n assert candidate(strs = ['hello', 'ohell', 'lohel', 'ollhe', 'elohl', '', '', '', 'a', 'a', 'a', 'a', 'a']) == [['hello', 'ohell', 'lohel', 'ollhe', 'elohl'], ['', '', ''], ['a', 'a', 'a', 'a', 'a']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'rat', 'tar', 'art', 'rom', 'mor', 'arm', 'rmo']) == [['listen', 'silent', 'enlist'], ['google', 'gooegl'], ['rat', 'tar', 'art'], ['rom', 'mor', 'rmo'], ['arm']]\n assert candidate(strs = ['aabbcc', 'abcabc', 'aabbbc', 'aacbbc', 'aabcc', 'abcacb', 'abacbc', 'bbaacc', 'abccba', 'bcaacb']) == [['aabbcc', 'abcabc', 'aacbbc', 'abcacb', 'abacbc', 'bbaacc', 'abccba', 'bcaacb'], ['aabbbc'], ['aabcc']]\n assert candidate(strs = ['listen', 'silent', 'enlist', 'google', 'gooegl', 'inlets', 'banana']) == [['listen', 'silent', 'enlist', 'inlets'], ['google', 'gooegl'], ['banana']]\n assert candidate(strs = ['abcde', 'edcba', 'bcdea', 'decab', 'cabed', 'edbac', 'baced', 'deabc', 'ebadc', 'acbed']) == [['abcde', 'edcba', 'bcdea', 'decab', 'cabed', 'edbac', 'baced', 'deabc', 'ebadc', 'acbed']]\n assert candidate(strs = ['abc', 'bcd', 'cab', 'bac', 'bca', 'cba', 'xyz', 'zyx', 'yxz', 'zy', 'yz', 'z', 'a', 'b', 'c']) == [['abc', 'cab', 'bac', 'bca', 'cba'], ['bcd'], ['xyz', 'zyx', 'yxz'], ['zy', 'yz'], ['z'], ['a'], ['b'], ['c']]\n assert candidate(strs = ['a', 'b', 'c', 'aa', 'bb', 'cc', 'aaa', 'bbb', 'ccc', 'aaaa', 'bbbb', 'cccc']) == [['a'], ['b'], ['c'], ['aa'], ['bb'], ['cc'], ['aaa'], ['bbb'], ['ccc'], ['aaaa'], ['bbbb'], ['cccc']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'inhti', 'ytsud', 'ytsdu', 'gnith', 'dusty', 'study', 'night', 'thing', 'inhti', 'ytsud', 'ytsdu', 'gnith', 'dusty', 'study', 'night', 'thing', 'inhti', 'ytsud', 'ytsdu', 'gnith', 'dusty', 'study', 'night', 'thing', 'inhti', 'ytsud', 'ytsdu', 'gnith']) == [['dusty', 'study', 'ytsud', 'ytsdu', 'dusty', 'study', 'ytsud', 'ytsdu', 'dusty', 'study', 'ytsud', 'ytsdu', 'dusty', 'study', 'ytsud', 'ytsdu'], ['night', 'thing', 'gnith', 'night', 'thing', 'gnith', 'night', 'thing', 'gnith', 'night', 'thing', 'gnith'], ['inhti', 'inhti', 'inhti', 'inhti']]\n assert candidate(strs = ['ab', 'ba', 'abc', 'cba', 'bac', 'bca', 'cab', 'acb', 'abc', 'cba', 'bac', 'bca', 'cab', 'acb']) == [['ab', 'ba'], ['abc', 'cba', 'bac', 'bca', 'cab', 'acb', 'abc', 'cba', 'bac', 'bca', 'cab', 'acb']]\n assert candidate(strs = ['dusty', 'study', 'night', 'thing', 'sight', 'fling', 'tying', 'sting', 'dusty']) == [['dusty', 'study', 'dusty'], ['night', 'thing'], ['sight'], ['fling'], ['tying'], ['sting']]\n"}, "metadata": {"canonical_parameter_names": ["strs"], "leetcode_dataset_entry_point": "Solution().groupAnagrams", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var groupAnagrams = function(strs) {", "container": null, "callable": "groupAnagrams", "parameters": [{"name": "strs", "type": "string[]"}], "return_type": "string[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 50, "task_id": "powx-n", "difficulty": "Medium", "problem_description": "Implement pow(x, n), which calculates x raised to the power n (i.e., xn).\n \nExample 1:\n\nInput: x = 2.00000, n = 10\nOutput: 1024.00000\n\nExample 2:\n\nInput: x = 2.10000, n = 3\nOutput: 9.26100\n\nExample 3:\n\nInput: x = 2.00000, n = -2\nOutput: 0.25000\nExplanation: 2-2 = 1/22 = 1/4 = 0.25\n\n \nConstraints:\n\n-100.0 < x < 100.0\n-231 <= n <= 231-1\nn is an integer.\nEither x is not zero or n > 0.\n-104 <= xn <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(x = 3.0,n = 0) == 1\n assert candidate(x = 10.0,n = -3) == 0.001\n assert candidate(x = 5.0,n = 1) == 5.0\n assert candidate(x = 2.0,n = -2) == 0.25\n assert candidate(x = 0.1,n = 2) == 0.010000000000000002\n assert candidate(x = 1.5,n = 5) == 7.59375\n assert candidate(x = 2.1,n = 3) == 9.261000000000001\n assert candidate(x = 2.0,n = -1) == 0.5\n assert candidate(x = 0.5,n = 4) == 0.0625\n assert candidate(x = 2.0,n = 10) == 1024.0\n assert candidate(x = 0.99,n = 100) == 0.3660323412732289\n assert candidate(x = 1.0,n = -1000000) == 1.0\n assert candidate(x = 2.5,n = -5) == 0.01024\n assert candidate(x = 10.0,n = 5) == 100000.0\n assert candidate(x = -1.0,n = 2147483647) == -1.0\n assert candidate(x = -2.0,n = 12) == 4096.0\n assert candidate(x = 1.23456,n = 789) == 1.5963462056225718e+72\n assert candidate(x = 3.14,n = 7) == 3009.5913952479914\n assert candidate(x = -2.0,n = -3) == -0.125\n assert candidate(x = -1.0,n = 1000001) == -1.0\n assert candidate(x = 0.1,n = 10) == 1.0000000000000011e-10\n assert candidate(x = 0.1,n = 20) == 1.0000000000000022e-20\n assert candidate(x = 0.99999,n = -10000) == 1.1051714706643663\n assert candidate(x = -1.5,n = 2) == 2.25\n assert candidate(x = -0.5,n = 4) == 0.0625\n assert candidate(x = -0.5,n = 6) == 0.015625\n assert candidate(x = -1.0,n = -2147483648) == 1.0\n assert candidate(x = 9.87654,n = -321) == 0.0\n assert candidate(x = 2.5,n = 100) == 6.223015277861143e+39\n assert candidate(x = 10.0,n = 10) == 10000000000.0\n assert candidate(x = 1.0,n = 1000000) == 1.0\n assert candidate(x = 5.0,n = -3) == 0.008\n assert candidate(x = 1.0,n = -2147483648) == 1.0\n assert candidate(x = 1.0,n = 0) == 1\n assert candidate(x = 10.0,n = 2147483647) == inf\n assert candidate(x = 99.99999,n = 10) == 9.999990000004497e+19\n assert candidate(x = -0.5,n = 8) == 0.00390625\n assert candidate(x = 2.0,n = -1000) == 9.332636185032189e-302\n assert candidate(x = 2.0,n = 0) == 1\n assert candidate(x = 2.5,n = -3) == 0.064\n assert candidate(x = 10.0,n = 1000) == inf\n assert candidate(x = 0.99999,n = 1000) == 0.990049784246398\n assert candidate(x = -3.0,n = 4) == 81.0\n assert candidate(x = -3.0,n = -3) == -0.037037037037037035\n assert candidate(x = 0.1,n = -5) == 99999.99999999994\n assert candidate(x = 2.5,n = 20) == 90949470.17729282\n assert candidate(x = 1.00001,n = -1000000) == 4.5402199796741926e-05\n assert candidate(x = 0.1,n = -3) == 999.9999999999998\n assert candidate(x = -0.5,n = 3) == -0.125\n assert candidate(x = 1.73205,n = 12) == 728.9959212545092\n assert candidate(x = 10.0,n = 1) == 10.0\n assert candidate(x = -2.0,n = 4) == 16.0\n assert candidate(x = 0.1,n = 100) == 1.0000000000000108e-100\n assert candidate(x = 2.0,n = 2147483647) == inf\n assert candidate(x = 1e-05,n = 10000) == 0.0\n assert candidate(x = 0.0,n = 0) == 1\n assert candidate(x = 0.5,n = -5) == 32.0\n assert candidate(x = 3.0,n = 20) == 3486784401.0\n assert candidate(x = 3.0,n = 15) == 14348907.0\n assert candidate(x = 1.00001,n = 1000) == 1.0100501165820832\n assert candidate(x = 1.5,n = 2147483646) == inf\n assert candidate(x = 10.0,n = 100) == 1.0000000000000002e+100\n assert candidate(x = 2.0,n = -2147483648) == 0.0\n assert candidate(x = 1e-05,n = 1000000) == 0.0\n assert candidate(x = -1.0,n = 2147483646) == 1.0\n assert candidate(x = 1.5,n = 20) == 3325.256730079651\n assert candidate(x = -2.0,n = 3) == -8.0\n assert candidate(x = 1.2,n = -5) == 0.4018775720164609\n assert candidate(x = 0.1,n = -10) == 9999999999.999989\n assert candidate(x = 1.0,n = -1000) == 1.0\n assert candidate(x = 2.0,n = 100000000) == inf\n assert candidate(x = -2.0,n = 11) == -2048.0\n assert candidate(x = 3.5,n = 15) == 144884079.28292847\n assert candidate(x = 0.5,n = -10) == 1024.0\n assert candidate(x = 1.41421,n = 50) == 33550206.11671562\n assert candidate(x = 3.0,n = 13) == 1594323.0\n assert candidate(x = 0.99999,n = 1000000) == 4.539765980992338e-05\n assert candidate(x = 5.0,n = 0) == 1\n assert candidate(x = 2.0,n = -10) == 0.0009765625\n assert candidate(x = 1.0,n = -5) == 1.0\n assert candidate(x = 1.00001,n = -1000) == 0.9900498832512471\n assert candidate(x = -1.5,n = 5) == -7.59375\n assert candidate(x = 1.0,n = 2147483647) == 1.0\n"}, "metadata": {"canonical_parameter_names": ["x", "n"], "leetcode_dataset_entry_point": "Solution().myPow", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var myPow = function(x, n) {", "container": null, "callable": "myPow", "parameters": [{"name": "x", "type": "number"}, {"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 51, "task_id": "n-queens", "difficulty": "Hard", "problem_description": "The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.\nGiven an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.\nEach solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.\n \nExample 1:\n\n\nInput: n = 4\nOutput: [[\".Q..\",\"...Q\",\"Q...\",\"..Q.\"],[\"..Q.\",\"Q...\",\"...Q\",\".Q..\"]]\nExplanation: There exist two distinct solutions to the 4-queens puzzle as shown above\n\nExample 2:\n\nInput: n = 1\nOutput: [[\"Q\"]]\n\n \nConstraints:\n\n1 <= n <= 9\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == [['Q.......', '....Q...', '.......Q', '.....Q..', '..Q.....', '......Q.', '.Q......', '...Q....'], ['Q.......', '.....Q..', '.......Q', '..Q.....', '......Q.', '...Q....', '.Q......', '....Q...'], ['Q.......', '......Q.', '...Q....', '.....Q..', '.......Q', '.Q......', '....Q...', '..Q.....'], ['Q.......', '......Q.', '....Q...', '.......Q', '.Q......', '...Q....', '.....Q..', '..Q.....'], ['.Q......', '...Q....', '.....Q..', '.......Q', '..Q.....', 'Q.......', '......Q.', '....Q...'], ['.Q......', '....Q...', '......Q.', 'Q.......', '..Q.....', '.......Q', '.....Q..', '...Q....'], ['.Q......', '....Q...', '......Q.', '...Q....', 'Q.......', '.......Q', '.....Q..', '..Q.....'], ['.Q......', '.....Q..', 'Q.......', '......Q.', '...Q....', '.......Q', '..Q.....', '....Q...'], ['.Q......', '.....Q..', '.......Q', '..Q.....', 'Q.......', '...Q....', '......Q.', '....Q...'], ['.Q......', '......Q.', '..Q.....', '.....Q..', '.......Q', '....Q...', 'Q.......', '...Q....'], ['.Q......', '......Q.', '....Q...', '.......Q', 'Q.......', '...Q....', '.....Q..', '..Q.....'], ['.Q......', '.......Q', '.....Q..', 'Q.......', '..Q.....', '....Q...', '......Q.', '...Q....'], ['..Q.....', 'Q.......', '......Q.', '....Q...', '.......Q', '.Q......', '...Q....', '.....Q..'], ['..Q.....', '....Q...', '.Q......', '.......Q', 'Q.......', '......Q.', '...Q....', '.....Q..'], ['..Q.....', '....Q...', '.Q......', '.......Q', '.....Q..', '...Q....', '......Q.', 'Q.......'], ['..Q.....', '....Q...', '......Q.', 'Q.......', '...Q....', '.Q......', '.......Q', '.....Q..'], ['..Q.....', '....Q...', '.......Q', '...Q....', 'Q.......', '......Q.', '.Q......', '.....Q..'], ['..Q.....', '.....Q..', '.Q......', '....Q...', '.......Q', 'Q.......', '......Q.', '...Q....'], ['..Q.....', '.....Q..', '.Q......', '......Q.', 'Q.......', '...Q....', '.......Q', '....Q...'], ['..Q.....', '.....Q..', '.Q......', '......Q.', '....Q...', 'Q.......', '.......Q', '...Q....'], ['..Q.....', '.....Q..', '...Q....', 'Q.......', '.......Q', '....Q...', '......Q.', '.Q......'], ['..Q.....', '.....Q..', '...Q....', '.Q......', '.......Q', '....Q...', '......Q.', 'Q.......'], ['..Q.....', '.....Q..', '.......Q', 'Q.......', '...Q....', '......Q.', '....Q...', '.Q......'], ['..Q.....', '.....Q..', '.......Q', 'Q.......', '....Q...', '......Q.', '.Q......', '...Q....'], ['..Q.....', '.....Q..', '.......Q', '.Q......', '...Q....', 'Q.......', '......Q.', '....Q...'], ['..Q.....', '......Q.', '.Q......', '.......Q', '....Q...', 'Q.......', '...Q....', '.....Q..'], ['..Q.....', '......Q.', '.Q......', '.......Q', '.....Q..', '...Q....', 'Q.......', '....Q...'], ['..Q.....', '.......Q', '...Q....', '......Q.', 'Q.......', '.....Q..', '.Q......', '....Q...'], ['...Q....', 'Q.......', '....Q...', '.......Q', '.Q......', '......Q.', '..Q.....', '.....Q..'], ['...Q....', 'Q.......', '....Q...', '.......Q', '.....Q..', '..Q.....', '......Q.', '.Q......'], ['...Q....', '.Q......', '....Q...', '.......Q', '.....Q..', 'Q.......', '..Q.....', '......Q.'], ['...Q....', '.Q......', '......Q.', '..Q.....', '.....Q..', '.......Q', 'Q.......', '....Q...'], ['...Q....', '.Q......', '......Q.', '..Q.....', '.....Q..', '.......Q', '....Q...', 'Q.......'], ['...Q....', '.Q......', '......Q.', '....Q...', 'Q.......', '.......Q', '.....Q..', '..Q.....'], ['...Q....', '.Q......', '.......Q', '....Q...', '......Q.', 'Q.......', '..Q.....', '.....Q..'], ['...Q....', '.Q......', '.......Q', '.....Q..', 'Q.......', '..Q.....', '....Q...', '......Q.'], ['...Q....', '.....Q..', 'Q.......', '....Q...', '.Q......', '.......Q', '..Q.....', '......Q.'], ['...Q....', '.....Q..', '.......Q', '.Q......', '......Q.', 'Q.......', '..Q.....', '....Q...'], ['...Q....', '.....Q..', '.......Q', '..Q.....', 'Q.......', '......Q.', '....Q...', '.Q......'], ['...Q....', '......Q.', 'Q.......', '.......Q', '....Q...', '.Q......', '.....Q..', '..Q.....'], ['...Q....', '......Q.', '..Q.....', '.......Q', '.Q......', '....Q...', 'Q.......', '.....Q..'], ['...Q....', '......Q.', '....Q...', '.Q......', '.....Q..', 'Q.......', '..Q.....', '.......Q'], ['...Q....', '......Q.', '....Q...', '..Q.....', 'Q.......', '.....Q..', '.......Q', '.Q......'], ['...Q....', '.......Q', 'Q.......', '..Q.....', '.....Q..', '.Q......', '......Q.', '....Q...'], ['...Q....', '.......Q', 'Q.......', '....Q...', '......Q.', '.Q......', '.....Q..', '..Q.....'], ['...Q....', '.......Q', '....Q...', '..Q.....', 'Q.......', '......Q.', '.Q......', '.....Q..'], ['....Q...', 'Q.......', '...Q....', '.....Q..', '.......Q', '.Q......', '......Q.', '..Q.....'], ['....Q...', 'Q.......', '.......Q', '...Q....', '.Q......', '......Q.', '..Q.....', '.....Q..'], ['....Q...', 'Q.......', '.......Q', '.....Q..', '..Q.....', '......Q.', '.Q......', '...Q....'], ['....Q...', '.Q......', '...Q....', '.....Q..', '.......Q', '..Q.....', 'Q.......', '......Q.'], ['....Q...', '.Q......', '...Q....', '......Q.', '..Q.....', '.......Q', '.....Q..', 'Q.......'], ['....Q...', '.Q......', '.....Q..', 'Q.......', '......Q.', '...Q....', '.......Q', '..Q.....'], ['....Q...', '.Q......', '.......Q', 'Q.......', '...Q....', '......Q.', '..Q.....', '.....Q..'], ['....Q...', '..Q.....', 'Q.......', '.....Q..', '.......Q', '.Q......', '...Q....', '......Q.'], ['....Q...', '..Q.....', 'Q.......', '......Q.', '.Q......', '.......Q', '.....Q..', '...Q....'], ['....Q...', '..Q.....', '.......Q', '...Q....', '......Q.', 'Q.......', '.....Q..', '.Q......'], ['....Q...', '......Q.', 'Q.......', '..Q.....', '.......Q', '.....Q..', '...Q....', '.Q......'], ['....Q...', '......Q.', 'Q.......', '...Q....', '.Q......', '.......Q', '.....Q..', '..Q.....'], ['....Q...', '......Q.', '.Q......', '...Q....', '.......Q', 'Q.......', '..Q.....', '.....Q..'], ['....Q...', '......Q.', '.Q......', '.....Q..', '..Q.....', 'Q.......', '...Q....', '.......Q'], ['....Q...', '......Q.', '.Q......', '.....Q..', '..Q.....', 'Q.......', '.......Q', '...Q....'], ['....Q...', '......Q.', '...Q....', 'Q.......', '..Q.....', '.......Q', '.....Q..', '.Q......'], ['....Q...', '.......Q', '...Q....', 'Q.......', '..Q.....', '.....Q..', '.Q......', '......Q.'], ['....Q...', '.......Q', '...Q....', 'Q.......', '......Q.', '.Q......', '.....Q..', '..Q.....'], ['.....Q..', 'Q.......', '....Q...', '.Q......', '.......Q', '..Q.....', '......Q.', '...Q....'], ['.....Q..', '.Q......', '......Q.', 'Q.......', '..Q.....', '....Q...', '.......Q', '...Q....'], ['.....Q..', '.Q......', '......Q.', 'Q.......', '...Q....', '.......Q', '....Q...', '..Q.....'], ['.....Q..', '..Q.....', 'Q.......', '......Q.', '....Q...', '.......Q', '.Q......', '...Q....'], ['.....Q..', '..Q.....', 'Q.......', '.......Q', '...Q....', '.Q......', '......Q.', '....Q...'], ['.....Q..', '..Q.....', 'Q.......', '.......Q', '....Q...', '.Q......', '...Q....', '......Q.'], ['.....Q..', '..Q.....', '....Q...', '......Q.', 'Q.......', '...Q....', '.Q......', '.......Q'], ['.....Q..', '..Q.....', '....Q...', '.......Q', 'Q.......', '...Q....', '.Q......', '......Q.'], ['.....Q..', '..Q.....', '......Q.', '.Q......', '...Q....', '.......Q', 'Q.......', '....Q...'], ['.....Q..', '..Q.....', '......Q.', '.Q......', '.......Q', '....Q...', 'Q.......', '...Q....'], ['.....Q..', '..Q.....', '......Q.', '...Q....', 'Q.......', '.......Q', '.Q......', '....Q...'], ['.....Q..', '...Q....', 'Q.......', '....Q...', '.......Q', '.Q......', '......Q.', '..Q.....'], ['.....Q..', '...Q....', '.Q......', '.......Q', '....Q...', '......Q.', 'Q.......', '..Q.....'], ['.....Q..', '...Q....', '......Q.', 'Q.......', '..Q.....', '....Q...', '.Q......', '.......Q'], ['.....Q..', '...Q....', '......Q.', 'Q.......', '.......Q', '.Q......', '....Q...', '..Q.....'], ['.....Q..', '.......Q', '.Q......', '...Q....', 'Q.......', '......Q.', '....Q...', '..Q.....'], ['......Q.', 'Q.......', '..Q.....', '.......Q', '.....Q..', '...Q....', '.Q......', '....Q...'], ['......Q.', '.Q......', '...Q....', 'Q.......', '.......Q', '....Q...', '..Q.....', '.....Q..'], ['......Q.', '.Q......', '.....Q..', '..Q.....', 'Q.......', '...Q....', '.......Q', '....Q...'], ['......Q.', '..Q.....', 'Q.......', '.....Q..', '.......Q', '....Q...', '.Q......', '...Q....'], ['......Q.', '..Q.....', '.......Q', '.Q......', '....Q...', 'Q.......', '.....Q..', '...Q....'], ['......Q.', '...Q....', '.Q......', '....Q...', '.......Q', 'Q.......', '..Q.....', '.....Q..'], ['......Q.', '...Q....', '.Q......', '.......Q', '.....Q..', 'Q.......', '..Q.....', '....Q...'], ['......Q.', '....Q...', '..Q.....', 'Q.......', '.....Q..', '.......Q', '.Q......', '...Q....'], ['.......Q', '.Q......', '...Q....', 'Q.......', '......Q.', '....Q...', '..Q.....', '.....Q..'], ['.......Q', '.Q......', '....Q...', '..Q.....', 'Q.......', '......Q.', '...Q....', '.....Q..'], ['.......Q', '..Q.....', 'Q.......', '.....Q..', '.Q......', '....Q...', '......Q.', '...Q....'], ['.......Q', '...Q....', 'Q.......', '..Q.....', '.....Q..', '.Q......', '......Q.', '....Q...']]\n assert candidate(n = 3) == []\n assert candidate(n = 4) == [['.Q..', '...Q', 'Q...', '..Q.'], ['..Q.', 'Q...', '...Q', '.Q..']]\n assert candidate(n = 6) == [['.Q....', '...Q..', '.....Q', 'Q.....', '..Q...', '....Q.'], ['..Q...', '.....Q', '.Q....', '....Q.', 'Q.....', '...Q..'], ['...Q..', 'Q.....', '....Q.', '.Q....', '.....Q', '..Q...'], ['....Q.', '..Q...', 'Q.....', '.....Q', '...Q..', '.Q....']]\n assert candidate(n = 2) == []\n assert candidate(n = 1) == [['Q']]\n assert candidate(n = 7) == [['Q......', '..Q....', '....Q..', '......Q', '.Q.....', '...Q...', '.....Q.'], ['Q......', '...Q...', '......Q', '..Q....', '.....Q.', '.Q.....', '....Q..'], ['Q......', '....Q..', '.Q.....', '.....Q.', '..Q....', '......Q', '...Q...'], ['Q......', '.....Q.', '...Q...', '.Q.....', '......Q', '....Q..', '..Q....'], ['.Q.....', '...Q...', 'Q......', '......Q', '....Q..', '..Q....', '.....Q.'], ['.Q.....', '...Q...', '.....Q.', 'Q......', '..Q....', '....Q..', '......Q'], ['.Q.....', '....Q..', 'Q......', '...Q...', '......Q', '..Q....', '.....Q.'], ['.Q.....', '....Q..', '..Q....', 'Q......', '......Q', '...Q...', '.....Q.'], ['.Q.....', '....Q..', '......Q', '...Q...', 'Q......', '..Q....', '.....Q.'], ['.Q.....', '.....Q.', '..Q....', '......Q', '...Q...', 'Q......', '....Q..'], ['.Q.....', '......Q', '....Q..', '..Q....', 'Q......', '.....Q.', '...Q...'], ['..Q....', 'Q......', '.....Q.', '.Q.....', '....Q..', '......Q', '...Q...'], ['..Q....', 'Q......', '.....Q.', '...Q...', '.Q.....', '......Q', '....Q..'], ['..Q....', '....Q..', '......Q', '.Q.....', '...Q...', '.....Q.', 'Q......'], ['..Q....', '.....Q.', '.Q.....', '....Q..', 'Q......', '...Q...', '......Q'], ['..Q....', '......Q', '.Q.....', '...Q...', '.....Q.', 'Q......', '....Q..'], ['..Q....', '......Q', '...Q...', 'Q......', '....Q..', '.Q.....', '.....Q.'], ['...Q...', 'Q......', '..Q....', '.....Q.', '.Q.....', '......Q', '....Q..'], ['...Q...', 'Q......', '....Q..', '.Q.....', '.....Q.', '..Q....', '......Q'], ['...Q...', '.Q.....', '......Q', '....Q..', '..Q....', 'Q......', '.....Q.'], ['...Q...', '.....Q.', 'Q......', '..Q....', '....Q..', '......Q', '.Q.....'], ['...Q...', '......Q', '..Q....', '.....Q.', '.Q.....', '....Q..', 'Q......'], ['...Q...', '......Q', '....Q..', '.Q.....', '.....Q.', 'Q......', '..Q....'], ['....Q..', 'Q......', '...Q...', '......Q', '..Q....', '.....Q.', '.Q.....'], ['....Q..', 'Q......', '.....Q.', '...Q...', '.Q.....', '......Q', '..Q....'], ['....Q..', '.Q.....', '.....Q.', '..Q....', '......Q', '...Q...', 'Q......'], ['....Q..', '..Q....', 'Q......', '.....Q.', '...Q...', '.Q.....', '......Q'], ['....Q..', '......Q', '.Q.....', '...Q...', '.....Q.', 'Q......', '..Q....'], ['....Q..', '......Q', '.Q.....', '.....Q.', '..Q....', 'Q......', '...Q...'], ['.....Q.', 'Q......', '..Q....', '....Q..', '......Q', '.Q.....', '...Q...'], ['.....Q.', '.Q.....', '....Q..', 'Q......', '...Q...', '......Q', '..Q....'], ['.....Q.', '..Q....', 'Q......', '...Q...', '......Q', '....Q..', '.Q.....'], ['.....Q.', '..Q....', '....Q..', '......Q', 'Q......', '...Q...', '.Q.....'], ['.....Q.', '..Q....', '......Q', '...Q...', 'Q......', '....Q..', '.Q.....'], ['.....Q.', '...Q...', '.Q.....', '......Q', '....Q..', '..Q....', 'Q......'], ['.....Q.', '...Q...', '......Q', 'Q......', '..Q....', '....Q..', '.Q.....'], ['......Q', '.Q.....', '...Q...', '.....Q.', 'Q......', '..Q....', '....Q..'], ['......Q', '..Q....', '.....Q.', '.Q.....', '....Q..', 'Q......', '...Q...'], ['......Q', '...Q...', 'Q......', '....Q..', '.Q.....', '.....Q.', '..Q....'], ['......Q', '....Q..', '..Q....', 'Q......', '.....Q.', '...Q...', '.Q.....']]\n assert candidate(n = 5) == [['Q....', '..Q..', '....Q', '.Q...', '...Q.'], ['Q....', '...Q.', '.Q...', '....Q', '..Q..'], ['.Q...', '...Q.', 'Q....', '..Q..', '....Q'], ['.Q...', '....Q', '..Q..', 'Q....', '...Q.'], ['..Q..', 'Q....', '...Q.', '.Q...', '....Q'], ['..Q..', '....Q', '.Q...', '...Q.', 'Q....'], ['...Q.', 'Q....', '..Q..', '....Q', '.Q...'], ['...Q.', '.Q...', '....Q', '..Q..', 'Q....'], ['....Q', '.Q...', '...Q.', 'Q....', '..Q..'], ['....Q', '..Q..', 'Q....', '...Q.', '.Q...']]\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().solveNQueens", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var solveNQueens = function(n) {", "container": null, "callable": "solveNQueens", "parameters": [{"name": "n", "type": "number"}], "return_type": "string[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 52, "task_id": "n-queens-ii", "difficulty": "Hard", "problem_description": "The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.\nGiven an integer n, return the number of distinct solutions to the n-queens puzzle.\n \nExample 1:\n\n\nInput: n = 4\nOutput: 2\nExplanation: There are two distinct solutions to the 4-queens puzzle as shown.\n\nExample 2:\n\nInput: n = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= n <= 9\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == 92\n assert candidate(n = 3) == 0\n assert candidate(n = 4) == 2\n assert candidate(n = 9) == 352\n assert candidate(n = 6) == 4\n assert candidate(n = 2) == 0\n assert candidate(n = 1) == 1\n assert candidate(n = 7) == 40\n assert candidate(n = 5) == 10\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().totalNQueens", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var totalNQueens = function(n) {", "container": null, "callable": "totalNQueens", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 53, "task_id": "maximum-subarray", "difficulty": "Medium", "problem_description": "Given an integer array nums, find the subarray with the largest sum, and return its sum.\n \nExample 1:\n\nInput: nums = [-2,1,-3,4,-1,2,1,-5,4]\nOutput: 6\nExplanation: The subarray [4,-1,2,1] has the largest sum 6.\n\nExample 2:\n\nInput: nums = [1]\nOutput: 1\nExplanation: The subarray [1] has the largest sum 1.\n\nExample 3:\n\nInput: nums = [5,4,-1,7,8]\nOutput: 23\nExplanation: The subarray [5,4,-1,7,8] has the largest sum 23.\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-104 <= nums[i] <= 104\n\n \nFollow up: If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 1, 2, 3, 4, 5]) == 15\n assert candidate(nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4, 7]) == 12\n assert candidate(nums = [10000, -10000, 10000, -10000, 10000]) == 10000\n assert candidate(nums = [100, -1, 50, -1, 100]) == 248\n assert candidate(nums = [0, -3, 5, -2, 1, 3, -1, 2, -4, 2]) == 8\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [0, -3, 5, -2, 1, 3, -1, 2, -4, 2, 3]) == 9\n assert candidate(nums = [-5, -4, -3, -2, -1]) == -1\n assert candidate(nums = [-1, 0, -2, 0, -3, 0, -4, 0]) == 0\n assert candidate(nums = [1, -2, 3, 5, -3, 2]) == 8\n assert candidate(nums = [-2, 0, -1]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 15\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4]) == 4\n assert candidate(nums = [10000, -10000, 10000]) == 10000\n assert candidate(nums = [0, 0, 0, 0]) == 0\n assert candidate(nums = [-1, -2, -3, -4]) == -1\n assert candidate(nums = [-10000, 10000]) == 10000\n assert candidate(nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4]) == 6\n assert candidate(nums = [-10000, 10000, -10000, 10000, -10000, 10000]) == 10000\n assert candidate(nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4, 1, 2, 3]) == 11\n assert candidate(nums = [5, 4, -1, 7, 8]) == 23\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == 5\n assert candidate(nums = [5, -1, 3, -2, 4, -3, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == 11\n assert candidate(nums = [100, -1, -2, -3, 100, -1, -2, -3]) == 194\n assert candidate(nums = [-10, -20, -30, -40, -50, -60]) == -10\n assert candidate(nums = [5, -2, -3, 4, -1, -2, 1, 5, -3]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, -15, 6, 7, 8, 9, 10, -25, 11, 12, 13, 14, 15]) == 80\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15]) == 15\n assert candidate(nums = [10, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19]) == 19\n assert candidate(nums = [100, -100, 50, -50, 75, -75, 25, -25, 0, 0, 0]) == 100\n assert candidate(nums = [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0]) == 1\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(nums = [2, 3, -2, 5, -3, 4, -1, 2, 1, -5, 4, -6, 7, 8, -9, 10, 11, -12]) == 31\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [10000, -10000, 10000, -10000, 10000, -10000, 10000, -10000, 10000, -10000]) == 10000\n assert candidate(nums = [1, -3, 2, 1, -1, 3, -2, 3, 4, -5, 2, 1, -1, 2, 3, -4, 5, -6, 7, -8]) == 14\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 100]) == 100\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5, 6, 7, 8, 9, 10]) == 40\n assert candidate(nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4, 6, -1, 2, -1, 4, -3]) == 15\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == 1\n assert candidate(nums = [-21, 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 34, -35, 36, -37, 38, -39, 40]) == 40\n assert candidate(nums = [100, -1, 2, -3, -4, 5, 6, 7, -8, 9, 10, -11, 12, 13, -14]) == 137\n assert candidate(nums = [100, -100, 100, -100, 100, -100, 100, -100, 100, -100]) == 100\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50]) == 50\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9]) == 9\n assert candidate(nums = [10, -20, 30, -40, 50, -60, 70, -80, 90, -100, 110, -120, 130, -140, 150]) == 150\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == 45\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 20]) == 55\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5, 1, 2, 3, 4, 5]) == 15\n assert candidate(nums = [10, -5, 10, -5, 10, -5, 10, -5, 10, -5, 10, -5, 10, -5, 10, -5, 10, -5, 10, -5]) == 55\n assert candidate(nums = [5, 4, -1, 7, 8, -20, 15, -10, 25, -5, 10, -30, 40, -50, 60]) == 60\n assert candidate(nums = [-1, 0, 1, 2, -1, 0, 1, 2, -1, 0, 1, 2, -1, 0, 1, 2, -1, 0, 1, 2]) == 11\n assert candidate(nums = [-2, -3, -1, -5, -4]) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5, 1, 2, 3, 4, 5]) == 15\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 3\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, 7, 8, 9, 10, 11, -1, -2, -3, -4]) == 45\n assert candidate(nums = [-1000, 500, -300, 200, -100, 50, -25, 12, -6, 3, -1]) == 500\n assert candidate(nums = [-10000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10000]) == 10000\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5, 10]) == 15\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20]) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, -15, 6, 7, 8, 9, 10]) == 40\n assert candidate(nums = [-10, 0, -1, 3, 4, -5, 1, 2, -1, -2, 3, 4, -5, 6, 7, -8, 9, 10]) == 28\n assert candidate(nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4, -2, 3, 4, -1, 2, 1, -5, 4]) == 12\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == -1\n assert candidate(nums = [10000, -5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000]) == 10000\n assert candidate(nums = [5, 4, -1, 7, 8, -10, 12, 3, 4, -15, 20, -21, 22]) == 38\n assert candidate(nums = [1, 2, 3, 4, -10, 10, 20, -5, 5]) == 30\n assert candidate(nums = [-2, -3, -1, -5, -4, -6, -3, -1, -2]) == -1\n assert candidate(nums = [-2, -3, 4, -1, -2, 1, 5, -3, 4, -1, 2, 1, -5, 4]) == 10\n assert candidate(nums = [1000, -500, 200, -100, 50, -25, 12, -6, 3, -1, 0, -2, 1, 3, -1, 2]) == 1000\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 100]) == 100\n assert candidate(nums = [-10, -20, -30, -40, -50, 100, -1, -2, -3]) == 100\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 125, -125]) == 1000\n assert candidate(nums = [-1, 0, -2, 0, -3, 0, -4, 0, -5, 0, -6, 0, -7, 0, -8, 0]) == 0\n assert candidate(nums = [1, 2, 3, -6, 1, 2, 3, 4, -10, 5, 6, 7, 8]) == 26\n assert candidate(nums = [-10000, -9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991]) == -9991\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == 10\n assert candidate(nums = [1000, -500, 200, -300, 100, -200, 50, -10, 5, 1]) == 1000\n assert candidate(nums = [1, 2, 3, -6, 1, 2, 3, 4, 5, -10, 1, 2, 3, 4, 5, 6, 7]) == 33\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 125, -125, 62, -62, 31, -31, 15, -15]) == 1000\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == -1\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 100]) == 100\n assert candidate(nums = [100, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 100\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15]) == 15\n assert candidate(nums = [10, 20, 30, 40, 50, -100, 60, 70, 80, 90, 100]) == 450\n assert candidate(nums = [-1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2]) == 8\n assert candidate(nums = [100, -1, -2, -3, 100]) == 194\n assert candidate(nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4, 6, -1, 2, -1, 2, 3]) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210\n assert candidate(nums = [100, -1, -2, -3, 100, -1, -2, -3, 100]) == 288\n assert candidate(nums = [1, 2, 3, 4, 5, -15, 6, 7, 8, 9, 10, -25, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 170\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5, 10, 20, 30, -10, -20, -30]) == 60\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14]) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210\n assert candidate(nums = [0, -1, -2, -3, -4, -5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, 6, 7, 8, 9, 10]) == 65\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20]) == 19\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().maxSubArray", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxSubArray = function(nums) {", "container": null, "callable": "maxSubArray", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 54, "task_id": "spiral-matrix", "difficulty": "Medium", "problem_description": "Given an m x n matrix, return all elements of the matrix in spiral order.\n \nExample 1:\n\n\nInput: matrix = [[1,2,3],[4,5,6],[7,8,9]]\nOutput: [1,2,3,6,9,8,7,4,5]\n\nExample 2:\n\n\nInput: matrix = [[1,2,3,4],[5,6,7,8],[9,10,11,12]]\nOutput: [1,2,3,4,8,12,11,10,9,5,6,7]\n\n \nConstraints:\n\nm == matrix.length\nn == matrix[i].length\n1 <= m, n <= 10\n-100 <= matrix[i][j] <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[1], [2], [3], [4], [5]]) == [1, 2, 3, 4, 5]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(matrix = [[7], [9], [3]]) == [7, 9, 3]\n assert candidate(matrix = [[1]]) == [1]\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]]) == [1, 2, 4, 6, 8, 10, 9, 7, 5, 3]\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]) == [1, 2, 3, 4, 5, 10, 9, 8, 7, 6]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18]]) == [1, 2, 3, 4, 5, 6, 12, 18, 17, 16, 15, 14, 13, 7, 8, 9, 10, 11]\n assert candidate(matrix = [[1, 2], [3, 4]]) == [1, 2, 4, 3]\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == [1, 2, 3, 6, 9, 8, 7, 4, 5]\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6]]) == [1, 2, 3, 6, 5, 4]\n assert candidate(matrix = [[7]]) == [7]\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) == [1, 2, 3, 4, 8, 12, 11, 10, 9, 5, 6, 7]\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]) == [1, 2, 3, 4, 5, 10, 15, 20, 19, 18, 17, 16, 11, 6, 7, 8, 9, 14, 13, 12]\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]) == [1, 2, 3, 6, 9, 12, 11, 10, 7, 4, 5, 8]\n assert candidate(matrix = [[1, 2, 3], [6, 9, 8], [7, 4, 5]]) == [1, 2, 3, 8, 5, 4, 7, 6, 9]\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]]) == [1, 2, 3, 4, 5, 10, 15, 14, 13, 12, 11, 6, 7, 8, 9]\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30]]) == [1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 29, 28, 27, 26, 21, 16, 11, 6, 7, 8, 9, 14, 19, 24, 23, 22, 17, 12, 13, 18]\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == [1, 2, 3, 4, 5, 10, 15, 20, 25, 24, 23, 22, 21, 16, 11, 6, 7, 8, 9, 14, 19, 18, 17, 12, 13]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32], [33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48], [49, 50, 51, 52, 53, 54, 55, 56], [57, 58, 59, 60, 61, 62, 63, 64]]) == [1, 2, 3, 4, 5, 6, 7, 8, 16, 24, 32, 40, 48, 56, 64, 63, 62, 61, 60, 59, 58, 57, 49, 41, 33, 25, 17, 9, 10, 11, 12, 13, 14, 15, 23, 31, 39, 47, 55, 54, 53, 52, 51, 50, 42, 34, 26, 18, 19, 20, 21, 22, 30, 38, 46, 45, 44, 43, 35, 27, 28, 29, 37, 36]\n assert candidate(matrix = [[-1, 2, -3, 4, -5], [6, -7, 8, -9, 10], [-11, 12, -13, 14, -15], [16, -17, 18, -19, 20]]) == [-1, 2, -3, 4, -5, 10, -15, 20, -19, 18, -17, 16, -11, 6, -7, 8, -9, 14, -13, 12]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 81, 71, 61, 51, 41, 31, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19, 29, 39, 49, 59, 69, 79, 89, 88, 87, 86, 85, 84, 83, 82, 72, 62, 52, 42, 32, 22, 23, 24, 25, 26, 27, 28, 38, 48, 58, 68, 78, 77, 76, 75, 74, 73, 63, 53, 43, 33, 34, 35, 36, 37, 47, 57, 67, 66, 65, 64, 54, 44, 45, 46, 56, 55]\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], [17, 18, 19, 20], [21, 22, 23, 24]]) == [1, 2, 3, 4, 8, 12, 16, 20, 24, 23, 22, 21, 17, 13, 9, 5, 6, 7, 11, 15, 19, 18, 14, 10]\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16]]) == [1, 2, 4, 6, 8, 10, 12, 14, 16, 15, 13, 11, 9, 7, 5, 3]\n assert candidate(matrix = [[1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1]]) == [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48], [49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 24, 36, 48, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 37, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 35, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 26, 27, 28, 29, 30, 31, 32, 33, 34]\n assert candidate(matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9], [-10, -11, -12]]) == [-1, -2, -3, -6, -9, -12, -11, -10, -7, -4, -5, -8]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36]]) == [1, 2, 3, 4, 5, 6, 12, 18, 24, 30, 36, 35, 34, 33, 32, 31, 25, 19, 13, 7, 8, 9, 10, 11, 17, 23, 29, 28, 27, 26, 20, 14, 15, 16, 22, 21]\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], [17, 18, 19, 20]]) == [1, 2, 3, 4, 8, 12, 16, 20, 19, 18, 17, 13, 9, 5, 6, 7, 11, 15, 14, 10]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24]]) == [1, 2, 3, 4, 5, 6, 12, 18, 24, 23, 22, 21, 20, 19, 13, 7, 8, 9, 10, 11, 17, 16, 15, 14]\n assert candidate(matrix = [[0, -1, -2, -3, -4], [-5, -6, -7, -8, -9], [-10, -11, -12, -13, -14], [-15, -16, -17, -18, -19], [-20, -21, -22, -23, -24]]) == [0, -1, -2, -3, -4, -9, -14, -19, -24, -23, -22, -21, -20, -15, -10, -5, -6, -7, -8, -13, -18, -17, -16, -11, -12]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 41, 31, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19, 29, 39, 49, 48, 47, 46, 45, 44, 43, 42, 32, 22, 23, 24, 25, 26, 27, 28, 38, 37, 36, 35, 34, 33]\n assert candidate(matrix = [[-100, 100, -50, 50], [-20, 20, -30, 30], [-40, 40, -60, 60], [-70, 70, -80, 80]]) == [-100, 100, -50, 50, 30, 60, 80, -80, 70, -70, -40, -20, 20, -30, -60, 40]\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]]) == [1, 2, 4, 6, 8, 10, 12, 11, 9, 7, 5, 3]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32], [33, 34, 35, 36, 37, 38, 39, 40]]) == [1, 2, 3, 4, 5, 6, 7, 8, 16, 24, 32, 40, 39, 38, 37, 36, 35, 34, 33, 25, 17, 9, 10, 11, 12, 13, 14, 15, 23, 31, 30, 29, 28, 27, 26, 18, 19, 20, 21, 22]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 27, 36, 45, 54, 53, 52, 51, 50, 49, 48, 47, 46, 37, 28, 19, 10, 11, 12, 13, 14, 15, 16, 17, 26, 35, 44, 43, 42, 41, 40, 39, 38, 29, 20, 21, 22, 23, 24, 25, 34, 33, 32, 31, 30]\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], [17, 18, 19, 20], [21, 22, 23, 24], [25, 26, 27, 28], [29, 30, 31, 32], [33, 34, 35, 36], [37, 38, 39, 40]]) == [1, 2, 3, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 39, 38, 37, 33, 29, 25, 21, 17, 13, 9, 5, 6, 7, 11, 15, 19, 23, 27, 31, 35, 34, 30, 26, 22, 18, 14, 10]\n assert candidate(matrix = [[-1, -2, -3, -4], [-2, -3, -4, -5], [-3, -4, -5, -6], [-4, -5, -6, -7]]) == [-1, -2, -3, -4, -5, -6, -7, -6, -5, -4, -3, -2, -3, -4, -5, -4]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28], [29, 30, 31, 32, 33, 34, 35], [36, 37, 38, 39, 40, 41, 42]]) == [1, 2, 3, 4, 5, 6, 7, 14, 21, 28, 35, 42, 41, 40, 39, 38, 37, 36, 29, 22, 15, 8, 9, 10, 11, 12, 13, 20, 27, 34, 33, 32, 31, 30, 23, 16, 17, 18, 19, 26, 25, 24]\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]]) == [1, 2, 3, 6, 9, 12, 15, 14, 13, 10, 7, 4, 5, 8, 11]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54], [55, 56, 57, 58, 59, 60, 61, 62, 63], [64, 65, 66, 67, 68, 69, 70, 71, 72], [73, 74, 75, 76, 77, 78, 79, 80, 81]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 27, 36, 45, 54, 63, 72, 81, 80, 79, 78, 77, 76, 75, 74, 73, 64, 55, 46, 37, 28, 19, 10, 11, 12, 13, 14, 15, 16, 17, 26, 35, 44, 53, 62, 71, 70, 69, 68, 67, 66, 65, 56, 47, 38, 29, 20, 21, 22, 23, 24, 25, 34, 43, 52, 61, 60, 59, 58, 57, 48, 39, 30, 31, 32, 33, 42, 51, 50, 49, 40, 41]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32]]) == [1, 2, 3, 4, 5, 6, 7, 8, 16, 24, 32, 31, 30, 29, 28, 27, 26, 25, 17, 9, 10, 11, 12, 13, 14, 15, 23, 22, 21, 20, 19, 18]\n assert candidate(matrix = [[-1, 2, -3, 4, -5], [6, -7, 8, -9, 10], [11, -12, 13, -14, 15], [16, -17, 18, -19, 20]]) == [-1, 2, -3, 4, -5, 10, 15, 20, -19, 18, -17, 16, 11, 6, -7, 8, -9, -14, 13, -12]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30]]) == [1, 2, 3, 4, 5, 6, 12, 18, 24, 30, 29, 28, 27, 26, 25, 19, 13, 7, 8, 9, 10, 11, 17, 23, 22, 21, 20, 14, 15, 16]\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15], [16, 17, 18]]) == [1, 2, 3, 6, 9, 12, 15, 18, 17, 16, 13, 10, 7, 4, 5, 8, 11, 14]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28]]) == [1, 2, 3, 4, 5, 6, 7, 14, 21, 28, 27, 26, 25, 24, 23, 22, 15, 8, 9, 10, 11, 12, 13, 20, 19, 18, 17, 16]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19, 29, 28, 27, 26, 25, 24, 23, 22]\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55], [56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66], [67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77], [78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88], [89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99], [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 89, 78, 67, 56, 45, 34, 23, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 32, 43, 54, 65, 76, 87, 98, 97, 96, 95, 94, 93, 92, 91, 90, 79, 68, 57, 46, 35, 24, 25, 26, 27, 28, 29, 30, 31, 42, 53, 64, 75, 86, 85, 84, 83, 82, 81, 80, 69, 58, 47, 36, 37, 38, 39, 40, 41, 52, 63, 74, 73, 72, 71, 70, 59, 48, 49, 50, 51, 62, 61, 60]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 31, 21, 11, 12, 13, 14, 15, 16, 17, 18, 19, 29, 39, 38, 37, 36, 35, 34, 33, 32, 22, 23, 24, 25, 26, 27, 28]\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28], [29, 30, 31, 32, 33, 34, 35], [36, 37, 38, 39, 40, 41, 42], [43, 44, 45, 46, 47, 48, 49]]) == [1, 2, 3, 4, 5, 6, 7, 14, 21, 28, 35, 42, 49, 48, 47, 46, 45, 44, 43, 36, 29, 22, 15, 8, 9, 10, 11, 12, 13, 20, 27, 34, 41, 40, 39, 38, 37, 30, 23, 16, 17, 18, 19, 26, 33, 32, 31, 24, 25]\n assert candidate(matrix = [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n"}, "metadata": {"canonical_parameter_names": ["matrix"], "leetcode_dataset_entry_point": "Solution().spiralOrder", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var spiralOrder = function(matrix) {", "container": null, "callable": "spiralOrder", "parameters": [{"name": "matrix", "type": "number[][]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 55, "task_id": "jump-game", "difficulty": "Medium", "problem_description": "You are given an integer array nums. You are initially positioned at the array's first index, and each element in the array represents your maximum jump length at that position.\nReturn true if you can reach the last index, or false otherwise.\n \nExample 1:\n\nInput: nums = [2,3,1,1,4]\nOutput: true\nExplanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.\n\nExample 2:\n\nInput: nums = [3,2,1,0,4]\nOutput: false\nExplanation: You will always arrive at index 3 no matter what. Its maximum jump length is 0, which makes it impossible to reach the last index.\n\n \nConstraints:\n\n1 <= nums.length <= 104\n0 <= nums[i] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [2, 5, 0, 0]) == True\n assert candidate(nums = [1, 1, 1, 1, 1]) == True\n assert candidate(nums = [0]) == True\n assert candidate(nums = [5, 0, 0, 0, 0]) == True\n assert candidate(nums = [1, 2, 3]) == True\n assert candidate(nums = [2, 3, 1, 1, 4]) == True\n assert candidate(nums = [3, 2, 1, 0, 4]) == False\n assert candidate(nums = [1, 0, 1, 0]) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == True\n assert candidate(nums = [1, 2, 3, 4, 5]) == True\n assert candidate(nums = [5, 9, 4, 2, 1]) == True\n assert candidate(nums = [2, 0, 0]) == True\n assert candidate(nums = [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == False\n assert candidate(nums = [1, 3, 2, 1, 0, 4]) == False\n assert candidate(nums = [2, 3, 1, 1, 4, 2, 3, 1, 1, 1]) == True\n assert candidate(nums = [4, 2, 0, 0, 1, 1, 4, 4, 0, 4]) == True\n assert candidate(nums = [3, 0, 8, 2, 0, 0, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0]) == False\n assert candidate(nums = [1, 0, 3, 4, 5, 0]) == False\n assert candidate(nums = [2, 5, 0, 0, 1, 1, 1, 1, 0, 2]) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [10, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == True\n assert candidate(nums = [3, 0, 8, 2, 0, 0, 1]) == True\n assert candidate(nums = [2, 0, 0, 0, 1, 0]) == False\n assert candidate(nums = [2, 3, 0, 1, 4]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == True\n assert candidate(nums = [3, 2, 1, 3, 4, 2, 1, 0, 0, 0, 0]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == True\n assert candidate(nums = [2, 5, 0, 1, 3, 2, 1]) == True\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == False\n assert candidate(nums = [1, 3, 2, 0, 0, 0, 0, 0, 0, 1]) == False\n assert candidate(nums = [10, 0, 0, 0, 0, 0, 0, 0, 0, 9]) == True\n assert candidate(nums = [0, 2, 3, 1, 4, 2, 2, 1, 0, 1]) == False\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == True\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == False\n assert candidate(nums = [5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0]) == False\n assert candidate(nums = [3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == False\n assert candidate(nums = [1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [4, 3, 2, 1, 0, 0, 0, 0, 0]) == False\n assert candidate(nums = [2, 0, 0, 0, 1]) == False\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == True\n assert candidate(nums = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == False\n assert candidate(nums = [9, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == True\n assert candidate(nums = [1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0]) == False\n assert candidate(nums = [3, 2, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == False\n assert candidate(nums = [1, 2, 0, 2, 0, 1, 0, 0, 1, 0]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1]) == False\n assert candidate(nums = [2, 3, 1, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == False\n assert candidate(nums = [10, 2, 14, 1, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6]) == True\n assert candidate(nums = [2, 0, 2, 0, 1, 1]) == True\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == False\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == False\n assert candidate(nums = [2, 3, 1, 1, 4, 2, 1, 0, 1, 3, 1, 0, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 0, 0, 1]) == True\n assert candidate(nums = [0, 2, 3]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0]) == True\n assert candidate(nums = [1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 0]) == False\n assert candidate(nums = [4, 2, 0, 0, 1, 1, 4, 0, 0, 0, 1]) == True\n assert candidate(nums = [2, 5, 0, 0, 0, 0, 4, 1, 1, 1, 1]) == True\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().canJump", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canJump = function(nums) {", "container": null, "callable": "canJump", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 56, "task_id": "merge-intervals", "difficulty": "Medium", "problem_description": "Given an array of intervals where intervals[i] = [starti, endi], merge all overlapping intervals, and return an array of the non-overlapping intervals that cover all the intervals in the input.\n \nExample 1:\n\nInput: intervals = [[1,3],[2,6],[8,10],[15,18]]\nOutput: [[1,6],[8,10],[15,18]]\nExplanation: Since intervals [1,3] and [2,6] overlap, merge them into [1,6].\n\nExample 2:\n\nInput: intervals = [[1,4],[4,5]]\nOutput: [[1,5]]\nExplanation: Intervals [1,4] and [4,5] are considered overlapping.\n\n \nConstraints:\n\n1 <= intervals.length <= 104\nintervals[i].length == 2\n0 <= starti <= endi <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5]]) == [[1, 5]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16], [4, 9]]) == [[1, 2], [3, 10], [12, 16]]\n assert candidate(intervals = [[1, 3], [2, 6], [8, 10], [15, 18]]) == [[1, 6], [8, 10], [15, 18]]\n assert candidate(intervals = [[1, 3], [2, 5], [4, 8], [10, 12]]) == [[1, 8], [10, 12]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6]]) == [[1, 2], [3, 4], [5, 6]]\n assert candidate(intervals = [[1, 10], [2, 6], [9, 12]]) == [[1, 12]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3]]) == [[1, 1], [2, 2], [3, 3]]\n assert candidate(intervals = [[2, 3], [2, 2], [3, 3], [1, 3], [5, 7], [2, 2], [4, 6]]) == [[1, 3], [4, 7]]\n assert candidate(intervals = [[1, 4], [2, 3]]) == [[1, 4]]\n assert candidate(intervals = [[2, 3], [4, 5], [6, 7], [8, 9], [1, 10]]) == [[1, 10]]\n assert candidate(intervals = [[1, 10], [2, 6], [3, 5], [7, 9]]) == [[1, 10]]\n assert candidate(intervals = [[1, 10], [10, 20], [20, 30]]) == [[1, 30]]\n assert candidate(intervals = [[1, 3], [2, 2], [3, 4], [5, 7], [5, 9], [8, 10]]) == [[1, 4], [5, 10]]\n assert candidate(intervals = [[1, 2], [3, 10], [12, 16], [10, 19], [20, 24]]) == [[1, 2], [3, 19], [20, 24]]\n assert candidate(intervals = [[1, 4], [4, 5]]) == [[1, 5]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[0, 0], [1, 2], [2, 3], [4, 5]]) == [[0, 0], [1, 3], [4, 5]]\n assert candidate(intervals = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == [[1, 21]]\n assert candidate(intervals = [[1, 10], [11, 20], [21, 30], [31, 40], [15, 25]]) == [[1, 10], [11, 30], [31, 40]]\n assert candidate(intervals = [[1, 2], [3, 5], [4, 6], [7, 8], [9, 11], [10, 12], [13, 15]]) == [[1, 2], [3, 6], [7, 8], [9, 12], [13, 15]]\n assert candidate(intervals = [[1, 3], [5, 19], [11, 15], [2, 4], [8, 10], [7, 13]]) == [[1, 4], [5, 19]]\n assert candidate(intervals = [[1, 10], [10, 20], [20, 30], [30, 40], [40, 50]]) == [[1, 50]]\n assert candidate(intervals = [[5, 15], [20, 30], [10, 25], [35, 45], [40, 50]]) == [[5, 30], [35, 50]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20], [2, 4], [6, 8], [10, 12], [14, 16], [18, 20]]) == [[1, 4], [5, 8], [9, 12], [13, 16], [17, 20]]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == [[1, 10]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [1, 11], [6, 16], [11, 21], [16, 26], [21, 31], [26, 36], [31, 41], [36, 46], [41, 51], [46, 56]]) == [[1, 56]]\n assert candidate(intervals = [[1, 1000], [100, 200], [200, 300], [300, 400], [400, 500], [500, 600], [600, 700], [700, 800], [800, 900], [900, 1000]]) == [[1, 1000]]\n assert candidate(intervals = [[1, 5], [5, 10], [10, 15], [15, 20], [20, 25], [25, 30]]) == [[1, 30]]\n assert candidate(intervals = [[1, 100], [50, 60], [60, 70], [10, 20], [80, 90], [90, 100], [20, 30]]) == [[1, 100]]\n assert candidate(intervals = [[3, 6], [1, 2], [15, 18], [8, 10], [4, 5], [11, 13]]) == [[1, 2], [3, 6], [8, 10], [11, 13], [15, 18]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20], [21, 22], [23, 24], [25, 26], [27, 28], [29, 30], [1, 30]]) == [[1, 30]]\n assert candidate(intervals = [[1, 5], [6, 10], [11, 15], [16, 20], [21, 25], [22, 27], [28, 30]]) == [[1, 5], [6, 10], [11, 15], [16, 20], [21, 27], [28, 30]]\n assert candidate(intervals = [[1, 3], [3, 7], [8, 12], [12, 15], [16, 20], [19, 25], [25, 30], [30, 35]]) == [[1, 7], [8, 15], [16, 35]]\n assert candidate(intervals = [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) == [[1, 2]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45], [45, 50], [1, 100]]) == [[1, 100]]\n assert candidate(intervals = [[1, 1000], [500, 600], [700, 800], [850, 900], [950, 1050]]) == [[1, 1050]]\n assert candidate(intervals = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96], [6, 95], [7, 94], [8, 93], [9, 92], [10, 91]]) == [[1, 100]]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [1, 6]]) == [[1, 25]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [1, 4], [3, 6], [5, 8], [7, 10], [1, 6], [3, 8], [5, 10], [1, 8], [3, 10], [1, 10]]) == [[1, 10]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 9], [10, 15], [14, 20], [21, 25]]) == [[1, 2], [3, 5], [6, 9], [10, 20], [21, 25]]\n assert candidate(intervals = [[5, 8], [8, 10], [10, 12], [12, 14], [14, 16], [16, 18]]) == [[5, 18]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [1, 10]]) == [[1, 10]]\n assert candidate(intervals = [[1, 3], [5, 8], [4, 7], [9, 11], [12, 15], [13, 17]]) == [[1, 3], [4, 8], [9, 11], [12, 17]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21], [22, 23], [24, 25], [26, 27], [28, 29], [30, 31], [32, 33], [34, 35], [36, 37], [38, 39], [40, 41], [42, 43], [44, 45], [46, 47], [48, 49], [50, 51]]) == [[1, 2], [4, 5], [7, 8], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21], [22, 23], [24, 25], [26, 27], [28, 29], [30, 31], [32, 33], [34, 35], [36, 37], [38, 39], [40, 41], [42, 43], [44, 45], [46, 47], [48, 49], [50, 51]]\n assert candidate(intervals = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400], [50, 150], [100, 200], [150, 250], [200, 300], [250, 350]]) == [[50, 400]]\n assert candidate(intervals = [[1, 5], [5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40]]) == [[1, 40]]\n assert candidate(intervals = [[1, 1000], [200, 400], [500, 600], [300, 700], [800, 900], [100, 300]]) == [[1, 1000]]\n assert candidate(intervals = [[10, 20], [15, 25], [20, 30], [5, 15], [25, 35]]) == [[5, 35]]\n assert candidate(intervals = [[1, 100], [50, 75], [25, 50], [75, 100], [1, 50], [50, 100]]) == [[1, 100]]\n assert candidate(intervals = [[10, 20], [20, 30], [30, 40], [15, 25], [25, 35], [35, 45], [1, 10]]) == [[1, 45]]\n assert candidate(intervals = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [2, 10], [3, 9], [4, 8], [5, 7], [6, 6]]) == [[1, 10]]\n assert candidate(intervals = [[1, 100], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21], [22, 23], [24, 25], [26, 27], [28, 29], [30, 31], [32, 33], [34, 35], [36, 37], [38, 39], [40, 41], [42, 43], [44, 45], [46, 47], [48, 49], [50, 51], [52, 53], [54, 55], [56, 57], [58, 59], [60, 61], [62, 63], [64, 65], [66, 67], [68, 69], [70, 71], [72, 73], [74, 75], [76, 77], [78, 79], [80, 81], [82, 83], [84, 85], [86, 87], [88, 89], [90, 91], [92, 93], [94, 95], [96, 97], [98, 99]]) == [[1, 100]]\n assert candidate(intervals = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]\n assert candidate(intervals = [[2, 5], [10, 12], [7, 9], [1, 3], [14, 16]]) == [[1, 5], [7, 9], [10, 12], [14, 16]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [1, 10], [2, 9], [3, 8], [4, 7], [5, 6]]) == [[1, 10]]\n assert candidate(intervals = [[1, 5], [5, 10], [10, 15], [15, 20], [20, 25], [1, 25]]) == [[1, 25]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]\n assert candidate(intervals = [[0, 4], [2, 6], [5, 7], [8, 10], [11, 13], [12, 16], [15, 18]]) == [[0, 7], [8, 10], [11, 18]]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40]]) == [[5, 40]]\n assert candidate(intervals = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400], [350, 450]]) == [[100, 450]]\n assert candidate(intervals = [[1, 100], [50, 60], [60, 70], [80, 90], [90, 100]]) == [[1, 100]]\n assert candidate(intervals = [[1, 100], [50, 150], [100, 200], [250, 350], [300, 375]]) == [[1, 200], [250, 375]]\n assert candidate(intervals = [[1, 4], [2, 6], [8, 10], [15, 18], [16, 20], [21, 25]]) == [[1, 6], [8, 10], [15, 20], [21, 25]]\n assert candidate(intervals = [[1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [21, 25], [25, 29], [29, 33], [33, 37], [37, 41], [41, 45], [45, 49], [49, 53], [53, 57], [57, 61], [61, 65], [65, 69], [69, 73], [73, 77], [77, 81], [81, 85], [85, 89], [89, 93], [93, 97], [97, 101]]) == [[1, 101]]\n assert candidate(intervals = [[1, 100], [50, 75], [25, 60], [70, 80], [65, 90], [10, 50]]) == [[1, 100]]\n assert candidate(intervals = [[100, 200], [200, 300], [300, 400], [150, 250], [250, 350], [350, 450], [10, 110]]) == [[10, 450]]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [1, 10]]) == [[1, 10]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45], [45, 50], [50, 55], [55, 60]]) == [[5, 60]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 9], [11, 13], [14, 17], [18, 20], [19, 22]]) == [[1, 2], [3, 5], [6, 9], [11, 13], [14, 17], [18, 22]]\n assert candidate(intervals = [[1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [1, 3], [3, 6], [6, 9], [9, 12], [12, 15], [15, 18], [18, 21]]) == [[1, 21]]\n assert candidate(intervals = [[1, 50], [51, 100], [101, 150], [151, 200], [201, 250], [251, 300], [301, 350], [351, 400]]) == [[1, 50], [51, 100], [101, 150], [151, 200], [201, 250], [251, 300], [301, 350], [351, 400]]\n assert candidate(intervals = [[1, 3], [3, 7], [8, 10], [12, 15], [14, 17], [18, 20], [21, 22]]) == [[1, 7], [8, 10], [12, 17], [18, 20], [21, 22]]\n assert candidate(intervals = [[1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9]]) == [[1, 9]]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35]]) == [[5, 35]]\n assert candidate(intervals = [[1, 10], [10, 20], [20, 30], [30, 40], [40, 50], [1, 50]]) == [[1, 50]]\n assert candidate(intervals = [[5, 10], [15, 20], [10, 15], [25, 30], [30, 35], [20, 25]]) == [[5, 35]]\n assert candidate(intervals = [[1, 100], [50, 150], [25, 75], [125, 200], [76, 124]]) == [[1, 200]]\n assert candidate(intervals = [[1, 1000], [2, 999], [3, 998], [4, 997], [5, 996], [6, 995], [7, 994], [8, 993], [9, 992], [10, 991], [11, 990], [12, 989]]) == [[1, 1000]]\n assert candidate(intervals = [[1, 5], [2, 3], [4, 8], [7, 10], [11, 15], [14, 18], [17, 21], [20, 24], [23, 27], [26, 30], [29, 33], [32, 36], [35, 39], [38, 42], [41, 45], [44, 48], [47, 51], [46, 50], [45, 49], [44, 48], [43, 47], [42, 46], [41, 45], [40, 44], [39, 43], [38, 42], [37, 41], [36, 40], [35, 39], [34, 38], [33, 37], [32, 36], [31, 35], [30, 34], [29, 33], [28, 32], [27, 31], [26, 30], [25, 29], [24, 28], [23, 27], [22, 26], [21, 25], [20, 24], [19, 23], [18, 22], [17, 21], [16, 20], [15, 19], [14, 18], [13, 17], [12, 16], [11, 15], [10, 14], [9, 13], [8, 12], [7, 11], [6, 10], [5, 9], [4, 8], [3, 7], [2, 6], [1, 5]]) == [[1, 51]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20], [1, 20]]) == [[1, 20]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 5], [2, 4], [3, 6], [4, 8], [5, 10]]) == [[1, 10]]\n assert candidate(intervals = [[5, 10], [15, 20], [10, 15], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45], [45, 50], [5, 45]]) == [[5, 50]]\n assert candidate(intervals = [[1, 3], [5, 7], [2, 4], [6, 8]]) == [[1, 4], [5, 8]]\n assert candidate(intervals = [[1, 1000], [1001, 2000], [2001, 3000], [3001, 4000], [4001, 5000]]) == [[1, 1000], [1001, 2000], [2001, 3000], [3001, 4000], [4001, 5000]]\n assert candidate(intervals = [[1, 10], [11, 20], [21, 30], [31, 40], [41, 50], [51, 60], [61, 70], [71, 80], [81, 90], [91, 100], [1, 100], [5, 95], [15, 90], [25, 85], [35, 80]]) == [[1, 100]]\n assert candidate(intervals = [[1, 5], [2, 3], [4, 10], [11, 15], [14, 20]]) == [[1, 10], [11, 20]]\n assert candidate(intervals = [[8, 10], [1, 3], [2, 6], [15, 18], [10, 15]]) == [[1, 6], [8, 18]]\n assert candidate(intervals = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [1, 100], [5, 95], [15, 90], [25, 85], [35, 80]]) == [[1, 100]]\n"}, "metadata": {"canonical_parameter_names": ["intervals"], "leetcode_dataset_entry_point": "Solution().merge", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var merge = function(intervals) {", "container": null, "callable": "merge", "parameters": [{"name": "intervals", "type": "number[][]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 57, "task_id": "insert-interval", "difficulty": "Medium", "problem_description": "You are given an array of non-overlapping intervals intervals where intervals[i] = [starti, endi] represent the start and the end of the ith interval and intervals is sorted in ascending order by starti. You are also given an interval newInterval = [start, end] that represents the start and end of another interval.\nInsert newInterval into intervals such that intervals is still sorted in ascending order by starti and intervals still does not have any overlapping intervals (merge overlapping intervals if necessary).\nReturn intervals after the insertion.\nNote that you don't need to modify intervals in-place. You can make a new array and return it.\n \nExample 1:\n\nInput: intervals = [[1,3],[6,9]], newInterval = [2,5]\nOutput: [[1,5],[6,9]]\n\nExample 2:\n\nInput: intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]\nOutput: [[1,2],[3,10],[12,16]]\nExplanation: Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10].\n\n \nConstraints:\n\n0 <= intervals.length <= 104\nintervals[i].length == 2\n0 <= starti <= endi <= 105\nintervals is sorted by starti in ascending order.\nnewInterval.length == 2\n0 <= start <= end <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(intervals = [[1, 5]],newInterval = [2, 3]) == [[1, 5]]\n assert candidate(intervals = [[1, 5]],newInterval = [0, 3]) == [[0, 5]]\n assert candidate(intervals = [[1, 2], [3, 10], [12, 16]],newInterval = [10, 11]) == [[1, 2], [3, 11], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8]],newInterval = [1, 8]) == [[1, 8]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [13, 14]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 3], [5, 7]],newInterval = [4, 4]) == [[1, 3], [4, 4], [5, 7]]\n assert candidate(intervals = [],newInterval = [5, 7]) == [[5, 7]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8]],newInterval = [0, 9]) == [[0, 9]]\n assert candidate(intervals = [[1, 3], [6, 9]],newInterval = [10, 12]) == [[1, 3], [6, 9], [10, 12]]\n assert candidate(intervals = [[1, 3], [5, 7]],newInterval = [4, 6]) == [[1, 3], [4, 7]]\n assert candidate(intervals = [[1, 5]],newInterval = [0, 0]) == [[0, 0], [1, 5]]\n assert candidate(intervals = [[1, 5]],newInterval = [6, 8]) == [[1, 5], [6, 8]]\n assert candidate(intervals = [[1, 3], [6, 9]],newInterval = [2, 5]) == [[1, 5], [6, 9]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [4, 8]) == [[1, 2], [3, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [5, 6], [9, 10], [14, 15], [19, 20]],newInterval = [3, 18]) == [[1, 2], [3, 18], [19, 20]]\n assert candidate(intervals = [[1, 3], [8, 10], [15, 17]],newInterval = [4, 6]) == [[1, 3], [4, 6], [8, 10], [15, 17]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [1, 3]) == [[1, 4], [5, 6], [7, 8], [9, 10]]\n assert candidate(intervals = [[1, 5], [10, 15], [20, 25], [30, 35]],newInterval = [6, 14]) == [[1, 5], [6, 15], [20, 25], [30, 35]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8]],newInterval = [3, 3]) == [[1, 2], [3, 3], [4, 5], [7, 8]]\n assert candidate(intervals = [[2, 3], [5, 6], [8, 9], [11, 12], [14, 15]],newInterval = [7, 13]) == [[2, 3], [5, 6], [7, 13], [14, 15]]\n assert candidate(intervals = [],newInterval = [0, 0]) == [[0, 0]]\n assert candidate(intervals = [[1, 3], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [14, 16]) == [[1, 3], [4, 6], [8, 10], [12, 18]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [2, 16]) == [[1, 16], [17, 19]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [1, 18]) == [[1, 18], [19, 20]]\n assert candidate(intervals = [[1, 4], [7, 10], [12, 16], [20, 24]],newInterval = [5, 18]) == [[1, 4], [5, 18], [20, 24]]\n assert candidate(intervals = [[1, 2], [6, 7], [11, 12]],newInterval = [5, 6]) == [[1, 2], [5, 7], [11, 12]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [0, 20]) == [[0, 20]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [0, 20]) == [[0, 20]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [4, 11]) == [[1, 3], [4, 11], [12, 14], [16, 18]]\n assert candidate(intervals = [[1, 4], [9, 10], [11, 12], [13, 14]],newInterval = [5, 13]) == [[1, 4], [5, 14]]\n assert candidate(intervals = [[0, 2], [3, 6], [8, 10], [12, 14], [16, 19]],newInterval = [1, 18]) == [[0, 19]]\n assert candidate(intervals = [[1, 2]],newInterval = [3, 4]) == [[1, 2], [3, 4]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14]],newInterval = [1, 14]) == [[1, 14]]\n assert candidate(intervals = [[5, 10], [15, 20], [25, 30], [35, 40]],newInterval = [22, 28]) == [[5, 10], [15, 20], [22, 30], [35, 40]]\n assert candidate(intervals = [[1, 3], [8, 10], [15, 17], [20, 22]],newInterval = [4, 9]) == [[1, 3], [4, 10], [15, 17], [20, 22]]\n assert candidate(intervals = [[1, 2], [3, 6], [8, 10], [12, 15]],newInterval = [7, 9]) == [[1, 2], [3, 6], [7, 10], [12, 15]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [11, 15]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 15]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [2, 18]) == [[1, 19]]\n assert candidate(intervals = [[1, 2], [4, 7], [8, 10], [12, 15], [17, 20]],newInterval = [3, 18]) == [[1, 2], [3, 20]]\n assert candidate(intervals = [[1, 100], [200, 300], [400, 500]],newInterval = [150, 250]) == [[1, 100], [150, 300], [400, 500]]\n assert candidate(intervals = [[1, 5], [10, 15], [20, 25], [30, 35]],newInterval = [5, 30]) == [[1, 35]]\n assert candidate(intervals = [[1, 3], [5, 8], [10, 15], [16, 20]],newInterval = [4, 18]) == [[1, 3], [4, 20]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16], [19, 20]],newInterval = [10, 19]) == [[1, 2], [3, 5], [6, 7], [8, 20]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [2, 16]) == [[1, 16]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [17, 20]) == [[1, 3], [5, 7], [8, 10], [12, 14], [16, 20]]\n assert candidate(intervals = [[1, 3], [6, 9], [12, 15], [18, 21], [24, 27]],newInterval = [5, 20]) == [[1, 3], [5, 21], [24, 27]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [8, 14]) == [[1, 3], [5, 7], [8, 15], [17, 19]]\n assert candidate(intervals = [[1, 2], [5, 6], [9, 10], [13, 14], [17, 18]],newInterval = [3, 15]) == [[1, 2], [3, 15], [17, 18]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [17, 20]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16], [17, 20]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [7, 15]) == [[1, 2], [3, 5], [6, 16]]\n assert candidate(intervals = [],newInterval = [1, 5]) == [[1, 5]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [0, 15]) == [[0, 15]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14]],newInterval = [4, 11]) == [[1, 3], [4, 11], [12, 14]]\n assert candidate(intervals = [[1, 10], [20, 30], [40, 50]],newInterval = [15, 25]) == [[1, 10], [15, 30], [40, 50]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [3, 12]) == [[1, 2], [3, 16]]\n assert candidate(intervals = [[1, 10000]],newInterval = [5000, 15000]) == [[1, 15000]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 8], [9, 10], [12, 14], [16, 18]],newInterval = [3, 13]) == [[1, 2], [3, 14], [16, 18]]\n assert candidate(intervals = [[1, 5], [10, 15], [20, 25], [30, 35]],newInterval = [18, 22]) == [[1, 5], [10, 15], [18, 25], [30, 35]]\n assert candidate(intervals = [[5, 7], [10, 12], [15, 17], [20, 22]],newInterval = [8, 19]) == [[5, 7], [8, 19], [20, 22]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [3, 17]) == [[1, 2], [3, 18], [19, 20]]\n assert candidate(intervals = [[3, 5], [10, 12], [15, 18]],newInterval = [6, 11]) == [[3, 5], [6, 12], [15, 18]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [1, 3]) == [[1, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [0, 0]) == [[0, 0], [1, 2], [3, 4], [5, 6], [7, 8], [9, 10]]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5]],newInterval = [0, 6]) == [[0, 6]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [3, 5]) == [[1, 2], [3, 6], [8, 10], [12, 14], [16, 18]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [10, 11]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 11]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [2, 9]) == [[1, 10]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18], [20, 22], [24, 26], [28, 30]],newInterval = [3, 27]) == [[1, 2], [3, 27], [28, 30]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [0, 17]) == [[0, 17]]\n assert candidate(intervals = [[1, 2], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [3, 12]) == [[1, 2], [3, 12], [13, 15], [17, 19]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [5, 10]) == [[1, 2], [3, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [6, 12]) == [[1, 2], [3, 5], [6, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]],newInterval = [1, 12]) == [[1, 12]]\n assert candidate(intervals = [[1, 5], [6, 10], [11, 15], [16, 20]],newInterval = [1, 20]) == [[1, 20]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [18, 20]) == [[1, 3], [5, 7], [8, 10], [12, 14], [16, 20]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [7, 13]) == [[1, 2], [3, 4], [5, 6], [7, 14], [15, 16], [17, 18], [19, 20]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18], [20, 22], [24, 26], [28, 30]],newInterval = [5, 25]) == [[1, 2], [4, 26], [28, 30]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15]],newInterval = [2, 14]) == [[1, 15]]\n assert candidate(intervals = [[1, 2], [3, 4], [7, 9], [11, 13], [15, 17], [19, 21]],newInterval = [5, 16]) == [[1, 2], [3, 4], [5, 17], [19, 21]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [5, 9]) == [[1, 2], [4, 10], [12, 14], [16, 18]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [15, 20]],newInterval = [4, 10]) == [[1, 3], [4, 11], [15, 20]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [6, 9]) == [[1, 3], [5, 11], [13, 15], [17, 19]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [1, 9]) == [[1, 10], [12, 16]]\n assert candidate(intervals = [[1, 4], [6, 8], [10, 12], [14, 16]],newInterval = [5, 15]) == [[1, 4], [5, 16]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18], [20, 22], [24, 26], [28, 30]],newInterval = [1, 30]) == [[1, 30]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 9], [11, 13], [15, 17], [19, 21]],newInterval = [4, 18]) == [[1, 2], [3, 18], [19, 21]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14], [16, 17], [19, 20]],newInterval = [3, 19]) == [[1, 2], [3, 20]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14], [16, 17], [19, 20]],newInterval = [6, 18]) == [[1, 2], [4, 5], [6, 18], [19, 20]]\n assert candidate(intervals = [[1, 5], [10, 15], [20, 25], [30, 35], [40, 45]],newInterval = [22, 33]) == [[1, 5], [10, 15], [20, 35], [40, 45]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 7], [9, 10]],newInterval = [3, 8]) == [[1, 2], [3, 8], [9, 10]]\n assert candidate(intervals = [[1, 3], [5, 6], [7, 8], [11, 12], [13, 14]],newInterval = [2, 10]) == [[1, 10], [11, 12], [13, 14]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [14, 16]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8]],newInterval = [5, 7]) == [[1, 2], [4, 8]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [4, 10]) == [[1, 3], [4, 11], [13, 15], [17, 19]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [15, 17]) == [[1, 3], [5, 7], [8, 10], [12, 14], [15, 18]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [2, 19]) == [[1, 20]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 7], [9, 10], [12, 13]],newInterval = [3, 8]) == [[1, 2], [3, 8], [9, 10], [12, 13]]\n assert candidate(intervals = [[1, 10], [15, 20], [25, 30], [35, 40]],newInterval = [12, 28]) == [[1, 10], [12, 30], [35, 40]]\n assert candidate(intervals = [[1, 100]],newInterval = [50, 50]) == [[1, 100]]\n assert candidate(intervals = [[1, 10], [15, 20], [25, 30]],newInterval = [11, 19]) == [[1, 10], [11, 20], [25, 30]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [0, 1]) == [[0, 3], [5, 7], [8, 10], [12, 14], [16, 18]]\n assert candidate(intervals = [[1, 2]],newInterval = [0, 0]) == [[0, 0], [1, 2]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [0, 0]) == [[0, 0], [1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [0, 11]) == [[0, 11]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [5, 13]) == [[1, 2], [4, 14], [16, 18]]\n assert candidate(intervals = [[1, 3], [6, 9], [11, 12], [15, 18], [20, 22]],newInterval = [13, 16]) == [[1, 3], [6, 9], [11, 12], [13, 18], [20, 22]]\n assert candidate(intervals = [[1, 5], [10, 15], [20, 25]],newInterval = [6, 19]) == [[1, 5], [6, 19], [20, 25]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [15, 16]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14]],newInterval = [3, 12]) == [[1, 2], [3, 12], [13, 14]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [0, 1]) == [[0, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [10, 11]) == [[1, 2], [3, 5], [6, 7], [8, 11], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [10, 10]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [11, 12]) == [[1, 3], [5, 7], [8, 10], [11, 14], [16, 18]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [11, 12]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]]\n assert candidate(intervals = [[1, 3], [5, 7], [10, 12], [15, 18]],newInterval = [6, 11]) == [[1, 3], [5, 12], [15, 18]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 7], [9, 10], [12, 13]],newInterval = [3, 11]) == [[1, 2], [3, 11], [12, 13]]\n assert candidate(intervals = [[1, 2]],newInterval = [2, 2]) == [[1, 2]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [15, 18]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 18]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 12], [15, 18]],newInterval = [4, 11]) == [[1, 3], [4, 12], [15, 18]]\n assert candidate(intervals = [[1, 10], [14, 20], [22, 30], [32, 40]],newInterval = [12, 28]) == [[1, 10], [12, 30], [32, 40]]\n assert candidate(intervals = [[1, 2], [10, 15], [20, 25], [30, 35]],newInterval = [5, 19]) == [[1, 2], [5, 19], [20, 25], [30, 35]]\n assert candidate(intervals = [[1, 50]],newInterval = [25, 75]) == [[1, 75]]\n assert candidate(intervals = [[1, 2], [4, 10], [15, 20], [25, 30]],newInterval = [5, 18]) == [[1, 2], [4, 20], [25, 30]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [19, 20]) == [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18], [19, 20]]\n assert candidate(intervals = [[1, 2], [4, 5], [8, 9], [12, 13], [16, 17], [20, 21]],newInterval = [6, 14]) == [[1, 2], [4, 5], [6, 14], [16, 17], [20, 21]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [5, 15]) == [[1, 2], [3, 16]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 7], [9, 10], [12, 13]],newInterval = [5, 9]) == [[1, 2], [4, 10], [12, 13]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [11, 11]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 11]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 7], [8, 9], [10, 11]],newInterval = [5, 6]) == [[1, 2], [4, 7], [8, 9], [10, 11]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [17, 20]) == [[1, 2], [4, 6], [8, 10], [12, 14], [16, 20]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [12, 13]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [0, 1]) == [[0, 2], [3, 4], [5, 6], [7, 8], [9, 10]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [9, 11]) == [[1, 2], [3, 4], [5, 6], [7, 8], [9, 12], [13, 14], [15, 16], [17, 18], [19, 20]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [10, 18]) == [[1, 2], [3, 5], [6, 7], [8, 18]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [11, 12]],newInterval = [3, 10]) == [[1, 2], [3, 10], [11, 12]]\n assert candidate(intervals = [[1, 3], [5, 7], [8, 10], [12, 14], [16, 18]],newInterval = [14, 15]) == [[1, 3], [5, 7], [8, 10], [12, 15], [16, 18]]\n assert candidate(intervals = [[1, 2], [6, 7], [11, 12]],newInterval = [3, 5]) == [[1, 2], [3, 5], [6, 7], [11, 12]]\n assert candidate(intervals = [[1, 2], [5, 10], [15, 20], [25, 30], [35, 40]],newInterval = [0, 45]) == [[0, 45]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19]],newInterval = [0, 20]) == [[0, 20]]\n assert candidate(intervals = [[1, 3], [6, 10], [14, 16], [19, 22], [24, 26]],newInterval = [11, 15]) == [[1, 3], [6, 10], [11, 16], [19, 22], [24, 26]]\n assert candidate(intervals = [],newInterval = [1, 2]) == [[1, 2]]\n assert candidate(intervals = [[1, 3], [5, 6], [8, 10], [12, 14], [16, 18]],newInterval = [7, 13]) == [[1, 3], [5, 6], [7, 14], [16, 18]]\n assert candidate(intervals = [[1, 2], [6, 7], [11, 12]],newInterval = [1, 17]) == [[1, 17]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 12], [14, 16], [18, 20]],newInterval = [3, 17]) == [[1, 2], [3, 17], [18, 20]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14]],newInterval = [3, 7]) == [[1, 2], [3, 7], [8, 10], [12, 14]]\n assert candidate(intervals = [[1, 2], [4, 5], [8, 10], [12, 14], [16, 18]],newInterval = [6, 11]) == [[1, 2], [4, 5], [6, 11], [12, 14], [16, 18]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [1, 20]) == [[1, 20]]\n assert candidate(intervals = [[1, 3], [5, 7], [9, 11], [13, 15], [17, 19], [21, 23], [25, 27], [29, 31]],newInterval = [4, 29]) == [[1, 3], [4, 31]]\n assert candidate(intervals = [[1, 5], [10, 15], [20, 25], [30, 35], [40, 45]],newInterval = [26, 34]) == [[1, 5], [10, 15], [20, 25], [26, 35], [40, 45]]\n assert candidate(intervals = [[0, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [3, 15]) == [[0, 2], [3, 15], [16, 18]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [9, 15]) == [[1, 2], [4, 6], [8, 15], [16, 18]]\n assert candidate(intervals = [[1, 3], [6, 9], [13, 17], [20, 24], [27, 30]],newInterval = [11, 22]) == [[1, 3], [6, 9], [11, 24], [27, 30]]\n assert candidate(intervals = [[1, 3], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [2, 4]) == [[1, 6], [8, 10], [12, 14], [16, 18]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8]],newInterval = [0, 1]) == [[0, 2], [4, 5], [7, 8]]\n assert candidate(intervals = [[1, 2], [5, 8], [10, 15], [20, 25]],newInterval = [3, 23]) == [[1, 2], [3, 25]]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14], [16, 17]],newInterval = [3, 12]) == [[1, 2], [3, 12], [13, 14], [16, 17]]\n assert candidate(intervals = [[1, 2], [4, 5], [6, 10], [12, 18], [20, 25]],newInterval = [3, 11]) == [[1, 2], [3, 11], [12, 18], [20, 25]]\n assert candidate(intervals = [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]],newInterval = [16, 16]) == [[1, 2], [3, 5], [6, 7], [8, 10], [12, 16]]\n assert candidate(intervals = [[1, 2], [4, 6], [8, 10], [12, 14], [16, 18]],newInterval = [15, 17]) == [[1, 2], [4, 6], [8, 10], [12, 14], [15, 18]]\n assert candidate(intervals = [[1, 3], [6, 9], [12, 15], [18, 21], [24, 27]],newInterval = [10, 25]) == [[1, 3], [6, 9], [10, 27]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],newInterval = [8, 10]) == [[1, 2], [3, 4], [5, 6], [7, 10]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16]],newInterval = [0, 16]) == [[0, 16]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]],newInterval = [5, 15]) == [[1, 2], [3, 4], [5, 16], [17, 18], [19, 20]]\n assert candidate(intervals = [[1, 3], [6, 9], [13, 17], [20, 24], [27, 30], [33, 37], [40, 45]],newInterval = [11, 34]) == [[1, 3], [6, 9], [11, 37], [40, 45]]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16]],newInterval = [1, 16]) == [[1, 16]]\n assert candidate(intervals = [[1, 2]],newInterval = [0, 3]) == [[0, 3]]\n"}, "metadata": {"canonical_parameter_names": ["intervals", "newInterval"], "leetcode_dataset_entry_point": "Solution().insert", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var insert = function(intervals, newInterval) {", "container": null, "callable": "insert", "parameters": [{"name": "intervals", "type": "number[][]"}, {"name": "newInterval", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 58, "task_id": "length-of-last-word", "difficulty": "Easy", "problem_description": "Given a string s consisting of words and spaces, return the length of the last word in the string.\nA word is a maximal substring consisting of non-space characters only.\n \nExample 1:\n\nInput: s = \"Hello World\"\nOutput: 5\nExplanation: The last word is \"World\" with length 5.\n\nExample 2:\n\nInput: s = \" fly me to the moon \"\nOutput: 4\nExplanation: The last word is \"moon\" with length 4.\n\nExample 3:\n\nInput: s = \"luffy is still joyboy\"\nOutput: 6\nExplanation: The last word is \"joyboy\" with length 6.\n\n \nConstraints:\n\n1 <= s.length <= 104\ns consists of only English letters and spaces ' '.\nThere will be at least one word in s.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"Hello World\") == 5\n assert candidate(s = \" fly me to the moon \") == 4\n assert candidate(s = \"luffy is still joyboy\") == 6\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().lengthOfLastWord", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var lengthOfLastWord = function(s) {", "container": null, "callable": "lengthOfLastWord", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 59, "task_id": "spiral-matrix-ii", "difficulty": "Medium", "problem_description": "Given a positive integer n, generate an n x n matrix filled with elements from 1 to n2 in spiral order.\n \nExample 1:\n\n\nInput: n = 3\nOutput: [[1,2,3],[8,9,4],[7,6,5]]\n\nExample 2:\n\nInput: n = 1\nOutput: [[1]]\n\n \nConstraints:\n\n1 <= n <= 20\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == [[1, 2, 3], [8, 9, 4], [7, 6, 5]]\n assert candidate(n = 15) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 16], [55, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 70, 17], [54, 103, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 116, 71, 18], [53, 102, 143, 176, 177, 178, 179, 180, 181, 182, 183, 154, 117, 72, 19], [52, 101, 142, 175, 200, 201, 202, 203, 204, 205, 184, 155, 118, 73, 20], [51, 100, 141, 174, 199, 216, 217, 218, 219, 206, 185, 156, 119, 74, 21], [50, 99, 140, 173, 198, 215, 224, 225, 220, 207, 186, 157, 120, 75, 22], [49, 98, 139, 172, 197, 214, 223, 222, 221, 208, 187, 158, 121, 76, 23], [48, 97, 138, 171, 196, 213, 212, 211, 210, 209, 188, 159, 122, 77, 24], [47, 96, 137, 170, 195, 194, 193, 192, 191, 190, 189, 160, 123, 78, 25], [46, 95, 136, 169, 168, 167, 166, 165, 164, 163, 162, 161, 124, 79, 26], [45, 94, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 80, 27], [44, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 28], [43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29]]\n assert candidate(n = 4) == [[1, 2, 3, 4], [12, 13, 14, 5], [11, 16, 15, 6], [10, 9, 8, 7]]\n assert candidate(n = 20) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 21], [75, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 95, 22], [74, 143, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 161, 96, 23], [73, 142, 203, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 219, 162, 97, 24], [72, 141, 202, 255, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 269, 220, 163, 98, 25], [71, 140, 201, 254, 299, 336, 337, 338, 339, 340, 341, 342, 343, 344, 311, 270, 221, 164, 99, 26], [70, 139, 200, 253, 298, 335, 364, 365, 366, 367, 368, 369, 370, 345, 312, 271, 222, 165, 100, 27], [69, 138, 199, 252, 297, 334, 363, 384, 385, 386, 387, 388, 371, 346, 313, 272, 223, 166, 101, 28], [68, 137, 198, 251, 296, 333, 362, 383, 396, 397, 398, 389, 372, 347, 314, 273, 224, 167, 102, 29], [67, 136, 197, 250, 295, 332, 361, 382, 395, 400, 399, 390, 373, 348, 315, 274, 225, 168, 103, 30], [66, 135, 196, 249, 294, 331, 360, 381, 394, 393, 392, 391, 374, 349, 316, 275, 226, 169, 104, 31], [65, 134, 195, 248, 293, 330, 359, 380, 379, 378, 377, 376, 375, 350, 317, 276, 227, 170, 105, 32], [64, 133, 194, 247, 292, 329, 358, 357, 356, 355, 354, 353, 352, 351, 318, 277, 228, 171, 106, 33], [63, 132, 193, 246, 291, 328, 327, 326, 325, 324, 323, 322, 321, 320, 319, 278, 229, 172, 107, 34], [62, 131, 192, 245, 290, 289, 288, 287, 286, 285, 284, 283, 282, 281, 280, 279, 230, 173, 108, 35], [61, 130, 191, 244, 243, 242, 241, 240, 239, 238, 237, 236, 235, 234, 233, 232, 231, 174, 109, 36], [60, 129, 190, 189, 188, 187, 186, 185, 184, 183, 182, 181, 180, 179, 178, 177, 176, 175, 110, 37], [59, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 38], [58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39]]\n assert candidate(n = 2) == [[1, 2], [4, 3]]\n assert candidate(n = 1) == [[1]]\n assert candidate(n = 10) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [36, 37, 38, 39, 40, 41, 42, 43, 44, 11], [35, 64, 65, 66, 67, 68, 69, 70, 45, 12], [34, 63, 84, 85, 86, 87, 88, 71, 46, 13], [33, 62, 83, 96, 97, 98, 89, 72, 47, 14], [32, 61, 82, 95, 100, 99, 90, 73, 48, 15], [31, 60, 81, 94, 93, 92, 91, 74, 49, 16], [30, 59, 80, 79, 78, 77, 76, 75, 50, 17], [29, 58, 57, 56, 55, 54, 53, 52, 51, 18], [28, 27, 26, 25, 24, 23, 22, 21, 20, 19]]\n assert candidate(n = 5) == [[1, 2, 3, 4, 5], [16, 17, 18, 19, 6], [15, 24, 25, 20, 7], [14, 23, 22, 21, 8], [13, 12, 11, 10, 9]]\n assert candidate(n = 12) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 13], [43, 80, 81, 82, 83, 84, 85, 86, 87, 88, 55, 14], [42, 79, 108, 109, 110, 111, 112, 113, 114, 89, 56, 15], [41, 78, 107, 128, 129, 130, 131, 132, 115, 90, 57, 16], [40, 77, 106, 127, 140, 141, 142, 133, 116, 91, 58, 17], [39, 76, 105, 126, 139, 144, 143, 134, 117, 92, 59, 18], [38, 75, 104, 125, 138, 137, 136, 135, 118, 93, 60, 19], [37, 74, 103, 124, 123, 122, 121, 120, 119, 94, 61, 20], [36, 73, 102, 101, 100, 99, 98, 97, 96, 95, 62, 21], [35, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 22], [34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23]]\n assert candidate(n = 16) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 17], [59, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 75, 18], [58, 111, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 125, 76, 19], [57, 110, 155, 192, 193, 194, 195, 196, 197, 198, 199, 200, 167, 126, 77, 20], [56, 109, 154, 191, 220, 221, 222, 223, 224, 225, 226, 201, 168, 127, 78, 21], [55, 108, 153, 190, 219, 240, 241, 242, 243, 244, 227, 202, 169, 128, 79, 22], [54, 107, 152, 189, 218, 239, 252, 253, 254, 245, 228, 203, 170, 129, 80, 23], [53, 106, 151, 188, 217, 238, 251, 256, 255, 246, 229, 204, 171, 130, 81, 24], [52, 105, 150, 187, 216, 237, 250, 249, 248, 247, 230, 205, 172, 131, 82, 25], [51, 104, 149, 186, 215, 236, 235, 234, 233, 232, 231, 206, 173, 132, 83, 26], [50, 103, 148, 185, 214, 213, 212, 211, 210, 209, 208, 207, 174, 133, 84, 27], [49, 102, 147, 184, 183, 182, 181, 180, 179, 178, 177, 176, 175, 134, 85, 28], [48, 101, 146, 145, 144, 143, 142, 141, 140, 139, 138, 137, 136, 135, 86, 29], [47, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 30], [46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31]]\n assert candidate(n = 17) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 18], [63, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 80, 19], [62, 119, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 134, 81, 20], [61, 118, 167, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 180, 135, 82, 21], [60, 117, 166, 207, 240, 241, 242, 243, 244, 245, 246, 247, 218, 181, 136, 83, 22], [59, 116, 165, 206, 239, 264, 265, 266, 267, 268, 269, 248, 219, 182, 137, 84, 23], [58, 115, 164, 205, 238, 263, 280, 281, 282, 283, 270, 249, 220, 183, 138, 85, 24], [57, 114, 163, 204, 237, 262, 279, 288, 289, 284, 271, 250, 221, 184, 139, 86, 25], [56, 113, 162, 203, 236, 261, 278, 287, 286, 285, 272, 251, 222, 185, 140, 87, 26], [55, 112, 161, 202, 235, 260, 277, 276, 275, 274, 273, 252, 223, 186, 141, 88, 27], [54, 111, 160, 201, 234, 259, 258, 257, 256, 255, 254, 253, 224, 187, 142, 89, 28], [53, 110, 159, 200, 233, 232, 231, 230, 229, 228, 227, 226, 225, 188, 143, 90, 29], [52, 109, 158, 199, 198, 197, 196, 195, 194, 193, 192, 191, 190, 189, 144, 91, 30], [51, 108, 157, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 92, 31], [50, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 32], [49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33]]\n assert candidate(n = 8) == [[1, 2, 3, 4, 5, 6, 7, 8], [28, 29, 30, 31, 32, 33, 34, 9], [27, 48, 49, 50, 51, 52, 35, 10], [26, 47, 60, 61, 62, 53, 36, 11], [25, 46, 59, 64, 63, 54, 37, 12], [24, 45, 58, 57, 56, 55, 38, 13], [23, 44, 43, 42, 41, 40, 39, 14], [22, 21, 20, 19, 18, 17, 16, 15]]\n assert candidate(n = 18) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 19], [67, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 85, 20], [66, 127, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 143, 86, 21], [65, 126, 179, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 193, 144, 87, 22], [64, 125, 178, 223, 260, 261, 262, 263, 264, 265, 266, 267, 268, 235, 194, 145, 88, 23], [63, 124, 177, 222, 259, 288, 289, 290, 291, 292, 293, 294, 269, 236, 195, 146, 89, 24], [62, 123, 176, 221, 258, 287, 308, 309, 310, 311, 312, 295, 270, 237, 196, 147, 90, 25], [61, 122, 175, 220, 257, 286, 307, 320, 321, 322, 313, 296, 271, 238, 197, 148, 91, 26], [60, 121, 174, 219, 256, 285, 306, 319, 324, 323, 314, 297, 272, 239, 198, 149, 92, 27], [59, 120, 173, 218, 255, 284, 305, 318, 317, 316, 315, 298, 273, 240, 199, 150, 93, 28], [58, 119, 172, 217, 254, 283, 304, 303, 302, 301, 300, 299, 274, 241, 200, 151, 94, 29], [57, 118, 171, 216, 253, 282, 281, 280, 279, 278, 277, 276, 275, 242, 201, 152, 95, 30], [56, 117, 170, 215, 252, 251, 250, 249, 248, 247, 246, 245, 244, 243, 202, 153, 96, 31], [55, 116, 169, 214, 213, 212, 211, 210, 209, 208, 207, 206, 205, 204, 203, 154, 97, 32], [54, 115, 168, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 98, 33], [53, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 34], [52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35]]\n assert candidate(n = 19) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 20], [71, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 90, 21], [70, 135, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 152, 91, 22], [69, 134, 191, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 206, 153, 92, 23], [68, 133, 190, 239, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 252, 207, 154, 93, 24], [67, 132, 189, 238, 279, 312, 313, 314, 315, 316, 317, 318, 319, 290, 253, 208, 155, 94, 25], [66, 131, 188, 237, 278, 311, 336, 337, 338, 339, 340, 341, 320, 291, 254, 209, 156, 95, 26], [65, 130, 187, 236, 277, 310, 335, 352, 353, 354, 355, 342, 321, 292, 255, 210, 157, 96, 27], [64, 129, 186, 235, 276, 309, 334, 351, 360, 361, 356, 343, 322, 293, 256, 211, 158, 97, 28], [63, 128, 185, 234, 275, 308, 333, 350, 359, 358, 357, 344, 323, 294, 257, 212, 159, 98, 29], [62, 127, 184, 233, 274, 307, 332, 349, 348, 347, 346, 345, 324, 295, 258, 213, 160, 99, 30], [61, 126, 183, 232, 273, 306, 331, 330, 329, 328, 327, 326, 325, 296, 259, 214, 161, 100, 31], [60, 125, 182, 231, 272, 305, 304, 303, 302, 301, 300, 299, 298, 297, 260, 215, 162, 101, 32], [59, 124, 181, 230, 271, 270, 269, 268, 267, 266, 265, 264, 263, 262, 261, 216, 163, 102, 33], [58, 123, 180, 229, 228, 227, 226, 225, 224, 223, 222, 221, 220, 219, 218, 217, 164, 103, 34], [57, 122, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 104, 35], [56, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 36], [55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37]]\n assert candidate(n = 11) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 12], [39, 72, 73, 74, 75, 76, 77, 78, 79, 50, 13], [38, 71, 96, 97, 98, 99, 100, 101, 80, 51, 14], [37, 70, 95, 112, 113, 114, 115, 102, 81, 52, 15], [36, 69, 94, 111, 120, 121, 116, 103, 82, 53, 16], [35, 68, 93, 110, 119, 118, 117, 104, 83, 54, 17], [34, 67, 92, 109, 108, 107, 106, 105, 84, 55, 18], [33, 66, 91, 90, 89, 88, 87, 86, 85, 56, 19], [32, 65, 64, 63, 62, 61, 60, 59, 58, 57, 20], [31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21]]\n assert candidate(n = 14) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 15], [51, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 65, 16], [50, 95, 132, 133, 134, 135, 136, 137, 138, 139, 140, 107, 66, 17], [49, 94, 131, 160, 161, 162, 163, 164, 165, 166, 141, 108, 67, 18], [48, 93, 130, 159, 180, 181, 182, 183, 184, 167, 142, 109, 68, 19], [47, 92, 129, 158, 179, 192, 193, 194, 185, 168, 143, 110, 69, 20], [46, 91, 128, 157, 178, 191, 196, 195, 186, 169, 144, 111, 70, 21], [45, 90, 127, 156, 177, 190, 189, 188, 187, 170, 145, 112, 71, 22], [44, 89, 126, 155, 176, 175, 174, 173, 172, 171, 146, 113, 72, 23], [43, 88, 125, 154, 153, 152, 151, 150, 149, 148, 147, 114, 73, 24], [42, 87, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 74, 25], [41, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 26], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27]]\n assert candidate(n = 9) == [[1, 2, 3, 4, 5, 6, 7, 8, 9], [32, 33, 34, 35, 36, 37, 38, 39, 10], [31, 56, 57, 58, 59, 60, 61, 40, 11], [30, 55, 72, 73, 74, 75, 62, 41, 12], [29, 54, 71, 80, 81, 76, 63, 42, 13], [28, 53, 70, 79, 78, 77, 64, 43, 14], [27, 52, 69, 68, 67, 66, 65, 44, 15], [26, 51, 50, 49, 48, 47, 46, 45, 16], [25, 24, 23, 22, 21, 20, 19, 18, 17]]\n assert candidate(n = 6) == [[1, 2, 3, 4, 5, 6], [20, 21, 22, 23, 24, 7], [19, 32, 33, 34, 25, 8], [18, 31, 36, 35, 26, 9], [17, 30, 29, 28, 27, 10], [16, 15, 14, 13, 12, 11]]\n assert candidate(n = 7) == [[1, 2, 3, 4, 5, 6, 7], [24, 25, 26, 27, 28, 29, 8], [23, 40, 41, 42, 43, 30, 9], [22, 39, 48, 49, 44, 31, 10], [21, 38, 47, 46, 45, 32, 11], [20, 37, 36, 35, 34, 33, 12], [19, 18, 17, 16, 15, 14, 13]]\n assert candidate(n = 13) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 14], [47, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 60, 15], [46, 87, 120, 121, 122, 123, 124, 125, 126, 127, 98, 61, 16], [45, 86, 119, 144, 145, 146, 147, 148, 149, 128, 99, 62, 17], [44, 85, 118, 143, 160, 161, 162, 163, 150, 129, 100, 63, 18], [43, 84, 117, 142, 159, 168, 169, 164, 151, 130, 101, 64, 19], [42, 83, 116, 141, 158, 167, 166, 165, 152, 131, 102, 65, 20], [41, 82, 115, 140, 157, 156, 155, 154, 153, 132, 103, 66, 21], [40, 81, 114, 139, 138, 137, 136, 135, 134, 133, 104, 67, 22], [39, 80, 113, 112, 111, 110, 109, 108, 107, 106, 105, 68, 23], [38, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 24], [37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25]]\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().generateMatrix", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var generateMatrix = function(n) {", "container": null, "callable": "generateMatrix", "parameters": [{"name": "n", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 60, "task_id": "permutation-sequence", "difficulty": "Hard", "problem_description": "The set [1, 2, 3, ..., n] contains a total of n! unique permutations.\nBy listing and labeling all of the permutations in order, we get the following sequence for n = 3:\n\n\"123\"\n\"132\"\n\"213\"\n\"231\"\n\"312\"\n\"321\"\n\nGiven n and k, return the kth permutation sequence.\n \nExample 1:\nInput: n = 3, k = 3\nOutput: \"213\"\nExample 2:\nInput: n = 4, k = 9\nOutput: \"2314\"\nExample 3:\nInput: n = 3, k = 1\nOutput: \"123\"\n\n \nConstraints:\n\n1 <= n <= 9\n1 <= k <= n!\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3,k = 1) == \"123\"\n assert candidate(n = 8,k = 40320) == \"87654321\"\n assert candidate(n = 4,k = 9) == \"2314\"\n assert candidate(n = 9,k = 362880) == \"987654321\"\n assert candidate(n = 5,k = 10) == \"13452\"\n assert candidate(n = 3,k = 3) == \"213\"\n assert candidate(n = 2,k = 1) == \"12\"\n assert candidate(n = 2,k = 2) == \"21\"\n assert candidate(n = 6,k = 720) == \"654321\"\n assert candidate(n = 7,k = 5040) == \"7654321\"\n assert candidate(n = 5,k = 1) == \"12345\"\n assert candidate(n = 5,k = 120) == \"54321\"\n assert candidate(n = 9,k = 362879) == \"987654312\"\n assert candidate(n = 5,k = 60) == \"32541\"\n assert candidate(n = 8,k = 25921) == \"62134578\"\n assert candidate(n = 4,k = 11) == \"2413\"\n assert candidate(n = 9,k = 181440) == \"549876321\"\n assert candidate(n = 6,k = 399) == \"425316\"\n assert candidate(n = 7,k = 1) == \"1234567\"\n assert candidate(n = 8,k = 30240) == \"68754321\"\n assert candidate(n = 6,k = 359) == \"365412\"\n assert candidate(n = 5,k = 119) == \"54312\"\n assert candidate(n = 4,k = 19) == \"4123\"\n assert candidate(n = 6,k = 719) == \"654312\"\n assert candidate(n = 8,k = 1) == \"12345678\"\n assert candidate(n = 8,k = 20161) == \"51234678\"\n assert candidate(n = 9,k = 123456) == \"416589732\"\n assert candidate(n = 8,k = 40321) == \"1234567\"\n assert candidate(n = 8,k = 20160) == \"48765321\"\n assert candidate(n = 6,k = 100) == \"162453\"\n assert candidate(n = 6,k = 360) == \"365421\"\n assert candidate(n = 4,k = 15) == \"3214\"\n assert candidate(n = 9,k = 270000) == \"764985321\"\n assert candidate(n = 9,k = 100000) == \"358926471\"\n assert candidate(n = 7,k = 2521) == \"4512367\"\n assert candidate(n = 7,k = 3500) == \"5716243\"\n assert candidate(n = 9,k = 50000) == \"239574186\"\n assert candidate(n = 9,k = 326592) == \"917548632\"\n assert candidate(n = 7,k = 5041) == \"123456\"\n assert candidate(n = 9,k = 274567) == \"784315269\"\n assert candidate(n = 6,k = 391) == \"423156\"\n assert candidate(n = 6,k = 500) == \"516243\"\n assert candidate(n = 6,k = 1) == \"123456\"\n assert candidate(n = 8,k = 25000) == \"58624371\"\n assert candidate(n = 8,k = 12345) == \"35184627\"\n assert candidate(n = 9,k = 181441) == \"561234789\"\n assert candidate(n = 4,k = 24) == \"4321\"\n assert candidate(n = 7,k = 5000) == \"7642153\"\n assert candidate(n = 7,k = 1000) == \"2436571\"\n assert candidate(n = 5,k = 24) == \"15432\"\n assert candidate(n = 7,k = 2520) == \"4376521\"\n assert candidate(n = 4,k = 4) == \"1342\"\n assert candidate(n = 4,k = 10) == \"2341\"\n assert candidate(n = 5,k = 100) == \"51342\"\n assert candidate(n = 9,k = 98765) == \"357214968\"\n assert candidate(n = 7,k = 5039) == \"7654312\"\n assert candidate(n = 6,k = 397) == \"425136\"\n assert candidate(n = 6,k = 361) == \"412356\"\n"}, "metadata": {"canonical_parameter_names": ["n", "k"], "leetcode_dataset_entry_point": "Solution().getPermutation", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getPermutation = function(n, k) {", "container": null, "callable": "getPermutation", "parameters": [{"name": "n", "type": "number"}, {"name": "k", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 61, "task_id": "rotate-list", "difficulty": "Medium", "problem_description": "Given the head of a linked list, rotate the list to the right by k places.\n \nExample 1:\n\n\nInput: head = [1,2,3,4,5], k = 2\nOutput: [4,5,1,2,3]\n\nExample 2:\n\n\nInput: head = [0,1,2], k = 4\nOutput: [2,0,1]\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 500].\n-100 <= Node.val <= 100\n0 <= k <= 2 * 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([-100, 100, 0]),k = 1), list_node([0, -100, 100]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),k = 9), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([0, 1, 2]),k = 4), list_node([2, 0, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),k = 5), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2]),k = 0), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),k = 3), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),k = 2), list_node([4, 5, 1, 2, 3]))\n assert candidate(head = list_node([]),k = 0) == None\n assert is_same_list(candidate(head = list_node([1, 2]),k = 3), list_node([2, 1]))\n assert is_same_list(candidate(head = list_node([1]),k = 0), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),k = 6), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([1, 2]),k = 1), list_node([2, 1]))\n assert is_same_list(candidate(head = list_node([-1, 0, 1]),k = 1), list_node([1, -1, 0]))\n assert is_same_list(candidate(head = list_node([1]),k = 1), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),k = 10), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),k = 3), list_node([7, 8, 9, 1, 2, 3, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 0), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),k = 7), list_node([2, 1, 5, 4, 3]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),k = 25), list_node([60, 70, 80, 90, 100, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([1]),k = 100), list_node([1]))\n assert is_same_list(candidate(head = list_node([7, 6, 5, 4, 3, 2, 1]),k = 10), list_node([3, 2, 1, 7, 6, 5, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 0), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),k = 15), list_node([4, 5, 6, 7, 8, 9, 1, 2, 3]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]),k = 11), list_node([20, 2, 4, 6, 8, 10, 12, 14, 16, 18]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 5), list_node([16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5]),k = 2), list_node([-4, -5, -1, -2, -3]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 3), list_node([3, 2, 1, 10, 9, 8, 7, 6, 5, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 20), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 15), list_node([6, 7, 8, 9, 10, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 500), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),k = 100), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([0]),k = 500), list_node([0]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0]),k = 9), list_node([8, 7, 6, 5, 4, 3, 2, 1, 0, 9]))\n assert is_same_list(candidate(head = list_node([3, 1, 2]),k = 3), list_node([3, 1, 2]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),k = 15), list_node([60, 70, 80, 90, 100, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),k = 1), list_node([1, 5, 4, 3, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 0), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),k = 501), list_node([100, 10, 20, 30, 40, 50, 60, 70, 80, 90]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),k = 5), list_node([-6, -7, -8, -9, -10, -1, -2, -3, -4, -5]))\n assert is_same_list(candidate(head = list_node([0]),k = 0), list_node([0]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50]),k = 1000000000), list_node([10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),k = 5), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([7, 1, 3, 9, 2, 5, 8, 6]),k = 3), list_node([5, 8, 6, 7, 1, 3, 9, 2]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 4294967295), list_node([3, 2, 1, 9, 8, 7, 6, 5, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 9), list_node([7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60]),k = 600000000), list_node([10, 20, 30, 40, 50, 60]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),k = 15), list_node([-6, -7, -8, -9, -10, -1, -2, -3, -4, -5]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]),k = 19), list_node([3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 1]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 2, 3, 8, 4, 7, 6]),k = 3), list_node([4, 7, 6, 5, 1, 9, 2, 3, 8]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 25), list_node([6, 7, 8, 9, 10, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1]),k = 1000000000), list_node([1]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 9), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),k = 10), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),k = 19), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([7, 7, 7, 7, 7]),k = 10), list_node([7, 7, 7, 7, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),k = 25), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n assert candidate(head = list_node([]),k = 3) == None\n assert is_same_list(candidate(head = list_node([-1, 0, 1, -2, 2, -3, 3]),k = 7), list_node([-1, 0, 1, -2, 2, -3, 3]))\n assert is_same_list(candidate(head = list_node([1]),k = 10), list_node([1]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),k = 2), list_node([2, 1, 5, 4, 3]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),k = 10), list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]))\n assert candidate(head = list_node([]),k = 1) == None\n assert is_same_list(candidate(head = list_node([100, -100, 50, -50, 25, -25, 12, -12]),k = 10), list_node([12, -12, 100, -100, 50, -50, 25, -25]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),k = 2147483647), list_node([3, 1, 2]))\n assert is_same_list(candidate(head = list_node([1]),k = 1000), list_node([1]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),k = 8), list_node([-3, -4, -5, -6, -7, -8, -9, -10, -1, -2]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 7), list_node([7, 6, 5, 4, 3, 2, 1, 9, 8]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 11), list_node([10, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([5]),k = 0), list_node([5]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),k = 3), list_node([3, 2, 1, 5, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 18), list_node([3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 100), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 19), list_node([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5]),k = 7), list_node([-4, -5, -1, -2, -3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 1), list_node([10, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 5), list_node([6, 7, 8, 9, 10, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([5, 6, 7, 8, 9, 10, 11]),k = 500000000), list_node([9, 10, 11, 5, 6, 7, 8]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),k = 5), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 3), list_node([8, 9, 10, 1, 2, 3, 4, 5, 6, 7]))\n assert is_same_list(candidate(head = list_node([2, 1]),k = 1), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),k = 21), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 20), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-100, 100, -50, 50, -25, 25]),k = 2), list_node([-25, 25, -100, 100, -50, 50]))\n assert is_same_list(candidate(head = list_node([-100, 0, 100]),k = 2), list_node([0, 100, -100]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),k = 9), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([9, 9, 9, 9, 9]),k = 10), list_node([9, 9, 9, 9, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),k = 7), list_node([9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8]))\n assert is_same_list(candidate(head = list_node([5]),k = 1000000000), list_node([5]))\n assert candidate(head = list_node([]),k = 5) == None\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),k = 20), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]),k = 13), list_node([6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 2, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),k = 7), list_node([6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]),k = 10), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),k = 9), list_node([2, 3, 4, 5, 6, 7, 8, 9, 10, 1]))\n assert is_same_list(candidate(head = list_node([-100, 0, 100]),k = 1), list_node([100, -100, 0]))\n assert is_same_list(candidate(head = list_node([3, 3, 3, 3, 3]),k = 10), list_node([3, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),k = 15), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6]))\n assert is_same_list(candidate(head = list_node([10, -20, 30, -40, 50]),k = 3), list_node([30, -40, 50, 10, -20]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),k = 50), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),k = 3), list_node([-8, -9, -10, -1, -2, -3, -4, -5, -6, -7]))\n"}, "metadata": {"canonical_parameter_names": ["head", "k"], "leetcode_dataset_entry_point": "Solution().rotateRight", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var rotateRight = function(head, k) {", "container": null, "callable": "rotateRight", "parameters": [{"name": "head", "type": "ListNode"}, {"name": "k", "type": "number"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 62, "task_id": "unique-paths", "difficulty": "Medium", "problem_description": "There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.\nGiven the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.\nThe test cases are generated so that the answer will be less than or equal to 2 * 109.\n \nExample 1:\n\n\nInput: m = 3, n = 7\nOutput: 28\n\nExample 2:\n\nInput: m = 3, n = 2\nOutput: 3\nExplanation: From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:\n1. Right -> Down -> Down\n2. Down -> Down -> Right\n3. Down -> Right -> Down\n\n \nConstraints:\n\n1 <= m, n <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(m = 20,n = 30) == 11541847896480\n assert candidate(m = 1,n = 100) == 1\n assert candidate(m = 3,n = 7) == 28\n assert candidate(m = 5,n = 5) == 70\n assert candidate(m = 10,n = 10) == 48620\n assert candidate(m = 5,n = 3) == 15\n assert candidate(m = 30,n = 20) == 11541847896480\n assert candidate(m = 1,n = 1) == 1\n assert candidate(m = 3,n = 2) == 3\n assert candidate(m = 100,n = 1) == 1\n assert candidate(m = 40,n = 30) == 13750991318793417920\n assert candidate(m = 67,n = 33) == 65814642035034133075191231\n assert candidate(m = 30,n = 30) == 30067266499541040\n assert candidate(m = 5,n = 95) == 3612280\n assert candidate(m = 15,n = 15) == 40116600\n assert candidate(m = 1,n = 50) == 1\n assert candidate(m = 30,n = 40) == 13750991318793417920\n assert candidate(m = 99,n = 99) == 5716592448890534420436582360196242777068052430850904489000\n assert candidate(m = 25,n = 75) == 45931679871275969889300\n assert candidate(m = 90,n = 10) == 1573664496040\n assert candidate(m = 75,n = 75) == 23362265873332749085315221863910685052043000\n assert candidate(m = 30,n = 25) == 779255311989700\n assert candidate(m = 75,n = 25) == 45931679871275969889300\n assert candidate(m = 30,n = 70) == 6230496325796261023265040\n assert candidate(m = 100,n = 5) == 4421275\n assert candidate(m = 80,n = 80) == 23156006494021191956342707682359261381151378400\n assert candidate(m = 40,n = 10) == 1677106640\n assert candidate(m = 80,n = 20) == 86623575014757120480\n assert candidate(m = 5,n = 8) == 330\n assert candidate(m = 99,n = 1) == 1\n assert candidate(m = 5,n = 100) == 4421275\n assert candidate(m = 99,n = 2) == 99\n assert candidate(m = 10,n = 90) == 1573664496040\n assert candidate(m = 60,n = 60) == 24356699707654619143838606602026720\n assert candidate(m = 2,n = 99) == 99\n assert candidate(m = 1,n = 99) == 1\n assert candidate(m = 45,n = 35) == 14429347509452441488650\n assert candidate(m = 55,n = 45) == 15362117803534044899180148240\n assert candidate(m = 50,n = 2) == 50\n assert candidate(m = 60,n = 40) == 3332420398982499757882998720\n assert candidate(m = 50,n = 50) == 25477612258980856902730428600\n assert candidate(m = 100,n = 100) == 22750883079422934966181954039568885395604168260154104734000\n assert candidate(m = 15,n = 5) == 3060\n assert candidate(m = 99,n = 100) == 11375441539711467483090977019784442697802084130077052367000\n assert candidate(m = 20,n = 80) == 86623575014757120480\n assert candidate(m = 15,n = 20) == 818809200\n assert candidate(m = 45,n = 55) == 15362117803534044899180148240\n assert candidate(m = 25,n = 25) == 32247603683100\n assert candidate(m = 2,n = 50) == 50\n assert candidate(m = 40,n = 60) == 3332420398982499757882998720\n assert candidate(m = 50,n = 1) == 1\n assert candidate(m = 70,n = 30) == 6230496325796261023265040\n assert candidate(m = 15,n = 25) == 9669554100\n assert candidate(m = 33,n = 67) == 65814642035034133075191231\n assert candidate(m = 35,n = 45) == 14429347509452441488650\n"}, "metadata": {"canonical_parameter_names": ["m", "n"], "leetcode_dataset_entry_point": "Solution().uniquePaths", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var uniquePaths = function(m, n) {", "container": null, "callable": "uniquePaths", "parameters": [{"name": "m", "type": "number"}, {"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 63, "task_id": "unique-paths-ii", "difficulty": "Medium", "problem_description": "You are given an m x n integer array grid. There is a robot initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.\nAn obstacle and space are marked as 1 or 0 respectively in grid. A path that the robot takes cannot include any square that is an obstacle.\nReturn the number of possible unique paths that the robot can take to reach the bottom-right corner.\nThe testcases are generated so that the answer will be less than or equal to 2 * 109.\n \nExample 1:\n\n\nInput: obstacleGrid = [[0,0,0],[0,1,0],[0,0,0]]\nOutput: 2\nExplanation: There is one obstacle in the middle of the 3x3 grid above.\nThere are two ways to reach the bottom-right corner:\n1. Right -> Right -> Down -> Down\n2. Down -> Down -> Right -> Right\n\nExample 2:\n\n\nInput: obstacleGrid = [[0,1],[0,0]]\nOutput: 1\n\n \nConstraints:\n\nm == obstacleGrid.length\nn == obstacleGrid[i].length\n1 <= m, n <= 100\nobstacleGrid[i][j] is 0 or 1.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(obstacleGrid = [[1, 0], [0, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]]) == 17\n assert candidate(obstacleGrid = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 1, 0, 0]]) == 7\n assert candidate(obstacleGrid = [[0, 1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 0]]) == 7\n assert candidate(obstacleGrid = [[1]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]) == 6\n assert candidate(obstacleGrid = [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0]]) == 4\n assert candidate(obstacleGrid = [[0, 0, 1, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0]]) == 7\n assert candidate(obstacleGrid = [[0]]) == 1\n assert candidate(obstacleGrid = [[0, 0, 0], [0, 1, 0], [0, 0, 0]]) == 2\n assert candidate(obstacleGrid = [[0, 0], [0, 0]]) == 2\n assert candidate(obstacleGrid = [[0, 0], [0, 1]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) == 11\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 35\n assert candidate(obstacleGrid = [[0, 1], [0, 0]]) == 1\n assert candidate(obstacleGrid = [[0, 0], [1, 0]]) == 1\n assert candidate(obstacleGrid = [[0, 0, 0], [0, 0, 0], [0, 0, 1]]) == 0\n assert candidate(obstacleGrid = [[0, 0], [1, 1], [0, 0]]) == 0\n assert candidate(obstacleGrid = [[1, 0, 0], [0, 1, 0], [0, 0, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) == 8\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 86\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0]]) == 11\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [1, 1, 1, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 1\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]]) == 87\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 35\n assert candidate(obstacleGrid = [[1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 1], [0, 0, 0, 0, 0], [1, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 24\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]) == 303\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0]]) == 13\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 53\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 26\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 33\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 540\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 1078\n assert candidate(obstacleGrid = [[0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0]]) == 2\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]) == 231\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 252\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 282\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 77\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]) == 25\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 47\n assert candidate(obstacleGrid = [[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 1, 0]]) == 4\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0]]) == 101\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0], [0, 0, 0, 1, 0], [1, 1, 1, 1, 0], [0, 0, 0, 0, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]]) == 14\n assert candidate(obstacleGrid = [[0, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 38\n assert candidate(obstacleGrid = [[0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 1058\n assert candidate(obstacleGrid = [[0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 0]]) == 5\n assert candidate(obstacleGrid = [[0, 1, 1, 1, 0], [0, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0], [0, 1, 0, 1, 0]]) == 3\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0]]) == 19\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 133\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 400\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 68\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 2\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 25\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 1871\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0]]) == 5\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 264\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 0]]) == 15\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0]]) == 10\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]]) == 72\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 239\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]) == 161\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 9446\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 4\n assert candidate(obstacleGrid = [[0, 1, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 1, 0], [1, 1, 0, 0, 0], [0, 0, 0, 0, 0]]) == 3\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]]) == 7\n assert candidate(obstacleGrid = [[0, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0]]) == 3\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]]) == 850\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0]]) == 14\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 6\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0]]) == 24\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]]) == 17\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]]) == 37\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 3225\n assert candidate(obstacleGrid = [[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0]]) == 16\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]]) == 24\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0], [0, 0, 1, 0, 0], [0, 0, 1, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]]) == 5\n assert candidate(obstacleGrid = [[0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0]]) == 11\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 27\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]]) == 190\n assert candidate(obstacleGrid = [[0, 1, 0, 1, 0], [1, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 1, 0, 1, 0]]) == 0\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 2513\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 1], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]]) == 39\n assert candidate(obstacleGrid = [[0, 1, 0, 1, 0], [0, 0, 0, 0, 0], [1, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0]]) == 7\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 20\n assert candidate(obstacleGrid = [[0, 1, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]) == 2\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 0]]) == 18\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 4588\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 53812\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0]]) == 72\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 184756\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 34\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 167\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 37\n assert candidate(obstacleGrid = [[0, 0, 0, 1, 0], [0, 0, 0, 0, 0], [1, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 20\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0]]) == 20\n assert candidate(obstacleGrid = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1]]) == 0\n"}, "metadata": {"canonical_parameter_names": ["obstacleGrid"], "leetcode_dataset_entry_point": "Solution().uniquePathsWithObstacles", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var uniquePathsWithObstacles = function(obstacleGrid) {", "container": null, "callable": "uniquePathsWithObstacles", "parameters": [{"name": "obstacleGrid", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 64, "task_id": "minimum-path-sum", "difficulty": "Medium", "problem_description": "Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right, which minimizes the sum of all numbers along its path.\nNote: You can only move either down or right at any point in time.\n \nExample 1:\n\n\nInput: grid = [[1,3,1],[1,5,1],[4,2,1]]\nOutput: 7\nExplanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.\n\nExample 2:\n\nInput: grid = [[1,2,3],[4,5,6]]\nOutput: 12\n\n \nConstraints:\n\nm == grid.length\nn == grid[i].length\n1 <= m, n <= 200\n0 <= grid[i][j] <= 200\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(grid = [[1, 2, 3], [4, 5, 6]]) == 12\n assert candidate(grid = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]) == 60\n assert candidate(grid = [[10, 15, 20], [25, 30, 35], [40, 45, 50]]) == 130\n assert candidate(grid = [[1]]) == 1\n assert candidate(grid = [[7]]) == 7\n assert candidate(grid = [[1, 2], [3, 4]]) == 7\n assert candidate(grid = [[1, 2], [3, 4], [5, 6]]) == 13\n assert candidate(grid = [[1, 3, 1], [1, 5, 1], [4, 2, 1]]) == 7\n assert candidate(grid = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) == 30\n assert candidate(grid = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [1, 1, 1, 1, 1], [9, 7, 5, 3, 1]]) == 9\n assert candidate(grid = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 3, 1, 5, 1], [2, 1, 2, 3, 4]]) == 17\n assert candidate(grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]]) == 48\n assert candidate(grid = [[9, 1, 4, 3, 2], [1, 2, 5, 6, 7], [3, 6, 8, 5, 4], [2, 5, 7, 8, 1], [6, 7, 8, 9, 10]]) == 41\n assert candidate(grid = [[5, 9, 6], [11, 5, 2], [3, 12, 4], [15, 7, 8]]) == 33\n assert candidate(grid = [[7, 1, 3, 4, 2], [5, 6, 7, 2, 1], [3, 2, 1, 5, 6], [4, 3, 2, 1, 5], [6, 7, 8, 9, 1]]) == 26\n assert candidate(grid = [[10, 20, 30, 40], [20, 30, 40, 50], [30, 40, 50, 60], [40, 50, 60, 70]]) == 280\n assert candidate(grid = [[50, 40, 30, 20, 10], [45, 41, 36, 31, 21], [40, 35, 30, 25, 15], [35, 30, 25, 20, 10], [30, 25, 20, 15, 5]]) == 201\n assert candidate(grid = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]) == 46\n assert candidate(grid = [[1, 1, 1, 1, 1, 1], [1, 2, 3, 4, 5, 1], [1, 3, 5, 7, 9, 1], [1, 5, 9, 13, 17, 1], [1, 7, 15, 21, 28, 1], [1, 1, 1, 1, 1, 1]]) == 11\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == 14\n assert candidate(grid = [[5, 3, 2, 1], [1, 2, 10, 1], [4, 3, 2, 20], [7, 1, 6, 5]]) == 23\n assert candidate(grid = [[1, 5, 7, 9, 11], [2, 4, 6, 8, 10], [10, 8, 6, 4, 2], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20]]) == 64\n assert candidate(grid = [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]) == 2\n assert candidate(grid = [[9, 5, 4, 9, 6, 5, 6, 9, 8], [2, 9, 4, 7, 6, 7, 5, 7, 5], [5, 9, 9, 3, 8, 4, 7, 8, 5], [8, 4, 5, 9, 6, 7, 4, 9, 5], [6, 4, 3, 2, 7, 1, 8, 9, 5], [2, 9, 1, 5, 4, 8, 9, 1, 5], [9, 5, 5, 1, 3, 5, 1, 3, 5], [2, 9, 3, 8, 7, 5, 9, 2, 1], [9, 5, 1, 5, 3, 5, 6, 9, 5]]) == 62\n assert candidate(grid = [[1, 9, 9, 9, 9, 9, 9], [1, 1, 9, 9, 9, 9, 9], [1, 1, 1, 9, 9, 9, 9], [1, 1, 1, 1, 9, 9, 9], [1, 1, 1, 1, 1, 9, 9], [1, 1, 1, 1, 1, 1, 9], [1, 1, 1, 1, 1, 1, 1]]) == 13\n assert candidate(grid = [[9, 8, 7, 6, 5], [4, 3, 2, 1, 0], [9, 8, 7, 6, 5], [4, 3, 2, 1, 0], [9, 8, 7, 6, 5]]) == 29\n assert candidate(grid = [[0, 1, 2, 3, 4], [4, 3, 2, 1, 0], [0, 1, 2, 3, 4], [4, 3, 2, 1, 0], [0, 1, 2, 3, 4]]) == 14\n assert candidate(grid = [[1, 2, 3], [6, 5, 4], [7, 8, 9]]) == 19\n assert candidate(grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]) == 33\n assert candidate(grid = [[1, 3, 5, 7, 9, 11], [2, 4, 6, 8, 10, 12], [13, 15, 17, 19, 21, 23], [24, 22, 20, 18, 16, 14]]) == 80\n assert candidate(grid = [[9, 1, 4, 8, 7], [6, 5, 3, 2, 1], [9, 1, 4, 8, 7], [6, 5, 3, 2, 1], [9, 1, 4, 8, 7]]) == 33\n assert candidate(grid = [[20, 30, 40], [5, 15, 25], [10, 20, 30], [1, 2, 3]]) == 41\n assert candidate(grid = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]]) == 75\n assert candidate(grid = [[0, 1, 2, 3, 4, 5, 6], [6, 5, 4, 3, 2, 1, 0], [1, 3, 5, 7, 9, 11, 13], [13, 11, 9, 7, 5, 3, 1], [0, 2, 4, 6, 8, 10, 12]]) == 38\n assert candidate(grid = [[9, 8, 7, 6, 5], [4, 3, 2, 1, 0], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [9, 8, 7, 6, 5]]) == 37\n assert candidate(grid = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == 9\n assert candidate(grid = [[10, 15, 20, 25], [30, 35, 40, 45], [50, 55, 60, 65], [70, 75, 80, 85], [90, 95, 100, 105]]) == 370\n assert candidate(grid = [[1, 3, 20, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]]) == 11\n assert candidate(grid = [[7, 5, 12, 6, 8], [9, 6, 10, 3, 7], [8, 15, 4, 2, 9], [7, 11, 12, 5, 3], [6, 10, 7, 4, 8]]) == 49\n assert candidate(grid = [[7, 1, 3, 4, 1], [2, 1, 3, 1, 1], [1, 5, 1, 2, 2], [3, 2, 4, 3, 2], [4, 1, 5, 2, 3]]) == 21\n assert candidate(grid = [[100, 200, 150], [50, 100, 125], [175, 200, 250], [225, 150, 300]]) == 900\n assert candidate(grid = [[1, 4, 5, 2, 3], [1, 2, 8, 9, 3], [3, 7, 6, 2, 1], [5, 5, 4, 2, 3]]) == 22\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 1], [1, 2, 3, 3, 3, 2, 1], [1, 2, 3, 4, 3, 2, 1], [1, 2, 3, 3, 3, 2, 1], [1, 2, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1, 1]]) == 13\n assert candidate(grid = [[1, 3, 5, 7, 9, 11, 13], [2, 4, 6, 8, 10, 12, 14], [13, 11, 9, 7, 5, 3, 1], [14, 12, 10, 8, 6, 4, 2], [15, 17, 19, 21, 23, 25, 27]]) == 66\n assert candidate(grid = [[1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6]]) == 26\n assert candidate(grid = [[1, 5, 3], [2, 9, 4], [5, 6, 7], [8, 9, 10]]) == 30\n assert candidate(grid = [[5, 4, 3, 2, 1], [4, 3, 2, 1, 5], [3, 2, 1, 5, 4], [2, 1, 5, 4, 3], [1, 5, 4, 3, 2]]) == 29\n assert candidate(grid = [[1, 9, 1, 9, 1, 9], [9, 1, 9, 1, 9, 1], [1, 9, 1, 9, 1, 9], [9, 1, 9, 1, 9, 1], [1, 9, 1, 9, 1, 9]]) == 50\n assert candidate(grid = [[1, 3, 1, 5], [2, 1, 2, 1], [5, 3, 1, 1], [4, 2, 1, 1]]) == 9\n assert candidate(grid = [[0, 3, 1, 2, 9], [3, 4, 1, 3, 8], [5, 6, 7, 8, 9], [1, 9, 8, 7, 6], [9, 8, 7, 6, 5]]) == 34\n assert candidate(grid = [[200, 0, 0, 0], [0, 200, 0, 0], [0, 0, 200, 0], [0, 0, 0, 200]]) == 400\n assert candidate(grid = [[1, 1, 1, 1, 1], [1, 2, 2, 2, 1], [1, 2, 3, 2, 1], [1, 2, 2, 2, 1], [1, 1, 1, 1, 1]]) == 9\n assert candidate(grid = [[1], [1], [1], [1], [1]]) == 5\n assert candidate(grid = [[10, 3, 12, 5, 8], [7, 4, 6, 9, 2], [1, 14, 11, 13, 7], [15, 8, 10, 4, 12], [9, 6, 3, 16, 5]]) == 58\n assert candidate(grid = [[9, 1, 4, 8, 7], [6, 3, 5, 9, 2], [2, 8, 0, 1, 5], [3, 6, 9, 4, 6], [6, 8, 2, 4, 0]]) == 27\n assert candidate(grid = [[2, 1, 2, 5, 1, 2], [5, 2, 3, 1, 3, 5], [1, 1, 2, 1, 2, 1], [2, 1, 1, 1, 1, 1], [1, 1, 2, 3, 1, 1]]) == 12\n assert candidate(grid = [[5, 3, 2, 1], [6, 7, 8, 9], [1, 2, 3, 4], [5, 4, 3, 2]]) == 22\n assert candidate(grid = [[1, 2, 5], [3, 1, 1], [1, 5, 1]]) == 6\n assert candidate(grid = [[1, 9, 9, 9, 9], [1, 1, 9, 9, 9], [1, 1, 1, 9, 9], [1, 1, 1, 1, 9], [1, 1, 1, 1, 1]]) == 9\n assert candidate(grid = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 3, 5, 7, 9], [9, 7, 5, 3, 1], [2, 4, 6, 8, 10]]) == 32\n assert candidate(grid = [[1, 100, 200, 300, 400], [1, 1, 1, 1, 1], [100, 100, 100, 100, 100], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == 108\n assert candidate(grid = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]) == 0\n assert candidate(grid = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]) == 11\n assert candidate(grid = [[10, 33, 14, 7, 24], [13, 4, 7, 6, 23], [6, 15, 66, 3, 18], [8, 41, 9, 12, 32], [1, 5, 3, 9, 20]]) == 75\n assert candidate(grid = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == 85\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == 12\n assert candidate(grid = [[1, 3, 8, 7, 3, 6], [1, 1, 7, 1, 2, 8], [4, 9, 10, 5, 1, 6], [6, 7, 2, 8, 2, 5], [3, 4, 9, 1, 8, 4]]) == 25\n assert candidate(grid = [[1, 3, 1, 1], [1, 5, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]) == 7\n assert candidate(grid = [[1, 9, 1, 9, 1, 9, 1], [9, 1, 9, 1, 9, 1, 9], [1, 9, 1, 9, 1, 9, 1], [9, 1, 9, 1, 9, 1, 9], [1, 9, 1, 9, 1, 9, 1], [9, 1, 9, 1, 9, 1, 9], [1, 9, 1, 9, 1, 9, 1]]) == 61\n assert candidate(grid = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [3, 5, 7, 9, 11], [4, 6, 8, 10, 12], [5, 7, 9, 11, 13]]) == 55\n assert candidate(grid = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 0\n assert candidate(grid = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]) == 10\n assert candidate(grid = [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]) == 7\n assert candidate(grid = [[10, 11, 12, 13], [14, 15, 16, 17], [18, 19, 20, 21], [22, 23, 24, 25]]) == 109\n assert candidate(grid = [[7, 8, 9, 10, 11, 12], [6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]) == 46\n assert candidate(grid = [[100, 200, 300], [400, 500, 600], [700, 800, 900]]) == 2100\n assert candidate(grid = [[5, 3, 2, 7], [8, 6, 4, 3], [1, 2, 6, 5], [9, 7, 4, 8]]) == 30\n"}, "metadata": {"canonical_parameter_names": ["grid"], "leetcode_dataset_entry_point": "Solution().minPathSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minPathSum = function(grid) {", "container": null, "callable": "minPathSum", "parameters": [{"name": "grid", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 65, "task_id": "valid-number", "difficulty": "Hard", "problem_description": "Given a string s, return whether s is a valid number.\n\nFor example, all the following are valid numbers: \"2\", \"0089\", \"-0.1\", \"+3.14\", \"4.\", \"-.9\", \"2e10\", \"-90E3\", \"3e+7\", \"+6e-1\", \"53.5e93\", \"-123.456e789\", while the following are not valid numbers: \"abc\", \"1a\", \"1e\", \"e3\", \"99e2.5\", \"--6\", \"-+3\", \"95a54e53\".\nFormally, a valid number is defined using one of the following definitions:\n\nAn integer number followed by an optional exponent.\nA decimal number followed by an optional exponent.\n\nAn integer number is defined with an optional sign '-' or '+' followed by digits.\nA decimal number is defined with an optional sign '-' or '+' followed by one of the following definitions:\n\nDigits followed by a dot '.'.\nDigits followed by a dot '.' followed by digits.\nA dot '.' followed by digits.\n\nAn exponent is defined with an exponent notation 'e' or 'E' followed by an integer number.\nThe digits are defined as one or more digits.\n \nExample 1:\n\nInput: s = \"0\"\nOutput: true\n\nExample 2:\n\nInput: s = \"e\"\nOutput: false\n\nExample 3:\n\nInput: s = \".\"\nOutput: false\n\n \nConstraints:\n\n1 <= s.length <= 20\ns consists of only English letters (both uppercase and lowercase), digits (0-9), plus '+', minus '-', or dot '.'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"0089\") == True\n assert candidate(s = \"-123.456e789\") == True\n assert candidate(s = \"95a54e53\") == False\n assert candidate(s = \"e3\") == False\n assert candidate(s = \"4.\") == True\n assert candidate(s = \"2e10\") == True\n assert candidate(s = \"1a\") == False\n assert candidate(s = \"-+3\") == False\n assert candidate(s = \"0\") == True\n assert candidate(s = \"99e2.5\") == False\n assert candidate(s = \".\") == False\n assert candidate(s = \"-.9\") == True\n assert candidate(s = \"3e+7\") == True\n assert candidate(s = \"-90E3\") == True\n assert candidate(s = \"+3.14\") == True\n assert candidate(s = \"abc\") == False\n assert candidate(s = \"+6e-1\") == True\n assert candidate(s = \"53.5e93\") == True\n assert candidate(s = \"-0.1\") == True\n assert candidate(s = \"2\") == True\n assert candidate(s = \"1e\") == False\n assert candidate(s = \"--6\") == False\n assert candidate(s = \"e\") == False\n assert candidate(s = \"-.e+1\") == False\n assert candidate(s = \"e+10\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16\") == False\n assert candidate(s = \"1..\") == False\n assert candidate(s = \"-0.000000000000000001E-1\") == True\n assert candidate(s = \"-e\") == False\n assert candidate(s = \"1+1e1\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e-15\") == False\n assert candidate(s = \"1e+1.e-\") == False\n assert candidate(s = \"1.23456789012345678901234567890E+10\") == True\n assert candidate(s = \"+.0000000000000000001\") == True\n assert candidate(s = \"12345678901234567890.12345678901234567890\") == True\n assert candidate(s = \"1.2.3\") == False\n assert candidate(s = \"3.14159265358979323846\") == True\n assert candidate(s = \"1E1E1\") == False\n assert candidate(s = \"1.2e+2e3\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e-12\") == False\n assert candidate(s = \"--123\") == False\n assert candidate(s = \"-1.0e+0\") == True\n assert candidate(s = \".1e10\") == True\n assert candidate(s = \"1e+308\") == True\n assert candidate(s = \"-e1\") == False\n assert candidate(s = \"1.e2.e3\") == False\n assert candidate(s = \"e.1\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e-13\") == False\n assert candidate(s = \"1e+1.e+2e3\") == False\n assert candidate(s = \"1.e+2e+3e-4\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17e+18e+19e+20\") == False\n assert candidate(s = \"1e+1.e+.3\") == False\n assert candidate(s = \"+1000000000000000000000000000000.0\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17e+18e-19\") == False\n assert candidate(s = \"0.000001\") == True\n assert candidate(s = \"1.0e+0\") == True\n assert candidate(s = \"1.e+2e+3e+4\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e-9\") == False\n assert candidate(s = \"1.e2.3\") == False\n assert candidate(s = \"-0.000000000000000000e-1234567890\") == True\n assert candidate(s = \"0.000000001\") == True\n assert candidate(s = \"-00000.00000E+00000\") == True\n assert candidate(s = \"1e1000\") == True\n assert candidate(s = \"1e+1.e\") == False\n assert candidate(s = \"1e+1.e+\") == False\n assert candidate(s = \"1.2e-+3\") == False\n assert candidate(s = \"1e+1.e-2\") == False\n assert candidate(s = \"1e+1.e+2.3e4\") == False\n assert candidate(s = \"1e+1.e2.3\") == False\n assert candidate(s = \"1e+1.e+1.e2e\") == False\n assert candidate(s = \"2.e5\") == True\n assert candidate(s = \"3.14159E+0\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17e-18\") == False\n assert candidate(s = \"1.2e2.3\") == False\n assert candidate(s = \"-6.02214076E+23\") == True\n assert candidate(s = \"+0E-0\") == True\n assert candidate(s = \"1e+1.e+2\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e-10\") == False\n assert candidate(s = \"1.e+2e3\") == False\n assert candidate(s = \"1.e-+2\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17e+18\") == False\n assert candidate(s = \"-0.e-1\") == True\n assert candidate(s = \"-1.2.3e4\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5\") == False\n assert candidate(s = \"1.e+2e-3\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17\") == False\n assert candidate(s = \"+\") == False\n assert candidate(s = \"e10\") == False\n assert candidate(s = \"1e+1e\") == False\n assert candidate(s = \"9.87654321E+123\") == True\n assert candidate(s = \"e-\") == False\n assert candidate(s = \".0e-0\") == True\n assert candidate(s = \"-1.e2\") == True\n assert candidate(s = \"1e-e\") == False\n assert candidate(s = \"+.e+2\") == False\n assert candidate(s = \"3.1415926535897932384626433832795\") == True\n assert candidate(s = \"0.000000000000000000e0\") == True\n assert candidate(s = \"1e+-\") == False\n assert candidate(s = \"-+3.14159\") == False\n assert candidate(s = \"1..2\") == False\n assert candidate(s = \"-0.0001\") == True\n assert candidate(s = \"0e0\") == True\n assert candidate(s = \"1.0000000000000000000e-1\") == True\n assert candidate(s = \"-1e-99\") == True\n assert candidate(s = \"1e+1.e+1.e+2.3e4\") == False\n assert candidate(s = \"1.e+2e+3\") == False\n assert candidate(s = \"-1.e-1000\") == True\n assert candidate(s = \"12345.67890E+12345.67890\") == False\n assert candidate(s = \".000000000000000000\") == True\n assert candidate(s = \"1e+1.e+1.e+\") == False\n assert candidate(s = \"1.2e-3.2\") == False\n assert candidate(s = \"1e+1.e+1.e+.3\") == False\n assert candidate(s = \"e-.\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11\") == False\n assert candidate(s = \"-1e-20\") == True\n assert candidate(s = \"1e+99\") == True\n assert candidate(s = \"1e+1.e2\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7\") == False\n assert candidate(s = \"6.02214076E+23\") == True\n assert candidate(s = \"e.e\") == False\n assert candidate(s = \"-2.71828182845904523536028747135266249775724709369999E+0\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9\") == False\n assert candidate(s = \"-1E-10\") == True\n assert candidate(s = \".e1\") == False\n assert candidate(s = \"-0.000000000000000000e-0\") == True\n assert candidate(s = \"+1.e+2\") == True\n assert candidate(s = \"1e+1.e+-\") == False\n assert candidate(s = \"2e0\") == True\n assert candidate(s = \"e+\") == False\n assert candidate(s = \"0.123456789012345678901234567890\") == True\n assert candidate(s = \"-e-\") == False\n assert candidate(s = \"+.e\") == False\n assert candidate(s = \"1e+1.e+1.e+1.e+.3\") == False\n assert candidate(s = \"-12345678901234567890.12345678901234567890\") == True\n assert candidate(s = \"-9.e-10\") == True\n assert candidate(s = \"1e+1.e+1.e+1.e2\") == False\n assert candidate(s = \"1e+1.e+1.e+1.e+2\") == False\n assert candidate(s = \".1234567890e+123\") == True\n assert candidate(s = \"1e2.3\") == False\n assert candidate(s = \"1e+1.e+1.e\") == False\n assert candidate(s = \"123.456e+789.0\") == False\n assert candidate(s = \"-3.14159E+0\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e-14\") == False\n assert candidate(s = \"1e+1e-1\") == False\n assert candidate(s = \"1e+2+3\") == False\n assert candidate(s = \"-.\") == False\n assert candidate(s = \"1e+1.e+1.e+2e3\") == False\n assert candidate(s = \"+.e+1\") == False\n assert candidate(s = \"0e-0\") == True\n assert candidate(s = \"1E+10\") == True\n assert candidate(s = \"1.0e+10\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e-17\") == False\n assert candidate(s = \"1e+1.e+1.e-\") == False\n assert candidate(s = \"+1.2.3\") == False\n assert candidate(s = \"12345678901234567890\") == True\n assert candidate(s = \".0e1\") == True\n assert candidate(s = \"1e+1.e+1.e+-\") == False\n assert candidate(s = \"0.e+0\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13\") == False\n assert candidate(s = \"+0000.0000E-0000\") == True\n assert candidate(s = \"1e+1.e+1e2\") == False\n assert candidate(s = \"e+-\") == False\n assert candidate(s = \"+.e-1\") == False\n assert candidate(s = \"1e+1.e+1.e+1e2\") == False\n assert candidate(s = \"1e+e\") == False\n assert candidate(s = \"1e+.2\") == False\n assert candidate(s = \"+.123E+45\") == True\n assert candidate(s = \"9.99999999999999999999999999999e+99\") == True\n assert candidate(s = \"+.8\") == True\n assert candidate(s = \"1e0\") == True\n assert candidate(s = \"1E+20\") == True\n assert candidate(s = \"-00.000000e-0000\") == True\n assert candidate(s = \"1e-+2\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e-8\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e-11\") == False\n assert candidate(s = \"5.\") == True\n assert candidate(s = \"0.000000000000000000e-0\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15\") == False\n assert candidate(s = \"0000123.000456\") == True\n assert candidate(s = \"1e+1.e+1.e-2\") == False\n assert candidate(s = \".e\") == False\n assert candidate(s = \"1e+1.e+1.e+1.e-2\") == False\n assert candidate(s = \"1e2+3\") == False\n assert candidate(s = \"1e+2e\") == False\n assert candidate(s = \"e+e\") == False\n assert candidate(s = \"e-1\") == False\n assert candidate(s = \"-0.00000000000000000000000000001\") == True\n assert candidate(s = \"-5.55555555555555555555555555555E-55\") == True\n assert candidate(s = \"1e+1.2\") == False\n assert candidate(s = \"0000000000000000000.000000000000000000\") == True\n assert candidate(s = \".0e+0\") == True\n assert candidate(s = \"123e\") == False\n assert candidate(s = \"1e+1.e+1.e+1.e2e\") == False\n assert candidate(s = \"1e-0\") == True\n assert candidate(s = \"2.71828182845904523536028747135266249775724709369999E+0\") == True\n assert candidate(s = \"0.E-00000\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e-6\") == False\n assert candidate(s = \"-12345678901234567890E-1234567890\") == True\n assert candidate(s = ('-.',)) == False\n assert candidate(s = \".0000000000000000001\") == True\n assert candidate(s = \"0.000000000000000001\") == True\n assert candidate(s = \"1e++2\") == False\n assert candidate(s = \"1e2e3\") == False\n assert candidate(s = \"1e+1.e+1.e+1.e\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14\") == False\n assert candidate(s = \".0\") == True\n assert candidate(s = \"-12345678901234567890.1234567890\") == True\n assert candidate(s = \"00000.00000e+00000\") == True\n assert candidate(s = \"1e.+2\") == False\n assert candidate(s = \"123.4567890123456789e+987654321.0\") == False\n assert candidate(s = \"1.234567890123456789\") == True\n assert candidate(s = \"-0.000000000000000000E+00000\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12\") == False\n assert candidate(s = \"12345678901234567890e-1234567890\") == True\n assert candidate(s = \"1e+1.e+1.e+1.e+2.3e4\") == False\n assert candidate(s = \"1.e+1\") == True\n assert candidate(s = \"+.e+\") == False\n assert candidate(s = \"1e--2\") == False\n assert candidate(s = \"1.e+2e+3e+4e-5\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8\") == False\n assert candidate(s = \"12345678901234567890E+1234567890\") == True\n assert candidate(s = \"e.\") == False\n assert candidate(s = \"123.456.789\") == False\n assert candidate(s = \"1.e-1\") == True\n assert candidate(s = \"1.2e+2.e3\") == False\n assert candidate(s = \"-.e-1\") == False\n assert candidate(s = \".e-10\") == False\n assert candidate(s = \"0.e-0\") == True\n assert candidate(s = \"999999999999999999e-1\") == True\n assert candidate(s = \"1e-+\") == False\n assert candidate(s = \"+.0\") == True\n assert candidate(s = \"1e+1e+2\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6\") == False\n assert candidate(s = \"00000.00000e-00000\") == True\n assert candidate(s = \"1.e+2.3\") == False\n assert candidate(s = \"0.000000000000000000e+0\") == True\n assert candidate(s = \"+1e-10\") == True\n assert candidate(s = \"1e+-2\") == False\n assert candidate(s = \"1e.e\") == False\n assert candidate(s = \"1e+1.e+1.e2\") == False\n assert candidate(s = \"+.1234567890123456789e+10\") == True\n assert candidate(s = \"1e+1.e+1.e+2\") == False\n assert candidate(s = \"1e-.2\") == False\n assert candidate(s = \"00000000000000000000\") == True\n assert candidate(s = \"1.2e-3e2\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17e+18e+19e-20\") == False\n assert candidate(s = \".e-\") == False\n assert candidate(s = \"1.23.45\") == False\n assert candidate(s = \"1000000000000000000.0\") == True\n assert candidate(s = \"-1.23456789E+987654321\") == True\n assert candidate(s = \"-.0000000000000000001\") == True\n assert candidate(s = \"1.e+2.e3\") == False\n assert candidate(s = \"+0.000000000000000000e+0\") == True\n assert candidate(s = \"3.141592653589793\") == True\n assert candidate(s = \"123E123E123\") == False\n assert candidate(s = \"-9.87654321E-123\") == True\n assert candidate(s = \"+0.E+0\") == True\n assert candidate(s = \"123e-456\") == True\n assert candidate(s = \"-9.87654321e-987\") == True\n assert candidate(s = \"-\") == False\n assert candidate(s = \"0e+0\") == True\n assert candidate(s = \"1.234E+10\") == True\n assert candidate(s = \"1e-308\") == True\n assert candidate(s = \"1e-+1\") == False\n assert candidate(s = \"000000.000000e0000\") == True\n assert candidate(s = \"1.0E+1.0\") == False\n assert candidate(s = \"000000000\") == True\n assert candidate(s = \"1.e\") == False\n assert candidate(s = \"-9876543210e+987654321\") == True\n assert candidate(s = \"-.e-2\") == False\n assert candidate(s = \"1.e+-2\") == False\n assert candidate(s = \"123456789012345678901234567890.\") == True\n assert candidate(s = \"+-123\") == False\n assert candidate(s = \"1.2e+2.3\") == False\n assert candidate(s = \"e1\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e-16\") == False\n assert candidate(s = \"1.234e+10\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e-7\") == False\n assert candidate(s = \".1234567890\") == True\n assert candidate(s = \"1.e+\") == False\n assert candidate(s = \"9.9e99\") == True\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10e+11e+12e+13e+14e+15e+16e+17e+18e+19\") == False\n assert candidate(s = \"123.e+10\") == True\n assert candidate(s = \"1.e+2.3e4\") == False\n assert candidate(s = \"-1.0000000000000000000e-1\") == True\n assert candidate(s = \"-123.4567890123456789E+123456789\") == True\n assert candidate(s = \"-9.99999999999999999999999999999e-99\") == True\n assert candidate(s = \"1e+\") == False\n assert candidate(s = \"1e.-2\") == False\n assert candidate(s = \"1.e+.3\") == False\n assert candidate(s = \"3.14159E-10\") == True\n assert candidate(s = \"0e-5\") == True\n assert candidate(s = \"-0000.0000E+0000\") == True\n assert candidate(s = \".1234567890123456789E-987654321\") == True\n assert candidate(s = \".e+\") == False\n assert candidate(s = \"1.e+2e+3e+4e+5e+6e+7e+8e+9e+10\") == False\n assert candidate(s = \"e+1e2\") == False\n assert candidate(s = \"1e+1.e2e\") == False\n assert candidate(s = \"+.\") == False\n assert candidate(s = \"1e+1.e+1.e+1.e+2e3\") == False\n assert candidate(s = \"+.1e1\") == True\n assert candidate(s = \"0.0000001e+10\") == True\n assert candidate(s = \"1.2.3.4\") == False\n assert candidate(s = \"2e-300\") == True\n assert candidate(s = \"-1.e-2\") == True\n assert candidate(s = \"4.2e\") == False\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().isNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isNumber = function(s) {", "container": null, "callable": "isNumber", "parameters": [{"name": "s", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 66, "task_id": "plus-one", "difficulty": "Easy", "problem_description": "You are given a large integer represented as an integer array digits, where each digits[i] is the ith digit of the integer. The digits are ordered from most significant to least significant in left-to-right order. The large integer does not contain any leading 0's.\nIncrement the large integer by one and return the resulting array of digits.\n \nExample 1:\n\nInput: digits = [1,2,3]\nOutput: [1,2,4]\nExplanation: The array represents the integer 123.\nIncrementing by one gives 123 + 1 = 124.\nThus, the result should be [1,2,4].\n\nExample 2:\n\nInput: digits = [4,3,2,1]\nOutput: [4,3,2,2]\nExplanation: The array represents the integer 4321.\nIncrementing by one gives 4321 + 1 = 4322.\nThus, the result should be [4,3,2,2].\n\nExample 3:\n\nInput: digits = [9]\nOutput: [1,0]\nExplanation: The array represents the integer 9.\nIncrementing by one gives 9 + 1 = 10.\nThus, the result should be [1,0].\n\n \nConstraints:\n\n1 <= digits.length <= 100\n0 <= digits[i] <= 9\ndigits does not contain any leading 0's.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(digits = [5, 8, 9, 9, 9]) == [5, 9, 0, 0, 0]\n assert candidate(digits = [2, 0, 0, 0, 0]) == [2, 0, 0, 0, 1]\n assert candidate(digits = [1, 0, 0, 0]) == [1, 0, 0, 1]\n assert candidate(digits = [1, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [2, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 2, 3]) == [1, 2, 4]\n assert candidate(digits = [1, 2, 9]) == [1, 3, 0]\n assert candidate(digits = [9]) == [1, 0]\n assert candidate(digits = [2, 9, 9]) == [3, 0, 0]\n assert candidate(digits = [5, 6, 7, 8, 9]) == [5, 6, 7, 9, 0]\n assert candidate(digits = [4, 3, 2, 1]) == [4, 3, 2, 2]\n assert candidate(digits = [0]) == [1]\n assert candidate(digits = [1, 0, 0]) == [1, 0, 1]\n assert candidate(digits = [1, 9, 9, 9, 9]) == [2, 0, 0, 0, 0]\n assert candidate(digits = [5, 6, 8, 6, 9, 9, 4, 9, 3, 9]) == [5, 6, 8, 6, 9, 9, 4, 9, 4, 0]\n assert candidate(digits = [0, 0, 0, 1]) == [0, 0, 0, 2]\n assert candidate(digits = [9, 9, 9]) == [1, 0, 0, 0]\n assert candidate(digits = [1, 9, 9]) == [2, 0, 0]\n assert candidate(digits = [8, 9, 9, 9]) == [9, 0, 0, 0]\n assert candidate(digits = [1, 8, 6, 4, 5, 2, 3, 7, 9, 1]) == [1, 8, 6, 4, 5, 2, 3, 7, 9, 2]\n assert candidate(digits = [1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7]\n assert candidate(digits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 2]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5]) == [5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 6]\n assert candidate(digits = [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [8, 9, 9, 9, 9, 9, 9, 9, 9, 8, 9]) == [8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0]\n assert candidate(digits = [9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 1]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [1, 8, 7, 6, 5, 4, 3, 2, 1, 1]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 9, 0]\n assert candidate(digits = [3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3]) == [3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 4]\n assert candidate(digits = [0, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [2, 4, 9, 9, 9, 9, 9, 9, 9, 9]) == [2, 5, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [9, 0, 9, 0, 9, 0, 9, 0, 9, 0]) == [9, 0, 9, 0, 9, 0, 9, 0, 9, 1]\n assert candidate(digits = [0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1]\n assert candidate(digits = [2, 5, 9, 9, 9, 9, 9]) == [2, 6, 0, 0, 0, 0, 0]\n assert candidate(digits = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 0]\n assert candidate(digits = [5, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [5, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3]) == [4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 4]\n assert candidate(digits = [8, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [9, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [2, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [3, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 9]) == [1, 2, 3, 4, 5, 6, 7, 9, 0, 0]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [1, 2, 3, 4, 5, 6, 7, 9, 0]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9]) == [8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 9, 0]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1]\n assert candidate(digits = [2, 4, 6, 8, 0, 1, 3, 5, 7, 9]) == [2, 4, 6, 8, 0, 1, 3, 5, 8, 0]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4]\n assert candidate(digits = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == [1, 0, 1, 0, 1, 0, 1, 0, 1, 1]\n assert candidate(digits = [1, 0, 0, 0, 0]) == [1, 0, 0, 0, 1]\n assert candidate(digits = [1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8]\n assert candidate(digits = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [7, 8, 9, 9, 9, 9, 9, 9, 9, 8, 7]) == [7, 8, 9, 9, 9, 9, 9, 9, 9, 8, 8]\n assert candidate(digits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]\n assert candidate(digits = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(digits = [5, 9, 5, 9, 5, 9, 5, 9, 5, 9]) == [5, 9, 5, 9, 5, 9, 5, 9, 6, 0]\n assert candidate(digits = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 1]\n assert candidate(digits = [0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0]) == [0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1]\n assert candidate(digits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n assert candidate(digits = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7, 7, 7, 7, 7, 7, 7, 7, 7, 8]\n"}, "metadata": {"canonical_parameter_names": ["digits"], "leetcode_dataset_entry_point": "Solution().plusOne", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var plusOne = function(digits) {", "container": null, "callable": "plusOne", "parameters": [{"name": "digits", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 67, "task_id": "add-binary", "difficulty": "Easy", "problem_description": "Given two binary strings a and b, return their sum as a binary string.\n \nExample 1:\nInput: a = \"11\", b = \"1\"\nOutput: \"100\"\nExample 2:\nInput: a = \"1010\", b = \"1011\"\nOutput: \"10101\"\n\n \nConstraints:\n\n1 <= a.length, b.length <= 104\na and b consist only of '0' or '1' characters.\nEach string does not contain leading zeros except for the zero itself.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(a = \"11\",b = \"1\") == \"100\"\n assert candidate(a = \"1101001\",b = \"1000111\") == \"10110000\"\n assert candidate(a = \"1101\",b = \"1001\") == \"10110\"\n assert candidate(a = \"1000000000000000000000000000000\",b = \"1\") == \"1000000000000000000000000000001\"\n assert candidate(a = \"1000\",b = \"1100\") == \"10100\"\n assert candidate(a = \"1111\",b = \"1\") == \"10000\"\n assert candidate(a = \"1\",b = \"11111111\") == \"100000000\"\n assert candidate(a = \"110010\",b = \"100111\") == \"1011001\"\n assert candidate(a = \"1111\",b = \"1111\") == \"11110\"\n assert candidate(a = \"111\",b = \"111\") == \"1110\"\n assert candidate(a = \"0\",b = \"101010\") == \"101010\"\n assert candidate(a = \"1\",b = \"1\") == \"10\"\n assert candidate(a = \"1001\",b = \"10\") == \"1011\"\n assert candidate(a = \"1010\",b = \"1011\") == \"10101\"\n assert candidate(a = \"0\",b = \"0\") == \"0\"\n assert candidate(a = \"1\",b = \"0\") == \"1\"\n assert candidate(a = \"1100101\",b = \"100010\") == \"10000111\"\n assert candidate(a = \"1111111111\",b = \"1111111111\") == \"11111111110\"\n assert candidate(a = \"11111111111111111111\",b = \"10101010101010101010\") == \"110101010101010101001\"\n assert candidate(a = \"11111111111111111111\",b = \"1\") == \"100000000000000000000\"\n assert candidate(a = \"1001001001001001001001001001001001001001001001001001001001001001001001001001\",b = \"1111111111111111111111111111111111111111111111111111111111111111111111111111\") == \"11001001001001001001001001001001001001001001001001001001001001001001001001000\"\n assert candidate(a = \"1101100101\",b = \"1010011011\") == \"11000000000\"\n assert candidate(a = \"11111111111111111111111111111111\",b = \"1\") == \"100000000000000000000000000000000\"\n assert candidate(a = \"1010101010101010101010101010101010101010101010101010\",b = \"1010101010101010101010101010101010101010101010101010\") == \"10101010101010101010101010101010101010101010101010100\"\n assert candidate(a = \"11111111111111111111\",b = \"11111111111111111111\") == \"111111111111111111110\"\n assert candidate(a = \"10101010101010101010\",b = \"01010101010101010101\") == \"11111111111111111111\"\n assert candidate(a = \"11110000000000000000\",b = \"11110000000000000000\") == \"111100000000000000000\"\n assert candidate(a = \"11011010101110110001110011100001111111011000111100111101\",b = \"11101010101110110001110011100001111111011000111100111100\") == \"111000101011101100011100111000011111110110001111001111001\"\n assert candidate(a = \"1\",b = \"1111111111111111111111111111111\") == \"10000000000000000000000000000000\"\n assert candidate(a = \"1100110011001100110011001100110011001100110011001100\",b = \"1\") == \"1100110011001100110011001100110011001100110011001101\"\n assert candidate(a = \"1010101010\",b = \"1010101010\") == \"10101010100\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111111111111111\",b = \"1000000000000000000000000000000000000000000000000000000000000000\") == \"10111111111111111111111111111111111111111111111111111111111111111\"\n assert candidate(a = \"100000000000000000000000000000000\",b = \"100000000000000000000000000000000\") == \"1000000000000000000000000000000000\"\n assert candidate(a = \"10000000000000000000000000000000\",b = \"1\") == \"10000000000000000000000000000001\"\n assert candidate(a = \"10000000000000000000000000000000000000000000000000000000000000000\",b = \"1\") == \"10000000000000000000000000000000000000000000000000000000000000001\"\n assert candidate(a = \"1010101010101010101010101010\",b = \"0101010101010101010101010101\") == \"1111111111111111111111111111\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111111111111111\",b = \"10\") == \"10000000000000000000000000000000000000000000000000000000000000001\"\n assert candidate(a = \"10110110110110110110\",b = \"10011001100110011001\") == \"101010000011101001111\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111111111111111\",b = \"1111111111111111111111111111111111111111111111111111111111111111\") == \"11111111111111111111111111111111111111111111111111111111111111110\"\n assert candidate(a = \"1\",b = \"10000000000000000000000000000000\") == \"10000000000000000000000000000001\"\n assert candidate(a = \"1010101010101010101010101010101\",b = \"1010101010101010101010101010101\") == \"10101010101010101010101010101010\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111111111111111\",b = \"1\") == \"10000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(a = \"10101010101010101010101010101010\",b = \"1\") == \"10101010101010101010101010101011\"\n assert candidate(a = \"11100001110001110001110001110001\",b = \"11110000111100001111000011110000\") == \"111010010101110000000110101100001\"\n assert candidate(a = \"1\",b = \"11111111111111111111111111111111\") == \"100000000000000000000000000000000\"\n assert candidate(a = \"11000000000000000000000000000000\",b = \"11000000000000000000000000000000\") == \"110000000000000000000000000000000\"\n assert candidate(a = \"1101010101010101010101010101010101010101010101010101010101010101\",b = \"1010101010101010101010101010101010101010101010101010101010101010\") == \"10111111111111111111111111111111111111111111111111111111111111111\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111111111111111\",b = \"1000000000000000000000000000000000000000000000000000000000000001\") == \"11000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(a = \"11001100110011001100\",b = \"11110000111100001111\") == \"110111101101111011011\"\n assert candidate(a = \"11011011011011011011011011011011\",b = \"10101010101010101010101010101010\") == \"110000110000110000110000110000101\"\n assert candidate(a = \"10101010101010101010101010101010\",b = \"11111111111111111111111111111111\") == \"110101010101010101010101010101001\"\n assert candidate(a = \"10101010101010101010101010101010\",b = \"101010101010101010101010101010101\") == \"111111111111111111111111111111111\"\n assert candidate(a = \"1111111111111111111111111111110\",b = \"1\") == \"1111111111111111111111111111111\"\n assert candidate(a = \"1\",b = \"10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\") == \"10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\"\n assert candidate(a = \"101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010\",b = \"101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010\") == \"1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010100\"\n assert candidate(a = \"111111111111111111111111111111111\",b = \"1\") == \"1000000000000000000000000000000000\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111\",b = \"1\") == \"10000000000000000000000000000000000000000000000000000\"\n assert candidate(a = \"1010101010101010\",b = \"0101010101010101\") == \"1111111111111111\"\n assert candidate(a = \"10000000000000000000000000000000\",b = \"11111111111111111111111111111111\") == \"101111111111111111111111111111111\"\n assert candidate(a = \"10010010010010010010010010010010\",b = \"10010010010010010010010010010010\") == \"100100100100100100100100100100100\"\n assert candidate(a = \"1010101010101010101010101010101010101010101010101010101010101010\",b = \"1010101010101010101010101010101010101010101010101010101010101010\") == \"10101010101010101010101010101010101010101010101010101010101010100\"\n assert candidate(a = \"1111000011110000\",b = \"0000111100001111\") == \"1111111111111111\"\n assert candidate(a = \"10000000000000000000\",b = \"11111111111111111111\") == \"101111111111111111111\"\n assert candidate(a = \"1000000000000000000000000000000000000000000000000000000000000000\",b = \"1000000000000000000000000000000000000000000000000000000000000001\") == \"10000000000000000000000000000000000000000000000000000000000000001\"\n assert candidate(a = \"110011001100110011001100\",b = \"001100110011001100110011\") == \"111111111111111111111111\"\n assert candidate(a = \"11001100110011001100110011001100\",b = \"11001100110011001100110011001100\") == \"110011001100110011001100110011000\"\n assert candidate(a = \"10011100111001110011100111001110\",b = \"11100011100011100011100011100011\") == \"110000000011101010111001010110001\"\n assert candidate(a = \"11000000000000000000000000000000\",b = \"1\") == \"11000000000000000000000000000001\"\n assert candidate(a = \"10000000000000000000\",b = \"10000000000000000000\") == \"100000000000000000000\"\n assert candidate(a = \"1110001110001110\",b = \"0001110001110001\") == \"1111111111111111\"\n assert candidate(a = \"11001100110011001100110011001100110011001100110011001100110011001100\",b = \"1010101010101010101010101010101010101010101010101010101010101010101\") == \"100100010001000100010001000100010001000100010001000100010001000100001\"\n assert candidate(a = \"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\",b = \"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\") == \"11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110\"\n assert candidate(a = \"11001100110011001100\",b = \"11001100110011001100\") == \"110011001100110011000\"\n assert candidate(a = \"11111111111111111111111111111111\",b = \"11111111111111111111111111111111\") == \"111111111111111111111111111111110\"\n assert candidate(a = \"10101010101010101010\",b = \"10101010101010101010\") == \"101010101010101010100\"\n assert candidate(a = \"11011011011011011011\",b = \"10010010010010010010\") == \"101101101101101101101\"\n assert candidate(a = \"1\",b = \"1100000000000000000000000000000000000000000000000000000000000000\") == \"1100000000000000000000000000000000000000000000000000000000000001\"\n assert candidate(a = \"1100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110\",b = \"10101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010\") == \"1100110011100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010000\"\n assert candidate(a = \"10110110110110110110\",b = \"01001001001001001001\") == \"11111111111111111111\"\n assert candidate(a = \"1000000000000000000000000000000\",b = \"1000000000000000000000000000000\") == \"10000000000000000000000000000000\"\n assert candidate(a = \"11100011100011100011100011100011\",b = \"11100011100011100011100011100011\") == \"111000111000111000111000111000110\"\n assert candidate(a = \"10101010101010101010101010101010\",b = \"10101010101010101010101010101010\") == \"101010101010101010101010101010100\"\n assert candidate(a = \"11010101010101010101\",b = \"10101010101010101010\") == \"101111111111111111111\"\n assert candidate(a = \"10101010101010101010101010101010101010101010101010101010101010101\",b = \"10101010101010101010101010101010101010101010101010101010101010101\") == \"101010101010101010101010101010101010101010101010101010101010101010\"\n assert candidate(a = \"1111111111\",b = \"1\") == \"10000000000\"\n assert candidate(a = \"1101010101010101010101010101010101010101010101010101010101010101\",b = \"1010101010101010101010101010101010101010101010101010101010101011\") == \"11000000000000000000000000000000000000000000000000000000000000000\"\n"}, "metadata": {"canonical_parameter_names": ["a", "b"], "leetcode_dataset_entry_point": "Solution().addBinary", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var addBinary = function(a, b) {", "container": null, "callable": "addBinary", "parameters": [{"name": "a", "type": "string"}, {"name": "b", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 68, "task_id": "text-justification", "difficulty": "Hard", "problem_description": "Given an array of strings words and a width maxWidth, format the text such that each line has exactly maxWidth characters and is fully (left and right) justified.\nYou should pack your words in a greedy approach; that is, pack as many words as you can in each line. Pad extra spaces ' ' when necessary so that each line has exactly maxWidth characters.\nExtra spaces between words should be distributed as evenly as possible. If the number of spaces on a line does not divide evenly between words, the empty slots on the left will be assigned more spaces than the slots on the right.\nFor the last line of text, it should be left-justified, and no extra space is inserted between words.\nNote:\n\nA word is defined as a character sequence consisting of non-space characters only.\nEach word's length is guaranteed to be greater than 0 and not exceed maxWidth.\nThe input array words contains at least one word.\n\n \nExample 1:\n\nInput: words = [\"This\", \"is\", \"an\", \"example\", \"of\", \"text\", \"justification.\"], maxWidth = 16\nOutput:\n[\n   \"This    is    an\",\n   \"example  of text\",\n   \"justification.  \"\n]\nExample 2:\n\nInput: words = [\"What\",\"must\",\"be\",\"acknowledgment\",\"shall\",\"be\"], maxWidth = 16\nOutput:\n[\n  \"What   must   be\",\n  \"acknowledgment  \",\n  \"shall be        \"\n]\nExplanation: Note that the last line is \"shall be \" instead of \"shall be\", because the last line must be left-justified instead of fully-justified.\nNote that the second line is also left-justified because it contains only one word.\nExample 3:\n\nInput: words = [\"Science\",\"is\",\"what\",\"we\",\"understand\",\"well\",\"enough\",\"to\",\"explain\",\"to\",\"a\",\"computer.\",\"Art\",\"is\",\"everything\",\"else\",\"we\",\"do\"], maxWidth = 20\nOutput:\n[\n  \"Science  is  what we\",\n \"understand      well\",\n  \"enough to explain to\",\n  \"a  computer.  Art is\",\n  \"everything  else  we\",\n  \"do                  \"\n]\n \nConstraints:\n\n1 <= words.length <= 300\n1 <= words[i].length <= 20\nwords[i] consists of only English letters and symbols.\n1 <= maxWidth <= 100\nwords[i].length <= maxWidth\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(words = ['Try', 'your', 'best', 'to', 'be', 'like', 'them', 'at', 'best', 'you', 'can', 'be', 'like', 'them.'],maxWidth = 20) == ['Try your best to be', 'like them at best', 'you can be like', 'them. ']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e'],maxWidth = 3) == ['a b', 'c d', 'e ']\n assert candidate(words = ['What', 'must', 'be', 'acknowledgment', 'shall', 'be'],maxWidth = 16) == ['What must be', 'acknowledgment ', 'shall be ']\n assert candidate(words = ['Listen', 'to', 'many', 'people', 'so', 'that', 'you', 'can', 'speak', 'to', 'none.'],maxWidth = 15) == ['Listen to many', 'people so that', 'you can speak', 'to none. ']\n assert candidate(words = ['short', 'longwordhere', 'longwordhere', 'short'],maxWidth = 20) == ['short longwordhere', 'longwordhere short ']\n assert candidate(words = ['a'],maxWidth = 2) == ['a ']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e'],maxWidth = 3) == ['a b', 'c d', 'e ']\n assert candidate(words = ['Science', 'is', 'what', 'we', 'understand', 'well', 'enough', 'to', 'explain', 'to', 'a', 'computer.', 'Art', 'is', 'everything', 'else', 'we', 'do'],maxWidth = 20) == ['Science is what we', 'understand well', 'enough to explain to', 'a computer. Art is', 'everything else we', 'do ']\n assert candidate(words = ['Listen', 'to', 'many', 'people', 'so', 'you', 'can', 'speak', 'to', 'all', 'people'],maxWidth = 7) == ['Listen ', 'to many', 'people ', 'so you', 'can ', 'speak ', 'to all', 'people ']\n assert candidate(words = ['This', 'is', 'an', 'example', 'of', 'text', 'justification.'],maxWidth = 16) == ['This is an', 'example of text', 'justification. ']\n assert candidate(words = ['Lorem', 'ipsum', 'dolor', 'sit', 'amet,', 'consectetur', 'adipiscing', 'elit.', 'Vestibulum', 'bibendum', 'porttitor', 'diam,'],maxWidth = 20) == ['Lorem ipsum dolor', 'sit amet,', 'consectetur ', 'adipiscing elit.', 'Vestibulum bibendum', 'porttitor diam, ']\n assert candidate(words = ['Even', 'though', 'the', 'path', 'may', 'seem', 'long', 'and', 'difficult.'],maxWidth = 18) == ['Even though the', 'path may seem long', 'and difficult. ']\n assert candidate(words = ['OneWordHereIsVeryLongIndeedAndItWillCauseSomeIssuesWithTheAlgorithmIfNotHandledProperly'],maxWidth = 50) == ['OneWordHereIsVeryLongIndeedAndItWillCauseSomeIssuesWithTheAlgorithmIfNotHandledProperly']\n assert candidate(words = ['Longer', 'words', 'and', 'evenlongerwords', 'are', 'here'],maxWidth = 25) == ['Longer words and', 'evenlongerwords are here ']\n assert candidate(words = ['Pack', 'my', 'box', 'with', 'five', 'dozen', 'liquor', 'jugs'],maxWidth = 20) == ['Pack my box with', 'five dozen liquor', 'jugs ']\n assert candidate(words = ['In', 'the', 'middle', 'of', 'the', 'night', 'the', 'old', 'owl', 'wisely', 'spread', 'his', 'wings'],maxWidth = 35) == ['In the middle of the night the old', 'owl wisely spread his wings ']\n assert candidate(words = ['Do', 'what', 'you', 'can', 'with', 'all', 'you', 'have,', 'wherever', 'you', 'are.'],maxWidth = 23) == ['Do what you can with', 'all you have, wherever', 'you are. ']\n assert candidate(words = ['Keep', 'your', 'face', 'always', 'toward', 'the', 'sunset.'],maxWidth = 21) == ['Keep your face always', 'toward the sunset. ']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't'],maxWidth = 5) == ['a b c', 'd e f', 'g h i', 'j k l', 'm n o', 'p q r', 's t ']\n assert candidate(words = ['Look', 'into', 'the', 'distance', 'where', 'you', 'can', 'see', 'the', 'futuristic', 'cityscape'],maxWidth = 35) == ['Look into the distance where you', 'can see the futuristic cityscape ']\n assert candidate(words = ['Why', 'do', 'we', 'fall', 'ape', 'not', 'to', 'rise'],maxWidth = 8) == ['Why do', 'we fall', 'ape not', 'to rise ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be', 'that', 'is', 'the', 'question'],maxWidth = 12) == ['To be or not', 'to be that', 'is the', 'question ']\n assert candidate(words = ['Listen', 'to', 'many,', 'speak', 'to', 'a', 'few.'],maxWidth = 15) == ['Listen to many,', 'speak to a few.']\n assert candidate(words = ['Success', 'is', 'not', 'final,', 'failure', 'is', 'not', 'fatal:', 'It', 'is', 'the', 'courage', 'to', 'continue', 'that', 'counts.'],maxWidth = 25) == ['Success is not final,', 'failure is not fatal: It', 'is the courage to', 'continue that counts. ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be', 'that', 'is', 'the', 'question'],maxWidth = 15) == ['To be or not to', 'be that is the', 'question ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be,that', 'is', 'the', 'question:'],maxWidth = 10) == ['To be or', 'not to', 'be,that is', 'the ', 'question: ']\n assert candidate(words = ['Python', 'programming', 'is', 'fun,and', 'effective.'],maxWidth = 25) == ['Python programming is', 'fun,and effective. ']\n assert candidate(words = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'],maxWidth = 5) == ['A B C', 'D E F', 'G H I', 'J ']\n assert candidate(words = ['Programming', 'is', 'not', 'about', 'what', 'you', 'know;', 'it', 'is', 'about', 'what', 'you', 'can', 'figure', 'out.'],maxWidth = 25) == ['Programming is not about', 'what you know; it is', 'about what you can figure', 'out. ']\n assert candidate(words = ['One', 'ring', 'to', 'rule', 'them', 'all,', 'One', 'ring', 'to', 'find', 'them.'],maxWidth = 18) == ['One ring to rule', 'them all, One ring', 'to find them. ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be,', 'that', 'is', 'the', 'question:'],maxWidth = 25) == ['To be or not to be, that', 'is the question: ']\n assert candidate(words = ['Left', 'justified', 'line'],maxWidth = 30) == ['Left justified line ']\n assert candidate(words = ['In', 'order', 'to', 'write', 'about', 'life,', 'one', 'must', 'live', 'it.'],maxWidth = 22) == ['In order to write', 'about life, one must', 'live it. ']\n assert candidate(words = ['The', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog'],maxWidth = 20) == ['The quick brown fox', 'jumps over the lazy', 'dog ']\n assert candidate(words = ['Sometimes', 'the', 'wisest', 'course', 'requires', 'a', 'great', 'deal', 'of', 'courage'],maxWidth = 25) == ['Sometimes the wisest', 'course requires a great', 'deal of courage ']\n assert candidate(words = ['The', 'only', 'way', 'to', 'do', 'great', 'work', 'is', 'to', 'love', 'what', 'you', 'do.'],maxWidth = 25) == ['The only way to do great', 'work is to love what you', 'do. ']\n assert candidate(words = ['How', 'much', 'wood', 'would', 'a', 'woodchuck', 'chuck', 'if', 'a', 'woodchuck', 'could', 'chuck', 'wood'],maxWidth = 20) == ['How much wood would', 'a woodchuck chuck if', 'a woodchuck could', 'chuck wood ']\n assert candidate(words = ['Sometimes', 'you', 'have', 'to', 'run', 'before', 'you', 'can', 'walk'],maxWidth = 20) == ['Sometimes you have', 'to run before you', 'can walk ']\n assert candidate(words = ['So', 'musing', 'on', 'the', 'marvel', 'of', 'this', 'theatre,'],maxWidth = 25) == ['So musing on the marvel', 'of this theatre, ']\n assert candidate(words = ['Knowledge', 'is', 'a', 'treasure,', 'and', 'practice', 'is', 'the', 'key', 'to', 'mastering', 'it.'],maxWidth = 28) == ['Knowledge is a treasure, and', 'practice is the key to', 'mastering it. ']\n assert candidate(words = ['Do', 'not', 'wait', 'to', 'strike', 'till', 'the', 'iron', 'is', 'hot;', 'but', 'make', 'it', 'hot', 'by', 'striking.'],maxWidth = 22) == ['Do not wait to strike', 'till the iron is hot;', 'but make it hot by', 'striking. ']\n assert candidate(words = ['Just', 'one', 'word'],maxWidth = 50) == ['Just one word ']\n assert candidate(words = ['The', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog.'],maxWidth = 15) == ['The quick brown', 'fox jumps over', 'the lazy dog. ']\n assert candidate(words = ['Lorem', 'ipsum', 'dolor', 'sit', 'amet,', 'consectetur', 'adipiscing', 'elit'],maxWidth = 20) == ['Lorem ipsum dolor', 'sit amet,', 'consectetur ', 'adipiscing elit ']\n assert candidate(words = ['The', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog'],maxWidth = 15) == ['The quick brown', 'fox jumps over', 'the lazy dog ']\n assert candidate(words = ['a', 'very', 'long', 'sentence', 'that', 'needs', 'to', 'be', 'formatted', 'correctly', 'with', 'various', 'spaces'],maxWidth = 10) == ['a very', 'long ', 'sentence ', 'that needs', 'to be', 'formatted ', 'correctly ', 'with ', 'various ', 'spaces ']\n assert candidate(words = ['Lorem', 'ipsum', 'dolor', 'sit', 'amet,', 'consectetur', 'adipiscing', 'elit.'],maxWidth = 12) == ['Lorem ipsum', 'dolor sit', 'amet, ', 'consectetur ', 'adipiscing ', 'elit. ']\n assert candidate(words = ['There', 'is', 'no', 'royal', 'road', 'to', 'learning.'],maxWidth = 20) == ['There is no royal', 'road to learning. ']\n assert candidate(words = ['word'],maxWidth = 1) == ['word']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o'],maxWidth = 5) == ['a b c', 'd e f', 'g h i', 'j k l', 'm n o']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be', 'that', 'is', 'the', 'question'],maxWidth = 15) == ['To be or not to', 'be that is the', 'question ']\n assert candidate(words = ['A', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog.'],maxWidth = 15) == ['A quick brown', 'fox jumps over', 'the lazy dog. ']\n assert candidate(words = ['Short', 'words', 'only'],maxWidth = 5) == ['Short', 'words', 'only ']\n assert candidate(words = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'],maxWidth = 5) == ['A B C', 'D E F', 'G H I', 'J K L', 'M N O', 'P Q R', 'S T U', 'V W X', 'Y Z ']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z'],maxWidth = 6) == ['a b c', 'd e f', 'g h i', 'j k l', 'm n o', 'p q r', 's t u', 'v w x', 'y z ']\n assert candidate(words = ['The', 'best', 'way', 'to', 'predict', 'the', 'future', 'is', 'to', 'create', 'it.'],maxWidth = 20) == ['The best way to', 'predict the future', 'is to create it. ']\n assert candidate(words = ['SingleWord'],maxWidth = 10) == ['SingleWord']\n assert candidate(words = ['Failure', 'is', 'not', 'the', 'opposite', 'of', 'success;', 'it', 'is', 'part', 'of', 'success.'],maxWidth = 30) == ['Failure is not the opposite of', 'success; it is part of', 'success. ']\n assert candidate(words = ['Lorem', 'ipsum', 'dolor', 'sit', 'amet,', 'consectetur', 'adipiscing', 'elit.'],maxWidth = 20) == ['Lorem ipsum dolor', 'sit amet,', 'consectetur ', 'adipiscing elit. ']\n assert candidate(words = ['Listen', 'to', 'many,', 'speak', 'to', 'a', 'few.'],maxWidth = 6) == ['Listen', 'to ', 'many, ', 'speak ', 'to a', 'few. ']\n assert candidate(words = ['Equal', 'space', 'distribution'],maxWidth = 20) == ['Equal space', 'distribution ']\n assert candidate(words = ['Lorem', 'ipsum', 'dolor', 'sit', 'amet,', 'consectetur', 'adipiscing', 'elit.'],maxWidth = 20) == ['Lorem ipsum dolor', 'sit amet,', 'consectetur ', 'adipiscing elit. ']\n assert candidate(words = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'],maxWidth = 5) == ['A B C', 'D E F', 'G H I', 'J K L', 'M N O', 'P Q R', 'S T U', 'V W X', 'Y Z ']\n assert candidate(words = ['A', 'brave', 'new', 'world,'],maxWidth = 30) == ['A brave new world, ']\n assert candidate(words = ['Listen', 'to', 'the', 'wind.', 'It', 'is', 'talking', 'to', 'you.'],maxWidth = 20) == ['Listen to the wind.', 'It is talking to', 'you. ']\n assert candidate(words = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T'],maxWidth = 20) == ['A B C D E F G H I J', 'K L M N O P Q R S T ']\n assert candidate(words = ['Let', 'us', 'hope', 'it', 'will', 'never', 'come', 'to', 'war'],maxWidth = 15) == ['Let us hope it', 'will never come', 'to war ']\n assert candidate(words = ['Equal', 'rights', 'for', 'all'],maxWidth = 10) == ['Equal ', 'rights for', 'all ']\n assert candidate(words = ['all', 'the', 'world', 'is', 'a', 'stage', 'and', 'all', 'the', 'men', 'and', 'women', 'merely', 'players'],maxWidth = 25) == ['all the world is a stage', 'and all the men and women', 'merely players ']\n assert candidate(words = ['One', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine', 'ten'],maxWidth = 12) == ['One two', 'three four', 'five six', 'seven eight', 'nine ten ']\n assert candidate(words = ['It', 'is', 'during', 'our', 'darkest', 'hours', 'that', 'we', 'must', 'trust', 'in', 'the', 'light.'],maxWidth = 24) == ['It is during our darkest', 'hours that we must trust', 'in the light. ']\n assert candidate(words = ['Once', 'upon', 'a', 'time', 'in', 'a', 'land', 'far', 'far', 'away'],maxWidth = 25) == ['Once upon a time in a', 'land far far away ']\n assert candidate(words = ['LongWord1234567890', 'Short', 'AnotherLongWord1234567', 'Tiny', 'Word'],maxWidth = 25) == ['LongWord1234567890 Short', 'AnotherLongWord1234567 ', 'Tiny Word ']\n assert candidate(words = ['We', 'are', 'now', 'a', 'great', 'nation', '', 'must', 'make', 'amends', 'that', 'we', 'have', 'wronged', 'visitors', 'from', 'other', 'lands'],maxWidth = 12) == ['We are now a', 'great nation', ' must make', 'amends that', 'we have', 'wronged ', 'visitors ', 'from other', 'lands ']\n assert candidate(words = ['Sometimes', 'we', 'have', 'to', 'let', 'go', 'of', 'the', 'past,to', 'move', 'forward.'],maxWidth = 22) == ['Sometimes we have to', 'let go of the past,to', 'move forward. ']\n assert candidate(words = ['A', 'journey', 'of', 'a', 'thousand', 'miles', 'begins', 'with', 'a', 'single', 'step'],maxWidth = 30) == ['A journey of a thousand miles', 'begins with a single step ']\n assert candidate(words = ['The', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog'],maxWidth = 10) == ['The quick', 'brown fox', 'jumps over', 'the lazy', 'dog ']\n assert candidate(words = ['One', 'two', 'three', 'four', 'five', 'six', 'seven'],maxWidth = 10) == ['One two', 'three four', 'five six', 'seven ']\n assert candidate(words = ['Short', 'words', 'only'],maxWidth = 10) == ['Short ', 'words only']\n assert candidate(words = ['Life', 'is', 'either', 'a', 'great', 'adventure', 'or', 'nothing.'],maxWidth = 19) == ['Life is either a', 'great adventure or', 'nothing. ']\n assert candidate(words = ['The', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog'],maxWidth = 20) == ['The quick brown fox', 'jumps over the lazy', 'dog ']\n assert candidate(words = ['Justification', 'is', 'a', 'bit', 'tricky,', 'especially', 'when', 'the', 'words', 'are', 'short.', 'Here', 'we', 'go.'],maxWidth = 20) == ['Justification is a', 'bit tricky,', 'especially when the', 'words are short.', 'Here we go. ']\n assert candidate(words = ['Here', 'is', 'a', 'longer', 'word', 'that', 'will', 'require', 'some', 'additional', 'spaces', 'to', 'justify'],maxWidth = 30) == ['Here is a longer word that', 'will require some additional', 'spaces to justify ']\n assert candidate(words = ['It', 'is', 'a', 'truth', 'universally', 'acknowledged', 'that', 'a', 'single', 'man', 'in', 'possession', 'of', 'a', 'good', 'fortune'],maxWidth = 20) == ['It is a truth', 'universally ', 'acknowledged that a', 'single man in', 'possession of a good', 'fortune ']\n assert candidate(words = ['If', 'you', 'set', 'your', 'goals', 'beyond', 'your', 'abilities,', 'you', 'will', 'never', 'achieve', 'them.'],maxWidth = 25) == ['If you set your goals', 'beyond your abilities,', 'you will never achieve', 'them. ']\n assert candidate(words = ['The', 'world', 'is', 'a', 'book', 'and', 'those', 'who', 'do', 'not', 'travel', 'read', 'only', 'one', 'page.'],maxWidth = 25) == ['The world is a book and', 'those who do not travel', 'read only one page. ']\n assert candidate(words = ['Every', 'great', 'developer', 'you', 'know', 'got', 'where', 'he', 'is', 'by', 'solving', 'problems', 'they', 'were', 'uncomfortable', 'solving', 'before.'],maxWidth = 40) == ['Every great developer you know got where', 'he is by solving problems they were', 'uncomfortable solving before. ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be', 'that', 'is', 'the', 'question'],maxWidth = 25) == ['To be or not to be that', 'is the question ']\n assert candidate(words = ['Once', 'upon', 'a', 'time', 'in', 'a', 'land', 'far', 'far', 'away'],maxWidth = 22) == ['Once upon a time in a', 'land far far away ']\n assert candidate(words = ['I', 'have', 'a', 'dream'],maxWidth = 10) == ['I have a', 'dream ']\n assert candidate(words = ['Programming', 'is', 'the', 'art', 'of', 'telling', 'another', 'person', 'what', 'to', 'do', 'in', 'a', 'language', 'that', 'the', 'other', 'person', 'can', 'understand'],maxWidth = 60) == ['Programming is the art of telling another person what to do', 'in a language that the other person can understand ']\n assert candidate(words = ['One', 'small', 'step', 'for', 'man', 'one', 'giants', 'leap', 'for', 'mankind'],maxWidth = 30) == ['One small step for man one', 'giants leap for mankind ']\n assert candidate(words = ['This', 'is', 'a', 'test', 'for', 'justification', 'algorithm', 'to', 'see', 'how', 'it', 'works', 'with', 'longer', 'texts'],maxWidth = 25) == ['This is a test for', 'justification algorithm', 'to see how it works with', 'longer texts ']\n assert candidate(words = ['One', 'word', 'in', 'each', 'line'],maxWidth = 1) == ['One', 'word', 'in', 'each', 'line']\n assert candidate(words = ['All', 'the', 'world’s', 'a', 'stage,', 'And', 'all', 'the', 'men', 'and', 'women', 'merely', 'players.'],maxWidth = 20) == ['All the world’s a', 'stage, And all the', 'men and women merely', 'players. ']\n assert candidate(words = ['Continuous', 'learning', 'is', 'the', 'only', 'way', 'to', 'remain', 'relevant', 'in', 'the', 'fast-paced', 'world', 'of', 'technology.'],maxWidth = 40) == ['Continuous learning is the only way to', 'remain relevant in the fast-paced world', 'of technology. ']\n assert candidate(words = ['The', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog'],maxWidth = 10) == ['The quick', 'brown fox', 'jumps over', 'the lazy', 'dog ']\n assert candidate(words = ['The', 'best', 'time', 'of', 'our', 'lives', 'The', 'worst', 'time', 'of', 'our', 'lives'],maxWidth = 20) == ['The best time of our', 'lives The worst time', 'of our lives ']\n assert candidate(words = ['A', 'simple', 'sentence.'],maxWidth = 20) == ['A simple sentence. ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be', 'that', 'is', 'the', 'question'],maxWidth = 20) == ['To be or not to be', 'that is the question']\n assert candidate(words = ['SingleLongWordThatExceedsTheMaxWidthAndNeedsToBeHandledProperly'],maxWidth = 30) == ['SingleLongWordThatExceedsTheMaxWidthAndNeedsToBeHandledProperly']\n assert candidate(words = ['Pneumonoultramicroscopicsilicovolcanoconiosis'],maxWidth = 40) == ['Pneumonoultramicroscopicsilicovolcanoconiosis']\n assert candidate(words = ['Believe', 'you', 'can', 'and', 'you', 're', 'halfway', 'there.'],maxWidth = 15) == ['Believe you can', 'and you re', 'halfway there. ']\n assert candidate(words = ['To', 'be', 'or', 'not', 'to', 'be,', 'that', 'is', 'the', 'question:'],maxWidth = 10) == ['To be or', 'not to be,', 'that is', 'the ', 'question: ']\n assert candidate(words = ['This', 'is', 'an', 'example', 'of', 'a', 'longer', 'text', 'that', 'will', 'be', 'used', 'to', 'test', 'the', 'algorithm'],maxWidth = 15) == ['This is an', 'example of a', 'longer text', 'that will be', 'used to test', 'the algorithm ']\n assert candidate(words = ['One', 'Two', 'Three', 'Four', 'Five'],maxWidth = 10) == ['One Two', 'Three Four', 'Five ']\n assert candidate(words = ['Many', 'spaces', 'should', 'go', 'here'],maxWidth = 23) == ['Many spaces should go', 'here ']\n assert candidate(words = ['Pack', 'my', 'box', 'with', 'five', 'dozen', 'liquor', 'jugs.'],maxWidth = 20) == ['Pack my box with', 'five dozen liquor', 'jugs. ']\n"}, "metadata": {"canonical_parameter_names": ["words", "maxWidth"], "leetcode_dataset_entry_point": "Solution().fullJustify", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var fullJustify = function(words, maxWidth) {", "container": null, "callable": "fullJustify", "parameters": [{"name": "words", "type": "string[]"}, {"name": "maxWidth", "type": "number"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 69, "task_id": "sqrtx", "difficulty": "Easy", "problem_description": "Given a non-negative integer x, return the square root of x rounded down to the nearest integer. The returned integer should be non-negative as well.\nYou must not use any built-in exponent function or operator.\n\nFor example, do not use pow(x, 0.5) in c++ or x ** 0.5 in python.\n\n \nExample 1:\n\nInput: x = 4\nOutput: 2\nExplanation: The square root of 4 is 2, so we return 2.\n\nExample 2:\n\nInput: x = 8\nOutput: 2\nExplanation: The square root of 8 is 2.82842..., and since we round it down to the nearest integer, 2 is returned.\n\n \nConstraints:\n\n0 <= x <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(x = 2147483647) == 46340\n assert candidate(x = 26) == 5\n assert candidate(x = 4) == 2\n assert candidate(x = 1) == 1\n assert candidate(x = 25) == 5\n assert candidate(x = 0) == 0\n assert candidate(x = 101) == 10\n assert candidate(x = 100) == 10\n assert candidate(x = 8) == 2\n assert candidate(x = 1025) == 32\n assert candidate(x = 10) == 3\n assert candidate(x = 1234567890123456789) == 1111111106\n assert candidate(x = 40000000000) == 200000\n assert candidate(x = 18014398509481984) == 134217728\n assert candidate(x = 16384) == 128\n assert candidate(x = 1000) == 31\n assert candidate(x = 1524157875) == 39040\n assert candidate(x = 2147483646) == 46340\n assert candidate(x = 99) == 9\n assert candidate(x = 4294967296) == 65536\n assert candidate(x = 225) == 15\n assert candidate(x = 1522756) == 1234\n assert candidate(x = 17) == 4\n assert candidate(x = 2147395600) == 46340\n assert candidate(x = 15) == 3\n assert candidate(x = 18446744073709551615) == 4294967295\n assert candidate(x = 16777215) == 4095\n assert candidate(x = 1000000) == 1000\n assert candidate(x = 18014398509481983) == 134217727\n assert candidate(x = 1000000001) == 31622\n assert candidate(x = 169) == 13\n assert candidate(x = 150) == 12\n assert candidate(x = 2) == 1\n assert candidate(x = 141421356237) == 376060\n assert candidate(x = 10000) == 100\n assert candidate(x = 4294967295) == 65535\n assert candidate(x = 361) == 19\n assert candidate(x = 30) == 5\n assert candidate(x = 987654321) == 31426\n assert candidate(x = 999999999) == 31622\n assert candidate(x = 499999999) == 22360\n assert candidate(x = 2048) == 45\n assert candidate(x = 1024) == 32\n assert candidate(x = 1048575) == 1023\n assert candidate(x = 16777216) == 4096\n assert candidate(x = 256) == 16\n assert candidate(x = 131072) == 362\n assert candidate(x = 2097152) == 1448\n assert candidate(x = 441) == 21\n assert candidate(x = 1048576) == 1024\n assert candidate(x = 65536) == 256\n assert candidate(x = 10000000) == 3162\n assert candidate(x = 49) == 7\n assert candidate(x = 144) == 12\n assert candidate(x = 121) == 11\n assert candidate(x = 1234567890123456788) == 1111111106\n assert candidate(x = 4096) == 64\n assert candidate(x = 196) == 14\n assert candidate(x = 9223372036854775807) == 3037000499\n assert candidate(x = 123456789) == 11111\n assert candidate(x = 289) == 17\n assert candidate(x = 324) == 18\n assert candidate(x = 24) == 4\n assert candidate(x = 16) == 4\n assert candidate(x = 1000000000) == 31622\n assert candidate(x = 3) == 1\n assert candidate(x = 36028797018963968) == 189812531\n"}, "metadata": {"canonical_parameter_names": ["x"], "leetcode_dataset_entry_point": "Solution().mySqrt", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var mySqrt = function(x) {", "container": null, "callable": "mySqrt", "parameters": [{"name": "x", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 70, "task_id": "climbing-stairs", "difficulty": "Easy", "problem_description": "You are climbing a staircase. It takes n steps to reach the top.\nEach time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?\n \nExample 1:\n\nInput: n = 2\nOutput: 2\nExplanation: There are two ways to climb to the top.\n1. 1 step + 1 step\n2. 2 steps\n\nExample 2:\n\nInput: n = 3\nOutput: 3\nExplanation: There are three ways to climb to the top.\n1. 1 step + 1 step + 1 step\n2. 1 step + 2 steps\n3. 2 steps + 1 step\n\n \nConstraints:\n\n1 <= n <= 45\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == 3\n assert candidate(n = 45) == 1836311903\n assert candidate(n = 4) == 5\n assert candidate(n = 20) == 10946\n assert candidate(n = 2) == 2\n assert candidate(n = 1) == 1\n assert candidate(n = 10) == 89\n assert candidate(n = 5) == 8\n assert candidate(n = 30) == 1346269\n assert candidate(n = 15) == 987\n assert candidate(n = 40) == 165580141\n assert candidate(n = 12) == 233\n assert candidate(n = 35) == 14930352\n assert candidate(n = 18) == 4181\n assert candidate(n = 7) == 21\n assert candidate(n = 25) == 121393\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().climbStairs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var climbStairs = function(n) {", "container": null, "callable": "climbStairs", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 71, "task_id": "simplify-path", "difficulty": "Medium", "problem_description": "You are given an absolute path for a Unix-style file system, which always begins with a slash '/'. Your task is to transform this absolute path into its simplified canonical path.\nThe rules of a Unix-style file system are as follows:\n\nA single period '.' represents the current directory.\nA double period '..' represents the previous/parent directory.\nMultiple consecutive slashes such as '//' and '///' are treated as a single slash '/'.\nAny sequence of periods that does not match the rules above should be treated as a valid directory or file name. For example, '...' and '....' are valid directory or file names.\n\nThe simplified canonical path should follow these rules:\n\nThe path must start with a single slash '/'.\nDirectories within the path must be separated by exactly one slash '/'.\nThe path must not end with a slash '/', unless it is the root directory.\nThe path must not have any single or double periods ('.' and '..') used to denote current or parent directories.\n\nReturn the simplified canonical path.\n \nExample 1:\n\nInput: path = \"/home/\"\nOutput: \"/home\"\nExplanation:\nThe trailing slash should be removed.\n\nExample 2:\n\nInput: path = \"/home//foo/\"\nOutput: \"/home/foo\"\nExplanation:\nMultiple consecutive slashes are replaced by a single one.\n\nExample 3:\n\nInput: path = \"/home/user/Documents/../Pictures\"\nOutput: \"/home/user/Pictures\"\nExplanation:\nA double period \"..\" refers to the directory up a level (the parent directory).\n\nExample 4:\n\nInput: path = \"/../\"\nOutput: \"/\"\nExplanation:\nGoing one level up from the root directory is not possible.\n\nExample 5:\n\nInput: path = \"/.../a/../b/c/../d/./\"\nOutput: \"/.../b/d\"\nExplanation:\n\"...\" is a valid name for a directory in this problem.\n\n \nConstraints:\n\n1 <= path.length <= 3000\npath consists of English letters, digits, period '.', slash '/' or '_'.\npath is a valid absolute Unix path.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(path = \"/.../a/../b/c/../d/./\") == \"/.../b/d\"\n assert candidate(path = \"/a/../../b/../c///.//\") == \"/c\"\n assert candidate(path = \"/a/b/c/d/e/f/g/../../..\") == \"/a/b/c/d\"\n assert candidate(path = \"/a/b/c/d/e/../../..//f/\") == \"/a/b/f\"\n assert candidate(path = \"/a/b/c/../\") == \"/a/b\"\n assert candidate(path = \"/a/b/c/d/e/../../../..///f/\") == \"/a/f\"\n assert candidate(path = \"/a/b/c/d/e/../../../\") == \"/a/b\"\n assert candidate(path = \"/a/b/c/d/\") == \"/a/b/c/d\"\n assert candidate(path = \"/a/b/c/d/e/../../../../f/\") == \"/a/f\"\n assert candidate(path = \"/a/b/c/d/../../..\") == \"/a\"\n assert candidate(path = \"/a//b////c/d//././/..\") == \"/a/b/c\"\n assert candidate(path = \"/home/\") == \"/home\"\n assert candidate(path = \"/a/b/c/d/e/./../../f/\") == \"/a/b/c/f\"\n assert candidate(path = \"/a/..\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/..\") == \"/a/b/c/d/e/f\"\n assert candidate(path = \"/a/b/c/../../d/e/\") == \"/a/d/e\"\n assert candidate(path = \"/a/b/c/d/e/f/..\") == \"/a/b/c/d/e\"\n assert candidate(path = \"/a/b/c/d/e/f/g/../..\") == \"/a/b/c/d/e\"\n assert candidate(path = \"/a/b/c/../../\") == \"/a\"\n assert candidate(path = \"/a/./b/../c/../../d/../../../e/../../../../f/\") == \"/f\"\n assert candidate(path = \"/home/user/Documents/../Pictures\") == \"/home/user/Pictures\"\n assert candidate(path = \"/a/./b/../../c/\") == \"/c\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/f/g\") == \"/a/b/c/d/e/f/g\"\n assert candidate(path = \"/a/b/c/d/e/../../..///f/\") == \"/a/b/f\"\n assert candidate(path = \"/a/./b/./c/./d/\") == \"/a/b/c/d\"\n assert candidate(path = \"/home//foo/\") == \"/home/foo\"\n assert candidate(path = \"/a/./b/./c/./\") == \"/a/b/c\"\n assert candidate(path = \"/a/b/c/./././\") == \"/a/b/c\"\n assert candidate(path = \"/a/b/c/d/e/../../../..//f/\") == \"/a/f\"\n assert candidate(path = \"/../\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../.././..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../..//\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../../../../\") == \"/\"\n assert candidate(path = \"/home/user/.../a/b/../../c/d/./e/f/../g/h/i/j/k/l/m/n/o/p/../../../q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../\") == \"/home/user/.../c/d/e/g/h/i/j/k/l/m\"\n assert candidate(path = \"/..////../home/user/Documents\") == \"/home/user/Documents\"\n assert candidate(path = \"/valid/./..../name/./with/./multiple/./dots/./in/./it\") == \"/valid/..../name/with/multiple/dots/in/it\"\n assert candidate(path = \"/a/b/c/d/./e/../../f/g/\") == \"/a/b/c/f/g\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../...\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/...\"\n assert candidate(path = \"/valid/directory/name/./with/./multiple/./dots/./in/./it\") == \"/valid/directory/name/with/multiple/dots/in/it\"\n assert candidate(path = \"/x/y/z/..../...../......./........\") == \"/x/y/z/..../...../......./........\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../...\") == \"/a/b/c/d/e/f/g/h/i/j/...\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../..////\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../..\") == \"/a/b/c/d/e/f/g/h/i\"\n assert candidate(path = \"/.../a/b/c/d/e/./f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/../../../\") == \"/.../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/home/user/../../../var/log/../../usr/local/bin/\") == \"/usr/local/bin\"\n assert candidate(path = \"/home/user/./././Documents/\") == \"/home/user/Documents\"\n assert candidate(path = \"/home/user/.../Documents/.../Pictures/././../Videos\") == \"/home/user/.../Documents/.../Videos\"\n assert candidate(path = \"/x/y/z/....//....//....//....\") == \"/x/y/z/..../..../..../....\"\n assert candidate(path = \"/home/user////....///.....///home/./../..///\") == \"/home/user/....\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./\") == \"/home/user/Pictures\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../...\") == \"/a/b/c/d/e/f/...\"\n assert candidate(path = \"/start/..//end\") == \"/end\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/..///./../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/a/b/c/././../d/e/f/..\") == \"/a/b/d/e\"\n assert candidate(path = \"/home/user////....///.....///home\") == \"/home/user/..../...../home\"\n assert candidate(path = \"/a/./b/./c/./d/./e/./f/./g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y\"\n assert candidate(path = \"/home/user/.../Documents/././../Pictures/././..///\") == \"/home/user/...\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../.././..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../..///\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../..//////\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m\"\n assert candidate(path = \"/one/two/three/../../../four/five/six/../../seven\") == \"/four/seven\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./../Videos/./../Music/./../Downloads/./../Documents/./../Pictures/./../Videos\") == \"/home/user/Videos\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../.././..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../...\") == \"/...\"\n assert candidate(path = \"/a/./b/./c/./d/./e/./f/./g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../...\") == \"/a/b/c/d/e/f/g/h/i/j/k/...\"\n assert candidate(path = \"/...../a/b/../../c/d/e/f/../g/h\") == \"/...../c/d/e/g/h\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../../..\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/././\") == \"/a/b/c/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/valid/./name/./with/./multiple/./dots/./in/./..../it\") == \"/valid/name/with/multiple/dots/in/..../it\"\n assert candidate(path = \"/user/./home/./.././..././....\") == \"/user/.../....\"\n assert candidate(path = \"/home/user////....///.....///home/./../..\") == \"/home/user/....\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/./\") == \"/a/b/c/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/../../../../e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/.../d/e/f/../../g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/../../../../z\") == \"/a/b/c/.../d/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/z\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./../Videos/./../Music/./../Downloads/./../\") == \"/home/user\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/..///././././..///\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x\"\n assert candidate(path = \"/home/user//...///....//.....//home\") == \"/home/user/.../..../...../home\"\n assert candidate(path = \"/a/b/c/d/e/f/g/../../../..//../m/n/o/p/\") == \"/a/b/m/n/o/p\"\n assert candidate(path = \"/home/user/.../Documents/././../Pictures/././..///././././..\") == \"/home/user\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../../../../../...\") == \"/...\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../...\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/...\"\n assert candidate(path = \"/....\") == \"/....\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../..///u/\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../..\") == \"/a/b/c/d/e/f/g\"\n assert candidate(path = \"/a/./b/./c/./d/./e\") == \"/a/b/c/d/e\"\n assert candidate(path = \"/many/../../dots/../../../in/../../../../path/../../../../../root\") == \"/root\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../../../../..\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/./f/g/././h/./i/./j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/home////user/..///Documents///\") == \"/home/Documents\"\n assert candidate(path = \"/home/user/.../a/b/../../c/d/./e/f/../g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/home/user/.../c/d/e/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/f/g/../../../../../../\") == \"/a\"\n assert candidate(path = \"/a/b/c/d/e/f/g/../../.././../../\") == \"/a/b\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/../../\") == \"/a/b/c/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x\"\n assert candidate(path = \"/.../a/b/c/d/e/./f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/../../\") == \"/.../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/home/user////....///.....///home/./../..///./../..///./../..\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./../Videos/./../Music/./../Downloads/./../Documents/./../\") == \"/home/user\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../...\") == \"/a/b/...\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../../...\") == \"/...\"\n assert candidate(path = \"/home/user/.../a/b/../../c/d/./e/f/../g/h/i/j/k/l/m/n/o/p/../../../q/r/s/t/u/v/w/x/y/z/../../../../\") == \"/home/user/.../c/d/e/g/h/i/j/k/l/m/q/r/s/t/u/v\"\n assert candidate(path = \"/home/user////....///.....///home/./../..///./..\") == \"/home/user\"\n assert candidate(path = \"/x/y/z/../../../../w/x/y\") == \"/w/x/y\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./../Videos/./../Music/./../Downloads/./../Documents/./../Pictures\") == \"/home/user/Pictures\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../\") == \"/a/b/c/d\"\n assert candidate(path = \"/home/user////....///.....///home/./..\") == \"/home/user/..../.....\"\n assert candidate(path = \"/x/y/z/../../w/../../v/..///u/\") == \"/u\"\n assert candidate(path = \"/home/user/././././././././././././././././././././././././././././././././\") == \"/home/user\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p\"\n assert candidate(path = \"/home/user/.../Documents/../Pictures/./../Videos\") == \"/home/user/.../Videos\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/.../d/e/f/../../g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/../../z\") == \"/a/b/c/.../d/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/z\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/../../h/i/../../j/k/../../l/m/../../n/o/p/../../q/r/s/t/../../u/v/w/x/../../y/z\") == \"/a/b/c/n/q/r/u/v/y/z\"\n assert candidate(path = \"/user/..///////...///////\") == \"/...\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/././././..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../..\") == \"/a/b/c\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/nested/../../deep/../../..\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/././././..//..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/./.././..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v\"\n assert candidate(path = \"/usr/local/../../local/bin/../../../bin\") == \"/bin\"\n assert candidate(path = \"/a/b/c/.../d/e/f/../../g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/.../d/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/../../d/e/../../f/g/h/../../../i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/var/log/../log/./error.log\") == \"/var/log/error.log\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../...\") == \"/a/b/c/d/e/f/g/...\"\n assert candidate(path = \"/valid/./name/./with/./multiple/./dots/./..../in/./it\") == \"/valid/name/with/multiple/dots/..../in/it\"\n assert candidate(path = \"/a/b/c/d/e/f/g/./.././h/i/j/k/l/..\") == \"/a/b/c/d/e/f/h/i/j/k\"\n assert candidate(path = \"/multiple/////slashes/are/here/./../still/reduced\") == \"/multiple/slashes/are/still/reduced\"\n assert candidate(path = \"/home/user/.../a/b/../../c/d/./e/f/../g/h/i/j/k/l/m/n/o/p/../../../q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/home/user/.../c/d/e/g/h/i/j/k/l/m/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/foo/./bar/./baz/../qux/../.././quux\") == \"/foo/quux\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/./././././././././././././././././././././././././././././././././.././././././././././././././././././././././././././././././././././././././././.\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y\"\n assert candidate(path = \"/home/user/.../Documents/././../Pictures/././..\") == \"/home/user/...\"\n assert candidate(path = \"/home/user////....///.....///home/./../..///./../..\") == \"/home\"\n assert candidate(path = \"/home/user/.../Documents/.../Pictures/././../Videos///\") == \"/home/user/.../Documents/.../Videos\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/./\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../\") == \"/a/b\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j\"\n assert candidate(path = \"/.../a/b/c/d/e/./f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/../\") == \"/.../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../...\") == \"/a/b/c/...\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./../Videos/./../Music/./../Downloads/./../Documents/./../Pictures/./../Videos/./../Music/./../Downloads\") == \"/home/user/Downloads\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/./i/../../j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/f/g/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/valid/./name/./with/./multiple/./..../dots/./in/./it\") == \"/valid/name/with/multiple/..../dots/in/it\"\n assert candidate(path = \"/a/b/c/././././././d/e/f/../g/h/i/j/k/l/m/n/o/p/../../../q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/g/h/i/j/k/l/m/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/././h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z\") == \"/a/b/c/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/home/user/../../../../../../\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p\"\n assert candidate(path = \"/.../a/./b/./c/./d/./e\") == \"/.../a/b/c/d/e\"\n assert candidate(path = \"/a/b/c/d/e/f/g/./.././.././../../\") == \"/a/b/c\"\n assert candidate(path = \"/a/b/c/../../d/e/../../f/g/h/./../\") == \"/a/f/g\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../...\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/...\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/..////..////..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l\"\n assert candidate(path = \"/home/user////....///.....///home/./../..///./../..///./..\") == \"/\"\n assert candidate(path = \"/x/y/z/../../../../../../../../../\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../..\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../../../../../\") == \"/\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/../../../\") == \"/a/b/c/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w\"\n assert candidate(path = \"/trailing/./slashes/./should/./be/./removed\") == \"/trailing/slashes/should/be/removed\"\n assert candidate(path = \"/home/user/../../root///\") == \"/root\"\n assert candidate(path = \"/a/b/c/./../../d/e/./f/../g\") == \"/a/d/e/g\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h\"\n assert candidate(path = \"/home/user/./Documents/../Pictures/./Vacation/../../Pictures\") == \"/home/user/Pictures\"\n assert candidate(path = \"/x/y/z/./././././././\") == \"/x/y/z\"\n assert candidate(path = \"/x/y/z/....//....//....//....//a/b/c/d\") == \"/x/y/z/..../..../..../..../a/b/c/d\"\n assert candidate(path = \"/a/b/c/d/e/../../f/g/./h/./i/./j/./k/./l/./m/./n/./o/./p/./q/./r/./s/./t/./u/./v/./w/./x/./y/./z/../\") == \"/a/b/c/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y\"\n assert candidate(path = \"/a/b/c/d/././././e/f/g/../././h\") == \"/a/b/c/d/e/f/h\"\n assert candidate(path = \"/home/user////....///.....///home/./../..///./../..///\") == \"/home\"\n assert candidate(path = \"/home/user/./Documents/./../Pictures/./../Videos/./../Music/./../Downloads/./../Documents/./../Pictures/./../Videos/./../Music\") == \"/home/user/Music\"\n assert candidate(path = \"/user//.///...///file\") == \"/user/.../file\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../..\") == \"/a/b/c/d/e\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../..////////\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\") == \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../\") == \"/a/b/c/d/e/f\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../..///..\") == \"/a/b/c/d/e/f/g/h/i/j/k/l\"\n assert candidate(path = \"/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/../../../../../../../../../../../../../../../../../../../../../../../../..\") == \"/a\"\n"}, "metadata": {"canonical_parameter_names": ["path"], "leetcode_dataset_entry_point": "Solution().simplifyPath", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var simplifyPath = function(path) {", "container": null, "callable": "simplifyPath", "parameters": [{"name": "path", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 72, "task_id": "edit-distance", "difficulty": "Medium", "problem_description": "Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.\nYou have the following three operations permitted on a word:\n\nInsert a character\nDelete a character\nReplace a character\n\n \nExample 1:\n\nInput: word1 = \"horse\", word2 = \"ros\"\nOutput: 3\nExplanation: \nhorse -> rorse (replace 'h' with 'r')\nrorse -> rose (remove 'r')\nrose -> ros (remove 'e')\n\nExample 2:\n\nInput: word1 = \"intention\", word2 = \"execution\"\nOutput: 5\nExplanation: \nintention -> inention (remove 't')\ninention -> enention (replace 'i' with 'e')\nenention -> exention (replace 'n' with 'x')\nexention -> exection (replace 'n' with 'c')\nexection -> execution (insert 'u')\n\n \nConstraints:\n\n0 <= word1.length, word2.length <= 500\nword1 and word2 consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(word1 = \"park\",word2 = \"spake\") == 3\n assert candidate(word1 = \"algorithm\",word2 = \"altruistic\") == 6\n assert candidate(word1 = \"abc\",word2 = \"\") == 3\n assert candidate(word1 = \"horse\",word2 = \"ros\") == 3\n assert candidate(word1 = \"a\",word2 = \"b\") == 1\n assert candidate(word1 = \"kitten\",word2 = \"sitting\") == 3\n assert candidate(word1 = \"a\",word2 = \"a\") == 0\n assert candidate(word1 = \"a\",word2 = \"\") == 1\n assert candidate(word1 = \"abcdefghij\",word2 = \"jihgfedcba\") == 10\n assert candidate(word1 = \"\",word2 = \"a\") == 1\n assert candidate(word1 = \"\",word2 = \"abc\") == 3\n assert candidate(word1 = \"abc\",word2 = \"abc\") == 0\n assert candidate(word1 = \"intention\",word2 = \"execution\") == 5\n assert candidate(word1 = \"abcd\",word2 = \"dcba\") == 4\n assert candidate(word1 = \"\",word2 = \"\") == 0\n assert candidate(word1 = \"abc\",word2 = \"def\") == 3\n assert candidate(word1 = \"flaw\",word2 = \"lawn\") == 2\n assert candidate(word1 = \"example\",word2 = \"samples\") == 3\n assert candidate(word1 = \"abbreviation\",word2 = \"acceleration\") == 6\n assert candidate(word1 = \"abcdefghijklmnopqrstuvwxyz\",word2 = \"zyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(word1 = \"acknowledgment\",word2 = \"acknowledge\") == 3\n assert candidate(word1 = \"xylophone\",word2 = \"xylophone\") == 0\n assert candidate(word1 = \"dynamic\",word2 = \"programming\") == 8\n assert candidate(word1 = \"embarrassing\",word2 = \"aberration\") == 7\n assert candidate(word1 = \"supercalifragilisticexpialidocious\",word2 = \"supercalifragilisticexpialidociousness\") == 4\n assert candidate(word1 = \"sequential\",word2 = \"sequentialization\") == 7\n assert candidate(word1 = \"algorithm\",word2 = \"alligator\") == 6\n assert candidate(word1 = \"distance\",word2 = \"distinction\") == 5\n assert candidate(word1 = \"irreversible\",word2 = \"reversible\") == 2\n assert candidate(word1 = \"serendipity\",word2 = \"inspiration\") == 10\n assert candidate(word1 = \"karolin\",word2 = \"kathrin\") == 3\n assert candidate(word1 = \"representative\",word2 = \"reproductive\") == 6\n assert candidate(word1 = \"congratulations\",word2 = \"congratulate\") == 4\n assert candidate(word1 = \"supercalifragilisticexpialidocious\",word2 = \"pseudopseudohypoparathyroidism\") == 30\n assert candidate(word1 = \"qwerty\",word2 = \"azerty\") == 2\n assert candidate(word1 = \"mississippi\",word2 = \"mispelling\") == 7\n assert candidate(word1 = \"levenshtein\",word2 = \"levenshtein\") == 0\n assert candidate(word1 = \"sequential\",word2 = \"concurrent\") == 9\n assert candidate(word1 = \"psychological\",word2 = \"psychologist\") == 3\n assert candidate(word1 = \"interpretation\",word2 = \"interpretive\") == 4\n assert candidate(word1 = \"transient\",word2 = \"transitory\") == 4\n assert candidate(word1 = \"abcdefgh\",word2 = \"xyz\") == 8\n assert candidate(word1 = \"algorithmic\",word2 = \"algebraic\") == 6\n assert candidate(word1 = \"transformation\",word2 = \"transfiguration\") == 4\n assert candidate(word1 = \"edit\",word2 = \"editing\") == 3\n assert candidate(word1 = \"levenshtein\",word2 = \"levenschtein\") == 1\n assert candidate(word1 = \"abracadabra\",word2 = \"barbarian\") == 8\n assert candidate(word1 = \"encyclopedia\",word2 = \"encyclopedic\") == 1\n assert candidate(word1 = \"transformation\",word2 = \"transmogrification\") == 6\n assert candidate(word1 = \"complexity\",word2 = \"simplicity\") == 4\n assert candidate(word1 = \"transformation\",word2 = \"transformation\") == 0\n assert candidate(word1 = \"transformation\",word2 = \"transform\") == 5\n assert candidate(word1 = \"abcdexyz\",word2 = \"abcd\") == 4\n assert candidate(word1 = \"zoology\",word2 = \"botany\") == 5\n assert candidate(word1 = \"computation\",word2 = \"computational\") == 2\n assert candidate(word1 = \"pharmaceuticals\",word2 = \"pharmacology\") == 8\n assert candidate(word1 = \"distance\",word2 = \"difference\") == 5\n assert candidate(word1 = \"reciprocal\",word2 = \"perpendicular\") == 10\n assert candidate(word1 = \"development\",word2 = \"evolution\") == 7\n assert candidate(word1 = \"amplification\",word2 = \"attenuation\") == 7\n assert candidate(word1 = \"thermodynamics\",word2 = \"thermodynamic\") == 1\n assert candidate(word1 = \"metamorphosis\",word2 = \"metaphysics\") == 5\n assert candidate(word1 = \"quantum\",word2 = \"quark\") == 4\n assert candidate(word1 = \"repetition\",word2 = \"repetitions\") == 1\n assert candidate(word1 = \"transform\",word2 = \"transformation\") == 5\n assert candidate(word1 = \"sequence\",word2 = \"consequence\") == 3\n assert candidate(word1 = \"abbreviation\",word2 = \"contraction\") == 8\n assert candidate(word1 = \"development\",word2 = \"independently\") == 9\n assert candidate(word1 = \"distance\",word2 = \"distant\") == 2\n assert candidate(word1 = \"mississippi\",word2 = \"mississipi\") == 1\n assert candidate(word1 = \"biographical\",word2 = \"biographies\") == 3\n assert candidate(word1 = \"optimization\",word2 = \"maximization\") == 3\n assert candidate(word1 = \"photosynthesis\",word2 = \"photosynthetic\") == 2\n assert candidate(word1 = \"supercalifragilisticexpialidocious\",word2 = \"pneumonoultramicroscopicsilicovolcanoconiosis\") == 31\n assert candidate(word1 = \"algorithm\",word2 = \"altruism\") == 5\n assert candidate(word1 = \"representation\",word2 = \"representative\") == 2\n assert candidate(word1 = \"reptile\",word2 = \"reptilian\") == 3\n assert candidate(word1 = \"abacaxi\",word2 = \"abacax\") == 1\n assert candidate(word1 = \"mississippi\",word2 = \"misisippi\") == 2\n assert candidate(word1 = \"electrical\",word2 = \"electronic\") == 4\n assert candidate(word1 = \"photograph\",word2 = \"photography\") == 1\n assert candidate(word1 = \"python\",word2 = \"typhon\") == 2\n assert candidate(word1 = \"kayak\",word2 = \"racecar\") == 5\n assert candidate(word1 = \"optimization\",word2 = \"minimization\") == 3\n assert candidate(word1 = \"biological\",word2 = \"biographic\") == 7\n assert candidate(word1 = \"congratulations\",word2 = \"congratulations\") == 0\n assert candidate(word1 = \"photography\",word2 = \"photomontage\") == 7\n assert candidate(word1 = \"babble\",word2 = \"bubble\") == 1\n assert candidate(word1 = \"transformation\",word2 = \"transmute\") == 7\n assert candidate(word1 = \"supercalifragilisticexpialidocious\",word2 = \"antidisestablishmentarianism\") == 26\n assert candidate(word1 = \"semantically\",word2 = \"syntactically\") == 4\n assert candidate(word1 = \"synchronous\",word2 = \"asynchronous\") == 1\n assert candidate(word1 = \"evolution\",word2 = \"revolution\") == 1\n assert candidate(word1 = \"abcdefghij\",word2 = \"zyxwvutsrqponmlkjihgfedcba\") == 25\n assert candidate(word1 = \"misunderstanding\",word2 = \"understanding\") == 3\n assert candidate(word1 = \"combinatorics\",word2 = \"computation\") == 7\n assert candidate(word1 = \"electromagnetic\",word2 = \"electroencephalography\") == 13\n assert candidate(word1 = \"permutation\",word2 = \"combination\") == 6\n assert candidate(word1 = \"subsequence\",word2 = \"supersequence\") == 3\n assert candidate(word1 = \"lumberjack\",word2 = \"lumbersome\") == 4\n assert candidate(word1 = \"optimization\",word2 = \"information\") == 7\n assert candidate(word1 = \"interpolation\",word2 = \"interpretation\") == 3\n assert candidate(word1 = \"magnificent\",word2 = \"magnanimous\") == 6\n assert candidate(word1 = \"xylophone\",word2 = \"xylography\") == 6\n assert candidate(word1 = \"biochemistry\",word2 = \"bioinformatics\") == 10\n assert candidate(word1 = \"exaggeration\",word2 = \"aggrandizement\") == 10\n assert candidate(word1 = \"abcde\",word2 = \"fghij\") == 5\n assert candidate(word1 = \"mississippi\",word2 = \"mispell\") == 8\n assert candidate(word1 = \"interpolation\",word2 = \"internationalization\") == 8\n assert candidate(word1 = \"entomology\",word2 = \"herpetology\") == 5\n assert candidate(word1 = \"interference\",word2 = \"interferometer\") == 5\n assert candidate(word1 = \"communication\",word2 = \"communism\") == 6\n assert candidate(word1 = \"characterization\",word2 = \"categorization\") == 6\n assert candidate(word1 = \"abracadabra\",word2 = \"cabracadabara\") == 2\n assert candidate(word1 = \"transformation\",word2 = \"transference\") == 7\n assert candidate(word1 = \"decomposition\",word2 = \"discombobulation\") == 7\n assert candidate(word1 = \"intermediate\",word2 = \"interim\") == 6\n assert candidate(word1 = \"interpolation\",word2 = \"intrapolation\") == 2\n assert candidate(word1 = \"visualization\",word2 = \"representation\") == 9\n assert candidate(word1 = \"abbreviation\",word2 = \"elision\") == 7\n assert candidate(word1 = \"metamorphism\",word2 = \"metempsychosis\") == 8\n assert candidate(word1 = \"encyclopedia\",word2 = \"encyclopedia\") == 0\n assert candidate(word1 = \"interdisciplinary\",word2 = \"transdisciplinary\") == 5\n assert candidate(word1 = \"unbelievable\",word2 = \"believable\") == 2\n assert candidate(word1 = \"abracadabra\",word2 = \"cadabra\") == 4\n assert candidate(word1 = \"hydrostatic\",word2 = \"hydrodynamics\") == 5\n assert candidate(word1 = \"parallel\",word2 = \"perpendicular\") == 10\n assert candidate(word1 = \"administration\",word2 = \"administrative\") == 2\n assert candidate(word1 = \"cosmology\",word2 = \"cosmonautics\") == 7\n assert candidate(word1 = \"development\",word2 = \"develpoment\") == 2\n assert candidate(word1 = \"photosynthesis\",word2 = \"photography\") == 8\n assert candidate(word1 = \"biochemistry\",word2 = \"biological\") == 8\n"}, "metadata": {"canonical_parameter_names": ["word1", "word2"], "leetcode_dataset_entry_point": "Solution().minDistance", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minDistance = function(word1, word2) {", "container": null, "callable": "minDistance", "parameters": [{"name": "word1", "type": "string"}, {"name": "word2", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 74, "task_id": "search-a-2d-matrix", "difficulty": "Medium", "problem_description": "You are given an m x n integer matrix matrix with the following two properties:\n\nEach row is sorted in non-decreasing order.\nThe first integer of each row is greater than the last integer of the previous row.\n\nGiven an integer target, return true if target is in matrix or false otherwise.\nYou must write a solution in O(log(m * n)) time complexity.\n \nExample 1:\n\n\nInput: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3\nOutput: true\n\nExample 2:\n\n\nInput: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13\nOutput: false\n\n \nConstraints:\n\nm == matrix.length\nn == matrix[i].length\n1 <= m, n <= 100\n-104 <= matrix[i][j], target <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20]],target = 10) == True\n assert candidate(matrix = [[-10, -5, -3], [0, 3, 10], [15, 20, 25]],target = 3) == True\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [7, 8, 11, 13], [15, 16, 18, 20]],target = 0) == True\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],target = 5) == True\n assert candidate(matrix = [[1]],target = 1) == True\n assert candidate(matrix = [[-10, -8, -6, -4], [-3, -1, 1, 3], [5, 7, 9, 11]],target = 10) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]],target = 0) == False\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [7, 8, 11, 13], [15, 16, 18, 20]],target = 20) == True\n assert candidate(matrix = [[-10, -8, -6, -4], [-3, -1, 1, 3], [5, 7, 9, 11]],target = -5) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]],target = 8) == True\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 13) == False\n assert candidate(matrix = [[1]],target = 2) == False\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [8, 9, 10, 12]],target = -3) == True\n assert candidate(matrix = [[1, 3, 5, 7]],target = 5) == True\n assert candidate(matrix = [[-10, -5, -3], [0, 3, 10], [15, 20, 25]],target = 1) == False\n assert candidate(matrix = [[1, 3, 5]],target = 5) == True\n assert candidate(matrix = [[-10, -5, -3, -2], [-1, 0, 2, 3], [4, 5, 7, 8]],target = 11) == False\n assert candidate(matrix = [[1]],target = 0) == False\n assert candidate(matrix = [[1, 3]],target = 3) == True\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [7, 8, 11, 13], [15, 16, 18, 20]],target = -10) == True\n assert candidate(matrix = [[1, 3, 5, 7]],target = 8) == False\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],target = 10) == False\n assert candidate(matrix = [[-10, -5, -3, -2], [-1, 0, 2, 3], [4, 5, 7, 8]],target = -3) == True\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],target = 0) == False\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [8, 9, 10, 12]],target = 15) == False\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [7, 8, 11, 13], [15, 16, 18, 20]],target = 21) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 3) == True\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [7, 8, 11, 13], [15, 16, 18, 20]],target = 11) == True\n assert candidate(matrix = [[-10, -5, -3, -1], [0, 2, 3, 5], [7, 8, 11, 13], [15, 16, 18, 20]],target = -11) == False\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6]],target = 6) == True\n assert candidate(matrix = [[1, 3, 5]],target = 6) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 60) == True\n assert candidate(matrix = [[1, 3]],target = 1) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10]],target = 10) == True\n assert candidate(matrix = [[1, 3]],target = 2) == False\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6]],target = 7) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 1) == True\n assert candidate(matrix = [[-1000, -950, -900, -850], [-800, -750, -700, -650], [-600, -550, -500, -450], [-400, -350, -300, -250], [-200, -150, -100, -50]],target = -325) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60], [61, 62, 63, 64], [65, 66, 67, 68]],target = 1) == True\n assert candidate(matrix = [[1, 3, 5], [7, 9, 11], [13, 15, 17]],target = 18) == False\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-4, -2, 2, 4, 8], [6, 7, 12, 13, 14], [15, 16, 18, 19, 20], [21, 22, 23, 24, 25]],target = 12) == True\n assert candidate(matrix = [[-1, 0, 1, 2, 3], [4, 5, 6, 7, 8], [9, 10, 11, 12, 13], [14, 15, 16, 17, 18], [19, 20, 21, 22, 23]],target = 0) == True\n assert candidate(matrix = [[10, 20, 30, 40, 50], [60, 70, 80, 90, 100], [110, 120, 130, 140, 150], [160, 170, 180, 190, 200]],target = 150) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15], [17, 19, 21, 23, 25, 27, 29, 31], [33, 35, 37, 39, 41, 43, 45, 47], [49, 51, 53, 55, 57, 59, 61, 63]],target = 62) == False\n assert candidate(matrix = [[-10000]],target = -10000) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 25) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29]],target = 20) == True\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60], [61, 62, 63, 64], [65, 66, 67, 68]],target = 35) == False\n assert candidate(matrix = [[-100, -90, -80, -70], [-60, -50, -40, -30], [-20, -10, 0, 10], [20, 30, 40, 50]],target = 5) == False\n assert candidate(matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]],target = 0) == False\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -88) == True\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]],target = 10) == True\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 61) == False\n assert candidate(matrix = [[-4, -3, -2, -1, 0], [1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]],target = -2) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 5) == False\n assert candidate(matrix = [[1, 4, 7, 10, 13], [2, 5, 8, 11, 14], [3, 6, 9, 12, 15], [16, 19, 22, 25, 28], [17, 20, 23, 26, 29]],target = 18) == False\n assert candidate(matrix = [[1, 3, 5, 7], [9, 11, 13, 15], [17, 19, 21, 23], [25, 27, 29, 31], [33, 35, 37, 39], [41, 43, 45, 47], [49, 51, 53, 55], [57, 59, 61, 63]],target = 64) == False\n assert candidate(matrix = [[-100, -90, -80, -70], [-60, -50, -40, -30], [-20, -10, 0, 10], [20, 30, 40, 50]],target = -55) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29], [31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59], [61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89], [91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119]],target = 119) == True\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9]],target = -6) == False\n assert candidate(matrix = [[-1, 0, 3, 5, 9, 12], [13, 18, 20, 23, 28, 31], [32, 34, 36, 39, 42, 45], [46, 48, 51, 54, 57, 60]],target = 61) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 5) == False\n assert candidate(matrix = [[-100, -90, -80, -70], [-60, -50, -40, -30], [-20, -10, 0, 10], [20, 30, 40, 50]],target = -45) == False\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -83) == True\n assert candidate(matrix = [[-5, -2, -1], [0, 3, 5], [8, 9, 10]],target = -3) == False\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16], [17, 18, 19, 20]],target = 1) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 20) == False\n assert candidate(matrix = [[1, 3, 5], [7, 9, 11], [13, 15, 17]],target = 14) == False\n assert candidate(matrix = [[-1000, -999, -998, -997, -996], [-995, -994, -993, -992, -991], [-990, -989, -988, -987, -986], [-985, -984, -983, -982, -981], [-980, -979, -978, -977, -976]],target = -987) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [11, 13, 15, 17, 19], [21, 23, 25, 27, 29], [31, 33, 35, 37, 39], [41, 43, 45, 47, 49]],target = 38) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 20) == False\n assert candidate(matrix = [[-1000, -999, -998, -997, -996], [-995, -994, -993, -992, -991], [-990, -989, -988, -987, -986]],target = -987) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]],target = 15) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [11, 13, 15, 17, 19], [21, 23, 25, 27, 29], [31, 33, 35, 37, 39], [41, 43, 45, 47, 49]],target = 0) == False\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15], [16, 17, 18], [19, 20, 21], [22, 23, 24], [25, 26, 27], [28, 29, 30], [31, 32, 33]],target = 17) == True\n assert candidate(matrix = [[-100, -99, -98, -97], [-96, -95, -94, -93], [-92, -91, -90, -89], [-88, -87, -86, -85]],target = -90) == True\n assert candidate(matrix = [[-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, -1]],target = -1) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [11, 13, 15, 17, 19], [21, 23, 25, 27, 29], [31, 33, 35, 37, 39]],target = 20) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11], [13, 15, 17, 19, 21, 23], [25, 27, 29, 31, 33, 35], [37, 39, 41, 43, 45, 47], [49, 51, 53, 55, 57, 59]],target = 30) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 25) == False\n assert candidate(matrix = [[10, 11, 12, 13, 14, 15]],target = 15) == True\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9]],target = 10) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]],target = 27) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 13) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]],target = 31) == False\n assert candidate(matrix = [[-100, -90, -80, -70, -60], [-50, -40, -30, -20, -10], [0, 10, 20, 30, 40], [50, 60, 70, 80, 90], [100, 110, 120, 130, 140]],target = -35) == False\n assert candidate(matrix = [[-1, 0, 3, 5, 9, 12], [13, 18, 20, 23, 28, 31], [32, 34, 36, 39, 42, 45], [46, 48, 51, 54, 57, 60]],target = 45) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]],target = 22) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40]],target = 25) == True\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 35) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60], [61, 62, 63, 64], [65, 66, 67, 68]],target = 68) == True\n assert candidate(matrix = [[-100, -98, -95, -93], [-88, -86, -82, -80], [-74, -70, -66, -62], [-58, -54, -50, -46]],target = -66) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 26) == False\n assert candidate(matrix = [[1, 5, 9, 13], [17, 21, 25, 29], [33, 37, 41, 45], [49, 53, 57, 61]],target = 18) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60], [61, 62, 63, 64], [65, 66, 67, 68], [69, 70, 71, 72]],target = 67) == True\n assert candidate(matrix = [[-5, -2, -1], [0, 3, 5], [8, 9, 10]],target = 11) == False\n assert candidate(matrix = [[-100, -90, -80, -70], [-60, -50, -40, -30], [-20, -10, 0, 10], [20, 30, 40, 50]],target = 0) == True\n assert candidate(matrix = [[-10000, -9999, -9998, -9997], [-9996, -9995, -9994, -9993], [-9992, -9991, -9990, -9989], [-9988, -9987, -9986, -9985]],target = -9990) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = -5) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = 0) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 0) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 13) == True\n assert candidate(matrix = [[-10, -8, -6, -4, -2], [0, 2, 4, 6, 8], [10, 12, 14, 16, 18], [20, 22, 24, 26, 28], [30, 32, 34, 36, 38]],target = -5) == False\n assert candidate(matrix = [[10], [11], [12], [13], [14], [15]],target = 15) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [41, 43, 45, 47, 49, 51, 53, 55, 57, 59], [61, 63, 65, 67, 69, 71, 73, 75, 77, 79]],target = 40) == False\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],target = 1) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 51) == False\n assert candidate(matrix = [[-1000, -500, -250, -100], [-50, -25, -10, 0], [5, 10, 25, 50], [100, 250, 500, 1000]],target = 0) == True\n assert candidate(matrix = [[-1, 0, 3, 5, 9, 12], [13, 18, 20, 23, 28, 31], [32, 34, 36, 39, 42, 45], [46, 48, 51, 54, 57, 60]],target = -2) == False\n assert candidate(matrix = [[1], [2], [3]],target = 2) == True\n assert candidate(matrix = [[-5, -3, -1, 1, 3], [5, 7, 9, 11, 13], [15, 17, 19, 21, 23], [25, 27, 29, 31, 33], [35, 37, 39, 41, 43]],target = 42) == False\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [50, 51, 52, 53, 54, 55, 56, 57, 58, 59], [60, 61, 62, 63, 64, 65, 66, 67, 68, 69], [70, 71, 72, 73, 74, 75, 76, 77, 78, 79], [80, 81, 82, 83, 84, 85, 86, 87, 88, 89]],target = 75) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [11, 13, 15, 17, 19], [21, 23, 25, 27, 29], [31, 33, 35, 37, 39], [41, 43, 45, 47, 49]],target = 50) == False\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9]],target = -1) == True\n assert candidate(matrix = [[1, 5, 9, 13, 17, 21], [25, 29, 33, 37, 41, 45], [49, 53, 57, 61, 65, 69], [73, 77, 81, 85, 89, 93], [97, 101, 105, 109, 113, 117]],target = 97) == True\n assert candidate(matrix = [[-9999, -9997, -9995, -9993], [-9991, -9989, -9987, -9985], [-9983, -9981, -9979, -9977], [-9975, -9973, -9971, -9969]],target = -9996) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]],target = 5) == True\n assert candidate(matrix = [[-1000, -500, -250, -100], [-50, -25, -10, 0], [5, 10, 25, 50], [100, 250, 500, 1000]],target = -300) == False\n assert candidate(matrix = [[10000]],target = 10000) == True\n assert candidate(matrix = [[1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009], [1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019], [1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029], [1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039]],target = 1025) == True\n assert candidate(matrix = [[1, 2, 3]],target = 2) == True\n assert candidate(matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]],target = -5) == False\n assert candidate(matrix = [[-10000, -9999, -9998], [-9997, -9996, -9995], [-9994, -9993, -9992], [-9991, -9990, -9989], [-9988, -9987, -9986]],target = -9992) == True\n assert candidate(matrix = [[-1000, -500, -250, -100], [-50, -25, -10, 0], [5, 10, 25, 50], [100, 250, 500, 1000]],target = 2000) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]],target = 11) == False\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60], [70, 71, 72, 73]],target = 70) == True\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],target = 18) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19], [20, 21, 22, 23, 24], [25, 26, 27, 28, 29]],target = 29) == True\n assert candidate(matrix = [[-10000, -9000, -8000, -7000], [-6000, -5000, -4000, -3000], [-2000, -1000, 0, 1000], [2000, 3000, 4000, 5000]],target = -5000) == True\n assert candidate(matrix = [[-1, 1, 3], [5, 7, 9], [11, 13, 15]],target = 0) == False\n assert candidate(matrix = [[-1000, -900, -800], [-700, -600, -500], [-400, -300, -200], [-100, -50, 0], [50, 100, 150]],target = -450) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]],target = 42) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]],target = 25) == True\n assert candidate(matrix = [[-5, -4, -3, -2, -1, 0, 1, 2, 3, 4], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34]],target = 17) == True\n assert candidate(matrix = [[-3, -2, -1, 0, 1, 2, 3], [4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23, 24]],target = 13) == True\n assert candidate(matrix = [[-1000, -999, -998, -997, -996], [-995, -994, -993, -992, -991], [-990, -989, -988, -987, -986], [-985, -984, -983, -982, -981]],target = -993) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13], [15, 17, 19, 21, 23, 25, 27], [29, 31, 33, 35, 37, 39, 41]],target = 28) == False\n assert candidate(matrix = [[10000, 10001, 10002], [10003, 10004, 10005], [10006, 10007, 10008]],target = 10004) == True\n assert candidate(matrix = [[-50, -49, -48, -47, -46], [-45, -44, -43, -42, -41], [-40, -39, -38, -37, -36], [-35, -34, -33, -32, -31], [-30, -29, -28, -27, -26]],target = -33) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 31) == False\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9]],target = 9) == True\n assert candidate(matrix = [[-100, -90, -80, -70], [-60, -50, -40, -30], [-20, -10, 0, 10], [20, 30, 40, 50]],target = -101) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 26) == False\n"}, "metadata": {"canonical_parameter_names": ["matrix", "target"], "leetcode_dataset_entry_point": "Solution().searchMatrix", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var searchMatrix = function(matrix, target) {", "container": null, "callable": "searchMatrix", "parameters": [{"name": "matrix", "type": "number[][]"}, {"name": "target", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 76, "task_id": "minimum-window-substring", "difficulty": "Hard", "problem_description": "Given two strings s and t of lengths m and n respectively, return the minimum window substring of s such that every character in t (including duplicates) is included in the window. If there is no such substring, return the empty string \"\".\nThe testcases will be generated such that the answer is unique.\n \nExample 1:\n\nInput: s = \"ADOBECODEBANC\", t = \"ABC\"\nOutput: \"BANC\"\nExplanation: The minimum window substring \"BANC\" includes 'A', 'B', and 'C' from string t.\n\nExample 2:\n\nInput: s = \"a\", t = \"a\"\nOutput: \"a\"\nExplanation: The entire string s is the minimum window.\n\nExample 3:\n\nInput: s = \"a\", t = \"aa\"\nOutput: \"\"\nExplanation: Both 'a's from t must be included in the window.\nSince the largest window of s only has one 'a', return empty string.\n\n \nConstraints:\n\nm == s.length\nn == t.length\n1 <= m, n <= 105\ns and t consist of uppercase and lowercase English letters.\n\n \nFollow up: Could you find an algorithm that runs in O(m + n) time?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"acbbaca\",t = \"aba\") == \"baca\"\n assert candidate(s = \"aabbcc\",t = \"abc\") == \"abbc\"\n assert candidate(s = \"aaaaaaa\",t = \"aa\") == \"aa\"\n assert candidate(s = \"a\",t = \"aa\") == \"\"\n assert candidate(s = \"abcd\",t = \"bd\") == \"bcd\"\n assert candidate(s = \"ab\",t = \"b\") == \"b\"\n assert candidate(s = \"aa\",t = \"aa\") == \"aa\"\n assert candidate(s = \"ADOBECODEBANC\",t = \"ABC\") == \"BANC\"\n assert candidate(s = \"fgrheahtfeqcrha\",t = \"harf\") == \"fgrhea\"\n assert candidate(s = \"aaaaaaaaaaaabbbbbcdd\",t = \"abcdd\") == \"abbbbbcdd\"\n assert candidate(s = \"abcde\",t = \"f\") == \"\"\n assert candidate(s = \"ab\",t = \"a\") == \"a\"\n assert candidate(s = \"abababab\",t = \"abab\") == \"abab\"\n assert candidate(s = \"a\",t = \"a\") == \"a\"\n assert candidate(s = \"aafffrbb\",t = \"ffab\") == \"afffrb\"\n assert candidate(s = \"bba\",t = \"ab\") == \"ba\"\n assert candidate(s = \"cbbbaaaaabbbcccccbbaa\",t = \"aaabbbccc\") == \"aaabbbccc\"\n assert candidate(s = \"abcabcabc\",t = \"abc\") == \"abc\"\n assert candidate(s = \"cabwefgewcwaefgcf\",t = \"cae\") == \"cwae\"\n assert candidate(s = \"abcabcabc\",t = \"aaa\") == \"abcabca\"\n assert candidate(s = \"abc\",t = \"abc\") == \"abc\"\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\",t = \"aaaaaaaaaaaaaaaaaaaaaaaaa\") == \"aaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"zjwsxeyrhtlnejzjwsxeyrhtlnej\",t = \"nejxyz\") == \"nejzjwsxey\"\n assert candidate(s = \"abcdefghijk\",t = \"jihgfedcba\") == \"abcdefghij\"\n assert candidate(s = \"abacabadabacaba\",t = \"abc\") == \"bac\"\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",t = \"cba\") == \"abc\"\n assert candidate(s = \"aabbccddeeffgghhii\",t = \"abcdefghi\") == \"abbccddeeffgghhi\"\n assert candidate(s = \"aaaaaaaaaabbbbbbcccccc\",t = \"abc\") == \"abbbbbbc\"\n assert candidate(s = \"mississippi\",t = \"issip\") == \"issip\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzz\",t = \"zzz\") == \"zzz\"\n assert candidate(s = \"xyxzyxzyxzyxzyx\",t = \"xzy\") == \"yxz\"\n assert candidate(s = \"abcdefg\",t = \"zyxwvutsrqponmlkjihgfedcba\") == \"\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zyxwvutsrqponmlkjihgfedcba\") == \"abbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyz\"\n assert candidate(s = \"xyzxzyzxzyzzyzyxzyzyxzyzyx\",t = \"xyzzyxzyzyzx\") == \"xyzxzyzxzyzzy\"\n assert candidate(s = \"aaabbbaaabbbccc\",t = \"aabbcc\") == \"aabbbcc\"\n assert candidate(s = \"zzzzzzzzzzz\",t = \"z\") == \"z\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"abcdef\") == \"abbccddeef\"\n assert candidate(s = \"aabbccddeeffgghhii\",t = \"aabbccddeeffgghhii\") == \"aabbccddeeffgghhii\"\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabcabcabc\",t = \"aabbcc\") == \"abcabc\"\n assert candidate(s = \"bbaabbbbbaabbbbaaabbbbaaabbababababab\",t = \"bbbbaaaa\") == \"aabbbbaa\"\n assert candidate(s = \"mississippi\",t = \"issi\") == \"issi\"\n assert candidate(s = \"aaabbcccccccdddeee\",t = \"abcde\") == \"abbcccccccddde\"\n assert candidate(s = \"zxcvbnmasdfghjklqwertyuiop\",t = \"opq\") == \"qwertyuiop\"\n assert candidate(s = \"aaaaaaaaaaaabbbbbbcccccccc\",t = \"abc\") == \"abbbbbbc\"\n assert candidate(s = \"abcabcabcabcabcabc\",t = \"cba\") == \"abc\"\n assert candidate(s = \"xyzzxyzzxyzz\",t = \"xyz\") == \"xyz\"\n assert candidate(s = \"aaaaaaaaaaaabbbbbbbbbbbcccccccccc\",t = \"abc\") == \"abbbbbbbbbbbc\"\n assert candidate(s = \"xyzzzyxzyxzyxzyxzy\",t = \"zyxzyxz\") == \"xyzzzyx\"\n assert candidate(s = \"ababababababab\",t = \"abba\") == \"abab\"\n assert candidate(s = \"abcdabcdeabcdf\",t = \"abcfed\") == \"eabcdf\"\n assert candidate(s = \"abababababababababab\",t = \"aabbcc\") == \"\"\n assert candidate(s = \"abcdefg\",t = \"xyz\") == \"\"\n assert candidate(s = \"aabbccddeeffgghhii\",t = \"aabbcc\") == \"aabbcc\"\n assert candidate(s = \"ababcabcabcabcabcabcabcabcabcabcabcabc\",t = \"abcabcabc\") == \"abcabcabc\"\n assert candidate(s = \"hellohellohello\",t = \"lle\") == \"ell\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcba\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"sadjhasjhdjahsjdhasjhadsjhsahjdahjdsjahjdhasjdhajsdhasjdhajsdjasdhasjdhsa\",t = \"hasjdh\") == \"hasjhd\"\n assert candidate(s = \"bancbbancbbanc\",t = \"abc\") == \"banc\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzzzzzzzzzzzzzz\",t = \"abcdefghijklmnopqrstuvwxyz\") == \"abbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyz\"\n assert candidate(s = \"thisisaverylongstringthatweneedtolookinto\",t = \"tin\") == \"int\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzz\") == \"zzzzzzzz\"\n assert candidate(s = \"bbaaaaaaabbbbcccc\",t = \"aabbbccc\") == \"aabbbbccc\"\n assert candidate(s = \"abababababababab\",t = \"abab\") == \"abab\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"mnopqrstuvwxyz\") == \"mnnooppqqrrssttuuvvwwxxyyz\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\",t = \"qwertyuiopzxcvbnm\") == \"zxcvbnmqwertyuiop\"\n assert candidate(s = \"xyzzyxzyzyxzyzxzyzxzyxzyzyxzyx\",t = \"xyz\") == \"xyz\"\n assert candidate(s = \"abcbacbacbacbacbacbacbacbacbacbacbacbacbacbac\",t = \"acbcba\") == \"abcbac\"\n assert candidate(s = \"abccbaacz\",t = \"abc\") == \"abc\"\n assert candidate(s = \"abracadabra\",t = \"rac\") == \"rac\"\n assert candidate(s = \"aaaaaaaaaabbbbbbbbbbcccccccccc\",t = \"abc\") == \"abbbbbbbbbbc\"\n assert candidate(s = \"bbaaacccaaaabbbccc\",t = \"aabbbccc\") == \"aabbbccc\"\n assert candidate(s = \"bancancode\",t = \"abc\") == \"banc\"\n assert candidate(s = \"abcdefgabcdefg\",t = \"abcd\") == \"abcd\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\",t = \"qwertyuiop\") == \"qwertyuiop\"\n assert candidate(s = \"aaaaaaaaaa\",t = \"aaa\") == \"aaa\"\n assert candidate(s = \"ababababababababababababababababababab\",t = \"aba\") == \"aba\"\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcccccccccccccccccccccccccccccccccc\",t = \"abc\") == \"abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbc\"\n assert candidate(s = \"abcdeffeghijk\",t = \"efg\") == \"feg\"\n assert candidate(s = \"abcabcabcabcabc\",t = \"cba\") == \"abc\"\n"}, "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().minWindow", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minWindow = function(s, t) {", "container": null, "callable": "minWindow", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 77, "task_id": "combinations", "difficulty": "Medium", "problem_description": "Given two integers n and k, return all possible combinations of k numbers chosen from the range [1, n].\nYou may return the answer in any order.\n \nExample 1:\n\nInput: n = 4, k = 2\nOutput: [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]\nExplanation: There are 4 choose 2 = 6 total combinations.\nNote that combinations are unordered, i.e., [1,2] and [2,1] are considered to be the same combination.\n\nExample 2:\n\nInput: n = 1, k = 1\nOutput: [[1]]\nExplanation: There is 1 choose 1 = 1 total combination.\n\n \nConstraints:\n\n1 <= n <= 20\n1 <= k <= n\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 10,k = 5) == [[1, 2, 3, 4, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 9, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 9, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 9, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 9, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 9, 10], [1, 2, 8, 9, 10], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9], [1, 3, 4, 5, 10], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9], [1, 3, 4, 6, 10], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 8, 9], [1, 3, 4, 8, 10], [1, 3, 4, 9, 10], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9], [1, 3, 5, 6, 10], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9], [1, 3, 5, 7, 10], [1, 3, 5, 8, 9], [1, 3, 5, 8, 10], [1, 3, 5, 9, 10], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9], [1, 3, 6, 7, 10], [1, 3, 6, 8, 9], [1, 3, 6, 8, 10], [1, 3, 6, 9, 10], [1, 3, 7, 8, 9], [1, 3, 7, 8, 10], [1, 3, 7, 9, 10], [1, 3, 8, 9, 10], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9], [1, 4, 5, 6, 10], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9], [1, 4, 5, 7, 10], [1, 4, 5, 8, 9], [1, 4, 5, 8, 10], [1, 4, 5, 9, 10], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9], [1, 4, 6, 7, 10], [1, 4, 6, 8, 9], [1, 4, 6, 8, 10], [1, 4, 6, 9, 10], [1, 4, 7, 8, 9], [1, 4, 7, 8, 10], [1, 4, 7, 9, 10], [1, 4, 8, 9, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9], [1, 5, 6, 7, 10], [1, 5, 6, 8, 9], [1, 5, 6, 8, 10], [1, 5, 6, 9, 10], [1, 5, 7, 8, 9], [1, 5, 7, 8, 10], [1, 5, 7, 9, 10], [1, 5, 8, 9, 10], [1, 6, 7, 8, 9], [1, 6, 7, 8, 10], [1, 6, 7, 9, 10], [1, 6, 8, 9, 10], [1, 7, 8, 9, 10], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9], [2, 3, 4, 5, 10], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9], [2, 3, 4, 6, 10], [2, 3, 4, 7, 8], [2, 3, 4, 7, 9], [2, 3, 4, 7, 10], [2, 3, 4, 8, 9], [2, 3, 4, 8, 10], [2, 3, 4, 9, 10], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8], [2, 3, 5, 6, 9], [2, 3, 5, 6, 10], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9], [2, 3, 5, 7, 10], [2, 3, 5, 8, 9], [2, 3, 5, 8, 10], [2, 3, 5, 9, 10], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9], [2, 3, 6, 7, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 10], [2, 3, 6, 9, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 10], [2, 3, 7, 9, 10], [2, 3, 8, 9, 10], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9], [2, 4, 5, 6, 10], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9], [2, 4, 5, 7, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 10], [2, 4, 5, 9, 10], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9], [2, 4, 6, 7, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 10], [2, 4, 6, 9, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 10], [2, 4, 7, 9, 10], [2, 4, 8, 9, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9], [2, 5, 6, 7, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 10], [2, 5, 6, 9, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 10], [2, 5, 7, 9, 10], [2, 5, 8, 9, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 10], [2, 6, 7, 9, 10], [2, 6, 8, 9, 10], [2, 7, 8, 9, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9], [3, 4, 5, 6, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9], [3, 4, 5, 7, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 10], [3, 4, 5, 9, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9], [3, 4, 6, 7, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 10], [3, 4, 6, 9, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 10], [3, 4, 7, 9, 10], [3, 4, 8, 9, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9], [3, 5, 6, 7, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 10], [3, 5, 6, 9, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 10], [3, 5, 7, 9, 10], [3, 5, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 9, 10], [3, 6, 8, 9, 10], [3, 7, 8, 9, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 9, 10], [4, 5, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 9, 10], [4, 6, 8, 9, 10], [4, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 9, 10], [5, 6, 8, 9, 10], [5, 7, 8, 9, 10], [6, 7, 8, 9, 10]]\n assert candidate(n = 6,k = 4) == [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 5, 6], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 5, 6], [1, 4, 5, 6], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 5, 6], [2, 4, 5, 6], [3, 4, 5, 6]]\n assert candidate(n = 1,k = 1) == [[1]]\n assert candidate(n = 4,k = 2) == [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]]\n assert candidate(n = 6,k = 1) == [[1], [2], [3], [4], [5], [6]]\n assert candidate(n = 5,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 4], [1, 3, 5], [1, 4, 5], [2, 3, 4], [2, 3, 5], [2, 4, 5], [3, 4, 5]]\n assert candidate(n = 9,k = 4) == [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 3, 9], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4, 8], [1, 2, 4, 9], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 5, 9], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 6, 9], [1, 2, 7, 8], [1, 2, 7, 9], [1, 2, 8, 9], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 4, 9], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 5, 9], [1, 3, 6, 7], [1, 3, 6, 8], [1, 3, 6, 9], [1, 3, 7, 8], [1, 3, 7, 9], [1, 3, 8, 9], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5, 8], [1, 4, 5, 9], [1, 4, 6, 7], [1, 4, 6, 8], [1, 4, 6, 9], [1, 4, 7, 8], [1, 4, 7, 9], [1, 4, 8, 9], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 6, 9], [1, 5, 7, 8], [1, 5, 7, 9], [1, 5, 8, 9], [1, 6, 7, 8], [1, 6, 7, 9], [1, 6, 8, 9], [1, 7, 8, 9], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4, 8], [2, 3, 4, 9], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5, 8], [2, 3, 5, 9], [2, 3, 6, 7], [2, 3, 6, 8], [2, 3, 6, 9], [2, 3, 7, 8], [2, 3, 7, 9], [2, 3, 8, 9], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5, 8], [2, 4, 5, 9], [2, 4, 6, 7], [2, 4, 6, 8], [2, 4, 6, 9], [2, 4, 7, 8], [2, 4, 7, 9], [2, 4, 8, 9], [2, 5, 6, 7], [2, 5, 6, 8], [2, 5, 6, 9], [2, 5, 7, 8], [2, 5, 7, 9], [2, 5, 8, 9], [2, 6, 7, 8], [2, 6, 7, 9], [2, 6, 8, 9], [2, 7, 8, 9], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5, 8], [3, 4, 5, 9], [3, 4, 6, 7], [3, 4, 6, 8], [3, 4, 6, 9], [3, 4, 7, 8], [3, 4, 7, 9], [3, 4, 8, 9], [3, 5, 6, 7], [3, 5, 6, 8], [3, 5, 6, 9], [3, 5, 7, 8], [3, 5, 7, 9], [3, 5, 8, 9], [3, 6, 7, 8], [3, 6, 7, 9], [3, 6, 8, 9], [3, 7, 8, 9], [4, 5, 6, 7], [4, 5, 6, 8], [4, 5, 6, 9], [4, 5, 7, 8], [4, 5, 7, 9], [4, 5, 8, 9], [4, 6, 7, 8], [4, 6, 7, 9], [4, 6, 8, 9], [4, 7, 8, 9], [5, 6, 7, 8], [5, 6, 7, 9], [5, 6, 8, 9], [5, 7, 8, 9], [6, 7, 8, 9]]\n assert candidate(n = 17,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 2, 11], [1, 2, 12], [1, 2, 13], [1, 2, 14], [1, 2, 15], [1, 2, 16], [1, 2, 17], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 3, 10], [1, 3, 11], [1, 3, 12], [1, 3, 13], [1, 3, 14], [1, 3, 15], [1, 3, 16], [1, 3, 17], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 4, 10], [1, 4, 11], [1, 4, 12], [1, 4, 13], [1, 4, 14], [1, 4, 15], [1, 4, 16], [1, 4, 17], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 10], [1, 5, 11], [1, 5, 12], [1, 5, 13], [1, 5, 14], [1, 5, 15], [1, 5, 16], [1, 5, 17], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 10], [1, 6, 11], [1, 6, 12], [1, 6, 13], [1, 6, 14], [1, 6, 15], [1, 6, 16], [1, 6, 17], [1, 7, 8], [1, 7, 9], [1, 7, 10], [1, 7, 11], [1, 7, 12], [1, 7, 13], [1, 7, 14], [1, 7, 15], [1, 7, 16], [1, 7, 17], [1, 8, 9], [1, 8, 10], [1, 8, 11], [1, 8, 12], [1, 8, 13], [1, 8, 14], [1, 8, 15], [1, 8, 16], [1, 8, 17], [1, 9, 10], [1, 9, 11], [1, 9, 12], [1, 9, 13], [1, 9, 14], [1, 9, 15], [1, 9, 16], [1, 9, 17], [1, 10, 11], [1, 10, 12], [1, 10, 13], [1, 10, 14], [1, 10, 15], [1, 10, 16], [1, 10, 17], [1, 11, 12], [1, 11, 13], [1, 11, 14], [1, 11, 15], [1, 11, 16], [1, 11, 17], [1, 12, 13], [1, 12, 14], [1, 12, 15], [1, 12, 16], [1, 12, 17], [1, 13, 14], [1, 13, 15], [1, 13, 16], [1, 13, 17], [1, 14, 15], [1, 14, 16], [1, 14, 17], [1, 15, 16], [1, 15, 17], [1, 16, 17], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], [2, 3, 10], [2, 3, 11], [2, 3, 12], [2, 3, 13], [2, 3, 14], [2, 3, 15], [2, 3, 16], [2, 3, 17], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 4, 10], [2, 4, 11], [2, 4, 12], [2, 4, 13], [2, 4, 14], [2, 4, 15], [2, 4, 16], [2, 4, 17], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9], [2, 5, 10], [2, 5, 11], [2, 5, 12], [2, 5, 13], [2, 5, 14], [2, 5, 15], [2, 5, 16], [2, 5, 17], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 6, 10], [2, 6, 11], [2, 6, 12], [2, 6, 13], [2, 6, 14], [2, 6, 15], [2, 6, 16], [2, 6, 17], [2, 7, 8], [2, 7, 9], [2, 7, 10], [2, 7, 11], [2, 7, 12], [2, 7, 13], [2, 7, 14], [2, 7, 15], [2, 7, 16], [2, 7, 17], [2, 8, 9], [2, 8, 10], [2, 8, 11], [2, 8, 12], [2, 8, 13], [2, 8, 14], [2, 8, 15], [2, 8, 16], [2, 8, 17], [2, 9, 10], [2, 9, 11], [2, 9, 12], [2, 9, 13], [2, 9, 14], [2, 9, 15], [2, 9, 16], [2, 9, 17], [2, 10, 11], [2, 10, 12], [2, 10, 13], [2, 10, 14], [2, 10, 15], [2, 10, 16], [2, 10, 17], [2, 11, 12], [2, 11, 13], [2, 11, 14], [2, 11, 15], [2, 11, 16], [2, 11, 17], [2, 12, 13], [2, 12, 14], [2, 12, 15], [2, 12, 16], [2, 12, 17], [2, 13, 14], [2, 13, 15], [2, 13, 16], [2, 13, 17], [2, 14, 15], [2, 14, 16], [2, 14, 17], [2, 15, 16], [2, 15, 17], [2, 16, 17], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 4, 10], [3, 4, 11], [3, 4, 12], [3, 4, 13], [3, 4, 14], [3, 4, 15], [3, 4, 16], [3, 4, 17], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 5, 10], [3, 5, 11], [3, 5, 12], [3, 5, 13], [3, 5, 14], [3, 5, 15], [3, 5, 16], [3, 5, 17], [3, 6, 7], [3, 6, 8], [3, 6, 9], [3, 6, 10], [3, 6, 11], [3, 6, 12], [3, 6, 13], [3, 6, 14], [3, 6, 15], [3, 6, 16], [3, 6, 17], [3, 7, 8], [3, 7, 9], [3, 7, 10], [3, 7, 11], [3, 7, 12], [3, 7, 13], [3, 7, 14], [3, 7, 15], [3, 7, 16], [3, 7, 17], [3, 8, 9], [3, 8, 10], [3, 8, 11], [3, 8, 12], [3, 8, 13], [3, 8, 14], [3, 8, 15], [3, 8, 16], [3, 8, 17], [3, 9, 10], [3, 9, 11], [3, 9, 12], [3, 9, 13], [3, 9, 14], [3, 9, 15], [3, 9, 16], [3, 9, 17], [3, 10, 11], [3, 10, 12], [3, 10, 13], [3, 10, 14], [3, 10, 15], [3, 10, 16], [3, 10, 17], [3, 11, 12], [3, 11, 13], [3, 11, 14], [3, 11, 15], [3, 11, 16], [3, 11, 17], [3, 12, 13], [3, 12, 14], [3, 12, 15], [3, 12, 16], [3, 12, 17], [3, 13, 14], [3, 13, 15], [3, 13, 16], [3, 13, 17], [3, 14, 15], [3, 14, 16], [3, 14, 17], [3, 15, 16], [3, 15, 17], [3, 16, 17], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 5, 10], [4, 5, 11], [4, 5, 12], [4, 5, 13], [4, 5, 14], [4, 5, 15], [4, 5, 16], [4, 5, 17], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 6, 10], [4, 6, 11], [4, 6, 12], [4, 6, 13], [4, 6, 14], [4, 6, 15], [4, 6, 16], [4, 6, 17], [4, 7, 8], [4, 7, 9], [4, 7, 10], [4, 7, 11], [4, 7, 12], [4, 7, 13], [4, 7, 14], [4, 7, 15], [4, 7, 16], [4, 7, 17], [4, 8, 9], [4, 8, 10], [4, 8, 11], [4, 8, 12], [4, 8, 13], [4, 8, 14], [4, 8, 15], [4, 8, 16], [4, 8, 17], [4, 9, 10], [4, 9, 11], [4, 9, 12], [4, 9, 13], [4, 9, 14], [4, 9, 15], [4, 9, 16], [4, 9, 17], [4, 10, 11], [4, 10, 12], [4, 10, 13], [4, 10, 14], [4, 10, 15], [4, 10, 16], [4, 10, 17], [4, 11, 12], [4, 11, 13], [4, 11, 14], [4, 11, 15], [4, 11, 16], [4, 11, 17], [4, 12, 13], [4, 12, 14], [4, 12, 15], [4, 12, 16], [4, 12, 17], [4, 13, 14], [4, 13, 15], [4, 13, 16], [4, 13, 17], [4, 14, 15], [4, 14, 16], [4, 14, 17], [4, 15, 16], [4, 15, 17], [4, 16, 17], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 6, 10], [5, 6, 11], [5, 6, 12], [5, 6, 13], [5, 6, 14], [5, 6, 15], [5, 6, 16], [5, 6, 17], [5, 7, 8], [5, 7, 9], [5, 7, 10], [5, 7, 11], [5, 7, 12], [5, 7, 13], [5, 7, 14], [5, 7, 15], [5, 7, 16], [5, 7, 17], [5, 8, 9], [5, 8, 10], [5, 8, 11], [5, 8, 12], [5, 8, 13], [5, 8, 14], [5, 8, 15], [5, 8, 16], [5, 8, 17], [5, 9, 10], [5, 9, 11], [5, 9, 12], [5, 9, 13], [5, 9, 14], [5, 9, 15], [5, 9, 16], [5, 9, 17], [5, 10, 11], [5, 10, 12], [5, 10, 13], [5, 10, 14], [5, 10, 15], [5, 10, 16], [5, 10, 17], [5, 11, 12], [5, 11, 13], [5, 11, 14], [5, 11, 15], [5, 11, 16], [5, 11, 17], [5, 12, 13], [5, 12, 14], [5, 12, 15], [5, 12, 16], [5, 12, 17], [5, 13, 14], [5, 13, 15], [5, 13, 16], [5, 13, 17], [5, 14, 15], [5, 14, 16], [5, 14, 17], [5, 15, 16], [5, 15, 17], [5, 16, 17], [6, 7, 8], [6, 7, 9], [6, 7, 10], [6, 7, 11], [6, 7, 12], [6, 7, 13], [6, 7, 14], [6, 7, 15], [6, 7, 16], [6, 7, 17], [6, 8, 9], [6, 8, 10], [6, 8, 11], [6, 8, 12], [6, 8, 13], [6, 8, 14], [6, 8, 15], [6, 8, 16], [6, 8, 17], [6, 9, 10], [6, 9, 11], [6, 9, 12], [6, 9, 13], [6, 9, 14], [6, 9, 15], [6, 9, 16], [6, 9, 17], [6, 10, 11], [6, 10, 12], [6, 10, 13], [6, 10, 14], [6, 10, 15], [6, 10, 16], [6, 10, 17], [6, 11, 12], [6, 11, 13], [6, 11, 14], [6, 11, 15], [6, 11, 16], [6, 11, 17], [6, 12, 13], [6, 12, 14], [6, 12, 15], [6, 12, 16], [6, 12, 17], [6, 13, 14], [6, 13, 15], [6, 13, 16], [6, 13, 17], [6, 14, 15], [6, 14, 16], [6, 14, 17], [6, 15, 16], [6, 15, 17], [6, 16, 17], [7, 8, 9], [7, 8, 10], [7, 8, 11], [7, 8, 12], [7, 8, 13], [7, 8, 14], [7, 8, 15], [7, 8, 16], [7, 8, 17], [7, 9, 10], [7, 9, 11], [7, 9, 12], [7, 9, 13], [7, 9, 14], [7, 9, 15], [7, 9, 16], [7, 9, 17], [7, 10, 11], [7, 10, 12], [7, 10, 13], [7, 10, 14], [7, 10, 15], [7, 10, 16], [7, 10, 17], [7, 11, 12], [7, 11, 13], [7, 11, 14], [7, 11, 15], [7, 11, 16], [7, 11, 17], [7, 12, 13], [7, 12, 14], [7, 12, 15], [7, 12, 16], [7, 12, 17], [7, 13, 14], [7, 13, 15], [7, 13, 16], [7, 13, 17], [7, 14, 15], [7, 14, 16], [7, 14, 17], [7, 15, 16], [7, 15, 17], [7, 16, 17], [8, 9, 10], [8, 9, 11], [8, 9, 12], [8, 9, 13], [8, 9, 14], [8, 9, 15], [8, 9, 16], [8, 9, 17], [8, 10, 11], [8, 10, 12], [8, 10, 13], [8, 10, 14], [8, 10, 15], [8, 10, 16], [8, 10, 17], [8, 11, 12], [8, 11, 13], [8, 11, 14], [8, 11, 15], [8, 11, 16], [8, 11, 17], [8, 12, 13], [8, 12, 14], [8, 12, 15], [8, 12, 16], [8, 12, 17], [8, 13, 14], [8, 13, 15], [8, 13, 16], [8, 13, 17], [8, 14, 15], [8, 14, 16], [8, 14, 17], [8, 15, 16], [8, 15, 17], [8, 16, 17], [9, 10, 11], [9, 10, 12], [9, 10, 13], [9, 10, 14], [9, 10, 15], [9, 10, 16], [9, 10, 17], [9, 11, 12], [9, 11, 13], [9, 11, 14], [9, 11, 15], [9, 11, 16], [9, 11, 17], [9, 12, 13], [9, 12, 14], [9, 12, 15], [9, 12, 16], [9, 12, 17], [9, 13, 14], [9, 13, 15], [9, 13, 16], [9, 13, 17], [9, 14, 15], [9, 14, 16], [9, 14, 17], [9, 15, 16], [9, 15, 17], [9, 16, 17], [10, 11, 12], [10, 11, 13], [10, 11, 14], [10, 11, 15], [10, 11, 16], [10, 11, 17], [10, 12, 13], [10, 12, 14], [10, 12, 15], [10, 12, 16], [10, 12, 17], [10, 13, 14], [10, 13, 15], [10, 13, 16], [10, 13, 17], [10, 14, 15], [10, 14, 16], [10, 14, 17], [10, 15, 16], [10, 15, 17], [10, 16, 17], [11, 12, 13], [11, 12, 14], [11, 12, 15], [11, 12, 16], [11, 12, 17], [11, 13, 14], [11, 13, 15], [11, 13, 16], [11, 13, 17], [11, 14, 15], [11, 14, 16], [11, 14, 17], [11, 15, 16], [11, 15, 17], [11, 16, 17], [12, 13, 14], [12, 13, 15], [12, 13, 16], [12, 13, 17], [12, 14, 15], [12, 14, 16], [12, 14, 17], [12, 15, 16], [12, 15, 17], [12, 16, 17], [13, 14, 15], [13, 14, 16], [13, 14, 17], [13, 15, 16], [13, 15, 17], [13, 16, 17], [14, 15, 16], [14, 15, 17], [14, 16, 17], [15, 16, 17]]\n assert candidate(n = 9,k = 5) == [[1, 2, 3, 4, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9], [1, 2, 3, 8, 9], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9], [1, 2, 4, 8, 9], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9], [1, 2, 5, 8, 9], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9], [1, 2, 6, 8, 9], [1, 2, 7, 8, 9], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9], [1, 3, 4, 8, 9], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9], [1, 3, 5, 8, 9], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9], [1, 3, 6, 8, 9], [1, 3, 7, 8, 9], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9], [1, 4, 5, 8, 9], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9], [1, 4, 6, 8, 9], [1, 4, 7, 8, 9], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9], [1, 5, 6, 8, 9], [1, 5, 7, 8, 9], [1, 6, 7, 8, 9], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9], [2, 3, 4, 7, 8], [2, 3, 4, 7, 9], [2, 3, 4, 8, 9], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8], [2, 3, 5, 6, 9], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9], [2, 3, 5, 8, 9], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9], [2, 3, 6, 8, 9], [2, 3, 7, 8, 9], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9], [2, 4, 5, 8, 9], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9], [2, 4, 6, 8, 9], [2, 4, 7, 8, 9], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9], [2, 5, 6, 8, 9], [2, 5, 7, 8, 9], [2, 6, 7, 8, 9], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9], [3, 4, 5, 8, 9], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9], [3, 4, 6, 8, 9], [3, 4, 7, 8, 9], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9], [3, 5, 6, 8, 9], [3, 5, 7, 8, 9], [3, 6, 7, 8, 9], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9], [4, 5, 6, 8, 9], [4, 5, 7, 8, 9], [4, 6, 7, 8, 9], [5, 6, 7, 8, 9]]\n assert candidate(n = 9,k = 9) == [[1, 2, 3, 4, 5, 6, 7, 8, 9]]\n assert candidate(n = 13,k = 2) == [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [9, 10], [9, 11], [9, 12], [9, 13], [10, 11], [10, 12], [10, 13], [11, 12], [11, 13], [12, 13]]\n assert candidate(n = 11,k = 10) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9, 11], [1, 2, 3, 4, 5, 6, 7, 8, 10, 11], [1, 2, 3, 4, 5, 6, 7, 9, 10, 11], [1, 2, 3, 4, 5, 6, 8, 9, 10, 11], [1, 2, 3, 4, 5, 7, 8, 9, 10, 11], [1, 2, 3, 4, 6, 7, 8, 9, 10, 11], [1, 2, 3, 5, 6, 7, 8, 9, 10, 11], [1, 2, 4, 5, 6, 7, 8, 9, 10, 11], [1, 3, 4, 5, 6, 7, 8, 9, 10, 11], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]\n assert candidate(n = 7,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 5, 6], [1, 5, 7], [1, 6, 7], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 5, 6], [2, 5, 7], [2, 6, 7], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 5, 6], [3, 5, 7], [3, 6, 7], [4, 5, 6], [4, 5, 7], [4, 6, 7], [5, 6, 7]]\n assert candidate(n = 9,k = 8) == [[1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 9], [2, 3, 4, 5, 6, 7, 8, 9]]\n assert candidate(n = 15,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 2, 11], [1, 2, 12], [1, 2, 13], [1, 2, 14], [1, 2, 15], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 3, 10], [1, 3, 11], [1, 3, 12], [1, 3, 13], [1, 3, 14], [1, 3, 15], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 4, 10], [1, 4, 11], [1, 4, 12], [1, 4, 13], [1, 4, 14], [1, 4, 15], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 10], [1, 5, 11], [1, 5, 12], [1, 5, 13], [1, 5, 14], [1, 5, 15], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 10], [1, 6, 11], [1, 6, 12], [1, 6, 13], [1, 6, 14], [1, 6, 15], [1, 7, 8], [1, 7, 9], [1, 7, 10], [1, 7, 11], [1, 7, 12], [1, 7, 13], [1, 7, 14], [1, 7, 15], [1, 8, 9], [1, 8, 10], [1, 8, 11], [1, 8, 12], [1, 8, 13], [1, 8, 14], [1, 8, 15], [1, 9, 10], [1, 9, 11], [1, 9, 12], [1, 9, 13], [1, 9, 14], [1, 9, 15], [1, 10, 11], [1, 10, 12], [1, 10, 13], [1, 10, 14], [1, 10, 15], [1, 11, 12], [1, 11, 13], [1, 11, 14], [1, 11, 15], [1, 12, 13], [1, 12, 14], [1, 12, 15], [1, 13, 14], [1, 13, 15], [1, 14, 15], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], [2, 3, 10], [2, 3, 11], [2, 3, 12], [2, 3, 13], [2, 3, 14], [2, 3, 15], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 4, 10], [2, 4, 11], [2, 4, 12], [2, 4, 13], [2, 4, 14], [2, 4, 15], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9], [2, 5, 10], [2, 5, 11], [2, 5, 12], [2, 5, 13], [2, 5, 14], [2, 5, 15], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 6, 10], [2, 6, 11], [2, 6, 12], [2, 6, 13], [2, 6, 14], [2, 6, 15], [2, 7, 8], [2, 7, 9], [2, 7, 10], [2, 7, 11], [2, 7, 12], [2, 7, 13], [2, 7, 14], [2, 7, 15], [2, 8, 9], [2, 8, 10], [2, 8, 11], [2, 8, 12], [2, 8, 13], [2, 8, 14], [2, 8, 15], [2, 9, 10], [2, 9, 11], [2, 9, 12], [2, 9, 13], [2, 9, 14], [2, 9, 15], [2, 10, 11], [2, 10, 12], [2, 10, 13], [2, 10, 14], [2, 10, 15], [2, 11, 12], [2, 11, 13], [2, 11, 14], [2, 11, 15], [2, 12, 13], [2, 12, 14], [2, 12, 15], [2, 13, 14], [2, 13, 15], [2, 14, 15], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 4, 10], [3, 4, 11], [3, 4, 12], [3, 4, 13], [3, 4, 14], [3, 4, 15], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 5, 10], [3, 5, 11], [3, 5, 12], [3, 5, 13], [3, 5, 14], [3, 5, 15], [3, 6, 7], [3, 6, 8], [3, 6, 9], [3, 6, 10], [3, 6, 11], [3, 6, 12], [3, 6, 13], [3, 6, 14], [3, 6, 15], [3, 7, 8], [3, 7, 9], [3, 7, 10], [3, 7, 11], [3, 7, 12], [3, 7, 13], [3, 7, 14], [3, 7, 15], [3, 8, 9], [3, 8, 10], [3, 8, 11], [3, 8, 12], [3, 8, 13], [3, 8, 14], [3, 8, 15], [3, 9, 10], [3, 9, 11], [3, 9, 12], [3, 9, 13], [3, 9, 14], [3, 9, 15], [3, 10, 11], [3, 10, 12], [3, 10, 13], [3, 10, 14], [3, 10, 15], [3, 11, 12], [3, 11, 13], [3, 11, 14], [3, 11, 15], [3, 12, 13], [3, 12, 14], [3, 12, 15], [3, 13, 14], [3, 13, 15], [3, 14, 15], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 5, 10], [4, 5, 11], [4, 5, 12], [4, 5, 13], [4, 5, 14], [4, 5, 15], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 6, 10], [4, 6, 11], [4, 6, 12], [4, 6, 13], [4, 6, 14], [4, 6, 15], [4, 7, 8], [4, 7, 9], [4, 7, 10], [4, 7, 11], [4, 7, 12], [4, 7, 13], [4, 7, 14], [4, 7, 15], [4, 8, 9], [4, 8, 10], [4, 8, 11], [4, 8, 12], [4, 8, 13], [4, 8, 14], [4, 8, 15], [4, 9, 10], [4, 9, 11], [4, 9, 12], [4, 9, 13], [4, 9, 14], [4, 9, 15], [4, 10, 11], [4, 10, 12], [4, 10, 13], [4, 10, 14], [4, 10, 15], [4, 11, 12], [4, 11, 13], [4, 11, 14], [4, 11, 15], [4, 12, 13], [4, 12, 14], [4, 12, 15], [4, 13, 14], [4, 13, 15], [4, 14, 15], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 6, 10], [5, 6, 11], [5, 6, 12], [5, 6, 13], [5, 6, 14], [5, 6, 15], [5, 7, 8], [5, 7, 9], [5, 7, 10], [5, 7, 11], [5, 7, 12], [5, 7, 13], [5, 7, 14], [5, 7, 15], [5, 8, 9], [5, 8, 10], [5, 8, 11], [5, 8, 12], [5, 8, 13], [5, 8, 14], [5, 8, 15], [5, 9, 10], [5, 9, 11], [5, 9, 12], [5, 9, 13], [5, 9, 14], [5, 9, 15], [5, 10, 11], [5, 10, 12], [5, 10, 13], [5, 10, 14], [5, 10, 15], [5, 11, 12], [5, 11, 13], [5, 11, 14], [5, 11, 15], [5, 12, 13], [5, 12, 14], [5, 12, 15], [5, 13, 14], [5, 13, 15], [5, 14, 15], [6, 7, 8], [6, 7, 9], [6, 7, 10], [6, 7, 11], [6, 7, 12], [6, 7, 13], [6, 7, 14], [6, 7, 15], [6, 8, 9], [6, 8, 10], [6, 8, 11], [6, 8, 12], [6, 8, 13], [6, 8, 14], [6, 8, 15], [6, 9, 10], [6, 9, 11], [6, 9, 12], [6, 9, 13], [6, 9, 14], [6, 9, 15], [6, 10, 11], [6, 10, 12], [6, 10, 13], [6, 10, 14], [6, 10, 15], [6, 11, 12], [6, 11, 13], [6, 11, 14], [6, 11, 15], [6, 12, 13], [6, 12, 14], [6, 12, 15], [6, 13, 14], [6, 13, 15], [6, 14, 15], [7, 8, 9], [7, 8, 10], [7, 8, 11], [7, 8, 12], [7, 8, 13], [7, 8, 14], [7, 8, 15], [7, 9, 10], [7, 9, 11], [7, 9, 12], [7, 9, 13], [7, 9, 14], [7, 9, 15], [7, 10, 11], [7, 10, 12], [7, 10, 13], [7, 10, 14], [7, 10, 15], [7, 11, 12], [7, 11, 13], [7, 11, 14], [7, 11, 15], [7, 12, 13], [7, 12, 14], [7, 12, 15], [7, 13, 14], [7, 13, 15], [7, 14, 15], [8, 9, 10], [8, 9, 11], [8, 9, 12], [8, 9, 13], [8, 9, 14], [8, 9, 15], [8, 10, 11], [8, 10, 12], [8, 10, 13], [8, 10, 14], [8, 10, 15], [8, 11, 12], [8, 11, 13], [8, 11, 14], [8, 11, 15], [8, 12, 13], [8, 12, 14], [8, 12, 15], [8, 13, 14], [8, 13, 15], [8, 14, 15], [9, 10, 11], [9, 10, 12], [9, 10, 13], [9, 10, 14], [9, 10, 15], [9, 11, 12], [9, 11, 13], [9, 11, 14], [9, 11, 15], [9, 12, 13], [9, 12, 14], [9, 12, 15], [9, 13, 14], [9, 13, 15], [9, 14, 15], [10, 11, 12], [10, 11, 13], [10, 11, 14], [10, 11, 15], [10, 12, 13], [10, 12, 14], [10, 12, 15], [10, 13, 14], [10, 13, 15], [10, 14, 15], [11, 12, 13], [11, 12, 14], [11, 12, 15], [11, 13, 14], [11, 13, 15], [11, 14, 15], [12, 13, 14], [12, 13, 15], [12, 14, 15], [13, 14, 15]]\n assert candidate(n = 8,k = 6) == [[1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 7, 8], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 7, 8], [1, 2, 3, 6, 7, 8], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 7, 8], [1, 2, 4, 6, 7, 8], [1, 2, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 7, 8], [1, 3, 4, 6, 7, 8], [1, 3, 5, 6, 7, 8], [1, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 7, 8], [2, 3, 4, 6, 7, 8], [2, 3, 5, 6, 7, 8], [2, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 8]]\n assert candidate(n = 10,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 3, 10], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 4, 10], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 10], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 10], [1, 7, 8], [1, 7, 9], [1, 7, 10], [1, 8, 9], [1, 8, 10], [1, 9, 10], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], [2, 3, 10], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 4, 10], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9], [2, 5, 10], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 6, 10], [2, 7, 8], [2, 7, 9], [2, 7, 10], [2, 8, 9], [2, 8, 10], [2, 9, 10], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 4, 10], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 5, 10], [3, 6, 7], [3, 6, 8], [3, 6, 9], [3, 6, 10], [3, 7, 8], [3, 7, 9], [3, 7, 10], [3, 8, 9], [3, 8, 10], [3, 9, 10], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 5, 10], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 6, 10], [4, 7, 8], [4, 7, 9], [4, 7, 10], [4, 8, 9], [4, 8, 10], [4, 9, 10], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 6, 10], [5, 7, 8], [5, 7, 9], [5, 7, 10], [5, 8, 9], [5, 8, 10], [5, 9, 10], [6, 7, 8], [6, 7, 9], [6, 7, 10], [6, 8, 9], [6, 8, 10], [6, 9, 10], [7, 8, 9], [7, 8, 10], [7, 9, 10], [8, 9, 10]]\n assert candidate(n = 10,k = 9) == [[1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10]]\n assert candidate(n = 13,k = 10) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9, 11], [1, 2, 3, 4, 5, 6, 7, 8, 9, 12], [1, 2, 3, 4, 5, 6, 7, 8, 9, 13], [1, 2, 3, 4, 5, 6, 7, 8, 10, 11], [1, 2, 3, 4, 5, 6, 7, 8, 10, 12], [1, 2, 3, 4, 5, 6, 7, 8, 10, 13], [1, 2, 3, 4, 5, 6, 7, 8, 11, 12], [1, 2, 3, 4, 5, 6, 7, 8, 11, 13], [1, 2, 3, 4, 5, 6, 7, 8, 12, 13], [1, 2, 3, 4, 5, 6, 7, 9, 10, 11], [1, 2, 3, 4, 5, 6, 7, 9, 10, 12], [1, 2, 3, 4, 5, 6, 7, 9, 10, 13], [1, 2, 3, 4, 5, 6, 7, 9, 11, 12], [1, 2, 3, 4, 5, 6, 7, 9, 11, 13], [1, 2, 3, 4, 5, 6, 7, 9, 12, 13], [1, 2, 3, 4, 5, 6, 7, 10, 11, 12], [1, 2, 3, 4, 5, 6, 7, 10, 11, 13], [1, 2, 3, 4, 5, 6, 7, 10, 12, 13], [1, 2, 3, 4, 5, 6, 7, 11, 12, 13], [1, 2, 3, 4, 5, 6, 8, 9, 10, 11], [1, 2, 3, 4, 5, 6, 8, 9, 10, 12], [1, 2, 3, 4, 5, 6, 8, 9, 10, 13], [1, 2, 3, 4, 5, 6, 8, 9, 11, 12], [1, 2, 3, 4, 5, 6, 8, 9, 11, 13], [1, 2, 3, 4, 5, 6, 8, 9, 12, 13], [1, 2, 3, 4, 5, 6, 8, 10, 11, 12], [1, 2, 3, 4, 5, 6, 8, 10, 11, 13], [1, 2, 3, 4, 5, 6, 8, 10, 12, 13], [1, 2, 3, 4, 5, 6, 8, 11, 12, 13], [1, 2, 3, 4, 5, 6, 9, 10, 11, 12], [1, 2, 3, 4, 5, 6, 9, 10, 11, 13], [1, 2, 3, 4, 5, 6, 9, 10, 12, 13], [1, 2, 3, 4, 5, 6, 9, 11, 12, 13], [1, 2, 3, 4, 5, 6, 10, 11, 12, 13], [1, 2, 3, 4, 5, 7, 8, 9, 10, 11], [1, 2, 3, 4, 5, 7, 8, 9, 10, 12], [1, 2, 3, 4, 5, 7, 8, 9, 10, 13], [1, 2, 3, 4, 5, 7, 8, 9, 11, 12], [1, 2, 3, 4, 5, 7, 8, 9, 11, 13], [1, 2, 3, 4, 5, 7, 8, 9, 12, 13], [1, 2, 3, 4, 5, 7, 8, 10, 11, 12], [1, 2, 3, 4, 5, 7, 8, 10, 11, 13], [1, 2, 3, 4, 5, 7, 8, 10, 12, 13], [1, 2, 3, 4, 5, 7, 8, 11, 12, 13], [1, 2, 3, 4, 5, 7, 9, 10, 11, 12], [1, 2, 3, 4, 5, 7, 9, 10, 11, 13], [1, 2, 3, 4, 5, 7, 9, 10, 12, 13], [1, 2, 3, 4, 5, 7, 9, 11, 12, 13], [1, 2, 3, 4, 5, 7, 10, 11, 12, 13], [1, 2, 3, 4, 5, 8, 9, 10, 11, 12], [1, 2, 3, 4, 5, 8, 9, 10, 11, 13], [1, 2, 3, 4, 5, 8, 9, 10, 12, 13], [1, 2, 3, 4, 5, 8, 9, 11, 12, 13], [1, 2, 3, 4, 5, 8, 10, 11, 12, 13], [1, 2, 3, 4, 5, 9, 10, 11, 12, 13], [1, 2, 3, 4, 6, 7, 8, 9, 10, 11], [1, 2, 3, 4, 6, 7, 8, 9, 10, 12], [1, 2, 3, 4, 6, 7, 8, 9, 10, 13], [1, 2, 3, 4, 6, 7, 8, 9, 11, 12], [1, 2, 3, 4, 6, 7, 8, 9, 11, 13], [1, 2, 3, 4, 6, 7, 8, 9, 12, 13], [1, 2, 3, 4, 6, 7, 8, 10, 11, 12], [1, 2, 3, 4, 6, 7, 8, 10, 11, 13], [1, 2, 3, 4, 6, 7, 8, 10, 12, 13], [1, 2, 3, 4, 6, 7, 8, 11, 12, 13], [1, 2, 3, 4, 6, 7, 9, 10, 11, 12], [1, 2, 3, 4, 6, 7, 9, 10, 11, 13], [1, 2, 3, 4, 6, 7, 9, 10, 12, 13], [1, 2, 3, 4, 6, 7, 9, 11, 12, 13], [1, 2, 3, 4, 6, 7, 10, 11, 12, 13], [1, 2, 3, 4, 6, 8, 9, 10, 11, 12], [1, 2, 3, 4, 6, 8, 9, 10, 11, 13], [1, 2, 3, 4, 6, 8, 9, 10, 12, 13], [1, 2, 3, 4, 6, 8, 9, 11, 12, 13], [1, 2, 3, 4, 6, 8, 10, 11, 12, 13], [1, 2, 3, 4, 6, 9, 10, 11, 12, 13], [1, 2, 3, 4, 7, 8, 9, 10, 11, 12], [1, 2, 3, 4, 7, 8, 9, 10, 11, 13], [1, 2, 3, 4, 7, 8, 9, 10, 12, 13], [1, 2, 3, 4, 7, 8, 9, 11, 12, 13], [1, 2, 3, 4, 7, 8, 10, 11, 12, 13], [1, 2, 3, 4, 7, 9, 10, 11, 12, 13], [1, 2, 3, 4, 8, 9, 10, 11, 12, 13], [1, 2, 3, 5, 6, 7, 8, 9, 10, 11], [1, 2, 3, 5, 6, 7, 8, 9, 10, 12], [1, 2, 3, 5, 6, 7, 8, 9, 10, 13], [1, 2, 3, 5, 6, 7, 8, 9, 11, 12], [1, 2, 3, 5, 6, 7, 8, 9, 11, 13], [1, 2, 3, 5, 6, 7, 8, 9, 12, 13], [1, 2, 3, 5, 6, 7, 8, 10, 11, 12], [1, 2, 3, 5, 6, 7, 8, 10, 11, 13], [1, 2, 3, 5, 6, 7, 8, 10, 12, 13], [1, 2, 3, 5, 6, 7, 8, 11, 12, 13], [1, 2, 3, 5, 6, 7, 9, 10, 11, 12], [1, 2, 3, 5, 6, 7, 9, 10, 11, 13], [1, 2, 3, 5, 6, 7, 9, 10, 12, 13], [1, 2, 3, 5, 6, 7, 9, 11, 12, 13], [1, 2, 3, 5, 6, 7, 10, 11, 12, 13], [1, 2, 3, 5, 6, 8, 9, 10, 11, 12], [1, 2, 3, 5, 6, 8, 9, 10, 11, 13], [1, 2, 3, 5, 6, 8, 9, 10, 12, 13], [1, 2, 3, 5, 6, 8, 9, 11, 12, 13], [1, 2, 3, 5, 6, 8, 10, 11, 12, 13], [1, 2, 3, 5, 6, 9, 10, 11, 12, 13], [1, 2, 3, 5, 7, 8, 9, 10, 11, 12], [1, 2, 3, 5, 7, 8, 9, 10, 11, 13], [1, 2, 3, 5, 7, 8, 9, 10, 12, 13], [1, 2, 3, 5, 7, 8, 9, 11, 12, 13], [1, 2, 3, 5, 7, 8, 10, 11, 12, 13], [1, 2, 3, 5, 7, 9, 10, 11, 12, 13], [1, 2, 3, 5, 8, 9, 10, 11, 12, 13], [1, 2, 3, 6, 7, 8, 9, 10, 11, 12], [1, 2, 3, 6, 7, 8, 9, 10, 11, 13], [1, 2, 3, 6, 7, 8, 9, 10, 12, 13], [1, 2, 3, 6, 7, 8, 9, 11, 12, 13], [1, 2, 3, 6, 7, 8, 10, 11, 12, 13], [1, 2, 3, 6, 7, 9, 10, 11, 12, 13], [1, 2, 3, 6, 8, 9, 10, 11, 12, 13], [1, 2, 3, 7, 8, 9, 10, 11, 12, 13], [1, 2, 4, 5, 6, 7, 8, 9, 10, 11], [1, 2, 4, 5, 6, 7, 8, 9, 10, 12], [1, 2, 4, 5, 6, 7, 8, 9, 10, 13], [1, 2, 4, 5, 6, 7, 8, 9, 11, 12], [1, 2, 4, 5, 6, 7, 8, 9, 11, 13], [1, 2, 4, 5, 6, 7, 8, 9, 12, 13], [1, 2, 4, 5, 6, 7, 8, 10, 11, 12], [1, 2, 4, 5, 6, 7, 8, 10, 11, 13], [1, 2, 4, 5, 6, 7, 8, 10, 12, 13], [1, 2, 4, 5, 6, 7, 8, 11, 12, 13], [1, 2, 4, 5, 6, 7, 9, 10, 11, 12], [1, 2, 4, 5, 6, 7, 9, 10, 11, 13], [1, 2, 4, 5, 6, 7, 9, 10, 12, 13], [1, 2, 4, 5, 6, 7, 9, 11, 12, 13], [1, 2, 4, 5, 6, 7, 10, 11, 12, 13], [1, 2, 4, 5, 6, 8, 9, 10, 11, 12], [1, 2, 4, 5, 6, 8, 9, 10, 11, 13], [1, 2, 4, 5, 6, 8, 9, 10, 12, 13], [1, 2, 4, 5, 6, 8, 9, 11, 12, 13], [1, 2, 4, 5, 6, 8, 10, 11, 12, 13], [1, 2, 4, 5, 6, 9, 10, 11, 12, 13], [1, 2, 4, 5, 7, 8, 9, 10, 11, 12], [1, 2, 4, 5, 7, 8, 9, 10, 11, 13], [1, 2, 4, 5, 7, 8, 9, 10, 12, 13], [1, 2, 4, 5, 7, 8, 9, 11, 12, 13], [1, 2, 4, 5, 7, 8, 10, 11, 12, 13], [1, 2, 4, 5, 7, 9, 10, 11, 12, 13], [1, 2, 4, 5, 8, 9, 10, 11, 12, 13], [1, 2, 4, 6, 7, 8, 9, 10, 11, 12], [1, 2, 4, 6, 7, 8, 9, 10, 11, 13], [1, 2, 4, 6, 7, 8, 9, 10, 12, 13], [1, 2, 4, 6, 7, 8, 9, 11, 12, 13], [1, 2, 4, 6, 7, 8, 10, 11, 12, 13], [1, 2, 4, 6, 7, 9, 10, 11, 12, 13], [1, 2, 4, 6, 8, 9, 10, 11, 12, 13], [1, 2, 4, 7, 8, 9, 10, 11, 12, 13], [1, 2, 5, 6, 7, 8, 9, 10, 11, 12], [1, 2, 5, 6, 7, 8, 9, 10, 11, 13], [1, 2, 5, 6, 7, 8, 9, 10, 12, 13], [1, 2, 5, 6, 7, 8, 9, 11, 12, 13], [1, 2, 5, 6, 7, 8, 10, 11, 12, 13], [1, 2, 5, 6, 7, 9, 10, 11, 12, 13], [1, 2, 5, 6, 8, 9, 10, 11, 12, 13], [1, 2, 5, 7, 8, 9, 10, 11, 12, 13], [1, 2, 6, 7, 8, 9, 10, 11, 12, 13], [1, 3, 4, 5, 6, 7, 8, 9, 10, 11], [1, 3, 4, 5, 6, 7, 8, 9, 10, 12], [1, 3, 4, 5, 6, 7, 8, 9, 10, 13], [1, 3, 4, 5, 6, 7, 8, 9, 11, 12], [1, 3, 4, 5, 6, 7, 8, 9, 11, 13], [1, 3, 4, 5, 6, 7, 8, 9, 12, 13], [1, 3, 4, 5, 6, 7, 8, 10, 11, 12], [1, 3, 4, 5, 6, 7, 8, 10, 11, 13], [1, 3, 4, 5, 6, 7, 8, 10, 12, 13], [1, 3, 4, 5, 6, 7, 8, 11, 12, 13], [1, 3, 4, 5, 6, 7, 9, 10, 11, 12], [1, 3, 4, 5, 6, 7, 9, 10, 11, 13], [1, 3, 4, 5, 6, 7, 9, 10, 12, 13], [1, 3, 4, 5, 6, 7, 9, 11, 12, 13], [1, 3, 4, 5, 6, 7, 10, 11, 12, 13], [1, 3, 4, 5, 6, 8, 9, 10, 11, 12], [1, 3, 4, 5, 6, 8, 9, 10, 11, 13], [1, 3, 4, 5, 6, 8, 9, 10, 12, 13], [1, 3, 4, 5, 6, 8, 9, 11, 12, 13], [1, 3, 4, 5, 6, 8, 10, 11, 12, 13], [1, 3, 4, 5, 6, 9, 10, 11, 12, 13], [1, 3, 4, 5, 7, 8, 9, 10, 11, 12], [1, 3, 4, 5, 7, 8, 9, 10, 11, 13], [1, 3, 4, 5, 7, 8, 9, 10, 12, 13], [1, 3, 4, 5, 7, 8, 9, 11, 12, 13], [1, 3, 4, 5, 7, 8, 10, 11, 12, 13], [1, 3, 4, 5, 7, 9, 10, 11, 12, 13], [1, 3, 4, 5, 8, 9, 10, 11, 12, 13], [1, 3, 4, 6, 7, 8, 9, 10, 11, 12], [1, 3, 4, 6, 7, 8, 9, 10, 11, 13], [1, 3, 4, 6, 7, 8, 9, 10, 12, 13], [1, 3, 4, 6, 7, 8, 9, 11, 12, 13], [1, 3, 4, 6, 7, 8, 10, 11, 12, 13], [1, 3, 4, 6, 7, 9, 10, 11, 12, 13], [1, 3, 4, 6, 8, 9, 10, 11, 12, 13], [1, 3, 4, 7, 8, 9, 10, 11, 12, 13], [1, 3, 5, 6, 7, 8, 9, 10, 11, 12], [1, 3, 5, 6, 7, 8, 9, 10, 11, 13], [1, 3, 5, 6, 7, 8, 9, 10, 12, 13], [1, 3, 5, 6, 7, 8, 9, 11, 12, 13], [1, 3, 5, 6, 7, 8, 10, 11, 12, 13], [1, 3, 5, 6, 7, 9, 10, 11, 12, 13], [1, 3, 5, 6, 8, 9, 10, 11, 12, 13], [1, 3, 5, 7, 8, 9, 10, 11, 12, 13], [1, 3, 6, 7, 8, 9, 10, 11, 12, 13], [1, 4, 5, 6, 7, 8, 9, 10, 11, 12], [1, 4, 5, 6, 7, 8, 9, 10, 11, 13], [1, 4, 5, 6, 7, 8, 9, 10, 12, 13], [1, 4, 5, 6, 7, 8, 9, 11, 12, 13], [1, 4, 5, 6, 7, 8, 10, 11, 12, 13], [1, 4, 5, 6, 7, 9, 10, 11, 12, 13], [1, 4, 5, 6, 8, 9, 10, 11, 12, 13], [1, 4, 5, 7, 8, 9, 10, 11, 12, 13], [1, 4, 6, 7, 8, 9, 10, 11, 12, 13], [1, 5, 6, 7, 8, 9, 10, 11, 12, 13], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [2, 3, 4, 5, 6, 7, 8, 9, 10, 12], [2, 3, 4, 5, 6, 7, 8, 9, 10, 13], [2, 3, 4, 5, 6, 7, 8, 9, 11, 12], [2, 3, 4, 5, 6, 7, 8, 9, 11, 13], [2, 3, 4, 5, 6, 7, 8, 9, 12, 13], [2, 3, 4, 5, 6, 7, 8, 10, 11, 12], [2, 3, 4, 5, 6, 7, 8, 10, 11, 13], [2, 3, 4, 5, 6, 7, 8, 10, 12, 13], [2, 3, 4, 5, 6, 7, 8, 11, 12, 13], [2, 3, 4, 5, 6, 7, 9, 10, 11, 12], [2, 3, 4, 5, 6, 7, 9, 10, 11, 13], [2, 3, 4, 5, 6, 7, 9, 10, 12, 13], [2, 3, 4, 5, 6, 7, 9, 11, 12, 13], [2, 3, 4, 5, 6, 7, 10, 11, 12, 13], [2, 3, 4, 5, 6, 8, 9, 10, 11, 12], [2, 3, 4, 5, 6, 8, 9, 10, 11, 13], [2, 3, 4, 5, 6, 8, 9, 10, 12, 13], [2, 3, 4, 5, 6, 8, 9, 11, 12, 13], [2, 3, 4, 5, 6, 8, 10, 11, 12, 13], [2, 3, 4, 5, 6, 9, 10, 11, 12, 13], [2, 3, 4, 5, 7, 8, 9, 10, 11, 12], [2, 3, 4, 5, 7, 8, 9, 10, 11, 13], [2, 3, 4, 5, 7, 8, 9, 10, 12, 13], [2, 3, 4, 5, 7, 8, 9, 11, 12, 13], [2, 3, 4, 5, 7, 8, 10, 11, 12, 13], [2, 3, 4, 5, 7, 9, 10, 11, 12, 13], [2, 3, 4, 5, 8, 9, 10, 11, 12, 13], [2, 3, 4, 6, 7, 8, 9, 10, 11, 12], [2, 3, 4, 6, 7, 8, 9, 10, 11, 13], [2, 3, 4, 6, 7, 8, 9, 10, 12, 13], [2, 3, 4, 6, 7, 8, 9, 11, 12, 13], [2, 3, 4, 6, 7, 8, 10, 11, 12, 13], [2, 3, 4, 6, 7, 9, 10, 11, 12, 13], [2, 3, 4, 6, 8, 9, 10, 11, 12, 13], [2, 3, 4, 7, 8, 9, 10, 11, 12, 13], [2, 3, 5, 6, 7, 8, 9, 10, 11, 12], [2, 3, 5, 6, 7, 8, 9, 10, 11, 13], [2, 3, 5, 6, 7, 8, 9, 10, 12, 13], [2, 3, 5, 6, 7, 8, 9, 11, 12, 13], [2, 3, 5, 6, 7, 8, 10, 11, 12, 13], [2, 3, 5, 6, 7, 9, 10, 11, 12, 13], [2, 3, 5, 6, 8, 9, 10, 11, 12, 13], [2, 3, 5, 7, 8, 9, 10, 11, 12, 13], [2, 3, 6, 7, 8, 9, 10, 11, 12, 13], [2, 4, 5, 6, 7, 8, 9, 10, 11, 12], [2, 4, 5, 6, 7, 8, 9, 10, 11, 13], [2, 4, 5, 6, 7, 8, 9, 10, 12, 13], [2, 4, 5, 6, 7, 8, 9, 11, 12, 13], [2, 4, 5, 6, 7, 8, 10, 11, 12, 13], [2, 4, 5, 6, 7, 9, 10, 11, 12, 13], [2, 4, 5, 6, 8, 9, 10, 11, 12, 13], [2, 4, 5, 7, 8, 9, 10, 11, 12, 13], [2, 4, 6, 7, 8, 9, 10, 11, 12, 13], [2, 5, 6, 7, 8, 9, 10, 11, 12, 13], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [3, 4, 5, 6, 7, 8, 9, 10, 11, 13], [3, 4, 5, 6, 7, 8, 9, 10, 12, 13], [3, 4, 5, 6, 7, 8, 9, 11, 12, 13], [3, 4, 5, 6, 7, 8, 10, 11, 12, 13], [3, 4, 5, 6, 7, 9, 10, 11, 12, 13], [3, 4, 5, 6, 8, 9, 10, 11, 12, 13], [3, 4, 5, 7, 8, 9, 10, 11, 12, 13], [3, 4, 6, 7, 8, 9, 10, 11, 12, 13], [3, 5, 6, 7, 8, 9, 10, 11, 12, 13], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]]\n assert candidate(n = 14,k = 2) == [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [10, 11], [10, 12], [10, 13], [10, 14], [11, 12], [11, 13], [11, 14], [12, 13], [12, 14], [13, 14]]\n assert candidate(n = 7,k = 2) == [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [4, 5], [4, 6], [4, 7], [5, 6], [5, 7], [6, 7]]\n assert candidate(n = 17,k = 2) == [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [4, 10], [4, 11], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 12], [5, 13], [5, 14], [5, 15], [5, 16], [5, 17], [6, 7], [6, 8], [6, 9], [6, 10], [6, 11], [6, 12], [6, 13], [6, 14], [6, 15], [6, 16], [6, 17], [7, 8], [7, 9], [7, 10], [7, 11], [7, 12], [7, 13], [7, 14], [7, 15], [7, 16], [7, 17], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14], [8, 15], [8, 16], [8, 17], [9, 10], [9, 11], [9, 12], [9, 13], [9, 14], [9, 15], [9, 16], [9, 17], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [11, 12], [11, 13], [11, 14], [11, 15], [11, 16], [11, 17], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [13, 14], [13, 15], [13, 16], [13, 17], [14, 15], [14, 16], [14, 17], [15, 16], [15, 17], [16, 17]]\n assert candidate(n = 12,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 2, 11], [1, 2, 12], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 3, 10], [1, 3, 11], [1, 3, 12], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 4, 10], [1, 4, 11], [1, 4, 12], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 10], [1, 5, 11], [1, 5, 12], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 10], [1, 6, 11], [1, 6, 12], [1, 7, 8], [1, 7, 9], [1, 7, 10], [1, 7, 11], [1, 7, 12], [1, 8, 9], [1, 8, 10], [1, 8, 11], [1, 8, 12], [1, 9, 10], [1, 9, 11], [1, 9, 12], [1, 10, 11], [1, 10, 12], [1, 11, 12], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], [2, 3, 10], [2, 3, 11], [2, 3, 12], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 4, 10], [2, 4, 11], [2, 4, 12], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9], [2, 5, 10], [2, 5, 11], [2, 5, 12], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 6, 10], [2, 6, 11], [2, 6, 12], [2, 7, 8], [2, 7, 9], [2, 7, 10], [2, 7, 11], [2, 7, 12], [2, 8, 9], [2, 8, 10], [2, 8, 11], [2, 8, 12], [2, 9, 10], [2, 9, 11], [2, 9, 12], [2, 10, 11], [2, 10, 12], [2, 11, 12], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 4, 10], [3, 4, 11], [3, 4, 12], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 5, 10], [3, 5, 11], [3, 5, 12], [3, 6, 7], [3, 6, 8], [3, 6, 9], [3, 6, 10], [3, 6, 11], [3, 6, 12], [3, 7, 8], [3, 7, 9], [3, 7, 10], [3, 7, 11], [3, 7, 12], [3, 8, 9], [3, 8, 10], [3, 8, 11], [3, 8, 12], [3, 9, 10], [3, 9, 11], [3, 9, 12], [3, 10, 11], [3, 10, 12], [3, 11, 12], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 5, 10], [4, 5, 11], [4, 5, 12], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 6, 10], [4, 6, 11], [4, 6, 12], [4, 7, 8], [4, 7, 9], [4, 7, 10], [4, 7, 11], [4, 7, 12], [4, 8, 9], [4, 8, 10], [4, 8, 11], [4, 8, 12], [4, 9, 10], [4, 9, 11], [4, 9, 12], [4, 10, 11], [4, 10, 12], [4, 11, 12], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 6, 10], [5, 6, 11], [5, 6, 12], [5, 7, 8], [5, 7, 9], [5, 7, 10], [5, 7, 11], [5, 7, 12], [5, 8, 9], [5, 8, 10], [5, 8, 11], [5, 8, 12], [5, 9, 10], [5, 9, 11], [5, 9, 12], [5, 10, 11], [5, 10, 12], [5, 11, 12], [6, 7, 8], [6, 7, 9], [6, 7, 10], [6, 7, 11], [6, 7, 12], [6, 8, 9], [6, 8, 10], [6, 8, 11], [6, 8, 12], [6, 9, 10], [6, 9, 11], [6, 9, 12], [6, 10, 11], [6, 10, 12], [6, 11, 12], [7, 8, 9], [7, 8, 10], [7, 8, 11], [7, 8, 12], [7, 9, 10], [7, 9, 11], [7, 9, 12], [7, 10, 11], [7, 10, 12], [7, 11, 12], [8, 9, 10], [8, 9, 11], [8, 9, 12], [8, 10, 11], [8, 10, 12], [8, 11, 12], [9, 10, 11], [9, 10, 12], [9, 11, 12], [10, 11, 12]]\n assert candidate(n = 11,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 2, 11], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 3, 9], [1, 3, 10], [1, 3, 11], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 4, 9], [1, 4, 10], [1, 4, 11], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 10], [1, 5, 11], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 10], [1, 6, 11], [1, 7, 8], [1, 7, 9], [1, 7, 10], [1, 7, 11], [1, 8, 9], [1, 8, 10], [1, 8, 11], [1, 9, 10], [1, 9, 11], [1, 10, 11], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 3, 9], [2, 3, 10], [2, 3, 11], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 4, 10], [2, 4, 11], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 5, 9], [2, 5, 10], [2, 5, 11], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 6, 10], [2, 6, 11], [2, 7, 8], [2, 7, 9], [2, 7, 10], [2, 7, 11], [2, 8, 9], [2, 8, 10], [2, 8, 11], [2, 9, 10], [2, 9, 11], [2, 10, 11], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 4, 10], [3, 4, 11], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 5, 10], [3, 5, 11], [3, 6, 7], [3, 6, 8], [3, 6, 9], [3, 6, 10], [3, 6, 11], [3, 7, 8], [3, 7, 9], [3, 7, 10], [3, 7, 11], [3, 8, 9], [3, 8, 10], [3, 8, 11], [3, 9, 10], [3, 9, 11], [3, 10, 11], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 5, 10], [4, 5, 11], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 6, 10], [4, 6, 11], [4, 7, 8], [4, 7, 9], [4, 7, 10], [4, 7, 11], [4, 8, 9], [4, 8, 10], [4, 8, 11], [4, 9, 10], [4, 9, 11], [4, 10, 11], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 6, 10], [5, 6, 11], [5, 7, 8], [5, 7, 9], [5, 7, 10], [5, 7, 11], [5, 8, 9], [5, 8, 10], [5, 8, 11], [5, 9, 10], [5, 9, 11], [5, 10, 11], [6, 7, 8], [6, 7, 9], [6, 7, 10], [6, 7, 11], [6, 8, 9], [6, 8, 10], [6, 8, 11], [6, 9, 10], [6, 9, 11], [6, 10, 11], [7, 8, 9], [7, 8, 10], [7, 8, 11], [7, 9, 10], [7, 9, 11], [7, 10, 11], [8, 9, 10], [8, 9, 11], [8, 10, 11], [9, 10, 11]]\n assert candidate(n = 8,k = 3) == [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 6, 7], [1, 6, 8], [1, 7, 8], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 3, 8], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 6, 7], [2, 6, 8], [2, 7, 8], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 6, 7], [3, 6, 8], [3, 7, 8], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 6, 7], [4, 6, 8], [4, 7, 8], [5, 6, 7], [5, 6, 8], [5, 7, 8], [6, 7, 8]]\n assert candidate(n = 8,k = 4) == [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4, 8], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 7, 8], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 6, 7], [1, 3, 6, 8], [1, 3, 7, 8], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5, 8], [1, 4, 6, 7], [1, 4, 6, 8], [1, 4, 7, 8], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 7, 8], [1, 6, 7, 8], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4, 8], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5, 8], [2, 3, 6, 7], [2, 3, 6, 8], [2, 3, 7, 8], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5, 8], [2, 4, 6, 7], [2, 4, 6, 8], [2, 4, 7, 8], [2, 5, 6, 7], [2, 5, 6, 8], [2, 5, 7, 8], [2, 6, 7, 8], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5, 8], [3, 4, 6, 7], [3, 4, 6, 8], [3, 4, 7, 8], [3, 5, 6, 7], [3, 5, 6, 8], [3, 5, 7, 8], [3, 6, 7, 8], [4, 5, 6, 7], [4, 5, 6, 8], [4, 5, 7, 8], [4, 6, 7, 8], [5, 6, 7, 8]]\n assert candidate(n = 13,k = 5) == [[1, 2, 3, 4, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4, 11], [1, 2, 3, 4, 12], [1, 2, 3, 4, 13], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5, 11], [1, 2, 3, 5, 12], [1, 2, 3, 5, 13], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6, 11], [1, 2, 3, 6, 12], [1, 2, 3, 6, 13], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7, 11], [1, 2, 3, 7, 12], [1, 2, 3, 7, 13], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8, 11], [1, 2, 3, 8, 12], [1, 2, 3, 8, 13], [1, 2, 3, 9, 10], [1, 2, 3, 9, 11], [1, 2, 3, 9, 12], [1, 2, 3, 9, 13], [1, 2, 3, 10, 11], [1, 2, 3, 10, 12], [1, 2, 3, 10, 13], [1, 2, 3, 11, 12], [1, 2, 3, 11, 13], [1, 2, 3, 12, 13], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5, 11], [1, 2, 4, 5, 12], [1, 2, 4, 5, 13], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6, 11], [1, 2, 4, 6, 12], [1, 2, 4, 6, 13], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7, 11], [1, 2, 4, 7, 12], [1, 2, 4, 7, 13], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8, 11], [1, 2, 4, 8, 12], [1, 2, 4, 8, 13], [1, 2, 4, 9, 10], [1, 2, 4, 9, 11], [1, 2, 4, 9, 12], [1, 2, 4, 9, 13], [1, 2, 4, 10, 11], [1, 2, 4, 10, 12], [1, 2, 4, 10, 13], [1, 2, 4, 11, 12], [1, 2, 4, 11, 13], [1, 2, 4, 12, 13], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6, 11], [1, 2, 5, 6, 12], [1, 2, 5, 6, 13], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7, 11], [1, 2, 5, 7, 12], [1, 2, 5, 7, 13], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8, 11], [1, 2, 5, 8, 12], [1, 2, 5, 8, 13], [1, 2, 5, 9, 10], [1, 2, 5, 9, 11], [1, 2, 5, 9, 12], [1, 2, 5, 9, 13], [1, 2, 5, 10, 11], [1, 2, 5, 10, 12], [1, 2, 5, 10, 13], [1, 2, 5, 11, 12], [1, 2, 5, 11, 13], [1, 2, 5, 12, 13], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 7, 11], [1, 2, 6, 7, 12], [1, 2, 6, 7, 13], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 8, 11], [1, 2, 6, 8, 12], [1, 2, 6, 8, 13], [1, 2, 6, 9, 10], [1, 2, 6, 9, 11], [1, 2, 6, 9, 12], [1, 2, 6, 9, 13], [1, 2, 6, 10, 11], [1, 2, 6, 10, 12], [1, 2, 6, 10, 13], [1, 2, 6, 11, 12], [1, 2, 6, 11, 13], [1, 2, 6, 12, 13], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 8, 11], [1, 2, 7, 8, 12], [1, 2, 7, 8, 13], [1, 2, 7, 9, 10], [1, 2, 7, 9, 11], [1, 2, 7, 9, 12], [1, 2, 7, 9, 13], [1, 2, 7, 10, 11], [1, 2, 7, 10, 12], [1, 2, 7, 10, 13], [1, 2, 7, 11, 12], [1, 2, 7, 11, 13], [1, 2, 7, 12, 13], [1, 2, 8, 9, 10], [1, 2, 8, 9, 11], [1, 2, 8, 9, 12], [1, 2, 8, 9, 13], [1, 2, 8, 10, 11], [1, 2, 8, 10, 12], [1, 2, 8, 10, 13], [1, 2, 8, 11, 12], [1, 2, 8, 11, 13], [1, 2, 8, 12, 13], [1, 2, 9, 10, 11], [1, 2, 9, 10, 12], [1, 2, 9, 10, 13], [1, 2, 9, 11, 12], [1, 2, 9, 11, 13], [1, 2, 9, 12, 13], [1, 2, 10, 11, 12], [1, 2, 10, 11, 13], [1, 2, 10, 12, 13], [1, 2, 11, 12, 13], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9], [1, 3, 4, 5, 10], [1, 3, 4, 5, 11], [1, 3, 4, 5, 12], [1, 3, 4, 5, 13], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9], [1, 3, 4, 6, 10], [1, 3, 4, 6, 11], [1, 3, 4, 6, 12], [1, 3, 4, 6, 13], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 7, 11], [1, 3, 4, 7, 12], [1, 3, 4, 7, 13], [1, 3, 4, 8, 9], [1, 3, 4, 8, 10], [1, 3, 4, 8, 11], [1, 3, 4, 8, 12], [1, 3, 4, 8, 13], [1, 3, 4, 9, 10], [1, 3, 4, 9, 11], [1, 3, 4, 9, 12], [1, 3, 4, 9, 13], [1, 3, 4, 10, 11], [1, 3, 4, 10, 12], [1, 3, 4, 10, 13], [1, 3, 4, 11, 12], [1, 3, 4, 11, 13], [1, 3, 4, 12, 13], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9], [1, 3, 5, 6, 10], [1, 3, 5, 6, 11], [1, 3, 5, 6, 12], [1, 3, 5, 6, 13], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9], [1, 3, 5, 7, 10], [1, 3, 5, 7, 11], [1, 3, 5, 7, 12], [1, 3, 5, 7, 13], [1, 3, 5, 8, 9], [1, 3, 5, 8, 10], [1, 3, 5, 8, 11], [1, 3, 5, 8, 12], [1, 3, 5, 8, 13], [1, 3, 5, 9, 10], [1, 3, 5, 9, 11], [1, 3, 5, 9, 12], [1, 3, 5, 9, 13], [1, 3, 5, 10, 11], [1, 3, 5, 10, 12], [1, 3, 5, 10, 13], [1, 3, 5, 11, 12], [1, 3, 5, 11, 13], [1, 3, 5, 12, 13], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9], [1, 3, 6, 7, 10], [1, 3, 6, 7, 11], [1, 3, 6, 7, 12], [1, 3, 6, 7, 13], [1, 3, 6, 8, 9], [1, 3, 6, 8, 10], [1, 3, 6, 8, 11], [1, 3, 6, 8, 12], [1, 3, 6, 8, 13], [1, 3, 6, 9, 10], [1, 3, 6, 9, 11], [1, 3, 6, 9, 12], [1, 3, 6, 9, 13], [1, 3, 6, 10, 11], [1, 3, 6, 10, 12], [1, 3, 6, 10, 13], [1, 3, 6, 11, 12], [1, 3, 6, 11, 13], [1, 3, 6, 12, 13], [1, 3, 7, 8, 9], [1, 3, 7, 8, 10], [1, 3, 7, 8, 11], [1, 3, 7, 8, 12], [1, 3, 7, 8, 13], [1, 3, 7, 9, 10], [1, 3, 7, 9, 11], [1, 3, 7, 9, 12], [1, 3, 7, 9, 13], [1, 3, 7, 10, 11], [1, 3, 7, 10, 12], [1, 3, 7, 10, 13], [1, 3, 7, 11, 12], [1, 3, 7, 11, 13], [1, 3, 7, 12, 13], [1, 3, 8, 9, 10], [1, 3, 8, 9, 11], [1, 3, 8, 9, 12], [1, 3, 8, 9, 13], [1, 3, 8, 10, 11], [1, 3, 8, 10, 12], [1, 3, 8, 10, 13], [1, 3, 8, 11, 12], [1, 3, 8, 11, 13], [1, 3, 8, 12, 13], [1, 3, 9, 10, 11], [1, 3, 9, 10, 12], [1, 3, 9, 10, 13], [1, 3, 9, 11, 12], [1, 3, 9, 11, 13], [1, 3, 9, 12, 13], [1, 3, 10, 11, 12], [1, 3, 10, 11, 13], [1, 3, 10, 12, 13], [1, 3, 11, 12, 13], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9], [1, 4, 5, 6, 10], [1, 4, 5, 6, 11], [1, 4, 5, 6, 12], [1, 4, 5, 6, 13], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9], [1, 4, 5, 7, 10], [1, 4, 5, 7, 11], [1, 4, 5, 7, 12], [1, 4, 5, 7, 13], [1, 4, 5, 8, 9], [1, 4, 5, 8, 10], [1, 4, 5, 8, 11], [1, 4, 5, 8, 12], [1, 4, 5, 8, 13], [1, 4, 5, 9, 10], [1, 4, 5, 9, 11], [1, 4, 5, 9, 12], [1, 4, 5, 9, 13], [1, 4, 5, 10, 11], [1, 4, 5, 10, 12], [1, 4, 5, 10, 13], [1, 4, 5, 11, 12], [1, 4, 5, 11, 13], [1, 4, 5, 12, 13], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9], [1, 4, 6, 7, 10], [1, 4, 6, 7, 11], [1, 4, 6, 7, 12], [1, 4, 6, 7, 13], [1, 4, 6, 8, 9], [1, 4, 6, 8, 10], [1, 4, 6, 8, 11], [1, 4, 6, 8, 12], [1, 4, 6, 8, 13], [1, 4, 6, 9, 10], [1, 4, 6, 9, 11], [1, 4, 6, 9, 12], [1, 4, 6, 9, 13], [1, 4, 6, 10, 11], [1, 4, 6, 10, 12], [1, 4, 6, 10, 13], [1, 4, 6, 11, 12], [1, 4, 6, 11, 13], [1, 4, 6, 12, 13], [1, 4, 7, 8, 9], [1, 4, 7, 8, 10], [1, 4, 7, 8, 11], [1, 4, 7, 8, 12], [1, 4, 7, 8, 13], [1, 4, 7, 9, 10], [1, 4, 7, 9, 11], [1, 4, 7, 9, 12], [1, 4, 7, 9, 13], [1, 4, 7, 10, 11], [1, 4, 7, 10, 12], [1, 4, 7, 10, 13], [1, 4, 7, 11, 12], [1, 4, 7, 11, 13], [1, 4, 7, 12, 13], [1, 4, 8, 9, 10], [1, 4, 8, 9, 11], [1, 4, 8, 9, 12], [1, 4, 8, 9, 13], [1, 4, 8, 10, 11], [1, 4, 8, 10, 12], [1, 4, 8, 10, 13], [1, 4, 8, 11, 12], [1, 4, 8, 11, 13], [1, 4, 8, 12, 13], [1, 4, 9, 10, 11], [1, 4, 9, 10, 12], [1, 4, 9, 10, 13], [1, 4, 9, 11, 12], [1, 4, 9, 11, 13], [1, 4, 9, 12, 13], [1, 4, 10, 11, 12], [1, 4, 10, 11, 13], [1, 4, 10, 12, 13], [1, 4, 11, 12, 13], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9], [1, 5, 6, 7, 10], [1, 5, 6, 7, 11], [1, 5, 6, 7, 12], [1, 5, 6, 7, 13], [1, 5, 6, 8, 9], [1, 5, 6, 8, 10], [1, 5, 6, 8, 11], [1, 5, 6, 8, 12], [1, 5, 6, 8, 13], [1, 5, 6, 9, 10], [1, 5, 6, 9, 11], [1, 5, 6, 9, 12], [1, 5, 6, 9, 13], [1, 5, 6, 10, 11], [1, 5, 6, 10, 12], [1, 5, 6, 10, 13], [1, 5, 6, 11, 12], [1, 5, 6, 11, 13], [1, 5, 6, 12, 13], [1, 5, 7, 8, 9], [1, 5, 7, 8, 10], [1, 5, 7, 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7, 8, 10], [4, 6, 7, 8, 11], [4, 6, 7, 8, 12], [4, 6, 7, 8, 13], [4, 6, 7, 9, 10], [4, 6, 7, 9, 11], [4, 6, 7, 9, 12], [4, 6, 7, 9, 13], [4, 6, 7, 10, 11], [4, 6, 7, 10, 12], [4, 6, 7, 10, 13], [4, 6, 7, 11, 12], [4, 6, 7, 11, 13], [4, 6, 7, 12, 13], [4, 6, 8, 9, 10], [4, 6, 8, 9, 11], [4, 6, 8, 9, 12], [4, 6, 8, 9, 13], [4, 6, 8, 10, 11], [4, 6, 8, 10, 12], [4, 6, 8, 10, 13], [4, 6, 8, 11, 12], [4, 6, 8, 11, 13], [4, 6, 8, 12, 13], [4, 6, 9, 10, 11], [4, 6, 9, 10, 12], [4, 6, 9, 10, 13], [4, 6, 9, 11, 12], [4, 6, 9, 11, 13], [4, 6, 9, 12, 13], [4, 6, 10, 11, 12], [4, 6, 10, 11, 13], [4, 6, 10, 12, 13], [4, 6, 11, 12, 13], [4, 7, 8, 9, 10], [4, 7, 8, 9, 11], [4, 7, 8, 9, 12], [4, 7, 8, 9, 13], [4, 7, 8, 10, 11], [4, 7, 8, 10, 12], [4, 7, 8, 10, 13], [4, 7, 8, 11, 12], [4, 7, 8, 11, 13], [4, 7, 8, 12, 13], [4, 7, 9, 10, 11], [4, 7, 9, 10, 12], [4, 7, 9, 10, 13], [4, 7, 9, 11, 12], [4, 7, 9, 11, 13], [4, 7, 9, 12, 13], [4, 7, 10, 11, 12], [4, 7, 10, 11, 13], [4, 7, 10, 12, 13], [4, 7, 11, 12, 13], [4, 8, 9, 10, 11], [4, 8, 9, 10, 12], [4, 8, 9, 10, 13], [4, 8, 9, 11, 12], [4, 8, 9, 11, 13], [4, 8, 9, 12, 13], [4, 8, 10, 11, 12], [4, 8, 10, 11, 13], [4, 8, 10, 12, 13], [4, 8, 11, 12, 13], [4, 9, 10, 11, 12], [4, 9, 10, 11, 13], [4, 9, 10, 12, 13], [4, 9, 11, 12, 13], [4, 10, 11, 12, 13], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8, 11], [5, 6, 7, 8, 12], [5, 6, 7, 8, 13], [5, 6, 7, 9, 10], [5, 6, 7, 9, 11], [5, 6, 7, 9, 12], [5, 6, 7, 9, 13], [5, 6, 7, 10, 11], [5, 6, 7, 10, 12], [5, 6, 7, 10, 13], [5, 6, 7, 11, 12], [5, 6, 7, 11, 13], [5, 6, 7, 12, 13], [5, 6, 8, 9, 10], [5, 6, 8, 9, 11], [5, 6, 8, 9, 12], [5, 6, 8, 9, 13], [5, 6, 8, 10, 11], [5, 6, 8, 10, 12], [5, 6, 8, 10, 13], [5, 6, 8, 11, 12], [5, 6, 8, 11, 13], [5, 6, 8, 12, 13], [5, 6, 9, 10, 11], [5, 6, 9, 10, 12], [5, 6, 9, 10, 13], [5, 6, 9, 11, 12], [5, 6, 9, 11, 13], [5, 6, 9, 12, 13], [5, 6, 10, 11, 12], [5, 6, 10, 11, 13], [5, 6, 10, 12, 13], [5, 6, 11, 12, 13], [5, 7, 8, 9, 10], [5, 7, 8, 9, 11], [5, 7, 8, 9, 12], [5, 7, 8, 9, 13], [5, 7, 8, 10, 11], [5, 7, 8, 10, 12], [5, 7, 8, 10, 13], [5, 7, 8, 11, 12], [5, 7, 8, 11, 13], [5, 7, 8, 12, 13], [5, 7, 9, 10, 11], [5, 7, 9, 10, 12], [5, 7, 9, 10, 13], [5, 7, 9, 11, 12], [5, 7, 9, 11, 13], [5, 7, 9, 12, 13], [5, 7, 10, 11, 12], [5, 7, 10, 11, 13], [5, 7, 10, 12, 13], [5, 7, 11, 12, 13], [5, 8, 9, 10, 11], [5, 8, 9, 10, 12], [5, 8, 9, 10, 13], [5, 8, 9, 11, 12], [5, 8, 9, 11, 13], [5, 8, 9, 12, 13], [5, 8, 10, 11, 12], [5, 8, 10, 11, 13], [5, 8, 10, 12, 13], [5, 8, 11, 12, 13], [5, 9, 10, 11, 12], [5, 9, 10, 11, 13], [5, 9, 10, 12, 13], [5, 9, 11, 12, 13], [5, 10, 11, 12, 13], [6, 7, 8, 9, 10], [6, 7, 8, 9, 11], [6, 7, 8, 9, 12], [6, 7, 8, 9, 13], [6, 7, 8, 10, 11], [6, 7, 8, 10, 12], [6, 7, 8, 10, 13], [6, 7, 8, 11, 12], [6, 7, 8, 11, 13], [6, 7, 8, 12, 13], [6, 7, 9, 10, 11], [6, 7, 9, 10, 12], [6, 7, 9, 10, 13], [6, 7, 9, 11, 12], [6, 7, 9, 11, 13], [6, 7, 9, 12, 13], [6, 7, 10, 11, 12], [6, 7, 10, 11, 13], [6, 7, 10, 12, 13], [6, 7, 11, 12, 13], [6, 8, 9, 10, 11], [6, 8, 9, 10, 12], [6, 8, 9, 10, 13], [6, 8, 9, 11, 12], [6, 8, 9, 11, 13], [6, 8, 9, 12, 13], [6, 8, 10, 11, 12], [6, 8, 10, 11, 13], [6, 8, 10, 12, 13], [6, 8, 11, 12, 13], [6, 9, 10, 11, 12], [6, 9, 10, 11, 13], [6, 9, 10, 12, 13], [6, 9, 11, 12, 13], [6, 10, 11, 12, 13], [7, 8, 9, 10, 11], [7, 8, 9, 10, 12], [7, 8, 9, 10, 13], [7, 8, 9, 11, 12], [7, 8, 9, 11, 13], [7, 8, 9, 12, 13], [7, 8, 10, 11, 12], [7, 8, 10, 11, 13], [7, 8, 10, 12, 13], [7, 8, 11, 12, 13], [7, 9, 10, 11, 12], [7, 9, 10, 11, 13], [7, 9, 10, 12, 13], [7, 9, 11, 12, 13], [7, 10, 11, 12, 13], [8, 9, 10, 11, 12], [8, 9, 10, 11, 13], [8, 9, 10, 12, 13], [8, 9, 11, 12, 13], [8, 10, 11, 12, 13], [9, 10, 11, 12, 13]]\n assert candidate(n = 8,k = 5) == [[1, 2, 3, 4, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8], [1, 2, 3, 7, 8], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8], [1, 2, 4, 7, 8], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8], [1, 2, 5, 7, 8], [1, 2, 6, 7, 8], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8], [1, 3, 4, 7, 8], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8], [1, 3, 5, 7, 8], [1, 3, 6, 7, 8], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8], [1, 4, 5, 7, 8], [1, 4, 6, 7, 8], [1, 5, 6, 7, 8], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8], [2, 3, 4, 7, 8], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8], [2, 3, 5, 7, 8], [2, 3, 6, 7, 8], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8], [2, 4, 5, 7, 8], [2, 4, 6, 7, 8], [2, 5, 6, 7, 8], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8], [3, 4, 5, 7, 8], [3, 4, 6, 7, 8], [3, 5, 6, 7, 8], [4, 5, 6, 7, 8]]\n assert candidate(n = 9,k = 2) == [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [3, 9], [4, 5], [4, 6], [4, 7], [4, 8], [4, 9], [5, 6], [5, 7], [5, 8], [5, 9], [6, 7], [6, 8], [6, 9], [7, 8], [7, 9], [8, 9]]\n assert candidate(n = 7,k = 5) == [[1, 2, 3, 4, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 6, 7], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 6, 7], [1, 2, 5, 6, 7], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 6, 7], [1, 3, 5, 6, 7], [1, 4, 5, 6, 7], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 6, 7], [2, 3, 5, 6, 7], [2, 4, 5, 6, 7], [3, 4, 5, 6, 7]]\n assert candidate(n = 11,k = 6) == [[1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5, 11], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6, 11], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7, 11], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8, 11], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 10, 11], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6, 11], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7, 11], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9, 11], [1, 2, 3, 5, 10, 11], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8, 11], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9, 11], [1, 2, 3, 6, 10, 11], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8, 11], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9, 11], [1, 2, 3, 7, 10, 11], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9, 11], [1, 2, 3, 8, 10, 11], [1, 2, 3, 9, 10, 11], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6, 11], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8, 11], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9, 11], [1, 2, 4, 5, 10, 11], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7, 11], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8, 11], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9, 11], [1, 2, 4, 6, 10, 11], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8, 11], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9, 11], [1, 2, 4, 7, 10, 11], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9, 11], [1, 2, 4, 8, 10, 11], [1, 2, 4, 9, 10, 11], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7, 11], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8, 11], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9, 11], [1, 2, 5, 6, 10, 11], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8, 11], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9, 11], [1, 2, 5, 7, 10, 11], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9, 11], [1, 2, 5, 8, 10, 11], [1, 2, 5, 9, 10, 11], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8, 11], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 9, 11], [1, 2, 6, 7, 10, 11], [1, 2, 6, 8, 9, 10], [1, 2, 6, 8, 9, 11], [1, 2, 6, 8, 10, 11], [1, 2, 6, 9, 10, 11], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9, 11], [1, 2, 7, 8, 10, 11], [1, 2, 7, 9, 10, 11], [1, 2, 8, 9, 10, 11], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 10], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7, 11], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8, 11], [1, 3, 4, 5, 9, 10], [1, 3, 4, 5, 9, 11], [1, 3, 4, 5, 10, 11], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 7, 11], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8, 11], [1, 3, 4, 6, 9, 10], [1, 3, 4, 6, 9, 11], [1, 3, 4, 6, 10, 11], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8, 11], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 9, 11], [1, 3, 4, 7, 10, 11], [1, 3, 4, 8, 9, 10], [1, 3, 4, 8, 9, 11], [1, 3, 4, 8, 10, 11], [1, 3, 4, 9, 10, 11], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7, 11], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8, 11], [1, 3, 5, 6, 9, 10], [1, 3, 5, 6, 9, 11], [1, 3, 5, 6, 10, 11], [1, 3, 5, 7, 8, 9], [1, 3, 5, 7, 8, 10], [1, 3, 5, 7, 8, 11], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 9, 11], [1, 3, 5, 7, 10, 11], [1, 3, 5, 8, 9, 10], [1, 3, 5, 8, 9, 11], [1, 3, 5, 8, 10, 11], [1, 3, 5, 9, 10, 11], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8, 11], [1, 3, 6, 7, 9, 10], [1, 3, 6, 7, 9, 11], [1, 3, 6, 7, 10, 11], [1, 3, 6, 8, 9, 10], [1, 3, 6, 8, 9, 11], [1, 3, 6, 8, 10, 11], [1, 3, 6, 9, 10, 11], [1, 3, 7, 8, 9, 10], [1, 3, 7, 8, 9, 11], [1, 3, 7, 8, 10, 11], [1, 3, 7, 9, 10, 11], [1, 3, 8, 9, 10, 11], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 7, 11], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8, 11], [1, 4, 5, 6, 9, 10], [1, 4, 5, 6, 9, 11], [1, 4, 5, 6, 10, 11], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8, 11], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 9, 11], [1, 4, 5, 7, 10, 11], [1, 4, 5, 8, 9, 10], [1, 4, 5, 8, 9, 11], [1, 4, 5, 8, 10, 11], [1, 4, 5, 9, 10, 11], [1, 4, 6, 7, 8, 9], [1, 4, 6, 7, 8, 10], [1, 4, 6, 7, 8, 11], [1, 4, 6, 7, 9, 10], [1, 4, 6, 7, 9, 11], [1, 4, 6, 7, 10, 11], [1, 4, 6, 8, 9, 10], [1, 4, 6, 8, 9, 11], [1, 4, 6, 8, 10, 11], [1, 4, 6, 9, 10, 11], [1, 4, 7, 8, 9, 10], [1, 4, 7, 8, 9, 11], [1, 4, 7, 8, 10, 11], [1, 4, 7, 9, 10, 11], [1, 4, 8, 9, 10, 11], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8, 11], [1, 5, 6, 7, 9, 10], [1, 5, 6, 7, 9, 11], [1, 5, 6, 7, 10, 11], [1, 5, 6, 8, 9, 10], [1, 5, 6, 8, 9, 11], [1, 5, 6, 8, 10, 11], [1, 5, 6, 9, 10, 11], [1, 5, 7, 8, 9, 10], [1, 5, 7, 8, 9, 11], [1, 5, 7, 8, 10, 11], [1, 5, 7, 9, 10, 11], [1, 5, 8, 9, 10, 11], [1, 6, 7, 8, 9, 10], [1, 6, 7, 8, 9, 11], [1, 6, 7, 8, 10, 11], [1, 6, 7, 9, 10, 11], [1, 6, 8, 9, 10, 11], [1, 7, 8, 9, 10, 11], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6, 11], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7, 11], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 8, 10], [2, 3, 4, 5, 8, 11], [2, 3, 4, 5, 9, 10], [2, 3, 4, 5, 9, 11], [2, 3, 4, 5, 10, 11], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 10], [2, 3, 4, 6, 7, 11], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8, 11], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 9, 11], [2, 3, 4, 6, 10, 11], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8, 11], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 9, 11], [2, 3, 4, 7, 10, 11], [2, 3, 4, 8, 9, 10], [2, 3, 4, 8, 9, 11], [2, 3, 4, 8, 10, 11], [2, 3, 4, 9, 10, 11], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7, 11], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 8, 10], [2, 3, 5, 6, 8, 11], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 9, 11], [2, 3, 5, 6, 10, 11], [2, 3, 5, 7, 8, 9], [2, 3, 5, 7, 8, 10], [2, 3, 5, 7, 8, 11], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 9, 11], [2, 3, 5, 7, 10, 11], [2, 3, 5, 8, 9, 10], [2, 3, 5, 8, 9, 11], [2, 3, 5, 8, 10, 11], [2, 3, 5, 9, 10, 11], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8, 11], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 9, 11], [2, 3, 6, 7, 10, 11], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 9, 11], [2, 3, 6, 8, 10, 11], [2, 3, 6, 9, 10, 11], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9, 11], [2, 3, 7, 8, 10, 11], [2, 3, 7, 9, 10, 11], [2, 3, 8, 9, 10, 11], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7, 11], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8, 11], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9, 11], [2, 4, 5, 6, 10, 11], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8, 11], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9, 11], [2, 4, 5, 7, 10, 11], [2, 4, 5, 8, 9, 10], [2, 4, 5, 8, 9, 11], [2, 4, 5, 8, 10, 11], [2, 4, 5, 9, 10, 11], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8, 11], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 9, 11], [2, 4, 6, 7, 10, 11], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 9, 11], [2, 4, 6, 8, 10, 11], [2, 4, 6, 9, 10, 11], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 9, 11], [2, 4, 7, 8, 10, 11], [2, 4, 7, 9, 10, 11], [2, 4, 8, 9, 10, 11], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8, 11], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9, 11], [2, 5, 6, 7, 10, 11], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9, 11], [2, 5, 6, 8, 10, 11], [2, 5, 6, 9, 10, 11], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9, 11], [2, 5, 7, 8, 10, 11], [2, 5, 7, 9, 10, 11], [2, 5, 8, 9, 10, 11], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9, 11], [2, 6, 7, 8, 10, 11], [2, 6, 7, 9, 10, 11], [2, 6, 8, 9, 10, 11], [2, 7, 8, 9, 10, 11], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7, 11], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8, 11], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9, 11], [3, 4, 5, 6, 10, 11], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8, 11], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9, 11], [3, 4, 5, 7, 10, 11], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9, 11], [3, 4, 5, 8, 10, 11], [3, 4, 5, 9, 10, 11], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8, 11], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9, 11], [3, 4, 6, 7, 10, 11], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9, 11], [3, 4, 6, 8, 10, 11], [3, 4, 6, 9, 10, 11], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9, 11], [3, 4, 7, 8, 10, 11], [3, 4, 7, 9, 10, 11], [3, 4, 8, 9, 10, 11], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8, 11], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9, 11], [3, 5, 6, 7, 10, 11], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9, 11], [3, 5, 6, 8, 10, 11], [3, 5, 6, 9, 10, 11], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9, 11], [3, 5, 7, 8, 10, 11], [3, 5, 7, 9, 10, 11], [3, 5, 8, 9, 10, 11], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9, 11], [3, 6, 7, 8, 10, 11], [3, 6, 7, 9, 10, 11], [3, 6, 8, 9, 10, 11], [3, 7, 8, 9, 10, 11], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8, 11], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9, 11], [4, 5, 6, 7, 10, 11], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9, 11], [4, 5, 6, 8, 10, 11], [4, 5, 6, 9, 10, 11], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9, 11], [4, 5, 7, 8, 10, 11], [4, 5, 7, 9, 10, 11], [4, 5, 8, 9, 10, 11], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9, 11], [4, 6, 7, 8, 10, 11], [4, 6, 7, 9, 10, 11], [4, 6, 8, 9, 10, 11], [4, 7, 8, 9, 10, 11], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9, 11], [5, 6, 7, 8, 10, 11], [5, 6, 7, 9, 10, 11], [5, 6, 8, 9, 10, 11], [5, 7, 8, 9, 10, 11], [6, 7, 8, 9, 10, 11]]\n assert candidate(n = 16,k = 4) == [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3, 11], [1, 2, 3, 12], [1, 2, 3, 13], [1, 2, 3, 14], [1, 2, 3, 15], [1, 2, 3, 16], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4, 8], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4, 11], [1, 2, 4, 12], [1, 2, 4, 13], [1, 2, 4, 14], [1, 2, 4, 15], [1, 2, 4, 16], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5, 11], [1, 2, 5, 12], [1, 2, 5, 13], [1, 2, 5, 14], [1, 2, 5, 15], [1, 2, 5, 16], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6, 11], [1, 2, 6, 12], [1, 2, 6, 13], [1, 2, 6, 14], [1, 2, 6, 15], [1, 2, 6, 16], [1, 2, 7, 8], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7, 11], [1, 2, 7, 12], [1, 2, 7, 13], [1, 2, 7, 14], [1, 2, 7, 15], [1, 2, 7, 16], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8, 11], [1, 2, 8, 12], [1, 2, 8, 13], [1, 2, 8, 14], [1, 2, 8, 15], [1, 2, 8, 16], [1, 2, 9, 10], [1, 2, 9, 11], [1, 2, 9, 12], [1, 2, 9, 13], [1, 2, 9, 14], [1, 2, 9, 15], [1, 2, 9, 16], [1, 2, 10, 11], [1, 2, 10, 12], [1, 2, 10, 13], [1, 2, 10, 14], [1, 2, 10, 15], [1, 2, 10, 16], [1, 2, 11, 12], [1, 2, 11, 13], [1, 2, 11, 14], [1, 2, 11, 15], [1, 2, 11, 16], [1, 2, 12, 13], [1, 2, 12, 14], [1, 2, 12, 15], [1, 2, 12, 16], [1, 2, 13, 14], [1, 2, 13, 15], [1, 2, 13, 16], [1, 2, 14, 15], [1, 2, 14, 16], [1, 2, 15, 16], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 4, 9], [1, 3, 4, 10], [1, 3, 4, 11], [1, 3, 4, 12], [1, 3, 4, 13], [1, 3, 4, 14], [1, 3, 4, 15], [1, 3, 4, 16], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 5, 9], [1, 3, 5, 10], [1, 3, 5, 11], [1, 3, 5, 12], [1, 3, 5, 13], [1, 3, 5, 14], [1, 3, 5, 15], [1, 3, 5, 16], [1, 3, 6, 7], [1, 3, 6, 8], [1, 3, 6, 9], [1, 3, 6, 10], [1, 3, 6, 11], [1, 3, 6, 12], [1, 3, 6, 13], [1, 3, 6, 14], [1, 3, 6, 15], [1, 3, 6, 16], [1, 3, 7, 8], [1, 3, 7, 9], [1, 3, 7, 10], [1, 3, 7, 11], [1, 3, 7, 12], [1, 3, 7, 13], [1, 3, 7, 14], [1, 3, 7, 15], [1, 3, 7, 16], [1, 3, 8, 9], [1, 3, 8, 10], [1, 3, 8, 11], [1, 3, 8, 12], [1, 3, 8, 13], [1, 3, 8, 14], [1, 3, 8, 15], [1, 3, 8, 16], [1, 3, 9, 10], [1, 3, 9, 11], [1, 3, 9, 12], [1, 3, 9, 13], [1, 3, 9, 14], [1, 3, 9, 15], [1, 3, 9, 16], [1, 3, 10, 11], [1, 3, 10, 12], [1, 3, 10, 13], [1, 3, 10, 14], [1, 3, 10, 15], [1, 3, 10, 16], [1, 3, 11, 12], [1, 3, 11, 13], [1, 3, 11, 14], [1, 3, 11, 15], [1, 3, 11, 16], [1, 3, 12, 13], [1, 3, 12, 14], [1, 3, 12, 15], [1, 3, 12, 16], [1, 3, 13, 14], [1, 3, 13, 15], [1, 3, 13, 16], [1, 3, 14, 15], [1, 3, 14, 16], [1, 3, 15, 16], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5, 8], [1, 4, 5, 9], [1, 4, 5, 10], [1, 4, 5, 11], [1, 4, 5, 12], [1, 4, 5, 13], [1, 4, 5, 14], [1, 4, 5, 15], [1, 4, 5, 16], [1, 4, 6, 7], [1, 4, 6, 8], [1, 4, 6, 9], [1, 4, 6, 10], [1, 4, 6, 11], [1, 4, 6, 12], [1, 4, 6, 13], [1, 4, 6, 14], [1, 4, 6, 15], [1, 4, 6, 16], [1, 4, 7, 8], [1, 4, 7, 9], [1, 4, 7, 10], [1, 4, 7, 11], [1, 4, 7, 12], [1, 4, 7, 13], [1, 4, 7, 14], [1, 4, 7, 15], [1, 4, 7, 16], [1, 4, 8, 9], [1, 4, 8, 10], [1, 4, 8, 11], [1, 4, 8, 12], [1, 4, 8, 13], [1, 4, 8, 14], [1, 4, 8, 15], [1, 4, 8, 16], [1, 4, 9, 10], [1, 4, 9, 11], [1, 4, 9, 12], [1, 4, 9, 13], [1, 4, 9, 14], [1, 4, 9, 15], [1, 4, 9, 16], [1, 4, 10, 11], [1, 4, 10, 12], [1, 4, 10, 13], [1, 4, 10, 14], [1, 4, 10, 15], [1, 4, 10, 16], [1, 4, 11, 12], [1, 4, 11, 13], [1, 4, 11, 14], [1, 4, 11, 15], [1, 4, 11, 16], [1, 4, 12, 13], [1, 4, 12, 14], [1, 4, 12, 15], [1, 4, 12, 16], [1, 4, 13, 14], [1, 4, 13, 15], [1, 4, 13, 16], [1, 4, 14, 15], [1, 4, 14, 16], [1, 4, 15, 16], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 6, 9], [1, 5, 6, 10], [1, 5, 6, 11], [1, 5, 6, 12], [1, 5, 6, 13], [1, 5, 6, 14], [1, 5, 6, 15], [1, 5, 6, 16], [1, 5, 7, 8], [1, 5, 7, 9], [1, 5, 7, 10], [1, 5, 7, 11], [1, 5, 7, 12], [1, 5, 7, 13], [1, 5, 7, 14], [1, 5, 7, 15], [1, 5, 7, 16], [1, 5, 8, 9], [1, 5, 8, 10], [1, 5, 8, 11], [1, 5, 8, 12], [1, 5, 8, 13], [1, 5, 8, 14], [1, 5, 8, 15], [1, 5, 8, 16], [1, 5, 9, 10], [1, 5, 9, 11], [1, 5, 9, 12], [1, 5, 9, 13], [1, 5, 9, 14], [1, 5, 9, 15], [1, 5, 9, 16], [1, 5, 10, 11], [1, 5, 10, 12], [1, 5, 10, 13], [1, 5, 10, 14], [1, 5, 10, 15], [1, 5, 10, 16], [1, 5, 11, 12], [1, 5, 11, 13], [1, 5, 11, 14], [1, 5, 11, 15], [1, 5, 11, 16], [1, 5, 12, 13], [1, 5, 12, 14], [1, 5, 12, 15], [1, 5, 12, 16], [1, 5, 13, 14], [1, 5, 13, 15], [1, 5, 13, 16], [1, 5, 14, 15], [1, 5, 14, 16], [1, 5, 15, 16], [1, 6, 7, 8], [1, 6, 7, 9], [1, 6, 7, 10], [1, 6, 7, 11], [1, 6, 7, 12], [1, 6, 7, 13], [1, 6, 7, 14], [1, 6, 7, 15], [1, 6, 7, 16], [1, 6, 8, 9], [1, 6, 8, 10], [1, 6, 8, 11], [1, 6, 8, 12], [1, 6, 8, 13], [1, 6, 8, 14], [1, 6, 8, 15], [1, 6, 8, 16], [1, 6, 9, 10], [1, 6, 9, 11], [1, 6, 9, 12], [1, 6, 9, 13], [1, 6, 9, 14], [1, 6, 9, 15], [1, 6, 9, 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14], [4, 7, 8, 15], [4, 7, 8, 16], [4, 7, 9, 10], [4, 7, 9, 11], [4, 7, 9, 12], [4, 7, 9, 13], [4, 7, 9, 14], [4, 7, 9, 15], [4, 7, 9, 16], [4, 7, 10, 11], [4, 7, 10, 12], [4, 7, 10, 13], [4, 7, 10, 14], [4, 7, 10, 15], [4, 7, 10, 16], [4, 7, 11, 12], [4, 7, 11, 13], [4, 7, 11, 14], [4, 7, 11, 15], [4, 7, 11, 16], [4, 7, 12, 13], [4, 7, 12, 14], [4, 7, 12, 15], [4, 7, 12, 16], [4, 7, 13, 14], [4, 7, 13, 15], [4, 7, 13, 16], [4, 7, 14, 15], [4, 7, 14, 16], [4, 7, 15, 16], [4, 8, 9, 10], [4, 8, 9, 11], [4, 8, 9, 12], [4, 8, 9, 13], [4, 8, 9, 14], [4, 8, 9, 15], [4, 8, 9, 16], [4, 8, 10, 11], [4, 8, 10, 12], [4, 8, 10, 13], [4, 8, 10, 14], [4, 8, 10, 15], [4, 8, 10, 16], [4, 8, 11, 12], [4, 8, 11, 13], [4, 8, 11, 14], [4, 8, 11, 15], [4, 8, 11, 16], [4, 8, 12, 13], [4, 8, 12, 14], [4, 8, 12, 15], [4, 8, 12, 16], [4, 8, 13, 14], [4, 8, 13, 15], [4, 8, 13, 16], [4, 8, 14, 15], [4, 8, 14, 16], [4, 8, 15, 16], [4, 9, 10, 11], [4, 9, 10, 12], [4, 9, 10, 13], [4, 9, 10, 14], [4, 9, 10, 15], [4, 9, 10, 16], [4, 9, 11, 12], [4, 9, 11, 13], [4, 9, 11, 14], [4, 9, 11, 15], [4, 9, 11, 16], [4, 9, 12, 13], [4, 9, 12, 14], [4, 9, 12, 15], [4, 9, 12, 16], [4, 9, 13, 14], [4, 9, 13, 15], [4, 9, 13, 16], [4, 9, 14, 15], [4, 9, 14, 16], [4, 9, 15, 16], [4, 10, 11, 12], [4, 10, 11, 13], [4, 10, 11, 14], [4, 10, 11, 15], [4, 10, 11, 16], [4, 10, 12, 13], [4, 10, 12, 14], [4, 10, 12, 15], [4, 10, 12, 16], [4, 10, 13, 14], [4, 10, 13, 15], [4, 10, 13, 16], [4, 10, 14, 15], [4, 10, 14, 16], [4, 10, 15, 16], [4, 11, 12, 13], [4, 11, 12, 14], [4, 11, 12, 15], [4, 11, 12, 16], [4, 11, 13, 14], [4, 11, 13, 15], [4, 11, 13, 16], [4, 11, 14, 15], [4, 11, 14, 16], [4, 11, 15, 16], [4, 12, 13, 14], [4, 12, 13, 15], [4, 12, 13, 16], [4, 12, 14, 15], [4, 12, 14, 16], [4, 12, 15, 16], [4, 13, 14, 15], [4, 13, 14, 16], [4, 13, 15, 16], [4, 14, 15, 16], [5, 6, 7, 8], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7, 11], [5, 6, 7, 12], [5, 6, 7, 13], [5, 6, 7, 14], [5, 6, 7, 15], [5, 6, 7, 16], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8, 11], [5, 6, 8, 12], [5, 6, 8, 13], [5, 6, 8, 14], [5, 6, 8, 15], [5, 6, 8, 16], [5, 6, 9, 10], [5, 6, 9, 11], [5, 6, 9, 12], [5, 6, 9, 13], [5, 6, 9, 14], [5, 6, 9, 15], [5, 6, 9, 16], [5, 6, 10, 11], [5, 6, 10, 12], [5, 6, 10, 13], [5, 6, 10, 14], [5, 6, 10, 15], [5, 6, 10, 16], [5, 6, 11, 12], [5, 6, 11, 13], [5, 6, 11, 14], [5, 6, 11, 15], [5, 6, 11, 16], [5, 6, 12, 13], [5, 6, 12, 14], [5, 6, 12, 15], [5, 6, 12, 16], [5, 6, 13, 14], [5, 6, 13, 15], [5, 6, 13, 16], [5, 6, 14, 15], [5, 6, 14, 16], [5, 6, 15, 16], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8, 11], [5, 7, 8, 12], [5, 7, 8, 13], [5, 7, 8, 14], [5, 7, 8, 15], [5, 7, 8, 16], [5, 7, 9, 10], [5, 7, 9, 11], [5, 7, 9, 12], [5, 7, 9, 13], [5, 7, 9, 14], [5, 7, 9, 15], [5, 7, 9, 16], [5, 7, 10, 11], [5, 7, 10, 12], [5, 7, 10, 13], [5, 7, 10, 14], [5, 7, 10, 15], [5, 7, 10, 16], [5, 7, 11, 12], [5, 7, 11, 13], [5, 7, 11, 14], [5, 7, 11, 15], [5, 7, 11, 16], [5, 7, 12, 13], [5, 7, 12, 14], [5, 7, 12, 15], [5, 7, 12, 16], [5, 7, 13, 14], [5, 7, 13, 15], [5, 7, 13, 16], [5, 7, 14, 15], [5, 7, 14, 16], [5, 7, 15, 16], [5, 8, 9, 10], [5, 8, 9, 11], [5, 8, 9, 12], [5, 8, 9, 13], [5, 8, 9, 14], [5, 8, 9, 15], [5, 8, 9, 16], [5, 8, 10, 11], [5, 8, 10, 12], [5, 8, 10, 13], [5, 8, 10, 14], [5, 8, 10, 15], [5, 8, 10, 16], [5, 8, 11, 12], [5, 8, 11, 13], [5, 8, 11, 14], [5, 8, 11, 15], [5, 8, 11, 16], [5, 8, 12, 13], [5, 8, 12, 14], [5, 8, 12, 15], [5, 8, 12, 16], [5, 8, 13, 14], [5, 8, 13, 15], [5, 8, 13, 16], [5, 8, 14, 15], [5, 8, 14, 16], [5, 8, 15, 16], [5, 9, 10, 11], [5, 9, 10, 12], [5, 9, 10, 13], [5, 9, 10, 14], [5, 9, 10, 15], [5, 9, 10, 16], [5, 9, 11, 12], [5, 9, 11, 13], [5, 9, 11, 14], [5, 9, 11, 15], [5, 9, 11, 16], [5, 9, 12, 13], [5, 9, 12, 14], [5, 9, 12, 15], [5, 9, 12, 16], [5, 9, 13, 14], [5, 9, 13, 15], [5, 9, 13, 16], [5, 9, 14, 15], [5, 9, 14, 16], [5, 9, 15, 16], [5, 10, 11, 12], [5, 10, 11, 13], [5, 10, 11, 14], [5, 10, 11, 15], [5, 10, 11, 16], [5, 10, 12, 13], [5, 10, 12, 14], [5, 10, 12, 15], [5, 10, 12, 16], [5, 10, 13, 14], [5, 10, 13, 15], [5, 10, 13, 16], [5, 10, 14, 15], [5, 10, 14, 16], [5, 10, 15, 16], [5, 11, 12, 13], [5, 11, 12, 14], [5, 11, 12, 15], [5, 11, 12, 16], [5, 11, 13, 14], [5, 11, 13, 15], [5, 11, 13, 16], [5, 11, 14, 15], [5, 11, 14, 16], [5, 11, 15, 16], [5, 12, 13, 14], [5, 12, 13, 15], [5, 12, 13, 16], [5, 12, 14, 15], [5, 12, 14, 16], [5, 12, 15, 16], [5, 13, 14, 15], [5, 13, 14, 16], [5, 13, 15, 16], [5, 14, 15, 16], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8, 11], [6, 7, 8, 12], [6, 7, 8, 13], [6, 7, 8, 14], [6, 7, 8, 15], [6, 7, 8, 16], [6, 7, 9, 10], [6, 7, 9, 11], [6, 7, 9, 12], [6, 7, 9, 13], [6, 7, 9, 14], [6, 7, 9, 15], [6, 7, 9, 16], [6, 7, 10, 11], [6, 7, 10, 12], [6, 7, 10, 13], [6, 7, 10, 14], [6, 7, 10, 15], [6, 7, 10, 16], [6, 7, 11, 12], [6, 7, 11, 13], [6, 7, 11, 14], [6, 7, 11, 15], [6, 7, 11, 16], [6, 7, 12, 13], [6, 7, 12, 14], [6, 7, 12, 15], [6, 7, 12, 16], [6, 7, 13, 14], [6, 7, 13, 15], [6, 7, 13, 16], [6, 7, 14, 15], [6, 7, 14, 16], [6, 7, 15, 16], [6, 8, 9, 10], [6, 8, 9, 11], [6, 8, 9, 12], [6, 8, 9, 13], [6, 8, 9, 14], [6, 8, 9, 15], [6, 8, 9, 16], [6, 8, 10, 11], [6, 8, 10, 12], [6, 8, 10, 13], [6, 8, 10, 14], [6, 8, 10, 15], [6, 8, 10, 16], [6, 8, 11, 12], [6, 8, 11, 13], [6, 8, 11, 14], [6, 8, 11, 15], [6, 8, 11, 16], [6, 8, 12, 13], [6, 8, 12, 14], [6, 8, 12, 15], [6, 8, 12, 16], [6, 8, 13, 14], [6, 8, 13, 15], [6, 8, 13, 16], [6, 8, 14, 15], [6, 8, 14, 16], [6, 8, 15, 16], [6, 9, 10, 11], [6, 9, 10, 12], [6, 9, 10, 13], [6, 9, 10, 14], [6, 9, 10, 15], [6, 9, 10, 16], [6, 9, 11, 12], [6, 9, 11, 13], [6, 9, 11, 14], [6, 9, 11, 15], [6, 9, 11, 16], [6, 9, 12, 13], [6, 9, 12, 14], [6, 9, 12, 15], [6, 9, 12, 16], [6, 9, 13, 14], [6, 9, 13, 15], [6, 9, 13, 16], [6, 9, 14, 15], [6, 9, 14, 16], [6, 9, 15, 16], [6, 10, 11, 12], [6, 10, 11, 13], [6, 10, 11, 14], [6, 10, 11, 15], [6, 10, 11, 16], [6, 10, 12, 13], [6, 10, 12, 14], [6, 10, 12, 15], [6, 10, 12, 16], [6, 10, 13, 14], [6, 10, 13, 15], [6, 10, 13, 16], [6, 10, 14, 15], [6, 10, 14, 16], [6, 10, 15, 16], [6, 11, 12, 13], [6, 11, 12, 14], [6, 11, 12, 15], [6, 11, 12, 16], [6, 11, 13, 14], [6, 11, 13, 15], [6, 11, 13, 16], [6, 11, 14, 15], [6, 11, 14, 16], [6, 11, 15, 16], [6, 12, 13, 14], [6, 12, 13, 15], [6, 12, 13, 16], [6, 12, 14, 15], [6, 12, 14, 16], [6, 12, 15, 16], [6, 13, 14, 15], [6, 13, 14, 16], [6, 13, 15, 16], [6, 14, 15, 16], [7, 8, 9, 10], [7, 8, 9, 11], [7, 8, 9, 12], [7, 8, 9, 13], [7, 8, 9, 14], [7, 8, 9, 15], [7, 8, 9, 16], [7, 8, 10, 11], [7, 8, 10, 12], [7, 8, 10, 13], [7, 8, 10, 14], [7, 8, 10, 15], [7, 8, 10, 16], [7, 8, 11, 12], [7, 8, 11, 13], [7, 8, 11, 14], [7, 8, 11, 15], [7, 8, 11, 16], [7, 8, 12, 13], [7, 8, 12, 14], [7, 8, 12, 15], [7, 8, 12, 16], [7, 8, 13, 14], [7, 8, 13, 15], [7, 8, 13, 16], [7, 8, 14, 15], [7, 8, 14, 16], [7, 8, 15, 16], [7, 9, 10, 11], [7, 9, 10, 12], [7, 9, 10, 13], [7, 9, 10, 14], [7, 9, 10, 15], [7, 9, 10, 16], [7, 9, 11, 12], [7, 9, 11, 13], [7, 9, 11, 14], [7, 9, 11, 15], [7, 9, 11, 16], [7, 9, 12, 13], [7, 9, 12, 14], [7, 9, 12, 15], [7, 9, 12, 16], [7, 9, 13, 14], [7, 9, 13, 15], [7, 9, 13, 16], [7, 9, 14, 15], [7, 9, 14, 16], [7, 9, 15, 16], [7, 10, 11, 12], [7, 10, 11, 13], [7, 10, 11, 14], [7, 10, 11, 15], [7, 10, 11, 16], [7, 10, 12, 13], [7, 10, 12, 14], [7, 10, 12, 15], [7, 10, 12, 16], [7, 10, 13, 14], [7, 10, 13, 15], [7, 10, 13, 16], [7, 10, 14, 15], [7, 10, 14, 16], [7, 10, 15, 16], [7, 11, 12, 13], [7, 11, 12, 14], [7, 11, 12, 15], [7, 11, 12, 16], [7, 11, 13, 14], [7, 11, 13, 15], [7, 11, 13, 16], [7, 11, 14, 15], [7, 11, 14, 16], [7, 11, 15, 16], [7, 12, 13, 14], [7, 12, 13, 15], [7, 12, 13, 16], [7, 12, 14, 15], [7, 12, 14, 16], [7, 12, 15, 16], [7, 13, 14, 15], [7, 13, 14, 16], [7, 13, 15, 16], [7, 14, 15, 16], [8, 9, 10, 11], [8, 9, 10, 12], [8, 9, 10, 13], [8, 9, 10, 14], [8, 9, 10, 15], [8, 9, 10, 16], [8, 9, 11, 12], [8, 9, 11, 13], [8, 9, 11, 14], [8, 9, 11, 15], [8, 9, 11, 16], [8, 9, 12, 13], [8, 9, 12, 14], [8, 9, 12, 15], [8, 9, 12, 16], [8, 9, 13, 14], [8, 9, 13, 15], [8, 9, 13, 16], [8, 9, 14, 15], [8, 9, 14, 16], [8, 9, 15, 16], [8, 10, 11, 12], [8, 10, 11, 13], [8, 10, 11, 14], [8, 10, 11, 15], [8, 10, 11, 16], [8, 10, 12, 13], [8, 10, 12, 14], [8, 10, 12, 15], [8, 10, 12, 16], [8, 10, 13, 14], [8, 10, 13, 15], [8, 10, 13, 16], [8, 10, 14, 15], [8, 10, 14, 16], [8, 10, 15, 16], [8, 11, 12, 13], [8, 11, 12, 14], [8, 11, 12, 15], [8, 11, 12, 16], [8, 11, 13, 14], [8, 11, 13, 15], [8, 11, 13, 16], [8, 11, 14, 15], [8, 11, 14, 16], [8, 11, 15, 16], [8, 12, 13, 14], [8, 12, 13, 15], [8, 12, 13, 16], [8, 12, 14, 15], [8, 12, 14, 16], [8, 12, 15, 16], [8, 13, 14, 15], [8, 13, 14, 16], [8, 13, 15, 16], [8, 14, 15, 16], [9, 10, 11, 12], [9, 10, 11, 13], [9, 10, 11, 14], [9, 10, 11, 15], [9, 10, 11, 16], [9, 10, 12, 13], [9, 10, 12, 14], [9, 10, 12, 15], [9, 10, 12, 16], [9, 10, 13, 14], [9, 10, 13, 15], [9, 10, 13, 16], [9, 10, 14, 15], [9, 10, 14, 16], [9, 10, 15, 16], [9, 11, 12, 13], [9, 11, 12, 14], [9, 11, 12, 15], [9, 11, 12, 16], [9, 11, 13, 14], [9, 11, 13, 15], [9, 11, 13, 16], [9, 11, 14, 15], [9, 11, 14, 16], [9, 11, 15, 16], [9, 12, 13, 14], [9, 12, 13, 15], [9, 12, 13, 16], [9, 12, 14, 15], [9, 12, 14, 16], [9, 12, 15, 16], [9, 13, 14, 15], [9, 13, 14, 16], [9, 13, 15, 16], [9, 14, 15, 16], [10, 11, 12, 13], [10, 11, 12, 14], [10, 11, 12, 15], [10, 11, 12, 16], [10, 11, 13, 14], [10, 11, 13, 15], [10, 11, 13, 16], [10, 11, 14, 15], [10, 11, 14, 16], [10, 11, 15, 16], [10, 12, 13, 14], [10, 12, 13, 15], [10, 12, 13, 16], [10, 12, 14, 15], [10, 12, 14, 16], [10, 12, 15, 16], [10, 13, 14, 15], [10, 13, 14, 16], [10, 13, 15, 16], [10, 14, 15, 16], [11, 12, 13, 14], [11, 12, 13, 15], [11, 12, 13, 16], [11, 12, 14, 15], [11, 12, 14, 16], [11, 12, 15, 16], [11, 13, 14, 15], [11, 13, 14, 16], [11, 13, 15, 16], [11, 14, 15, 16], [12, 13, 14, 15], [12, 13, 14, 16], [12, 13, 15, 16], [12, 14, 15, 16], [13, 14, 15, 16]]\n assert candidate(n = 12,k = 4) == [[1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3, 11], [1, 2, 3, 12], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4, 8], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4, 11], [1, 2, 4, 12], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5, 11], [1, 2, 5, 12], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6, 11], [1, 2, 6, 12], [1, 2, 7, 8], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7, 11], [1, 2, 7, 12], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8, 11], [1, 2, 8, 12], [1, 2, 9, 10], [1, 2, 9, 11], [1, 2, 9, 12], [1, 2, 10, 11], [1, 2, 10, 12], [1, 2, 11, 12], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 4, 9], [1, 3, 4, 10], [1, 3, 4, 11], [1, 3, 4, 12], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 5, 9], [1, 3, 5, 10], [1, 3, 5, 11], [1, 3, 5, 12], [1, 3, 6, 7], [1, 3, 6, 8], [1, 3, 6, 9], [1, 3, 6, 10], [1, 3, 6, 11], [1, 3, 6, 12], [1, 3, 7, 8], [1, 3, 7, 9], [1, 3, 7, 10], [1, 3, 7, 11], [1, 3, 7, 12], [1, 3, 8, 9], [1, 3, 8, 10], [1, 3, 8, 11], [1, 3, 8, 12], [1, 3, 9, 10], [1, 3, 9, 11], [1, 3, 9, 12], [1, 3, 10, 11], [1, 3, 10, 12], [1, 3, 11, 12], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5, 8], [1, 4, 5, 9], [1, 4, 5, 10], [1, 4, 5, 11], [1, 4, 5, 12], [1, 4, 6, 7], [1, 4, 6, 8], [1, 4, 6, 9], [1, 4, 6, 10], [1, 4, 6, 11], [1, 4, 6, 12], [1, 4, 7, 8], [1, 4, 7, 9], [1, 4, 7, 10], [1, 4, 7, 11], [1, 4, 7, 12], [1, 4, 8, 9], [1, 4, 8, 10], [1, 4, 8, 11], [1, 4, 8, 12], [1, 4, 9, 10], [1, 4, 9, 11], [1, 4, 9, 12], [1, 4, 10, 11], [1, 4, 10, 12], [1, 4, 11, 12], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 6, 9], [1, 5, 6, 10], [1, 5, 6, 11], [1, 5, 6, 12], [1, 5, 7, 8], [1, 5, 7, 9], [1, 5, 7, 10], [1, 5, 7, 11], [1, 5, 7, 12], [1, 5, 8, 9], [1, 5, 8, 10], [1, 5, 8, 11], [1, 5, 8, 12], [1, 5, 9, 10], [1, 5, 9, 11], [1, 5, 9, 12], [1, 5, 10, 11], [1, 5, 10, 12], [1, 5, 11, 12], [1, 6, 7, 8], [1, 6, 7, 9], [1, 6, 7, 10], [1, 6, 7, 11], [1, 6, 7, 12], [1, 6, 8, 9], [1, 6, 8, 10], [1, 6, 8, 11], [1, 6, 8, 12], [1, 6, 9, 10], [1, 6, 9, 11], [1, 6, 9, 12], [1, 6, 10, 11], [1, 6, 10, 12], [1, 6, 11, 12], [1, 7, 8, 9], [1, 7, 8, 10], [1, 7, 8, 11], [1, 7, 8, 12], [1, 7, 9, 10], [1, 7, 9, 11], [1, 7, 9, 12], [1, 7, 10, 11], [1, 7, 10, 12], [1, 7, 11, 12], [1, 8, 9, 10], [1, 8, 9, 11], [1, 8, 9, 12], [1, 8, 10, 11], [1, 8, 10, 12], [1, 8, 11, 12], [1, 9, 10, 11], [1, 9, 10, 12], [1, 9, 11, 12], [1, 10, 11, 12], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4, 8], [2, 3, 4, 9], [2, 3, 4, 10], [2, 3, 4, 11], [2, 3, 4, 12], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5, 8], [2, 3, 5, 9], [2, 3, 5, 10], [2, 3, 5, 11], [2, 3, 5, 12], [2, 3, 6, 7], [2, 3, 6, 8], [2, 3, 6, 9], [2, 3, 6, 10], [2, 3, 6, 11], [2, 3, 6, 12], [2, 3, 7, 8], [2, 3, 7, 9], [2, 3, 7, 10], [2, 3, 7, 11], [2, 3, 7, 12], [2, 3, 8, 9], [2, 3, 8, 10], [2, 3, 8, 11], [2, 3, 8, 12], [2, 3, 9, 10], [2, 3, 9, 11], [2, 3, 9, 12], [2, 3, 10, 11], [2, 3, 10, 12], [2, 3, 11, 12], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5, 8], [2, 4, 5, 9], [2, 4, 5, 10], [2, 4, 5, 11], [2, 4, 5, 12], [2, 4, 6, 7], [2, 4, 6, 8], [2, 4, 6, 9], [2, 4, 6, 10], [2, 4, 6, 11], [2, 4, 6, 12], [2, 4, 7, 8], [2, 4, 7, 9], [2, 4, 7, 10], [2, 4, 7, 11], [2, 4, 7, 12], [2, 4, 8, 9], [2, 4, 8, 10], [2, 4, 8, 11], [2, 4, 8, 12], [2, 4, 9, 10], [2, 4, 9, 11], [2, 4, 9, 12], [2, 4, 10, 11], [2, 4, 10, 12], [2, 4, 11, 12], [2, 5, 6, 7], [2, 5, 6, 8], [2, 5, 6, 9], [2, 5, 6, 10], [2, 5, 6, 11], [2, 5, 6, 12], [2, 5, 7, 8], [2, 5, 7, 9], [2, 5, 7, 10], [2, 5, 7, 11], [2, 5, 7, 12], [2, 5, 8, 9], [2, 5, 8, 10], [2, 5, 8, 11], [2, 5, 8, 12], [2, 5, 9, 10], [2, 5, 9, 11], [2, 5, 9, 12], [2, 5, 10, 11], [2, 5, 10, 12], [2, 5, 11, 12], [2, 6, 7, 8], [2, 6, 7, 9], [2, 6, 7, 10], [2, 6, 7, 11], [2, 6, 7, 12], [2, 6, 8, 9], [2, 6, 8, 10], [2, 6, 8, 11], [2, 6, 8, 12], [2, 6, 9, 10], [2, 6, 9, 11], [2, 6, 9, 12], [2, 6, 10, 11], [2, 6, 10, 12], [2, 6, 11, 12], [2, 7, 8, 9], [2, 7, 8, 10], [2, 7, 8, 11], [2, 7, 8, 12], [2, 7, 9, 10], [2, 7, 9, 11], [2, 7, 9, 12], [2, 7, 10, 11], [2, 7, 10, 12], [2, 7, 11, 12], [2, 8, 9, 10], [2, 8, 9, 11], [2, 8, 9, 12], [2, 8, 10, 11], [2, 8, 10, 12], [2, 8, 11, 12], [2, 9, 10, 11], [2, 9, 10, 12], [2, 9, 11, 12], [2, 10, 11, 12], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5, 8], [3, 4, 5, 9], [3, 4, 5, 10], [3, 4, 5, 11], [3, 4, 5, 12], [3, 4, 6, 7], [3, 4, 6, 8], [3, 4, 6, 9], [3, 4, 6, 10], [3, 4, 6, 11], [3, 4, 6, 12], [3, 4, 7, 8], [3, 4, 7, 9], [3, 4, 7, 10], [3, 4, 7, 11], [3, 4, 7, 12], [3, 4, 8, 9], [3, 4, 8, 10], [3, 4, 8, 11], [3, 4, 8, 12], [3, 4, 9, 10], [3, 4, 9, 11], [3, 4, 9, 12], [3, 4, 10, 11], [3, 4, 10, 12], [3, 4, 11, 12], [3, 5, 6, 7], [3, 5, 6, 8], [3, 5, 6, 9], [3, 5, 6, 10], [3, 5, 6, 11], [3, 5, 6, 12], [3, 5, 7, 8], [3, 5, 7, 9], [3, 5, 7, 10], [3, 5, 7, 11], [3, 5, 7, 12], [3, 5, 8, 9], [3, 5, 8, 10], [3, 5, 8, 11], [3, 5, 8, 12], [3, 5, 9, 10], [3, 5, 9, 11], [3, 5, 9, 12], [3, 5, 10, 11], [3, 5, 10, 12], [3, 5, 11, 12], [3, 6, 7, 8], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7, 11], [3, 6, 7, 12], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8, 11], [3, 6, 8, 12], [3, 6, 9, 10], [3, 6, 9, 11], [3, 6, 9, 12], [3, 6, 10, 11], [3, 6, 10, 12], [3, 6, 11, 12], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8, 11], [3, 7, 8, 12], [3, 7, 9, 10], [3, 7, 9, 11], [3, 7, 9, 12], [3, 7, 10, 11], [3, 7, 10, 12], [3, 7, 11, 12], [3, 8, 9, 10], [3, 8, 9, 11], [3, 8, 9, 12], [3, 8, 10, 11], [3, 8, 10, 12], [3, 8, 11, 12], [3, 9, 10, 11], [3, 9, 10, 12], [3, 9, 11, 12], [3, 10, 11, 12], [4, 5, 6, 7], [4, 5, 6, 8], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6, 11], [4, 5, 6, 12], [4, 5, 7, 8], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7, 11], [4, 5, 7, 12], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8, 11], [4, 5, 8, 12], [4, 5, 9, 10], [4, 5, 9, 11], [4, 5, 9, 12], [4, 5, 10, 11], [4, 5, 10, 12], [4, 5, 11, 12], [4, 6, 7, 8], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7, 11], [4, 6, 7, 12], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8, 11], [4, 6, 8, 12], [4, 6, 9, 10], [4, 6, 9, 11], [4, 6, 9, 12], [4, 6, 10, 11], [4, 6, 10, 12], [4, 6, 11, 12], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8, 11], [4, 7, 8, 12], [4, 7, 9, 10], [4, 7, 9, 11], [4, 7, 9, 12], [4, 7, 10, 11], [4, 7, 10, 12], [4, 7, 11, 12], [4, 8, 9, 10], [4, 8, 9, 11], [4, 8, 9, 12], [4, 8, 10, 11], [4, 8, 10, 12], [4, 8, 11, 12], [4, 9, 10, 11], [4, 9, 10, 12], [4, 9, 11, 12], [4, 10, 11, 12], [5, 6, 7, 8], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7, 11], [5, 6, 7, 12], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8, 11], [5, 6, 8, 12], [5, 6, 9, 10], [5, 6, 9, 11], [5, 6, 9, 12], [5, 6, 10, 11], [5, 6, 10, 12], [5, 6, 11, 12], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8, 11], [5, 7, 8, 12], [5, 7, 9, 10], [5, 7, 9, 11], [5, 7, 9, 12], [5, 7, 10, 11], [5, 7, 10, 12], [5, 7, 11, 12], [5, 8, 9, 10], [5, 8, 9, 11], [5, 8, 9, 12], [5, 8, 10, 11], [5, 8, 10, 12], [5, 8, 11, 12], [5, 9, 10, 11], [5, 9, 10, 12], [5, 9, 11, 12], [5, 10, 11, 12], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8, 11], [6, 7, 8, 12], [6, 7, 9, 10], [6, 7, 9, 11], [6, 7, 9, 12], [6, 7, 10, 11], [6, 7, 10, 12], [6, 7, 11, 12], [6, 8, 9, 10], [6, 8, 9, 11], [6, 8, 9, 12], [6, 8, 10, 11], [6, 8, 10, 12], [6, 8, 11, 12], [6, 9, 10, 11], [6, 9, 10, 12], [6, 9, 11, 12], [6, 10, 11, 12], [7, 8, 9, 10], [7, 8, 9, 11], [7, 8, 9, 12], [7, 8, 10, 11], [7, 8, 10, 12], [7, 8, 11, 12], [7, 9, 10, 11], [7, 9, 10, 12], [7, 9, 11, 12], [7, 10, 11, 12], [8, 9, 10, 11], [8, 9, 10, 12], [8, 9, 11, 12], [8, 10, 11, 12], [9, 10, 11, 12]]\n assert candidate(n = 12,k = 6) == [[1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5, 11], [1, 2, 3, 4, 5, 12], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6, 11], [1, 2, 3, 4, 6, 12], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7, 11], [1, 2, 3, 4, 7, 12], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8, 11], [1, 2, 3, 4, 8, 12], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9, 11], [1, 2, 3, 4, 9, 12], [1, 2, 3, 4, 10, 11], [1, 2, 3, 4, 10, 12], [1, 2, 3, 4, 11, 12], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6, 11], [1, 2, 3, 5, 6, 12], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7, 11], [1, 2, 3, 5, 7, 12], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8, 11], [1, 2, 3, 5, 8, 12], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9, 11], [1, 2, 3, 5, 9, 12], [1, 2, 3, 5, 10, 11], [1, 2, 3, 5, 10, 12], [1, 2, 3, 5, 11, 12], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 7, 12], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8, 11], [1, 2, 3, 6, 8, 12], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9, 11], [1, 2, 3, 6, 9, 12], [1, 2, 3, 6, 10, 11], [1, 2, 3, 6, 10, 12], [1, 2, 3, 6, 11, 12], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8, 11], [1, 2, 3, 7, 8, 12], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9, 11], [1, 2, 3, 7, 9, 12], [1, 2, 3, 7, 10, 11], [1, 2, 3, 7, 10, 12], [1, 2, 3, 7, 11, 12], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9, 11], [1, 2, 3, 8, 9, 12], [1, 2, 3, 8, 10, 11], [1, 2, 3, 8, 10, 12], [1, 2, 3, 8, 11, 12], [1, 2, 3, 9, 10, 11], [1, 2, 3, 9, 10, 12], [1, 2, 3, 9, 11, 12], [1, 2, 3, 10, 11, 12], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6, 11], [1, 2, 4, 5, 6, 12], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7, 11], [1, 2, 4, 5, 7, 12], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8, 11], [1, 2, 4, 5, 8, 12], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9, 11], [1, 2, 4, 5, 9, 12], [1, 2, 4, 5, 10, 11], [1, 2, 4, 5, 10, 12], [1, 2, 4, 5, 11, 12], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7, 11], [1, 2, 4, 6, 7, 12], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8, 11], [1, 2, 4, 6, 8, 12], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9, 11], [1, 2, 4, 6, 9, 12], [1, 2, 4, 6, 10, 11], [1, 2, 4, 6, 10, 12], [1, 2, 4, 6, 11, 12], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8, 11], [1, 2, 4, 7, 8, 12], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9, 11], [1, 2, 4, 7, 9, 12], [1, 2, 4, 7, 10, 11], [1, 2, 4, 7, 10, 12], [1, 2, 4, 7, 11, 12], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9, 11], [1, 2, 4, 8, 9, 12], [1, 2, 4, 8, 10, 11], [1, 2, 4, 8, 10, 12], [1, 2, 4, 8, 11, 12], [1, 2, 4, 9, 10, 11], [1, 2, 4, 9, 10, 12], [1, 2, 4, 9, 11, 12], [1, 2, 4, 10, 11, 12], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7, 11], [1, 2, 5, 6, 7, 12], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8, 11], [1, 2, 5, 6, 8, 12], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9, 11], [1, 2, 5, 6, 9, 12], [1, 2, 5, 6, 10, 11], [1, 2, 5, 6, 10, 12], [1, 2, 5, 6, 11, 12], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8, 11], [1, 2, 5, 7, 8, 12], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9, 11], [1, 2, 5, 7, 9, 12], [1, 2, 5, 7, 10, 11], [1, 2, 5, 7, 10, 12], [1, 2, 5, 7, 11, 12], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9, 11], [1, 2, 5, 8, 9, 12], [1, 2, 5, 8, 10, 11], [1, 2, 5, 8, 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12], [3, 4, 7, 8, 11, 12], [3, 4, 7, 9, 10, 11], [3, 4, 7, 9, 10, 12], [3, 4, 7, 9, 11, 12], [3, 4, 7, 10, 11, 12], [3, 4, 8, 9, 10, 11], [3, 4, 8, 9, 10, 12], [3, 4, 8, 9, 11, 12], [3, 4, 8, 10, 11, 12], [3, 4, 9, 10, 11, 12], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8, 11], [3, 5, 6, 7, 8, 12], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9, 11], [3, 5, 6, 7, 9, 12], [3, 5, 6, 7, 10, 11], [3, 5, 6, 7, 10, 12], [3, 5, 6, 7, 11, 12], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9, 11], [3, 5, 6, 8, 9, 12], [3, 5, 6, 8, 10, 11], [3, 5, 6, 8, 10, 12], [3, 5, 6, 8, 11, 12], [3, 5, 6, 9, 10, 11], [3, 5, 6, 9, 10, 12], [3, 5, 6, 9, 11, 12], [3, 5, 6, 10, 11, 12], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9, 11], [3, 5, 7, 8, 9, 12], [3, 5, 7, 8, 10, 11], [3, 5, 7, 8, 10, 12], [3, 5, 7, 8, 11, 12], [3, 5, 7, 9, 10, 11], [3, 5, 7, 9, 10, 12], [3, 5, 7, 9, 11, 12], [3, 5, 7, 10, 11, 12], [3, 5, 8, 9, 10, 11], [3, 5, 8, 9, 10, 12], [3, 5, 8, 9, 11, 12], [3, 5, 8, 10, 11, 12], [3, 5, 9, 10, 11, 12], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9, 11], [3, 6, 7, 8, 9, 12], [3, 6, 7, 8, 10, 11], [3, 6, 7, 8, 10, 12], [3, 6, 7, 8, 11, 12], [3, 6, 7, 9, 10, 11], [3, 6, 7, 9, 10, 12], [3, 6, 7, 9, 11, 12], [3, 6, 7, 10, 11, 12], [3, 6, 8, 9, 10, 11], [3, 6, 8, 9, 10, 12], [3, 6, 8, 9, 11, 12], [3, 6, 8, 10, 11, 12], [3, 6, 9, 10, 11, 12], [3, 7, 8, 9, 10, 11], [3, 7, 8, 9, 10, 12], [3, 7, 8, 9, 11, 12], [3, 7, 8, 10, 11, 12], [3, 7, 9, 10, 11, 12], [3, 8, 9, 10, 11, 12], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8, 11], [4, 5, 6, 7, 8, 12], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9, 11], [4, 5, 6, 7, 9, 12], [4, 5, 6, 7, 10, 11], [4, 5, 6, 7, 10, 12], [4, 5, 6, 7, 11, 12], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9, 11], [4, 5, 6, 8, 9, 12], [4, 5, 6, 8, 10, 11], [4, 5, 6, 8, 10, 12], [4, 5, 6, 8, 11, 12], [4, 5, 6, 9, 10, 11], [4, 5, 6, 9, 10, 12], [4, 5, 6, 9, 11, 12], [4, 5, 6, 10, 11, 12], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9, 11], [4, 5, 7, 8, 9, 12], [4, 5, 7, 8, 10, 11], [4, 5, 7, 8, 10, 12], [4, 5, 7, 8, 11, 12], [4, 5, 7, 9, 10, 11], [4, 5, 7, 9, 10, 12], [4, 5, 7, 9, 11, 12], [4, 5, 7, 10, 11, 12], [4, 5, 8, 9, 10, 11], [4, 5, 8, 9, 10, 12], [4, 5, 8, 9, 11, 12], [4, 5, 8, 10, 11, 12], [4, 5, 9, 10, 11, 12], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9, 11], [4, 6, 7, 8, 9, 12], [4, 6, 7, 8, 10, 11], [4, 6, 7, 8, 10, 12], [4, 6, 7, 8, 11, 12], [4, 6, 7, 9, 10, 11], [4, 6, 7, 9, 10, 12], [4, 6, 7, 9, 11, 12], [4, 6, 7, 10, 11, 12], [4, 6, 8, 9, 10, 11], [4, 6, 8, 9, 10, 12], [4, 6, 8, 9, 11, 12], [4, 6, 8, 10, 11, 12], [4, 6, 9, 10, 11, 12], [4, 7, 8, 9, 10, 11], [4, 7, 8, 9, 10, 12], [4, 7, 8, 9, 11, 12], [4, 7, 8, 10, 11, 12], [4, 7, 9, 10, 11, 12], [4, 8, 9, 10, 11, 12], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9, 11], [5, 6, 7, 8, 9, 12], [5, 6, 7, 8, 10, 11], [5, 6, 7, 8, 10, 12], [5, 6, 7, 8, 11, 12], [5, 6, 7, 9, 10, 11], [5, 6, 7, 9, 10, 12], [5, 6, 7, 9, 11, 12], [5, 6, 7, 10, 11, 12], [5, 6, 8, 9, 10, 11], [5, 6, 8, 9, 10, 12], [5, 6, 8, 9, 11, 12], [5, 6, 8, 10, 11, 12], [5, 6, 9, 10, 11, 12], [5, 7, 8, 9, 10, 11], [5, 7, 8, 9, 10, 12], [5, 7, 8, 9, 11, 12], [5, 7, 8, 10, 11, 12], [5, 7, 9, 10, 11, 12], [5, 8, 9, 10, 11, 12], [6, 7, 8, 9, 10, 11], [6, 7, 8, 9, 10, 12], [6, 7, 8, 9, 11, 12], [6, 7, 8, 10, 11, 12], [6, 7, 9, 10, 11, 12], [6, 8, 9, 10, 11, 12], [7, 8, 9, 10, 11, 12]]\n assert candidate(n = 20,k = 1) == [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]]\n assert candidate(n = 10,k = 7) == [[1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 10], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 8, 10], [1, 3, 4, 5, 6, 9, 10], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 7, 8, 10], [1, 3, 4, 5, 7, 9, 10], [1, 3, 4, 5, 8, 9, 10], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 6, 7, 8, 10], [1, 3, 4, 6, 7, 9, 10], [1, 3, 4, 6, 8, 9, 10], [1, 3, 4, 7, 8, 9, 10], [1, 3, 5, 6, 7, 8, 9], [1, 3, 5, 6, 7, 8, 10], [1, 3, 5, 6, 7, 9, 10], [1, 3, 5, 6, 8, 9, 10], [1, 3, 5, 7, 8, 9, 10], [1, 3, 6, 7, 8, 9, 10], [1, 4, 5, 6, 7, 8, 9], [1, 4, 5, 6, 7, 8, 10], [1, 4, 5, 6, 7, 9, 10], [1, 4, 5, 6, 8, 9, 10], [1, 4, 5, 7, 8, 9, 10], [1, 4, 6, 7, 8, 9, 10], [1, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 10], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 8, 10], [2, 3, 4, 5, 6, 9, 10], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 7, 8, 10], [2, 3, 4, 5, 7, 9, 10], [2, 3, 4, 5, 8, 9, 10], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 6, 7, 8, 10], [2, 3, 4, 6, 7, 9, 10], [2, 3, 4, 6, 8, 9, 10], [2, 3, 4, 7, 8, 9, 10], [2, 3, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 10], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5, 6, 8, 9, 10], [2, 3, 5, 7, 8, 9, 10], [2, 3, 6, 7, 8, 9, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 7, 8, 9, 10], [2, 4, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9, 10]]\n"}, "metadata": {"canonical_parameter_names": ["n", "k"], "leetcode_dataset_entry_point": "Solution().combine", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var combine = function(n, k) {", "container": null, "callable": "combine", "parameters": [{"name": "n", "type": "number"}, {"name": "k", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 78, "task_id": "subsets", "difficulty": "Medium", "problem_description": "Given an integer array nums of unique elements, return all possible subsets (the power set).\nThe solution set must not contain duplicate subsets. Return the solution in any order.\n \nExample 1:\n\nInput: nums = [1,2,3]\nOutput: [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]\n\nExample 2:\n\nInput: nums = [0]\nOutput: [[],[0]]\n\n \nConstraints:\n\n1 <= nums.length <= 10\n-10 <= nums[i] <= 10\nAll the numbers of nums are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [6, 1, 5, 2, 4]) == [[], [4], [2], [2, 4], [5], [5, 4], [5, 2], [5, 2, 4], [1], [1, 4], [1, 2], [1, 2, 4], [1, 5], [1, 5, 4], [1, 5, 2], [1, 5, 2, 4], [6], [6, 4], [6, 2], [6, 2, 4], [6, 5], [6, 5, 4], [6, 5, 2], [6, 5, 2, 4], [6, 1], [6, 1, 4], [6, 1, 2], [6, 1, 2, 4], [6, 1, 5], [6, 1, 5, 4], [6, 1, 5, 2], [6, 1, 5, 2, 4]]\n assert candidate(nums = [-2, -1, 0, 1, 2]) == [[], [2], [1], [1, 2], [0], [0, 2], [0, 1], [0, 1, 2], [-1], [-1, 2], [-1, 1], [-1, 1, 2], [-1, 0], [-1, 0, 2], [-1, 0, 1], [-1, 0, 1, 2], [-2], [-2, 2], [-2, 1], [-2, 1, 2], [-2, 0], [-2, 0, 2], [-2, 0, 1], [-2, 0, 1, 2], [-2, -1], [-2, -1, 2], [-2, -1, 1], [-2, -1, 1, 2], [-2, -1, 0], [-2, -1, 0, 2], [-2, -1, 0, 1], [-2, -1, 0, 1, 2]]\n assert candidate(nums = [-2, -3, -1, 0]) == [[], [0], [-1], [-1, 0], [-3], [-3, 0], [-3, -1], [-3, -1, 0], [-2], [-2, 0], [-2, -1], [-2, -1, 0], [-2, -3], [-2, -3, 0], [-2, -3, -1], [-2, -3, -1, 0]]\n assert candidate(nums = [-2, -3, -1]) == [[], [-1], [-3], [-3, -1], [-2], [-2, -1], [-2, -3], [-2, -3, -1]]\n assert candidate(nums = [6, 2, 8, 1, 3]) == [[], [3], [1], [1, 3], [8], [8, 3], [8, 1], [8, 1, 3], [2], [2, 3], [2, 1], [2, 1, 3], [2, 8], [2, 8, 3], [2, 8, 1], [2, 8, 1, 3], [6], [6, 3], [6, 1], [6, 1, 3], [6, 8], [6, 8, 3], [6, 8, 1], [6, 8, 1, 3], [6, 2], [6, 2, 3], [6, 2, 1], [6, 2, 1, 3], [6, 2, 8], [6, 2, 8, 3], [6, 2, 8, 1], [6, 2, 8, 1, 3]]\n assert candidate(nums = [2, 4, 6, 8, 10]) == [[], [10], [8], [8, 10], [6], [6, 10], [6, 8], [6, 8, 10], [4], [4, 10], [4, 8], [4, 8, 10], [4, 6], [4, 6, 10], [4, 6, 8], [4, 6, 8, 10], [2], [2, 10], [2, 8], [2, 8, 10], [2, 6], [2, 6, 10], [2, 6, 8], [2, 6, 8, 10], [2, 4], [2, 4, 10], [2, 4, 8], [2, 4, 8, 10], [2, 4, 6], [2, 4, 6, 10], [2, 4, 6, 8], [2, 4, 6, 8, 10]]\n assert candidate(nums = [1, 3, 5, 7, 9]) == [[], [9], [7], [7, 9], [5], [5, 9], [5, 7], [5, 7, 9], [3], [3, 9], [3, 7], [3, 7, 9], [3, 5], [3, 5, 9], [3, 5, 7], [3, 5, 7, 9], [1], [1, 9], [1, 7], [1, 7, 9], [1, 5], [1, 5, 9], [1, 5, 7], [1, 5, 7, 9], [1, 3], [1, 3, 9], [1, 3, 7], [1, 3, 7, 9], [1, 3, 5], [1, 3, 5, 9], [1, 3, 5, 7], [1, 3, 5, 7, 9]]\n assert candidate(nums = [10]) == [[], [10]]\n assert candidate(nums = [1]) == [[], [1]]\n assert candidate(nums = [-5, 0, 5]) == [[], [5], [0], [0, 5], [-5], [-5, 5], [-5, 0], [-5, 0, 5]]\n assert candidate(nums = [1, 2, 3, 4]) == [[], [4], [3], [3, 4], [2], [2, 4], [2, 3], [2, 3, 4], [1], [1, 4], [1, 3], [1, 3, 4], [1, 2], [1, 2, 4], [1, 2, 3], [1, 2, 3, 4]]\n assert candidate(nums = [-5, -4, -3, -2, -1]) == [[], [-1], [-2], [-2, -1], [-3], [-3, -1], [-3, -2], [-3, -2, -1], [-4], [-4, -1], [-4, -2], [-4, -2, -1], [-4, -3], [-4, -3, -1], [-4, -3, -2], [-4, -3, -2, -1], [-5], [-5, -1], [-5, -2], [-5, -2, -1], [-5, -3], [-5, -3, -1], [-5, -3, -2], [-5, -3, -2, -1], [-5, -4], [-5, -4, -1], [-5, -4, -2], [-5, -4, -2, -1], [-5, -4, -3], [-5, -4, -3, -1], [-5, -4, -3, -2], [-5, -4, -3, -2, -1]]\n assert candidate(nums = [1, 3, 5, 7, 9, 11]) == [[], [11], [9], [9, 11], [7], [7, 11], [7, 9], [7, 9, 11], [5], [5, 11], [5, 9], [5, 9, 11], [5, 7], [5, 7, 11], [5, 7, 9], [5, 7, 9, 11], [3], [3, 11], [3, 9], [3, 9, 11], [3, 7], [3, 7, 11], [3, 7, 9], [3, 7, 9, 11], [3, 5], [3, 5, 11], [3, 5, 9], [3, 5, 9, 11], [3, 5, 7], [3, 5, 7, 11], [3, 5, 7, 9], [3, 5, 7, 9, 11], [1], [1, 11], [1, 9], [1, 9, 11], [1, 7], [1, 7, 11], [1, 7, 9], [1, 7, 9, 11], [1, 5], [1, 5, 11], [1, 5, 9], [1, 5, 9, 11], [1, 5, 7], [1, 5, 7, 11], [1, 5, 7, 9], [1, 5, 7, 9, 11], [1, 3], [1, 3, 11], [1, 3, 9], [1, 3, 9, 11], [1, 3, 7], [1, 3, 7, 11], [1, 3, 7, 9], [1, 3, 7, 9, 11], [1, 3, 5], [1, 3, 5, 11], [1, 3, 5, 9], [1, 3, 5, 9, 11], [1, 3, 5, 7], [1, 3, 5, 7, 11], [1, 3, 5, 7, 9], [1, 3, 5, 7, 9, 11]]\n assert candidate(nums = [5, -1, 4]) == [[], [4], [-1], [-1, 4], [5], [5, 4], [5, -1], [5, -1, 4]]\n assert candidate(nums = [0]) == [[], [0]]\n assert candidate(nums = [-10, 10]) == [[], [10], [-10], [-10, 10]]\n assert candidate(nums = [5, 10, 15]) == [[], [15], [10], [10, 15], [5], [5, 15], [5, 10], [5, 10, 15]]\n assert candidate(nums = [5, -1, 2]) == [[], [2], [-1], [-1, 2], [5], [5, 2], [5, -1], [5, -1, 2]]\n assert candidate(nums = [10, -5, 0, 3]) == [[], [3], [0], [0, 3], [-5], [-5, 3], [-5, 0], [-5, 0, 3], [10], [10, 3], [10, 0], [10, 0, 3], [10, -5], [10, -5, 3], [10, -5, 0], [10, -5, 0, 3]]\n assert candidate(nums = [1, 2]) == [[], [2], [1], [1, 2]]\n assert candidate(nums = [10, -10, 0]) == [[], [0], [-10], [-10, 0], [10], [10, 0], [10, -10], [10, -10, 0]]\n assert candidate(nums = [1, 2, 3]) == [[], [3], [2], [2, 3], [1], [1, 3], [1, 2], [1, 2, 3]]\n assert candidate(nums = [5, -1, 3]) == [[], [3], [-1], [-1, 3], [5], [5, 3], [5, -1], [5, -1, 3]]\n assert candidate(nums = [7]) == [[], [7]]\n assert candidate(nums = [5, -3, 7, 1]) == [[], [1], [7], [7, 1], [-3], [-3, 1], [-3, 7], [-3, 7, 1], [5], [5, 1], [5, 7], [5, 7, 1], [5, -3], [5, -3, 1], [5, -3, 7], [5, -3, 7, 1]]\n assert candidate(nums = [3, 1, 2]) == [[], [2], [1], [1, 2], [3], [3, 2], [3, 1], [3, 1, 2]]\n assert candidate(nums = [-1, 0, 1]) == [[], [1], [0], [0, 1], [-1], [-1, 1], [-1, 0], [-1, 0, 1]]\n assert candidate(nums = [-2, -4, -6, -8]) == [[], [-8], [-6], [-6, -8], [-4], [-4, -8], [-4, -6], [-4, -6, -8], [-2], [-2, -8], [-2, -6], [-2, -6, -8], [-2, -4], [-2, -4, -8], [-2, -4, -6], [-2, -4, -6, -8]]\n assert candidate(nums = [2, 4, 6, 8]) == [[], [8], [6], [6, 8], [4], [4, 8], [4, 6], [4, 6, 8], [2], [2, 8], [2, 6], [2, 6, 8], [2, 4], [2, 4, 8], [2, 4, 6], [2, 4, 6, 8]]\n assert candidate(nums = [-10, -5, -3, -1, 0, 1, 3, 5, 10]) == [[], [10], [5], [5, 10], [3], [3, 10], [3, 5], [3, 5, 10], [1], [1, 10], [1, 5], [1, 5, 10], [1, 3], [1, 3, 10], [1, 3, 5], [1, 3, 5, 10], [0], [0, 10], [0, 5], [0, 5, 10], [0, 3], [0, 3, 10], [0, 3, 5], [0, 3, 5, 10], [0, 1], [0, 1, 10], [0, 1, 5], [0, 1, 5, 10], [0, 1, 3], [0, 1, 3, 10], [0, 1, 3, 5], [0, 1, 3, 5, 10], [-1], [-1, 10], [-1, 5], [-1, 5, 10], [-1, 3], [-1, 3, 10], [-1, 3, 5], [-1, 3, 5, 10], [-1, 1], [-1, 1, 10], [-1, 1, 5], [-1, 1, 5, 10], [-1, 1, 3], [-1, 1, 3, 10], [-1, 1, 3, 5], [-1, 1, 3, 5, 10], [-1, 0], [-1, 0, 10], [-1, 0, 5], [-1, 0, 5, 10], [-1, 0, 3], [-1, 0, 3, 10], [-1, 0, 3, 5], [-1, 0, 3, 5, 10], [-1, 0, 1], [-1, 0, 1, 10], [-1, 0, 1, 5], [-1, 0, 1, 5, 10], [-1, 0, 1, 3], [-1, 0, 1, 3, 10], [-1, 0, 1, 3, 5], [-1, 0, 1, 3, 5, 10], [-3], [-3, 10], [-3, 5], [-3, 5, 10], [-3, 3], [-3, 3, 10], [-3, 3, 5], [-3, 3, 5, 10], [-3, 1], [-3, 1, 10], [-3, 1, 5], [-3, 1, 5, 10], [-3, 1, 3], [-3, 1, 3, 10], [-3, 1, 3, 5], [-3, 1, 3, 5, 10], [-3, 0], [-3, 0, 10], [-3, 0, 5], [-3, 0, 5, 10], [-3, 0, 3], [-3, 0, 3, 10], [-3, 0, 3, 5], [-3, 0, 3, 5, 10], [-3, 0, 1], [-3, 0, 1, 10], [-3, 0, 1, 5], [-3, 0, 1, 5, 10], [-3, 0, 1, 3], [-3, 0, 1, 3, 10], [-3, 0, 1, 3, 5], [-3, 0, 1, 3, 5, 10], [-3, -1], [-3, -1, 10], [-3, -1, 5], [-3, -1, 5, 10], [-3, -1, 3], [-3, -1, 3, 10], [-3, -1, 3, 5], [-3, -1, 3, 5, 10], [-3, -1, 1], [-3, -1, 1, 10], [-3, -1, 1, 5], [-3, -1, 1, 5, 10], [-3, -1, 1, 3], [-3, -1, 1, 3, 10], [-3, -1, 1, 3, 5], [-3, -1, 1, 3, 5, 10], [-3, -1, 0], [-3, -1, 0, 10], [-3, -1, 0, 5], [-3, -1, 0, 5, 10], [-3, -1, 0, 3], [-3, -1, 0, 3, 10], [-3, -1, 0, 3, 5], [-3, -1, 0, 3, 5, 10], [-3, -1, 0, 1], [-3, -1, 0, 1, 10], [-3, -1, 0, 1, 5], [-3, -1, 0, 1, 5, 10], [-3, -1, 0, 1, 3], [-3, -1, 0, 1, 3, 10], [-3, -1, 0, 1, 3, 5], [-3, -1, 0, 1, 3, 5, 10], [-5], [-5, 10], [-5, 5], [-5, 5, 10], [-5, 3], [-5, 3, 10], [-5, 3, 5], [-5, 3, 5, 10], [-5, 1], [-5, 1, 10], [-5, 1, 5], [-5, 1, 5, 10], [-5, 1, 3], [-5, 1, 3, 10], [-5, 1, 3, 5], [-5, 1, 3, 5, 10], [-5, 0], [-5, 0, 10], [-5, 0, 5], [-5, 0, 5, 10], [-5, 0, 3], [-5, 0, 3, 10], [-5, 0, 3, 5], [-5, 0, 3, 5, 10], [-5, 0, 1], [-5, 0, 1, 10], [-5, 0, 1, 5], [-5, 0, 1, 5, 10], [-5, 0, 1, 3], [-5, 0, 1, 3, 10], [-5, 0, 1, 3, 5], [-5, 0, 1, 3, 5, 10], [-5, -1], [-5, -1, 10], [-5, -1, 5], [-5, -1, 5, 10], [-5, -1, 3], [-5, -1, 3, 10], [-5, -1, 3, 5], [-5, -1, 3, 5, 10], [-5, -1, 1], [-5, -1, 1, 10], [-5, -1, 1, 5], [-5, -1, 1, 5, 10], [-5, -1, 1, 3], [-5, -1, 1, 3, 10], [-5, -1, 1, 3, 5], [-5, -1, 1, 3, 5, 10], [-5, -1, 0], [-5, -1, 0, 10], [-5, -1, 0, 5], [-5, -1, 0, 5, 10], [-5, -1, 0, 3], [-5, -1, 0, 3, 10], [-5, -1, 0, 3, 5], [-5, -1, 0, 3, 5, 10], [-5, -1, 0, 1], [-5, -1, 0, 1, 10], [-5, -1, 0, 1, 5], [-5, -1, 0, 1, 5, 10], [-5, -1, 0, 1, 3], [-5, -1, 0, 1, 3, 10], [-5, -1, 0, 1, 3, 5], [-5, -1, 0, 1, 3, 5, 10], [-5, -3], [-5, -3, 10], [-5, -3, 5], [-5, -3, 5, 10], [-5, -3, 3], [-5, -3, 3, 10], [-5, -3, 3, 5], [-5, -3, 3, 5, 10], [-5, -3, 1], [-5, -3, 1, 10], [-5, -3, 1, 5], [-5, -3, 1, 5, 10], [-5, -3, 1, 3], [-5, -3, 1, 3, 10], [-5, -3, 1, 3, 5], [-5, -3, 1, 3, 5, 10], [-5, -3, 0], [-5, -3, 0, 10], [-5, -3, 0, 5], [-5, -3, 0, 5, 10], [-5, -3, 0, 3], [-5, -3, 0, 3, 10], [-5, -3, 0, 3, 5], [-5, -3, 0, 3, 5, 10], [-5, -3, 0, 1], [-5, -3, 0, 1, 10], [-5, -3, 0, 1, 5], [-5, -3, 0, 1, 5, 10], [-5, -3, 0, 1, 3], [-5, -3, 0, 1, 3, 10], [-5, -3, 0, 1, 3, 5], [-5, -3, 0, 1, 3, 5, 10], [-5, -3, -1], [-5, -3, -1, 10], [-5, -3, -1, 5], [-5, -3, -1, 5, 10], [-5, -3, -1, 3], [-5, -3, -1, 3, 10], [-5, -3, -1, 3, 5], [-5, -3, -1, 3, 5, 10], [-5, -3, -1, 1], [-5, -3, -1, 1, 10], [-5, -3, -1, 1, 5], [-5, -3, -1, 1, 5, 10], [-5, -3, -1, 1, 3], [-5, -3, -1, 1, 3, 10], [-5, -3, -1, 1, 3, 5], [-5, -3, -1, 1, 3, 5, 10], [-5, -3, -1, 0], [-5, -3, -1, 0, 10], [-5, -3, -1, 0, 5], [-5, -3, -1, 0, 5, 10], [-5, -3, -1, 0, 3], [-5, -3, -1, 0, 3, 10], [-5, -3, -1, 0, 3, 5], [-5, -3, -1, 0, 3, 5, 10], [-5, -3, -1, 0, 1], [-5, -3, -1, 0, 1, 10], [-5, -3, -1, 0, 1, 5], [-5, -3, -1, 0, 1, 5, 10], [-5, -3, -1, 0, 1, 3], [-5, -3, -1, 0, 1, 3, 10], [-5, -3, -1, 0, 1, 3, 5], [-5, -3, -1, 0, 1, 3, 5, 10], [-10], [-10, 10], [-10, 5], [-10, 5, 10], [-10, 3], [-10, 3, 10], [-10, 3, 5], [-10, 3, 5, 10], [-10, 1], [-10, 1, 10], [-10, 1, 5], [-10, 1, 5, 10], [-10, 1, 3], [-10, 1, 3, 10], [-10, 1, 3, 5], [-10, 1, 3, 5, 10], [-10, 0], [-10, 0, 10], [-10, 0, 5], [-10, 0, 5, 10], [-10, 0, 3], [-10, 0, 3, 10], [-10, 0, 3, 5], [-10, 0, 3, 5, 10], [-10, 0, 1], [-10, 0, 1, 10], [-10, 0, 1, 5], [-10, 0, 1, 5, 10], [-10, 0, 1, 3], [-10, 0, 1, 3, 10], [-10, 0, 1, 3, 5], [-10, 0, 1, 3, 5, 10], [-10, -1], [-10, -1, 10], [-10, -1, 5], [-10, -1, 5, 10], [-10, -1, 3], [-10, -1, 3, 10], [-10, -1, 3, 5], [-10, -1, 3, 5, 10], [-10, -1, 1], [-10, -1, 1, 10], [-10, -1, 1, 5], [-10, -1, 1, 5, 10], [-10, -1, 1, 3], [-10, -1, 1, 3, 10], [-10, -1, 1, 3, 5], [-10, -1, 1, 3, 5, 10], [-10, -1, 0], [-10, -1, 0, 10], [-10, -1, 0, 5], [-10, -1, 0, 5, 10], [-10, -1, 0, 3], [-10, -1, 0, 3, 10], [-10, -1, 0, 3, 5], [-10, -1, 0, 3, 5, 10], [-10, -1, 0, 1], [-10, -1, 0, 1, 10], [-10, -1, 0, 1, 5], [-10, -1, 0, 1, 5, 10], [-10, -1, 0, 1, 3], [-10, -1, 0, 1, 3, 10], [-10, -1, 0, 1, 3, 5], [-10, -1, 0, 1, 3, 5, 10], [-10, -3], [-10, -3, 10], [-10, -3, 5], [-10, -3, 5, 10], [-10, -3, 3], [-10, -3, 3, 10], [-10, -3, 3, 5], [-10, -3, 3, 5, 10], [-10, -3, 1], [-10, -3, 1, 10], [-10, -3, 1, 5], [-10, -3, 1, 5, 10], [-10, -3, 1, 3], [-10, -3, 1, 3, 10], [-10, -3, 1, 3, 5], [-10, -3, 1, 3, 5, 10], [-10, -3, 0], [-10, -3, 0, 10], [-10, -3, 0, 5], [-10, -3, 0, 5, 10], [-10, -3, 0, 3], [-10, -3, 0, 3, 10], [-10, -3, 0, 3, 5], [-10, -3, 0, 3, 5, 10], [-10, -3, 0, 1], [-10, -3, 0, 1, 10], [-10, -3, 0, 1, 5], [-10, -3, 0, 1, 5, 10], [-10, -3, 0, 1, 3], [-10, -3, 0, 1, 3, 10], [-10, -3, 0, 1, 3, 5], [-10, -3, 0, 1, 3, 5, 10], [-10, -3, -1], [-10, -3, -1, 10], [-10, -3, -1, 5], [-10, -3, -1, 5, 10], [-10, -3, -1, 3], [-10, -3, -1, 3, 10], [-10, -3, -1, 3, 5], [-10, -3, -1, 3, 5, 10], [-10, -3, -1, 1], [-10, -3, -1, 1, 10], [-10, -3, -1, 1, 5], [-10, -3, -1, 1, 5, 10], [-10, -3, -1, 1, 3], [-10, -3, -1, 1, 3, 10], [-10, -3, -1, 1, 3, 5], [-10, -3, -1, 1, 3, 5, 10], [-10, -3, -1, 0], [-10, -3, -1, 0, 10], [-10, -3, -1, 0, 5], [-10, -3, -1, 0, 5, 10], [-10, -3, -1, 0, 3], [-10, -3, -1, 0, 3, 10], [-10, -3, -1, 0, 3, 5], [-10, -3, -1, 0, 3, 5, 10], [-10, -3, -1, 0, 1], [-10, -3, -1, 0, 1, 10], [-10, -3, -1, 0, 1, 5], [-10, -3, -1, 0, 1, 5, 10], [-10, -3, -1, 0, 1, 3], [-10, -3, -1, 0, 1, 3, 10], [-10, -3, -1, 0, 1, 3, 5], [-10, -3, -1, 0, 1, 3, 5, 10], [-10, -5], [-10, -5, 10], [-10, -5, 5], [-10, -5, 5, 10], [-10, -5, 3], [-10, -5, 3, 10], [-10, -5, 3, 5], [-10, -5, 3, 5, 10], [-10, -5, 1], [-10, -5, 1, 10], [-10, -5, 1, 5], [-10, -5, 1, 5, 10], [-10, -5, 1, 3], [-10, -5, 1, 3, 10], [-10, -5, 1, 3, 5], [-10, -5, 1, 3, 5, 10], [-10, -5, 0], [-10, -5, 0, 10], [-10, -5, 0, 5], [-10, -5, 0, 5, 10], [-10, -5, 0, 3], [-10, -5, 0, 3, 10], [-10, -5, 0, 3, 5], [-10, -5, 0, 3, 5, 10], [-10, -5, 0, 1], [-10, -5, 0, 1, 10], [-10, -5, 0, 1, 5], [-10, -5, 0, 1, 5, 10], [-10, -5, 0, 1, 3], [-10, -5, 0, 1, 3, 10], [-10, -5, 0, 1, 3, 5], [-10, -5, 0, 1, 3, 5, 10], [-10, -5, -1], [-10, -5, -1, 10], [-10, -5, -1, 5], [-10, -5, -1, 5, 10], [-10, -5, -1, 3], [-10, -5, -1, 3, 10], [-10, -5, -1, 3, 5], [-10, -5, -1, 3, 5, 10], [-10, -5, -1, 1], [-10, -5, -1, 1, 10], [-10, -5, -1, 1, 5], [-10, -5, -1, 1, 5, 10], [-10, -5, -1, 1, 3], [-10, -5, -1, 1, 3, 10], [-10, -5, -1, 1, 3, 5], [-10, -5, -1, 1, 3, 5, 10], [-10, -5, -1, 0], [-10, -5, -1, 0, 10], [-10, -5, -1, 0, 5], [-10, -5, -1, 0, 5, 10], [-10, -5, -1, 0, 3], [-10, -5, -1, 0, 3, 10], [-10, -5, -1, 0, 3, 5], [-10, -5, -1, 0, 3, 5, 10], [-10, -5, -1, 0, 1], [-10, -5, -1, 0, 1, 10], [-10, -5, -1, 0, 1, 5], [-10, -5, -1, 0, 1, 5, 10], [-10, -5, -1, 0, 1, 3], [-10, -5, -1, 0, 1, 3, 10], [-10, -5, -1, 0, 1, 3, 5], [-10, -5, -1, 0, 1, 3, 5, 10], [-10, -5, -3], [-10, -5, -3, 10], [-10, -5, -3, 5], [-10, -5, -3, 5, 10], [-10, -5, -3, 3], [-10, -5, -3, 3, 10], [-10, -5, -3, 3, 5], [-10, -5, -3, 3, 5, 10], [-10, -5, -3, 1], [-10, -5, -3, 1, 10], [-10, -5, -3, 1, 5], [-10, -5, -3, 1, 5, 10], [-10, -5, -3, 1, 3], [-10, -5, -3, 1, 3, 10], [-10, -5, -3, 1, 3, 5], [-10, -5, -3, 1, 3, 5, 10], [-10, -5, -3, 0], [-10, -5, -3, 0, 10], [-10, -5, -3, 0, 5], [-10, -5, -3, 0, 5, 10], [-10, -5, -3, 0, 3], [-10, -5, -3, 0, 3, 10], [-10, -5, -3, 0, 3, 5], [-10, -5, -3, 0, 3, 5, 10], [-10, -5, -3, 0, 1], [-10, -5, -3, 0, 1, 10], [-10, -5, -3, 0, 1, 5], [-10, -5, -3, 0, 1, 5, 10], [-10, -5, -3, 0, 1, 3], [-10, -5, -3, 0, 1, 3, 10], [-10, -5, -3, 0, 1, 3, 5], [-10, -5, -3, 0, 1, 3, 5, 10], [-10, -5, -3, -1], [-10, -5, -3, -1, 10], [-10, -5, -3, -1, 5], [-10, -5, -3, -1, 5, 10], [-10, -5, -3, -1, 3], [-10, -5, -3, -1, 3, 10], [-10, -5, -3, -1, 3, 5], [-10, -5, -3, -1, 3, 5, 10], [-10, -5, -3, -1, 1], [-10, -5, -3, -1, 1, 10], [-10, -5, -3, -1, 1, 5], [-10, -5, -3, -1, 1, 5, 10], [-10, -5, -3, -1, 1, 3], [-10, -5, -3, -1, 1, 3, 10], [-10, -5, -3, -1, 1, 3, 5], [-10, -5, -3, -1, 1, 3, 5, 10], [-10, -5, -3, -1, 0], [-10, -5, -3, -1, 0, 10], [-10, -5, -3, -1, 0, 5], [-10, -5, -3, -1, 0, 5, 10], [-10, -5, -3, -1, 0, 3], [-10, -5, -3, -1, 0, 3, 10], [-10, -5, -3, -1, 0, 3, 5], [-10, -5, -3, -1, 0, 3, 5, 10], [-10, -5, -3, -1, 0, 1], [-10, -5, -3, -1, 0, 1, 10], [-10, -5, -3, -1, 0, 1, 5], [-10, -5, -3, -1, 0, 1, 5, 10], [-10, -5, -3, -1, 0, 1, 3], [-10, -5, -3, -1, 0, 1, 3, 10], [-10, -5, -3, -1, 0, 1, 3, 5], [-10, -5, -3, -1, 0, 1, 3, 5, 10]]\n assert candidate(nums = [10, -5, 0, 7]) == [[], [7], [0], [0, 7], [-5], [-5, 7], [-5, 0], [-5, 0, 7], [10], [10, 7], [10, 0], [10, 0, 7], [10, -5], [10, -5, 7], [10, -5, 0], [10, -5, 0, 7]]\n assert candidate(nums = [1, 10, 100, 1000, 10000]) == [[], [10000], [1000], [1000, 10000], [100], [100, 10000], [100, 1000], [100, 1000, 10000], [10], [10, 10000], [10, 1000], [10, 1000, 10000], [10, 100], [10, 100, 10000], [10, 100, 1000], [10, 100, 1000, 10000], [1], [1, 10000], [1, 1000], [1, 1000, 10000], [1, 100], [1, 100, 10000], [1, 100, 1000], [1, 100, 1000, 10000], [1, 10], [1, 10, 10000], [1, 10, 1000], [1, 10, 1000, 10000], [1, 10, 100], [1, 10, 100, 10000], [1, 10, 100, 1000], [1, 10, 100, 1000, 10000]]\n assert candidate(nums = [9, 7, 5, 3, 1, -1, -3, -5, -7, -9]) == [[], [-9], [-7], [-7, -9], [-5], [-5, -9], [-5, -7], [-5, -7, -9], [-3], [-3, -9], [-3, -7], [-3, -7, -9], [-3, -5], [-3, -5, -9], [-3, -5, -7], [-3, -5, -7, -9], [-1], [-1, -9], [-1, -7], [-1, -7, -9], [-1, -5], [-1, -5, -9], [-1, -5, -7], [-1, -5, -7, -9], [-1, -3], [-1, -3, -9], [-1, -3, -7], [-1, -3, -7, -9], [-1, -3, -5], [-1, -3, -5, -9], [-1, -3, -5, -7], [-1, -3, -5, -7, -9], [1], [1, -9], [1, -7], [1, -7, -9], [1, -5], [1, -5, -9], [1, -5, -7], [1, -5, -7, -9], [1, -3], [1, -3, -9], [1, -3, -7], [1, -3, -7, -9], [1, -3, -5], [1, -3, -5, -9], [1, -3, -5, -7], [1, -3, -5, -7, -9], [1, -1], [1, -1, -9], [1, -1, -7], [1, -1, -7, -9], [1, -1, -5], [1, -1, -5, -9], [1, -1, -5, -7], [1, -1, -5, -7, -9], [1, -1, -3], [1, -1, -3, -9], [1, -1, -3, -7], [1, -1, -3, -7, -9], [1, -1, -3, -5], [1, -1, -3, -5, -9], [1, -1, -3, -5, -7], [1, -1, -3, -5, -7, -9], [3], [3, -9], [3, -7], [3, -7, -9], [3, -5], [3, -5, -9], [3, -5, -7], [3, -5, -7, -9], [3, -3], [3, -3, -9], [3, -3, -7], [3, -3, -7, -9], [3, -3, -5], [3, -3, -5, -9], [3, -3, -5, -7], [3, -3, -5, -7, -9], [3, -1], [3, -1, -9], [3, -1, -7], [3, -1, -7, -9], [3, -1, -5], [3, -1, -5, -9], [3, -1, -5, -7], [3, -1, -5, -7, -9], [3, -1, -3], [3, -1, -3, -9], [3, -1, -3, -7], [3, -1, -3, -7, -9], [3, -1, -3, -5], [3, -1, -3, -5, -9], [3, -1, -3, -5, -7], [3, -1, -3, -5, -7, -9], [3, 1], [3, 1, -9], [3, 1, -7], [3, 1, -7, -9], [3, 1, -5], [3, 1, -5, -9], [3, 1, -5, -7], [3, 1, -5, -7, -9], [3, 1, -3], [3, 1, -3, -9], [3, 1, -3, -7], [3, 1, -3, -7, -9], [3, 1, -3, -5], [3, 1, -3, -5, -9], [3, 1, -3, -5, -7], [3, 1, -3, -5, -7, -9], [3, 1, -1], [3, 1, -1, -9], [3, 1, -1, -7], [3, 1, -1, -7, -9], [3, 1, -1, -5], [3, 1, -1, -5, -9], [3, 1, -1, -5, -7], [3, 1, -1, -5, -7, -9], [3, 1, -1, -3], [3, 1, -1, -3, -9], [3, 1, -1, -3, -7], [3, 1, -1, -3, -7, -9], [3, 1, -1, -3, -5], [3, 1, -1, -3, -5, -9], [3, 1, -1, -3, -5, -7], [3, 1, -1, -3, -5, -7, -9], [5], [5, -9], [5, -7], [5, -7, -9], [5, -5], [5, -5, -9], [5, -5, -7], [5, -5, -7, -9], [5, -3], [5, -3, -9], [5, -3, -7], [5, -3, -7, -9], [5, -3, -5], [5, -3, -5, -9], [5, -3, -5, -7], [5, -3, -5, -7, -9], [5, -1], [5, -1, -9], [5, -1, -7], [5, -1, -7, -9], [5, -1, -5], [5, -1, -5, -9], [5, -1, -5, -7], [5, -1, -5, -7, -9], [5, -1, -3], [5, -1, -3, -9], [5, -1, -3, -7], [5, -1, -3, -7, -9], [5, -1, -3, -5], [5, -1, -3, -5, -9], [5, -1, -3, -5, -7], [5, -1, -3, -5, -7, -9], [5, 1], [5, 1, -9], [5, 1, -7], [5, 1, -7, -9], [5, 1, -5], [5, 1, -5, -9], [5, 1, -5, -7], [5, 1, -5, -7, -9], [5, 1, -3], [5, 1, -3, -9], [5, 1, -3, -7], [5, 1, -3, -7, -9], [5, 1, -3, -5], [5, 1, -3, -5, -9], [5, 1, -3, -5, -7], [5, 1, -3, -5, -7, -9], [5, 1, -1], [5, 1, -1, -9], [5, 1, -1, -7], [5, 1, -1, -7, -9], [5, 1, -1, -5], [5, 1, -1, -5, -9], [5, 1, -1, -5, -7], [5, 1, -1, -5, -7, -9], [5, 1, -1, -3], [5, 1, -1, -3, -9], [5, 1, -1, -3, -7], [5, 1, -1, -3, -7, -9], [5, 1, -1, -3, -5], [5, 1, -1, -3, -5, -9], [5, 1, -1, -3, -5, -7], [5, 1, -1, -3, -5, -7, -9], [5, 3], [5, 3, -9], [5, 3, -7], [5, 3, -7, -9], [5, 3, -5], [5, 3, -5, -9], [5, 3, -5, -7], [5, 3, -5, -7, -9], [5, 3, -3], [5, 3, -3, -9], [5, 3, -3, -7], [5, 3, -3, -7, -9], [5, 3, -3, -5], [5, 3, -3, -5, -9], [5, 3, -3, -5, -7], [5, 3, -3, -5, -7, -9], [5, 3, -1], [5, 3, -1, -9], [5, 3, -1, -7], [5, 3, -1, -7, -9], [5, 3, -1, -5], [5, 3, -1, -5, -9], [5, 3, -1, -5, -7], [5, 3, -1, -5, -7, -9], [5, 3, -1, -3], [5, 3, -1, -3, -9], [5, 3, -1, -3, -7], [5, 3, -1, -3, -7, -9], [5, 3, -1, -3, -5], [5, 3, -1, -3, -5, -9], [5, 3, -1, -3, -5, -7], [5, 3, -1, -3, -5, -7, -9], [5, 3, 1], [5, 3, 1, -9], [5, 3, 1, -7], [5, 3, 1, -7, -9], [5, 3, 1, -5], [5, 3, 1, -5, -9], [5, 3, 1, -5, -7], [5, 3, 1, -5, -7, -9], [5, 3, 1, -3], [5, 3, 1, -3, -9], [5, 3, 1, -3, -7], [5, 3, 1, -3, -7, -9], [5, 3, 1, -3, -5], [5, 3, 1, -3, -5, -9], [5, 3, 1, -3, -5, -7], [5, 3, 1, -3, -5, -7, -9], [5, 3, 1, -1], [5, 3, 1, -1, -9], [5, 3, 1, -1, -7], [5, 3, 1, -1, -7, -9], [5, 3, 1, -1, -5], [5, 3, 1, -1, -5, -9], [5, 3, 1, -1, -5, -7], [5, 3, 1, -1, -5, -7, -9], [5, 3, 1, -1, -3], [5, 3, 1, -1, -3, -9], [5, 3, 1, -1, -3, -7], [5, 3, 1, -1, -3, -7, -9], [5, 3, 1, -1, -3, -5], [5, 3, 1, -1, -3, -5, -9], [5, 3, 1, -1, -3, -5, -7], [5, 3, 1, -1, -3, -5, -7, -9], [7], [7, -9], [7, -7], [7, -7, -9], [7, -5], [7, -5, -9], [7, -5, -7], [7, -5, -7, -9], [7, -3], [7, -3, -9], [7, -3, -7], [7, -3, -7, -9], [7, -3, -5], [7, -3, -5, -9], [7, -3, -5, -7], [7, -3, -5, -7, -9], [7, -1], [7, -1, -9], [7, -1, -7], [7, -1, -7, -9], [7, -1, -5], [7, -1, -5, -9], [7, -1, -5, -7], [7, -1, -5, -7, -9], [7, -1, -3], [7, -1, -3, -9], [7, -1, -3, -7], [7, -1, -3, -7, -9], [7, -1, -3, -5], [7, -1, -3, -5, -9], [7, -1, -3, -5, -7], [7, -1, -3, -5, -7, -9], [7, 1], [7, 1, -9], [7, 1, -7], [7, 1, -7, -9], [7, 1, -5], [7, 1, -5, -9], [7, 1, -5, -7], [7, 1, -5, -7, -9], [7, 1, -3], [7, 1, -3, -9], [7, 1, -3, -7], [7, 1, -3, -7, -9], [7, 1, -3, -5], [7, 1, -3, -5, -9], [7, 1, -3, -5, -7], [7, 1, -3, -5, -7, -9], [7, 1, -1], [7, 1, -1, -9], [7, 1, -1, -7], [7, 1, -1, -7, -9], [7, 1, -1, -5], [7, 1, -1, -5, -9], [7, 1, -1, -5, -7], [7, 1, -1, -5, -7, -9], [7, 1, -1, -3], [7, 1, -1, -3, -9], [7, 1, -1, -3, -7], [7, 1, -1, -3, -7, -9], [7, 1, -1, -3, -5], [7, 1, -1, -3, -5, -9], [7, 1, -1, -3, -5, -7], [7, 1, -1, -3, -5, -7, -9], [7, 3], [7, 3, -9], [7, 3, -7], [7, 3, -7, -9], [7, 3, -5], [7, 3, -5, -9], [7, 3, -5, -7], [7, 3, -5, -7, -9], [7, 3, -3], [7, 3, -3, -9], [7, 3, -3, -7], [7, 3, -3, -7, -9], [7, 3, -3, -5], [7, 3, -3, -5, -9], [7, 3, -3, -5, -7], [7, 3, -3, -5, -7, -9], [7, 3, -1], [7, 3, -1, -9], [7, 3, -1, -7], [7, 3, -1, -7, -9], [7, 3, -1, -5], [7, 3, -1, -5, -9], [7, 3, -1, -5, -7], [7, 3, -1, -5, -7, -9], [7, 3, -1, -3], [7, 3, -1, -3, -9], [7, 3, -1, -3, -7], [7, 3, -1, -3, -7, -9], [7, 3, -1, -3, -5], [7, 3, -1, -3, -5, -9], [7, 3, -1, -3, -5, -7], [7, 3, -1, -3, -5, -7, -9], [7, 3, 1], [7, 3, 1, -9], [7, 3, 1, -7], [7, 3, 1, -7, -9], [7, 3, 1, -5], [7, 3, 1, -5, -9], [7, 3, 1, -5, -7], [7, 3, 1, -5, -7, -9], [7, 3, 1, -3], [7, 3, 1, -3, -9], [7, 3, 1, -3, -7], [7, 3, 1, -3, -7, -9], [7, 3, 1, -3, -5], [7, 3, 1, -3, -5, -9], [7, 3, 1, -3, -5, -7], [7, 3, 1, -3, -5, -7, -9], [7, 3, 1, -1], [7, 3, 1, -1, -9], [7, 3, 1, -1, -7], [7, 3, 1, -1, -7, -9], [7, 3, 1, -1, -5], [7, 3, 1, -1, -5, -9], [7, 3, 1, -1, -5, -7], [7, 3, 1, -1, -5, -7, -9], [7, 3, 1, -1, -3], [7, 3, 1, -1, -3, -9], [7, 3, 1, -1, -3, -7], [7, 3, 1, -1, -3, -7, -9], [7, 3, 1, -1, -3, -5], [7, 3, 1, -1, -3, -5, -9], [7, 3, 1, -1, -3, -5, -7], [7, 3, 1, -1, -3, -5, -7, -9], [7, 5], [7, 5, -9], [7, 5, -7], [7, 5, -7, -9], [7, 5, -5], [7, 5, -5, -9], [7, 5, -5, -7], [7, 5, -5, -7, -9], [7, 5, -3], [7, 5, -3, -9], [7, 5, -3, -7], [7, 5, -3, -7, -9], [7, 5, -3, -5], [7, 5, -3, -5, -9], [7, 5, -3, -5, -7], [7, 5, -3, -5, -7, -9], [7, 5, -1], [7, 5, -1, -9], [7, 5, -1, -7], [7, 5, -1, -7, -9], [7, 5, -1, -5], [7, 5, -1, -5, -9], [7, 5, -1, -5, -7], [7, 5, -1, -5, -7, -9], [7, 5, -1, -3], [7, 5, -1, -3, -9], [7, 5, -1, -3, -7], [7, 5, -1, -3, -7, -9], [7, 5, -1, -3, -5], [7, 5, -1, -3, -5, -9], [7, 5, -1, -3, -5, -7], [7, 5, -1, -3, -5, -7, -9], [7, 5, 1], [7, 5, 1, -9], [7, 5, 1, -7], [7, 5, 1, -7, -9], [7, 5, 1, -5], [7, 5, 1, -5, -9], [7, 5, 1, -5, -7], [7, 5, 1, -5, -7, -9], [7, 5, 1, -3], [7, 5, 1, -3, -9], [7, 5, 1, -3, -7], [7, 5, 1, -3, -7, -9], [7, 5, 1, -3, -5], [7, 5, 1, -3, -5, -9], [7, 5, 1, -3, -5, -7], [7, 5, 1, -3, -5, -7, -9], [7, 5, 1, -1], [7, 5, 1, -1, -9], [7, 5, 1, -1, -7], [7, 5, 1, -1, -7, -9], [7, 5, 1, -1, -5], [7, 5, 1, -1, -5, -9], [7, 5, 1, -1, -5, -7], [7, 5, 1, -1, -5, -7, -9], [7, 5, 1, -1, -3], [7, 5, 1, -1, -3, -9], [7, 5, 1, -1, -3, -7], [7, 5, 1, -1, -3, -7, -9], [7, 5, 1, -1, -3, -5], [7, 5, 1, -1, -3, -5, -9], [7, 5, 1, -1, -3, -5, -7], [7, 5, 1, -1, -3, -5, -7, -9], [7, 5, 3], [7, 5, 3, 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-1, -5], [9, 7, 5, 3, -1, -5, -9], [9, 7, 5, 3, -1, -5, -7], [9, 7, 5, 3, -1, -5, -7, -9], [9, 7, 5, 3, -1, -3], [9, 7, 5, 3, -1, -3, -9], [9, 7, 5, 3, -1, -3, -7], [9, 7, 5, 3, -1, -3, -7, -9], [9, 7, 5, 3, -1, -3, -5], [9, 7, 5, 3, -1, -3, -5, -9], [9, 7, 5, 3, -1, -3, -5, -7], [9, 7, 5, 3, -1, -3, -5, -7, -9], [9, 7, 5, 3, 1], [9, 7, 5, 3, 1, -9], [9, 7, 5, 3, 1, -7], [9, 7, 5, 3, 1, -7, -9], [9, 7, 5, 3, 1, -5], [9, 7, 5, 3, 1, -5, -9], [9, 7, 5, 3, 1, -5, -7], [9, 7, 5, 3, 1, -5, -7, -9], [9, 7, 5, 3, 1, -3], [9, 7, 5, 3, 1, -3, -9], [9, 7, 5, 3, 1, -3, -7], [9, 7, 5, 3, 1, -3, -7, -9], [9, 7, 5, 3, 1, -3, -5], [9, 7, 5, 3, 1, -3, -5, -9], [9, 7, 5, 3, 1, -3, -5, -7], [9, 7, 5, 3, 1, -3, -5, -7, -9], [9, 7, 5, 3, 1, -1], [9, 7, 5, 3, 1, -1, -9], [9, 7, 5, 3, 1, -1, -7], [9, 7, 5, 3, 1, -1, -7, -9], [9, 7, 5, 3, 1, -1, -5], [9, 7, 5, 3, 1, -1, -5, -9], [9, 7, 5, 3, 1, -1, -5, -7], [9, 7, 5, 3, 1, -1, -5, -7, -9], [9, 7, 5, 3, 1, -1, -3], [9, 7, 5, 3, 1, -1, -3, -9], [9, 7, 5, 3, 1, -1, -3, -7], [9, 7, 5, 3, 1, -1, -3, -7, -9], [9, 7, 5, 3, 1, -1, -3, -5], [9, 7, 5, 3, 1, -1, -3, -5, -9], [9, 7, 5, 3, 1, -1, -3, -5, -7], [9, 7, 5, 3, 1, -1, -3, -5, -7, -9]]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35]) == [[], [35], [30], [30, 35], [25], [25, 35], [25, 30], [25, 30, 35], [20], [20, 35], [20, 30], [20, 30, 35], [20, 25], [20, 25, 35], [20, 25, 30], [20, 25, 30, 35], [15], [15, 35], [15, 30], [15, 30, 35], [15, 25], [15, 25, 35], [15, 25, 30], [15, 25, 30, 35], [15, 20], [15, 20, 35], [15, 20, 30], [15, 20, 30, 35], [15, 20, 25], [15, 20, 25, 35], [15, 20, 25, 30], [15, 20, 25, 30, 35], [10], [10, 35], [10, 30], [10, 30, 35], [10, 25], [10, 25, 35], [10, 25, 30], [10, 25, 30, 35], [10, 20], [10, 20, 35], [10, 20, 30], [10, 20, 30, 35], [10, 20, 25], [10, 20, 25, 35], [10, 20, 25, 30], [10, 20, 25, 30, 35], [10, 15], [10, 15, 35], [10, 15, 30], [10, 15, 30, 35], [10, 15, 25], [10, 15, 25, 35], [10, 15, 25, 30], [10, 15, 25, 30, 35], [10, 15, 20], [10, 15, 20, 35], [10, 15, 20, 30], [10, 15, 20, 30, 35], [10, 15, 20, 25], [10, 15, 20, 25, 35], [10, 15, 20, 25, 30], [10, 15, 20, 25, 30, 35], [5], [5, 35], [5, 30], [5, 30, 35], [5, 25], [5, 25, 35], [5, 25, 30], [5, 25, 30, 35], [5, 20], [5, 20, 35], [5, 20, 30], [5, 20, 30, 35], [5, 20, 25], [5, 20, 25, 35], [5, 20, 25, 30], [5, 20, 25, 30, 35], [5, 15], [5, 15, 35], [5, 15, 30], [5, 15, 30, 35], [5, 15, 25], [5, 15, 25, 35], [5, 15, 25, 30], [5, 15, 25, 30, 35], [5, 15, 20], [5, 15, 20, 35], [5, 15, 20, 30], [5, 15, 20, 30, 35], [5, 15, 20, 25], [5, 15, 20, 25, 35], [5, 15, 20, 25, 30], [5, 15, 20, 25, 30, 35], [5, 10], [5, 10, 35], [5, 10, 30], [5, 10, 30, 35], [5, 10, 25], [5, 10, 25, 35], [5, 10, 25, 30], [5, 10, 25, 30, 35], [5, 10, 20], [5, 10, 20, 35], [5, 10, 20, 30], [5, 10, 20, 30, 35], [5, 10, 20, 25], [5, 10, 20, 25, 35], [5, 10, 20, 25, 30], [5, 10, 20, 25, 30, 35], [5, 10, 15], [5, 10, 15, 35], [5, 10, 15, 30], [5, 10, 15, 30, 35], [5, 10, 15, 25], [5, 10, 15, 25, 35], [5, 10, 15, 25, 30], [5, 10, 15, 25, 30, 35], [5, 10, 15, 20], [5, 10, 15, 20, 35], [5, 10, 15, 20, 30], [5, 10, 15, 20, 30, 35], [5, 10, 15, 20, 25], [5, 10, 15, 20, 25, 35], [5, 10, 15, 20, 25, 30], [5, 10, 15, 20, 25, 30, 35]]\n assert candidate(nums = [1, 11, 21, 31, 41, 51, 61, 71, 81, 91]) == [[], [91], [81], [81, 91], [71], [71, 91], [71, 81], [71, 81, 91], [61], [61, 91], [61, 81], [61, 81, 91], [61, 71], [61, 71, 91], [61, 71, 81], [61, 71, 81, 91], [51], [51, 91], [51, 81], [51, 81, 91], [51, 71], [51, 71, 91], [51, 71, 81], [51, 71, 81, 91], [51, 61], [51, 61, 91], [51, 61, 81], [51, 61, 81, 91], [51, 61, 71], [51, 61, 71, 91], [51, 61, 71, 81], [51, 61, 71, 81, 91], [41], [41, 91], [41, 81], [41, 81, 91], [41, 71], [41, 71, 91], [41, 71, 81], [41, 71, 81, 91], [41, 61], [41, 61, 91], [41, 61, 81], [41, 61, 81, 91], [41, 61, 71], [41, 61, 71, 91], [41, 61, 71, 81], [41, 61, 71, 81, 91], [41, 51], [41, 51, 91], [41, 51, 81], [41, 51, 81, 91], [41, 51, 71], [41, 51, 71, 91], [41, 51, 71, 81], [41, 51, 71, 81, 91], [41, 51, 61], [41, 51, 61, 91], [41, 51, 61, 81], [41, 51, 61, 81, 91], [41, 51, 61, 71], [41, 51, 61, 71, 91], [41, 51, 61, 71, 81], [41, 51, 61, 71, 81, 91], [31], [31, 91], [31, 81], [31, 81, 91], [31, 71], [31, 71, 91], [31, 71, 81], [31, 71, 81, 91], [31, 61], [31, 61, 91], [31, 61, 81], [31, 61, 81, 91], [31, 61, 71], [31, 61, 71, 91], [31, 61, 71, 81], [31, 61, 71, 81, 91], [31, 51], [31, 51, 91], [31, 51, 81], [31, 51, 81, 91], [31, 51, 71], [31, 51, 71, 91], [31, 51, 71, 81], [31, 51, 71, 81, 91], [31, 51, 61], [31, 51, 61, 91], [31, 51, 61, 81], [31, 51, 61, 81, 91], [31, 51, 61, 71], [31, 51, 61, 71, 91], [31, 51, 61, 71, 81], [31, 51, 61, 71, 81, 91], [31, 41], [31, 41, 91], [31, 41, 81], [31, 41, 81, 91], [31, 41, 71], [31, 41, 71, 91], [31, 41, 71, 81], [31, 41, 71, 81, 91], [31, 41, 61], [31, 41, 61, 91], [31, 41, 61, 81], [31, 41, 61, 81, 91], [31, 41, 61, 71], [31, 41, 61, 71, 91], [31, 41, 61, 71, 81], [31, 41, 61, 71, 81, 91], [31, 41, 51], [31, 41, 51, 91], [31, 41, 51, 81], [31, 41, 51, 81, 91], [31, 41, 51, 71], [31, 41, 51, 71, 91], [31, 41, 51, 71, 81], [31, 41, 51, 71, 81, 91], [31, 41, 51, 61], [31, 41, 51, 61, 91], [31, 41, 51, 61, 81], [31, 41, 51, 61, 81, 91], [31, 41, 51, 61, 71], [31, 41, 51, 61, 71, 91], [31, 41, 51, 61, 71, 81], [31, 41, 51, 61, 71, 81, 91], [21], [21, 91], [21, 81], [21, 81, 91], [21, 71], [21, 71, 91], [21, 71, 81], [21, 71, 81, 91], [21, 61], [21, 61, 91], [21, 61, 81], [21, 61, 81, 91], [21, 61, 71], [21, 61, 71, 91], [21, 61, 71, 81], [21, 61, 71, 81, 91], [21, 51], [21, 51, 91], [21, 51, 81], [21, 51, 81, 91], [21, 51, 71], [21, 51, 71, 91], [21, 51, 71, 81], [21, 51, 71, 81, 91], [21, 51, 61], [21, 51, 61, 91], [21, 51, 61, 81], [21, 51, 61, 81, 91], [21, 51, 61, 71], [21, 51, 61, 71, 91], [21, 51, 61, 71, 81], [21, 51, 61, 71, 81, 91], [21, 41], [21, 41, 91], [21, 41, 81], [21, 41, 81, 91], [21, 41, 71], [21, 41, 71, 91], [21, 41, 71, 81], [21, 41, 71, 81, 91], [21, 41, 61], [21, 41, 61, 91], [21, 41, 61, 81], [21, 41, 61, 81, 91], [21, 41, 61, 71], [21, 41, 61, 71, 91], [21, 41, 61, 71, 81], [21, 41, 61, 71, 81, 91], [21, 41, 51], [21, 41, 51, 91], [21, 41, 51, 81], [21, 41, 51, 81, 91], [21, 41, 51, 71], [21, 41, 51, 71, 91], [21, 41, 51, 71, 81], [21, 41, 51, 71, 81, 91], [21, 41, 51, 61], [21, 41, 51, 61, 91], [21, 41, 51, 61, 81], [21, 41, 51, 61, 81, 91], [21, 41, 51, 61, 71], [21, 41, 51, 61, 71, 91], [21, 41, 51, 61, 71, 81], [21, 41, 51, 61, 71, 81, 91], [21, 31], [21, 31, 91], [21, 31, 81], [21, 31, 81, 91], [21, 31, 71], [21, 31, 71, 91], [21, 31, 71, 81], [21, 31, 71, 81, 91], [21, 31, 61], [21, 31, 61, 91], [21, 31, 61, 81], [21, 31, 61, 81, 91], [21, 31, 61, 71], [21, 31, 61, 71, 91], [21, 31, 61, 71, 81], [21, 31, 61, 71, 81, 91], [21, 31, 51], [21, 31, 51, 91], [21, 31, 51, 81], [21, 31, 51, 81, 91], [21, 31, 51, 71], [21, 31, 51, 71, 91], [21, 31, 51, 71, 81], [21, 31, 51, 71, 81, 91], [21, 31, 51, 61], [21, 31, 51, 61, 91], [21, 31, 51, 61, 81], [21, 31, 51, 61, 81, 91], [21, 31, 51, 61, 71], [21, 31, 51, 61, 71, 91], [21, 31, 51, 61, 71, 81], [21, 31, 51, 61, 71, 81, 91], [21, 31, 41], [21, 31, 41, 91], [21, 31, 41, 81], [21, 31, 41, 81, 91], [21, 31, 41, 71], [21, 31, 41, 71, 91], [21, 31, 41, 71, 81], [21, 31, 41, 71, 81, 91], [21, 31, 41, 61], [21, 31, 41, 61, 91], [21, 31, 41, 61, 81], [21, 31, 41, 61, 81, 91], [21, 31, 41, 61, 71], [21, 31, 41, 61, 71, 91], [21, 31, 41, 61, 71, 81], [21, 31, 41, 61, 71, 81, 91], [21, 31, 41, 51], [21, 31, 41, 51, 91], [21, 31, 41, 51, 81], [21, 31, 41, 51, 81, 91], [21, 31, 41, 51, 71], [21, 31, 41, 51, 71, 91], [21, 31, 41, 51, 71, 81], [21, 31, 41, 51, 71, 81, 91], [21, 31, 41, 51, 61], [21, 31, 41, 51, 61, 91], [21, 31, 41, 51, 61, 81], [21, 31, 41, 51, 61, 81, 91], [21, 31, 41, 51, 61, 71], [21, 31, 41, 51, 61, 71, 91], [21, 31, 41, 51, 61, 71, 81], [21, 31, 41, 51, 61, 71, 81, 91], [11], [11, 91], [11, 81], [11, 81, 91], [11, 71], [11, 71, 91], [11, 71, 81], [11, 71, 81, 91], [11, 61], [11, 61, 91], [11, 61, 81], [11, 61, 81, 91], [11, 61, 71], [11, 61, 71, 91], [11, 61, 71, 81], [11, 61, 71, 81, 91], [11, 51], [11, 51, 91], [11, 51, 81], [11, 51, 81, 91], [11, 51, 71], [11, 51, 71, 91], [11, 51, 71, 81], [11, 51, 71, 81, 91], [11, 51, 61], [11, 51, 61, 91], [11, 51, 61, 81], [11, 51, 61, 81, 91], [11, 51, 61, 71], [11, 51, 61, 71, 91], [11, 51, 61, 71, 81], [11, 51, 61, 71, 81, 91], [11, 41], [11, 41, 91], [11, 41, 81], [11, 41, 81, 91], [11, 41, 71], [11, 41, 71, 91], [11, 41, 71, 81], [11, 41, 71, 81, 91], [11, 41, 61], [11, 41, 61, 91], [11, 41, 61, 81], [11, 41, 61, 81, 91], [11, 41, 61, 71], [11, 41, 61, 71, 91], [11, 41, 61, 71, 81], [11, 41, 61, 71, 81, 91], [11, 41, 51], [11, 41, 51, 91], [11, 41, 51, 81], [11, 41, 51, 81, 91], [11, 41, 51, 71], [11, 41, 51, 71, 91], [11, 41, 51, 71, 81], [11, 41, 51, 71, 81, 91], [11, 41, 51, 61], [11, 41, 51, 61, 91], [11, 41, 51, 61, 81], [11, 41, 51, 61, 81, 91], [11, 41, 51, 61, 71], [11, 41, 51, 61, 71, 91], [11, 41, 51, 61, 71, 81], [11, 41, 51, 61, 71, 81, 91], [11, 31], [11, 31, 91], [11, 31, 81], [11, 31, 81, 91], [11, 31, 71], [11, 31, 71, 91], [11, 31, 71, 81], [11, 31, 71, 81, 91], [11, 31, 61], [11, 31, 61, 91], [11, 31, 61, 81], [11, 31, 61, 81, 91], [11, 31, 61, 71], [11, 31, 61, 71, 91], [11, 31, 61, 71, 81], [11, 31, 61, 71, 81, 91], [11, 31, 51], [11, 31, 51, 91], [11, 31, 51, 81], [11, 31, 51, 81, 91], [11, 31, 51, 71], [11, 31, 51, 71, 91], [11, 31, 51, 71, 81], [11, 31, 51, 71, 81, 91], [11, 31, 51, 61], [11, 31, 51, 61, 91], [11, 31, 51, 61, 81], [11, 31, 51, 61, 81, 91], [11, 31, 51, 61, 71], [11, 31, 51, 61, 71, 91], [11, 31, 51, 61, 71, 81], [11, 31, 51, 61, 71, 81, 91], [11, 31, 41], [11, 31, 41, 91], [11, 31, 41, 81], [11, 31, 41, 81, 91], [11, 31, 41, 71], [11, 31, 41, 71, 91], [11, 31, 41, 71, 81], [11, 31, 41, 71, 81, 91], [11, 31, 41, 61], [11, 31, 41, 61, 91], [11, 31, 41, 61, 81], [11, 31, 41, 61, 81, 91], [11, 31, 41, 61, 71], [11, 31, 41, 61, 71, 91], [11, 31, 41, 61, 71, 81], [11, 31, 41, 61, 71, 81, 91], [11, 31, 41, 51], [11, 31, 41, 51, 91], [11, 31, 41, 51, 81], [11, 31, 41, 51, 81, 91], [11, 31, 41, 51, 71], [11, 31, 41, 51, 71, 91], [11, 31, 41, 51, 71, 81], [11, 31, 41, 51, 71, 81, 91], [11, 31, 41, 51, 61], [11, 31, 41, 51, 61, 91], [11, 31, 41, 51, 61, 81], [11, 31, 41, 51, 61, 81, 91], [11, 31, 41, 51, 61, 71], [11, 31, 41, 51, 61, 71, 91], [11, 31, 41, 51, 61, 71, 81], [11, 31, 41, 51, 61, 71, 81, 91], [11, 21], [11, 21, 91], [11, 21, 81], [11, 21, 81, 91], [11, 21, 71], [11, 21, 71, 91], [11, 21, 71, 81], [11, 21, 71, 81, 91], [11, 21, 61], [11, 21, 61, 91], [11, 21, 61, 81], [11, 21, 61, 81, 91], [11, 21, 61, 71], [11, 21, 61, 71, 91], [11, 21, 61, 71, 81], [11, 21, 61, 71, 81, 91], [11, 21, 51], [11, 21, 51, 91], [11, 21, 51, 81], [11, 21, 51, 81, 91], [11, 21, 51, 71], [11, 21, 51, 71, 91], [11, 21, 51, 71, 81], [11, 21, 51, 71, 81, 91], [11, 21, 51, 61], [11, 21, 51, 61, 91], [11, 21, 51, 61, 81], [11, 21, 51, 61, 81, 91], [11, 21, 51, 61, 71], [11, 21, 51, 61, 71, 91], [11, 21, 51, 61, 71, 81], [11, 21, 51, 61, 71, 81, 91], [11, 21, 41], [11, 21, 41, 91], [11, 21, 41, 81], [11, 21, 41, 81, 91], [11, 21, 41, 71], [11, 21, 41, 71, 91], [11, 21, 41, 71, 81], [11, 21, 41, 71, 81, 91], [11, 21, 41, 61], [11, 21, 41, 61, 91], [11, 21, 41, 61, 81], [11, 21, 41, 61, 81, 91], [11, 21, 41, 61, 71], [11, 21, 41, 61, 71, 91], [11, 21, 41, 61, 71, 81], [11, 21, 41, 61, 71, 81, 91], [11, 21, 41, 51], [11, 21, 41, 51, 91], [11, 21, 41, 51, 81], [11, 21, 41, 51, 81, 91], [11, 21, 41, 51, 71], [11, 21, 41, 51, 71, 91], [11, 21, 41, 51, 71, 81], [11, 21, 41, 51, 71, 81, 91], [11, 21, 41, 51, 61], [11, 21, 41, 51, 61, 91], [11, 21, 41, 51, 61, 81], [11, 21, 41, 51, 61, 81, 91], [11, 21, 41, 51, 61, 71], [11, 21, 41, 51, 61, 71, 91], [11, 21, 41, 51, 61, 71, 81], [11, 21, 41, 51, 61, 71, 81, 91], [11, 21, 31], [11, 21, 31, 91], [11, 21, 31, 81], [11, 21, 31, 81, 91], [11, 21, 31, 71], [11, 21, 31, 71, 91], [11, 21, 31, 71, 81], [11, 21, 31, 71, 81, 91], [11, 21, 31, 61], [11, 21, 31, 61, 91], [11, 21, 31, 61, 81], [11, 21, 31, 61, 81, 91], [11, 21, 31, 61, 71], [11, 21, 31, 61, 71, 91], [11, 21, 31, 61, 71, 81], [11, 21, 31, 61, 71, 81, 91], [11, 21, 31, 51], [11, 21, 31, 51, 91], [11, 21, 31, 51, 81], [11, 21, 31, 51, 81, 91], [11, 21, 31, 51, 71], [11, 21, 31, 51, 71, 91], [11, 21, 31, 51, 71, 81], [11, 21, 31, 51, 71, 81, 91], [11, 21, 31, 51, 61], [11, 21, 31, 51, 61, 91], [11, 21, 31, 51, 61, 81], [11, 21, 31, 51, 61, 81, 91], [11, 21, 31, 51, 61, 71], [11, 21, 31, 51, 61, 71, 91], [11, 21, 31, 51, 61, 71, 81], [11, 21, 31, 51, 61, 71, 81, 91], [11, 21, 31, 41], [11, 21, 31, 41, 91], [11, 21, 31, 41, 81], [11, 21, 31, 41, 81, 91], [11, 21, 31, 41, 71], [11, 21, 31, 41, 71, 91], [11, 21, 31, 41, 71, 81], [11, 21, 31, 41, 71, 81, 91], [11, 21, 31, 41, 61], [11, 21, 31, 41, 61, 91], [11, 21, 31, 41, 61, 81], [11, 21, 31, 41, 61, 81, 91], [11, 21, 31, 41, 61, 71], [11, 21, 31, 41, 61, 71, 91], [11, 21, 31, 41, 61, 71, 81], [11, 21, 31, 41, 61, 71, 81, 91], [11, 21, 31, 41, 51], [11, 21, 31, 41, 51, 91], [11, 21, 31, 41, 51, 81], [11, 21, 31, 41, 51, 81, 91], [11, 21, 31, 41, 51, 71], [11, 21, 31, 41, 51, 71, 91], [11, 21, 31, 41, 51, 71, 81], [11, 21, 31, 41, 51, 71, 81, 91], [11, 21, 31, 41, 51, 61], [11, 21, 31, 41, 51, 61, 91], [11, 21, 31, 41, 51, 61, 81], [11, 21, 31, 41, 51, 61, 81, 91], [11, 21, 31, 41, 51, 61, 71], [11, 21, 31, 41, 51, 61, 71, 91], [11, 21, 31, 41, 51, 61, 71, 81], [11, 21, 31, 41, 51, 61, 71, 81, 91], [1], [1, 91], [1, 81], [1, 81, 91], [1, 71], [1, 71, 91], [1, 71, 81], [1, 71, 81, 91], [1, 61], [1, 61, 91], [1, 61, 81], [1, 61, 81, 91], [1, 61, 71], [1, 61, 71, 91], [1, 61, 71, 81], [1, 61, 71, 81, 91], [1, 51], [1, 51, 91], [1, 51, 81], [1, 51, 81, 91], [1, 51, 71], [1, 51, 71, 91], [1, 51, 71, 81], [1, 51, 71, 81, 91], [1, 51, 61], [1, 51, 61, 91], [1, 51, 61, 81], [1, 51, 61, 81, 91], [1, 51, 61, 71], [1, 51, 61, 71, 91], [1, 51, 61, 71, 81], [1, 51, 61, 71, 81, 91], [1, 41], [1, 41, 91], [1, 41, 81], [1, 41, 81, 91], [1, 41, 71], [1, 41, 71, 91], [1, 41, 71, 81], [1, 41, 71, 81, 91], [1, 41, 61], [1, 41, 61, 91], [1, 41, 61, 81], [1, 41, 61, 81, 91], [1, 41, 61, 71], [1, 41, 61, 71, 91], [1, 41, 61, 71, 81], [1, 41, 61, 71, 81, 91], [1, 41, 51], [1, 41, 51, 91], [1, 41, 51, 81], [1, 41, 51, 81, 91], [1, 41, 51, 71], [1, 41, 51, 71, 91], [1, 41, 51, 71, 81], [1, 41, 51, 71, 81, 91], [1, 41, 51, 61], [1, 41, 51, 61, 91], [1, 41, 51, 61, 81], [1, 41, 51, 61, 81, 91], [1, 41, 51, 61, 71], [1, 41, 51, 61, 71, 91], [1, 41, 51, 61, 71, 81], [1, 41, 51, 61, 71, 81, 91], [1, 31], [1, 31, 91], [1, 31, 81], [1, 31, 81, 91], [1, 31, 71], [1, 31, 71, 91], [1, 31, 71, 81], [1, 31, 71, 81, 91], [1, 31, 61], [1, 31, 61, 91], [1, 31, 61, 81], [1, 31, 61, 81, 91], [1, 31, 61, 71], [1, 31, 61, 71, 91], [1, 31, 61, 71, 81], [1, 31, 61, 71, 81, 91], [1, 31, 51], [1, 31, 51, 91], [1, 31, 51, 81], [1, 31, 51, 81, 91], [1, 31, 51, 71], [1, 31, 51, 71, 91], [1, 31, 51, 71, 81], [1, 31, 51, 71, 81, 91], [1, 31, 51, 61], [1, 31, 51, 61, 91], [1, 31, 51, 61, 81], [1, 31, 51, 61, 81, 91], [1, 31, 51, 61, 71], [1, 31, 51, 61, 71, 91], [1, 31, 51, 61, 71, 81], [1, 31, 51, 61, 71, 81, 91], [1, 31, 41], [1, 31, 41, 91], [1, 31, 41, 81], [1, 31, 41, 81, 91], [1, 31, 41, 71], [1, 31, 41, 71, 91], [1, 31, 41, 71, 81], [1, 31, 41, 71, 81, 91], [1, 31, 41, 61], [1, 31, 41, 61, 91], [1, 31, 41, 61, 81], [1, 31, 41, 61, 81, 91], [1, 31, 41, 61, 71], [1, 31, 41, 61, 71, 91], [1, 31, 41, 61, 71, 81], [1, 31, 41, 61, 71, 81, 91], [1, 31, 41, 51], [1, 31, 41, 51, 91], [1, 31, 41, 51, 81], [1, 31, 41, 51, 81, 91], [1, 31, 41, 51, 71], [1, 31, 41, 51, 71, 91], [1, 31, 41, 51, 71, 81], [1, 31, 41, 51, 71, 81, 91], [1, 31, 41, 51, 61], [1, 31, 41, 51, 61, 91], [1, 31, 41, 51, 61, 81], [1, 31, 41, 51, 61, 81, 91], [1, 31, 41, 51, 61, 71], [1, 31, 41, 51, 61, 71, 91], [1, 31, 41, 51, 61, 71, 81], [1, 31, 41, 51, 61, 71, 81, 91], [1, 21], [1, 21, 91], [1, 21, 81], [1, 21, 81, 91], [1, 21, 71], [1, 21, 71, 91], [1, 21, 71, 81], [1, 21, 71, 81, 91], [1, 21, 61], [1, 21, 61, 91], [1, 21, 61, 81], [1, 21, 61, 81, 91], [1, 21, 61, 71], [1, 21, 61, 71, 91], [1, 21, 61, 71, 81], [1, 21, 61, 71, 81, 91], [1, 21, 51], [1, 21, 51, 91], [1, 21, 51, 81], [1, 21, 51, 81, 91], [1, 21, 51, 71], [1, 21, 51, 71, 91], [1, 21, 51, 71, 81], [1, 21, 51, 71, 81, 91], [1, 21, 51, 61], [1, 21, 51, 61, 91], [1, 21, 51, 61, 81], [1, 21, 51, 61, 81, 91], [1, 21, 51, 61, 71], [1, 21, 51, 61, 71, 91], [1, 21, 51, 61, 71, 81], [1, 21, 51, 61, 71, 81, 91], [1, 21, 41], [1, 21, 41, 91], [1, 21, 41, 81], [1, 21, 41, 81, 91], [1, 21, 41, 71], [1, 21, 41, 71, 91], [1, 21, 41, 71, 81], [1, 21, 41, 71, 81, 91], [1, 21, 41, 61], [1, 21, 41, 61, 91], [1, 21, 41, 61, 81], [1, 21, 41, 61, 81, 91], [1, 21, 41, 61, 71], [1, 21, 41, 61, 71, 91], [1, 21, 41, 61, 71, 81], [1, 21, 41, 61, 71, 81, 91], [1, 21, 41, 51], [1, 21, 41, 51, 91], [1, 21, 41, 51, 81], [1, 21, 41, 51, 81, 91], [1, 21, 41, 51, 71], [1, 21, 41, 51, 71, 91], [1, 21, 41, 51, 71, 81], [1, 21, 41, 51, 71, 81, 91], [1, 21, 41, 51, 61], [1, 21, 41, 51, 61, 91], [1, 21, 41, 51, 61, 81], [1, 21, 41, 51, 61, 81, 91], [1, 21, 41, 51, 61, 71], [1, 21, 41, 51, 61, 71, 91], [1, 21, 41, 51, 61, 71, 81], [1, 21, 41, 51, 61, 71, 81, 91], [1, 21, 31], [1, 21, 31, 91], [1, 21, 31, 81], [1, 21, 31, 81, 91], [1, 21, 31, 71], [1, 21, 31, 71, 91], [1, 21, 31, 71, 81], [1, 21, 31, 71, 81, 91], [1, 21, 31, 61], [1, 21, 31, 61, 91], [1, 21, 31, 61, 81], [1, 21, 31, 61, 81, 91], [1, 21, 31, 61, 71], [1, 21, 31, 61, 71, 91], [1, 21, 31, 61, 71, 81], [1, 21, 31, 61, 71, 81, 91], [1, 21, 31, 51], [1, 21, 31, 51, 91], [1, 21, 31, 51, 81], [1, 21, 31, 51, 81, 91], [1, 21, 31, 51, 71], [1, 21, 31, 51, 71, 91], [1, 21, 31, 51, 71, 81], [1, 21, 31, 51, 71, 81, 91], [1, 21, 31, 51, 61], [1, 21, 31, 51, 61, 91], [1, 21, 31, 51, 61, 81], [1, 21, 31, 51, 61, 81, 91], [1, 21, 31, 51, 61, 71], [1, 21, 31, 51, 61, 71, 91], [1, 21, 31, 51, 61, 71, 81], [1, 21, 31, 51, 61, 71, 81, 91], [1, 21, 31, 41], [1, 21, 31, 41, 91], [1, 21, 31, 41, 81], [1, 21, 31, 41, 81, 91], [1, 21, 31, 41, 71], [1, 21, 31, 41, 71, 91], [1, 21, 31, 41, 71, 81], [1, 21, 31, 41, 71, 81, 91], [1, 21, 31, 41, 61], [1, 21, 31, 41, 61, 91], [1, 21, 31, 41, 61, 81], [1, 21, 31, 41, 61, 81, 91], [1, 21, 31, 41, 61, 71], [1, 21, 31, 41, 61, 71, 91], [1, 21, 31, 41, 61, 71, 81], [1, 21, 31, 41, 61, 71, 81, 91], [1, 21, 31, 41, 51], [1, 21, 31, 41, 51, 91], [1, 21, 31, 41, 51, 81], [1, 21, 31, 41, 51, 81, 91], [1, 21, 31, 41, 51, 71], [1, 21, 31, 41, 51, 71, 91], [1, 21, 31, 41, 51, 71, 81], [1, 21, 31, 41, 51, 71, 81, 91], [1, 21, 31, 41, 51, 61], [1, 21, 31, 41, 51, 61, 91], [1, 21, 31, 41, 51, 61, 81], [1, 21, 31, 41, 51, 61, 81, 91], [1, 21, 31, 41, 51, 61, 71], [1, 21, 31, 41, 51, 61, 71, 91], [1, 21, 31, 41, 51, 61, 71, 81], [1, 21, 31, 41, 51, 61, 71, 81, 91], [1, 11], [1, 11, 91], [1, 11, 81], [1, 11, 81, 91], [1, 11, 71], [1, 11, 71, 91], [1, 11, 71, 81], [1, 11, 71, 81, 91], [1, 11, 61], [1, 11, 61, 91], [1, 11, 61, 81], [1, 11, 61, 81, 91], [1, 11, 61, 71], [1, 11, 61, 71, 91], [1, 11, 61, 71, 81], [1, 11, 61, 71, 81, 91], [1, 11, 51], [1, 11, 51, 91], [1, 11, 51, 81], [1, 11, 51, 81, 91], [1, 11, 51, 71], [1, 11, 51, 71, 91], [1, 11, 51, 71, 81], [1, 11, 51, 71, 81, 91], [1, 11, 51, 61], [1, 11, 51, 61, 91], [1, 11, 51, 61, 81], [1, 11, 51, 61, 81, 91], [1, 11, 51, 61, 71], [1, 11, 51, 61, 71, 91], [1, 11, 51, 61, 71, 81], [1, 11, 51, 61, 71, 81, 91], [1, 11, 41], [1, 11, 41, 91], [1, 11, 41, 81], [1, 11, 41, 81, 91], [1, 11, 41, 71], [1, 11, 41, 71, 91], [1, 11, 41, 71, 81], [1, 11, 41, 71, 81, 91], [1, 11, 41, 61], [1, 11, 41, 61, 91], [1, 11, 41, 61, 81], [1, 11, 41, 61, 81, 91], [1, 11, 41, 61, 71], [1, 11, 41, 61, 71, 91], [1, 11, 41, 61, 71, 81], [1, 11, 41, 61, 71, 81, 91], [1, 11, 41, 51], [1, 11, 41, 51, 91], [1, 11, 41, 51, 81], [1, 11, 41, 51, 81, 91], [1, 11, 41, 51, 71], [1, 11, 41, 51, 71, 91], [1, 11, 41, 51, 71, 81], [1, 11, 41, 51, 71, 81, 91], [1, 11, 41, 51, 61], [1, 11, 41, 51, 61, 91], [1, 11, 41, 51, 61, 81], [1, 11, 41, 51, 61, 81, 91], [1, 11, 41, 51, 61, 71], [1, 11, 41, 51, 61, 71, 91], [1, 11, 41, 51, 61, 71, 81], [1, 11, 41, 51, 61, 71, 81, 91], [1, 11, 31], [1, 11, 31, 91], [1, 11, 31, 81], [1, 11, 31, 81, 91], [1, 11, 31, 71], [1, 11, 31, 71, 91], [1, 11, 31, 71, 81], [1, 11, 31, 71, 81, 91], [1, 11, 31, 61], [1, 11, 31, 61, 91], [1, 11, 31, 61, 81], [1, 11, 31, 61, 81, 91], [1, 11, 31, 61, 71], [1, 11, 31, 61, 71, 91], [1, 11, 31, 61, 71, 81], [1, 11, 31, 61, 71, 81, 91], [1, 11, 31, 51], [1, 11, 31, 51, 91], [1, 11, 31, 51, 81], [1, 11, 31, 51, 81, 91], [1, 11, 31, 51, 71], [1, 11, 31, 51, 71, 91], [1, 11, 31, 51, 71, 81], [1, 11, 31, 51, 71, 81, 91], [1, 11, 31, 51, 61], [1, 11, 31, 51, 61, 91], [1, 11, 31, 51, 61, 81], [1, 11, 31, 51, 61, 81, 91], [1, 11, 31, 51, 61, 71], [1, 11, 31, 51, 61, 71, 91], [1, 11, 31, 51, 61, 71, 81], [1, 11, 31, 51, 61, 71, 81, 91], [1, 11, 31, 41], [1, 11, 31, 41, 91], [1, 11, 31, 41, 81], [1, 11, 31, 41, 81, 91], [1, 11, 31, 41, 71], [1, 11, 31, 41, 71, 91], [1, 11, 31, 41, 71, 81], [1, 11, 31, 41, 71, 81, 91], [1, 11, 31, 41, 61], [1, 11, 31, 41, 61, 91], [1, 11, 31, 41, 61, 81], [1, 11, 31, 41, 61, 81, 91], [1, 11, 31, 41, 61, 71], [1, 11, 31, 41, 61, 71, 91], [1, 11, 31, 41, 61, 71, 81], [1, 11, 31, 41, 61, 71, 81, 91], [1, 11, 31, 41, 51], [1, 11, 31, 41, 51, 91], [1, 11, 31, 41, 51, 81], [1, 11, 31, 41, 51, 81, 91], [1, 11, 31, 41, 51, 71], [1, 11, 31, 41, 51, 71, 91], [1, 11, 31, 41, 51, 71, 81], [1, 11, 31, 41, 51, 71, 81, 91], [1, 11, 31, 41, 51, 61], [1, 11, 31, 41, 51, 61, 91], [1, 11, 31, 41, 51, 61, 81], [1, 11, 31, 41, 51, 61, 81, 91], [1, 11, 31, 41, 51, 61, 71], [1, 11, 31, 41, 51, 61, 71, 91], [1, 11, 31, 41, 51, 61, 71, 81], [1, 11, 31, 41, 51, 61, 71, 81, 91], [1, 11, 21], [1, 11, 21, 91], [1, 11, 21, 81], [1, 11, 21, 81, 91], [1, 11, 21, 71], [1, 11, 21, 71, 91], [1, 11, 21, 71, 81], [1, 11, 21, 71, 81, 91], [1, 11, 21, 61], [1, 11, 21, 61, 91], [1, 11, 21, 61, 81], [1, 11, 21, 61, 81, 91], [1, 11, 21, 61, 71], [1, 11, 21, 61, 71, 91], [1, 11, 21, 61, 71, 81], [1, 11, 21, 61, 71, 81, 91], [1, 11, 21, 51], [1, 11, 21, 51, 91], [1, 11, 21, 51, 81], [1, 11, 21, 51, 81, 91], [1, 11, 21, 51, 71], [1, 11, 21, 51, 71, 91], [1, 11, 21, 51, 71, 81], [1, 11, 21, 51, 71, 81, 91], [1, 11, 21, 51, 61], [1, 11, 21, 51, 61, 91], [1, 11, 21, 51, 61, 81], [1, 11, 21, 51, 61, 81, 91], [1, 11, 21, 51, 61, 71], [1, 11, 21, 51, 61, 71, 91], [1, 11, 21, 51, 61, 71, 81], [1, 11, 21, 51, 61, 71, 81, 91], [1, 11, 21, 41], [1, 11, 21, 41, 91], [1, 11, 21, 41, 81], [1, 11, 21, 41, 81, 91], [1, 11, 21, 41, 71], [1, 11, 21, 41, 71, 91], [1, 11, 21, 41, 71, 81], [1, 11, 21, 41, 71, 81, 91], [1, 11, 21, 41, 61], [1, 11, 21, 41, 61, 91], [1, 11, 21, 41, 61, 81], [1, 11, 21, 41, 61, 81, 91], [1, 11, 21, 41, 61, 71], [1, 11, 21, 41, 61, 71, 91], [1, 11, 21, 41, 61, 71, 81], [1, 11, 21, 41, 61, 71, 81, 91], [1, 11, 21, 41, 51], [1, 11, 21, 41, 51, 91], [1, 11, 21, 41, 51, 81], [1, 11, 21, 41, 51, 81, 91], [1, 11, 21, 41, 51, 71], [1, 11, 21, 41, 51, 71, 91], [1, 11, 21, 41, 51, 71, 81], [1, 11, 21, 41, 51, 71, 81, 91], [1, 11, 21, 41, 51, 61], [1, 11, 21, 41, 51, 61, 91], [1, 11, 21, 41, 51, 61, 81], [1, 11, 21, 41, 51, 61, 81, 91], [1, 11, 21, 41, 51, 61, 71], [1, 11, 21, 41, 51, 61, 71, 91], [1, 11, 21, 41, 51, 61, 71, 81], [1, 11, 21, 41, 51, 61, 71, 81, 91], [1, 11, 21, 31], [1, 11, 21, 31, 91], [1, 11, 21, 31, 81], [1, 11, 21, 31, 81, 91], [1, 11, 21, 31, 71], [1, 11, 21, 31, 71, 91], [1, 11, 21, 31, 71, 81], [1, 11, 21, 31, 71, 81, 91], [1, 11, 21, 31, 61], [1, 11, 21, 31, 61, 91], [1, 11, 21, 31, 61, 81], [1, 11, 21, 31, 61, 81, 91], [1, 11, 21, 31, 61, 71], [1, 11, 21, 31, 61, 71, 91], [1, 11, 21, 31, 61, 71, 81], [1, 11, 21, 31, 61, 71, 81, 91], [1, 11, 21, 31, 51], [1, 11, 21, 31, 51, 91], [1, 11, 21, 31, 51, 81], [1, 11, 21, 31, 51, 81, 91], [1, 11, 21, 31, 51, 71], [1, 11, 21, 31, 51, 71, 91], [1, 11, 21, 31, 51, 71, 81], [1, 11, 21, 31, 51, 71, 81, 91], [1, 11, 21, 31, 51, 61], [1, 11, 21, 31, 51, 61, 91], [1, 11, 21, 31, 51, 61, 81], [1, 11, 21, 31, 51, 61, 81, 91], [1, 11, 21, 31, 51, 61, 71], [1, 11, 21, 31, 51, 61, 71, 91], [1, 11, 21, 31, 51, 61, 71, 81], [1, 11, 21, 31, 51, 61, 71, 81, 91], [1, 11, 21, 31, 41], [1, 11, 21, 31, 41, 91], [1, 11, 21, 31, 41, 81], [1, 11, 21, 31, 41, 81, 91], [1, 11, 21, 31, 41, 71], [1, 11, 21, 31, 41, 71, 91], [1, 11, 21, 31, 41, 71, 81], [1, 11, 21, 31, 41, 71, 81, 91], [1, 11, 21, 31, 41, 61], [1, 11, 21, 31, 41, 61, 91], [1, 11, 21, 31, 41, 61, 81], [1, 11, 21, 31, 41, 61, 81, 91], [1, 11, 21, 31, 41, 61, 71], [1, 11, 21, 31, 41, 61, 71, 91], [1, 11, 21, 31, 41, 61, 71, 81], [1, 11, 21, 31, 41, 61, 71, 81, 91], [1, 11, 21, 31, 41, 51], [1, 11, 21, 31, 41, 51, 91], [1, 11, 21, 31, 41, 51, 81], [1, 11, 21, 31, 41, 51, 81, 91], [1, 11, 21, 31, 41, 51, 71], [1, 11, 21, 31, 41, 51, 71, 91], [1, 11, 21, 31, 41, 51, 71, 81], [1, 11, 21, 31, 41, 51, 71, 81, 91], [1, 11, 21, 31, 41, 51, 61], [1, 11, 21, 31, 41, 51, 61, 91], [1, 11, 21, 31, 41, 51, 61, 81], [1, 11, 21, 31, 41, 51, 61, 81, 91], [1, 11, 21, 31, 41, 51, 61, 71], [1, 11, 21, 31, 41, 51, 61, 71, 91], [1, 11, 21, 31, 41, 51, 61, 71, 81], [1, 11, 21, 31, 41, 51, 61, 71, 81, 91]]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == [[], [1000], [900], [900, 1000], [800], [800, 1000], [800, 900], [800, 900, 1000], [700], [700, 1000], [700, 900], [700, 900, 1000], [700, 800], [700, 800, 1000], [700, 800, 900], [700, 800, 900, 1000], [600], [600, 1000], [600, 900], [600, 900, 1000], [600, 800], [600, 800, 1000], [600, 800, 900], [600, 800, 900, 1000], [600, 700], [600, 700, 1000], [600, 700, 900], [600, 700, 900, 1000], [600, 700, 800], [600, 700, 800, 1000], [600, 700, 800, 900], [600, 700, 800, 900, 1000], [500], [500, 1000], [500, 900], [500, 900, 1000], [500, 800], [500, 800, 1000], [500, 800, 900], [500, 800, 900, 1000], [500, 700], [500, 700, 1000], [500, 700, 900], [500, 700, 900, 1000], [500, 700, 800], [500, 700, 800, 1000], [500, 700, 800, 900], [500, 700, 800, 900, 1000], [500, 600], [500, 600, 1000], [500, 600, 900], [500, 600, 900, 1000], [500, 600, 800], [500, 600, 800, 1000], [500, 600, 800, 900], [500, 600, 800, 900, 1000], [500, 600, 700], [500, 600, 700, 1000], [500, 600, 700, 900], [500, 600, 700, 900, 1000], [500, 600, 700, 800], [500, 600, 700, 800, 1000], [500, 600, 700, 800, 900], [500, 600, 700, 800, 900, 1000], [400], [400, 1000], [400, 900], [400, 900, 1000], [400, 800], [400, 800, 1000], [400, 800, 900], [400, 800, 900, 1000], [400, 700], [400, 700, 1000], [400, 700, 900], [400, 700, 900, 1000], [400, 700, 800], [400, 700, 800, 1000], [400, 700, 800, 900], [400, 700, 800, 900, 1000], [400, 600], [400, 600, 1000], [400, 600, 900], [400, 600, 900, 1000], [400, 600, 800], [400, 600, 800, 1000], [400, 600, 800, 900], [400, 600, 800, 900, 1000], [400, 600, 700], [400, 600, 700, 1000], [400, 600, 700, 900], [400, 600, 700, 900, 1000], [400, 600, 700, 800], [400, 600, 700, 800, 1000], [400, 600, 700, 800, 900], [400, 600, 700, 800, 900, 1000], [400, 500], [400, 500, 1000], [400, 500, 900], [400, 500, 900, 1000], [400, 500, 800], [400, 500, 800, 1000], [400, 500, 800, 900], [400, 500, 800, 900, 1000], [400, 500, 700], [400, 500, 700, 1000], [400, 500, 700, 900], [400, 500, 700, 900, 1000], [400, 500, 700, 800], [400, 500, 700, 800, 1000], [400, 500, 700, 800, 900], [400, 500, 700, 800, 900, 1000], [400, 500, 600], [400, 500, 600, 1000], [400, 500, 600, 900], [400, 500, 600, 900, 1000], [400, 500, 600, 800], [400, 500, 600, 800, 1000], [400, 500, 600, 800, 900], [400, 500, 600, 800, 900, 1000], [400, 500, 600, 700], [400, 500, 600, 700, 1000], [400, 500, 600, 700, 900], [400, 500, 600, 700, 900, 1000], [400, 500, 600, 700, 800], [400, 500, 600, 700, 800, 1000], [400, 500, 600, 700, 800, 900], [400, 500, 600, 700, 800, 900, 1000], [300], [300, 1000], [300, 900], [300, 900, 1000], [300, 800], [300, 800, 1000], [300, 800, 900], [300, 800, 900, 1000], [300, 700], [300, 700, 1000], [300, 700, 900], [300, 700, 900, 1000], [300, 700, 800], [300, 700, 800, 1000], [300, 700, 800, 900], [300, 700, 800, 900, 1000], [300, 600], [300, 600, 1000], [300, 600, 900], [300, 600, 900, 1000], [300, 600, 800], [300, 600, 800, 1000], [300, 600, 800, 900], [300, 600, 800, 900, 1000], [300, 600, 700], [300, 600, 700, 1000], [300, 600, 700, 900], [300, 600, 700, 900, 1000], [300, 600, 700, 800], [300, 600, 700, 800, 1000], [300, 600, 700, 800, 900], [300, 600, 700, 800, 900, 1000], [300, 500], [300, 500, 1000], [300, 500, 900], [300, 500, 900, 1000], [300, 500, 800], [300, 500, 800, 1000], [300, 500, 800, 900], [300, 500, 800, 900, 1000], [300, 500, 700], [300, 500, 700, 1000], [300, 500, 700, 900], [300, 500, 700, 900, 1000], [300, 500, 700, 800], [300, 500, 700, 800, 1000], [300, 500, 700, 800, 900], [300, 500, 700, 800, 900, 1000], [300, 500, 600], [300, 500, 600, 1000], [300, 500, 600, 900], [300, 500, 600, 900, 1000], [300, 500, 600, 800], [300, 500, 600, 800, 1000], [300, 500, 600, 800, 900], [300, 500, 600, 800, 900, 1000], [300, 500, 600, 700], [300, 500, 600, 700, 1000], [300, 500, 600, 700, 900], [300, 500, 600, 700, 900, 1000], [300, 500, 600, 700, 800], [300, 500, 600, 700, 800, 1000], [300, 500, 600, 700, 800, 900], [300, 500, 600, 700, 800, 900, 1000], [300, 400], [300, 400, 1000], [300, 400, 900], [300, 400, 900, 1000], [300, 400, 800], [300, 400, 800, 1000], [300, 400, 800, 900], [300, 400, 800, 900, 1000], [300, 400, 700], [300, 400, 700, 1000], [300, 400, 700, 900], [300, 400, 700, 900, 1000], [300, 400, 700, 800], [300, 400, 700, 800, 1000], [300, 400, 700, 800, 900], [300, 400, 700, 800, 900, 1000], [300, 400, 600], [300, 400, 600, 1000], [300, 400, 600, 900], [300, 400, 600, 900, 1000], [300, 400, 600, 800], [300, 400, 600, 800, 1000], [300, 400, 600, 800, 900], [300, 400, 600, 800, 900, 1000], [300, 400, 600, 700], [300, 400, 600, 700, 1000], [300, 400, 600, 700, 900], [300, 400, 600, 700, 900, 1000], [300, 400, 600, 700, 800], [300, 400, 600, 700, 800, 1000], [300, 400, 600, 700, 800, 900], [300, 400, 600, 700, 800, 900, 1000], [300, 400, 500], [300, 400, 500, 1000], [300, 400, 500, 900], [300, 400, 500, 900, 1000], [300, 400, 500, 800], [300, 400, 500, 800, 1000], [300, 400, 500, 800, 900], [300, 400, 500, 800, 900, 1000], [300, 400, 500, 700], [300, 400, 500, 700, 1000], [300, 400, 500, 700, 900], [300, 400, 500, 700, 900, 1000], [300, 400, 500, 700, 800], [300, 400, 500, 700, 800, 1000], [300, 400, 500, 700, 800, 900], [300, 400, 500, 700, 800, 900, 1000], [300, 400, 500, 600], [300, 400, 500, 600, 1000], [300, 400, 500, 600, 900], [300, 400, 500, 600, 900, 1000], [300, 400, 500, 600, 800], [300, 400, 500, 600, 800, 1000], [300, 400, 500, 600, 800, 900], [300, 400, 500, 600, 800, 900, 1000], [300, 400, 500, 600, 700], [300, 400, 500, 600, 700, 1000], [300, 400, 500, 600, 700, 900], [300, 400, 500, 600, 700, 900, 1000], [300, 400, 500, 600, 700, 800], [300, 400, 500, 600, 700, 800, 1000], [300, 400, 500, 600, 700, 800, 900], [300, 400, 500, 600, 700, 800, 900, 1000], [200], [200, 1000], [200, 900], [200, 900, 1000], [200, 800], [200, 800, 1000], [200, 800, 900], [200, 800, 900, 1000], [200, 700], [200, 700, 1000], [200, 700, 900], [200, 700, 900, 1000], [200, 700, 800], [200, 700, 800, 1000], [200, 700, 800, 900], [200, 700, 800, 900, 1000], [200, 600], [200, 600, 1000], [200, 600, 900], [200, 600, 900, 1000], [200, 600, 800], [200, 600, 800, 1000], [200, 600, 800, 900], [200, 600, 800, 900, 1000], [200, 600, 700], [200, 600, 700, 1000], [200, 600, 700, 900], [200, 600, 700, 900, 1000], [200, 600, 700, 800], [200, 600, 700, 800, 1000], [200, 600, 700, 800, 900], [200, 600, 700, 800, 900, 1000], [200, 500], [200, 500, 1000], [200, 500, 900], [200, 500, 900, 1000], [200, 500, 800], [200, 500, 800, 1000], [200, 500, 800, 900], [200, 500, 800, 900, 1000], [200, 500, 700], [200, 500, 700, 1000], [200, 500, 700, 900], [200, 500, 700, 900, 1000], [200, 500, 700, 800], [200, 500, 700, 800, 1000], [200, 500, 700, 800, 900], [200, 500, 700, 800, 900, 1000], [200, 500, 600], [200, 500, 600, 1000], [200, 500, 600, 900], [200, 500, 600, 900, 1000], [200, 500, 600, 800], [200, 500, 600, 800, 1000], [200, 500, 600, 800, 900], [200, 500, 600, 800, 900, 1000], [200, 500, 600, 700], [200, 500, 600, 700, 1000], [200, 500, 600, 700, 900], [200, 500, 600, 700, 900, 1000], [200, 500, 600, 700, 800], [200, 500, 600, 700, 800, 1000], [200, 500, 600, 700, 800, 900], [200, 500, 600, 700, 800, 900, 1000], [200, 400], [200, 400, 1000], [200, 400, 900], [200, 400, 900, 1000], [200, 400, 800], [200, 400, 800, 1000], [200, 400, 800, 900], [200, 400, 800, 900, 1000], [200, 400, 700], [200, 400, 700, 1000], [200, 400, 700, 900], [200, 400, 700, 900, 1000], [200, 400, 700, 800], [200, 400, 700, 800, 1000], [200, 400, 700, 800, 900], [200, 400, 700, 800, 900, 1000], [200, 400, 600], [200, 400, 600, 1000], [200, 400, 600, 900], [200, 400, 600, 900, 1000], [200, 400, 600, 800], [200, 400, 600, 800, 1000], [200, 400, 600, 800, 900], [200, 400, 600, 800, 900, 1000], [200, 400, 600, 700], [200, 400, 600, 700, 1000], [200, 400, 600, 700, 900], [200, 400, 600, 700, 900, 1000], [200, 400, 600, 700, 800], [200, 400, 600, 700, 800, 1000], [200, 400, 600, 700, 800, 900], [200, 400, 600, 700, 800, 900, 1000], [200, 400, 500], [200, 400, 500, 1000], [200, 400, 500, 900], [200, 400, 500, 900, 1000], [200, 400, 500, 800], [200, 400, 500, 800, 1000], [200, 400, 500, 800, 900], [200, 400, 500, 800, 900, 1000], [200, 400, 500, 700], [200, 400, 500, 700, 1000], [200, 400, 500, 700, 900], [200, 400, 500, 700, 900, 1000], [200, 400, 500, 700, 800], [200, 400, 500, 700, 800, 1000], [200, 400, 500, 700, 800, 900], [200, 400, 500, 700, 800, 900, 1000], [200, 400, 500, 600], [200, 400, 500, 600, 1000], [200, 400, 500, 600, 900], [200, 400, 500, 600, 900, 1000], [200, 400, 500, 600, 800], [200, 400, 500, 600, 800, 1000], [200, 400, 500, 600, 800, 900], [200, 400, 500, 600, 800, 900, 1000], [200, 400, 500, 600, 700], [200, 400, 500, 600, 700, 1000], [200, 400, 500, 600, 700, 900], [200, 400, 500, 600, 700, 900, 1000], [200, 400, 500, 600, 700, 800], [200, 400, 500, 600, 700, 800, 1000], [200, 400, 500, 600, 700, 800, 900], [200, 400, 500, 600, 700, 800, 900, 1000], [200, 300], [200, 300, 1000], [200, 300, 900], [200, 300, 900, 1000], [200, 300, 800], [200, 300, 800, 1000], [200, 300, 800, 900], [200, 300, 800, 900, 1000], [200, 300, 700], [200, 300, 700, 1000], [200, 300, 700, 900], [200, 300, 700, 900, 1000], [200, 300, 700, 800], [200, 300, 700, 800, 1000], [200, 300, 700, 800, 900], [200, 300, 700, 800, 900, 1000], [200, 300, 600], [200, 300, 600, 1000], [200, 300, 600, 900], [200, 300, 600, 900, 1000], [200, 300, 600, 800], [200, 300, 600, 800, 1000], [200, 300, 600, 800, 900], [200, 300, 600, 800, 900, 1000], [200, 300, 600, 700], [200, 300, 600, 700, 1000], [200, 300, 600, 700, 900], [200, 300, 600, 700, 900, 1000], [200, 300, 600, 700, 800], [200, 300, 600, 700, 800, 1000], [200, 300, 600, 700, 800, 900], [200, 300, 600, 700, 800, 900, 1000], [200, 300, 500], [200, 300, 500, 1000], [200, 300, 500, 900], [200, 300, 500, 900, 1000], [200, 300, 500, 800], [200, 300, 500, 800, 1000], [200, 300, 500, 800, 900], [200, 300, 500, 800, 900, 1000], [200, 300, 500, 700], [200, 300, 500, 700, 1000], [200, 300, 500, 700, 900], [200, 300, 500, 700, 900, 1000], [200, 300, 500, 700, 800], [200, 300, 500, 700, 800, 1000], [200, 300, 500, 700, 800, 900], [200, 300, 500, 700, 800, 900, 1000], [200, 300, 500, 600], [200, 300, 500, 600, 1000], [200, 300, 500, 600, 900], [200, 300, 500, 600, 900, 1000], [200, 300, 500, 600, 800], [200, 300, 500, 600, 800, 1000], [200, 300, 500, 600, 800, 900], [200, 300, 500, 600, 800, 900, 1000], [200, 300, 500, 600, 700], [200, 300, 500, 600, 700, 1000], [200, 300, 500, 600, 700, 900], [200, 300, 500, 600, 700, 900, 1000], [200, 300, 500, 600, 700, 800], [200, 300, 500, 600, 700, 800, 1000], [200, 300, 500, 600, 700, 800, 900], [200, 300, 500, 600, 700, 800, 900, 1000], [200, 300, 400], [200, 300, 400, 1000], [200, 300, 400, 900], [200, 300, 400, 900, 1000], [200, 300, 400, 800], [200, 300, 400, 800, 1000], [200, 300, 400, 800, 900], [200, 300, 400, 800, 900, 1000], [200, 300, 400, 700], [200, 300, 400, 700, 1000], [200, 300, 400, 700, 900], [200, 300, 400, 700, 900, 1000], [200, 300, 400, 700, 800], [200, 300, 400, 700, 800, 1000], [200, 300, 400, 700, 800, 900], [200, 300, 400, 700, 800, 900, 1000], [200, 300, 400, 600], [200, 300, 400, 600, 1000], [200, 300, 400, 600, 900], [200, 300, 400, 600, 900, 1000], [200, 300, 400, 600, 800], [200, 300, 400, 600, 800, 1000], [200, 300, 400, 600, 800, 900], [200, 300, 400, 600, 800, 900, 1000], [200, 300, 400, 600, 700], [200, 300, 400, 600, 700, 1000], [200, 300, 400, 600, 700, 900], [200, 300, 400, 600, 700, 900, 1000], [200, 300, 400, 600, 700, 800], [200, 300, 400, 600, 700, 800, 1000], [200, 300, 400, 600, 700, 800, 900], [200, 300, 400, 600, 700, 800, 900, 1000], [200, 300, 400, 500], [200, 300, 400, 500, 1000], [200, 300, 400, 500, 900], [200, 300, 400, 500, 900, 1000], [200, 300, 400, 500, 800], [200, 300, 400, 500, 800, 1000], [200, 300, 400, 500, 800, 900], [200, 300, 400, 500, 800, 900, 1000], [200, 300, 400, 500, 700], [200, 300, 400, 500, 700, 1000], [200, 300, 400, 500, 700, 900], [200, 300, 400, 500, 700, 900, 1000], [200, 300, 400, 500, 700, 800], [200, 300, 400, 500, 700, 800, 1000], [200, 300, 400, 500, 700, 800, 900], [200, 300, 400, 500, 700, 800, 900, 1000], [200, 300, 400, 500, 600], [200, 300, 400, 500, 600, 1000], [200, 300, 400, 500, 600, 900], [200, 300, 400, 500, 600, 900, 1000], [200, 300, 400, 500, 600, 800], [200, 300, 400, 500, 600, 800, 1000], [200, 300, 400, 500, 600, 800, 900], [200, 300, 400, 500, 600, 800, 900, 1000], [200, 300, 400, 500, 600, 700], [200, 300, 400, 500, 600, 700, 1000], [200, 300, 400, 500, 600, 700, 900], [200, 300, 400, 500, 600, 700, 900, 1000], [200, 300, 400, 500, 600, 700, 800], [200, 300, 400, 500, 600, 700, 800, 1000], [200, 300, 400, 500, 600, 700, 800, 900], [200, 300, 400, 500, 600, 700, 800, 900, 1000], [100], [100, 1000], [100, 900], [100, 900, 1000], [100, 800], [100, 800, 1000], [100, 800, 900], [100, 800, 900, 1000], [100, 700], [100, 700, 1000], [100, 700, 900], [100, 700, 900, 1000], [100, 700, 800], [100, 700, 800, 1000], [100, 700, 800, 900], [100, 700, 800, 900, 1000], [100, 600], [100, 600, 1000], [100, 600, 900], [100, 600, 900, 1000], [100, 600, 800], [100, 600, 800, 1000], [100, 600, 800, 900], [100, 600, 800, 900, 1000], [100, 600, 700], [100, 600, 700, 1000], [100, 600, 700, 900], [100, 600, 700, 900, 1000], [100, 600, 700, 800], [100, 600, 700, 800, 1000], [100, 600, 700, 800, 900], [100, 600, 700, 800, 900, 1000], [100, 500], [100, 500, 1000], [100, 500, 900], [100, 500, 900, 1000], [100, 500, 800], [100, 500, 800, 1000], [100, 500, 800, 900], [100, 500, 800, 900, 1000], [100, 500, 700], [100, 500, 700, 1000], [100, 500, 700, 900], [100, 500, 700, 900, 1000], [100, 500, 700, 800], [100, 500, 700, 800, 1000], [100, 500, 700, 800, 900], [100, 500, 700, 800, 900, 1000], [100, 500, 600], [100, 500, 600, 1000], [100, 500, 600, 900], [100, 500, 600, 900, 1000], [100, 500, 600, 800], [100, 500, 600, 800, 1000], [100, 500, 600, 800, 900], [100, 500, 600, 800, 900, 1000], [100, 500, 600, 700], [100, 500, 600, 700, 1000], [100, 500, 600, 700, 900], [100, 500, 600, 700, 900, 1000], [100, 500, 600, 700, 800], [100, 500, 600, 700, 800, 1000], [100, 500, 600, 700, 800, 900], [100, 500, 600, 700, 800, 900, 1000], [100, 400], [100, 400, 1000], [100, 400, 900], [100, 400, 900, 1000], [100, 400, 800], [100, 400, 800, 1000], [100, 400, 800, 900], [100, 400, 800, 900, 1000], [100, 400, 700], [100, 400, 700, 1000], [100, 400, 700, 900], [100, 400, 700, 900, 1000], [100, 400, 700, 800], [100, 400, 700, 800, 1000], [100, 400, 700, 800, 900], [100, 400, 700, 800, 900, 1000], [100, 400, 600], [100, 400, 600, 1000], [100, 400, 600, 900], [100, 400, 600, 900, 1000], [100, 400, 600, 800], [100, 400, 600, 800, 1000], [100, 400, 600, 800, 900], [100, 400, 600, 800, 900, 1000], [100, 400, 600, 700], [100, 400, 600, 700, 1000], [100, 400, 600, 700, 900], [100, 400, 600, 700, 900, 1000], [100, 400, 600, 700, 800], [100, 400, 600, 700, 800, 1000], [100, 400, 600, 700, 800, 900], [100, 400, 600, 700, 800, 900, 1000], [100, 400, 500], [100, 400, 500, 1000], [100, 400, 500, 900], [100, 400, 500, 900, 1000], [100, 400, 500, 800], [100, 400, 500, 800, 1000], [100, 400, 500, 800, 900], [100, 400, 500, 800, 900, 1000], [100, 400, 500, 700], [100, 400, 500, 700, 1000], [100, 400, 500, 700, 900], [100, 400, 500, 700, 900, 1000], [100, 400, 500, 700, 800], [100, 400, 500, 700, 800, 1000], [100, 400, 500, 700, 800, 900], [100, 400, 500, 700, 800, 900, 1000], [100, 400, 500, 600], [100, 400, 500, 600, 1000], [100, 400, 500, 600, 900], [100, 400, 500, 600, 900, 1000], [100, 400, 500, 600, 800], [100, 400, 500, 600, 800, 1000], [100, 400, 500, 600, 800, 900], [100, 400, 500, 600, 800, 900, 1000], [100, 400, 500, 600, 700], [100, 400, 500, 600, 700, 1000], [100, 400, 500, 600, 700, 900], [100, 400, 500, 600, 700, 900, 1000], [100, 400, 500, 600, 700, 800], [100, 400, 500, 600, 700, 800, 1000], [100, 400, 500, 600, 700, 800, 900], [100, 400, 500, 600, 700, 800, 900, 1000], [100, 300], [100, 300, 1000], [100, 300, 900], [100, 300, 900, 1000], [100, 300, 800], [100, 300, 800, 1000], [100, 300, 800, 900], [100, 300, 800, 900, 1000], [100, 300, 700], [100, 300, 700, 1000], [100, 300, 700, 900], [100, 300, 700, 900, 1000], [100, 300, 700, 800], [100, 300, 700, 800, 1000], [100, 300, 700, 800, 900], [100, 300, 700, 800, 900, 1000], [100, 300, 600], [100, 300, 600, 1000], [100, 300, 600, 900], [100, 300, 600, 900, 1000], [100, 300, 600, 800], [100, 300, 600, 800, 1000], [100, 300, 600, 800, 900], [100, 300, 600, 800, 900, 1000], [100, 300, 600, 700], [100, 300, 600, 700, 1000], [100, 300, 600, 700, 900], [100, 300, 600, 700, 900, 1000], [100, 300, 600, 700, 800], [100, 300, 600, 700, 800, 1000], [100, 300, 600, 700, 800, 900], [100, 300, 600, 700, 800, 900, 1000], [100, 300, 500], [100, 300, 500, 1000], [100, 300, 500, 900], [100, 300, 500, 900, 1000], [100, 300, 500, 800], [100, 300, 500, 800, 1000], [100, 300, 500, 800, 900], [100, 300, 500, 800, 900, 1000], [100, 300, 500, 700], [100, 300, 500, 700, 1000], [100, 300, 500, 700, 900], [100, 300, 500, 700, 900, 1000], [100, 300, 500, 700, 800], [100, 300, 500, 700, 800, 1000], [100, 300, 500, 700, 800, 900], [100, 300, 500, 700, 800, 900, 1000], [100, 300, 500, 600], [100, 300, 500, 600, 1000], [100, 300, 500, 600, 900], [100, 300, 500, 600, 900, 1000], [100, 300, 500, 600, 800], [100, 300, 500, 600, 800, 1000], [100, 300, 500, 600, 800, 900], [100, 300, 500, 600, 800, 900, 1000], [100, 300, 500, 600, 700], [100, 300, 500, 600, 700, 1000], [100, 300, 500, 600, 700, 900], [100, 300, 500, 600, 700, 900, 1000], [100, 300, 500, 600, 700, 800], [100, 300, 500, 600, 700, 800, 1000], [100, 300, 500, 600, 700, 800, 900], [100, 300, 500, 600, 700, 800, 900, 1000], [100, 300, 400], [100, 300, 400, 1000], [100, 300, 400, 900], [100, 300, 400, 900, 1000], [100, 300, 400, 800], [100, 300, 400, 800, 1000], [100, 300, 400, 800, 900], [100, 300, 400, 800, 900, 1000], [100, 300, 400, 700], [100, 300, 400, 700, 1000], [100, 300, 400, 700, 900], [100, 300, 400, 700, 900, 1000], [100, 300, 400, 700, 800], [100, 300, 400, 700, 800, 1000], [100, 300, 400, 700, 800, 900], [100, 300, 400, 700, 800, 900, 1000], [100, 300, 400, 600], [100, 300, 400, 600, 1000], [100, 300, 400, 600, 900], [100, 300, 400, 600, 900, 1000], [100, 300, 400, 600, 800], [100, 300, 400, 600, 800, 1000], [100, 300, 400, 600, 800, 900], [100, 300, 400, 600, 800, 900, 1000], [100, 300, 400, 600, 700], [100, 300, 400, 600, 700, 1000], [100, 300, 400, 600, 700, 900], [100, 300, 400, 600, 700, 900, 1000], [100, 300, 400, 600, 700, 800], [100, 300, 400, 600, 700, 800, 1000], [100, 300, 400, 600, 700, 800, 900], [100, 300, 400, 600, 700, 800, 900, 1000], [100, 300, 400, 500], [100, 300, 400, 500, 1000], [100, 300, 400, 500, 900], [100, 300, 400, 500, 900, 1000], [100, 300, 400, 500, 800], [100, 300, 400, 500, 800, 1000], [100, 300, 400, 500, 800, 900], [100, 300, 400, 500, 800, 900, 1000], [100, 300, 400, 500, 700], [100, 300, 400, 500, 700, 1000], [100, 300, 400, 500, 700, 900], [100, 300, 400, 500, 700, 900, 1000], [100, 300, 400, 500, 700, 800], [100, 300, 400, 500, 700, 800, 1000], [100, 300, 400, 500, 700, 800, 900], [100, 300, 400, 500, 700, 800, 900, 1000], [100, 300, 400, 500, 600], [100, 300, 400, 500, 600, 1000], [100, 300, 400, 500, 600, 900], [100, 300, 400, 500, 600, 900, 1000], [100, 300, 400, 500, 600, 800], [100, 300, 400, 500, 600, 800, 1000], [100, 300, 400, 500, 600, 800, 900], [100, 300, 400, 500, 600, 800, 900, 1000], [100, 300, 400, 500, 600, 700], [100, 300, 400, 500, 600, 700, 1000], [100, 300, 400, 500, 600, 700, 900], [100, 300, 400, 500, 600, 700, 900, 1000], [100, 300, 400, 500, 600, 700, 800], [100, 300, 400, 500, 600, 700, 800, 1000], [100, 300, 400, 500, 600, 700, 800, 900], [100, 300, 400, 500, 600, 700, 800, 900, 1000], [100, 200], [100, 200, 1000], [100, 200, 900], [100, 200, 900, 1000], [100, 200, 800], [100, 200, 800, 1000], [100, 200, 800, 900], [100, 200, 800, 900, 1000], [100, 200, 700], [100, 200, 700, 1000], [100, 200, 700, 900], [100, 200, 700, 900, 1000], [100, 200, 700, 800], [100, 200, 700, 800, 1000], [100, 200, 700, 800, 900], [100, 200, 700, 800, 900, 1000], [100, 200, 600], [100, 200, 600, 1000], [100, 200, 600, 900], [100, 200, 600, 900, 1000], [100, 200, 600, 800], [100, 200, 600, 800, 1000], [100, 200, 600, 800, 900], [100, 200, 600, 800, 900, 1000], [100, 200, 600, 700], [100, 200, 600, 700, 1000], [100, 200, 600, 700, 900], [100, 200, 600, 700, 900, 1000], [100, 200, 600, 700, 800], [100, 200, 600, 700, 800, 1000], [100, 200, 600, 700, 800, 900], [100, 200, 600, 700, 800, 900, 1000], [100, 200, 500], [100, 200, 500, 1000], [100, 200, 500, 900], [100, 200, 500, 900, 1000], [100, 200, 500, 800], [100, 200, 500, 800, 1000], [100, 200, 500, 800, 900], [100, 200, 500, 800, 900, 1000], [100, 200, 500, 700], [100, 200, 500, 700, 1000], [100, 200, 500, 700, 900], [100, 200, 500, 700, 900, 1000], [100, 200, 500, 700, 800], [100, 200, 500, 700, 800, 1000], [100, 200, 500, 700, 800, 900], [100, 200, 500, 700, 800, 900, 1000], [100, 200, 500, 600], [100, 200, 500, 600, 1000], [100, 200, 500, 600, 900], [100, 200, 500, 600, 900, 1000], [100, 200, 500, 600, 800], [100, 200, 500, 600, 800, 1000], [100, 200, 500, 600, 800, 900], [100, 200, 500, 600, 800, 900, 1000], [100, 200, 500, 600, 700], [100, 200, 500, 600, 700, 1000], [100, 200, 500, 600, 700, 900], [100, 200, 500, 600, 700, 900, 1000], [100, 200, 500, 600, 700, 800], [100, 200, 500, 600, 700, 800, 1000], [100, 200, 500, 600, 700, 800, 900], [100, 200, 500, 600, 700, 800, 900, 1000], [100, 200, 400], [100, 200, 400, 1000], [100, 200, 400, 900], [100, 200, 400, 900, 1000], [100, 200, 400, 800], [100, 200, 400, 800, 1000], [100, 200, 400, 800, 900], [100, 200, 400, 800, 900, 1000], [100, 200, 400, 700], [100, 200, 400, 700, 1000], [100, 200, 400, 700, 900], [100, 200, 400, 700, 900, 1000], [100, 200, 400, 700, 800], [100, 200, 400, 700, 800, 1000], [100, 200, 400, 700, 800, 900], [100, 200, 400, 700, 800, 900, 1000], [100, 200, 400, 600], [100, 200, 400, 600, 1000], [100, 200, 400, 600, 900], [100, 200, 400, 600, 900, 1000], [100, 200, 400, 600, 800], [100, 200, 400, 600, 800, 1000], [100, 200, 400, 600, 800, 900], [100, 200, 400, 600, 800, 900, 1000], [100, 200, 400, 600, 700], [100, 200, 400, 600, 700, 1000], [100, 200, 400, 600, 700, 900], [100, 200, 400, 600, 700, 900, 1000], [100, 200, 400, 600, 700, 800], [100, 200, 400, 600, 700, 800, 1000], [100, 200, 400, 600, 700, 800, 900], [100, 200, 400, 600, 700, 800, 900, 1000], [100, 200, 400, 500], [100, 200, 400, 500, 1000], [100, 200, 400, 500, 900], [100, 200, 400, 500, 900, 1000], [100, 200, 400, 500, 800], [100, 200, 400, 500, 800, 1000], [100, 200, 400, 500, 800, 900], [100, 200, 400, 500, 800, 900, 1000], [100, 200, 400, 500, 700], [100, 200, 400, 500, 700, 1000], [100, 200, 400, 500, 700, 900], [100, 200, 400, 500, 700, 900, 1000], [100, 200, 400, 500, 700, 800], [100, 200, 400, 500, 700, 800, 1000], [100, 200, 400, 500, 700, 800, 900], [100, 200, 400, 500, 700, 800, 900, 1000], [100, 200, 400, 500, 600], [100, 200, 400, 500, 600, 1000], [100, 200, 400, 500, 600, 900], [100, 200, 400, 500, 600, 900, 1000], [100, 200, 400, 500, 600, 800], [100, 200, 400, 500, 600, 800, 1000], [100, 200, 400, 500, 600, 800, 900], [100, 200, 400, 500, 600, 800, 900, 1000], [100, 200, 400, 500, 600, 700], [100, 200, 400, 500, 600, 700, 1000], [100, 200, 400, 500, 600, 700, 900], [100, 200, 400, 500, 600, 700, 900, 1000], [100, 200, 400, 500, 600, 700, 800], [100, 200, 400, 500, 600, 700, 800, 1000], [100, 200, 400, 500, 600, 700, 800, 900], [100, 200, 400, 500, 600, 700, 800, 900, 1000], [100, 200, 300], [100, 200, 300, 1000], [100, 200, 300, 900], [100, 200, 300, 900, 1000], [100, 200, 300, 800], [100, 200, 300, 800, 1000], [100, 200, 300, 800, 900], [100, 200, 300, 800, 900, 1000], [100, 200, 300, 700], [100, 200, 300, 700, 1000], [100, 200, 300, 700, 900], [100, 200, 300, 700, 900, 1000], [100, 200, 300, 700, 800], [100, 200, 300, 700, 800, 1000], [100, 200, 300, 700, 800, 900], [100, 200, 300, 700, 800, 900, 1000], [100, 200, 300, 600], [100, 200, 300, 600, 1000], [100, 200, 300, 600, 900], [100, 200, 300, 600, 900, 1000], [100, 200, 300, 600, 800], [100, 200, 300, 600, 800, 1000], [100, 200, 300, 600, 800, 900], [100, 200, 300, 600, 800, 900, 1000], [100, 200, 300, 600, 700], [100, 200, 300, 600, 700, 1000], [100, 200, 300, 600, 700, 900], [100, 200, 300, 600, 700, 900, 1000], [100, 200, 300, 600, 700, 800], [100, 200, 300, 600, 700, 800, 1000], [100, 200, 300, 600, 700, 800, 900], [100, 200, 300, 600, 700, 800, 900, 1000], [100, 200, 300, 500], [100, 200, 300, 500, 1000], [100, 200, 300, 500, 900], [100, 200, 300, 500, 900, 1000], [100, 200, 300, 500, 800], [100, 200, 300, 500, 800, 1000], [100, 200, 300, 500, 800, 900], [100, 200, 300, 500, 800, 900, 1000], [100, 200, 300, 500, 700], [100, 200, 300, 500, 700, 1000], [100, 200, 300, 500, 700, 900], [100, 200, 300, 500, 700, 900, 1000], [100, 200, 300, 500, 700, 800], [100, 200, 300, 500, 700, 800, 1000], [100, 200, 300, 500, 700, 800, 900], [100, 200, 300, 500, 700, 800, 900, 1000], [100, 200, 300, 500, 600], [100, 200, 300, 500, 600, 1000], [100, 200, 300, 500, 600, 900], [100, 200, 300, 500, 600, 900, 1000], [100, 200, 300, 500, 600, 800], [100, 200, 300, 500, 600, 800, 1000], [100, 200, 300, 500, 600, 800, 900], [100, 200, 300, 500, 600, 800, 900, 1000], [100, 200, 300, 500, 600, 700], [100, 200, 300, 500, 600, 700, 1000], [100, 200, 300, 500, 600, 700, 900], [100, 200, 300, 500, 600, 700, 900, 1000], [100, 200, 300, 500, 600, 700, 800], [100, 200, 300, 500, 600, 700, 800, 1000], [100, 200, 300, 500, 600, 700, 800, 900], [100, 200, 300, 500, 600, 700, 800, 900, 1000], [100, 200, 300, 400], [100, 200, 300, 400, 1000], [100, 200, 300, 400, 900], [100, 200, 300, 400, 900, 1000], [100, 200, 300, 400, 800], [100, 200, 300, 400, 800, 1000], [100, 200, 300, 400, 800, 900], [100, 200, 300, 400, 800, 900, 1000], [100, 200, 300, 400, 700], [100, 200, 300, 400, 700, 1000], [100, 200, 300, 400, 700, 900], [100, 200, 300, 400, 700, 900, 1000], [100, 200, 300, 400, 700, 800], [100, 200, 300, 400, 700, 800, 1000], [100, 200, 300, 400, 700, 800, 900], [100, 200, 300, 400, 700, 800, 900, 1000], [100, 200, 300, 400, 600], [100, 200, 300, 400, 600, 1000], [100, 200, 300, 400, 600, 900], [100, 200, 300, 400, 600, 900, 1000], [100, 200, 300, 400, 600, 800], [100, 200, 300, 400, 600, 800, 1000], [100, 200, 300, 400, 600, 800, 900], [100, 200, 300, 400, 600, 800, 900, 1000], [100, 200, 300, 400, 600, 700], [100, 200, 300, 400, 600, 700, 1000], [100, 200, 300, 400, 600, 700, 900], [100, 200, 300, 400, 600, 700, 900, 1000], [100, 200, 300, 400, 600, 700, 800], [100, 200, 300, 400, 600, 700, 800, 1000], [100, 200, 300, 400, 600, 700, 800, 900], [100, 200, 300, 400, 600, 700, 800, 900, 1000], [100, 200, 300, 400, 500], [100, 200, 300, 400, 500, 1000], [100, 200, 300, 400, 500, 900], [100, 200, 300, 400, 500, 900, 1000], [100, 200, 300, 400, 500, 800], [100, 200, 300, 400, 500, 800, 1000], [100, 200, 300, 400, 500, 800, 900], [100, 200, 300, 400, 500, 800, 900, 1000], [100, 200, 300, 400, 500, 700], [100, 200, 300, 400, 500, 700, 1000], [100, 200, 300, 400, 500, 700, 900], [100, 200, 300, 400, 500, 700, 900, 1000], [100, 200, 300, 400, 500, 700, 800], [100, 200, 300, 400, 500, 700, 800, 1000], [100, 200, 300, 400, 500, 700, 800, 900], [100, 200, 300, 400, 500, 700, 800, 900, 1000], [100, 200, 300, 400, 500, 600], [100, 200, 300, 400, 500, 600, 1000], [100, 200, 300, 400, 500, 600, 900], [100, 200, 300, 400, 500, 600, 900, 1000], [100, 200, 300, 400, 500, 600, 800], [100, 200, 300, 400, 500, 600, 800, 1000], [100, 200, 300, 400, 500, 600, 800, 900], [100, 200, 300, 400, 500, 600, 800, 900, 1000], [100, 200, 300, 400, 500, 600, 700], [100, 200, 300, 400, 500, 600, 700, 1000], [100, 200, 300, 400, 500, 600, 700, 900], [100, 200, 300, 400, 500, 600, 700, 900, 1000], [100, 200, 300, 400, 500, 600, 700, 800], [100, 200, 300, 400, 500, 600, 700, 800, 1000], [100, 200, 300, 400, 500, 600, 700, 800, 900], [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]]\n assert candidate(nums = [10, 20, 30, 40, 50, 60]) == [[], [60], [50], [50, 60], [40], [40, 60], [40, 50], [40, 50, 60], [30], [30, 60], [30, 50], [30, 50, 60], [30, 40], [30, 40, 60], [30, 40, 50], [30, 40, 50, 60], [20], [20, 60], [20, 50], [20, 50, 60], [20, 40], [20, 40, 60], [20, 40, 50], [20, 40, 50, 60], [20, 30], [20, 30, 60], [20, 30, 50], [20, 30, 50, 60], [20, 30, 40], [20, 30, 40, 60], [20, 30, 40, 50], [20, 30, 40, 50, 60], [10], [10, 60], [10, 50], [10, 50, 60], [10, 40], [10, 40, 60], [10, 40, 50], [10, 40, 50, 60], [10, 30], [10, 30, 60], [10, 30, 50], [10, 30, 50, 60], [10, 30, 40], [10, 30, 40, 60], [10, 30, 40, 50], [10, 30, 40, 50, 60], [10, 20], [10, 20, 60], [10, 20, 50], [10, 20, 50, 60], [10, 20, 40], [10, 20, 40, 60], [10, 20, 40, 50], [10, 20, 40, 50, 60], [10, 20, 30], [10, 20, 30, 60], [10, 20, 30, 50], [10, 20, 30, 50, 60], [10, 20, 30, 40], [10, 20, 30, 40, 60], [10, 20, 30, 40, 50], [10, 20, 30, 40, 50, 60]]\n assert candidate(nums = [-2, 0, 2, 4, 6, 8, 10, 12, 14, 16]) == [[], [16], [14], [14, 16], [12], [12, 16], [12, 14], [12, 14, 16], [10], [10, 16], [10, 14], [10, 14, 16], [10, 12], [10, 12, 16], [10, 12, 14], [10, 12, 14, 16], [8], [8, 16], [8, 14], [8, 14, 16], [8, 12], [8, 12, 16], [8, 12, 14], [8, 12, 14, 16], [8, 10], [8, 10, 16], [8, 10, 14], [8, 10, 14, 16], [8, 10, 12], [8, 10, 12, 16], [8, 10, 12, 14], [8, 10, 12, 14, 16], [6], [6, 16], [6, 14], [6, 14, 16], [6, 12], [6, 12, 16], [6, 12, 14], [6, 12, 14, 16], [6, 10], [6, 10, 16], [6, 10, 14], [6, 10, 14, 16], [6, 10, 12], [6, 10, 12, 16], [6, 10, 12, 14], [6, 10, 12, 14, 16], [6, 8], [6, 8, 16], [6, 8, 14], [6, 8, 14, 16], [6, 8, 12], [6, 8, 12, 16], [6, 8, 12, 14], [6, 8, 12, 14, 16], [6, 8, 10], [6, 8, 10, 16], [6, 8, 10, 14], [6, 8, 10, 14, 16], [6, 8, 10, 12], [6, 8, 10, 12, 16], [6, 8, 10, 12, 14], [6, 8, 10, 12, 14, 16], [4], [4, 16], [4, 14], [4, 14, 16], [4, 12], [4, 12, 16], [4, 12, 14], [4, 12, 14, 16], [4, 10], [4, 10, 16], [4, 10, 14], [4, 10, 14, 16], [4, 10, 12], [4, 10, 12, 16], [4, 10, 12, 14], [4, 10, 12, 14, 16], [4, 8], [4, 8, 16], [4, 8, 14], [4, 8, 14, 16], [4, 8, 12], [4, 8, 12, 16], [4, 8, 12, 14], [4, 8, 12, 14, 16], [4, 8, 10], [4, 8, 10, 16], [4, 8, 10, 14], [4, 8, 10, 14, 16], [4, 8, 10, 12], [4, 8, 10, 12, 16], [4, 8, 10, 12, 14], [4, 8, 10, 12, 14, 16], [4, 6], [4, 6, 16], [4, 6, 14], [4, 6, 14, 16], [4, 6, 12], [4, 6, 12, 16], [4, 6, 12, 14], [4, 6, 12, 14, 16], [4, 6, 10], [4, 6, 10, 16], [4, 6, 10, 14], [4, 6, 10, 14, 16], [4, 6, 10, 12], [4, 6, 10, 12, 16], [4, 6, 10, 12, 14], [4, 6, 10, 12, 14, 16], [4, 6, 8], [4, 6, 8, 16], [4, 6, 8, 14], [4, 6, 8, 14, 16], [4, 6, 8, 12], [4, 6, 8, 12, 16], [4, 6, 8, 12, 14], [4, 6, 8, 12, 14, 16], [4, 6, 8, 10], [4, 6, 8, 10, 16], [4, 6, 8, 10, 14], [4, 6, 8, 10, 14, 16], [4, 6, 8, 10, 12], [4, 6, 8, 10, 12, 16], [4, 6, 8, 10, 12, 14], [4, 6, 8, 10, 12, 14, 16], [2], [2, 16], [2, 14], [2, 14, 16], [2, 12], [2, 12, 16], [2, 12, 14], [2, 12, 14, 16], [2, 10], [2, 10, 16], [2, 10, 14], [2, 10, 14, 16], [2, 10, 12], [2, 10, 12, 16], [2, 10, 12, 14], [2, 10, 12, 14, 16], [2, 8], [2, 8, 16], [2, 8, 14], [2, 8, 14, 16], [2, 8, 12], [2, 8, 12, 16], [2, 8, 12, 14], [2, 8, 12, 14, 16], [2, 8, 10], [2, 8, 10, 16], [2, 8, 10, 14], [2, 8, 10, 14, 16], [2, 8, 10, 12], [2, 8, 10, 12, 16], [2, 8, 10, 12, 14], [2, 8, 10, 12, 14, 16], [2, 6], [2, 6, 16], [2, 6, 14], [2, 6, 14, 16], [2, 6, 12], [2, 6, 12, 16], [2, 6, 12, 14], [2, 6, 12, 14, 16], [2, 6, 10], [2, 6, 10, 16], [2, 6, 10, 14], [2, 6, 10, 14, 16], [2, 6, 10, 12], [2, 6, 10, 12, 16], [2, 6, 10, 12, 14], [2, 6, 10, 12, 14, 16], [2, 6, 8], [2, 6, 8, 16], [2, 6, 8, 14], [2, 6, 8, 14, 16], [2, 6, 8, 12], [2, 6, 8, 12, 16], [2, 6, 8, 12, 14], [2, 6, 8, 12, 14, 16], [2, 6, 8, 10], [2, 6, 8, 10, 16], [2, 6, 8, 10, 14], [2, 6, 8, 10, 14, 16], [2, 6, 8, 10, 12], [2, 6, 8, 10, 12, 16], [2, 6, 8, 10, 12, 14], [2, 6, 8, 10, 12, 14, 16], [2, 4], [2, 4, 16], [2, 4, 14], [2, 4, 14, 16], [2, 4, 12], [2, 4, 12, 16], [2, 4, 12, 14], [2, 4, 12, 14, 16], [2, 4, 10], [2, 4, 10, 16], [2, 4, 10, 14], [2, 4, 10, 14, 16], [2, 4, 10, 12], [2, 4, 10, 12, 16], [2, 4, 10, 12, 14], [2, 4, 10, 12, 14, 16], [2, 4, 8], [2, 4, 8, 16], [2, 4, 8, 14], [2, 4, 8, 14, 16], [2, 4, 8, 12], [2, 4, 8, 12, 16], [2, 4, 8, 12, 14], [2, 4, 8, 12, 14, 16], [2, 4, 8, 10], [2, 4, 8, 10, 16], [2, 4, 8, 10, 14], [2, 4, 8, 10, 14, 16], [2, 4, 8, 10, 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16], [-2, 0, 4], [-2, 0, 4, 16], [-2, 0, 4, 14], [-2, 0, 4, 14, 16], [-2, 0, 4, 12], [-2, 0, 4, 12, 16], [-2, 0, 4, 12, 14], [-2, 0, 4, 12, 14, 16], [-2, 0, 4, 10], [-2, 0, 4, 10, 16], [-2, 0, 4, 10, 14], [-2, 0, 4, 10, 14, 16], [-2, 0, 4, 10, 12], [-2, 0, 4, 10, 12, 16], [-2, 0, 4, 10, 12, 14], [-2, 0, 4, 10, 12, 14, 16], [-2, 0, 4, 8], [-2, 0, 4, 8, 16], [-2, 0, 4, 8, 14], [-2, 0, 4, 8, 14, 16], [-2, 0, 4, 8, 12], [-2, 0, 4, 8, 12, 16], [-2, 0, 4, 8, 12, 14], [-2, 0, 4, 8, 12, 14, 16], [-2, 0, 4, 8, 10], [-2, 0, 4, 8, 10, 16], [-2, 0, 4, 8, 10, 14], [-2, 0, 4, 8, 10, 14, 16], [-2, 0, 4, 8, 10, 12], [-2, 0, 4, 8, 10, 12, 16], [-2, 0, 4, 8, 10, 12, 14], [-2, 0, 4, 8, 10, 12, 14, 16], [-2, 0, 4, 6], [-2, 0, 4, 6, 16], [-2, 0, 4, 6, 14], [-2, 0, 4, 6, 14, 16], [-2, 0, 4, 6, 12], [-2, 0, 4, 6, 12, 16], [-2, 0, 4, 6, 12, 14], [-2, 0, 4, 6, 12, 14, 16], [-2, 0, 4, 6, 10], [-2, 0, 4, 6, 10, 16], [-2, 0, 4, 6, 10, 14], [-2, 0, 4, 6, 10, 14, 16], [-2, 0, 4, 6, 10, 12], [-2, 0, 4, 6, 10, 12, 16], [-2, 0, 4, 6, 10, 12, 14], [-2, 0, 4, 6, 10, 12, 14, 16], [-2, 0, 4, 6, 8], [-2, 0, 4, 6, 8, 16], [-2, 0, 4, 6, 8, 14], [-2, 0, 4, 6, 8, 14, 16], [-2, 0, 4, 6, 8, 12], [-2, 0, 4, 6, 8, 12, 16], [-2, 0, 4, 6, 8, 12, 14], [-2, 0, 4, 6, 8, 12, 14, 16], [-2, 0, 4, 6, 8, 10], [-2, 0, 4, 6, 8, 10, 16], [-2, 0, 4, 6, 8, 10, 14], [-2, 0, 4, 6, 8, 10, 14, 16], [-2, 0, 4, 6, 8, 10, 12], [-2, 0, 4, 6, 8, 10, 12, 16], [-2, 0, 4, 6, 8, 10, 12, 14], [-2, 0, 4, 6, 8, 10, 12, 14, 16], [-2, 0, 2], [-2, 0, 2, 16], [-2, 0, 2, 14], [-2, 0, 2, 14, 16], [-2, 0, 2, 12], [-2, 0, 2, 12, 16], [-2, 0, 2, 12, 14], [-2, 0, 2, 12, 14, 16], [-2, 0, 2, 10], [-2, 0, 2, 10, 16], [-2, 0, 2, 10, 14], [-2, 0, 2, 10, 14, 16], [-2, 0, 2, 10, 12], [-2, 0, 2, 10, 12, 16], [-2, 0, 2, 10, 12, 14], [-2, 0, 2, 10, 12, 14, 16], [-2, 0, 2, 8], [-2, 0, 2, 8, 16], [-2, 0, 2, 8, 14], [-2, 0, 2, 8, 14, 16], [-2, 0, 2, 8, 12], [-2, 0, 2, 8, 12, 16], [-2, 0, 2, 8, 12, 14], [-2, 0, 2, 8, 12, 14, 16], [-2, 0, 2, 8, 10], [-2, 0, 2, 8, 10, 16], [-2, 0, 2, 8, 10, 14], [-2, 0, 2, 8, 10, 14, 16], [-2, 0, 2, 8, 10, 12], [-2, 0, 2, 8, 10, 12, 16], [-2, 0, 2, 8, 10, 12, 14], [-2, 0, 2, 8, 10, 12, 14, 16], [-2, 0, 2, 6], [-2, 0, 2, 6, 16], [-2, 0, 2, 6, 14], [-2, 0, 2, 6, 14, 16], [-2, 0, 2, 6, 12], [-2, 0, 2, 6, 12, 16], [-2, 0, 2, 6, 12, 14], [-2, 0, 2, 6, 12, 14, 16], [-2, 0, 2, 6, 10], [-2, 0, 2, 6, 10, 16], [-2, 0, 2, 6, 10, 14], [-2, 0, 2, 6, 10, 14, 16], [-2, 0, 2, 6, 10, 12], [-2, 0, 2, 6, 10, 12, 16], [-2, 0, 2, 6, 10, 12, 14], [-2, 0, 2, 6, 10, 12, 14, 16], [-2, 0, 2, 6, 8], [-2, 0, 2, 6, 8, 16], [-2, 0, 2, 6, 8, 14], [-2, 0, 2, 6, 8, 14, 16], [-2, 0, 2, 6, 8, 12], [-2, 0, 2, 6, 8, 12, 16], [-2, 0, 2, 6, 8, 12, 14], [-2, 0, 2, 6, 8, 12, 14, 16], [-2, 0, 2, 6, 8, 10], [-2, 0, 2, 6, 8, 10, 16], [-2, 0, 2, 6, 8, 10, 14], [-2, 0, 2, 6, 8, 10, 14, 16], [-2, 0, 2, 6, 8, 10, 12], [-2, 0, 2, 6, 8, 10, 12, 16], [-2, 0, 2, 6, 8, 10, 12, 14], [-2, 0, 2, 6, 8, 10, 12, 14, 16], [-2, 0, 2, 4], [-2, 0, 2, 4, 16], [-2, 0, 2, 4, 14], [-2, 0, 2, 4, 14, 16], [-2, 0, 2, 4, 12], [-2, 0, 2, 4, 12, 16], [-2, 0, 2, 4, 12, 14], [-2, 0, 2, 4, 12, 14, 16], [-2, 0, 2, 4, 10], [-2, 0, 2, 4, 10, 16], [-2, 0, 2, 4, 10, 14], [-2, 0, 2, 4, 10, 14, 16], [-2, 0, 2, 4, 10, 12], [-2, 0, 2, 4, 10, 12, 16], [-2, 0, 2, 4, 10, 12, 14], [-2, 0, 2, 4, 10, 12, 14, 16], [-2, 0, 2, 4, 8], [-2, 0, 2, 4, 8, 16], [-2, 0, 2, 4, 8, 14], [-2, 0, 2, 4, 8, 14, 16], [-2, 0, 2, 4, 8, 12], [-2, 0, 2, 4, 8, 12, 16], [-2, 0, 2, 4, 8, 12, 14], [-2, 0, 2, 4, 8, 12, 14, 16], [-2, 0, 2, 4, 8, 10], [-2, 0, 2, 4, 8, 10, 16], [-2, 0, 2, 4, 8, 10, 14], [-2, 0, 2, 4, 8, 10, 14, 16], [-2, 0, 2, 4, 8, 10, 12], [-2, 0, 2, 4, 8, 10, 12, 16], [-2, 0, 2, 4, 8, 10, 12, 14], [-2, 0, 2, 4, 8, 10, 12, 14, 16], [-2, 0, 2, 4, 6], [-2, 0, 2, 4, 6, 16], [-2, 0, 2, 4, 6, 14], [-2, 0, 2, 4, 6, 14, 16], [-2, 0, 2, 4, 6, 12], [-2, 0, 2, 4, 6, 12, 16], [-2, 0, 2, 4, 6, 12, 14], [-2, 0, 2, 4, 6, 12, 14, 16], [-2, 0, 2, 4, 6, 10], [-2, 0, 2, 4, 6, 10, 16], [-2, 0, 2, 4, 6, 10, 14], [-2, 0, 2, 4, 6, 10, 14, 16], [-2, 0, 2, 4, 6, 10, 12], [-2, 0, 2, 4, 6, 10, 12, 16], [-2, 0, 2, 4, 6, 10, 12, 14], [-2, 0, 2, 4, 6, 10, 12, 14, 16], [-2, 0, 2, 4, 6, 8], [-2, 0, 2, 4, 6, 8, 16], [-2, 0, 2, 4, 6, 8, 14], [-2, 0, 2, 4, 6, 8, 14, 16], [-2, 0, 2, 4, 6, 8, 12], [-2, 0, 2, 4, 6, 8, 12, 16], [-2, 0, 2, 4, 6, 8, 12, 14], [-2, 0, 2, 4, 6, 8, 12, 14, 16], [-2, 0, 2, 4, 6, 8, 10], [-2, 0, 2, 4, 6, 8, 10, 16], [-2, 0, 2, 4, 6, 8, 10, 14], [-2, 0, 2, 4, 6, 8, 10, 14, 16], [-2, 0, 2, 4, 6, 8, 10, 12], [-2, 0, 2, 4, 6, 8, 10, 12, 16], [-2, 0, 2, 4, 6, 8, 10, 12, 14], [-2, 0, 2, 4, 6, 8, 10, 12, 14, 16]]\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3]) == [[], [3], [2], [2, 3], [1], [1, 3], [1, 2], [1, 2, 3], [0], [0, 3], [0, 2], [0, 2, 3], [0, 1], [0, 1, 3], [0, 1, 2], [0, 1, 2, 3], [-1], [-1, 3], [-1, 2], [-1, 2, 3], [-1, 1], [-1, 1, 3], [-1, 1, 2], [-1, 1, 2, 3], [-1, 0], [-1, 0, 3], [-1, 0, 2], [-1, 0, 2, 3], [-1, 0, 1], [-1, 0, 1, 3], [-1, 0, 1, 2], [-1, 0, 1, 2, 3], [-2], [-2, 3], [-2, 2], [-2, 2, 3], [-2, 1], [-2, 1, 3], [-2, 1, 2], [-2, 1, 2, 3], [-2, 0], [-2, 0, 3], [-2, 0, 2], [-2, 0, 2, 3], [-2, 0, 1], [-2, 0, 1, 3], [-2, 0, 1, 2], [-2, 0, 1, 2, 3], [-2, -1], [-2, -1, 3], [-2, -1, 2], [-2, -1, 2, 3], [-2, -1, 1], [-2, -1, 1, 3], [-2, -1, 1, 2], [-2, -1, 1, 2, 3], [-2, -1, 0], [-2, -1, 0, 3], [-2, -1, 0, 2], [-2, -1, 0, 2, 3], [-2, -1, 0, 1], [-2, -1, 0, 1, 3], [-2, -1, 0, 1, 2], [-2, -1, 0, 1, 2, 3], [-3], [-3, 3], [-3, 2], [-3, 2, 3], [-3, 1], [-3, 1, 3], [-3, 1, 2], [-3, 1, 2, 3], [-3, 0], [-3, 0, 3], [-3, 0, 2], [-3, 0, 2, 3], [-3, 0, 1], [-3, 0, 1, 3], [-3, 0, 1, 2], [-3, 0, 1, 2, 3], [-3, -1], [-3, -1, 3], [-3, -1, 2], [-3, -1, 2, 3], [-3, -1, 1], [-3, -1, 1, 3], [-3, -1, 1, 2], [-3, -1, 1, 2, 3], [-3, -1, 0], [-3, -1, 0, 3], [-3, -1, 0, 2], [-3, -1, 0, 2, 3], [-3, -1, 0, 1], [-3, -1, 0, 1, 3], [-3, -1, 0, 1, 2], [-3, -1, 0, 1, 2, 3], [-3, -2], [-3, -2, 3], [-3, -2, 2], [-3, -2, 2, 3], [-3, -2, 1], [-3, -2, 1, 3], [-3, -2, 1, 2], [-3, -2, 1, 2, 3], [-3, -2, 0], [-3, -2, 0, 3], [-3, -2, 0, 2], [-3, -2, 0, 2, 3], [-3, -2, 0, 1], [-3, -2, 0, 1, 3], [-3, -2, 0, 1, 2], [-3, -2, 0, 1, 2, 3], [-3, -2, -1], [-3, -2, -1, 3], [-3, -2, -1, 2], [-3, -2, -1, 2, 3], [-3, -2, -1, 1], [-3, -2, -1, 1, 3], [-3, -2, -1, 1, 2], [-3, -2, -1, 1, 2, 3], [-3, -2, -1, 0], [-3, -2, -1, 0, 3], [-3, -2, -1, 0, 2], [-3, -2, -1, 0, 2, 3], [-3, -2, -1, 0, 1], [-3, -2, -1, 0, 1, 3], [-3, -2, -1, 0, 1, 2], [-3, -2, -1, 0, 1, 2, 3]]\n assert candidate(nums = [10, -5, 0, 7]) == [[], [7], [0], [0, 7], [-5], [-5, 7], [-5, 0], [-5, 0, 7], [10], [10, 7], [10, 0], [10, 0, 7], [10, -5], [10, -5, 7], [10, -5, 0], [10, -5, 0, 7]]\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70]) == [[], [-70], [-60], [-60, -70], [-50], [-50, -70], [-50, -60], [-50, -60, -70], [-40], [-40, -70], [-40, -60], [-40, -60, -70], [-40, -50], [-40, -50, -70], [-40, -50, -60], [-40, -50, -60, -70], [-30], [-30, -70], [-30, -60], [-30, -60, -70], [-30, -50], [-30, -50, -70], [-30, -50, -60], [-30, -50, -60, -70], [-30, -40], [-30, -40, -70], [-30, -40, -60], [-30, -40, -60, -70], [-30, -40, -50], [-30, -40, -50, -70], [-30, -40, -50, -60], [-30, -40, -50, -60, -70], [-20], [-20, -70], [-20, -60], [-20, -60, -70], [-20, -50], [-20, -50, -70], [-20, -50, -60], [-20, -50, -60, -70], [-20, -40], [-20, -40, -70], [-20, -40, -60], [-20, -40, -60, -70], [-20, -40, -50], [-20, -40, -50, -70], [-20, -40, -50, -60], [-20, -40, -50, -60, -70], [-20, -30], [-20, -30, -70], [-20, -30, -60], [-20, -30, -60, -70], [-20, -30, -50], [-20, -30, -50, -70], [-20, -30, -50, -60], [-20, -30, -50, -60, -70], [-20, -30, -40], [-20, -30, -40, -70], [-20, -30, -40, -60], [-20, -30, -40, -60, -70], [-20, -30, -40, -50], [-20, -30, -40, -50, -70], [-20, -30, -40, -50, -60], [-20, -30, -40, -50, -60, -70], [-10], [-10, -70], [-10, -60], [-10, -60, -70], [-10, -50], [-10, -50, -70], [-10, -50, -60], [-10, -50, -60, -70], [-10, -40], [-10, -40, -70], [-10, -40, -60], [-10, -40, -60, -70], [-10, -40, -50], [-10, -40, -50, -70], [-10, -40, -50, -60], [-10, -40, -50, -60, -70], [-10, -30], [-10, -30, -70], [-10, -30, -60], [-10, -30, -60, -70], [-10, -30, -50], [-10, -30, -50, -70], [-10, -30, -50, -60], [-10, -30, -50, -60, -70], [-10, -30, -40], [-10, -30, -40, -70], [-10, -30, -40, -60], [-10, -30, -40, -60, -70], [-10, -30, -40, -50], [-10, -30, -40, -50, -70], [-10, -30, -40, -50, -60], [-10, -30, -40, -50, -60, -70], [-10, -20], [-10, -20, -70], [-10, -20, -60], [-10, -20, -60, -70], [-10, -20, -50], [-10, -20, -50, -70], [-10, -20, -50, -60], [-10, -20, -50, -60, -70], [-10, -20, -40], [-10, -20, -40, -70], [-10, -20, -40, -60], [-10, -20, -40, -60, -70], [-10, -20, -40, -50], [-10, -20, -40, -50, -70], [-10, -20, -40, -50, -60], [-10, -20, -40, -50, -60, -70], [-10, -20, -30], [-10, -20, -30, -70], [-10, -20, -30, -60], [-10, -20, -30, -60, -70], [-10, -20, -30, -50], [-10, -20, -30, -50, -70], [-10, -20, -30, -50, -60], [-10, -20, -30, -50, -60, -70], [-10, -20, -30, -40], [-10, -20, -30, -40, -70], [-10, -20, -30, -40, -60], [-10, -20, -30, -40, -60, -70], [-10, -20, -30, -40, -50], [-10, -20, -30, -40, -50, -70], [-10, -20, -30, -40, -50, -60], [-10, -20, -30, -40, -50, -60, -70]]\n assert candidate(nums = [-1, 0, 1, -2, 2, -3, 3]) == [[], [3], [-3], [-3, 3], [2], [2, 3], [2, -3], [2, -3, 3], [-2], [-2, 3], [-2, -3], [-2, -3, 3], [-2, 2], [-2, 2, 3], [-2, 2, -3], [-2, 2, -3, 3], [1], [1, 3], [1, -3], [1, -3, 3], [1, 2], [1, 2, 3], [1, 2, -3], [1, 2, -3, 3], [1, -2], [1, -2, 3], [1, -2, -3], [1, -2, -3, 3], [1, -2, 2], [1, -2, 2, 3], [1, -2, 2, -3], [1, -2, 2, -3, 3], [0], [0, 3], [0, -3], [0, -3, 3], [0, 2], [0, 2, 3], [0, 2, -3], [0, 2, -3, 3], [0, -2], [0, -2, 3], [0, -2, -3], [0, -2, -3, 3], [0, -2, 2], [0, -2, 2, 3], [0, -2, 2, -3], [0, -2, 2, -3, 3], [0, 1], [0, 1, 3], [0, 1, -3], [0, 1, -3, 3], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, -3], [0, 1, 2, -3, 3], [0, 1, -2], [0, 1, -2, 3], [0, 1, -2, -3], [0, 1, -2, -3, 3], [0, 1, -2, 2], [0, 1, -2, 2, 3], [0, 1, -2, 2, -3], [0, 1, -2, 2, -3, 3], [-1], [-1, 3], [-1, -3], [-1, -3, 3], [-1, 2], [-1, 2, 3], [-1, 2, -3], [-1, 2, -3, 3], [-1, -2], [-1, -2, 3], [-1, -2, -3], [-1, -2, -3, 3], [-1, -2, 2], [-1, -2, 2, 3], [-1, -2, 2, -3], [-1, -2, 2, -3, 3], [-1, 1], [-1, 1, 3], [-1, 1, -3], [-1, 1, -3, 3], [-1, 1, 2], [-1, 1, 2, 3], [-1, 1, 2, -3], [-1, 1, 2, -3, 3], [-1, 1, -2], [-1, 1, -2, 3], [-1, 1, -2, -3], [-1, 1, -2, -3, 3], [-1, 1, -2, 2], [-1, 1, -2, 2, 3], [-1, 1, -2, 2, -3], [-1, 1, -2, 2, -3, 3], [-1, 0], [-1, 0, 3], [-1, 0, -3], [-1, 0, -3, 3], [-1, 0, 2], [-1, 0, 2, 3], [-1, 0, 2, -3], [-1, 0, 2, -3, 3], [-1, 0, -2], [-1, 0, -2, 3], [-1, 0, -2, -3], [-1, 0, -2, -3, 3], [-1, 0, -2, 2], [-1, 0, -2, 2, 3], [-1, 0, -2, 2, -3], [-1, 0, -2, 2, -3, 3], [-1, 0, 1], [-1, 0, 1, 3], [-1, 0, 1, -3], [-1, 0, 1, -3, 3], [-1, 0, 1, 2], [-1, 0, 1, 2, 3], [-1, 0, 1, 2, -3], [-1, 0, 1, 2, -3, 3], [-1, 0, 1, -2], [-1, 0, 1, -2, 3], [-1, 0, 1, -2, -3], [-1, 0, 1, -2, -3, 3], [-1, 0, 1, -2, 2], [-1, 0, 1, -2, 2, 3], [-1, 0, 1, -2, 2, -3], [-1, 0, 1, -2, 2, -3, 3]]\n assert candidate(nums = [8, 6, 4, 2, 0, -2, -4, -6, -8]) == [[], [-8], [-6], [-6, -8], [-4], [-4, -8], [-4, -6], [-4, -6, -8], [-2], [-2, -8], [-2, -6], [-2, -6, -8], [-2, -4], [-2, -4, -8], [-2, -4, -6], [-2, -4, -6, -8], [0], [0, -8], [0, -6], [0, -6, -8], [0, -4], [0, -4, -8], [0, -4, -6], [0, -4, -6, -8], [0, -2], [0, -2, -8], [0, -2, -6], [0, -2, -6, -8], [0, -2, -4], [0, -2, -4, -8], [0, -2, -4, -6], [0, -2, -4, -6, -8], [2], [2, -8], [2, -6], [2, -6, -8], [2, -4], [2, -4, -8], [2, -4, -6], [2, -4, -6, -8], [2, -2], [2, -2, -8], [2, -2, -6], [2, -2, -6, -8], [2, -2, -4], [2, -2, -4, -8], [2, -2, -4, -6], [2, -2, -4, -6, -8], [2, 0], [2, 0, -8], [2, 0, -6], [2, 0, -6, -8], [2, 0, -4], [2, 0, -4, -8], [2, 0, -4, -6], [2, 0, -4, -6, -8], [2, 0, -2], [2, 0, -2, -8], [2, 0, -2, -6], [2, 0, -2, -6, -8], [2, 0, -2, -4], [2, 0, -2, -4, -8], [2, 0, -2, -4, -6], [2, 0, -2, -4, -6, -8], [4], [4, -8], [4, -6], [4, -6, -8], [4, -4], [4, -4, -8], [4, -4, -6], [4, -4, -6, -8], [4, -2], [4, -2, -8], [4, -2, -6], [4, -2, -6, -8], [4, -2, -4], [4, -2, -4, -8], [4, -2, -4, -6], [4, -2, -4, -6, -8], [4, 0], [4, 0, -8], [4, 0, -6], [4, 0, -6, -8], [4, 0, -4], [4, 0, -4, -8], [4, 0, -4, -6], [4, 0, -4, -6, -8], [4, 0, -2], [4, 0, -2, -8], [4, 0, -2, -6], [4, 0, -2, -6, -8], [4, 0, -2, -4], [4, 0, -2, -4, -8], [4, 0, -2, -4, -6], [4, 0, -2, -4, -6, -8], [4, 2], [4, 2, -8], [4, 2, -6], [4, 2, -6, -8], [4, 2, -4], [4, 2, -4, -8], [4, 2, -4, -6], [4, 2, -4, -6, -8], [4, 2, -2], [4, 2, -2, -8], [4, 2, -2, -6], [4, 2, -2, -6, -8], [4, 2, -2, -4], [4, 2, -2, -4, -8], [4, 2, -2, -4, -6], [4, 2, -2, -4, -6, -8], [4, 2, 0], [4, 2, 0, -8], [4, 2, 0, -6], [4, 2, 0, -6, -8], [4, 2, 0, -4], [4, 2, 0, -4, -8], [4, 2, 0, -4, -6], [4, 2, 0, -4, -6, -8], [4, 2, 0, -2], [4, 2, 0, -2, -8], [4, 2, 0, -2, -6], [4, 2, 0, -2, -6, -8], [4, 2, 0, -2, -4], [4, 2, 0, -2, -4, -8], [4, 2, 0, -2, -4, -6], [4, 2, 0, -2, -4, -6, -8], [6], [6, -8], [6, -6], [6, -6, -8], [6, -4], [6, -4, -8], [6, -4, -6], [6, -4, -6, -8], [6, -2], [6, -2, -8], [6, -2, -6], [6, -2, -6, -8], [6, -2, -4], [6, -2, -4, -8], [6, -2, -4, -6], [6, -2, -4, -6, -8], [6, 0], [6, 0, -8], [6, 0, -6], [6, 0, -6, -8], [6, 0, -4], [6, 0, -4, -8], [6, 0, -4, -6], [6, 0, -4, -6, -8], [6, 0, -2], [6, 0, -2, -8], [6, 0, -2, -6], [6, 0, -2, -6, -8], [6, 0, -2, -4], [6, 0, -2, -4, -8], [6, 0, -2, -4, -6], [6, 0, -2, -4, -6, -8], [6, 2], [6, 2, -8], [6, 2, -6], [6, 2, -6, -8], [6, 2, -4], [6, 2, -4, -8], [6, 2, -4, -6], [6, 2, -4, -6, -8], [6, 2, -2], [6, 2, -2, -8], [6, 2, -2, -6], [6, 2, -2, -6, -8], [6, 2, -2, -4], [6, 2, -2, -4, -8], [6, 2, -2, -4, -6], [6, 2, -2, -4, -6, -8], [6, 2, 0], [6, 2, 0, -8], [6, 2, 0, -6], [6, 2, 0, -6, -8], [6, 2, 0, -4], [6, 2, 0, -4, -8], [6, 2, 0, -4, -6], [6, 2, 0, -4, -6, -8], [6, 2, 0, -2], [6, 2, 0, -2, -8], [6, 2, 0, -2, -6], [6, 2, 0, -2, -6, -8], [6, 2, 0, -2, -4], [6, 2, 0, -2, -4, -8], [6, 2, 0, -2, -4, -6], [6, 2, 0, -2, -4, -6, -8], [6, 4], [6, 4, -8], [6, 4, -6], [6, 4, -6, -8], [6, 4, -4], [6, 4, -4, -8], [6, 4, -4, -6], [6, 4, -4, -6, -8], [6, 4, -2], [6, 4, -2, -8], [6, 4, -2, -6], [6, 4, -2, -6, -8], [6, 4, -2, -4], [6, 4, -2, -4, -8], [6, 4, -2, -4, -6], [6, 4, -2, -4, -6, -8], [6, 4, 0], [6, 4, 0, -8], [6, 4, 0, -6], [6, 4, 0, -6, -8], [6, 4, 0, -4], [6, 4, 0, -4, -8], [6, 4, 0, -4, -6], [6, 4, 0, -4, -6, -8], [6, 4, 0, -2], [6, 4, 0, -2, -8], [6, 4, 0, -2, -6], [6, 4, 0, -2, -6, -8], [6, 4, 0, -2, -4], [6, 4, 0, -2, -4, -8], [6, 4, 0, -2, -4, -6], [6, 4, 0, -2, -4, -6, -8], [6, 4, 2], [6, 4, 2, -8], [6, 4, 2, -6], [6, 4, 2, -6, -8], [6, 4, 2, -4], [6, 4, 2, -4, -8], [6, 4, 2, -4, -6], [6, 4, 2, -4, -6, -8], [6, 4, 2, -2], [6, 4, 2, -2, -8], [6, 4, 2, -2, -6], [6, 4, 2, -2, -6, -8], [6, 4, 2, -2, -4], [6, 4, 2, -2, -4, -8], [6, 4, 2, -2, -4, -6], [6, 4, 2, -2, -4, -6, -8], [6, 4, 2, 0], [6, 4, 2, 0, -8], [6, 4, 2, 0, -6], [6, 4, 2, 0, -6, -8], [6, 4, 2, 0, -4], [6, 4, 2, 0, -4, -8], [6, 4, 2, 0, -4, -6], [6, 4, 2, 0, -4, -6, -8], [6, 4, 2, 0, -2], [6, 4, 2, 0, -2, -8], [6, 4, 2, 0, -2, -6], [6, 4, 2, 0, -2, -6, -8], [6, 4, 2, 0, -2, -4], [6, 4, 2, 0, -2, -4, -8], [6, 4, 2, 0, -2, -4, -6], [6, 4, 2, 0, -2, -4, -6, -8], [8], [8, -8], [8, -6], [8, -6, -8], [8, -4], [8, -4, -8], [8, -4, -6], [8, -4, -6, -8], [8, -2], [8, -2, -8], [8, -2, -6], [8, -2, -6, -8], [8, -2, -4], [8, -2, -4, -8], [8, -2, -4, -6], [8, -2, -4, -6, -8], [8, 0], [8, 0, -8], [8, 0, -6], [8, 0, -6, -8], [8, 0, -4], [8, 0, -4, -8], [8, 0, -4, -6], [8, 0, -4, -6, -8], [8, 0, -2], [8, 0, -2, -8], [8, 0, -2, -6], [8, 0, -2, -6, -8], [8, 0, -2, -4], [8, 0, -2, -4, -8], [8, 0, -2, -4, -6], [8, 0, -2, -4, -6, -8], [8, 2], [8, 2, -8], [8, 2, -6], [8, 2, -6, -8], [8, 2, -4], [8, 2, -4, -8], [8, 2, -4, -6], [8, 2, -4, -6, -8], [8, 2, -2], [8, 2, -2, -8], [8, 2, -2, -6], [8, 2, -2, -6, -8], [8, 2, -2, -4], [8, 2, -2, -4, -8], [8, 2, -2, -4, -6], [8, 2, -2, -4, -6, -8], [8, 2, 0], [8, 2, 0, -8], [8, 2, 0, -6], [8, 2, 0, -6, -8], [8, 2, 0, -4], [8, 2, 0, -4, -8], [8, 2, 0, -4, -6], [8, 2, 0, -4, -6, -8], [8, 2, 0, -2], [8, 2, 0, -2, -8], [8, 2, 0, -2, -6], [8, 2, 0, -2, -6, -8], [8, 2, 0, -2, -4], [8, 2, 0, -2, -4, -8], [8, 2, 0, -2, -4, -6], [8, 2, 0, -2, -4, -6, -8], [8, 4], [8, 4, -8], [8, 4, -6], [8, 4, -6, -8], [8, 4, -4], [8, 4, -4, -8], [8, 4, -4, -6], [8, 4, -4, -6, -8], [8, 4, -2], [8, 4, -2, -8], [8, 4, -2, -6], [8, 4, -2, -6, -8], [8, 4, -2, -4], [8, 4, -2, -4, -8], [8, 4, -2, -4, -6], [8, 4, -2, -4, -6, -8], [8, 4, 0], [8, 4, 0, -8], [8, 4, 0, -6], [8, 4, 0, -6, -8], [8, 4, 0, -4], [8, 4, 0, -4, -8], [8, 4, 0, -4, -6], [8, 4, 0, -4, -6, -8], [8, 4, 0, -2], [8, 4, 0, -2, -8], [8, 4, 0, -2, -6], [8, 4, 0, -2, -6, -8], [8, 4, 0, -2, -4], [8, 4, 0, -2, -4, -8], [8, 4, 0, -2, -4, -6], [8, 4, 0, -2, -4, -6, -8], [8, 4, 2], [8, 4, 2, -8], [8, 4, 2, -6], [8, 4, 2, -6, -8], [8, 4, 2, -4], [8, 4, 2, -4, -8], [8, 4, 2, -4, -6], [8, 4, 2, -4, -6, -8], [8, 4, 2, -2], [8, 4, 2, -2, -8], [8, 4, 2, -2, -6], [8, 4, 2, -2, -6, -8], [8, 4, 2, -2, -4], [8, 4, 2, -2, -4, -8], [8, 4, 2, -2, -4, -6], [8, 4, 2, -2, -4, -6, -8], [8, 4, 2, 0], [8, 4, 2, 0, -8], [8, 4, 2, 0, -6], [8, 4, 2, 0, -6, -8], [8, 4, 2, 0, -4], [8, 4, 2, 0, -4, -8], [8, 4, 2, 0, -4, -6], [8, 4, 2, 0, -4, -6, -8], [8, 4, 2, 0, -2], [8, 4, 2, 0, -2, -8], [8, 4, 2, 0, -2, -6], [8, 4, 2, 0, -2, -6, -8], [8, 4, 2, 0, -2, -4], [8, 4, 2, 0, -2, -4, -8], [8, 4, 2, 0, -2, -4, -6], [8, 4, 2, 0, -2, -4, -6, -8], [8, 6], [8, 6, -8], [8, 6, -6], [8, 6, -6, -8], [8, 6, -4], [8, 6, -4, -8], [8, 6, -4, -6], [8, 6, -4, -6, -8], [8, 6, -2], [8, 6, -2, -8], [8, 6, -2, -6], [8, 6, -2, -6, -8], [8, 6, -2, -4], [8, 6, -2, -4, -8], [8, 6, -2, -4, -6], [8, 6, -2, -4, -6, -8], [8, 6, 0], [8, 6, 0, -8], [8, 6, 0, -6], [8, 6, 0, -6, -8], [8, 6, 0, -4], [8, 6, 0, -4, -8], [8, 6, 0, -4, -6], [8, 6, 0, -4, -6, -8], [8, 6, 0, -2], [8, 6, 0, -2, -8], [8, 6, 0, -2, -6], [8, 6, 0, -2, -6, -8], [8, 6, 0, -2, -4], [8, 6, 0, -2, -4, -8], [8, 6, 0, -2, -4, -6], [8, 6, 0, -2, -4, -6, -8], [8, 6, 2], [8, 6, 2, -8], [8, 6, 2, -6], [8, 6, 2, -6, -8], [8, 6, 2, -4], [8, 6, 2, -4, -8], [8, 6, 2, -4, -6], [8, 6, 2, -4, -6, -8], [8, 6, 2, -2], [8, 6, 2, -2, -8], [8, 6, 2, -2, -6], [8, 6, 2, -2, -6, -8], [8, 6, 2, -2, -4], [8, 6, 2, -2, -4, -8], [8, 6, 2, -2, -4, -6], [8, 6, 2, -2, -4, -6, -8], [8, 6, 2, 0], [8, 6, 2, 0, -8], [8, 6, 2, 0, -6], [8, 6, 2, 0, -6, -8], [8, 6, 2, 0, -4], [8, 6, 2, 0, -4, -8], [8, 6, 2, 0, -4, -6], [8, 6, 2, 0, -4, -6, -8], [8, 6, 2, 0, -2], [8, 6, 2, 0, -2, -8], [8, 6, 2, 0, -2, -6], [8, 6, 2, 0, -2, -6, -8], [8, 6, 2, 0, -2, -4], [8, 6, 2, 0, -2, -4, -8], [8, 6, 2, 0, -2, -4, -6], [8, 6, 2, 0, -2, -4, -6, -8], [8, 6, 4], [8, 6, 4, -8], [8, 6, 4, -6], [8, 6, 4, -6, -8], [8, 6, 4, -4], [8, 6, 4, -4, -8], [8, 6, 4, -4, -6], [8, 6, 4, -4, -6, -8], [8, 6, 4, -2], [8, 6, 4, -2, -8], [8, 6, 4, -2, -6], [8, 6, 4, -2, -6, -8], [8, 6, 4, -2, -4], [8, 6, 4, -2, -4, -8], [8, 6, 4, -2, -4, -6], [8, 6, 4, -2, -4, -6, -8], [8, 6, 4, 0], [8, 6, 4, 0, -8], [8, 6, 4, 0, -6], [8, 6, 4, 0, -6, -8], [8, 6, 4, 0, -4], [8, 6, 4, 0, -4, -8], [8, 6, 4, 0, -4, -6], [8, 6, 4, 0, -4, -6, -8], [8, 6, 4, 0, -2], [8, 6, 4, 0, -2, -8], [8, 6, 4, 0, -2, -6], [8, 6, 4, 0, -2, -6, -8], [8, 6, 4, 0, -2, -4], [8, 6, 4, 0, -2, -4, -8], [8, 6, 4, 0, -2, -4, -6], [8, 6, 4, 0, -2, -4, -6, -8], [8, 6, 4, 2], [8, 6, 4, 2, -8], [8, 6, 4, 2, -6], [8, 6, 4, 2, -6, -8], [8, 6, 4, 2, -4], [8, 6, 4, 2, -4, -8], [8, 6, 4, 2, -4, -6], [8, 6, 4, 2, -4, -6, -8], [8, 6, 4, 2, -2], [8, 6, 4, 2, -2, -8], [8, 6, 4, 2, -2, -6], [8, 6, 4, 2, -2, -6, -8], [8, 6, 4, 2, -2, -4], [8, 6, 4, 2, -2, -4, -8], [8, 6, 4, 2, -2, -4, -6], [8, 6, 4, 2, -2, -4, -6, -8], [8, 6, 4, 2, 0], [8, 6, 4, 2, 0, -8], [8, 6, 4, 2, 0, -6], [8, 6, 4, 2, 0, -6, -8], [8, 6, 4, 2, 0, -4], [8, 6, 4, 2, 0, -4, -8], [8, 6, 4, 2, 0, -4, -6], [8, 6, 4, 2, 0, -4, -6, -8], [8, 6, 4, 2, 0, -2], [8, 6, 4, 2, 0, -2, -8], [8, 6, 4, 2, 0, -2, -6], [8, 6, 4, 2, 0, -2, -6, -8], [8, 6, 4, 2, 0, -2, -4], [8, 6, 4, 2, 0, -2, -4, -8], [8, 6, 4, 2, 0, -2, -4, -6], [8, 6, 4, 2, 0, -2, -4, -6, -8]]\n assert candidate(nums = [7, 14, 21, 28, 35]) == [[], [35], [28], [28, 35], [21], [21, 35], [21, 28], [21, 28, 35], [14], [14, 35], [14, 28], [14, 28, 35], [14, 21], [14, 21, 35], [14, 21, 28], [14, 21, 28, 35], [7], [7, 35], [7, 28], [7, 28, 35], [7, 21], [7, 21, 35], [7, 21, 28], [7, 21, 28, 35], [7, 14], [7, 14, 35], [7, 14, 28], [7, 14, 28, 35], [7, 14, 21], [7, 14, 21, 35], [7, 14, 21, 28], [7, 14, 21, 28, 35]]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [[], [19], [17], [17, 19], [15], [15, 19], [15, 17], [15, 17, 19], [13], [13, 19], [13, 17], [13, 17, 19], [13, 15], [13, 15, 19], [13, 15, 17], [13, 15, 17, 19], [11], [11, 19], [11, 17], [11, 17, 19], [11, 15], [11, 15, 19], [11, 15, 17], [11, 15, 17, 19], [11, 13], [11, 13, 19], [11, 13, 17], [11, 13, 17, 19], [11, 13, 15], [11, 13, 15, 19], [11, 13, 15, 17], [11, 13, 15, 17, 19], [9], [9, 19], [9, 17], [9, 17, 19], [9, 15], [9, 15, 19], [9, 15, 17], [9, 15, 17, 19], [9, 13], [9, 13, 19], [9, 13, 17], [9, 13, 17, 19], [9, 13, 15], [9, 13, 15, 19], [9, 13, 15, 17], [9, 13, 15, 17, 19], [9, 11], [9, 11, 19], [9, 11, 17], [9, 11, 17, 19], [9, 11, 15], [9, 11, 15, 19], [9, 11, 15, 17], [9, 11, 15, 17, 19], [9, 11, 13], [9, 11, 13, 19], [9, 11, 13, 17], [9, 11, 13, 17, 19], [9, 11, 13, 15], [9, 11, 13, 15, 19], [9, 11, 13, 15, 17], [9, 11, 13, 15, 17, 19], [7], [7, 19], [7, 17], [7, 17, 19], [7, 15], [7, 15, 19], [7, 15, 17], [7, 15, 17, 19], [7, 13], [7, 13, 19], [7, 13, 17], [7, 13, 17, 19], [7, 13, 15], [7, 13, 15, 19], [7, 13, 15, 17], [7, 13, 15, 17, 19], [7, 11], [7, 11, 19], [7, 11, 17], [7, 11, 17, 19], [7, 11, 15], [7, 11, 15, 19], [7, 11, 15, 17], [7, 11, 15, 17, 19], [7, 11, 13], [7, 11, 13, 19], [7, 11, 13, 17], [7, 11, 13, 17, 19], [7, 11, 13, 15], [7, 11, 13, 15, 19], [7, 11, 13, 15, 17], [7, 11, 13, 15, 17, 19], [7, 9], [7, 9, 19], [7, 9, 17], [7, 9, 17, 19], [7, 9, 15], [7, 9, 15, 19], [7, 9, 15, 17], [7, 9, 15, 17, 19], [7, 9, 13], [7, 9, 13, 19], [7, 9, 13, 17], [7, 9, 13, 17, 19], [7, 9, 13, 15], [7, 9, 13, 15, 19], [7, 9, 13, 15, 17], [7, 9, 13, 15, 17, 19], [7, 9, 11], [7, 9, 11, 19], [7, 9, 11, 17], [7, 9, 11, 17, 19], [7, 9, 11, 15], [7, 9, 11, 15, 19], [7, 9, 11, 15, 17], [7, 9, 11, 15, 17, 19], [7, 9, 11, 13], [7, 9, 11, 13, 19], [7, 9, 11, 13, 17], [7, 9, 11, 13, 17, 19], [7, 9, 11, 13, 15], [7, 9, 11, 13, 15, 19], [7, 9, 11, 13, 15, 17], [7, 9, 11, 13, 15, 17, 19], [5], [5, 19], [5, 17], [5, 17, 19], [5, 15], [5, 15, 19], [5, 15, 17], [5, 15, 17, 19], [5, 13], [5, 13, 19], [5, 13, 17], [5, 13, 17, 19], [5, 13, 15], [5, 13, 15, 19], [5, 13, 15, 17], [5, 13, 15, 17, 19], [5, 11], [5, 11, 19], [5, 11, 17], [5, 11, 17, 19], [5, 11, 15], [5, 11, 15, 19], [5, 11, 15, 17], [5, 11, 15, 17, 19], [5, 11, 13], [5, 11, 13, 19], [5, 11, 13, 17], [5, 11, 13, 17, 19], [5, 11, 13, 15], [5, 11, 13, 15, 19], [5, 11, 13, 15, 17], [5, 11, 13, 15, 17, 19], 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15], [1, 3, 13, 15, 19], [1, 3, 13, 15, 17], [1, 3, 13, 15, 17, 19], [1, 3, 11], [1, 3, 11, 19], [1, 3, 11, 17], [1, 3, 11, 17, 19], [1, 3, 11, 15], [1, 3, 11, 15, 19], [1, 3, 11, 15, 17], [1, 3, 11, 15, 17, 19], [1, 3, 11, 13], [1, 3, 11, 13, 19], [1, 3, 11, 13, 17], [1, 3, 11, 13, 17, 19], [1, 3, 11, 13, 15], [1, 3, 11, 13, 15, 19], [1, 3, 11, 13, 15, 17], [1, 3, 11, 13, 15, 17, 19], [1, 3, 9], [1, 3, 9, 19], [1, 3, 9, 17], [1, 3, 9, 17, 19], [1, 3, 9, 15], [1, 3, 9, 15, 19], [1, 3, 9, 15, 17], [1, 3, 9, 15, 17, 19], [1, 3, 9, 13], [1, 3, 9, 13, 19], [1, 3, 9, 13, 17], [1, 3, 9, 13, 17, 19], [1, 3, 9, 13, 15], [1, 3, 9, 13, 15, 19], [1, 3, 9, 13, 15, 17], [1, 3, 9, 13, 15, 17, 19], [1, 3, 9, 11], [1, 3, 9, 11, 19], [1, 3, 9, 11, 17], [1, 3, 9, 11, 17, 19], [1, 3, 9, 11, 15], [1, 3, 9, 11, 15, 19], [1, 3, 9, 11, 15, 17], [1, 3, 9, 11, 15, 17, 19], [1, 3, 9, 11, 13], [1, 3, 9, 11, 13, 19], [1, 3, 9, 11, 13, 17], [1, 3, 9, 11, 13, 17, 19], [1, 3, 9, 11, 13, 15], [1, 3, 9, 11, 13, 15, 19], [1, 3, 9, 11, 13, 15, 17], [1, 3, 9, 11, 13, 15, 17, 19], [1, 3, 7], [1, 3, 7, 19], [1, 3, 7, 17], [1, 3, 7, 17, 19], [1, 3, 7, 15], [1, 3, 7, 15, 19], [1, 3, 7, 15, 17], [1, 3, 7, 15, 17, 19], [1, 3, 7, 13], [1, 3, 7, 13, 19], [1, 3, 7, 13, 17], [1, 3, 7, 13, 17, 19], [1, 3, 7, 13, 15], [1, 3, 7, 13, 15, 19], [1, 3, 7, 13, 15, 17], [1, 3, 7, 13, 15, 17, 19], [1, 3, 7, 11], [1, 3, 7, 11, 19], [1, 3, 7, 11, 17], [1, 3, 7, 11, 17, 19], [1, 3, 7, 11, 15], [1, 3, 7, 11, 15, 19], [1, 3, 7, 11, 15, 17], [1, 3, 7, 11, 15, 17, 19], [1, 3, 7, 11, 13], [1, 3, 7, 11, 13, 19], [1, 3, 7, 11, 13, 17], [1, 3, 7, 11, 13, 17, 19], [1, 3, 7, 11, 13, 15], [1, 3, 7, 11, 13, 15, 19], [1, 3, 7, 11, 13, 15, 17], [1, 3, 7, 11, 13, 15, 17, 19], [1, 3, 7, 9], [1, 3, 7, 9, 19], [1, 3, 7, 9, 17], [1, 3, 7, 9, 17, 19], [1, 3, 7, 9, 15], [1, 3, 7, 9, 15, 19], [1, 3, 7, 9, 15, 17], [1, 3, 7, 9, 15, 17, 19], [1, 3, 7, 9, 13], [1, 3, 7, 9, 13, 19], [1, 3, 7, 9, 13, 17], [1, 3, 7, 9, 13, 17, 19], [1, 3, 7, 9, 13, 15], [1, 3, 7, 9, 13, 15, 19], [1, 3, 7, 9, 13, 15, 17], [1, 3, 7, 9, 13, 15, 17, 19], [1, 3, 7, 9, 11], [1, 3, 7, 9, 11, 19], [1, 3, 7, 9, 11, 17], [1, 3, 7, 9, 11, 17, 19], [1, 3, 7, 9, 11, 15], [1, 3, 7, 9, 11, 15, 19], [1, 3, 7, 9, 11, 15, 17], [1, 3, 7, 9, 11, 15, 17, 19], [1, 3, 7, 9, 11, 13], [1, 3, 7, 9, 11, 13, 19], [1, 3, 7, 9, 11, 13, 17], [1, 3, 7, 9, 11, 13, 17, 19], [1, 3, 7, 9, 11, 13, 15], [1, 3, 7, 9, 11, 13, 15, 19], [1, 3, 7, 9, 11, 13, 15, 17], [1, 3, 7, 9, 11, 13, 15, 17, 19], [1, 3, 5], [1, 3, 5, 19], [1, 3, 5, 17], [1, 3, 5, 17, 19], [1, 3, 5, 15], [1, 3, 5, 15, 19], [1, 3, 5, 15, 17], [1, 3, 5, 15, 17, 19], [1, 3, 5, 13], [1, 3, 5, 13, 19], [1, 3, 5, 13, 17], [1, 3, 5, 13, 17, 19], [1, 3, 5, 13, 15], [1, 3, 5, 13, 15, 19], [1, 3, 5, 13, 15, 17], [1, 3, 5, 13, 15, 17, 19], [1, 3, 5, 11], [1, 3, 5, 11, 19], [1, 3, 5, 11, 17], [1, 3, 5, 11, 17, 19], [1, 3, 5, 11, 15], [1, 3, 5, 11, 15, 19], [1, 3, 5, 11, 15, 17], [1, 3, 5, 11, 15, 17, 19], [1, 3, 5, 11, 13], [1, 3, 5, 11, 13, 19], [1, 3, 5, 11, 13, 17], [1, 3, 5, 11, 13, 17, 19], [1, 3, 5, 11, 13, 15], [1, 3, 5, 11, 13, 15, 19], [1, 3, 5, 11, 13, 15, 17], [1, 3, 5, 11, 13, 15, 17, 19], [1, 3, 5, 9], [1, 3, 5, 9, 19], [1, 3, 5, 9, 17], [1, 3, 5, 9, 17, 19], [1, 3, 5, 9, 15], [1, 3, 5, 9, 15, 19], [1, 3, 5, 9, 15, 17], [1, 3, 5, 9, 15, 17, 19], [1, 3, 5, 9, 13], [1, 3, 5, 9, 13, 19], [1, 3, 5, 9, 13, 17], [1, 3, 5, 9, 13, 17, 19], [1, 3, 5, 9, 13, 15], [1, 3, 5, 9, 13, 15, 19], [1, 3, 5, 9, 13, 15, 17], [1, 3, 5, 9, 13, 15, 17, 19], [1, 3, 5, 9, 11], [1, 3, 5, 9, 11, 19], [1, 3, 5, 9, 11, 17], [1, 3, 5, 9, 11, 17, 19], [1, 3, 5, 9, 11, 15], [1, 3, 5, 9, 11, 15, 19], [1, 3, 5, 9, 11, 15, 17], [1, 3, 5, 9, 11, 15, 17, 19], [1, 3, 5, 9, 11, 13], [1, 3, 5, 9, 11, 13, 19], [1, 3, 5, 9, 11, 13, 17], [1, 3, 5, 9, 11, 13, 17, 19], [1, 3, 5, 9, 11, 13, 15], [1, 3, 5, 9, 11, 13, 15, 19], [1, 3, 5, 9, 11, 13, 15, 17], [1, 3, 5, 9, 11, 13, 15, 17, 19], [1, 3, 5, 7], [1, 3, 5, 7, 19], [1, 3, 5, 7, 17], [1, 3, 5, 7, 17, 19], [1, 3, 5, 7, 15], [1, 3, 5, 7, 15, 19], [1, 3, 5, 7, 15, 17], [1, 3, 5, 7, 15, 17, 19], [1, 3, 5, 7, 13], [1, 3, 5, 7, 13, 19], [1, 3, 5, 7, 13, 17], [1, 3, 5, 7, 13, 17, 19], [1, 3, 5, 7, 13, 15], [1, 3, 5, 7, 13, 15, 19], [1, 3, 5, 7, 13, 15, 17], [1, 3, 5, 7, 13, 15, 17, 19], [1, 3, 5, 7, 11], [1, 3, 5, 7, 11, 19], [1, 3, 5, 7, 11, 17], [1, 3, 5, 7, 11, 17, 19], [1, 3, 5, 7, 11, 15], [1, 3, 5, 7, 11, 15, 19], [1, 3, 5, 7, 11, 15, 17], [1, 3, 5, 7, 11, 15, 17, 19], [1, 3, 5, 7, 11, 13], [1, 3, 5, 7, 11, 13, 19], [1, 3, 5, 7, 11, 13, 17], [1, 3, 5, 7, 11, 13, 17, 19], [1, 3, 5, 7, 11, 13, 15], [1, 3, 5, 7, 11, 13, 15, 19], [1, 3, 5, 7, 11, 13, 15, 17], [1, 3, 5, 7, 11, 13, 15, 17, 19], [1, 3, 5, 7, 9], [1, 3, 5, 7, 9, 19], [1, 3, 5, 7, 9, 17], [1, 3, 5, 7, 9, 17, 19], [1, 3, 5, 7, 9, 15], [1, 3, 5, 7, 9, 15, 19], [1, 3, 5, 7, 9, 15, 17], [1, 3, 5, 7, 9, 15, 17, 19], [1, 3, 5, 7, 9, 13], [1, 3, 5, 7, 9, 13, 19], [1, 3, 5, 7, 9, 13, 17], [1, 3, 5, 7, 9, 13, 17, 19], [1, 3, 5, 7, 9, 13, 15], [1, 3, 5, 7, 9, 13, 15, 19], [1, 3, 5, 7, 9, 13, 15, 17], [1, 3, 5, 7, 9, 13, 15, 17, 19], [1, 3, 5, 7, 9, 11], [1, 3, 5, 7, 9, 11, 19], [1, 3, 5, 7, 9, 11, 17], [1, 3, 5, 7, 9, 11, 17, 19], [1, 3, 5, 7, 9, 11, 15], [1, 3, 5, 7, 9, 11, 15, 19], [1, 3, 5, 7, 9, 11, 15, 17], [1, 3, 5, 7, 9, 11, 15, 17, 19], [1, 3, 5, 7, 9, 11, 13], [1, 3, 5, 7, 9, 11, 13, 19], [1, 3, 5, 7, 9, 11, 13, 17], [1, 3, 5, 7, 9, 11, 13, 17, 19], [1, 3, 5, 7, 9, 11, 13, 15], [1, 3, 5, 7, 9, 11, 13, 15, 19], [1, 3, 5, 7, 9, 11, 13, 15, 17], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]]\n assert candidate(nums = [7, 14, 28, 56, 112]) == [[], [112], [56], [56, 112], [28], [28, 112], [28, 56], [28, 56, 112], [14], [14, 112], [14, 56], [14, 56, 112], [14, 28], [14, 28, 112], [14, 28, 56], [14, 28, 56, 112], [7], [7, 112], [7, 56], [7, 56, 112], [7, 28], [7, 28, 112], [7, 28, 56], [7, 28, 56, 112], [7, 14], [7, 14, 112], [7, 14, 56], [7, 14, 56, 112], [7, 14, 28], [7, 14, 28, 112], [7, 14, 28, 56], [7, 14, 28, 56, 112]]\n assert candidate(nums = [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8]) == [[], [8], [6], [6, 8], [4], [4, 8], [4, 6], [4, 6, 8], [2], [2, 8], [2, 6], [2, 6, 8], [2, 4], [2, 4, 8], [2, 4, 6], [2, 4, 6, 8], [0], [0, 8], [0, 6], [0, 6, 8], [0, 4], [0, 4, 8], [0, 4, 6], [0, 4, 6, 8], [0, 2], [0, 2, 8], [0, 2, 6], [0, 2, 6, 8], [0, 2, 4], [0, 2, 4, 8], [0, 2, 4, 6], [0, 2, 4, 6, 8], [-2], [-2, 8], [-2, 6], [-2, 6, 8], [-2, 4], [-2, 4, 8], [-2, 4, 6], [-2, 4, 6, 8], [-2, 2], [-2, 2, 8], [-2, 2, 6], [-2, 2, 6, 8], [-2, 2, 4], [-2, 2, 4, 8], [-2, 2, 4, 6], [-2, 2, 4, 6, 8], [-2, 0], [-2, 0, 8], [-2, 0, 6], [-2, 0, 6, 8], [-2, 0, 4], [-2, 0, 4, 8], [-2, 0, 4, 6], [-2, 0, 4, 6, 8], [-2, 0, 2], [-2, 0, 2, 8], [-2, 0, 2, 6], [-2, 0, 2, 6, 8], [-2, 0, 2, 4], [-2, 0, 2, 4, 8], [-2, 0, 2, 4, 6], [-2, 0, 2, 4, 6, 8], [-4], [-4, 8], [-4, 6], [-4, 6, 8], [-4, 4], [-4, 4, 8], [-4, 4, 6], [-4, 4, 6, 8], [-4, 2], [-4, 2, 8], [-4, 2, 6], [-4, 2, 6, 8], [-4, 2, 4], [-4, 2, 4, 8], [-4, 2, 4, 6], [-4, 2, 4, 6, 8], [-4, 0], [-4, 0, 8], [-4, 0, 6], [-4, 0, 6, 8], [-4, 0, 4], [-4, 0, 4, 8], [-4, 0, 4, 6], [-4, 0, 4, 6, 8], [-4, 0, 2], [-4, 0, 2, 8], [-4, 0, 2, 6], [-4, 0, 2, 6, 8], [-4, 0, 2, 4], [-4, 0, 2, 4, 8], [-4, 0, 2, 4, 6], [-4, 0, 2, 4, 6, 8], [-4, -2], [-4, -2, 8], [-4, -2, 6], [-4, -2, 6, 8], [-4, -2, 4], [-4, -2, 4, 8], [-4, -2, 4, 6], [-4, -2, 4, 6, 8], [-4, -2, 2], [-4, -2, 2, 8], [-4, -2, 2, 6], [-4, -2, 2, 6, 8], [-4, -2, 2, 4], [-4, -2, 2, 4, 8], [-4, -2, 2, 4, 6], [-4, -2, 2, 4, 6, 8], [-4, -2, 0], [-4, -2, 0, 8], [-4, -2, 0, 6], [-4, -2, 0, 6, 8], [-4, -2, 0, 4], [-4, -2, 0, 4, 8], [-4, -2, 0, 4, 6], [-4, -2, 0, 4, 6, 8], [-4, -2, 0, 2], [-4, -2, 0, 2, 8], [-4, -2, 0, 2, 6], [-4, -2, 0, 2, 6, 8], [-4, -2, 0, 2, 4], [-4, -2, 0, 2, 4, 8], [-4, -2, 0, 2, 4, 6], [-4, -2, 0, 2, 4, 6, 8], [-6], [-6, 8], [-6, 6], [-6, 6, 8], [-6, 4], [-6, 4, 8], [-6, 4, 6], [-6, 4, 6, 8], [-6, 2], [-6, 2, 8], [-6, 2, 6], [-6, 2, 6, 8], [-6, 2, 4], [-6, 2, 4, 8], [-6, 2, 4, 6], [-6, 2, 4, 6, 8], [-6, 0], [-6, 0, 8], [-6, 0, 6], [-6, 0, 6, 8], [-6, 0, 4], [-6, 0, 4, 8], [-6, 0, 4, 6], [-6, 0, 4, 6, 8], [-6, 0, 2], [-6, 0, 2, 8], [-6, 0, 2, 6], [-6, 0, 2, 6, 8], [-6, 0, 2, 4], [-6, 0, 2, 4, 8], [-6, 0, 2, 4, 6], [-6, 0, 2, 4, 6, 8], [-6, -2], [-6, -2, 8], [-6, -2, 6], [-6, -2, 6, 8], [-6, -2, 4], [-6, -2, 4, 8], [-6, -2, 4, 6], [-6, -2, 4, 6, 8], [-6, -2, 2], [-6, -2, 2, 8], [-6, -2, 2, 6], [-6, -2, 2, 6, 8], [-6, -2, 2, 4], [-6, -2, 2, 4, 8], [-6, -2, 2, 4, 6], [-6, -2, 2, 4, 6, 8], [-6, -2, 0], [-6, -2, 0, 8], [-6, -2, 0, 6], [-6, -2, 0, 6, 8], [-6, -2, 0, 4], [-6, -2, 0, 4, 8], [-6, -2, 0, 4, 6], [-6, -2, 0, 4, 6, 8], [-6, -2, 0, 2], [-6, -2, 0, 2, 8], [-6, -2, 0, 2, 6], [-6, -2, 0, 2, 6, 8], [-6, -2, 0, 2, 4], [-6, -2, 0, 2, 4, 8], [-6, -2, 0, 2, 4, 6], [-6, -2, 0, 2, 4, 6, 8], [-6, -4], [-6, -4, 8], [-6, -4, 6], [-6, -4, 6, 8], [-6, -4, 4], [-6, -4, 4, 8], [-6, -4, 4, 6], [-6, -4, 4, 6, 8], [-6, -4, 2], [-6, -4, 2, 8], [-6, -4, 2, 6], [-6, -4, 2, 6, 8], [-6, -4, 2, 4], [-6, -4, 2, 4, 8], [-6, -4, 2, 4, 6], [-6, -4, 2, 4, 6, 8], [-6, -4, 0], [-6, -4, 0, 8], [-6, -4, 0, 6], [-6, -4, 0, 6, 8], [-6, -4, 0, 4], [-6, -4, 0, 4, 8], [-6, -4, 0, 4, 6], [-6, -4, 0, 4, 6, 8], [-6, -4, 0, 2], [-6, -4, 0, 2, 8], [-6, -4, 0, 2, 6], [-6, -4, 0, 2, 6, 8], [-6, -4, 0, 2, 4], [-6, -4, 0, 2, 4, 8], [-6, -4, 0, 2, 4, 6], [-6, -4, 0, 2, 4, 6, 8], [-6, -4, -2], [-6, -4, -2, 8], [-6, -4, -2, 6], [-6, -4, -2, 6, 8], [-6, -4, -2, 4], [-6, -4, -2, 4, 8], [-6, -4, -2, 4, 6], [-6, -4, -2, 4, 6, 8], [-6, -4, -2, 2], [-6, -4, -2, 2, 8], [-6, -4, -2, 2, 6], [-6, -4, -2, 2, 6, 8], [-6, -4, -2, 2, 4], [-6, -4, -2, 2, 4, 8], [-6, -4, -2, 2, 4, 6], [-6, -4, -2, 2, 4, 6, 8], [-6, -4, -2, 0], [-6, -4, -2, 0, 8], [-6, -4, -2, 0, 6], [-6, -4, -2, 0, 6, 8], [-6, -4, -2, 0, 4], [-6, -4, -2, 0, 4, 8], [-6, -4, -2, 0, 4, 6], [-6, -4, -2, 0, 4, 6, 8], [-6, -4, -2, 0, 2], [-6, -4, -2, 0, 2, 8], [-6, -4, -2, 0, 2, 6], [-6, -4, -2, 0, 2, 6, 8], [-6, -4, -2, 0, 2, 4], [-6, -4, -2, 0, 2, 4, 8], [-6, -4, -2, 0, 2, 4, 6], [-6, -4, -2, 0, 2, 4, 6, 8], [-8], [-8, 8], [-8, 6], [-8, 6, 8], [-8, 4], [-8, 4, 8], [-8, 4, 6], [-8, 4, 6, 8], [-8, 2], [-8, 2, 8], [-8, 2, 6], [-8, 2, 6, 8], [-8, 2, 4], [-8, 2, 4, 8], [-8, 2, 4, 6], [-8, 2, 4, 6, 8], [-8, 0], [-8, 0, 8], [-8, 0, 6], [-8, 0, 6, 8], [-8, 0, 4], [-8, 0, 4, 8], [-8, 0, 4, 6], [-8, 0, 4, 6, 8], [-8, 0, 2], [-8, 0, 2, 8], [-8, 0, 2, 6], [-8, 0, 2, 6, 8], [-8, 0, 2, 4], [-8, 0, 2, 4, 8], [-8, 0, 2, 4, 6], [-8, 0, 2, 4, 6, 8], [-8, -2], [-8, -2, 8], [-8, -2, 6], [-8, -2, 6, 8], [-8, -2, 4], [-8, -2, 4, 8], [-8, -2, 4, 6], [-8, -2, 4, 6, 8], [-8, -2, 2], [-8, -2, 2, 8], [-8, -2, 2, 6], [-8, -2, 2, 6, 8], [-8, -2, 2, 4], [-8, -2, 2, 4, 8], [-8, -2, 2, 4, 6], [-8, -2, 2, 4, 6, 8], [-8, -2, 0], [-8, -2, 0, 8], [-8, -2, 0, 6], [-8, -2, 0, 6, 8], [-8, -2, 0, 4], [-8, -2, 0, 4, 8], [-8, -2, 0, 4, 6], [-8, -2, 0, 4, 6, 8], [-8, -2, 0, 2], [-8, -2, 0, 2, 8], [-8, -2, 0, 2, 6], [-8, -2, 0, 2, 6, 8], [-8, -2, 0, 2, 4], [-8, -2, 0, 2, 4, 8], 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8], [-10, -6, -4, -2, 0, 4, 6], [-10, -6, -4, -2, 0, 4, 6, 8], [-10, -6, -4, -2, 0, 2], [-10, -6, -4, -2, 0, 2, 8], [-10, -6, -4, -2, 0, 2, 6], [-10, -6, -4, -2, 0, 2, 6, 8], [-10, -6, -4, -2, 0, 2, 4], [-10, -6, -4, -2, 0, 2, 4, 8], [-10, -6, -4, -2, 0, 2, 4, 6], [-10, -6, -4, -2, 0, 2, 4, 6, 8], [-10, -8], [-10, -8, 8], [-10, -8, 6], [-10, -8, 6, 8], [-10, -8, 4], [-10, -8, 4, 8], [-10, -8, 4, 6], [-10, -8, 4, 6, 8], [-10, -8, 2], [-10, -8, 2, 8], [-10, -8, 2, 6], [-10, -8, 2, 6, 8], [-10, -8, 2, 4], [-10, -8, 2, 4, 8], [-10, -8, 2, 4, 6], [-10, -8, 2, 4, 6, 8], [-10, -8, 0], [-10, -8, 0, 8], [-10, -8, 0, 6], [-10, -8, 0, 6, 8], [-10, -8, 0, 4], [-10, -8, 0, 4, 8], [-10, -8, 0, 4, 6], [-10, -8, 0, 4, 6, 8], [-10, -8, 0, 2], [-10, -8, 0, 2, 8], [-10, -8, 0, 2, 6], [-10, -8, 0, 2, 6, 8], [-10, -8, 0, 2, 4], [-10, -8, 0, 2, 4, 8], [-10, -8, 0, 2, 4, 6], [-10, -8, 0, 2, 4, 6, 8], [-10, -8, -2], [-10, -8, -2, 8], [-10, -8, -2, 6], [-10, -8, -2, 6, 8], [-10, -8, -2, 4], [-10, -8, -2, 4, 8], [-10, -8, -2, 4, 6], [-10, -8, -2, 4, 6, 8], [-10, -8, -2, 2], [-10, -8, -2, 2, 8], [-10, -8, -2, 2, 6], [-10, -8, -2, 2, 6, 8], [-10, -8, -2, 2, 4], [-10, -8, -2, 2, 4, 8], [-10, -8, -2, 2, 4, 6], [-10, -8, -2, 2, 4, 6, 8], [-10, -8, -2, 0], [-10, -8, -2, 0, 8], [-10, -8, -2, 0, 6], [-10, -8, -2, 0, 6, 8], [-10, -8, -2, 0, 4], [-10, -8, -2, 0, 4, 8], [-10, -8, -2, 0, 4, 6], [-10, -8, -2, 0, 4, 6, 8], [-10, -8, -2, 0, 2], [-10, -8, -2, 0, 2, 8], [-10, -8, -2, 0, 2, 6], [-10, -8, -2, 0, 2, 6, 8], [-10, -8, -2, 0, 2, 4], [-10, -8, -2, 0, 2, 4, 8], [-10, -8, -2, 0, 2, 4, 6], [-10, -8, -2, 0, 2, 4, 6, 8], [-10, -8, -4], [-10, -8, -4, 8], [-10, -8, -4, 6], [-10, -8, -4, 6, 8], [-10, -8, -4, 4], [-10, -8, -4, 4, 8], [-10, -8, -4, 4, 6], [-10, -8, -4, 4, 6, 8], [-10, -8, -4, 2], [-10, -8, -4, 2, 8], [-10, -8, -4, 2, 6], [-10, -8, -4, 2, 6, 8], [-10, -8, -4, 2, 4], [-10, -8, -4, 2, 4, 8], [-10, -8, -4, 2, 4, 6], [-10, -8, -4, 2, 4, 6, 8], [-10, -8, -4, 0], [-10, -8, -4, 0, 8], [-10, -8, -4, 0, 6], [-10, -8, -4, 0, 6, 8], [-10, -8, -4, 0, 4], [-10, -8, -4, 0, 4, 8], [-10, -8, -4, 0, 4, 6], [-10, -8, -4, 0, 4, 6, 8], [-10, -8, -4, 0, 2], [-10, -8, -4, 0, 2, 8], [-10, -8, -4, 0, 2, 6], [-10, -8, -4, 0, 2, 6, 8], [-10, -8, -4, 0, 2, 4], [-10, -8, -4, 0, 2, 4, 8], [-10, -8, -4, 0, 2, 4, 6], [-10, -8, -4, 0, 2, 4, 6, 8], [-10, -8, -4, -2], [-10, -8, -4, -2, 8], [-10, -8, -4, -2, 6], [-10, -8, -4, -2, 6, 8], [-10, -8, -4, -2, 4], [-10, -8, -4, -2, 4, 8], [-10, -8, -4, -2, 4, 6], [-10, -8, -4, -2, 4, 6, 8], [-10, -8, -4, -2, 2], [-10, -8, -4, -2, 2, 8], [-10, -8, -4, -2, 2, 6], [-10, -8, -4, -2, 2, 6, 8], [-10, -8, -4, -2, 2, 4], [-10, -8, -4, -2, 2, 4, 8], [-10, -8, -4, -2, 2, 4, 6], [-10, -8, -4, -2, 2, 4, 6, 8], [-10, -8, -4, -2, 0], [-10, -8, -4, -2, 0, 8], [-10, -8, -4, -2, 0, 6], [-10, -8, -4, -2, 0, 6, 8], [-10, -8, -4, -2, 0, 4], [-10, -8, -4, -2, 0, 4, 8], [-10, -8, -4, -2, 0, 4, 6], [-10, -8, -4, -2, 0, 4, 6, 8], [-10, -8, -4, -2, 0, 2], [-10, -8, -4, -2, 0, 2, 8], [-10, -8, -4, -2, 0, 2, 6], [-10, -8, -4, -2, 0, 2, 6, 8], [-10, -8, -4, -2, 0, 2, 4], [-10, -8, -4, -2, 0, 2, 4, 8], [-10, -8, -4, -2, 0, 2, 4, 6], [-10, -8, -4, -2, 0, 2, 4, 6, 8], [-10, -8, -6], [-10, -8, -6, 8], [-10, -8, -6, 6], [-10, -8, -6, 6, 8], [-10, -8, -6, 4], [-10, -8, -6, 4, 8], [-10, -8, -6, 4, 6], [-10, -8, -6, 4, 6, 8], [-10, -8, -6, 2], [-10, -8, -6, 2, 8], [-10, -8, -6, 2, 6], [-10, -8, -6, 2, 6, 8], [-10, -8, -6, 2, 4], [-10, -8, -6, 2, 4, 8], [-10, -8, -6, 2, 4, 6], [-10, -8, -6, 2, 4, 6, 8], [-10, -8, -6, 0], [-10, -8, -6, 0, 8], [-10, -8, -6, 0, 6], [-10, -8, -6, 0, 6, 8], [-10, -8, -6, 0, 4], [-10, -8, -6, 0, 4, 8], [-10, -8, -6, 0, 4, 6], [-10, -8, -6, 0, 4, 6, 8], [-10, -8, -6, 0, 2], [-10, -8, -6, 0, 2, 8], [-10, -8, -6, 0, 2, 6], [-10, -8, -6, 0, 2, 6, 8], [-10, -8, -6, 0, 2, 4], [-10, -8, -6, 0, 2, 4, 8], [-10, -8, -6, 0, 2, 4, 6], [-10, -8, -6, 0, 2, 4, 6, 8], [-10, -8, -6, -2], [-10, -8, -6, -2, 8], [-10, -8, -6, -2, 6], [-10, -8, -6, -2, 6, 8], [-10, -8, -6, -2, 4], [-10, -8, -6, -2, 4, 8], [-10, -8, -6, -2, 4, 6], [-10, -8, -6, -2, 4, 6, 8], [-10, -8, -6, -2, 2], [-10, -8, -6, -2, 2, 8], [-10, -8, -6, -2, 2, 6], [-10, -8, -6, -2, 2, 6, 8], [-10, -8, -6, -2, 2, 4], [-10, -8, -6, -2, 2, 4, 8], [-10, -8, -6, -2, 2, 4, 6], [-10, -8, -6, -2, 2, 4, 6, 8], [-10, -8, -6, -2, 0], [-10, -8, -6, -2, 0, 8], [-10, -8, -6, -2, 0, 6], [-10, -8, -6, -2, 0, 6, 8], [-10, -8, -6, -2, 0, 4], [-10, -8, -6, -2, 0, 4, 8], [-10, -8, -6, -2, 0, 4, 6], [-10, -8, -6, -2, 0, 4, 6, 8], [-10, -8, -6, -2, 0, 2], [-10, -8, -6, -2, 0, 2, 8], [-10, -8, -6, -2, 0, 2, 6], [-10, -8, -6, -2, 0, 2, 6, 8], [-10, -8, -6, -2, 0, 2, 4], [-10, -8, -6, -2, 0, 2, 4, 8], [-10, -8, -6, -2, 0, 2, 4, 6], [-10, -8, -6, -2, 0, 2, 4, 6, 8], [-10, -8, -6, -4], [-10, -8, -6, -4, 8], [-10, -8, -6, -4, 6], [-10, -8, -6, -4, 6, 8], [-10, -8, -6, -4, 4], [-10, -8, -6, -4, 4, 8], [-10, -8, -6, -4, 4, 6], [-10, -8, -6, -4, 4, 6, 8], [-10, -8, -6, -4, 2], [-10, -8, -6, -4, 2, 8], [-10, -8, -6, -4, 2, 6], [-10, -8, -6, -4, 2, 6, 8], [-10, -8, -6, -4, 2, 4], [-10, -8, -6, -4, 2, 4, 8], [-10, -8, -6, -4, 2, 4, 6], [-10, -8, -6, -4, 2, 4, 6, 8], [-10, -8, -6, -4, 0], [-10, -8, -6, -4, 0, 8], [-10, -8, -6, -4, 0, 6], [-10, -8, -6, -4, 0, 6, 8], [-10, -8, -6, -4, 0, 4], [-10, -8, -6, -4, 0, 4, 8], [-10, -8, -6, -4, 0, 4, 6], [-10, -8, -6, -4, 0, 4, 6, 8], [-10, -8, -6, -4, 0, 2], [-10, -8, -6, -4, 0, 2, 8], [-10, -8, -6, -4, 0, 2, 6], [-10, -8, -6, -4, 0, 2, 6, 8], [-10, -8, -6, -4, 0, 2, 4], [-10, -8, -6, -4, 0, 2, 4, 8], [-10, -8, -6, -4, 0, 2, 4, 6], [-10, -8, -6, -4, 0, 2, 4, 6, 8], [-10, -8, -6, -4, -2], [-10, -8, -6, -4, -2, 8], [-10, -8, -6, -4, -2, 6], [-10, -8, -6, -4, -2, 6, 8], [-10, -8, -6, -4, -2, 4], [-10, -8, -6, -4, -2, 4, 8], [-10, -8, -6, -4, -2, 4, 6], [-10, -8, -6, -4, -2, 4, 6, 8], [-10, -8, -6, -4, -2, 2], [-10, -8, -6, -4, -2, 2, 8], [-10, -8, -6, -4, -2, 2, 6], [-10, -8, -6, -4, -2, 2, 6, 8], [-10, -8, -6, -4, -2, 2, 4], [-10, -8, -6, -4, -2, 2, 4, 8], [-10, -8, -6, -4, -2, 2, 4, 6], [-10, -8, -6, -4, -2, 2, 4, 6, 8], [-10, -8, -6, -4, -2, 0], [-10, -8, -6, -4, -2, 0, 8], [-10, -8, -6, -4, -2, 0, 6], [-10, -8, -6, -4, -2, 0, 6, 8], [-10, -8, -6, -4, -2, 0, 4], [-10, -8, -6, -4, -2, 0, 4, 8], [-10, -8, -6, -4, -2, 0, 4, 6], [-10, -8, -6, -4, -2, 0, 4, 6, 8], [-10, -8, -6, -4, -2, 0, 2], [-10, -8, -6, -4, -2, 0, 2, 8], [-10, -8, -6, -4, -2, 0, 2, 6], [-10, -8, -6, -4, -2, 0, 2, 6, 8], [-10, -8, -6, -4, -2, 0, 2, 4], [-10, -8, -6, -4, -2, 0, 2, 4, 8], [-10, -8, -6, -4, -2, 0, 2, 4, 6], [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8]]\n assert candidate(nums = [0, 1, 2, 3, 4, 5]) == [[], [5], [4], [4, 5], [3], [3, 5], [3, 4], [3, 4, 5], [2], [2, 5], [2, 4], [2, 4, 5], [2, 3], [2, 3, 5], [2, 3, 4], [2, 3, 4, 5], [1], [1, 5], [1, 4], [1, 4, 5], [1, 3], [1, 3, 5], [1, 3, 4], [1, 3, 4, 5], [1, 2], [1, 2, 5], [1, 2, 4], [1, 2, 4, 5], [1, 2, 3], [1, 2, 3, 5], [1, 2, 3, 4], [1, 2, 3, 4, 5], [0], [0, 5], [0, 4], [0, 4, 5], [0, 3], [0, 3, 5], [0, 3, 4], [0, 3, 4, 5], [0, 2], [0, 2, 5], [0, 2, 4], [0, 2, 4, 5], [0, 2, 3], [0, 2, 3, 5], [0, 2, 3, 4], [0, 2, 3, 4, 5], [0, 1], [0, 1, 5], [0, 1, 4], [0, 1, 4, 5], [0, 1, 3], [0, 1, 3, 5], [0, 1, 3, 4], [0, 1, 3, 4, 5], [0, 1, 2], [0, 1, 2, 5], [0, 1, 2, 4], [0, 1, 2, 4, 5], [0, 1, 2, 3], [0, 1, 2, 3, 5], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 5]]\n assert candidate(nums = [1, 2, 3, 4]) == [[], [4], [3], [3, 4], [2], [2, 4], [2, 3], [2, 3, 4], [1], [1, 4], [1, 3], [1, 3, 4], [1, 2], [1, 2, 4], [1, 2, 3], [1, 2, 3, 4]]\n assert candidate(nums = [0, 1, 10, 100, 1000, 10000]) == [[], [10000], [1000], [1000, 10000], [100], [100, 10000], [100, 1000], [100, 1000, 10000], [10], [10, 10000], [10, 1000], [10, 1000, 10000], [10, 100], [10, 100, 10000], [10, 100, 1000], [10, 100, 1000, 10000], [1], [1, 10000], [1, 1000], [1, 1000, 10000], [1, 100], [1, 100, 10000], [1, 100, 1000], [1, 100, 1000, 10000], [1, 10], [1, 10, 10000], [1, 10, 1000], [1, 10, 1000, 10000], [1, 10, 100], [1, 10, 100, 10000], [1, 10, 100, 1000], [1, 10, 100, 1000, 10000], [0], [0, 10000], [0, 1000], [0, 1000, 10000], [0, 100], [0, 100, 10000], [0, 100, 1000], [0, 100, 1000, 10000], [0, 10], [0, 10, 10000], [0, 10, 1000], [0, 10, 1000, 10000], [0, 10, 100], [0, 10, 100, 10000], [0, 10, 100, 1000], [0, 10, 100, 1000, 10000], [0, 1], [0, 1, 10000], [0, 1, 1000], [0, 1, 1000, 10000], [0, 1, 100], [0, 1, 100, 10000], [0, 1, 100, 1000], [0, 1, 100, 1000, 10000], [0, 1, 10], [0, 1, 10, 10000], [0, 1, 10, 1000], [0, 1, 10, 1000, 10000], [0, 1, 10, 100], [0, 1, 10, 100, 10000], [0, 1, 10, 100, 1000], [0, 1, 10, 100, 1000, 10000]]\n assert candidate(nums = [-5, -10, -15, -20, -25, -30, -35]) == [[], [-35], [-30], [-30, -35], [-25], [-25, -35], [-25, -30], [-25, -30, -35], [-20], [-20, -35], [-20, -30], [-20, -30, -35], [-20, -25], [-20, -25, -35], [-20, -25, -30], [-20, -25, -30, -35], [-15], [-15, -35], [-15, -30], [-15, -30, -35], [-15, -25], [-15, -25, -35], [-15, -25, -30], [-15, -25, -30, -35], [-15, -20], [-15, -20, -35], [-15, -20, -30], [-15, -20, -30, -35], [-15, -20, -25], [-15, -20, -25, -35], [-15, -20, -25, -30], [-15, -20, -25, -30, -35], [-10], [-10, -35], [-10, -30], [-10, -30, -35], [-10, -25], [-10, -25, -35], [-10, -25, -30], [-10, -25, -30, -35], [-10, -20], [-10, -20, -35], [-10, -20, -30], [-10, -20, -30, -35], [-10, -20, -25], [-10, -20, -25, -35], [-10, -20, -25, -30], [-10, -20, -25, -30, -35], [-10, -15], [-10, -15, -35], [-10, -15, -30], [-10, -15, -30, -35], [-10, -15, -25], [-10, -15, -25, -35], [-10, -15, -25, -30], [-10, -15, -25, -30, -35], [-10, -15, -20], [-10, -15, -20, -35], [-10, -15, -20, -30], [-10, -15, -20, -30, -35], [-10, -15, -20, -25], [-10, -15, -20, -25, -35], [-10, -15, -20, -25, -30], [-10, -15, -20, -25, -30, -35], [-5], [-5, -35], [-5, -30], [-5, -30, -35], [-5, -25], [-5, -25, -35], [-5, -25, -30], [-5, -25, -30, -35], [-5, -20], [-5, -20, -35], [-5, -20, -30], [-5, -20, -30, -35], [-5, -20, -25], [-5, -20, -25, -35], [-5, -20, -25, -30], [-5, -20, -25, -30, -35], [-5, -15], [-5, -15, -35], [-5, -15, -30], [-5, -15, -30, -35], [-5, -15, -25], [-5, -15, -25, -35], [-5, -15, -25, -30], [-5, -15, -25, -30, -35], [-5, -15, -20], [-5, -15, -20, -35], [-5, -15, -20, -30], [-5, -15, -20, -30, -35], [-5, -15, -20, -25], [-5, -15, -20, -25, -35], [-5, -15, -20, -25, -30], [-5, -15, -20, -25, -30, -35], [-5, -10], [-5, -10, -35], [-5, -10, -30], [-5, -10, -30, -35], [-5, -10, -25], [-5, -10, -25, -35], [-5, -10, -25, -30], [-5, -10, -25, -30, -35], [-5, -10, -20], [-5, -10, -20, -35], [-5, -10, -20, -30], [-5, -10, -20, -30, -35], [-5, -10, -20, -25], [-5, -10, -20, -25, -35], [-5, -10, -20, -25, -30], [-5, -10, -20, -25, -30, -35], [-5, -10, -15], [-5, -10, -15, -35], [-5, -10, -15, -30], [-5, -10, -15, -30, -35], [-5, -10, -15, -25], [-5, -10, -15, -25, -35], [-5, -10, -15, -25, -30], [-5, -10, -15, -25, -30, -35], [-5, -10, -15, -20], [-5, -10, -15, -20, -35], [-5, -10, -15, -20, -30], [-5, -10, -15, -20, -30, -35], [-5, -10, -15, -20, -25], [-5, -10, -15, -20, -25, -35], [-5, -10, -15, -20, -25, -30], [-5, -10, -15, -20, -25, -30, -35]]\n assert candidate(nums = [7, 1, 5, 3]) == [[], [3], [5], [5, 3], [1], [1, 3], [1, 5], [1, 5, 3], [7], [7, 3], [7, 5], [7, 5, 3], [7, 1], [7, 1, 3], [7, 1, 5], [7, 1, 5, 3]]\n assert candidate(nums = [-1, -2, -3, -4, -5]) == [[], [-5], [-4], [-4, -5], [-3], [-3, -5], [-3, -4], [-3, -4, -5], [-2], [-2, -5], [-2, -4], [-2, -4, -5], [-2, -3], [-2, -3, -5], [-2, -3, -4], [-2, -3, -4, -5], [-1], [-1, -5], [-1, -4], [-1, -4, -5], [-1, -3], [-1, -3, -5], [-1, -3, -4], [-1, -3, -4, -5], [-1, -2], [-1, -2, -5], [-1, -2, -4], [-1, -2, -4, -5], [-1, -2, -3], [-1, -2, -3, -5], [-1, -2, -3, -4], [-1, -2, -3, -4, -5]]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [[], [9], [8], [8, 9], [7], [7, 9], [7, 8], [7, 8, 9], [6], [6, 9], [6, 8], [6, 8, 9], [6, 7], [6, 7, 9], [6, 7, 8], [6, 7, 8, 9], [5], [5, 9], [5, 8], [5, 8, 9], [5, 7], [5, 7, 9], [5, 7, 8], [5, 7, 8, 9], [5, 6], [5, 6, 9], [5, 6, 8], [5, 6, 8, 9], [5, 6, 7], [5, 6, 7, 9], [5, 6, 7, 8], [5, 6, 7, 8, 9], [4], [4, 9], [4, 8], [4, 8, 9], [4, 7], [4, 7, 9], [4, 7, 8], [4, 7, 8, 9], [4, 6], [4, 6, 9], [4, 6, 8], [4, 6, 8, 9], [4, 6, 7], [4, 6, 7, 9], [4, 6, 7, 8], [4, 6, 7, 8, 9], [4, 5], [4, 5, 9], [4, 5, 8], [4, 5, 8, 9], [4, 5, 7], [4, 5, 7, 9], [4, 5, 7, 8], [4, 5, 7, 8, 9], [4, 5, 6], [4, 5, 6, 9], [4, 5, 6, 8], [4, 5, 6, 8, 9], [4, 5, 6, 7], [4, 5, 6, 7, 9], [4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9], [3], [3, 9], [3, 8], [3, 8, 9], [3, 7], [3, 7, 9], [3, 7, 8], [3, 7, 8, 9], [3, 6], [3, 6, 9], [3, 6, 8], [3, 6, 8, 9], [3, 6, 7], [3, 6, 7, 9], [3, 6, 7, 8], [3, 6, 7, 8, 9], [3, 5], [3, 5, 9], [3, 5, 8], [3, 5, 8, 9], [3, 5, 7], [3, 5, 7, 9], [3, 5, 7, 8], [3, 5, 7, 8, 9], [3, 5, 6], [3, 5, 6, 9], [3, 5, 6, 8], [3, 5, 6, 8, 9], [3, 5, 6, 7], [3, 5, 6, 7, 9], [3, 5, 6, 7, 8], [3, 5, 6, 7, 8, 9], [3, 4], [3, 4, 9], [3, 4, 8], [3, 4, 8, 9], [3, 4, 7], [3, 4, 7, 9], [3, 4, 7, 8], [3, 4, 7, 8, 9], [3, 4, 6], [3, 4, 6, 9], [3, 4, 6, 8], [3, 4, 6, 8, 9], [3, 4, 6, 7], [3, 4, 6, 7, 9], [3, 4, 6, 7, 8], [3, 4, 6, 7, 8, 9], [3, 4, 5], [3, 4, 5, 9], [3, 4, 5, 8], [3, 4, 5, 8, 9], [3, 4, 5, 7], [3, 4, 5, 7, 9], [3, 4, 5, 7, 8], [3, 4, 5, 7, 8, 9], [3, 4, 5, 6], [3, 4, 5, 6, 9], [3, 4, 5, 6, 8], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 8, 9], [2], [2, 9], [2, 8], [2, 8, 9], [2, 7], [2, 7, 9], [2, 7, 8], [2, 7, 8, 9], [2, 6], [2, 6, 9], [2, 6, 8], [2, 6, 8, 9], [2, 6, 7], [2, 6, 7, 9], [2, 6, 7, 8], [2, 6, 7, 8, 9], [2, 5], [2, 5, 9], [2, 5, 8], [2, 5, 8, 9], [2, 5, 7], [2, 5, 7, 9], [2, 5, 7, 8], [2, 5, 7, 8, 9], [2, 5, 6], [2, 5, 6, 9], [2, 5, 6, 8], [2, 5, 6, 8, 9], [2, 5, 6, 7], [2, 5, 6, 7, 9], [2, 5, 6, 7, 8], [2, 5, 6, 7, 8, 9], [2, 4], [2, 4, 9], [2, 4, 8], [2, 4, 8, 9], [2, 4, 7], [2, 4, 7, 9], [2, 4, 7, 8], [2, 4, 7, 8, 9], [2, 4, 6], [2, 4, 6, 9], [2, 4, 6, 8], [2, 4, 6, 8, 9], [2, 4, 6, 7], [2, 4, 6, 7, 9], [2, 4, 6, 7, 8], [2, 4, 6, 7, 8, 9], [2, 4, 5], [2, 4, 5, 9], [2, 4, 5, 8], [2, 4, 5, 8, 9], [2, 4, 5, 7], [2, 4, 5, 7, 9], [2, 4, 5, 7, 8], [2, 4, 5, 7, 8, 9], [2, 4, 5, 6], [2, 4, 5, 6, 9], [2, 4, 5, 6, 8], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 7], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 8, 9], [2, 3], [2, 3, 9], [2, 3, 8], [2, 3, 8, 9], [2, 3, 7], [2, 3, 7, 9], [2, 3, 7, 8], [2, 3, 7, 8, 9], [2, 3, 6], [2, 3, 6, 9], [2, 3, 6, 8], [2, 3, 6, 8, 9], [2, 3, 6, 7], [2, 3, 6, 7, 9], [2, 3, 6, 7, 8], [2, 3, 6, 7, 8, 9], [2, 3, 5], [2, 3, 5, 9], [2, 3, 5, 8], [2, 3, 5, 8, 9], [2, 3, 5, 7], [2, 3, 5, 7, 9], [2, 3, 5, 7, 8], [2, 3, 5, 7, 8, 9], [2, 3, 5, 6], [2, 3, 5, 6, 9], [2, 3, 5, 6, 8], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 7], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 8, 9], [2, 3, 4], [2, 3, 4, 9], [2, 3, 4, 8], [2, 3, 4, 8, 9], [2, 3, 4, 7], [2, 3, 4, 7, 9], [2, 3, 4, 7, 8], [2, 3, 4, 7, 8, 9], [2, 3, 4, 6], [2, 3, 4, 6, 9], [2, 3, 4, 6, 8], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 7], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 5], [2, 3, 4, 5, 9], [2, 3, 4, 5, 8], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 7], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 8, 9], [1], [1, 9], [1, 8], [1, 8, 9], [1, 7], [1, 7, 9], [1, 7, 8], [1, 7, 8, 9], [1, 6], [1, 6, 9], [1, 6, 8], [1, 6, 8, 9], [1, 6, 7], [1, 6, 7, 9], [1, 6, 7, 8], [1, 6, 7, 8, 9], [1, 5], [1, 5, 9], [1, 5, 8], [1, 5, 8, 9], [1, 5, 7], [1, 5, 7, 9], [1, 5, 7, 8], [1, 5, 7, 8, 9], [1, 5, 6], [1, 5, 6, 9], [1, 5, 6, 8], [1, 5, 6, 8, 9], [1, 5, 6, 7], [1, 5, 6, 7, 9], [1, 5, 6, 7, 8], [1, 5, 6, 7, 8, 9], [1, 4], [1, 4, 9], [1, 4, 8], [1, 4, 8, 9], [1, 4, 7], [1, 4, 7, 9], [1, 4, 7, 8], [1, 4, 7, 8, 9], [1, 4, 6], [1, 4, 6, 9], [1, 4, 6, 8], [1, 4, 6, 8, 9], [1, 4, 6, 7], [1, 4, 6, 7, 9], [1, 4, 6, 7, 8], [1, 4, 6, 7, 8, 9], [1, 4, 5], [1, 4, 5, 9], [1, 4, 5, 8], [1, 4, 5, 8, 9], [1, 4, 5, 7], [1, 4, 5, 7, 9], [1, 4, 5, 7, 8], [1, 4, 5, 7, 8, 9], [1, 4, 5, 6], [1, 4, 5, 6, 9], [1, 4, 5, 6, 8], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 7], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 8, 9], [1, 3], [1, 3, 9], [1, 3, 8], [1, 3, 8, 9], [1, 3, 7], [1, 3, 7, 9], [1, 3, 7, 8], [1, 3, 7, 8, 9], [1, 3, 6], [1, 3, 6, 9], [1, 3, 6, 8], [1, 3, 6, 8, 9], [1, 3, 6, 7], [1, 3, 6, 7, 9], [1, 3, 6, 7, 8], [1, 3, 6, 7, 8, 9], [1, 3, 5], [1, 3, 5, 9], [1, 3, 5, 8], [1, 3, 5, 8, 9], [1, 3, 5, 7], [1, 3, 5, 7, 9], [1, 3, 5, 7, 8], [1, 3, 5, 7, 8, 9], [1, 3, 5, 6], [1, 3, 5, 6, 9], [1, 3, 5, 6, 8], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 7], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 8, 9], [1, 3, 4], [1, 3, 4, 9], [1, 3, 4, 8], [1, 3, 4, 8, 9], [1, 3, 4, 7], [1, 3, 4, 7, 9], [1, 3, 4, 7, 8], [1, 3, 4, 7, 8, 9], [1, 3, 4, 6], [1, 3, 4, 6, 9], [1, 3, 4, 6, 8], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 7], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 5], [1, 3, 4, 5, 9], [1, 3, 4, 5, 8], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 7], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 6], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 8, 9], [1, 2], [1, 2, 9], [1, 2, 8], [1, 2, 8, 9], [1, 2, 7], [1, 2, 7, 9], [1, 2, 7, 8], [1, 2, 7, 8, 9], [1, 2, 6], [1, 2, 6, 9], [1, 2, 6, 8], [1, 2, 6, 8, 9], [1, 2, 6, 7], [1, 2, 6, 7, 9], [1, 2, 6, 7, 8], [1, 2, 6, 7, 8, 9], [1, 2, 5], [1, 2, 5, 9], [1, 2, 5, 8], [1, 2, 5, 8, 9], [1, 2, 5, 7], [1, 2, 5, 7, 9], [1, 2, 5, 7, 8], [1, 2, 5, 7, 8, 9], [1, 2, 5, 6], [1, 2, 5, 6, 9], [1, 2, 5, 6, 8], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 7], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 8, 9], [1, 2, 4], [1, 2, 4, 9], [1, 2, 4, 8], [1, 2, 4, 8, 9], [1, 2, 4, 7], [1, 2, 4, 7, 9], [1, 2, 4, 7, 8], [1, 2, 4, 7, 8, 9], [1, 2, 4, 6], [1, 2, 4, 6, 9], [1, 2, 4, 6, 8], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 7], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 5], [1, 2, 4, 5, 9], [1, 2, 4, 5, 8], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 7], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 6], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 3], [1, 2, 3, 9], [1, 2, 3, 8], [1, 2, 3, 8, 9], [1, 2, 3, 7], [1, 2, 3, 7, 9], [1, 2, 3, 7, 8], [1, 2, 3, 7, 8, 9], [1, 2, 3, 6], [1, 2, 3, 6, 9], [1, 2, 3, 6, 8], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 7], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 5], [1, 2, 3, 5, 9], [1, 2, 3, 5, 8], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 7], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 6], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 4], [1, 2, 3, 4, 9], [1, 2, 3, 4, 8], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 7], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 6], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8, 9], [0], [0, 9], [0, 8], [0, 8, 9], [0, 7], [0, 7, 9], [0, 7, 8], [0, 7, 8, 9], [0, 6], [0, 6, 9], [0, 6, 8], [0, 6, 8, 9], [0, 6, 7], [0, 6, 7, 9], [0, 6, 7, 8], [0, 6, 7, 8, 9], [0, 5], [0, 5, 9], [0, 5, 8], [0, 5, 8, 9], [0, 5, 7], [0, 5, 7, 9], [0, 5, 7, 8], [0, 5, 7, 8, 9], [0, 5, 6], [0, 5, 6, 9], [0, 5, 6, 8], [0, 5, 6, 8, 9], [0, 5, 6, 7], [0, 5, 6, 7, 9], [0, 5, 6, 7, 8], [0, 5, 6, 7, 8, 9], [0, 4], [0, 4, 9], [0, 4, 8], [0, 4, 8, 9], [0, 4, 7], [0, 4, 7, 9], [0, 4, 7, 8], [0, 4, 7, 8, 9], [0, 4, 6], [0, 4, 6, 9], [0, 4, 6, 8], [0, 4, 6, 8, 9], [0, 4, 6, 7], [0, 4, 6, 7, 9], [0, 4, 6, 7, 8], [0, 4, 6, 7, 8, 9], [0, 4, 5], [0, 4, 5, 9], [0, 4, 5, 8], [0, 4, 5, 8, 9], [0, 4, 5, 7], [0, 4, 5, 7, 9], [0, 4, 5, 7, 8], [0, 4, 5, 7, 8, 9], [0, 4, 5, 6], [0, 4, 5, 6, 9], [0, 4, 5, 6, 8], [0, 4, 5, 6, 8, 9], [0, 4, 5, 6, 7], [0, 4, 5, 6, 7, 9], [0, 4, 5, 6, 7, 8], [0, 4, 5, 6, 7, 8, 9], [0, 3], [0, 3, 9], [0, 3, 8], [0, 3, 8, 9], [0, 3, 7], [0, 3, 7, 9], [0, 3, 7, 8], [0, 3, 7, 8, 9], [0, 3, 6], [0, 3, 6, 9], [0, 3, 6, 8], [0, 3, 6, 8, 9], [0, 3, 6, 7], [0, 3, 6, 7, 9], [0, 3, 6, 7, 8], [0, 3, 6, 7, 8, 9], [0, 3, 5], [0, 3, 5, 9], [0, 3, 5, 8], [0, 3, 5, 8, 9], [0, 3, 5, 7], [0, 3, 5, 7, 9], [0, 3, 5, 7, 8], [0, 3, 5, 7, 8, 9], [0, 3, 5, 6], [0, 3, 5, 6, 9], [0, 3, 5, 6, 8], [0, 3, 5, 6, 8, 9], [0, 3, 5, 6, 7], [0, 3, 5, 6, 7, 9], [0, 3, 5, 6, 7, 8], [0, 3, 5, 6, 7, 8, 9], [0, 3, 4], [0, 3, 4, 9], [0, 3, 4, 8], [0, 3, 4, 8, 9], [0, 3, 4, 7], [0, 3, 4, 7, 9], [0, 3, 4, 7, 8], [0, 3, 4, 7, 8, 9], [0, 3, 4, 6], [0, 3, 4, 6, 9], [0, 3, 4, 6, 8], [0, 3, 4, 6, 8, 9], [0, 3, 4, 6, 7], [0, 3, 4, 6, 7, 9], [0, 3, 4, 6, 7, 8], [0, 3, 4, 6, 7, 8, 9], [0, 3, 4, 5], [0, 3, 4, 5, 9], [0, 3, 4, 5, 8], [0, 3, 4, 5, 8, 9], [0, 3, 4, 5, 7], [0, 3, 4, 5, 7, 9], [0, 3, 4, 5, 7, 8], [0, 3, 4, 5, 7, 8, 9], [0, 3, 4, 5, 6], [0, 3, 4, 5, 6, 9], [0, 3, 4, 5, 6, 8], [0, 3, 4, 5, 6, 8, 9], [0, 3, 4, 5, 6, 7], [0, 3, 4, 5, 6, 7, 9], [0, 3, 4, 5, 6, 7, 8], [0, 3, 4, 5, 6, 7, 8, 9], [0, 2], [0, 2, 9], [0, 2, 8], [0, 2, 8, 9], [0, 2, 7], [0, 2, 7, 9], [0, 2, 7, 8], [0, 2, 7, 8, 9], [0, 2, 6], [0, 2, 6, 9], [0, 2, 6, 8], [0, 2, 6, 8, 9], [0, 2, 6, 7], [0, 2, 6, 7, 9], [0, 2, 6, 7, 8], [0, 2, 6, 7, 8, 9], [0, 2, 5], [0, 2, 5, 9], [0, 2, 5, 8], [0, 2, 5, 8, 9], [0, 2, 5, 7], [0, 2, 5, 7, 9], [0, 2, 5, 7, 8], [0, 2, 5, 7, 8, 9], [0, 2, 5, 6], [0, 2, 5, 6, 9], [0, 2, 5, 6, 8], [0, 2, 5, 6, 8, 9], [0, 2, 5, 6, 7], [0, 2, 5, 6, 7, 9], [0, 2, 5, 6, 7, 8], [0, 2, 5, 6, 7, 8, 9], [0, 2, 4], [0, 2, 4, 9], [0, 2, 4, 8], [0, 2, 4, 8, 9], [0, 2, 4, 7], [0, 2, 4, 7, 9], [0, 2, 4, 7, 8], [0, 2, 4, 7, 8, 9], [0, 2, 4, 6], [0, 2, 4, 6, 9], [0, 2, 4, 6, 8], [0, 2, 4, 6, 8, 9], [0, 2, 4, 6, 7], [0, 2, 4, 6, 7, 9], [0, 2, 4, 6, 7, 8], [0, 2, 4, 6, 7, 8, 9], [0, 2, 4, 5], [0, 2, 4, 5, 9], [0, 2, 4, 5, 8], [0, 2, 4, 5, 8, 9], [0, 2, 4, 5, 7], [0, 2, 4, 5, 7, 9], [0, 2, 4, 5, 7, 8], [0, 2, 4, 5, 7, 8, 9], [0, 2, 4, 5, 6], [0, 2, 4, 5, 6, 9], [0, 2, 4, 5, 6, 8], [0, 2, 4, 5, 6, 8, 9], [0, 2, 4, 5, 6, 7], [0, 2, 4, 5, 6, 7, 9], [0, 2, 4, 5, 6, 7, 8], [0, 2, 4, 5, 6, 7, 8, 9], [0, 2, 3], [0, 2, 3, 9], [0, 2, 3, 8], [0, 2, 3, 8, 9], [0, 2, 3, 7], [0, 2, 3, 7, 9], [0, 2, 3, 7, 8], [0, 2, 3, 7, 8, 9], [0, 2, 3, 6], [0, 2, 3, 6, 9], [0, 2, 3, 6, 8], [0, 2, 3, 6, 8, 9], [0, 2, 3, 6, 7], [0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 8], [0, 2, 3, 6, 7, 8, 9], [0, 2, 3, 5], [0, 2, 3, 5, 9], [0, 2, 3, 5, 8], [0, 2, 3, 5, 8, 9], [0, 2, 3, 5, 7], [0, 2, 3, 5, 7, 9], [0, 2, 3, 5, 7, 8], [0, 2, 3, 5, 7, 8, 9], [0, 2, 3, 5, 6], [0, 2, 3, 5, 6, 9], [0, 2, 3, 5, 6, 8], [0, 2, 3, 5, 6, 8, 9], [0, 2, 3, 5, 6, 7], [0, 2, 3, 5, 6, 7, 9], [0, 2, 3, 5, 6, 7, 8], [0, 2, 3, 5, 6, 7, 8, 9], [0, 2, 3, 4], [0, 2, 3, 4, 9], [0, 2, 3, 4, 8], [0, 2, 3, 4, 8, 9], [0, 2, 3, 4, 7], [0, 2, 3, 4, 7, 9], [0, 2, 3, 4, 7, 8], [0, 2, 3, 4, 7, 8, 9], [0, 2, 3, 4, 6], [0, 2, 3, 4, 6, 9], [0, 2, 3, 4, 6, 8], [0, 2, 3, 4, 6, 8, 9], [0, 2, 3, 4, 6, 7], [0, 2, 3, 4, 6, 7, 9], [0, 2, 3, 4, 6, 7, 8], [0, 2, 3, 4, 6, 7, 8, 9], [0, 2, 3, 4, 5], [0, 2, 3, 4, 5, 9], [0, 2, 3, 4, 5, 8], [0, 2, 3, 4, 5, 8, 9], [0, 2, 3, 4, 5, 7], [0, 2, 3, 4, 5, 7, 9], [0, 2, 3, 4, 5, 7, 8], [0, 2, 3, 4, 5, 7, 8, 9], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 6, 9], [0, 2, 3, 4, 5, 6, 8], [0, 2, 3, 4, 5, 6, 8, 9], [0, 2, 3, 4, 5, 6, 7], [0, 2, 3, 4, 5, 6, 7, 9], [0, 2, 3, 4, 5, 6, 7, 8], [0, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1], [0, 1, 9], [0, 1, 8], [0, 1, 8, 9], [0, 1, 7], [0, 1, 7, 9], [0, 1, 7, 8], [0, 1, 7, 8, 9], [0, 1, 6], [0, 1, 6, 9], [0, 1, 6, 8], [0, 1, 6, 8, 9], [0, 1, 6, 7], [0, 1, 6, 7, 9], [0, 1, 6, 7, 8], [0, 1, 6, 7, 8, 9], [0, 1, 5], [0, 1, 5, 9], [0, 1, 5, 8], [0, 1, 5, 8, 9], [0, 1, 5, 7], [0, 1, 5, 7, 9], [0, 1, 5, 7, 8], [0, 1, 5, 7, 8, 9], [0, 1, 5, 6], [0, 1, 5, 6, 9], [0, 1, 5, 6, 8], [0, 1, 5, 6, 8, 9], [0, 1, 5, 6, 7], [0, 1, 5, 6, 7, 9], [0, 1, 5, 6, 7, 8], [0, 1, 5, 6, 7, 8, 9], [0, 1, 4], [0, 1, 4, 9], [0, 1, 4, 8], [0, 1, 4, 8, 9], [0, 1, 4, 7], [0, 1, 4, 7, 9], [0, 1, 4, 7, 8], [0, 1, 4, 7, 8, 9], [0, 1, 4, 6], [0, 1, 4, 6, 9], [0, 1, 4, 6, 8], [0, 1, 4, 6, 8, 9], [0, 1, 4, 6, 7], [0, 1, 4, 6, 7, 9], [0, 1, 4, 6, 7, 8], [0, 1, 4, 6, 7, 8, 9], [0, 1, 4, 5], [0, 1, 4, 5, 9], [0, 1, 4, 5, 8], [0, 1, 4, 5, 8, 9], [0, 1, 4, 5, 7], [0, 1, 4, 5, 7, 9], [0, 1, 4, 5, 7, 8], [0, 1, 4, 5, 7, 8, 9], [0, 1, 4, 5, 6], [0, 1, 4, 5, 6, 9], [0, 1, 4, 5, 6, 8], [0, 1, 4, 5, 6, 8, 9], [0, 1, 4, 5, 6, 7], [0, 1, 4, 5, 6, 7, 9], [0, 1, 4, 5, 6, 7, 8], [0, 1, 4, 5, 6, 7, 8, 9], [0, 1, 3], [0, 1, 3, 9], [0, 1, 3, 8], [0, 1, 3, 8, 9], [0, 1, 3, 7], [0, 1, 3, 7, 9], [0, 1, 3, 7, 8], [0, 1, 3, 7, 8, 9], [0, 1, 3, 6], [0, 1, 3, 6, 9], [0, 1, 3, 6, 8], [0, 1, 3, 6, 8, 9], [0, 1, 3, 6, 7], [0, 1, 3, 6, 7, 9], [0, 1, 3, 6, 7, 8], [0, 1, 3, 6, 7, 8, 9], [0, 1, 3, 5], [0, 1, 3, 5, 9], [0, 1, 3, 5, 8], [0, 1, 3, 5, 8, 9], [0, 1, 3, 5, 7], [0, 1, 3, 5, 7, 9], [0, 1, 3, 5, 7, 8], [0, 1, 3, 5, 7, 8, 9], [0, 1, 3, 5, 6], [0, 1, 3, 5, 6, 9], [0, 1, 3, 5, 6, 8], [0, 1, 3, 5, 6, 8, 9], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6, 7, 9], [0, 1, 3, 5, 6, 7, 8], [0, 1, 3, 5, 6, 7, 8, 9], [0, 1, 3, 4], [0, 1, 3, 4, 9], [0, 1, 3, 4, 8], [0, 1, 3, 4, 8, 9], [0, 1, 3, 4, 7], [0, 1, 3, 4, 7, 9], [0, 1, 3, 4, 7, 8], [0, 1, 3, 4, 7, 8, 9], [0, 1, 3, 4, 6], [0, 1, 3, 4, 6, 9], [0, 1, 3, 4, 6, 8], [0, 1, 3, 4, 6, 8, 9], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 7, 9], [0, 1, 3, 4, 6, 7, 8], [0, 1, 3, 4, 6, 7, 8, 9], [0, 1, 3, 4, 5], [0, 1, 3, 4, 5, 9], [0, 1, 3, 4, 5, 8], [0, 1, 3, 4, 5, 8, 9], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5, 7, 9], [0, 1, 3, 4, 5, 7, 8], [0, 1, 3, 4, 5, 7, 8, 9], [0, 1, 3, 4, 5, 6], [0, 1, 3, 4, 5, 6, 9], [0, 1, 3, 4, 5, 6, 8], [0, 1, 3, 4, 5, 6, 8, 9], [0, 1, 3, 4, 5, 6, 7], [0, 1, 3, 4, 5, 6, 7, 9], [0, 1, 3, 4, 5, 6, 7, 8], [0, 1, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2], [0, 1, 2, 9], [0, 1, 2, 8], [0, 1, 2, 8, 9], [0, 1, 2, 7], [0, 1, 2, 7, 9], [0, 1, 2, 7, 8], [0, 1, 2, 7, 8, 9], [0, 1, 2, 6], [0, 1, 2, 6, 9], [0, 1, 2, 6, 8], [0, 1, 2, 6, 8, 9], [0, 1, 2, 6, 7], [0, 1, 2, 6, 7, 9], [0, 1, 2, 6, 7, 8], [0, 1, 2, 6, 7, 8, 9], [0, 1, 2, 5], [0, 1, 2, 5, 9], [0, 1, 2, 5, 8], [0, 1, 2, 5, 8, 9], [0, 1, 2, 5, 7], [0, 1, 2, 5, 7, 9], [0, 1, 2, 5, 7, 8], [0, 1, 2, 5, 7, 8, 9], [0, 1, 2, 5, 6], [0, 1, 2, 5, 6, 9], [0, 1, 2, 5, 6, 8], [0, 1, 2, 5, 6, 8, 9], [0, 1, 2, 5, 6, 7], [0, 1, 2, 5, 6, 7, 9], [0, 1, 2, 5, 6, 7, 8], [0, 1, 2, 5, 6, 7, 8, 9], [0, 1, 2, 4], [0, 1, 2, 4, 9], [0, 1, 2, 4, 8], [0, 1, 2, 4, 8, 9], [0, 1, 2, 4, 7], [0, 1, 2, 4, 7, 9], [0, 1, 2, 4, 7, 8], [0, 1, 2, 4, 7, 8, 9], [0, 1, 2, 4, 6], [0, 1, 2, 4, 6, 9], [0, 1, 2, 4, 6, 8], [0, 1, 2, 4, 6, 8, 9], [0, 1, 2, 4, 6, 7], [0, 1, 2, 4, 6, 7, 9], [0, 1, 2, 4, 6, 7, 8], [0, 1, 2, 4, 6, 7, 8, 9], [0, 1, 2, 4, 5], [0, 1, 2, 4, 5, 9], [0, 1, 2, 4, 5, 8], [0, 1, 2, 4, 5, 8, 9], [0, 1, 2, 4, 5, 7], [0, 1, 2, 4, 5, 7, 9], [0, 1, 2, 4, 5, 7, 8], [0, 1, 2, 4, 5, 7, 8, 9], [0, 1, 2, 4, 5, 6], [0, 1, 2, 4, 5, 6, 9], [0, 1, 2, 4, 5, 6, 8], [0, 1, 2, 4, 5, 6, 8, 9], [0, 1, 2, 4, 5, 6, 7], [0, 1, 2, 4, 5, 6, 7, 9], [0, 1, 2, 4, 5, 6, 7, 8], [0, 1, 2, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3], [0, 1, 2, 3, 9], [0, 1, 2, 3, 8], [0, 1, 2, 3, 8, 9], [0, 1, 2, 3, 7], [0, 1, 2, 3, 7, 9], [0, 1, 2, 3, 7, 8], [0, 1, 2, 3, 7, 8, 9], [0, 1, 2, 3, 6], [0, 1, 2, 3, 6, 9], [0, 1, 2, 3, 6, 8], [0, 1, 2, 3, 6, 8, 9], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6, 7, 9], [0, 1, 2, 3, 6, 7, 8], [0, 1, 2, 3, 6, 7, 8, 9], [0, 1, 2, 3, 5], [0, 1, 2, 3, 5, 9], [0, 1, 2, 3, 5, 8], [0, 1, 2, 3, 5, 8, 9], [0, 1, 2, 3, 5, 7], [0, 1, 2, 3, 5, 7, 9], [0, 1, 2, 3, 5, 7, 8], [0, 1, 2, 3, 5, 7, 8, 9], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 6, 9], [0, 1, 2, 3, 5, 6, 8], [0, 1, 2, 3, 5, 6, 8, 9], [0, 1, 2, 3, 5, 6, 7], [0, 1, 2, 3, 5, 6, 7, 9], [0, 1, 2, 3, 5, 6, 7, 8], [0, 1, 2, 3, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 9], [0, 1, 2, 3, 4, 8], [0, 1, 2, 3, 4, 8, 9], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4, 7, 9], [0, 1, 2, 3, 4, 7, 8], [0, 1, 2, 3, 4, 7, 8, 9], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 6, 9], [0, 1, 2, 3, 4, 6, 8], [0, 1, 2, 3, 4, 6, 8, 9], [0, 1, 2, 3, 4, 6, 7], [0, 1, 2, 3, 4, 6, 7, 9], [0, 1, 2, 3, 4, 6, 7, 8], [0, 1, 2, 3, 4, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5, 9], [0, 1, 2, 3, 4, 5, 8], [0, 1, 2, 3, 4, 5, 8, 9], [0, 1, 2, 3, 4, 5, 7], [0, 1, 2, 3, 4, 5, 7, 9], [0, 1, 2, 3, 4, 5, 7, 8], [0, 1, 2, 3, 4, 5, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6, 9], [0, 1, 2, 3, 4, 5, 6, 8], [0, 1, 2, 3, 4, 5, 6, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]\n assert candidate(nums = [-3, 1, 4, -2, 5, -6, 7, -8, 9, -10]) == [[], [-10], [9], [9, -10], [-8], [-8, -10], [-8, 9], [-8, 9, -10], [7], [7, -10], [7, 9], [7, 9, -10], [7, -8], [7, -8, -10], [7, -8, 9], [7, -8, 9, -10], [-6], [-6, -10], [-6, 9], [-6, 9, -10], [-6, -8], [-6, -8, -10], [-6, -8, 9], [-6, -8, 9, -10], [-6, 7], [-6, 7, -10], [-6, 7, 9], [-6, 7, 9, -10], [-6, 7, -8], [-6, 7, -8, -10], [-6, 7, -8, 9], [-6, 7, -8, 9, -10], [5], [5, -10], [5, 9], [5, 9, -10], [5, -8], [5, -8, -10], [5, -8, 9], [5, -8, 9, -10], [5, 7], [5, 7, -10], [5, 7, 9], [5, 7, 9, -10], [5, 7, -8], [5, 7, -8, -10], [5, 7, -8, 9], [5, 7, -8, 9, -10], [5, -6], [5, -6, -10], [5, -6, 9], [5, -6, 9, -10], [5, -6, -8], [5, -6, -8, -10], [5, -6, -8, 9], [5, -6, -8, 9, -10], [5, -6, 7], [5, -6, 7, -10], [5, -6, 7, 9], [5, -6, 7, 9, -10], [5, -6, 7, -8], [5, -6, 7, -8, -10], [5, -6, 7, -8, 9], [5, -6, 7, -8, 9, -10], [-2], [-2, -10], [-2, 9], [-2, 9, -10], [-2, -8], [-2, -8, -10], [-2, -8, 9], [-2, -8, 9, -10], [-2, 7], [-2, 7, -10], [-2, 7, 9], [-2, 7, 9, -10], [-2, 7, -8], [-2, 7, -8, -10], [-2, 7, -8, 9], [-2, 7, -8, 9, -10], [-2, -6], [-2, -6, -10], [-2, -6, 9], [-2, -6, 9, -10], [-2, -6, -8], [-2, -6, -8, -10], [-2, -6, -8, 9], [-2, -6, -8, 9, -10], [-2, -6, 7], [-2, -6, 7, -10], [-2, -6, 7, 9], [-2, -6, 7, 9, -10], [-2, -6, 7, -8], [-2, -6, 7, -8, -10], [-2, -6, 7, -8, 9], [-2, -6, 7, -8, 9, -10], [-2, 5], [-2, 5, -10], [-2, 5, 9], [-2, 5, 9, -10], [-2, 5, -8], [-2, 5, -8, -10], [-2, 5, -8, 9], [-2, 5, -8, 9, -10], [-2, 5, 7], [-2, 5, 7, -10], [-2, 5, 7, 9], [-2, 5, 7, 9, -10], [-2, 5, 7, -8], [-2, 5, 7, -8, -10], [-2, 5, 7, -8, 9], [-2, 5, 7, -8, 9, -10], [-2, 5, -6], [-2, 5, -6, -10], [-2, 5, -6, 9], [-2, 5, -6, 9, -10], [-2, 5, -6, -8], [-2, 5, -6, -8, -10], [-2, 5, -6, -8, 9], [-2, 5, -6, -8, 9, -10], [-2, 5, -6, 7], [-2, 5, -6, 7, -10], [-2, 5, -6, 7, 9], [-2, 5, -6, 7, 9, -10], [-2, 5, -6, 7, -8], [-2, 5, -6, 7, -8, -10], [-2, 5, -6, 7, -8, 9], [-2, 5, -6, 7, -8, 9, -10], [4], [4, -10], [4, 9], [4, 9, -10], [4, -8], [4, -8, -10], [4, -8, 9], [4, -8, 9, -10], [4, 7], [4, 7, -10], [4, 7, 9], [4, 7, 9, -10], [4, 7, -8], [4, 7, -8, -10], [4, 7, -8, 9], [4, 7, -8, 9, -10], [4, -6], [4, -6, -10], [4, -6, 9], [4, -6, 9, -10], [4, -6, -8], [4, -6, -8, -10], [4, -6, -8, 9], [4, -6, -8, 9, -10], [4, -6, 7], [4, -6, 7, -10], [4, -6, 7, 9], [4, -6, 7, 9, -10], [4, -6, 7, -8], [4, -6, 7, -8, -10], [4, -6, 7, -8, 9], [4, -6, 7, -8, 9, -10], [4, 5], [4, 5, -10], [4, 5, 9], [4, 5, 9, -10], [4, 5, -8], [4, 5, -8, -10], [4, 5, -8, 9], [4, 5, -8, 9, -10], [4, 5, 7], [4, 5, 7, -10], [4, 5, 7, 9], [4, 5, 7, 9, -10], [4, 5, 7, -8], [4, 5, 7, -8, -10], [4, 5, 7, -8, 9], [4, 5, 7, -8, 9, -10], [4, 5, -6], [4, 5, -6, -10], [4, 5, -6, 9], [4, 5, -6, 9, -10], [4, 5, -6, -8], [4, 5, -6, -8, -10], [4, 5, -6, -8, 9], [4, 5, -6, -8, 9, -10], [4, 5, -6, 7], [4, 5, -6, 7, -10], [4, 5, -6, 7, 9], [4, 5, -6, 7, 9, -10], [4, 5, -6, 7, -8], [4, 5, -6, 7, -8, -10], [4, 5, -6, 7, -8, 9], [4, 5, -6, 7, -8, 9, -10], [4, -2], [4, -2, -10], [4, -2, 9], [4, -2, 9, -10], [4, -2, -8], [4, -2, -8, -10], [4, -2, -8, 9], [4, -2, -8, 9, -10], [4, -2, 7], [4, -2, 7, -10], [4, -2, 7, 9], [4, -2, 7, 9, -10], [4, -2, 7, -8], [4, -2, 7, -8, -10], [4, -2, 7, -8, 9], [4, -2, 7, -8, 9, -10], [4, -2, -6], [4, -2, -6, -10], [4, -2, -6, 9], [4, -2, -6, 9, -10], [4, -2, -6, -8], [4, -2, -6, -8, -10], [4, -2, -6, -8, 9], [4, -2, -6, -8, 9, -10], [4, -2, -6, 7], [4, -2, -6, 7, -10], [4, -2, -6, 7, 9], [4, -2, -6, 7, 9, -10], [4, -2, -6, 7, -8], [4, -2, -6, 7, -8, -10], [4, -2, -6, 7, -8, 9], [4, -2, -6, 7, -8, 9, -10], [4, -2, 5], [4, -2, 5, -10], [4, -2, 5, 9], [4, -2, 5, 9, -10], [4, -2, 5, -8], [4, -2, 5, -8, -10], [4, -2, 5, -8, 9], [4, -2, 5, -8, 9, -10], [4, -2, 5, 7], [4, -2, 5, 7, -10], [4, -2, 5, 7, 9], [4, -2, 5, 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-8], [-3, 4, -2, 5, -8, -10], [-3, 4, -2, 5, -8, 9], [-3, 4, -2, 5, -8, 9, -10], [-3, 4, -2, 5, 7], [-3, 4, -2, 5, 7, -10], [-3, 4, -2, 5, 7, 9], [-3, 4, -2, 5, 7, 9, -10], [-3, 4, -2, 5, 7, -8], [-3, 4, -2, 5, 7, -8, -10], [-3, 4, -2, 5, 7, -8, 9], [-3, 4, -2, 5, 7, -8, 9, -10], [-3, 4, -2, 5, -6], [-3, 4, -2, 5, -6, -10], [-3, 4, -2, 5, -6, 9], [-3, 4, -2, 5, -6, 9, -10], [-3, 4, -2, 5, -6, -8], [-3, 4, -2, 5, -6, -8, -10], [-3, 4, -2, 5, -6, -8, 9], [-3, 4, -2, 5, -6, -8, 9, -10], [-3, 4, -2, 5, -6, 7], [-3, 4, -2, 5, -6, 7, -10], [-3, 4, -2, 5, -6, 7, 9], [-3, 4, -2, 5, -6, 7, 9, -10], [-3, 4, -2, 5, -6, 7, -8], [-3, 4, -2, 5, -6, 7, -8, -10], [-3, 4, -2, 5, -6, 7, -8, 9], [-3, 4, -2, 5, -6, 7, -8, 9, -10], [-3, 1], [-3, 1, -10], [-3, 1, 9], [-3, 1, 9, -10], [-3, 1, -8], [-3, 1, -8, -10], [-3, 1, -8, 9], [-3, 1, -8, 9, -10], [-3, 1, 7], [-3, 1, 7, -10], [-3, 1, 7, 9], [-3, 1, 7, 9, -10], [-3, 1, 7, -8], [-3, 1, 7, -8, -10], [-3, 1, 7, -8, 9], [-3, 1, 7, -8, 9, -10], [-3, 1, -6], [-3, 1, -6, -10], [-3, 1, -6, 9], [-3, 1, -6, 9, -10], [-3, 1, -6, -8], [-3, 1, -6, -8, -10], [-3, 1, -6, -8, 9], [-3, 1, -6, -8, 9, -10], [-3, 1, -6, 7], [-3, 1, -6, 7, -10], [-3, 1, -6, 7, 9], [-3, 1, -6, 7, 9, -10], [-3, 1, -6, 7, -8], [-3, 1, -6, 7, -8, -10], [-3, 1, -6, 7, -8, 9], [-3, 1, -6, 7, -8, 9, -10], [-3, 1, 5], [-3, 1, 5, -10], [-3, 1, 5, 9], [-3, 1, 5, 9, -10], [-3, 1, 5, -8], [-3, 1, 5, -8, -10], [-3, 1, 5, -8, 9], [-3, 1, 5, -8, 9, -10], [-3, 1, 5, 7], [-3, 1, 5, 7, -10], [-3, 1, 5, 7, 9], [-3, 1, 5, 7, 9, -10], [-3, 1, 5, 7, -8], [-3, 1, 5, 7, -8, -10], [-3, 1, 5, 7, -8, 9], [-3, 1, 5, 7, -8, 9, -10], [-3, 1, 5, -6], [-3, 1, 5, -6, -10], [-3, 1, 5, -6, 9], [-3, 1, 5, -6, 9, -10], [-3, 1, 5, -6, -8], [-3, 1, 5, -6, -8, -10], [-3, 1, 5, -6, -8, 9], [-3, 1, 5, -6, -8, 9, -10], [-3, 1, 5, -6, 7], [-3, 1, 5, -6, 7, -10], [-3, 1, 5, -6, 7, 9], [-3, 1, 5, -6, 7, 9, -10], [-3, 1, 5, -6, 7, -8], [-3, 1, 5, -6, 7, -8, -10], [-3, 1, 5, -6, 7, -8, 9], [-3, 1, 5, -6, 7, -8, 9, -10], [-3, 1, -2], [-3, 1, -2, -10], [-3, 1, -2, 9], [-3, 1, -2, 9, -10], [-3, 1, -2, -8], [-3, 1, -2, -8, -10], [-3, 1, -2, -8, 9], [-3, 1, -2, -8, 9, -10], [-3, 1, -2, 7], [-3, 1, -2, 7, -10], [-3, 1, -2, 7, 9], [-3, 1, -2, 7, 9, -10], [-3, 1, -2, 7, -8], [-3, 1, -2, 7, -8, -10], [-3, 1, -2, 7, -8, 9], [-3, 1, -2, 7, -8, 9, -10], [-3, 1, -2, -6], [-3, 1, -2, -6, -10], [-3, 1, -2, -6, 9], [-3, 1, -2, -6, 9, -10], [-3, 1, -2, -6, -8], [-3, 1, -2, -6, -8, -10], [-3, 1, -2, -6, -8, 9], [-3, 1, -2, -6, -8, 9, -10], [-3, 1, -2, -6, 7], [-3, 1, -2, -6, 7, -10], [-3, 1, -2, -6, 7, 9], [-3, 1, -2, -6, 7, 9, -10], [-3, 1, -2, -6, 7, -8], [-3, 1, -2, -6, 7, -8, -10], [-3, 1, -2, -6, 7, -8, 9], [-3, 1, -2, -6, 7, -8, 9, -10], [-3, 1, -2, 5], [-3, 1, -2, 5, -10], [-3, 1, -2, 5, 9], [-3, 1, -2, 5, 9, -10], [-3, 1, -2, 5, -8], [-3, 1, -2, 5, -8, -10], [-3, 1, -2, 5, -8, 9], [-3, 1, -2, 5, -8, 9, -10], [-3, 1, -2, 5, 7], [-3, 1, -2, 5, 7, -10], [-3, 1, -2, 5, 7, 9], [-3, 1, -2, 5, 7, 9, -10], [-3, 1, -2, 5, 7, -8], [-3, 1, -2, 5, 7, -8, -10], [-3, 1, -2, 5, 7, -8, 9], [-3, 1, -2, 5, 7, -8, 9, -10], [-3, 1, -2, 5, -6], [-3, 1, -2, 5, -6, -10], [-3, 1, -2, 5, -6, 9], [-3, 1, -2, 5, -6, 9, -10], [-3, 1, -2, 5, -6, -8], [-3, 1, -2, 5, -6, -8, -10], [-3, 1, -2, 5, -6, -8, 9], [-3, 1, -2, 5, -6, -8, 9, -10], [-3, 1, -2, 5, -6, 7], [-3, 1, -2, 5, -6, 7, -10], [-3, 1, -2, 5, -6, 7, 9], [-3, 1, -2, 5, -6, 7, 9, -10], [-3, 1, -2, 5, -6, 7, -8], [-3, 1, -2, 5, -6, 7, -8, -10], [-3, 1, -2, 5, -6, 7, -8, 9], [-3, 1, -2, 5, -6, 7, -8, 9, -10], [-3, 1, 4], [-3, 1, 4, -10], [-3, 1, 4, 9], [-3, 1, 4, 9, -10], [-3, 1, 4, -8], [-3, 1, 4, -8, -10], [-3, 1, 4, -8, 9], [-3, 1, 4, -8, 9, -10], [-3, 1, 4, 7], [-3, 1, 4, 7, -10], [-3, 1, 4, 7, 9], [-3, 1, 4, 7, 9, -10], [-3, 1, 4, 7, -8], [-3, 1, 4, 7, -8, -10], [-3, 1, 4, 7, -8, 9], [-3, 1, 4, 7, -8, 9, -10], [-3, 1, 4, -6], [-3, 1, 4, -6, -10], [-3, 1, 4, -6, 9], [-3, 1, 4, -6, 9, -10], [-3, 1, 4, -6, -8], [-3, 1, 4, -6, -8, -10], [-3, 1, 4, -6, -8, 9], [-3, 1, 4, -6, -8, 9, -10], [-3, 1, 4, -6, 7], [-3, 1, 4, -6, 7, -10], [-3, 1, 4, -6, 7, 9], [-3, 1, 4, -6, 7, 9, -10], [-3, 1, 4, -6, 7, -8], [-3, 1, 4, -6, 7, -8, -10], [-3, 1, 4, -6, 7, -8, 9], [-3, 1, 4, -6, 7, -8, 9, -10], [-3, 1, 4, 5], [-3, 1, 4, 5, -10], [-3, 1, 4, 5, 9], [-3, 1, 4, 5, 9, -10], [-3, 1, 4, 5, -8], [-3, 1, 4, 5, -8, -10], [-3, 1, 4, 5, -8, 9], [-3, 1, 4, 5, -8, 9, -10], [-3, 1, 4, 5, 7], [-3, 1, 4, 5, 7, -10], [-3, 1, 4, 5, 7, 9], [-3, 1, 4, 5, 7, 9, -10], [-3, 1, 4, 5, 7, -8], [-3, 1, 4, 5, 7, -8, -10], [-3, 1, 4, 5, 7, -8, 9], [-3, 1, 4, 5, 7, -8, 9, -10], [-3, 1, 4, 5, -6], [-3, 1, 4, 5, -6, -10], [-3, 1, 4, 5, -6, 9], [-3, 1, 4, 5, -6, 9, -10], [-3, 1, 4, 5, -6, -8], [-3, 1, 4, 5, -6, -8, -10], [-3, 1, 4, 5, -6, -8, 9], [-3, 1, 4, 5, -6, -8, 9, -10], [-3, 1, 4, 5, -6, 7], [-3, 1, 4, 5, -6, 7, -10], [-3, 1, 4, 5, -6, 7, 9], [-3, 1, 4, 5, -6, 7, 9, -10], [-3, 1, 4, 5, -6, 7, -8], [-3, 1, 4, 5, -6, 7, -8, -10], [-3, 1, 4, 5, -6, 7, -8, 9], [-3, 1, 4, 5, -6, 7, -8, 9, -10], [-3, 1, 4, -2], [-3, 1, 4, -2, -10], [-3, 1, 4, -2, 9], [-3, 1, 4, -2, 9, -10], [-3, 1, 4, -2, -8], [-3, 1, 4, -2, -8, -10], [-3, 1, 4, -2, -8, 9], [-3, 1, 4, -2, -8, 9, -10], [-3, 1, 4, -2, 7], [-3, 1, 4, -2, 7, -10], [-3, 1, 4, -2, 7, 9], [-3, 1, 4, -2, 7, 9, -10], [-3, 1, 4, -2, 7, -8], [-3, 1, 4, -2, 7, -8, -10], [-3, 1, 4, -2, 7, -8, 9], [-3, 1, 4, -2, 7, -8, 9, -10], [-3, 1, 4, -2, -6], [-3, 1, 4, -2, -6, -10], [-3, 1, 4, -2, -6, 9], [-3, 1, 4, -2, -6, 9, -10], [-3, 1, 4, -2, -6, -8], [-3, 1, 4, -2, -6, -8, -10], [-3, 1, 4, -2, -6, -8, 9], [-3, 1, 4, -2, -6, -8, 9, -10], [-3, 1, 4, -2, -6, 7], [-3, 1, 4, -2, -6, 7, -10], [-3, 1, 4, -2, -6, 7, 9], [-3, 1, 4, -2, -6, 7, 9, -10], [-3, 1, 4, -2, -6, 7, -8], [-3, 1, 4, -2, -6, 7, -8, -10], [-3, 1, 4, -2, -6, 7, -8, 9], [-3, 1, 4, -2, -6, 7, -8, 9, -10], [-3, 1, 4, -2, 5], [-3, 1, 4, -2, 5, -10], [-3, 1, 4, -2, 5, 9], [-3, 1, 4, -2, 5, 9, -10], [-3, 1, 4, -2, 5, -8], [-3, 1, 4, -2, 5, -8, -10], [-3, 1, 4, -2, 5, -8, 9], [-3, 1, 4, -2, 5, -8, 9, -10], [-3, 1, 4, -2, 5, 7], [-3, 1, 4, -2, 5, 7, -10], [-3, 1, 4, -2, 5, 7, 9], [-3, 1, 4, -2, 5, 7, 9, -10], [-3, 1, 4, -2, 5, 7, -8], [-3, 1, 4, -2, 5, 7, -8, -10], [-3, 1, 4, -2, 5, 7, -8, 9], [-3, 1, 4, -2, 5, 7, -8, 9, -10], [-3, 1, 4, -2, 5, -6], [-3, 1, 4, -2, 5, -6, -10], [-3, 1, 4, -2, 5, -6, 9], [-3, 1, 4, -2, 5, -6, 9, -10], [-3, 1, 4, -2, 5, -6, -8], [-3, 1, 4, -2, 5, -6, -8, -10], [-3, 1, 4, -2, 5, -6, -8, 9], [-3, 1, 4, -2, 5, -6, -8, 9, -10], [-3, 1, 4, -2, 5, -6, 7], [-3, 1, 4, -2, 5, -6, 7, -10], [-3, 1, 4, -2, 5, -6, 7, 9], [-3, 1, 4, -2, 5, -6, 7, 9, -10], [-3, 1, 4, -2, 5, -6, 7, -8], [-3, 1, 4, -2, 5, -6, 7, -8, -10], [-3, 1, 4, -2, 5, -6, 7, -8, 9], [-3, 1, 4, -2, 5, -6, 7, -8, 9, -10]]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [[], [-10], [-9], [-9, -10], [-8], [-8, -10], [-8, -9], [-8, -9, -10], [-7], [-7, -10], [-7, -9], [-7, -9, -10], [-7, -8], [-7, -8, -10], [-7, -8, -9], [-7, -8, -9, -10], [-6], [-6, -10], [-6, -9], [-6, -9, -10], [-6, -8], [-6, -8, -10], [-6, -8, -9], [-6, -8, -9, -10], [-6, -7], [-6, -7, -10], [-6, -7, -9], [-6, -7, -9, -10], [-6, -7, -8], [-6, -7, -8, -10], [-6, -7, -8, -9], [-6, -7, -8, -9, -10], [-5], [-5, -10], [-5, -9], [-5, -9, -10], [-5, -8], [-5, -8, -10], [-5, -8, -9], [-5, -8, -9, -10], [-5, -7], [-5, -7, -10], [-5, -7, -9], [-5, -7, -9, -10], [-5, -7, -8], [-5, -7, -8, -10], [-5, -7, -8, -9], [-5, -7, -8, -9, -10], [-5, -6], [-5, -6, -10], [-5, -6, -9], [-5, -6, -9, -10], [-5, -6, -8], [-5, -6, -8, -10], [-5, -6, -8, -9], [-5, -6, -8, -9, -10], [-5, -6, -7], [-5, -6, -7, -10], [-5, -6, -7, -9], [-5, -6, -7, -9, -10], [-5, -6, -7, -8], [-5, -6, -7, -8, -10], [-5, -6, -7, -8, -9], [-5, -6, -7, -8, -9, -10], [-4], [-4, -10], [-4, -9], [-4, -9, -10], [-4, -8], [-4, -8, -10], [-4, -8, -9], [-4, -8, -9, -10], [-4, -7], [-4, -7, -10], [-4, -7, -9], [-4, -7, -9, -10], [-4, -7, -8], [-4, -7, -8, -10], [-4, -7, -8, -9], [-4, -7, -8, -9, -10], [-4, -6], [-4, -6, 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-3, -4, -9, -10], [-1, -2, -3, -4, -8], [-1, -2, -3, -4, -8, -10], [-1, -2, -3, -4, -8, -9], [-1, -2, -3, -4, -8, -9, -10], [-1, -2, -3, -4, -7], [-1, -2, -3, -4, -7, -10], [-1, -2, -3, -4, -7, -9], [-1, -2, -3, -4, -7, -9, -10], [-1, -2, -3, -4, -7, -8], [-1, -2, -3, -4, -7, -8, -10], [-1, -2, -3, -4, -7, -8, -9], [-1, -2, -3, -4, -7, -8, -9, -10], [-1, -2, -3, -4, -6], [-1, -2, -3, -4, -6, -10], [-1, -2, -3, -4, -6, -9], [-1, -2, -3, -4, -6, -9, -10], [-1, -2, -3, -4, -6, -8], [-1, -2, -3, -4, -6, -8, -10], [-1, -2, -3, -4, -6, -8, -9], [-1, -2, -3, -4, -6, -8, -9, -10], [-1, -2, -3, -4, -6, -7], [-1, -2, -3, -4, -6, -7, -10], [-1, -2, -3, -4, -6, -7, -9], [-1, -2, -3, -4, -6, -7, -9, -10], [-1, -2, -3, -4, -6, -7, -8], [-1, -2, -3, -4, -6, -7, -8, -10], [-1, -2, -3, -4, -6, -7, -8, -9], [-1, -2, -3, -4, -6, -7, -8, -9, -10], [-1, -2, -3, -4, -5], [-1, -2, -3, -4, -5, -10], [-1, -2, -3, -4, -5, -9], [-1, -2, -3, -4, -5, -9, -10], [-1, -2, -3, -4, -5, -8], [-1, -2, -3, -4, -5, -8, -10], [-1, -2, -3, -4, -5, -8, -9], [-1, -2, -3, -4, -5, -8, -9, -10], [-1, -2, -3, -4, -5, -7], [-1, -2, -3, -4, -5, -7, -10], [-1, -2, -3, -4, -5, -7, -9], [-1, -2, -3, -4, -5, -7, -9, -10], [-1, -2, -3, -4, -5, -7, -8], [-1, -2, -3, -4, -5, -7, -8, -10], [-1, -2, -3, -4, -5, -7, -8, -9], [-1, -2, -3, -4, -5, -7, -8, -9, -10], [-1, -2, -3, -4, -5, -6], [-1, -2, -3, -4, -5, -6, -10], [-1, -2, -3, -4, -5, -6, -9], [-1, -2, -3, -4, -5, -6, -9, -10], [-1, -2, -3, -4, -5, -6, -8], [-1, -2, -3, -4, -5, -6, -8, -10], [-1, -2, -3, -4, -5, -6, -8, -9], [-1, -2, -3, -4, -5, -6, -8, -9, -10], [-1, -2, -3, -4, -5, -6, -7], [-1, -2, -3, -4, -5, -6, -7, -10], [-1, -2, -3, -4, -5, -6, -7, -9], [-1, -2, -3, -4, -5, -6, -7, -9, -10], [-1, -2, -3, -4, -5, -6, -7, -8], [-1, -2, -3, -4, -5, -6, -7, -8, -10], [-1, -2, -3, -4, -5, -6, -7, -8, -9], [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]]\n assert candidate(nums = [-3, -1, 2, 4, 6, 8]) == [[], [8], [6], [6, 8], [4], [4, 8], [4, 6], [4, 6, 8], [2], [2, 8], [2, 6], [2, 6, 8], [2, 4], [2, 4, 8], [2, 4, 6], [2, 4, 6, 8], [-1], [-1, 8], [-1, 6], [-1, 6, 8], [-1, 4], [-1, 4, 8], [-1, 4, 6], [-1, 4, 6, 8], [-1, 2], [-1, 2, 8], [-1, 2, 6], [-1, 2, 6, 8], [-1, 2, 4], [-1, 2, 4, 8], [-1, 2, 4, 6], [-1, 2, 4, 6, 8], [-3], [-3, 8], [-3, 6], [-3, 6, 8], [-3, 4], [-3, 4, 8], [-3, 4, 6], [-3, 4, 6, 8], [-3, 2], [-3, 2, 8], [-3, 2, 6], [-3, 2, 6, 8], [-3, 2, 4], [-3, 2, 4, 8], [-3, 2, 4, 6], [-3, 2, 4, 6, 8], [-3, -1], [-3, -1, 8], [-3, -1, 6], [-3, -1, 6, 8], [-3, -1, 4], [-3, -1, 4, 8], [-3, -1, 4, 6], [-3, -1, 4, 6, 8], [-3, -1, 2], [-3, -1, 2, 8], [-3, -1, 2, 6], [-3, -1, 2, 6, 8], [-3, -1, 2, 4], [-3, -1, 2, 4, 8], [-3, -1, 2, 4, 6], [-3, -1, 2, 4, 6, 8]]\n assert candidate(nums = [-1, 0, 1, 2, 3]) == [[], [3], [2], [2, 3], [1], [1, 3], [1, 2], [1, 2, 3], [0], [0, 3], [0, 2], [0, 2, 3], [0, 1], [0, 1, 3], [0, 1, 2], [0, 1, 2, 3], [-1], [-1, 3], [-1, 2], [-1, 2, 3], [-1, 1], [-1, 1, 3], [-1, 1, 2], [-1, 1, 2, 3], [-1, 0], [-1, 0, 3], [-1, 0, 2], [-1, 0, 2, 3], [-1, 0, 1], [-1, 0, 1, 3], [-1, 0, 1, 2], [-1, 0, 1, 2, 3]]\n assert candidate(nums = [5, 4, 3, 2, 1]) == [[], [1], [2], [2, 1], [3], [3, 1], [3, 2], [3, 2, 1], [4], [4, 1], [4, 2], [4, 2, 1], [4, 3], [4, 3, 1], [4, 3, 2], [4, 3, 2, 1], [5], [5, 1], [5, 2], [5, 2, 1], [5, 3], [5, 3, 1], [5, 3, 2], [5, 3, 2, 1], [5, 4], [5, 4, 1], [5, 4, 2], [5, 4, 2, 1], [5, 4, 3], [5, 4, 3, 1], [5, 4, 3, 2], [5, 4, 3, 2, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [[], [10], [9], [9, 10], [8], [8, 10], [8, 9], [8, 9, 10], [7], [7, 10], [7, 9], [7, 9, 10], [7, 8], [7, 8, 10], [7, 8, 9], [7, 8, 9, 10], [6], [6, 10], [6, 9], [6, 9, 10], [6, 8], [6, 8, 10], [6, 8, 9], [6, 8, 9, 10], [6, 7], [6, 7, 10], [6, 7, 9], [6, 7, 9, 10], [6, 7, 8], [6, 7, 8, 10], [6, 7, 8, 9], [6, 7, 8, 9, 10], [5], [5, 10], [5, 9], [5, 9, 10], [5, 8], [5, 8, 10], [5, 8, 9], [5, 8, 9, 10], [5, 7], [5, 7, 10], [5, 7, 9], [5, 7, 9, 10], [5, 7, 8], [5, 7, 8, 10], [5, 7, 8, 9], [5, 7, 8, 9, 10], [5, 6], [5, 6, 10], [5, 6, 9], [5, 6, 9, 10], [5, 6, 8], [5, 6, 8, 10], [5, 6, 8, 9], [5, 6, 8, 9, 10], [5, 6, 7], [5, 6, 7, 10], [5, 6, 7, 9], [5, 6, 7, 9, 10], [5, 6, 7, 8], [5, 6, 7, 8, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 9, 10], [4], [4, 10], [4, 9], [4, 9, 10], [4, 8], [4, 8, 10], [4, 8, 9], [4, 8, 9, 10], [4, 7], [4, 7, 10], [4, 7, 9], [4, 7, 9, 10], [4, 7, 8], [4, 7, 8, 10], [4, 7, 8, 9], [4, 7, 8, 9, 10], [4, 6], [4, 6, 10], [4, 6, 9], [4, 6, 9, 10], [4, 6, 8], [4, 6, 8, 10], [4, 6, 8, 9], [4, 6, 8, 9, 10], [4, 6, 7], [4, 6, 7, 10], [4, 6, 7, 9], [4, 6, 7, 9, 10], [4, 6, 7, 8], [4, 6, 7, 8, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 9, 10], [4, 5], [4, 5, 10], [4, 5, 9], [4, 5, 9, 10], [4, 5, 8], [4, 5, 8, 10], [4, 5, 8, 9], [4, 5, 8, 9, 10], [4, 5, 7], [4, 5, 7, 10], [4, 5, 7, 9], [4, 5, 7, 9, 10], [4, 5, 7, 8], [4, 5, 7, 8, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 9, 10], [4, 5, 6], [4, 5, 6, 10], [4, 5, 6, 9], [4, 5, 6, 9, 10], [4, 5, 6, 8], [4, 5, 6, 8, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 9, 10], [4, 5, 6, 7], [4, 5, 6, 7, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 9, 10], [3], [3, 10], [3, 9], [3, 9, 10], [3, 8], [3, 8, 10], [3, 8, 9], [3, 8, 9, 10], [3, 7], [3, 7, 10], [3, 7, 9], [3, 7, 9, 10], [3, 7, 8], [3, 7, 8, 10], [3, 7, 8, 9], [3, 7, 8, 9, 10], [3, 6], [3, 6, 10], [3, 6, 9], [3, 6, 9, 10], [3, 6, 8], [3, 6, 8, 10], [3, 6, 8, 9], [3, 6, 8, 9, 10], [3, 6, 7], [3, 6, 7, 10], [3, 6, 7, 9], [3, 6, 7, 9, 10], [3, 6, 7, 8], [3, 6, 7, 8, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 9, 10], [3, 5], [3, 5, 10], [3, 5, 9], [3, 5, 9, 10], [3, 5, 8], [3, 5, 8, 10], [3, 5, 8, 9], [3, 5, 8, 9, 10], [3, 5, 7], [3, 5, 7, 10], [3, 5, 7, 9], [3, 5, 7, 9, 10], [3, 5, 7, 8], [3, 5, 7, 8, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 9, 10], [3, 5, 6], [3, 5, 6, 10], [3, 5, 6, 9], [3, 5, 6, 9, 10], [3, 5, 6, 8], [3, 5, 6, 8, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 9, 10], [3, 5, 6, 7], [3, 5, 6, 7, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 9, 10], [3, 4], [3, 4, 10], [3, 4, 9], [3, 4, 9, 10], [3, 4, 8], [3, 4, 8, 10], [3, 4, 8, 9], [3, 4, 8, 9, 10], [3, 4, 7], [3, 4, 7, 10], [3, 4, 7, 9], [3, 4, 7, 9, 10], [3, 4, 7, 8], [3, 4, 7, 8, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 9, 10], [3, 4, 6], [3, 4, 6, 10], [3, 4, 6, 9], [3, 4, 6, 9, 10], [3, 4, 6, 8], [3, 4, 6, 8, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 9, 10], [3, 4, 6, 7], [3, 4, 6, 7, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 9, 10], [3, 4, 5], [3, 4, 5, 10], [3, 4, 5, 9], [3, 4, 5, 9, 10], [3, 4, 5, 8], [3, 4, 5, 8, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 9, 10], [3, 4, 5, 7], [3, 4, 5, 7, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 6], [3, 4, 5, 6, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 8], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 9, 10], [2], [2, 10], [2, 9], [2, 9, 10], [2, 8], [2, 8, 10], [2, 8, 9], [2, 8, 9, 10], [2, 7], [2, 7, 10], [2, 7, 9], [2, 7, 9, 10], [2, 7, 8], [2, 7, 8, 10], [2, 7, 8, 9], [2, 7, 8, 9, 10], [2, 6], [2, 6, 10], [2, 6, 9], [2, 6, 9, 10], [2, 6, 8], [2, 6, 8, 10], [2, 6, 8, 9], [2, 6, 8, 9, 10], [2, 6, 7], [2, 6, 7, 10], [2, 6, 7, 9], [2, 6, 7, 9, 10], [2, 6, 7, 8], [2, 6, 7, 8, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 9, 10], [2, 5], [2, 5, 10], [2, 5, 9], [2, 5, 9, 10], [2, 5, 8], [2, 5, 8, 10], [2, 5, 8, 9], [2, 5, 8, 9, 10], [2, 5, 7], [2, 5, 7, 10], [2, 5, 7, 9], [2, 5, 7, 9, 10], [2, 5, 7, 8], [2, 5, 7, 8, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 9, 10], [2, 5, 6], [2, 5, 6, 10], [2, 5, 6, 9], [2, 5, 6, 9, 10], [2, 5, 6, 8], [2, 5, 6, 8, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 9, 10], [2, 5, 6, 7], [2, 5, 6, 7, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 9, 10], [2, 4], [2, 4, 10], [2, 4, 9], [2, 4, 9, 10], [2, 4, 8], [2, 4, 8, 10], [2, 4, 8, 9], [2, 4, 8, 9, 10], [2, 4, 7], [2, 4, 7, 10], [2, 4, 7, 9], [2, 4, 7, 9, 10], [2, 4, 7, 8], [2, 4, 7, 8, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 9, 10], [2, 4, 6], [2, 4, 6, 10], [2, 4, 6, 9], [2, 4, 6, 9, 10], [2, 4, 6, 8], [2, 4, 6, 8, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 9, 10], [2, 4, 6, 7], [2, 4, 6, 7, 10], [2, 4, 6, 7, 9], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 8], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 9, 10], [2, 4, 5], [2, 4, 5, 10], [2, 4, 5, 9], [2, 4, 5, 9, 10], [2, 4, 5, 8], [2, 4, 5, 8, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 9, 10], [2, 4, 5, 7], [2, 4, 5, 7, 10], [2, 4, 5, 7, 9], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 8], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 9, 10], [2, 4, 5, 6], [2, 4, 5, 6, 10], [2, 4, 5, 6, 9], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 8], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 6, 7], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 9, 10], [2, 3], [2, 3, 10], [2, 3, 9], [2, 3, 9, 10], [2, 3, 8], [2, 3, 8, 10], [2, 3, 8, 9], [2, 3, 8, 9, 10], [2, 3, 7], [2, 3, 7, 10], [2, 3, 7, 9], [2, 3, 7, 9, 10], [2, 3, 7, 8], [2, 3, 7, 8, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 9, 10], [2, 3, 6], [2, 3, 6, 10], [2, 3, 6, 9], [2, 3, 6, 9, 10], [2, 3, 6, 8], [2, 3, 6, 8, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 9, 10], [2, 3, 6, 7], [2, 3, 6, 7, 10], [2, 3, 6, 7, 9], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 8], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 9, 10], [2, 3, 5], [2, 3, 5, 10], [2, 3, 5, 9], [2, 3, 5, 9, 10], [2, 3, 5, 8], [2, 3, 5, 8, 10], [2, 3, 5, 8, 9], [2, 3, 5, 8, 9, 10], [2, 3, 5, 7], [2, 3, 5, 7, 10], [2, 3, 5, 7, 9], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 8], [2, 3, 5, 7, 8, 10], [2, 3, 5, 7, 8, 9], [2, 3, 5, 7, 8, 9, 10], [2, 3, 5, 6], [2, 3, 5, 6, 10], [2, 3, 5, 6, 9], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 8], [2, 3, 5, 6, 8, 10], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 8, 9, 10], [2, 3, 5, 6, 7], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 8, 10], [2, 3, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 9, 10], [2, 3, 4], [2, 3, 4, 10], [2, 3, 4, 9], [2, 3, 4, 9, 10], [2, 3, 4, 8], [2, 3, 4, 8, 10], [2, 3, 4, 8, 9], [2, 3, 4, 8, 9, 10], [2, 3, 4, 7], [2, 3, 4, 7, 10], [2, 3, 4, 7, 9], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 8], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 9, 10], [2, 3, 4, 6], [2, 3, 4, 6, 10], [2, 3, 4, 6, 9], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 8], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 9, 10], [2, 3, 4, 6, 7], [2, 3, 4, 6, 7, 10], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 9, 10], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 8, 10], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 6, 7, 8, 9, 10], [2, 3, 4, 5], [2, 3, 4, 5, 10], [2, 3, 4, 5, 9], [2, 3, 4, 5, 9, 10], [2, 3, 4, 5, 8], [2, 3, 4, 5, 8, 10], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 8, 9, 10], [2, 3, 4, 5, 7], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 9, 10], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 8, 10], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 7, 8, 9, 10], [2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 9, 10], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 8, 10], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 8, 9, 10], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 7, 10], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 9, 10], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 8, 10], [2, 3, 4, 5, 6, 7, 8, 9], [2, 3, 4, 5, 6, 7, 8, 9, 10], [1], [1, 10], [1, 9], [1, 9, 10], [1, 8], [1, 8, 10], [1, 8, 9], [1, 8, 9, 10], [1, 7], [1, 7, 10], [1, 7, 9], [1, 7, 9, 10], [1, 7, 8], [1, 7, 8, 10], [1, 7, 8, 9], [1, 7, 8, 9, 10], [1, 6], [1, 6, 10], [1, 6, 9], [1, 6, 9, 10], [1, 6, 8], [1, 6, 8, 10], [1, 6, 8, 9], [1, 6, 8, 9, 10], [1, 6, 7], [1, 6, 7, 10], [1, 6, 7, 9], [1, 6, 7, 9, 10], [1, 6, 7, 8], [1, 6, 7, 8, 10], [1, 6, 7, 8, 9], [1, 6, 7, 8, 9, 10], [1, 5], [1, 5, 10], [1, 5, 9], [1, 5, 9, 10], [1, 5, 8], [1, 5, 8, 10], [1, 5, 8, 9], [1, 5, 8, 9, 10], [1, 5, 7], [1, 5, 7, 10], [1, 5, 7, 9], [1, 5, 7, 9, 10], [1, 5, 7, 8], [1, 5, 7, 8, 10], [1, 5, 7, 8, 9], [1, 5, 7, 8, 9, 10], [1, 5, 6], [1, 5, 6, 10], [1, 5, 6, 9], [1, 5, 6, 9, 10], [1, 5, 6, 8], [1, 5, 6, 8, 10], [1, 5, 6, 8, 9], [1, 5, 6, 8, 9, 10], [1, 5, 6, 7], [1, 5, 6, 7, 10], [1, 5, 6, 7, 9], [1, 5, 6, 7, 9, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 9, 10], [1, 4], [1, 4, 10], [1, 4, 9], [1, 4, 9, 10], [1, 4, 8], [1, 4, 8, 10], [1, 4, 8, 9], [1, 4, 8, 9, 10], [1, 4, 7], [1, 4, 7, 10], [1, 4, 7, 9], [1, 4, 7, 9, 10], [1, 4, 7, 8], [1, 4, 7, 8, 10], [1, 4, 7, 8, 9], [1, 4, 7, 8, 9, 10], [1, 4, 6], [1, 4, 6, 10], [1, 4, 6, 9], [1, 4, 6, 9, 10], [1, 4, 6, 8], [1, 4, 6, 8, 10], [1, 4, 6, 8, 9], [1, 4, 6, 8, 9, 10], [1, 4, 6, 7], [1, 4, 6, 7, 10], [1, 4, 6, 7, 9], [1, 4, 6, 7, 9, 10], [1, 4, 6, 7, 8], [1, 4, 6, 7, 8, 10], [1, 4, 6, 7, 8, 9], [1, 4, 6, 7, 8, 9, 10], [1, 4, 5], [1, 4, 5, 10], [1, 4, 5, 9], [1, 4, 5, 9, 10], [1, 4, 5, 8], [1, 4, 5, 8, 10], [1, 4, 5, 8, 9], [1, 4, 5, 8, 9, 10], [1, 4, 5, 7], [1, 4, 5, 7, 10], [1, 4, 5, 7, 9], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 8], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 9, 10], [1, 4, 5, 6], [1, 4, 5, 6, 10], [1, 4, 5, 6, 9], [1, 4, 5, 6, 9, 10], [1, 4, 5, 6, 8], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 9, 10], [1, 4, 5, 6, 7], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 9, 10], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 8, 10], [1, 4, 5, 6, 7, 8, 9], [1, 4, 5, 6, 7, 8, 9, 10], [1, 3], [1, 3, 10], [1, 3, 9], [1, 3, 9, 10], [1, 3, 8], [1, 3, 8, 10], [1, 3, 8, 9], [1, 3, 8, 9, 10], [1, 3, 7], [1, 3, 7, 10], [1, 3, 7, 9], [1, 3, 7, 9, 10], [1, 3, 7, 8], [1, 3, 7, 8, 10], [1, 3, 7, 8, 9], [1, 3, 7, 8, 9, 10], [1, 3, 6], [1, 3, 6, 10], [1, 3, 6, 9], [1, 3, 6, 9, 10], [1, 3, 6, 8], [1, 3, 6, 8, 10], [1, 3, 6, 8, 9], [1, 3, 6, 8, 9, 10], [1, 3, 6, 7], [1, 3, 6, 7, 10], [1, 3, 6, 7, 9], [1, 3, 6, 7, 9, 10], [1, 3, 6, 7, 8], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 9, 10], [1, 3, 5], [1, 3, 5, 10], [1, 3, 5, 9], [1, 3, 5, 9, 10], [1, 3, 5, 8], [1, 3, 5, 8, 10], [1, 3, 5, 8, 9], [1, 3, 5, 8, 9, 10], [1, 3, 5, 7], [1, 3, 5, 7, 10], [1, 3, 5, 7, 9], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 8], [1, 3, 5, 7, 8, 10], [1, 3, 5, 7, 8, 9], [1, 3, 5, 7, 8, 9, 10], [1, 3, 5, 6], [1, 3, 5, 6, 10], [1, 3, 5, 6, 9], [1, 3, 5, 6, 9, 10], [1, 3, 5, 6, 8], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 9, 10], [1, 3, 5, 6, 7], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 9, 10], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 8, 10], [1, 3, 5, 6, 7, 8, 9], [1, 3, 5, 6, 7, 8, 9, 10], [1, 3, 4], [1, 3, 4, 10], [1, 3, 4, 9], [1, 3, 4, 9, 10], [1, 3, 4, 8], [1, 3, 4, 8, 10], [1, 3, 4, 8, 9], [1, 3, 4, 8, 9, 10], [1, 3, 4, 7], [1, 3, 4, 7, 10], [1, 3, 4, 7, 9], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 8], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 9, 10], [1, 3, 4, 6], [1, 3, 4, 6, 10], [1, 3, 4, 6, 9], [1, 3, 4, 6, 9, 10], [1, 3, 4, 6, 8], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 9, 10], [1, 3, 4, 6, 7], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 9, 10], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 8, 10], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 6, 7, 8, 9, 10], [1, 3, 4, 5], [1, 3, 4, 5, 10], [1, 3, 4, 5, 9], [1, 3, 4, 5, 9, 10], [1, 3, 4, 5, 8], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 9, 10], [1, 3, 4, 5, 7], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 9, 10], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 8, 10], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 7, 8, 9, 10], [1, 3, 4, 5, 6], [1, 3, 4, 5, 6, 10], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 9, 10], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 8, 10], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 8, 9, 10], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 7, 10], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 9, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 8, 10], [1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2], [1, 2, 10], [1, 2, 9], [1, 2, 9, 10], [1, 2, 8], [1, 2, 8, 10], [1, 2, 8, 9], [1, 2, 8, 9, 10], [1, 2, 7], [1, 2, 7, 10], [1, 2, 7, 9], [1, 2, 7, 9, 10], [1, 2, 7, 8], [1, 2, 7, 8, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 9, 10], [1, 2, 6], [1, 2, 6, 10], [1, 2, 6, 9], [1, 2, 6, 9, 10], [1, 2, 6, 8], [1, 2, 6, 8, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 9, 10], [1, 2, 6, 7], [1, 2, 6, 7, 10], [1, 2, 6, 7, 9], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 9, 10], [1, 2, 5], [1, 2, 5, 10], [1, 2, 5, 9], [1, 2, 5, 9, 10], [1, 2, 5, 8], [1, 2, 5, 8, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 9, 10], [1, 2, 5, 7], [1, 2, 5, 7, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 6], [1, 2, 5, 6, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 4], [1, 2, 4, 10], [1, 2, 4, 9], [1, 2, 4, 9, 10], [1, 2, 4, 8], [1, 2, 4, 8, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 9, 10], [1, 2, 4, 7], [1, 2, 4, 7, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 6], [1, 2, 4, 6, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 5], [1, 2, 4, 5, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3], [1, 2, 3, 10], [1, 2, 3, 9], [1, 2, 3, 9, 10], [1, 2, 3, 8], [1, 2, 3, 8, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 9, 10], [1, 2, 3, 7], [1, 2, 3, 7, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 6], [1, 2, 3, 6, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 5], [1, 2, 3, 5, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4], [1, 2, 3, 4, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]\n assert candidate(nums = [0, 1, 2, 3, 4]) == [[], [4], [3], [3, 4], [2], [2, 4], [2, 3], [2, 3, 4], [1], [1, 4], [1, 3], [1, 3, 4], [1, 2], [1, 2, 4], [1, 2, 3], [1, 2, 3, 4], [0], [0, 4], [0, 3], [0, 3, 4], [0, 2], [0, 2, 4], [0, 2, 3], [0, 2, 3, 4], [0, 1], [0, 1, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 2], [0, 1, 2, 4], [0, 1, 2, 3], [0, 1, 2, 3, 4]]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == [[], [-5], [5], [5, -5], [-4], [-4, -5], [-4, 5], [-4, 5, -5], [4], [4, -5], [4, 5], [4, 5, -5], [4, -4], [4, -4, -5], [4, -4, 5], [4, -4, 5, -5], [-3], [-3, -5], [-3, 5], [-3, 5, -5], [-3, -4], [-3, -4, -5], [-3, -4, 5], [-3, -4, 5, -5], [-3, 4], [-3, 4, -5], [-3, 4, 5], [-3, 4, 5, -5], [-3, 4, -4], [-3, 4, -4, -5], [-3, 4, -4, 5], [-3, 4, -4, 5, -5], [3], [3, -5], [3, 5], [3, 5, -5], [3, -4], [3, -4, -5], [3, -4, 5], [3, -4, 5, -5], [3, 4], [3, 4, -5], [3, 4, 5], [3, 4, 5, -5], [3, 4, -4], [3, 4, -4, -5], [3, 4, -4, 5], [3, 4, -4, 5, -5], [3, -3], [3, -3, -5], [3, -3, 5], [3, -3, 5, -5], [3, -3, -4], [3, -3, -4, -5], [3, -3, -4, 5], [3, -3, -4, 5, -5], [3, -3, 4], [3, -3, 4, -5], [3, -3, 4, 5], [3, -3, 4, 5, -5], [3, -3, 4, -4], [3, -3, 4, -4, -5], [3, -3, 4, -4, 5], [3, -3, 4, -4, 5, -5], [-2], [-2, -5], [-2, 5], [-2, 5, -5], [-2, -4], [-2, -4, -5], [-2, -4, 5], [-2, -4, 5, -5], [-2, 4], [-2, 4, -5], [-2, 4, 5], [-2, 4, 5, -5], [-2, 4, -4], [-2, 4, -4, -5], [-2, 4, -4, 5], [-2, 4, -4, 5, -5], [-2, -3], [-2, -3, -5], [-2, -3, 5], [-2, -3, 5, -5], [-2, -3, -4], [-2, -3, -4, -5], [-2, -3, -4, 5], [-2, -3, -4, 5, -5], [-2, -3, 4], [-2, -3, 4, -5], [-2, -3, 4, 5], [-2, -3, 4, 5, -5], [-2, -3, 4, -4], [-2, -3, 4, -4, -5], [-2, -3, 4, -4, 5], [-2, -3, 4, -4, 5, -5], [-2, 3], [-2, 3, -5], [-2, 3, 5], [-2, 3, 5, -5], [-2, 3, -4], [-2, 3, -4, -5], [-2, 3, -4, 5], [-2, 3, -4, 5, -5], [-2, 3, 4], [-2, 3, 4, -5], [-2, 3, 4, 5], [-2, 3, 4, 5, -5], [-2, 3, 4, -4], [-2, 3, 4, -4, -5], [-2, 3, 4, -4, 5], [-2, 3, 4, -4, 5, -5], [-2, 3, -3], [-2, 3, -3, -5], [-2, 3, -3, 5], [-2, 3, -3, 5, -5], [-2, 3, -3, -4], [-2, 3, -3, -4, -5], [-2, 3, -3, -4, 5], [-2, 3, -3, -4, 5, -5], [-2, 3, -3, 4], [-2, 3, -3, 4, -5], [-2, 3, -3, 4, 5], [-2, 3, -3, 4, 5, -5], [-2, 3, -3, 4, -4], [-2, 3, -3, 4, -4, -5], [-2, 3, -3, 4, -4, 5], [-2, 3, -3, 4, -4, 5, -5], [2], [2, -5], [2, 5], [2, 5, -5], [2, -4], [2, -4, -5], [2, -4, 5], [2, -4, 5, -5], [2, 4], [2, 4, -5], [2, 4, 5], [2, 4, 5, -5], [2, 4, -4], [2, 4, -4, -5], [2, 4, -4, 5], [2, 4, -4, 5, -5], [2, -3], [2, -3, -5], [2, -3, 5], [2, -3, 5, -5], [2, -3, -4], [2, -3, -4, -5], [2, -3, -4, 5], [2, -3, -4, 5, -5], [2, -3, 4], [2, -3, 4, -5], [2, -3, 4, 5], [2, -3, 4, 5, -5], [2, -3, 4, -4], [2, -3, 4, -4, -5], [2, -3, 4, -4, 5], [2, -3, 4, -4, 5, -5], [2, 3], [2, 3, -5], [2, 3, 5], [2, 3, 5, -5], [2, 3, -4], [2, 3, -4, -5], [2, 3, -4, 5], [2, 3, -4, 5, -5], [2, 3, 4], [2, 3, 4, -5], [2, 3, 4, 5], [2, 3, 4, 5, -5], [2, 3, 4, -4], [2, 3, 4, -4, -5], [2, 3, 4, -4, 5], [2, 3, 4, -4, 5, -5], [2, 3, -3], [2, 3, -3, -5], [2, 3, -3, 5], [2, 3, -3, 5, -5], [2, 3, -3, -4], [2, 3, -3, -4, -5], [2, 3, -3, -4, 5], [2, 3, -3, -4, 5, -5], [2, 3, -3, 4], [2, 3, -3, 4, -5], [2, 3, -3, 4, 5], [2, 3, -3, 4, 5, -5], [2, 3, -3, 4, -4], [2, 3, -3, 4, -4, -5], [2, 3, -3, 4, -4, 5], [2, 3, -3, 4, -4, 5, -5], [2, -2], [2, -2, -5], [2, -2, 5], [2, -2, 5, -5], [2, -2, -4], [2, -2, -4, -5], [2, -2, -4, 5], [2, -2, -4, 5, -5], [2, -2, 4], [2, -2, 4, -5], [2, -2, 4, 5], [2, -2, 4, 5, -5], [2, -2, 4, -4], [2, -2, 4, -4, -5], [2, -2, 4, -4, 5], [2, -2, 4, -4, 5, -5], [2, -2, -3], [2, -2, -3, -5], [2, -2, -3, 5], [2, -2, -3, 5, -5], [2, -2, -3, -4], [2, -2, -3, -4, -5], [2, -2, -3, -4, 5], [2, -2, -3, -4, 5, -5], [2, -2, -3, 4], [2, -2, -3, 4, -5], [2, -2, -3, 4, 5], [2, -2, -3, 4, 5, -5], [2, -2, -3, 4, -4], [2, -2, -3, 4, -4, -5], [2, -2, -3, 4, -4, 5], [2, -2, -3, 4, -4, 5, -5], [2, -2, 3], [2, -2, 3, -5], [2, -2, 3, 5], [2, -2, 3, 5, -5], [2, -2, 3, -4], [2, -2, 3, -4, -5], [2, -2, 3, -4, 5], [2, -2, 3, -4, 5, -5], [2, -2, 3, 4], [2, -2, 3, 4, -5], [2, -2, 3, 4, 5], [2, -2, 3, 4, 5, -5], [2, -2, 3, 4, -4], [2, -2, 3, 4, -4, -5], [2, -2, 3, 4, -4, 5], [2, -2, 3, 4, -4, 5, -5], [2, -2, 3, -3], [2, -2, 3, -3, -5], [2, -2, 3, -3, 5], [2, -2, 3, -3, 5, -5], [2, -2, 3, -3, -4], [2, -2, 3, -3, -4, -5], [2, -2, 3, -3, -4, 5], [2, -2, 3, -3, -4, 5, -5], [2, -2, 3, -3, 4], [2, -2, 3, -3, 4, -5], [2, -2, 3, -3, 4, 5], [2, -2, 3, -3, 4, 5, -5], [2, -2, 3, -3, 4, -4], [2, -2, 3, -3, 4, -4, -5], [2, -2, 3, -3, 4, -4, 5], [2, -2, 3, -3, 4, -4, 5, -5], [-1], [-1, -5], [-1, 5], [-1, 5, -5], [-1, -4], [-1, -4, -5], [-1, -4, 5], [-1, -4, 5, -5], [-1, 4], [-1, 4, -5], [-1, 4, 5], [-1, 4, 5, -5], [-1, 4, -4], [-1, 4, -4, -5], [-1, 4, -4, 5], [-1, 4, -4, 5, -5], [-1, -3], [-1, -3, -5], [-1, -3, 5], [-1, -3, 5, -5], [-1, -3, -4], [-1, -3, -4, -5], [-1, -3, -4, 5], [-1, -3, -4, 5, -5], [-1, -3, 4], [-1, -3, 4, -5], [-1, -3, 4, 5], [-1, -3, 4, 5, -5], [-1, -3, 4, -4], [-1, -3, 4, -4, -5], [-1, -3, 4, -4, 5], [-1, -3, 4, -4, 5, -5], [-1, 3], [-1, 3, -5], [-1, 3, 5], [-1, 3, 5, -5], [-1, 3, -4], [-1, 3, -4, -5], [-1, 3, -4, 5], [-1, 3, -4, 5, -5], [-1, 3, 4], [-1, 3, 4, -5], [-1, 3, 4, 5], [-1, 3, 4, 5, -5], [-1, 3, 4, -4], [-1, 3, 4, -4, -5], [-1, 3, 4, -4, 5], [-1, 3, 4, -4, 5, -5], [-1, 3, -3], [-1, 3, -3, -5], [-1, 3, -3, 5], [-1, 3, -3, 5, -5], [-1, 3, -3, -4], [-1, 3, -3, -4, -5], [-1, 3, -3, -4, 5], [-1, 3, -3, -4, 5, -5], [-1, 3, -3, 4], [-1, 3, -3, 4, -5], [-1, 3, -3, 4, 5], [-1, 3, -3, 4, 5, -5], [-1, 3, -3, 4, -4], [-1, 3, -3, 4, -4, -5], [-1, 3, -3, 4, -4, 5], [-1, 3, -3, 4, -4, 5, -5], [-1, -2], [-1, -2, -5], [-1, -2, 5], [-1, -2, 5, -5], [-1, -2, -4], [-1, -2, -4, -5], [-1, -2, -4, 5], [-1, -2, -4, 5, -5], [-1, -2, 4], [-1, -2, 4, -5], [-1, -2, 4, 5], [-1, -2, 4, 5, -5], [-1, -2, 4, -4], [-1, -2, 4, -4, -5], [-1, -2, 4, -4, 5], [-1, -2, 4, -4, 5, -5], [-1, -2, -3], [-1, -2, -3, -5], [-1, -2, -3, 5], [-1, -2, -3, 5, -5], [-1, -2, -3, -4], [-1, -2, -3, -4, -5], [-1, -2, -3, -4, 5], [-1, -2, -3, -4, 5, -5], [-1, -2, -3, 4], [-1, -2, -3, 4, -5], [-1, -2, -3, 4, 5], [-1, -2, -3, 4, 5, -5], [-1, -2, -3, 4, -4], [-1, -2, -3, 4, -4, -5], [-1, -2, -3, 4, -4, 5], [-1, -2, -3, 4, -4, 5, -5], [-1, -2, 3], [-1, -2, 3, -5], [-1, -2, 3, 5], [-1, -2, 3, 5, -5], [-1, -2, 3, -4], [-1, -2, 3, -4, -5], [-1, -2, 3, -4, 5], [-1, -2, 3, -4, 5, -5], [-1, -2, 3, 4], [-1, -2, 3, 4, -5], [-1, -2, 3, 4, 5], [-1, -2, 3, 4, 5, -5], [-1, -2, 3, 4, -4], [-1, -2, 3, 4, -4, -5], [-1, -2, 3, 4, -4, 5], [-1, -2, 3, 4, -4, 5, -5], [-1, -2, 3, -3], [-1, -2, 3, -3, -5], [-1, -2, 3, -3, 5], [-1, -2, 3, -3, 5, -5], [-1, -2, 3, -3, -4], [-1, -2, 3, -3, -4, -5], [-1, -2, 3, -3, -4, 5], [-1, -2, 3, -3, -4, 5, -5], [-1, -2, 3, -3, 4], [-1, -2, 3, -3, 4, -5], [-1, -2, 3, -3, 4, 5], [-1, -2, 3, -3, 4, 5, -5], [-1, -2, 3, -3, 4, -4], [-1, -2, 3, -3, 4, -4, -5], [-1, -2, 3, -3, 4, -4, 5], [-1, -2, 3, -3, 4, -4, 5, -5], [-1, 2], [-1, 2, -5], [-1, 2, 5], [-1, 2, 5, -5], [-1, 2, -4], [-1, 2, -4, -5], [-1, 2, -4, 5], [-1, 2, -4, 5, -5], [-1, 2, 4], [-1, 2, 4, -5], [-1, 2, 4, 5], [-1, 2, 4, 5, -5], [-1, 2, 4, -4], [-1, 2, 4, -4, -5], [-1, 2, 4, -4, 5], [-1, 2, 4, -4, 5, -5], [-1, 2, -3], [-1, 2, -3, -5], [-1, 2, -3, 5], [-1, 2, -3, 5, -5], [-1, 2, -3, -4], [-1, 2, -3, -4, -5], [-1, 2, -3, -4, 5], [-1, 2, -3, -4, 5, -5], [-1, 2, -3, 4], [-1, 2, -3, 4, -5], [-1, 2, -3, 4, 5], [-1, 2, -3, 4, 5, -5], [-1, 2, -3, 4, -4], [-1, 2, -3, 4, -4, -5], [-1, 2, -3, 4, -4, 5], [-1, 2, -3, 4, -4, 5, -5], [-1, 2, 3], [-1, 2, 3, -5], [-1, 2, 3, 5], [-1, 2, 3, 5, -5], [-1, 2, 3, -4], [-1, 2, 3, -4, -5], [-1, 2, 3, -4, 5], [-1, 2, 3, -4, 5, -5], [-1, 2, 3, 4], [-1, 2, 3, 4, -5], [-1, 2, 3, 4, 5], [-1, 2, 3, 4, 5, -5], [-1, 2, 3, 4, -4], [-1, 2, 3, 4, -4, -5], [-1, 2, 3, 4, -4, 5], [-1, 2, 3, 4, -4, 5, -5], [-1, 2, 3, -3], [-1, 2, 3, -3, -5], [-1, 2, 3, -3, 5], [-1, 2, 3, -3, 5, -5], [-1, 2, 3, -3, -4], [-1, 2, 3, -3, -4, -5], [-1, 2, 3, -3, -4, 5], [-1, 2, 3, -3, -4, 5, -5], [-1, 2, 3, -3, 4], [-1, 2, 3, -3, 4, -5], [-1, 2, 3, -3, 4, 5], [-1, 2, 3, -3, 4, 5, -5], [-1, 2, 3, -3, 4, -4], [-1, 2, 3, -3, 4, -4, -5], [-1, 2, 3, -3, 4, -4, 5], [-1, 2, 3, -3, 4, -4, 5, -5], [-1, 2, -2], [-1, 2, -2, -5], [-1, 2, -2, 5], [-1, 2, -2, 5, -5], [-1, 2, -2, -4], [-1, 2, -2, -4, -5], [-1, 2, -2, -4, 5], [-1, 2, -2, -4, 5, -5], [-1, 2, -2, 4], [-1, 2, -2, 4, -5], [-1, 2, -2, 4, 5], [-1, 2, -2, 4, 5, -5], [-1, 2, -2, 4, -4], [-1, 2, -2, 4, -4, -5], [-1, 2, -2, 4, -4, 5], [-1, 2, -2, 4, -4, 5, -5], [-1, 2, -2, -3], [-1, 2, -2, -3, -5], [-1, 2, -2, -3, 5], [-1, 2, -2, -3, 5, -5], [-1, 2, -2, -3, -4], [-1, 2, -2, -3, -4, -5], [-1, 2, -2, -3, -4, 5], [-1, 2, -2, -3, -4, 5, -5], [-1, 2, -2, -3, 4], [-1, 2, -2, -3, 4, -5], [-1, 2, -2, -3, 4, 5], [-1, 2, -2, -3, 4, 5, -5], [-1, 2, -2, -3, 4, -4], [-1, 2, -2, -3, 4, -4, -5], [-1, 2, -2, -3, 4, -4, 5], [-1, 2, -2, -3, 4, -4, 5, -5], [-1, 2, -2, 3], [-1, 2, -2, 3, -5], [-1, 2, -2, 3, 5], [-1, 2, -2, 3, 5, -5], [-1, 2, -2, 3, -4], [-1, 2, -2, 3, -4, -5], [-1, 2, -2, 3, -4, 5], [-1, 2, -2, 3, -4, 5, -5], [-1, 2, -2, 3, 4], [-1, 2, -2, 3, 4, -5], [-1, 2, -2, 3, 4, 5], [-1, 2, -2, 3, 4, 5, -5], [-1, 2, -2, 3, 4, -4], [-1, 2, -2, 3, 4, -4, -5], [-1, 2, -2, 3, 4, -4, 5], [-1, 2, -2, 3, 4, -4, 5, -5], [-1, 2, -2, 3, -3], [-1, 2, -2, 3, -3, -5], [-1, 2, -2, 3, -3, 5], [-1, 2, -2, 3, -3, 5, -5], [-1, 2, -2, 3, -3, -4], [-1, 2, -2, 3, -3, -4, -5], [-1, 2, -2, 3, -3, -4, 5], [-1, 2, -2, 3, -3, -4, 5, -5], [-1, 2, -2, 3, -3, 4], [-1, 2, -2, 3, -3, 4, -5], [-1, 2, -2, 3, -3, 4, 5], [-1, 2, -2, 3, -3, 4, 5, -5], [-1, 2, -2, 3, -3, 4, -4], [-1, 2, -2, 3, -3, 4, -4, -5], [-1, 2, -2, 3, -3, 4, -4, 5], [-1, 2, -2, 3, -3, 4, -4, 5, -5], [1], [1, -5], [1, 5], [1, 5, -5], [1, -4], [1, -4, -5], [1, -4, 5], [1, -4, 5, -5], [1, 4], [1, 4, -5], [1, 4, 5], [1, 4, 5, -5], [1, 4, -4], [1, 4, -4, -5], [1, 4, -4, 5], [1, 4, -4, 5, -5], [1, -3], [1, -3, -5], [1, -3, 5], [1, -3, 5, -5], [1, -3, -4], [1, -3, -4, -5], [1, -3, -4, 5], [1, -3, -4, 5, -5], [1, -3, 4], [1, -3, 4, -5], [1, -3, 4, 5], [1, -3, 4, 5, -5], [1, -3, 4, -4], [1, -3, 4, -4, -5], [1, -3, 4, -4, 5], [1, -3, 4, -4, 5, -5], [1, 3], [1, 3, -5], [1, 3, 5], [1, 3, 5, -5], [1, 3, -4], [1, 3, -4, -5], [1, 3, -4, 5], [1, 3, -4, 5, -5], [1, 3, 4], [1, 3, 4, -5], [1, 3, 4, 5], [1, 3, 4, 5, -5], [1, 3, 4, -4], [1, 3, 4, -4, -5], [1, 3, 4, -4, 5], [1, 3, 4, -4, 5, -5], [1, 3, -3], [1, 3, -3, -5], [1, 3, -3, 5], [1, 3, -3, 5, -5], [1, 3, -3, -4], [1, 3, -3, -4, -5], [1, 3, -3, -4, 5], [1, 3, -3, -4, 5, -5], [1, 3, -3, 4], [1, 3, -3, 4, -5], [1, 3, -3, 4, 5], [1, 3, -3, 4, 5, -5], [1, 3, -3, 4, -4], [1, 3, -3, 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2, -2, 3, 5, -5], [1, -1, 2, -2, 3, -4], [1, -1, 2, -2, 3, -4, -5], [1, -1, 2, -2, 3, -4, 5], [1, -1, 2, -2, 3, -4, 5, -5], [1, -1, 2, -2, 3, 4], [1, -1, 2, -2, 3, 4, -5], [1, -1, 2, -2, 3, 4, 5], [1, -1, 2, -2, 3, 4, 5, -5], [1, -1, 2, -2, 3, 4, -4], [1, -1, 2, -2, 3, 4, -4, -5], [1, -1, 2, -2, 3, 4, -4, 5], [1, -1, 2, -2, 3, 4, -4, 5, -5], [1, -1, 2, -2, 3, -3], [1, -1, 2, -2, 3, -3, -5], [1, -1, 2, -2, 3, -3, 5], [1, -1, 2, -2, 3, -3, 5, -5], [1, -1, 2, -2, 3, -3, -4], [1, -1, 2, -2, 3, -3, -4, -5], [1, -1, 2, -2, 3, -3, -4, 5], [1, -1, 2, -2, 3, -3, -4, 5, -5], [1, -1, 2, -2, 3, -3, 4], [1, -1, 2, -2, 3, -3, 4, -5], [1, -1, 2, -2, 3, -3, 4, 5], [1, -1, 2, -2, 3, -3, 4, 5, -5], [1, -1, 2, -2, 3, -3, 4, -4], [1, -1, 2, -2, 3, -3, 4, -4, -5], [1, -1, 2, -2, 3, -3, 4, -4, 5], [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == [[], [-1], [-2], [-2, -1], [-3], [-3, -1], [-3, -2], [-3, -2, -1], [-4], [-4, -1], [-4, -2], [-4, -2, -1], [-4, -3], [-4, -3, -1], [-4, -3, -2], [-4, -3, -2, -1], [-5], [-5, -1], [-5, -2], [-5, -2, -1], [-5, -3], [-5, -3, -1], [-5, -3, -2], [-5, -3, -2, -1], [-5, -4], [-5, -4, -1], [-5, -4, -2], [-5, -4, -2, -1], [-5, -4, -3], [-5, -4, -3, -1], [-5, -4, -3, -2], [-5, -4, -3, -2, -1], [-6], [-6, -1], [-6, -2], [-6, -2, -1], [-6, -3], [-6, -3, -1], [-6, -3, -2], [-6, -3, -2, -1], [-6, -4], [-6, -4, -1], [-6, -4, -2], [-6, -4, -2, -1], [-6, -4, -3], [-6, -4, -3, -1], [-6, -4, -3, -2], [-6, -4, -3, -2, -1], [-6, -5], [-6, -5, -1], [-6, -5, -2], [-6, -5, -2, -1], [-6, -5, -3], [-6, -5, -3, -1], [-6, -5, -3, -2], [-6, -5, -3, -2, -1], [-6, -5, -4], [-6, -5, -4, -1], [-6, -5, -4, -2], [-6, -5, -4, -2, -1], [-6, -5, -4, -3], [-6, -5, -4, -3, -1], [-6, -5, -4, -3, -2], [-6, -5, -4, -3, -2, -1], [-7], [-7, -1], [-7, -2], [-7, -2, -1], [-7, -3], [-7, -3, -1], [-7, -3, -2], [-7, -3, -2, -1], [-7, -4], [-7, -4, -1], [-7, -4, -2], [-7, -4, -2, -1], [-7, -4, -3], [-7, -4, -3, -1], [-7, -4, -3, -2], [-7, -4, -3, -2, -1], [-7, -5], [-7, -5, -1], [-7, -5, -2], [-7, -5, -2, -1], [-7, -5, -3], [-7, -5, -3, -1], [-7, -5, -3, -2], [-7, -5, -3, -2, -1], [-7, -5, -4], [-7, -5, -4, -1], [-7, -5, -4, -2], [-7, -5, -4, -2, -1], [-7, -5, -4, -3], [-7, -5, -4, -3, -1], [-7, -5, -4, -3, -2], [-7, -5, -4, -3, -2, -1], [-7, -6], [-7, -6, -1], [-7, -6, -2], [-7, -6, -2, -1], [-7, -6, -3], [-7, -6, -3, -1], [-7, -6, -3, -2], [-7, -6, -3, -2, -1], [-7, -6, -4], [-7, -6, -4, -1], [-7, -6, -4, -2], [-7, -6, -4, -2, -1], [-7, -6, -4, -3], [-7, -6, -4, -3, -1], [-7, -6, -4, -3, -2], [-7, -6, -4, -3, -2, -1], [-7, -6, -5], [-7, -6, -5, -1], [-7, -6, -5, -2], [-7, -6, -5, -2, -1], [-7, -6, -5, -3], [-7, -6, -5, -3, -1], [-7, -6, -5, -3, -2], [-7, -6, -5, -3, -2, -1], [-7, -6, -5, -4], [-7, -6, -5, -4, -1], [-7, -6, -5, -4, -2], [-7, -6, -5, -4, -2, -1], [-7, -6, -5, -4, -3], [-7, -6, -5, -4, -3, -1], [-7, -6, -5, -4, -3, -2], [-7, -6, -5, -4, -3, -2, -1], [-8], [-8, -1], [-8, -2], [-8, -2, -1], [-8, -3], [-8, -3, -1], [-8, -3, -2], [-8, -3, -2, -1], [-8, -4], [-8, -4, -1], [-8, -4, -2], [-8, -4, -2, -1], [-8, -4, -3], [-8, -4, -3, -1], [-8, -4, -3, -2], [-8, -4, -3, -2, -1], [-8, -5], [-8, -5, -1], [-8, -5, -2], [-8, -5, -2, -1], [-8, -5, -3], [-8, -5, -3, -1], [-8, -5, -3, -2], [-8, -5, -3, -2, -1], [-8, -5, -4], [-8, -5, -4, -1], [-8, -5, -4, -2], [-8, -5, -4, -2, -1], [-8, -5, -4, -3], [-8, -5, -4, -3, -1], [-8, -5, -4, -3, -2], [-8, -5, -4, -3, -2, -1], [-8, -6], [-8, -6, -1], [-8, -6, -2], [-8, -6, -2, -1], [-8, -6, -3], [-8, -6, -3, -1], [-8, -6, -3, -2], [-8, -6, -3, -2, -1], [-8, -6, -4], [-8, -6, -4, -1], [-8, -6, -4, -2], [-8, -6, -4, -2, -1], [-8, -6, -4, -3], [-8, -6, -4, -3, -1], [-8, -6, -4, -3, -2], [-8, -6, -4, -3, -2, -1], [-8, -6, -5], [-8, -6, -5, -1], [-8, -6, -5, -2], [-8, -6, -5, -2, -1], [-8, -6, -5, -3], [-8, -6, -5, -3, -1], [-8, -6, -5, -3, -2], [-8, -6, -5, -3, -2, -1], [-8, -6, -5, -4], [-8, -6, -5, -4, -1], [-8, -6, -5, -4, -2], [-8, -6, -5, -4, -2, -1], 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-4], [-10, -9, -7, -6, -5, -4, -1], [-10, -9, -7, -6, -5, -4, -2], [-10, -9, -7, -6, -5, -4, -2, -1], [-10, -9, -7, -6, -5, -4, -3], [-10, -9, -7, -6, -5, -4, -3, -1], [-10, -9, -7, -6, -5, -4, -3, -2], [-10, -9, -7, -6, -5, -4, -3, -2, -1], [-10, -9, -8], [-10, -9, -8, -1], [-10, -9, -8, -2], [-10, -9, -8, -2, -1], [-10, -9, -8, -3], [-10, -9, -8, -3, -1], [-10, -9, -8, -3, -2], [-10, -9, -8, -3, -2, -1], [-10, -9, -8, -4], [-10, -9, -8, -4, -1], [-10, -9, -8, -4, -2], [-10, -9, -8, -4, -2, -1], [-10, -9, -8, -4, -3], [-10, -9, -8, -4, -3, -1], [-10, -9, -8, -4, -3, -2], [-10, -9, -8, -4, -3, -2, -1], [-10, -9, -8, -5], [-10, -9, -8, -5, -1], [-10, -9, -8, -5, -2], [-10, -9, -8, -5, -2, -1], [-10, -9, -8, -5, -3], [-10, -9, -8, -5, -3, -1], [-10, -9, -8, -5, -3, -2], [-10, -9, -8, -5, -3, -2, -1], [-10, -9, -8, -5, -4], [-10, -9, -8, -5, -4, -1], [-10, -9, -8, -5, -4, -2], [-10, -9, -8, -5, -4, -2, -1], [-10, -9, -8, -5, -4, -3], [-10, -9, -8, -5, -4, -3, -1], [-10, -9, -8, -5, -4, -3, -2], [-10, -9, -8, -5, -4, -3, -2, -1], [-10, -9, -8, -6], [-10, -9, -8, -6, -1], [-10, -9, -8, -6, -2], [-10, -9, -8, -6, -2, -1], [-10, -9, -8, -6, -3], [-10, -9, -8, -6, -3, -1], [-10, -9, -8, -6, -3, -2], [-10, -9, -8, -6, -3, -2, -1], [-10, -9, -8, -6, -4], [-10, -9, -8, -6, -4, -1], [-10, -9, -8, -6, -4, -2], [-10, -9, -8, -6, -4, -2, -1], [-10, -9, -8, -6, -4, -3], [-10, -9, -8, -6, -4, -3, -1], [-10, -9, -8, -6, -4, -3, -2], [-10, -9, -8, -6, -4, -3, -2, -1], [-10, -9, -8, -6, -5], [-10, -9, -8, -6, -5, -1], [-10, -9, -8, -6, -5, -2], [-10, -9, -8, -6, -5, -2, -1], [-10, -9, -8, -6, -5, -3], [-10, -9, -8, -6, -5, -3, -1], [-10, -9, -8, -6, -5, -3, -2], [-10, -9, -8, -6, -5, -3, -2, -1], [-10, -9, -8, -6, -5, -4], [-10, -9, -8, -6, -5, -4, -1], [-10, -9, -8, -6, -5, -4, -2], [-10, -9, -8, -6, -5, -4, -2, -1], [-10, -9, -8, -6, -5, -4, -3], [-10, -9, -8, -6, -5, -4, -3, -1], [-10, -9, -8, -6, -5, -4, -3, -2], [-10, -9, -8, -6, -5, -4, -3, -2, -1], [-10, -9, -8, -7], [-10, -9, -8, -7, -1], [-10, -9, -8, -7, -2], [-10, -9, -8, -7, -2, -1], [-10, -9, -8, -7, -3], [-10, -9, -8, -7, -3, -1], [-10, -9, -8, -7, -3, -2], [-10, -9, -8, -7, -3, -2, -1], [-10, -9, -8, -7, -4], [-10, -9, -8, -7, -4, -1], [-10, -9, -8, -7, -4, -2], [-10, -9, -8, -7, -4, -2, -1], [-10, -9, -8, -7, -4, -3], [-10, -9, -8, -7, -4, -3, -1], [-10, -9, -8, -7, -4, -3, -2], [-10, -9, -8, -7, -4, -3, -2, -1], [-10, -9, -8, -7, -5], [-10, -9, -8, -7, -5, -1], [-10, -9, -8, -7, -5, -2], [-10, -9, -8, -7, -5, -2, -1], [-10, -9, -8, -7, -5, -3], [-10, -9, -8, -7, -5, -3, -1], [-10, -9, -8, -7, -5, -3, -2], [-10, -9, -8, -7, -5, -3, -2, -1], [-10, -9, -8, -7, -5, -4], [-10, -9, -8, -7, -5, -4, -1], [-10, -9, -8, -7, -5, -4, -2], [-10, -9, -8, -7, -5, -4, -2, -1], [-10, -9, -8, -7, -5, -4, -3], [-10, -9, -8, -7, -5, -4, -3, -1], [-10, -9, -8, -7, -5, -4, -3, -2], [-10, -9, -8, -7, -5, -4, -3, -2, -1], [-10, -9, -8, -7, -6], [-10, -9, -8, -7, -6, -1], [-10, -9, -8, -7, -6, -2], [-10, -9, -8, -7, -6, -2, -1], [-10, -9, -8, -7, -6, -3], [-10, -9, -8, -7, -6, -3, -1], [-10, -9, -8, -7, -6, -3, -2], [-10, -9, -8, -7, -6, -3, -2, -1], [-10, -9, -8, -7, -6, -4], [-10, -9, -8, -7, -6, -4, -1], [-10, -9, -8, -7, -6, -4, -2], [-10, -9, -8, -7, -6, -4, -2, -1], [-10, -9, -8, -7, -6, -4, -3], [-10, -9, -8, -7, -6, -4, -3, -1], [-10, -9, -8, -7, -6, -4, -3, -2], [-10, -9, -8, -7, -6, -4, -3, -2, -1], [-10, -9, -8, -7, -6, -5], [-10, -9, -8, -7, -6, -5, -1], [-10, -9, -8, -7, -6, -5, -2], [-10, -9, -8, -7, -6, -5, -2, -1], [-10, -9, -8, -7, -6, -5, -3], [-10, -9, -8, -7, -6, -5, -3, -1], [-10, -9, -8, -7, -6, -5, -3, -2], [-10, -9, -8, -7, -6, -5, -3, -2, -1], [-10, -9, -8, -7, -6, -5, -4], [-10, -9, -8, -7, -6, -5, -4, -1], [-10, -9, -8, -7, -6, -5, -4, -2], [-10, -9, -8, -7, -6, -5, -4, -2, -1], [-10, -9, -8, -7, -6, -5, -4, -3], [-10, -9, -8, -7, -6, -5, -4, -3, -1], [-10, -9, -8, -7, -6, -5, -4, -3, -2], [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == [[], [100], [90], [90, 100], [80], [80, 100], [80, 90], [80, 90, 100], [70], [70, 100], [70, 90], [70, 90, 100], [70, 80], [70, 80, 100], [70, 80, 90], [70, 80, 90, 100], [60], [60, 100], [60, 90], [60, 90, 100], [60, 80], [60, 80, 100], [60, 80, 90], [60, 80, 90, 100], [60, 70], [60, 70, 100], [60, 70, 90], [60, 70, 90, 100], [60, 70, 80], [60, 70, 80, 100], [60, 70, 80, 90], [60, 70, 80, 90, 100], [50], [50, 100], [50, 90], [50, 90, 100], [50, 80], [50, 80, 100], [50, 80, 90], [50, 80, 90, 100], [50, 70], [50, 70, 100], [50, 70, 90], [50, 70, 90, 100], [50, 70, 80], [50, 70, 80, 100], [50, 70, 80, 90], [50, 70, 80, 90, 100], [50, 60], [50, 60, 100], [50, 60, 90], [50, 60, 90, 100], [50, 60, 80], [50, 60, 80, 100], [50, 60, 80, 90], [50, 60, 80, 90, 100], [50, 60, 70], [50, 60, 70, 100], [50, 60, 70, 90], [50, 60, 70, 90, 100], [50, 60, 70, 80], [50, 60, 70, 80, 100], [50, 60, 70, 80, 90], [50, 60, 70, 80, 90, 100], [40], [40, 100], [40, 90], [40, 90, 100], [40, 80], [40, 80, 100], [40, 80, 90], [40, 80, 90, 100], [40, 70], [40, 70, 100], [40, 70, 90], [40, 70, 90, 100], [40, 70, 80], [40, 70, 80, 100], [40, 70, 80, 90], [40, 70, 80, 90, 100], [40, 60], [40, 60, 100], [40, 60, 90], [40, 60, 90, 100], [40, 60, 80], [40, 60, 80, 100], [40, 60, 80, 90], [40, 60, 80, 90, 100], [40, 60, 70], [40, 60, 70, 100], [40, 60, 70, 90], [40, 60, 70, 90, 100], [40, 60, 70, 80], [40, 60, 70, 80, 100], [40, 60, 70, 80, 90], [40, 60, 70, 80, 90, 100], [40, 50], [40, 50, 100], [40, 50, 90], [40, 50, 90, 100], [40, 50, 80], [40, 50, 80, 100], [40, 50, 80, 90], [40, 50, 80, 90, 100], [40, 50, 70], [40, 50, 70, 100], [40, 50, 70, 90], [40, 50, 70, 90, 100], [40, 50, 70, 80], [40, 50, 70, 80, 100], [40, 50, 70, 80, 90], [40, 50, 70, 80, 90, 100], [40, 50, 60], [40, 50, 60, 100], [40, 50, 60, 90], [40, 50, 60, 90, 100], [40, 50, 60, 80], [40, 50, 60, 80, 100], [40, 50, 60, 80, 90], [40, 50, 60, 80, 90, 100], [40, 50, 60, 70], [40, 50, 60, 70, 100], [40, 50, 60, 70, 90], [40, 50, 60, 70, 90, 100], [40, 50, 60, 70, 80], [40, 50, 60, 70, 80, 100], [40, 50, 60, 70, 80, 90], [40, 50, 60, 70, 80, 90, 100], [30], [30, 100], [30, 90], [30, 90, 100], [30, 80], [30, 80, 100], [30, 80, 90], [30, 80, 90, 100], [30, 70], [30, 70, 100], [30, 70, 90], [30, 70, 90, 100], [30, 70, 80], [30, 70, 80, 100], [30, 70, 80, 90], [30, 70, 80, 90, 100], [30, 60], [30, 60, 100], [30, 60, 90], [30, 60, 90, 100], [30, 60, 80], [30, 60, 80, 100], [30, 60, 80, 90], [30, 60, 80, 90, 100], [30, 60, 70], [30, 60, 70, 100], [30, 60, 70, 90], [30, 60, 70, 90, 100], [30, 60, 70, 80], [30, 60, 70, 80, 100], [30, 60, 70, 80, 90], [30, 60, 70, 80, 90, 100], [30, 50], [30, 50, 100], [30, 50, 90], [30, 50, 90, 100], [30, 50, 80], [30, 50, 80, 100], [30, 50, 80, 90], [30, 50, 80, 90, 100], [30, 50, 70], [30, 50, 70, 100], [30, 50, 70, 90], [30, 50, 70, 90, 100], [30, 50, 70, 80], [30, 50, 70, 80, 100], [30, 50, 70, 80, 90], [30, 50, 70, 80, 90, 100], [30, 50, 60], [30, 50, 60, 100], [30, 50, 60, 90], [30, 50, 60, 90, 100], [30, 50, 60, 80], [30, 50, 60, 80, 100], [30, 50, 60, 80, 90], [30, 50, 60, 80, 90, 100], [30, 50, 60, 70], [30, 50, 60, 70, 100], [30, 50, 60, 70, 90], [30, 50, 60, 70, 90, 100], [30, 50, 60, 70, 80], [30, 50, 60, 70, 80, 100], [30, 50, 60, 70, 80, 90], [30, 50, 60, 70, 80, 90, 100], [30, 40], [30, 40, 100], [30, 40, 90], [30, 40, 90, 100], [30, 40, 80], [30, 40, 80, 100], [30, 40, 80, 90], [30, 40, 80, 90, 100], [30, 40, 70], [30, 40, 70, 100], [30, 40, 70, 90], [30, 40, 70, 90, 100], [30, 40, 70, 80], [30, 40, 70, 80, 100], [30, 40, 70, 80, 90], [30, 40, 70, 80, 90, 100], [30, 40, 60], [30, 40, 60, 100], [30, 40, 60, 90], [30, 40, 60, 90, 100], [30, 40, 60, 80], [30, 40, 60, 80, 100], [30, 40, 60, 80, 90], [30, 40, 60, 80, 90, 100], [30, 40, 60, 70], [30, 40, 60, 70, 100], [30, 40, 60, 70, 90], [30, 40, 60, 70, 90, 100], [30, 40, 60, 70, 80], [30, 40, 60, 70, 80, 100], [30, 40, 60, 70, 80, 90], [30, 40, 60, 70, 80, 90, 100], [30, 40, 50], [30, 40, 50, 100], [30, 40, 50, 90], [30, 40, 50, 90, 100], [30, 40, 50, 80], [30, 40, 50, 80, 100], [30, 40, 50, 80, 90], [30, 40, 50, 80, 90, 100], [30, 40, 50, 70], [30, 40, 50, 70, 100], [30, 40, 50, 70, 90], [30, 40, 50, 70, 90, 100], [30, 40, 50, 70, 80], [30, 40, 50, 70, 80, 100], [30, 40, 50, 70, 80, 90], [30, 40, 50, 70, 80, 90, 100], [30, 40, 50, 60], [30, 40, 50, 60, 100], [30, 40, 50, 60, 90], [30, 40, 50, 60, 90, 100], [30, 40, 50, 60, 80], [30, 40, 50, 60, 80, 100], [30, 40, 50, 60, 80, 90], [30, 40, 50, 60, 80, 90, 100], [30, 40, 50, 60, 70], [30, 40, 50, 60, 70, 100], [30, 40, 50, 60, 70, 90], [30, 40, 50, 60, 70, 90, 100], [30, 40, 50, 60, 70, 80], [30, 40, 50, 60, 70, 80, 100], [30, 40, 50, 60, 70, 80, 90], [30, 40, 50, 60, 70, 80, 90, 100], [20], [20, 100], [20, 90], [20, 90, 100], [20, 80], [20, 80, 100], [20, 80, 90], [20, 80, 90, 100], [20, 70], [20, 70, 100], [20, 70, 90], [20, 70, 90, 100], [20, 70, 80], [20, 70, 80, 100], [20, 70, 80, 90], [20, 70, 80, 90, 100], [20, 60], [20, 60, 100], [20, 60, 90], [20, 60, 90, 100], [20, 60, 80], [20, 60, 80, 100], [20, 60, 80, 90], [20, 60, 80, 90, 100], [20, 60, 70], [20, 60, 70, 100], [20, 60, 70, 90], [20, 60, 70, 90, 100], [20, 60, 70, 80], [20, 60, 70, 80, 100], [20, 60, 70, 80, 90], [20, 60, 70, 80, 90, 100], [20, 50], [20, 50, 100], [20, 50, 90], [20, 50, 90, 100], [20, 50, 80], [20, 50, 80, 100], [20, 50, 80, 90], [20, 50, 80, 90, 100], [20, 50, 70], [20, 50, 70, 100], [20, 50, 70, 90], [20, 50, 70, 90, 100], [20, 50, 70, 80], [20, 50, 70, 80, 100], [20, 50, 70, 80, 90], [20, 50, 70, 80, 90, 100], [20, 50, 60], [20, 50, 60, 100], [20, 50, 60, 90], [20, 50, 60, 90, 100], [20, 50, 60, 80], [20, 50, 60, 80, 100], [20, 50, 60, 80, 90], [20, 50, 60, 80, 90, 100], [20, 50, 60, 70], [20, 50, 60, 70, 100], [20, 50, 60, 70, 90], [20, 50, 60, 70, 90, 100], [20, 50, 60, 70, 80], [20, 50, 60, 70, 80, 100], [20, 50, 60, 70, 80, 90], [20, 50, 60, 70, 80, 90, 100], [20, 40], [20, 40, 100], [20, 40, 90], 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70, 80, 90], [10, 20, 30, 40, 60, 70, 80, 90, 100], [10, 20, 30, 40, 50], [10, 20, 30, 40, 50, 100], [10, 20, 30, 40, 50, 90], [10, 20, 30, 40, 50, 90, 100], [10, 20, 30, 40, 50, 80], [10, 20, 30, 40, 50, 80, 100], [10, 20, 30, 40, 50, 80, 90], [10, 20, 30, 40, 50, 80, 90, 100], [10, 20, 30, 40, 50, 70], [10, 20, 30, 40, 50, 70, 100], [10, 20, 30, 40, 50, 70, 90], [10, 20, 30, 40, 50, 70, 90, 100], [10, 20, 30, 40, 50, 70, 80], [10, 20, 30, 40, 50, 70, 80, 100], [10, 20, 30, 40, 50, 70, 80, 90], [10, 20, 30, 40, 50, 70, 80, 90, 100], [10, 20, 30, 40, 50, 60], [10, 20, 30, 40, 50, 60, 100], [10, 20, 30, 40, 50, 60, 90], [10, 20, 30, 40, 50, 60, 90, 100], [10, 20, 30, 40, 50, 60, 80], [10, 20, 30, 40, 50, 60, 80, 100], [10, 20, 30, 40, 50, 60, 80, 90], [10, 20, 30, 40, 50, 60, 80, 90, 100], [10, 20, 30, 40, 50, 60, 70], [10, 20, 30, 40, 50, 60, 70, 100], [10, 20, 30, 40, 50, 60, 70, 90], [10, 20, 30, 40, 50, 60, 70, 90, 100], [10, 20, 30, 40, 50, 60, 70, 80], [10, 20, 30, 40, 50, 60, 70, 80, 100], [10, 20, 30, 40, 50, 60, 70, 80, 90], [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6]) == [[], [6], [5], [5, 6], [4], [4, 6], [4, 5], [4, 5, 6], [3], [3, 6], [3, 5], [3, 5, 6], [3, 4], [3, 4, 6], [3, 4, 5], [3, 4, 5, 6], [2], [2, 6], [2, 5], [2, 5, 6], [2, 4], [2, 4, 6], [2, 4, 5], [2, 4, 5, 6], [2, 3], [2, 3, 6], [2, 3, 5], [2, 3, 5, 6], [2, 3, 4], [2, 3, 4, 6], [2, 3, 4, 5], [2, 3, 4, 5, 6], [1], [1, 6], [1, 5], [1, 5, 6], [1, 4], [1, 4, 6], [1, 4, 5], [1, 4, 5, 6], [1, 3], [1, 3, 6], [1, 3, 5], [1, 3, 5, 6], [1, 3, 4], [1, 3, 4, 6], [1, 3, 4, 5], [1, 3, 4, 5, 6], [1, 2], [1, 2, 6], [1, 2, 5], [1, 2, 5, 6], [1, 2, 4], [1, 2, 4, 6], [1, 2, 4, 5], [1, 2, 4, 5, 6], [1, 2, 3], [1, 2, 3, 6], [1, 2, 3, 5], [1, 2, 3, 5, 6], [1, 2, 3, 4], [1, 2, 3, 4, 6], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 6]]\n assert candidate(nums = [10, 20, 30, 40, 50]) == [[], [50], [40], [40, 50], [30], [30, 50], [30, 40], [30, 40, 50], [20], [20, 50], [20, 40], [20, 40, 50], [20, 30], [20, 30, 50], [20, 30, 40], [20, 30, 40, 50], [10], [10, 50], [10, 40], [10, 40, 50], [10, 30], [10, 30, 50], [10, 30, 40], [10, 30, 40, 50], [10, 20], [10, 20, 50], [10, 20, 40], [10, 20, 40, 50], [10, 20, 30], [10, 20, 30, 50], [10, 20, 30, 40], [10, 20, 30, 40, 50]]\n assert candidate(nums = [-5, 0, 5, 10, 15]) == [[], [15], [10], [10, 15], [5], [5, 15], [5, 10], [5, 10, 15], [0], [0, 15], [0, 10], [0, 10, 15], [0, 5], [0, 5, 15], [0, 5, 10], [0, 5, 10, 15], [-5], [-5, 15], [-5, 10], [-5, 10, 15], [-5, 5], [-5, 5, 15], [-5, 5, 10], [-5, 5, 10, 15], [-5, 0], [-5, 0, 15], [-5, 0, 10], [-5, 0, 10, 15], [-5, 0, 5], [-5, 0, 5, 15], [-5, 0, 5, 10], [-5, 0, 5, 10, 15]]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [[], [0], [1], [1, 0], [2], [2, 0], [2, 1], [2, 1, 0], [3], [3, 0], [3, 1], [3, 1, 0], [3, 2], [3, 2, 0], [3, 2, 1], [3, 2, 1, 0], [4], [4, 0], [4, 1], [4, 1, 0], [4, 2], [4, 2, 0], [4, 2, 1], [4, 2, 1, 0], [4, 3], [4, 3, 0], [4, 3, 1], [4, 3, 1, 0], [4, 3, 2], [4, 3, 2, 0], [4, 3, 2, 1], [4, 3, 2, 1, 0], [5], [5, 0], [5, 1], [5, 1, 0], [5, 2], [5, 2, 0], [5, 2, 1], [5, 2, 1, 0], [5, 3], [5, 3, 0], [5, 3, 1], [5, 3, 1, 0], [5, 3, 2], [5, 3, 2, 0], [5, 3, 2, 1], [5, 3, 2, 1, 0], [5, 4], [5, 4, 0], [5, 4, 1], [5, 4, 1, 0], [5, 4, 2], [5, 4, 2, 0], [5, 4, 2, 1], [5, 4, 2, 1, 0], [5, 4, 3], [5, 4, 3, 0], [5, 4, 3, 1], [5, 4, 3, 1, 0], [5, 4, 3, 2], [5, 4, 3, 2, 0], [5, 4, 3, 2, 1], [5, 4, 3, 2, 1, 0], [6], [6, 0], [6, 1], [6, 1, 0], [6, 2], [6, 2, 0], [6, 2, 1], [6, 2, 1, 0], [6, 3], [6, 3, 0], [6, 3, 1], [6, 3, 1, 0], [6, 3, 2], [6, 3, 2, 0], [6, 3, 2, 1], [6, 3, 2, 1, 0], [6, 4], [6, 4, 0], [6, 4, 1], [6, 4, 1, 0], [6, 4, 2], [6, 4, 2, 0], [6, 4, 2, 1], [6, 4, 2, 1, 0], [6, 4, 3], [6, 4, 3, 0], [6, 4, 3, 1], [6, 4, 3, 1, 0], [6, 4, 3, 2], [6, 4, 3, 2, 0], [6, 4, 3, 2, 1], [6, 4, 3, 2, 1, 0], [6, 5], [6, 5, 0], [6, 5, 1], [6, 5, 1, 0], [6, 5, 2], [6, 5, 2, 0], [6, 5, 2, 1], [6, 5, 2, 1, 0], [6, 5, 3], [6, 5, 3, 0], [6, 5, 3, 1], [6, 5, 3, 1, 0], [6, 5, 3, 2], [6, 5, 3, 2, 0], [6, 5, 3, 2, 1], [6, 5, 3, 2, 1, 0], [6, 5, 4], [6, 5, 4, 0], [6, 5, 4, 1], [6, 5, 4, 1, 0], [6, 5, 4, 2], [6, 5, 4, 2, 0], [6, 5, 4, 2, 1], [6, 5, 4, 2, 1, 0], [6, 5, 4, 3], [6, 5, 4, 3, 0], [6, 5, 4, 3, 1], [6, 5, 4, 3, 1, 0], [6, 5, 4, 3, 2], [6, 5, 4, 3, 2, 0], [6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 2, 1, 0], [7], [7, 0], [7, 1], [7, 1, 0], [7, 2], [7, 2, 0], [7, 2, 1], [7, 2, 1, 0], [7, 3], [7, 3, 0], [7, 3, 1], [7, 3, 1, 0], [7, 3, 2], [7, 3, 2, 0], [7, 3, 2, 1], [7, 3, 2, 1, 0], [7, 4], [7, 4, 0], [7, 4, 1], [7, 4, 1, 0], [7, 4, 2], [7, 4, 2, 0], [7, 4, 2, 1], [7, 4, 2, 1, 0], [7, 4, 3], [7, 4, 3, 0], [7, 4, 3, 1], [7, 4, 3, 1, 0], [7, 4, 3, 2], [7, 4, 3, 2, 0], [7, 4, 3, 2, 1], [7, 4, 3, 2, 1, 0], [7, 5], [7, 5, 0], [7, 5, 1], [7, 5, 1, 0], [7, 5, 2], [7, 5, 2, 0], [7, 5, 2, 1], [7, 5, 2, 1, 0], [7, 5, 3], [7, 5, 3, 0], [7, 5, 3, 1], [7, 5, 3, 1, 0], [7, 5, 3, 2], [7, 5, 3, 2, 0], [7, 5, 3, 2, 1], [7, 5, 3, 2, 1, 0], [7, 5, 4], [7, 5, 4, 0], [7, 5, 4, 1], [7, 5, 4, 1, 0], [7, 5, 4, 2], [7, 5, 4, 2, 0], [7, 5, 4, 2, 1], [7, 5, 4, 2, 1, 0], [7, 5, 4, 3], [7, 5, 4, 3, 0], [7, 5, 4, 3, 1], [7, 5, 4, 3, 1, 0], [7, 5, 4, 3, 2], [7, 5, 4, 3, 2, 0], [7, 5, 4, 3, 2, 1], [7, 5, 4, 3, 2, 1, 0], [7, 6], [7, 6, 0], [7, 6, 1], [7, 6, 1, 0], [7, 6, 2], [7, 6, 2, 0], [7, 6, 2, 1], [7, 6, 2, 1, 0], [7, 6, 3], [7, 6, 3, 0], [7, 6, 3, 1], [7, 6, 3, 1, 0], [7, 6, 3, 2], [7, 6, 3, 2, 0], [7, 6, 3, 2, 1], [7, 6, 3, 2, 1, 0], [7, 6, 4], [7, 6, 4, 0], [7, 6, 4, 1], [7, 6, 4, 1, 0], [7, 6, 4, 2], [7, 6, 4, 2, 0], [7, 6, 4, 2, 1], [7, 6, 4, 2, 1, 0], [7, 6, 4, 3], [7, 6, 4, 3, 0], [7, 6, 4, 3, 1], [7, 6, 4, 3, 1, 0], [7, 6, 4, 3, 2], [7, 6, 4, 3, 2, 0], [7, 6, 4, 3, 2, 1], [7, 6, 4, 3, 2, 1, 0], [7, 6, 5], [7, 6, 5, 0], [7, 6, 5, 1], [7, 6, 5, 1, 0], [7, 6, 5, 2], [7, 6, 5, 2, 0], [7, 6, 5, 2, 1], [7, 6, 5, 2, 1, 0], [7, 6, 5, 3], [7, 6, 5, 3, 0], [7, 6, 5, 3, 1], [7, 6, 5, 3, 1, 0], [7, 6, 5, 3, 2], [7, 6, 5, 3, 2, 0], [7, 6, 5, 3, 2, 1], [7, 6, 5, 3, 2, 1, 0], [7, 6, 5, 4], [7, 6, 5, 4, 0], [7, 6, 5, 4, 1], [7, 6, 5, 4, 1, 0], [7, 6, 5, 4, 2], [7, 6, 5, 4, 2, 0], [7, 6, 5, 4, 2, 1], [7, 6, 5, 4, 2, 1, 0], [7, 6, 5, 4, 3], [7, 6, 5, 4, 3, 0], [7, 6, 5, 4, 3, 1], [7, 6, 5, 4, 3, 1, 0], [7, 6, 5, 4, 3, 2], [7, 6, 5, 4, 3, 2, 0], [7, 6, 5, 4, 3, 2, 1], [7, 6, 5, 4, 3, 2, 1, 0], [8], [8, 0], [8, 1], [8, 1, 0], [8, 2], [8, 2, 0], [8, 2, 1], [8, 2, 1, 0], [8, 3], [8, 3, 0], [8, 3, 1], [8, 3, 1, 0], [8, 3, 2], [8, 3, 2, 0], [8, 3, 2, 1], [8, 3, 2, 1, 0], [8, 4], [8, 4, 0], [8, 4, 1], [8, 4, 1, 0], [8, 4, 2], [8, 4, 2, 0], [8, 4, 2, 1], [8, 4, 2, 1, 0], [8, 4, 3], [8, 4, 3, 0], [8, 4, 3, 1], [8, 4, 3, 1, 0], [8, 4, 3, 2], [8, 4, 3, 2, 0], [8, 4, 3, 2, 1], [8, 4, 3, 2, 1, 0], [8, 5], [8, 5, 0], [8, 5, 1], [8, 5, 1, 0], [8, 5, 2], [8, 5, 2, 0], [8, 5, 2, 1], [8, 5, 2, 1, 0], [8, 5, 3], [8, 5, 3, 0], [8, 5, 3, 1], [8, 5, 3, 1, 0], [8, 5, 3, 2], [8, 5, 3, 2, 0], [8, 5, 3, 2, 1], [8, 5, 3, 2, 1, 0], [8, 5, 4], [8, 5, 4, 0], [8, 5, 4, 1], [8, 5, 4, 1, 0], [8, 5, 4, 2], [8, 5, 4, 2, 0], [8, 5, 4, 2, 1], [8, 5, 4, 2, 1, 0], [8, 5, 4, 3], [8, 5, 4, 3, 0], [8, 5, 4, 3, 1], [8, 5, 4, 3, 1, 0], [8, 5, 4, 3, 2], [8, 5, 4, 3, 2, 0], [8, 5, 4, 3, 2, 1], [8, 5, 4, 3, 2, 1, 0], [8, 6], [8, 6, 0], [8, 6, 1], [8, 6, 1, 0], [8, 6, 2], [8, 6, 2, 0], [8, 6, 2, 1], [8, 6, 2, 1, 0], [8, 6, 3], [8, 6, 3, 0], [8, 6, 3, 1], [8, 6, 3, 1, 0], [8, 6, 3, 2], [8, 6, 3, 2, 0], [8, 6, 3, 2, 1], [8, 6, 3, 2, 1, 0], [8, 6, 4], [8, 6, 4, 0], [8, 6, 4, 1], [8, 6, 4, 1, 0], [8, 6, 4, 2], [8, 6, 4, 2, 0], [8, 6, 4, 2, 1], [8, 6, 4, 2, 1, 0], [8, 6, 4, 3], [8, 6, 4, 3, 0], [8, 6, 4, 3, 1], [8, 6, 4, 3, 1, 0], [8, 6, 4, 3, 2], [8, 6, 4, 3, 2, 0], [8, 6, 4, 3, 2, 1], [8, 6, 4, 3, 2, 1, 0], [8, 6, 5], [8, 6, 5, 0], [8, 6, 5, 1], [8, 6, 5, 1, 0], [8, 6, 5, 2], [8, 6, 5, 2, 0], [8, 6, 5, 2, 1], [8, 6, 5, 2, 1, 0], [8, 6, 5, 3], [8, 6, 5, 3, 0], [8, 6, 5, 3, 1], [8, 6, 5, 3, 1, 0], [8, 6, 5, 3, 2], [8, 6, 5, 3, 2, 0], [8, 6, 5, 3, 2, 1], [8, 6, 5, 3, 2, 1, 0], [8, 6, 5, 4], [8, 6, 5, 4, 0], [8, 6, 5, 4, 1], [8, 6, 5, 4, 1, 0], [8, 6, 5, 4, 2], [8, 6, 5, 4, 2, 0], [8, 6, 5, 4, 2, 1], [8, 6, 5, 4, 2, 1, 0], [8, 6, 5, 4, 3], [8, 6, 5, 4, 3, 0], [8, 6, 5, 4, 3, 1], [8, 6, 5, 4, 3, 1, 0], [8, 6, 5, 4, 3, 2], [8, 6, 5, 4, 3, 2, 0], [8, 6, 5, 4, 3, 2, 1], [8, 6, 5, 4, 3, 2, 1, 0], [8, 7], [8, 7, 0], [8, 7, 1], [8, 7, 1, 0], [8, 7, 2], [8, 7, 2, 0], [8, 7, 2, 1], [8, 7, 2, 1, 0], [8, 7, 3], [8, 7, 3, 0], [8, 7, 3, 1], [8, 7, 3, 1, 0], [8, 7, 3, 2], [8, 7, 3, 2, 0], [8, 7, 3, 2, 1], [8, 7, 3, 2, 1, 0], [8, 7, 4], [8, 7, 4, 0], [8, 7, 4, 1], [8, 7, 4, 1, 0], [8, 7, 4, 2], [8, 7, 4, 2, 0], [8, 7, 4, 2, 1], [8, 7, 4, 2, 1, 0], [8, 7, 4, 3], [8, 7, 4, 3, 0], [8, 7, 4, 3, 1], [8, 7, 4, 3, 1, 0], [8, 7, 4, 3, 2], [8, 7, 4, 3, 2, 0], [8, 7, 4, 3, 2, 1], [8, 7, 4, 3, 2, 1, 0], [8, 7, 5], [8, 7, 5, 0], [8, 7, 5, 1], [8, 7, 5, 1, 0], [8, 7, 5, 2], [8, 7, 5, 2, 0], [8, 7, 5, 2, 1], [8, 7, 5, 2, 1, 0], [8, 7, 5, 3], [8, 7, 5, 3, 0], [8, 7, 5, 3, 1], [8, 7, 5, 3, 1, 0], [8, 7, 5, 3, 2], [8, 7, 5, 3, 2, 0], [8, 7, 5, 3, 2, 1], [8, 7, 5, 3, 2, 1, 0], [8, 7, 5, 4], [8, 7, 5, 4, 0], [8, 7, 5, 4, 1], [8, 7, 5, 4, 1, 0], [8, 7, 5, 4, 2], [8, 7, 5, 4, 2, 0], [8, 7, 5, 4, 2, 1], [8, 7, 5, 4, 2, 1, 0], [8, 7, 5, 4, 3], [8, 7, 5, 4, 3, 0], [8, 7, 5, 4, 3, 1], [8, 7, 5, 4, 3, 1, 0], [8, 7, 5, 4, 3, 2], [8, 7, 5, 4, 3, 2, 0], [8, 7, 5, 4, 3, 2, 1], [8, 7, 5, 4, 3, 2, 1, 0], [8, 7, 6], [8, 7, 6, 0], [8, 7, 6, 1], [8, 7, 6, 1, 0], [8, 7, 6, 2], [8, 7, 6, 2, 0], [8, 7, 6, 2, 1], [8, 7, 6, 2, 1, 0], [8, 7, 6, 3], [8, 7, 6, 3, 0], [8, 7, 6, 3, 1], [8, 7, 6, 3, 1, 0], [8, 7, 6, 3, 2], [8, 7, 6, 3, 2, 0], [8, 7, 6, 3, 2, 1], [8, 7, 6, 3, 2, 1, 0], [8, 7, 6, 4], [8, 7, 6, 4, 0], [8, 7, 6, 4, 1], [8, 7, 6, 4, 1, 0], [8, 7, 6, 4, 2], [8, 7, 6, 4, 2, 0], [8, 7, 6, 4, 2, 1], [8, 7, 6, 4, 2, 1, 0], [8, 7, 6, 4, 3], [8, 7, 6, 4, 3, 0], [8, 7, 6, 4, 3, 1], [8, 7, 6, 4, 3, 1, 0], [8, 7, 6, 4, 3, 2], [8, 7, 6, 4, 3, 2, 0], [8, 7, 6, 4, 3, 2, 1], [8, 7, 6, 4, 3, 2, 1, 0], [8, 7, 6, 5], [8, 7, 6, 5, 0], [8, 7, 6, 5, 1], [8, 7, 6, 5, 1, 0], [8, 7, 6, 5, 2], [8, 7, 6, 5, 2, 0], [8, 7, 6, 5, 2, 1], [8, 7, 6, 5, 2, 1, 0], [8, 7, 6, 5, 3], [8, 7, 6, 5, 3, 0], [8, 7, 6, 5, 3, 1], [8, 7, 6, 5, 3, 1, 0], [8, 7, 6, 5, 3, 2], [8, 7, 6, 5, 3, 2, 0], [8, 7, 6, 5, 3, 2, 1], [8, 7, 6, 5, 3, 2, 1, 0], [8, 7, 6, 5, 4], [8, 7, 6, 5, 4, 0], [8, 7, 6, 5, 4, 1], [8, 7, 6, 5, 4, 1, 0], [8, 7, 6, 5, 4, 2], [8, 7, 6, 5, 4, 2, 0], [8, 7, 6, 5, 4, 2, 1], [8, 7, 6, 5, 4, 2, 1, 0], [8, 7, 6, 5, 4, 3], [8, 7, 6, 5, 4, 3, 0], [8, 7, 6, 5, 4, 3, 1], [8, 7, 6, 5, 4, 3, 1, 0], [8, 7, 6, 5, 4, 3, 2], [8, 7, 6, 5, 4, 3, 2, 0], [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1, 0], [9], [9, 0], [9, 1], [9, 1, 0], [9, 2], [9, 2, 0], [9, 2, 1], [9, 2, 1, 0], [9, 3], [9, 3, 0], [9, 3, 1], [9, 3, 1, 0], [9, 3, 2], [9, 3, 2, 0], [9, 3, 2, 1], [9, 3, 2, 1, 0], [9, 4], [9, 4, 0], [9, 4, 1], [9, 4, 1, 0], [9, 4, 2], [9, 4, 2, 0], [9, 4, 2, 1], [9, 4, 2, 1, 0], [9, 4, 3], [9, 4, 3, 0], [9, 4, 3, 1], [9, 4, 3, 1, 0], [9, 4, 3, 2], [9, 4, 3, 2, 0], [9, 4, 3, 2, 1], [9, 4, 3, 2, 1, 0], [9, 5], [9, 5, 0], [9, 5, 1], [9, 5, 1, 0], [9, 5, 2], [9, 5, 2, 0], [9, 5, 2, 1], [9, 5, 2, 1, 0], [9, 5, 3], [9, 5, 3, 0], [9, 5, 3, 1], [9, 5, 3, 1, 0], [9, 5, 3, 2], [9, 5, 3, 2, 0], [9, 5, 3, 2, 1], [9, 5, 3, 2, 1, 0], [9, 5, 4], [9, 5, 4, 0], [9, 5, 4, 1], [9, 5, 4, 1, 0], [9, 5, 4, 2], [9, 5, 4, 2, 0], [9, 5, 4, 2, 1], [9, 5, 4, 2, 1, 0], [9, 5, 4, 3], [9, 5, 4, 3, 0], [9, 5, 4, 3, 1], [9, 5, 4, 3, 1, 0], [9, 5, 4, 3, 2], [9, 5, 4, 3, 2, 0], [9, 5, 4, 3, 2, 1], [9, 5, 4, 3, 2, 1, 0], [9, 6], [9, 6, 0], [9, 6, 1], [9, 6, 1, 0], [9, 6, 2], [9, 6, 2, 0], [9, 6, 2, 1], [9, 6, 2, 1, 0], [9, 6, 3], [9, 6, 3, 0], [9, 6, 3, 1], [9, 6, 3, 1, 0], [9, 6, 3, 2], [9, 6, 3, 2, 0], [9, 6, 3, 2, 1], [9, 6, 3, 2, 1, 0], [9, 6, 4], [9, 6, 4, 0], [9, 6, 4, 1], [9, 6, 4, 1, 0], [9, 6, 4, 2], [9, 6, 4, 2, 0], [9, 6, 4, 2, 1], [9, 6, 4, 2, 1, 0], [9, 6, 4, 3], [9, 6, 4, 3, 0], [9, 6, 4, 3, 1], [9, 6, 4, 3, 1, 0], [9, 6, 4, 3, 2], [9, 6, 4, 3, 2, 0], [9, 6, 4, 3, 2, 1], [9, 6, 4, 3, 2, 1, 0], [9, 6, 5], [9, 6, 5, 0], [9, 6, 5, 1], [9, 6, 5, 1, 0], [9, 6, 5, 2], [9, 6, 5, 2, 0], [9, 6, 5, 2, 1], [9, 6, 5, 2, 1, 0], [9, 6, 5, 3], [9, 6, 5, 3, 0], [9, 6, 5, 3, 1], [9, 6, 5, 3, 1, 0], [9, 6, 5, 3, 2], [9, 6, 5, 3, 2, 0], [9, 6, 5, 3, 2, 1], [9, 6, 5, 3, 2, 1, 0], [9, 6, 5, 4], [9, 6, 5, 4, 0], [9, 6, 5, 4, 1], [9, 6, 5, 4, 1, 0], [9, 6, 5, 4, 2], [9, 6, 5, 4, 2, 0], [9, 6, 5, 4, 2, 1], [9, 6, 5, 4, 2, 1, 0], [9, 6, 5, 4, 3], [9, 6, 5, 4, 3, 0], [9, 6, 5, 4, 3, 1], [9, 6, 5, 4, 3, 1, 0], [9, 6, 5, 4, 3, 2], [9, 6, 5, 4, 3, 2, 0], [9, 6, 5, 4, 3, 2, 1], [9, 6, 5, 4, 3, 2, 1, 0], [9, 7], [9, 7, 0], [9, 7, 1], [9, 7, 1, 0], [9, 7, 2], [9, 7, 2, 0], [9, 7, 2, 1], [9, 7, 2, 1, 0], [9, 7, 3], [9, 7, 3, 0], [9, 7, 3, 1], [9, 7, 3, 1, 0], [9, 7, 3, 2], [9, 7, 3, 2, 0], [9, 7, 3, 2, 1], [9, 7, 3, 2, 1, 0], [9, 7, 4], [9, 7, 4, 0], [9, 7, 4, 1], [9, 7, 4, 1, 0], [9, 7, 4, 2], [9, 7, 4, 2, 0], [9, 7, 4, 2, 1], [9, 7, 4, 2, 1, 0], [9, 7, 4, 3], [9, 7, 4, 3, 0], [9, 7, 4, 3, 1], [9, 7, 4, 3, 1, 0], [9, 7, 4, 3, 2], [9, 7, 4, 3, 2, 0], [9, 7, 4, 3, 2, 1], [9, 7, 4, 3, 2, 1, 0], [9, 7, 5], [9, 7, 5, 0], [9, 7, 5, 1], [9, 7, 5, 1, 0], [9, 7, 5, 2], [9, 7, 5, 2, 0], [9, 7, 5, 2, 1], [9, 7, 5, 2, 1, 0], [9, 7, 5, 3], [9, 7, 5, 3, 0], [9, 7, 5, 3, 1], [9, 7, 5, 3, 1, 0], [9, 7, 5, 3, 2], [9, 7, 5, 3, 2, 0], [9, 7, 5, 3, 2, 1], [9, 7, 5, 3, 2, 1, 0], [9, 7, 5, 4], [9, 7, 5, 4, 0], [9, 7, 5, 4, 1], [9, 7, 5, 4, 1, 0], [9, 7, 5, 4, 2], [9, 7, 5, 4, 2, 0], [9, 7, 5, 4, 2, 1], [9, 7, 5, 4, 2, 1, 0], [9, 7, 5, 4, 3], [9, 7, 5, 4, 3, 0], [9, 7, 5, 4, 3, 1], [9, 7, 5, 4, 3, 1, 0], [9, 7, 5, 4, 3, 2], [9, 7, 5, 4, 3, 2, 0], [9, 7, 5, 4, 3, 2, 1], [9, 7, 5, 4, 3, 2, 1, 0], [9, 7, 6], [9, 7, 6, 0], [9, 7, 6, 1], [9, 7, 6, 1, 0], [9, 7, 6, 2], [9, 7, 6, 2, 0], [9, 7, 6, 2, 1], [9, 7, 6, 2, 1, 0], [9, 7, 6, 3], [9, 7, 6, 3, 0], [9, 7, 6, 3, 1], [9, 7, 6, 3, 1, 0], [9, 7, 6, 3, 2], [9, 7, 6, 3, 2, 0], [9, 7, 6, 3, 2, 1], [9, 7, 6, 3, 2, 1, 0], [9, 7, 6, 4], [9, 7, 6, 4, 0], [9, 7, 6, 4, 1], [9, 7, 6, 4, 1, 0], [9, 7, 6, 4, 2], [9, 7, 6, 4, 2, 0], [9, 7, 6, 4, 2, 1], [9, 7, 6, 4, 2, 1, 0], [9, 7, 6, 4, 3], [9, 7, 6, 4, 3, 0], [9, 7, 6, 4, 3, 1], [9, 7, 6, 4, 3, 1, 0], [9, 7, 6, 4, 3, 2], [9, 7, 6, 4, 3, 2, 0], [9, 7, 6, 4, 3, 2, 1], [9, 7, 6, 4, 3, 2, 1, 0], [9, 7, 6, 5], [9, 7, 6, 5, 0], [9, 7, 6, 5, 1], [9, 7, 6, 5, 1, 0], [9, 7, 6, 5, 2], [9, 7, 6, 5, 2, 0], [9, 7, 6, 5, 2, 1], [9, 7, 6, 5, 2, 1, 0], [9, 7, 6, 5, 3], [9, 7, 6, 5, 3, 0], [9, 7, 6, 5, 3, 1], [9, 7, 6, 5, 3, 1, 0], [9, 7, 6, 5, 3, 2], [9, 7, 6, 5, 3, 2, 0], [9, 7, 6, 5, 3, 2, 1], [9, 7, 6, 5, 3, 2, 1, 0], [9, 7, 6, 5, 4], [9, 7, 6, 5, 4, 0], [9, 7, 6, 5, 4, 1], [9, 7, 6, 5, 4, 1, 0], [9, 7, 6, 5, 4, 2], [9, 7, 6, 5, 4, 2, 0], [9, 7, 6, 5, 4, 2, 1], [9, 7, 6, 5, 4, 2, 1, 0], [9, 7, 6, 5, 4, 3], [9, 7, 6, 5, 4, 3, 0], [9, 7, 6, 5, 4, 3, 1], [9, 7, 6, 5, 4, 3, 1, 0], [9, 7, 6, 5, 4, 3, 2], [9, 7, 6, 5, 4, 3, 2, 0], [9, 7, 6, 5, 4, 3, 2, 1], [9, 7, 6, 5, 4, 3, 2, 1, 0], [9, 8], [9, 8, 0], [9, 8, 1], [9, 8, 1, 0], [9, 8, 2], [9, 8, 2, 0], [9, 8, 2, 1], [9, 8, 2, 1, 0], [9, 8, 3], [9, 8, 3, 0], [9, 8, 3, 1], [9, 8, 3, 1, 0], [9, 8, 3, 2], [9, 8, 3, 2, 0], [9, 8, 3, 2, 1], [9, 8, 3, 2, 1, 0], [9, 8, 4], [9, 8, 4, 0], [9, 8, 4, 1], [9, 8, 4, 1, 0], [9, 8, 4, 2], [9, 8, 4, 2, 0], [9, 8, 4, 2, 1], [9, 8, 4, 2, 1, 0], [9, 8, 4, 3], [9, 8, 4, 3, 0], [9, 8, 4, 3, 1], [9, 8, 4, 3, 1, 0], [9, 8, 4, 3, 2], [9, 8, 4, 3, 2, 0], [9, 8, 4, 3, 2, 1], [9, 8, 4, 3, 2, 1, 0], [9, 8, 5], [9, 8, 5, 0], [9, 8, 5, 1], [9, 8, 5, 1, 0], [9, 8, 5, 2], [9, 8, 5, 2, 0], [9, 8, 5, 2, 1], [9, 8, 5, 2, 1, 0], [9, 8, 5, 3], [9, 8, 5, 3, 0], [9, 8, 5, 3, 1], [9, 8, 5, 3, 1, 0], [9, 8, 5, 3, 2], [9, 8, 5, 3, 2, 0], [9, 8, 5, 3, 2, 1], [9, 8, 5, 3, 2, 1, 0], [9, 8, 5, 4], [9, 8, 5, 4, 0], [9, 8, 5, 4, 1], [9, 8, 5, 4, 1, 0], [9, 8, 5, 4, 2], [9, 8, 5, 4, 2, 0], [9, 8, 5, 4, 2, 1], [9, 8, 5, 4, 2, 1, 0], [9, 8, 5, 4, 3], [9, 8, 5, 4, 3, 0], [9, 8, 5, 4, 3, 1], [9, 8, 5, 4, 3, 1, 0], [9, 8, 5, 4, 3, 2], [9, 8, 5, 4, 3, 2, 0], [9, 8, 5, 4, 3, 2, 1], [9, 8, 5, 4, 3, 2, 1, 0], [9, 8, 6], [9, 8, 6, 0], [9, 8, 6, 1], [9, 8, 6, 1, 0], [9, 8, 6, 2], [9, 8, 6, 2, 0], [9, 8, 6, 2, 1], [9, 8, 6, 2, 1, 0], [9, 8, 6, 3], [9, 8, 6, 3, 0], [9, 8, 6, 3, 1], [9, 8, 6, 3, 1, 0], [9, 8, 6, 3, 2], [9, 8, 6, 3, 2, 0], [9, 8, 6, 3, 2, 1], [9, 8, 6, 3, 2, 1, 0], [9, 8, 6, 4], [9, 8, 6, 4, 0], [9, 8, 6, 4, 1], [9, 8, 6, 4, 1, 0], [9, 8, 6, 4, 2], [9, 8, 6, 4, 2, 0], [9, 8, 6, 4, 2, 1], [9, 8, 6, 4, 2, 1, 0], [9, 8, 6, 4, 3], [9, 8, 6, 4, 3, 0], [9, 8, 6, 4, 3, 1], [9, 8, 6, 4, 3, 1, 0], [9, 8, 6, 4, 3, 2], [9, 8, 6, 4, 3, 2, 0], [9, 8, 6, 4, 3, 2, 1], [9, 8, 6, 4, 3, 2, 1, 0], [9, 8, 6, 5], [9, 8, 6, 5, 0], [9, 8, 6, 5, 1], [9, 8, 6, 5, 1, 0], [9, 8, 6, 5, 2], [9, 8, 6, 5, 2, 0], [9, 8, 6, 5, 2, 1], [9, 8, 6, 5, 2, 1, 0], [9, 8, 6, 5, 3], [9, 8, 6, 5, 3, 0], [9, 8, 6, 5, 3, 1], [9, 8, 6, 5, 3, 1, 0], [9, 8, 6, 5, 3, 2], [9, 8, 6, 5, 3, 2, 0], [9, 8, 6, 5, 3, 2, 1], [9, 8, 6, 5, 3, 2, 1, 0], [9, 8, 6, 5, 4], [9, 8, 6, 5, 4, 0], [9, 8, 6, 5, 4, 1], [9, 8, 6, 5, 4, 1, 0], [9, 8, 6, 5, 4, 2], [9, 8, 6, 5, 4, 2, 0], [9, 8, 6, 5, 4, 2, 1], [9, 8, 6, 5, 4, 2, 1, 0], [9, 8, 6, 5, 4, 3], [9, 8, 6, 5, 4, 3, 0], [9, 8, 6, 5, 4, 3, 1], [9, 8, 6, 5, 4, 3, 1, 0], [9, 8, 6, 5, 4, 3, 2], [9, 8, 6, 5, 4, 3, 2, 0], [9, 8, 6, 5, 4, 3, 2, 1], [9, 8, 6, 5, 4, 3, 2, 1, 0], [9, 8, 7], [9, 8, 7, 0], [9, 8, 7, 1], [9, 8, 7, 1, 0], [9, 8, 7, 2], [9, 8, 7, 2, 0], [9, 8, 7, 2, 1], [9, 8, 7, 2, 1, 0], [9, 8, 7, 3], [9, 8, 7, 3, 0], [9, 8, 7, 3, 1], [9, 8, 7, 3, 1, 0], [9, 8, 7, 3, 2], [9, 8, 7, 3, 2, 0], [9, 8, 7, 3, 2, 1], [9, 8, 7, 3, 2, 1, 0], [9, 8, 7, 4], [9, 8, 7, 4, 0], [9, 8, 7, 4, 1], [9, 8, 7, 4, 1, 0], [9, 8, 7, 4, 2], [9, 8, 7, 4, 2, 0], [9, 8, 7, 4, 2, 1], [9, 8, 7, 4, 2, 1, 0], [9, 8, 7, 4, 3], [9, 8, 7, 4, 3, 0], [9, 8, 7, 4, 3, 1], [9, 8, 7, 4, 3, 1, 0], [9, 8, 7, 4, 3, 2], [9, 8, 7, 4, 3, 2, 0], [9, 8, 7, 4, 3, 2, 1], [9, 8, 7, 4, 3, 2, 1, 0], [9, 8, 7, 5], [9, 8, 7, 5, 0], [9, 8, 7, 5, 1], [9, 8, 7, 5, 1, 0], [9, 8, 7, 5, 2], [9, 8, 7, 5, 2, 0], [9, 8, 7, 5, 2, 1], [9, 8, 7, 5, 2, 1, 0], [9, 8, 7, 5, 3], [9, 8, 7, 5, 3, 0], [9, 8, 7, 5, 3, 1], [9, 8, 7, 5, 3, 1, 0], [9, 8, 7, 5, 3, 2], [9, 8, 7, 5, 3, 2, 0], [9, 8, 7, 5, 3, 2, 1], [9, 8, 7, 5, 3, 2, 1, 0], [9, 8, 7, 5, 4], [9, 8, 7, 5, 4, 0], [9, 8, 7, 5, 4, 1], [9, 8, 7, 5, 4, 1, 0], [9, 8, 7, 5, 4, 2], [9, 8, 7, 5, 4, 2, 0], [9, 8, 7, 5, 4, 2, 1], [9, 8, 7, 5, 4, 2, 1, 0], [9, 8, 7, 5, 4, 3], [9, 8, 7, 5, 4, 3, 0], [9, 8, 7, 5, 4, 3, 1], [9, 8, 7, 5, 4, 3, 1, 0], [9, 8, 7, 5, 4, 3, 2], [9, 8, 7, 5, 4, 3, 2, 0], [9, 8, 7, 5, 4, 3, 2, 1], [9, 8, 7, 5, 4, 3, 2, 1, 0], [9, 8, 7, 6], [9, 8, 7, 6, 0], [9, 8, 7, 6, 1], [9, 8, 7, 6, 1, 0], [9, 8, 7, 6, 2], [9, 8, 7, 6, 2, 0], [9, 8, 7, 6, 2, 1], [9, 8, 7, 6, 2, 1, 0], [9, 8, 7, 6, 3], [9, 8, 7, 6, 3, 0], [9, 8, 7, 6, 3, 1], [9, 8, 7, 6, 3, 1, 0], [9, 8, 7, 6, 3, 2], [9, 8, 7, 6, 3, 2, 0], [9, 8, 7, 6, 3, 2, 1], [9, 8, 7, 6, 3, 2, 1, 0], [9, 8, 7, 6, 4], [9, 8, 7, 6, 4, 0], [9, 8, 7, 6, 4, 1], [9, 8, 7, 6, 4, 1, 0], [9, 8, 7, 6, 4, 2], [9, 8, 7, 6, 4, 2, 0], [9, 8, 7, 6, 4, 2, 1], [9, 8, 7, 6, 4, 2, 1, 0], [9, 8, 7, 6, 4, 3], [9, 8, 7, 6, 4, 3, 0], [9, 8, 7, 6, 4, 3, 1], [9, 8, 7, 6, 4, 3, 1, 0], [9, 8, 7, 6, 4, 3, 2], [9, 8, 7, 6, 4, 3, 2, 0], [9, 8, 7, 6, 4, 3, 2, 1], [9, 8, 7, 6, 4, 3, 2, 1, 0], [9, 8, 7, 6, 5], [9, 8, 7, 6, 5, 0], [9, 8, 7, 6, 5, 1], [9, 8, 7, 6, 5, 1, 0], [9, 8, 7, 6, 5, 2], [9, 8, 7, 6, 5, 2, 0], [9, 8, 7, 6, 5, 2, 1], [9, 8, 7, 6, 5, 2, 1, 0], [9, 8, 7, 6, 5, 3], [9, 8, 7, 6, 5, 3, 0], [9, 8, 7, 6, 5, 3, 1], [9, 8, 7, 6, 5, 3, 1, 0], [9, 8, 7, 6, 5, 3, 2], [9, 8, 7, 6, 5, 3, 2, 0], [9, 8, 7, 6, 5, 3, 2, 1], [9, 8, 7, 6, 5, 3, 2, 1, 0], [9, 8, 7, 6, 5, 4], [9, 8, 7, 6, 5, 4, 0], [9, 8, 7, 6, 5, 4, 1], [9, 8, 7, 6, 5, 4, 1, 0], [9, 8, 7, 6, 5, 4, 2], [9, 8, 7, 6, 5, 4, 2, 0], [9, 8, 7, 6, 5, 4, 2, 1], [9, 8, 7, 6, 5, 4, 2, 1, 0], [9, 8, 7, 6, 5, 4, 3], [9, 8, 7, 6, 5, 4, 3, 0], [9, 8, 7, 6, 5, 4, 3, 1], [9, 8, 7, 6, 5, 4, 3, 1, 0], [9, 8, 7, 6, 5, 4, 3, 2], [9, 8, 7, 6, 5, 4, 3, 2, 0], [9, 8, 7, 6, 5, 4, 3, 2, 1], [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]]\n assert candidate(nums = [-5, 0, 5, 10]) == [[], [10], [5], [5, 10], [0], [0, 10], [0, 5], [0, 5, 10], [-5], [-5, 10], [-5, 5], [-5, 5, 10], [-5, 0], [-5, 0, 10], [-5, 0, 5], [-5, 0, 5, 10]]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [[], [0], [1], [1, 0], [2], [2, 0], [2, 1], [2, 1, 0], [3], [3, 0], [3, 1], [3, 1, 0], [3, 2], [3, 2, 0], [3, 2, 1], [3, 2, 1, 0], [4], [4, 0], [4, 1], [4, 1, 0], [4, 2], [4, 2, 0], [4, 2, 1], [4, 2, 1, 0], [4, 3], [4, 3, 0], [4, 3, 1], [4, 3, 1, 0], [4, 3, 2], [4, 3, 2, 0], [4, 3, 2, 1], [4, 3, 2, 1, 0], [5], [5, 0], [5, 1], [5, 1, 0], [5, 2], [5, 2, 0], [5, 2, 1], [5, 2, 1, 0], [5, 3], [5, 3, 0], [5, 3, 1], [5, 3, 1, 0], [5, 3, 2], [5, 3, 2, 0], [5, 3, 2, 1], [5, 3, 2, 1, 0], [5, 4], [5, 4, 0], [5, 4, 1], [5, 4, 1, 0], [5, 4, 2], [5, 4, 2, 0], [5, 4, 2, 1], [5, 4, 2, 1, 0], [5, 4, 3], [5, 4, 3, 0], [5, 4, 3, 1], [5, 4, 3, 1, 0], [5, 4, 3, 2], [5, 4, 3, 2, 0], [5, 4, 3, 2, 1], [5, 4, 3, 2, 1, 0], [6], [6, 0], [6, 1], [6, 1, 0], [6, 2], [6, 2, 0], [6, 2, 1], [6, 2, 1, 0], [6, 3], [6, 3, 0], [6, 3, 1], [6, 3, 1, 0], [6, 3, 2], [6, 3, 2, 0], [6, 3, 2, 1], [6, 3, 2, 1, 0], [6, 4], [6, 4, 0], [6, 4, 1], [6, 4, 1, 0], [6, 4, 2], [6, 4, 2, 0], [6, 4, 2, 1], [6, 4, 2, 1, 0], [6, 4, 3], [6, 4, 3, 0], [6, 4, 3, 1], [6, 4, 3, 1, 0], [6, 4, 3, 2], [6, 4, 3, 2, 0], [6, 4, 3, 2, 1], [6, 4, 3, 2, 1, 0], [6, 5], [6, 5, 0], [6, 5, 1], [6, 5, 1, 0], [6, 5, 2], [6, 5, 2, 0], [6, 5, 2, 1], [6, 5, 2, 1, 0], [6, 5, 3], [6, 5, 3, 0], [6, 5, 3, 1], [6, 5, 3, 1, 0], [6, 5, 3, 2], [6, 5, 3, 2, 0], [6, 5, 3, 2, 1], [6, 5, 3, 2, 1, 0], [6, 5, 4], [6, 5, 4, 0], [6, 5, 4, 1], [6, 5, 4, 1, 0], [6, 5, 4, 2], [6, 5, 4, 2, 0], [6, 5, 4, 2, 1], [6, 5, 4, 2, 1, 0], [6, 5, 4, 3], [6, 5, 4, 3, 0], [6, 5, 4, 3, 1], [6, 5, 4, 3, 1, 0], [6, 5, 4, 3, 2], [6, 5, 4, 3, 2, 0], [6, 5, 4, 3, 2, 1], [6, 5, 4, 3, 2, 1, 0], [7], [7, 0], [7, 1], [7, 1, 0], [7, 2], [7, 2, 0], [7, 2, 1], [7, 2, 1, 0], [7, 3], [7, 3, 0], [7, 3, 1], [7, 3, 1, 0], [7, 3, 2], [7, 3, 2, 0], [7, 3, 2, 1], [7, 3, 2, 1, 0], [7, 4], [7, 4, 0], [7, 4, 1], [7, 4, 1, 0], [7, 4, 2], [7, 4, 2, 0], [7, 4, 2, 1], [7, 4, 2, 1, 0], [7, 4, 3], [7, 4, 3, 0], [7, 4, 3, 1], [7, 4, 3, 1, 0], [7, 4, 3, 2], [7, 4, 3, 2, 0], [7, 4, 3, 2, 1], [7, 4, 3, 2, 1, 0], [7, 5], [7, 5, 0], [7, 5, 1], [7, 5, 1, 0], [7, 5, 2], [7, 5, 2, 0], [7, 5, 2, 1], [7, 5, 2, 1, 0], [7, 5, 3], [7, 5, 3, 0], [7, 5, 3, 1], [7, 5, 3, 1, 0], [7, 5, 3, 2], [7, 5, 3, 2, 0], [7, 5, 3, 2, 1], [7, 5, 3, 2, 1, 0], [7, 5, 4], [7, 5, 4, 0], [7, 5, 4, 1], [7, 5, 4, 1, 0], [7, 5, 4, 2], [7, 5, 4, 2, 0], [7, 5, 4, 2, 1], [7, 5, 4, 2, 1, 0], [7, 5, 4, 3], [7, 5, 4, 3, 0], [7, 5, 4, 3, 1], [7, 5, 4, 3, 1, 0], [7, 5, 4, 3, 2], [7, 5, 4, 3, 2, 0], [7, 5, 4, 3, 2, 1], [7, 5, 4, 3, 2, 1, 0], [7, 6], [7, 6, 0], [7, 6, 1], [7, 6, 1, 0], [7, 6, 2], [7, 6, 2, 0], [7, 6, 2, 1], [7, 6, 2, 1, 0], [7, 6, 3], [7, 6, 3, 0], [7, 6, 3, 1], [7, 6, 3, 1, 0], [7, 6, 3, 2], [7, 6, 3, 2, 0], [7, 6, 3, 2, 1], [7, 6, 3, 2, 1, 0], [7, 6, 4], [7, 6, 4, 0], [7, 6, 4, 1], [7, 6, 4, 1, 0], [7, 6, 4, 2], [7, 6, 4, 2, 0], [7, 6, 4, 2, 1], [7, 6, 4, 2, 1, 0], [7, 6, 4, 3], [7, 6, 4, 3, 0], [7, 6, 4, 3, 1], [7, 6, 4, 3, 1, 0], [7, 6, 4, 3, 2], [7, 6, 4, 3, 2, 0], [7, 6, 4, 3, 2, 1], [7, 6, 4, 3, 2, 1, 0], [7, 6, 5], [7, 6, 5, 0], [7, 6, 5, 1], [7, 6, 5, 1, 0], [7, 6, 5, 2], [7, 6, 5, 2, 0], [7, 6, 5, 2, 1], [7, 6, 5, 2, 1, 0], [7, 6, 5, 3], [7, 6, 5, 3, 0], [7, 6, 5, 3, 1], [7, 6, 5, 3, 1, 0], [7, 6, 5, 3, 2], [7, 6, 5, 3, 2, 0], [7, 6, 5, 3, 2, 1], [7, 6, 5, 3, 2, 1, 0], [7, 6, 5, 4], [7, 6, 5, 4, 0], [7, 6, 5, 4, 1], [7, 6, 5, 4, 1, 0], [7, 6, 5, 4, 2], [7, 6, 5, 4, 2, 0], [7, 6, 5, 4, 2, 1], [7, 6, 5, 4, 2, 1, 0], [7, 6, 5, 4, 3], [7, 6, 5, 4, 3, 0], [7, 6, 5, 4, 3, 1], [7, 6, 5, 4, 3, 1, 0], [7, 6, 5, 4, 3, 2], [7, 6, 5, 4, 3, 2, 0], [7, 6, 5, 4, 3, 2, 1], [7, 6, 5, 4, 3, 2, 1, 0], [8], [8, 0], [8, 1], [8, 1, 0], [8, 2], [8, 2, 0], [8, 2, 1], [8, 2, 1, 0], [8, 3], [8, 3, 0], [8, 3, 1], [8, 3, 1, 0], [8, 3, 2], [8, 3, 2, 0], [8, 3, 2, 1], [8, 3, 2, 1, 0], [8, 4], [8, 4, 0], [8, 4, 1], [8, 4, 1, 0], [8, 4, 2], [8, 4, 2, 0], [8, 4, 2, 1], [8, 4, 2, 1, 0], [8, 4, 3], [8, 4, 3, 0], [8, 4, 3, 1], [8, 4, 3, 1, 0], [8, 4, 3, 2], [8, 4, 3, 2, 0], [8, 4, 3, 2, 1], [8, 4, 3, 2, 1, 0], [8, 5], [8, 5, 0], [8, 5, 1], [8, 5, 1, 0], [8, 5, 2], [8, 5, 2, 0], [8, 5, 2, 1], [8, 5, 2, 1, 0], [8, 5, 3], [8, 5, 3, 0], [8, 5, 3, 1], [8, 5, 3, 1, 0], [8, 5, 3, 2], [8, 5, 3, 2, 0], [8, 5, 3, 2, 1], [8, 5, 3, 2, 1, 0], [8, 5, 4], [8, 5, 4, 0], [8, 5, 4, 1], [8, 5, 4, 1, 0], [8, 5, 4, 2], [8, 5, 4, 2, 0], [8, 5, 4, 2, 1], [8, 5, 4, 2, 1, 0], [8, 5, 4, 3], [8, 5, 4, 3, 0], [8, 5, 4, 3, 1], [8, 5, 4, 3, 1, 0], [8, 5, 4, 3, 2], [8, 5, 4, 3, 2, 0], [8, 5, 4, 3, 2, 1], [8, 5, 4, 3, 2, 1, 0], [8, 6], [8, 6, 0], [8, 6, 1], [8, 6, 1, 0], [8, 6, 2], [8, 6, 2, 0], [8, 6, 2, 1], [8, 6, 2, 1, 0], [8, 6, 3], [8, 6, 3, 0], [8, 6, 3, 1], [8, 6, 3, 1, 0], [8, 6, 3, 2], [8, 6, 3, 2, 0], [8, 6, 3, 2, 1], [8, 6, 3, 2, 1, 0], [8, 6, 4], [8, 6, 4, 0], [8, 6, 4, 1], [8, 6, 4, 1, 0], [8, 6, 4, 2], [8, 6, 4, 2, 0], [8, 6, 4, 2, 1], [8, 6, 4, 2, 1, 0], [8, 6, 4, 3], [8, 6, 4, 3, 0], [8, 6, 4, 3, 1], [8, 6, 4, 3, 1, 0], [8, 6, 4, 3, 2], [8, 6, 4, 3, 2, 0], [8, 6, 4, 3, 2, 1], [8, 6, 4, 3, 2, 1, 0], [8, 6, 5], [8, 6, 5, 0], [8, 6, 5, 1], [8, 6, 5, 1, 0], [8, 6, 5, 2], [8, 6, 5, 2, 0], [8, 6, 5, 2, 1], [8, 6, 5, 2, 1, 0], [8, 6, 5, 3], [8, 6, 5, 3, 0], [8, 6, 5, 3, 1], [8, 6, 5, 3, 1, 0], [8, 6, 5, 3, 2], [8, 6, 5, 3, 2, 0], [8, 6, 5, 3, 2, 1], [8, 6, 5, 3, 2, 1, 0], [8, 6, 5, 4], [8, 6, 5, 4, 0], [8, 6, 5, 4, 1], [8, 6, 5, 4, 1, 0], [8, 6, 5, 4, 2], [8, 6, 5, 4, 2, 0], [8, 6, 5, 4, 2, 1], [8, 6, 5, 4, 2, 1, 0], [8, 6, 5, 4, 3], [8, 6, 5, 4, 3, 0], [8, 6, 5, 4, 3, 1], [8, 6, 5, 4, 3, 1, 0], [8, 6, 5, 4, 3, 2], [8, 6, 5, 4, 3, 2, 0], [8, 6, 5, 4, 3, 2, 1], [8, 6, 5, 4, 3, 2, 1, 0], [8, 7], [8, 7, 0], [8, 7, 1], [8, 7, 1, 0], [8, 7, 2], [8, 7, 2, 0], [8, 7, 2, 1], [8, 7, 2, 1, 0], [8, 7, 3], [8, 7, 3, 0], [8, 7, 3, 1], [8, 7, 3, 1, 0], [8, 7, 3, 2], [8, 7, 3, 2, 0], [8, 7, 3, 2, 1], [8, 7, 3, 2, 1, 0], [8, 7, 4], [8, 7, 4, 0], [8, 7, 4, 1], [8, 7, 4, 1, 0], [8, 7, 4, 2], [8, 7, 4, 2, 0], [8, 7, 4, 2, 1], [8, 7, 4, 2, 1, 0], [8, 7, 4, 3], [8, 7, 4, 3, 0], [8, 7, 4, 3, 1], [8, 7, 4, 3, 1, 0], [8, 7, 4, 3, 2], [8, 7, 4, 3, 2, 0], [8, 7, 4, 3, 2, 1], [8, 7, 4, 3, 2, 1, 0], [8, 7, 5], [8, 7, 5, 0], [8, 7, 5, 1], [8, 7, 5, 1, 0], [8, 7, 5, 2], [8, 7, 5, 2, 0], [8, 7, 5, 2, 1], [8, 7, 5, 2, 1, 0], [8, 7, 5, 3], [8, 7, 5, 3, 0], [8, 7, 5, 3, 1], [8, 7, 5, 3, 1, 0], [8, 7, 5, 3, 2], [8, 7, 5, 3, 2, 0], [8, 7, 5, 3, 2, 1], [8, 7, 5, 3, 2, 1, 0], [8, 7, 5, 4], [8, 7, 5, 4, 0], [8, 7, 5, 4, 1], [8, 7, 5, 4, 1, 0], [8, 7, 5, 4, 2], [8, 7, 5, 4, 2, 0], [8, 7, 5, 4, 2, 1], [8, 7, 5, 4, 2, 1, 0], [8, 7, 5, 4, 3], [8, 7, 5, 4, 3, 0], [8, 7, 5, 4, 3, 1], [8, 7, 5, 4, 3, 1, 0], [8, 7, 5, 4, 3, 2], [8, 7, 5, 4, 3, 2, 0], [8, 7, 5, 4, 3, 2, 1], [8, 7, 5, 4, 3, 2, 1, 0], [8, 7, 6], [8, 7, 6, 0], [8, 7, 6, 1], [8, 7, 6, 1, 0], [8, 7, 6, 2], [8, 7, 6, 2, 0], [8, 7, 6, 2, 1], [8, 7, 6, 2, 1, 0], [8, 7, 6, 3], [8, 7, 6, 3, 0], [8, 7, 6, 3, 1], [8, 7, 6, 3, 1, 0], [8, 7, 6, 3, 2], [8, 7, 6, 3, 2, 0], [8, 7, 6, 3, 2, 1], [8, 7, 6, 3, 2, 1, 0], [8, 7, 6, 4], [8, 7, 6, 4, 0], [8, 7, 6, 4, 1], [8, 7, 6, 4, 1, 0], [8, 7, 6, 4, 2], [8, 7, 6, 4, 2, 0], [8, 7, 6, 4, 2, 1], [8, 7, 6, 4, 2, 1, 0], [8, 7, 6, 4, 3], [8, 7, 6, 4, 3, 0], [8, 7, 6, 4, 3, 1], [8, 7, 6, 4, 3, 1, 0], [8, 7, 6, 4, 3, 2], [8, 7, 6, 4, 3, 2, 0], [8, 7, 6, 4, 3, 2, 1], [8, 7, 6, 4, 3, 2, 1, 0], [8, 7, 6, 5], [8, 7, 6, 5, 0], [8, 7, 6, 5, 1], [8, 7, 6, 5, 1, 0], [8, 7, 6, 5, 2], [8, 7, 6, 5, 2, 0], [8, 7, 6, 5, 2, 1], [8, 7, 6, 5, 2, 1, 0], [8, 7, 6, 5, 3], [8, 7, 6, 5, 3, 0], [8, 7, 6, 5, 3, 1], [8, 7, 6, 5, 3, 1, 0], [8, 7, 6, 5, 3, 2], [8, 7, 6, 5, 3, 2, 0], [8, 7, 6, 5, 3, 2, 1], [8, 7, 6, 5, 3, 2, 1, 0], [8, 7, 6, 5, 4], [8, 7, 6, 5, 4, 0], [8, 7, 6, 5, 4, 1], [8, 7, 6, 5, 4, 1, 0], [8, 7, 6, 5, 4, 2], [8, 7, 6, 5, 4, 2, 0], [8, 7, 6, 5, 4, 2, 1], [8, 7, 6, 5, 4, 2, 1, 0], [8, 7, 6, 5, 4, 3], [8, 7, 6, 5, 4, 3, 0], [8, 7, 6, 5, 4, 3, 1], [8, 7, 6, 5, 4, 3, 1, 0], [8, 7, 6, 5, 4, 3, 2], [8, 7, 6, 5, 4, 3, 2, 0], [8, 7, 6, 5, 4, 3, 2, 1], [8, 7, 6, 5, 4, 3, 2, 1, 0], [9], [9, 0], [9, 1], [9, 1, 0], [9, 2], [9, 2, 0], [9, 2, 1], [9, 2, 1, 0], [9, 3], [9, 3, 0], [9, 3, 1], [9, 3, 1, 0], [9, 3, 2], [9, 3, 2, 0], [9, 3, 2, 1], [9, 3, 2, 1, 0], [9, 4], [9, 4, 0], [9, 4, 1], [9, 4, 1, 0], [9, 4, 2], [9, 4, 2, 0], [9, 4, 2, 1], [9, 4, 2, 1, 0], [9, 4, 3], [9, 4, 3, 0], [9, 4, 3, 1], [9, 4, 3, 1, 0], [9, 4, 3, 2], [9, 4, 3, 2, 0], [9, 4, 3, 2, 1], [9, 4, 3, 2, 1, 0], [9, 5], [9, 5, 0], [9, 5, 1], [9, 5, 1, 0], [9, 5, 2], [9, 5, 2, 0], [9, 5, 2, 1], [9, 5, 2, 1, 0], [9, 5, 3], [9, 5, 3, 0], [9, 5, 3, 1], [9, 5, 3, 1, 0], [9, 5, 3, 2], [9, 5, 3, 2, 0], [9, 5, 3, 2, 1], [9, 5, 3, 2, 1, 0], [9, 5, 4], [9, 5, 4, 0], [9, 5, 4, 1], [9, 5, 4, 1, 0], [9, 5, 4, 2], [9, 5, 4, 2, 0], [9, 5, 4, 2, 1], [9, 5, 4, 2, 1, 0], [9, 5, 4, 3], [9, 5, 4, 3, 0], [9, 5, 4, 3, 1], [9, 5, 4, 3, 1, 0], [9, 5, 4, 3, 2], [9, 5, 4, 3, 2, 0], [9, 5, 4, 3, 2, 1], [9, 5, 4, 3, 2, 1, 0], [9, 6], [9, 6, 0], [9, 6, 1], [9, 6, 1, 0], [9, 6, 2], [9, 6, 2, 0], [9, 6, 2, 1], [9, 6, 2, 1, 0], [9, 6, 3], [9, 6, 3, 0], [9, 6, 3, 1], [9, 6, 3, 1, 0], [9, 6, 3, 2], [9, 6, 3, 2, 0], [9, 6, 3, 2, 1], [9, 6, 3, 2, 1, 0], [9, 6, 4], [9, 6, 4, 0], [9, 6, 4, 1], [9, 6, 4, 1, 0], [9, 6, 4, 2], [9, 6, 4, 2, 0], [9, 6, 4, 2, 1], [9, 6, 4, 2, 1, 0], [9, 6, 4, 3], [9, 6, 4, 3, 0], [9, 6, 4, 3, 1], [9, 6, 4, 3, 1, 0], [9, 6, 4, 3, 2], [9, 6, 4, 3, 2, 0], [9, 6, 4, 3, 2, 1], [9, 6, 4, 3, 2, 1, 0], [9, 6, 5], [9, 6, 5, 0], [9, 6, 5, 1], [9, 6, 5, 1, 0], [9, 6, 5, 2], [9, 6, 5, 2, 0], [9, 6, 5, 2, 1], [9, 6, 5, 2, 1, 0], [9, 6, 5, 3], [9, 6, 5, 3, 0], [9, 6, 5, 3, 1], [9, 6, 5, 3, 1, 0], [9, 6, 5, 3, 2], [9, 6, 5, 3, 2, 0], [9, 6, 5, 3, 2, 1], [9, 6, 5, 3, 2, 1, 0], [9, 6, 5, 4], [9, 6, 5, 4, 0], [9, 6, 5, 4, 1], [9, 6, 5, 4, 1, 0], [9, 6, 5, 4, 2], [9, 6, 5, 4, 2, 0], [9, 6, 5, 4, 2, 1], [9, 6, 5, 4, 2, 1, 0], [9, 6, 5, 4, 3], [9, 6, 5, 4, 3, 0], [9, 6, 5, 4, 3, 1], [9, 6, 5, 4, 3, 1, 0], [9, 6, 5, 4, 3, 2], [9, 6, 5, 4, 3, 2, 0], [9, 6, 5, 4, 3, 2, 1], [9, 6, 5, 4, 3, 2, 1, 0], [9, 7], [9, 7, 0], [9, 7, 1], [9, 7, 1, 0], [9, 7, 2], [9, 7, 2, 0], [9, 7, 2, 1], [9, 7, 2, 1, 0], [9, 7, 3], [9, 7, 3, 0], [9, 7, 3, 1], [9, 7, 3, 1, 0], [9, 7, 3, 2], [9, 7, 3, 2, 0], [9, 7, 3, 2, 1], [9, 7, 3, 2, 1, 0], [9, 7, 4], [9, 7, 4, 0], [9, 7, 4, 1], [9, 7, 4, 1, 0], [9, 7, 4, 2], [9, 7, 4, 2, 0], [9, 7, 4, 2, 1], [9, 7, 4, 2, 1, 0], [9, 7, 4, 3], [9, 7, 4, 3, 0], [9, 7, 4, 3, 1], [9, 7, 4, 3, 1, 0], [9, 7, 4, 3, 2], [9, 7, 4, 3, 2, 0], [9, 7, 4, 3, 2, 1], [9, 7, 4, 3, 2, 1, 0], [9, 7, 5], [9, 7, 5, 0], [9, 7, 5, 1], [9, 7, 5, 1, 0], [9, 7, 5, 2], [9, 7, 5, 2, 0], [9, 7, 5, 2, 1], [9, 7, 5, 2, 1, 0], [9, 7, 5, 3], [9, 7, 5, 3, 0], [9, 7, 5, 3, 1], [9, 7, 5, 3, 1, 0], [9, 7, 5, 3, 2], [9, 7, 5, 3, 2, 0], [9, 7, 5, 3, 2, 1], [9, 7, 5, 3, 2, 1, 0], [9, 7, 5, 4], [9, 7, 5, 4, 0], [9, 7, 5, 4, 1], [9, 7, 5, 4, 1, 0], [9, 7, 5, 4, 2], [9, 7, 5, 4, 2, 0], [9, 7, 5, 4, 2, 1], [9, 7, 5, 4, 2, 1, 0], [9, 7, 5, 4, 3], [9, 7, 5, 4, 3, 0], [9, 7, 5, 4, 3, 1], [9, 7, 5, 4, 3, 1, 0], [9, 7, 5, 4, 3, 2], [9, 7, 5, 4, 3, 2, 0], [9, 7, 5, 4, 3, 2, 1], [9, 7, 5, 4, 3, 2, 1, 0], [9, 7, 6], [9, 7, 6, 0], [9, 7, 6, 1], [9, 7, 6, 1, 0], [9, 7, 6, 2], [9, 7, 6, 2, 0], [9, 7, 6, 2, 1], [9, 7, 6, 2, 1, 0], [9, 7, 6, 3], [9, 7, 6, 3, 0], [9, 7, 6, 3, 1], [9, 7, 6, 3, 1, 0], [9, 7, 6, 3, 2], [9, 7, 6, 3, 2, 0], [9, 7, 6, 3, 2, 1], [9, 7, 6, 3, 2, 1, 0], [9, 7, 6, 4], [9, 7, 6, 4, 0], [9, 7, 6, 4, 1], [9, 7, 6, 4, 1, 0], [9, 7, 6, 4, 2], [9, 7, 6, 4, 2, 0], [9, 7, 6, 4, 2, 1], [9, 7, 6, 4, 2, 1, 0], [9, 7, 6, 4, 3], [9, 7, 6, 4, 3, 0], [9, 7, 6, 4, 3, 1], [9, 7, 6, 4, 3, 1, 0], [9, 7, 6, 4, 3, 2], [9, 7, 6, 4, 3, 2, 0], [9, 7, 6, 4, 3, 2, 1], [9, 7, 6, 4, 3, 2, 1, 0], [9, 7, 6, 5], [9, 7, 6, 5, 0], [9, 7, 6, 5, 1], [9, 7, 6, 5, 1, 0], [9, 7, 6, 5, 2], [9, 7, 6, 5, 2, 0], [9, 7, 6, 5, 2, 1], [9, 7, 6, 5, 2, 1, 0], [9, 7, 6, 5, 3], [9, 7, 6, 5, 3, 0], [9, 7, 6, 5, 3, 1], [9, 7, 6, 5, 3, 1, 0], [9, 7, 6, 5, 3, 2], [9, 7, 6, 5, 3, 2, 0], [9, 7, 6, 5, 3, 2, 1], [9, 7, 6, 5, 3, 2, 1, 0], [9, 7, 6, 5, 4], [9, 7, 6, 5, 4, 0], [9, 7, 6, 5, 4, 1], [9, 7, 6, 5, 4, 1, 0], [9, 7, 6, 5, 4, 2], [9, 7, 6, 5, 4, 2, 0], [9, 7, 6, 5, 4, 2, 1], [9, 7, 6, 5, 4, 2, 1, 0], [9, 7, 6, 5, 4, 3], [9, 7, 6, 5, 4, 3, 0], [9, 7, 6, 5, 4, 3, 1], [9, 7, 6, 5, 4, 3, 1, 0], [9, 7, 6, 5, 4, 3, 2], [9, 7, 6, 5, 4, 3, 2, 0], [9, 7, 6, 5, 4, 3, 2, 1], [9, 7, 6, 5, 4, 3, 2, 1, 0], [9, 8], [9, 8, 0], [9, 8, 1], [9, 8, 1, 0], [9, 8, 2], [9, 8, 2, 0], [9, 8, 2, 1], [9, 8, 2, 1, 0], [9, 8, 3], [9, 8, 3, 0], [9, 8, 3, 1], [9, 8, 3, 1, 0], [9, 8, 3, 2], [9, 8, 3, 2, 0], [9, 8, 3, 2, 1], [9, 8, 3, 2, 1, 0], [9, 8, 4], [9, 8, 4, 0], [9, 8, 4, 1], [9, 8, 4, 1, 0], [9, 8, 4, 2], [9, 8, 4, 2, 0], [9, 8, 4, 2, 1], [9, 8, 4, 2, 1, 0], [9, 8, 4, 3], [9, 8, 4, 3, 0], [9, 8, 4, 3, 1], [9, 8, 4, 3, 1, 0], [9, 8, 4, 3, 2], [9, 8, 4, 3, 2, 0], [9, 8, 4, 3, 2, 1], [9, 8, 4, 3, 2, 1, 0], [9, 8, 5], [9, 8, 5, 0], [9, 8, 5, 1], [9, 8, 5, 1, 0], [9, 8, 5, 2], [9, 8, 5, 2, 0], [9, 8, 5, 2, 1], [9, 8, 5, 2, 1, 0], [9, 8, 5, 3], [9, 8, 5, 3, 0], [9, 8, 5, 3, 1], [9, 8, 5, 3, 1, 0], [9, 8, 5, 3, 2], [9, 8, 5, 3, 2, 0], [9, 8, 5, 3, 2, 1], [9, 8, 5, 3, 2, 1, 0], [9, 8, 5, 4], [9, 8, 5, 4, 0], [9, 8, 5, 4, 1], [9, 8, 5, 4, 1, 0], [9, 8, 5, 4, 2], [9, 8, 5, 4, 2, 0], [9, 8, 5, 4, 2, 1], [9, 8, 5, 4, 2, 1, 0], [9, 8, 5, 4, 3], [9, 8, 5, 4, 3, 0], [9, 8, 5, 4, 3, 1], [9, 8, 5, 4, 3, 1, 0], [9, 8, 5, 4, 3, 2], [9, 8, 5, 4, 3, 2, 0], [9, 8, 5, 4, 3, 2, 1], [9, 8, 5, 4, 3, 2, 1, 0], [9, 8, 6], [9, 8, 6, 0], [9, 8, 6, 1], [9, 8, 6, 1, 0], [9, 8, 6, 2], [9, 8, 6, 2, 0], [9, 8, 6, 2, 1], [9, 8, 6, 2, 1, 0], [9, 8, 6, 3], [9, 8, 6, 3, 0], [9, 8, 6, 3, 1], [9, 8, 6, 3, 1, 0], [9, 8, 6, 3, 2], [9, 8, 6, 3, 2, 0], [9, 8, 6, 3, 2, 1], [9, 8, 6, 3, 2, 1, 0], [9, 8, 6, 4], [9, 8, 6, 4, 0], [9, 8, 6, 4, 1], [9, 8, 6, 4, 1, 0], [9, 8, 6, 4, 2], [9, 8, 6, 4, 2, 0], [9, 8, 6, 4, 2, 1], [9, 8, 6, 4, 2, 1, 0], [9, 8, 6, 4, 3], [9, 8, 6, 4, 3, 0], [9, 8, 6, 4, 3, 1], [9, 8, 6, 4, 3, 1, 0], [9, 8, 6, 4, 3, 2], [9, 8, 6, 4, 3, 2, 0], [9, 8, 6, 4, 3, 2, 1], [9, 8, 6, 4, 3, 2, 1, 0], [9, 8, 6, 5], [9, 8, 6, 5, 0], [9, 8, 6, 5, 1], [9, 8, 6, 5, 1, 0], [9, 8, 6, 5, 2], [9, 8, 6, 5, 2, 0], [9, 8, 6, 5, 2, 1], [9, 8, 6, 5, 2, 1, 0], [9, 8, 6, 5, 3], [9, 8, 6, 5, 3, 0], [9, 8, 6, 5, 3, 1], [9, 8, 6, 5, 3, 1, 0], [9, 8, 6, 5, 3, 2], [9, 8, 6, 5, 3, 2, 0], [9, 8, 6, 5, 3, 2, 1], [9, 8, 6, 5, 3, 2, 1, 0], [9, 8, 6, 5, 4], [9, 8, 6, 5, 4, 0], [9, 8, 6, 5, 4, 1], [9, 8, 6, 5, 4, 1, 0], [9, 8, 6, 5, 4, 2], [9, 8, 6, 5, 4, 2, 0], [9, 8, 6, 5, 4, 2, 1], [9, 8, 6, 5, 4, 2, 1, 0], [9, 8, 6, 5, 4, 3], [9, 8, 6, 5, 4, 3, 0], [9, 8, 6, 5, 4, 3, 1], [9, 8, 6, 5, 4, 3, 1, 0], [9, 8, 6, 5, 4, 3, 2], [9, 8, 6, 5, 4, 3, 2, 0], [9, 8, 6, 5, 4, 3, 2, 1], [9, 8, 6, 5, 4, 3, 2, 1, 0], [9, 8, 7], [9, 8, 7, 0], [9, 8, 7, 1], [9, 8, 7, 1, 0], [9, 8, 7, 2], [9, 8, 7, 2, 0], [9, 8, 7, 2, 1], [9, 8, 7, 2, 1, 0], [9, 8, 7, 3], [9, 8, 7, 3, 0], [9, 8, 7, 3, 1], [9, 8, 7, 3, 1, 0], [9, 8, 7, 3, 2], [9, 8, 7, 3, 2, 0], [9, 8, 7, 3, 2, 1], [9, 8, 7, 3, 2, 1, 0], [9, 8, 7, 4], [9, 8, 7, 4, 0], [9, 8, 7, 4, 1], [9, 8, 7, 4, 1, 0], [9, 8, 7, 4, 2], [9, 8, 7, 4, 2, 0], [9, 8, 7, 4, 2, 1], [9, 8, 7, 4, 2, 1, 0], [9, 8, 7, 4, 3], [9, 8, 7, 4, 3, 0], [9, 8, 7, 4, 3, 1], [9, 8, 7, 4, 3, 1, 0], [9, 8, 7, 4, 3, 2], [9, 8, 7, 4, 3, 2, 0], [9, 8, 7, 4, 3, 2, 1], [9, 8, 7, 4, 3, 2, 1, 0], [9, 8, 7, 5], [9, 8, 7, 5, 0], [9, 8, 7, 5, 1], [9, 8, 7, 5, 1, 0], [9, 8, 7, 5, 2], [9, 8, 7, 5, 2, 0], [9, 8, 7, 5, 2, 1], [9, 8, 7, 5, 2, 1, 0], [9, 8, 7, 5, 3], [9, 8, 7, 5, 3, 0], [9, 8, 7, 5, 3, 1], [9, 8, 7, 5, 3, 1, 0], [9, 8, 7, 5, 3, 2], [9, 8, 7, 5, 3, 2, 0], [9, 8, 7, 5, 3, 2, 1], [9, 8, 7, 5, 3, 2, 1, 0], [9, 8, 7, 5, 4], [9, 8, 7, 5, 4, 0], [9, 8, 7, 5, 4, 1], [9, 8, 7, 5, 4, 1, 0], [9, 8, 7, 5, 4, 2], [9, 8, 7, 5, 4, 2, 0], [9, 8, 7, 5, 4, 2, 1], [9, 8, 7, 5, 4, 2, 1, 0], [9, 8, 7, 5, 4, 3], [9, 8, 7, 5, 4, 3, 0], [9, 8, 7, 5, 4, 3, 1], [9, 8, 7, 5, 4, 3, 1, 0], [9, 8, 7, 5, 4, 3, 2], [9, 8, 7, 5, 4, 3, 2, 0], [9, 8, 7, 5, 4, 3, 2, 1], [9, 8, 7, 5, 4, 3, 2, 1, 0], [9, 8, 7, 6], [9, 8, 7, 6, 0], [9, 8, 7, 6, 1], [9, 8, 7, 6, 1, 0], [9, 8, 7, 6, 2], [9, 8, 7, 6, 2, 0], [9, 8, 7, 6, 2, 1], [9, 8, 7, 6, 2, 1, 0], [9, 8, 7, 6, 3], [9, 8, 7, 6, 3, 0], [9, 8, 7, 6, 3, 1], [9, 8, 7, 6, 3, 1, 0], [9, 8, 7, 6, 3, 2], [9, 8, 7, 6, 3, 2, 0], [9, 8, 7, 6, 3, 2, 1], [9, 8, 7, 6, 3, 2, 1, 0], [9, 8, 7, 6, 4], [9, 8, 7, 6, 4, 0], [9, 8, 7, 6, 4, 1], [9, 8, 7, 6, 4, 1, 0], [9, 8, 7, 6, 4, 2], [9, 8, 7, 6, 4, 2, 0], [9, 8, 7, 6, 4, 2, 1], [9, 8, 7, 6, 4, 2, 1, 0], [9, 8, 7, 6, 4, 3], [9, 8, 7, 6, 4, 3, 0], [9, 8, 7, 6, 4, 3, 1], [9, 8, 7, 6, 4, 3, 1, 0], [9, 8, 7, 6, 4, 3, 2], [9, 8, 7, 6, 4, 3, 2, 0], [9, 8, 7, 6, 4, 3, 2, 1], [9, 8, 7, 6, 4, 3, 2, 1, 0], [9, 8, 7, 6, 5], [9, 8, 7, 6, 5, 0], [9, 8, 7, 6, 5, 1], [9, 8, 7, 6, 5, 1, 0], [9, 8, 7, 6, 5, 2], [9, 8, 7, 6, 5, 2, 0], [9, 8, 7, 6, 5, 2, 1], [9, 8, 7, 6, 5, 2, 1, 0], [9, 8, 7, 6, 5, 3], [9, 8, 7, 6, 5, 3, 0], [9, 8, 7, 6, 5, 3, 1], [9, 8, 7, 6, 5, 3, 1, 0], [9, 8, 7, 6, 5, 3, 2], [9, 8, 7, 6, 5, 3, 2, 0], [9, 8, 7, 6, 5, 3, 2, 1], [9, 8, 7, 6, 5, 3, 2, 1, 0], [9, 8, 7, 6, 5, 4], [9, 8, 7, 6, 5, 4, 0], [9, 8, 7, 6, 5, 4, 1], [9, 8, 7, 6, 5, 4, 1, 0], [9, 8, 7, 6, 5, 4, 2], [9, 8, 7, 6, 5, 4, 2, 0], [9, 8, 7, 6, 5, 4, 2, 1], [9, 8, 7, 6, 5, 4, 2, 1, 0], [9, 8, 7, 6, 5, 4, 3], [9, 8, 7, 6, 5, 4, 3, 0], [9, 8, 7, 6, 5, 4, 3, 1], [9, 8, 7, 6, 5, 4, 3, 1, 0], [9, 8, 7, 6, 5, 4, 3, 2], [9, 8, 7, 6, 5, 4, 3, 2, 0], [9, 8, 7, 6, 5, 4, 3, 2, 1], [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]]\n assert candidate(nums = [5, 3, 8, 6, 2, 7, 4, 1]) == [[], [1], [4], [4, 1], [7], [7, 1], [7, 4], [7, 4, 1], [2], [2, 1], [2, 4], [2, 4, 1], [2, 7], [2, 7, 1], [2, 7, 4], [2, 7, 4, 1], [6], [6, 1], [6, 4], [6, 4, 1], [6, 7], [6, 7, 1], [6, 7, 4], [6, 7, 4, 1], [6, 2], [6, 2, 1], [6, 2, 4], [6, 2, 4, 1], [6, 2, 7], [6, 2, 7, 1], [6, 2, 7, 4], [6, 2, 7, 4, 1], [8], [8, 1], [8, 4], [8, 4, 1], [8, 7], [8, 7, 1], [8, 7, 4], [8, 7, 4, 1], [8, 2], [8, 2, 1], [8, 2, 4], [8, 2, 4, 1], [8, 2, 7], [8, 2, 7, 1], [8, 2, 7, 4], [8, 2, 7, 4, 1], [8, 6], [8, 6, 1], [8, 6, 4], [8, 6, 4, 1], [8, 6, 7], [8, 6, 7, 1], [8, 6, 7, 4], [8, 6, 7, 4, 1], [8, 6, 2], [8, 6, 2, 1], [8, 6, 2, 4], [8, 6, 2, 4, 1], [8, 6, 2, 7], [8, 6, 2, 7, 1], [8, 6, 2, 7, 4], [8, 6, 2, 7, 4, 1], [3], [3, 1], [3, 4], [3, 4, 1], [3, 7], [3, 7, 1], [3, 7, 4], [3, 7, 4, 1], [3, 2], [3, 2, 1], [3, 2, 4], [3, 2, 4, 1], [3, 2, 7], [3, 2, 7, 1], [3, 2, 7, 4], [3, 2, 7, 4, 1], [3, 6], [3, 6, 1], [3, 6, 4], [3, 6, 4, 1], [3, 6, 7], [3, 6, 7, 1], [3, 6, 7, 4], [3, 6, 7, 4, 1], [3, 6, 2], [3, 6, 2, 1], [3, 6, 2, 4], [3, 6, 2, 4, 1], [3, 6, 2, 7], [3, 6, 2, 7, 1], [3, 6, 2, 7, 4], [3, 6, 2, 7, 4, 1], [3, 8], [3, 8, 1], [3, 8, 4], [3, 8, 4, 1], [3, 8, 7], [3, 8, 7, 1], [3, 8, 7, 4], [3, 8, 7, 4, 1], [3, 8, 2], [3, 8, 2, 1], [3, 8, 2, 4], [3, 8, 2, 4, 1], [3, 8, 2, 7], [3, 8, 2, 7, 1], [3, 8, 2, 7, 4], [3, 8, 2, 7, 4, 1], [3, 8, 6], [3, 8, 6, 1], [3, 8, 6, 4], [3, 8, 6, 4, 1], [3, 8, 6, 7], [3, 8, 6, 7, 1], [3, 8, 6, 7, 4], [3, 8, 6, 7, 4, 1], [3, 8, 6, 2], [3, 8, 6, 2, 1], [3, 8, 6, 2, 4], [3, 8, 6, 2, 4, 1], [3, 8, 6, 2, 7], [3, 8, 6, 2, 7, 1], [3, 8, 6, 2, 7, 4], [3, 8, 6, 2, 7, 4, 1], [5], [5, 1], [5, 4], [5, 4, 1], [5, 7], [5, 7, 1], [5, 7, 4], [5, 7, 4, 1], [5, 2], [5, 2, 1], [5, 2, 4], [5, 2, 4, 1], [5, 2, 7], [5, 2, 7, 1], [5, 2, 7, 4], [5, 2, 7, 4, 1], [5, 6], [5, 6, 1], [5, 6, 4], [5, 6, 4, 1], [5, 6, 7], [5, 6, 7, 1], [5, 6, 7, 4], [5, 6, 7, 4, 1], [5, 6, 2], [5, 6, 2, 1], [5, 6, 2, 4], [5, 6, 2, 4, 1], [5, 6, 2, 7], [5, 6, 2, 7, 1], [5, 6, 2, 7, 4], [5, 6, 2, 7, 4, 1], [5, 8], [5, 8, 1], [5, 8, 4], [5, 8, 4, 1], [5, 8, 7], [5, 8, 7, 1], [5, 8, 7, 4], [5, 8, 7, 4, 1], [5, 8, 2], [5, 8, 2, 1], [5, 8, 2, 4], [5, 8, 2, 4, 1], [5, 8, 2, 7], [5, 8, 2, 7, 1], [5, 8, 2, 7, 4], [5, 8, 2, 7, 4, 1], [5, 8, 6], [5, 8, 6, 1], [5, 8, 6, 4], [5, 8, 6, 4, 1], [5, 8, 6, 7], [5, 8, 6, 7, 1], [5, 8, 6, 7, 4], [5, 8, 6, 7, 4, 1], [5, 8, 6, 2], [5, 8, 6, 2, 1], [5, 8, 6, 2, 4], [5, 8, 6, 2, 4, 1], [5, 8, 6, 2, 7], [5, 8, 6, 2, 7, 1], [5, 8, 6, 2, 7, 4], [5, 8, 6, 2, 7, 4, 1], [5, 3], [5, 3, 1], [5, 3, 4], [5, 3, 4, 1], [5, 3, 7], [5, 3, 7, 1], [5, 3, 7, 4], [5, 3, 7, 4, 1], [5, 3, 2], [5, 3, 2, 1], [5, 3, 2, 4], [5, 3, 2, 4, 1], [5, 3, 2, 7], [5, 3, 2, 7, 1], [5, 3, 2, 7, 4], [5, 3, 2, 7, 4, 1], [5, 3, 6], [5, 3, 6, 1], [5, 3, 6, 4], [5, 3, 6, 4, 1], [5, 3, 6, 7], [5, 3, 6, 7, 1], [5, 3, 6, 7, 4], [5, 3, 6, 7, 4, 1], [5, 3, 6, 2], [5, 3, 6, 2, 1], [5, 3, 6, 2, 4], [5, 3, 6, 2, 4, 1], [5, 3, 6, 2, 7], [5, 3, 6, 2, 7, 1], [5, 3, 6, 2, 7, 4], [5, 3, 6, 2, 7, 4, 1], [5, 3, 8], [5, 3, 8, 1], [5, 3, 8, 4], [5, 3, 8, 4, 1], [5, 3, 8, 7], [5, 3, 8, 7, 1], [5, 3, 8, 7, 4], [5, 3, 8, 7, 4, 1], [5, 3, 8, 2], [5, 3, 8, 2, 1], [5, 3, 8, 2, 4], [5, 3, 8, 2, 4, 1], [5, 3, 8, 2, 7], [5, 3, 8, 2, 7, 1], [5, 3, 8, 2, 7, 4], [5, 3, 8, 2, 7, 4, 1], [5, 3, 8, 6], [5, 3, 8, 6, 1], [5, 3, 8, 6, 4], [5, 3, 8, 6, 4, 1], [5, 3, 8, 6, 7], [5, 3, 8, 6, 7, 1], [5, 3, 8, 6, 7, 4], [5, 3, 8, 6, 7, 4, 1], [5, 3, 8, 6, 2], [5, 3, 8, 6, 2, 1], [5, 3, 8, 6, 2, 4], [5, 3, 8, 6, 2, 4, 1], [5, 3, 8, 6, 2, 7], [5, 3, 8, 6, 2, 7, 1], [5, 3, 8, 6, 2, 7, 4], [5, 3, 8, 6, 2, 7, 4, 1]]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4]) == [[], [-4], [4], [4, -4], [-3], [-3, -4], [-3, 4], [-3, 4, -4], [3], [3, -4], [3, 4], [3, 4, -4], [3, -3], [3, -3, -4], [3, -3, 4], [3, -3, 4, -4], [-2], [-2, -4], [-2, 4], [-2, 4, -4], [-2, -3], [-2, -3, -4], [-2, -3, 4], [-2, -3, 4, -4], [-2, 3], [-2, 3, -4], [-2, 3, 4], [-2, 3, 4, -4], [-2, 3, -3], [-2, 3, -3, -4], [-2, 3, -3, 4], [-2, 3, -3, 4, -4], [2], [2, -4], [2, 4], [2, 4, -4], [2, -3], [2, -3, -4], [2, -3, 4], [2, -3, 4, -4], [2, 3], [2, 3, -4], [2, 3, 4], [2, 3, 4, -4], [2, 3, -3], [2, 3, -3, -4], [2, 3, -3, 4], [2, 3, -3, 4, -4], [2, -2], [2, -2, -4], [2, -2, 4], [2, -2, 4, -4], [2, -2, -3], [2, -2, -3, -4], [2, -2, -3, 4], [2, -2, -3, 4, -4], [2, -2, 3], [2, -2, 3, -4], [2, -2, 3, 4], [2, -2, 3, 4, -4], [2, -2, 3, -3], [2, -2, 3, -3, -4], [2, -2, 3, -3, 4], [2, -2, 3, -3, 4, -4], [-1], [-1, -4], [-1, 4], [-1, 4, -4], [-1, -3], [-1, -3, -4], [-1, -3, 4], [-1, -3, 4, -4], [-1, 3], [-1, 3, -4], [-1, 3, 4], [-1, 3, 4, -4], [-1, 3, -3], [-1, 3, -3, -4], [-1, 3, -3, 4], [-1, 3, -3, 4, -4], [-1, -2], [-1, -2, -4], [-1, -2, 4], [-1, -2, 4, -4], [-1, -2, -3], [-1, -2, -3, -4], [-1, -2, -3, 4], [-1, -2, -3, 4, -4], [-1, -2, 3], [-1, -2, 3, -4], [-1, -2, 3, 4], [-1, -2, 3, 4, -4], [-1, -2, 3, -3], [-1, -2, 3, -3, -4], [-1, -2, 3, -3, 4], [-1, -2, 3, -3, 4, -4], [-1, 2], [-1, 2, -4], [-1, 2, 4], [-1, 2, 4, -4], [-1, 2, -3], [-1, 2, -3, -4], [-1, 2, -3, 4], [-1, 2, -3, 4, -4], [-1, 2, 3], [-1, 2, 3, -4], [-1, 2, 3, 4], [-1, 2, 3, 4, -4], [-1, 2, 3, -3], [-1, 2, 3, -3, -4], [-1, 2, 3, -3, 4], [-1, 2, 3, -3, 4, -4], [-1, 2, -2], [-1, 2, -2, -4], [-1, 2, -2, 4], [-1, 2, -2, 4, -4], [-1, 2, -2, -3], [-1, 2, -2, -3, -4], [-1, 2, -2, -3, 4], [-1, 2, -2, -3, 4, -4], [-1, 2, -2, 3], [-1, 2, -2, 3, -4], [-1, 2, -2, 3, 4], [-1, 2, -2, 3, 4, -4], [-1, 2, -2, 3, -3], [-1, 2, -2, 3, -3, -4], [-1, 2, -2, 3, -3, 4], [-1, 2, -2, 3, -3, 4, -4], [1], [1, -4], [1, 4], [1, 4, -4], [1, -3], [1, -3, -4], [1, -3, 4], [1, -3, 4, -4], [1, 3], [1, 3, -4], [1, 3, 4], [1, 3, 4, -4], [1, 3, -3], [1, 3, -3, -4], [1, 3, -3, 4], [1, 3, -3, 4, -4], [1, -2], [1, -2, -4], [1, -2, 4], [1, -2, 4, -4], [1, -2, -3], [1, -2, -3, -4], [1, -2, -3, 4], [1, -2, -3, 4, -4], [1, -2, 3], [1, -2, 3, -4], [1, -2, 3, 4], [1, -2, 3, 4, -4], [1, -2, 3, -3], [1, -2, 3, -3, -4], [1, -2, 3, -3, 4], [1, -2, 3, -3, 4, -4], [1, 2], [1, 2, -4], [1, 2, 4], [1, 2, 4, -4], [1, 2, -3], [1, 2, -3, -4], [1, 2, -3, 4], [1, 2, -3, 4, -4], [1, 2, 3], [1, 2, 3, -4], [1, 2, 3, 4], [1, 2, 3, 4, -4], [1, 2, 3, -3], [1, 2, 3, -3, -4], [1, 2, 3, -3, 4], [1, 2, 3, -3, 4, -4], [1, 2, -2], [1, 2, -2, -4], [1, 2, -2, 4], [1, 2, -2, 4, -4], [1, 2, -2, -3], [1, 2, -2, -3, -4], [1, 2, -2, -3, 4], [1, 2, -2, -3, 4, -4], [1, 2, -2, 3], [1, 2, -2, 3, -4], [1, 2, -2, 3, 4], [1, 2, -2, 3, 4, -4], [1, 2, -2, 3, -3], [1, 2, -2, 3, -3, -4], [1, 2, -2, 3, -3, 4], [1, 2, -2, 3, -3, 4, -4], [1, -1], [1, -1, -4], [1, -1, 4], [1, -1, 4, -4], [1, -1, -3], [1, -1, -3, -4], [1, -1, -3, 4], [1, -1, -3, 4, -4], [1, -1, 3], [1, -1, 3, -4], [1, -1, 3, 4], [1, -1, 3, 4, -4], [1, -1, 3, -3], [1, -1, 3, -3, -4], [1, -1, 3, -3, 4], [1, -1, 3, -3, 4, -4], [1, -1, -2], [1, -1, -2, -4], [1, -1, -2, 4], [1, -1, -2, 4, -4], [1, -1, -2, -3], [1, -1, -2, -3, -4], [1, -1, -2, -3, 4], [1, -1, -2, -3, 4, -4], [1, -1, -2, 3], [1, -1, -2, 3, -4], [1, -1, -2, 3, 4], [1, -1, -2, 3, 4, -4], [1, -1, -2, 3, -3], [1, -1, -2, 3, -3, -4], [1, -1, -2, 3, -3, 4], [1, -1, -2, 3, -3, 4, -4], [1, -1, 2], [1, -1, 2, -4], [1, -1, 2, 4], [1, -1, 2, 4, -4], [1, -1, 2, -3], [1, -1, 2, -3, -4], [1, -1, 2, -3, 4], [1, -1, 2, -3, 4, -4], [1, -1, 2, 3], [1, -1, 2, 3, -4], [1, -1, 2, 3, 4], [1, -1, 2, 3, 4, -4], [1, -1, 2, 3, -3], [1, -1, 2, 3, -3, -4], [1, -1, 2, 3, -3, 4], [1, -1, 2, 3, -3, 4, -4], [1, -1, 2, -2], [1, -1, 2, -2, -4], [1, -1, 2, -2, 4], [1, -1, 2, -2, 4, -4], [1, -1, 2, -2, -3], [1, -1, 2, -2, -3, -4], [1, -1, 2, -2, -3, 4], [1, -1, 2, -2, -3, 4, -4], [1, -1, 2, -2, 3], [1, -1, 2, -2, 3, -4], [1, -1, 2, -2, 3, 4], [1, -1, 2, -2, 3, 4, -4], [1, -1, 2, -2, 3, -3], [1, -1, 2, -2, 3, -3, -4], [1, -1, 2, -2, 3, -3, 4], [1, -1, 2, -2, 3, -3, 4, -4]]\n assert candidate(nums = [10, -5, 0, 7, 11]) == [[], [11], [7], [7, 11], [0], [0, 11], [0, 7], [0, 7, 11], [-5], [-5, 11], [-5, 7], [-5, 7, 11], [-5, 0], [-5, 0, 11], [-5, 0, 7], [-5, 0, 7, 11], [10], [10, 11], [10, 7], [10, 7, 11], [10, 0], [10, 0, 11], [10, 0, 7], [10, 0, 7, 11], [10, -5], [10, -5, 11], [10, -5, 7], [10, -5, 7, 11], [10, -5, 0], [10, -5, 0, 11], [10, -5, 0, 7], [10, -5, 0, 7, 11]]\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]) == [[], [95], [85], [85, 95], [75], [75, 95], [75, 85], [75, 85, 95], [65], [65, 95], [65, 85], [65, 85, 95], [65, 75], [65, 75, 95], [65, 75, 85], [65, 75, 85, 95], [55], [55, 95], [55, 85], [55, 85, 95], [55, 75], [55, 75, 95], [55, 75, 85], [55, 75, 85, 95], [55, 65], [55, 65, 95], [55, 65, 85], [55, 65, 85, 95], [55, 65, 75], [55, 65, 75, 95], [55, 65, 75, 85], [55, 65, 75, 85, 95], [45], [45, 95], [45, 85], [45, 85, 95], [45, 75], [45, 75, 95], [45, 75, 85], [45, 75, 85, 95], [45, 65], [45, 65, 95], [45, 65, 85], [45, 65, 85, 95], [45, 65, 75], [45, 65, 75, 95], [45, 65, 75, 85], [45, 65, 75, 85, 95], [45, 55], [45, 55, 95], [45, 55, 85], [45, 55, 85, 95], [45, 55, 75], [45, 55, 75, 95], [45, 55, 75, 85], [45, 55, 75, 85, 95], [45, 55, 65], [45, 55, 65, 95], [45, 55, 65, 85], [45, 55, 65, 85, 95], [45, 55, 65, 75], [45, 55, 65, 75, 95], [45, 55, 65, 75, 85], [45, 55, 65, 75, 85, 95], [35], [35, 95], [35, 85], [35, 85, 95], [35, 75], [35, 75, 95], [35, 75, 85], [35, 75, 85, 95], [35, 65], [35, 65, 95], [35, 65, 85], [35, 65, 85, 95], [35, 65, 75], [35, 65, 75, 95], [35, 65, 75, 85], [35, 65, 75, 85, 95], [35, 55], [35, 55, 95], [35, 55, 85], [35, 55, 85, 95], [35, 55, 75], [35, 55, 75, 95], [35, 55, 75, 85], [35, 55, 75, 85, 95], [35, 55, 65], [35, 55, 65, 95], [35, 55, 65, 85], [35, 55, 65, 85, 95], [35, 55, 65, 75], [35, 55, 65, 75, 95], [35, 55, 65, 75, 85], [35, 55, 65, 75, 85, 95], [35, 45], [35, 45, 95], [35, 45, 85], [35, 45, 85, 95], [35, 45, 75], [35, 45, 75, 95], [35, 45, 75, 85], [35, 45, 75, 85, 95], [35, 45, 65], [35, 45, 65, 95], [35, 45, 65, 85], [35, 45, 65, 85, 95], [35, 45, 65, 75], [35, 45, 65, 75, 95], [35, 45, 65, 75, 85], [35, 45, 65, 75, 85, 95], [35, 45, 55], [35, 45, 55, 95], [35, 45, 55, 85], [35, 45, 55, 85, 95], [35, 45, 55, 75], [35, 45, 55, 75, 95], [35, 45, 55, 75, 85], [35, 45, 55, 75, 85, 95], [35, 45, 55, 65], [35, 45, 55, 65, 95], [35, 45, 55, 65, 85], [35, 45, 55, 65, 85, 95], [35, 45, 55, 65, 75], [35, 45, 55, 65, 75, 95], [35, 45, 55, 65, 75, 85], [35, 45, 55, 65, 75, 85, 95], [25], [25, 95], [25, 85], [25, 85, 95], [25, 75], [25, 75, 95], [25, 75, 85], [25, 75, 85, 95], [25, 65], [25, 65, 95], [25, 65, 85], [25, 65, 85, 95], [25, 65, 75], [25, 65, 75, 95], [25, 65, 75, 85], [25, 65, 75, 85, 95], [25, 55], [25, 55, 95], [25, 55, 85], [25, 55, 85, 95], [25, 55, 75], [25, 55, 75, 95], [25, 55, 75, 85], [25, 55, 75, 85, 95], [25, 55, 65], [25, 55, 65, 95], [25, 55, 65, 85], [25, 55, 65, 85, 95], [25, 55, 65, 75], [25, 55, 65, 75, 95], [25, 55, 65, 75, 85], [25, 55, 65, 75, 85, 95], [25, 45], [25, 45, 95], [25, 45, 85], [25, 45, 85, 95], [25, 45, 75], [25, 45, 75, 95], [25, 45, 75, 85], [25, 45, 75, 85, 95], [25, 45, 65], [25, 45, 65, 95], [25, 45, 65, 85], [25, 45, 65, 85, 95], [25, 45, 65, 75], [25, 45, 65, 75, 95], [25, 45, 65, 75, 85], [25, 45, 65, 75, 85, 95], [25, 45, 55], [25, 45, 55, 95], [25, 45, 55, 85], [25, 45, 55, 85, 95], [25, 45, 55, 75], [25, 45, 55, 75, 95], [25, 45, 55, 75, 85], [25, 45, 55, 75, 85, 95], [25, 45, 55, 65], [25, 45, 55, 65, 95], [25, 45, 55, 65, 85], [25, 45, 55, 65, 85, 95], [25, 45, 55, 65, 75], [25, 45, 55, 65, 75, 95], [25, 45, 55, 65, 75, 85], [25, 45, 55, 65, 75, 85, 95], [25, 35], [25, 35, 95], [25, 35, 85], [25, 35, 85, 95], [25, 35, 75], [25, 35, 75, 95], [25, 35, 75, 85], [25, 35, 75, 85, 95], [25, 35, 65], [25, 35, 65, 95], [25, 35, 65, 85], [25, 35, 65, 85, 95], [25, 35, 65, 75], [25, 35, 65, 75, 95], [25, 35, 65, 75, 85], [25, 35, 65, 75, 85, 95], [25, 35, 55], [25, 35, 55, 95], [25, 35, 55, 85], [25, 35, 55, 85, 95], [25, 35, 55, 75], [25, 35, 55, 75, 95], [25, 35, 55, 75, 85], [25, 35, 55, 75, 85, 95], [25, 35, 55, 65], [25, 35, 55, 65, 95], [25, 35, 55, 65, 85], [25, 35, 55, 65, 85, 95], [25, 35, 55, 65, 75], [25, 35, 55, 65, 75, 95], [25, 35, 55, 65, 75, 85], [25, 35, 55, 65, 75, 85, 95], [25, 35, 45], [25, 35, 45, 95], [25, 35, 45, 85], [25, 35, 45, 85, 95], [25, 35, 45, 75], [25, 35, 45, 75, 95], [25, 35, 45, 75, 85], [25, 35, 45, 75, 85, 95], [25, 35, 45, 65], [25, 35, 45, 65, 95], [25, 35, 45, 65, 85], [25, 35, 45, 65, 85, 95], [25, 35, 45, 65, 75], [25, 35, 45, 65, 75, 95], [25, 35, 45, 65, 75, 85], [25, 35, 45, 65, 75, 85, 95], [25, 35, 45, 55], [25, 35, 45, 55, 95], [25, 35, 45, 55, 85], [25, 35, 45, 55, 85, 95], [25, 35, 45, 55, 75], [25, 35, 45, 55, 75, 95], [25, 35, 45, 55, 75, 85], [25, 35, 45, 55, 75, 85, 95], [25, 35, 45, 55, 65], [25, 35, 45, 55, 65, 95], [25, 35, 45, 55, 65, 85], [25, 35, 45, 55, 65, 85, 95], [25, 35, 45, 55, 65, 75], [25, 35, 45, 55, 65, 75, 95], [25, 35, 45, 55, 65, 75, 85], [25, 35, 45, 55, 65, 75, 85, 95], [15], [15, 95], [15, 85], [15, 85, 95], [15, 75], [15, 75, 95], [15, 75, 85], [15, 75, 85, 95], [15, 65], [15, 65, 95], [15, 65, 85], [15, 65, 85, 95], [15, 65, 75], [15, 65, 75, 95], [15, 65, 75, 85], [15, 65, 75, 85, 95], [15, 55], [15, 55, 95], [15, 55, 85], [15, 55, 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75, 85], [5, 15, 25, 45, 55, 75, 85, 95], [5, 15, 25, 45, 55, 65], [5, 15, 25, 45, 55, 65, 95], [5, 15, 25, 45, 55, 65, 85], [5, 15, 25, 45, 55, 65, 85, 95], [5, 15, 25, 45, 55, 65, 75], [5, 15, 25, 45, 55, 65, 75, 95], [5, 15, 25, 45, 55, 65, 75, 85], [5, 15, 25, 45, 55, 65, 75, 85, 95], [5, 15, 25, 35], [5, 15, 25, 35, 95], [5, 15, 25, 35, 85], [5, 15, 25, 35, 85, 95], [5, 15, 25, 35, 75], [5, 15, 25, 35, 75, 95], [5, 15, 25, 35, 75, 85], [5, 15, 25, 35, 75, 85, 95], [5, 15, 25, 35, 65], [5, 15, 25, 35, 65, 95], [5, 15, 25, 35, 65, 85], [5, 15, 25, 35, 65, 85, 95], [5, 15, 25, 35, 65, 75], [5, 15, 25, 35, 65, 75, 95], [5, 15, 25, 35, 65, 75, 85], [5, 15, 25, 35, 65, 75, 85, 95], [5, 15, 25, 35, 55], [5, 15, 25, 35, 55, 95], [5, 15, 25, 35, 55, 85], [5, 15, 25, 35, 55, 85, 95], [5, 15, 25, 35, 55, 75], [5, 15, 25, 35, 55, 75, 95], [5, 15, 25, 35, 55, 75, 85], [5, 15, 25, 35, 55, 75, 85, 95], [5, 15, 25, 35, 55, 65], [5, 15, 25, 35, 55, 65, 95], [5, 15, 25, 35, 55, 65, 85], [5, 15, 25, 35, 55, 65, 85, 95], [5, 15, 25, 35, 55, 65, 75], [5, 15, 25, 35, 55, 65, 75, 95], [5, 15, 25, 35, 55, 65, 75, 85], [5, 15, 25, 35, 55, 65, 75, 85, 95], [5, 15, 25, 35, 45], [5, 15, 25, 35, 45, 95], [5, 15, 25, 35, 45, 85], [5, 15, 25, 35, 45, 85, 95], [5, 15, 25, 35, 45, 75], [5, 15, 25, 35, 45, 75, 95], [5, 15, 25, 35, 45, 75, 85], [5, 15, 25, 35, 45, 75, 85, 95], [5, 15, 25, 35, 45, 65], [5, 15, 25, 35, 45, 65, 95], [5, 15, 25, 35, 45, 65, 85], [5, 15, 25, 35, 45, 65, 85, 95], [5, 15, 25, 35, 45, 65, 75], [5, 15, 25, 35, 45, 65, 75, 95], [5, 15, 25, 35, 45, 65, 75, 85], [5, 15, 25, 35, 45, 65, 75, 85, 95], [5, 15, 25, 35, 45, 55], [5, 15, 25, 35, 45, 55, 95], [5, 15, 25, 35, 45, 55, 85], [5, 15, 25, 35, 45, 55, 85, 95], [5, 15, 25, 35, 45, 55, 75], [5, 15, 25, 35, 45, 55, 75, 95], [5, 15, 25, 35, 45, 55, 75, 85], [5, 15, 25, 35, 45, 55, 75, 85, 95], [5, 15, 25, 35, 45, 55, 65], [5, 15, 25, 35, 45, 55, 65, 95], [5, 15, 25, 35, 45, 55, 65, 85], [5, 15, 25, 35, 45, 55, 65, 85, 95], [5, 15, 25, 35, 45, 55, 65, 75], [5, 15, 25, 35, 45, 55, 65, 75, 95], [5, 15, 25, 35, 45, 55, 65, 75, 85], [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [[], [9], [8], [8, 9], [7], [7, 9], [7, 8], [7, 8, 9], [6], [6, 9], [6, 8], [6, 8, 9], [6, 7], [6, 7, 9], [6, 7, 8], [6, 7, 8, 9], [5], [5, 9], [5, 8], [5, 8, 9], [5, 7], [5, 7, 9], [5, 7, 8], [5, 7, 8, 9], [5, 6], [5, 6, 9], [5, 6, 8], [5, 6, 8, 9], [5, 6, 7], [5, 6, 7, 9], [5, 6, 7, 8], [5, 6, 7, 8, 9], [4], [4, 9], [4, 8], [4, 8, 9], [4, 7], [4, 7, 9], [4, 7, 8], [4, 7, 8, 9], [4, 6], [4, 6, 9], [4, 6, 8], [4, 6, 8, 9], [4, 6, 7], [4, 6, 7, 9], [4, 6, 7, 8], [4, 6, 7, 8, 9], [4, 5], [4, 5, 9], [4, 5, 8], [4, 5, 8, 9], [4, 5, 7], [4, 5, 7, 9], [4, 5, 7, 8], [4, 5, 7, 8, 9], [4, 5, 6], [4, 5, 6, 9], [4, 5, 6, 8], [4, 5, 6, 8, 9], [4, 5, 6, 7], [4, 5, 6, 7, 9], [4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9], [3], [3, 9], [3, 8], [3, 8, 9], [3, 7], [3, 7, 9], [3, 7, 8], [3, 7, 8, 9], [3, 6], [3, 6, 9], [3, 6, 8], [3, 6, 8, 9], [3, 6, 7], [3, 6, 7, 9], [3, 6, 7, 8], [3, 6, 7, 8, 9], [3, 5], [3, 5, 9], [3, 5, 8], [3, 5, 8, 9], [3, 5, 7], [3, 5, 7, 9], [3, 5, 7, 8], [3, 5, 7, 8, 9], [3, 5, 6], [3, 5, 6, 9], [3, 5, 6, 8], [3, 5, 6, 8, 9], [3, 5, 6, 7], [3, 5, 6, 7, 9], [3, 5, 6, 7, 8], [3, 5, 6, 7, 8, 9], [3, 4], [3, 4, 9], [3, 4, 8], [3, 4, 8, 9], [3, 4, 7], [3, 4, 7, 9], [3, 4, 7, 8], [3, 4, 7, 8, 9], [3, 4, 6], [3, 4, 6, 9], [3, 4, 6, 8], [3, 4, 6, 8, 9], [3, 4, 6, 7], [3, 4, 6, 7, 9], [3, 4, 6, 7, 8], [3, 4, 6, 7, 8, 9], [3, 4, 5], [3, 4, 5, 9], [3, 4, 5, 8], [3, 4, 5, 8, 9], [3, 4, 5, 7], [3, 4, 5, 7, 9], [3, 4, 5, 7, 8], [3, 4, 5, 7, 8, 9], [3, 4, 5, 6], [3, 4, 5, 6, 9], [3, 4, 5, 6, 8], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 8, 9], [2], [2, 9], [2, 8], [2, 8, 9], [2, 7], [2, 7, 9], [2, 7, 8], [2, 7, 8, 9], [2, 6], [2, 6, 9], [2, 6, 8], [2, 6, 8, 9], [2, 6, 7], [2, 6, 7, 9], [2, 6, 7, 8], [2, 6, 7, 8, 9], [2, 5], [2, 5, 9], [2, 5, 8], [2, 5, 8, 9], [2, 5, 7], [2, 5, 7, 9], [2, 5, 7, 8], [2, 5, 7, 8, 9], [2, 5, 6], [2, 5, 6, 9], [2, 5, 6, 8], [2, 5, 6, 8, 9], [2, 5, 6, 7], [2, 5, 6, 7, 9], [2, 5, 6, 7, 8], [2, 5, 6, 7, 8, 9], [2, 4], [2, 4, 9], [2, 4, 8], [2, 4, 8, 9], [2, 4, 7], [2, 4, 7, 9], [2, 4, 7, 8], [2, 4, 7, 8, 9], [2, 4, 6], [2, 4, 6, 9], [2, 4, 6, 8], [2, 4, 6, 8, 9], [2, 4, 6, 7], [2, 4, 6, 7, 9], [2, 4, 6, 7, 8], [2, 4, 6, 7, 8, 9], [2, 4, 5], [2, 4, 5, 9], [2, 4, 5, 8], [2, 4, 5, 8, 9], [2, 4, 5, 7], [2, 4, 5, 7, 9], [2, 4, 5, 7, 8], [2, 4, 5, 7, 8, 9], [2, 4, 5, 6], [2, 4, 5, 6, 9], [2, 4, 5, 6, 8], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 7], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 8, 9], [2, 3], [2, 3, 9], [2, 3, 8], [2, 3, 8, 9], [2, 3, 7], [2, 3, 7, 9], [2, 3, 7, 8], [2, 3, 7, 8, 9], [2, 3, 6], [2, 3, 6, 9], [2, 3, 6, 8], [2, 3, 6, 8, 9], [2, 3, 6, 7], [2, 3, 6, 7, 9], [2, 3, 6, 7, 8], [2, 3, 6, 7, 8, 9], [2, 3, 5], [2, 3, 5, 9], [2, 3, 5, 8], [2, 3, 5, 8, 9], [2, 3, 5, 7], [2, 3, 5, 7, 9], [2, 3, 5, 7, 8], [2, 3, 5, 7, 8, 9], [2, 3, 5, 6], [2, 3, 5, 6, 9], [2, 3, 5, 6, 8], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 7], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 8, 9], [2, 3, 4], [2, 3, 4, 9], [2, 3, 4, 8], [2, 3, 4, 8, 9], [2, 3, 4, 7], [2, 3, 4, 7, 9], [2, 3, 4, 7, 8], [2, 3, 4, 7, 8, 9], [2, 3, 4, 6], [2, 3, 4, 6, 9], [2, 3, 4, 6, 8], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 7], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 5], [2, 3, 4, 5, 9], [2, 3, 4, 5, 8], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 7], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 8, 9], [1], [1, 9], [1, 8], [1, 8, 9], [1, 7], [1, 7, 9], [1, 7, 8], [1, 7, 8, 9], [1, 6], [1, 6, 9], [1, 6, 8], [1, 6, 8, 9], [1, 6, 7], [1, 6, 7, 9], [1, 6, 7, 8], [1, 6, 7, 8, 9], [1, 5], [1, 5, 9], [1, 5, 8], [1, 5, 8, 9], [1, 5, 7], [1, 5, 7, 9], [1, 5, 7, 8], [1, 5, 7, 8, 9], [1, 5, 6], [1, 5, 6, 9], [1, 5, 6, 8], [1, 5, 6, 8, 9], [1, 5, 6, 7], [1, 5, 6, 7, 9], [1, 5, 6, 7, 8], [1, 5, 6, 7, 8, 9], [1, 4], [1, 4, 9], [1, 4, 8], [1, 4, 8, 9], [1, 4, 7], [1, 4, 7, 9], [1, 4, 7, 8], [1, 4, 7, 8, 9], [1, 4, 6], [1, 4, 6, 9], [1, 4, 6, 8], [1, 4, 6, 8, 9], [1, 4, 6, 7], [1, 4, 6, 7, 9], [1, 4, 6, 7, 8], [1, 4, 6, 7, 8, 9], [1, 4, 5], [1, 4, 5, 9], [1, 4, 5, 8], [1, 4, 5, 8, 9], [1, 4, 5, 7], [1, 4, 5, 7, 9], [1, 4, 5, 7, 8], [1, 4, 5, 7, 8, 9], [1, 4, 5, 6], [1, 4, 5, 6, 9], [1, 4, 5, 6, 8], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 7], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 8, 9], [1, 3], [1, 3, 9], [1, 3, 8], [1, 3, 8, 9], [1, 3, 7], [1, 3, 7, 9], [1, 3, 7, 8], [1, 3, 7, 8, 9], [1, 3, 6], [1, 3, 6, 9], [1, 3, 6, 8], [1, 3, 6, 8, 9], [1, 3, 6, 7], [1, 3, 6, 7, 9], [1, 3, 6, 7, 8], [1, 3, 6, 7, 8, 9], [1, 3, 5], [1, 3, 5, 9], [1, 3, 5, 8], [1, 3, 5, 8, 9], [1, 3, 5, 7], [1, 3, 5, 7, 9], [1, 3, 5, 7, 8], [1, 3, 5, 7, 8, 9], [1, 3, 5, 6], [1, 3, 5, 6, 9], [1, 3, 5, 6, 8], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 7], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 8, 9], [1, 3, 4], [1, 3, 4, 9], [1, 3, 4, 8], [1, 3, 4, 8, 9], [1, 3, 4, 7], [1, 3, 4, 7, 9], [1, 3, 4, 7, 8], [1, 3, 4, 7, 8, 9], [1, 3, 4, 6], [1, 3, 4, 6, 9], [1, 3, 4, 6, 8], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 7], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 5], [1, 3, 4, 5, 9], [1, 3, 4, 5, 8], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 7], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 6], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 8, 9], [1, 2], [1, 2, 9], [1, 2, 8], [1, 2, 8, 9], [1, 2, 7], [1, 2, 7, 9], [1, 2, 7, 8], [1, 2, 7, 8, 9], [1, 2, 6], [1, 2, 6, 9], [1, 2, 6, 8], [1, 2, 6, 8, 9], [1, 2, 6, 7], [1, 2, 6, 7, 9], [1, 2, 6, 7, 8], [1, 2, 6, 7, 8, 9], [1, 2, 5], [1, 2, 5, 9], [1, 2, 5, 8], [1, 2, 5, 8, 9], [1, 2, 5, 7], [1, 2, 5, 7, 9], [1, 2, 5, 7, 8], [1, 2, 5, 7, 8, 9], [1, 2, 5, 6], [1, 2, 5, 6, 9], [1, 2, 5, 6, 8], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 7], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 8, 9], [1, 2, 4], [1, 2, 4, 9], [1, 2, 4, 8], [1, 2, 4, 8, 9], [1, 2, 4, 7], [1, 2, 4, 7, 9], [1, 2, 4, 7, 8], [1, 2, 4, 7, 8, 9], [1, 2, 4, 6], [1, 2, 4, 6, 9], [1, 2, 4, 6, 8], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 7], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 5], [1, 2, 4, 5, 9], [1, 2, 4, 5, 8], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 7], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 6], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 3], [1, 2, 3, 9], [1, 2, 3, 8], [1, 2, 3, 8, 9], [1, 2, 3, 7], [1, 2, 3, 7, 9], [1, 2, 3, 7, 8], [1, 2, 3, 7, 8, 9], [1, 2, 3, 6], [1, 2, 3, 6, 9], [1, 2, 3, 6, 8], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 7], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 5], [1, 2, 3, 5, 9], [1, 2, 3, 5, 8], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 7], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 6], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 4], [1, 2, 3, 4, 9], [1, 2, 3, 4, 8], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 7], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 6], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 8, 9], [0], [0, 9], [0, 8], [0, 8, 9], [0, 7], [0, 7, 9], [0, 7, 8], [0, 7, 8, 9], [0, 6], [0, 6, 9], [0, 6, 8], [0, 6, 8, 9], [0, 6, 7], [0, 6, 7, 9], [0, 6, 7, 8], [0, 6, 7, 8, 9], [0, 5], [0, 5, 9], [0, 5, 8], [0, 5, 8, 9], [0, 5, 7], [0, 5, 7, 9], [0, 5, 7, 8], [0, 5, 7, 8, 9], [0, 5, 6], [0, 5, 6, 9], [0, 5, 6, 8], [0, 5, 6, 8, 9], [0, 5, 6, 7], [0, 5, 6, 7, 9], [0, 5, 6, 7, 8], [0, 5, 6, 7, 8, 9], [0, 4], [0, 4, 9], [0, 4, 8], [0, 4, 8, 9], [0, 4, 7], [0, 4, 7, 9], [0, 4, 7, 8], [0, 4, 7, 8, 9], [0, 4, 6], [0, 4, 6, 9], [0, 4, 6, 8], [0, 4, 6, 8, 9], [0, 4, 6, 7], [0, 4, 6, 7, 9], [0, 4, 6, 7, 8], [0, 4, 6, 7, 8, 9], [0, 4, 5], [0, 4, 5, 9], [0, 4, 5, 8], [0, 4, 5, 8, 9], [0, 4, 5, 7], [0, 4, 5, 7, 9], [0, 4, 5, 7, 8], [0, 4, 5, 7, 8, 9], [0, 4, 5, 6], [0, 4, 5, 6, 9], [0, 4, 5, 6, 8], [0, 4, 5, 6, 8, 9], [0, 4, 5, 6, 7], [0, 4, 5, 6, 7, 9], [0, 4, 5, 6, 7, 8], [0, 4, 5, 6, 7, 8, 9], [0, 3], [0, 3, 9], [0, 3, 8], [0, 3, 8, 9], [0, 3, 7], [0, 3, 7, 9], [0, 3, 7, 8], [0, 3, 7, 8, 9], [0, 3, 6], [0, 3, 6, 9], [0, 3, 6, 8], [0, 3, 6, 8, 9], [0, 3, 6, 7], [0, 3, 6, 7, 9], [0, 3, 6, 7, 8], [0, 3, 6, 7, 8, 9], [0, 3, 5], [0, 3, 5, 9], [0, 3, 5, 8], [0, 3, 5, 8, 9], [0, 3, 5, 7], [0, 3, 5, 7, 9], [0, 3, 5, 7, 8], [0, 3, 5, 7, 8, 9], [0, 3, 5, 6], [0, 3, 5, 6, 9], [0, 3, 5, 6, 8], [0, 3, 5, 6, 8, 9], [0, 3, 5, 6, 7], [0, 3, 5, 6, 7, 9], [0, 3, 5, 6, 7, 8], [0, 3, 5, 6, 7, 8, 9], [0, 3, 4], [0, 3, 4, 9], [0, 3, 4, 8], [0, 3, 4, 8, 9], [0, 3, 4, 7], [0, 3, 4, 7, 9], [0, 3, 4, 7, 8], [0, 3, 4, 7, 8, 9], [0, 3, 4, 6], [0, 3, 4, 6, 9], [0, 3, 4, 6, 8], [0, 3, 4, 6, 8, 9], [0, 3, 4, 6, 7], [0, 3, 4, 6, 7, 9], [0, 3, 4, 6, 7, 8], [0, 3, 4, 6, 7, 8, 9], [0, 3, 4, 5], [0, 3, 4, 5, 9], [0, 3, 4, 5, 8], [0, 3, 4, 5, 8, 9], [0, 3, 4, 5, 7], [0, 3, 4, 5, 7, 9], [0, 3, 4, 5, 7, 8], [0, 3, 4, 5, 7, 8, 9], [0, 3, 4, 5, 6], [0, 3, 4, 5, 6, 9], [0, 3, 4, 5, 6, 8], [0, 3, 4, 5, 6, 8, 9], [0, 3, 4, 5, 6, 7], [0, 3, 4, 5, 6, 7, 9], [0, 3, 4, 5, 6, 7, 8], [0, 3, 4, 5, 6, 7, 8, 9], [0, 2], [0, 2, 9], [0, 2, 8], [0, 2, 8, 9], [0, 2, 7], [0, 2, 7, 9], [0, 2, 7, 8], [0, 2, 7, 8, 9], [0, 2, 6], [0, 2, 6, 9], [0, 2, 6, 8], [0, 2, 6, 8, 9], [0, 2, 6, 7], [0, 2, 6, 7, 9], [0, 2, 6, 7, 8], [0, 2, 6, 7, 8, 9], [0, 2, 5], [0, 2, 5, 9], [0, 2, 5, 8], [0, 2, 5, 8, 9], [0, 2, 5, 7], [0, 2, 5, 7, 9], [0, 2, 5, 7, 8], [0, 2, 5, 7, 8, 9], [0, 2, 5, 6], [0, 2, 5, 6, 9], [0, 2, 5, 6, 8], [0, 2, 5, 6, 8, 9], [0, 2, 5, 6, 7], [0, 2, 5, 6, 7, 9], [0, 2, 5, 6, 7, 8], [0, 2, 5, 6, 7, 8, 9], [0, 2, 4], [0, 2, 4, 9], [0, 2, 4, 8], [0, 2, 4, 8, 9], [0, 2, 4, 7], [0, 2, 4, 7, 9], [0, 2, 4, 7, 8], [0, 2, 4, 7, 8, 9], [0, 2, 4, 6], [0, 2, 4, 6, 9], [0, 2, 4, 6, 8], [0, 2, 4, 6, 8, 9], [0, 2, 4, 6, 7], [0, 2, 4, 6, 7, 9], [0, 2, 4, 6, 7, 8], [0, 2, 4, 6, 7, 8, 9], [0, 2, 4, 5], [0, 2, 4, 5, 9], [0, 2, 4, 5, 8], [0, 2, 4, 5, 8, 9], [0, 2, 4, 5, 7], [0, 2, 4, 5, 7, 9], [0, 2, 4, 5, 7, 8], [0, 2, 4, 5, 7, 8, 9], [0, 2, 4, 5, 6], [0, 2, 4, 5, 6, 9], [0, 2, 4, 5, 6, 8], [0, 2, 4, 5, 6, 8, 9], [0, 2, 4, 5, 6, 7], [0, 2, 4, 5, 6, 7, 9], [0, 2, 4, 5, 6, 7, 8], [0, 2, 4, 5, 6, 7, 8, 9], [0, 2, 3], [0, 2, 3, 9], [0, 2, 3, 8], [0, 2, 3, 8, 9], [0, 2, 3, 7], [0, 2, 3, 7, 9], [0, 2, 3, 7, 8], [0, 2, 3, 7, 8, 9], [0, 2, 3, 6], [0, 2, 3, 6, 9], [0, 2, 3, 6, 8], [0, 2, 3, 6, 8, 9], [0, 2, 3, 6, 7], [0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 8], [0, 2, 3, 6, 7, 8, 9], [0, 2, 3, 5], [0, 2, 3, 5, 9], [0, 2, 3, 5, 8], [0, 2, 3, 5, 8, 9], [0, 2, 3, 5, 7], [0, 2, 3, 5, 7, 9], [0, 2, 3, 5, 7, 8], [0, 2, 3, 5, 7, 8, 9], [0, 2, 3, 5, 6], [0, 2, 3, 5, 6, 9], [0, 2, 3, 5, 6, 8], [0, 2, 3, 5, 6, 8, 9], [0, 2, 3, 5, 6, 7], [0, 2, 3, 5, 6, 7, 9], [0, 2, 3, 5, 6, 7, 8], [0, 2, 3, 5, 6, 7, 8, 9], [0, 2, 3, 4], [0, 2, 3, 4, 9], [0, 2, 3, 4, 8], [0, 2, 3, 4, 8, 9], [0, 2, 3, 4, 7], [0, 2, 3, 4, 7, 9], [0, 2, 3, 4, 7, 8], [0, 2, 3, 4, 7, 8, 9], [0, 2, 3, 4, 6], [0, 2, 3, 4, 6, 9], [0, 2, 3, 4, 6, 8], [0, 2, 3, 4, 6, 8, 9], [0, 2, 3, 4, 6, 7], [0, 2, 3, 4, 6, 7, 9], [0, 2, 3, 4, 6, 7, 8], [0, 2, 3, 4, 6, 7, 8, 9], [0, 2, 3, 4, 5], [0, 2, 3, 4, 5, 9], [0, 2, 3, 4, 5, 8], [0, 2, 3, 4, 5, 8, 9], [0, 2, 3, 4, 5, 7], [0, 2, 3, 4, 5, 7, 9], [0, 2, 3, 4, 5, 7, 8], [0, 2, 3, 4, 5, 7, 8, 9], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 6, 9], [0, 2, 3, 4, 5, 6, 8], [0, 2, 3, 4, 5, 6, 8, 9], [0, 2, 3, 4, 5, 6, 7], [0, 2, 3, 4, 5, 6, 7, 9], [0, 2, 3, 4, 5, 6, 7, 8], [0, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1], [0, 1, 9], [0, 1, 8], [0, 1, 8, 9], [0, 1, 7], [0, 1, 7, 9], [0, 1, 7, 8], [0, 1, 7, 8, 9], [0, 1, 6], [0, 1, 6, 9], [0, 1, 6, 8], [0, 1, 6, 8, 9], [0, 1, 6, 7], [0, 1, 6, 7, 9], [0, 1, 6, 7, 8], [0, 1, 6, 7, 8, 9], [0, 1, 5], [0, 1, 5, 9], [0, 1, 5, 8], [0, 1, 5, 8, 9], [0, 1, 5, 7], [0, 1, 5, 7, 9], [0, 1, 5, 7, 8], [0, 1, 5, 7, 8, 9], [0, 1, 5, 6], [0, 1, 5, 6, 9], [0, 1, 5, 6, 8], [0, 1, 5, 6, 8, 9], [0, 1, 5, 6, 7], [0, 1, 5, 6, 7, 9], [0, 1, 5, 6, 7, 8], [0, 1, 5, 6, 7, 8, 9], [0, 1, 4], [0, 1, 4, 9], [0, 1, 4, 8], [0, 1, 4, 8, 9], [0, 1, 4, 7], [0, 1, 4, 7, 9], [0, 1, 4, 7, 8], [0, 1, 4, 7, 8, 9], [0, 1, 4, 6], [0, 1, 4, 6, 9], [0, 1, 4, 6, 8], [0, 1, 4, 6, 8, 9], [0, 1, 4, 6, 7], [0, 1, 4, 6, 7, 9], [0, 1, 4, 6, 7, 8], [0, 1, 4, 6, 7, 8, 9], [0, 1, 4, 5], [0, 1, 4, 5, 9], [0, 1, 4, 5, 8], [0, 1, 4, 5, 8, 9], [0, 1, 4, 5, 7], [0, 1, 4, 5, 7, 9], [0, 1, 4, 5, 7, 8], [0, 1, 4, 5, 7, 8, 9], [0, 1, 4, 5, 6], [0, 1, 4, 5, 6, 9], [0, 1, 4, 5, 6, 8], [0, 1, 4, 5, 6, 8, 9], [0, 1, 4, 5, 6, 7], [0, 1, 4, 5, 6, 7, 9], [0, 1, 4, 5, 6, 7, 8], [0, 1, 4, 5, 6, 7, 8, 9], [0, 1, 3], [0, 1, 3, 9], [0, 1, 3, 8], [0, 1, 3, 8, 9], [0, 1, 3, 7], [0, 1, 3, 7, 9], [0, 1, 3, 7, 8], [0, 1, 3, 7, 8, 9], [0, 1, 3, 6], [0, 1, 3, 6, 9], [0, 1, 3, 6, 8], [0, 1, 3, 6, 8, 9], [0, 1, 3, 6, 7], [0, 1, 3, 6, 7, 9], [0, 1, 3, 6, 7, 8], [0, 1, 3, 6, 7, 8, 9], [0, 1, 3, 5], [0, 1, 3, 5, 9], [0, 1, 3, 5, 8], [0, 1, 3, 5, 8, 9], [0, 1, 3, 5, 7], [0, 1, 3, 5, 7, 9], [0, 1, 3, 5, 7, 8], [0, 1, 3, 5, 7, 8, 9], [0, 1, 3, 5, 6], [0, 1, 3, 5, 6, 9], [0, 1, 3, 5, 6, 8], [0, 1, 3, 5, 6, 8, 9], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6, 7, 9], [0, 1, 3, 5, 6, 7, 8], [0, 1, 3, 5, 6, 7, 8, 9], [0, 1, 3, 4], [0, 1, 3, 4, 9], [0, 1, 3, 4, 8], [0, 1, 3, 4, 8, 9], [0, 1, 3, 4, 7], [0, 1, 3, 4, 7, 9], [0, 1, 3, 4, 7, 8], [0, 1, 3, 4, 7, 8, 9], [0, 1, 3, 4, 6], [0, 1, 3, 4, 6, 9], [0, 1, 3, 4, 6, 8], [0, 1, 3, 4, 6, 8, 9], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 7, 9], [0, 1, 3, 4, 6, 7, 8], [0, 1, 3, 4, 6, 7, 8, 9], [0, 1, 3, 4, 5], [0, 1, 3, 4, 5, 9], [0, 1, 3, 4, 5, 8], [0, 1, 3, 4, 5, 8, 9], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5, 7, 9], [0, 1, 3, 4, 5, 7, 8], [0, 1, 3, 4, 5, 7, 8, 9], [0, 1, 3, 4, 5, 6], [0, 1, 3, 4, 5, 6, 9], [0, 1, 3, 4, 5, 6, 8], [0, 1, 3, 4, 5, 6, 8, 9], [0, 1, 3, 4, 5, 6, 7], [0, 1, 3, 4, 5, 6, 7, 9], [0, 1, 3, 4, 5, 6, 7, 8], [0, 1, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2], [0, 1, 2, 9], [0, 1, 2, 8], [0, 1, 2, 8, 9], [0, 1, 2, 7], [0, 1, 2, 7, 9], [0, 1, 2, 7, 8], [0, 1, 2, 7, 8, 9], [0, 1, 2, 6], [0, 1, 2, 6, 9], [0, 1, 2, 6, 8], [0, 1, 2, 6, 8, 9], [0, 1, 2, 6, 7], [0, 1, 2, 6, 7, 9], [0, 1, 2, 6, 7, 8], [0, 1, 2, 6, 7, 8, 9], [0, 1, 2, 5], [0, 1, 2, 5, 9], [0, 1, 2, 5, 8], [0, 1, 2, 5, 8, 9], [0, 1, 2, 5, 7], [0, 1, 2, 5, 7, 9], [0, 1, 2, 5, 7, 8], [0, 1, 2, 5, 7, 8, 9], [0, 1, 2, 5, 6], [0, 1, 2, 5, 6, 9], [0, 1, 2, 5, 6, 8], [0, 1, 2, 5, 6, 8, 9], [0, 1, 2, 5, 6, 7], [0, 1, 2, 5, 6, 7, 9], [0, 1, 2, 5, 6, 7, 8], [0, 1, 2, 5, 6, 7, 8, 9], [0, 1, 2, 4], [0, 1, 2, 4, 9], [0, 1, 2, 4, 8], [0, 1, 2, 4, 8, 9], [0, 1, 2, 4, 7], [0, 1, 2, 4, 7, 9], [0, 1, 2, 4, 7, 8], [0, 1, 2, 4, 7, 8, 9], [0, 1, 2, 4, 6], [0, 1, 2, 4, 6, 9], [0, 1, 2, 4, 6, 8], [0, 1, 2, 4, 6, 8, 9], [0, 1, 2, 4, 6, 7], [0, 1, 2, 4, 6, 7, 9], [0, 1, 2, 4, 6, 7, 8], [0, 1, 2, 4, 6, 7, 8, 9], [0, 1, 2, 4, 5], [0, 1, 2, 4, 5, 9], [0, 1, 2, 4, 5, 8], [0, 1, 2, 4, 5, 8, 9], [0, 1, 2, 4, 5, 7], [0, 1, 2, 4, 5, 7, 9], [0, 1, 2, 4, 5, 7, 8], [0, 1, 2, 4, 5, 7, 8, 9], [0, 1, 2, 4, 5, 6], [0, 1, 2, 4, 5, 6, 9], [0, 1, 2, 4, 5, 6, 8], [0, 1, 2, 4, 5, 6, 8, 9], [0, 1, 2, 4, 5, 6, 7], [0, 1, 2, 4, 5, 6, 7, 9], [0, 1, 2, 4, 5, 6, 7, 8], [0, 1, 2, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3], [0, 1, 2, 3, 9], [0, 1, 2, 3, 8], [0, 1, 2, 3, 8, 9], [0, 1, 2, 3, 7], [0, 1, 2, 3, 7, 9], [0, 1, 2, 3, 7, 8], [0, 1, 2, 3, 7, 8, 9], [0, 1, 2, 3, 6], [0, 1, 2, 3, 6, 9], [0, 1, 2, 3, 6, 8], [0, 1, 2, 3, 6, 8, 9], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6, 7, 9], [0, 1, 2, 3, 6, 7, 8], [0, 1, 2, 3, 6, 7, 8, 9], [0, 1, 2, 3, 5], [0, 1, 2, 3, 5, 9], [0, 1, 2, 3, 5, 8], [0, 1, 2, 3, 5, 8, 9], [0, 1, 2, 3, 5, 7], [0, 1, 2, 3, 5, 7, 9], [0, 1, 2, 3, 5, 7, 8], [0, 1, 2, 3, 5, 7, 8, 9], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 6, 9], [0, 1, 2, 3, 5, 6, 8], [0, 1, 2, 3, 5, 6, 8, 9], [0, 1, 2, 3, 5, 6, 7], [0, 1, 2, 3, 5, 6, 7, 9], [0, 1, 2, 3, 5, 6, 7, 8], [0, 1, 2, 3, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 9], [0, 1, 2, 3, 4, 8], [0, 1, 2, 3, 4, 8, 9], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4, 7, 9], [0, 1, 2, 3, 4, 7, 8], [0, 1, 2, 3, 4, 7, 8, 9], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 6, 9], [0, 1, 2, 3, 4, 6, 8], [0, 1, 2, 3, 4, 6, 8, 9], [0, 1, 2, 3, 4, 6, 7], [0, 1, 2, 3, 4, 6, 7, 9], [0, 1, 2, 3, 4, 6, 7, 8], [0, 1, 2, 3, 4, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5, 9], [0, 1, 2, 3, 4, 5, 8], [0, 1, 2, 3, 4, 5, 8, 9], [0, 1, 2, 3, 4, 5, 7], [0, 1, 2, 3, 4, 5, 7, 9], [0, 1, 2, 3, 4, 5, 7, 8], [0, 1, 2, 3, 4, 5, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6, 9], [0, 1, 2, 3, 4, 5, 6, 8], [0, 1, 2, 3, 4, 5, 6, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == [[], [50], [45], [45, 50], [40], [40, 50], [40, 45], [40, 45, 50], [35], [35, 50], [35, 45], [35, 45, 50], [35, 40], [35, 40, 50], [35, 40, 45], [35, 40, 45, 50], [30], [30, 50], [30, 45], [30, 45, 50], [30, 40], [30, 40, 50], [30, 40, 45], [30, 40, 45, 50], [30, 35], [30, 35, 50], [30, 35, 45], [30, 35, 45, 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40], [5, 10, 25, 40, 50], [5, 10, 25, 40, 45], [5, 10, 25, 40, 45, 50], [5, 10, 25, 35], [5, 10, 25, 35, 50], [5, 10, 25, 35, 45], [5, 10, 25, 35, 45, 50], [5, 10, 25, 35, 40], [5, 10, 25, 35, 40, 50], [5, 10, 25, 35, 40, 45], [5, 10, 25, 35, 40, 45, 50], [5, 10, 25, 30], [5, 10, 25, 30, 50], [5, 10, 25, 30, 45], [5, 10, 25, 30, 45, 50], [5, 10, 25, 30, 40], [5, 10, 25, 30, 40, 50], [5, 10, 25, 30, 40, 45], [5, 10, 25, 30, 40, 45, 50], [5, 10, 25, 30, 35], [5, 10, 25, 30, 35, 50], [5, 10, 25, 30, 35, 45], [5, 10, 25, 30, 35, 45, 50], [5, 10, 25, 30, 35, 40], [5, 10, 25, 30, 35, 40, 50], [5, 10, 25, 30, 35, 40, 45], [5, 10, 25, 30, 35, 40, 45, 50], [5, 10, 20], [5, 10, 20, 50], [5, 10, 20, 45], [5, 10, 20, 45, 50], [5, 10, 20, 40], [5, 10, 20, 40, 50], [5, 10, 20, 40, 45], [5, 10, 20, 40, 45, 50], [5, 10, 20, 35], [5, 10, 20, 35, 50], [5, 10, 20, 35, 45], [5, 10, 20, 35, 45, 50], [5, 10, 20, 35, 40], [5, 10, 20, 35, 40, 50], [5, 10, 20, 35, 40, 45], [5, 10, 20, 35, 40, 45, 50], [5, 10, 20, 30], [5, 10, 20, 30, 50], [5, 10, 20, 30, 45], [5, 10, 20, 30, 45, 50], [5, 10, 20, 30, 40], [5, 10, 20, 30, 40, 50], [5, 10, 20, 30, 40, 45], [5, 10, 20, 30, 40, 45, 50], [5, 10, 20, 30, 35], [5, 10, 20, 30, 35, 50], [5, 10, 20, 30, 35, 45], [5, 10, 20, 30, 35, 45, 50], [5, 10, 20, 30, 35, 40], [5, 10, 20, 30, 35, 40, 50], [5, 10, 20, 30, 35, 40, 45], [5, 10, 20, 30, 35, 40, 45, 50], [5, 10, 20, 25], [5, 10, 20, 25, 50], [5, 10, 20, 25, 45], [5, 10, 20, 25, 45, 50], [5, 10, 20, 25, 40], [5, 10, 20, 25, 40, 50], [5, 10, 20, 25, 40, 45], [5, 10, 20, 25, 40, 45, 50], [5, 10, 20, 25, 35], [5, 10, 20, 25, 35, 50], [5, 10, 20, 25, 35, 45], [5, 10, 20, 25, 35, 45, 50], [5, 10, 20, 25, 35, 40], [5, 10, 20, 25, 35, 40, 50], [5, 10, 20, 25, 35, 40, 45], [5, 10, 20, 25, 35, 40, 45, 50], [5, 10, 20, 25, 30], [5, 10, 20, 25, 30, 50], [5, 10, 20, 25, 30, 45], [5, 10, 20, 25, 30, 45, 50], [5, 10, 20, 25, 30, 40], [5, 10, 20, 25, 30, 40, 50], [5, 10, 20, 25, 30, 40, 45], [5, 10, 20, 25, 30, 40, 45, 50], [5, 10, 20, 25, 30, 35], [5, 10, 20, 25, 30, 35, 50], [5, 10, 20, 25, 30, 35, 45], [5, 10, 20, 25, 30, 35, 45, 50], [5, 10, 20, 25, 30, 35, 40], [5, 10, 20, 25, 30, 35, 40, 50], [5, 10, 20, 25, 30, 35, 40, 45], [5, 10, 20, 25, 30, 35, 40, 45, 50], [5, 10, 15], [5, 10, 15, 50], [5, 10, 15, 45], [5, 10, 15, 45, 50], [5, 10, 15, 40], [5, 10, 15, 40, 50], [5, 10, 15, 40, 45], [5, 10, 15, 40, 45, 50], [5, 10, 15, 35], [5, 10, 15, 35, 50], [5, 10, 15, 35, 45], [5, 10, 15, 35, 45, 50], [5, 10, 15, 35, 40], [5, 10, 15, 35, 40, 50], [5, 10, 15, 35, 40, 45], [5, 10, 15, 35, 40, 45, 50], [5, 10, 15, 30], [5, 10, 15, 30, 50], [5, 10, 15, 30, 45], [5, 10, 15, 30, 45, 50], [5, 10, 15, 30, 40], [5, 10, 15, 30, 40, 50], [5, 10, 15, 30, 40, 45], [5, 10, 15, 30, 40, 45, 50], [5, 10, 15, 30, 35], [5, 10, 15, 30, 35, 50], [5, 10, 15, 30, 35, 45], [5, 10, 15, 30, 35, 45, 50], [5, 10, 15, 30, 35, 40], [5, 10, 15, 30, 35, 40, 50], [5, 10, 15, 30, 35, 40, 45], [5, 10, 15, 30, 35, 40, 45, 50], [5, 10, 15, 25], [5, 10, 15, 25, 50], [5, 10, 15, 25, 45], [5, 10, 15, 25, 45, 50], [5, 10, 15, 25, 40], [5, 10, 15, 25, 40, 50], [5, 10, 15, 25, 40, 45], [5, 10, 15, 25, 40, 45, 50], [5, 10, 15, 25, 35], [5, 10, 15, 25, 35, 50], [5, 10, 15, 25, 35, 45], [5, 10, 15, 25, 35, 45, 50], [5, 10, 15, 25, 35, 40], [5, 10, 15, 25, 35, 40, 50], [5, 10, 15, 25, 35, 40, 45], [5, 10, 15, 25, 35, 40, 45, 50], [5, 10, 15, 25, 30], [5, 10, 15, 25, 30, 50], [5, 10, 15, 25, 30, 45], [5, 10, 15, 25, 30, 45, 50], [5, 10, 15, 25, 30, 40], [5, 10, 15, 25, 30, 40, 50], [5, 10, 15, 25, 30, 40, 45], [5, 10, 15, 25, 30, 40, 45, 50], [5, 10, 15, 25, 30, 35], [5, 10, 15, 25, 30, 35, 50], [5, 10, 15, 25, 30, 35, 45], [5, 10, 15, 25, 30, 35, 45, 50], [5, 10, 15, 25, 30, 35, 40], [5, 10, 15, 25, 30, 35, 40, 50], [5, 10, 15, 25, 30, 35, 40, 45], [5, 10, 15, 25, 30, 35, 40, 45, 50], [5, 10, 15, 20], [5, 10, 15, 20, 50], [5, 10, 15, 20, 45], [5, 10, 15, 20, 45, 50], [5, 10, 15, 20, 40], [5, 10, 15, 20, 40, 50], [5, 10, 15, 20, 40, 45], [5, 10, 15, 20, 40, 45, 50], [5, 10, 15, 20, 35], [5, 10, 15, 20, 35, 50], [5, 10, 15, 20, 35, 45], [5, 10, 15, 20, 35, 45, 50], [5, 10, 15, 20, 35, 40], [5, 10, 15, 20, 35, 40, 50], [5, 10, 15, 20, 35, 40, 45], [5, 10, 15, 20, 35, 40, 45, 50], [5, 10, 15, 20, 30], [5, 10, 15, 20, 30, 50], [5, 10, 15, 20, 30, 45], [5, 10, 15, 20, 30, 45, 50], [5, 10, 15, 20, 30, 40], [5, 10, 15, 20, 30, 40, 50], [5, 10, 15, 20, 30, 40, 45], [5, 10, 15, 20, 30, 40, 45, 50], [5, 10, 15, 20, 30, 35], [5, 10, 15, 20, 30, 35, 50], [5, 10, 15, 20, 30, 35, 45], [5, 10, 15, 20, 30, 35, 45, 50], [5, 10, 15, 20, 30, 35, 40], [5, 10, 15, 20, 30, 35, 40, 50], [5, 10, 15, 20, 30, 35, 40, 45], [5, 10, 15, 20, 30, 35, 40, 45, 50], [5, 10, 15, 20, 25], [5, 10, 15, 20, 25, 50], [5, 10, 15, 20, 25, 45], [5, 10, 15, 20, 25, 45, 50], [5, 10, 15, 20, 25, 40], [5, 10, 15, 20, 25, 40, 50], [5, 10, 15, 20, 25, 40, 45], [5, 10, 15, 20, 25, 40, 45, 50], [5, 10, 15, 20, 25, 35], [5, 10, 15, 20, 25, 35, 50], [5, 10, 15, 20, 25, 35, 45], [5, 10, 15, 20, 25, 35, 45, 50], [5, 10, 15, 20, 25, 35, 40], [5, 10, 15, 20, 25, 35, 40, 50], [5, 10, 15, 20, 25, 35, 40, 45], [5, 10, 15, 20, 25, 35, 40, 45, 50], [5, 10, 15, 20, 25, 30], [5, 10, 15, 20, 25, 30, 50], [5, 10, 15, 20, 25, 30, 45], [5, 10, 15, 20, 25, 30, 45, 50], [5, 10, 15, 20, 25, 30, 40], [5, 10, 15, 20, 25, 30, 40, 50], [5, 10, 15, 20, 25, 30, 40, 45], [5, 10, 15, 20, 25, 30, 40, 45, 50], [5, 10, 15, 20, 25, 30, 35], [5, 10, 15, 20, 25, 30, 35, 50], [5, 10, 15, 20, 25, 30, 35, 45], [5, 10, 15, 20, 25, 30, 35, 45, 50], [5, 10, 15, 20, 25, 30, 35, 40], [5, 10, 15, 20, 25, 30, 35, 40, 50], [5, 10, 15, 20, 25, 30, 35, 40, 45], [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]]\n assert candidate(nums = [5, 1, 4, 2, 3]) == [[], [3], [2], [2, 3], [4], [4, 3], [4, 2], [4, 2, 3], [1], [1, 3], [1, 2], [1, 2, 3], [1, 4], [1, 4, 3], [1, 4, 2], [1, 4, 2, 3], [5], [5, 3], [5, 2], [5, 2, 3], [5, 4], [5, 4, 3], [5, 4, 2], [5, 4, 2, 3], [5, 1], [5, 1, 3], [5, 1, 2], [5, 1, 2, 3], [5, 1, 4], [5, 1, 4, 3], [5, 1, 4, 2], [5, 1, 4, 2, 3]]\n assert candidate(nums = [1, -1, 2, -2, 3, -3]) == [[], [-3], [3], [3, -3], [-2], [-2, -3], [-2, 3], [-2, 3, -3], [2], [2, -3], [2, 3], [2, 3, -3], [2, -2], [2, -2, -3], [2, -2, 3], [2, -2, 3, -3], [-1], [-1, -3], [-1, 3], [-1, 3, -3], [-1, -2], [-1, -2, -3], [-1, -2, 3], [-1, -2, 3, -3], [-1, 2], [-1, 2, -3], [-1, 2, 3], [-1, 2, 3, -3], [-1, 2, -2], [-1, 2, -2, -3], [-1, 2, -2, 3], [-1, 2, -2, 3, -3], [1], [1, -3], [1, 3], [1, 3, -3], [1, -2], [1, -2, -3], [1, -2, 3], [1, -2, 3, -3], [1, 2], [1, 2, -3], [1, 2, 3], [1, 2, 3, -3], [1, 2, -2], [1, 2, -2, -3], [1, 2, -2, 3], [1, 2, -2, 3, -3], [1, -1], [1, -1, -3], [1, -1, 3], [1, -1, 3, -3], [1, -1, -2], [1, -1, -2, -3], [1, -1, -2, 3], [1, -1, -2, 3, -3], [1, -1, 2], [1, -1, 2, -3], [1, -1, 2, 3], [1, -1, 2, 3, -3], [1, -1, 2, -2], [1, -1, 2, -2, -3], [1, -1, 2, -2, 3], [1, -1, 2, -2, 3, -3]]\n assert candidate(nums = [7, 11, 13, 17]) == [[], [17], [13], [13, 17], [11], [11, 17], [11, 13], [11, 13, 17], [7], [7, 17], [7, 13], [7, 13, 17], [7, 11], [7, 11, 17], [7, 11, 13], [7, 11, 13, 17]]\n assert candidate(nums = [8, 6, 7, 5, 3, 0, 9]) == [[], [9], [0], [0, 9], [3], [3, 9], [3, 0], [3, 0, 9], [5], [5, 9], [5, 0], [5, 0, 9], [5, 3], [5, 3, 9], [5, 3, 0], [5, 3, 0, 9], [7], [7, 9], [7, 0], [7, 0, 9], [7, 3], [7, 3, 9], [7, 3, 0], [7, 3, 0, 9], [7, 5], [7, 5, 9], [7, 5, 0], [7, 5, 0, 9], [7, 5, 3], [7, 5, 3, 9], [7, 5, 3, 0], [7, 5, 3, 0, 9], [6], [6, 9], [6, 0], [6, 0, 9], [6, 3], [6, 3, 9], [6, 3, 0], [6, 3, 0, 9], [6, 5], [6, 5, 9], [6, 5, 0], [6, 5, 0, 9], [6, 5, 3], [6, 5, 3, 9], [6, 5, 3, 0], [6, 5, 3, 0, 9], [6, 7], [6, 7, 9], [6, 7, 0], [6, 7, 0, 9], [6, 7, 3], [6, 7, 3, 9], [6, 7, 3, 0], [6, 7, 3, 0, 9], [6, 7, 5], [6, 7, 5, 9], [6, 7, 5, 0], [6, 7, 5, 0, 9], [6, 7, 5, 3], [6, 7, 5, 3, 9], [6, 7, 5, 3, 0], [6, 7, 5, 3, 0, 9], [8], [8, 9], [8, 0], [8, 0, 9], [8, 3], [8, 3, 9], [8, 3, 0], [8, 3, 0, 9], [8, 5], [8, 5, 9], [8, 5, 0], [8, 5, 0, 9], [8, 5, 3], [8, 5, 3, 9], [8, 5, 3, 0], [8, 5, 3, 0, 9], [8, 7], [8, 7, 9], [8, 7, 0], [8, 7, 0, 9], [8, 7, 3], [8, 7, 3, 9], [8, 7, 3, 0], [8, 7, 3, 0, 9], [8, 7, 5], [8, 7, 5, 9], [8, 7, 5, 0], [8, 7, 5, 0, 9], [8, 7, 5, 3], [8, 7, 5, 3, 9], [8, 7, 5, 3, 0], [8, 7, 5, 3, 0, 9], [8, 6], [8, 6, 9], [8, 6, 0], [8, 6, 0, 9], [8, 6, 3], [8, 6, 3, 9], [8, 6, 3, 0], [8, 6, 3, 0, 9], [8, 6, 5], [8, 6, 5, 9], [8, 6, 5, 0], [8, 6, 5, 0, 9], [8, 6, 5, 3], [8, 6, 5, 3, 9], [8, 6, 5, 3, 0], [8, 6, 5, 3, 0, 9], [8, 6, 7], [8, 6, 7, 9], [8, 6, 7, 0], [8, 6, 7, 0, 9], [8, 6, 7, 3], [8, 6, 7, 3, 9], [8, 6, 7, 3, 0], [8, 6, 7, 3, 0, 9], [8, 6, 7, 5], [8, 6, 7, 5, 9], [8, 6, 7, 5, 0], [8, 6, 7, 5, 0, 9], [8, 6, 7, 5, 3], [8, 6, 7, 5, 3, 9], [8, 6, 7, 5, 3, 0], [8, 6, 7, 5, 3, 0, 9]]\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == [[], [-100], [-90], [-90, -100], [-80], [-80, -100], [-80, -90], [-80, -90, -100], [-70], [-70, -100], [-70, -90], [-70, -90, -100], [-70, -80], [-70, -80, -100], [-70, -80, -90], [-70, -80, -90, -100], [-60], [-60, -100], [-60, -90], [-60, -90, -100], [-60, -80], [-60, -80, -100], [-60, -80, -90], [-60, -80, -90, -100], [-60, -70], [-60, -70, -100], [-60, -70, -90], [-60, -70, -90, -100], [-60, -70, -80], [-60, -70, -80, -100], [-60, -70, -80, -90], [-60, -70, -80, -90, -100], [-50], [-50, -100], [-50, -90], [-50, -90, -100], [-50, -80], [-50, -80, -100], [-50, -80, -90], [-50, -80, -90, -100], [-50, -70], [-50, -70, -100], [-50, -70, -90], [-50, -70, -90, -100], [-50, -70, -80], [-50, -70, -80, -100], [-50, -70, -80, -90], [-50, -70, -80, -90, -100], [-50, -60], [-50, -60, -100], [-50, -60, -90], [-50, -60, -90, -100], [-50, -60, -80], [-50, -60, -80, -100], [-50, -60, -80, -90], [-50, -60, -80, -90, -100], [-50, -60, -70], [-50, -60, -70, -100], [-50, -60, -70, -90], [-50, -60, -70, -90, -100], [-50, -60, -70, -80], [-50, -60, -70, -80, -100], [-50, -60, -70, -80, -90], [-50, -60, -70, -80, -90, -100], [-40], [-40, -100], [-40, -90], [-40, -90, -100], [-40, -80], [-40, -80, -100], [-40, -80, -90], [-40, -80, -90, -100], [-40, -70], [-40, -70, -100], [-40, -70, -90], [-40, -70, -90, -100], [-40, -70, -80], [-40, -70, -80, -100], [-40, -70, -80, -90], [-40, -70, -80, -90, -100], [-40, -60], [-40, -60, -100], [-40, -60, -90], [-40, -60, -90, -100], [-40, -60, -80], [-40, -60, -80, -100], [-40, -60, -80, -90], [-40, -60, -80, -90, -100], [-40, -60, -70], [-40, -60, -70, -100], [-40, -60, -70, -90], [-40, -60, -70, -90, -100], [-40, -60, -70, -80], [-40, -60, -70, -80, -100], [-40, -60, -70, -80, -90], [-40, -60, -70, -80, -90, -100], [-40, -50], [-40, -50, -100], [-40, -50, -90], [-40, -50, -90, -100], [-40, -50, -80], [-40, -50, -80, -100], [-40, -50, -80, -90], [-40, -50, -80, -90, -100], [-40, -50, -70], [-40, -50, -70, -100], [-40, -50, -70, -90], [-40, -50, -70, -90, -100], [-40, -50, -70, -80], [-40, -50, -70, -80, -100], [-40, -50, -70, -80, -90], [-40, -50, -70, -80, -90, -100], [-40, -50, -60], [-40, -50, -60, -100], [-40, -50, -60, -90], [-40, -50, -60, -90, -100], [-40, -50, -60, -80], [-40, -50, -60, -80, -100], [-40, -50, -60, -80, -90], [-40, -50, -60, -80, -90, -100], [-40, -50, -60, -70], [-40, -50, -60, -70, -100], [-40, -50, -60, -70, -90], [-40, -50, -60, -70, -90, -100], [-40, -50, -60, -70, -80], [-40, -50, -60, -70, -80, -100], [-40, -50, -60, -70, -80, -90], [-40, -50, -60, -70, -80, -90, -100], [-30], [-30, -100], [-30, -90], [-30, -90, -100], [-30, -80], [-30, -80, -100], [-30, -80, -90], [-30, -80, -90, -100], [-30, -70], [-30, -70, -100], [-30, -70, -90], [-30, -70, -90, -100], [-30, -70, -80], [-30, -70, -80, -100], [-30, -70, -80, -90], [-30, -70, -80, -90, -100], [-30, -60], [-30, -60, -100], [-30, -60, -90], [-30, -60, -90, -100], [-30, -60, -80], [-30, -60, -80, -100], [-30, -60, -80, -90], [-30, -60, -80, -90, -100], [-30, -60, -70], [-30, -60, -70, -100], [-30, -60, -70, -90], [-30, -60, -70, -90, -100], [-30, -60, -70, -80], [-30, -60, -70, -80, -100], [-30, -60, -70, -80, -90], [-30, -60, -70, -80, -90, -100], [-30, -50], [-30, -50, -100], [-30, -50, -90], [-30, -50, -90, -100], [-30, -50, -80], [-30, -50, -80, -100], [-30, -50, -80, -90], [-30, -50, -80, -90, -100], [-30, -50, -70], [-30, -50, -70, -100], [-30, -50, -70, -90], [-30, -50, -70, -90, -100], [-30, -50, -70, -80], [-30, -50, -70, -80, -100], [-30, -50, -70, -80, -90], [-30, -50, -70, -80, -90, -100], [-30, -50, -60], [-30, -50, -60, -100], [-30, -50, -60, -90], [-30, -50, -60, -90, -100], [-30, -50, -60, -80], [-30, -50, -60, -80, -100], [-30, -50, -60, -80, -90], [-30, -50, -60, -80, -90, -100], [-30, -50, -60, -70], [-30, -50, -60, -70, -100], [-30, -50, -60, -70, -90], [-30, -50, -60, -70, -90, -100], [-30, -50, -60, -70, -80], [-30, -50, -60, -70, -80, -100], [-30, -50, -60, -70, -80, -90], [-30, -50, -60, -70, -80, -90, -100], [-30, -40], [-30, -40, -100], [-30, -40, -90], [-30, -40, -90, -100], [-30, -40, -80], [-30, -40, -80, -100], [-30, -40, -80, 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-60], [-10, -20, -40, -50, -60, -100], [-10, -20, -40, -50, -60, -90], [-10, -20, -40, -50, -60, -90, -100], [-10, -20, -40, -50, -60, -80], [-10, -20, -40, -50, -60, -80, -100], [-10, -20, -40, -50, -60, -80, -90], [-10, -20, -40, -50, -60, -80, -90, -100], [-10, -20, -40, -50, -60, -70], [-10, -20, -40, -50, -60, -70, -100], [-10, -20, -40, -50, -60, -70, -90], [-10, -20, -40, -50, -60, -70, -90, -100], [-10, -20, -40, -50, -60, -70, -80], [-10, -20, -40, -50, -60, -70, -80, -100], [-10, -20, -40, -50, -60, -70, -80, -90], [-10, -20, -40, -50, -60, -70, -80, -90, -100], [-10, -20, -30], [-10, -20, -30, -100], [-10, -20, -30, -90], [-10, -20, -30, -90, -100], [-10, -20, -30, -80], [-10, -20, -30, -80, -100], [-10, -20, -30, -80, -90], [-10, -20, -30, -80, -90, -100], [-10, -20, -30, -70], [-10, -20, -30, -70, -100], [-10, -20, -30, -70, -90], [-10, -20, -30, -70, -90, -100], [-10, -20, -30, -70, -80], [-10, -20, -30, -70, -80, -100], [-10, -20, -30, -70, -80, -90], [-10, -20, -30, 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-50, -70, -80, -90], [-10, -20, -30, -50, -70, -80, -90, -100], [-10, -20, -30, -50, -60], [-10, -20, -30, -50, -60, -100], [-10, -20, -30, -50, -60, -90], [-10, -20, -30, -50, -60, -90, -100], [-10, -20, -30, -50, -60, -80], [-10, -20, -30, -50, -60, -80, -100], [-10, -20, -30, -50, -60, -80, -90], [-10, -20, -30, -50, -60, -80, -90, -100], [-10, -20, -30, -50, -60, -70], [-10, -20, -30, -50, -60, -70, -100], [-10, -20, -30, -50, -60, -70, -90], [-10, -20, -30, -50, -60, -70, -90, -100], [-10, -20, -30, -50, -60, -70, -80], [-10, -20, -30, -50, -60, -70, -80, -100], [-10, -20, -30, -50, -60, -70, -80, -90], [-10, -20, -30, -50, -60, -70, -80, -90, -100], [-10, -20, -30, -40], [-10, -20, -30, -40, -100], [-10, -20, -30, -40, -90], [-10, -20, -30, -40, -90, -100], [-10, -20, -30, -40, -80], [-10, -20, -30, -40, -80, -100], [-10, -20, -30, -40, -80, -90], [-10, -20, -30, -40, -80, -90, -100], [-10, -20, -30, -40, -70], [-10, -20, -30, -40, -70, -100], [-10, -20, -30, -40, -70, -90], [-10, -20, -30, -40, -70, -90, -100], [-10, -20, -30, -40, -70, -80], [-10, -20, -30, -40, -70, -80, -100], [-10, -20, -30, -40, -70, -80, -90], [-10, -20, -30, -40, -70, -80, -90, -100], [-10, -20, -30, -40, -60], [-10, -20, -30, -40, -60, -100], [-10, -20, -30, -40, -60, -90], [-10, -20, -30, -40, -60, -90, -100], [-10, -20, -30, -40, -60, -80], [-10, -20, -30, -40, -60, -80, -100], [-10, -20, -30, -40, -60, -80, -90], [-10, -20, -30, -40, -60, -80, -90, -100], [-10, -20, -30, -40, -60, -70], [-10, -20, -30, -40, -60, -70, -100], [-10, -20, -30, -40, -60, -70, -90], [-10, -20, -30, -40, -60, -70, -90, -100], [-10, -20, -30, -40, -60, -70, -80], [-10, -20, -30, -40, -60, -70, -80, -100], [-10, -20, -30, -40, -60, -70, -80, -90], [-10, -20, -30, -40, -60, -70, -80, -90, -100], [-10, -20, -30, -40, -50], [-10, -20, -30, -40, -50, -100], [-10, -20, -30, -40, -50, -90], [-10, -20, -30, -40, -50, -90, -100], [-10, -20, -30, -40, -50, -80], [-10, -20, -30, -40, -50, -80, -100], [-10, -20, -30, -40, -50, -80, -90], [-10, -20, -30, -40, -50, -80, -90, -100], [-10, -20, -30, -40, -50, -70], [-10, -20, -30, -40, -50, -70, -100], [-10, -20, -30, -40, -50, -70, -90], [-10, -20, -30, -40, -50, -70, -90, -100], [-10, -20, -30, -40, -50, -70, -80], [-10, -20, -30, -40, -50, -70, -80, -100], [-10, -20, -30, -40, -50, -70, -80, -90], [-10, -20, -30, -40, -50, -70, -80, -90, -100], [-10, -20, -30, -40, -50, -60], [-10, -20, -30, -40, -50, -60, -100], [-10, -20, -30, -40, -50, -60, -90], [-10, -20, -30, -40, -50, -60, -90, -100], [-10, -20, -30, -40, -50, -60, -80], [-10, -20, -30, -40, -50, -60, -80, -100], [-10, -20, -30, -40, -50, -60, -80, -90], [-10, -20, -30, -40, -50, -60, -80, -90, -100], [-10, -20, -30, -40, -50, -60, -70], [-10, -20, -30, -40, -50, -60, -70, -100], [-10, -20, -30, -40, -50, -60, -70, -90], [-10, -20, -30, -40, -50, -60, -70, -90, -100], [-10, -20, -30, -40, -50, -60, -70, -80], [-10, -20, -30, -40, -50, -60, -70, -80, -100], [-10, -20, -30, -40, -50, -60, -70, -80, -90], [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100]]\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14]) == [[], [14], [12], [12, 14], [10], [10, 14], [10, 12], [10, 12, 14], [8], [8, 14], [8, 12], [8, 12, 14], [8, 10], [8, 10, 14], [8, 10, 12], [8, 10, 12, 14], [6], [6, 14], [6, 12], [6, 12, 14], [6, 10], [6, 10, 14], [6, 10, 12], [6, 10, 12, 14], [6, 8], [6, 8, 14], [6, 8, 12], [6, 8, 12, 14], [6, 8, 10], [6, 8, 10, 14], [6, 8, 10, 12], [6, 8, 10, 12, 14], [4], [4, 14], [4, 12], [4, 12, 14], [4, 10], [4, 10, 14], [4, 10, 12], [4, 10, 12, 14], [4, 8], [4, 8, 14], [4, 8, 12], [4, 8, 12, 14], [4, 8, 10], [4, 8, 10, 14], [4, 8, 10, 12], [4, 8, 10, 12, 14], [4, 6], [4, 6, 14], [4, 6, 12], [4, 6, 12, 14], [4, 6, 10], [4, 6, 10, 14], [4, 6, 10, 12], [4, 6, 10, 12, 14], [4, 6, 8], [4, 6, 8, 14], [4, 6, 8, 12], [4, 6, 8, 12, 14], [4, 6, 8, 10], [4, 6, 8, 10, 14], [4, 6, 8, 10, 12], [4, 6, 8, 10, 12, 14], [2], [2, 14], [2, 12], [2, 12, 14], [2, 10], [2, 10, 14], [2, 10, 12], [2, 10, 12, 14], [2, 8], [2, 8, 14], [2, 8, 12], [2, 8, 12, 14], [2, 8, 10], [2, 8, 10, 14], [2, 8, 10, 12], [2, 8, 10, 12, 14], [2, 6], [2, 6, 14], [2, 6, 12], [2, 6, 12, 14], [2, 6, 10], [2, 6, 10, 14], [2, 6, 10, 12], [2, 6, 10, 12, 14], [2, 6, 8], [2, 6, 8, 14], [2, 6, 8, 12], [2, 6, 8, 12, 14], [2, 6, 8, 10], [2, 6, 8, 10, 14], [2, 6, 8, 10, 12], [2, 6, 8, 10, 12, 14], [2, 4], [2, 4, 14], [2, 4, 12], [2, 4, 12, 14], [2, 4, 10], [2, 4, 10, 14], [2, 4, 10, 12], [2, 4, 10, 12, 14], [2, 4, 8], [2, 4, 8, 14], [2, 4, 8, 12], [2, 4, 8, 12, 14], [2, 4, 8, 10], [2, 4, 8, 10, 14], [2, 4, 8, 10, 12], [2, 4, 8, 10, 12, 14], [2, 4, 6], [2, 4, 6, 14], [2, 4, 6, 12], [2, 4, 6, 12, 14], [2, 4, 6, 10], [2, 4, 6, 10, 14], [2, 4, 6, 10, 12], [2, 4, 6, 10, 12, 14], [2, 4, 6, 8], [2, 4, 6, 8, 14], [2, 4, 6, 8, 12], [2, 4, 6, 8, 12, 14], [2, 4, 6, 8, 10], [2, 4, 6, 8, 10, 14], [2, 4, 6, 8, 10, 12], [2, 4, 6, 8, 10, 12, 14]]\n assert candidate(nums = [10, -10, 5, -5, 0]) == [[], [0], [-5], [-5, 0], [5], [5, 0], [5, -5], [5, -5, 0], [-10], [-10, 0], [-10, -5], [-10, -5, 0], [-10, 5], [-10, 5, 0], [-10, 5, -5], [-10, 5, -5, 0], [10], [10, 0], [10, -5], [10, -5, 0], [10, 5], [10, 5, 0], [10, 5, -5], [10, 5, -5, 0], [10, -10], [10, -10, 0], [10, -10, -5], [10, -10, -5, 0], [10, -10, 5], [10, -10, 5, 0], [10, -10, 5, -5], [10, -10, 5, -5, 0]]\n assert candidate(nums = [-10, -5, 0, 5, 10]) == [[], [10], [5], [5, 10], [0], [0, 10], [0, 5], [0, 5, 10], [-5], [-5, 10], [-5, 5], [-5, 5, 10], [-5, 0], [-5, 0, 10], [-5, 0, 5], [-5, 0, 5, 10], [-10], [-10, 10], [-10, 5], [-10, 5, 10], [-10, 0], [-10, 0, 10], [-10, 0, 5], [-10, 0, 5, 10], [-10, -5], [-10, -5, 10], [-10, -5, 5], [-10, -5, 5, 10], [-10, -5, 0], [-10, -5, 0, 10], [-10, -5, 0, 5], [-10, -5, 0, 5, 10]]\n assert candidate(nums = [1, 100, 1000, 10000, 100000, 1000000]) == [[], [1000000], [100000], [100000, 1000000], [10000], [10000, 1000000], [10000, 100000], [10000, 100000, 1000000], [1000], [1000, 1000000], [1000, 100000], [1000, 100000, 1000000], [1000, 10000], [1000, 10000, 1000000], [1000, 10000, 100000], [1000, 10000, 100000, 1000000], [100], [100, 1000000], [100, 100000], [100, 100000, 1000000], [100, 10000], [100, 10000, 1000000], [100, 10000, 100000], [100, 10000, 100000, 1000000], [100, 1000], [100, 1000, 1000000], [100, 1000, 100000], [100, 1000, 100000, 1000000], [100, 1000, 10000], [100, 1000, 10000, 1000000], [100, 1000, 10000, 100000], [100, 1000, 10000, 100000, 1000000], [1], [1, 1000000], [1, 100000], [1, 100000, 1000000], [1, 10000], [1, 10000, 1000000], [1, 10000, 100000], [1, 10000, 100000, 1000000], [1, 1000], [1, 1000, 1000000], [1, 1000, 100000], [1, 1000, 100000, 1000000], [1, 1000, 10000], [1, 1000, 10000, 1000000], [1, 1000, 10000, 100000], [1, 1000, 10000, 100000, 1000000], [1, 100], [1, 100, 1000000], [1, 100, 100000], [1, 100, 100000, 1000000], [1, 100, 10000], [1, 100, 10000, 1000000], [1, 100, 10000, 100000], [1, 100, 10000, 100000, 1000000], [1, 100, 1000], [1, 100, 1000, 1000000], [1, 100, 1000, 100000], [1, 100, 1000, 100000, 1000000], [1, 100, 1000, 10000], [1, 100, 1000, 10000, 1000000], [1, 100, 1000, 10000, 100000], [1, 100, 1000, 10000, 100000, 1000000]]\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == [[], [8], [7], [7, 8], [6], [6, 8], [6, 7], [6, 7, 8], [5], [5, 8], [5, 7], [5, 7, 8], [5, 6], [5, 6, 8], [5, 6, 7], [5, 6, 7, 8], [4], [4, 8], [4, 7], [4, 7, 8], [4, 6], [4, 6, 8], [4, 6, 7], [4, 6, 7, 8], [4, 5], [4, 5, 8], [4, 5, 7], [4, 5, 7, 8], [4, 5, 6], [4, 5, 6, 8], [4, 5, 6, 7], [4, 5, 6, 7, 8], [3], [3, 8], [3, 7], [3, 7, 8], [3, 6], [3, 6, 8], [3, 6, 7], [3, 6, 7, 8], [3, 5], [3, 5, 8], [3, 5, 7], [3, 5, 7, 8], [3, 5, 6], [3, 5, 6, 8], [3, 5, 6, 7], [3, 5, 6, 7, 8], [3, 4], [3, 4, 8], [3, 4, 7], [3, 4, 7, 8], [3, 4, 6], [3, 4, 6, 8], [3, 4, 6, 7], [3, 4, 6, 7, 8], [3, 4, 5], [3, 4, 5, 8], [3, 4, 5, 7], [3, 4, 5, 7, 8], [3, 4, 5, 6], [3, 4, 5, 6, 8], [3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 8], [2], [2, 8], [2, 7], [2, 7, 8], [2, 6], [2, 6, 8], [2, 6, 7], [2, 6, 7, 8], [2, 5], [2, 5, 8], [2, 5, 7], [2, 5, 7, 8], [2, 5, 6], [2, 5, 6, 8], [2, 5, 6, 7], [2, 5, 6, 7, 8], [2, 4], [2, 4, 8], [2, 4, 7], [2, 4, 7, 8], [2, 4, 6], [2, 4, 6, 8], [2, 4, 6, 7], [2, 4, 6, 7, 8], [2, 4, 5], [2, 4, 5, 8], [2, 4, 5, 7], [2, 4, 5, 7, 8], [2, 4, 5, 6], [2, 4, 5, 6, 8], [2, 4, 5, 6, 7], [2, 4, 5, 6, 7, 8], [2, 3], [2, 3, 8], [2, 3, 7], [2, 3, 7, 8], [2, 3, 6], [2, 3, 6, 8], [2, 3, 6, 7], [2, 3, 6, 7, 8], [2, 3, 5], [2, 3, 5, 8], [2, 3, 5, 7], [2, 3, 5, 7, 8], [2, 3, 5, 6], [2, 3, 5, 6, 8], [2, 3, 5, 6, 7], [2, 3, 5, 6, 7, 8], [2, 3, 4], [2, 3, 4, 8], [2, 3, 4, 7], [2, 3, 4, 7, 8], [2, 3, 4, 6], [2, 3, 4, 6, 8], [2, 3, 4, 6, 7], [2, 3, 4, 6, 7, 8], [2, 3, 4, 5], [2, 3, 4, 5, 8], [2, 3, 4, 5, 7], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 7, 8], [1], [1, 8], [1, 7], [1, 7, 8], [1, 6], [1, 6, 8], [1, 6, 7], [1, 6, 7, 8], [1, 5], [1, 5, 8], [1, 5, 7], [1, 5, 7, 8], [1, 5, 6], [1, 5, 6, 8], [1, 5, 6, 7], [1, 5, 6, 7, 8], [1, 4], [1, 4, 8], [1, 4, 7], [1, 4, 7, 8], [1, 4, 6], [1, 4, 6, 8], [1, 4, 6, 7], [1, 4, 6, 7, 8], [1, 4, 5], [1, 4, 5, 8], [1, 4, 5, 7], [1, 4, 5, 7, 8], [1, 4, 5, 6], [1, 4, 5, 6, 8], [1, 4, 5, 6, 7], [1, 4, 5, 6, 7, 8], [1, 3], [1, 3, 8], [1, 3, 7], [1, 3, 7, 8], [1, 3, 6], [1, 3, 6, 8], [1, 3, 6, 7], [1, 3, 6, 7, 8], [1, 3, 5], [1, 3, 5, 8], [1, 3, 5, 7], [1, 3, 5, 7, 8], [1, 3, 5, 6], [1, 3, 5, 6, 8], [1, 3, 5, 6, 7], [1, 3, 5, 6, 7, 8], [1, 3, 4], [1, 3, 4, 8], [1, 3, 4, 7], [1, 3, 4, 7, 8], [1, 3, 4, 6], [1, 3, 4, 6, 8], [1, 3, 4, 6, 7], [1, 3, 4, 6, 7, 8], [1, 3, 4, 5], [1, 3, 4, 5, 8], [1, 3, 4, 5, 7], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 6], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 7, 8], [1, 2], [1, 2, 8], [1, 2, 7], [1, 2, 7, 8], [1, 2, 6], [1, 2, 6, 8], [1, 2, 6, 7], [1, 2, 6, 7, 8], [1, 2, 5], [1, 2, 5, 8], [1, 2, 5, 7], [1, 2, 5, 7, 8], [1, 2, 5, 6], [1, 2, 5, 6, 8], [1, 2, 5, 6, 7], [1, 2, 5, 6, 7, 8], [1, 2, 4], [1, 2, 4, 8], [1, 2, 4, 7], [1, 2, 4, 7, 8], [1, 2, 4, 6], [1, 2, 4, 6, 8], [1, 2, 4, 6, 7], [1, 2, 4, 6, 7, 8], [1, 2, 4, 5], [1, 2, 4, 5, 8], [1, 2, 4, 5, 7], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 6], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 7, 8], [1, 2, 3], [1, 2, 3, 8], [1, 2, 3, 7], [1, 2, 3, 7, 8], [1, 2, 3, 6], [1, 2, 3, 6, 8], [1, 2, 3, 6, 7], [1, 2, 3, 6, 7, 8], [1, 2, 3, 5], [1, 2, 3, 5, 8], [1, 2, 3, 5, 7], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 6], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 4], [1, 2, 3, 4, 8], [1, 2, 3, 4, 7], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 6], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 7, 8], [0], [0, 8], [0, 7], [0, 7, 8], [0, 6], [0, 6, 8], [0, 6, 7], [0, 6, 7, 8], [0, 5], [0, 5, 8], [0, 5, 7], [0, 5, 7, 8], [0, 5, 6], [0, 5, 6, 8], [0, 5, 6, 7], [0, 5, 6, 7, 8], [0, 4], [0, 4, 8], [0, 4, 7], [0, 4, 7, 8], [0, 4, 6], [0, 4, 6, 8], [0, 4, 6, 7], [0, 4, 6, 7, 8], [0, 4, 5], [0, 4, 5, 8], [0, 4, 5, 7], [0, 4, 5, 7, 8], [0, 4, 5, 6], [0, 4, 5, 6, 8], [0, 4, 5, 6, 7], [0, 4, 5, 6, 7, 8], [0, 3], [0, 3, 8], [0, 3, 7], [0, 3, 7, 8], [0, 3, 6], [0, 3, 6, 8], [0, 3, 6, 7], [0, 3, 6, 7, 8], [0, 3, 5], [0, 3, 5, 8], [0, 3, 5, 7], [0, 3, 5, 7, 8], [0, 3, 5, 6], [0, 3, 5, 6, 8], [0, 3, 5, 6, 7], [0, 3, 5, 6, 7, 8], [0, 3, 4], [0, 3, 4, 8], [0, 3, 4, 7], [0, 3, 4, 7, 8], [0, 3, 4, 6], [0, 3, 4, 6, 8], [0, 3, 4, 6, 7], [0, 3, 4, 6, 7, 8], [0, 3, 4, 5], [0, 3, 4, 5, 8], [0, 3, 4, 5, 7], [0, 3, 4, 5, 7, 8], [0, 3, 4, 5, 6], [0, 3, 4, 5, 6, 8], [0, 3, 4, 5, 6, 7], [0, 3, 4, 5, 6, 7, 8], [0, 2], [0, 2, 8], [0, 2, 7], [0, 2, 7, 8], [0, 2, 6], [0, 2, 6, 8], [0, 2, 6, 7], [0, 2, 6, 7, 8], [0, 2, 5], [0, 2, 5, 8], [0, 2, 5, 7], [0, 2, 5, 7, 8], [0, 2, 5, 6], [0, 2, 5, 6, 8], [0, 2, 5, 6, 7], [0, 2, 5, 6, 7, 8], [0, 2, 4], [0, 2, 4, 8], [0, 2, 4, 7], [0, 2, 4, 7, 8], [0, 2, 4, 6], [0, 2, 4, 6, 8], [0, 2, 4, 6, 7], [0, 2, 4, 6, 7, 8], [0, 2, 4, 5], [0, 2, 4, 5, 8], [0, 2, 4, 5, 7], [0, 2, 4, 5, 7, 8], [0, 2, 4, 5, 6], [0, 2, 4, 5, 6, 8], [0, 2, 4, 5, 6, 7], [0, 2, 4, 5, 6, 7, 8], [0, 2, 3], [0, 2, 3, 8], [0, 2, 3, 7], [0, 2, 3, 7, 8], [0, 2, 3, 6], [0, 2, 3, 6, 8], [0, 2, 3, 6, 7], [0, 2, 3, 6, 7, 8], [0, 2, 3, 5], [0, 2, 3, 5, 8], [0, 2, 3, 5, 7], [0, 2, 3, 5, 7, 8], [0, 2, 3, 5, 6], [0, 2, 3, 5, 6, 8], [0, 2, 3, 5, 6, 7], [0, 2, 3, 5, 6, 7, 8], [0, 2, 3, 4], [0, 2, 3, 4, 8], [0, 2, 3, 4, 7], [0, 2, 3, 4, 7, 8], [0, 2, 3, 4, 6], [0, 2, 3, 4, 6, 8], [0, 2, 3, 4, 6, 7], [0, 2, 3, 4, 6, 7, 8], [0, 2, 3, 4, 5], [0, 2, 3, 4, 5, 8], [0, 2, 3, 4, 5, 7], [0, 2, 3, 4, 5, 7, 8], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 6, 8], [0, 2, 3, 4, 5, 6, 7], [0, 2, 3, 4, 5, 6, 7, 8], [0, 1], [0, 1, 8], [0, 1, 7], [0, 1, 7, 8], [0, 1, 6], [0, 1, 6, 8], [0, 1, 6, 7], [0, 1, 6, 7, 8], [0, 1, 5], [0, 1, 5, 8], [0, 1, 5, 7], [0, 1, 5, 7, 8], [0, 1, 5, 6], [0, 1, 5, 6, 8], [0, 1, 5, 6, 7], [0, 1, 5, 6, 7, 8], [0, 1, 4], [0, 1, 4, 8], [0, 1, 4, 7], [0, 1, 4, 7, 8], [0, 1, 4, 6], [0, 1, 4, 6, 8], [0, 1, 4, 6, 7], [0, 1, 4, 6, 7, 8], [0, 1, 4, 5], [0, 1, 4, 5, 8], [0, 1, 4, 5, 7], [0, 1, 4, 5, 7, 8], [0, 1, 4, 5, 6], [0, 1, 4, 5, 6, 8], [0, 1, 4, 5, 6, 7], [0, 1, 4, 5, 6, 7, 8], [0, 1, 3], [0, 1, 3, 8], [0, 1, 3, 7], [0, 1, 3, 7, 8], [0, 1, 3, 6], [0, 1, 3, 6, 8], [0, 1, 3, 6, 7], [0, 1, 3, 6, 7, 8], [0, 1, 3, 5], [0, 1, 3, 5, 8], [0, 1, 3, 5, 7], [0, 1, 3, 5, 7, 8], [0, 1, 3, 5, 6], [0, 1, 3, 5, 6, 8], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6, 7, 8], [0, 1, 3, 4], [0, 1, 3, 4, 8], [0, 1, 3, 4, 7], [0, 1, 3, 4, 7, 8], [0, 1, 3, 4, 6], [0, 1, 3, 4, 6, 8], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 7, 8], [0, 1, 3, 4, 5], [0, 1, 3, 4, 5, 8], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5, 7, 8], [0, 1, 3, 4, 5, 6], [0, 1, 3, 4, 5, 6, 8], [0, 1, 3, 4, 5, 6, 7], [0, 1, 3, 4, 5, 6, 7, 8], [0, 1, 2], [0, 1, 2, 8], [0, 1, 2, 7], [0, 1, 2, 7, 8], [0, 1, 2, 6], [0, 1, 2, 6, 8], [0, 1, 2, 6, 7], [0, 1, 2, 6, 7, 8], [0, 1, 2, 5], [0, 1, 2, 5, 8], [0, 1, 2, 5, 7], [0, 1, 2, 5, 7, 8], [0, 1, 2, 5, 6], [0, 1, 2, 5, 6, 8], [0, 1, 2, 5, 6, 7], [0, 1, 2, 5, 6, 7, 8], [0, 1, 2, 4], [0, 1, 2, 4, 8], [0, 1, 2, 4, 7], [0, 1, 2, 4, 7, 8], [0, 1, 2, 4, 6], [0, 1, 2, 4, 6, 8], [0, 1, 2, 4, 6, 7], [0, 1, 2, 4, 6, 7, 8], [0, 1, 2, 4, 5], [0, 1, 2, 4, 5, 8], [0, 1, 2, 4, 5, 7], [0, 1, 2, 4, 5, 7, 8], [0, 1, 2, 4, 5, 6], [0, 1, 2, 4, 5, 6, 8], [0, 1, 2, 4, 5, 6, 7], [0, 1, 2, 4, 5, 6, 7, 8], [0, 1, 2, 3], [0, 1, 2, 3, 8], [0, 1, 2, 3, 7], [0, 1, 2, 3, 7, 8], [0, 1, 2, 3, 6], [0, 1, 2, 3, 6, 8], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6, 7, 8], [0, 1, 2, 3, 5], [0, 1, 2, 3, 5, 8], [0, 1, 2, 3, 5, 7], [0, 1, 2, 3, 5, 7, 8], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 6, 8], [0, 1, 2, 3, 5, 6, 7], [0, 1, 2, 3, 5, 6, 7, 8], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 8], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4, 7, 8], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 6, 8], [0, 1, 2, 3, 4, 6, 7], [0, 1, 2, 3, 4, 6, 7, 8], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5, 8], [0, 1, 2, 3, 4, 5, 7], [0, 1, 2, 3, 4, 5, 7, 8], [0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 6, 8], [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 7, 8], [-1], [-1, 8], [-1, 7], [-1, 7, 8], [-1, 6], [-1, 6, 8], [-1, 6, 7], [-1, 6, 7, 8], [-1, 5], [-1, 5, 8], [-1, 5, 7], [-1, 5, 7, 8], [-1, 5, 6], [-1, 5, 6, 8], [-1, 5, 6, 7], [-1, 5, 6, 7, 8], [-1, 4], [-1, 4, 8], [-1, 4, 7], [-1, 4, 7, 8], [-1, 4, 6], [-1, 4, 6, 8], [-1, 4, 6, 7], [-1, 4, 6, 7, 8], [-1, 4, 5], [-1, 4, 5, 8], [-1, 4, 5, 7], [-1, 4, 5, 7, 8], [-1, 4, 5, 6], [-1, 4, 5, 6, 8], [-1, 4, 5, 6, 7], [-1, 4, 5, 6, 7, 8], [-1, 3], [-1, 3, 8], [-1, 3, 7], [-1, 3, 7, 8], [-1, 3, 6], [-1, 3, 6, 8], [-1, 3, 6, 7], [-1, 3, 6, 7, 8], [-1, 3, 5], [-1, 3, 5, 8], [-1, 3, 5, 7], [-1, 3, 5, 7, 8], [-1, 3, 5, 6], [-1, 3, 5, 6, 8], [-1, 3, 5, 6, 7], [-1, 3, 5, 6, 7, 8], [-1, 3, 4], [-1, 3, 4, 8], [-1, 3, 4, 7], [-1, 3, 4, 7, 8], [-1, 3, 4, 6], [-1, 3, 4, 6, 8], [-1, 3, 4, 6, 7], [-1, 3, 4, 6, 7, 8], [-1, 3, 4, 5], [-1, 3, 4, 5, 8], [-1, 3, 4, 5, 7], [-1, 3, 4, 5, 7, 8], [-1, 3, 4, 5, 6], [-1, 3, 4, 5, 6, 8], [-1, 3, 4, 5, 6, 7], [-1, 3, 4, 5, 6, 7, 8], [-1, 2], [-1, 2, 8], [-1, 2, 7], [-1, 2, 7, 8], [-1, 2, 6], [-1, 2, 6, 8], [-1, 2, 6, 7], [-1, 2, 6, 7, 8], [-1, 2, 5], [-1, 2, 5, 8], [-1, 2, 5, 7], [-1, 2, 5, 7, 8], [-1, 2, 5, 6], [-1, 2, 5, 6, 8], [-1, 2, 5, 6, 7], [-1, 2, 5, 6, 7, 8], [-1, 2, 4], [-1, 2, 4, 8], [-1, 2, 4, 7], [-1, 2, 4, 7, 8], [-1, 2, 4, 6], [-1, 2, 4, 6, 8], [-1, 2, 4, 6, 7], [-1, 2, 4, 6, 7, 8], [-1, 2, 4, 5], [-1, 2, 4, 5, 8], [-1, 2, 4, 5, 7], [-1, 2, 4, 5, 7, 8], [-1, 2, 4, 5, 6], [-1, 2, 4, 5, 6, 8], [-1, 2, 4, 5, 6, 7], [-1, 2, 4, 5, 6, 7, 8], [-1, 2, 3], [-1, 2, 3, 8], [-1, 2, 3, 7], [-1, 2, 3, 7, 8], [-1, 2, 3, 6], [-1, 2, 3, 6, 8], [-1, 2, 3, 6, 7], [-1, 2, 3, 6, 7, 8], [-1, 2, 3, 5], [-1, 2, 3, 5, 8], [-1, 2, 3, 5, 7], [-1, 2, 3, 5, 7, 8], [-1, 2, 3, 5, 6], [-1, 2, 3, 5, 6, 8], [-1, 2, 3, 5, 6, 7], [-1, 2, 3, 5, 6, 7, 8], [-1, 2, 3, 4], [-1, 2, 3, 4, 8], [-1, 2, 3, 4, 7], [-1, 2, 3, 4, 7, 8], [-1, 2, 3, 4, 6], [-1, 2, 3, 4, 6, 8], [-1, 2, 3, 4, 6, 7], [-1, 2, 3, 4, 6, 7, 8], [-1, 2, 3, 4, 5], [-1, 2, 3, 4, 5, 8], [-1, 2, 3, 4, 5, 7], [-1, 2, 3, 4, 5, 7, 8], [-1, 2, 3, 4, 5, 6], [-1, 2, 3, 4, 5, 6, 8], [-1, 2, 3, 4, 5, 6, 7], [-1, 2, 3, 4, 5, 6, 7, 8], [-1, 1], [-1, 1, 8], [-1, 1, 7], [-1, 1, 7, 8], [-1, 1, 6], [-1, 1, 6, 8], [-1, 1, 6, 7], [-1, 1, 6, 7, 8], [-1, 1, 5], [-1, 1, 5, 8], [-1, 1, 5, 7], [-1, 1, 5, 7, 8], [-1, 1, 5, 6], [-1, 1, 5, 6, 8], [-1, 1, 5, 6, 7], [-1, 1, 5, 6, 7, 8], [-1, 1, 4], [-1, 1, 4, 8], [-1, 1, 4, 7], [-1, 1, 4, 7, 8], [-1, 1, 4, 6], [-1, 1, 4, 6, 8], [-1, 1, 4, 6, 7], [-1, 1, 4, 6, 7, 8], [-1, 1, 4, 5], [-1, 1, 4, 5, 8], [-1, 1, 4, 5, 7], [-1, 1, 4, 5, 7, 8], [-1, 1, 4, 5, 6], [-1, 1, 4, 5, 6, 8], [-1, 1, 4, 5, 6, 7], [-1, 1, 4, 5, 6, 7, 8], [-1, 1, 3], [-1, 1, 3, 8], [-1, 1, 3, 7], [-1, 1, 3, 7, 8], [-1, 1, 3, 6], [-1, 1, 3, 6, 8], [-1, 1, 3, 6, 7], [-1, 1, 3, 6, 7, 8], [-1, 1, 3, 5], [-1, 1, 3, 5, 8], [-1, 1, 3, 5, 7], [-1, 1, 3, 5, 7, 8], [-1, 1, 3, 5, 6], [-1, 1, 3, 5, 6, 8], [-1, 1, 3, 5, 6, 7], [-1, 1, 3, 5, 6, 7, 8], [-1, 1, 3, 4], [-1, 1, 3, 4, 8], [-1, 1, 3, 4, 7], [-1, 1, 3, 4, 7, 8], [-1, 1, 3, 4, 6], [-1, 1, 3, 4, 6, 8], [-1, 1, 3, 4, 6, 7], [-1, 1, 3, 4, 6, 7, 8], [-1, 1, 3, 4, 5], [-1, 1, 3, 4, 5, 8], [-1, 1, 3, 4, 5, 7], [-1, 1, 3, 4, 5, 7, 8], [-1, 1, 3, 4, 5, 6], [-1, 1, 3, 4, 5, 6, 8], [-1, 1, 3, 4, 5, 6, 7], [-1, 1, 3, 4, 5, 6, 7, 8], [-1, 1, 2], [-1, 1, 2, 8], [-1, 1, 2, 7], [-1, 1, 2, 7, 8], [-1, 1, 2, 6], [-1, 1, 2, 6, 8], [-1, 1, 2, 6, 7], [-1, 1, 2, 6, 7, 8], [-1, 1, 2, 5], [-1, 1, 2, 5, 8], [-1, 1, 2, 5, 7], [-1, 1, 2, 5, 7, 8], [-1, 1, 2, 5, 6], [-1, 1, 2, 5, 6, 8], [-1, 1, 2, 5, 6, 7], [-1, 1, 2, 5, 6, 7, 8], [-1, 1, 2, 4], [-1, 1, 2, 4, 8], [-1, 1, 2, 4, 7], [-1, 1, 2, 4, 7, 8], [-1, 1, 2, 4, 6], [-1, 1, 2, 4, 6, 8], [-1, 1, 2, 4, 6, 7], [-1, 1, 2, 4, 6, 7, 8], [-1, 1, 2, 4, 5], [-1, 1, 2, 4, 5, 8], [-1, 1, 2, 4, 5, 7], [-1, 1, 2, 4, 5, 7, 8], [-1, 1, 2, 4, 5, 6], [-1, 1, 2, 4, 5, 6, 8], [-1, 1, 2, 4, 5, 6, 7], [-1, 1, 2, 4, 5, 6, 7, 8], [-1, 1, 2, 3], [-1, 1, 2, 3, 8], [-1, 1, 2, 3, 7], [-1, 1, 2, 3, 7, 8], [-1, 1, 2, 3, 6], [-1, 1, 2, 3, 6, 8], [-1, 1, 2, 3, 6, 7], [-1, 1, 2, 3, 6, 7, 8], [-1, 1, 2, 3, 5], [-1, 1, 2, 3, 5, 8], [-1, 1, 2, 3, 5, 7], [-1, 1, 2, 3, 5, 7, 8], [-1, 1, 2, 3, 5, 6], [-1, 1, 2, 3, 5, 6, 8], [-1, 1, 2, 3, 5, 6, 7], [-1, 1, 2, 3, 5, 6, 7, 8], [-1, 1, 2, 3, 4], [-1, 1, 2, 3, 4, 8], [-1, 1, 2, 3, 4, 7], [-1, 1, 2, 3, 4, 7, 8], [-1, 1, 2, 3, 4, 6], [-1, 1, 2, 3, 4, 6, 8], [-1, 1, 2, 3, 4, 6, 7], [-1, 1, 2, 3, 4, 6, 7, 8], [-1, 1, 2, 3, 4, 5], [-1, 1, 2, 3, 4, 5, 8], [-1, 1, 2, 3, 4, 5, 7], [-1, 1, 2, 3, 4, 5, 7, 8], [-1, 1, 2, 3, 4, 5, 6], [-1, 1, 2, 3, 4, 5, 6, 8], [-1, 1, 2, 3, 4, 5, 6, 7], [-1, 1, 2, 3, 4, 5, 6, 7, 8], [-1, 0], [-1, 0, 8], [-1, 0, 7], [-1, 0, 7, 8], [-1, 0, 6], [-1, 0, 6, 8], [-1, 0, 6, 7], [-1, 0, 6, 7, 8], [-1, 0, 5], [-1, 0, 5, 8], [-1, 0, 5, 7], [-1, 0, 5, 7, 8], [-1, 0, 5, 6], [-1, 0, 5, 6, 8], [-1, 0, 5, 6, 7], [-1, 0, 5, 6, 7, 8], [-1, 0, 4], [-1, 0, 4, 8], [-1, 0, 4, 7], [-1, 0, 4, 7, 8], [-1, 0, 4, 6], [-1, 0, 4, 6, 8], [-1, 0, 4, 6, 7], [-1, 0, 4, 6, 7, 8], [-1, 0, 4, 5], [-1, 0, 4, 5, 8], [-1, 0, 4, 5, 7], [-1, 0, 4, 5, 7, 8], [-1, 0, 4, 5, 6], [-1, 0, 4, 5, 6, 8], [-1, 0, 4, 5, 6, 7], [-1, 0, 4, 5, 6, 7, 8], [-1, 0, 3], [-1, 0, 3, 8], [-1, 0, 3, 7], [-1, 0, 3, 7, 8], [-1, 0, 3, 6], [-1, 0, 3, 6, 8], [-1, 0, 3, 6, 7], [-1, 0, 3, 6, 7, 8], [-1, 0, 3, 5], [-1, 0, 3, 5, 8], [-1, 0, 3, 5, 7], [-1, 0, 3, 5, 7, 8], [-1, 0, 3, 5, 6], [-1, 0, 3, 5, 6, 8], [-1, 0, 3, 5, 6, 7], [-1, 0, 3, 5, 6, 7, 8], [-1, 0, 3, 4], [-1, 0, 3, 4, 8], [-1, 0, 3, 4, 7], [-1, 0, 3, 4, 7, 8], [-1, 0, 3, 4, 6], [-1, 0, 3, 4, 6, 8], [-1, 0, 3, 4, 6, 7], [-1, 0, 3, 4, 6, 7, 8], [-1, 0, 3, 4, 5], [-1, 0, 3, 4, 5, 8], [-1, 0, 3, 4, 5, 7], [-1, 0, 3, 4, 5, 7, 8], [-1, 0, 3, 4, 5, 6], [-1, 0, 3, 4, 5, 6, 8], [-1, 0, 3, 4, 5, 6, 7], [-1, 0, 3, 4, 5, 6, 7, 8], [-1, 0, 2], [-1, 0, 2, 8], [-1, 0, 2, 7], [-1, 0, 2, 7, 8], [-1, 0, 2, 6], [-1, 0, 2, 6, 8], [-1, 0, 2, 6, 7], [-1, 0, 2, 6, 7, 8], [-1, 0, 2, 5], [-1, 0, 2, 5, 8], [-1, 0, 2, 5, 7], [-1, 0, 2, 5, 7, 8], [-1, 0, 2, 5, 6], [-1, 0, 2, 5, 6, 8], [-1, 0, 2, 5, 6, 7], [-1, 0, 2, 5, 6, 7, 8], [-1, 0, 2, 4], [-1, 0, 2, 4, 8], [-1, 0, 2, 4, 7], [-1, 0, 2, 4, 7, 8], [-1, 0, 2, 4, 6], [-1, 0, 2, 4, 6, 8], [-1, 0, 2, 4, 6, 7], [-1, 0, 2, 4, 6, 7, 8], [-1, 0, 2, 4, 5], [-1, 0, 2, 4, 5, 8], [-1, 0, 2, 4, 5, 7], [-1, 0, 2, 4, 5, 7, 8], [-1, 0, 2, 4, 5, 6], [-1, 0, 2, 4, 5, 6, 8], [-1, 0, 2, 4, 5, 6, 7], [-1, 0, 2, 4, 5, 6, 7, 8], [-1, 0, 2, 3], [-1, 0, 2, 3, 8], [-1, 0, 2, 3, 7], [-1, 0, 2, 3, 7, 8], [-1, 0, 2, 3, 6], [-1, 0, 2, 3, 6, 8], [-1, 0, 2, 3, 6, 7], [-1, 0, 2, 3, 6, 7, 8], [-1, 0, 2, 3, 5], [-1, 0, 2, 3, 5, 8], [-1, 0, 2, 3, 5, 7], [-1, 0, 2, 3, 5, 7, 8], [-1, 0, 2, 3, 5, 6], [-1, 0, 2, 3, 5, 6, 8], [-1, 0, 2, 3, 5, 6, 7], [-1, 0, 2, 3, 5, 6, 7, 8], [-1, 0, 2, 3, 4], [-1, 0, 2, 3, 4, 8], [-1, 0, 2, 3, 4, 7], [-1, 0, 2, 3, 4, 7, 8], [-1, 0, 2, 3, 4, 6], [-1, 0, 2, 3, 4, 6, 8], [-1, 0, 2, 3, 4, 6, 7], [-1, 0, 2, 3, 4, 6, 7, 8], [-1, 0, 2, 3, 4, 5], [-1, 0, 2, 3, 4, 5, 8], [-1, 0, 2, 3, 4, 5, 7], [-1, 0, 2, 3, 4, 5, 7, 8], [-1, 0, 2, 3, 4, 5, 6], [-1, 0, 2, 3, 4, 5, 6, 8], [-1, 0, 2, 3, 4, 5, 6, 7], [-1, 0, 2, 3, 4, 5, 6, 7, 8], [-1, 0, 1], [-1, 0, 1, 8], [-1, 0, 1, 7], [-1, 0, 1, 7, 8], [-1, 0, 1, 6], [-1, 0, 1, 6, 8], [-1, 0, 1, 6, 7], [-1, 0, 1, 6, 7, 8], [-1, 0, 1, 5], [-1, 0, 1, 5, 8], [-1, 0, 1, 5, 7], [-1, 0, 1, 5, 7, 8], [-1, 0, 1, 5, 6], [-1, 0, 1, 5, 6, 8], [-1, 0, 1, 5, 6, 7], [-1, 0, 1, 5, 6, 7, 8], [-1, 0, 1, 4], [-1, 0, 1, 4, 8], [-1, 0, 1, 4, 7], [-1, 0, 1, 4, 7, 8], [-1, 0, 1, 4, 6], [-1, 0, 1, 4, 6, 8], [-1, 0, 1, 4, 6, 7], [-1, 0, 1, 4, 6, 7, 8], [-1, 0, 1, 4, 5], [-1, 0, 1, 4, 5, 8], [-1, 0, 1, 4, 5, 7], [-1, 0, 1, 4, 5, 7, 8], [-1, 0, 1, 4, 5, 6], [-1, 0, 1, 4, 5, 6, 8], [-1, 0, 1, 4, 5, 6, 7], [-1, 0, 1, 4, 5, 6, 7, 8], [-1, 0, 1, 3], [-1, 0, 1, 3, 8], [-1, 0, 1, 3, 7], [-1, 0, 1, 3, 7, 8], [-1, 0, 1, 3, 6], [-1, 0, 1, 3, 6, 8], [-1, 0, 1, 3, 6, 7], [-1, 0, 1, 3, 6, 7, 8], [-1, 0, 1, 3, 5], [-1, 0, 1, 3, 5, 8], [-1, 0, 1, 3, 5, 7], [-1, 0, 1, 3, 5, 7, 8], [-1, 0, 1, 3, 5, 6], [-1, 0, 1, 3, 5, 6, 8], [-1, 0, 1, 3, 5, 6, 7], [-1, 0, 1, 3, 5, 6, 7, 8], [-1, 0, 1, 3, 4], [-1, 0, 1, 3, 4, 8], [-1, 0, 1, 3, 4, 7], [-1, 0, 1, 3, 4, 7, 8], [-1, 0, 1, 3, 4, 6], [-1, 0, 1, 3, 4, 6, 8], [-1, 0, 1, 3, 4, 6, 7], [-1, 0, 1, 3, 4, 6, 7, 8], [-1, 0, 1, 3, 4, 5], [-1, 0, 1, 3, 4, 5, 8], [-1, 0, 1, 3, 4, 5, 7], [-1, 0, 1, 3, 4, 5, 7, 8], [-1, 0, 1, 3, 4, 5, 6], [-1, 0, 1, 3, 4, 5, 6, 8], [-1, 0, 1, 3, 4, 5, 6, 7], [-1, 0, 1, 3, 4, 5, 6, 7, 8], [-1, 0, 1, 2], [-1, 0, 1, 2, 8], [-1, 0, 1, 2, 7], [-1, 0, 1, 2, 7, 8], [-1, 0, 1, 2, 6], [-1, 0, 1, 2, 6, 8], [-1, 0, 1, 2, 6, 7], [-1, 0, 1, 2, 6, 7, 8], [-1, 0, 1, 2, 5], [-1, 0, 1, 2, 5, 8], [-1, 0, 1, 2, 5, 7], [-1, 0, 1, 2, 5, 7, 8], [-1, 0, 1, 2, 5, 6], [-1, 0, 1, 2, 5, 6, 8], [-1, 0, 1, 2, 5, 6, 7], [-1, 0, 1, 2, 5, 6, 7, 8], [-1, 0, 1, 2, 4], [-1, 0, 1, 2, 4, 8], [-1, 0, 1, 2, 4, 7], [-1, 0, 1, 2, 4, 7, 8], [-1, 0, 1, 2, 4, 6], [-1, 0, 1, 2, 4, 6, 8], [-1, 0, 1, 2, 4, 6, 7], [-1, 0, 1, 2, 4, 6, 7, 8], [-1, 0, 1, 2, 4, 5], [-1, 0, 1, 2, 4, 5, 8], [-1, 0, 1, 2, 4, 5, 7], [-1, 0, 1, 2, 4, 5, 7, 8], [-1, 0, 1, 2, 4, 5, 6], [-1, 0, 1, 2, 4, 5, 6, 8], [-1, 0, 1, 2, 4, 5, 6, 7], [-1, 0, 1, 2, 4, 5, 6, 7, 8], [-1, 0, 1, 2, 3], [-1, 0, 1, 2, 3, 8], [-1, 0, 1, 2, 3, 7], [-1, 0, 1, 2, 3, 7, 8], [-1, 0, 1, 2, 3, 6], [-1, 0, 1, 2, 3, 6, 8], [-1, 0, 1, 2, 3, 6, 7], [-1, 0, 1, 2, 3, 6, 7, 8], [-1, 0, 1, 2, 3, 5], [-1, 0, 1, 2, 3, 5, 8], [-1, 0, 1, 2, 3, 5, 7], [-1, 0, 1, 2, 3, 5, 7, 8], [-1, 0, 1, 2, 3, 5, 6], [-1, 0, 1, 2, 3, 5, 6, 8], [-1, 0, 1, 2, 3, 5, 6, 7], [-1, 0, 1, 2, 3, 5, 6, 7, 8], [-1, 0, 1, 2, 3, 4], [-1, 0, 1, 2, 3, 4, 8], [-1, 0, 1, 2, 3, 4, 7], [-1, 0, 1, 2, 3, 4, 7, 8], [-1, 0, 1, 2, 3, 4, 6], [-1, 0, 1, 2, 3, 4, 6, 8], [-1, 0, 1, 2, 3, 4, 6, 7], [-1, 0, 1, 2, 3, 4, 6, 7, 8], [-1, 0, 1, 2, 3, 4, 5], [-1, 0, 1, 2, 3, 4, 5, 8], [-1, 0, 1, 2, 3, 4, 5, 7], [-1, 0, 1, 2, 3, 4, 5, 7, 8], [-1, 0, 1, 2, 3, 4, 5, 6], [-1, 0, 1, 2, 3, 4, 5, 6, 8], [-1, 0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]]\n assert candidate(nums = [-9, -7, -5, -3, -1, 1, 3, 5, 7, 9]) == [[], [9], [7], [7, 9], [5], [5, 9], [5, 7], [5, 7, 9], [3], [3, 9], [3, 7], [3, 7, 9], [3, 5], [3, 5, 9], [3, 5, 7], [3, 5, 7, 9], [1], [1, 9], [1, 7], [1, 7, 9], [1, 5], [1, 5, 9], [1, 5, 7], [1, 5, 7, 9], [1, 3], [1, 3, 9], [1, 3, 7], [1, 3, 7, 9], [1, 3, 5], [1, 3, 5, 9], [1, 3, 5, 7], [1, 3, 5, 7, 9], [-1], [-1, 9], [-1, 7], [-1, 7, 9], [-1, 5], [-1, 5, 9], [-1, 5, 7], [-1, 5, 7, 9], [-1, 3], [-1, 3, 9], [-1, 3, 7], [-1, 3, 7, 9], [-1, 3, 5], [-1, 3, 5, 9], [-1, 3, 5, 7], [-1, 3, 5, 7, 9], [-1, 1], [-1, 1, 9], [-1, 1, 7], [-1, 1, 7, 9], [-1, 1, 5], [-1, 1, 5, 9], [-1, 1, 5, 7], [-1, 1, 5, 7, 9], [-1, 1, 3], [-1, 1, 3, 9], [-1, 1, 3, 7], [-1, 1, 3, 7, 9], [-1, 1, 3, 5], [-1, 1, 3, 5, 9], [-1, 1, 3, 5, 7], [-1, 1, 3, 5, 7, 9], [-3], [-3, 9], [-3, 7], [-3, 7, 9], [-3, 5], [-3, 5, 9], [-3, 5, 7], [-3, 5, 7, 9], [-3, 3], [-3, 3, 9], [-3, 3, 7], [-3, 3, 7, 9], [-3, 3, 5], [-3, 3, 5, 9], [-3, 3, 5, 7], [-3, 3, 5, 7, 9], [-3, 1], [-3, 1, 9], [-3, 1, 7], [-3, 1, 7, 9], [-3, 1, 5], [-3, 1, 5, 9], [-3, 1, 5, 7], [-3, 1, 5, 7, 9], [-3, 1, 3], [-3, 1, 3, 9], [-3, 1, 3, 7], [-3, 1, 3, 7, 9], [-3, 1, 3, 5], [-3, 1, 3, 5, 9], [-3, 1, 3, 5, 7], [-3, 1, 3, 5, 7, 9], [-3, -1], [-3, -1, 9], [-3, -1, 7], [-3, -1, 7, 9], [-3, -1, 5], [-3, -1, 5, 9], [-3, -1, 5, 7], [-3, -1, 5, 7, 9], [-3, -1, 3], [-3, -1, 3, 9], [-3, -1, 3, 7], [-3, -1, 3, 7, 9], [-3, -1, 3, 5], [-3, -1, 3, 5, 9], [-3, -1, 3, 5, 7], [-3, -1, 3, 5, 7, 9], [-3, -1, 1], [-3, -1, 1, 9], [-3, -1, 1, 7], [-3, -1, 1, 7, 9], [-3, -1, 1, 5], [-3, -1, 1, 5, 9], [-3, -1, 1, 5, 7], [-3, -1, 1, 5, 7, 9], [-3, -1, 1, 3], [-3, -1, 1, 3, 9], [-3, -1, 1, 3, 7], [-3, -1, 1, 3, 7, 9], [-3, -1, 1, 3, 5], [-3, -1, 1, 3, 5, 9], [-3, -1, 1, 3, 5, 7], [-3, -1, 1, 3, 5, 7, 9], [-5], [-5, 9], [-5, 7], [-5, 7, 9], [-5, 5], [-5, 5, 9], [-5, 5, 7], [-5, 5, 7, 9], [-5, 3], [-5, 3, 9], [-5, 3, 7], [-5, 3, 7, 9], [-5, 3, 5], [-5, 3, 5, 9], [-5, 3, 5, 7], [-5, 3, 5, 7, 9], [-5, 1], [-5, 1, 9], [-5, 1, 7], [-5, 1, 7, 9], [-5, 1, 5], [-5, 1, 5, 9], [-5, 1, 5, 7], [-5, 1, 5, 7, 9], [-5, 1, 3], [-5, 1, 3, 9], [-5, 1, 3, 7], [-5, 1, 3, 7, 9], [-5, 1, 3, 5], [-5, 1, 3, 5, 9], [-5, 1, 3, 5, 7], [-5, 1, 3, 5, 7, 9], [-5, -1], [-5, -1, 9], [-5, -1, 7], [-5, -1, 7, 9], [-5, -1, 5], [-5, -1, 5, 9], [-5, -1, 5, 7], [-5, -1, 5, 7, 9], [-5, -1, 3], [-5, -1, 3, 9], [-5, -1, 3, 7], [-5, -1, 3, 7, 9], [-5, -1, 3, 5], [-5, -1, 3, 5, 9], [-5, -1, 3, 5, 7], [-5, -1, 3, 5, 7, 9], [-5, -1, 1], [-5, -1, 1, 9], [-5, -1, 1, 7], [-5, -1, 1, 7, 9], [-5, -1, 1, 5], [-5, -1, 1, 5, 9], [-5, -1, 1, 5, 7], [-5, -1, 1, 5, 7, 9], [-5, -1, 1, 3], [-5, -1, 1, 3, 9], [-5, -1, 1, 3, 7], [-5, -1, 1, 3, 7, 9], [-5, -1, 1, 3, 5], [-5, -1, 1, 3, 5, 9], [-5, -1, 1, 3, 5, 7], [-5, -1, 1, 3, 5, 7, 9], [-5, -3], [-5, -3, 9], [-5, -3, 7], [-5, -3, 7, 9], [-5, -3, 5], [-5, -3, 5, 9], [-5, -3, 5, 7], [-5, -3, 5, 7, 9], [-5, -3, 3], [-5, -3, 3, 9], [-5, -3, 3, 7], [-5, -3, 3, 7, 9], [-5, -3, 3, 5], [-5, -3, 3, 5, 9], [-5, -3, 3, 5, 7], [-5, -3, 3, 5, 7, 9], [-5, -3, 1], [-5, -3, 1, 9], [-5, -3, 1, 7], [-5, -3, 1, 7, 9], [-5, -3, 1, 5], [-5, -3, 1, 5, 9], [-5, -3, 1, 5, 7], [-5, -3, 1, 5, 7, 9], [-5, -3, 1, 3], [-5, -3, 1, 3, 9], [-5, -3, 1, 3, 7], [-5, -3, 1, 3, 7, 9], [-5, -3, 1, 3, 5], [-5, -3, 1, 3, 5, 9], [-5, -3, 1, 3, 5, 7], [-5, -3, 1, 3, 5, 7, 9], [-5, -3, -1], [-5, -3, -1, 9], [-5, -3, -1, 7], [-5, -3, -1, 7, 9], [-5, -3, -1, 5], [-5, -3, -1, 5, 9], [-5, -3, -1, 5, 7], [-5, -3, -1, 5, 7, 9], [-5, -3, -1, 3], [-5, -3, -1, 3, 9], [-5, -3, -1, 3, 7], [-5, -3, -1, 3, 7, 9], [-5, -3, -1, 3, 5], [-5, -3, -1, 3, 5, 9], [-5, -3, -1, 3, 5, 7], [-5, -3, -1, 3, 5, 7, 9], [-5, -3, -1, 1], [-5, -3, -1, 1, 9], [-5, -3, -1, 1, 7], [-5, -3, -1, 1, 7, 9], [-5, -3, -1, 1, 5], [-5, -3, -1, 1, 5, 9], [-5, -3, -1, 1, 5, 7], [-5, -3, -1, 1, 5, 7, 9], [-5, -3, -1, 1, 3], [-5, -3, -1, 1, 3, 9], [-5, -3, -1, 1, 3, 7], [-5, -3, -1, 1, 3, 7, 9], [-5, -3, -1, 1, 3, 5], [-5, -3, -1, 1, 3, 5, 9], [-5, -3, -1, 1, 3, 5, 7], [-5, -3, -1, 1, 3, 5, 7, 9], [-7], [-7, 9], [-7, 7], [-7, 7, 9], [-7, 5], [-7, 5, 9], [-7, 5, 7], [-7, 5, 7, 9], [-7, 3], [-7, 3, 9], [-7, 3, 7], [-7, 3, 7, 9], [-7, 3, 5], [-7, 3, 5, 9], [-7, 3, 5, 7], [-7, 3, 5, 7, 9], [-7, 1], [-7, 1, 9], [-7, 1, 7], [-7, 1, 7, 9], [-7, 1, 5], [-7, 1, 5, 9], [-7, 1, 5, 7], [-7, 1, 5, 7, 9], [-7, 1, 3], [-7, 1, 3, 9], [-7, 1, 3, 7], [-7, 1, 3, 7, 9], [-7, 1, 3, 5], [-7, 1, 3, 5, 9], [-7, 1, 3, 5, 7], [-7, 1, 3, 5, 7, 9], [-7, -1], [-7, -1, 9], [-7, -1, 7], [-7, -1, 7, 9], [-7, -1, 5], [-7, -1, 5, 9], [-7, -1, 5, 7], [-7, -1, 5, 7, 9], [-7, -1, 3], [-7, -1, 3, 9], [-7, -1, 3, 7], [-7, -1, 3, 7, 9], [-7, -1, 3, 5], [-7, -1, 3, 5, 9], [-7, -1, 3, 5, 7], [-7, -1, 3, 5, 7, 9], [-7, -1, 1], [-7, -1, 1, 9], [-7, -1, 1, 7], [-7, -1, 1, 7, 9], [-7, -1, 1, 5], [-7, -1, 1, 5, 9], [-7, -1, 1, 5, 7], [-7, -1, 1, 5, 7, 9], [-7, -1, 1, 3], [-7, -1, 1, 3, 9], [-7, -1, 1, 3, 7], [-7, -1, 1, 3, 7, 9], [-7, -1, 1, 3, 5], [-7, -1, 1, 3, 5, 9], [-7, -1, 1, 3, 5, 7], [-7, -1, 1, 3, 5, 7, 9], [-7, -3], [-7, -3, 9], [-7, -3, 7], [-7, -3, 7, 9], [-7, -3, 5], [-7, -3, 5, 9], [-7, -3, 5, 7], [-7, -3, 5, 7, 9], [-7, -3, 3], [-7, -3, 3, 9], [-7, -3, 3, 7], [-7, -3, 3, 7, 9], [-7, -3, 3, 5], [-7, -3, 3, 5, 9], [-7, -3, 3, 5, 7], [-7, -3, 3, 5, 7, 9], [-7, -3, 1], [-7, -3, 1, 9], [-7, -3, 1, 7], [-7, -3, 1, 7, 9], [-7, -3, 1, 5], [-7, -3, 1, 5, 9], [-7, -3, 1, 5, 7], [-7, -3, 1, 5, 7, 9], [-7, -3, 1, 3], [-7, -3, 1, 3, 9], [-7, -3, 1, 3, 7], [-7, -3, 1, 3, 7, 9], [-7, -3, 1, 3, 5], [-7, -3, 1, 3, 5, 9], [-7, -3, 1, 3, 5, 7], [-7, -3, 1, 3, 5, 7, 9], [-7, -3, -1], [-7, -3, -1, 9], [-7, -3, -1, 7], [-7, -3, -1, 7, 9], [-7, -3, -1, 5], [-7, -3, -1, 5, 9], [-7, -3, -1, 5, 7], [-7, -3, -1, 5, 7, 9], [-7, -3, -1, 3], [-7, -3, -1, 3, 9], [-7, -3, -1, 3, 7], [-7, -3, -1, 3, 7, 9], [-7, -3, -1, 3, 5], [-7, -3, -1, 3, 5, 9], [-7, -3, -1, 3, 5, 7], [-7, -3, -1, 3, 5, 7, 9], [-7, -3, -1, 1], [-7, -3, -1, 1, 9], [-7, -3, -1, 1, 7], [-7, -3, -1, 1, 7, 9], [-7, -3, -1, 1, 5], [-7, -3, -1, 1, 5, 9], [-7, -3, -1, 1, 5, 7], [-7, -3, -1, 1, 5, 7, 9], [-7, -3, -1, 1, 3], [-7, -3, -1, 1, 3, 9], [-7, -3, -1, 1, 3, 7], [-7, -3, -1, 1, 3, 7, 9], [-7, -3, -1, 1, 3, 5], [-7, -3, -1, 1, 3, 5, 9], [-7, -3, -1, 1, 3, 5, 7], [-7, -3, -1, 1, 3, 5, 7, 9], [-7, -5], [-7, -5, 9], [-7, -5, 7], [-7, -5, 7, 9], [-7, -5, 5], [-7, -5, 5, 9], [-7, -5, 5, 7], [-7, -5, 5, 7, 9], [-7, -5, 3], [-7, -5, 3, 9], [-7, -5, 3, 7], [-7, -5, 3, 7, 9], [-7, -5, 3, 5], [-7, -5, 3, 5, 9], [-7, -5, 3, 5, 7], [-7, -5, 3, 5, 7, 9], [-7, -5, 1], [-7, -5, 1, 9], [-7, -5, 1, 7], [-7, -5, 1, 7, 9], [-7, -5, 1, 5], [-7, -5, 1, 5, 9], [-7, -5, 1, 5, 7], [-7, -5, 1, 5, 7, 9], [-7, -5, 1, 3], [-7, -5, 1, 3, 9], [-7, -5, 1, 3, 7], [-7, -5, 1, 3, 7, 9], [-7, -5, 1, 3, 5], [-7, -5, 1, 3, 5, 9], [-7, -5, 1, 3, 5, 7], [-7, -5, 1, 3, 5, 7, 9], [-7, -5, -1], [-7, -5, -1, 9], [-7, -5, -1, 7], [-7, -5, -1, 7, 9], [-7, -5, -1, 5], [-7, -5, -1, 5, 9], [-7, -5, -1, 5, 7], [-7, -5, -1, 5, 7, 9], [-7, -5, -1, 3], [-7, -5, -1, 3, 9], [-7, -5, -1, 3, 7], [-7, -5, -1, 3, 7, 9], [-7, -5, -1, 3, 5], [-7, -5, -1, 3, 5, 9], [-7, -5, -1, 3, 5, 7], [-7, -5, -1, 3, 5, 7, 9], [-7, -5, -1, 1], [-7, -5, -1, 1, 9], [-7, -5, -1, 1, 7], [-7, -5, -1, 1, 7, 9], [-7, -5, -1, 1, 5], [-7, -5, -1, 1, 5, 9], [-7, -5, -1, 1, 5, 7], [-7, -5, -1, 1, 5, 7, 9], [-7, -5, -1, 1, 3], [-7, -5, -1, 1, 3, 9], [-7, -5, -1, 1, 3, 7], [-7, -5, -1, 1, 3, 7, 9], [-7, -5, -1, 1, 3, 5], [-7, -5, -1, 1, 3, 5, 9], [-7, -5, -1, 1, 3, 5, 7], [-7, -5, -1, 1, 3, 5, 7, 9], [-7, -5, -3], [-7, -5, -3, 9], [-7, -5, -3, 7], [-7, -5, -3, 7, 9], [-7, -5, -3, 5], [-7, -5, -3, 5, 9], [-7, -5, -3, 5, 7], [-7, -5, -3, 5, 7, 9], [-7, -5, -3, 3], [-7, -5, -3, 3, 9], [-7, -5, -3, 3, 7], [-7, -5, -3, 3, 7, 9], [-7, -5, -3, 3, 5], [-7, -5, -3, 3, 5, 9], [-7, -5, -3, 3, 5, 7], [-7, -5, -3, 3, 5, 7, 9], [-7, -5, -3, 1], [-7, -5, -3, 1, 9], [-7, -5, -3, 1, 7], [-7, -5, -3, 1, 7, 9], [-7, -5, -3, 1, 5], [-7, -5, -3, 1, 5, 9], [-7, -5, -3, 1, 5, 7], [-7, -5, -3, 1, 5, 7, 9], [-7, -5, -3, 1, 3], [-7, -5, -3, 1, 3, 9], [-7, -5, -3, 1, 3, 7], [-7, -5, -3, 1, 3, 7, 9], [-7, -5, -3, 1, 3, 5], [-7, -5, -3, 1, 3, 5, 9], [-7, -5, -3, 1, 3, 5, 7], [-7, -5, -3, 1, 3, 5, 7, 9], [-7, -5, -3, -1], [-7, -5, -3, -1, 9], [-7, -5, -3, -1, 7], [-7, -5, -3, -1, 7, 9], [-7, -5, -3, -1, 5], [-7, -5, -3, -1, 5, 9], [-7, -5, -3, -1, 5, 7], [-7, -5, -3, -1, 5, 7, 9], [-7, -5, -3, -1, 3], [-7, -5, -3, -1, 3, 9], [-7, -5, -3, -1, 3, 7], [-7, -5, -3, -1, 3, 7, 9], [-7, -5, -3, -1, 3, 5], [-7, -5, -3, -1, 3, 5, 9], [-7, -5, -3, -1, 3, 5, 7], [-7, -5, -3, -1, 3, 5, 7, 9], [-7, -5, -3, -1, 1], [-7, -5, -3, -1, 1, 9], [-7, -5, -3, -1, 1, 7], [-7, -5, -3, -1, 1, 7, 9], [-7, -5, -3, -1, 1, 5], [-7, -5, -3, -1, 1, 5, 9], [-7, -5, -3, -1, 1, 5, 7], [-7, -5, -3, -1, 1, 5, 7, 9], [-7, -5, -3, -1, 1, 3], [-7, -5, -3, -1, 1, 3, 9], [-7, -5, -3, -1, 1, 3, 7], [-7, -5, -3, -1, 1, 3, 7, 9], [-7, -5, -3, -1, 1, 3, 5], [-7, -5, -3, -1, 1, 3, 5, 9], [-7, -5, -3, -1, 1, 3, 5, 7], [-7, -5, -3, -1, 1, 3, 5, 7, 9], [-9], [-9, 9], [-9, 7], [-9, 7, 9], [-9, 5], [-9, 5, 9], [-9, 5, 7], [-9, 5, 7, 9], [-9, 3], [-9, 3, 9], [-9, 3, 7], [-9, 3, 7, 9], [-9, 3, 5], [-9, 3, 5, 9], [-9, 3, 5, 7], [-9, 3, 5, 7, 9], [-9, 1], [-9, 1, 9], [-9, 1, 7], [-9, 1, 7, 9], [-9, 1, 5], [-9, 1, 5, 9], [-9, 1, 5, 7], [-9, 1, 5, 7, 9], [-9, 1, 3], [-9, 1, 3, 9], [-9, 1, 3, 7], [-9, 1, 3, 7, 9], [-9, 1, 3, 5], [-9, 1, 3, 5, 9], [-9, 1, 3, 5, 7], [-9, 1, 3, 5, 7, 9], [-9, -1], [-9, -1, 9], [-9, -1, 7], [-9, -1, 7, 9], [-9, -1, 5], [-9, -1, 5, 9], [-9, -1, 5, 7], [-9, -1, 5, 7, 9], [-9, -1, 3], [-9, -1, 3, 9], [-9, -1, 3, 7], [-9, -1, 3, 7, 9], [-9, -1, 3, 5], [-9, -1, 3, 5, 9], [-9, -1, 3, 5, 7], [-9, -1, 3, 5, 7, 9], [-9, -1, 1], [-9, -1, 1, 9], [-9, -1, 1, 7], [-9, -1, 1, 7, 9], [-9, -1, 1, 5], [-9, -1, 1, 5, 9], [-9, -1, 1, 5, 7], [-9, -1, 1, 5, 7, 9], [-9, -1, 1, 3], [-9, -1, 1, 3, 9], [-9, -1, 1, 3, 7], [-9, -1, 1, 3, 7, 9], [-9, -1, 1, 3, 5], [-9, -1, 1, 3, 5, 9], [-9, -1, 1, 3, 5, 7], [-9, -1, 1, 3, 5, 7, 9], [-9, -3], [-9, -3, 9], [-9, -3, 7], [-9, -3, 7, 9], [-9, -3, 5], [-9, -3, 5, 9], [-9, -3, 5, 7], [-9, -3, 5, 7, 9], [-9, -3, 3], [-9, -3, 3, 9], [-9, -3, 3, 7], [-9, -3, 3, 7, 9], [-9, -3, 3, 5], [-9, -3, 3, 5, 9], [-9, -3, 3, 5, 7], [-9, -3, 3, 5, 7, 9], [-9, -3, 1], [-9, -3, 1, 9], [-9, -3, 1, 7], [-9, -3, 1, 7, 9], [-9, -3, 1, 5], [-9, -3, 1, 5, 9], [-9, -3, 1, 5, 7], [-9, -3, 1, 5, 7, 9], [-9, -3, 1, 3], [-9, -3, 1, 3, 9], [-9, -3, 1, 3, 7], [-9, -3, 1, 3, 7, 9], [-9, -3, 1, 3, 5], [-9, -3, 1, 3, 5, 9], [-9, -3, 1, 3, 5, 7], [-9, -3, 1, 3, 5, 7, 9], [-9, -3, -1], [-9, -3, -1, 9], [-9, -3, -1, 7], [-9, -3, -1, 7, 9], [-9, -3, -1, 5], [-9, -3, -1, 5, 9], [-9, -3, -1, 5, 7], [-9, -3, -1, 5, 7, 9], [-9, -3, -1, 3], [-9, -3, -1, 3, 9], [-9, -3, -1, 3, 7], [-9, -3, -1, 3, 7, 9], [-9, -3, -1, 3, 5], [-9, -3, -1, 3, 5, 9], [-9, -3, -1, 3, 5, 7], [-9, -3, -1, 3, 5, 7, 9], [-9, -3, -1, 1], [-9, -3, -1, 1, 9], [-9, -3, -1, 1, 7], [-9, -3, -1, 1, 7, 9], [-9, -3, -1, 1, 5], [-9, -3, -1, 1, 5, 9], [-9, -3, -1, 1, 5, 7], [-9, -3, -1, 1, 5, 7, 9], [-9, -3, -1, 1, 3], [-9, -3, -1, 1, 3, 9], [-9, -3, -1, 1, 3, 7], [-9, -3, -1, 1, 3, 7, 9], [-9, -3, -1, 1, 3, 5], [-9, -3, -1, 1, 3, 5, 9], [-9, -3, -1, 1, 3, 5, 7], [-9, -3, -1, 1, 3, 5, 7, 9], [-9, -5], [-9, -5, 9], [-9, -5, 7], [-9, -5, 7, 9], [-9, -5, 5], [-9, -5, 5, 9], [-9, -5, 5, 7], [-9, -5, 5, 7, 9], [-9, -5, 3], [-9, -5, 3, 9], [-9, -5, 3, 7], [-9, -5, 3, 7, 9], [-9, -5, 3, 5], [-9, -5, 3, 5, 9], [-9, -5, 3, 5, 7], [-9, -5, 3, 5, 7, 9], [-9, -5, 1], [-9, -5, 1, 9], [-9, -5, 1, 7], [-9, -5, 1, 7, 9], [-9, -5, 1, 5], [-9, -5, 1, 5, 9], [-9, -5, 1, 5, 7], [-9, -5, 1, 5, 7, 9], [-9, -5, 1, 3], [-9, -5, 1, 3, 9], [-9, -5, 1, 3, 7], [-9, -5, 1, 3, 7, 9], [-9, -5, 1, 3, 5], [-9, -5, 1, 3, 5, 9], [-9, -5, 1, 3, 5, 7], [-9, -5, 1, 3, 5, 7, 9], [-9, -5, -1], [-9, -5, -1, 9], [-9, -5, -1, 7], [-9, -5, -1, 7, 9], [-9, -5, -1, 5], [-9, -5, -1, 5, 9], [-9, -5, -1, 5, 7], [-9, -5, -1, 5, 7, 9], [-9, -5, -1, 3], [-9, -5, -1, 3, 9], [-9, -5, -1, 3, 7], [-9, -5, -1, 3, 7, 9], [-9, -5, -1, 3, 5], [-9, -5, -1, 3, 5, 9], [-9, -5, -1, 3, 5, 7], [-9, -5, -1, 3, 5, 7, 9], [-9, -5, -1, 1], [-9, -5, -1, 1, 9], [-9, -5, -1, 1, 7], [-9, -5, -1, 1, 7, 9], [-9, -5, -1, 1, 5], [-9, -5, -1, 1, 5, 9], [-9, -5, -1, 1, 5, 7], [-9, -5, -1, 1, 5, 7, 9], [-9, -5, -1, 1, 3], [-9, -5, -1, 1, 3, 9], [-9, -5, -1, 1, 3, 7], [-9, -5, -1, 1, 3, 7, 9], [-9, -5, -1, 1, 3, 5], [-9, -5, -1, 1, 3, 5, 9], [-9, -5, -1, 1, 3, 5, 7], [-9, -5, -1, 1, 3, 5, 7, 9], [-9, -5, -3], [-9, -5, -3, 9], [-9, -5, -3, 7], [-9, -5, -3, 7, 9], [-9, -5, -3, 5], [-9, -5, -3, 5, 9], [-9, -5, -3, 5, 7], [-9, -5, -3, 5, 7, 9], [-9, -5, -3, 3], [-9, -5, -3, 3, 9], [-9, -5, -3, 3, 7], [-9, -5, -3, 3, 7, 9], [-9, -5, -3, 3, 5], [-9, -5, -3, 3, 5, 9], [-9, -5, -3, 3, 5, 7], [-9, -5, -3, 3, 5, 7, 9], [-9, -5, -3, 1], [-9, -5, -3, 1, 9], [-9, -5, -3, 1, 7], [-9, -5, -3, 1, 7, 9], [-9, -5, -3, 1, 5], [-9, -5, -3, 1, 5, 9], [-9, -5, -3, 1, 5, 7], [-9, -5, -3, 1, 5, 7, 9], [-9, -5, -3, 1, 3], [-9, -5, -3, 1, 3, 9], [-9, -5, -3, 1, 3, 7], [-9, -5, -3, 1, 3, 7, 9], [-9, -5, -3, 1, 3, 5], [-9, -5, -3, 1, 3, 5, 9], [-9, -5, -3, 1, 3, 5, 7], [-9, -5, -3, 1, 3, 5, 7, 9], [-9, -5, -3, -1], [-9, -5, -3, -1, 9], [-9, -5, -3, -1, 7], [-9, -5, -3, -1, 7, 9], [-9, -5, -3, -1, 5], [-9, -5, -3, -1, 5, 9], [-9, -5, -3, -1, 5, 7], [-9, -5, -3, -1, 5, 7, 9], [-9, -5, -3, -1, 3], [-9, -5, -3, -1, 3, 9], [-9, -5, -3, -1, 3, 7], [-9, -5, -3, -1, 3, 7, 9], [-9, -5, -3, -1, 3, 5], [-9, -5, -3, -1, 3, 5, 9], [-9, -5, -3, -1, 3, 5, 7], [-9, -5, -3, -1, 3, 5, 7, 9], [-9, -5, -3, -1, 1], [-9, -5, -3, -1, 1, 9], [-9, -5, -3, -1, 1, 7], [-9, -5, -3, -1, 1, 7, 9], [-9, -5, -3, -1, 1, 5], [-9, -5, -3, -1, 1, 5, 9], [-9, -5, -3, -1, 1, 5, 7], [-9, -5, -3, -1, 1, 5, 7, 9], [-9, -5, -3, -1, 1, 3], [-9, -5, -3, -1, 1, 3, 9], [-9, -5, -3, -1, 1, 3, 7], [-9, -5, -3, -1, 1, 3, 7, 9], [-9, -5, -3, -1, 1, 3, 5], [-9, -5, -3, -1, 1, 3, 5, 9], [-9, -5, -3, -1, 1, 3, 5, 7], [-9, -5, -3, -1, 1, 3, 5, 7, 9], [-9, -7], [-9, -7, 9], [-9, -7, 7], [-9, -7, 7, 9], [-9, -7, 5], [-9, -7, 5, 9], [-9, -7, 5, 7], [-9, -7, 5, 7, 9], [-9, -7, 3], [-9, -7, 3, 9], [-9, -7, 3, 7], [-9, -7, 3, 7, 9], [-9, -7, 3, 5], [-9, -7, 3, 5, 9], [-9, -7, 3, 5, 7], [-9, -7, 3, 5, 7, 9], [-9, -7, 1], [-9, -7, 1, 9], [-9, -7, 1, 7], [-9, -7, 1, 7, 9], [-9, -7, 1, 5], [-9, -7, 1, 5, 9], [-9, -7, 1, 5, 7], [-9, -7, 1, 5, 7, 9], [-9, -7, 1, 3], [-9, -7, 1, 3, 9], [-9, -7, 1, 3, 7], [-9, -7, 1, 3, 7, 9], [-9, -7, 1, 3, 5], [-9, -7, 1, 3, 5, 9], [-9, -7, 1, 3, 5, 7], [-9, -7, 1, 3, 5, 7, 9], [-9, -7, -1], [-9, -7, -1, 9], [-9, -7, -1, 7], [-9, -7, -1, 7, 9], [-9, -7, -1, 5], [-9, -7, -1, 5, 9], [-9, -7, -1, 5, 7], [-9, -7, -1, 5, 7, 9], [-9, -7, -1, 3], [-9, -7, -1, 3, 9], [-9, -7, -1, 3, 7], [-9, -7, -1, 3, 7, 9], [-9, -7, -1, 3, 5], [-9, -7, -1, 3, 5, 9], [-9, -7, -1, 3, 5, 7], [-9, -7, -1, 3, 5, 7, 9], [-9, -7, -1, 1], [-9, -7, -1, 1, 9], [-9, -7, -1, 1, 7], [-9, -7, -1, 1, 7, 9], [-9, -7, -1, 1, 5], [-9, -7, -1, 1, 5, 9], [-9, -7, -1, 1, 5, 7], [-9, -7, -1, 1, 5, 7, 9], [-9, -7, -1, 1, 3], [-9, -7, -1, 1, 3, 9], [-9, -7, -1, 1, 3, 7], [-9, -7, -1, 1, 3, 7, 9], [-9, -7, -1, 1, 3, 5], [-9, -7, -1, 1, 3, 5, 9], [-9, -7, -1, 1, 3, 5, 7], [-9, -7, -1, 1, 3, 5, 7, 9], [-9, -7, -3], [-9, -7, -3, 9], [-9, -7, -3, 7], [-9, -7, -3, 7, 9], [-9, -7, -3, 5], [-9, -7, -3, 5, 9], [-9, -7, -3, 5, 7], [-9, -7, -3, 5, 7, 9], [-9, -7, -3, 3], [-9, -7, -3, 3, 9], [-9, -7, -3, 3, 7], [-9, -7, -3, 3, 7, 9], [-9, -7, -3, 3, 5], [-9, -7, -3, 3, 5, 9], [-9, -7, -3, 3, 5, 7], [-9, -7, -3, 3, 5, 7, 9], [-9, -7, -3, 1], [-9, -7, -3, 1, 9], [-9, -7, -3, 1, 7], [-9, -7, -3, 1, 7, 9], [-9, -7, -3, 1, 5], [-9, -7, -3, 1, 5, 9], [-9, -7, -3, 1, 5, 7], [-9, -7, -3, 1, 5, 7, 9], [-9, -7, -3, 1, 3], [-9, -7, -3, 1, 3, 9], [-9, -7, -3, 1, 3, 7], [-9, -7, -3, 1, 3, 7, 9], [-9, -7, -3, 1, 3, 5], [-9, -7, -3, 1, 3, 5, 9], [-9, -7, -3, 1, 3, 5, 7], [-9, -7, -3, 1, 3, 5, 7, 9], [-9, -7, -3, -1], [-9, -7, -3, -1, 9], [-9, -7, -3, -1, 7], [-9, -7, -3, -1, 7, 9], [-9, -7, -3, -1, 5], [-9, -7, -3, -1, 5, 9], [-9, -7, -3, -1, 5, 7], [-9, -7, -3, -1, 5, 7, 9], [-9, -7, -3, -1, 3], [-9, -7, -3, -1, 3, 9], [-9, -7, -3, -1, 3, 7], [-9, -7, -3, -1, 3, 7, 9], [-9, -7, -3, -1, 3, 5], [-9, -7, -3, -1, 3, 5, 9], [-9, -7, -3, -1, 3, 5, 7], [-9, -7, -3, -1, 3, 5, 7, 9], [-9, -7, -3, -1, 1], [-9, -7, -3, -1, 1, 9], [-9, -7, -3, -1, 1, 7], [-9, -7, -3, -1, 1, 7, 9], [-9, -7, -3, -1, 1, 5], [-9, -7, -3, -1, 1, 5, 9], [-9, -7, -3, -1, 1, 5, 7], [-9, -7, -3, -1, 1, 5, 7, 9], [-9, -7, -3, -1, 1, 3], [-9, -7, -3, -1, 1, 3, 9], [-9, -7, -3, -1, 1, 3, 7], [-9, -7, -3, -1, 1, 3, 7, 9], [-9, -7, -3, -1, 1, 3, 5], [-9, -7, -3, -1, 1, 3, 5, 9], [-9, -7, -3, -1, 1, 3, 5, 7], [-9, -7, -3, -1, 1, 3, 5, 7, 9], [-9, -7, -5], [-9, -7, -5, 9], [-9, -7, -5, 7], [-9, -7, -5, 7, 9], [-9, -7, -5, 5], [-9, -7, -5, 5, 9], [-9, -7, -5, 5, 7], [-9, -7, -5, 5, 7, 9], [-9, -7, -5, 3], [-9, -7, -5, 3, 9], [-9, -7, -5, 3, 7], [-9, -7, -5, 3, 7, 9], [-9, -7, -5, 3, 5], [-9, -7, -5, 3, 5, 9], [-9, -7, -5, 3, 5, 7], [-9, -7, -5, 3, 5, 7, 9], [-9, -7, -5, 1], [-9, -7, -5, 1, 9], [-9, -7, -5, 1, 7], [-9, -7, -5, 1, 7, 9], [-9, -7, -5, 1, 5], [-9, -7, -5, 1, 5, 9], [-9, -7, -5, 1, 5, 7], [-9, -7, -5, 1, 5, 7, 9], [-9, -7, -5, 1, 3], [-9, -7, -5, 1, 3, 9], [-9, -7, -5, 1, 3, 7], [-9, -7, -5, 1, 3, 7, 9], [-9, -7, -5, 1, 3, 5], [-9, -7, -5, 1, 3, 5, 9], [-9, -7, -5, 1, 3, 5, 7], [-9, -7, -5, 1, 3, 5, 7, 9], [-9, -7, -5, -1], [-9, -7, -5, -1, 9], [-9, -7, -5, -1, 7], [-9, -7, -5, -1, 7, 9], [-9, -7, -5, -1, 5], [-9, -7, -5, -1, 5, 9], [-9, -7, -5, -1, 5, 7], [-9, -7, -5, -1, 5, 7, 9], [-9, -7, -5, -1, 3], [-9, -7, -5, -1, 3, 9], [-9, -7, -5, -1, 3, 7], [-9, -7, -5, -1, 3, 7, 9], [-9, -7, -5, -1, 3, 5], [-9, -7, -5, -1, 3, 5, 9], [-9, -7, -5, -1, 3, 5, 7], [-9, -7, -5, -1, 3, 5, 7, 9], [-9, -7, -5, -1, 1], [-9, -7, -5, -1, 1, 9], [-9, -7, -5, -1, 1, 7], [-9, -7, -5, -1, 1, 7, 9], [-9, -7, -5, -1, 1, 5], [-9, -7, -5, -1, 1, 5, 9], [-9, -7, -5, -1, 1, 5, 7], [-9, -7, -5, -1, 1, 5, 7, 9], [-9, -7, -5, -1, 1, 3], [-9, -7, -5, -1, 1, 3, 9], [-9, -7, -5, -1, 1, 3, 7], [-9, -7, -5, -1, 1, 3, 7, 9], [-9, -7, -5, -1, 1, 3, 5], [-9, -7, -5, -1, 1, 3, 5, 9], [-9, -7, -5, -1, 1, 3, 5, 7], [-9, -7, -5, -1, 1, 3, 5, 7, 9], [-9, -7, -5, -3], [-9, -7, -5, -3, 9], [-9, -7, -5, -3, 7], [-9, -7, -5, -3, 7, 9], [-9, -7, -5, -3, 5], [-9, -7, -5, -3, 5, 9], [-9, -7, -5, -3, 5, 7], [-9, -7, -5, -3, 5, 7, 9], [-9, -7, -5, -3, 3], [-9, -7, -5, -3, 3, 9], [-9, -7, -5, -3, 3, 7], [-9, -7, -5, -3, 3, 7, 9], [-9, -7, -5, -3, 3, 5], [-9, -7, -5, -3, 3, 5, 9], [-9, -7, -5, -3, 3, 5, 7], [-9, -7, -5, -3, 3, 5, 7, 9], [-9, -7, -5, -3, 1], [-9, -7, -5, -3, 1, 9], [-9, -7, -5, -3, 1, 7], [-9, -7, -5, -3, 1, 7, 9], [-9, -7, -5, -3, 1, 5], [-9, -7, -5, -3, 1, 5, 9], [-9, -7, -5, -3, 1, 5, 7], [-9, -7, -5, -3, 1, 5, 7, 9], [-9, -7, -5, -3, 1, 3], [-9, -7, -5, -3, 1, 3, 9], [-9, -7, -5, -3, 1, 3, 7], [-9, -7, -5, -3, 1, 3, 7, 9], [-9, -7, -5, -3, 1, 3, 5], [-9, -7, -5, -3, 1, 3, 5, 9], [-9, -7, -5, -3, 1, 3, 5, 7], [-9, -7, -5, -3, 1, 3, 5, 7, 9], [-9, -7, -5, -3, -1], [-9, -7, -5, -3, -1, 9], [-9, -7, -5, -3, -1, 7], [-9, -7, -5, -3, -1, 7, 9], [-9, -7, -5, -3, -1, 5], [-9, -7, -5, -3, -1, 5, 9], [-9, -7, -5, -3, -1, 5, 7], [-9, -7, -5, -3, -1, 5, 7, 9], [-9, -7, -5, -3, -1, 3], [-9, -7, -5, -3, -1, 3, 9], [-9, -7, -5, -3, -1, 3, 7], [-9, -7, -5, -3, -1, 3, 7, 9], [-9, -7, -5, -3, -1, 3, 5], [-9, -7, -5, -3, -1, 3, 5, 9], [-9, -7, -5, -3, -1, 3, 5, 7], [-9, -7, -5, -3, -1, 3, 5, 7, 9], [-9, -7, -5, -3, -1, 1], [-9, -7, -5, -3, -1, 1, 9], [-9, -7, -5, -3, -1, 1, 7], [-9, -7, -5, -3, -1, 1, 7, 9], [-9, -7, -5, -3, -1, 1, 5], [-9, -7, -5, -3, -1, 1, 5, 9], [-9, -7, -5, -3, -1, 1, 5, 7], [-9, -7, -5, -3, -1, 1, 5, 7, 9], [-9, -7, -5, -3, -1, 1, 3], [-9, -7, -5, -3, -1, 1, 3, 9], [-9, -7, -5, -3, -1, 1, 3, 7], [-9, -7, -5, -3, -1, 1, 3, 7, 9], [-9, -7, -5, -3, -1, 1, 3, 5], [-9, -7, -5, -3, -1, 1, 3, 5, 9], [-9, -7, -5, -3, -1, 1, 3, 5, 7], [-9, -7, -5, -3, -1, 1, 3, 5, 7, 9]]\n assert candidate(nums = [-5, -3, -1, 0, 1, 3, 5]) == [[], [5], [3], [3, 5], [1], [1, 5], [1, 3], [1, 3, 5], [0], [0, 5], [0, 3], [0, 3, 5], [0, 1], [0, 1, 5], [0, 1, 3], [0, 1, 3, 5], [-1], [-1, 5], [-1, 3], [-1, 3, 5], [-1, 1], [-1, 1, 5], [-1, 1, 3], [-1, 1, 3, 5], [-1, 0], [-1, 0, 5], [-1, 0, 3], [-1, 0, 3, 5], [-1, 0, 1], [-1, 0, 1, 5], [-1, 0, 1, 3], [-1, 0, 1, 3, 5], [-3], [-3, 5], [-3, 3], [-3, 3, 5], [-3, 1], [-3, 1, 5], [-3, 1, 3], [-3, 1, 3, 5], [-3, 0], [-3, 0, 5], [-3, 0, 3], [-3, 0, 3, 5], [-3, 0, 1], [-3, 0, 1, 5], [-3, 0, 1, 3], [-3, 0, 1, 3, 5], [-3, -1], [-3, -1, 5], [-3, -1, 3], [-3, -1, 3, 5], [-3, -1, 1], [-3, -1, 1, 5], [-3, -1, 1, 3], [-3, -1, 1, 3, 5], [-3, -1, 0], [-3, -1, 0, 5], [-3, -1, 0, 3], [-3, -1, 0, 3, 5], [-3, -1, 0, 1], [-3, -1, 0, 1, 5], [-3, -1, 0, 1, 3], [-3, -1, 0, 1, 3, 5], [-5], [-5, 5], [-5, 3], [-5, 3, 5], [-5, 1], [-5, 1, 5], [-5, 1, 3], [-5, 1, 3, 5], [-5, 0], [-5, 0, 5], [-5, 0, 3], [-5, 0, 3, 5], [-5, 0, 1], [-5, 0, 1, 5], [-5, 0, 1, 3], [-5, 0, 1, 3, 5], [-5, -1], [-5, -1, 5], [-5, -1, 3], [-5, -1, 3, 5], [-5, -1, 1], [-5, -1, 1, 5], [-5, -1, 1, 3], [-5, -1, 1, 3, 5], [-5, -1, 0], [-5, -1, 0, 5], [-5, -1, 0, 3], [-5, -1, 0, 3, 5], [-5, -1, 0, 1], [-5, -1, 0, 1, 5], [-5, -1, 0, 1, 3], [-5, -1, 0, 1, 3, 5], [-5, -3], [-5, -3, 5], [-5, -3, 3], [-5, -3, 3, 5], [-5, -3, 1], [-5, -3, 1, 5], [-5, -3, 1, 3], [-5, -3, 1, 3, 5], [-5, -3, 0], [-5, -3, 0, 5], [-5, -3, 0, 3], [-5, -3, 0, 3, 5], [-5, -3, 0, 1], [-5, -3, 0, 1, 5], [-5, -3, 0, 1, 3], [-5, -3, 0, 1, 3, 5], [-5, -3, -1], [-5, -3, -1, 5], [-5, -3, -1, 3], [-5, -3, -1, 3, 5], [-5, -3, -1, 1], [-5, -3, -1, 1, 5], [-5, -3, -1, 1, 3], [-5, -3, -1, 1, 3, 5], [-5, -3, -1, 0], [-5, -3, -1, 0, 5], [-5, -3, -1, 0, 3], [-5, -3, -1, 0, 3, 5], [-5, -3, -1, 0, 1], [-5, -3, -1, 0, 1, 5], [-5, -3, -1, 0, 1, 3], [-5, -3, -1, 0, 1, 3, 5]]\n assert candidate(nums = [1, 3, 5, 7, 9, 11]) == [[], [11], [9], [9, 11], [7], [7, 11], [7, 9], [7, 9, 11], [5], [5, 11], [5, 9], [5, 9, 11], [5, 7], [5, 7, 11], [5, 7, 9], [5, 7, 9, 11], [3], [3, 11], [3, 9], [3, 9, 11], [3, 7], [3, 7, 11], [3, 7, 9], [3, 7, 9, 11], [3, 5], [3, 5, 11], [3, 5, 9], [3, 5, 9, 11], [3, 5, 7], [3, 5, 7, 11], [3, 5, 7, 9], [3, 5, 7, 9, 11], [1], [1, 11], [1, 9], [1, 9, 11], [1, 7], [1, 7, 11], [1, 7, 9], [1, 7, 9, 11], [1, 5], [1, 5, 11], [1, 5, 9], [1, 5, 9, 11], [1, 5, 7], [1, 5, 7, 11], [1, 5, 7, 9], [1, 5, 7, 9, 11], [1, 3], [1, 3, 11], [1, 3, 9], [1, 3, 9, 11], [1, 3, 7], [1, 3, 7, 11], [1, 3, 7, 9], [1, 3, 7, 9, 11], [1, 3, 5], [1, 3, 5, 11], [1, 3, 5, 9], [1, 3, 5, 9, 11], [1, 3, 5, 7], [1, 3, 5, 7, 11], [1, 3, 5, 7, 9], [1, 3, 5, 7, 9, 11]]\n assert candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81]) == [[], [81], [64], [64, 81], [49], [49, 81], [49, 64], [49, 64, 81], [36], [36, 81], [36, 64], [36, 64, 81], [36, 49], [36, 49, 81], [36, 49, 64], [36, 49, 64, 81], [25], [25, 81], [25, 64], [25, 64, 81], [25, 49], [25, 49, 81], [25, 49, 64], [25, 49, 64, 81], [25, 36], [25, 36, 81], [25, 36, 64], [25, 36, 64, 81], [25, 36, 49], [25, 36, 49, 81], [25, 36, 49, 64], [25, 36, 49, 64, 81], [16], [16, 81], [16, 64], [16, 64, 81], [16, 49], [16, 49, 81], [16, 49, 64], [16, 49, 64, 81], [16, 36], [16, 36, 81], [16, 36, 64], [16, 36, 64, 81], [16, 36, 49], [16, 36, 49, 81], [16, 36, 49, 64], [16, 36, 49, 64, 81], [16, 25], [16, 25, 81], [16, 25, 64], [16, 25, 64, 81], [16, 25, 49], [16, 25, 49, 81], [16, 25, 49, 64], [16, 25, 49, 64, 81], [16, 25, 36], [16, 25, 36, 81], [16, 25, 36, 64], [16, 25, 36, 64, 81], [16, 25, 36, 49], [16, 25, 36, 49, 81], [16, 25, 36, 49, 64], [16, 25, 36, 49, 64, 81], [9], [9, 81], [9, 64], [9, 64, 81], [9, 49], [9, 49, 81], [9, 49, 64], [9, 49, 64, 81], [9, 36], [9, 36, 81], [9, 36, 64], [9, 36, 64, 81], [9, 36, 49], [9, 36, 49, 81], [9, 36, 49, 64], [9, 36, 49, 64, 81], [9, 25], [9, 25, 81], [9, 25, 64], [9, 25, 64, 81], [9, 25, 49], [9, 25, 49, 81], [9, 25, 49, 64], [9, 25, 49, 64, 81], [9, 25, 36], [9, 25, 36, 81], [9, 25, 36, 64], [9, 25, 36, 64, 81], [9, 25, 36, 49], [9, 25, 36, 49, 81], [9, 25, 36, 49, 64], [9, 25, 36, 49, 64, 81], [9, 16], [9, 16, 81], [9, 16, 64], [9, 16, 64, 81], [9, 16, 49], [9, 16, 49, 81], [9, 16, 49, 64], [9, 16, 49, 64, 81], [9, 16, 36], [9, 16, 36, 81], [9, 16, 36, 64], [9, 16, 36, 64, 81], [9, 16, 36, 49], [9, 16, 36, 49, 81], [9, 16, 36, 49, 64], [9, 16, 36, 49, 64, 81], [9, 16, 25], [9, 16, 25, 81], [9, 16, 25, 64], [9, 16, 25, 64, 81], [9, 16, 25, 49], [9, 16, 25, 49, 81], [9, 16, 25, 49, 64], [9, 16, 25, 49, 64, 81], [9, 16, 25, 36], [9, 16, 25, 36, 81], [9, 16, 25, 36, 64], [9, 16, 25, 36, 64, 81], [9, 16, 25, 36, 49], [9, 16, 25, 36, 49, 81], [9, 16, 25, 36, 49, 64], [9, 16, 25, 36, 49, 64, 81], [4], [4, 81], [4, 64], [4, 64, 81], [4, 49], [4, 49, 81], [4, 49, 64], [4, 49, 64, 81], [4, 36], [4, 36, 81], [4, 36, 64], [4, 36, 64, 81], [4, 36, 49], [4, 36, 49, 81], [4, 36, 49, 64], [4, 36, 49, 64, 81], [4, 25], [4, 25, 81], [4, 25, 64], [4, 25, 64, 81], [4, 25, 49], [4, 25, 49, 81], [4, 25, 49, 64], [4, 25, 49, 64, 81], [4, 25, 36], [4, 25, 36, 81], [4, 25, 36, 64], [4, 25, 36, 64, 81], [4, 25, 36, 49], [4, 25, 36, 49, 81], [4, 25, 36, 49, 64], [4, 25, 36, 49, 64, 81], [4, 16], [4, 16, 81], [4, 16, 64], [4, 16, 64, 81], [4, 16, 49], [4, 16, 49, 81], [4, 16, 49, 64], [4, 16, 49, 64, 81], [4, 16, 36], [4, 16, 36, 81], [4, 16, 36, 64], [4, 16, 36, 64, 81], [4, 16, 36, 49], [4, 16, 36, 49, 81], [4, 16, 36, 49, 64], [4, 16, 36, 49, 64, 81], [4, 16, 25], [4, 16, 25, 81], [4, 16, 25, 64], [4, 16, 25, 64, 81], [4, 16, 25, 49], [4, 16, 25, 49, 81], [4, 16, 25, 49, 64], [4, 16, 25, 49, 64, 81], [4, 16, 25, 36], [4, 16, 25, 36, 81], [4, 16, 25, 36, 64], [4, 16, 25, 36, 64, 81], [4, 16, 25, 36, 49], [4, 16, 25, 36, 49, 81], [4, 16, 25, 36, 49, 64], [4, 16, 25, 36, 49, 64, 81], [4, 9], [4, 9, 81], [4, 9, 64], [4, 9, 64, 81], [4, 9, 49], [4, 9, 49, 81], [4, 9, 49, 64], [4, 9, 49, 64, 81], [4, 9, 36], [4, 9, 36, 81], [4, 9, 36, 64], [4, 9, 36, 64, 81], [4, 9, 36, 49], [4, 9, 36, 49, 81], [4, 9, 36, 49, 64], [4, 9, 36, 49, 64, 81], [4, 9, 25], [4, 9, 25, 81], [4, 9, 25, 64], [4, 9, 25, 64, 81], [4, 9, 25, 49], [4, 9, 25, 49, 81], [4, 9, 25, 49, 64], [4, 9, 25, 49, 64, 81], [4, 9, 25, 36], [4, 9, 25, 36, 81], [4, 9, 25, 36, 64], [4, 9, 25, 36, 64, 81], [4, 9, 25, 36, 49], [4, 9, 25, 36, 49, 81], [4, 9, 25, 36, 49, 64], [4, 9, 25, 36, 49, 64, 81], [4, 9, 16], [4, 9, 16, 81], [4, 9, 16, 64], [4, 9, 16, 64, 81], [4, 9, 16, 49], [4, 9, 16, 49, 81], [4, 9, 16, 49, 64], [4, 9, 16, 49, 64, 81], [4, 9, 16, 36], [4, 9, 16, 36, 81], [4, 9, 16, 36, 64], [4, 9, 16, 36, 64, 81], [4, 9, 16, 36, 49], [4, 9, 16, 36, 49, 81], [4, 9, 16, 36, 49, 64], [4, 9, 16, 36, 49, 64, 81], [4, 9, 16, 25], [4, 9, 16, 25, 81], [4, 9, 16, 25, 64], [4, 9, 16, 25, 64, 81], [4, 9, 16, 25, 49], [4, 9, 16, 25, 49, 81], [4, 9, 16, 25, 49, 64], [4, 9, 16, 25, 49, 64, 81], [4, 9, 16, 25, 36], [4, 9, 16, 25, 36, 81], [4, 9, 16, 25, 36, 64], [4, 9, 16, 25, 36, 64, 81], [4, 9, 16, 25, 36, 49], [4, 9, 16, 25, 36, 49, 81], [4, 9, 16, 25, 36, 49, 64], [4, 9, 16, 25, 36, 49, 64, 81], [1], [1, 81], [1, 64], [1, 64, 81], [1, 49], [1, 49, 81], [1, 49, 64], [1, 49, 64, 81], [1, 36], [1, 36, 81], [1, 36, 64], [1, 36, 64, 81], [1, 36, 49], [1, 36, 49, 81], [1, 36, 49, 64], [1, 36, 49, 64, 81], [1, 25], [1, 25, 81], [1, 25, 64], [1, 25, 64, 81], [1, 25, 49], [1, 25, 49, 81], [1, 25, 49, 64], [1, 25, 49, 64, 81], [1, 25, 36], [1, 25, 36, 81], [1, 25, 36, 64], [1, 25, 36, 64, 81], [1, 25, 36, 49], [1, 25, 36, 49, 81], [1, 25, 36, 49, 64], [1, 25, 36, 49, 64, 81], [1, 16], [1, 16, 81], [1, 16, 64], [1, 16, 64, 81], [1, 16, 49], [1, 16, 49, 81], [1, 16, 49, 64], [1, 16, 49, 64, 81], [1, 16, 36], [1, 16, 36, 81], [1, 16, 36, 64], [1, 16, 36, 64, 81], [1, 16, 36, 49], [1, 16, 36, 49, 81], [1, 16, 36, 49, 64], [1, 16, 36, 49, 64, 81], [1, 16, 25], [1, 16, 25, 81], [1, 16, 25, 64], [1, 16, 25, 64, 81], [1, 16, 25, 49], [1, 16, 25, 49, 81], [1, 16, 25, 49, 64], [1, 16, 25, 49, 64, 81], [1, 16, 25, 36], [1, 16, 25, 36, 81], [1, 16, 25, 36, 64], [1, 16, 25, 36, 64, 81], [1, 16, 25, 36, 49], [1, 16, 25, 36, 49, 81], [1, 16, 25, 36, 49, 64], [1, 16, 25, 36, 49, 64, 81], [1, 9], [1, 9, 81], [1, 9, 64], [1, 9, 64, 81], [1, 9, 49], [1, 9, 49, 81], [1, 9, 49, 64], [1, 9, 49, 64, 81], [1, 9, 36], [1, 9, 36, 81], [1, 9, 36, 64], [1, 9, 36, 64, 81], [1, 9, 36, 49], [1, 9, 36, 49, 81], [1, 9, 36, 49, 64], [1, 9, 36, 49, 64, 81], [1, 9, 25], [1, 9, 25, 81], [1, 9, 25, 64], [1, 9, 25, 64, 81], [1, 9, 25, 49], [1, 9, 25, 49, 81], [1, 9, 25, 49, 64], [1, 9, 25, 49, 64, 81], [1, 9, 25, 36], [1, 9, 25, 36, 81], [1, 9, 25, 36, 64], [1, 9, 25, 36, 64, 81], [1, 9, 25, 36, 49], [1, 9, 25, 36, 49, 81], [1, 9, 25, 36, 49, 64], [1, 9, 25, 36, 49, 64, 81], [1, 9, 16], [1, 9, 16, 81], [1, 9, 16, 64], [1, 9, 16, 64, 81], [1, 9, 16, 49], [1, 9, 16, 49, 81], [1, 9, 16, 49, 64], [1, 9, 16, 49, 64, 81], [1, 9, 16, 36], [1, 9, 16, 36, 81], [1, 9, 16, 36, 64], [1, 9, 16, 36, 64, 81], [1, 9, 16, 36, 49], [1, 9, 16, 36, 49, 81], [1, 9, 16, 36, 49, 64], [1, 9, 16, 36, 49, 64, 81], [1, 9, 16, 25], [1, 9, 16, 25, 81], [1, 9, 16, 25, 64], [1, 9, 16, 25, 64, 81], [1, 9, 16, 25, 49], [1, 9, 16, 25, 49, 81], [1, 9, 16, 25, 49, 64], [1, 9, 16, 25, 49, 64, 81], [1, 9, 16, 25, 36], [1, 9, 16, 25, 36, 81], [1, 9, 16, 25, 36, 64], [1, 9, 16, 25, 36, 64, 81], [1, 9, 16, 25, 36, 49], [1, 9, 16, 25, 36, 49, 81], [1, 9, 16, 25, 36, 49, 64], [1, 9, 16, 25, 36, 49, 64, 81], [1, 4], [1, 4, 81], [1, 4, 64], [1, 4, 64, 81], [1, 4, 49], [1, 4, 49, 81], [1, 4, 49, 64], [1, 4, 49, 64, 81], [1, 4, 36], [1, 4, 36, 81], [1, 4, 36, 64], [1, 4, 36, 64, 81], [1, 4, 36, 49], [1, 4, 36, 49, 81], [1, 4, 36, 49, 64], [1, 4, 36, 49, 64, 81], [1, 4, 25], [1, 4, 25, 81], [1, 4, 25, 64], [1, 4, 25, 64, 81], [1, 4, 25, 49], [1, 4, 25, 49, 81], [1, 4, 25, 49, 64], [1, 4, 25, 49, 64, 81], [1, 4, 25, 36], [1, 4, 25, 36, 81], [1, 4, 25, 36, 64], [1, 4, 25, 36, 64, 81], [1, 4, 25, 36, 49], [1, 4, 25, 36, 49, 81], [1, 4, 25, 36, 49, 64], [1, 4, 25, 36, 49, 64, 81], [1, 4, 16], [1, 4, 16, 81], [1, 4, 16, 64], [1, 4, 16, 64, 81], [1, 4, 16, 49], [1, 4, 16, 49, 81], [1, 4, 16, 49, 64], [1, 4, 16, 49, 64, 81], [1, 4, 16, 36], [1, 4, 16, 36, 81], [1, 4, 16, 36, 64], [1, 4, 16, 36, 64, 81], [1, 4, 16, 36, 49], [1, 4, 16, 36, 49, 81], [1, 4, 16, 36, 49, 64], [1, 4, 16, 36, 49, 64, 81], [1, 4, 16, 25], [1, 4, 16, 25, 81], [1, 4, 16, 25, 64], [1, 4, 16, 25, 64, 81], [1, 4, 16, 25, 49], [1, 4, 16, 25, 49, 81], [1, 4, 16, 25, 49, 64], [1, 4, 16, 25, 49, 64, 81], [1, 4, 16, 25, 36], [1, 4, 16, 25, 36, 81], [1, 4, 16, 25, 36, 64], [1, 4, 16, 25, 36, 64, 81], [1, 4, 16, 25, 36, 49], [1, 4, 16, 25, 36, 49, 81], [1, 4, 16, 25, 36, 49, 64], [1, 4, 16, 25, 36, 49, 64, 81], [1, 4, 9], [1, 4, 9, 81], [1, 4, 9, 64], [1, 4, 9, 64, 81], [1, 4, 9, 49], [1, 4, 9, 49, 81], [1, 4, 9, 49, 64], [1, 4, 9, 49, 64, 81], [1, 4, 9, 36], [1, 4, 9, 36, 81], [1, 4, 9, 36, 64], [1, 4, 9, 36, 64, 81], [1, 4, 9, 36, 49], [1, 4, 9, 36, 49, 81], [1, 4, 9, 36, 49, 64], [1, 4, 9, 36, 49, 64, 81], [1, 4, 9, 25], [1, 4, 9, 25, 81], [1, 4, 9, 25, 64], [1, 4, 9, 25, 64, 81], [1, 4, 9, 25, 49], [1, 4, 9, 25, 49, 81], [1, 4, 9, 25, 49, 64], [1, 4, 9, 25, 49, 64, 81], [1, 4, 9, 25, 36], [1, 4, 9, 25, 36, 81], [1, 4, 9, 25, 36, 64], [1, 4, 9, 25, 36, 64, 81], [1, 4, 9, 25, 36, 49], [1, 4, 9, 25, 36, 49, 81], [1, 4, 9, 25, 36, 49, 64], [1, 4, 9, 25, 36, 49, 64, 81], [1, 4, 9, 16], [1, 4, 9, 16, 81], [1, 4, 9, 16, 64], [1, 4, 9, 16, 64, 81], [1, 4, 9, 16, 49], [1, 4, 9, 16, 49, 81], [1, 4, 9, 16, 49, 64], [1, 4, 9, 16, 49, 64, 81], [1, 4, 9, 16, 36], [1, 4, 9, 16, 36, 81], [1, 4, 9, 16, 36, 64], [1, 4, 9, 16, 36, 64, 81], [1, 4, 9, 16, 36, 49], [1, 4, 9, 16, 36, 49, 81], [1, 4, 9, 16, 36, 49, 64], [1, 4, 9, 16, 36, 49, 64, 81], [1, 4, 9, 16, 25], [1, 4, 9, 16, 25, 81], [1, 4, 9, 16, 25, 64], [1, 4, 9, 16, 25, 64, 81], [1, 4, 9, 16, 25, 49], [1, 4, 9, 16, 25, 49, 81], [1, 4, 9, 16, 25, 49, 64], [1, 4, 9, 16, 25, 49, 64, 81], [1, 4, 9, 16, 25, 36], [1, 4, 9, 16, 25, 36, 81], [1, 4, 9, 16, 25, 36, 64], [1, 4, 9, 16, 25, 36, 64, 81], [1, 4, 9, 16, 25, 36, 49], [1, 4, 9, 16, 25, 36, 49, 81], [1, 4, 9, 16, 25, 36, 49, 64], [1, 4, 9, 16, 25, 36, 49, 64, 81]]\n assert candidate(nums = [4, 8, 15, 16, 23, 42]) == [[], [42], [23], [23, 42], [16], [16, 42], [16, 23], [16, 23, 42], [15], [15, 42], [15, 23], [15, 23, 42], [15, 16], [15, 16, 42], [15, 16, 23], [15, 16, 23, 42], [8], [8, 42], [8, 23], [8, 23, 42], [8, 16], [8, 16, 42], [8, 16, 23], [8, 16, 23, 42], [8, 15], [8, 15, 42], [8, 15, 23], [8, 15, 23, 42], [8, 15, 16], [8, 15, 16, 42], [8, 15, 16, 23], [8, 15, 16, 23, 42], [4], [4, 42], [4, 23], [4, 23, 42], [4, 16], [4, 16, 42], [4, 16, 23], [4, 16, 23, 42], [4, 15], [4, 15, 42], [4, 15, 23], [4, 15, 23, 42], [4, 15, 16], [4, 15, 16, 42], [4, 15, 16, 23], [4, 15, 16, 23, 42], [4, 8], [4, 8, 42], [4, 8, 23], [4, 8, 23, 42], [4, 8, 16], [4, 8, 16, 42], [4, 8, 16, 23], [4, 8, 16, 23, 42], [4, 8, 15], [4, 8, 15, 42], [4, 8, 15, 23], [4, 8, 15, 23, 42], [4, 8, 15, 16], [4, 8, 15, 16, 42], [4, 8, 15, 16, 23], [4, 8, 15, 16, 23, 42]]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().subsets", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var subsets = function(nums) {", "container": null, "callable": "subsets", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 79, "task_id": "word-search", "difficulty": "Medium", "problem_description": "Given an m x n grid of characters board and a string word, return true if word exists in the grid.\nThe word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.\n \nExample 1:\n\n\nInput: board = [[\"A\",\"B\",\"C\",\"E\"],[\"S\",\"F\",\"C\",\"S\"],[\"A\",\"D\",\"E\",\"E\"]], word = \"ABCCED\"\nOutput: true\n\nExample 2:\n\n\nInput: board = [[\"A\",\"B\",\"C\",\"E\"],[\"S\",\"F\",\"C\",\"S\"],[\"A\",\"D\",\"E\",\"E\"]], word = \"SEE\"\nOutput: true\n\nExample 3:\n\n\nInput: board = [[\"A\",\"B\",\"C\",\"E\"],[\"S\",\"F\",\"C\",\"S\"],[\"A\",\"D\",\"E\",\"E\"]], word = \"ABCB\"\nOutput: false\n\n \nConstraints:\n\nm == board.length\nn = board[i].length\n1 <= m, n <= 6\n1 <= word.length <= 15\nboard and word consists of only lowercase and uppercase English letters.\n\n \nFollow up: Could you use search pruning to make your solution faster with a larger board?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = [['A', 'B'], ['C', 'D']],word = \"BD\") == True\n assert candidate(board = [['A', 'B'], ['C', 'D']],word = \"AC\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"ABCB\") == False\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"ASADB\") == False\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"ABCB\") == False\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'E', 'S'], ['A', 'D', 'E', 'E']],word = \"ABCESEEEFS\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"Z\") == False\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"AB\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"ABCCED\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"SEE\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"E\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"SEE\") == True\n assert candidate(board = [['A', 'B'], ['C', 'D']],word = \"AB\") == True\n assert candidate(board = [['A', 'B'], ['C', 'D']],word = \"CD\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"ASAD\") == True\n assert candidate(board = [['A']],word = \"A\") == True\n assert candidate(board = [['A', 'B', 'C', 'E'], ['S', 'F', 'C', 'S'], ['A', 'D', 'E', 'E']],word = \"ABCCED\") == True\n"}, "metadata": {"canonical_parameter_names": ["board", "word"], "leetcode_dataset_entry_point": "Solution().exist", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var exist = function(board, word) {", "container": null, "callable": "exist", "parameters": [{"name": "board", "type": "character[][]"}, {"name": "word", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 80, "task_id": "remove-duplicates-from-sorted-array-ii", "difficulty": "Medium", "problem_description": "Given an integer array nums sorted in non-decreasing order, remove some duplicates in-place such that each unique element appears at most twice. The relative order of the elements should be kept the same.\nSince it is impossible to change the length of the array in some languages, you must instead have the result be placed in the first part of the array nums. More formally, if there are k elements after removing the duplicates, then the first k elements of nums should hold the final result. It does not matter what you leave beyond the first k elements.\nReturn k after placing the final result in the first k slots of nums.\nDo not allocate extra space for another array. You must do this by modifying the input array in-place with O(1) extra memory.\nCustom Judge:\nThe judge will test your solution with the following code:\n\nint[] nums = [...]; // Input array\nint[] expectedNums = [...]; // The expected answer with correct length\n\nint k = removeDuplicates(nums); // Calls your implementation\n\nassert k == expectedNums.length;\nfor (int i = 0; i < k; i++) {\n assert nums[i] == expectedNums[i];\n}\n\nIf all assertions pass, then your solution will be accepted.\n \nExample 1:\n\nInput: nums = [1,1,1,2,2,3]\nOutput: 5, nums = [1,1,2,2,3,_]\nExplanation: Your function should return k = 5, with the first five elements of nums being 1, 1, 2, 2 and 3 respectively.\nIt does not matter what you leave beyond the returned k (hence they are underscores).\n\nExample 2:\n\nInput: nums = [0,0,1,1,1,1,2,3,3]\nOutput: 7, nums = [0,0,1,1,2,3,3,_,_]\nExplanation: Your function should return k = 7, with the first seven elements of nums being 0, 0, 1, 1, 2, 3 and 3 respectively.\nIt does not matter what you leave beyond the returned k (hence they are underscores).\n\n \nConstraints:\n\n1 <= nums.length <= 3 * 104\n-104 <= nums[i] <= 104\nnums is sorted in non-decreasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 2\n assert candidate(nums = [1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 3]) == 6\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 3]) == 9\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 4, 4]) == 8\n assert candidate(nums = [1, 1, 1, 2, 2, 3]) == 5\n assert candidate(nums = [0, 0, 1, 1, 1, 1, 2, 3, 3]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5]) == 5\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5]) == 9\n assert candidate(nums = [1, 1, 2]) == 3\n assert candidate(nums = [-10000, -10000, 10000, 10000, 10000]) == 4\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4]) == 8\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 9]) == 14\n assert candidate(nums = [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3]) == 9\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 7\n assert candidate(nums = [1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 17\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 10\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]) == 6\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5]) == 10\n assert candidate(nums = [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 3]) == 10\n assert candidate(nums = [1, 1]) == 2\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 18\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12]) == 23\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4]) == 8\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 20\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 20\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 9]) == 18\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3]) == 10\n assert candidate(nums = [-1, -1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9]) == 22\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]) == 4\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7]) == 14\n assert candidate(nums = [-100, -100, -99, -99, -98, -98, -98, -97, -97, -96, -96, -95, -95, -95, -95]) == 12\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20]) == 24\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 30\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == 12\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 4\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11, 11]) == 22\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 6\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 20\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 20\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6]) == 11\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9]) == 17\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5]) == 12\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == 12\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7]) == 14\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6]) == 11\n assert candidate(nums = [-1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3]) == 10\n assert candidate(nums = [1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 19\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9]) == 16\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 20\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 9\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 19\n assert candidate(nums = [-1, -1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 24\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8]) == 15\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 20\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6]) == 16\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6]) == 11\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]) == 20\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9]) == 18\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 4\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10]) == 19\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9]) == 17\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 11\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8]) == 18\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9]) == 18\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 20\n assert candidate(nums = [1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == 15\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == 12\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13]) == 26\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6]) == 12\n assert candidate(nums = [-10000, -9999, -9999, -9998, -9997, -9997, -9997, -9996, -9995, -9995, -9994, -9994, -9993, -9993, -9992, -9992, -9991, -9991, -9990, -9990]) == 19\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == 28\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 11\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6]) == 12\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == 29\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13]) == 25\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6]) == 12\n assert candidate(nums = [-10, -10, -10, -9, -9, -8, -8, -8, -8, -8, -7, -7, -7, -7, -6, -6, -6, -6, -6, -5, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0]) == 22\n assert candidate(nums = [1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 9\n assert candidate(nums = [-10000, -10000, -9999, -9998, -9998, -9998, -9997, -9997, -9997, -9997, -9996, -9996, -9996, -9995, -9995]) == 11\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7]) == 13\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9]) == 18\n assert candidate(nums = [-3, -3, -3, -2, -2, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5]) == 17\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 12\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5]) == 10\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 13]) == 25\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6]) == 11\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 20\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3]) == 6\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6]) == 12\n assert candidate(nums = [-10000, -10000, -10000, -10000, -9999, -9999, -9998, -9998, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 18\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10]) == 19\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 12\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6]) == 12\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13]) == 26\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 2\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7]) == 14\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6]) == 11\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9]) == 19\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15]) == 21\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7]) == 13\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 4\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().removeDuplicates", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeDuplicates = function(nums) {", "container": null, "callable": "removeDuplicates", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 81, "task_id": "search-in-rotated-sorted-array-ii", "difficulty": "Medium", "problem_description": "There is an integer array nums sorted in non-decreasing order (not necessarily with distinct values).\nBefore being passed to your function, nums is rotated at an unknown pivot index k (0 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]] (0-indexed). For example, [0,1,2,4,4,4,5,6,6,7] might be rotated at pivot index 5 and become [4,5,6,6,7,0,1,2,4,4].\nGiven the array nums after the rotation and an integer target, return true if target is in nums, or false if it is not in nums.\nYou must decrease the overall operation steps as much as possible.\n \nExample 1:\nInput: nums = [2,5,6,0,0,1,2], target = 0\nOutput: true\nExample 2:\nInput: nums = [2,5,6,0,0,1,2], target = 3\nOutput: false\n\n \nConstraints:\n\n1 <= nums.length <= 5000\n-104 <= nums[i] <= 104\nnums is guaranteed to be rotated at some pivot.\n-104 <= target <= 104\n\n \nFollow up: This problem is similar to Search in Rotated Sorted Array, but nums may contain duplicates. Would this affect the runtime complexity? How and why?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 6) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1],target = 2) == True\n assert candidate(nums = [4, 5, 6, 6, 7, 0, 1, 2, 4, 4],target = 4) == True\n assert candidate(nums = [3, 1],target = 2) == False\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 3) == False\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2],target = 0) == True\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3],target = 1) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1],target = 3) == False\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 1],target = 1) == True\n assert candidate(nums = [3, 1],target = 1) == True\n assert candidate(nums = [1],target = 1) == True\n assert candidate(nums = [5, 1, 3],target = 3) == True\n assert candidate(nums = [2, 5, 6, 0, 0, 1, 2],target = 3) == False\n assert candidate(nums = [4, 5, 6, 6, 7, 0, 1, 2, 4, 4],target = 7) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == True\n assert candidate(nums = [2, 5, 6, 0, 0, 1, 2],target = 0) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],target = 1) == True\n assert candidate(nums = [5, 1, 3],target = 5) == True\n assert candidate(nums = [1, 3, 5],target = 1) == True\n assert candidate(nums = [1, 0, 1, 1, 1],target = 0) == True\n assert candidate(nums = [1],target = 0) == False\n assert candidate(nums = [1],target = 2) == False\n assert candidate(nums = [1, 3, 5],target = 5) == True\n assert candidate(nums = [3, 1],target = 3) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 3, 4, 2],target = 3) == True\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8, 10],target = 7) == False\n assert candidate(nums = [7, 8, 9, 1, 2, 3, 4, 5, 6],target = 9) == True\n assert candidate(nums = [6, 7, 1, 2, 3, 4, 5],target = 3) == True\n assert candidate(nums = [5, 5, 5, 1, 2, 3, 4, 5],target = 6) == False\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2, 3],target = 6) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0],target = 18) == True\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2, 3],target = 10) == False\n assert candidate(nums = [6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5],target = 10) == True\n assert candidate(nums = [11, 13, 15, 17, 19, 21, 3, 5, 7, 9],target = 3) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 0, 1, 2, 3, 4],target = 9) == True\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 0],target = 0) == True\n assert candidate(nums = [15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],target = 3) == True\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 15) == True\n assert candidate(nums = [5, 5, 5, 1, 2, 3, 4, 5],target = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0],target = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0],target = 19) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == True\n assert candidate(nums = [2, 2, 2, 0, 2, 2],target = 0) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 2, 3, 4],target = 1) == True\n assert candidate(nums = [2, 2, 2, 0, 1, 2],target = 3) == False\n assert candidate(nums = [2, 2, 2, 0, 1, 2],target = 0) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 15) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == False\n assert candidate(nums = [5, 1, 3, 4, 5, 5, 5, 5, 5],target = 1) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 0, 1, 2, 3, 4],target = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0],target = 20) == False\n assert candidate(nums = [3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 1) == True\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2, 3],target = 0) == True\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 0, 1],target = 0) == True\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8, 10],target = 5) == False\n assert candidate(nums = [9, 9, 9, 9, 9, 1, 1, 1, 1, 1],target = 1) == True\n assert candidate(nums = [1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 3) == True\n assert candidate(nums = [4, 5, 6, 7, 8, 1, 2, 3],target = 8) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2],target = 3) == True\n assert candidate(nums = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8],target = 1) == False\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],target = 9) == True\n assert candidate(nums = [4, 4, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 4, 4, 4, 4],target = 0) == True\n assert candidate(nums = [5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5],target = 1) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 1) == False\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4],target = 0) == True\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],target = 25) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4],target = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7],target = 5) == True\n assert candidate(nums = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8],target = 0) == True\n assert candidate(nums = [3, 4, 5, 6, 1, 2],target = 1) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 7) == True\n assert candidate(nums = [10, 10, 10, 10, 10, 1, 2, 3, 4, 5],target = 1) == True\n assert candidate(nums = [10, 15, 20, 25, 30, 5, 10],target = 25) == True\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 4, 6, 8, 10],target = 17) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],target = 29) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1],target = 2) == True\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().search", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var search = function(nums, target) {", "container": null, "callable": "search", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 82, "task_id": "remove-duplicates-from-sorted-list-ii", "difficulty": "Medium", "problem_description": "Given the head of a sorted linked list, delete all nodes that have duplicate numbers, leaving only distinct numbers from the original list. Return the linked list sorted as well.\n \nExample 1:\n\n\nInput: head = [1,2,3,3,4,4,5]\nOutput: [1,2,5]\n\nExample 2:\n\n\nInput: head = [1,1,1,2,3]\nOutput: [2,3]\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 300].\n-100 <= Node.val <= 100\nThe list is guaranteed to be sorted in ascending order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert candidate(head = list_node([])) == None\n assert is_same_list(candidate(head = list_node([-100, -100, -99, -98, -98, -97, -96, -96, -95])), list_node([-99, -97, -95]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 3, 4, 4, 5])), list_node([2, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 5, 5])), list_node([1, 4]))\n assert is_same_list(candidate(head = list_node([-100, 100, -100, 100])), list_node([-100, 100, -100, 100]))\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5])), list_node([1]))\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 3])), list_node([2, 3]))\n assert is_same_list(candidate(head = list_node([-100, 100])), list_node([-100, 100]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 4, 4, 5, 5])), list_node([1, 3]))\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -97, -97, -96])), list_node([-100, -98, -96]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -98, -97, -97, -96, -95, -94, -94, -93])), list_node([-100, -99, -96, -95, -93]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 3, 4, 4, 5])), list_node([1, 2, 5]))\n assert candidate(head = list_node([0, 0, 0, 0, 0])) == None\n assert candidate(head = list_node([1, 1, 1, 1, 1])) == None\n assert candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == None\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 12, 12, 13])), list_node([1, 3, 5, 6, 7, 9, 11, 13]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7])), list_node([7]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11])), list_node([1, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 15, 15, 16, 17, 17, 18, 19, 20, 20, 20])), list_node([2, 3, 4, 6, 7, 9, 11, 13, 14, 16, 18, 19]))\n assert is_same_list(candidate(head = list_node([-1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 5, 5])), list_node([3, 4]))\n assert candidate(head = list_node([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10])) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 21, 22, 23, 24, 25, 25, 25, 26, 27, 28, 29, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30]))\n assert candidate(head = list_node([1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6])), list_node([1]))\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10])) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 14, 15, 16, 16, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10, 10])), list_node([6, 7, 8, 9]))\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])) == None\n assert candidate(head = list_node([-100, -100, -99, -99, -98, -98, -97, -97, -96, -96])) == None\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20])), list_node([1, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 10])), list_node([1, 2, 3, 4, 6, 7, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10])), list_node([1, 2, 3, 4]))\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10])), list_node([2, 3, 6]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15])), list_node([1, 4]))\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])) == None\n assert is_same_list(candidate(head = list_node([-100, -100, -100, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9])), list_node([4]))\n assert is_same_list(candidate(head = list_node([-10, -10, -9, -9, -8, -8, -7, -7, -6, -5, -4, -3, -2, -1, 0, 0, 0, 0, 1, 2, 2, 3, 3, 4, 5, 5, 5])), list_node([-6, -5, -4, -3, -2, -1, 1, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 11])), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9])), list_node([1]))\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16])), list_node([2]))\n assert is_same_list(candidate(head = list_node([-100, -100, 0, 0, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9])), list_node([1, 3, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10])), list_node([1]))\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13])) == None\n assert candidate(head = list_node([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])) == None\n assert is_same_list(candidate(head = list_node([-100, -50, -50, -10, 0, 0, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9, 100])), list_node([-100, -10, 1, 4, 6, 7, 9, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 2, 3, 4, 5, 5, 5])), list_node([2, 3, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9])) == None\n assert candidate(head = list_node([-10, -10, -9, -9, -8, -8, -7, -7, -6, -6, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5])), list_node([2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-1, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5])), list_node([-1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19]))\n assert candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 9, 10, 10, 10])), list_node([4, 7, 9]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6])), list_node([2, 6]))\n assert candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10])) == None\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17])) == None\n assert is_same_list(candidate(head = list_node([-100, -100, -50, -50, 0, 0, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6])), list_node([1, 3, 6]))\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7])), list_node([3, 7]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9])), list_node([4]))\n assert candidate(head = list_node([1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5])) == None\n assert candidate(head = list_node([1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3])) == None\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert candidate(head = list_node([-10, -10, -10, -9, -9, -8, -8, -7, -7, -6, -6, -5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54, 55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70, 71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78, 79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100])) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15])), list_node([1, 2]))\n assert candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9])) == None\n assert candidate(head = list_node([0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 10, 10, 10])), list_node([6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9])), list_node([2]))\n assert is_same_list(candidate(head = list_node([-5, -4, -4, -3, -3, -2, -1, -1, 0, 0, 1, 2, 2, 3, 3, 4, 5, 5, 6])), list_node([-5, -2, 1, 4, 6]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15])), list_node([1, 3, 4, 6, 8, 9, 10, 12, 13, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6])), list_node([1]))\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -98, -97, -96, -96, -96, -95, -94, -94, -93, -92, -91, -91, -90, -89, -89, -88, -87, -87, -87, -86, -85, -85, -84, -83, -83, -83, -82, -81, -81, -80, -79, -79, -78, -77, -77, -76, -75, -75, -74, -73, -73, -72, -71, -71, -70, -69, -69, -68, -67, -67, -66, -65, -65, -64, -63, -63, -62, -61, -61, -60, -59, -59, -58, -57, -57, -56, -55, -55, -54, -53, -53, -52, -51, -51, -50, -49, -49, -48, -47, -47, -46, -45, -45, -44, -43, -43, -42, -41, -41, -40, -39, -39, -38, -37, -37, -36, -35, -35, -34, -33, -33, -32, -31, -31, -30, -29, -29, -28, -27, -27, -26, -25, -25, -24, -23, -23, -22, -21, -21, -20, -19, -19, -18, -17, -17, -16, -15, -15, -14, -13, -13, -12, -11, -11, -10, -9, -9, -8, -7, -7, -6, -5, -5, -4, -3, -3, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([-100, -97, -95, -93, -92, -90, -88, -86, -84, -82, -80, -78, -76, -74, -72, -70, -68, -66, -64, -62, -60, -58, -56, -54, -52, -50, -48, -46, -44, -42, -40, -38, -36, -34, -32, -30, -28, -26, -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2]))\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -98, -97, -96, -96, -95, -94, -93, -93, -92])), list_node([-100, -97, -95, -94, -92]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11])), list_node([2, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12])), list_node([1, 2, 4, 7, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 14, 15])), list_node([1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 15]))\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == None\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26, 27, 28, 29, 30, 30])), list_node([2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 20])), list_node([4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -98, -97, -96, -95, -95, -94, -94, -93, -92, -92, -91, -91])), list_node([-100, -99, -97, -96, -93]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 6])), list_node([3, 6]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8])), list_node([1, 8]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().deleteDuplicates", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var deleteDuplicates = function(head) {", "container": null, "callable": "deleteDuplicates", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 83, "task_id": "remove-duplicates-from-sorted-list", "difficulty": "Easy", "problem_description": "Given the head of a sorted linked list, delete all duplicates such that each element appears only once. Return the linked list sorted as well.\n \nExample 1:\n\n\nInput: head = [1,1,2]\nOutput: [1,2]\n\nExample 2:\n\n\nInput: head = [1,1,2,3,3]\nOutput: [1,2,3]\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 300].\n-100 <= Node.val <= 100\nThe list is guaranteed to be sorted in ascending order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([-100, 0, 0, 1, 1, 2, 2, 3, 3, 100])), list_node([-100, 0, 1, 2, 3, 100]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([-100, -100, -99, -98, -98, -97, -97, -96])), list_node([-100, -99, -98, -97, -96]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0])), list_node([0]))\n assert candidate(head = list_node([])) == None\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 4, 4, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-100, 0, 100])), list_node([-100, 0, 100]))\n assert is_same_list(candidate(head = list_node([-100, -50, -50, -25, -25, 0, 0, 50, 50, 100])), list_node([-100, -50, -25, 0, 50, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 2])), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([-3, -2, -1, -1, 0, 1, 2, 2, 3])), list_node([-3, -2, -1, 0, 1, 2, 3]))\n assert is_same_list(candidate(head = list_node([-1, 0, 0, 1, 1, 2])), list_node([-1, 0, 1, 2]))\n assert is_same_list(candidate(head = list_node([-100, 0, 0, 1, 1, 2, 3, 3, 100])), list_node([-100, 0, 1, 2, 3, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 3, 3])), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([100, 100, 100])), list_node([100]))\n assert is_same_list(candidate(head = list_node([50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50])), list_node([50]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20])), list_node([-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10])), list_node([10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2])), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([-100, -50, -25, -25, -10, -10, -5, -5, 0, 0, 5, 5, 10, 10, 25, 25, 50, 50, 100, 100])), list_node([-100, -50, -25, -10, -5, 0, 5, 10, 25, 50, 100]))\n assert is_same_list(candidate(head = list_node([-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3])), list_node([-1, 0, 1, 2, 3]))\n assert is_same_list(candidate(head = list_node([-50, -50, -40, -40, -30, -30, -20, -20, -10, -10, 0, 0, 10, 10, 20, 20, 30, 30, 40, 40, 50, 50])), list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -97, -97, -96, -95, -95, -94, -93, -93, -92, -91, -91, -90, -89, -89, -88, -87, -87, -86, -85, -85, -84, -83, -83, -82, -81, -81, -80, -79, -79, -78, -77, -77, -76, -75, -75, -74, -73, -73, -72, -71, -71, -70, -69, -69, -68, -67, -67, -66, -65, -65, -64, -63, -63, -62, -61, -61, -60, -59, -59, -58, -57, -57, -56, -55, -55, -54, -53, -53, -52, -51, -51, -50, -49, -49, -48, -47, -47, -46, -45, -45, -44, -43, -43, -42, -41, -41, -40, -39, -39, -38, -37, -37, -36, -35, -35, -34, -33, -33, -32, -31, -31, -30, -29, -29, -28, -27, -27, -26, -25, -25, -24, -23, -23, -22, -21, -21, -20, -19, -19, -18, -17, -17, -16, -15, -15, -14, -13, -13, -12, -11, -11, -10, -9, -9, -8, -7, -7, -6, -5, -5, -4, -3, -3, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-50, -50, -50, -50, -50, -25, -25, -25, -25, -10, -10, -5, -5, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5])), list_node([-50, -25, -10, -5, -1, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-99, -99, -98, -98, -97, -97, -96, -96, -95, -95, -94, -94, -93, -93, -92, -92, -91, -91, -90, -90])), list_node([-99, -98, -97, -96, -95, -94, -93, -92, -91, -90]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -98, -97, -97, -96, -95, -94, -94, -93, -93, -92, -91, -91, -90, -89, -88, -88, -87])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87]))\n assert is_same_list(candidate(head = list_node([50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 54, 54, 54, 54, 54, 55, 55, 55])), list_node([50, 51, 52, 53, 54, 55]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81]))\n assert is_same_list(candidate(head = list_node([100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100])), list_node([100]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 8, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([-100, -50, -50, -50, -50, -25, -25, -25, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 100, 100])), list_node([-100, -50, -25, -1, 0, 1, 2, 3, 100]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6, 6, 6, 6, 7])), list_node([-1, 0, 1, 2, 3, 4, 5, 6, 7]))\n assert is_same_list(candidate(head = list_node([-100, -100, -100, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 100, 100])), list_node([-100, 0, 1, 2, 3, 100]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70])), list_node([-99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([-99, -99, -98, -98, -97, -97, -96, -96, -95, -95, -94, -94, -93, -93, -92, -92, -91, -91, -90, -90])), list_node([-99, -98, -97, -96, -95, -94, -93, -92, -91, -90]))\n assert is_same_list(candidate(head = list_node([-10, -9, -9, -8, -7, -7, -6, -5, -4, -4, -3, -2, -2, -1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([-50, -50, -50, -50, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40])), list_node([-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100])), list_node([-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]))\n assert is_same_list(candidate(head = list_node([-3, -3, -2, -2, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30])), list_node([-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([-1, 0, 1]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]))\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -98, -97, -97, -96, -96, -95, -95, -94, -94, -93, -93, -92, -92, -91, -91, -90, -90])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1])), list_node([0, 1]))\n assert is_same_list(candidate(head = list_node([-100, -100, -100, -50, -50, 0, 0, 1, 1, 2, 2, 2, 3, 3, 100, 100])), list_node([-100, -50, 0, 1, 2, 3, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -98, -97, -97, -96, -96, -95, -95, -94, -94, -93, -93])), list_node([-100, -99, -98, -97, -96, -95, -94, -93]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([-100, -100, -100, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([-100, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-10, 0, 1, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 19, 20])), list_node([-10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2])), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([-100, -100, -50, -50, -50, 0, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8, 9, 10])), list_node([-100, -50, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3])), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 100, 100, 100, 100])), list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]))\n assert is_same_list(candidate(head = list_node([-5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5])), list_node([-5]))\n assert is_same_list(candidate(head = list_node([-50, -50, -50, -25, -25, -25, -25, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 50, 50, 50, 50])), list_node([-50, -25, 0, 1, 2, 50]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60])), list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60]))\n assert is_same_list(candidate(head = list_node([100, 100, 100, 100, 100, 100, 100, 100, 100, 100])), list_node([100]))\n assert is_same_list(candidate(head = list_node([-100, -100, -100, -50, -50, -50, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 100, 100, 100])), list_node([-100, -50, 0, 1, 2, 3, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3])), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([-100, -100, -99, -99, -98, -97, -97, -96, -95, -95, -94])), list_node([-100, -99, -98, -97, -96, -95, -94]))\n assert is_same_list(candidate(head = list_node([-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5])), list_node([-1, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 60, 60, 60, 60, 60, 61, 61, 61, 61, 61, 62, 62, 62, 62, 62, 63, 63, 63, 63, 63, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 68, 68, 68, 68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72, 73, 73, 73, 73, 73, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 78, 78, 78, 78, 78, 79, 79, 79, 79, 79, 80, 80, 80, 80, 80, 81, 81, 81, 81, 81, 82, 82, 82, 82, 82, 83, 83, 83, 83, 83, 84, 84, 84, 84, 84, 85, 85, 85, 85, 85, 86, 86, 86, 86, 86, 87, 87, 87, 87, 87, 88, 88, 88, 88, 88, 89, 89, 89, 89, 89, 90, 90, 90, 90, 90, 91, 91, 91, 91, 91, 92, 92, 92, 92, 92, 93, 93, 93, 93, 93, 94, 94, 94, 94, 94, 95, 95, 95, 95, 95, 96, 96, 96, 96, 96, 97, 97, 97, 97, 97, 98, 98, 98, 98, 98, 99, 99, 99, 99, 99, 100, 100, 100, 100, 100])), list_node([50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]))\n assert is_same_list(candidate(head = list_node([-100, -50, -50, -40, -40, -30, -30, -20, -20, -10, -10, 0, 0, 10, 10, 20, 20, 30, 30, 40, 40, 50, 50, 100, 100])), list_node([-100, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 100]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([-100, -99, -99, -98, -98, -97, -97, -96, -96, -95, -95, -94, -94, -93, -93, -92, -92, -91, -91, -90, -90, -89, -89, -88, -88, -87, -87, -86, -86, -85, -85, -84, -84, -83, -83, -82, -82, -81, -81])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81]))\n assert is_same_list(candidate(head = list_node([50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50])), list_node([50]))\n assert is_same_list(candidate(head = list_node([-100, -100, -100, -100, -100, -100, -100, -100, -100, -100])), list_node([-100]))\n assert is_same_list(candidate(head = list_node([-50, -40, -30, -20, -10, -10, -10, -5, -5, 0, 0, 0, 5, 5, 5, 10, 10, 15, 15, 20, 20, 25, 25, 30, 30, 35, 35, 40, 40, 50, 50])), list_node([-50, -40, -30, -20, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 50]))\n assert is_same_list(candidate(head = list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81, -80, -79, -78, -77, -76, -75, -74, -73, -72, -71, -70, -69, -68, -67, -66, -65, -64, -63, -62, -61, -60, -59, -58, -57, -56, -55, -54, -53, -52, -51, -50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]))\n assert is_same_list(candidate(head = list_node([-100, -50, 0, 50, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100])), list_node([-100, -50, 0, 50, 100]))\n assert is_same_list(candidate(head = list_node([50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50])), list_node([50]))\n assert is_same_list(candidate(head = list_node([-100, 100])), list_node([-100, 100]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3])), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([-50, -49, -49, -48, -47, -47, -46, -45, -45, -44, -43, -43, -42, -41, -40, -40, -39, -38, -38, -37, -36, -35, -35])), list_node([-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85]))\n assert is_same_list(candidate(head = list_node([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10])), list_node([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81])), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90, -89, -88, -87, -86, -85, -84, -83, -82, -81]))\n assert is_same_list(candidate(head = list_node([-100, -98, -96, -94, -92, -90, -88, -86, -84, -82, -80, -78, -76, -74, -72, -70, -68, -66, -64, -62, -60, -58, -56, -54, -52, -50, -48, -46, -44, -42, -40, -38, -36, -34, -32, -30, -28, -26, -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100])), list_node([-100, -98, -96, -94, -92, -90, -88, -86, -84, -82, -80, -78, -76, -74, -72, -70, -68, -66, -64, -62, -60, -58, -56, -54, -52, -50, -48, -46, -44, -42, -40, -38, -36, -34, -32, -30, -28, -26, -24, -22, -20, -18, -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100]))\n assert is_same_list(candidate(head = list_node([100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100])), list_node([100]))\n assert is_same_list(candidate(head = list_node([-1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5])), list_node([-1, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-50, -50, -49, -48, -47, -47, -46, -45, -44, -44, -43, -42, -41, -41, -40])), list_node([-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40]))\n assert is_same_list(candidate(head = list_node([-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100])), list_node([-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]))\n assert is_same_list(candidate(head = list_node([-50, -40, -40, -30, -20, -20, -20, -10, -10, 0, 0, 0, 10, 20, 30, 40, 40, 50, 50])), list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([50, 50, 50, 50, 50, 50, 50, 51, 52, 52, 52, 53, 54, 55, 55, 56, 57, 58, 58, 59])), list_node([50, 51, 52, 53, 54, 55, 56, 57, 58, 59]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().deleteDuplicates", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var deleteDuplicates = function(head) {", "container": null, "callable": "deleteDuplicates", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 84, "task_id": "largest-rectangle-in-histogram", "difficulty": "Hard", "problem_description": "Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram.\n \nExample 1:\n\n\nInput: heights = [2,1,5,6,2,3]\nOutput: 10\nExplanation: The above is a histogram where width of each bar is 1.\nThe largest rectangle is shown in the red area, which has an area = 10 units.\n\nExample 2:\n\n\nInput: heights = [2,4]\nOutput: 4\n\n \nConstraints:\n\n1 <= heights.length <= 105\n0 <= heights[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(heights = [1]) == 1\n assert candidate(heights = [1, 0, 1, 0, 1]) == 1\n assert candidate(heights = [10000, 10000, 10000, 10000, 10000]) == 50000\n assert candidate(heights = [0]) == 0\n assert candidate(heights = [1, 2, 3, 4, 5]) == 9\n assert candidate(heights = [0, 1, 0, 1, 0]) == 1\n assert candidate(heights = [2, 1, 2]) == 3\n assert candidate(heights = [4, 2, 0, 3, 2, 5, 6, 0, 0, 1]) == 10\n assert candidate(heights = [3, 6, 5, 7, 4, 8, 1, 0]) == 20\n assert candidate(heights = [3]) == 3\n assert candidate(heights = [2, 4]) == 4\n assert candidate(heights = [10000, 10000, 10000, 10000]) == 40000\n assert candidate(heights = [3, 6, 5, 7, 4, 8, 1, 0, 9]) == 20\n assert candidate(heights = [0, 0, 0, 0, 0]) == 0\n assert candidate(heights = [0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1]) == 9\n assert candidate(heights = [2, 1, 5, 6, 2, 3]) == 10\n assert candidate(heights = [3, 3, 3, 3, 3, 3, 3, 3, 3]) == 27\n assert candidate(heights = [1, 1, 1, 1, 1]) == 5\n assert candidate(heights = [5, 4, 3, 2, 1]) == 9\n assert candidate(heights = [3, 1, 3, 1, 3]) == 5\n assert candidate(heights = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 30\n assert candidate(heights = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3]) == 16\n assert candidate(heights = [10, 15, 10, 20, 25, 30, 20, 15, 10]) == 90\n assert candidate(heights = [5, 4, 3, 2, 1, 2, 3, 4, 5]) == 9\n assert candidate(heights = [1, 2, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == 14\n assert candidate(heights = [1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1]) == 15\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 60\n assert candidate(heights = [3, 6, 5, 7, 4, 8, 1, 0, 2]) == 20\n assert candidate(heights = [5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5]) == 9\n assert candidate(heights = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 30\n assert candidate(heights = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 30\n assert candidate(heights = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 25\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == 30\n assert candidate(heights = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991]) == 99910\n assert candidate(heights = [3, 6, 5, 7, 4, 8, 1, 0, 2, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 55\n assert candidate(heights = [5, 2, 5, 2, 5, 2, 5, 2, 5, 2]) == 20\n assert candidate(heights = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 55\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 110\n assert candidate(heights = [6, 2, 5, 4, 5, 1, 6, 2, 3, 3, 2, 6, 5, 3, 2, 1]) == 18\n assert candidate(heights = [3, 6, 5, 7, 4, 8, 1, 0, 9, 2, 5, 6, 4, 3, 7, 8, 9, 10, 11, 12]) == 42\n assert candidate(heights = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 113\n assert candidate(heights = [10, 20, 10, 30, 10, 40, 10, 50, 10, 60, 10]) == 110\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 66\n assert candidate(heights = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 27, 24, 21, 18, 15, 12, 9, 6, 3]) == 165\n assert candidate(heights = [10000, 0, 10000, 0, 10000, 0]) == 10000\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 55\n assert candidate(heights = [5, 3, 5, 6, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1]) == 28\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 30\n assert candidate(heights = [1, 3, 2, 1, 5, 4, 2, 1]) == 8\n assert candidate(heights = [4, 2, 0, 3, 2, 5]) == 6\n assert candidate(heights = [100, 200, 300, 400, 300, 200, 100]) == 1000\n assert candidate(heights = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == 10\n assert candidate(heights = [1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1]) == 28\n assert candidate(heights = [6, 2, 5, 4, 5, 1, 6, 3]) == 12\n assert candidate(heights = [2, 1, 5, 6, 2, 3, 2, 1, 5, 6, 2, 3]) == 12\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(heights = [2, 1, 5, 6, 2, 3, 1, 4, 2, 1]) == 10\n assert candidate(heights = [0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(heights = [4, 2, 0, 3, 2, 5, 3, 1]) == 8\n assert candidate(heights = [5, 5, 1, 5, 5]) == 10\n assert candidate(heights = [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0]) == 10\n assert candidate(heights = [1, 3, 2, 1, 2, 3, 1]) == 7\n assert candidate(heights = [5, 6, 2, 8, 9, 1, 4, 3, 7, 10]) == 16\n assert candidate(heights = [5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5]) == 25\n assert candidate(heights = [5, 8, 6, 2, 7, 8, 5, 9, 5, 3, 8, 6, 7, 9, 5, 2, 8]) == 34\n assert candidate(heights = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(heights = [10000, 0, 10000, 0, 10000, 0, 10000, 0]) == 10000\n assert candidate(heights = [2, 1, 5, 6, 2, 3, 2, 5, 6, 7, 8, 9, 10]) == 30\n assert candidate(heights = [1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 21]) == 66\n assert candidate(heights = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 21\n assert candidate(heights = [2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4]) == 40\n assert candidate(heights = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 18\n assert candidate(heights = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == 10\n assert candidate(heights = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 20\n assert candidate(heights = [1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(heights = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 25\n assert candidate(heights = [2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 26\n assert candidate(heights = [1, 3, 2, 1, 3, 2, 1]) == 7\n assert candidate(heights = [5, 5, 1, 7, 1, 1, 5, 2, 7, 6]) == 12\n assert candidate(heights = [5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5]) == 25\n assert candidate(heights = [2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 25\n assert candidate(heights = [6, 2, 5, 4, 5, 1, 6]) == 12\n assert candidate(heights = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 21\n assert candidate(heights = [5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 55\n assert candidate(heights = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == 15\n assert candidate(heights = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(heights = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == 160\n assert candidate(heights = [1, 3, 2, 1, 2, 3, 1, 2, 3, 4, 3, 2, 1, 2, 3, 1]) == 16\n assert candidate(heights = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 21\n assert candidate(heights = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(heights = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]) == 5500\n assert candidate(heights = [1, 0, 0, 0, 1, 0, 0, 0, 1]) == 1\n assert candidate(heights = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 20\n assert candidate(heights = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 1\n assert candidate(heights = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 17\n assert candidate(heights = [2, 1, 3, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 2, 3, 2, 1, 2, 3, 2, 1]) == 28\n"}, "metadata": {"canonical_parameter_names": ["heights"], "leetcode_dataset_entry_point": "Solution().largestRectangleArea", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var largestRectangleArea = function(heights) {", "container": null, "callable": "largestRectangleArea", "parameters": [{"name": "heights", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 85, "task_id": "maximal-rectangle", "difficulty": "Hard", "problem_description": "Given a rows x cols binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.\n \nExample 1:\n\n\nInput: matrix = [[\"1\",\"0\",\"1\",\"0\",\"0\"],[\"1\",\"0\",\"1\",\"1\",\"1\"],[\"1\",\"1\",\"1\",\"1\",\"1\"],[\"1\",\"0\",\"0\",\"1\",\"0\"]]\nOutput: 6\nExplanation: The maximal rectangle is shown in the above picture.\n\nExample 2:\n\nInput: matrix = [[\"0\"]]\nOutput: 0\n\nExample 3:\n\nInput: matrix = [[\"1\"]]\nOutput: 1\n\n \nConstraints:\n\nrows == matrix.length\ncols == matrix[i].length\n1 <= row, cols <= 200\nmatrix[i][j] is '0' or '1'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [['1']]) == 1\n assert candidate(matrix = [['0', '1', '0', '1'], ['1', '0', '1', '0'], ['0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1'], ['1', '1']]) == 4\n assert candidate(matrix = [['0']]) == 0\n assert candidate(matrix = [['1', '1', '0', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['0', '0', '1', '1', '1']]) == 10\n assert candidate(matrix = [['0', '0', '0'], ['0', '0', '0']]) == 0\n assert candidate(matrix = [['1', '0', '1', '0', '0'], ['1', '0', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '1', '0']]) == 6\n assert candidate(matrix = [['1', '1', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1']]) == 16\n assert candidate(matrix = [['1', '0'], ['0', '1']]) == 1\n assert candidate(matrix = [['1', '0', '1'], ['0', '0', '1'], ['1', '0', '1']]) == 3\n assert candidate(matrix = [['1', '1', '1'], ['1', '1', '1'], ['1', '1', '1']]) == 9\n assert candidate(matrix = [['0', '0'], ['0', '0']]) == 0\n assert candidate(matrix = [['1', '1', '0', '1'], ['1', '1', '0', '1'], ['1', '1', '1', '1']]) == 6\n assert candidate(matrix = [['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '0', '0'], ['1', '1', '0', '0']]) == 8\n assert candidate(matrix = [['0', '1', '1', '0'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['0', '1', '1', '0']]) == 8\n assert candidate(matrix = [['1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '1', '0'], ['1', '1', '1', '1', '1']]) == 5\n assert candidate(matrix = [['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '0', '0', '1'], ['1', '0', '0', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1']]) == 8\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1']]) == 16\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 10\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '0', '1'], ['1', '0', '0', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 10\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 30\n assert candidate(matrix = [['0', '1', '0', '1'], ['1', '0', '1', '0'], ['0', '1', '0', '1'], ['1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '1', '0', '1'], ['1', '1', '1', '1'], ['0', '1', '1', '0'], ['1', '1', '1', '1'], ['1', '0', '1', '0']]) == 6\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 25\n assert candidate(matrix = [['1', '1', '0', '0'], ['1', '1', '0', '0'], ['0', '0', '1', '1'], ['0', '0', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '0', '0', '0', '0', '1', '1'], ['1', '1', '1', '1', '0', '0', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 16\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1']]) == 10\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1', '0', '0', '1'], ['1', '1', '1', '1', '1'], ['0', '1', '0', '1', '0'], ['1', '1', '1', '1', '1']]) == 5\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '0', '1'], ['1', '0', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1']]) == 6\n assert candidate(matrix = [['0', '0', '0', '0', '0', '0'], ['0', '1', '1', '1', '1', '0'], ['0', '1', '1', '1', '1', '0'], ['0', '1', '1', '1', '1', '0'], ['0', '0', '0', '0', '0', '0']]) == 12\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '0', '1'], ['1', '1', '1', '1', '1']]) == 12\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1']]) == 5\n assert candidate(matrix = [['1', '0', '0', '1', '1', '0', '1'], ['1', '0', '0', '1', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '1', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 10\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '0', '0', '1'], ['1', '1', '0', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 12\n assert candidate(matrix = [['1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1'], ['0', '1', '1', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1']]) == 6\n assert candidate(matrix = [['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1']]) == 10\n assert candidate(matrix = [['1', '1', '1', '1'], ['1', '1', '0', '1'], ['1', '1', '1', '1'], ['0', '1', '1', '1']]) == 6\n assert candidate(matrix = [['0', '1', '1', '1', '0'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['0', '1', '1', '1', '0']]) == 12\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 20\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1']]) == 5\n assert candidate(matrix = [['1', '1', '1'], ['1', '1', '1'], ['1', '1', '1'], ['0', '0', '0'], ['1', '1', '1'], ['1', '1', '1'], ['1', '1', '1']]) == 9\n assert candidate(matrix = [['0', '0', '0', '1', '0'], ['0', '0', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['0', '0', '0', '1', '0']]) == 6\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 7\n assert candidate(matrix = [['1', '1', '0', '0', '1'], ['1', '1', '0', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1']]) == 6\n assert candidate(matrix = [['1', '0', '0', '1', '0'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '1', '0']]) == 10\n assert candidate(matrix = [['0', '1', '1', '0'], ['1', '1', '1', '1'], ['0', '1', '1', '0'], ['1', '1', '1', '1']]) == 8\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '1', '1', '1']]) == 21\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '0', '0', '1', '1']]) == 12\n assert candidate(matrix = [['1', '0', '1', '1'], ['1', '1', '1', '1'], ['0', '1', '1', '1'], ['1', '0', '1', '1']]) == 8\n assert candidate(matrix = [['1', '0', '0', '1'], ['0', '0', '0', '0'], ['1', '0', '0', '1'], ['1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '0', '0'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '0', '0'], ['0', '0', '0', '0', '0']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 15\n assert candidate(matrix = [['1', '1', '1', '1'], ['1', '1', '0', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1']]) == 8\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0'], ['1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0']]) == 6\n assert candidate(matrix = [['0', '1', '1', '1', '0', '0', '1'], ['0', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '0', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1', '0']]) == 10\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '0', '0', '1', '1'], ['1', '1', '0', '0', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1']]) == 16\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['0', '0', '1', '1', '1'], ['0', '0', '1', '1', '1'], ['0', '0', '1', '1', '1']]) == 12\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '0', '0', '0', '1'], ['1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1'], ['1', '0', '0', '0', '1']]) == 4\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1']]) == 5\n assert candidate(matrix = [['0', '0', '0', '0'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['0', '0', '0', '0']]) == 8\n"}, "metadata": {"canonical_parameter_names": ["matrix"], "leetcode_dataset_entry_point": "Solution().maximalRectangle", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maximalRectangle = function(matrix) {", "container": null, "callable": "maximalRectangle", "parameters": [{"name": "matrix", "type": "character[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 86, "task_id": "partition-list", "difficulty": "Medium", "problem_description": "Given the head of a linked list and a value x, partition it such that all nodes less than x come before nodes greater than or equal to x.\nYou should preserve the original relative order of the nodes in each of the two partitions.\n \nExample 1:\n\n\nInput: head = [1,4,3,2,5,2], x = 3\nOutput: [1,2,2,4,3,5]\n\nExample 2:\n\nInput: head = [2,1], x = 2\nOutput: [1,2]\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 200].\n-100 <= Node.val <= 100\n-200 <= x <= 200\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(head = list_node([]),x = 0) == None\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),x = 3), list_node([2, 1, 5, 4, 3]))\n assert is_same_list(candidate(head = list_node([100, -100, 50, 0, -50]),x = 0), list_node([-100, -50, 100, 50, 0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1]),x = 2), list_node([1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),x = 3), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 4, 3, 2, 5, 2]),x = 3), list_node([1, 2, 2, 4, 3, 5]))\n assert is_same_list(candidate(head = list_node([5, 1, 2, 3, 4]),x = 3), list_node([1, 2, 5, 3, 4]))\n assert is_same_list(candidate(head = list_node([-100, 100, 0]),x = 0), list_node([-100, 100, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),x = 6), list_node([1, 2, 3, 4, 5]))\n assert candidate(head = list_node([]),x = 5) == None\n assert is_same_list(candidate(head = list_node([2, 1]),x = 2), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 5), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([100, 50, 0, -50, -100]),x = 0), list_node([-50, -100, 100, 50, 0]))\n assert is_same_list(candidate(head = list_node([200, -200, 100, -100, 50, -50, 0, 25, -25, 75, -75, 125, -125, 150, -150]),x = -50), list_node([-200, -100, -75, -125, -150, 200, 100, 50, -50, 0, 25, -25, 75, 125, 150]))\n assert is_same_list(candidate(head = list_node([10, 5, 10, 5, 10, 5, 10, 5]),x = 7), list_node([5, 5, 5, 5, 10, 10, 10, 10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]),x = 100), list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),x = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 5), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0]),x = 0), list_node([0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),x = 6), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6]))\n assert is_same_list(candidate(head = list_node([10, 10, 10, 5, 5, 5, 1, 1, 1, 0, 0, 0]),x = 5), list_node([1, 1, 1, 0, 0, 0, 10, 10, 10, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),x = 10), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([-50, -40, -30, -20, -10]),x = -25), list_node([-50, -40, -30, -20, -10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0]),x = 0), list_node([0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([100, -100, 50, -50, 25, -25, 0]),x = 0), list_node([-100, -50, -25, 100, 50, 25, 0]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91]),x = 95), list_node([94, 93, 92, 91, 100, 99, 98, 97, 96, 95]))\n assert is_same_list(candidate(head = list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3]),x = 3), list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5]),x = 5), list_node([1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([50, 20, 60, 30, 40, 50, 10, 90]),x = 50), list_node([20, 30, 40, 10, 50, 60, 50, 90]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),x = 5), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),x = 8), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([50, 40, 30, 20, 10, 0, -10, -20, -30, -40]),x = 0), list_node([-10, -20, -30, -40, 50, 40, 30, 20, 10, 0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2]),x = 2), list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),x = 5), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),x = 1), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),x = 5), list_node([4, 3, 2, 1, 10, 9, 8, 7, 6, 5]))\n assert is_same_list(candidate(head = list_node([5, 1, 8, 0, 3, 9, 2, 7]),x = 5), list_node([1, 0, 3, 2, 5, 8, 9, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 5.5), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]),x = 0), list_node([-10, -20, -30, -40, -50, 50, 40, 30, 20, 10, 0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),x = 1), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([2, 2, 2, 2, 2, 1, 1, 1, 1, 1]),x = 2), list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),x = 2), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95]),x = 98), list_node([97, 96, 95, 100, 99, 98]))\n assert is_same_list(candidate(head = list_node([50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]),x = 30), list_node([20, 10, 0, -10, -20, -30, -40, -50, 50, 40, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 11), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 0), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1]),x = 2), list_node([1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7]),x = 8), list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7]))\n assert is_same_list(candidate(head = list_node([3, 3, 3, 3, 3]),x = 3), list_node([3, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0]),x = 4), list_node([3, 2, 1, 0, 9, 8, 7, 6, 5, 4]))\n assert is_same_list(candidate(head = list_node([0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5]),x = 0), list_node([-1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),x = 5), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([100, -100, 50, -50, 25, -25, 75, -75, 0]),x = 0), list_node([-100, -50, -25, -75, 100, 50, 25, 75, 0]))\n assert is_same_list(candidate(head = list_node([5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 5), list_node([1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),x = 0), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 5, 3, 2, 4, 6, 2, 3, 1, 5]),x = 4), list_node([1, 3, 2, 2, 3, 1, 5, 4, 6, 5]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 10]),x = 5), list_node([1, 3, 2, 4, 5, 7, 6, 9, 8, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]),x = 2), list_node([1, 1, 1, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3]))\n assert is_same_list(candidate(head = list_node([50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]),x = -20), list_node([-30, -40, -50, 50, 40, 30, 20, 10, 0, -10, -20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5]),x = 5), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),x = 6), list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6]))\n assert is_same_list(candidate(head = list_node([-50, 50, -50, 50, -50, 50, -50, 50, -50, 50]),x = 0), list_node([-50, -50, -50, -50, -50, 50, 50, 50, 50, 50]))\n assert is_same_list(candidate(head = list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),x = 8), list_node([7, 6, 5, 4, 3, 2, 1, 15, 14, 13, 12, 11, 10, 9, 8]))\n assert is_same_list(candidate(head = list_node([-100, 0, 100, 50, -50, 25, -25]),x = 0), list_node([-100, -50, -25, 0, 100, 50, 25]))\n assert is_same_list(candidate(head = list_node([91, 92, 93, 94, 95, 96, 97, 98, 99, 100]),x = 95), list_node([91, 92, 93, 94, 95, 96, 97, 98, 99, 100]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 5, 6, 7, 8, 9, 10]),x = 7), list_node([1, 3, 2, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),x = 10), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]),x = 6), list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),x = 0), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91]),x = -95), list_node([-100, -99, -98, -97, -96, -95, -94, -93, -92, -91]))\n assert is_same_list(candidate(head = list_node([5, 1, 8, 3, 6, 2, 7, 4]),x = 5), list_node([1, 3, 2, 4, 5, 8, 6, 7]))\n assert is_same_list(candidate(head = list_node([10, 15, 5, 20, 1, 9, 11]),x = 10), list_node([5, 1, 9, 10, 15, 20, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]),x = 5), list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),x = 5), list_node([4, 3, 2, 1, 10, 9, 8, 7, 6, 5]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),x = 0), list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]))\n assert is_same_list(candidate(head = list_node([100, -100, 50, 0, 25, -50]),x = 0), list_node([-100, -50, 100, 50, 0, 25]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),x = 2), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([100, -100, 50, -50, 25, -25, 0, 0, 0, 0]),x = 0), list_node([-100, -50, -25, 100, 50, 25, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),x = 1), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50]),x = 0), list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5]),x = 3), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5]))\n assert is_same_list(candidate(head = list_node([5, 1, 3, 5, 1, 3, 5, 1, 3, 5]),x = 3), list_node([1, 1, 1, 5, 3, 5, 3, 5, 3, 5]))\n assert is_same_list(candidate(head = list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7]),x = 7), list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7]))\n assert is_same_list(candidate(head = list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3]),x = 3), list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 2, 1, 3, 2]),x = 2), list_node([1, 1, 3, 2, 4, 2, 3, 2]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 2, 4, 1, 5, 3, 2, 1]),x = 2), list_node([1, 1, 1, 3, 2, 2, 4, 5, 3, 2]))\n assert is_same_list(candidate(head = list_node([100, -100, 50, -50, 0, 25, -25, 75, -75]),x = 0), list_node([-100, -50, -25, -75, 100, 50, 0, 25, 75]))\n assert is_same_list(candidate(head = list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7]),x = 6), list_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),x = 6), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([7, 3, 5, 8, 5, 10, 2, 1]),x = 5), list_node([3, 2, 1, 7, 5, 8, 5, 10]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]),x = 5), list_node([3, 1, 4, 1, 2, 3, 5, 9, 6, 5, 5]))\n assert is_same_list(candidate(head = list_node([20, 18, 16, 14, 12, 10, 8, 6, 4, 2]),x = 11), list_node([10, 8, 6, 4, 2, 20, 18, 16, 14, 12]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]),x = 0), list_node([-1, -2, -3, -4, -5, 5, 4, 3, 2, 1, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),x = -1), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 2, 5, 4, 3, 2, 1, 0]),x = 2), list_node([1, 1, 0, 3, 2, 2, 5, 4, 3, 2]))\n assert is_same_list(candidate(head = list_node([-5, -3, -1, 0, 2, 4, 6, 8, 10]),x = 0), list_node([-5, -3, -1, 0, 2, 4, 6, 8, 10]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 10]),x = 5), list_node([1, 3, 2, 4, 5, 7, 9, 6, 8, 10]))\n assert is_same_list(candidate(head = list_node([100, 50, 25, 12, 6, 3, 1, -1, -3, -6, -12, -25, -50, -100]),x = 0), list_node([-1, -3, -6, -12, -25, -50, -100, 100, 50, 25, 12, 6, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),x = 0), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 2, 3, 1, 4, 2, 3]),x = 3), list_node([1, 2, 2, 1, 2, 3, 4, 3, 4, 3]))\n assert is_same_list(candidate(head = list_node([10, 10, 10, 10, 10, 10, 10, 10, 10, 10]),x = 5), list_node([10, 10, 10, 10, 10, 10, 10, 10, 10, 10]))\n"}, "metadata": {"canonical_parameter_names": ["head", "x"], "leetcode_dataset_entry_point": "Solution().partition", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var partition = function(head, x) {", "container": null, "callable": "partition", "parameters": [{"name": "head", "type": "ListNode"}, {"name": "x", "type": "number"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 87, "task_id": "scramble-string", "difficulty": "Hard", "problem_description": "We can scramble a string s to get a string t using the following algorithm:\n\nIf the length of the string is 1, stop.\nIf the length of the string is > 1, do the following:\n\t\nSplit the string into two non-empty substrings at a random index, i.e., if the string is s, divide it to x and y where s = x + y.\nRandomly decide to swap the two substrings or to keep them in the same order. i.e., after this step, s may become s = x + y or s = y + x.\nApply step 1 recursively on each of the two substrings x and y.\n\n\n\nGiven two strings s1 and s2 of the same length, return true if s2 is a scrambled string of s1, otherwise, return false.\n \nExample 1:\n\nInput: s1 = \"great\", s2 = \"rgeat\"\nOutput: true\nExplanation: One possible scenario applied on s1 is:\n\"great\" --> \"gr/eat\" // divide at random index.\n\"gr/eat\" --> \"gr/eat\" // random decision is not to swap the two substrings and keep them in order.\n\"gr/eat\" --> \"g/r / e/at\" // apply the same algorithm recursively on both substrings. divide at random index each of them.\n\"g/r / e/at\" --> \"r/g / e/at\" // random decision was to swap the first substring and to keep the second substring in the same order.\n\"r/g / e/at\" --> \"r/g / e/ a/t\" // again apply the algorithm recursively, divide \"at\" to \"a/t\".\n\"r/g / e/ a/t\" --> \"r/g / e/ a/t\" // random decision is to keep both substrings in the same order.\nThe algorithm stops now, and the result string is \"rgeat\" which is s2.\nAs one possible scenario led s1 to be scrambled to s2, we return true.\n\nExample 2:\n\nInput: s1 = \"abcde\", s2 = \"caebd\"\nOutput: false\n\nExample 3:\n\nInput: s1 = \"a\", s2 = \"a\"\nOutput: true\n\n \nConstraints:\n\ns1.length == s2.length\n1 <= s1.length <= 30\ns1 and s2 consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s1 = \"abcdefghij\",s2 = \"ihgfedcbaj\") == True\n assert candidate(s1 = \"noon\",s2 = \"onon\") == True\n assert candidate(s1 = \"abc\",s2 = \"cab\") == True\n assert candidate(s1 = \"abcdefghijklmnop\",s2 = \"ponmlkjihgfedcba\") == True\n assert candidate(s1 = \"abcde\",s2 = \"caebd\") == False\n assert candidate(s1 = \"abcdefghijk\",s2 = \"abcdefghijk\") == True\n assert candidate(s1 = \"abc\",s2 = \"bca\") == True\n assert candidate(s1 = \"abcdefgh\",s2 = \"hgfedcba\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"ijabcdefgh\") == True\n assert candidate(s1 = \"eebaacbcbcadaaedceaaacadccd\",s2 = \"eadcaacabaddaceacbceaabe\") == False\n assert candidate(s1 = \"ab\",s2 = \"ba\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"jihgfedcba\") == True\n assert candidate(s1 = \"aabbcc\",s2 = \"abcabc\") == True\n assert candidate(s1 = \"aabbcc\",s2 = \"ccbbaa\") == True\n assert candidate(s1 = \"great\",s2 = \"rgeat\") == True\n assert candidate(s1 = \"abcd\",s2 = \"abcd\") == True\n assert candidate(s1 = \"abcd\",s2 = \"bdac\") == False\n assert candidate(s1 = \"hello\",s2 = \"lohel\") == True\n assert candidate(s1 = \"abcd\",s2 = \"dcba\") == True\n assert candidate(s1 = \"aabb\",s2 = \"baba\") == True\n assert candidate(s1 = \"abcdefgh\",s2 = \"efghabcd\") == True\n assert candidate(s1 = \"eebaacb\",s2 = \"aceebbb\") == False\n assert candidate(s1 = \"xstjzkfpqczbdy\",s2 = \"bdyxzcqpzkjfst\") == True\n assert candidate(s1 = \"hello\",s2 = \"olelh\") == True\n assert candidate(s1 = \"xyzz\",s2 = \"zzyx\") == True\n assert candidate(s1 = \"xyz\",s2 = \"zyx\") == True\n assert candidate(s1 = \"abcdefg\",s2 = \"efgabcd\") == True\n assert candidate(s1 = \"abcdefghijk\",s2 = \"kabcdefghij\") == True\n assert candidate(s1 = \"a\",s2 = \"a\") == True\n assert candidate(s1 = \"algorithm\",s2 = \"logarithm\") == True\n assert candidate(s1 = \"introduction\",s2 = \"oitrnuduinc\") == False\n assert candidate(s1 = \"abcdabcd\",s2 = \"ddddcccc\") == False\n assert candidate(s1 = \"abcdexyz\",s2 = \"zyxdecba\") == True\n assert candidate(s1 = \"abcdxyz\",s2 = \"yzabcdx\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"efghijklabdc\") == False\n assert candidate(s1 = \"recursion\",s2 = \"rursiicno\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"jihgfecdba\") == True\n assert candidate(s1 = \"abcdefgh\",s2 = \"abcdghfe\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"abijhgfedc\") == True\n assert candidate(s1 = \"xylophone\",s2 = \"eponhloxy\") == True\n assert candidate(s1 = \"abcdefg\",s2 = \"gfedcba\") == True\n assert candidate(s1 = \"scramble\",s2 = \"elmacrbs\") == True\n assert candidate(s1 = \"interview\",s2 = \"wetneivrt\") == False\n assert candidate(s1 = \"abababab\",s2 = \"babababa\") == True\n assert candidate(s1 = \"backtracking\",s2 = \"tcgakknbirn\") == False\n assert candidate(s1 = \"abcdefgh\",s2 = \"ghfedcba\") == True\n assert candidate(s1 = \"abcdexyz\",s2 = \"xyzexbcd\") == False\n assert candidate(s1 = \"abcdefgh\",s2 = \"cdabefgh\") == True\n assert candidate(s1 = \"qwertyuiop\",s2 = \"yuiopqwert\") == True\n assert candidate(s1 = \"intention\",s2 = \"tennotiin\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"jihgfedabc\") == True\n assert candidate(s1 = \"abcd\",s2 = \"cdab\") == True\n assert candidate(s1 = \"scramble\",s2 = \"melbrcsa\") == True\n assert candidate(s1 = \"abcdexyz\",s2 = \"xyzabcde\") == True\n assert candidate(s1 = \"algorithm\",s2 = \"rhtaglmoi\") == False\n assert candidate(s1 = \"optimization\",s2 = \"tivioonpmzas\") == False\n assert candidate(s1 = \"interview\",s2 = \"ewrotnive\") == False\n assert candidate(s1 = \"programming\",s2 = \"gnimmargorp\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"efghabcdij\") == True\n assert candidate(s1 = \"recursion\",s2 = \"suoncire\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"abcdjihgfe\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"fedcbaighj\") == True\n assert candidate(s1 = \"waterbottle\",s2 = \"elbottlewat\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"ghfedcbaab\") == False\n assert candidate(s1 = \"scramble\",s2 = \"leacrbms\") == True\n assert candidate(s1 = \"scramble\",s2 = \"rscmable\") == True\n assert candidate(s1 = \"algorithm\",s2 = \"rhtlgmaoi\") == False\n assert candidate(s1 = \"scrambledstring\",s2 = \"stgimrebldstring\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"mnopqrjkl\") == False\n assert candidate(s1 = \"abcdefghijk\",s2 = \"efghijkabcd\") == True\n assert candidate(s1 = \"abracadabra\",s2 = \"carrabbadaba\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"ihgfedcbaa\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"hgfedcbaij\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"abcdghfjie\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"abcdefghij\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"ihgfjedcba\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"ijklabefgh\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"ghijefabcd\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"ihgfjklmno\") == False\n assert candidate(s1 = \"interview\",s2 = \"reterivne\") == False\n assert candidate(s1 = \"python\",s2 = \"nohtyp\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"bcdefghiaj\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"cdabefghij\") == True\n assert candidate(s1 = \"abcdabcd\",s2 = \"dcbacabd\") == True\n assert candidate(s1 = \"scramble\",s2 = \"blecrmas\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"cbadefghij\") == True\n assert candidate(s1 = \"optimization\",s2 = \"nizationopti\") == False\n assert candidate(s1 = \"intvw\",s2 = \"nvtiw\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"cdefghijab\") == True\n assert candidate(s1 = \"intervw\",s2 = \"wvnreit\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"efghijabcd\") == True\n assert candidate(s1 = \"optimization\",s2 = \"nizaitpmosio\") == False\n assert candidate(s1 = \"algorithm\",s2 = \"rhtgmialo\") == False\n assert candidate(s1 = \"interview\",s2 = \"terviewin\") == True\n assert candidate(s1 = \"abcdabcd\",s2 = \"abcdabcd\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"jabcdefghi\") == True\n assert candidate(s1 = \"abcdefghijk\",s2 = \"kjiabcdefgh\") == True\n assert candidate(s1 = \"abab\",s2 = \"baba\") == True\n assert candidate(s1 = \"scramble\",s2 = \"melcarbs\") == False\n assert candidate(s1 = \"thisisatest\",s2 = \"tsaistestihis\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"fghebacijd\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"ijklabcdefgh\") == False\n assert candidate(s1 = \"scramble\",s2 = \"ercmsbal\") == False\n assert candidate(s1 = \"scramblestring\",s2 = \"gterinmbscrl\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"cbadefghji\") == True\n assert candidate(s1 = \"introduction\",s2 = \"ntrioduicton\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"abjihgfedc\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"abcdefghijab\") == True\n assert candidate(s1 = \"recursion\",s2 = \"insrucero\") == False\n"}, "metadata": {"canonical_parameter_names": ["s1", "s2"], "leetcode_dataset_entry_point": "Solution().isScramble", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isScramble = function(s1, s2) {", "container": null, "callable": "isScramble", "parameters": [{"name": "s1", "type": "string"}, {"name": "s2", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 89, "task_id": "gray-code", "difficulty": "Medium", "problem_description": "An n-bit gray code sequence is a sequence of 2n integers where:\n\nEvery integer is in the inclusive range [0, 2n - 1],\nThe first integer is 0,\nAn integer appears no more than once in the sequence,\nThe binary representation of every pair of adjacent integers differs by exactly one bit, and\nThe binary representation of the first and last integers differs by exactly one bit.\n\nGiven an integer n, return any valid n-bit gray code sequence.\n \nExample 1:\n\nInput: n = 2\nOutput: [0,1,3,2]\nExplanation:\nThe binary representation of [0,1,3,2] is [00,01,11,10].\n- 00 and 01 differ by one bit\n- 01 and 11 differ by one bit\n- 11 and 10 differ by one bit\n- 10 and 00 differ by one bit\n[0,2,3,1] is also a valid gray code sequence, whose binary representation is [00,10,11,01].\n- 00 and 10 differ by one bit\n- 10 and 11 differ by one bit\n- 11 and 01 differ by one bit\n- 01 and 00 differ by one bit\n\nExample 2:\n\nInput: n = 1\nOutput: [0,1]\n\n \nConstraints:\n\n1 <= n <= 16\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == [0, 1, 3, 2, 6, 7, 5, 4]\n assert candidate(n = 4) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8]\n assert candidate(n = 2) == [0, 1, 3, 2]\n assert candidate(n = 1) == [0, 1]\n assert candidate(n = 10) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64, 192, 193, 195, 194, 198, 199, 197, 196, 204, 205, 207, 206, 202, 203, 201, 200, 216, 217, 219, 218, 222, 223, 221, 220, 212, 213, 215, 214, 210, 211, 209, 208, 240, 241, 243, 242, 246, 247, 245, 244, 252, 253, 255, 254, 250, 251, 249, 248, 232, 233, 235, 234, 238, 239, 237, 236, 228, 229, 231, 230, 226, 227, 225, 224, 160, 161, 163, 162, 166, 167, 165, 164, 172, 173, 175, 174, 170, 171, 169, 168, 184, 185, 187, 186, 190, 191, 189, 188, 180, 181, 183, 182, 178, 179, 177, 176, 144, 145, 147, 146, 150, 151, 149, 148, 156, 157, 159, 158, 154, 155, 153, 152, 136, 137, 139, 138, 142, 143, 141, 140, 132, 133, 135, 134, 130, 131, 129, 128, 384, 385, 387, 386, 390, 391, 389, 388, 396, 397, 399, 398, 394, 395, 393, 392, 408, 409, 411, 410, 414, 415, 413, 412, 404, 405, 407, 406, 402, 403, 401, 400, 432, 433, 435, 434, 438, 439, 437, 436, 444, 445, 447, 446, 442, 443, 441, 440, 424, 425, 427, 426, 430, 431, 429, 428, 420, 421, 423, 422, 418, 419, 417, 416, 480, 481, 483, 482, 486, 487, 485, 484, 492, 493, 495, 494, 490, 491, 489, 488, 504, 505, 507, 506, 510, 511, 509, 508, 500, 501, 503, 502, 498, 499, 497, 496, 464, 465, 467, 466, 470, 471, 469, 468, 476, 477, 479, 478, 474, 475, 473, 472, 456, 457, 459, 458, 462, 463, 461, 460, 452, 453, 455, 454, 450, 451, 449, 448, 320, 321, 323, 322, 326, 327, 325, 324, 332, 333, 335, 334, 330, 331, 329, 328, 344, 345, 347, 346, 350, 351, 349, 348, 340, 341, 343, 342, 338, 339, 337, 336, 368, 369, 371, 370, 374, 375, 373, 372, 380, 381, 383, 382, 378, 379, 377, 376, 360, 361, 363, 362, 366, 367, 365, 364, 356, 357, 359, 358, 354, 355, 353, 352, 288, 289, 291, 290, 294, 295, 293, 292, 300, 301, 303, 302, 298, 299, 297, 296, 312, 313, 315, 314, 318, 319, 317, 316, 308, 309, 311, 310, 306, 307, 305, 304, 272, 273, 275, 274, 278, 279, 277, 276, 284, 285, 287, 286, 282, 283, 281, 280, 264, 265, 267, 266, 270, 271, 269, 268, 260, 261, 263, 262, 258, 259, 257, 256, 768, 769, 771, 770, 774, 775, 773, 772, 780, 781, 783, 782, 778, 779, 777, 776, 792, 793, 795, 794, 798, 799, 797, 796, 788, 789, 791, 790, 786, 787, 785, 784, 816, 817, 819, 818, 822, 823, 821, 820, 828, 829, 831, 830, 826, 827, 825, 824, 808, 809, 811, 810, 814, 815, 813, 812, 804, 805, 807, 806, 802, 803, 801, 800, 864, 865, 867, 866, 870, 871, 869, 868, 876, 877, 879, 878, 874, 875, 873, 872, 888, 889, 891, 890, 894, 895, 893, 892, 884, 885, 887, 886, 882, 883, 881, 880, 848, 849, 851, 850, 854, 855, 853, 852, 860, 861, 863, 862, 858, 859, 857, 856, 840, 841, 843, 842, 846, 847, 845, 844, 836, 837, 839, 838, 834, 835, 833, 832, 960, 961, 963, 962, 966, 967, 965, 964, 972, 973, 975, 974, 970, 971, 969, 968, 984, 985, 987, 986, 990, 991, 989, 988, 980, 981, 983, 982, 978, 979, 977, 976, 1008, 1009, 1011, 1010, 1014, 1015, 1013, 1012, 1020, 1021, 1023, 1022, 1018, 1019, 1017, 1016, 1000, 1001, 1003, 1002, 1006, 1007, 1005, 1004, 996, 997, 999, 998, 994, 995, 993, 992, 928, 929, 931, 930, 934, 935, 933, 932, 940, 941, 943, 942, 938, 939, 937, 936, 952, 953, 955, 954, 958, 959, 957, 956, 948, 949, 951, 950, 946, 947, 945, 944, 912, 913, 915, 914, 918, 919, 917, 916, 924, 925, 927, 926, 922, 923, 921, 920, 904, 905, 907, 906, 910, 911, 909, 908, 900, 901, 903, 902, 898, 899, 897, 896, 640, 641, 643, 642, 646, 647, 645, 644, 652, 653, 655, 654, 650, 651, 649, 648, 664, 665, 667, 666, 670, 671, 669, 668, 660, 661, 663, 662, 658, 659, 657, 656, 688, 689, 691, 690, 694, 695, 693, 692, 700, 701, 703, 702, 698, 699, 697, 696, 680, 681, 683, 682, 686, 687, 685, 684, 676, 677, 679, 678, 674, 675, 673, 672, 736, 737, 739, 738, 742, 743, 741, 740, 748, 749, 751, 750, 746, 747, 745, 744, 760, 761, 763, 762, 766, 767, 765, 764, 756, 757, 759, 758, 754, 755, 753, 752, 720, 721, 723, 722, 726, 727, 725, 724, 732, 733, 735, 734, 730, 731, 729, 728, 712, 713, 715, 714, 718, 719, 717, 716, 708, 709, 711, 710, 706, 707, 705, 704, 576, 577, 579, 578, 582, 583, 581, 580, 588, 589, 591, 590, 586, 587, 585, 584, 600, 601, 603, 602, 606, 607, 605, 604, 596, 597, 599, 598, 594, 595, 593, 592, 624, 625, 627, 626, 630, 631, 629, 628, 636, 637, 639, 638, 634, 635, 633, 632, 616, 617, 619, 618, 622, 623, 621, 620, 612, 613, 615, 614, 610, 611, 609, 608, 544, 545, 547, 546, 550, 551, 549, 548, 556, 557, 559, 558, 554, 555, 553, 552, 568, 569, 571, 570, 574, 575, 573, 572, 564, 565, 567, 566, 562, 563, 561, 560, 528, 529, 531, 530, 534, 535, 533, 532, 540, 541, 543, 542, 538, 539, 537, 536, 520, 521, 523, 522, 526, 527, 525, 524, 516, 517, 519, 518, 514, 515, 513, 512]\n assert candidate(n = 5) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16]\n assert candidate(n = 8) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64, 192, 193, 195, 194, 198, 199, 197, 196, 204, 205, 207, 206, 202, 203, 201, 200, 216, 217, 219, 218, 222, 223, 221, 220, 212, 213, 215, 214, 210, 211, 209, 208, 240, 241, 243, 242, 246, 247, 245, 244, 252, 253, 255, 254, 250, 251, 249, 248, 232, 233, 235, 234, 238, 239, 237, 236, 228, 229, 231, 230, 226, 227, 225, 224, 160, 161, 163, 162, 166, 167, 165, 164, 172, 173, 175, 174, 170, 171, 169, 168, 184, 185, 187, 186, 190, 191, 189, 188, 180, 181, 183, 182, 178, 179, 177, 176, 144, 145, 147, 146, 150, 151, 149, 148, 156, 157, 159, 158, 154, 155, 153, 152, 136, 137, 139, 138, 142, 143, 141, 140, 132, 133, 135, 134, 130, 131, 129, 128]\n assert candidate(n = 11) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64, 192, 193, 195, 194, 198, 199, 197, 196, 204, 205, 207, 206, 202, 203, 201, 200, 216, 217, 219, 218, 222, 223, 221, 220, 212, 213, 215, 214, 210, 211, 209, 208, 240, 241, 243, 242, 246, 247, 245, 244, 252, 253, 255, 254, 250, 251, 249, 248, 232, 233, 235, 234, 238, 239, 237, 236, 228, 229, 231, 230, 226, 227, 225, 224, 160, 161, 163, 162, 166, 167, 165, 164, 172, 173, 175, 174, 170, 171, 169, 168, 184, 185, 187, 186, 190, 191, 189, 188, 180, 181, 183, 182, 178, 179, 177, 176, 144, 145, 147, 146, 150, 151, 149, 148, 156, 157, 159, 158, 154, 155, 153, 152, 136, 137, 139, 138, 142, 143, 141, 140, 132, 133, 135, 134, 130, 131, 129, 128, 384, 385, 387, 386, 390, 391, 389, 388, 396, 397, 399, 398, 394, 395, 393, 392, 408, 409, 411, 410, 414, 415, 413, 412, 404, 405, 407, 406, 402, 403, 401, 400, 432, 433, 435, 434, 438, 439, 437, 436, 444, 445, 447, 446, 442, 443, 441, 440, 424, 425, 427, 426, 430, 431, 429, 428, 420, 421, 423, 422, 418, 419, 417, 416, 480, 481, 483, 482, 486, 487, 485, 484, 492, 493, 495, 494, 490, 491, 489, 488, 504, 505, 507, 506, 510, 511, 509, 508, 500, 501, 503, 502, 498, 499, 497, 496, 464, 465, 467, 466, 470, 471, 469, 468, 476, 477, 479, 478, 474, 475, 473, 472, 456, 457, 459, 458, 462, 463, 461, 460, 452, 453, 455, 454, 450, 451, 449, 448, 320, 321, 323, 322, 326, 327, 325, 324, 332, 333, 335, 334, 330, 331, 329, 328, 344, 345, 347, 346, 350, 351, 349, 348, 340, 341, 343, 342, 338, 339, 337, 336, 368, 369, 371, 370, 374, 375, 373, 372, 380, 381, 383, 382, 378, 379, 377, 376, 360, 361, 363, 362, 366, 367, 365, 364, 356, 357, 359, 358, 354, 355, 353, 352, 288, 289, 291, 290, 294, 295, 293, 292, 300, 301, 303, 302, 298, 299, 297, 296, 312, 313, 315, 314, 318, 319, 317, 316, 308, 309, 311, 310, 306, 307, 305, 304, 272, 273, 275, 274, 278, 279, 277, 276, 284, 285, 287, 286, 282, 283, 281, 280, 264, 265, 267, 266, 270, 271, 269, 268, 260, 261, 263, 262, 258, 259, 257, 256, 768, 769, 771, 770, 774, 775, 773, 772, 780, 781, 783, 782, 778, 779, 777, 776, 792, 793, 795, 794, 798, 799, 797, 796, 788, 789, 791, 790, 786, 787, 785, 784, 816, 817, 819, 818, 822, 823, 821, 820, 828, 829, 831, 830, 826, 827, 825, 824, 808, 809, 811, 810, 814, 815, 813, 812, 804, 805, 807, 806, 802, 803, 801, 800, 864, 865, 867, 866, 870, 871, 869, 868, 876, 877, 879, 878, 874, 875, 873, 872, 888, 889, 891, 890, 894, 895, 893, 892, 884, 885, 887, 886, 882, 883, 881, 880, 848, 849, 851, 850, 854, 855, 853, 852, 860, 861, 863, 862, 858, 859, 857, 856, 840, 841, 843, 842, 846, 847, 845, 844, 836, 837, 839, 838, 834, 835, 833, 832, 960, 961, 963, 962, 966, 967, 965, 964, 972, 973, 975, 974, 970, 971, 969, 968, 984, 985, 987, 986, 990, 991, 989, 988, 980, 981, 983, 982, 978, 979, 977, 976, 1008, 1009, 1011, 1010, 1014, 1015, 1013, 1012, 1020, 1021, 1023, 1022, 1018, 1019, 1017, 1016, 1000, 1001, 1003, 1002, 1006, 1007, 1005, 1004, 996, 997, 999, 998, 994, 995, 993, 992, 928, 929, 931, 930, 934, 935, 933, 932, 940, 941, 943, 942, 938, 939, 937, 936, 952, 953, 955, 954, 958, 959, 957, 956, 948, 949, 951, 950, 946, 947, 945, 944, 912, 913, 915, 914, 918, 919, 917, 916, 924, 925, 927, 926, 922, 923, 921, 920, 904, 905, 907, 906, 910, 911, 909, 908, 900, 901, 903, 902, 898, 899, 897, 896, 640, 641, 643, 642, 646, 647, 645, 644, 652, 653, 655, 654, 650, 651, 649, 648, 664, 665, 667, 666, 670, 671, 669, 668, 660, 661, 663, 662, 658, 659, 657, 656, 688, 689, 691, 690, 694, 695, 693, 692, 700, 701, 703, 702, 698, 699, 697, 696, 680, 681, 683, 682, 686, 687, 685, 684, 676, 677, 679, 678, 674, 675, 673, 672, 736, 737, 739, 738, 742, 743, 741, 740, 748, 749, 751, 750, 746, 747, 745, 744, 760, 761, 763, 762, 766, 767, 765, 764, 756, 757, 759, 758, 754, 755, 753, 752, 720, 721, 723, 722, 726, 727, 725, 724, 732, 733, 735, 734, 730, 731, 729, 728, 712, 713, 715, 714, 718, 719, 717, 716, 708, 709, 711, 710, 706, 707, 705, 704, 576, 577, 579, 578, 582, 583, 581, 580, 588, 589, 591, 590, 586, 587, 585, 584, 600, 601, 603, 602, 606, 607, 605, 604, 596, 597, 599, 598, 594, 595, 593, 592, 624, 625, 627, 626, 630, 631, 629, 628, 636, 637, 639, 638, 634, 635, 633, 632, 616, 617, 619, 618, 622, 623, 621, 620, 612, 613, 615, 614, 610, 611, 609, 608, 544, 545, 547, 546, 550, 551, 549, 548, 556, 557, 559, 558, 554, 555, 553, 552, 568, 569, 571, 570, 574, 575, 573, 572, 564, 565, 567, 566, 562, 563, 561, 560, 528, 529, 531, 530, 534, 535, 533, 532, 540, 541, 543, 542, 538, 539, 537, 536, 520, 521, 523, 522, 526, 527, 525, 524, 516, 517, 519, 518, 514, 515, 513, 512, 1536, 1537, 1539, 1538, 1542, 1543, 1541, 1540, 1548, 1549, 1551, 1550, 1546, 1547, 1545, 1544, 1560, 1561, 1563, 1562, 1566, 1567, 1565, 1564, 1556, 1557, 1559, 1558, 1554, 1555, 1553, 1552, 1584, 1585, 1587, 1586, 1590, 1591, 1589, 1588, 1596, 1597, 1599, 1598, 1594, 1595, 1593, 1592, 1576, 1577, 1579, 1578, 1582, 1583, 1581, 1580, 1572, 1573, 1575, 1574, 1570, 1571, 1569, 1568, 1632, 1633, 1635, 1634, 1638, 1639, 1637, 1636, 1644, 1645, 1647, 1646, 1642, 1643, 1641, 1640, 1656, 1657, 1659, 1658, 1662, 1663, 1661, 1660, 1652, 1653, 1655, 1654, 1650, 1651, 1649, 1648, 1616, 1617, 1619, 1618, 1622, 1623, 1621, 1620, 1628, 1629, 1631, 1630, 1626, 1627, 1625, 1624, 1608, 1609, 1611, 1610, 1614, 1615, 1613, 1612, 1604, 1605, 1607, 1606, 1602, 1603, 1601, 1600, 1728, 1729, 1731, 1730, 1734, 1735, 1733, 1732, 1740, 1741, 1743, 1742, 1738, 1739, 1737, 1736, 1752, 1753, 1755, 1754, 1758, 1759, 1757, 1756, 1748, 1749, 1751, 1750, 1746, 1747, 1745, 1744, 1776, 1777, 1779, 1778, 1782, 1783, 1781, 1780, 1788, 1789, 1791, 1790, 1786, 1787, 1785, 1784, 1768, 1769, 1771, 1770, 1774, 1775, 1773, 1772, 1764, 1765, 1767, 1766, 1762, 1763, 1761, 1760, 1696, 1697, 1699, 1698, 1702, 1703, 1701, 1700, 1708, 1709, 1711, 1710, 1706, 1707, 1705, 1704, 1720, 1721, 1723, 1722, 1726, 1727, 1725, 1724, 1716, 1717, 1719, 1718, 1714, 1715, 1713, 1712, 1680, 1681, 1683, 1682, 1686, 1687, 1685, 1684, 1692, 1693, 1695, 1694, 1690, 1691, 1689, 1688, 1672, 1673, 1675, 1674, 1678, 1679, 1677, 1676, 1668, 1669, 1671, 1670, 1666, 1667, 1665, 1664, 1920, 1921, 1923, 1922, 1926, 1927, 1925, 1924, 1932, 1933, 1935, 1934, 1930, 1931, 1929, 1928, 1944, 1945, 1947, 1946, 1950, 1951, 1949, 1948, 1940, 1941, 1943, 1942, 1938, 1939, 1937, 1936, 1968, 1969, 1971, 1970, 1974, 1975, 1973, 1972, 1980, 1981, 1983, 1982, 1978, 1979, 1977, 1976, 1960, 1961, 1963, 1962, 1966, 1967, 1965, 1964, 1956, 1957, 1959, 1958, 1954, 1955, 1953, 1952, 2016, 2017, 2019, 2018, 2022, 2023, 2021, 2020, 2028, 2029, 2031, 2030, 2026, 2027, 2025, 2024, 2040, 2041, 2043, 2042, 2046, 2047, 2045, 2044, 2036, 2037, 2039, 2038, 2034, 2035, 2033, 2032, 2000, 2001, 2003, 2002, 2006, 2007, 2005, 2004, 2012, 2013, 2015, 2014, 2010, 2011, 2009, 2008, 1992, 1993, 1995, 1994, 1998, 1999, 1997, 1996, 1988, 1989, 1991, 1990, 1986, 1987, 1985, 1984, 1856, 1857, 1859, 1858, 1862, 1863, 1861, 1860, 1868, 1869, 1871, 1870, 1866, 1867, 1865, 1864, 1880, 1881, 1883, 1882, 1886, 1887, 1885, 1884, 1876, 1877, 1879, 1878, 1874, 1875, 1873, 1872, 1904, 1905, 1907, 1906, 1910, 1911, 1909, 1908, 1916, 1917, 1919, 1918, 1914, 1915, 1913, 1912, 1896, 1897, 1899, 1898, 1902, 1903, 1901, 1900, 1892, 1893, 1895, 1894, 1890, 1891, 1889, 1888, 1824, 1825, 1827, 1826, 1830, 1831, 1829, 1828, 1836, 1837, 1839, 1838, 1834, 1835, 1833, 1832, 1848, 1849, 1851, 1850, 1854, 1855, 1853, 1852, 1844, 1845, 1847, 1846, 1842, 1843, 1841, 1840, 1808, 1809, 1811, 1810, 1814, 1815, 1813, 1812, 1820, 1821, 1823, 1822, 1818, 1819, 1817, 1816, 1800, 1801, 1803, 1802, 1806, 1807, 1805, 1804, 1796, 1797, 1799, 1798, 1794, 1795, 1793, 1792, 1280, 1281, 1283, 1282, 1286, 1287, 1285, 1284, 1292, 1293, 1295, 1294, 1290, 1291, 1289, 1288, 1304, 1305, 1307, 1306, 1310, 1311, 1309, 1308, 1300, 1301, 1303, 1302, 1298, 1299, 1297, 1296, 1328, 1329, 1331, 1330, 1334, 1335, 1333, 1332, 1340, 1341, 1343, 1342, 1338, 1339, 1337, 1336, 1320, 1321, 1323, 1322, 1326, 1327, 1325, 1324, 1316, 1317, 1319, 1318, 1314, 1315, 1313, 1312, 1376, 1377, 1379, 1378, 1382, 1383, 1381, 1380, 1388, 1389, 1391, 1390, 1386, 1387, 1385, 1384, 1400, 1401, 1403, 1402, 1406, 1407, 1405, 1404, 1396, 1397, 1399, 1398, 1394, 1395, 1393, 1392, 1360, 1361, 1363, 1362, 1366, 1367, 1365, 1364, 1372, 1373, 1375, 1374, 1370, 1371, 1369, 1368, 1352, 1353, 1355, 1354, 1358, 1359, 1357, 1356, 1348, 1349, 1351, 1350, 1346, 1347, 1345, 1344, 1472, 1473, 1475, 1474, 1478, 1479, 1477, 1476, 1484, 1485, 1487, 1486, 1482, 1483, 1481, 1480, 1496, 1497, 1499, 1498, 1502, 1503, 1501, 1500, 1492, 1493, 1495, 1494, 1490, 1491, 1489, 1488, 1520, 1521, 1523, 1522, 1526, 1527, 1525, 1524, 1532, 1533, 1535, 1534, 1530, 1531, 1529, 1528, 1512, 1513, 1515, 1514, 1518, 1519, 1517, 1516, 1508, 1509, 1511, 1510, 1506, 1507, 1505, 1504, 1440, 1441, 1443, 1442, 1446, 1447, 1445, 1444, 1452, 1453, 1455, 1454, 1450, 1451, 1449, 1448, 1464, 1465, 1467, 1466, 1470, 1471, 1469, 1468, 1460, 1461, 1463, 1462, 1458, 1459, 1457, 1456, 1424, 1425, 1427, 1426, 1430, 1431, 1429, 1428, 1436, 1437, 1439, 1438, 1434, 1435, 1433, 1432, 1416, 1417, 1419, 1418, 1422, 1423, 1421, 1420, 1412, 1413, 1415, 1414, 1410, 1411, 1409, 1408, 1152, 1153, 1155, 1154, 1158, 1159, 1157, 1156, 1164, 1165, 1167, 1166, 1162, 1163, 1161, 1160, 1176, 1177, 1179, 1178, 1182, 1183, 1181, 1180, 1172, 1173, 1175, 1174, 1170, 1171, 1169, 1168, 1200, 1201, 1203, 1202, 1206, 1207, 1205, 1204, 1212, 1213, 1215, 1214, 1210, 1211, 1209, 1208, 1192, 1193, 1195, 1194, 1198, 1199, 1197, 1196, 1188, 1189, 1191, 1190, 1186, 1187, 1185, 1184, 1248, 1249, 1251, 1250, 1254, 1255, 1253, 1252, 1260, 1261, 1263, 1262, 1258, 1259, 1257, 1256, 1272, 1273, 1275, 1274, 1278, 1279, 1277, 1276, 1268, 1269, 1271, 1270, 1266, 1267, 1265, 1264, 1232, 1233, 1235, 1234, 1238, 1239, 1237, 1236, 1244, 1245, 1247, 1246, 1242, 1243, 1241, 1240, 1224, 1225, 1227, 1226, 1230, 1231, 1229, 1228, 1220, 1221, 1223, 1222, 1218, 1219, 1217, 1216, 1088, 1089, 1091, 1090, 1094, 1095, 1093, 1092, 1100, 1101, 1103, 1102, 1098, 1099, 1097, 1096, 1112, 1113, 1115, 1114, 1118, 1119, 1117, 1116, 1108, 1109, 1111, 1110, 1106, 1107, 1105, 1104, 1136, 1137, 1139, 1138, 1142, 1143, 1141, 1140, 1148, 1149, 1151, 1150, 1146, 1147, 1145, 1144, 1128, 1129, 1131, 1130, 1134, 1135, 1133, 1132, 1124, 1125, 1127, 1126, 1122, 1123, 1121, 1120, 1056, 1057, 1059, 1058, 1062, 1063, 1061, 1060, 1068, 1069, 1071, 1070, 1066, 1067, 1065, 1064, 1080, 1081, 1083, 1082, 1086, 1087, 1085, 1084, 1076, 1077, 1079, 1078, 1074, 1075, 1073, 1072, 1040, 1041, 1043, 1042, 1046, 1047, 1045, 1044, 1052, 1053, 1055, 1054, 1050, 1051, 1049, 1048, 1032, 1033, 1035, 1034, 1038, 1039, 1037, 1036, 1028, 1029, 1031, 1030, 1026, 1027, 1025, 1024]\n assert candidate(n = 12) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64, 192, 193, 195, 194, 198, 199, 197, 196, 204, 205, 207, 206, 202, 203, 201, 200, 216, 217, 219, 218, 222, 223, 221, 220, 212, 213, 215, 214, 210, 211, 209, 208, 240, 241, 243, 242, 246, 247, 245, 244, 252, 253, 255, 254, 250, 251, 249, 248, 232, 233, 235, 234, 238, 239, 237, 236, 228, 229, 231, 230, 226, 227, 225, 224, 160, 161, 163, 162, 166, 167, 165, 164, 172, 173, 175, 174, 170, 171, 169, 168, 184, 185, 187, 186, 190, 191, 189, 188, 180, 181, 183, 182, 178, 179, 177, 176, 144, 145, 147, 146, 150, 151, 149, 148, 156, 157, 159, 158, 154, 155, 153, 152, 136, 137, 139, 138, 142, 143, 141, 140, 132, 133, 135, 134, 130, 131, 129, 128, 384, 385, 387, 386, 390, 391, 389, 388, 396, 397, 399, 398, 394, 395, 393, 392, 408, 409, 411, 410, 414, 415, 413, 412, 404, 405, 407, 406, 402, 403, 401, 400, 432, 433, 435, 434, 438, 439, 437, 436, 444, 445, 447, 446, 442, 443, 441, 440, 424, 425, 427, 426, 430, 431, 429, 428, 420, 421, 423, 422, 418, 419, 417, 416, 480, 481, 483, 482, 486, 487, 485, 484, 492, 493, 495, 494, 490, 491, 489, 488, 504, 505, 507, 506, 510, 511, 509, 508, 500, 501, 503, 502, 498, 499, 497, 496, 464, 465, 467, 466, 470, 471, 469, 468, 476, 477, 479, 478, 474, 475, 473, 472, 456, 457, 459, 458, 462, 463, 461, 460, 452, 453, 455, 454, 450, 451, 449, 448, 320, 321, 323, 322, 326, 327, 325, 324, 332, 333, 335, 334, 330, 331, 329, 328, 344, 345, 347, 346, 350, 351, 349, 348, 340, 341, 343, 342, 338, 339, 337, 336, 368, 369, 371, 370, 374, 375, 373, 372, 380, 381, 383, 382, 378, 379, 377, 376, 360, 361, 363, 362, 366, 367, 365, 364, 356, 357, 359, 358, 354, 355, 353, 352, 288, 289, 291, 290, 294, 295, 293, 292, 300, 301, 303, 302, 298, 299, 297, 296, 312, 313, 315, 314, 318, 319, 317, 316, 308, 309, 311, 310, 306, 307, 305, 304, 272, 273, 275, 274, 278, 279, 277, 276, 284, 285, 287, 286, 282, 283, 281, 280, 264, 265, 267, 266, 270, 271, 269, 268, 260, 261, 263, 262, 258, 259, 257, 256, 768, 769, 771, 770, 774, 775, 773, 772, 780, 781, 783, 782, 778, 779, 777, 776, 792, 793, 795, 794, 798, 799, 797, 796, 788, 789, 791, 790, 786, 787, 785, 784, 816, 817, 819, 818, 822, 823, 821, 820, 828, 829, 831, 830, 826, 827, 825, 824, 808, 809, 811, 810, 814, 815, 813, 812, 804, 805, 807, 806, 802, 803, 801, 800, 864, 865, 867, 866, 870, 871, 869, 868, 876, 877, 879, 878, 874, 875, 873, 872, 888, 889, 891, 890, 894, 895, 893, 892, 884, 885, 887, 886, 882, 883, 881, 880, 848, 849, 851, 850, 854, 855, 853, 852, 860, 861, 863, 862, 858, 859, 857, 856, 840, 841, 843, 842, 846, 847, 845, 844, 836, 837, 839, 838, 834, 835, 833, 832, 960, 961, 963, 962, 966, 967, 965, 964, 972, 973, 975, 974, 970, 971, 969, 968, 984, 985, 987, 986, 990, 991, 989, 988, 980, 981, 983, 982, 978, 979, 977, 976, 1008, 1009, 1011, 1010, 1014, 1015, 1013, 1012, 1020, 1021, 1023, 1022, 1018, 1019, 1017, 1016, 1000, 1001, 1003, 1002, 1006, 1007, 1005, 1004, 996, 997, 999, 998, 994, 995, 993, 992, 928, 929, 931, 930, 934, 935, 933, 932, 940, 941, 943, 942, 938, 939, 937, 936, 952, 953, 955, 954, 958, 959, 957, 956, 948, 949, 951, 950, 946, 947, 945, 944, 912, 913, 915, 914, 918, 919, 917, 916, 924, 925, 927, 926, 922, 923, 921, 920, 904, 905, 907, 906, 910, 911, 909, 908, 900, 901, 903, 902, 898, 899, 897, 896, 640, 641, 643, 642, 646, 647, 645, 644, 652, 653, 655, 654, 650, 651, 649, 648, 664, 665, 667, 666, 670, 671, 669, 668, 660, 661, 663, 662, 658, 659, 657, 656, 688, 689, 691, 690, 694, 695, 693, 692, 700, 701, 703, 702, 698, 699, 697, 696, 680, 681, 683, 682, 686, 687, 685, 684, 676, 677, 679, 678, 674, 675, 673, 672, 736, 737, 739, 738, 742, 743, 741, 740, 748, 749, 751, 750, 746, 747, 745, 744, 760, 761, 763, 762, 766, 767, 765, 764, 756, 757, 759, 758, 754, 755, 753, 752, 720, 721, 723, 722, 726, 727, 725, 724, 732, 733, 735, 734, 730, 731, 729, 728, 712, 713, 715, 714, 718, 719, 717, 716, 708, 709, 711, 710, 706, 707, 705, 704, 576, 577, 579, 578, 582, 583, 581, 580, 588, 589, 591, 590, 586, 587, 585, 584, 600, 601, 603, 602, 606, 607, 605, 604, 596, 597, 599, 598, 594, 595, 593, 592, 624, 625, 627, 626, 630, 631, 629, 628, 636, 637, 639, 638, 634, 635, 633, 632, 616, 617, 619, 618, 622, 623, 621, 620, 612, 613, 615, 614, 610, 611, 609, 608, 544, 545, 547, 546, 550, 551, 549, 548, 556, 557, 559, 558, 554, 555, 553, 552, 568, 569, 571, 570, 574, 575, 573, 572, 564, 565, 567, 566, 562, 563, 561, 560, 528, 529, 531, 530, 534, 535, 533, 532, 540, 541, 543, 542, 538, 539, 537, 536, 520, 521, 523, 522, 526, 527, 525, 524, 516, 517, 519, 518, 514, 515, 513, 512, 1536, 1537, 1539, 1538, 1542, 1543, 1541, 1540, 1548, 1549, 1551, 1550, 1546, 1547, 1545, 1544, 1560, 1561, 1563, 1562, 1566, 1567, 1565, 1564, 1556, 1557, 1559, 1558, 1554, 1555, 1553, 1552, 1584, 1585, 1587, 1586, 1590, 1591, 1589, 1588, 1596, 1597, 1599, 1598, 1594, 1595, 1593, 1592, 1576, 1577, 1579, 1578, 1582, 1583, 1581, 1580, 1572, 1573, 1575, 1574, 1570, 1571, 1569, 1568, 1632, 1633, 1635, 1634, 1638, 1639, 1637, 1636, 1644, 1645, 1647, 1646, 1642, 1643, 1641, 1640, 1656, 1657, 1659, 1658, 1662, 1663, 1661, 1660, 1652, 1653, 1655, 1654, 1650, 1651, 1649, 1648, 1616, 1617, 1619, 1618, 1622, 1623, 1621, 1620, 1628, 1629, 1631, 1630, 1626, 1627, 1625, 1624, 1608, 1609, 1611, 1610, 1614, 1615, 1613, 1612, 1604, 1605, 1607, 1606, 1602, 1603, 1601, 1600, 1728, 1729, 1731, 1730, 1734, 1735, 1733, 1732, 1740, 1741, 1743, 1742, 1738, 1739, 1737, 1736, 1752, 1753, 1755, 1754, 1758, 1759, 1757, 1756, 1748, 1749, 1751, 1750, 1746, 1747, 1745, 1744, 1776, 1777, 1779, 1778, 1782, 1783, 1781, 1780, 1788, 1789, 1791, 1790, 1786, 1787, 1785, 1784, 1768, 1769, 1771, 1770, 1774, 1775, 1773, 1772, 1764, 1765, 1767, 1766, 1762, 1763, 1761, 1760, 1696, 1697, 1699, 1698, 1702, 1703, 1701, 1700, 1708, 1709, 1711, 1710, 1706, 1707, 1705, 1704, 1720, 1721, 1723, 1722, 1726, 1727, 1725, 1724, 1716, 1717, 1719, 1718, 1714, 1715, 1713, 1712, 1680, 1681, 1683, 1682, 1686, 1687, 1685, 1684, 1692, 1693, 1695, 1694, 1690, 1691, 1689, 1688, 1672, 1673, 1675, 1674, 1678, 1679, 1677, 1676, 1668, 1669, 1671, 1670, 1666, 1667, 1665, 1664, 1920, 1921, 1923, 1922, 1926, 1927, 1925, 1924, 1932, 1933, 1935, 1934, 1930, 1931, 1929, 1928, 1944, 1945, 1947, 1946, 1950, 1951, 1949, 1948, 1940, 1941, 1943, 1942, 1938, 1939, 1937, 1936, 1968, 1969, 1971, 1970, 1974, 1975, 1973, 1972, 1980, 1981, 1983, 1982, 1978, 1979, 1977, 1976, 1960, 1961, 1963, 1962, 1966, 1967, 1965, 1964, 1956, 1957, 1959, 1958, 1954, 1955, 1953, 1952, 2016, 2017, 2019, 2018, 2022, 2023, 2021, 2020, 2028, 2029, 2031, 2030, 2026, 2027, 2025, 2024, 2040, 2041, 2043, 2042, 2046, 2047, 2045, 2044, 2036, 2037, 2039, 2038, 2034, 2035, 2033, 2032, 2000, 2001, 2003, 2002, 2006, 2007, 2005, 2004, 2012, 2013, 2015, 2014, 2010, 2011, 2009, 2008, 1992, 1993, 1995, 1994, 1998, 1999, 1997, 1996, 1988, 1989, 1991, 1990, 1986, 1987, 1985, 1984, 1856, 1857, 1859, 1858, 1862, 1863, 1861, 1860, 1868, 1869, 1871, 1870, 1866, 1867, 1865, 1864, 1880, 1881, 1883, 1882, 1886, 1887, 1885, 1884, 1876, 1877, 1879, 1878, 1874, 1875, 1873, 1872, 1904, 1905, 1907, 1906, 1910, 1911, 1909, 1908, 1916, 1917, 1919, 1918, 1914, 1915, 1913, 1912, 1896, 1897, 1899, 1898, 1902, 1903, 1901, 1900, 1892, 1893, 1895, 1894, 1890, 1891, 1889, 1888, 1824, 1825, 1827, 1826, 1830, 1831, 1829, 1828, 1836, 1837, 1839, 1838, 1834, 1835, 1833, 1832, 1848, 1849, 1851, 1850, 1854, 1855, 1853, 1852, 1844, 1845, 1847, 1846, 1842, 1843, 1841, 1840, 1808, 1809, 1811, 1810, 1814, 1815, 1813, 1812, 1820, 1821, 1823, 1822, 1818, 1819, 1817, 1816, 1800, 1801, 1803, 1802, 1806, 1807, 1805, 1804, 1796, 1797, 1799, 1798, 1794, 1795, 1793, 1792, 1280, 1281, 1283, 1282, 1286, 1287, 1285, 1284, 1292, 1293, 1295, 1294, 1290, 1291, 1289, 1288, 1304, 1305, 1307, 1306, 1310, 1311, 1309, 1308, 1300, 1301, 1303, 1302, 1298, 1299, 1297, 1296, 1328, 1329, 1331, 1330, 1334, 1335, 1333, 1332, 1340, 1341, 1343, 1342, 1338, 1339, 1337, 1336, 1320, 1321, 1323, 1322, 1326, 1327, 1325, 1324, 1316, 1317, 1319, 1318, 1314, 1315, 1313, 1312, 1376, 1377, 1379, 1378, 1382, 1383, 1381, 1380, 1388, 1389, 1391, 1390, 1386, 1387, 1385, 1384, 1400, 1401, 1403, 1402, 1406, 1407, 1405, 1404, 1396, 1397, 1399, 1398, 1394, 1395, 1393, 1392, 1360, 1361, 1363, 1362, 1366, 1367, 1365, 1364, 1372, 1373, 1375, 1374, 1370, 1371, 1369, 1368, 1352, 1353, 1355, 1354, 1358, 1359, 1357, 1356, 1348, 1349, 1351, 1350, 1346, 1347, 1345, 1344, 1472, 1473, 1475, 1474, 1478, 1479, 1477, 1476, 1484, 1485, 1487, 1486, 1482, 1483, 1481, 1480, 1496, 1497, 1499, 1498, 1502, 1503, 1501, 1500, 1492, 1493, 1495, 1494, 1490, 1491, 1489, 1488, 1520, 1521, 1523, 1522, 1526, 1527, 1525, 1524, 1532, 1533, 1535, 1534, 1530, 1531, 1529, 1528, 1512, 1513, 1515, 1514, 1518, 1519, 1517, 1516, 1508, 1509, 1511, 1510, 1506, 1507, 1505, 1504, 1440, 1441, 1443, 1442, 1446, 1447, 1445, 1444, 1452, 1453, 1455, 1454, 1450, 1451, 1449, 1448, 1464, 1465, 1467, 1466, 1470, 1471, 1469, 1468, 1460, 1461, 1463, 1462, 1458, 1459, 1457, 1456, 1424, 1425, 1427, 1426, 1430, 1431, 1429, 1428, 1436, 1437, 1439, 1438, 1434, 1435, 1433, 1432, 1416, 1417, 1419, 1418, 1422, 1423, 1421, 1420, 1412, 1413, 1415, 1414, 1410, 1411, 1409, 1408, 1152, 1153, 1155, 1154, 1158, 1159, 1157, 1156, 1164, 1165, 1167, 1166, 1162, 1163, 1161, 1160, 1176, 1177, 1179, 1178, 1182, 1183, 1181, 1180, 1172, 1173, 1175, 1174, 1170, 1171, 1169, 1168, 1200, 1201, 1203, 1202, 1206, 1207, 1205, 1204, 1212, 1213, 1215, 1214, 1210, 1211, 1209, 1208, 1192, 1193, 1195, 1194, 1198, 1199, 1197, 1196, 1188, 1189, 1191, 1190, 1186, 1187, 1185, 1184, 1248, 1249, 1251, 1250, 1254, 1255, 1253, 1252, 1260, 1261, 1263, 1262, 1258, 1259, 1257, 1256, 1272, 1273, 1275, 1274, 1278, 1279, 1277, 1276, 1268, 1269, 1271, 1270, 1266, 1267, 1265, 1264, 1232, 1233, 1235, 1234, 1238, 1239, 1237, 1236, 1244, 1245, 1247, 1246, 1242, 1243, 1241, 1240, 1224, 1225, 1227, 1226, 1230, 1231, 1229, 1228, 1220, 1221, 1223, 1222, 1218, 1219, 1217, 1216, 1088, 1089, 1091, 1090, 1094, 1095, 1093, 1092, 1100, 1101, 1103, 1102, 1098, 1099, 1097, 1096, 1112, 1113, 1115, 1114, 1118, 1119, 1117, 1116, 1108, 1109, 1111, 1110, 1106, 1107, 1105, 1104, 1136, 1137, 1139, 1138, 1142, 1143, 1141, 1140, 1148, 1149, 1151, 1150, 1146, 1147, 1145, 1144, 1128, 1129, 1131, 1130, 1134, 1135, 1133, 1132, 1124, 1125, 1127, 1126, 1122, 1123, 1121, 1120, 1056, 1057, 1059, 1058, 1062, 1063, 1061, 1060, 1068, 1069, 1071, 1070, 1066, 1067, 1065, 1064, 1080, 1081, 1083, 1082, 1086, 1087, 1085, 1084, 1076, 1077, 1079, 1078, 1074, 1075, 1073, 1072, 1040, 1041, 1043, 1042, 1046, 1047, 1045, 1044, 1052, 1053, 1055, 1054, 1050, 1051, 1049, 1048, 1032, 1033, 1035, 1034, 1038, 1039, 1037, 1036, 1028, 1029, 1031, 1030, 1026, 1027, 1025, 1024, 3072, 3073, 3075, 3074, 3078, 3079, 3077, 3076, 3084, 3085, 3087, 3086, 3082, 3083, 3081, 3080, 3096, 3097, 3099, 3098, 3102, 3103, 3101, 3100, 3092, 3093, 3095, 3094, 3090, 3091, 3089, 3088, 3120, 3121, 3123, 3122, 3126, 3127, 3125, 3124, 3132, 3133, 3135, 3134, 3130, 3131, 3129, 3128, 3112, 3113, 3115, 3114, 3118, 3119, 3117, 3116, 3108, 3109, 3111, 3110, 3106, 3107, 3105, 3104, 3168, 3169, 3171, 3170, 3174, 3175, 3173, 3172, 3180, 3181, 3183, 3182, 3178, 3179, 3177, 3176, 3192, 3193, 3195, 3194, 3198, 3199, 3197, 3196, 3188, 3189, 3191, 3190, 3186, 3187, 3185, 3184, 3152, 3153, 3155, 3154, 3158, 3159, 3157, 3156, 3164, 3165, 3167, 3166, 3162, 3163, 3161, 3160, 3144, 3145, 3147, 3146, 3150, 3151, 3149, 3148, 3140, 3141, 3143, 3142, 3138, 3139, 3137, 3136, 3264, 3265, 3267, 3266, 3270, 3271, 3269, 3268, 3276, 3277, 3279, 3278, 3274, 3275, 3273, 3272, 3288, 3289, 3291, 3290, 3294, 3295, 3293, 3292, 3284, 3285, 3287, 3286, 3282, 3283, 3281, 3280, 3312, 3313, 3315, 3314, 3318, 3319, 3317, 3316, 3324, 3325, 3327, 3326, 3322, 3323, 3321, 3320, 3304, 3305, 3307, 3306, 3310, 3311, 3309, 3308, 3300, 3301, 3303, 3302, 3298, 3299, 3297, 3296, 3232, 3233, 3235, 3234, 3238, 3239, 3237, 3236, 3244, 3245, 3247, 3246, 3242, 3243, 3241, 3240, 3256, 3257, 3259, 3258, 3262, 3263, 3261, 3260, 3252, 3253, 3255, 3254, 3250, 3251, 3249, 3248, 3216, 3217, 3219, 3218, 3222, 3223, 3221, 3220, 3228, 3229, 3231, 3230, 3226, 3227, 3225, 3224, 3208, 3209, 3211, 3210, 3214, 3215, 3213, 3212, 3204, 3205, 3207, 3206, 3202, 3203, 3201, 3200, 3456, 3457, 3459, 3458, 3462, 3463, 3461, 3460, 3468, 3469, 3471, 3470, 3466, 3467, 3465, 3464, 3480, 3481, 3483, 3482, 3486, 3487, 3485, 3484, 3476, 3477, 3479, 3478, 3474, 3475, 3473, 3472, 3504, 3505, 3507, 3506, 3510, 3511, 3509, 3508, 3516, 3517, 3519, 3518, 3514, 3515, 3513, 3512, 3496, 3497, 3499, 3498, 3502, 3503, 3501, 3500, 3492, 3493, 3495, 3494, 3490, 3491, 3489, 3488, 3552, 3553, 3555, 3554, 3558, 3559, 3557, 3556, 3564, 3565, 3567, 3566, 3562, 3563, 3561, 3560, 3576, 3577, 3579, 3578, 3582, 3583, 3581, 3580, 3572, 3573, 3575, 3574, 3570, 3571, 3569, 3568, 3536, 3537, 3539, 3538, 3542, 3543, 3541, 3540, 3548, 3549, 3551, 3550, 3546, 3547, 3545, 3544, 3528, 3529, 3531, 3530, 3534, 3535, 3533, 3532, 3524, 3525, 3527, 3526, 3522, 3523, 3521, 3520, 3392, 3393, 3395, 3394, 3398, 3399, 3397, 3396, 3404, 3405, 3407, 3406, 3402, 3403, 3401, 3400, 3416, 3417, 3419, 3418, 3422, 3423, 3421, 3420, 3412, 3413, 3415, 3414, 3410, 3411, 3409, 3408, 3440, 3441, 3443, 3442, 3446, 3447, 3445, 3444, 3452, 3453, 3455, 3454, 3450, 3451, 3449, 3448, 3432, 3433, 3435, 3434, 3438, 3439, 3437, 3436, 3428, 3429, 3431, 3430, 3426, 3427, 3425, 3424, 3360, 3361, 3363, 3362, 3366, 3367, 3365, 3364, 3372, 3373, 3375, 3374, 3370, 3371, 3369, 3368, 3384, 3385, 3387, 3386, 3390, 3391, 3389, 3388, 3380, 3381, 3383, 3382, 3378, 3379, 3377, 3376, 3344, 3345, 3347, 3346, 3350, 3351, 3349, 3348, 3356, 3357, 3359, 3358, 3354, 3355, 3353, 3352, 3336, 3337, 3339, 3338, 3342, 3343, 3341, 3340, 3332, 3333, 3335, 3334, 3330, 3331, 3329, 3328, 3840, 3841, 3843, 3842, 3846, 3847, 3845, 3844, 3852, 3853, 3855, 3854, 3850, 3851, 3849, 3848, 3864, 3865, 3867, 3866, 3870, 3871, 3869, 3868, 3860, 3861, 3863, 3862, 3858, 3859, 3857, 3856, 3888, 3889, 3891, 3890, 3894, 3895, 3893, 3892, 3900, 3901, 3903, 3902, 3898, 3899, 3897, 3896, 3880, 3881, 3883, 3882, 3886, 3887, 3885, 3884, 3876, 3877, 3879, 3878, 3874, 3875, 3873, 3872, 3936, 3937, 3939, 3938, 3942, 3943, 3941, 3940, 3948, 3949, 3951, 3950, 3946, 3947, 3945, 3944, 3960, 3961, 3963, 3962, 3966, 3967, 3965, 3964, 3956, 3957, 3959, 3958, 3954, 3955, 3953, 3952, 3920, 3921, 3923, 3922, 3926, 3927, 3925, 3924, 3932, 3933, 3935, 3934, 3930, 3931, 3929, 3928, 3912, 3913, 3915, 3914, 3918, 3919, 3917, 3916, 3908, 3909, 3911, 3910, 3906, 3907, 3905, 3904, 4032, 4033, 4035, 4034, 4038, 4039, 4037, 4036, 4044, 4045, 4047, 4046, 4042, 4043, 4041, 4040, 4056, 4057, 4059, 4058, 4062, 4063, 4061, 4060, 4052, 4053, 4055, 4054, 4050, 4051, 4049, 4048, 4080, 4081, 4083, 4082, 4086, 4087, 4085, 4084, 4092, 4093, 4095, 4094, 4090, 4091, 4089, 4088, 4072, 4073, 4075, 4074, 4078, 4079, 4077, 4076, 4068, 4069, 4071, 4070, 4066, 4067, 4065, 4064, 4000, 4001, 4003, 4002, 4006, 4007, 4005, 4004, 4012, 4013, 4015, 4014, 4010, 4011, 4009, 4008, 4024, 4025, 4027, 4026, 4030, 4031, 4029, 4028, 4020, 4021, 4023, 4022, 4018, 4019, 4017, 4016, 3984, 3985, 3987, 3986, 3990, 3991, 3989, 3988, 3996, 3997, 3999, 3998, 3994, 3995, 3993, 3992, 3976, 3977, 3979, 3978, 3982, 3983, 3981, 3980, 3972, 3973, 3975, 3974, 3970, 3971, 3969, 3968, 3712, 3713, 3715, 3714, 3718, 3719, 3717, 3716, 3724, 3725, 3727, 3726, 3722, 3723, 3721, 3720, 3736, 3737, 3739, 3738, 3742, 3743, 3741, 3740, 3732, 3733, 3735, 3734, 3730, 3731, 3729, 3728, 3760, 3761, 3763, 3762, 3766, 3767, 3765, 3764, 3772, 3773, 3775, 3774, 3770, 3771, 3769, 3768, 3752, 3753, 3755, 3754, 3758, 3759, 3757, 3756, 3748, 3749, 3751, 3750, 3746, 3747, 3745, 3744, 3808, 3809, 3811, 3810, 3814, 3815, 3813, 3812, 3820, 3821, 3823, 3822, 3818, 3819, 3817, 3816, 3832, 3833, 3835, 3834, 3838, 3839, 3837, 3836, 3828, 3829, 3831, 3830, 3826, 3827, 3825, 3824, 3792, 3793, 3795, 3794, 3798, 3799, 3797, 3796, 3804, 3805, 3807, 3806, 3802, 3803, 3801, 3800, 3784, 3785, 3787, 3786, 3790, 3791, 3789, 3788, 3780, 3781, 3783, 3782, 3778, 3779, 3777, 3776, 3648, 3649, 3651, 3650, 3654, 3655, 3653, 3652, 3660, 3661, 3663, 3662, 3658, 3659, 3657, 3656, 3672, 3673, 3675, 3674, 3678, 3679, 3677, 3676, 3668, 3669, 3671, 3670, 3666, 3667, 3665, 3664, 3696, 3697, 3699, 3698, 3702, 3703, 3701, 3700, 3708, 3709, 3711, 3710, 3706, 3707, 3705, 3704, 3688, 3689, 3691, 3690, 3694, 3695, 3693, 3692, 3684, 3685, 3687, 3686, 3682, 3683, 3681, 3680, 3616, 3617, 3619, 3618, 3622, 3623, 3621, 3620, 3628, 3629, 3631, 3630, 3626, 3627, 3625, 3624, 3640, 3641, 3643, 3642, 3646, 3647, 3645, 3644, 3636, 3637, 3639, 3638, 3634, 3635, 3633, 3632, 3600, 3601, 3603, 3602, 3606, 3607, 3605, 3604, 3612, 3613, 3615, 3614, 3610, 3611, 3609, 3608, 3592, 3593, 3595, 3594, 3598, 3599, 3597, 3596, 3588, 3589, 3591, 3590, 3586, 3587, 3585, 3584, 2560, 2561, 2563, 2562, 2566, 2567, 2565, 2564, 2572, 2573, 2575, 2574, 2570, 2571, 2569, 2568, 2584, 2585, 2587, 2586, 2590, 2591, 2589, 2588, 2580, 2581, 2583, 2582, 2578, 2579, 2577, 2576, 2608, 2609, 2611, 2610, 2614, 2615, 2613, 2612, 2620, 2621, 2623, 2622, 2618, 2619, 2617, 2616, 2600, 2601, 2603, 2602, 2606, 2607, 2605, 2604, 2596, 2597, 2599, 2598, 2594, 2595, 2593, 2592, 2656, 2657, 2659, 2658, 2662, 2663, 2661, 2660, 2668, 2669, 2671, 2670, 2666, 2667, 2665, 2664, 2680, 2681, 2683, 2682, 2686, 2687, 2685, 2684, 2676, 2677, 2679, 2678, 2674, 2675, 2673, 2672, 2640, 2641, 2643, 2642, 2646, 2647, 2645, 2644, 2652, 2653, 2655, 2654, 2650, 2651, 2649, 2648, 2632, 2633, 2635, 2634, 2638, 2639, 2637, 2636, 2628, 2629, 2631, 2630, 2626, 2627, 2625, 2624, 2752, 2753, 2755, 2754, 2758, 2759, 2757, 2756, 2764, 2765, 2767, 2766, 2762, 2763, 2761, 2760, 2776, 2777, 2779, 2778, 2782, 2783, 2781, 2780, 2772, 2773, 2775, 2774, 2770, 2771, 2769, 2768, 2800, 2801, 2803, 2802, 2806, 2807, 2805, 2804, 2812, 2813, 2815, 2814, 2810, 2811, 2809, 2808, 2792, 2793, 2795, 2794, 2798, 2799, 2797, 2796, 2788, 2789, 2791, 2790, 2786, 2787, 2785, 2784, 2720, 2721, 2723, 2722, 2726, 2727, 2725, 2724, 2732, 2733, 2735, 2734, 2730, 2731, 2729, 2728, 2744, 2745, 2747, 2746, 2750, 2751, 2749, 2748, 2740, 2741, 2743, 2742, 2738, 2739, 2737, 2736, 2704, 2705, 2707, 2706, 2710, 2711, 2709, 2708, 2716, 2717, 2719, 2718, 2714, 2715, 2713, 2712, 2696, 2697, 2699, 2698, 2702, 2703, 2701, 2700, 2692, 2693, 2695, 2694, 2690, 2691, 2689, 2688, 2944, 2945, 2947, 2946, 2950, 2951, 2949, 2948, 2956, 2957, 2959, 2958, 2954, 2955, 2953, 2952, 2968, 2969, 2971, 2970, 2974, 2975, 2973, 2972, 2964, 2965, 2967, 2966, 2962, 2963, 2961, 2960, 2992, 2993, 2995, 2994, 2998, 2999, 2997, 2996, 3004, 3005, 3007, 3006, 3002, 3003, 3001, 3000, 2984, 2985, 2987, 2986, 2990, 2991, 2989, 2988, 2980, 2981, 2983, 2982, 2978, 2979, 2977, 2976, 3040, 3041, 3043, 3042, 3046, 3047, 3045, 3044, 3052, 3053, 3055, 3054, 3050, 3051, 3049, 3048, 3064, 3065, 3067, 3066, 3070, 3071, 3069, 3068, 3060, 3061, 3063, 3062, 3058, 3059, 3057, 3056, 3024, 3025, 3027, 3026, 3030, 3031, 3029, 3028, 3036, 3037, 3039, 3038, 3034, 3035, 3033, 3032, 3016, 3017, 3019, 3018, 3022, 3023, 3021, 3020, 3012, 3013, 3015, 3014, 3010, 3011, 3009, 3008, 2880, 2881, 2883, 2882, 2886, 2887, 2885, 2884, 2892, 2893, 2895, 2894, 2890, 2891, 2889, 2888, 2904, 2905, 2907, 2906, 2910, 2911, 2909, 2908, 2900, 2901, 2903, 2902, 2898, 2899, 2897, 2896, 2928, 2929, 2931, 2930, 2934, 2935, 2933, 2932, 2940, 2941, 2943, 2942, 2938, 2939, 2937, 2936, 2920, 2921, 2923, 2922, 2926, 2927, 2925, 2924, 2916, 2917, 2919, 2918, 2914, 2915, 2913, 2912, 2848, 2849, 2851, 2850, 2854, 2855, 2853, 2852, 2860, 2861, 2863, 2862, 2858, 2859, 2857, 2856, 2872, 2873, 2875, 2874, 2878, 2879, 2877, 2876, 2868, 2869, 2871, 2870, 2866, 2867, 2865, 2864, 2832, 2833, 2835, 2834, 2838, 2839, 2837, 2836, 2844, 2845, 2847, 2846, 2842, 2843, 2841, 2840, 2824, 2825, 2827, 2826, 2830, 2831, 2829, 2828, 2820, 2821, 2823, 2822, 2818, 2819, 2817, 2816, 2304, 2305, 2307, 2306, 2310, 2311, 2309, 2308, 2316, 2317, 2319, 2318, 2314, 2315, 2313, 2312, 2328, 2329, 2331, 2330, 2334, 2335, 2333, 2332, 2324, 2325, 2327, 2326, 2322, 2323, 2321, 2320, 2352, 2353, 2355, 2354, 2358, 2359, 2357, 2356, 2364, 2365, 2367, 2366, 2362, 2363, 2361, 2360, 2344, 2345, 2347, 2346, 2350, 2351, 2349, 2348, 2340, 2341, 2343, 2342, 2338, 2339, 2337, 2336, 2400, 2401, 2403, 2402, 2406, 2407, 2405, 2404, 2412, 2413, 2415, 2414, 2410, 2411, 2409, 2408, 2424, 2425, 2427, 2426, 2430, 2431, 2429, 2428, 2420, 2421, 2423, 2422, 2418, 2419, 2417, 2416, 2384, 2385, 2387, 2386, 2390, 2391, 2389, 2388, 2396, 2397, 2399, 2398, 2394, 2395, 2393, 2392, 2376, 2377, 2379, 2378, 2382, 2383, 2381, 2380, 2372, 2373, 2375, 2374, 2370, 2371, 2369, 2368, 2496, 2497, 2499, 2498, 2502, 2503, 2501, 2500, 2508, 2509, 2511, 2510, 2506, 2507, 2505, 2504, 2520, 2521, 2523, 2522, 2526, 2527, 2525, 2524, 2516, 2517, 2519, 2518, 2514, 2515, 2513, 2512, 2544, 2545, 2547, 2546, 2550, 2551, 2549, 2548, 2556, 2557, 2559, 2558, 2554, 2555, 2553, 2552, 2536, 2537, 2539, 2538, 2542, 2543, 2541, 2540, 2532, 2533, 2535, 2534, 2530, 2531, 2529, 2528, 2464, 2465, 2467, 2466, 2470, 2471, 2469, 2468, 2476, 2477, 2479, 2478, 2474, 2475, 2473, 2472, 2488, 2489, 2491, 2490, 2494, 2495, 2493, 2492, 2484, 2485, 2487, 2486, 2482, 2483, 2481, 2480, 2448, 2449, 2451, 2450, 2454, 2455, 2453, 2452, 2460, 2461, 2463, 2462, 2458, 2459, 2457, 2456, 2440, 2441, 2443, 2442, 2446, 2447, 2445, 2444, 2436, 2437, 2439, 2438, 2434, 2435, 2433, 2432, 2176, 2177, 2179, 2178, 2182, 2183, 2181, 2180, 2188, 2189, 2191, 2190, 2186, 2187, 2185, 2184, 2200, 2201, 2203, 2202, 2206, 2207, 2205, 2204, 2196, 2197, 2199, 2198, 2194, 2195, 2193, 2192, 2224, 2225, 2227, 2226, 2230, 2231, 2229, 2228, 2236, 2237, 2239, 2238, 2234, 2235, 2233, 2232, 2216, 2217, 2219, 2218, 2222, 2223, 2221, 2220, 2212, 2213, 2215, 2214, 2210, 2211, 2209, 2208, 2272, 2273, 2275, 2274, 2278, 2279, 2277, 2276, 2284, 2285, 2287, 2286, 2282, 2283, 2281, 2280, 2296, 2297, 2299, 2298, 2302, 2303, 2301, 2300, 2292, 2293, 2295, 2294, 2290, 2291, 2289, 2288, 2256, 2257, 2259, 2258, 2262, 2263, 2261, 2260, 2268, 2269, 2271, 2270, 2266, 2267, 2265, 2264, 2248, 2249, 2251, 2250, 2254, 2255, 2253, 2252, 2244, 2245, 2247, 2246, 2242, 2243, 2241, 2240, 2112, 2113, 2115, 2114, 2118, 2119, 2117, 2116, 2124, 2125, 2127, 2126, 2122, 2123, 2121, 2120, 2136, 2137, 2139, 2138, 2142, 2143, 2141, 2140, 2132, 2133, 2135, 2134, 2130, 2131, 2129, 2128, 2160, 2161, 2163, 2162, 2166, 2167, 2165, 2164, 2172, 2173, 2175, 2174, 2170, 2171, 2169, 2168, 2152, 2153, 2155, 2154, 2158, 2159, 2157, 2156, 2148, 2149, 2151, 2150, 2146, 2147, 2145, 2144, 2080, 2081, 2083, 2082, 2086, 2087, 2085, 2084, 2092, 2093, 2095, 2094, 2090, 2091, 2089, 2088, 2104, 2105, 2107, 2106, 2110, 2111, 2109, 2108, 2100, 2101, 2103, 2102, 2098, 2099, 2097, 2096, 2064, 2065, 2067, 2066, 2070, 2071, 2069, 2068, 2076, 2077, 2079, 2078, 2074, 2075, 2073, 2072, 2056, 2057, 2059, 2058, 2062, 2063, 2061, 2060, 2052, 2053, 2055, 2054, 2050, 2051, 2049, 2048]\n assert candidate(n = 9) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64, 192, 193, 195, 194, 198, 199, 197, 196, 204, 205, 207, 206, 202, 203, 201, 200, 216, 217, 219, 218, 222, 223, 221, 220, 212, 213, 215, 214, 210, 211, 209, 208, 240, 241, 243, 242, 246, 247, 245, 244, 252, 253, 255, 254, 250, 251, 249, 248, 232, 233, 235, 234, 238, 239, 237, 236, 228, 229, 231, 230, 226, 227, 225, 224, 160, 161, 163, 162, 166, 167, 165, 164, 172, 173, 175, 174, 170, 171, 169, 168, 184, 185, 187, 186, 190, 191, 189, 188, 180, 181, 183, 182, 178, 179, 177, 176, 144, 145, 147, 146, 150, 151, 149, 148, 156, 157, 159, 158, 154, 155, 153, 152, 136, 137, 139, 138, 142, 143, 141, 140, 132, 133, 135, 134, 130, 131, 129, 128, 384, 385, 387, 386, 390, 391, 389, 388, 396, 397, 399, 398, 394, 395, 393, 392, 408, 409, 411, 410, 414, 415, 413, 412, 404, 405, 407, 406, 402, 403, 401, 400, 432, 433, 435, 434, 438, 439, 437, 436, 444, 445, 447, 446, 442, 443, 441, 440, 424, 425, 427, 426, 430, 431, 429, 428, 420, 421, 423, 422, 418, 419, 417, 416, 480, 481, 483, 482, 486, 487, 485, 484, 492, 493, 495, 494, 490, 491, 489, 488, 504, 505, 507, 506, 510, 511, 509, 508, 500, 501, 503, 502, 498, 499, 497, 496, 464, 465, 467, 466, 470, 471, 469, 468, 476, 477, 479, 478, 474, 475, 473, 472, 456, 457, 459, 458, 462, 463, 461, 460, 452, 453, 455, 454, 450, 451, 449, 448, 320, 321, 323, 322, 326, 327, 325, 324, 332, 333, 335, 334, 330, 331, 329, 328, 344, 345, 347, 346, 350, 351, 349, 348, 340, 341, 343, 342, 338, 339, 337, 336, 368, 369, 371, 370, 374, 375, 373, 372, 380, 381, 383, 382, 378, 379, 377, 376, 360, 361, 363, 362, 366, 367, 365, 364, 356, 357, 359, 358, 354, 355, 353, 352, 288, 289, 291, 290, 294, 295, 293, 292, 300, 301, 303, 302, 298, 299, 297, 296, 312, 313, 315, 314, 318, 319, 317, 316, 308, 309, 311, 310, 306, 307, 305, 304, 272, 273, 275, 274, 278, 279, 277, 276, 284, 285, 287, 286, 282, 283, 281, 280, 264, 265, 267, 266, 270, 271, 269, 268, 260, 261, 263, 262, 258, 259, 257, 256]\n assert candidate(n = 6) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32]\n assert candidate(n = 7) == [0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64]\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().grayCode", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var grayCode = function(n) {", "container": null, "callable": "grayCode", "parameters": [{"name": "n", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 90, "task_id": "subsets-ii", "difficulty": "Medium", "problem_description": "Given an integer array nums that may contain duplicates, return all possible subsets (the power set).\nThe solution set must not contain duplicate subsets. Return the solution in any order.\n \nExample 1:\nInput: nums = [1,2,2]\nOutput: [[],[1],[1,2],[1,2,2],[2],[2,2]]\nExample 2:\nInput: nums = [0]\nOutput: [[],[0]]\n\n \nConstraints:\n\n1 <= nums.length <= 10\n-10 <= nums[i] <= 10\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-1, 1, -1, 1]) == [[-1, -1, 1, 1], [-1, -1, 1], [-1, -1], [-1, 1, 1], [-1, 1], [-1], [1, 1], [1], []]\n assert candidate(nums = [1, 2, 2, 3]) == [[1, 2, 2, 3], [1, 2, 2], [1, 2, 3], [1, 2], [1, 3], [1], [2, 2, 3], [2, 2], [2, 3], [2], [3], []]\n assert candidate(nums = [1, 1, 2, 2]) == [[1, 1, 2, 2], [1, 1, 2], [1, 1], [1, 2, 2], [1, 2], [1], [2, 2], [2], []]\n assert candidate(nums = [-1, -1, 0, 1, 1, 2]) == [[-1, -1, 0, 1, 1, 2], [-1, -1, 0, 1, 1], [-1, -1, 0, 1, 2], [-1, -1, 0, 1], [-1, -1, 0, 2], [-1, -1, 0], [-1, -1, 1, 1, 2], [-1, -1, 1, 1], [-1, -1, 1, 2], [-1, -1, 1], [-1, -1, 2], [-1, -1], [-1, 0, 1, 1, 2], [-1, 0, 1, 1], [-1, 0, 1, 2], [-1, 0, 1], [-1, 0, 2], [-1, 0], [-1, 1, 1, 2], [-1, 1, 1], [-1, 1, 2], [-1, 1], [-1, 2], [-1], [0, 1, 1, 2], [0, 1, 1], [0, 1, 2], [0, 1], [0, 2], [0], [1, 1, 2], [1, 1], [1, 2], [1], [2], []]\n assert candidate(nums = [1, 1, 2, 2, 3, 3]) == [[1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [1, 2, 3, 4]) == [[1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], [1, 3], [1, 4], [1], [2, 3, 4], [2, 3], [2, 4], [2], [3, 4], [3], [4], []]\n assert candidate(nums = [2, 1, 2]) == [[1, 2, 2], [1, 2], [1], [2, 2], [2], []]\n assert candidate(nums = [1, 2, 2]) == [[1, 2, 2], [1, 2], [1], [2, 2], [2], []]\n assert candidate(nums = [5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5], [5], []]\n assert candidate(nums = [-1, -2, -3, -4, -5]) == [[-5, -4, -3, -2, -1], [-5, -4, -3, -2], [-5, -4, -3, -1], [-5, -4, -3], [-5, -4, -2, -1], [-5, -4, -2], [-5, -4, -1], [-5, -4], [-5, -3, -2, -1], [-5, -3, -2], [-5, -3, -1], [-5, -3], [-5, -2, -1], [-5, -2], [-5, -1], [-5], [-4, -3, -2, -1], [-4, -3, -2], [-4, -3, -1], [-4, -3], [-4, -2, -1], [-4, -2], [-4, -1], [-4], [-3, -2, -1], [-3, -2], [-3, -1], [-3], [-2, -1], [-2], [-1], []]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0], [0], []]\n assert candidate(nums = [1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [1], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [2], [3, 4, 5], [3, 4], [3, 5], [3], [4, 5], [4], [5], []]\n assert candidate(nums = [1, 2, 2, 3, 3]) == [[1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [1, 1, 1, 2, 2, 2]) == [[1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1], [1, 1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 2], [1, 1], [1, 2, 2, 2], [1, 2, 2], [1, 2], [1], [2, 2, 2], [2, 2], [2], []]\n assert candidate(nums = [10, 10, 10]) == [[10, 10, 10], [10, 10], [10], []]\n assert candidate(nums = [0]) == [[0], []]\n assert candidate(nums = [-1, -1, -1, 0]) == [[-1, -1, -1, 0], [-1, -1, -1], [-1, -1, 0], [-1, -1], [-1, 0], [-1], [0], []]\n assert candidate(nums = [0, 0, 0, 0]) == [[0, 0, 0, 0], [0, 0, 0], [0, 0], [0], []]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4]) == [[1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 3, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 3, 4, 4, 4], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 3, 4, 4, 4], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4], [2, 4, 4], [2, 4], [2], [3, 3, 3, 4, 4, 4], [3, 3, 3, 4, 4], [3, 3, 3, 4], [3, 3, 3], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4], [3, 4, 4], [3, 4], [3], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [4, 4, 4, 1, 4]) == [[1, 4, 4, 4, 4], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [4, 4, 4, 4], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [1, 2, 3]) == [[1, 2, 3], [1, 2], [1, 3], [1], [2, 3], [2], [3], []]\n assert candidate(nums = [-1, -1, 2]) == [[-1, -1, 2], [-1, -1], [-1, 2], [-1], [2], []]\n assert candidate(nums = [5]) == [[5], []]\n assert candidate(nums = [2, 2, 2, 2, 2]) == [[2, 2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2], [2, 2], [2], []]\n assert candidate(nums = [-1, 0, 1]) == [[-1, 0, 1], [-1, 0], [-1, 1], [-1], [0, 1], [0], [1], []]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0], [0], []]\n assert candidate(nums = [4, 4, 4, 1, 4]) == [[1, 4, 4, 4, 4], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [4, 4, 4, 4], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8], [1, 2, 4, 9, 10], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 9, 10], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 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5, 8], [3, 5, 9, 10], [3, 5, 9], [3, 5, 10], [3, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8], [3, 6, 9, 10], [3, 6, 9], [3, 6, 10], [3, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8], [3, 7, 9, 10], [3, 7, 9], [3, 7, 10], [3, 7], [3, 8, 9, 10], [3, 8, 9], [3, 8, 10], [3, 8], [3, 9, 10], [3, 9], [3, 10], [3], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [4], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [5], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [6], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [7], [8, 9, 10], [8, 9], [8, 10], [8], [9, 10], [9], [10], []]\n assert candidate(nums = [-2, -2, -1, -1, 0, 0, 1, 1, 2, 2]) == [[-2, -2, -1, -1, 0, 0, 1, 1, 2, 2], [-2, -2, -1, -1, 0, 0, 1, 1, 2], [-2, -2, -1, -1, 0, 0, 1, 1], [-2, -2, -1, -1, 0, 0, 1, 2, 2], [-2, -2, -1, -1, 0, 0, 1, 2], [-2, -2, -1, -1, 0, 0, 1], [-2, -2, -1, -1, 0, 0, 2, 2], [-2, -2, -1, -1, 0, 0, 2], [-2, -2, -1, -1, 0, 0], [-2, -2, -1, -1, 0, 1, 1, 2, 2], [-2, -2, -1, -1, 0, 1, 1, 2], [-2, -2, -1, -1, 0, 1, 1], [-2, -2, -1, -1, 0, 1, 2, 2], [-2, -2, -1, -1, 0, 1, 2], [-2, -2, -1, -1, 0, 1], [-2, -2, -1, -1, 0, 2, 2], [-2, -2, -1, -1, 0, 2], [-2, -2, -1, -1, 0], [-2, -2, -1, -1, 1, 1, 2, 2], [-2, -2, -1, -1, 1, 1, 2], [-2, -2, -1, -1, 1, 1], [-2, -2, -1, -1, 1, 2, 2], [-2, -2, -1, -1, 1, 2], [-2, -2, -1, -1, 1], [-2, -2, -1, -1, 2, 2], [-2, -2, -1, -1, 2], [-2, -2, -1, -1], [-2, -2, -1, 0, 0, 1, 1, 2, 2], [-2, -2, -1, 0, 0, 1, 1, 2], [-2, -2, -1, 0, 0, 1, 1], [-2, -2, -1, 0, 0, 1, 2, 2], [-2, -2, -1, 0, 0, 1, 2], [-2, -2, -1, 0, 0, 1], [-2, -2, -1, 0, 0, 2, 2], [-2, -2, -1, 0, 0, 2], [-2, -2, -1, 0, 0], [-2, -2, -1, 0, 1, 1, 2, 2], [-2, -2, -1, 0, 1, 1, 2], [-2, -2, -1, 0, 1, 1], [-2, -2, -1, 0, 1, 2, 2], [-2, -2, -1, 0, 1, 2], [-2, -2, -1, 0, 1], [-2, -2, -1, 0, 2, 2], [-2, -2, -1, 0, 2], [-2, -2, -1, 0], [-2, -2, -1, 1, 1, 2, 2], [-2, -2, -1, 1, 1, 2], [-2, -2, -1, 1, 1], [-2, -2, -1, 1, 2, 2], [-2, -2, -1, 1, 2], [-2, -2, -1, 1], [-2, -2, -1, 2, 2], [-2, -2, -1, 2], [-2, -2, -1], [-2, -2, 0, 0, 1, 1, 2, 2], [-2, -2, 0, 0, 1, 1, 2], [-2, -2, 0, 0, 1, 1], [-2, -2, 0, 0, 1, 2, 2], [-2, -2, 0, 0, 1, 2], [-2, -2, 0, 0, 1], [-2, -2, 0, 0, 2, 2], [-2, -2, 0, 0, 2], [-2, -2, 0, 0], [-2, -2, 0, 1, 1, 2, 2], [-2, -2, 0, 1, 1, 2], [-2, -2, 0, 1, 1], [-2, -2, 0, 1, 2, 2], [-2, -2, 0, 1, 2], [-2, -2, 0, 1], [-2, -2, 0, 2, 2], [-2, -2, 0, 2], [-2, -2, 0], [-2, -2, 1, 1, 2, 2], [-2, -2, 1, 1, 2], [-2, -2, 1, 1], [-2, -2, 1, 2, 2], [-2, -2, 1, 2], [-2, -2, 1], [-2, -2, 2, 2], [-2, -2, 2], [-2, -2], [-2, -1, -1, 0, 0, 1, 1, 2, 2], [-2, -1, -1, 0, 0, 1, 1, 2], [-2, -1, -1, 0, 0, 1, 1], [-2, -1, -1, 0, 0, 1, 2, 2], [-2, -1, -1, 0, 0, 1, 2], [-2, -1, -1, 0, 0, 1], [-2, -1, -1, 0, 0, 2, 2], [-2, -1, -1, 0, 0, 2], [-2, -1, -1, 0, 0], [-2, -1, -1, 0, 1, 1, 2, 2], [-2, -1, -1, 0, 1, 1, 2], [-2, -1, -1, 0, 1, 1], [-2, -1, -1, 0, 1, 2, 2], [-2, -1, -1, 0, 1, 2], [-2, -1, -1, 0, 1], [-2, -1, -1, 0, 2, 2], [-2, -1, -1, 0, 2], [-2, -1, -1, 0], [-2, -1, -1, 1, 1, 2, 2], [-2, -1, -1, 1, 1, 2], [-2, -1, -1, 1, 1], [-2, -1, -1, 1, 2, 2], [-2, -1, -1, 1, 2], [-2, -1, -1, 1], [-2, -1, -1, 2, 2], [-2, -1, -1, 2], [-2, -1, -1], [-2, -1, 0, 0, 1, 1, 2, 2], [-2, -1, 0, 0, 1, 1, 2], [-2, -1, 0, 0, 1, 1], [-2, -1, 0, 0, 1, 2, 2], [-2, -1, 0, 0, 1, 2], [-2, -1, 0, 0, 1], [-2, -1, 0, 0, 2, 2], [-2, -1, 0, 0, 2], [-2, -1, 0, 0], [-2, -1, 0, 1, 1, 2, 2], [-2, -1, 0, 1, 1, 2], [-2, -1, 0, 1, 1], [-2, -1, 0, 1, 2, 2], [-2, -1, 0, 1, 2], [-2, -1, 0, 1], [-2, -1, 0, 2, 2], [-2, -1, 0, 2], [-2, -1, 0], [-2, -1, 1, 1, 2, 2], [-2, -1, 1, 1, 2], [-2, -1, 1, 1], [-2, -1, 1, 2, 2], [-2, -1, 1, 2], [-2, -1, 1], [-2, -1, 2, 2], [-2, -1, 2], [-2, -1], [-2, 0, 0, 1, 1, 2, 2], [-2, 0, 0, 1, 1, 2], [-2, 0, 0, 1, 1], [-2, 0, 0, 1, 2, 2], [-2, 0, 0, 1, 2], [-2, 0, 0, 1], [-2, 0, 0, 2, 2], [-2, 0, 0, 2], [-2, 0, 0], [-2, 0, 1, 1, 2, 2], [-2, 0, 1, 1, 2], [-2, 0, 1, 1], [-2, 0, 1, 2, 2], [-2, 0, 1, 2], [-2, 0, 1], [-2, 0, 2, 2], [-2, 0, 2], [-2, 0], [-2, 1, 1, 2, 2], [-2, 1, 1, 2], [-2, 1, 1], [-2, 1, 2, 2], [-2, 1, 2], [-2, 1], [-2, 2, 2], [-2, 2], [-2], [-1, -1, 0, 0, 1, 1, 2, 2], [-1, -1, 0, 0, 1, 1, 2], [-1, -1, 0, 0, 1, 1], [-1, -1, 0, 0, 1, 2, 2], [-1, -1, 0, 0, 1, 2], [-1, -1, 0, 0, 1], [-1, -1, 0, 0, 2, 2], [-1, -1, 0, 0, 2], [-1, -1, 0, 0], [-1, -1, 0, 1, 1, 2, 2], [-1, -1, 0, 1, 1, 2], [-1, -1, 0, 1, 1], [-1, -1, 0, 1, 2, 2], [-1, -1, 0, 1, 2], [-1, -1, 0, 1], [-1, -1, 0, 2, 2], [-1, -1, 0, 2], [-1, -1, 0], [-1, -1, 1, 1, 2, 2], [-1, -1, 1, 1, 2], [-1, -1, 1, 1], [-1, -1, 1, 2, 2], [-1, -1, 1, 2], [-1, -1, 1], [-1, -1, 2, 2], [-1, -1, 2], [-1, -1], [-1, 0, 0, 1, 1, 2, 2], [-1, 0, 0, 1, 1, 2], [-1, 0, 0, 1, 1], [-1, 0, 0, 1, 2, 2], [-1, 0, 0, 1, 2], [-1, 0, 0, 1], [-1, 0, 0, 2, 2], [-1, 0, 0, 2], [-1, 0, 0], [-1, 0, 1, 1, 2, 2], [-1, 0, 1, 1, 2], [-1, 0, 1, 1], [-1, 0, 1, 2, 2], [-1, 0, 1, 2], [-1, 0, 1], [-1, 0, 2, 2], [-1, 0, 2], [-1, 0], [-1, 1, 1, 2, 2], [-1, 1, 1, 2], [-1, 1, 1], [-1, 1, 2, 2], [-1, 1, 2], [-1, 1], [-1, 2, 2], [-1, 2], [-1], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2], [0, 0, 1, 1], [0, 0, 1, 2, 2], [0, 0, 1, 2], [0, 0, 1], [0, 0, 2, 2], [0, 0, 2], [0, 0], [0, 1, 1, 2, 2], [0, 1, 1, 2], [0, 1, 1], [0, 1, 2, 2], [0, 1, 2], [0, 1], [0, 2, 2], [0, 2], [0], [1, 1, 2, 2], [1, 1, 2], [1, 1], [1, 2, 2], [1, 2], [1], [2, 2], [2], []]\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == [[-4, -3, -2, -1, 0, 1, 2, 3, 4, 5], [-4, -3, -2, -1, 0, 1, 2, 3, 4], [-4, -3, -2, -1, 0, 1, 2, 3, 5], [-4, -3, -2, -1, 0, 1, 2, 3], [-4, -3, -2, -1, 0, 1, 2, 4, 5], [-4, -3, -2, -1, 0, 1, 2, 4], [-4, -3, -2, -1, 0, 1, 2, 5], [-4, -3, -2, -1, 0, 1, 2], [-4, -3, -2, -1, 0, 1, 3, 4, 5], [-4, -3, -2, -1, 0, 1, 3, 4], [-4, -3, -2, -1, 0, 1, 3, 5], [-4, -3, -2, -1, 0, 1, 3], [-4, -3, -2, -1, 0, 1, 4, 5], [-4, -3, -2, -1, 0, 1, 4], [-4, -3, -2, -1, 0, 1, 5], [-4, -3, -2, -1, 0, 1], [-4, -3, -2, -1, 0, 2, 3, 4, 5], [-4, -3, -2, -1, 0, 2, 3, 4], [-4, -3, -2, -1, 0, 2, 3, 5], [-4, -3, -2, -1, 0, 2, 3], [-4, -3, -2, -1, 0, 2, 4, 5], [-4, -3, -2, -1, 0, 2, 4], [-4, -3, -2, -1, 0, 2, 5], [-4, -3, -2, -1, 0, 2], [-4, -3, -2, -1, 0, 3, 4, 5], [-4, -3, -2, -1, 0, 3, 4], [-4, -3, -2, -1, 0, 3, 5], [-4, -3, -2, -1, 0, 3], [-4, -3, -2, -1, 0, 4, 5], [-4, -3, -2, -1, 0, 4], [-4, -3, -2, -1, 0, 5], [-4, -3, -2, -1, 0], [-4, -3, -2, -1, 1, 2, 3, 4, 5], [-4, -3, -2, -1, 1, 2, 3, 4], [-4, -3, -2, -1, 1, 2, 3, 5], [-4, -3, -2, -1, 1, 2, 3], [-4, -3, -2, -1, 1, 2, 4, 5], [-4, -3, -2, -1, 1, 2, 4], [-4, -3, -2, -1, 1, 2, 5], [-4, -3, -2, -1, 1, 2], [-4, -3, -2, -1, 1, 3, 4, 5], [-4, -3, -2, -1, 1, 3, 4], [-4, -3, -2, -1, 1, 3, 5], [-4, -3, -2, -1, 1, 3], [-4, -3, -2, -1, 1, 4, 5], [-4, -3, -2, -1, 1, 4], [-4, -3, -2, -1, 1, 5], [-4, -3, -2, -1, 1], [-4, -3, -2, -1, 2, 3, 4, 5], [-4, -3, -2, -1, 2, 3, 4], [-4, -3, -2, -1, 2, 3, 5], [-4, -3, -2, -1, 2, 3], [-4, -3, -2, -1, 2, 4, 5], [-4, -3, -2, -1, 2, 4], [-4, -3, -2, -1, 2, 5], [-4, -3, -2, -1, 2], [-4, -3, -2, -1, 3, 4, 5], [-4, -3, -2, -1, 3, 4], [-4, -3, -2, -1, 3, 5], [-4, -3, -2, -1, 3], [-4, -3, -2, -1, 4, 5], [-4, -3, -2, -1, 4], [-4, -3, -2, -1, 5], [-4, -3, -2, -1], [-4, -3, -2, 0, 1, 2, 3, 4, 5], [-4, -3, -2, 0, 1, 2, 3, 4], [-4, -3, -2, 0, 1, 2, 3, 5], [-4, -3, -2, 0, 1, 2, 3], [-4, -3, -2, 0, 1, 2, 4, 5], [-4, -3, -2, 0, 1, 2, 4], [-4, -3, -2, 0, 1, 2, 5], [-4, -3, -2, 0, 1, 2], [-4, -3, -2, 0, 1, 3, 4, 5], [-4, -3, -2, 0, 1, 3, 4], [-4, -3, -2, 0, 1, 3, 5], [-4, -3, -2, 0, 1, 3], [-4, -3, -2, 0, 1, 4, 5], [-4, -3, -2, 0, 1, 4], [-4, -3, -2, 0, 1, 5], [-4, -3, -2, 0, 1], [-4, -3, -2, 0, 2, 3, 4, 5], [-4, -3, -2, 0, 2, 3, 4], [-4, -3, -2, 0, 2, 3, 5], [-4, -3, -2, 0, 2, 3], [-4, -3, -2, 0, 2, 4, 5], [-4, -3, -2, 0, 2, 4], [-4, -3, -2, 0, 2, 5], [-4, -3, -2, 0, 2], [-4, -3, -2, 0, 3, 4, 5], [-4, -3, -2, 0, 3, 4], [-4, -3, -2, 0, 3, 5], [-4, -3, -2, 0, 3], [-4, -3, -2, 0, 4, 5], [-4, -3, -2, 0, 4], [-4, -3, -2, 0, 5], [-4, -3, -2, 0], [-4, -3, -2, 1, 2, 3, 4, 5], [-4, -3, -2, 1, 2, 3, 4], [-4, -3, -2, 1, 2, 3, 5], [-4, -3, -2, 1, 2, 3], [-4, -3, -2, 1, 2, 4, 5], [-4, -3, -2, 1, 2, 4], [-4, -3, -2, 1, 2, 5], [-4, -3, -2, 1, 2], [-4, -3, -2, 1, 3, 4, 5], [-4, -3, -2, 1, 3, 4], [-4, -3, -2, 1, 3, 5], [-4, -3, -2, 1, 3], [-4, -3, -2, 1, 4, 5], [-4, -3, -2, 1, 4], [-4, -3, -2, 1, 5], [-4, -3, -2, 1], [-4, -3, -2, 2, 3, 4, 5], [-4, -3, -2, 2, 3, 4], [-4, -3, -2, 2, 3, 5], [-4, -3, -2, 2, 3], [-4, -3, -2, 2, 4, 5], [-4, -3, -2, 2, 4], [-4, -3, -2, 2, 5], [-4, -3, -2, 2], [-4, -3, -2, 3, 4, 5], [-4, -3, -2, 3, 4], [-4, -3, -2, 3, 5], [-4, -3, -2, 3], [-4, -3, -2, 4, 5], [-4, -3, -2, 4], [-4, -3, -2, 5], [-4, -3, -2], [-4, -3, -1, 0, 1, 2, 3, 4, 5], [-4, -3, -1, 0, 1, 2, 3, 4], [-4, -3, -1, 0, 1, 2, 3, 5], [-4, -3, -1, 0, 1, 2, 3], [-4, -3, -1, 0, 1, 2, 4, 5], [-4, -3, -1, 0, 1, 2, 4], [-4, -3, -1, 0, 1, 2, 5], [-4, -3, -1, 0, 1, 2], [-4, -3, -1, 0, 1, 3, 4, 5], [-4, -3, -1, 0, 1, 3, 4], [-4, -3, -1, 0, 1, 3, 5], [-4, -3, -1, 0, 1, 3], [-4, -3, -1, 0, 1, 4, 5], [-4, -3, -1, 0, 1, 4], [-4, -3, -1, 0, 1, 5], [-4, -3, -1, 0, 1], [-4, -3, -1, 0, 2, 3, 4, 5], [-4, -3, -1, 0, 2, 3, 4], [-4, -3, -1, 0, 2, 3, 5], [-4, -3, -1, 0, 2, 3], [-4, -3, -1, 0, 2, 4, 5], [-4, -3, -1, 0, 2, 4], [-4, -3, -1, 0, 2, 5], [-4, -3, -1, 0, 2], [-4, -3, -1, 0, 3, 4, 5], [-4, -3, -1, 0, 3, 4], [-4, -3, -1, 0, 3, 5], [-4, -3, -1, 0, 3], [-4, -3, -1, 0, 4, 5], [-4, -3, -1, 0, 4], [-4, -3, -1, 0, 5], [-4, -3, -1, 0], [-4, -3, -1, 1, 2, 3, 4, 5], [-4, -3, -1, 1, 2, 3, 4], [-4, -3, -1, 1, 2, 3, 5], [-4, -3, -1, 1, 2, 3], [-4, -3, -1, 1, 2, 4, 5], [-4, -3, -1, 1, 2, 4], [-4, -3, -1, 1, 2, 5], [-4, -3, -1, 1, 2], [-4, -3, -1, 1, 3, 4, 5], [-4, -3, -1, 1, 3, 4], [-4, -3, -1, 1, 3, 5], [-4, -3, -1, 1, 3], [-4, -3, -1, 1, 4, 5], [-4, -3, -1, 1, 4], [-4, -3, -1, 1, 5], [-4, -3, -1, 1], [-4, -3, -1, 2, 3, 4, 5], [-4, -3, -1, 2, 3, 4], [-4, -3, -1, 2, 3, 5], [-4, -3, -1, 2, 3], [-4, -3, -1, 2, 4, 5], [-4, -3, -1, 2, 4], [-4, -3, -1, 2, 5], [-4, -3, -1, 2], [-4, -3, -1, 3, 4, 5], [-4, -3, -1, 3, 4], [-4, -3, -1, 3, 5], [-4, -3, -1, 3], [-4, -3, -1, 4, 5], [-4, -3, -1, 4], [-4, -3, -1, 5], [-4, -3, -1], [-4, -3, 0, 1, 2, 3, 4, 5], [-4, -3, 0, 1, 2, 3, 4], [-4, -3, 0, 1, 2, 3, 5], [-4, -3, 0, 1, 2, 3], [-4, -3, 0, 1, 2, 4, 5], [-4, -3, 0, 1, 2, 4], [-4, -3, 0, 1, 2, 5], [-4, -3, 0, 1, 2], [-4, -3, 0, 1, 3, 4, 5], [-4, -3, 0, 1, 3, 4], [-4, -3, 0, 1, 3, 5], [-4, -3, 0, 1, 3], [-4, -3, 0, 1, 4, 5], [-4, -3, 0, 1, 4], [-4, -3, 0, 1, 5], [-4, -3, 0, 1], [-4, -3, 0, 2, 3, 4, 5], [-4, -3, 0, 2, 3, 4], [-4, -3, 0, 2, 3, 5], [-4, -3, 0, 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5], [-3, -2, 1, 3], [-3, -2, 1, 4, 5], [-3, -2, 1, 4], [-3, -2, 1, 5], [-3, -2, 1], [-3, -2, 2, 3, 4, 5], [-3, -2, 2, 3, 4], [-3, -2, 2, 3, 5], [-3, -2, 2, 3], [-3, -2, 2, 4, 5], [-3, -2, 2, 4], [-3, -2, 2, 5], [-3, -2, 2], [-3, -2, 3, 4, 5], [-3, -2, 3, 4], [-3, -2, 3, 5], [-3, -2, 3], [-3, -2, 4, 5], [-3, -2, 4], [-3, -2, 5], [-3, -2], [-3, -1, 0, 1, 2, 3, 4, 5], [-3, -1, 0, 1, 2, 3, 4], [-3, -1, 0, 1, 2, 3, 5], [-3, -1, 0, 1, 2, 3], [-3, -1, 0, 1, 2, 4, 5], [-3, -1, 0, 1, 2, 4], [-3, -1, 0, 1, 2, 5], [-3, -1, 0, 1, 2], [-3, -1, 0, 1, 3, 4, 5], [-3, -1, 0, 1, 3, 4], [-3, -1, 0, 1, 3, 5], [-3, -1, 0, 1, 3], [-3, -1, 0, 1, 4, 5], [-3, -1, 0, 1, 4], [-3, -1, 0, 1, 5], [-3, -1, 0, 1], [-3, -1, 0, 2, 3, 4, 5], [-3, -1, 0, 2, 3, 4], [-3, -1, 0, 2, 3, 5], [-3, -1, 0, 2, 3], [-3, -1, 0, 2, 4, 5], [-3, -1, 0, 2, 4], [-3, -1, 0, 2, 5], [-3, -1, 0, 2], [-3, -1, 0, 3, 4, 5], [-3, -1, 0, 3, 4], [-3, -1, 0, 3, 5], [-3, -1, 0, 3], [-3, -1, 0, 4, 5], [-3, -1, 0, 4], [-3, -1, 0, 5], [-3, -1, 0], [-3, -1, 1, 2, 3, 4, 5], [-3, -1, 1, 2, 3, 4], [-3, -1, 1, 2, 3, 5], [-3, -1, 1, 2, 3], [-3, -1, 1, 2, 4, 5], [-3, -1, 1, 2, 4], [-3, -1, 1, 2, 5], [-3, -1, 1, 2], [-3, -1, 1, 3, 4, 5], [-3, -1, 1, 3, 4], [-3, -1, 1, 3, 5], [-3, -1, 1, 3], [-3, -1, 1, 4, 5], [-3, -1, 1, 4], [-3, -1, 1, 5], [-3, -1, 1], [-3, -1, 2, 3, 4, 5], [-3, -1, 2, 3, 4], [-3, -1, 2, 3, 5], [-3, -1, 2, 3], [-3, -1, 2, 4, 5], [-3, -1, 2, 4], [-3, -1, 2, 5], [-3, -1, 2], [-3, -1, 3, 4, 5], [-3, -1, 3, 4], [-3, -1, 3, 5], [-3, -1, 3], [-3, -1, 4, 5], [-3, -1, 4], [-3, -1, 5], [-3, -1], [-3, 0, 1, 2, 3, 4, 5], [-3, 0, 1, 2, 3, 4], [-3, 0, 1, 2, 3, 5], [-3, 0, 1, 2, 3], [-3, 0, 1, 2, 4, 5], [-3, 0, 1, 2, 4], [-3, 0, 1, 2, 5], [-3, 0, 1, 2], [-3, 0, 1, 3, 4, 5], [-3, 0, 1, 3, 4], [-3, 0, 1, 3, 5], [-3, 0, 1, 3], [-3, 0, 1, 4, 5], [-3, 0, 1, 4], [-3, 0, 1, 5], [-3, 0, 1], [-3, 0, 2, 3, 4, 5], [-3, 0, 2, 3, 4], [-3, 0, 2, 3, 5], [-3, 0, 2, 3], [-3, 0, 2, 4, 5], [-3, 0, 2, 4], [-3, 0, 2, 5], [-3, 0, 2], [-3, 0, 3, 4, 5], [-3, 0, 3, 4], [-3, 0, 3, 5], [-3, 0, 3], [-3, 0, 4, 5], [-3, 0, 4], [-3, 0, 5], [-3, 0], [-3, 1, 2, 3, 4, 5], [-3, 1, 2, 3, 4], [-3, 1, 2, 3, 5], [-3, 1, 2, 3], [-3, 1, 2, 4, 5], [-3, 1, 2, 4], [-3, 1, 2, 5], [-3, 1, 2], [-3, 1, 3, 4, 5], [-3, 1, 3, 4], [-3, 1, 3, 5], [-3, 1, 3], [-3, 1, 4, 5], [-3, 1, 4], [-3, 1, 5], [-3, 1], [-3, 2, 3, 4, 5], [-3, 2, 3, 4], [-3, 2, 3, 5], [-3, 2, 3], [-3, 2, 4, 5], [-3, 2, 4], [-3, 2, 5], [-3, 2], [-3, 3, 4, 5], [-3, 3, 4], [-3, 3, 5], [-3, 3], [-3, 4, 5], [-3, 4], [-3, 5], [-3], [-2, -1, 0, 1, 2, 3, 4, 5], [-2, -1, 0, 1, 2, 3, 4], [-2, -1, 0, 1, 2, 3, 5], [-2, -1, 0, 1, 2, 3], [-2, -1, 0, 1, 2, 4, 5], [-2, -1, 0, 1, 2, 4], [-2, -1, 0, 1, 2, 5], [-2, -1, 0, 1, 2], [-2, -1, 0, 1, 3, 4, 5], [-2, -1, 0, 1, 3, 4], [-2, -1, 0, 1, 3, 5], [-2, -1, 0, 1, 3], [-2, -1, 0, 1, 4, 5], [-2, -1, 0, 1, 4], [-2, -1, 0, 1, 5], [-2, -1, 0, 1], [-2, -1, 0, 2, 3, 4, 5], [-2, -1, 0, 2, 3, 4], [-2, -1, 0, 2, 3, 5], [-2, -1, 0, 2, 3], [-2, -1, 0, 2, 4, 5], [-2, -1, 0, 2, 4], [-2, -1, 0, 2, 5], [-2, -1, 0, 2], [-2, -1, 0, 3, 4, 5], [-2, -1, 0, 3, 4], [-2, -1, 0, 3, 5], [-2, -1, 0, 3], [-2, -1, 0, 4, 5], [-2, -1, 0, 4], [-2, -1, 0, 5], [-2, -1, 0], [-2, -1, 1, 2, 3, 4, 5], [-2, -1, 1, 2, 3, 4], [-2, -1, 1, 2, 3, 5], [-2, -1, 1, 2, 3], [-2, -1, 1, 2, 4, 5], [-2, -1, 1, 2, 4], [-2, -1, 1, 2, 5], [-2, -1, 1, 2], [-2, -1, 1, 3, 4, 5], [-2, -1, 1, 3, 4], [-2, -1, 1, 3, 5], [-2, -1, 1, 3], [-2, -1, 1, 4, 5], [-2, -1, 1, 4], [-2, -1, 1, 5], [-2, -1, 1], [-2, -1, 2, 3, 4, 5], [-2, -1, 2, 3, 4], [-2, -1, 2, 3, 5], [-2, -1, 2, 3], [-2, -1, 2, 4, 5], [-2, -1, 2, 4], [-2, -1, 2, 5], [-2, -1, 2], [-2, -1, 3, 4, 5], [-2, -1, 3, 4], [-2, -1, 3, 5], [-2, -1, 3], [-2, -1, 4, 5], [-2, -1, 4], [-2, -1, 5], [-2, -1], [-2, 0, 1, 2, 3, 4, 5], [-2, 0, 1, 2, 3, 4], [-2, 0, 1, 2, 3, 5], [-2, 0, 1, 2, 3], [-2, 0, 1, 2, 4, 5], [-2, 0, 1, 2, 4], [-2, 0, 1, 2, 5], [-2, 0, 1, 2], [-2, 0, 1, 3, 4, 5], [-2, 0, 1, 3, 4], [-2, 0, 1, 3, 5], [-2, 0, 1, 3], [-2, 0, 1, 4, 5], [-2, 0, 1, 4], [-2, 0, 1, 5], [-2, 0, 1], [-2, 0, 2, 3, 4, 5], [-2, 0, 2, 3, 4], [-2, 0, 2, 3, 5], [-2, 0, 2, 3], [-2, 0, 2, 4, 5], [-2, 0, 2, 4], [-2, 0, 2, 5], [-2, 0, 2], [-2, 0, 3, 4, 5], [-2, 0, 3, 4], [-2, 0, 3, 5], [-2, 0, 3], [-2, 0, 4, 5], [-2, 0, 4], [-2, 0, 5], [-2, 0], [-2, 1, 2, 3, 4, 5], [-2, 1, 2, 3, 4], [-2, 1, 2, 3, 5], [-2, 1, 2, 3], [-2, 1, 2, 4, 5], [-2, 1, 2, 4], [-2, 1, 2, 5], [-2, 1, 2], [-2, 1, 3, 4, 5], [-2, 1, 3, 4], [-2, 1, 3, 5], [-2, 1, 3], [-2, 1, 4, 5], [-2, 1, 4], [-2, 1, 5], [-2, 1], [-2, 2, 3, 4, 5], [-2, 2, 3, 4], [-2, 2, 3, 5], [-2, 2, 3], [-2, 2, 4, 5], [-2, 2, 4], [-2, 2, 5], [-2, 2], [-2, 3, 4, 5], [-2, 3, 4], [-2, 3, 5], [-2, 3], [-2, 4, 5], [-2, 4], [-2, 5], [-2], [-1, 0, 1, 2, 3, 4, 5], [-1, 0, 1, 2, 3, 4], [-1, 0, 1, 2, 3, 5], [-1, 0, 1, 2, 3], [-1, 0, 1, 2, 4, 5], [-1, 0, 1, 2, 4], [-1, 0, 1, 2, 5], [-1, 0, 1, 2], [-1, 0, 1, 3, 4, 5], [-1, 0, 1, 3, 4], [-1, 0, 1, 3, 5], [-1, 0, 1, 3], [-1, 0, 1, 4, 5], [-1, 0, 1, 4], [-1, 0, 1, 5], [-1, 0, 1], [-1, 0, 2, 3, 4, 5], [-1, 0, 2, 3, 4], [-1, 0, 2, 3, 5], [-1, 0, 2, 3], [-1, 0, 2, 4, 5], [-1, 0, 2, 4], [-1, 0, 2, 5], [-1, 0, 2], [-1, 0, 3, 4, 5], [-1, 0, 3, 4], [-1, 0, 3, 5], [-1, 0, 3], [-1, 0, 4, 5], [-1, 0, 4], [-1, 0, 5], [-1, 0], [-1, 1, 2, 3, 4, 5], [-1, 1, 2, 3, 4], [-1, 1, 2, 3, 5], [-1, 1, 2, 3], [-1, 1, 2, 4, 5], [-1, 1, 2, 4], [-1, 1, 2, 5], [-1, 1, 2], [-1, 1, 3, 4, 5], [-1, 1, 3, 4], [-1, 1, 3, 5], [-1, 1, 3], [-1, 1, 4, 5], [-1, 1, 4], [-1, 1, 5], [-1, 1], [-1, 2, 3, 4, 5], [-1, 2, 3, 4], [-1, 2, 3, 5], [-1, 2, 3], [-1, 2, 4, 5], [-1, 2, 4], [-1, 2, 5], [-1, 2], [-1, 3, 4, 5], [-1, 3, 4], [-1, 3, 5], [-1, 3], [-1, 4, 5], [-1, 4], [-1, 5], [-1], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5], [0, 1, 2, 3], [0, 1, 2, 4, 5], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2], [0, 1, 3, 4, 5], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3], [0, 1, 4, 5], [0, 1, 4], [0, 1, 5], [0, 1], [0, 2, 3, 4, 5], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3], [0, 2, 4, 5], [0, 2, 4], [0, 2, 5], [0, 2], [0, 3, 4, 5], [0, 3, 4], [0, 3, 5], [0, 3], [0, 4, 5], [0, 4], [0, 5], [0], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [1], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [2], [3, 4, 5], [3, 4], [3, 5], [3], [4, 5], [4], [5], []]\n assert candidate(nums = [0, -1, -1, 0, 1, 1, -2, -2]) == [[-2, -2, -1, -1, 0, 0, 1, 1], [-2, -2, -1, -1, 0, 0, 1], [-2, -2, -1, -1, 0, 0], [-2, -2, -1, -1, 0, 1, 1], [-2, -2, -1, -1, 0, 1], [-2, -2, -1, -1, 0], [-2, -2, -1, -1, 1, 1], [-2, -2, -1, -1, 1], [-2, -2, -1, -1], [-2, -2, -1, 0, 0, 1, 1], [-2, -2, -1, 0, 0, 1], [-2, -2, -1, 0, 0], [-2, -2, -1, 0, 1, 1], [-2, -2, -1, 0, 1], [-2, -2, -1, 0], [-2, -2, -1, 1, 1], [-2, -2, -1, 1], [-2, -2, -1], [-2, -2, 0, 0, 1, 1], [-2, -2, 0, 0, 1], [-2, -2, 0, 0], [-2, -2, 0, 1, 1], [-2, -2, 0, 1], [-2, -2, 0], [-2, -2, 1, 1], [-2, -2, 1], [-2, -2], [-2, -1, -1, 0, 0, 1, 1], [-2, -1, -1, 0, 0, 1], [-2, -1, -1, 0, 0], [-2, -1, -1, 0, 1, 1], [-2, -1, -1, 0, 1], [-2, -1, -1, 0], [-2, -1, -1, 1, 1], [-2, -1, -1, 1], [-2, -1, -1], [-2, -1, 0, 0, 1, 1], [-2, -1, 0, 0, 1], [-2, -1, 0, 0], [-2, -1, 0, 1, 1], [-2, -1, 0, 1], [-2, -1, 0], [-2, -1, 1, 1], [-2, -1, 1], [-2, -1], [-2, 0, 0, 1, 1], [-2, 0, 0, 1], [-2, 0, 0], [-2, 0, 1, 1], [-2, 0, 1], [-2, 0], [-2, 1, 1], [-2, 1], [-2], [-1, -1, 0, 0, 1, 1], [-1, -1, 0, 0, 1], [-1, -1, 0, 0], [-1, -1, 0, 1, 1], [-1, -1, 0, 1], [-1, -1, 0], [-1, -1, 1, 1], [-1, -1, 1], [-1, -1], [-1, 0, 0, 1, 1], [-1, 0, 0, 1], [-1, 0, 0], [-1, 0, 1, 1], [-1, 0, 1], [-1, 0], [-1, 1, 1], [-1, 1], [-1], [0, 0, 1, 1], [0, 0, 1], [0, 0], [0, 1, 1], [0, 1], [0], [1, 1], [1], []]\n assert candidate(nums = [4, 4, 4, 3, 3, 2, 2, 1, 1]) == [[1, 1, 2, 2, 3, 3, 4, 4, 4], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 4], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 4], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 4], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 4], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4], [1, 1, 2, 3], [1, 1, 2, 4, 4, 4], [1, 1, 2, 4, 4], [1, 1, 2, 4], [1, 1, 2], [1, 1, 3, 3, 4, 4, 4], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4], [1, 1, 3, 3], [1, 1, 3, 4, 4, 4], [1, 1, 3, 4, 4], [1, 1, 3, 4], [1, 1, 3], [1, 1, 4, 4, 4], [1, 1, 4, 4], [1, 1, 4], [1, 1], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4], [2, 4, 4], [2, 4], [2], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4], [3, 4, 4], [3, 4], [3], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [0, 1, 2, 3, 4, 5]) == [[0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5], [0, 1, 2, 3], [0, 1, 2, 4, 5], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2], [0, 1, 3, 4, 5], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3], [0, 1, 4, 5], [0, 1, 4], [0, 1, 5], [0, 1], [0, 2, 3, 4, 5], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3], [0, 2, 4, 5], [0, 2, 4], [0, 2, 5], [0, 2], [0, 3, 4, 5], [0, 3, 4], [0, 3, 5], [0, 3], [0, 4, 5], [0, 4], [0, 5], [0], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [1], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [2], [3, 4, 5], [3, 4], [3, 5], [3], [4, 5], [4], [5], []]\n assert candidate(nums = [1, 2, 3, 3, 2, 1, 1, 2, 3]) == [[1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3], [1, 1, 1, 3], [1, 1, 1], [1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3, 3], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [1], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [2], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 0]) == [[0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 7], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 6, 7], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5, 6, 7], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 7], [0, 1, 2, 3, 5], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6], [0, 1, 2, 3, 7], [0, 1, 2, 3], [0, 1, 2, 4, 5, 6, 7], [0, 1, 2, 4, 5, 6], [0, 1, 2, 4, 5, 7], [0, 1, 2, 4, 5], [0, 1, 2, 4, 6, 7], [0, 1, 2, 4, 6], [0, 1, 2, 4, 7], [0, 1, 2, 4], [0, 1, 2, 5, 6, 7], [0, 1, 2, 5, 6], [0, 1, 2, 5, 7], [0, 1, 2, 5], [0, 1, 2, 6, 7], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 2], [0, 1, 3, 4, 5, 6, 7], [0, 1, 3, 4, 5, 6], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6], [0, 1, 3, 4, 7], [0, 1, 3, 4], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6], [0, 1, 3, 5, 7], [0, 1, 3, 5], [0, 1, 3, 6, 7], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 3], [0, 1, 4, 5, 6, 7], [0, 1, 4, 5, 6], [0, 1, 4, 5, 7], [0, 1, 4, 5], [0, 1, 4, 6, 7], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 4], [0, 1, 5, 6, 7], [0, 1, 5, 6], [0, 1, 5, 7], [0, 1, 5], [0, 1, 6, 7], [0, 1, 6], [0, 1, 7], [0, 1], [0, 2, 3, 4, 5, 6, 7], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 7], [0, 2, 3, 4, 5], [0, 2, 3, 4, 6, 7], [0, 2, 3, 4, 6], [0, 2, 3, 4, 7], [0, 2, 3, 4], [0, 2, 3, 5, 6, 7], [0, 2, 3, 5, 6], [0, 2, 3, 5, 7], [0, 2, 3, 5], [0, 2, 3, 6, 7], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 3], [0, 2, 4, 5, 6, 7], [0, 2, 4, 5, 6], [0, 2, 4, 5, 7], [0, 2, 4, 5], [0, 2, 4, 6, 7], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 4], [0, 2, 5, 6, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 5], [0, 2, 6, 7], [0, 2, 6], [0, 2, 7], [0, 2], [0, 3, 4, 5, 6, 7], [0, 3, 4, 5, 6], [0, 3, 4, 5, 7], [0, 3, 4, 5], [0, 3, 4, 6, 7], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 4], [0, 3, 5, 6, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 5], [0, 3, 6, 7], [0, 3, 6], [0, 3, 7], [0, 3], [0, 4, 5, 6, 7], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 5], [0, 4, 6, 7], [0, 4, 6], [0, 4, 7], [0, 4], [0, 5, 6, 7], [0, 5, 6], [0, 5, 7], [0, 5], [0, 6, 7], [0, 6], [0, 7], [0], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5], [1, 2, 3, 6, 7], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5], [1, 2, 4, 6, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4], [1, 2, 5, 6, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5], [1, 2, 6, 7], [1, 2, 6], [1, 2, 7], [1, 2], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5], [1, 3, 4, 6, 7], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4], [1, 3, 5, 6, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5], [1, 3, 6, 7], [1, 3, 6], [1, 3, 7], [1, 3], [1, 4, 5, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5], [1, 4, 6, 7], [1, 4, 6], [1, 4, 7], [1, 4], [1, 5, 6, 7], [1, 5, 6], [1, 5, 7], [1, 5], [1, 6, 7], [1, 6], [1, 7], [1], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5], [2, 3, 4, 6, 7], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4], [2, 3, 5, 6, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5], [2, 3, 6, 7], [2, 3, 6], [2, 3, 7], [2, 3], [2, 4, 5, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5], [2, 4, 6, 7], [2, 4, 6], [2, 4, 7], [2, 4], [2, 5, 6, 7], [2, 5, 6], [2, 5, 7], [2, 5], [2, 6, 7], [2, 6], [2, 7], [2], [3, 4, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5], [3, 4, 6, 7], [3, 4, 6], [3, 4, 7], [3, 4], [3, 5, 6, 7], [3, 5, 6], [3, 5, 7], [3, 5], [3, 6, 7], [3, 6], [3, 7], [3], [4, 5, 6, 7], [4, 5, 6], [4, 5, 7], [4, 5], [4, 6, 7], [4, 6], [4, 7], [4], [5, 6, 7], [5, 6], [5, 7], [5], [6, 7], [6], [7], []]\n assert candidate(nums = [1, 2, 2, 3, 3, 3]) == [[1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [2], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [1, 2, 2, 3, 3]) == [[1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 4]) == [[1, 1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 1, 2, 2, 3], [1, 1, 1, 1, 2, 2, 4], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 1, 2, 3, 3], [1, 1, 1, 1, 2, 3, 4], [1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 2, 4], [1, 1, 1, 1, 2], [1, 1, 1, 1, 3, 3, 4], [1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 3, 4], [1, 1, 1, 1, 3], [1, 1, 1, 1, 4], [1, 1, 1, 1], [1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2, 4], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3, 4], [1, 1, 1, 2, 3], [1, 1, 1, 2, 4], [1, 1, 1, 2], [1, 1, 1, 3, 3, 4], [1, 1, 1, 3, 3], [1, 1, 1, 3, 4], [1, 1, 1, 3], [1, 1, 1, 4], [1, 1, 1], [1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3, 4], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2, 4], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4], [1, 1, 2, 3], [1, 1, 2, 4], [1, 1, 2], [1, 1, 3, 3, 4], [1, 1, 3, 3], [1, 1, 3, 4], [1, 1, 3], [1, 1, 4], [1, 1], [1, 2, 2, 2, 3, 3, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4], [1, 3], [1, 4], [1], [2, 2, 2, 3, 3, 4], [2, 2, 2, 3, 3], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4], [2, 2, 2], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4], [2, 3], [2, 4], [2], [3, 3, 4], [3, 3], [3, 4], [3], [4], []]\n assert candidate(nums = [3, 1, 2, 2, 1]) == [[1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3], [1, 1], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3], [1, 2], [1, 3], [1], [2, 2, 3], [2, 2], [2, 3], [2], [3], []]\n assert candidate(nums = [-1, -1, -1, 0, 0, 1, 1]) == [[-1, -1, -1, 0, 0, 1, 1], [-1, -1, -1, 0, 0, 1], [-1, -1, -1, 0, 0], [-1, -1, -1, 0, 1, 1], [-1, -1, -1, 0, 1], [-1, -1, -1, 0], [-1, -1, -1, 1, 1], [-1, -1, -1, 1], [-1, -1, -1], [-1, -1, 0, 0, 1, 1], [-1, -1, 0, 0, 1], [-1, -1, 0, 0], [-1, -1, 0, 1, 1], [-1, -1, 0, 1], [-1, -1, 0], [-1, -1, 1, 1], [-1, -1, 1], [-1, -1], [-1, 0, 0, 1, 1], [-1, 0, 0, 1], [-1, 0, 0], [-1, 0, 1, 1], [-1, 0, 1], [-1, 0], [-1, 1, 1], [-1, 1], [-1], [0, 0, 1, 1], [0, 0, 1], [0, 0], [0, 1, 1], [0, 1], [0], [1, 1], [1], []]\n assert candidate(nums = [-5, -5, -4, -4, -3, -2, -1, 0, 0, 1]) == [[-5, -5, -4, -4, -3, -2, -1, 0, 0, 1], [-5, -5, -4, -4, -3, -2, -1, 0, 0], [-5, -5, -4, -4, -3, -2, -1, 0, 1], [-5, -5, -4, -4, -3, -2, -1, 0], [-5, -5, -4, -4, -3, -2, -1, 1], [-5, -5, -4, -4, -3, -2, -1], [-5, -5, -4, -4, -3, -2, 0, 0, 1], [-5, -5, -4, -4, -3, -2, 0, 0], [-5, -5, -4, -4, -3, -2, 0, 1], [-5, -5, -4, -4, -3, -2, 0], [-5, -5, -4, -4, -3, -2, 1], [-5, -5, -4, -4, -3, -2], [-5, -5, -4, -4, -3, -1, 0, 0, 1], [-5, -5, -4, -4, -3, -1, 0, 0], [-5, -5, -4, -4, -3, -1, 0, 1], [-5, -5, -4, -4, -3, -1, 0], [-5, -5, -4, -4, -3, -1, 1], [-5, -5, -4, -4, -3, -1], [-5, -5, -4, -4, -3, 0, 0, 1], [-5, -5, -4, -4, -3, 0, 0], [-5, -5, -4, -4, -3, 0, 1], [-5, -5, -4, -4, -3, 0], [-5, -5, -4, -4, -3, 1], [-5, -5, -4, -4, -3], [-5, -5, -4, -4, -2, -1, 0, 0, 1], [-5, -5, -4, -4, -2, -1, 0, 0], [-5, -5, -4, -4, -2, -1, 0, 1], [-5, -5, -4, -4, -2, -1, 0], [-5, -5, -4, -4, -2, -1, 1], [-5, -5, -4, -4, -2, -1], [-5, -5, -4, -4, -2, 0, 0, 1], [-5, -5, -4, -4, -2, 0, 0], [-5, -5, -4, -4, -2, 0, 1], [-5, -5, -4, -4, -2, 0], [-5, -5, -4, -4, -2, 1], [-5, -5, -4, -4, -2], [-5, -5, -4, -4, -1, 0, 0, 1], [-5, -5, -4, -4, -1, 0, 0], [-5, -5, -4, -4, -1, 0, 1], [-5, -5, -4, -4, -1, 0], [-5, -5, -4, -4, -1, 1], [-5, -5, -4, -4, -1], [-5, -5, -4, -4, 0, 0, 1], [-5, -5, -4, -4, 0, 0], [-5, -5, -4, -4, 0, 1], [-5, -5, -4, -4, 0], [-5, -5, -4, -4, 1], [-5, -5, -4, -4], [-5, -5, -4, -3, -2, -1, 0, 0, 1], [-5, -5, -4, -3, -2, -1, 0, 0], [-5, -5, -4, -3, -2, -1, 0, 1], [-5, -5, -4, -3, -2, -1, 0], [-5, -5, -4, -3, -2, -1, 1], [-5, -5, -4, -3, -2, -1], [-5, -5, -4, -3, -2, 0, 0, 1], [-5, -5, -4, -3, -2, 0, 0], [-5, -5, -4, -3, -2, 0, 1], [-5, -5, -4, -3, -2, 0], [-5, -5, -4, -3, -2, 1], [-5, -5, -4, -3, -2], [-5, -5, -4, -3, -1, 0, 0, 1], [-5, -5, -4, -3, -1, 0, 0], [-5, -5, -4, -3, -1, 0, 1], [-5, -5, -4, -3, -1, 0], [-5, -5, -4, -3, -1, 1], [-5, -5, -4, -3, -1], [-5, -5, -4, -3, 0, 0, 1], [-5, -5, -4, -3, 0, 0], [-5, -5, -4, -3, 0, 1], [-5, -5, -4, -3, 0], [-5, -5, -4, -3, 1], [-5, -5, -4, -3], [-5, -5, -4, -2, -1, 0, 0, 1], [-5, -5, -4, -2, -1, 0, 0], [-5, -5, -4, -2, -1, 0, 1], [-5, -5, -4, -2, -1, 0], [-5, -5, -4, -2, -1, 1], [-5, -5, -4, -2, -1], [-5, -5, -4, -2, 0, 0, 1], [-5, -5, -4, -2, 0, 0], [-5, -5, -4, -2, 0, 1], [-5, -5, -4, -2, 0], [-5, -5, -4, -2, 1], [-5, -5, -4, -2], [-5, -5, -4, -1, 0, 0, 1], [-5, -5, -4, -1, 0, 0], [-5, -5, -4, -1, 0, 1], [-5, -5, -4, -1, 0], [-5, -5, -4, -1, 1], [-5, -5, -4, -1], [-5, -5, -4, 0, 0, 1], [-5, -5, -4, 0, 0], [-5, -5, -4, 0, 1], [-5, -5, -4, 0], [-5, -5, -4, 1], [-5, -5, -4], [-5, -5, -3, -2, -1, 0, 0, 1], [-5, -5, -3, -2, -1, 0, 0], [-5, -5, -3, -2, -1, 0, 1], [-5, -5, -3, -2, -1, 0], [-5, -5, -3, -2, -1, 1], [-5, -5, -3, -2, -1], [-5, -5, -3, -2, 0, 0, 1], [-5, -5, -3, -2, 0, 0], [-5, -5, -3, -2, 0, 1], [-5, -5, -3, -2, 0], [-5, -5, -3, -2, 1], [-5, -5, -3, -2], [-5, -5, -3, -1, 0, 0, 1], [-5, -5, -3, -1, 0, 0], [-5, -5, -3, -1, 0, 1], [-5, -5, -3, -1, 0], [-5, -5, -3, -1, 1], [-5, -5, -3, -1], [-5, -5, -3, 0, 0, 1], [-5, -5, -3, 0, 0], [-5, -5, -3, 0, 1], [-5, -5, -3, 0], [-5, -5, -3, 1], [-5, -5, -3], [-5, -5, -2, -1, 0, 0, 1], [-5, -5, -2, -1, 0, 0], [-5, -5, -2, -1, 0, 1], [-5, -5, -2, -1, 0], [-5, -5, -2, -1, 1], [-5, -5, -2, -1], [-5, -5, -2, 0, 0, 1], [-5, -5, -2, 0, 0], [-5, -5, -2, 0, 1], [-5, -5, -2, 0], [-5, -5, -2, 1], [-5, -5, -2], [-5, -5, -1, 0, 0, 1], [-5, -5, -1, 0, 0], [-5, -5, -1, 0, 1], [-5, -5, -1, 0], [-5, -5, -1, 1], [-5, -5, -1], [-5, -5, 0, 0, 1], [-5, -5, 0, 0], [-5, -5, 0, 1], [-5, -5, 0], [-5, -5, 1], [-5, -5], [-5, -4, -4, -3, -2, -1, 0, 0, 1], [-5, -4, -4, -3, -2, -1, 0, 0], [-5, -4, -4, -3, -2, -1, 0, 1], [-5, -4, -4, -3, -2, -1, 0], [-5, -4, -4, -3, -2, -1, 1], [-5, -4, -4, -3, -2, -1], [-5, -4, -4, -3, -2, 0, 0, 1], [-5, -4, -4, -3, -2, 0, 0], [-5, -4, -4, -3, -2, 0, 1], [-5, -4, -4, -3, -2, 0], [-5, -4, -4, -3, -2, 1], [-5, -4, -4, -3, -2], [-5, -4, -4, -3, -1, 0, 0, 1], [-5, -4, -4, -3, -1, 0, 0], [-5, -4, -4, -3, -1, 0, 1], [-5, -4, -4, -3, -1, 0], [-5, -4, -4, -3, -1, 1], [-5, -4, -4, -3, -1], [-5, -4, -4, -3, 0, 0, 1], [-5, -4, -4, -3, 0, 0], [-5, -4, -4, -3, 0, 1], [-5, -4, -4, -3, 0], [-5, -4, -4, -3, 1], [-5, -4, -4, -3], [-5, -4, -4, -2, -1, 0, 0, 1], [-5, -4, -4, -2, -1, 0, 0], [-5, -4, -4, -2, -1, 0, 1], [-5, -4, -4, -2, -1, 0], [-5, -4, -4, -2, -1, 1], [-5, -4, -4, -2, -1], [-5, -4, -4, -2, 0, 0, 1], [-5, -4, -4, -2, 0, 0], [-5, -4, -4, -2, 0, 1], [-5, -4, -4, -2, 0], [-5, -4, -4, -2, 1], [-5, -4, -4, -2], [-5, -4, -4, -1, 0, 0, 1], [-5, -4, -4, -1, 0, 0], [-5, -4, -4, -1, 0, 1], [-5, -4, -4, -1, 0], [-5, -4, -4, -1, 1], [-5, -4, -4, -1], [-5, -4, -4, 0, 0, 1], [-5, -4, -4, 0, 0], [-5, -4, -4, 0, 1], [-5, -4, -4, 0], [-5, -4, -4, 1], [-5, -4, -4], [-5, -4, -3, -2, -1, 0, 0, 1], [-5, -4, -3, -2, -1, 0, 0], [-5, -4, -3, -2, -1, 0, 1], [-5, -4, -3, -2, -1, 0], [-5, -4, -3, -2, -1, 1], [-5, -4, -3, -2, -1], [-5, -4, -3, -2, 0, 0, 1], [-5, -4, -3, -2, 0, 0], [-5, -4, -3, -2, 0, 1], [-5, -4, -3, -2, 0], [-5, -4, -3, -2, 1], [-5, -4, -3, -2], [-5, -4, -3, -1, 0, 0, 1], [-5, -4, -3, -1, 0, 0], [-5, -4, -3, -1, 0, 1], [-5, -4, -3, -1, 0], [-5, -4, -3, -1, 1], [-5, -4, -3, -1], [-5, -4, -3, 0, 0, 1], [-5, -4, -3, 0, 0], [-5, -4, -3, 0, 1], [-5, -4, -3, 0], [-5, -4, -3, 1], [-5, -4, -3], [-5, -4, -2, -1, 0, 0, 1], [-5, -4, -2, -1, 0, 0], [-5, -4, -2, -1, 0, 1], [-5, -4, -2, -1, 0], [-5, -4, -2, -1, 1], [-5, -4, -2, -1], [-5, -4, -2, 0, 0, 1], [-5, -4, -2, 0, 0], [-5, -4, -2, 0, 1], [-5, -4, -2, 0], [-5, -4, -2, 1], [-5, -4, -2], [-5, -4, -1, 0, 0, 1], [-5, -4, -1, 0, 0], [-5, -4, -1, 0, 1], [-5, -4, -1, 0], [-5, -4, -1, 1], [-5, -4, -1], [-5, -4, 0, 0, 1], [-5, -4, 0, 0], [-5, -4, 0, 1], [-5, -4, 0], [-5, -4, 1], [-5, -4], [-5, -3, -2, -1, 0, 0, 1], [-5, -3, -2, -1, 0, 0], [-5, -3, -2, -1, 0, 1], [-5, -3, -2, -1, 0], [-5, -3, -2, -1, 1], [-5, -3, -2, -1], [-5, -3, -2, 0, 0, 1], [-5, -3, -2, 0, 0], [-5, -3, -2, 0, 1], [-5, -3, -2, 0], [-5, -3, -2, 1], [-5, -3, -2], [-5, -3, -1, 0, 0, 1], [-5, -3, -1, 0, 0], [-5, -3, -1, 0, 1], [-5, -3, -1, 0], [-5, -3, -1, 1], [-5, -3, -1], [-5, -3, 0, 0, 1], [-5, -3, 0, 0], [-5, -3, 0, 1], [-5, -3, 0], [-5, -3, 1], [-5, -3], [-5, -2, -1, 0, 0, 1], [-5, -2, -1, 0, 0], [-5, -2, -1, 0, 1], [-5, -2, -1, 0], [-5, -2, -1, 1], [-5, -2, -1], [-5, -2, 0, 0, 1], [-5, -2, 0, 0], [-5, -2, 0, 1], [-5, -2, 0], [-5, -2, 1], [-5, -2], [-5, -1, 0, 0, 1], [-5, -1, 0, 0], [-5, -1, 0, 1], [-5, -1, 0], [-5, -1, 1], [-5, -1], [-5, 0, 0, 1], [-5, 0, 0], [-5, 0, 1], [-5, 0], [-5, 1], [-5], [-4, -4, -3, -2, -1, 0, 0, 1], [-4, -4, -3, -2, -1, 0, 0], [-4, -4, -3, -2, -1, 0, 1], [-4, -4, -3, -2, -1, 0], [-4, -4, -3, -2, -1, 1], [-4, -4, -3, -2, -1], [-4, -4, -3, -2, 0, 0, 1], [-4, -4, -3, -2, 0, 0], [-4, -4, -3, -2, 0, 1], [-4, -4, -3, -2, 0], [-4, -4, -3, -2, 1], [-4, -4, -3, -2], [-4, -4, -3, -1, 0, 0, 1], [-4, -4, -3, -1, 0, 0], [-4, -4, -3, -1, 0, 1], [-4, -4, -3, -1, 0], [-4, -4, -3, -1, 1], [-4, -4, -3, -1], [-4, -4, -3, 0, 0, 1], [-4, -4, -3, 0, 0], [-4, -4, -3, 0, 1], [-4, -4, -3, 0], [-4, -4, -3, 1], [-4, -4, -3], [-4, -4, -2, -1, 0, 0, 1], [-4, -4, -2, -1, 0, 0], [-4, -4, -2, -1, 0, 1], [-4, -4, -2, -1, 0], [-4, -4, -2, -1, 1], [-4, -4, -2, -1], [-4, -4, -2, 0, 0, 1], [-4, -4, -2, 0, 0], [-4, -4, -2, 0, 1], [-4, -4, -2, 0], [-4, -4, -2, 1], [-4, -4, -2], [-4, -4, -1, 0, 0, 1], [-4, -4, -1, 0, 0], [-4, -4, -1, 0, 1], [-4, -4, -1, 0], [-4, -4, -1, 1], [-4, -4, -1], [-4, -4, 0, 0, 1], [-4, -4, 0, 0], [-4, -4, 0, 1], [-4, -4, 0], [-4, -4, 1], [-4, -4], [-4, -3, -2, -1, 0, 0, 1], [-4, -3, -2, -1, 0, 0], [-4, -3, -2, -1, 0, 1], [-4, -3, -2, -1, 0], [-4, -3, -2, -1, 1], [-4, -3, -2, -1], [-4, -3, -2, 0, 0, 1], [-4, -3, -2, 0, 0], [-4, -3, -2, 0, 1], [-4, -3, -2, 0], [-4, -3, -2, 1], [-4, -3, -2], [-4, -3, -1, 0, 0, 1], [-4, -3, -1, 0, 0], [-4, -3, -1, 0, 1], [-4, -3, -1, 0], [-4, -3, -1, 1], [-4, -3, -1], [-4, -3, 0, 0, 1], [-4, -3, 0, 0], [-4, -3, 0, 1], [-4, -3, 0], [-4, -3, 1], [-4, -3], [-4, -2, -1, 0, 0, 1], [-4, -2, -1, 0, 0], [-4, -2, -1, 0, 1], [-4, -2, -1, 0], [-4, -2, -1, 1], [-4, -2, -1], [-4, -2, 0, 0, 1], [-4, -2, 0, 0], [-4, -2, 0, 1], [-4, -2, 0], [-4, -2, 1], [-4, -2], [-4, -1, 0, 0, 1], [-4, -1, 0, 0], [-4, -1, 0, 1], [-4, -1, 0], [-4, -1, 1], [-4, -1], [-4, 0, 0, 1], [-4, 0, 0], [-4, 0, 1], [-4, 0], [-4, 1], [-4], [-3, -2, -1, 0, 0, 1], [-3, -2, -1, 0, 0], [-3, -2, -1, 0, 1], [-3, -2, -1, 0], [-3, -2, -1, 1], [-3, -2, -1], [-3, -2, 0, 0, 1], [-3, -2, 0, 0], [-3, -2, 0, 1], [-3, -2, 0], [-3, -2, 1], [-3, -2], [-3, -1, 0, 0, 1], [-3, -1, 0, 0], [-3, -1, 0, 1], [-3, -1, 0], [-3, -1, 1], [-3, -1], [-3, 0, 0, 1], [-3, 0, 0], [-3, 0, 1], [-3, 0], [-3, 1], [-3], [-2, -1, 0, 0, 1], [-2, -1, 0, 0], [-2, -1, 0, 1], [-2, -1, 0], [-2, -1, 1], [-2, -1], [-2, 0, 0, 1], [-2, 0, 0], [-2, 0, 1], [-2, 0], [-2, 1], [-2], [-1, 0, 0, 1], [-1, 0, 0], [-1, 0, 1], [-1, 0], [-1, 1], [-1], [0, 0, 1], [0, 0], [0, 1], [0], [1], []]\n assert candidate(nums = [4, 4, 4, 3, 3, 2, 1, 0]) == [[0, 1, 2, 3, 3, 4, 4, 4], [0, 1, 2, 3, 3, 4, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 3], [0, 1, 2, 3, 4, 4, 4], [0, 1, 2, 3, 4, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3], [0, 1, 2, 4, 4, 4], [0, 1, 2, 4, 4], [0, 1, 2, 4], [0, 1, 2], [0, 1, 3, 3, 4, 4, 4], [0, 1, 3, 3, 4, 4], [0, 1, 3, 3, 4], [0, 1, 3, 3], [0, 1, 3, 4, 4, 4], [0, 1, 3, 4, 4], [0, 1, 3, 4], [0, 1, 3], [0, 1, 4, 4, 4], [0, 1, 4, 4], [0, 1, 4], [0, 1], [0, 2, 3, 3, 4, 4, 4], [0, 2, 3, 3, 4, 4], [0, 2, 3, 3, 4], [0, 2, 3, 3], [0, 2, 3, 4, 4, 4], [0, 2, 3, 4, 4], [0, 2, 3, 4], [0, 2, 3], [0, 2, 4, 4, 4], [0, 2, 4, 4], [0, 2, 4], [0, 2], [0, 3, 3, 4, 4, 4], [0, 3, 3, 4, 4], [0, 3, 3, 4], [0, 3, 3], [0, 3, 4, 4, 4], [0, 3, 4, 4], [0, 3, 4], [0, 3], [0, 4, 4, 4], [0, 4, 4], [0, 4], [0], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4], [2, 4, 4], [2, 4], [2], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4], [3, 4, 4], [3, 4], [3], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [-1, -1, 0, 0, 1, 1]) == [[-1, -1, 0, 0, 1, 1], [-1, -1, 0, 0, 1], [-1, -1, 0, 0], [-1, -1, 0, 1, 1], [-1, -1, 0, 1], [-1, -1, 0], [-1, -1, 1, 1], [-1, -1, 1], [-1, -1], [-1, 0, 0, 1, 1], [-1, 0, 0, 1], [-1, 0, 0], [-1, 0, 1, 1], [-1, 0, 1], [-1, 0], [-1, 1, 1], [-1, 1], [-1], [0, 0, 1, 1], [0, 0, 1], [0, 0], [0, 1, 1], [0, 1], [0], [1, 1], [1], []]\n assert candidate(nums = [7, 3, 3, 7, 3, 7]) == [[3, 3, 3, 7, 7, 7], [3, 3, 3, 7, 7], [3, 3, 3, 7], [3, 3, 3], [3, 3, 7, 7, 7], [3, 3, 7, 7], [3, 3, 7], [3, 3], [3, 7, 7, 7], [3, 7, 7], [3, 7], [3], [7, 7, 7], [7, 7], [7], []]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == [[1, 2, 2, 3, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4, 4], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4, 4], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4, 4], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4, 4], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 3, 4, 4, 4, 4], [1, 3, 3, 3, 4, 4, 4], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3], [1, 3, 3, 4, 4, 4, 4], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4, 4], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4, 4], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [2, 2, 3, 3, 3, 4, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 4, 4], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4, 4], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4, 4], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 3, 4, 4, 4, 4], [2, 3, 3, 3, 4, 4, 4], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3], [2, 3, 3, 4, 4, 4, 4], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4, 4], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4, 4], [2, 4, 4, 4], [2, 4, 4], [2, 4], [2], [3, 3, 3, 4, 4, 4, 4], [3, 3, 3, 4, 4, 4], [3, 3, 3, 4, 4], [3, 3, 3, 4], [3, 3, 3], [3, 3, 4, 4, 4, 4], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4, 4], [3, 4, 4, 4], [3, 4, 4], [3, 4], [3], [4, 4, 4, 4], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [-2, -2, -2, 0, 0, 1, 1]) == [[-2, -2, -2, 0, 0, 1, 1], [-2, -2, -2, 0, 0, 1], [-2, -2, -2, 0, 0], [-2, -2, -2, 0, 1, 1], [-2, -2, -2, 0, 1], [-2, -2, -2, 0], [-2, -2, -2, 1, 1], [-2, -2, -2, 1], [-2, -2, -2], [-2, -2, 0, 0, 1, 1], [-2, -2, 0, 0, 1], [-2, -2, 0, 0], [-2, -2, 0, 1, 1], [-2, -2, 0, 1], [-2, -2, 0], [-2, -2, 1, 1], [-2, -2, 1], [-2, -2], [-2, 0, 0, 1, 1], [-2, 0, 0, 1], [-2, 0, 0], [-2, 0, 1, 1], [-2, 0, 1], [-2, 0], [-2, 1, 1], [-2, 1], [-2], [0, 0, 1, 1], [0, 0, 1], [0, 0], [0, 1, 1], [0, 1], [0], [1, 1], [1], []]\n assert candidate(nums = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == [[1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 2, 2, 3, 3, 5], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5, 5], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 2, 2, 4, 4, 5], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5, 5], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5, 5], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 3, 4, 4, 5, 5], [1, 1, 3, 3, 4, 4, 5], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 3, 4, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5, 5], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 4, 5, 5], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5, 5], [1, 1, 5], [1, 1], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5], [1, 5], [1], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5], [2, 5], [2], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5], [3, 5], [3], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5], [4, 5], [4], [5, 5], [5], []]\n assert candidate(nums = [6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]) == [[6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9], [6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9], [6, 6, 6, 7, 7, 7, 8, 8, 8, 9], [6, 6, 6, 7, 7, 7, 8, 8, 8], [6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9], [6, 6, 6, 7, 7, 7, 8, 8, 9, 9], [6, 6, 6, 7, 7, 7, 8, 8, 9], [6, 6, 6, 7, 7, 7, 8, 8], [6, 6, 6, 7, 7, 7, 8, 9, 9, 9], [6, 6, 6, 7, 7, 7, 8, 9, 9], [6, 6, 6, 7, 7, 7, 8, 9], [6, 6, 6, 7, 7, 7, 8], [6, 6, 6, 7, 7, 7, 9, 9, 9], [6, 6, 6, 7, 7, 7, 9, 9], [6, 6, 6, 7, 7, 7, 9], [6, 6, 6, 7, 7, 7], [6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9], [6, 6, 6, 7, 7, 8, 8, 8, 9, 9], [6, 6, 6, 7, 7, 8, 8, 8, 9], [6, 6, 6, 7, 7, 8, 8, 8], [6, 6, 6, 7, 7, 8, 8, 9, 9, 9], [6, 6, 6, 7, 7, 8, 8, 9, 9], [6, 6, 6, 7, 7, 8, 8, 9], [6, 6, 6, 7, 7, 8, 8], [6, 6, 6, 7, 7, 8, 9, 9, 9], [6, 6, 6, 7, 7, 8, 9, 9], [6, 6, 6, 7, 7, 8, 9], [6, 6, 6, 7, 7, 8], [6, 6, 6, 7, 7, 9, 9, 9], [6, 6, 6, 7, 7, 9, 9], [6, 6, 6, 7, 7, 9], [6, 6, 6, 7, 7], [6, 6, 6, 7, 8, 8, 8, 9, 9, 9], [6, 6, 6, 7, 8, 8, 8, 9, 9], [6, 6, 6, 7, 8, 8, 8, 9], [6, 6, 6, 7, 8, 8, 8], [6, 6, 6, 7, 8, 8, 9, 9, 9], [6, 6, 6, 7, 8, 8, 9, 9], [6, 6, 6, 7, 8, 8, 9], [6, 6, 6, 7, 8, 8], [6, 6, 6, 7, 8, 9, 9, 9], [6, 6, 6, 7, 8, 9, 9], [6, 6, 6, 7, 8, 9], [6, 6, 6, 7, 8], [6, 6, 6, 7, 9, 9, 9], [6, 6, 6, 7, 9, 9], [6, 6, 6, 7, 9], [6, 6, 6, 7], [6, 6, 6, 8, 8, 8, 9, 9, 9], [6, 6, 6, 8, 8, 8, 9, 9], [6, 6, 6, 8, 8, 8, 9], [6, 6, 6, 8, 8, 8], [6, 6, 6, 8, 8, 9, 9, 9], [6, 6, 6, 8, 8, 9, 9], [6, 6, 6, 8, 8, 9], [6, 6, 6, 8, 8], [6, 6, 6, 8, 9, 9, 9], [6, 6, 6, 8, 9, 9], [6, 6, 6, 8, 9], [6, 6, 6, 8], [6, 6, 6, 9, 9, 9], [6, 6, 6, 9, 9], [6, 6, 6, 9], [6, 6, 6], [6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9], [6, 6, 7, 7, 7, 8, 8, 8, 9, 9], [6, 6, 7, 7, 7, 8, 8, 8, 9], [6, 6, 7, 7, 7, 8, 8, 8], [6, 6, 7, 7, 7, 8, 8, 9, 9, 9], [6, 6, 7, 7, 7, 8, 8, 9, 9], [6, 6, 7, 7, 7, 8, 8, 9], [6, 6, 7, 7, 7, 8, 8], [6, 6, 7, 7, 7, 8, 9, 9, 9], [6, 6, 7, 7, 7, 8, 9, 9], [6, 6, 7, 7, 7, 8, 9], [6, 6, 7, 7, 7, 8], [6, 6, 7, 7, 7, 9, 9, 9], [6, 6, 7, 7, 7, 9, 9], [6, 6, 7, 7, 7, 9], [6, 6, 7, 7, 7], [6, 6, 7, 7, 8, 8, 8, 9, 9, 9], [6, 6, 7, 7, 8, 8, 8, 9, 9], [6, 6, 7, 7, 8, 8, 8, 9], [6, 6, 7, 7, 8, 8, 8], [6, 6, 7, 7, 8, 8, 9, 9, 9], [6, 6, 7, 7, 8, 8, 9, 9], [6, 6, 7, 7, 8, 8, 9], [6, 6, 7, 7, 8, 8], [6, 6, 7, 7, 8, 9, 9, 9], [6, 6, 7, 7, 8, 9, 9], [6, 6, 7, 7, 8, 9], [6, 6, 7, 7, 8], [6, 6, 7, 7, 9, 9, 9], [6, 6, 7, 7, 9, 9], [6, 6, 7, 7, 9], [6, 6, 7, 7], [6, 6, 7, 8, 8, 8, 9, 9, 9], [6, 6, 7, 8, 8, 8, 9, 9], [6, 6, 7, 8, 8, 8, 9], [6, 6, 7, 8, 8, 8], [6, 6, 7, 8, 8, 9, 9, 9], [6, 6, 7, 8, 8, 9, 9], [6, 6, 7, 8, 8, 9], [6, 6, 7, 8, 8], [6, 6, 7, 8, 9, 9, 9], [6, 6, 7, 8, 9, 9], [6, 6, 7, 8, 9], [6, 6, 7, 8], [6, 6, 7, 9, 9, 9], [6, 6, 7, 9, 9], [6, 6, 7, 9], [6, 6, 7], [6, 6, 8, 8, 8, 9, 9, 9], [6, 6, 8, 8, 8, 9, 9], [6, 6, 8, 8, 8, 9], [6, 6, 8, 8, 8], [6, 6, 8, 8, 9, 9, 9], [6, 6, 8, 8, 9, 9], [6, 6, 8, 8, 9], [6, 6, 8, 8], [6, 6, 8, 9, 9, 9], [6, 6, 8, 9, 9], [6, 6, 8, 9], [6, 6, 8], [6, 6, 9, 9, 9], [6, 6, 9, 9], [6, 6, 9], [6, 6], [6, 7, 7, 7, 8, 8, 8, 9, 9, 9], [6, 7, 7, 7, 8, 8, 8, 9, 9], [6, 7, 7, 7, 8, 8, 8, 9], [6, 7, 7, 7, 8, 8, 8], [6, 7, 7, 7, 8, 8, 9, 9, 9], [6, 7, 7, 7, 8, 8, 9, 9], [6, 7, 7, 7, 8, 8, 9], [6, 7, 7, 7, 8, 8], [6, 7, 7, 7, 8, 9, 9, 9], [6, 7, 7, 7, 8, 9, 9], [6, 7, 7, 7, 8, 9], [6, 7, 7, 7, 8], [6, 7, 7, 7, 9, 9, 9], [6, 7, 7, 7, 9, 9], [6, 7, 7, 7, 9], [6, 7, 7, 7], [6, 7, 7, 8, 8, 8, 9, 9, 9], [6, 7, 7, 8, 8, 8, 9, 9], [6, 7, 7, 8, 8, 8, 9], [6, 7, 7, 8, 8, 8], [6, 7, 7, 8, 8, 9, 9, 9], [6, 7, 7, 8, 8, 9, 9], [6, 7, 7, 8, 8, 9], [6, 7, 7, 8, 8], [6, 7, 7, 8, 9, 9, 9], [6, 7, 7, 8, 9, 9], [6, 7, 7, 8, 9], [6, 7, 7, 8], [6, 7, 7, 9, 9, 9], [6, 7, 7, 9, 9], [6, 7, 7, 9], [6, 7, 7], [6, 7, 8, 8, 8, 9, 9, 9], [6, 7, 8, 8, 8, 9, 9], [6, 7, 8, 8, 8, 9], [6, 7, 8, 8, 8], [6, 7, 8, 8, 9, 9, 9], [6, 7, 8, 8, 9, 9], [6, 7, 8, 8, 9], [6, 7, 8, 8], [6, 7, 8, 9, 9, 9], [6, 7, 8, 9, 9], [6, 7, 8, 9], [6, 7, 8], [6, 7, 9, 9, 9], [6, 7, 9, 9], [6, 7, 9], [6, 7], [6, 8, 8, 8, 9, 9, 9], [6, 8, 8, 8, 9, 9], [6, 8, 8, 8, 9], [6, 8, 8, 8], [6, 8, 8, 9, 9, 9], [6, 8, 8, 9, 9], [6, 8, 8, 9], [6, 8, 8], [6, 8, 9, 9, 9], [6, 8, 9, 9], [6, 8, 9], [6, 8], [6, 9, 9, 9], [6, 9, 9], [6, 9], [6], [7, 7, 7, 8, 8, 8, 9, 9, 9], [7, 7, 7, 8, 8, 8, 9, 9], [7, 7, 7, 8, 8, 8, 9], [7, 7, 7, 8, 8, 8], [7, 7, 7, 8, 8, 9, 9, 9], [7, 7, 7, 8, 8, 9, 9], [7, 7, 7, 8, 8, 9], [7, 7, 7, 8, 8], [7, 7, 7, 8, 9, 9, 9], [7, 7, 7, 8, 9, 9], [7, 7, 7, 8, 9], [7, 7, 7, 8], [7, 7, 7, 9, 9, 9], [7, 7, 7, 9, 9], [7, 7, 7, 9], [7, 7, 7], [7, 7, 8, 8, 8, 9, 9, 9], [7, 7, 8, 8, 8, 9, 9], [7, 7, 8, 8, 8, 9], [7, 7, 8, 8, 8], [7, 7, 8, 8, 9, 9, 9], [7, 7, 8, 8, 9, 9], [7, 7, 8, 8, 9], [7, 7, 8, 8], [7, 7, 8, 9, 9, 9], [7, 7, 8, 9, 9], [7, 7, 8, 9], [7, 7, 8], [7, 7, 9, 9, 9], [7, 7, 9, 9], [7, 7, 9], [7, 7], [7, 8, 8, 8, 9, 9, 9], [7, 8, 8, 8, 9, 9], [7, 8, 8, 8, 9], [7, 8, 8, 8], [7, 8, 8, 9, 9, 9], [7, 8, 8, 9, 9], [7, 8, 8, 9], [7, 8, 8], [7, 8, 9, 9, 9], [7, 8, 9, 9], [7, 8, 9], [7, 8], [7, 9, 9, 9], [7, 9, 9], [7, 9], [7], [8, 8, 8, 9, 9, 9], [8, 8, 8, 9, 9], [8, 8, 8, 9], [8, 8, 8], [8, 8, 9, 9, 9], [8, 8, 9, 9], [8, 8, 9], [8, 8], [8, 9, 9, 9], [8, 9, 9], [8, 9], [8], [9, 9, 9], [9, 9], [9], []]\n assert candidate(nums = [1, 2, 3, 2]) == [[1, 2, 2, 3], [1, 2, 2], [1, 2, 3], [1, 2], [1, 3], [1], [2, 2, 3], [2, 2], [2, 3], [2], [3], []]\n assert candidate(nums = [-1, 1, 0, -1, 1]) == [[-1, -1, 0, 1, 1], [-1, -1, 0, 1], [-1, -1, 0], [-1, -1, 1, 1], [-1, -1, 1], [-1, -1], [-1, 0, 1, 1], [-1, 0, 1], [-1, 0], [-1, 1, 1], [-1, 1], [-1], [0, 1, 1], [0, 1], [0], [1, 1], [1], []]\n assert candidate(nums = [-2, -2, -1, 0, 0, 1, 1, 2]) == [[-2, -2, -1, 0, 0, 1, 1, 2], [-2, -2, -1, 0, 0, 1, 1], [-2, -2, -1, 0, 0, 1, 2], [-2, -2, -1, 0, 0, 1], [-2, -2, -1, 0, 0, 2], [-2, -2, -1, 0, 0], [-2, -2, -1, 0, 1, 1, 2], [-2, -2, -1, 0, 1, 1], [-2, -2, -1, 0, 1, 2], [-2, -2, -1, 0, 1], [-2, -2, -1, 0, 2], [-2, -2, -1, 0], [-2, -2, -1, 1, 1, 2], [-2, -2, -1, 1, 1], [-2, -2, -1, 1, 2], [-2, -2, -1, 1], [-2, -2, -1, 2], [-2, -2, -1], [-2, -2, 0, 0, 1, 1, 2], [-2, -2, 0, 0, 1, 1], [-2, -2, 0, 0, 1, 2], [-2, -2, 0, 0, 1], [-2, -2, 0, 0, 2], [-2, -2, 0, 0], [-2, -2, 0, 1, 1, 2], [-2, -2, 0, 1, 1], [-2, -2, 0, 1, 2], [-2, -2, 0, 1], [-2, -2, 0, 2], [-2, -2, 0], [-2, -2, 1, 1, 2], [-2, -2, 1, 1], [-2, -2, 1, 2], [-2, -2, 1], [-2, -2, 2], [-2, -2], [-2, -1, 0, 0, 1, 1, 2], [-2, -1, 0, 0, 1, 1], [-2, -1, 0, 0, 1, 2], [-2, -1, 0, 0, 1], [-2, -1, 0, 0, 2], [-2, -1, 0, 0], [-2, -1, 0, 1, 1, 2], [-2, -1, 0, 1, 1], [-2, -1, 0, 1, 2], [-2, -1, 0, 1], [-2, -1, 0, 2], [-2, -1, 0], [-2, -1, 1, 1, 2], [-2, -1, 1, 1], [-2, -1, 1, 2], [-2, -1, 1], [-2, -1, 2], [-2, -1], [-2, 0, 0, 1, 1, 2], [-2, 0, 0, 1, 1], [-2, 0, 0, 1, 2], [-2, 0, 0, 1], [-2, 0, 0, 2], [-2, 0, 0], [-2, 0, 1, 1, 2], [-2, 0, 1, 1], [-2, 0, 1, 2], [-2, 0, 1], [-2, 0, 2], [-2, 0], [-2, 1, 1, 2], [-2, 1, 1], [-2, 1, 2], [-2, 1], [-2, 2], [-2], [-1, 0, 0, 1, 1, 2], [-1, 0, 0, 1, 1], [-1, 0, 0, 1, 2], [-1, 0, 0, 1], [-1, 0, 0, 2], [-1, 0, 0], [-1, 0, 1, 1, 2], [-1, 0, 1, 1], [-1, 0, 1, 2], [-1, 0, 1], [-1, 0, 2], [-1, 0], [-1, 1, 1, 2], [-1, 1, 1], [-1, 1, 2], [-1, 1], [-1, 2], [-1], [0, 0, 1, 1, 2], [0, 0, 1, 1], [0, 0, 1, 2], [0, 0, 1], [0, 0, 2], [0, 0], [0, 1, 1, 2], [0, 1, 1], [0, 1, 2], [0, 1], [0, 2], [0], [1, 1, 2], [1, 1], [1, 2], [1], [2], []]\n assert candidate(nums = [-5, -5, -5, 0, 0, 5, 5]) == [[-5, -5, -5, 0, 0, 5, 5], [-5, -5, -5, 0, 0, 5], [-5, -5, -5, 0, 0], [-5, -5, -5, 0, 5, 5], [-5, -5, -5, 0, 5], [-5, -5, -5, 0], [-5, -5, -5, 5, 5], [-5, -5, -5, 5], [-5, -5, -5], [-5, -5, 0, 0, 5, 5], [-5, -5, 0, 0, 5], [-5, -5, 0, 0], [-5, -5, 0, 5, 5], [-5, -5, 0, 5], [-5, -5, 0], [-5, -5, 5, 5], [-5, -5, 5], [-5, -5], [-5, 0, 0, 5, 5], [-5, 0, 0, 5], [-5, 0, 0], [-5, 0, 5, 5], [-5, 0, 5], [-5, 0], [-5, 5, 5], [-5, 5], [-5], [0, 0, 5, 5], [0, 0, 5], [0, 0], [0, 5, 5], [0, 5], [0], [5, 5], [5], []]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0], [0], []]\n assert candidate(nums = [-2, -1, 0, 1, 2, 2, 3, 4, 4, 5]) == [[-2, -1, 0, 1, 2, 2, 3, 4, 4, 5], [-2, -1, 0, 1, 2, 2, 3, 4, 4], [-2, -1, 0, 1, 2, 2, 3, 4, 5], [-2, -1, 0, 1, 2, 2, 3, 4], [-2, -1, 0, 1, 2, 2, 3, 5], [-2, -1, 0, 1, 2, 2, 3], [-2, -1, 0, 1, 2, 2, 4, 4, 5], [-2, -1, 0, 1, 2, 2, 4, 4], [-2, -1, 0, 1, 2, 2, 4, 5], [-2, -1, 0, 1, 2, 2, 4], [-2, -1, 0, 1, 2, 2, 5], [-2, -1, 0, 1, 2, 2], [-2, -1, 0, 1, 2, 3, 4, 4, 5], [-2, -1, 0, 1, 2, 3, 4, 4], [-2, -1, 0, 1, 2, 3, 4, 5], [-2, -1, 0, 1, 2, 3, 4], [-2, -1, 0, 1, 2, 3, 5], [-2, -1, 0, 1, 2, 3], [-2, -1, 0, 1, 2, 4, 4, 5], [-2, -1, 0, 1, 2, 4, 4], [-2, -1, 0, 1, 2, 4, 5], [-2, -1, 0, 1, 2, 4], [-2, -1, 0, 1, 2, 5], [-2, -1, 0, 1, 2], [-2, -1, 0, 1, 3, 4, 4, 5], [-2, -1, 0, 1, 3, 4, 4], [-2, -1, 0, 1, 3, 4, 5], [-2, -1, 0, 1, 3, 4], [-2, -1, 0, 1, 3, 5], [-2, -1, 0, 1, 3], [-2, -1, 0, 1, 4, 4, 5], [-2, -1, 0, 1, 4, 4], [-2, -1, 0, 1, 4, 5], [-2, -1, 0, 1, 4], [-2, -1, 0, 1, 5], [-2, -1, 0, 1], [-2, -1, 0, 2, 2, 3, 4, 4, 5], [-2, -1, 0, 2, 2, 3, 4, 4], [-2, -1, 0, 2, 2, 3, 4, 5], [-2, -1, 0, 2, 2, 3, 4], [-2, -1, 0, 2, 2, 3, 5], [-2, -1, 0, 2, 2, 3], [-2, -1, 0, 2, 2, 4, 4, 5], [-2, -1, 0, 2, 2, 4, 4], [-2, -1, 0, 2, 2, 4, 5], [-2, -1, 0, 2, 2, 4], [-2, -1, 0, 2, 2, 5], [-2, -1, 0, 2, 2], [-2, -1, 0, 2, 3, 4, 4, 5], [-2, -1, 0, 2, 3, 4, 4], [-2, -1, 0, 2, 3, 4, 5], [-2, -1, 0, 2, 3, 4], [-2, -1, 0, 2, 3, 5], [-2, -1, 0, 2, 3], [-2, -1, 0, 2, 4, 4, 5], [-2, -1, 0, 2, 4, 4], [-2, -1, 0, 2, 4, 5], [-2, -1, 0, 2, 4], [-2, -1, 0, 2, 5], [-2, -1, 0, 2], [-2, -1, 0, 3, 4, 4, 5], [-2, -1, 0, 3, 4, 4], [-2, -1, 0, 3, 4, 5], [-2, -1, 0, 3, 4], [-2, -1, 0, 3, 5], [-2, -1, 0, 3], [-2, -1, 0, 4, 4, 5], [-2, -1, 0, 4, 4], [-2, -1, 0, 4, 5], [-2, -1, 0, 4], [-2, -1, 0, 5], [-2, -1, 0], [-2, -1, 1, 2, 2, 3, 4, 4, 5], [-2, -1, 1, 2, 2, 3, 4, 4], [-2, -1, 1, 2, 2, 3, 4, 5], [-2, -1, 1, 2, 2, 3, 4], [-2, -1, 1, 2, 2, 3, 5], [-2, -1, 1, 2, 2, 3], [-2, -1, 1, 2, 2, 4, 4, 5], [-2, -1, 1, 2, 2, 4, 4], [-2, -1, 1, 2, 2, 4, 5], [-2, -1, 1, 2, 2, 4], [-2, -1, 1, 2, 2, 5], [-2, -1, 1, 2, 2], [-2, -1, 1, 2, 3, 4, 4, 5], [-2, -1, 1, 2, 3, 4, 4], [-2, -1, 1, 2, 3, 4, 5], [-2, -1, 1, 2, 3, 4], [-2, -1, 1, 2, 3, 5], [-2, -1, 1, 2, 3], [-2, -1, 1, 2, 4, 4, 5], [-2, -1, 1, 2, 4, 4], [-2, -1, 1, 2, 4, 5], [-2, -1, 1, 2, 4], [-2, -1, 1, 2, 5], [-2, -1, 1, 2], [-2, -1, 1, 3, 4, 4, 5], [-2, -1, 1, 3, 4, 4], [-2, -1, 1, 3, 4, 5], [-2, -1, 1, 3, 4], [-2, -1, 1, 3, 5], [-2, -1, 1, 3], [-2, -1, 1, 4, 4, 5], [-2, -1, 1, 4, 4], [-2, -1, 1, 4, 5], [-2, -1, 1, 4], [-2, -1, 1, 5], [-2, -1, 1], [-2, -1, 2, 2, 3, 4, 4, 5], [-2, -1, 2, 2, 3, 4, 4], [-2, -1, 2, 2, 3, 4, 5], [-2, -1, 2, 2, 3, 4], [-2, -1, 2, 2, 3, 5], [-2, -1, 2, 2, 3], [-2, -1, 2, 2, 4, 4, 5], [-2, -1, 2, 2, 4, 4], [-2, -1, 2, 2, 4, 5], [-2, -1, 2, 2, 4], [-2, -1, 2, 2, 5], [-2, -1, 2, 2], [-2, -1, 2, 3, 4, 4, 5], [-2, -1, 2, 3, 4, 4], [-2, -1, 2, 3, 4, 5], [-2, -1, 2, 3, 4], [-2, -1, 2, 3, 5], [-2, -1, 2, 3], [-2, -1, 2, 4, 4, 5], [-2, -1, 2, 4, 4], [-2, -1, 2, 4, 5], [-2, -1, 2, 4], [-2, -1, 2, 5], [-2, -1, 2], [-2, -1, 3, 4, 4, 5], [-2, -1, 3, 4, 4], [-2, -1, 3, 4, 5], [-2, -1, 3, 4], [-2, -1, 3, 5], [-2, -1, 3], [-2, -1, 4, 4, 5], [-2, -1, 4, 4], [-2, -1, 4, 5], [-2, -1, 4], [-2, -1, 5], [-2, -1], [-2, 0, 1, 2, 2, 3, 4, 4, 5], [-2, 0, 1, 2, 2, 3, 4, 4], [-2, 0, 1, 2, 2, 3, 4, 5], [-2, 0, 1, 2, 2, 3, 4], [-2, 0, 1, 2, 2, 3, 5], [-2, 0, 1, 2, 2, 3], [-2, 0, 1, 2, 2, 4, 4, 5], [-2, 0, 1, 2, 2, 4, 4], [-2, 0, 1, 2, 2, 4, 5], [-2, 0, 1, 2, 2, 4], [-2, 0, 1, 2, 2, 5], [-2, 0, 1, 2, 2], [-2, 0, 1, 2, 3, 4, 4, 5], [-2, 0, 1, 2, 3, 4, 4], [-2, 0, 1, 2, 3, 4, 5], [-2, 0, 1, 2, 3, 4], [-2, 0, 1, 2, 3, 5], [-2, 0, 1, 2, 3], [-2, 0, 1, 2, 4, 4, 5], [-2, 0, 1, 2, 4, 4], [-2, 0, 1, 2, 4, 5], [-2, 0, 1, 2, 4], [-2, 0, 1, 2, 5], [-2, 0, 1, 2], [-2, 0, 1, 3, 4, 4, 5], [-2, 0, 1, 3, 4, 4], [-2, 0, 1, 3, 4, 5], [-2, 0, 1, 3, 4], [-2, 0, 1, 3, 5], [-2, 0, 1, 3], [-2, 0, 1, 4, 4, 5], [-2, 0, 1, 4, 4], [-2, 0, 1, 4, 5], [-2, 0, 1, 4], [-2, 0, 1, 5], [-2, 0, 1], [-2, 0, 2, 2, 3, 4, 4, 5], [-2, 0, 2, 2, 3, 4, 4], [-2, 0, 2, 2, 3, 4, 5], [-2, 0, 2, 2, 3, 4], [-2, 0, 2, 2, 3, 5], [-2, 0, 2, 2, 3], [-2, 0, 2, 2, 4, 4, 5], [-2, 0, 2, 2, 4, 4], [-2, 0, 2, 2, 4, 5], [-2, 0, 2, 2, 4], [-2, 0, 2, 2, 5], [-2, 0, 2, 2], [-2, 0, 2, 3, 4, 4, 5], [-2, 0, 2, 3, 4, 4], [-2, 0, 2, 3, 4, 5], [-2, 0, 2, 3, 4], [-2, 0, 2, 3, 5], [-2, 0, 2, 3], [-2, 0, 2, 4, 4, 5], [-2, 0, 2, 4, 4], [-2, 0, 2, 4, 5], [-2, 0, 2, 4], [-2, 0, 2, 5], [-2, 0, 2], [-2, 0, 3, 4, 4, 5], [-2, 0, 3, 4, 4], [-2, 0, 3, 4, 5], [-2, 0, 3, 4], [-2, 0, 3, 5], [-2, 0, 3], [-2, 0, 4, 4, 5], [-2, 0, 4, 4], [-2, 0, 4, 5], [-2, 0, 4], [-2, 0, 5], [-2, 0], [-2, 1, 2, 2, 3, 4, 4, 5], [-2, 1, 2, 2, 3, 4, 4], [-2, 1, 2, 2, 3, 4, 5], [-2, 1, 2, 2, 3, 4], [-2, 1, 2, 2, 3, 5], [-2, 1, 2, 2, 3], [-2, 1, 2, 2, 4, 4, 5], [-2, 1, 2, 2, 4, 4], [-2, 1, 2, 2, 4, 5], [-2, 1, 2, 2, 4], [-2, 1, 2, 2, 5], [-2, 1, 2, 2], [-2, 1, 2, 3, 4, 4, 5], [-2, 1, 2, 3, 4, 4], [-2, 1, 2, 3, 4, 5], [-2, 1, 2, 3, 4], [-2, 1, 2, 3, 5], [-2, 1, 2, 3], [-2, 1, 2, 4, 4, 5], [-2, 1, 2, 4, 4], [-2, 1, 2, 4, 5], [-2, 1, 2, 4], [-2, 1, 2, 5], [-2, 1, 2], [-2, 1, 3, 4, 4, 5], [-2, 1, 3, 4, 4], [-2, 1, 3, 4, 5], [-2, 1, 3, 4], [-2, 1, 3, 5], [-2, 1, 3], [-2, 1, 4, 4, 5], [-2, 1, 4, 4], [-2, 1, 4, 5], [-2, 1, 4], [-2, 1, 5], [-2, 1], [-2, 2, 2, 3, 4, 4, 5], [-2, 2, 2, 3, 4, 4], [-2, 2, 2, 3, 4, 5], [-2, 2, 2, 3, 4], [-2, 2, 2, 3, 5], [-2, 2, 2, 3], [-2, 2, 2, 4, 4, 5], [-2, 2, 2, 4, 4], [-2, 2, 2, 4, 5], [-2, 2, 2, 4], [-2, 2, 2, 5], [-2, 2, 2], [-2, 2, 3, 4, 4, 5], [-2, 2, 3, 4, 4], [-2, 2, 3, 4, 5], [-2, 2, 3, 4], [-2, 2, 3, 5], [-2, 2, 3], [-2, 2, 4, 4, 5], [-2, 2, 4, 4], [-2, 2, 4, 5], [-2, 2, 4], [-2, 2, 5], [-2, 2], [-2, 3, 4, 4, 5], [-2, 3, 4, 4], [-2, 3, 4, 5], [-2, 3, 4], [-2, 3, 5], [-2, 3], [-2, 4, 4, 5], [-2, 4, 4], [-2, 4, 5], [-2, 4], [-2, 5], [-2], [-1, 0, 1, 2, 2, 3, 4, 4, 5], [-1, 0, 1, 2, 2, 3, 4, 4], [-1, 0, 1, 2, 2, 3, 4, 5], [-1, 0, 1, 2, 2, 3, 4], [-1, 0, 1, 2, 2, 3, 5], [-1, 0, 1, 2, 2, 3], [-1, 0, 1, 2, 2, 4, 4, 5], [-1, 0, 1, 2, 2, 4, 4], [-1, 0, 1, 2, 2, 4, 5], [-1, 0, 1, 2, 2, 4], [-1, 0, 1, 2, 2, 5], [-1, 0, 1, 2, 2], [-1, 0, 1, 2, 3, 4, 4, 5], [-1, 0, 1, 2, 3, 4, 4], [-1, 0, 1, 2, 3, 4, 5], [-1, 0, 1, 2, 3, 4], [-1, 0, 1, 2, 3, 5], [-1, 0, 1, 2, 3], [-1, 0, 1, 2, 4, 4, 5], [-1, 0, 1, 2, 4, 4], [-1, 0, 1, 2, 4, 5], [-1, 0, 1, 2, 4], [-1, 0, 1, 2, 5], [-1, 0, 1, 2], [-1, 0, 1, 3, 4, 4, 5], [-1, 0, 1, 3, 4, 4], [-1, 0, 1, 3, 4, 5], [-1, 0, 1, 3, 4], [-1, 0, 1, 3, 5], [-1, 0, 1, 3], [-1, 0, 1, 4, 4, 5], [-1, 0, 1, 4, 4], [-1, 0, 1, 4, 5], [-1, 0, 1, 4], [-1, 0, 1, 5], [-1, 0, 1], [-1, 0, 2, 2, 3, 4, 4, 5], [-1, 0, 2, 2, 3, 4, 4], [-1, 0, 2, 2, 3, 4, 5], [-1, 0, 2, 2, 3, 4], [-1, 0, 2, 2, 3, 5], [-1, 0, 2, 2, 3], [-1, 0, 2, 2, 4, 4, 5], [-1, 0, 2, 2, 4, 4], [-1, 0, 2, 2, 4, 5], [-1, 0, 2, 2, 4], [-1, 0, 2, 2, 5], [-1, 0, 2, 2], [-1, 0, 2, 3, 4, 4, 5], [-1, 0, 2, 3, 4, 4], [-1, 0, 2, 3, 4, 5], [-1, 0, 2, 3, 4], [-1, 0, 2, 3, 5], [-1, 0, 2, 3], [-1, 0, 2, 4, 4, 5], [-1, 0, 2, 4, 4], [-1, 0, 2, 4, 5], [-1, 0, 2, 4], [-1, 0, 2, 5], [-1, 0, 2], [-1, 0, 3, 4, 4, 5], [-1, 0, 3, 4, 4], [-1, 0, 3, 4, 5], [-1, 0, 3, 4], [-1, 0, 3, 5], [-1, 0, 3], [-1, 0, 4, 4, 5], [-1, 0, 4, 4], [-1, 0, 4, 5], [-1, 0, 4], [-1, 0, 5], [-1, 0], [-1, 1, 2, 2, 3, 4, 4, 5], [-1, 1, 2, 2, 3, 4, 4], [-1, 1, 2, 2, 3, 4, 5], [-1, 1, 2, 2, 3, 4], [-1, 1, 2, 2, 3, 5], [-1, 1, 2, 2, 3], [-1, 1, 2, 2, 4, 4, 5], [-1, 1, 2, 2, 4, 4], [-1, 1, 2, 2, 4, 5], [-1, 1, 2, 2, 4], [-1, 1, 2, 2, 5], [-1, 1, 2, 2], [-1, 1, 2, 3, 4, 4, 5], [-1, 1, 2, 3, 4, 4], [-1, 1, 2, 3, 4, 5], [-1, 1, 2, 3, 4], [-1, 1, 2, 3, 5], [-1, 1, 2, 3], [-1, 1, 2, 4, 4, 5], [-1, 1, 2, 4, 4], [-1, 1, 2, 4, 5], [-1, 1, 2, 4], [-1, 1, 2, 5], [-1, 1, 2], [-1, 1, 3, 4, 4, 5], [-1, 1, 3, 4, 4], [-1, 1, 3, 4, 5], [-1, 1, 3, 4], [-1, 1, 3, 5], [-1, 1, 3], [-1, 1, 4, 4, 5], [-1, 1, 4, 4], [-1, 1, 4, 5], [-1, 1, 4], [-1, 1, 5], [-1, 1], [-1, 2, 2, 3, 4, 4, 5], [-1, 2, 2, 3, 4, 4], [-1, 2, 2, 3, 4, 5], [-1, 2, 2, 3, 4], [-1, 2, 2, 3, 5], [-1, 2, 2, 3], [-1, 2, 2, 4, 4, 5], [-1, 2, 2, 4, 4], [-1, 2, 2, 4, 5], [-1, 2, 2, 4], [-1, 2, 2, 5], [-1, 2, 2], [-1, 2, 3, 4, 4, 5], [-1, 2, 3, 4, 4], [-1, 2, 3, 4, 5], [-1, 2, 3, 4], [-1, 2, 3, 5], [-1, 2, 3], [-1, 2, 4, 4, 5], [-1, 2, 4, 4], [-1, 2, 4, 5], [-1, 2, 4], [-1, 2, 5], [-1, 2], [-1, 3, 4, 4, 5], [-1, 3, 4, 4], [-1, 3, 4, 5], [-1, 3, 4], [-1, 3, 5], [-1, 3], [-1, 4, 4, 5], [-1, 4, 4], [-1, 4, 5], [-1, 4], [-1, 5], [-1], [0, 1, 2, 2, 3, 4, 4, 5], [0, 1, 2, 2, 3, 4, 4], [0, 1, 2, 2, 3, 4, 5], [0, 1, 2, 2, 3, 4], [0, 1, 2, 2, 3, 5], [0, 1, 2, 2, 3], [0, 1, 2, 2, 4, 4, 5], [0, 1, 2, 2, 4, 4], [0, 1, 2, 2, 4, 5], [0, 1, 2, 2, 4], [0, 1, 2, 2, 5], [0, 1, 2, 2], [0, 1, 2, 3, 4, 4, 5], [0, 1, 2, 3, 4, 4], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5], [0, 1, 2, 3], [0, 1, 2, 4, 4, 5], [0, 1, 2, 4, 4], [0, 1, 2, 4, 5], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2], [0, 1, 3, 4, 4, 5], [0, 1, 3, 4, 4], [0, 1, 3, 4, 5], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3], [0, 1, 4, 4, 5], [0, 1, 4, 4], [0, 1, 4, 5], [0, 1, 4], [0, 1, 5], [0, 1], [0, 2, 2, 3, 4, 4, 5], [0, 2, 2, 3, 4, 4], [0, 2, 2, 3, 4, 5], [0, 2, 2, 3, 4], [0, 2, 2, 3, 5], [0, 2, 2, 3], [0, 2, 2, 4, 4, 5], [0, 2, 2, 4, 4], [0, 2, 2, 4, 5], [0, 2, 2, 4], [0, 2, 2, 5], [0, 2, 2], [0, 2, 3, 4, 4, 5], [0, 2, 3, 4, 4], [0, 2, 3, 4, 5], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3], [0, 2, 4, 4, 5], [0, 2, 4, 4], [0, 2, 4, 5], [0, 2, 4], [0, 2, 5], [0, 2], [0, 3, 4, 4, 5], [0, 3, 4, 4], [0, 3, 4, 5], [0, 3, 4], [0, 3, 5], [0, 3], [0, 4, 4, 5], [0, 4, 4], [0, 4, 5], [0, 4], [0, 5], [0], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5], [1, 4], [1, 5], [1], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5], [2, 4], [2, 5], [2], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5], [3, 4], [3, 5], [3], [4, 4, 5], [4, 4], [4, 5], [4], [5], []]\n assert candidate(nums = [4, 4, 3, 2, 2, 1, 1]) == [[1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4], [1, 1, 2, 2], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4], [1, 1, 2, 3], [1, 1, 2, 4, 4], [1, 1, 2, 4], [1, 1, 2], [1, 1, 3, 4, 4], [1, 1, 3, 4], [1, 1, 3], [1, 1, 4, 4], [1, 1, 4], [1, 1], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4], [1, 4], [1], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4], [2, 4], [2], [3, 4, 4], [3, 4], [3], [4, 4], [4], []]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4]) == [[1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4], [1, 1, 2, 3], [1, 1, 2, 4, 4], [1, 1, 2, 4], [1, 1, 2], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4], [1, 1, 3, 3], [1, 1, 3, 4, 4], [1, 1, 3, 4], [1, 1, 3], [1, 1, 4, 4], [1, 1, 4], [1, 1], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4], [1, 4], [1], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4], [2, 4], [2], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4], [3, 4], [3], [4, 4], [4], []]\n assert candidate(nums = [7, 7, 8, 8, 8, 9]) == [[7, 7, 8, 8, 8, 9], [7, 7, 8, 8, 8], [7, 7, 8, 8, 9], [7, 7, 8, 8], [7, 7, 8, 9], [7, 7, 8], [7, 7, 9], [7, 7], [7, 8, 8, 8, 9], [7, 8, 8, 8], [7, 8, 8, 9], [7, 8, 8], [7, 8, 9], [7, 8], [7, 9], [7], [8, 8, 8, 9], [8, 8, 8], [8, 8, 9], [8, 8], [8, 9], [8], [9], []]\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 2, 2]) == [[0, 0, 0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 1, 2, 2], [0, 0, 0, 0, 0, 1, 1, 2], [0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 2], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1, 2, 2], [0, 0, 0, 0, 1, 1, 2], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 1], [0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 2, 2], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 1], [0, 0, 0, 1, 2, 2], [0, 0, 0, 1, 2], [0, 0, 0, 1], [0, 0, 0, 2, 2], [0, 0, 0, 2], [0, 0, 0], [0, 0, 1, 1, 1, 2, 2], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2], [0, 0, 1, 1], [0, 0, 1, 2, 2], [0, 0, 1, 2], [0, 0, 1], [0, 0, 2, 2], [0, 0, 2], [0, 0], [0, 1, 1, 1, 2, 2], [0, 1, 1, 1, 2], [0, 1, 1, 1], [0, 1, 1, 2, 2], [0, 1, 1, 2], [0, 1, 1], [0, 1, 2, 2], [0, 1, 2], [0, 1], [0, 2, 2], [0, 2], [0], [1, 1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1], [1, 1, 2, 2], [1, 1, 2], [1, 1], [1, 2, 2], [1, 2], [1], [2, 2], [2], []]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == [[1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 2, 2, 3, 3, 5], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5, 5], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 2, 2, 4, 4, 5], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5, 5], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5, 5], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 3, 4, 4, 5, 5], [1, 1, 3, 3, 4, 4, 5], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 3, 4, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5, 5], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 4, 5, 5], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5, 5], [1, 1, 5], [1, 1], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5], [1, 5], [1], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5], [2, 5], [2], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5], [3, 5], [3], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5], [4, 5], [4], [5, 5], [5], []]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == [[1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 2, 2, 3, 3, 5], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5, 5], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 2, 2, 4, 4, 5], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5, 5], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5, 5], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 3, 4, 4, 5, 5], [1, 1, 3, 3, 4, 4, 5], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 3, 4, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5, 5], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 4, 5, 5], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5, 5], [1, 1, 5], [1, 1], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5], [1, 5], [1], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5], [2, 5], [2], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5], [3, 5], [3], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5], [4, 5], [4], [5, 5], [5], []]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3]) == [[1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3], [1, 1, 1, 3], [1, 1, 1], [1, 1, 2, 2, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 2, 3], [1, 1, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 3], [1, 1, 2, 2, 2, 2], [1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3, 3], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [1], [2, 2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2], [2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [2], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [10, 9, 9, 8, 8, 7, 7, 6, 6, 5]) == [[5, 6, 6, 7, 7, 8, 8, 9, 9, 10], [5, 6, 6, 7, 7, 8, 8, 9, 9], [5, 6, 6, 7, 7, 8, 8, 9, 10], [5, 6, 6, 7, 7, 8, 8, 9], [5, 6, 6, 7, 7, 8, 8, 10], [5, 6, 6, 7, 7, 8, 8], [5, 6, 6, 7, 7, 8, 9, 9, 10], [5, 6, 6, 7, 7, 8, 9, 9], [5, 6, 6, 7, 7, 8, 9, 10], [5, 6, 6, 7, 7, 8, 9], [5, 6, 6, 7, 7, 8, 10], [5, 6, 6, 7, 7, 8], [5, 6, 6, 7, 7, 9, 9, 10], [5, 6, 6, 7, 7, 9, 9], [5, 6, 6, 7, 7, 9, 10], [5, 6, 6, 7, 7, 9], [5, 6, 6, 7, 7, 10], [5, 6, 6, 7, 7], [5, 6, 6, 7, 8, 8, 9, 9, 10], [5, 6, 6, 7, 8, 8, 9, 9], [5, 6, 6, 7, 8, 8, 9, 10], [5, 6, 6, 7, 8, 8, 9], [5, 6, 6, 7, 8, 8, 10], [5, 6, 6, 7, 8, 8], [5, 6, 6, 7, 8, 9, 9, 10], [5, 6, 6, 7, 8, 9, 9], [5, 6, 6, 7, 8, 9, 10], [5, 6, 6, 7, 8, 9], [5, 6, 6, 7, 8, 10], [5, 6, 6, 7, 8], [5, 6, 6, 7, 9, 9, 10], [5, 6, 6, 7, 9, 9], [5, 6, 6, 7, 9, 10], [5, 6, 6, 7, 9], [5, 6, 6, 7, 10], [5, 6, 6, 7], [5, 6, 6, 8, 8, 9, 9, 10], [5, 6, 6, 8, 8, 9, 9], [5, 6, 6, 8, 8, 9, 10], [5, 6, 6, 8, 8, 9], [5, 6, 6, 8, 8, 10], [5, 6, 6, 8, 8], [5, 6, 6, 8, 9, 9, 10], [5, 6, 6, 8, 9, 9], [5, 6, 6, 8, 9, 10], [5, 6, 6, 8, 9], [5, 6, 6, 8, 10], [5, 6, 6, 8], [5, 6, 6, 9, 9, 10], [5, 6, 6, 9, 9], [5, 6, 6, 9, 10], [5, 6, 6, 9], [5, 6, 6, 10], [5, 6, 6], [5, 6, 7, 7, 8, 8, 9, 9, 10], [5, 6, 7, 7, 8, 8, 9, 9], [5, 6, 7, 7, 8, 8, 9, 10], [5, 6, 7, 7, 8, 8, 9], [5, 6, 7, 7, 8, 8, 10], [5, 6, 7, 7, 8, 8], [5, 6, 7, 7, 8, 9, 9, 10], [5, 6, 7, 7, 8, 9, 9], [5, 6, 7, 7, 8, 9, 10], [5, 6, 7, 7, 8, 9], [5, 6, 7, 7, 8, 10], [5, 6, 7, 7, 8], [5, 6, 7, 7, 9, 9, 10], [5, 6, 7, 7, 9, 9], [5, 6, 7, 7, 9, 10], [5, 6, 7, 7, 9], [5, 6, 7, 7, 10], [5, 6, 7, 7], [5, 6, 7, 8, 8, 9, 9, 10], [5, 6, 7, 8, 8, 9, 9], [5, 6, 7, 8, 8, 9, 10], [5, 6, 7, 8, 8, 9], [5, 6, 7, 8, 8, 10], [5, 6, 7, 8, 8], [5, 6, 7, 8, 9, 9, 10], [5, 6, 7, 8, 9, 9], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 9, 10], [5, 6, 7, 9, 9], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 8, 9, 9, 10], [5, 6, 8, 8, 9, 9], [5, 6, 8, 8, 9, 10], [5, 6, 8, 8, 9], [5, 6, 8, 8, 10], [5, 6, 8, 8], [5, 6, 8, 9, 9, 10], [5, 6, 8, 9, 9], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 9, 10], [5, 6, 9, 9], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 7, 8, 8, 9, 9, 10], [5, 7, 7, 8, 8, 9, 9], [5, 7, 7, 8, 8, 9, 10], [5, 7, 7, 8, 8, 9], [5, 7, 7, 8, 8, 10], [5, 7, 7, 8, 8], [5, 7, 7, 8, 9, 9, 10], [5, 7, 7, 8, 9, 9], [5, 7, 7, 8, 9, 10], [5, 7, 7, 8, 9], [5, 7, 7, 8, 10], [5, 7, 7, 8], [5, 7, 7, 9, 9, 10], [5, 7, 7, 9, 9], [5, 7, 7, 9, 10], [5, 7, 7, 9], [5, 7, 7, 10], [5, 7, 7], [5, 7, 8, 8, 9, 9, 10], [5, 7, 8, 8, 9, 9], [5, 7, 8, 8, 9, 10], [5, 7, 8, 8, 9], [5, 7, 8, 8, 10], [5, 7, 8, 8], [5, 7, 8, 9, 9, 10], [5, 7, 8, 9, 9], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 9, 10], [5, 7, 9, 9], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 8, 9, 9, 10], [5, 8, 8, 9, 9], [5, 8, 8, 9, 10], [5, 8, 8, 9], [5, 8, 8, 10], [5, 8, 8], [5, 8, 9, 9, 10], [5, 8, 9, 9], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 9, 10], [5, 9, 9], [5, 9, 10], [5, 9], [5, 10], [5], [6, 6, 7, 7, 8, 8, 9, 9, 10], [6, 6, 7, 7, 8, 8, 9, 9], [6, 6, 7, 7, 8, 8, 9, 10], [6, 6, 7, 7, 8, 8, 9], [6, 6, 7, 7, 8, 8, 10], [6, 6, 7, 7, 8, 8], [6, 6, 7, 7, 8, 9, 9, 10], [6, 6, 7, 7, 8, 9, 9], [6, 6, 7, 7, 8, 9, 10], [6, 6, 7, 7, 8, 9], [6, 6, 7, 7, 8, 10], [6, 6, 7, 7, 8], [6, 6, 7, 7, 9, 9, 10], [6, 6, 7, 7, 9, 9], [6, 6, 7, 7, 9, 10], [6, 6, 7, 7, 9], [6, 6, 7, 7, 10], [6, 6, 7, 7], [6, 6, 7, 8, 8, 9, 9, 10], [6, 6, 7, 8, 8, 9, 9], [6, 6, 7, 8, 8, 9, 10], [6, 6, 7, 8, 8, 9], [6, 6, 7, 8, 8, 10], [6, 6, 7, 8, 8], [6, 6, 7, 8, 9, 9, 10], [6, 6, 7, 8, 9, 9], [6, 6, 7, 8, 9, 10], [6, 6, 7, 8, 9], [6, 6, 7, 8, 10], [6, 6, 7, 8], [6, 6, 7, 9, 9, 10], [6, 6, 7, 9, 9], [6, 6, 7, 9, 10], [6, 6, 7, 9], [6, 6, 7, 10], [6, 6, 7], [6, 6, 8, 8, 9, 9, 10], [6, 6, 8, 8, 9, 9], [6, 6, 8, 8, 9, 10], [6, 6, 8, 8, 9], [6, 6, 8, 8, 10], [6, 6, 8, 8], [6, 6, 8, 9, 9, 10], [6, 6, 8, 9, 9], [6, 6, 8, 9, 10], [6, 6, 8, 9], [6, 6, 8, 10], [6, 6, 8], [6, 6, 9, 9, 10], [6, 6, 9, 9], [6, 6, 9, 10], [6, 6, 9], [6, 6, 10], [6, 6], [6, 7, 7, 8, 8, 9, 9, 10], [6, 7, 7, 8, 8, 9, 9], [6, 7, 7, 8, 8, 9, 10], [6, 7, 7, 8, 8, 9], [6, 7, 7, 8, 8, 10], [6, 7, 7, 8, 8], [6, 7, 7, 8, 9, 9, 10], [6, 7, 7, 8, 9, 9], [6, 7, 7, 8, 9, 10], [6, 7, 7, 8, 9], [6, 7, 7, 8, 10], [6, 7, 7, 8], [6, 7, 7, 9, 9, 10], [6, 7, 7, 9, 9], [6, 7, 7, 9, 10], [6, 7, 7, 9], [6, 7, 7, 10], [6, 7, 7], [6, 7, 8, 8, 9, 9, 10], [6, 7, 8, 8, 9, 9], [6, 7, 8, 8, 9, 10], [6, 7, 8, 8, 9], [6, 7, 8, 8, 10], [6, 7, 8, 8], [6, 7, 8, 9, 9, 10], [6, 7, 8, 9, 9], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 9, 10], [6, 7, 9, 9], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 8, 9, 9, 10], [6, 8, 8, 9, 9], [6, 8, 8, 9, 10], [6, 8, 8, 9], [6, 8, 8, 10], [6, 8, 8], [6, 8, 9, 9, 10], [6, 8, 9, 9], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 9, 10], [6, 9, 9], [6, 9, 10], [6, 9], [6, 10], [6], [7, 7, 8, 8, 9, 9, 10], [7, 7, 8, 8, 9, 9], [7, 7, 8, 8, 9, 10], [7, 7, 8, 8, 9], [7, 7, 8, 8, 10], [7, 7, 8, 8], [7, 7, 8, 9, 9, 10], [7, 7, 8, 9, 9], [7, 7, 8, 9, 10], [7, 7, 8, 9], [7, 7, 8, 10], [7, 7, 8], [7, 7, 9, 9, 10], [7, 7, 9, 9], [7, 7, 9, 10], [7, 7, 9], [7, 7, 10], [7, 7], [7, 8, 8, 9, 9, 10], [7, 8, 8, 9, 9], [7, 8, 8, 9, 10], [7, 8, 8, 9], [7, 8, 8, 10], [7, 8, 8], [7, 8, 9, 9, 10], [7, 8, 9, 9], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 9, 10], [7, 9, 9], [7, 9, 10], [7, 9], [7, 10], [7], [8, 8, 9, 9, 10], [8, 8, 9, 9], [8, 8, 9, 10], [8, 8, 9], [8, 8, 10], [8, 8], [8, 9, 9, 10], [8, 9, 9], [8, 9, 10], [8, 9], [8, 10], [8], [9, 9, 10], [9, 9], [9, 10], [9], [10], []]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == [[2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2], [2, 2], [2], []]\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 6, 7, 8]) == [[1, 2, 3, 4, 5, 5, 5, 6, 7, 8], [1, 2, 3, 4, 5, 5, 5, 6, 7], [1, 2, 3, 4, 5, 5, 5, 6, 8], [1, 2, 3, 4, 5, 5, 5, 6], [1, 2, 3, 4, 5, 5, 5, 7, 8], [1, 2, 3, 4, 5, 5, 5, 7], [1, 2, 3, 4, 5, 5, 5, 8], [1, 2, 3, 4, 5, 5, 5], [1, 2, 3, 4, 5, 5, 6, 7, 8], [1, 2, 3, 4, 5, 5, 6, 7], [1, 2, 3, 4, 5, 5, 6, 8], [1, 2, 3, 4, 5, 5, 6], [1, 2, 3, 4, 5, 5, 7, 8], [1, 2, 3, 4, 5, 5, 7], [1, 2, 3, 4, 5, 5, 8], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8], [1, 2, 3, 4], [1, 2, 3, 5, 5, 5, 6, 7, 8], [1, 2, 3, 5, 5, 5, 6, 7], [1, 2, 3, 5, 5, 5, 6, 8], [1, 2, 3, 5, 5, 5, 6], [1, 2, 3, 5, 5, 5, 7, 8], [1, 2, 3, 5, 5, 5, 7], [1, 2, 3, 5, 5, 5, 8], [1, 2, 3, 5, 5, 5], [1, 2, 3, 5, 5, 6, 7, 8], [1, 2, 3, 5, 5, 6, 7], [1, 2, 3, 5, 5, 6, 8], [1, 2, 3, 5, 5, 6], [1, 2, 3, 5, 5, 7, 8], [1, 2, 3, 5, 5, 7], [1, 2, 3, 5, 5, 8], [1, 2, 3, 5, 5], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8], [1, 2, 3, 6], [1, 2, 3, 7, 8], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 3], [1, 2, 4, 5, 5, 5, 6, 7, 8], [1, 2, 4, 5, 5, 5, 6, 7], [1, 2, 4, 5, 5, 5, 6, 8], [1, 2, 4, 5, 5, 5, 6], [1, 2, 4, 5, 5, 5, 7, 8], [1, 2, 4, 5, 5, 5, 7], [1, 2, 4, 5, 5, 5, 8], [1, 2, 4, 5, 5, 5], [1, 2, 4, 5, 5, 6, 7, 8], [1, 2, 4, 5, 5, 6, 7], [1, 2, 4, 5, 5, 6, 8], [1, 2, 4, 5, 5, 6], [1, 2, 4, 5, 5, 7, 8], [1, 2, 4, 5, 5, 7], [1, 2, 4, 5, 5, 8], [1, 2, 4, 5, 5], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8], [1, 2, 4, 6], [1, 2, 4, 7, 8], [1, 2, 4, 7], [1, 2, 4, 8], [1, 2, 4], [1, 2, 5, 5, 5, 6, 7, 8], [1, 2, 5, 5, 5, 6, 7], [1, 2, 5, 5, 5, 6, 8], [1, 2, 5, 5, 5, 6], [1, 2, 5, 5, 5, 7, 8], [1, 2, 5, 5, 5, 7], [1, 2, 5, 5, 5, 8], [1, 2, 5, 5, 5], [1, 2, 5, 5, 6, 7, 8], [1, 2, 5, 5, 6, 7], [1, 2, 5, 5, 6, 8], [1, 2, 5, 5, 6], [1, 2, 5, 5, 7, 8], [1, 2, 5, 5, 7], [1, 2, 5, 5, 8], [1, 2, 5, 5], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8], [1, 2, 5, 6], [1, 2, 5, 7, 8], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 5], [1, 2, 6, 7, 8], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 6], [1, 2, 7, 8], [1, 2, 7], [1, 2, 8], [1, 2], [1, 3, 4, 5, 5, 5, 6, 7, 8], [1, 3, 4, 5, 5, 5, 6, 7], [1, 3, 4, 5, 5, 5, 6, 8], [1, 3, 4, 5, 5, 5, 6], [1, 3, 4, 5, 5, 5, 7, 8], [1, 3, 4, 5, 5, 5, 7], [1, 3, 4, 5, 5, 5, 8], [1, 3, 4, 5, 5, 5], [1, 3, 4, 5, 5, 6, 7, 8], [1, 3, 4, 5, 5, 6, 7], [1, 3, 4, 5, 5, 6, 8], [1, 3, 4, 5, 5, 6], [1, 3, 4, 5, 5, 7, 8], [1, 3, 4, 5, 5, 7], [1, 3, 4, 5, 5, 8], [1, 3, 4, 5, 5], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8], [1, 3, 4, 5], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8], [1, 3, 4, 6], [1, 3, 4, 7, 8], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 4], [1, 3, 5, 5, 5, 6, 7, 8], [1, 3, 5, 5, 5, 6, 7], [1, 3, 5, 5, 5, 6, 8], [1, 3, 5, 5, 5, 6], [1, 3, 5, 5, 5, 7, 8], [1, 3, 5, 5, 5, 7], [1, 3, 5, 5, 5, 8], [1, 3, 5, 5, 5], [1, 3, 5, 5, 6, 7, 8], [1, 3, 5, 5, 6, 7], [1, 3, 5, 5, 6, 8], [1, 3, 5, 5, 6], [1, 3, 5, 5, 7, 8], [1, 3, 5, 5, 7], [1, 3, 5, 5, 8], [1, 3, 5, 5], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8], [1, 3, 5, 6], [1, 3, 5, 7, 8], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 5], [1, 3, 6, 7, 8], [1, 3, 6, 7], [1, 3, 6, 8], [1, 3, 6], [1, 3, 7, 8], [1, 3, 7], [1, 3, 8], [1, 3], [1, 4, 5, 5, 5, 6, 7, 8], [1, 4, 5, 5, 5, 6, 7], [1, 4, 5, 5, 5, 6, 8], [1, 4, 5, 5, 5, 6], [1, 4, 5, 5, 5, 7, 8], [1, 4, 5, 5, 5, 7], [1, 4, 5, 5, 5, 8], [1, 4, 5, 5, 5], [1, 4, 5, 5, 6, 7, 8], [1, 4, 5, 5, 6, 7], [1, 4, 5, 5, 6, 8], [1, 4, 5, 5, 6], [1, 4, 5, 5, 7, 8], [1, 4, 5, 5, 7], [1, 4, 5, 5, 8], [1, 4, 5, 5], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8], [1, 4, 5, 6], [1, 4, 5, 7, 8], [1, 4, 5, 7], [1, 4, 5, 8], [1, 4, 5], [1, 4, 6, 7, 8], [1, 4, 6, 7], [1, 4, 6, 8], [1, 4, 6], [1, 4, 7, 8], [1, 4, 7], [1, 4, 8], [1, 4], [1, 5, 5, 5, 6, 7, 8], [1, 5, 5, 5, 6, 7], [1, 5, 5, 5, 6, 8], [1, 5, 5, 5, 6], [1, 5, 5, 5, 7, 8], [1, 5, 5, 5, 7], [1, 5, 5, 5, 8], [1, 5, 5, 5], [1, 5, 5, 6, 7, 8], [1, 5, 5, 6, 7], [1, 5, 5, 6, 8], [1, 5, 5, 6], [1, 5, 5, 7, 8], [1, 5, 5, 7], [1, 5, 5, 8], [1, 5, 5], [1, 5, 6, 7, 8], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 6], [1, 5, 7, 8], [1, 5, 7], [1, 5, 8], [1, 5], [1, 6, 7, 8], [1, 6, 7], [1, 6, 8], [1, 6], [1, 7, 8], [1, 7], [1, 8], [1], [2, 3, 4, 5, 5, 5, 6, 7, 8], [2, 3, 4, 5, 5, 5, 6, 7], [2, 3, 4, 5, 5, 5, 6, 8], [2, 3, 4, 5, 5, 5, 6], [2, 3, 4, 5, 5, 5, 7, 8], [2, 3, 4, 5, 5, 5, 7], [2, 3, 4, 5, 5, 5, 8], [2, 3, 4, 5, 5, 5], [2, 3, 4, 5, 5, 6, 7, 8], [2, 3, 4, 5, 5, 6, 7], [2, 3, 4, 5, 5, 6, 8], [2, 3, 4, 5, 5, 6], [2, 3, 4, 5, 5, 7, 8], [2, 3, 4, 5, 5, 7], [2, 3, 4, 5, 5, 8], [2, 3, 4, 5, 5], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8], [2, 3, 4, 5], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8], [2, 3, 4, 6], [2, 3, 4, 7, 8], [2, 3, 4, 7], [2, 3, 4, 8], [2, 3, 4], [2, 3, 5, 5, 5, 6, 7, 8], [2, 3, 5, 5, 5, 6, 7], [2, 3, 5, 5, 5, 6, 8], [2, 3, 5, 5, 5, 6], [2, 3, 5, 5, 5, 7, 8], [2, 3, 5, 5, 5, 7], [2, 3, 5, 5, 5, 8], [2, 3, 5, 5, 5], [2, 3, 5, 5, 6, 7, 8], [2, 3, 5, 5, 6, 7], [2, 3, 5, 5, 6, 8], [2, 3, 5, 5, 6], [2, 3, 5, 5, 7, 8], [2, 3, 5, 5, 7], [2, 3, 5, 5, 8], [2, 3, 5, 5], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8], [2, 3, 5, 6], [2, 3, 5, 7, 8], [2, 3, 5, 7], [2, 3, 5, 8], [2, 3, 5], [2, 3, 6, 7, 8], [2, 3, 6, 7], [2, 3, 6, 8], [2, 3, 6], [2, 3, 7, 8], [2, 3, 7], [2, 3, 8], [2, 3], [2, 4, 5, 5, 5, 6, 7, 8], [2, 4, 5, 5, 5, 6, 7], [2, 4, 5, 5, 5, 6, 8], [2, 4, 5, 5, 5, 6], [2, 4, 5, 5, 5, 7, 8], [2, 4, 5, 5, 5, 7], [2, 4, 5, 5, 5, 8], [2, 4, 5, 5, 5], [2, 4, 5, 5, 6, 7, 8], [2, 4, 5, 5, 6, 7], [2, 4, 5, 5, 6, 8], [2, 4, 5, 5, 6], [2, 4, 5, 5, 7, 8], [2, 4, 5, 5, 7], [2, 4, 5, 5, 8], [2, 4, 5, 5], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8], [2, 4, 5, 6], [2, 4, 5, 7, 8], [2, 4, 5, 7], [2, 4, 5, 8], [2, 4, 5], [2, 4, 6, 7, 8], [2, 4, 6, 7], [2, 4, 6, 8], [2, 4, 6], [2, 4, 7, 8], [2, 4, 7], [2, 4, 8], [2, 4], [2, 5, 5, 5, 6, 7, 8], [2, 5, 5, 5, 6, 7], [2, 5, 5, 5, 6, 8], [2, 5, 5, 5, 6], [2, 5, 5, 5, 7, 8], [2, 5, 5, 5, 7], [2, 5, 5, 5, 8], [2, 5, 5, 5], [2, 5, 5, 6, 7, 8], [2, 5, 5, 6, 7], [2, 5, 5, 6, 8], [2, 5, 5, 6], [2, 5, 5, 7, 8], [2, 5, 5, 7], [2, 5, 5, 8], [2, 5, 5], [2, 5, 6, 7, 8], [2, 5, 6, 7], [2, 5, 6, 8], [2, 5, 6], [2, 5, 7, 8], [2, 5, 7], [2, 5, 8], [2, 5], [2, 6, 7, 8], [2, 6, 7], [2, 6, 8], [2, 6], [2, 7, 8], [2, 7], [2, 8], [2], [3, 4, 5, 5, 5, 6, 7, 8], [3, 4, 5, 5, 5, 6, 7], [3, 4, 5, 5, 5, 6, 8], [3, 4, 5, 5, 5, 6], [3, 4, 5, 5, 5, 7, 8], [3, 4, 5, 5, 5, 7], [3, 4, 5, 5, 5, 8], [3, 4, 5, 5, 5], [3, 4, 5, 5, 6, 7, 8], [3, 4, 5, 5, 6, 7], [3, 4, 5, 5, 6, 8], [3, 4, 5, 5, 6], [3, 4, 5, 5, 7, 8], [3, 4, 5, 5, 7], [3, 4, 5, 5, 8], [3, 4, 5, 5], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8], [3, 4, 5, 6], [3, 4, 5, 7, 8], [3, 4, 5, 7], [3, 4, 5, 8], [3, 4, 5], [3, 4, 6, 7, 8], [3, 4, 6, 7], [3, 4, 6, 8], [3, 4, 6], [3, 4, 7, 8], [3, 4, 7], [3, 4, 8], [3, 4], [3, 5, 5, 5, 6, 7, 8], [3, 5, 5, 5, 6, 7], [3, 5, 5, 5, 6, 8], [3, 5, 5, 5, 6], [3, 5, 5, 5, 7, 8], [3, 5, 5, 5, 7], [3, 5, 5, 5, 8], [3, 5, 5, 5], [3, 5, 5, 6, 7, 8], [3, 5, 5, 6, 7], [3, 5, 5, 6, 8], [3, 5, 5, 6], [3, 5, 5, 7, 8], [3, 5, 5, 7], [3, 5, 5, 8], [3, 5, 5], [3, 5, 6, 7, 8], [3, 5, 6, 7], [3, 5, 6, 8], [3, 5, 6], [3, 5, 7, 8], [3, 5, 7], [3, 5, 8], [3, 5], [3, 6, 7, 8], [3, 6, 7], [3, 6, 8], [3, 6], [3, 7, 8], [3, 7], [3, 8], [3], [4, 5, 5, 5, 6, 7, 8], [4, 5, 5, 5, 6, 7], [4, 5, 5, 5, 6, 8], [4, 5, 5, 5, 6], [4, 5, 5, 5, 7, 8], [4, 5, 5, 5, 7], [4, 5, 5, 5, 8], [4, 5, 5, 5], [4, 5, 5, 6, 7, 8], [4, 5, 5, 6, 7], [4, 5, 5, 6, 8], [4, 5, 5, 6], [4, 5, 5, 7, 8], [4, 5, 5, 7], [4, 5, 5, 8], [4, 5, 5], [4, 5, 6, 7, 8], [4, 5, 6, 7], [4, 5, 6, 8], [4, 5, 6], [4, 5, 7, 8], [4, 5, 7], [4, 5, 8], [4, 5], [4, 6, 7, 8], [4, 6, 7], [4, 6, 8], [4, 6], [4, 7, 8], [4, 7], [4, 8], [4], [5, 5, 5, 6, 7, 8], [5, 5, 5, 6, 7], [5, 5, 5, 6, 8], [5, 5, 5, 6], [5, 5, 5, 7, 8], [5, 5, 5, 7], [5, 5, 5, 8], [5, 5, 5], [5, 5, 6, 7, 8], [5, 5, 6, 7], [5, 5, 6, 8], [5, 5, 6], [5, 5, 7, 8], [5, 5, 7], [5, 5, 8], [5, 5], [5, 6, 7, 8], [5, 6, 7], [5, 6, 8], [5, 6], [5, 7, 8], [5, 7], [5, 8], [5], [6, 7, 8], [6, 7], [6, 8], [6], [7, 8], [7], [8], []]\n assert candidate(nums = [7, 6, 6, 5, 4, 4, 4, 3, 2, 1]) == [[1, 2, 3, 4, 4, 4, 5, 6, 6, 7], [1, 2, 3, 4, 4, 4, 5, 6, 6], [1, 2, 3, 4, 4, 4, 5, 6, 7], [1, 2, 3, 4, 4, 4, 5, 6], [1, 2, 3, 4, 4, 4, 5, 7], [1, 2, 3, 4, 4, 4, 5], [1, 2, 3, 4, 4, 4, 6, 6, 7], [1, 2, 3, 4, 4, 4, 6, 6], [1, 2, 3, 4, 4, 4, 6, 7], [1, 2, 3, 4, 4, 4, 6], [1, 2, 3, 4, 4, 4, 7], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4, 5, 6, 6, 7], [1, 2, 3, 4, 4, 5, 6, 6], [1, 2, 3, 4, 4, 5, 6, 7], [1, 2, 3, 4, 4, 5, 6], [1, 2, 3, 4, 4, 5, 7], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4, 6, 6, 7], [1, 2, 3, 4, 4, 6, 6], [1, 2, 3, 4, 4, 6, 7], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 4, 7], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 6, 6, 7], [1, 2, 3, 4, 5, 6, 6], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 6, 7], [1, 2, 3, 4, 6, 6], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4], [1, 2, 3, 5, 6, 6, 7], [1, 2, 3, 5, 6, 6], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5], [1, 2, 3, 6, 6, 7], [1, 2, 3, 6, 6], [1, 2, 3, 6, 7], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3], [1, 2, 4, 4, 4, 5, 6, 6, 7], [1, 2, 4, 4, 4, 5, 6, 6], [1, 2, 4, 4, 4, 5, 6, 7], [1, 2, 4, 4, 4, 5, 6], [1, 2, 4, 4, 4, 5, 7], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4, 6, 6, 7], [1, 2, 4, 4, 4, 6, 6], [1, 2, 4, 4, 4, 6, 7], [1, 2, 4, 4, 4, 6], [1, 2, 4, 4, 4, 7], [1, 2, 4, 4, 4], [1, 2, 4, 4, 5, 6, 6, 7], [1, 2, 4, 4, 5, 6, 6], [1, 2, 4, 4, 5, 6, 7], [1, 2, 4, 4, 5, 6], [1, 2, 4, 4, 5, 7], [1, 2, 4, 4, 5], [1, 2, 4, 4, 6, 6, 7], [1, 2, 4, 4, 6, 6], [1, 2, 4, 4, 6, 7], [1, 2, 4, 4, 6], [1, 2, 4, 4, 7], [1, 2, 4, 4], [1, 2, 4, 5, 6, 6, 7], [1, 2, 4, 5, 6, 6], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5], [1, 2, 4, 6, 6, 7], [1, 2, 4, 6, 6], [1, 2, 4, 6, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4], [1, 2, 5, 6, 6, 7], [1, 2, 5, 6, 6], [1, 2, 5, 6, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5], [1, 2, 6, 6, 7], [1, 2, 6, 6], [1, 2, 6, 7], [1, 2, 6], [1, 2, 7], [1, 2], [1, 3, 4, 4, 4, 5, 6, 6, 7], [1, 3, 4, 4, 4, 5, 6, 6], [1, 3, 4, 4, 4, 5, 6, 7], [1, 3, 4, 4, 4, 5, 6], [1, 3, 4, 4, 4, 5, 7], [1, 3, 4, 4, 4, 5], [1, 3, 4, 4, 4, 6, 6, 7], [1, 3, 4, 4, 4, 6, 6], [1, 3, 4, 4, 4, 6, 7], [1, 3, 4, 4, 4, 6], [1, 3, 4, 4, 4, 7], [1, 3, 4, 4, 4], [1, 3, 4, 4, 5, 6, 6, 7], [1, 3, 4, 4, 5, 6, 6], [1, 3, 4, 4, 5, 6, 7], [1, 3, 4, 4, 5, 6], [1, 3, 4, 4, 5, 7], [1, 3, 4, 4, 5], [1, 3, 4, 4, 6, 6, 7], [1, 3, 4, 4, 6, 6], [1, 3, 4, 4, 6, 7], [1, 3, 4, 4, 6], [1, 3, 4, 4, 7], [1, 3, 4, 4], [1, 3, 4, 5, 6, 6, 7], [1, 3, 4, 5, 6, 6], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5], [1, 3, 4, 6, 6, 7], [1, 3, 4, 6, 6], [1, 3, 4, 6, 7], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4], [1, 3, 5, 6, 6, 7], [1, 3, 5, 6, 6], [1, 3, 5, 6, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5], [1, 3, 6, 6, 7], [1, 3, 6, 6], [1, 3, 6, 7], [1, 3, 6], [1, 3, 7], [1, 3], [1, 4, 4, 4, 5, 6, 6, 7], [1, 4, 4, 4, 5, 6, 6], [1, 4, 4, 4, 5, 6, 7], [1, 4, 4, 4, 5, 6], [1, 4, 4, 4, 5, 7], [1, 4, 4, 4, 5], [1, 4, 4, 4, 6, 6, 7], [1, 4, 4, 4, 6, 6], [1, 4, 4, 4, 6, 7], [1, 4, 4, 4, 6], [1, 4, 4, 4, 7], [1, 4, 4, 4], [1, 4, 4, 5, 6, 6, 7], [1, 4, 4, 5, 6, 6], [1, 4, 4, 5, 6, 7], [1, 4, 4, 5, 6], [1, 4, 4, 5, 7], [1, 4, 4, 5], [1, 4, 4, 6, 6, 7], [1, 4, 4, 6, 6], [1, 4, 4, 6, 7], [1, 4, 4, 6], [1, 4, 4, 7], [1, 4, 4], [1, 4, 5, 6, 6, 7], [1, 4, 5, 6, 6], [1, 4, 5, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5], [1, 4, 6, 6, 7], [1, 4, 6, 6], [1, 4, 6, 7], [1, 4, 6], [1, 4, 7], [1, 4], [1, 5, 6, 6, 7], [1, 5, 6, 6], [1, 5, 6, 7], [1, 5, 6], [1, 5, 7], [1, 5], [1, 6, 6, 7], [1, 6, 6], [1, 6, 7], [1, 6], [1, 7], [1], [2, 3, 4, 4, 4, 5, 6, 6, 7], [2, 3, 4, 4, 4, 5, 6, 6], [2, 3, 4, 4, 4, 5, 6, 7], [2, 3, 4, 4, 4, 5, 6], [2, 3, 4, 4, 4, 5, 7], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4, 6, 6, 7], [2, 3, 4, 4, 4, 6, 6], [2, 3, 4, 4, 4, 6, 7], [2, 3, 4, 4, 4, 6], [2, 3, 4, 4, 4, 7], [2, 3, 4, 4, 4], [2, 3, 4, 4, 5, 6, 6, 7], [2, 3, 4, 4, 5, 6, 6], [2, 3, 4, 4, 5, 6, 7], [2, 3, 4, 4, 5, 6], [2, 3, 4, 4, 5, 7], [2, 3, 4, 4, 5], [2, 3, 4, 4, 6, 6, 7], [2, 3, 4, 4, 6, 6], [2, 3, 4, 4, 6, 7], [2, 3, 4, 4, 6], [2, 3, 4, 4, 7], [2, 3, 4, 4], [2, 3, 4, 5, 6, 6, 7], [2, 3, 4, 5, 6, 6], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5], [2, 3, 4, 6, 6, 7], [2, 3, 4, 6, 6], [2, 3, 4, 6, 7], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4], [2, 3, 5, 6, 6, 7], [2, 3, 5, 6, 6], [2, 3, 5, 6, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5], [2, 3, 6, 6, 7], [2, 3, 6, 6], [2, 3, 6, 7], [2, 3, 6], [2, 3, 7], [2, 3], [2, 4, 4, 4, 5, 6, 6, 7], [2, 4, 4, 4, 5, 6, 6], [2, 4, 4, 4, 5, 6, 7], [2, 4, 4, 4, 5, 6], [2, 4, 4, 4, 5, 7], [2, 4, 4, 4, 5], [2, 4, 4, 4, 6, 6, 7], [2, 4, 4, 4, 6, 6], [2, 4, 4, 4, 6, 7], [2, 4, 4, 4, 6], [2, 4, 4, 4, 7], [2, 4, 4, 4], [2, 4, 4, 5, 6, 6, 7], [2, 4, 4, 5, 6, 6], [2, 4, 4, 5, 6, 7], [2, 4, 4, 5, 6], [2, 4, 4, 5, 7], [2, 4, 4, 5], [2, 4, 4, 6, 6, 7], [2, 4, 4, 6, 6], [2, 4, 4, 6, 7], [2, 4, 4, 6], [2, 4, 4, 7], [2, 4, 4], [2, 4, 5, 6, 6, 7], [2, 4, 5, 6, 6], [2, 4, 5, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5], [2, 4, 6, 6, 7], [2, 4, 6, 6], [2, 4, 6, 7], [2, 4, 6], [2, 4, 7], [2, 4], [2, 5, 6, 6, 7], [2, 5, 6, 6], [2, 5, 6, 7], [2, 5, 6], [2, 5, 7], [2, 5], [2, 6, 6, 7], [2, 6, 6], [2, 6, 7], [2, 6], [2, 7], [2], [3, 4, 4, 4, 5, 6, 6, 7], [3, 4, 4, 4, 5, 6, 6], [3, 4, 4, 4, 5, 6, 7], [3, 4, 4, 4, 5, 6], [3, 4, 4, 4, 5, 7], [3, 4, 4, 4, 5], [3, 4, 4, 4, 6, 6, 7], [3, 4, 4, 4, 6, 6], [3, 4, 4, 4, 6, 7], [3, 4, 4, 4, 6], [3, 4, 4, 4, 7], [3, 4, 4, 4], [3, 4, 4, 5, 6, 6, 7], [3, 4, 4, 5, 6, 6], [3, 4, 4, 5, 6, 7], [3, 4, 4, 5, 6], [3, 4, 4, 5, 7], [3, 4, 4, 5], [3, 4, 4, 6, 6, 7], [3, 4, 4, 6, 6], [3, 4, 4, 6, 7], [3, 4, 4, 6], [3, 4, 4, 7], [3, 4, 4], [3, 4, 5, 6, 6, 7], [3, 4, 5, 6, 6], [3, 4, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5], [3, 4, 6, 6, 7], [3, 4, 6, 6], [3, 4, 6, 7], [3, 4, 6], [3, 4, 7], [3, 4], [3, 5, 6, 6, 7], [3, 5, 6, 6], [3, 5, 6, 7], [3, 5, 6], [3, 5, 7], [3, 5], [3, 6, 6, 7], [3, 6, 6], [3, 6, 7], [3, 6], [3, 7], [3], [4, 4, 4, 5, 6, 6, 7], [4, 4, 4, 5, 6, 6], [4, 4, 4, 5, 6, 7], [4, 4, 4, 5, 6], [4, 4, 4, 5, 7], [4, 4, 4, 5], [4, 4, 4, 6, 6, 7], [4, 4, 4, 6, 6], [4, 4, 4, 6, 7], [4, 4, 4, 6], [4, 4, 4, 7], [4, 4, 4], [4, 4, 5, 6, 6, 7], [4, 4, 5, 6, 6], [4, 4, 5, 6, 7], [4, 4, 5, 6], [4, 4, 5, 7], [4, 4, 5], [4, 4, 6, 6, 7], [4, 4, 6, 6], [4, 4, 6, 7], [4, 4, 6], [4, 4, 7], [4, 4], [4, 5, 6, 6, 7], [4, 5, 6, 6], [4, 5, 6, 7], [4, 5, 6], [4, 5, 7], [4, 5], [4, 6, 6, 7], [4, 6, 6], [4, 6, 7], [4, 6], [4, 7], [4], [5, 6, 6, 7], [5, 6, 6], [5, 6, 7], [5, 6], [5, 7], [5], [6, 6, 7], [6, 6], [6, 7], [6], [7], []]\n assert candidate(nums = [0, 0, 0, 1, 1, 2, 2, 2, 3, 3]) == [[0, 0, 0, 1, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 2, 3], [0, 0, 0, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3], [0, 0, 0, 1, 1, 2, 2], [0, 0, 0, 1, 1, 2, 3, 3], [0, 0, 0, 1, 1, 2, 3], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 1, 3, 3], [0, 0, 0, 1, 1, 3], [0, 0, 0, 1, 1], [0, 0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 2, 2, 2, 3], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 2, 2, 3, 3], [0, 0, 0, 1, 2, 2, 3], [0, 0, 0, 1, 2, 2], [0, 0, 0, 1, 2, 3, 3], [0, 0, 0, 1, 2, 3], [0, 0, 0, 1, 2], [0, 0, 0, 1, 3, 3], [0, 0, 0, 1, 3], [0, 0, 0, 1], [0, 0, 0, 2, 2, 2, 3, 3], [0, 0, 0, 2, 2, 2, 3], [0, 0, 0, 2, 2, 2], [0, 0, 0, 2, 2, 3, 3], [0, 0, 0, 2, 2, 3], [0, 0, 0, 2, 2], [0, 0, 0, 2, 3, 3], [0, 0, 0, 2, 3], [0, 0, 0, 2], [0, 0, 0, 3, 3], [0, 0, 0, 3], [0, 0, 0], [0, 0, 1, 1, 2, 2, 2, 3, 3], [0, 0, 1, 1, 2, 2, 2, 3], [0, 0, 1, 1, 2, 2, 2], [0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 1, 1, 2, 2, 3], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2, 3, 3], [0, 0, 1, 1, 2, 3], [0, 0, 1, 1, 2], [0, 0, 1, 1, 3, 3], [0, 0, 1, 1, 3], [0, 0, 1, 1], [0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 1, 2, 2, 2, 3], [0, 0, 1, 2, 2, 2], [0, 0, 1, 2, 2, 3, 3], [0, 0, 1, 2, 2, 3], [0, 0, 1, 2, 2], [0, 0, 1, 2, 3, 3], [0, 0, 1, 2, 3], [0, 0, 1, 2], [0, 0, 1, 3, 3], [0, 0, 1, 3], [0, 0, 1], [0, 0, 2, 2, 2, 3, 3], [0, 0, 2, 2, 2, 3], [0, 0, 2, 2, 2], [0, 0, 2, 2, 3, 3], [0, 0, 2, 2, 3], [0, 0, 2, 2], [0, 0, 2, 3, 3], [0, 0, 2, 3], [0, 0, 2], [0, 0, 3, 3], [0, 0, 3], [0, 0], [0, 1, 1, 2, 2, 2, 3, 3], [0, 1, 1, 2, 2, 2, 3], [0, 1, 1, 2, 2, 2], [0, 1, 1, 2, 2, 3, 3], [0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2], [0, 1, 1, 2, 3, 3], [0, 1, 1, 2, 3], [0, 1, 1, 2], [0, 1, 1, 3, 3], [0, 1, 1, 3], [0, 1, 1], [0, 1, 2, 2, 2, 3, 3], [0, 1, 2, 2, 2, 3], [0, 1, 2, 2, 2], [0, 1, 2, 2, 3, 3], [0, 1, 2, 2, 3], [0, 1, 2, 2], [0, 1, 2, 3, 3], [0, 1, 2, 3], [0, 1, 2], [0, 1, 3, 3], [0, 1, 3], [0, 1], [0, 2, 2, 2, 3, 3], [0, 2, 2, 2, 3], [0, 2, 2, 2], [0, 2, 2, 3, 3], [0, 2, 2, 3], [0, 2, 2], [0, 2, 3, 3], [0, 2, 3], [0, 2], [0, 3, 3], [0, 3], [0], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == [[6, 6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6], [6, 6, 6, 6], [6, 6, 6], [6, 6], [6], []]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 4]) == [[1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4], [2, 4, 4], [2, 4], [2], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4], [3, 4, 4], [3, 4], [3], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [4, 4, 4, 4, 5, 5, 5]) == [[4, 4, 4, 4, 5, 5, 5], [4, 4, 4, 4, 5, 5], [4, 4, 4, 4, 5], [4, 4, 4, 4], [4, 4, 4, 5, 5, 5], [4, 4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [4, 4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5, 5], [4, 5, 5], [4, 5], [4], [5, 5, 5], [5, 5], [5], []]\n assert candidate(nums = [3, 1, 2, 3, 2, 1]) == [[1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [5, 5, 4, 4, 4, 3, 3, 2, 2, 1]) == [[1, 2, 2, 3, 3, 4, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 4, 5], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4, 5, 5], [1, 2, 2, 4, 4, 4, 5], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 4, 5], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4, 5, 5], [1, 2, 3, 4, 4, 4, 5], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 4, 5, 5], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 4, 5, 5], [1, 3, 3, 4, 4, 4, 5], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 4, 5, 5], [1, 3, 4, 4, 4, 5], [1, 3, 4, 4, 4], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 4, 5, 5], [1, 4, 4, 4, 5], [1, 4, 4, 4], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5], [1, 5], [1], [2, 2, 3, 3, 4, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 4, 5], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4, 5, 5], [2, 2, 3, 4, 4, 4, 5], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 4, 5, 5], [2, 2, 4, 4, 4, 5], [2, 2, 4, 4, 4], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 4, 5, 5], [2, 3, 3, 4, 4, 4, 5], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 4, 5, 5], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 4, 5, 5], [2, 4, 4, 4, 5], [2, 4, 4, 4], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5], [2, 5], [2], [3, 3, 4, 4, 4, 5, 5], [3, 3, 4, 4, 4, 5], [3, 3, 4, 4, 4], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 4, 5, 5], [3, 4, 4, 4, 5], [3, 4, 4, 4], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5], [3, 5], [3], [4, 4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5], [4, 5], [4], [5, 5], [5], []]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8], [1, 2, 4, 9, 10], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 9, 10], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 7], [1, 2, 6, 8, 9, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 8], [1, 2, 6, 9, 10], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 8], [1, 2, 7, 9, 10], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7], [1, 2, 8, 9, 10], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8], [1, 2, 9, 10], [1, 2, 9], [1, 2, 10], [1, 2], [1, 3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 9, 10], 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9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [4], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [5], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [6], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [7], [8, 9, 10], [8, 9], [8, 10], [8], [9, 10], [9], [10], []]\n assert candidate(nums = [-1, -2, -3, -4, -5, 5, 4, 3, 2, 1]) == [[-5, -4, -3, -2, -1, 1, 2, 3, 4, 5], [-5, -4, -3, -2, -1, 1, 2, 3, 4], [-5, -4, -3, -2, -1, 1, 2, 3, 5], [-5, -4, -3, -2, -1, 1, 2, 3], [-5, -4, -3, -2, -1, 1, 2, 4, 5], [-5, -4, -3, -2, -1, 1, 2, 4], [-5, -4, -3, -2, -1, 1, 2, 5], [-5, -4, -3, -2, -1, 1, 2], [-5, -4, -3, -2, -1, 1, 3, 4, 5], [-5, -4, -3, -2, -1, 1, 3, 4], [-5, -4, -3, -2, -1, 1, 3, 5], [-5, -4, -3, -2, -1, 1, 3], [-5, -4, -3, -2, -1, 1, 4, 5], [-5, -4, -3, -2, -1, 1, 4], [-5, -4, -3, -2, -1, 1, 5], [-5, -4, -3, -2, -1, 1], [-5, -4, -3, -2, -1, 2, 3, 4, 5], [-5, -4, -3, -2, -1, 2, 3, 4], [-5, -4, -3, -2, -1, 2, 3, 5], [-5, -4, -3, -2, -1, 2, 3], [-5, -4, -3, -2, -1, 2, 4, 5], [-5, -4, -3, -2, -1, 2, 4], [-5, -4, -3, -2, -1, 2, 5], [-5, -4, -3, -2, -1, 2], [-5, -4, -3, -2, -1, 3, 4, 5], [-5, -4, -3, -2, -1, 3, 4], [-5, -4, -3, -2, -1, 3, 5], [-5, -4, -3, -2, -1, 3], [-5, -4, -3, -2, -1, 4, 5], [-5, -4, -3, -2, -1, 4], [-5, -4, -3, -2, -1, 5], [-5, -4, -3, -2, -1], [-5, -4, -3, -2, 1, 2, 3, 4, 5], [-5, -4, -3, -2, 1, 2, 3, 4], [-5, -4, -3, -2, 1, 2, 3, 5], [-5, -4, -3, -2, 1, 2, 3], [-5, -4, -3, -2, 1, 2, 4, 5], [-5, -4, -3, -2, 1, 2, 4], [-5, -4, -3, -2, 1, 2, 5], [-5, -4, -3, -2, 1, 2], [-5, -4, -3, -2, 1, 3, 4, 5], [-5, -4, -3, -2, 1, 3, 4], [-5, -4, -3, -2, 1, 3, 5], [-5, -4, -3, -2, 1, 3], [-5, -4, -3, -2, 1, 4, 5], [-5, -4, -3, -2, 1, 4], [-5, -4, -3, -2, 1, 5], [-5, -4, -3, -2, 1], [-5, -4, -3, -2, 2, 3, 4, 5], [-5, -4, -3, -2, 2, 3, 4], [-5, -4, -3, -2, 2, 3, 5], [-5, -4, -3, -2, 2, 3], [-5, -4, -3, -2, 2, 4, 5], [-5, -4, -3, -2, 2, 4], [-5, -4, -3, -2, 2, 5], [-5, -4, -3, -2, 2], [-5, -4, -3, -2, 3, 4, 5], [-5, -4, -3, -2, 3, 4], [-5, -4, -3, -2, 3, 5], [-5, -4, -3, -2, 3], [-5, -4, -3, -2, 4, 5], [-5, -4, -3, -2, 4], [-5, -4, -3, -2, 5], [-5, -4, -3, -2], [-5, -4, -3, -1, 1, 2, 3, 4, 5], [-5, -4, -3, -1, 1, 2, 3, 4], [-5, -4, -3, -1, 1, 2, 3, 5], [-5, -4, -3, -1, 1, 2, 3], [-5, -4, -3, -1, 1, 2, 4, 5], [-5, -4, -3, -1, 1, 2, 4], [-5, -4, -3, -1, 1, 2, 5], [-5, -4, -3, -1, 1, 2], [-5, -4, -3, -1, 1, 3, 4, 5], [-5, -4, -3, -1, 1, 3, 4], [-5, -4, -3, -1, 1, 3, 5], [-5, -4, -3, -1, 1, 3], [-5, -4, -3, -1, 1, 4, 5], [-5, -4, -3, -1, 1, 4], [-5, -4, -3, -1, 1, 5], [-5, -4, -3, -1, 1], [-5, -4, -3, -1, 2, 3, 4, 5], [-5, -4, -3, -1, 2, 3, 4], [-5, -4, -3, -1, 2, 3, 5], [-5, -4, -3, -1, 2, 3], [-5, -4, -3, -1, 2, 4, 5], [-5, -4, -3, -1, 2, 4], [-5, -4, -3, -1, 2, 5], [-5, -4, -3, -1, 2], [-5, -4, -3, -1, 3, 4, 5], [-5, -4, -3, -1, 3, 4], [-5, -4, -3, -1, 3, 5], [-5, -4, -3, -1, 3], [-5, -4, -3, -1, 4, 5], [-5, -4, -3, -1, 4], [-5, -4, -3, -1, 5], [-5, -4, -3, -1], [-5, -4, -3, 1, 2, 3, 4, 5], [-5, -4, -3, 1, 2, 3, 4], [-5, -4, -3, 1, 2, 3, 5], [-5, -4, -3, 1, 2, 3], [-5, -4, -3, 1, 2, 4, 5], [-5, -4, -3, 1, 2, 4], [-5, -4, -3, 1, 2, 5], [-5, -4, -3, 1, 2], [-5, -4, -3, 1, 3, 4, 5], [-5, -4, -3, 1, 3, 4], [-5, -4, -3, 1, 3, 5], [-5, -4, -3, 1, 3], [-5, -4, -3, 1, 4, 5], [-5, -4, -3, 1, 4], [-5, -4, -3, 1, 5], [-5, -4, -3, 1], [-5, -4, -3, 2, 3, 4, 5], [-5, -4, -3, 2, 3, 4], [-5, -4, -3, 2, 3, 5], [-5, -4, -3, 2, 3], [-5, -4, -3, 2, 4, 5], [-5, -4, -3, 2, 4], [-5, -4, -3, 2, 5], [-5, -4, -3, 2], [-5, -4, -3, 3, 4, 5], [-5, -4, -3, 3, 4], [-5, -4, -3, 3, 5], [-5, -4, -3, 3], [-5, -4, -3, 4, 5], [-5, -4, -3, 4], [-5, -4, -3, 5], [-5, -4, -3], [-5, -4, -2, -1, 1, 2, 3, 4, 5], [-5, -4, -2, -1, 1, 2, 3, 4], [-5, -4, -2, -1, 1, 2, 3, 5], [-5, -4, -2, -1, 1, 2, 3], [-5, -4, -2, -1, 1, 2, 4, 5], [-5, -4, -2, -1, 1, 2, 4], [-5, -4, -2, -1, 1, 2, 5], [-5, -4, -2, -1, 1, 2], [-5, -4, -2, -1, 1, 3, 4, 5], [-5, -4, -2, -1, 1, 3, 4], [-5, -4, -2, -1, 1, 3, 5], [-5, -4, -2, -1, 1, 3], [-5, -4, -2, -1, 1, 4, 5], [-5, -4, -2, -1, 1, 4], [-5, -4, -2, -1, 1, 5], [-5, -4, -2, -1, 1], [-5, -4, -2, -1, 2, 3, 4, 5], [-5, -4, -2, -1, 2, 3, 4], [-5, -4, -2, -1, 2, 3, 5], [-5, -4, -2, -1, 2, 3], [-5, -4, -2, -1, 2, 4, 5], [-5, -4, -2, -1, 2, 4], [-5, -4, -2, -1, 2, 5], [-5, -4, -2, -1, 2], [-5, -4, -2, -1, 3, 4, 5], [-5, -4, -2, -1, 3, 4], [-5, -4, -2, -1, 3, 5], [-5, -4, -2, -1, 3], [-5, -4, -2, -1, 4, 5], [-5, -4, -2, -1, 4], [-5, -4, -2, -1, 5], [-5, -4, -2, -1], [-5, -4, -2, 1, 2, 3, 4, 5], [-5, -4, -2, 1, 2, 3, 4], [-5, -4, -2, 1, 2, 3, 5], [-5, -4, -2, 1, 2, 3], [-5, -4, -2, 1, 2, 4, 5], [-5, -4, -2, 1, 2, 4], [-5, -4, -2, 1, 2, 5], [-5, -4, -2, 1, 2], [-5, -4, -2, 1, 3, 4, 5], [-5, -4, -2, 1, 3, 4], [-5, -4, -2, 1, 3, 5], [-5, -4, -2, 1, 3], [-5, -4, -2, 1, 4, 5], [-5, -4, -2, 1, 4], [-5, -4, -2, 1, 5], [-5, -4, -2, 1], [-5, -4, -2, 2, 3, 4, 5], [-5, -4, -2, 2, 3, 4], [-5, -4, -2, 2, 3, 5], [-5, -4, -2, 2, 3], [-5, -4, -2, 2, 4, 5], [-5, -4, -2, 2, 4], [-5, -4, -2, 2, 5], [-5, -4, -2, 2], [-5, -4, -2, 3, 4, 5], [-5, -4, -2, 3, 4], [-5, -4, -2, 3, 5], [-5, -4, -2, 3], [-5, -4, -2, 4, 5], [-5, -4, -2, 4], [-5, -4, -2, 5], [-5, -4, -2], [-5, -4, -1, 1, 2, 3, 4, 5], [-5, -4, -1, 1, 2, 3, 4], [-5, -4, -1, 1, 2, 3, 5], [-5, -4, -1, 1, 2, 3], [-5, -4, -1, 1, 2, 4, 5], [-5, -4, -1, 1, 2, 4], [-5, -4, -1, 1, 2, 5], [-5, -4, -1, 1, 2], [-5, -4, -1, 1, 3, 4, 5], [-5, -4, -1, 1, 3, 4], [-5, -4, -1, 1, 3, 5], [-5, -4, -1, 1, 3], [-5, -4, -1, 1, 4, 5], [-5, -4, -1, 1, 4], [-5, -4, -1, 1, 5], [-5, -4, -1, 1], [-5, -4, -1, 2, 3, 4, 5], [-5, -4, -1, 2, 3, 4], [-5, -4, -1, 2, 3, 5], [-5, -4, -1, 2, 3], [-5, -4, -1, 2, 4, 5], [-5, -4, -1, 2, 4], [-5, -4, -1, 2, 5], [-5, -4, -1, 2], [-5, -4, -1, 3, 4, 5], [-5, -4, -1, 3, 4], [-5, -4, -1, 3, 5], [-5, -4, -1, 3], [-5, -4, -1, 4, 5], [-5, -4, -1, 4], [-5, -4, -1, 5], [-5, -4, -1], [-5, -4, 1, 2, 3, 4, 5], [-5, -4, 1, 2, 3, 4], [-5, -4, 1, 2, 3, 5], [-5, -4, 1, 2, 3], [-5, -4, 1, 2, 4, 5], [-5, -4, 1, 2, 4], [-5, -4, 1, 2, 5], [-5, -4, 1, 2], [-5, -4, 1, 3, 4, 5], [-5, -4, 1, 3, 4], [-5, -4, 1, 3, 5], [-5, -4, 1, 3], [-5, -4, 1, 4, 5], [-5, -4, 1, 4], [-5, -4, 1, 5], [-5, -4, 1], [-5, -4, 2, 3, 4, 5], [-5, -4, 2, 3, 4], [-5, -4, 2, 3, 5], [-5, -4, 2, 3], [-5, -4, 2, 4, 5], [-5, -4, 2, 4], [-5, -4, 2, 5], [-5, -4, 2], [-5, -4, 3, 4, 5], [-5, -4, 3, 4], [-5, -4, 3, 5], [-5, -4, 3], [-5, -4, 4, 5], [-5, -4, 4], [-5, -4, 5], [-5, -4], [-5, -3, -2, -1, 1, 2, 3, 4, 5], [-5, -3, -2, -1, 1, 2, 3, 4], [-5, -3, -2, -1, 1, 2, 3, 5], [-5, -3, -2, -1, 1, 2, 3], [-5, -3, -2, -1, 1, 2, 4, 5], [-5, -3, -2, -1, 1, 2, 4], [-5, -3, -2, -1, 1, 2, 5], [-5, -3, -2, -1, 1, 2], [-5, -3, -2, -1, 1, 3, 4, 5], [-5, -3, -2, -1, 1, 3, 4], [-5, -3, -2, -1, 1, 3, 5], [-5, -3, -2, -1, 1, 3], [-5, -3, -2, -1, 1, 4, 5], 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1, 2, 5], [-2, -1, 1, 2], [-2, -1, 1, 3, 4, 5], [-2, -1, 1, 3, 4], [-2, -1, 1, 3, 5], [-2, -1, 1, 3], [-2, -1, 1, 4, 5], [-2, -1, 1, 4], [-2, -1, 1, 5], [-2, -1, 1], [-2, -1, 2, 3, 4, 5], [-2, -1, 2, 3, 4], [-2, -1, 2, 3, 5], [-2, -1, 2, 3], [-2, -1, 2, 4, 5], [-2, -1, 2, 4], [-2, -1, 2, 5], [-2, -1, 2], [-2, -1, 3, 4, 5], [-2, -1, 3, 4], [-2, -1, 3, 5], [-2, -1, 3], [-2, -1, 4, 5], [-2, -1, 4], [-2, -1, 5], [-2, -1], [-2, 1, 2, 3, 4, 5], [-2, 1, 2, 3, 4], [-2, 1, 2, 3, 5], [-2, 1, 2, 3], [-2, 1, 2, 4, 5], [-2, 1, 2, 4], [-2, 1, 2, 5], [-2, 1, 2], [-2, 1, 3, 4, 5], [-2, 1, 3, 4], [-2, 1, 3, 5], [-2, 1, 3], [-2, 1, 4, 5], [-2, 1, 4], [-2, 1, 5], [-2, 1], [-2, 2, 3, 4, 5], [-2, 2, 3, 4], [-2, 2, 3, 5], [-2, 2, 3], [-2, 2, 4, 5], [-2, 2, 4], [-2, 2, 5], [-2, 2], [-2, 3, 4, 5], [-2, 3, 4], [-2, 3, 5], [-2, 3], [-2, 4, 5], [-2, 4], [-2, 5], [-2], [-1, 1, 2, 3, 4, 5], [-1, 1, 2, 3, 4], [-1, 1, 2, 3, 5], [-1, 1, 2, 3], [-1, 1, 2, 4, 5], [-1, 1, 2, 4], [-1, 1, 2, 5], [-1, 1, 2], [-1, 1, 3, 4, 5], [-1, 1, 3, 4], [-1, 1, 3, 5], [-1, 1, 3], [-1, 1, 4, 5], [-1, 1, 4], [-1, 1, 5], [-1, 1], [-1, 2, 3, 4, 5], [-1, 2, 3, 4], [-1, 2, 3, 5], [-1, 2, 3], [-1, 2, 4, 5], [-1, 2, 4], [-1, 2, 5], [-1, 2], [-1, 3, 4, 5], [-1, 3, 4], [-1, 3, 5], [-1, 3], [-1, 4, 5], [-1, 4], [-1, 5], [-1], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [1], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [2], [3, 4, 5], [3, 4], [3, 5], [3], [4, 5], [4], [5], []]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0], [0], []]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8], [1, 2, 4, 9, 10], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 9, 10], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 7], [1, 2, 6, 8, 9, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 8], [1, 2, 6, 9, 10], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 8], [1, 2, 7, 9, 10], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7], [1, 2, 8, 9, 10], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8], [1, 2, 9, 10], [1, 2, 9], [1, 2, 10], [1, 2], [1, 3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 9, 10], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 10], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8, 9, 10], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 8, 10], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 9, 10], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 10], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7, 8, 9, 10], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 7, 8, 10], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 9, 10], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8, 9, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9, 10], [1, 3, 4, 5, 9], [1, 3, 4, 5, 10], [1, 3, 4, 5], [1, 3, 4, 6, 7, 8, 9, 10], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 6, 7, 8, 10], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 9, 10], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8, 9, 10], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9, 10], [1, 3, 4, 6, 9], [1, 3, 4, 6, 10], [1, 3, 4, 6], [1, 3, 4, 7, 8, 9, 10], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 7], [1, 3, 4, 8, 9, 10], [1, 3, 4, 8, 9], [1, 3, 4, 8, 10], [1, 3, 4, 8], [1, 3, 4, 9, 10], [1, 3, 4, 9], [1, 3, 4, 10], [1, 3, 4], [1, 3, 5, 6, 7, 8, 9, 10], [1, 3, 5, 6, 7, 8, 9], [1, 3, 5, 6, 7, 8, 10], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 9, 10], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8, 9, 10], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9, 10], [1, 3, 5, 6, 9], [1, 3, 5, 6, 10], [1, 3, 5, 6], [1, 3, 5, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 3, 5, 7, 8, 10], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 9], [1, 3, 5, 7, 10], [1, 3, 5, 7], [1, 3, 5, 8, 9, 10], [1, 3, 5, 8, 9], [1, 3, 5, 8, 10], [1, 3, 5, 8], [1, 3, 5, 9, 10], [1, 3, 5, 9], [1, 3, 5, 10], [1, 3, 5], [1, 3, 6, 7, 8, 9, 10], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9, 10], [1, 3, 6, 7, 9], [1, 3, 6, 7, 10], [1, 3, 6, 7], [1, 3, 6, 8, 9, 10], [1, 3, 6, 8, 9], [1, 3, 6, 8, 10], [1, 3, 6, 8], [1, 3, 6, 9, 10], [1, 3, 6, 9], [1, 3, 6, 10], [1, 3, 6], [1, 3, 7, 8, 9, 10], [1, 3, 7, 8, 9], [1, 3, 7, 8, 10], [1, 3, 7, 8], [1, 3, 7, 9, 10], [1, 3, 7, 9], [1, 3, 7, 10], [1, 3, 7], [1, 3, 8, 9, 10], [1, 3, 8, 9], [1, 3, 8, 10], [1, 3, 8], [1, 3, 9, 10], [1, 3, 9], [1, 3, 10], [1, 3], [1, 4, 5, 6, 7, 8, 9, 10], [1, 4, 5, 6, 7, 8, 9], [1, 4, 5, 6, 7, 8, 10], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 9, 10], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8, 9, 10], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9, 10], [1, 4, 5, 6, 9], [1, 4, 5, 6, 10], [1, 4, 5, 6], [1, 4, 5, 7, 8, 9, 10], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 9], [1, 4, 5, 7, 10], [1, 4, 5, 7], [1, 4, 5, 8, 9, 10], [1, 4, 5, 8, 9], [1, 4, 5, 8, 10], [1, 4, 5, 8], [1, 4, 5, 9, 10], [1, 4, 5, 9], [1, 4, 5, 10], [1, 4, 5], [1, 4, 6, 7, 8, 9, 10], [1, 4, 6, 7, 8, 9], [1, 4, 6, 7, 8, 10], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9, 10], [1, 4, 6, 7, 9], [1, 4, 6, 7, 10], [1, 4, 6, 7], [1, 4, 6, 8, 9, 10], [1, 4, 6, 8, 9], [1, 4, 6, 8, 10], [1, 4, 6, 8], [1, 4, 6, 9, 10], [1, 4, 6, 9], [1, 4, 6, 10], [1, 4, 6], [1, 4, 7, 8, 9, 10], [1, 4, 7, 8, 9], [1, 4, 7, 8, 10], [1, 4, 7, 8], [1, 4, 7, 9, 10], [1, 4, 7, 9], [1, 4, 7, 10], [1, 4, 7], [1, 4, 8, 9, 10], [1, 4, 8, 9], [1, 4, 8, 10], [1, 4, 8], [1, 4, 9, 10], [1, 4, 9], [1, 4, 10], [1, 4], [1, 5, 6, 7, 8, 9, 10], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9, 10], [1, 5, 6, 7, 9], [1, 5, 6, 7, 10], [1, 5, 6, 7], [1, 5, 6, 8, 9, 10], [1, 5, 6, 8, 9], [1, 5, 6, 8, 10], [1, 5, 6, 8], [1, 5, 6, 9, 10], [1, 5, 6, 9], [1, 5, 6, 10], [1, 5, 6], [1, 5, 7, 8, 9, 10], [1, 5, 7, 8, 9], [1, 5, 7, 8, 10], [1, 5, 7, 8], [1, 5, 7, 9, 10], [1, 5, 7, 9], [1, 5, 7, 10], [1, 5, 7], [1, 5, 8, 9, 10], [1, 5, 8, 9], [1, 5, 8, 10], [1, 5, 8], [1, 5, 9, 10], [1, 5, 9], [1, 5, 10], [1, 5], [1, 6, 7, 8, 9, 10], [1, 6, 7, 8, 9], [1, 6, 7, 8, 10], [1, 6, 7, 8], [1, 6, 7, 9, 10], [1, 6, 7, 9], [1, 6, 7, 10], [1, 6, 7], [1, 6, 8, 9, 10], [1, 6, 8, 9], [1, 6, 8, 10], [1, 6, 8], [1, 6, 9, 10], [1, 6, 9], [1, 6, 10], [1, 6], [1, 7, 8, 9, 10], [1, 7, 8, 9], [1, 7, 8, 10], [1, 7, 8], [1, 7, 9, 10], [1, 7, 9], [1, 7, 10], [1, 7], [1, 8, 9, 10], [1, 8, 9], [1, 8, 10], [1, 8], [1, 9, 10], [1, 9], [1, 10], [1], [2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9], [2, 3, 4, 5, 6, 7, 8, 10], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 9, 10], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 10], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8, 9, 10], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 8, 10], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 9, 10], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7, 8, 9, 10], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 7, 8, 10], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 9, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8, 9, 10], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 8, 10], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9, 10], [2, 3, 4, 5, 9], [2, 3, 4, 5, 10], [2, 3, 4, 5], [2, 3, 4, 6, 7, 8, 9, 10], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 6, 7, 8, 10], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 9, 10], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 10], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8, 9, 10], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 9], [2, 3, 4, 6, 10], [2, 3, 4, 6], [2, 3, 4, 7, 8, 9, 10], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 9], [2, 3, 4, 7, 10], [2, 3, 4, 7], [2, 3, 4, 8, 9, 10], [2, 3, 4, 8, 9], [2, 3, 4, 8, 10], [2, 3, 4, 8], [2, 3, 4, 9, 10], [2, 3, 4, 9], [2, 3, 4, 10], [2, 3, 4], [2, 3, 5, 6, 7, 8, 9, 10], [2, 3, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 10], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8, 9, 10], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 8, 10], [2, 3, 5, 6, 8], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 9], [2, 3, 5, 6, 10], [2, 3, 5, 6], [2, 3, 5, 7, 8, 9, 10], [2, 3, 5, 7, 8, 9], [2, 3, 5, 7, 8, 10], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 9], [2, 3, 5, 7, 10], [2, 3, 5, 7], [2, 3, 5, 8, 9, 10], [2, 3, 5, 8, 9], [2, 3, 5, 8, 10], [2, 3, 5, 8], [2, 3, 5, 9, 10], [2, 3, 5, 9], [2, 3, 5, 10], [2, 3, 5], [2, 3, 6, 7, 8, 9, 10], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 9], [2, 3, 6, 7, 10], [2, 3, 6, 7], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 10], [2, 3, 6, 8], [2, 3, 6, 9, 10], [2, 3, 6, 9], [2, 3, 6, 10], [2, 3, 6], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 10], [2, 3, 7, 8], [2, 3, 7, 9, 10], [2, 3, 7, 9], [2, 3, 7, 10], [2, 3, 7], [2, 3, 8, 9, 10], [2, 3, 8, 9], [2, 3, 8, 10], [2, 3, 8], [2, 3, 9, 10], [2, 3, 9], [2, 3, 10], [2, 3], [2, 4, 5, 6, 7, 8, 9, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9], [2, 4, 5, 6, 10], [2, 4, 5, 6], [2, 4, 5, 7, 8, 9, 10], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9], [2, 4, 5, 7, 10], [2, 4, 5, 7], [2, 4, 5, 8, 9, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 10], [2, 4, 5, 8], [2, 4, 5, 9, 10], [2, 4, 5, 9], [2, 4, 5, 10], [2, 4, 5], [2, 4, 6, 7, 8, 9, 10], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 9], [2, 4, 6, 7, 10], [2, 4, 6, 7], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 10], [2, 4, 6, 8], [2, 4, 6, 9, 10], [2, 4, 6, 9], [2, 4, 6, 10], [2, 4, 6], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 10], [2, 4, 7, 8], [2, 4, 7, 9, 10], [2, 4, 7, 9], [2, 4, 7, 10], [2, 4, 7], [2, 4, 8, 9, 10], [2, 4, 8, 9], [2, 4, 8, 10], [2, 4, 8], [2, 4, 9, 10], [2, 4, 9], [2, 4, 10], [2, 4], [2, 5, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 10], [2, 5, 6, 7], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 10], [2, 5, 6, 8], [2, 5, 6, 9, 10], [2, 5, 6, 9], [2, 5, 6, 10], [2, 5, 6], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 10], [2, 5, 7, 8], [2, 5, 7, 9, 10], [2, 5, 7, 9], [2, 5, 7, 10], [2, 5, 7], [2, 5, 8, 9, 10], [2, 5, 8, 9], [2, 5, 8, 10], [2, 5, 8], [2, 5, 9, 10], [2, 5, 9], [2, 5, 10], [2, 5], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 10], [2, 6, 7, 8], [2, 6, 7, 9, 10], [2, 6, 7, 9], [2, 6, 7, 10], [2, 6, 7], [2, 6, 8, 9, 10], [2, 6, 8, 9], [2, 6, 8, 10], [2, 6, 8], [2, 6, 9, 10], [2, 6, 9], [2, 6, 10], [2, 6], [2, 7, 8, 9, 10], [2, 7, 8, 9], [2, 7, 8, 10], [2, 7, 8], [2, 7, 9, 10], [2, 7, 9], [2, 7, 10], [2, 7], [2, 8, 9, 10], [2, 8, 9], [2, 8, 10], [2, 8], [2, 9, 10], [2, 9], [2, 10], [2], [3, 4, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 10], [3, 4, 5, 6], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 10], [3, 4, 5, 7], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 10], [3, 4, 5, 8], [3, 4, 5, 9, 10], [3, 4, 5, 9], [3, 4, 5, 10], [3, 4, 5], [3, 4, 6, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 10], [3, 4, 6, 7], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 10], [3, 4, 6, 8], [3, 4, 6, 9, 10], [3, 4, 6, 9], [3, 4, 6, 10], [3, 4, 6], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 10], [3, 4, 7, 8], [3, 4, 7, 9, 10], [3, 4, 7, 9], [3, 4, 7, 10], [3, 4, 7], [3, 4, 8, 9, 10], [3, 4, 8, 9], [3, 4, 8, 10], [3, 4, 8], [3, 4, 9, 10], [3, 4, 9], [3, 4, 10], [3, 4], [3, 5, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 10], [3, 5, 6, 7], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 10], [3, 5, 6, 8], [3, 5, 6, 9, 10], [3, 5, 6, 9], [3, 5, 6, 10], [3, 5, 6], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 10], [3, 5, 7, 8], [3, 5, 7, 9, 10], [3, 5, 7, 9], [3, 5, 7, 10], [3, 5, 7], [3, 5, 8, 9, 10], [3, 5, 8, 9], [3, 5, 8, 10], [3, 5, 8], [3, 5, 9, 10], [3, 5, 9], [3, 5, 10], [3, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8], [3, 6, 9, 10], [3, 6, 9], [3, 6, 10], [3, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8], [3, 7, 9, 10], [3, 7, 9], [3, 7, 10], [3, 7], [3, 8, 9, 10], [3, 8, 9], [3, 8, 10], [3, 8], [3, 9, 10], [3, 9], [3, 10], [3], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [4], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [5], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [6], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [7], [8, 9, 10], [8, 9], [8, 10], [8], [9, 10], [9], [10], []]\n assert candidate(nums = [-2, -1, 0, 0, 1, 2]) == [[-2, -1, 0, 0, 1, 2], [-2, -1, 0, 0, 1], [-2, -1, 0, 0, 2], [-2, -1, 0, 0], [-2, -1, 0, 1, 2], [-2, -1, 0, 1], [-2, -1, 0, 2], [-2, -1, 0], [-2, -1, 1, 2], [-2, -1, 1], [-2, -1, 2], [-2, -1], [-2, 0, 0, 1, 2], [-2, 0, 0, 1], [-2, 0, 0, 2], [-2, 0, 0], [-2, 0, 1, 2], [-2, 0, 1], [-2, 0, 2], [-2, 0], [-2, 1, 2], [-2, 1], [-2, 2], [-2], [-1, 0, 0, 1, 2], [-1, 0, 0, 1], [-1, 0, 0, 2], [-1, 0, 0], [-1, 0, 1, 2], [-1, 0, 1], [-1, 0, 2], [-1, 0], [-1, 1, 2], [-1, 1], [-1, 2], [-1], [0, 0, 1, 2], [0, 0, 1], [0, 0, 2], [0, 0], [0, 1, 2], [0, 1], [0, 2], [0], [1, 2], [1], [2], []]\n assert candidate(nums = [6, 6, 6, 6, 6, 6, 6]) == [[6, 6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6, 6], [6, 6, 6, 6, 6], [6, 6, 6, 6], [6, 6, 6], [6, 6], [6], []]\n assert candidate(nums = [10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8], [1, 2, 4, 9, 10], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 9, 10], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 7], [1, 2, 6, 8, 9, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 8], [1, 2, 6, 9, 10], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 8], [1, 2, 7, 9, 10], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7], [1, 2, 8, 9, 10], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8], [1, 2, 9, 10], [1, 2, 9], [1, 2, 10], [1, 2], [1, 3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 9, 10], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 10], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8, 9, 10], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 8, 10], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 9, 10], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 10], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7, 8, 9, 10], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 7, 8, 10], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 9, 10], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8, 9, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9, 10], [1, 3, 4, 5, 9], [1, 3, 4, 5, 10], [1, 3, 4, 5], [1, 3, 4, 6, 7, 8, 9, 10], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 6, 7, 8, 10], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 9, 10], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8, 9, 10], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9, 10], [1, 3, 4, 6, 9], [1, 3, 4, 6, 10], [1, 3, 4, 6], [1, 3, 4, 7, 8, 9, 10], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 7], [1, 3, 4, 8, 9, 10], [1, 3, 4, 8, 9], [1, 3, 4, 8, 10], [1, 3, 4, 8], [1, 3, 4, 9, 10], [1, 3, 4, 9], [1, 3, 4, 10], [1, 3, 4], [1, 3, 5, 6, 7, 8, 9, 10], [1, 3, 5, 6, 7, 8, 9], [1, 3, 5, 6, 7, 8, 10], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 9, 10], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8, 9, 10], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9, 10], [1, 3, 5, 6, 9], [1, 3, 5, 6, 10], [1, 3, 5, 6], [1, 3, 5, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 3, 5, 7, 8, 10], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 9], [1, 3, 5, 7, 10], [1, 3, 5, 7], [1, 3, 5, 8, 9, 10], [1, 3, 5, 8, 9], [1, 3, 5, 8, 10], [1, 3, 5, 8], [1, 3, 5, 9, 10], [1, 3, 5, 9], [1, 3, 5, 10], [1, 3, 5], [1, 3, 6, 7, 8, 9, 10], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9, 10], [1, 3, 6, 7, 9], [1, 3, 6, 7, 10], [1, 3, 6, 7], [1, 3, 6, 8, 9, 10], [1, 3, 6, 8, 9], [1, 3, 6, 8, 10], [1, 3, 6, 8], [1, 3, 6, 9, 10], [1, 3, 6, 9], [1, 3, 6, 10], [1, 3, 6], [1, 3, 7, 8, 9, 10], [1, 3, 7, 8, 9], [1, 3, 7, 8, 10], [1, 3, 7, 8], [1, 3, 7, 9, 10], [1, 3, 7, 9], [1, 3, 7, 10], [1, 3, 7], [1, 3, 8, 9, 10], [1, 3, 8, 9], [1, 3, 8, 10], [1, 3, 8], [1, 3, 9, 10], [1, 3, 9], [1, 3, 10], [1, 3], [1, 4, 5, 6, 7, 8, 9, 10], [1, 4, 5, 6, 7, 8, 9], [1, 4, 5, 6, 7, 8, 10], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 9, 10], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8, 9, 10], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9, 10], [1, 4, 5, 6, 9], [1, 4, 5, 6, 10], [1, 4, 5, 6], [1, 4, 5, 7, 8, 9, 10], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 9], [1, 4, 5, 7, 10], [1, 4, 5, 7], [1, 4, 5, 8, 9, 10], [1, 4, 5, 8, 9], [1, 4, 5, 8, 10], [1, 4, 5, 8], [1, 4, 5, 9, 10], [1, 4, 5, 9], [1, 4, 5, 10], [1, 4, 5], [1, 4, 6, 7, 8, 9, 10], [1, 4, 6, 7, 8, 9], [1, 4, 6, 7, 8, 10], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9, 10], [1, 4, 6, 7, 9], [1, 4, 6, 7, 10], [1, 4, 6, 7], [1, 4, 6, 8, 9, 10], [1, 4, 6, 8, 9], [1, 4, 6, 8, 10], [1, 4, 6, 8], [1, 4, 6, 9, 10], [1, 4, 6, 9], [1, 4, 6, 10], [1, 4, 6], [1, 4, 7, 8, 9, 10], [1, 4, 7, 8, 9], [1, 4, 7, 8, 10], [1, 4, 7, 8], [1, 4, 7, 9, 10], [1, 4, 7, 9], [1, 4, 7, 10], [1, 4, 7], [1, 4, 8, 9, 10], [1, 4, 8, 9], [1, 4, 8, 10], [1, 4, 8], [1, 4, 9, 10], [1, 4, 9], [1, 4, 10], [1, 4], [1, 5, 6, 7, 8, 9, 10], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9, 10], [1, 5, 6, 7, 9], [1, 5, 6, 7, 10], [1, 5, 6, 7], [1, 5, 6, 8, 9, 10], [1, 5, 6, 8, 9], [1, 5, 6, 8, 10], [1, 5, 6, 8], [1, 5, 6, 9, 10], [1, 5, 6, 9], [1, 5, 6, 10], [1, 5, 6], [1, 5, 7, 8, 9, 10], [1, 5, 7, 8, 9], [1, 5, 7, 8, 10], [1, 5, 7, 8], [1, 5, 7, 9, 10], [1, 5, 7, 9], [1, 5, 7, 10], [1, 5, 7], [1, 5, 8, 9, 10], [1, 5, 8, 9], [1, 5, 8, 10], [1, 5, 8], [1, 5, 9, 10], [1, 5, 9], [1, 5, 10], [1, 5], [1, 6, 7, 8, 9, 10], [1, 6, 7, 8, 9], [1, 6, 7, 8, 10], [1, 6, 7, 8], [1, 6, 7, 9, 10], [1, 6, 7, 9], [1, 6, 7, 10], [1, 6, 7], [1, 6, 8, 9, 10], [1, 6, 8, 9], [1, 6, 8, 10], [1, 6, 8], [1, 6, 9, 10], [1, 6, 9], [1, 6, 10], [1, 6], [1, 7, 8, 9, 10], [1, 7, 8, 9], [1, 7, 8, 10], [1, 7, 8], [1, 7, 9, 10], [1, 7, 9], [1, 7, 10], [1, 7], [1, 8, 9, 10], [1, 8, 9], [1, 8, 10], [1, 8], [1, 9, 10], [1, 9], [1, 10], [1], [2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9], [2, 3, 4, 5, 6, 7, 8, 10], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 9, 10], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 10], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8, 9, 10], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 8, 10], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 9, 10], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7, 8, 9, 10], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 7, 8, 10], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 9, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8, 9, 10], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 8, 10], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9, 10], [2, 3, 4, 5, 9], [2, 3, 4, 5, 10], [2, 3, 4, 5], [2, 3, 4, 6, 7, 8, 9, 10], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 6, 7, 8, 10], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 9, 10], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 10], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8, 9, 10], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 9], [2, 3, 4, 6, 10], [2, 3, 4, 6], [2, 3, 4, 7, 8, 9, 10], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 9], [2, 3, 4, 7, 10], [2, 3, 4, 7], [2, 3, 4, 8, 9, 10], [2, 3, 4, 8, 9], [2, 3, 4, 8, 10], [2, 3, 4, 8], [2, 3, 4, 9, 10], [2, 3, 4, 9], [2, 3, 4, 10], [2, 3, 4], [2, 3, 5, 6, 7, 8, 9, 10], [2, 3, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 10], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8, 9, 10], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 8, 10], [2, 3, 5, 6, 8], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 9], [2, 3, 5, 6, 10], [2, 3, 5, 6], [2, 3, 5, 7, 8, 9, 10], [2, 3, 5, 7, 8, 9], [2, 3, 5, 7, 8, 10], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 9], [2, 3, 5, 7, 10], [2, 3, 5, 7], [2, 3, 5, 8, 9, 10], [2, 3, 5, 8, 9], [2, 3, 5, 8, 10], [2, 3, 5, 8], [2, 3, 5, 9, 10], [2, 3, 5, 9], [2, 3, 5, 10], [2, 3, 5], [2, 3, 6, 7, 8, 9, 10], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 9], [2, 3, 6, 7, 10], [2, 3, 6, 7], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 10], [2, 3, 6, 8], [2, 3, 6, 9, 10], [2, 3, 6, 9], [2, 3, 6, 10], [2, 3, 6], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 10], [2, 3, 7, 8], [2, 3, 7, 9, 10], [2, 3, 7, 9], [2, 3, 7, 10], [2, 3, 7], [2, 3, 8, 9, 10], [2, 3, 8, 9], [2, 3, 8, 10], [2, 3, 8], [2, 3, 9, 10], [2, 3, 9], [2, 3, 10], [2, 3], [2, 4, 5, 6, 7, 8, 9, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9], [2, 4, 5, 6, 10], [2, 4, 5, 6], [2, 4, 5, 7, 8, 9, 10], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9], [2, 4, 5, 7, 10], [2, 4, 5, 7], [2, 4, 5, 8, 9, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 10], [2, 4, 5, 8], [2, 4, 5, 9, 10], [2, 4, 5, 9], [2, 4, 5, 10], [2, 4, 5], [2, 4, 6, 7, 8, 9, 10], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 9], [2, 4, 6, 7, 10], [2, 4, 6, 7], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 10], [2, 4, 6, 8], [2, 4, 6, 9, 10], [2, 4, 6, 9], [2, 4, 6, 10], [2, 4, 6], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 10], [2, 4, 7, 8], [2, 4, 7, 9, 10], [2, 4, 7, 9], [2, 4, 7, 10], [2, 4, 7], [2, 4, 8, 9, 10], [2, 4, 8, 9], [2, 4, 8, 10], [2, 4, 8], [2, 4, 9, 10], [2, 4, 9], [2, 4, 10], [2, 4], [2, 5, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 10], [2, 5, 6, 7], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 10], [2, 5, 6, 8], [2, 5, 6, 9, 10], [2, 5, 6, 9], [2, 5, 6, 10], [2, 5, 6], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 10], [2, 5, 7, 8], [2, 5, 7, 9, 10], [2, 5, 7, 9], [2, 5, 7, 10], [2, 5, 7], [2, 5, 8, 9, 10], [2, 5, 8, 9], [2, 5, 8, 10], [2, 5, 8], [2, 5, 9, 10], [2, 5, 9], [2, 5, 10], [2, 5], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 10], [2, 6, 7, 8], [2, 6, 7, 9, 10], [2, 6, 7, 9], [2, 6, 7, 10], [2, 6, 7], [2, 6, 8, 9, 10], [2, 6, 8, 9], [2, 6, 8, 10], [2, 6, 8], [2, 6, 9, 10], [2, 6, 9], [2, 6, 10], [2, 6], [2, 7, 8, 9, 10], [2, 7, 8, 9], [2, 7, 8, 10], [2, 7, 8], [2, 7, 9, 10], [2, 7, 9], [2, 7, 10], [2, 7], [2, 8, 9, 10], [2, 8, 9], [2, 8, 10], [2, 8], [2, 9, 10], [2, 9], [2, 10], [2], [3, 4, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 10], [3, 4, 5, 6], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 10], [3, 4, 5, 7], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 10], [3, 4, 5, 8], [3, 4, 5, 9, 10], [3, 4, 5, 9], [3, 4, 5, 10], [3, 4, 5], [3, 4, 6, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 10], [3, 4, 6, 7], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 10], [3, 4, 6, 8], [3, 4, 6, 9, 10], [3, 4, 6, 9], [3, 4, 6, 10], [3, 4, 6], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 10], [3, 4, 7, 8], [3, 4, 7, 9, 10], [3, 4, 7, 9], [3, 4, 7, 10], [3, 4, 7], [3, 4, 8, 9, 10], [3, 4, 8, 9], [3, 4, 8, 10], [3, 4, 8], [3, 4, 9, 10], [3, 4, 9], [3, 4, 10], [3, 4], [3, 5, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 10], [3, 5, 6, 7], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 10], [3, 5, 6, 8], [3, 5, 6, 9, 10], [3, 5, 6, 9], [3, 5, 6, 10], [3, 5, 6], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 10], [3, 5, 7, 8], [3, 5, 7, 9, 10], [3, 5, 7, 9], [3, 5, 7, 10], [3, 5, 7], [3, 5, 8, 9, 10], [3, 5, 8, 9], [3, 5, 8, 10], [3, 5, 8], [3, 5, 9, 10], [3, 5, 9], [3, 5, 10], [3, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8], [3, 6, 9, 10], [3, 6, 9], [3, 6, 10], [3, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8], [3, 7, 9, 10], [3, 7, 9], [3, 7, 10], [3, 7], [3, 8, 9, 10], [3, 8, 9], [3, 8, 10], [3, 8], [3, 9, 10], [3, 9], [3, 10], [3], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [4], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [5], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [6], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [7], [8, 9, 10], [8, 9], [8, 10], [8], [9, 10], [9], [10], []]\n assert candidate(nums = [0, 1, 1, 2, 2, 2, 3]) == [[0, 1, 1, 2, 2, 2, 3], [0, 1, 1, 2, 2, 2], [0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2], [0, 1, 1, 2, 3], [0, 1, 1, 2], [0, 1, 1, 3], [0, 1, 1], [0, 1, 2, 2, 2, 3], [0, 1, 2, 2, 2], [0, 1, 2, 2, 3], [0, 1, 2, 2], [0, 1, 2, 3], [0, 1, 2], [0, 1, 3], [0, 1], [0, 2, 2, 2, 3], [0, 2, 2, 2], [0, 2, 2, 3], [0, 2, 2], [0, 2, 3], [0, 2], [0, 3], [0], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3], [1, 1], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3], [1, 2], [1, 3], [1], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3], [2, 2], [2, 3], [2], [3], []]\n assert candidate(nums = [-1, -2, -3, -4, -5, -1, -2, -3, -4, -5]) == [[-5, -5, -4, -4, -3, -3, -2, -2, -1, -1], [-5, -5, -4, -4, -3, -3, -2, -2, -1], [-5, -5, -4, -4, -3, -3, -2, -2], [-5, -5, -4, -4, -3, -3, -2, -1, -1], [-5, -5, -4, -4, -3, -3, -2, -1], [-5, -5, -4, -4, -3, -3, -2], [-5, -5, -4, -4, -3, -3, -1, -1], [-5, -5, -4, -4, -3, -3, -1], [-5, -5, -4, -4, -3, -3], [-5, -5, -4, -4, -3, -2, -2, -1, -1], [-5, -5, -4, -4, -3, -2, -2, -1], [-5, -5, -4, -4, -3, -2, -2], [-5, -5, -4, -4, -3, -2, -1, -1], [-5, -5, -4, -4, -3, -2, -1], [-5, -5, -4, -4, -3, -2], [-5, -5, -4, -4, -3, -1, -1], [-5, -5, -4, -4, -3, -1], [-5, -5, -4, -4, -3], [-5, -5, -4, -4, -2, -2, -1, -1], [-5, -5, -4, -4, -2, -2, -1], [-5, -5, -4, -4, -2, -2], [-5, -5, -4, -4, -2, -1, -1], [-5, -5, -4, -4, -2, -1], [-5, -5, -4, -4, -2], [-5, -5, -4, -4, -1, -1], [-5, -5, -4, -4, -1], [-5, -5, -4, -4], [-5, -5, -4, -3, -3, -2, -2, -1, -1], [-5, -5, -4, -3, -3, -2, -2, -1], [-5, -5, -4, -3, -3, -2, -2], [-5, -5, -4, -3, -3, -2, -1, -1], [-5, -5, -4, -3, -3, -2, -1], [-5, -5, -4, -3, -3, -2], [-5, -5, -4, -3, -3, -1, -1], [-5, -5, -4, -3, -3, -1], [-5, -5, -4, -3, -3], [-5, -5, -4, -3, -2, -2, -1, -1], [-5, -5, -4, -3, -2, -2, -1], [-5, -5, -4, -3, -2, -2], [-5, -5, -4, -3, -2, -1, -1], [-5, -5, -4, -3, -2, -1], [-5, -5, -4, -3, -2], [-5, -5, -4, -3, -1, -1], [-5, -5, -4, -3, -1], [-5, -5, -4, -3], [-5, -5, -4, -2, -2, -1, -1], [-5, -5, -4, -2, -2, -1], [-5, -5, -4, -2, -2], [-5, -5, -4, -2, -1, -1], [-5, -5, -4, -2, -1], [-5, -5, -4, -2], [-5, -5, -4, -1, -1], [-5, -5, -4, -1], [-5, -5, -4], [-5, -5, -3, -3, -2, -2, -1, -1], [-5, -5, -3, -3, -2, -2, -1], [-5, -5, -3, -3, -2, -2], [-5, -5, -3, -3, -2, -1, -1], [-5, -5, -3, -3, -2, -1], [-5, -5, -3, -3, -2], [-5, -5, -3, -3, -1, -1], [-5, -5, -3, -3, -1], [-5, -5, -3, -3], [-5, -5, -3, -2, -2, -1, -1], [-5, -5, -3, -2, -2, -1], [-5, -5, -3, -2, -2], [-5, -5, -3, -2, -1, -1], [-5, -5, -3, -2, -1], [-5, -5, -3, -2], [-5, -5, -3, -1, -1], [-5, -5, -3, -1], [-5, -5, -3], [-5, -5, -2, -2, -1, -1], [-5, -5, -2, -2, -1], [-5, -5, -2, -2], [-5, -5, -2, -1, -1], [-5, -5, -2, -1], [-5, -5, -2], [-5, -5, -1, -1], [-5, -5, -1], [-5, -5], [-5, -4, -4, -3, -3, -2, -2, -1, -1], [-5, -4, -4, -3, -3, -2, -2, -1], [-5, -4, -4, -3, -3, -2, -2], [-5, -4, -4, -3, -3, -2, -1, -1], [-5, -4, -4, -3, -3, -2, -1], [-5, -4, -4, -3, -3, -2], [-5, -4, -4, -3, -3, -1, -1], [-5, -4, -4, -3, -3, -1], [-5, -4, -4, -3, -3], [-5, -4, -4, -3, -2, -2, -1, -1], [-5, -4, -4, -3, -2, -2, -1], [-5, -4, -4, -3, -2, -2], [-5, -4, -4, -3, -2, -1, -1], [-5, -4, -4, -3, -2, -1], [-5, -4, -4, -3, -2], [-5, -4, -4, -3, -1, -1], [-5, -4, -4, -3, -1], [-5, -4, -4, -3], [-5, -4, -4, -2, -2, -1, -1], [-5, -4, -4, -2, -2, -1], [-5, -4, -4, -2, -2], [-5, -4, -4, -2, -1, -1], [-5, -4, -4, -2, -1], [-5, -4, -4, -2], [-5, -4, -4, -1, -1], [-5, -4, -4, -1], [-5, -4, -4], [-5, -4, -3, -3, -2, -2, -1, -1], [-5, -4, -3, -3, -2, -2, -1], [-5, -4, -3, -3, -2, -2], [-5, -4, -3, -3, -2, -1, -1], [-5, -4, -3, -3, -2, -1], [-5, -4, -3, -3, -2], [-5, -4, -3, -3, -1, -1], [-5, -4, -3, -3, -1], [-5, -4, -3, -3], [-5, -4, -3, -2, -2, -1, -1], [-5, -4, -3, -2, -2, -1], [-5, -4, -3, -2, -2], [-5, -4, -3, -2, -1, -1], [-5, -4, -3, -2, -1], [-5, -4, -3, -2], [-5, -4, -3, -1, -1], [-5, -4, -3, -1], [-5, -4, -3], [-5, -4, -2, -2, -1, -1], [-5, -4, -2, -2, -1], [-5, -4, -2, -2], [-5, -4, -2, -1, -1], [-5, -4, -2, -1], [-5, -4, -2], [-5, -4, -1, -1], [-5, -4, -1], [-5, -4], [-5, -3, -3, -2, -2, -1, -1], [-5, -3, -3, -2, -2, -1], [-5, -3, -3, -2, -2], [-5, -3, -3, -2, -1, -1], [-5, -3, -3, -2, -1], [-5, -3, -3, -2], [-5, -3, -3, -1, -1], [-5, -3, -3, -1], [-5, -3, -3], [-5, -3, -2, -2, -1, -1], [-5, -3, -2, -2, -1], [-5, -3, -2, -2], [-5, -3, -2, -1, -1], [-5, -3, -2, -1], [-5, -3, -2], [-5, -3, -1, -1], [-5, -3, -1], [-5, -3], [-5, -2, -2, -1, -1], [-5, -2, -2, -1], [-5, -2, -2], [-5, -2, -1, -1], [-5, -2, -1], [-5, -2], [-5, -1, -1], [-5, -1], [-5], [-4, -4, -3, -3, -2, -2, -1, -1], [-4, -4, -3, -3, -2, -2, -1], [-4, -4, -3, -3, -2, -2], [-4, -4, -3, -3, -2, -1, -1], [-4, -4, -3, -3, -2, -1], [-4, -4, -3, -3, -2], [-4, -4, -3, -3, -1, -1], [-4, -4, -3, -3, -1], [-4, -4, -3, -3], [-4, -4, -3, -2, -2, -1, -1], [-4, -4, -3, -2, -2, -1], [-4, -4, -3, -2, -2], [-4, -4, -3, -2, -1, -1], [-4, -4, -3, -2, -1], [-4, -4, -3, -2], [-4, -4, -3, -1, -1], [-4, -4, -3, -1], [-4, -4, -3], [-4, -4, -2, -2, -1, -1], [-4, -4, -2, -2, -1], [-4, -4, -2, -2], [-4, -4, -2, -1, -1], [-4, -4, -2, -1], [-4, -4, -2], [-4, -4, -1, -1], [-4, -4, -1], [-4, -4], [-4, -3, -3, -2, -2, -1, -1], [-4, -3, -3, -2, -2, -1], [-4, -3, -3, -2, -2], [-4, -3, -3, -2, -1, -1], [-4, -3, -3, -2, -1], [-4, -3, -3, -2], [-4, -3, -3, -1, -1], [-4, -3, -3, -1], [-4, -3, -3], [-4, -3, -2, -2, -1, -1], [-4, -3, -2, -2, -1], [-4, -3, -2, -2], [-4, -3, -2, -1, -1], [-4, -3, -2, -1], [-4, -3, -2], [-4, -3, -1, -1], [-4, -3, -1], [-4, -3], [-4, -2, -2, -1, -1], [-4, -2, -2, -1], [-4, -2, -2], [-4, -2, -1, -1], [-4, -2, -1], [-4, -2], [-4, -1, -1], [-4, -1], [-4], [-3, -3, -2, -2, -1, -1], [-3, -3, -2, -2, -1], [-3, -3, -2, -2], [-3, -3, -2, -1, -1], [-3, -3, -2, -1], [-3, -3, -2], [-3, -3, -1, -1], [-3, -3, -1], [-3, -3], [-3, -2, -2, -1, -1], [-3, -2, -2, -1], [-3, -2, -2], [-3, -2, -1, -1], [-3, -2, -1], [-3, -2], [-3, -1, -1], [-3, -1], [-3], [-2, -2, -1, -1], [-2, -2, -1], [-2, -2], [-2, -1, -1], [-2, -1], [-2], [-1, -1], [-1], []]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2, 3, 4, 5, 6, 7, 9], [0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 8, 9], [0, 1, 2, 3, 4, 5, 6, 8], [0, 1, 2, 3, 4, 5, 6, 9], [0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 7, 8, 9], [0, 1, 2, 3, 4, 5, 7, 8], [0, 1, 2, 3, 4, 5, 7, 9], [0, 1, 2, 3, 4, 5, 7], [0, 1, 2, 3, 4, 5, 8, 9], [0, 1, 2, 3, 4, 5, 8], [0, 1, 2, 3, 4, 5, 9], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 6, 7, 8, 9], [0, 1, 2, 3, 4, 6, 7, 8], [0, 1, 2, 3, 4, 6, 7, 9], [0, 1, 2, 3, 4, 6, 7], [0, 1, 2, 3, 4, 6, 8, 9], [0, 1, 2, 3, 4, 6, 8], [0, 1, 2, 3, 4, 6, 9], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 7, 8, 9], [0, 1, 2, 3, 4, 7, 8], [0, 1, 2, 3, 4, 7, 9], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4, 8, 9], [0, 1, 2, 3, 4, 8], [0, 1, 2, 3, 4, 9], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5, 6, 7, 8, 9], [0, 1, 2, 3, 5, 6, 7, 8], [0, 1, 2, 3, 5, 6, 7, 9], [0, 1, 2, 3, 5, 6, 7], [0, 1, 2, 3, 5, 6, 8, 9], [0, 1, 2, 3, 5, 6, 8], [0, 1, 2, 3, 5, 6, 9], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 7, 8, 9], [0, 1, 2, 3, 5, 7, 8], [0, 1, 2, 3, 5, 7, 9], [0, 1, 2, 3, 5, 7], [0, 1, 2, 3, 5, 8, 9], [0, 1, 2, 3, 5, 8], [0, 1, 2, 3, 5, 9], [0, 1, 2, 3, 5], [0, 1, 2, 3, 6, 7, 8, 9], [0, 1, 2, 3, 6, 7, 8], [0, 1, 2, 3, 6, 7, 9], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6, 8, 9], [0, 1, 2, 3, 6, 8], [0, 1, 2, 3, 6, 9], [0, 1, 2, 3, 6], [0, 1, 2, 3, 7, 8, 9], [0, 1, 2, 3, 7, 8], [0, 1, 2, 3, 7, 9], [0, 1, 2, 3, 7], [0, 1, 2, 3, 8, 9], [0, 1, 2, 3, 8], [0, 1, 2, 3, 9], [0, 1, 2, 3], [0, 1, 2, 4, 5, 6, 7, 8, 9], [0, 1, 2, 4, 5, 6, 7, 8], [0, 1, 2, 4, 5, 6, 7, 9], [0, 1, 2, 4, 5, 6, 7], [0, 1, 2, 4, 5, 6, 8, 9], [0, 1, 2, 4, 5, 6, 8], [0, 1, 2, 4, 5, 6, 9], [0, 1, 2, 4, 5, 6], [0, 1, 2, 4, 5, 7, 8, 9], [0, 1, 2, 4, 5, 7, 8], [0, 1, 2, 4, 5, 7, 9], [0, 1, 2, 4, 5, 7], [0, 1, 2, 4, 5, 8, 9], [0, 1, 2, 4, 5, 8], [0, 1, 2, 4, 5, 9], [0, 1, 2, 4, 5], [0, 1, 2, 4, 6, 7, 8, 9], [0, 1, 2, 4, 6, 7, 8], [0, 1, 2, 4, 6, 7, 9], [0, 1, 2, 4, 6, 7], [0, 1, 2, 4, 6, 8, 9], [0, 1, 2, 4, 6, 8], [0, 1, 2, 4, 6, 9], [0, 1, 2, 4, 6], [0, 1, 2, 4, 7, 8, 9], [0, 1, 2, 4, 7, 8], [0, 1, 2, 4, 7, 9], [0, 1, 2, 4, 7], [0, 1, 2, 4, 8, 9], [0, 1, 2, 4, 8], [0, 1, 2, 4, 9], [0, 1, 2, 4], [0, 1, 2, 5, 6, 7, 8, 9], [0, 1, 2, 5, 6, 7, 8], [0, 1, 2, 5, 6, 7, 9], [0, 1, 2, 5, 6, 7], [0, 1, 2, 5, 6, 8, 9], [0, 1, 2, 5, 6, 8], [0, 1, 2, 5, 6, 9], [0, 1, 2, 5, 6], [0, 1, 2, 5, 7, 8, 9], [0, 1, 2, 5, 7, 8], [0, 1, 2, 5, 7, 9], [0, 1, 2, 5, 7], [0, 1, 2, 5, 8, 9], [0, 1, 2, 5, 8], [0, 1, 2, 5, 9], [0, 1, 2, 5], [0, 1, 2, 6, 7, 8, 9], [0, 1, 2, 6, 7, 8], [0, 1, 2, 6, 7, 9], [0, 1, 2, 6, 7], [0, 1, 2, 6, 8, 9], [0, 1, 2, 6, 8], [0, 1, 2, 6, 9], [0, 1, 2, 6], [0, 1, 2, 7, 8, 9], [0, 1, 2, 7, 8], [0, 1, 2, 7, 9], [0, 1, 2, 7], [0, 1, 2, 8, 9], [0, 1, 2, 8], [0, 1, 2, 9], [0, 1, 2], [0, 1, 3, 4, 5, 6, 7, 8, 9], [0, 1, 3, 4, 5, 6, 7, 8], [0, 1, 3, 4, 5, 6, 7, 9], [0, 1, 3, 4, 5, 6, 7], [0, 1, 3, 4, 5, 6, 8, 9], [0, 1, 3, 4, 5, 6, 8], [0, 1, 3, 4, 5, 6, 9], [0, 1, 3, 4, 5, 6], [0, 1, 3, 4, 5, 7, 8, 9], [0, 1, 3, 4, 5, 7, 8], [0, 1, 3, 4, 5, 7, 9], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5, 8, 9], [0, 1, 3, 4, 5, 8], [0, 1, 3, 4, 5, 9], [0, 1, 3, 4, 5], [0, 1, 3, 4, 6, 7, 8, 9], [0, 1, 3, 4, 6, 7, 8], [0, 1, 3, 4, 6, 7, 9], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 8, 9], [0, 1, 3, 4, 6, 8], [0, 1, 3, 4, 6, 9], [0, 1, 3, 4, 6], [0, 1, 3, 4, 7, 8, 9], [0, 1, 3, 4, 7, 8], [0, 1, 3, 4, 7, 9], [0, 1, 3, 4, 7], [0, 1, 3, 4, 8, 9], [0, 1, 3, 4, 8], [0, 1, 3, 4, 9], [0, 1, 3, 4], [0, 1, 3, 5, 6, 7, 8, 9], [0, 1, 3, 5, 6, 7, 8], [0, 1, 3, 5, 6, 7, 9], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6, 8, 9], [0, 1, 3, 5, 6, 8], [0, 1, 3, 5, 6, 9], [0, 1, 3, 5, 6], [0, 1, 3, 5, 7, 8, 9], [0, 1, 3, 5, 7, 8], [0, 1, 3, 5, 7, 9], [0, 1, 3, 5, 7], [0, 1, 3, 5, 8, 9], [0, 1, 3, 5, 8], [0, 1, 3, 5, 9], [0, 1, 3, 5], [0, 1, 3, 6, 7, 8, 9], [0, 1, 3, 6, 7, 8], [0, 1, 3, 6, 7, 9], [0, 1, 3, 6, 7], [0, 1, 3, 6, 8, 9], [0, 1, 3, 6, 8], [0, 1, 3, 6, 9], [0, 1, 3, 6], [0, 1, 3, 7, 8, 9], [0, 1, 3, 7, 8], [0, 1, 3, 7, 9], [0, 1, 3, 7], [0, 1, 3, 8, 9], [0, 1, 3, 8], [0, 1, 3, 9], [0, 1, 3], [0, 1, 4, 5, 6, 7, 8, 9], [0, 1, 4, 5, 6, 7, 8], [0, 1, 4, 5, 6, 7, 9], [0, 1, 4, 5, 6, 7], [0, 1, 4, 5, 6, 8, 9], [0, 1, 4, 5, 6, 8], [0, 1, 4, 5, 6, 9], [0, 1, 4, 5, 6], [0, 1, 4, 5, 7, 8, 9], [0, 1, 4, 5, 7, 8], [0, 1, 4, 5, 7, 9], [0, 1, 4, 5, 7], [0, 1, 4, 5, 8, 9], [0, 1, 4, 5, 8], [0, 1, 4, 5, 9], [0, 1, 4, 5], [0, 1, 4, 6, 7, 8, 9], [0, 1, 4, 6, 7, 8], [0, 1, 4, 6, 7, 9], [0, 1, 4, 6, 7], [0, 1, 4, 6, 8, 9], [0, 1, 4, 6, 8], [0, 1, 4, 6, 9], [0, 1, 4, 6], [0, 1, 4, 7, 8, 9], [0, 1, 4, 7, 8], [0, 1, 4, 7, 9], [0, 1, 4, 7], [0, 1, 4, 8, 9], [0, 1, 4, 8], [0, 1, 4, 9], [0, 1, 4], [0, 1, 5, 6, 7, 8, 9], [0, 1, 5, 6, 7, 8], [0, 1, 5, 6, 7, 9], [0, 1, 5, 6, 7], [0, 1, 5, 6, 8, 9], [0, 1, 5, 6, 8], [0, 1, 5, 6, 9], [0, 1, 5, 6], [0, 1, 5, 7, 8, 9], [0, 1, 5, 7, 8], [0, 1, 5, 7, 9], [0, 1, 5, 7], [0, 1, 5, 8, 9], [0, 1, 5, 8], [0, 1, 5, 9], [0, 1, 5], [0, 1, 6, 7, 8, 9], [0, 1, 6, 7, 8], [0, 1, 6, 7, 9], [0, 1, 6, 7], [0, 1, 6, 8, 9], [0, 1, 6, 8], [0, 1, 6, 9], [0, 1, 6], [0, 1, 7, 8, 9], [0, 1, 7, 8], [0, 1, 7, 9], [0, 1, 7], [0, 1, 8, 9], [0, 1, 8], [0, 1, 9], [0, 1], [0, 2, 3, 4, 5, 6, 7, 8, 9], [0, 2, 3, 4, 5, 6, 7, 8], [0, 2, 3, 4, 5, 6, 7, 9], [0, 2, 3, 4, 5, 6, 7], [0, 2, 3, 4, 5, 6, 8, 9], [0, 2, 3, 4, 5, 6, 8], [0, 2, 3, 4, 5, 6, 9], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 7, 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8, 9], [6, 8], [6, 9], [6], [7, 8, 9], [7, 8], [7, 9], [7], [8, 9], [8], [9], []]\n assert candidate(nums = [3, 3, 1, 1, 2, 2]) == [[1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [3, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, -1, -1, -1]) == [[-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 1], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 2], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 2], [-1, -1, -1, 0, 0, 0, 1, 1, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 1, 3], [-1, -1, -1, 0, 0, 0, 1, 1], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 2], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 2], [-1, -1, -1, 0, 0, 0, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 2, 3], [-1, -1, -1, 0, 0, 0, 1, 2], [-1, -1, -1, 0, 0, 0, 1, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 3, 3], [-1, -1, -1, 0, 0, 0, 1, 3], [-1, -1, -1, 0, 0, 0, 1], [-1, -1, -1, 0, 0, 0, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 2, 2, 2], [-1, -1, -1, 0, 0, 0, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 2, 2, 3], [-1, -1, -1, 0, 0, 0, 2, 2], [-1, -1, -1, 0, 0, 0, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 2, 3, 3], [-1, -1, -1, 0, 0, 0, 2, 3], [-1, -1, -1, 0, 0, 0, 2], [-1, -1, -1, 0, 0, 0, 3, 3, 3], [-1, -1, -1, 0, 0, 0, 3, 3], [-1, -1, -1, 0, 0, 0, 3], [-1, -1, -1, 0, 0, 0], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 2], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 2], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 2], [-1, -1, -1, 0, 0, 1, 1, 1, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 1, 3], [-1, -1, -1, 0, 0, 1, 1, 1], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 2], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 2, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 2], [-1, -1, -1, 0, 0, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 2, 3], [-1, -1, -1, 0, 0, 1, 1, 2], [-1, -1, -1, 0, 0, 1, 1, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 3, 3], [-1, -1, -1, 0, 0, 1, 1, 3], [-1, -1, -1, 0, 0, 1, 1], [-1, -1, -1, 0, 0, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 1, 2, 2, 2], [-1, -1, -1, 0, 0, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 2, 2, 3], [-1, -1, -1, 0, 0, 1, 2, 2], [-1, -1, -1, 0, 0, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 2, 3, 3], [-1, -1, -1, 0, 0, 1, 2, 3], [-1, -1, -1, 0, 0, 1, 2], [-1, -1, -1, 0, 0, 1, 3, 3, 3], [-1, -1, -1, 0, 0, 1, 3, 3], [-1, -1, -1, 0, 0, 1, 3], [-1, -1, -1, 0, 0, 1], [-1, -1, -1, 0, 0, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 2, 2, 2, 3], [-1, -1, -1, 0, 0, 2, 2, 2], [-1, -1, -1, 0, 0, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 2, 2, 3, 3], [-1, -1, -1, 0, 0, 2, 2, 3], [-1, -1, -1, 0, 0, 2, 2], [-1, -1, -1, 0, 0, 2, 3, 3, 3], [-1, -1, -1, 0, 0, 2, 3, 3], [-1, -1, -1, 0, 0, 2, 3], [-1, -1, -1, 0, 0, 2], [-1, -1, -1, 0, 0, 3, 3, 3], [-1, -1, -1, 0, 0, 3, 3], [-1, -1, -1, 0, 0, 3], [-1, -1, -1, 0, 0], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 2], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 2, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 2], [-1, -1, -1, 0, 1, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 2, 3], [-1, -1, -1, 0, 1, 1, 1, 2], [-1, -1, -1, 0, 1, 1, 1, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 3, 3], [-1, -1, -1, 0, 1, 1, 1, 3], [-1, -1, -1, 0, 1, 1, 1], [-1, -1, -1, 0, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 1, 1, 2, 2, 2], [-1, -1, -1, 0, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 1, 1, 2, 2, 3], [-1, -1, -1, 0, 1, 1, 2, 2], [-1, -1, -1, 0, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 2, 3, 3], [-1, -1, -1, 0, 1, 1, 2, 3], [-1, -1, -1, 0, 1, 1, 2], [-1, -1, -1, 0, 1, 1, 3, 3, 3], [-1, -1, -1, 0, 1, 1, 3, 3], [-1, -1, -1, 0, 1, 1, 3], [-1, -1, -1, 0, 1, 1], [-1, -1, -1, 0, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 1, 2, 2, 2, 3], [-1, -1, -1, 0, 1, 2, 2, 2], [-1, -1, -1, 0, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 2, 2, 3, 3], [-1, -1, -1, 0, 1, 2, 2, 3], [-1, -1, -1, 0, 1, 2, 2], [-1, -1, -1, 0, 1, 2, 3, 3, 3], [-1, -1, -1, 0, 1, 2, 3, 3], [-1, -1, -1, 0, 1, 2, 3], [-1, -1, -1, 0, 1, 2], [-1, -1, -1, 0, 1, 3, 3, 3], [-1, -1, -1, 0, 1, 3, 3], [-1, -1, -1, 0, 1, 3], [-1, -1, -1, 0, 1], [-1, -1, -1, 0, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 2, 2, 2, 3, 3], [-1, -1, -1, 0, 2, 2, 2, 3], [-1, -1, -1, 0, 2, 2, 2], [-1, -1, -1, 0, 2, 2, 3, 3, 3], [-1, -1, -1, 0, 2, 2, 3, 3], [-1, -1, -1, 0, 2, 2, 3], [-1, -1, -1, 0, 2, 2], [-1, -1, -1, 0, 2, 3, 3, 3], [-1, -1, -1, 0, 2, 3, 3], [-1, -1, -1, 0, 2, 3], [-1, -1, -1, 0, 2], [-1, -1, -1, 0, 3, 3, 3], [-1, -1, -1, 0, 3, 3], [-1, -1, -1, 0, 3], [-1, -1, -1, 0], [-1, -1, -1, 1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 1, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 1, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 1, 1, 1, 2, 2, 2], [-1, -1, -1, 1, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 1, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 1, 1, 1, 2, 2, 3], [-1, -1, -1, 1, 1, 1, 2, 2], [-1, -1, -1, 1, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 1, 1, 1, 2, 3, 3], [-1, -1, -1, 1, 1, 1, 2, 3], [-1, -1, -1, 1, 1, 1, 2], [-1, -1, -1, 1, 1, 1, 3, 3, 3], [-1, -1, -1, 1, 1, 1, 3, 3], [-1, -1, -1, 1, 1, 1, 3], [-1, -1, -1, 1, 1, 1], [-1, -1, -1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 1, 1, 2, 2, 2, 3], [-1, -1, -1, 1, 1, 2, 2, 2], [-1, -1, -1, 1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 1, 1, 2, 2, 3, 3], [-1, -1, -1, 1, 1, 2, 2, 3], [-1, -1, -1, 1, 1, 2, 2], [-1, -1, -1, 1, 1, 2, 3, 3, 3], [-1, -1, -1, 1, 1, 2, 3, 3], [-1, -1, -1, 1, 1, 2, 3], [-1, -1, -1, 1, 1, 2], [-1, -1, -1, 1, 1, 3, 3, 3], [-1, -1, -1, 1, 1, 3, 3], [-1, -1, -1, 1, 1, 3], [-1, -1, -1, 1, 1], [-1, -1, -1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 1, 2, 2, 2, 3, 3], [-1, -1, -1, 1, 2, 2, 2, 3], [-1, -1, -1, 1, 2, 2, 2], [-1, -1, -1, 1, 2, 2, 3, 3, 3], [-1, -1, -1, 1, 2, 2, 3, 3], [-1, -1, -1, 1, 2, 2, 3], [-1, -1, -1, 1, 2, 2], [-1, -1, -1, 1, 2, 3, 3, 3], [-1, -1, -1, 1, 2, 3, 3], [-1, -1, -1, 1, 2, 3], [-1, -1, -1, 1, 2], [-1, -1, -1, 1, 3, 3, 3], [-1, -1, -1, 1, 3, 3], [-1, -1, -1, 1, 3], [-1, -1, -1, 1], [-1, -1, -1, 2, 2, 2, 3, 3, 3], [-1, -1, -1, 2, 2, 2, 3, 3], [-1, -1, -1, 2, 2, 2, 3], [-1, -1, -1, 2, 2, 2], [-1, -1, -1, 2, 2, 3, 3, 3], [-1, -1, -1, 2, 2, 3, 3], [-1, -1, -1, 2, 2, 3], [-1, -1, -1, 2, 2], [-1, -1, -1, 2, 3, 3, 3], [-1, -1, -1, 2, 3, 3], [-1, -1, -1, 2, 3], [-1, -1, -1, 2], [-1, -1, -1, 3, 3, 3], [-1, -1, -1, 3, 3], [-1, -1, -1, 3], [-1, -1, -1], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 2], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 2], [-1, -1, 0, 0, 0, 1, 1, 1, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 1, 3], [-1, -1, 0, 0, 0, 1, 1, 1], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 2], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 2, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 2], [-1, -1, 0, 0, 0, 1, 1, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 2, 3], [-1, -1, 0, 0, 0, 1, 1, 2], [-1, -1, 0, 0, 0, 1, 1, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 3, 3], [-1, -1, 0, 0, 0, 1, 1, 3], [-1, -1, 0, 0, 0, 1, 1], [-1, -1, 0, 0, 0, 1, 2, 2, 2, 3, 3, 3], [-1, -1, 0, 0, 0, 1, 2, 2, 2, 3, 3], [-1, -1, 0, 0, 0, 1, 2, 2, 2, 3], [-1, -1, 0, 0, 0, 1, 2, 2, 2], [-1, -1, 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0, 1, 1, 2, 3, 3, 3], [-1, 0, 1, 1, 2, 3, 3], [-1, 0, 1, 1, 2, 3], [-1, 0, 1, 1, 2], [-1, 0, 1, 1, 3, 3, 3], [-1, 0, 1, 1, 3, 3], [-1, 0, 1, 1, 3], [-1, 0, 1, 1], [-1, 0, 1, 2, 2, 2, 3, 3, 3], [-1, 0, 1, 2, 2, 2, 3, 3], [-1, 0, 1, 2, 2, 2, 3], [-1, 0, 1, 2, 2, 2], [-1, 0, 1, 2, 2, 3, 3, 3], [-1, 0, 1, 2, 2, 3, 3], [-1, 0, 1, 2, 2, 3], [-1, 0, 1, 2, 2], [-1, 0, 1, 2, 3, 3, 3], [-1, 0, 1, 2, 3, 3], [-1, 0, 1, 2, 3], [-1, 0, 1, 2], [-1, 0, 1, 3, 3, 3], [-1, 0, 1, 3, 3], [-1, 0, 1, 3], [-1, 0, 1], [-1, 0, 2, 2, 2, 3, 3, 3], [-1, 0, 2, 2, 2, 3, 3], [-1, 0, 2, 2, 2, 3], [-1, 0, 2, 2, 2], [-1, 0, 2, 2, 3, 3, 3], [-1, 0, 2, 2, 3, 3], [-1, 0, 2, 2, 3], [-1, 0, 2, 2], [-1, 0, 2, 3, 3, 3], [-1, 0, 2, 3, 3], [-1, 0, 2, 3], [-1, 0, 2], [-1, 0, 3, 3, 3], [-1, 0, 3, 3], [-1, 0, 3], [-1, 0], [-1, 1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, 1, 1, 1, 2, 2, 2, 3, 3], [-1, 1, 1, 1, 2, 2, 2, 3], [-1, 1, 1, 1, 2, 2, 2], [-1, 1, 1, 1, 2, 2, 3, 3, 3], [-1, 1, 1, 1, 2, 2, 3, 3], [-1, 1, 1, 1, 2, 2, 3], [-1, 1, 1, 1, 2, 2], [-1, 1, 1, 1, 2, 3, 3, 3], [-1, 1, 1, 1, 2, 3, 3], [-1, 1, 1, 1, 2, 3], [-1, 1, 1, 1, 2], [-1, 1, 1, 1, 3, 3, 3], [-1, 1, 1, 1, 3, 3], [-1, 1, 1, 1, 3], [-1, 1, 1, 1], [-1, 1, 1, 2, 2, 2, 3, 3, 3], [-1, 1, 1, 2, 2, 2, 3, 3], [-1, 1, 1, 2, 2, 2, 3], [-1, 1, 1, 2, 2, 2], [-1, 1, 1, 2, 2, 3, 3, 3], [-1, 1, 1, 2, 2, 3, 3], [-1, 1, 1, 2, 2, 3], [-1, 1, 1, 2, 2], [-1, 1, 1, 2, 3, 3, 3], [-1, 1, 1, 2, 3, 3], [-1, 1, 1, 2, 3], [-1, 1, 1, 2], [-1, 1, 1, 3, 3, 3], [-1, 1, 1, 3, 3], [-1, 1, 1, 3], [-1, 1, 1], [-1, 1, 2, 2, 2, 3, 3, 3], [-1, 1, 2, 2, 2, 3, 3], [-1, 1, 2, 2, 2, 3], [-1, 1, 2, 2, 2], [-1, 1, 2, 2, 3, 3, 3], [-1, 1, 2, 2, 3, 3], [-1, 1, 2, 2, 3], [-1, 1, 2, 2], [-1, 1, 2, 3, 3, 3], [-1, 1, 2, 3, 3], [-1, 1, 2, 3], [-1, 1, 2], [-1, 1, 3, 3, 3], [-1, 1, 3, 3], [-1, 1, 3], [-1, 1], [-1, 2, 2, 2, 3, 3, 3], [-1, 2, 2, 2, 3, 3], [-1, 2, 2, 2, 3], [-1, 2, 2, 2], [-1, 2, 2, 3, 3, 3], [-1, 2, 2, 3, 3], [-1, 2, 2, 3], [-1, 2, 2], [-1, 2, 3, 3, 3], [-1, 2, 3, 3], [-1, 2, 3], [-1, 2], [-1, 3, 3, 3], [-1, 3, 3], [-1, 3], [-1], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3], [0, 0, 0, 1, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 3], [0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 1, 1, 1, 2, 3, 3, 3], [0, 0, 0, 1, 1, 1, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 3], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 3, 3, 3], [0, 0, 0, 1, 1, 1, 3, 3], [0, 0, 0, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 2, 3], [0, 0, 0, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3], [0, 0, 0, 1, 1, 2, 2], [0, 0, 0, 1, 1, 2, 3, 3, 3], [0, 0, 0, 1, 1, 2, 3, 3], [0, 0, 0, 1, 1, 2, 3], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 1, 3, 3, 3], [0, 0, 0, 1, 1, 3, 3], [0, 0, 0, 1, 1, 3], [0, 0, 0, 1, 1], [0, 0, 0, 1, 2, 2, 2, 3, 3, 3], [0, 0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 2, 2, 2, 3], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 2, 2, 3, 3, 3], [0, 0, 0, 1, 2, 2, 3, 3], [0, 0, 0, 1, 2, 2, 3], [0, 0, 0, 1, 2, 2], [0, 0, 0, 1, 2, 3, 3, 3], [0, 0, 0, 1, 2, 3, 3], [0, 0, 0, 1, 2, 3], [0, 0, 0, 1, 2], [0, 0, 0, 1, 3, 3, 3], [0, 0, 0, 1, 3, 3], [0, 0, 0, 1, 3], [0, 0, 0, 1], [0, 0, 0, 2, 2, 2, 3, 3, 3], [0, 0, 0, 2, 2, 2, 3, 3], [0, 0, 0, 2, 2, 2, 3], [0, 0, 0, 2, 2, 2], [0, 0, 0, 2, 2, 3, 3, 3], [0, 0, 0, 2, 2, 3, 3], [0, 0, 0, 2, 2, 3], [0, 0, 0, 2, 2], [0, 0, 0, 2, 3, 3, 3], [0, 0, 0, 2, 3, 3], [0, 0, 0, 2, 3], [0, 0, 0, 2], [0, 0, 0, 3, 3, 3], [0, 0, 0, 3, 3], [0, 0, 0, 3], [0, 0, 0], [0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [0, 0, 1, 1, 1, 2, 2, 2, 3, 3], [0, 0, 1, 1, 1, 2, 2, 2, 3], [0, 0, 1, 1, 1, 2, 2, 2], [0, 0, 1, 1, 1, 2, 2, 3, 3, 3], [0, 0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 1, 1, 1, 2, 2, 3], [0, 0, 1, 1, 1, 2, 2], [0, 0, 1, 1, 1, 2, 3, 3, 3], [0, 0, 1, 1, 1, 2, 3, 3], [0, 0, 1, 1, 1, 2, 3], [0, 0, 1, 1, 1, 2], [0, 0, 1, 1, 1, 3, 3, 3], [0, 0, 1, 1, 1, 3, 3], [0, 0, 1, 1, 1, 3], [0, 0, 1, 1, 1], [0, 0, 1, 1, 2, 2, 2, 3, 3, 3], [0, 0, 1, 1, 2, 2, 2, 3, 3], [0, 0, 1, 1, 2, 2, 2, 3], [0, 0, 1, 1, 2, 2, 2], [0, 0, 1, 1, 2, 2, 3, 3, 3], [0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 1, 1, 2, 2, 3], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2, 3, 3, 3], [0, 0, 1, 1, 2, 3, 3], [0, 0, 1, 1, 2, 3], [0, 0, 1, 1, 2], [0, 0, 1, 1, 3, 3, 3], [0, 0, 1, 1, 3, 3], [0, 0, 1, 1, 3], [0, 0, 1, 1], [0, 0, 1, 2, 2, 2, 3, 3, 3], [0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 1, 2, 2, 2, 3], [0, 0, 1, 2, 2, 2], [0, 0, 1, 2, 2, 3, 3, 3], [0, 0, 1, 2, 2, 3, 3], [0, 0, 1, 2, 2, 3], [0, 0, 1, 2, 2], [0, 0, 1, 2, 3, 3, 3], [0, 0, 1, 2, 3, 3], [0, 0, 1, 2, 3], [0, 0, 1, 2], [0, 0, 1, 3, 3, 3], [0, 0, 1, 3, 3], [0, 0, 1, 3], [0, 0, 1], [0, 0, 2, 2, 2, 3, 3, 3], [0, 0, 2, 2, 2, 3, 3], [0, 0, 2, 2, 2, 3], [0, 0, 2, 2, 2], [0, 0, 2, 2, 3, 3, 3], [0, 0, 2, 2, 3, 3], [0, 0, 2, 2, 3], [0, 0, 2, 2], [0, 0, 2, 3, 3, 3], [0, 0, 2, 3, 3], [0, 0, 2, 3], [0, 0, 2], [0, 0, 3, 3, 3], [0, 0, 3, 3], [0, 0, 3], [0, 0], [0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [0, 1, 1, 1, 2, 2, 2, 3, 3], [0, 1, 1, 1, 2, 2, 2, 3], [0, 1, 1, 1, 2, 2, 2], [0, 1, 1, 1, 2, 2, 3, 3, 3], [0, 1, 1, 1, 2, 2, 3, 3], [0, 1, 1, 1, 2, 2, 3], [0, 1, 1, 1, 2, 2], [0, 1, 1, 1, 2, 3, 3, 3], [0, 1, 1, 1, 2, 3, 3], [0, 1, 1, 1, 2, 3], [0, 1, 1, 1, 2], [0, 1, 1, 1, 3, 3, 3], [0, 1, 1, 1, 3, 3], [0, 1, 1, 1, 3], [0, 1, 1, 1], [0, 1, 1, 2, 2, 2, 3, 3, 3], [0, 1, 1, 2, 2, 2, 3, 3], [0, 1, 1, 2, 2, 2, 3], [0, 1, 1, 2, 2, 2], [0, 1, 1, 2, 2, 3, 3, 3], [0, 1, 1, 2, 2, 3, 3], [0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2], [0, 1, 1, 2, 3, 3, 3], [0, 1, 1, 2, 3, 3], [0, 1, 1, 2, 3], [0, 1, 1, 2], [0, 1, 1, 3, 3, 3], [0, 1, 1, 3, 3], [0, 1, 1, 3], [0, 1, 1], [0, 1, 2, 2, 2, 3, 3, 3], [0, 1, 2, 2, 2, 3, 3], [0, 1, 2, 2, 2, 3], [0, 1, 2, 2, 2], [0, 1, 2, 2, 3, 3, 3], [0, 1, 2, 2, 3, 3], [0, 1, 2, 2, 3], [0, 1, 2, 2], [0, 1, 2, 3, 3, 3], [0, 1, 2, 3, 3], [0, 1, 2, 3], [0, 1, 2], [0, 1, 3, 3, 3], [0, 1, 3, 3], [0, 1, 3], [0, 1], [0, 2, 2, 2, 3, 3, 3], [0, 2, 2, 2, 3, 3], [0, 2, 2, 2, 3], [0, 2, 2, 2], [0, 2, 2, 3, 3, 3], [0, 2, 2, 3, 3], [0, 2, 2, 3], [0, 2, 2], [0, 2, 3, 3, 3], [0, 2, 3, 3], [0, 2, 3], [0, 2], [0, 3, 3, 3], [0, 3, 3], [0, 3], [0], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3], [1, 1, 1, 3], [1, 1, 1], [1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3, 3], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [1], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [2], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == [[1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 2, 2, 3, 3, 5], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5, 5], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 2, 2, 4, 4, 5], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5, 5], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5, 5], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 3, 4, 4, 5, 5], [1, 1, 3, 3, 4, 4, 5], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 3, 4, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5, 5], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 4, 5, 5], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5, 5], [1, 1, 5], [1, 1], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5], [1, 5], [1], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5], [2, 5], [2], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5], [3, 5], [3], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5], [4, 5], [4], [5, 5], [5], []]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == [[1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 5], [1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 2, 2, 2, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 2, 3, 5], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 1, 2, 2, 2, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 2, 4, 4], [1, 1, 1, 2, 2, 2, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 4, 5, 5], [1, 1, 1, 2, 2, 2, 4, 5], [1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 2, 2, 2, 5, 5, 5], [1, 1, 1, 2, 2, 2, 5, 5], [1, 1, 1, 2, 2, 2, 5], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 5], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 1, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 1, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 4, 5], [1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 2, 2, 3, 5, 5, 5], [1, 1, 1, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 3, 5], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 4, 4, 4, 5], [1, 1, 1, 2, 2, 4, 4, 4], [1, 1, 1, 2, 2, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 1, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 4, 4], [1, 1, 1, 2, 2, 4, 5, 5, 5], [1, 1, 1, 2, 2, 4, 5, 5], [1, 1, 1, 2, 2, 4, 5], [1, 1, 1, 2, 2, 4], [1, 1, 1, 2, 2, 5, 5, 5], [1, 1, 1, 2, 2, 5, 5], [1, 1, 1, 2, 2, 5], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 3, 3, 3, 4, 4, 5], [1, 1, 1, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 3, 4, 5, 5], [1, 1, 1, 2, 3, 3, 3, 4, 5], [1, 1, 1, 2, 3, 3, 3, 4], [1, 1, 1, 2, 3, 3, 3, 5, 5, 5], [1, 1, 1, 2, 3, 3, 3, 5, 5], [1, 1, 1, 2, 3, 3, 3, 5], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 1, 2, 3, 3, 4, 4], [1, 1, 1, 2, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 3, 3, 4, 5, 5], [1, 1, 1, 2, 3, 3, 4, 5], [1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 2, 3, 3, 5, 5, 5], [1, 1, 1, 2, 3, 3, 5, 5], [1, 1, 1, 2, 3, 3, 5], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 3, 4, 4, 4, 5], [1, 1, 1, 2, 3, 4, 4, 4], [1, 1, 1, 2, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 3, 4, 4, 5, 5], [1, 1, 1, 2, 3, 4, 4, 5], [1, 1, 1, 2, 3, 4, 4], [1, 1, 1, 2, 3, 4, 5, 5, 5], [1, 1, 1, 2, 3, 4, 5, 5], [1, 1, 1, 2, 3, 4, 5], [1, 1, 1, 2, 3, 4], [1, 1, 1, 2, 3, 5, 5, 5], [1, 1, 1, 2, 3, 5, 5], [1, 1, 1, 2, 3, 5], [1, 1, 1, 2, 3], [1, 1, 1, 2, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 4, 4, 4, 5, 5], [1, 1, 1, 2, 4, 4, 4, 5], [1, 1, 1, 2, 4, 4, 4], [1, 1, 1, 2, 4, 4, 5, 5, 5], [1, 1, 1, 2, 4, 4, 5, 5], [1, 1, 1, 2, 4, 4, 5], [1, 1, 1, 2, 4, 4], [1, 1, 1, 2, 4, 5, 5, 5], [1, 1, 1, 2, 4, 5, 5], [1, 1, 1, 2, 4, 5], [1, 1, 1, 2, 4], [1, 1, 1, 2, 5, 5, 5], [1, 1, 1, 2, 5, 5], [1, 1, 1, 2, 5], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 3, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 3, 3, 3, 4, 4, 4, 5], [1, 1, 1, 3, 3, 3, 4, 4, 4], [1, 1, 1, 3, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 3, 3, 3, 4, 4, 5], [1, 1, 1, 3, 3, 3, 4, 4], [1, 1, 1, 3, 3, 3, 4, 5, 5, 5], [1, 1, 1, 3, 3, 3, 4, 5, 5], [1, 1, 1, 3, 3, 3, 4, 5], [1, 1, 1, 3, 3, 3, 4], [1, 1, 1, 3, 3, 3, 5, 5, 5], [1, 1, 1, 3, 3, 3, 5, 5], [1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 3, 3, 4, 4, 4, 5], [1, 1, 1, 3, 3, 4, 4, 4], [1, 1, 1, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 3, 3, 4, 4, 5, 5], [1, 1, 1, 3, 3, 4, 4, 5], [1, 1, 1, 3, 3, 4, 4], [1, 1, 1, 3, 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[1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4], [1, 2, 4, 4, 5, 5, 5], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5, 5], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5, 5], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 3, 3, 3, 4, 4, 4, 5, 5], [1, 3, 3, 3, 4, 4, 4, 5], [1, 3, 3, 3, 4, 4, 4], [1, 3, 3, 3, 4, 4, 5, 5, 5], [1, 3, 3, 3, 4, 4, 5, 5], [1, 3, 3, 3, 4, 4, 5], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 4, 5, 5, 5], [1, 3, 3, 3, 4, 5, 5], [1, 3, 3, 3, 4, 5], [1, 3, 3, 3, 4], [1, 3, 3, 3, 5, 5, 5], [1, 3, 3, 3, 5, 5], [1, 3, 3, 3, 5], [1, 3, 3, 3], [1, 3, 3, 4, 4, 4, 5, 5, 5], [1, 3, 3, 4, 4, 4, 5, 5], [1, 3, 3, 4, 4, 4, 5], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4, 5, 5, 5], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5, 5], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5, 5], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 4, 5, 5, 5], [1, 3, 4, 4, 4, 5, 5], [1, 3, 4, 4, 4, 5], [1, 3, 4, 4, 4], [1, 3, 4, 4, 5, 5, 5], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5, 5], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5, 5], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 4, 5, 5, 5], [1, 4, 4, 4, 5, 5], [1, 4, 4, 4, 5], [1, 4, 4, 4], [1, 4, 4, 5, 5, 5], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5, 5], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5, 5], [1, 5, 5], [1, 5], [1], [2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [2, 2, 2, 3, 3, 3, 4, 4, 4, 5], [2, 2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [2, 2, 2, 3, 3, 3, 4, 4, 5, 5], [2, 2, 2, 3, 3, 3, 4, 4, 5], [2, 2, 2, 3, 3, 3, 4, 4], [2, 2, 2, 3, 3, 3, 4, 5, 5, 5], [2, 2, 2, 3, 3, 3, 4, 5, 5], [2, 2, 2, 3, 3, 3, 4, 5], [2, 2, 2, 3, 3, 3, 4], [2, 2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 2, 3, 3, 3, 5, 5], [2, 2, 2, 3, 3, 3, 5], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [2, 2, 2, 3, 3, 4, 4, 4, 5, 5], [2, 2, 2, 3, 3, 4, 4, 4, 5], [2, 2, 2, 3, 3, 4, 4, 4], [2, 2, 2, 3, 3, 4, 4, 5, 5, 5], [2, 2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 2, 3, 3, 4, 4, 5], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 4, 5, 5, 5], [2, 2, 2, 3, 3, 4, 5, 5], [2, 2, 2, 3, 3, 4, 5], [2, 2, 2, 3, 3, 4], [2, 2, 2, 3, 3, 5, 5, 5], [2, 2, 2, 3, 3, 5, 5], [2, 2, 2, 3, 3, 5], [2, 2, 2, 3, 3], [2, 2, 2, 3, 4, 4, 4, 5, 5, 5], [2, 2, 2, 3, 4, 4, 4, 5, 5], [2, 2, 2, 3, 4, 4, 4, 5], [2, 2, 2, 3, 4, 4, 4], [2, 2, 2, 3, 4, 4, 5, 5, 5], [2, 2, 2, 3, 4, 4, 5, 5], [2, 2, 2, 3, 4, 4, 5], [2, 2, 2, 3, 4, 4], [2, 2, 2, 3, 4, 5, 5, 5], [2, 2, 2, 3, 4, 5, 5], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 4], [2, 2, 2, 3, 5, 5, 5], [2, 2, 2, 3, 5, 5], [2, 2, 2, 3, 5], [2, 2, 2, 3], [2, 2, 2, 4, 4, 4, 5, 5, 5], [2, 2, 2, 4, 4, 4, 5, 5], [2, 2, 2, 4, 4, 4, 5], [2, 2, 2, 4, 4, 4], [2, 2, 2, 4, 4, 5, 5, 5], [2, 2, 2, 4, 4, 5, 5], [2, 2, 2, 4, 4, 5], [2, 2, 2, 4, 4], [2, 2, 2, 4, 5, 5, 5], [2, 2, 2, 4, 5, 5], [2, 2, 2, 4, 5], [2, 2, 2, 4], [2, 2, 2, 5, 5, 5], [2, 2, 2, 5, 5], [2, 2, 2, 5], [2, 2, 2], [2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [2, 2, 3, 3, 3, 4, 4, 4, 5], [2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [2, 2, 3, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 3, 4, 4, 5], [2, 2, 3, 3, 3, 4, 4], [2, 2, 3, 3, 3, 4, 5, 5, 5], [2, 2, 3, 3, 3, 4, 5, 5], [2, 2, 3, 3, 3, 4, 5], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 3, 3, 3, 5, 5], [2, 2, 3, 3, 3, 5], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [2, 2, 3, 3, 4, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 4, 5], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4, 5, 5, 5], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5, 5], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5, 5], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4, 5, 5, 5], [2, 2, 3, 4, 4, 4, 5, 5], [2, 2, 3, 4, 4, 4, 5], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4, 5, 5, 5], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5, 5], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5, 5], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 4, 5, 5, 5], [2, 2, 4, 4, 4, 5, 5], [2, 2, 4, 4, 4, 5], [2, 2, 4, 4, 4], [2, 2, 4, 4, 5, 5, 5], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5, 5], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5, 5], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [2, 3, 3, 3, 4, 4, 4, 5, 5], [2, 3, 3, 3, 4, 4, 4, 5], [2, 3, 3, 3, 4, 4, 4], [2, 3, 3, 3, 4, 4, 5, 5, 5], [2, 3, 3, 3, 4, 4, 5, 5], [2, 3, 3, 3, 4, 4, 5], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4, 5, 5, 5], [2, 3, 3, 3, 4, 5, 5], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 5, 5, 5], [2, 3, 3, 3, 5, 5], [2, 3, 3, 3, 5], [2, 3, 3, 3], [2, 3, 3, 4, 4, 4, 5, 5, 5], [2, 3, 3, 4, 4, 4, 5, 5], [2, 3, 3, 4, 4, 4, 5], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4, 5, 5, 5], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5, 5], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5, 5], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 4, 5, 5, 5], [2, 3, 4, 4, 4, 5, 5], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4], [2, 3, 4, 4, 5, 5, 5], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5, 5], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5, 5], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 4, 5, 5, 5], [2, 4, 4, 4, 5, 5], [2, 4, 4, 4, 5], [2, 4, 4, 4], [2, 4, 4, 5, 5, 5], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5, 5], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5, 5], [2, 5, 5], [2, 5], [2], [3, 3, 3, 4, 4, 4, 5, 5, 5], [3, 3, 3, 4, 4, 4, 5, 5], [3, 3, 3, 4, 4, 4, 5], [3, 3, 3, 4, 4, 4], [3, 3, 3, 4, 4, 5, 5, 5], [3, 3, 3, 4, 4, 5, 5], [3, 3, 3, 4, 4, 5], [3, 3, 3, 4, 4], [3, 3, 3, 4, 5, 5, 5], [3, 3, 3, 4, 5, 5], [3, 3, 3, 4, 5], [3, 3, 3, 4], [3, 3, 3, 5, 5, 5], [3, 3, 3, 5, 5], [3, 3, 3, 5], [3, 3, 3], [3, 3, 4, 4, 4, 5, 5, 5], [3, 3, 4, 4, 4, 5, 5], [3, 3, 4, 4, 4, 5], [3, 3, 4, 4, 4], [3, 3, 4, 4, 5, 5, 5], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5, 5], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5, 5], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 4, 5, 5, 5], [3, 4, 4, 4, 5, 5], [3, 4, 4, 4, 5], [3, 4, 4, 4], [3, 4, 4, 5, 5, 5], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5, 5], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5, 5], [3, 5, 5], [3, 5], [3], [4, 4, 4, 5, 5, 5], [4, 4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [4, 4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5, 5], [4, 5, 5], [4, 5], [4], [5, 5, 5], [5, 5], [5], []]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7], [7, 7], [7], []]\n assert candidate(nums = [3, 3, 3, 2, 2, 1, 1, 1]) == [[1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3], [1, 1, 1, 3], [1, 1, 1], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3, 3], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [2], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [-10, -9, -8, -7, -6, -5, -4, -3, -2], [-10, -9, -8, -7, -6, -5, -4, -3, -1], [-10, -9, -8, -7, -6, -5, -4, -3], [-10, -9, -8, -7, -6, -5, -4, -2, -1], [-10, -9, -8, -7, -6, -5, -4, -2], [-10, -9, -8, -7, -6, -5, -4, -1], [-10, -9, -8, -7, -6, -5, -4], [-10, -9, -8, -7, -6, -5, -3, -2, -1], [-10, -9, -8, -7, -6, -5, -3, -2], [-10, -9, -8, -7, -6, -5, -3, -1], [-10, 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-4, -3, -1], [-7, -6, -4, -3], [-7, -6, -4, -2, -1], [-7, -6, -4, -2], [-7, -6, -4, -1], [-7, -6, -4], [-7, -6, -3, -2, -1], [-7, -6, -3, -2], [-7, -6, -3, -1], [-7, -6, -3], [-7, -6, -2, -1], [-7, -6, -2], [-7, -6, -1], [-7, -6], [-7, -5, -4, -3, -2, -1], [-7, -5, -4, -3, -2], [-7, -5, -4, -3, -1], [-7, -5, -4, -3], [-7, -5, -4, -2, -1], [-7, -5, -4, -2], [-7, -5, -4, -1], [-7, -5, -4], [-7, -5, -3, -2, -1], [-7, -5, -3, -2], [-7, -5, -3, -1], [-7, -5, -3], [-7, -5, -2, -1], [-7, -5, -2], [-7, -5, -1], [-7, -5], [-7, -4, -3, -2, -1], [-7, -4, -3, -2], [-7, -4, -3, -1], [-7, -4, -3], [-7, -4, -2, -1], [-7, -4, -2], [-7, -4, -1], [-7, -4], [-7, -3, -2, -1], [-7, -3, -2], [-7, -3, -1], [-7, -3], [-7, -2, -1], [-7, -2], [-7, -1], [-7], [-6, -5, -4, -3, -2, -1], [-6, -5, -4, -3, -2], [-6, -5, -4, -3, -1], [-6, -5, -4, -3], [-6, -5, -4, -2, -1], [-6, -5, -4, -2], [-6, -5, -4, -1], [-6, -5, -4], [-6, -5, -3, -2, -1], [-6, -5, -3, -2], [-6, -5, -3, -1], [-6, -5, -3], [-6, -5, -2, -1], [-6, -5, -2], [-6, -5, -1], [-6, -5], [-6, -4, -3, -2, -1], [-6, -4, -3, -2], [-6, -4, -3, -1], [-6, -4, -3], [-6, -4, -2, -1], [-6, -4, -2], [-6, -4, -1], [-6, -4], [-6, -3, -2, -1], [-6, -3, -2], [-6, -3, -1], [-6, -3], [-6, -2, -1], [-6, -2], [-6, -1], [-6], [-5, -4, -3, -2, -1], [-5, -4, -3, -2], [-5, -4, -3, -1], [-5, -4, -3], [-5, -4, -2, -1], [-5, -4, -2], [-5, -4, -1], [-5, -4], [-5, -3, -2, -1], [-5, -3, -2], [-5, -3, -1], [-5, -3], [-5, -2, -1], [-5, -2], [-5, -1], [-5], [-4, -3, -2, -1], [-4, -3, -2], [-4, -3, -1], [-4, -3], [-4, -2, -1], [-4, -2], [-4, -1], [-4], [-3, -2, -1], [-3, -2], [-3, -1], [-3], [-2, -1], [-2], [-1], []]\n assert candidate(nums = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == [[4, 4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4, 4], [4, 4, 4, 4, 4], [4, 4, 4, 4], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [-1, -2, -3, -2, -1]) == [[-3, -2, -2, -1, -1], [-3, -2, -2, -1], [-3, -2, -2], [-3, -2, -1, -1], [-3, -2, -1], [-3, -2], [-3, -1, -1], [-3, -1], [-3], [-2, -2, -1, -1], [-2, -2, -1], [-2, -2], [-2, -1, -1], [-2, -1], [-2], [-1, -1], [-1], []]\n assert candidate(nums = [-5, -5, -5, -5, 0, 0, 0, 5, 5, 5]) == [[-5, -5, -5, -5, 0, 0, 0, 5, 5, 5], [-5, -5, -5, -5, 0, 0, 0, 5, 5], [-5, -5, -5, -5, 0, 0, 0, 5], [-5, -5, -5, -5, 0, 0, 0], [-5, -5, -5, -5, 0, 0, 5, 5, 5], [-5, -5, -5, -5, 0, 0, 5, 5], [-5, -5, -5, -5, 0, 0, 5], [-5, -5, -5, -5, 0, 0], [-5, -5, -5, -5, 0, 5, 5, 5], [-5, -5, -5, -5, 0, 5, 5], [-5, -5, -5, -5, 0, 5], [-5, -5, -5, -5, 0], [-5, -5, -5, -5, 5, 5, 5], [-5, -5, -5, -5, 5, 5], [-5, -5, -5, -5, 5], [-5, -5, -5, -5], [-5, -5, -5, 0, 0, 0, 5, 5, 5], [-5, -5, -5, 0, 0, 0, 5, 5], [-5, -5, -5, 0, 0, 0, 5], [-5, -5, -5, 0, 0, 0], [-5, -5, -5, 0, 0, 5, 5, 5], [-5, -5, -5, 0, 0, 5, 5], [-5, -5, -5, 0, 0, 5], [-5, -5, -5, 0, 0], [-5, -5, -5, 0, 5, 5, 5], [-5, -5, -5, 0, 5, 5], [-5, -5, -5, 0, 5], [-5, -5, -5, 0], [-5, -5, -5, 5, 5, 5], [-5, -5, -5, 5, 5], [-5, -5, -5, 5], [-5, -5, -5], [-5, -5, 0, 0, 0, 5, 5, 5], [-5, -5, 0, 0, 0, 5, 5], [-5, -5, 0, 0, 0, 5], [-5, -5, 0, 0, 0], [-5, -5, 0, 0, 5, 5, 5], [-5, -5, 0, 0, 5, 5], [-5, -5, 0, 0, 5], [-5, -5, 0, 0], [-5, -5, 0, 5, 5, 5], [-5, -5, 0, 5, 5], [-5, -5, 0, 5], [-5, -5, 0], [-5, -5, 5, 5, 5], [-5, -5, 5, 5], [-5, -5, 5], [-5, -5], [-5, 0, 0, 0, 5, 5, 5], [-5, 0, 0, 0, 5, 5], [-5, 0, 0, 0, 5], [-5, 0, 0, 0], [-5, 0, 0, 5, 5, 5], [-5, 0, 0, 5, 5], [-5, 0, 0, 5], [-5, 0, 0], [-5, 0, 5, 5, 5], [-5, 0, 5, 5], [-5, 0, 5], [-5, 0], [-5, 5, 5, 5], [-5, 5, 5], [-5, 5], [-5], [0, 0, 0, 5, 5, 5], [0, 0, 0, 5, 5], [0, 0, 0, 5], [0, 0, 0], [0, 0, 5, 5, 5], [0, 0, 5, 5], [0, 0, 5], [0, 0], [0, 5, 5, 5], [0, 5, 5], [0, 5], [0], [5, 5, 5], [5, 5], [5], []]\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3]) == [[0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 1, 1, 2, 2, 3], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2, 3, 3], [0, 0, 1, 1, 2, 3], [0, 0, 1, 1, 2], [0, 0, 1, 1, 3, 3], [0, 0, 1, 1, 3], [0, 0, 1, 1], [0, 0, 1, 2, 2, 3, 3], [0, 0, 1, 2, 2, 3], [0, 0, 1, 2, 2], [0, 0, 1, 2, 3, 3], [0, 0, 1, 2, 3], [0, 0, 1, 2], [0, 0, 1, 3, 3], [0, 0, 1, 3], [0, 0, 1], [0, 0, 2, 2, 3, 3], [0, 0, 2, 2, 3], [0, 0, 2, 2], [0, 0, 2, 3, 3], [0, 0, 2, 3], [0, 0, 2], [0, 0, 3, 3], [0, 0, 3], [0, 0], [0, 1, 1, 2, 2, 3, 3], [0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2], [0, 1, 1, 2, 3, 3], [0, 1, 1, 2, 3], [0, 1, 1, 2], [0, 1, 1, 3, 3], [0, 1, 1, 3], [0, 1, 1], [0, 1, 2, 2, 3, 3], [0, 1, 2, 2, 3], [0, 1, 2, 2], [0, 1, 2, 3, 3], [0, 1, 2, 3], [0, 1, 2], [0, 1, 3, 3], [0, 1, 3], [0, 1], [0, 2, 2, 3, 3], [0, 2, 2, 3], [0, 2, 2], [0, 2, 3, 3], [0, 2, 3], [0, 2], [0, 3, 3], [0, 3], [0], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [-1, -2, -3, -4, -1, -2, -3, -4]) == [[-4, -4, -3, -3, -2, -2, -1, -1], [-4, -4, -3, -3, -2, -2, -1], [-4, -4, -3, -3, -2, -2], [-4, -4, -3, -3, -2, -1, -1], [-4, -4, -3, -3, -2, -1], [-4, -4, -3, -3, -2], [-4, -4, -3, -3, -1, -1], [-4, -4, -3, -3, -1], [-4, -4, -3, -3], [-4, -4, -3, -2, -2, -1, -1], [-4, -4, -3, -2, -2, -1], [-4, -4, -3, -2, -2], [-4, -4, -3, -2, -1, -1], [-4, -4, -3, -2, -1], [-4, -4, -3, -2], [-4, -4, -3, -1, -1], [-4, -4, -3, -1], [-4, -4, -3], [-4, -4, -2, -2, -1, -1], [-4, -4, -2, -2, -1], [-4, -4, -2, -2], [-4, -4, -2, -1, -1], [-4, -4, -2, -1], [-4, -4, -2], [-4, -4, -1, -1], [-4, -4, -1], [-4, -4], [-4, -3, -3, -2, -2, -1, -1], [-4, -3, -3, -2, -2, -1], [-4, -3, -3, -2, -2], [-4, -3, -3, -2, -1, -1], [-4, -3, -3, -2, -1], [-4, -3, -3, -2], [-4, -3, -3, -1, -1], [-4, -3, -3, -1], [-4, -3, -3], [-4, -3, -2, -2, -1, -1], [-4, -3, -2, -2, -1], [-4, -3, -2, -2], [-4, -3, -2, -1, -1], [-4, -3, -2, -1], [-4, -3, -2], [-4, -3, -1, -1], [-4, -3, -1], [-4, -3], [-4, -2, -2, -1, -1], [-4, -2, -2, -1], [-4, -2, -2], [-4, -2, -1, -1], [-4, -2, -1], [-4, -2], [-4, -1, -1], [-4, -1], [-4], [-3, -3, -2, -2, -1, -1], [-3, -3, -2, -2, -1], [-3, -3, -2, -2], [-3, -3, -2, -1, -1], [-3, -3, -2, -1], [-3, -3, -2], [-3, -3, -1, -1], [-3, -3, -1], [-3, -3], [-3, -2, -2, -1, -1], [-3, -2, -2, -1], [-3, -2, -2], [-3, -2, -1, -1], [-3, -2, -1], [-3, -2], [-3, -1, -1], [-3, -1], [-3], [-2, -2, -1, -1], [-2, -2, -1], [-2, -2], [-2, -1, -1], [-2, -1], [-2], [-1, -1], [-1], []]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4]) == [[1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 3, 3, 4], [1, 3, 3, 3], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4], [1, 3], [1, 4], [1], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [2, 3, 3, 3, 4], [2, 3, 3, 3], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4], [2, 3], [2, 4], [2], [3, 3, 3, 4], [3, 3, 3], [3, 3, 4], [3, 3], [3, 4], [3], [4], []]\n assert candidate(nums = [7, 8, 7, 8, 9]) == [[7, 7, 8, 8, 9], [7, 7, 8, 8], [7, 7, 8, 9], [7, 7, 8], [7, 7, 9], [7, 7], [7, 8, 8, 9], [7, 8, 8], [7, 8, 9], [7, 8], [7, 9], [7], [8, 8, 9], [8, 8], [8, 9], [8], [9], []]\n assert candidate(nums = [-10, 0, 10, -10, 0, 10, -10, 0, 10]) == [[-10, -10, -10, 0, 0, 0, 10, 10, 10], [-10, -10, -10, 0, 0, 0, 10, 10], [-10, -10, -10, 0, 0, 0, 10], [-10, -10, -10, 0, 0, 0], [-10, -10, -10, 0, 0, 10, 10, 10], [-10, -10, -10, 0, 0, 10, 10], [-10, -10, -10, 0, 0, 10], [-10, -10, -10, 0, 0], [-10, -10, -10, 0, 10, 10, 10], [-10, -10, -10, 0, 10, 10], [-10, -10, -10, 0, 10], [-10, -10, -10, 0], [-10, -10, -10, 10, 10, 10], [-10, -10, -10, 10, 10], [-10, -10, -10, 10], [-10, -10, -10], [-10, -10, 0, 0, 0, 10, 10, 10], [-10, -10, 0, 0, 0, 10, 10], [-10, -10, 0, 0, 0, 10], [-10, -10, 0, 0, 0], [-10, -10, 0, 0, 10, 10, 10], [-10, -10, 0, 0, 10, 10], [-10, -10, 0, 0, 10], [-10, -10, 0, 0], [-10, -10, 0, 10, 10, 10], [-10, -10, 0, 10, 10], [-10, -10, 0, 10], [-10, -10, 0], [-10, -10, 10, 10, 10], [-10, -10, 10, 10], [-10, -10, 10], [-10, -10], [-10, 0, 0, 0, 10, 10, 10], [-10, 0, 0, 0, 10, 10], [-10, 0, 0, 0, 10], [-10, 0, 0, 0], [-10, 0, 0, 10, 10, 10], [-10, 0, 0, 10, 10], [-10, 0, 0, 10], [-10, 0, 0], [-10, 0, 10, 10, 10], [-10, 0, 10, 10], [-10, 0, 10], [-10, 0], [-10, 10, 10, 10], [-10, 10, 10], [-10, 10], [-10], [0, 0, 0, 10, 10, 10], [0, 0, 0, 10, 10], [0, 0, 0, 10], [0, 0, 0], [0, 0, 10, 10, 10], [0, 0, 10, 10], [0, 0, 10], [0, 0], [0, 10, 10, 10], [0, 10, 10], [0, 10], [0], [10, 10, 10], [10, 10], [10], []]\n assert candidate(nums = [1, 2, 2, 3, 3, 3]) == [[1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [2], [3, 3, 3], [3, 3], [3], []]\n assert candidate(nums = [9, 9, 8, 8, 7, 7, 6, 6, 5, 5]) == [[5, 5, 6, 6, 7, 7, 8, 8, 9, 9], [5, 5, 6, 6, 7, 7, 8, 8, 9], [5, 5, 6, 6, 7, 7, 8, 8], [5, 5, 6, 6, 7, 7, 8, 9, 9], [5, 5, 6, 6, 7, 7, 8, 9], [5, 5, 6, 6, 7, 7, 8], [5, 5, 6, 6, 7, 7, 9, 9], [5, 5, 6, 6, 7, 7, 9], [5, 5, 6, 6, 7, 7], [5, 5, 6, 6, 7, 8, 8, 9, 9], [5, 5, 6, 6, 7, 8, 8, 9], [5, 5, 6, 6, 7, 8, 8], [5, 5, 6, 6, 7, 8, 9, 9], [5, 5, 6, 6, 7, 8, 9], [5, 5, 6, 6, 7, 8], [5, 5, 6, 6, 7, 9, 9], [5, 5, 6, 6, 7, 9], [5, 5, 6, 6, 7], [5, 5, 6, 6, 8, 8, 9, 9], [5, 5, 6, 6, 8, 8, 9], [5, 5, 6, 6, 8, 8], [5, 5, 6, 6, 8, 9, 9], [5, 5, 6, 6, 8, 9], [5, 5, 6, 6, 8], [5, 5, 6, 6, 9, 9], [5, 5, 6, 6, 9], [5, 5, 6, 6], [5, 5, 6, 7, 7, 8, 8, 9, 9], [5, 5, 6, 7, 7, 8, 8, 9], [5, 5, 6, 7, 7, 8, 8], [5, 5, 6, 7, 7, 8, 9, 9], [5, 5, 6, 7, 7, 8, 9], [5, 5, 6, 7, 7, 8], [5, 5, 6, 7, 7, 9, 9], [5, 5, 6, 7, 7, 9], [5, 5, 6, 7, 7], [5, 5, 6, 7, 8, 8, 9, 9], [5, 5, 6, 7, 8, 8, 9], [5, 5, 6, 7, 8, 8], [5, 5, 6, 7, 8, 9, 9], [5, 5, 6, 7, 8, 9], [5, 5, 6, 7, 8], [5, 5, 6, 7, 9, 9], [5, 5, 6, 7, 9], [5, 5, 6, 7], [5, 5, 6, 8, 8, 9, 9], [5, 5, 6, 8, 8, 9], [5, 5, 6, 8, 8], [5, 5, 6, 8, 9, 9], [5, 5, 6, 8, 9], [5, 5, 6, 8], [5, 5, 6, 9, 9], [5, 5, 6, 9], [5, 5, 6], [5, 5, 7, 7, 8, 8, 9, 9], [5, 5, 7, 7, 8, 8, 9], [5, 5, 7, 7, 8, 8], [5, 5, 7, 7, 8, 9, 9], [5, 5, 7, 7, 8, 9], [5, 5, 7, 7, 8], [5, 5, 7, 7, 9, 9], [5, 5, 7, 7, 9], [5, 5, 7, 7], [5, 5, 7, 8, 8, 9, 9], [5, 5, 7, 8, 8, 9], [5, 5, 7, 8, 8], [5, 5, 7, 8, 9, 9], [5, 5, 7, 8, 9], [5, 5, 7, 8], [5, 5, 7, 9, 9], [5, 5, 7, 9], [5, 5, 7], [5, 5, 8, 8, 9, 9], [5, 5, 8, 8, 9], [5, 5, 8, 8], [5, 5, 8, 9, 9], [5, 5, 8, 9], [5, 5, 8], [5, 5, 9, 9], [5, 5, 9], [5, 5], [5, 6, 6, 7, 7, 8, 8, 9, 9], [5, 6, 6, 7, 7, 8, 8, 9], [5, 6, 6, 7, 7, 8, 8], [5, 6, 6, 7, 7, 8, 9, 9], [5, 6, 6, 7, 7, 8, 9], [5, 6, 6, 7, 7, 8], [5, 6, 6, 7, 7, 9, 9], [5, 6, 6, 7, 7, 9], [5, 6, 6, 7, 7], [5, 6, 6, 7, 8, 8, 9, 9], [5, 6, 6, 7, 8, 8, 9], [5, 6, 6, 7, 8, 8], [5, 6, 6, 7, 8, 9, 9], [5, 6, 6, 7, 8, 9], [5, 6, 6, 7, 8], [5, 6, 6, 7, 9, 9], [5, 6, 6, 7, 9], [5, 6, 6, 7], [5, 6, 6, 8, 8, 9, 9], [5, 6, 6, 8, 8, 9], [5, 6, 6, 8, 8], [5, 6, 6, 8, 9, 9], [5, 6, 6, 8, 9], [5, 6, 6, 8], [5, 6, 6, 9, 9], [5, 6, 6, 9], [5, 6, 6], [5, 6, 7, 7, 8, 8, 9, 9], [5, 6, 7, 7, 8, 8, 9], [5, 6, 7, 7, 8, 8], [5, 6, 7, 7, 8, 9, 9], [5, 6, 7, 7, 8, 9], [5, 6, 7, 7, 8], [5, 6, 7, 7, 9, 9], [5, 6, 7, 7, 9], [5, 6, 7, 7], [5, 6, 7, 8, 8, 9, 9], [5, 6, 7, 8, 8, 9], [5, 6, 7, 8, 8], [5, 6, 7, 8, 9, 9], [5, 6, 7, 8, 9], [5, 6, 7, 8], [5, 6, 7, 9, 9], [5, 6, 7, 9], [5, 6, 7], [5, 6, 8, 8, 9, 9], [5, 6, 8, 8, 9], [5, 6, 8, 8], [5, 6, 8, 9, 9], [5, 6, 8, 9], [5, 6, 8], [5, 6, 9, 9], [5, 6, 9], [5, 6], [5, 7, 7, 8, 8, 9, 9], [5, 7, 7, 8, 8, 9], [5, 7, 7, 8, 8], [5, 7, 7, 8, 9, 9], [5, 7, 7, 8, 9], [5, 7, 7, 8], [5, 7, 7, 9, 9], [5, 7, 7, 9], [5, 7, 7], [5, 7, 8, 8, 9, 9], [5, 7, 8, 8, 9], [5, 7, 8, 8], [5, 7, 8, 9, 9], [5, 7, 8, 9], [5, 7, 8], [5, 7, 9, 9], [5, 7, 9], [5, 7], [5, 8, 8, 9, 9], [5, 8, 8, 9], [5, 8, 8], [5, 8, 9, 9], [5, 8, 9], [5, 8], [5, 9, 9], [5, 9], [5], [6, 6, 7, 7, 8, 8, 9, 9], [6, 6, 7, 7, 8, 8, 9], [6, 6, 7, 7, 8, 8], [6, 6, 7, 7, 8, 9, 9], [6, 6, 7, 7, 8, 9], [6, 6, 7, 7, 8], [6, 6, 7, 7, 9, 9], [6, 6, 7, 7, 9], [6, 6, 7, 7], [6, 6, 7, 8, 8, 9, 9], [6, 6, 7, 8, 8, 9], [6, 6, 7, 8, 8], [6, 6, 7, 8, 9, 9], [6, 6, 7, 8, 9], [6, 6, 7, 8], [6, 6, 7, 9, 9], [6, 6, 7, 9], [6, 6, 7], [6, 6, 8, 8, 9, 9], [6, 6, 8, 8, 9], [6, 6, 8, 8], [6, 6, 8, 9, 9], [6, 6, 8, 9], [6, 6, 8], [6, 6, 9, 9], [6, 6, 9], [6, 6], [6, 7, 7, 8, 8, 9, 9], [6, 7, 7, 8, 8, 9], [6, 7, 7, 8, 8], [6, 7, 7, 8, 9, 9], [6, 7, 7, 8, 9], [6, 7, 7, 8], [6, 7, 7, 9, 9], [6, 7, 7, 9], [6, 7, 7], [6, 7, 8, 8, 9, 9], [6, 7, 8, 8, 9], [6, 7, 8, 8], [6, 7, 8, 9, 9], [6, 7, 8, 9], [6, 7, 8], [6, 7, 9, 9], [6, 7, 9], [6, 7], [6, 8, 8, 9, 9], [6, 8, 8, 9], [6, 8, 8], [6, 8, 9, 9], [6, 8, 9], [6, 8], [6, 9, 9], [6, 9], [6], [7, 7, 8, 8, 9, 9], [7, 7, 8, 8, 9], [7, 7, 8, 8], [7, 7, 8, 9, 9], [7, 7, 8, 9], [7, 7, 8], [7, 7, 9, 9], [7, 7, 9], [7, 7], [7, 8, 8, 9, 9], [7, 8, 8, 9], [7, 8, 8], [7, 8, 9, 9], [7, 8, 9], [7, 8], [7, 9, 9], [7, 9], [7], [8, 8, 9, 9], [8, 8, 9], [8, 8], [8, 9, 9], [8, 9], [8], [9, 9], [9], []]\n assert candidate(nums = [7, 8, 8, 9, 9, 9, 9]) == [[7, 8, 8, 9, 9, 9, 9], [7, 8, 8, 9, 9, 9], [7, 8, 8, 9, 9], [7, 8, 8, 9], [7, 8, 8], [7, 8, 9, 9, 9, 9], [7, 8, 9, 9, 9], [7, 8, 9, 9], [7, 8, 9], [7, 8], [7, 9, 9, 9, 9], [7, 9, 9, 9], [7, 9, 9], [7, 9], [7], [8, 8, 9, 9, 9, 9], [8, 8, 9, 9, 9], [8, 8, 9, 9], [8, 8, 9], [8, 8], [8, 9, 9, 9, 9], [8, 9, 9, 9], [8, 9, 9], [8, 9], [8], [9, 9, 9, 9], [9, 9, 9], [9, 9], [9], []]\n assert candidate(nums = [4, 4, 4, 3, 3, 2, 1]) == [[1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4], [1, 4, 4], [1, 4], [1], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4], [2, 4, 4], [2, 4], [2], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4], [3, 4, 4], [3, 4], [3], [4, 4, 4], [4, 4], [4], []]\n assert candidate(nums = [3, 1, 2, 2, 3, 1]) == [[1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3], [1, 3], [1], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3], [2, 3], [2], [3, 3], [3], []]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5]) == [[1, 1, 2, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 2, 2, 2, 3, 3, 5], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 2, 2, 2, 3, 4, 5], [1, 1, 2, 2, 2, 3, 4], [1, 1, 2, 2, 2, 3, 5], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2, 4, 4, 5], [1, 1, 2, 2, 2, 4, 4], [1, 1, 2, 2, 2, 4, 5], [1, 1, 2, 2, 2, 4], [1, 1, 2, 2, 2, 5], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3, 5], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 5], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 3, 4, 4, 5], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5], [1, 1], [1, 2, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 2, 3, 3, 4, 4], [1, 2, 2, 2, 3, 3, 4, 5], [1, 2, 2, 2, 3, 3, 4], [1, 2, 2, 2, 3, 3, 5], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3, 4, 4, 5], [1, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 3, 4, 5], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 5], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4, 4, 5], [1, 2, 2, 2, 4, 4], [1, 2, 2, 2, 4, 5], [1, 2, 2, 2, 4], [1, 2, 2, 2, 5], [1, 2, 2, 2], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5], [1, 4], [1, 5], [1], [2, 2, 2, 3, 3, 4, 4, 5], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 4, 5], [2, 2, 2, 3, 3, 4], [2, 2, 2, 3, 3, 5], [2, 2, 2, 3, 3], [2, 2, 2, 3, 4, 4, 5], [2, 2, 2, 3, 4, 4], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 4], [2, 2, 2, 3, 5], [2, 2, 2, 3], [2, 2, 2, 4, 4, 5], [2, 2, 2, 4, 4], [2, 2, 2, 4, 5], [2, 2, 2, 4], [2, 2, 2, 5], [2, 2, 2], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5], [2, 4], [2, 5], [2], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5], [3, 3], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5], [3, 4], [3, 5], [3], [4, 4, 5], [4, 4], [4, 5], [4], [5], []]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().subsetsWithDup", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var subsetsWithDup = function(nums) {", "container": null, "callable": "subsetsWithDup", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 91, "task_id": "decode-ways", "difficulty": "Medium", "problem_description": "You have intercepted a secret message encoded as a string of numbers. The message is decoded via the following mapping:\n\"1\" -> 'A'\n\"2\" -> 'B'\n...\n\"25\" -> 'Y'\n\"26\" -> 'Z'\nHowever, while decoding the message, you realize that there are many different ways you can decode the message because some codes are contained in other codes (\"2\" and \"5\" vs \"25\").\nFor example, \"11106\" can be decoded into:\n\n\"AAJF\" with the grouping (1, 1, 10, 6)\n\"KJF\" with the grouping (11, 10, 6)\nThe grouping (1, 11, 06) is invalid because \"06\" is not a valid code (only \"6\" is valid).\n\nNote: there may be strings that are impossible to decode.\n\nGiven a string s containing only digits, return the number of ways to decode it. If the entire string cannot be decoded in any valid way, return 0.\nThe test cases are generated so that the answer fits in a 32-bit integer.\n \nExample 1:\n\nInput: s = \"12\"\nOutput: 2\nExplanation:\n\"12\" could be decoded as \"AB\" (1 2) or \"L\" (12).\n\nExample 2:\n\nInput: s = \"226\"\nOutput: 3\nExplanation:\n\"226\" could be decoded as \"BZ\" (2 26), \"VF\" (22 6), or \"BBF\" (2 2 6).\n\nExample 3:\n\nInput: s = \"06\"\nOutput: 0\nExplanation:\n\"06\" cannot be mapped to \"F\" because of the leading zero (\"6\" is different from \"06\"). In this case, the string is not a valid encoding, so return 0.\n\n \nConstraints:\n\n1 <= s.length <= 100\ns contains only digits and may contain leading zero(s).\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"100100100\") == 0\n assert candidate(s = \"101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010\") == 1\n assert candidate(s = \"1111001111001111001111001111001111001111001111001111001111\") == 0\n assert candidate(s = \"2611055971756562\") == 4\n assert candidate(s = \"10011\") == 0\n assert candidate(s = \"11106\") == 2\n assert candidate(s = \"30\") == 0\n assert candidate(s = \"10101010101010101010101010101010\") == 1\n assert candidate(s = \"260260260260260260260260260260260260260260260260260260260\") == 0\n assert candidate(s = \"50633191395000636099666\") == 0\n assert candidate(s = \"12212212212212212212212212212212\") == 3524578\n assert candidate(s = \"120123\") == 3\n assert candidate(s = \"1201234\") == 3\n assert candidate(s = \"999999999999999999999999999999999999999999999999999999999\") == 1\n assert candidate(s = \"1230123\") == 0\n assert candidate(s = \"1234567890\") == 0\n assert candidate(s = \"123456789\") == 3\n assert candidate(s = \"2626262626262626262626262626262626262626262626262626262626\") == 536870912\n assert candidate(s = \"1234567891011121314151617181920212223242526\") == 259584\n assert candidate(s = \"200\") == 0\n assert candidate(s = \"0\") == 0\n assert candidate(s = \"100\") == 0\n assert candidate(s = \"2121212121212121212121212121212121212121212121212121212121\") == 956722026041\n assert candidate(s = \"1231231231231231231231231231231231231231231231231231231231\") == 1162261467\n assert candidate(s = \"47575625458446174945557469461\") == 4\n assert candidate(s = \"2200\") == 0\n assert candidate(s = \"010\") == 0\n assert candidate(s = \"99999999999999999999999999999999\") == 1\n assert candidate(s = \"230\") == 0\n assert candidate(s = \"2020202020202020202020202020202020202020202020202020202020\") == 1\n assert candidate(s = \"99999\") == 1\n assert candidate(s = \"111122221111222211112222111122221111222211112222111122221111\") == 2504730781961\n assert candidate(s = \"3\") == 1\n assert candidate(s = \"11111111111111111111111111111111\") == 3524578\n assert candidate(s = \"27\") == 1\n assert candidate(s = \"1000000000000000000000000000000000000000000000000000000000\") == 0\n assert candidate(s = \"301\") == 0\n assert candidate(s = \"000\") == 0\n assert candidate(s = \"61105709526116709637291338570167016761\") == 0\n assert candidate(s = \"1010101010101010101010101010101010101010101010101010101010\") == 1\n assert candidate(s = \"10\") == 1\n assert candidate(s = \"1101101101101101101101101101101101101101101101101101101101\") == 1\n assert candidate(s = \"101010101010101010101010101010101010101010101010101010\") == 1\n assert candidate(s = \"110\") == 1\n assert candidate(s = \"12\") == 2\n assert candidate(s = \"226\") == 3\n assert candidate(s = \"1\") == 1\n assert candidate(s = \"2222002222002222002222002222002222002222002222002222002222\") == 0\n assert candidate(s = \"2323232323232323232323232323232323232323232323232323232323\") == 536870912\n assert candidate(s = \"1010101010101010101010101010101010101010101010101010101010101010\") == 1\n assert candidate(s = \"1000\") == 0\n assert candidate(s = \"1001001001001001001001001001001001\") == 0\n assert candidate(s = \"11111111111111111111111111111111111111111111111111\") == 20365011074\n assert candidate(s = \"111111111111111111111111111111111111111111111111111111\") == 139583862445\n assert candidate(s = \"2101\") == 1\n assert candidate(s = \"20\") == 1\n assert candidate(s = \"1212121212121212121212121212121212121212121212121212121212\") == 956722026041\n assert candidate(s = \"1111111111111111111111111111111111111111111111111111111111\") == 956722026041\n assert candidate(s = \"1001001001001001001001001001001001001001001001001001001001\") == 0\n assert candidate(s = \"06\") == 0\n assert candidate(s = \"1234567890123456789012345678901234567890123456789012345679\") == 0\n assert candidate(s = \"12321213213213213213213213213213213213213213213213\") == 114791256\n assert candidate(s = \"1111111111111111111111111111111111111111111111111111111111111\") == 4052739537881\n assert candidate(s = \"12211221122112211221122112211221122112211221122112211221122112\") == 6557470319842\n assert candidate(s = \"12345678987654321\") == 6\n assert candidate(s = \"22222222222222222222222222222222222222222222222222222222222\") == 1548008755920\n assert candidate(s = \"2525252525252525252525252525252525252525252525252525252525\") == 536870912\n assert candidate(s = \"12345678901234567890123456789012345678901234567890\") == 0\n assert candidate(s = \"1010101010101010101010101010101010101010101010101010101010101\") == 1\n assert candidate(s = \"10101010101010101010101010101010101010101010101010\") == 1\n assert candidate(s = \"121212121212121212121212121212121212121212121212121212121212121\") == 10610209857723\n assert candidate(s = \"1201201201201201201201201201201201201201201201201201201201\") == 1\n assert candidate(s = \"122522201\") == 10\n assert candidate(s = \"20202020202020202020202020202020202020202020202020202020202\") == 1\n assert candidate(s = \"2222222222222222222222222222222222222222222222222222222222\") == 956722026041\n assert candidate(s = \"200200200200200200200200200200200200200200200200200\") == 0\n assert candidate(s = \"25252525252525252525252525252525252525252525252525252525250\") == 0\n assert candidate(s = \"120120120120120\") == 1\n assert candidate(s = \"191919191919191919191919191919191919191919191919191919191919\") == 1073741824\n assert candidate(s = \"9999999999999999999999999999999999999999999999999999999999\") == 1\n assert candidate(s = \"112112112112112112112112112112112112112112112112112112112112\") == 2504730781961\n assert candidate(s = \"1234567890123456789012345678901234567890123456789012345678\") == 0\n assert candidate(s = \"112233445566778899\") == 8\n assert candidate(s = \"99999999999999999999999999999999999999\") == 1\n assert candidate(s = \"11111111111111111111111111111111111110\") == 24157817\n assert candidate(s = \"192939495969798991011121314151617181920212223242526272829\") == 173056\n assert candidate(s = \"20202020202020202020202020202020202020202020202020\") == 1\n assert candidate(s = \"1234567890987654321012345678909876543210\") == 0\n assert candidate(s = \"272727\") == 1\n assert candidate(s = \"21212121212121212121212121212121212121212121212121212121212121\") == 6557470319842\n assert candidate(s = \"3030303030303030303030303030303030303030303030303030303030303\") == 0\n assert candidate(s = \"22122212122212122212122212122212122212122212122212122212122\") == 1548008755920\n assert candidate(s = \"001\") == 0\n assert candidate(s = \"1122221122221122221122221122221122221122221122221122221122221\") == 4052739537881\n assert candidate(s = \"11110011110011110011110011110011110011110011110011\") == 0\n assert candidate(s = \"1111111111111111111111111111111111111111111111111111111112\") == 956722026041\n assert candidate(s = \"2511452311222112511452311222112511452311222112511\") == 143748000\n assert candidate(s = \"112112112112112112112112112112112112112112112112112112112112112\") == 10610209857723\n assert candidate(s = \"222222222222222222222222222222222222222222222222222222222222\") == 2504730781961\n assert candidate(s = \"1234567898765432123456789876543212345678987654321234567898\") == 375\n assert candidate(s = \"30515015150150150150150150150150150150150150150150\") == 0\n assert candidate(s = \"11213141516171819202122232425262728293031323334353637383940\") == 0\n assert candidate(s = \"212121212121212121212121212121212121212121212121212121212\") == 591286729879\n assert candidate(s = \"10203040506070809010111213141516171819202122232425262728293031\") == 0\n assert candidate(s = \"22111122111122111122111122111122111122111122111122111122111122\") == 6557470319842\n assert candidate(s = \"0102030405060708091011121314151617181920212223242526\") == 0\n assert candidate(s = \"11111111111111111111111111111111111111111111111111111111112\") == 1548008755920\n assert candidate(s = \"212221222122212221222122212221222122212221222122212221222122\") == 2504730781961\n assert candidate(s = \"11122211122211122211122211122211122211122211122211122211122211\") == 6557470319842\n assert candidate(s = \"01010101010101010101010101010101010101010101010101010101010\") == 0\n assert candidate(s = \"111222333444555666777888999000111222333444555666777888999000\") == 0\n assert candidate(s = \"1234567890123456789012345678901234567890123456789012345670\") == 0\n assert candidate(s = \"0000000000000000000000000000000000000000000000000000000000\") == 0\n assert candidate(s = \"1234056789\") == 0\n assert candidate(s = \"19019019019019019019019019019019019019019019019019\") == 0\n assert candidate(s = \"12223242526272829303132333435363738394041424344454647484950\") == 0\n assert candidate(s = \"11111111111111111111111111111111111111\") == 63245986\n assert candidate(s = \"30313233343536373839404142434445464748495051525354555657585960\") == 0\n assert candidate(s = \"21212121212121212121212121212121212121212121212121212121212\") == 1548008755920\n assert candidate(s = \"270029\") == 0\n assert candidate(s = \"11001100110011001100\") == 0\n assert candidate(s = \"12345678987654321234567898765432123456789\") == 75\n assert candidate(s = \"1122334455667788991011121314151617181920212223242526\") == 692224\n assert candidate(s = \"10101010101010101010101010101010101010101010101010101010101\") == 1\n assert candidate(s = \"273747576787980\") == 0\n assert candidate(s = \"129129129\") == 8\n assert candidate(s = \"112211221122112211221122112211221122112211221122112211221122112\") == 10610209857723\n assert candidate(s = \"301010\") == 0\n assert candidate(s = \"121212121212121212121212121212121212121212121212121212121212\") == 2504730781961\n assert candidate(s = \"1101111011111011111011111011111011111011111011111\") == 375000\n assert candidate(s = \"123456789012345678901234567890123456789012345678901234567890\") == 0\n assert candidate(s = \"1101010101010101010101010101010101010101010101010101010101\") == 1\n assert candidate(s = \"111000111000111000111000111000111000111000111000111000\") == 0\n assert candidate(s = \"1225232125\") == 50\n assert candidate(s = \"212223242526212223242526212223242526212223242526\") == 116985856\n assert candidate(s = \"262626262626262626262626262626262626262626262626262626262\") == 268435456\n assert candidate(s = \"0123456789\") == 0\n assert candidate(s = \"11223344556677889911223344556677889911223344556677889911\") == 1024\n assert candidate(s = \"11223344556677889910111213141516171819202122232425262728293031\") == 0\n assert candidate(s = \"26262626262626262626262626262626262626\") == 524288\n assert candidate(s = \"101010101010101010101010101010101010101010101010101010101010\") == 1\n assert candidate(s = \"111111111111111111111111111111111111111111111111111111111111\") == 2504730781961\n assert candidate(s = \"12222222222222222222222222222222222222222222222222222222222\") == 1548008755920\n assert candidate(s = \"22322322322322322322322322322322322322322322322322322322322\") == 2324522934\n assert candidate(s = \"12121212121212121212121212121212121212\") == 63245986\n assert candidate(s = \"1222222222222222222222222222222222222222222222222222222222\") == 956722026041\n assert candidate(s = \"25242322212019181716151413121110987654321\") == 51200\n assert candidate(s = \"101010101010101010101010101010101010101010101010101010101010100\") == 0\n assert candidate(s = \"101112131415161718192021222324252620212223242526\") == 8998912\n assert candidate(s = \"11111111111111111111111111111111111111111111111111111111110\") == 591286729879\n assert candidate(s = \"11121314151617181920212223242526\") == 86528\n assert candidate(s = \"22222222222222222222222222222222222222\") == 63245986\n assert candidate(s = \"1230011010101010101010101010101010101010101010101010101010\") == 0\n assert candidate(s = \"2727272727272727272727272727272727272727272727272727272727\") == 1\n assert candidate(s = \"1230450678901234567890\") == 0\n assert candidate(s = \"11223344556677889911223344556677889911223344556677889911222\") == 4096\n assert candidate(s = \"33333333333333333333333333333333333333333333333333333333333\") == 1\n assert candidate(s = \"21012101210121012101210121012101210121012101210121\") == 6144\n assert candidate(s = \"11111111111111111111111111111111111111111111111111111111111101\") == 1548008755920\n assert candidate(s = \"212121212121212121212121212121212121212121212121212121212121\") == 2504730781961\n assert candidate(s = \"12121212121212121212121212121212121212121212121212121212121212\") == 6557470319842\n assert candidate(s = \"112358132134558914423337761098765534211\") == 360\n assert candidate(s = \"262626262626262626262626262626262626262626262626262626262626\") == 1073741824\n assert candidate(s = \"102030405060708090\") == 0\n assert candidate(s = \"9999999999999999999999999999999999999999999999999\") == 1\n assert candidate(s = \"25252525252525252525252525252525252525252525252525\") == 33554432\n assert candidate(s = \"222333444555666777888999\") == 5\n assert candidate(s = \"272727272727272727272727272727272727272727272727272727272\") == 1\n assert candidate(s = \"101010\") == 1\n assert candidate(s = \"102233445566778899112233445566778899112233445566\") == 192\n assert candidate(s = \"110110110\") == 1\n assert candidate(s = \"110110110110110110110110110110110110110110110110110110110110\") == 1\n assert candidate(s = \"21211212211212122112121221121212211212122112121221121212211212\") == 6557470319842\n assert candidate(s = \"19191919191919191919191919191919191919191919191919191919191919\") == 2147483648\n assert candidate(s = \"26262626262626262626262626262626262626262626262626\") == 33554432\n assert candidate(s = \"112233445566778899112233445566778899112233445566\") == 512\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().numDecodings", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numDecodings = function(s) {", "container": null, "callable": "numDecodings", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 92, "task_id": "reverse-linked-list-ii", "difficulty": "Medium", "problem_description": "Given the head of a singly linked list and two integers left and right where left <= right, reverse the nodes of the list from position left to position right, and return the reversed list.\n \nExample 1:\n\n\nInput: head = [1,2,3,4,5], left = 2, right = 4\nOutput: [1,4,3,2,5]\n\nExample 2:\n\nInput: head = [5], left = 1, right = 1\nOutput: [5]\n\n \nConstraints:\n\nThe number of nodes in the list is n.\n1 <= n <= 500\n-500 <= Node.val <= 500\n1 <= left <= right <= n\n\n \nFollow up: Could you do it in one pass?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 3,right = 4), list_node([1, 2, 4, 3, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 2,right = 4), list_node([1, 4, 3, 2, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 3,right = 8), list_node([1, 2, 8, 7, 6, 5, 4, 3, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 2,right = 2), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50]),left = 1,right = 3), list_node([30, 20, 10, 40, 50]))\n assert is_same_list(candidate(head = list_node([1, 2, 3]),left = 1,right = 3), list_node([3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),left = 3,right = 7), list_node([1, 2, 7, 6, 5, 4, 3, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 2,right = 3), list_node([1, 3, 2, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 5,right = 5), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9]),left = 2,right = 3), list_node([1, 5, 3, 7, 9]))\n assert is_same_list(candidate(head = list_node([5]),left = 1,right = 1), list_node([5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 1,right = 1), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7]),left = 3,right = 5), list_node([1, 2, 5, 4, 3, 6, 7]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9]),left = 2,right = 4), list_node([1, 7, 5, 3, 9]))\n assert is_same_list(candidate(head = list_node([-1, 0, 1, 2, 3]),left = 2,right = 5), list_node([-1, 3, 2, 1, 0]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50]),left = 1,right = 5), list_node([50, 40, 30, 20, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),left = 1,right = 5), list_node([5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),left = 3,right = 8), list_node([-1, -2, -8, -7, -6, -5, -4, -3, -9, -10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),left = 7,right = 7), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),left = 4,right = 7), list_node([-1, -2, -3, -7, -6, -5, -4, -8, -9, -10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 8,right = 8), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),left = 5,right = 16), list_node([1, 2, 3, 4, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([500, -500, 500, -500, 500]),left = 2,right = 4), list_node([500, -500, 500, -500, 500]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),left = 6,right = 15), list_node([1, 2, 3, 4, 5, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),left = 8,right = 10), list_node([1, 2, 3, 4, 5, 6, 7, 10, 9, 8, 11, 12]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]),left = 5,right = 15), list_node([10, 20, 30, 40, 150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 5,right = 12), list_node([1, 2, 3, 4, 12, 11, 10, 9, 8, 7, 6, 5, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),left = 1,right = 12), list_node([12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 4,right = 8), list_node([1, 2, 3, 8, 7, 6, 5, 4, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 6,right = 11), list_node([1, 2, 3, 4, 5, 11, 10, 9, 8, 7, 6, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([500, 400, 300, 200, 100]),left = 2,right = 4), list_node([500, 200, 300, 400, 100]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 7,right = 7), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 13,right = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 14, 13]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 1,right = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 5,right = 5), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 11,right = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 14, 13, 12, 11]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),left = 2,right = 5), list_node([1, 5, 4, 3, 2, 6, 7, 8, 9, 10, 11, 12]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 3,right = 3), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 4,right = 10), list_node([1, 2, 3, 10, 9, 8, 7, 6, 5, 4, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),left = 5,right = 11), list_node([1, 2, 3, 4, 11, 10, 9, 8, 7, 6, 5, 12]))\n assert is_same_list(candidate(head = list_node([100, -200, 300, -400, 500]),left = 2,right = 4), list_node([100, -400, 300, -200, 500]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]),left = 3,right = 9), list_node([5, 4, -3, -2, -1, 0, 1, 2, 3, -4, -5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 6,right = 6), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 2,right = 9), list_node([1, 9, 8, 7, 6, 5, 4, 3, 2, 10]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15]),left = 4,right = 10), list_node([-1, -2, -3, -10, -9, -8, -7, -6, -5, -4, -11, -12, -13, -14, -15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 6,right = 10), list_node([1, 2, 3, 4, 5, 10, 9, 8, 7, 6]))\n assert is_same_list(candidate(head = list_node([-10, -20, -30, -40, -50]),left = 1,right = 3), list_node([-30, -20, -10, -40, -50]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1]),left = 2,right = 5), list_node([5, 1, 2, 3, 4]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),left = 2,right = 9), list_node([10, 2, 3, 4, 5, 6, 7, 8, 9, 1]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),left = 4,right = 7), list_node([10, 9, 8, 4, 5, 6, 7, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),left = 1,right = 2), list_node([3, 1, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800]),left = 2,right = 7), list_node([100, 700, 600, 500, 400, 300, 200, 800]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 5,right = 9), list_node([1, 2, 3, 4, 9, 8, 7, 6, 5, 10]))\n assert is_same_list(candidate(head = list_node([-100, -200, -300, -400, -500]),left = 1,right = 4), list_node([-400, -300, -200, -100, -500]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),left = 5,right = 15), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 1,right = 7), list_node([7, 6, 5, 4, 3, 2, 1, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),left = 4,right = 8), list_node([-1, -2, -3, -8, -7, -6, -5, -4, -9, -10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90]),left = 3,right = 7), list_node([10, 20, 70, 60, 50, 40, 30, 80, 90]))\n assert is_same_list(candidate(head = list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]),left = 3,right = 7), list_node([-10, -9, -4, -5, -6, -7, -8, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 9,right = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 10, 9]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]),left = 5,right = 5), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]))\n assert is_same_list(candidate(head = list_node([7, 6, 5, 4, 3, 2, 1]),left = 1,right = 1), list_node([7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 1,right = 1), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 1,right = 15), list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),left = 10,right = 20), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 1,right = 5), list_node([5, 4, 3, 2, 1, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 4,right = 12), list_node([1, 2, 3, 12, 11, 10, 9, 8, 7, 6, 5, 4, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),left = 3,right = 8), list_node([10, 20, 80, 70, 60, 50, 40, 30, 90, 100]))\n assert is_same_list(candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),left = 1,right = 5), list_node([4, 3, 2, 1, 0, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),left = 3,right = 7), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-10, -20, -30, -40, -50, -60, -70]),left = 2,right = 5), list_node([-10, -50, -40, -30, -20, -60, -70]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 1,right = 2), list_node([2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),left = 5,right = 9), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 7,right = 11), list_node([1, 2, 3, 4, 5, 6, 11, 10, 9, 8, 7, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]),left = 3,right = 7), list_node([-1, -2, -7, -6, -5, -4, -3, -8, -9, -10]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]),left = 1,right = 5), list_node([500, 400, 300, 200, 100, 600, 700, 800, 900, 1000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 2,right = 14), list_node([1, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 15]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600]),left = 1,right = 5), list_node([500, 400, 300, 200, 100, 600]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 5,right = 8), list_node([1, 2, 3, 4, 8, 7, 6, 5, 9, 10]))\n assert is_same_list(candidate(head = list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),left = 2,right = 14), list_node([15, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 10,right = 14), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 14, 13, 12, 11, 10, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 6,right = 12), list_node([1, 2, 3, 4, 5, 12, 11, 10, 9, 8, 7, 6, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 1,right = 10), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),left = 10,right = 30), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),left = 3,right = 8), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([-10, -20, -30, -40, -50]),left = 3,right = 5), list_node([-10, -20, -50, -40, -30]))\n assert is_same_list(candidate(head = list_node([50, 40, 30, 20, 10]),left = 2,right = 4), list_node([50, 20, 30, 40, 10]))\n assert is_same_list(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40]),left = 3,right = 5), list_node([5, 10, 25, 20, 15, 30, 35, 40]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]),left = 2,right = 8), list_node([9, 2, 3, 4, 5, 6, 7, 8, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),left = 2,right = 9), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([500, -500, 250, -250, 0, 1, 2, 3, 4, 5]),left = 2,right = 6), list_node([500, 1, 0, -250, 250, -500, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 5,right = 9), list_node([1, 2, 3, 4, 9, 8, 7, 6, 5, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),left = 9,right = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 15, 14, 13, 12, 11, 10, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 4,right = 7), list_node([1, 2, 3, 7, 6, 5, 4, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),left = 1,right = 10), list_node([100, 90, 80, 70, 60, 50, 40, 30, 20, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]),left = 4,right = 10), list_node([1, 2, 3, 10, 9, 8, 7, 6, 5, 4, 11, 12]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70]),left = 3,right = 6), list_node([10, 20, 60, 50, 40, 30, 70]))\n assert is_same_list(candidate(head = list_node([-500, 500, -500, 500, -500]),left = 1,right = 5), list_node([-500, 500, -500, 500, -500]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),left = 4,right = 9), list_node([1, 2, 3, 9, 8, 7, 6, 5, 4, 10]))\n"}, "metadata": {"canonical_parameter_names": ["head", "left", "right"], "leetcode_dataset_entry_point": "Solution().reverseBetween", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverseBetween = function(head, left, right) {", "container": null, "callable": "reverseBetween", "parameters": [{"name": "head", "type": "ListNode"}, {"name": "left", "type": "number"}, {"name": "right", "type": "number"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 93, "task_id": "restore-ip-addresses", "difficulty": "Medium", "problem_description": "A valid IP address consists of exactly four integers separated by single dots. Each integer is between 0 and 255 (inclusive) and cannot have leading zeros.\n\nFor example, \"0.1.2.201\" and \"192.168.1.1\" are valid IP addresses, but \"0.011.255.245\", \"192.168.1.312\" and \"192.168@1.1\" are invalid IP addresses.\n\nGiven a string s containing only digits, return all possible valid IP addresses that can be formed by inserting dots into s. You are not allowed to reorder or remove any digits in s. You may return the valid IP addresses in any order.\n \nExample 1:\n\nInput: s = \"25525511135\"\nOutput: [\"255.255.11.135\",\"255.255.111.35\"]\n\nExample 2:\n\nInput: s = \"0000\"\nOutput: [\"0.0.0.0\"]\n\nExample 3:\n\nInput: s = \"101023\"\nOutput: [\"1.0.10.23\",\"1.0.102.3\",\"10.1.0.23\",\"10.10.2.3\",\"101.0.2.3\"]\n\n \nConstraints:\n\n1 <= s.length <= 20\ns consists of digits only.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"101023\") == ['1.0.10.23', '1.0.102.3', '10.1.0.23', '10.10.2.3', '101.0.2.3']\n assert candidate(s = \"1111\") == ['1.1.1.1']\n assert candidate(s = \"9876543210\") == []\n assert candidate(s = \"00000000000000000000\") == []\n assert candidate(s = \"222333444\") == ['22.233.34.44', '222.33.34.44']\n assert candidate(s = \"0000\") == ['0.0.0.0']\n assert candidate(s = \"25525511135\") == ['255.255.11.135', '255.255.111.35']\n assert candidate(s = \"256256256256\") == []\n assert candidate(s = \"010010\") == ['0.10.0.10', '0.100.1.0']\n assert candidate(s = \"99999999999999999999\") == []\n assert candidate(s = \"11111111111111111111\") == []\n assert candidate(s = \"19216811\") == ['1.92.168.11', '19.2.168.11', '19.21.68.11', '19.216.8.11', '19.216.81.1', '192.1.68.11', '192.16.8.11', '192.16.81.1', '192.168.1.1']\n assert candidate(s = \"255025502550\") == []\n assert candidate(s = \"22222222\") == ['2.2.222.222', '2.22.22.222', '2.22.222.22', '2.222.2.222', '2.222.22.22', '2.222.222.2', '22.2.22.222', '22.2.222.22', '22.22.2.222', '22.22.22.22', '22.22.222.2', '22.222.2.22', '22.222.22.2', '222.2.2.222', '222.2.22.22', '222.2.222.2', '222.22.2.22', '222.22.22.2', '222.222.2.2']\n assert candidate(s = \"1\") == []\n assert candidate(s = \"123123123123\") == ['123.123.123.123']\n assert candidate(s = \"19216801\") == ['19.216.80.1', '192.16.80.1', '192.168.0.1']\n assert candidate(s = \"22222222222222222222\") == []\n assert candidate(s = \"123456789\") == ['123.45.67.89']\n assert candidate(s = \"100100100\") == ['10.0.100.100', '100.10.0.100', '100.100.10.0']\n assert candidate(s = \"001001001001001\") == []\n assert candidate(s = \"255255255255255255255255255255255255255255255255255255\") == []\n assert candidate(s = \"0100100\") == ['0.10.0.100', '0.100.10.0']\n assert candidate(s = \"0001000100010001\") == []\n assert candidate(s = \"1100110011001100\") == []\n assert candidate(s = \"19216811001\") == []\n assert candidate(s = \"2552552551113525525511135\") == []\n assert candidate(s = \"999999999\") == []\n assert candidate(s = \"1111111\") == ['1.1.11.111', '1.1.111.11', '1.11.1.111', '1.11.11.11', '1.11.111.1', '1.111.1.11', '1.111.11.1', '11.1.1.111', '11.1.11.11', '11.1.111.1', '11.11.1.11', '11.11.11.1', '11.111.1.1', '111.1.1.11', '111.1.11.1', '111.11.1.1']\n assert candidate(s = \"2552552550\") == ['255.255.25.50', '255.255.255.0']\n assert candidate(s = \"255000255000255\") == []\n assert candidate(s = \"255255255000\") == []\n assert candidate(s = \"255255255255255255255255255255255\") == []\n assert candidate(s = \"0000000000\") == []\n assert candidate(s = \"0000000000000000\") == []\n assert candidate(s = \"222222222222222222\") == []\n assert candidate(s = \"10000000000000000000\") == []\n assert candidate(s = \"1230456789\") == []\n assert candidate(s = \"01001001001001\") == []\n assert candidate(s = \"111111111111111111110\") == []\n assert candidate(s = \"255255255255255255255255255255255255255255255255255255255255255255\") == []\n assert candidate(s = \"000000000000000000000\") == []\n assert candidate(s = \"1111222233334444\") == []\n assert candidate(s = \"000256\") == []\n assert candidate(s = \"255255255100\") == ['255.255.255.100']\n assert candidate(s = \"123456789012\") == []\n assert candidate(s = \"01020304\") == []\n assert candidate(s = \"3333333333\") == []\n assert candidate(s = \"100100\") == ['1.0.0.100', '10.0.10.0', '100.1.0.0']\n assert candidate(s = \"012345678910\") == []\n assert candidate(s = \"12345678901234567\") == []\n assert candidate(s = \"02552552550\") == []\n assert candidate(s = \"111111111111\") == ['111.111.111.111']\n assert candidate(s = \"192168111111001\") == []\n assert candidate(s = \"00000001\") == []\n assert candidate(s = \"1230123012301230\") == []\n assert candidate(s = \"100100100100100\") == []\n assert candidate(s = \"999999999999999999\") == []\n assert candidate(s = \"000255255000\") == []\n assert candidate(s = \"0000100100100\") == []\n assert candidate(s = \"2550255255255255\") == []\n assert candidate(s = \"1001001001\") == ['100.100.100.1']\n assert candidate(s = \"1111111111111111\") == []\n assert candidate(s = \"1234567890123\") == []\n assert candidate(s = \"192168011001001\") == []\n assert candidate(s = \"12345678901234567890\") == []\n assert candidate(s = \"1921681111001\") == []\n assert candidate(s = \"222222222222\") == ['222.222.222.222']\n assert candidate(s = \"255255255255255255255\") == []\n assert candidate(s = \"255255255255255255255255255255255255255255255255255255255255\") == []\n assert candidate(s = \"000000000000\") == []\n assert candidate(s = \"1921680101\") == ['19.216.80.101', '192.16.80.101', '192.168.0.101']\n assert candidate(s = \"99999999\") == ['99.99.99.99']\n assert candidate(s = \"00000\") == []\n assert candidate(s = \"255255255255255255255255255255255255255255255\") == []\n assert candidate(s = \"102030405\") == []\n assert candidate(s = \"255255255255255255255255\") == []\n assert candidate(s = \"1001001001001001\") == []\n assert candidate(s = \"0102030405\") == []\n assert candidate(s = \"255255255255255255255255255255255255255255255255\") == []\n assert candidate(s = \"111222333\") == ['1.112.223.33', '11.12.223.33', '11.122.23.33', '11.122.233.3', '111.2.223.33', '111.22.23.33', '111.22.233.3', '111.222.3.33', '111.222.33.3']\n assert candidate(s = \"0000111122223333\") == []\n assert candidate(s = \"255255255255\") == ['255.255.255.255']\n assert candidate(s = \"1921681001\") == ['192.168.100.1']\n assert candidate(s = \"192168111001\") == []\n assert candidate(s = \"1000000000000000\") == []\n assert candidate(s = \"255025502550255\") == []\n assert candidate(s = \"19216811111001\") == []\n assert candidate(s = \"19216811111\") == ['192.168.11.111', '192.168.111.11']\n assert candidate(s = \"1234567890123456\") == []\n assert candidate(s = \"255000255000\") == []\n assert candidate(s = \"991871283712983712987123789\") == []\n assert candidate(s = \"0123456789\") == []\n assert candidate(s = \"1234567890123456789\") == []\n assert candidate(s = \"00000000\") == []\n assert candidate(s = \"11111\") == ['1.1.1.11', '1.1.11.1', '1.11.1.1', '11.1.1.1']\n assert candidate(s = \"255000000\") == []\n assert candidate(s = \"192168001001\") == []\n assert candidate(s = \"255255111350\") == []\n assert candidate(s = \"2552551113525525511135\") == []\n assert candidate(s = \"00010001000100010001\") == []\n assert candidate(s = \"123456789012345678\") == []\n assert candidate(s = \"0000255255255\") == []\n assert candidate(s = \"9999999999\") == []\n assert candidate(s = \"255255255255255\") == []\n assert candidate(s = \"01001001001001001001\") == []\n assert candidate(s = \"255255255255255255255255255255255255255255255255255255255255255\") == []\n assert candidate(s = \"255000255000255000\") == []\n assert candidate(s = \"2222222222\") == ['2.222.222.222', '22.22.222.222', '22.222.22.222', '22.222.222.22', '222.2.222.222', '222.22.22.222', '222.22.222.22', '222.222.2.222', '222.222.22.22', '222.222.222.2']\n assert candidate(s = \"2552551000\") == ['255.255.100.0']\n assert candidate(s = \"2552550000\") == []\n assert candidate(s = \"25502550255025502550255\") == []\n assert candidate(s = \"2550255025502550\") == []\n assert candidate(s = \"123123123123123123\") == []\n assert candidate(s = \"192168001\") == []\n assert candidate(s = \"12345678901234\") == []\n assert candidate(s = \"010010010010\") == []\n assert candidate(s = \"123456789012345\") == []\n assert candidate(s = \"1234567890\") == []\n assert candidate(s = \"0255025502550255\") == []\n assert candidate(s = \"9216811135\") == ['92.168.11.135', '92.168.111.35']\n assert candidate(s = \"001001001\") == []\n assert candidate(s = \"00112233445566778899\") == []\n assert candidate(s = \"11101110111011101110\") == []\n assert candidate(s = \"2222222222222222\") == []\n assert candidate(s = \"255255255255255255255255255255\") == []\n assert candidate(s = \"100100100100\") == ['100.100.100.100']\n assert candidate(s = \"19216801100101\") == []\n assert candidate(s = \"123456\") == ['1.2.34.56', '1.23.4.56', '1.23.45.6', '1.234.5.6', '12.3.4.56', '12.3.45.6', '12.34.5.6', '123.4.5.6']\n assert candidate(s = \"11111111\") == ['1.1.111.111', '1.11.11.111', '1.11.111.11', '1.111.1.111', '1.111.11.11', '1.111.111.1', '11.1.11.111', '11.1.111.11', '11.11.1.111', '11.11.11.11', '11.11.111.1', '11.111.1.11', '11.111.11.1', '111.1.1.111', '111.1.11.11', '111.1.111.1', '111.11.1.11', '111.11.11.1', '111.111.1.1']\n assert candidate(s = \"19216801001\") == []\n assert candidate(s = \"999999999999\") == []\n assert candidate(s = \"22222222222222222220\") == []\n assert candidate(s = \"10000000000000000001\") == []\n assert candidate(s = \"192168100\") == ['1.92.168.100', '19.2.168.100', '19.21.68.100', '19.216.8.100', '192.1.68.100', '192.16.8.100', '192.168.10.0']\n assert candidate(s = \"200200200200\") == ['200.200.200.200']\n assert candidate(s = \"25525511135111\") == []\n assert candidate(s = \"110110110110110\") == []\n assert candidate(s = \"255255255255255255255255255255255255255\") == []\n assert candidate(s = \"333333333333\") == []\n assert candidate(s = \"01001001001001001001001001001\") == []\n assert candidate(s = \"025525511135\") == []\n assert candidate(s = \"001001001001001001\") == []\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().restoreIpAddresses", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var restoreIpAddresses = function(s) {", "container": null, "callable": "restoreIpAddresses", "parameters": [{"name": "s", "type": "string"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 94, "task_id": "binary-tree-inorder-traversal", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, return the inorder traversal of its nodes' values.\n \nExample 1:\n\nInput: root = [1,null,2,3]\nOutput: [1,3,2]\nExplanation:\n\n\nExample 2:\n\nInput: root = [1,2,3,4,5,null,8,null,null,6,7,9]\nOutput: [4,2,6,5,7,1,3,9,8]\nExplanation:\n\n\nExample 3:\n\nInput: root = []\nOutput: []\n\nExample 4:\n\nInput: root = [1]\nOutput: [1]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 100].\n-100 <= Node.val <= 100\n\n \nFollow up: Recursive solution is trivial, could you do it iteratively?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 8, None, None, 6, 7, 9])) == [4, 2, 6, 5, 7, 1, 3, 9, 8]\n assert candidate(root = tree_node([1])) == [1]\n assert candidate(root = tree_node([1, None, 2, 3])) == [1, 3, 2]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, 18, 28, 32, None, 45])) == [5, 10, 12, 15, 20, 18, 25, 28, 30, 32, 35, 40, 45]\n assert candidate(root = tree_node([3, 1, 4, None, 2, None, None])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == [5, 10, 6, 15, 20]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == [3, 5, 7, 10, 15, 18]\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1])) == [1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, 4, None, None, 5])) == [1, 2]\n assert candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13])) == [1, 3, 4, 6, 7, 8, 10, 13, 14]\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])) == [0, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, 9])) == [1, 2, 3, 4, 5, 6, 9, 7, 8]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 18, 23, 27, 32, 37, 1, 3, 6, 8, 11, 13, 16, 19, 22, 24, 26, 28, 31, 33, 36, 38])) == [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38]\n assert candidate(root = tree_node([1, 2, None, None, 3, None, 4, None, 5])) == [2, 3, 4, 5, 1]\n assert candidate(root = tree_node([50, 25, 75, 10, 35, 60, 90, 5, 20, 30, 40, 55, 65, 85, 100])) == [5, 10, 20, 25, 30, 35, 40, 50, 55, 60, 65, 75, 85, 90, 100]\n assert candidate(root = tree_node([8, 5, 12, 4, 6, 10, 14, 2, None, None, 7, 9, 11, 13, 15])) == [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 15, 25, None, None, None, None, None, 90])) == [15, 20, 25, 30, 40, 50, 60, 70, 80, 90]\n assert candidate(root = tree_node([5, 1, 8, None, 4, None, None, None, 3, None, 6])) == [1, 4, 3, 6, 5, 8]\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, None, 25, 35, 47, None, None, 11, 14, 23, 37, None, None, None, None, 48, None, 49, 51])) == [49, 11, 51, 5, 14, 10, 23, 12, 37, 15, 20, 25, 30, 35, 40, 48, 47, 45, 50]\n assert candidate(root = tree_node([9, 6, 15, 5, 8, 12, 20, 2, 7, None, 11, 14, 18, 1, None, None, 4, None, None, None, None, 10, 13, None, None, None, None, None, None, None, 16, 17, 19, None, None, None, None, None, None, None, 21, None, None, None, None, None, None, 22])) == [2, 4, 5, 7, 6, 8, 11, 9, 10, 16, 14, 17, 13, 19, 12, 18, 15, 1, 20]\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, None, 9, None])) == [1, 2, 3, 4, 5, 6, 7, 9, 8]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, None, 17, 22, 28, 32, 38])) == [2, 5, 7, 10, 15, 17, 20, 22, 25, 28, 30, 32, 35, 38]\n assert candidate(root = tree_node([3, 1, 2])) == [1, 3, 2]\n assert candidate(root = tree_node([8, 5, 10, 3, 6, None, 12, None, None, None, None, 11, 14])) == [3, 5, 6, 8, 10, 11, 12, 14]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20])) == [3, 7, 9, 15, 20]\n assert candidate(root = tree_node([100, -50, None, -100, None, -75, None, -150, None, -200, None, -175, None, -225])) == [-225, -175, -200, -150, -75, -100, -50, 100]\n assert candidate(root = tree_node([5, 4, 6, None, 3, None, None, None, 2])) == [4, 3, 2, 5, 6]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, 0, 2, 6, None, None, 10])) == [0, 1, 2, 3, 6, 4, 5, 7, 10, 8, 9]\n assert candidate(root = tree_node([2, 1, 3, 4, 5])) == [4, 1, 5, 2, 3]\n assert candidate(root = tree_node([7, 3, 15, None, None, None, 20])) == [3, 7, 15, 20]\n assert candidate(root = tree_node([2, 1, None, 4, 3])) == [4, 1, 3, 2]\n assert candidate(root = tree_node([2, 1, 3, 4, 5, None, None, None, None, None, 6, 7])) == [4, 1, 5, 7, 6, 2, 3]\n assert candidate(root = tree_node([7, 3, 9, None, 4, 8, 10])) == [3, 4, 7, 8, 9, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [16, 8, 17, 4, 18, 9, 19, 2, 20, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [8, 4, 9, 2, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, 7, None, 17, 22, 27, 32, 40])) == [1, 5, 7, 10, 15, 17, 20, 22, 25, 27, 30, 32, 35, 40]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4, None, None, None, 5])) == [1, 2]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, None, None, 17])) == [3, 7, 9, 15, 20]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [4, 2, 5, 1, 6, 3, 7]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, None, 6])) == [1, 3, 5, 7, 6, 10, 15, 18]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == [16, 8, 17, 4, 18, 9, 19, 2, 20, 10, 21, 5, 22, 11, 23, 1, 24, 12, 25, 6, 13, 3, 14, 7, 15]\n assert candidate(root = tree_node([50, 25, 75, 10, 30, 60, 80, 5, 15, 27, 35, 55, 65, 77, 85])) == [5, 10, 15, 25, 27, 30, 35, 50, 55, 60, 65, 75, 77, 80, 85]\n assert candidate(root = tree_node([-10, -20, -30, -40, None, -50, -60])) == [-40, -20, -10, -50, -30, -60]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, 8, 17, 22])) == [3, 7, 9, 8, 15, 17, 20, 22]\n assert candidate(root = tree_node([2, 1, 3, None, 4, None, None, None, 5])) == [1, 4, 5, 2, 3]\n assert candidate(root = tree_node([7, 3, 15, None, None, None, 9])) == [3, 7, 15, 9]\n assert candidate(root = tree_node([25, 15, 30, 10, 20, 27, 35, 5, 12, 18, 23, 26, 29, 32, 40])) == [5, 10, 12, 15, 18, 20, 23, 25, 26, 27, 29, 30, 32, 35, 40]\n assert candidate(root = tree_node([8, 3, 10, None, 1, 6, None, 4, 7, 11, 14])) == [3, 4, 1, 7, 8, 11, 6, 14, 10]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, None, 10, 0, 2, None, None, 9, 11])) == [0, 1, 2, 3, 4, 5, 8, 9, 10, 11]\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 23, 27, 32, 37, 42, 47, 1, 7, 11, 13, 17, 22, 24, 26, 28, 31, 33, 36, 38, 41, 43, 46, 48])) == [46, 47, 48, 5, 1, 10, 7, 12, 11, 15, 13, 18, 17, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9])) == [1, 3, 4, 5, 7, 8, 9]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [1, 5, 3, 4, 6]\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 90, 110, 140, 160, 190])) == [10, 25, 35, 50, 60, 75, 90, 100, 110, 125, 140, 150, 160, 175, 190]\n assert candidate(root = tree_node([10, 5, 15, None, None, 12, 20, 11, 14, 13, 18, 17, 19, 16])) == [5, 10, 17, 11, 19, 12, 16, 14, 15, 13, 20, 18]\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 42, 48, 55, 1, 7, 11, 13, 17, 23, 27, 33, 37, 41, 43, 47, 51, 53, 57])) == [1, 5, 7, 10, 11, 12, 13, 15, 17, 18, 23, 20, 27, 25, 33, 30, 37, 35, 41, 40, 43, 42, 47, 45, 51, 48, 53, 50, 57, 55]\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3])) == [1, 2]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [7, 6, 5, 4, 3, 2, 1]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37])) == [3, 5, 7, 10, 13, 15, 17, 20, 23, 25, 27, 30, 33, 35, 37]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6])) == [1, 3, 5, 6, 7, 10, 13, 15, 18]\n assert candidate(root = tree_node([3, 1, 4, None, 2])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7, 0, None, None, None, None, None, None, 8])) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(root = tree_node([1, 3, 2, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99])) == [61, 29, 63, 13, 65, 31, 67, 5, 69, 33, 71, 15, 73, 35, 75, 3, 77, 37, 79, 17, 81, 39, 83, 7, 85, 41, 87, 19, 89, 43, 91, 1, 93, 45, 95, 21, 97, 47, 99, 9, 49, 23, 51, 2, 53, 25, 55, 11, 57, 27, 59]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20, None, None, 11, 18, 16, 25])) == [5, 10, 6, 15, 16, 11, 25, 20, 18]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([8, 5, 15, 3, 7, 12, 18, 1, 4, 6, 9, 11, 13, 17, 19])) == [1, 3, 4, 5, 6, 7, 9, 8, 11, 12, 13, 15, 17, 18, 19]\n assert candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75, 2, 7, 12, 18, 23, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 1, 3, 6, 8, 11, 13, 16, 19, 22, 24, 26, 28, 31, 33, 36, 38, 41, 43, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 71, 73, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])) == [79, 1, 80, 2, 81, 3, 82, 5, 83, 6, 84, 7, 85, 8, 86, 10, 87, 11, 88, 12, 89, 13, 90, 15, 91, 16, 92, 18, 93, 19, 94, 20, 95, 22, 96, 23, 97, 24, 98, 25, 99, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 78]\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7])) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(root = tree_node([10, None, 15, 12, 20, None, None, 11, 14, 13, 18, None, None, None, None, None, 19, 17])) == [10, 12, 15, 13, 11, 18, 17, 19, 20, 14]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4, None, None, None, 5, None, None, None, 6, None, None, None, 7])) == [1, 2]\n assert candidate(root = tree_node([8, 5, 12, 4, 6, 9, 13, 2, None, None, 7, 8, 11, 10])) == [2, 4, 5, 6, 7, 8, 8, 9, 11, 12, 10, 13]\n assert candidate(root = tree_node([3, 1, 4, None, 2, None, None, None, None, None, 5])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([100, -100, None, -99, None, -98, None, -97, None, -96, None, -95, None, -94, None, -93, None, -92, None, -91, None, -90, None, -89, None, -88, None, -87, None, -86, None, -85, None, -84, None, -83, None, -82, None, -81, None, -80, None, -79, None, -78, None, -77, None, -76, None, -75, None, -74, None, -73, None, -72, None, -71, None, -70, None, -69, None, -68, None, -67, None, -66, None, -65, None, -64, None, -63, None, -62, None, -61, None, -60, None, -59, None, -58, None, -57, None, -56, None, -55, None, -54, None, -53, None, -52, None, -51, None, -50, None, -49, None, -48, None, -47, None, -46, None, -45, None, -44, None, -43, None, -42, None, -41, None, -40, None, -39, None, -38, None, -37, None, -36, None, -35, None, -34, None, -33, None, -32, None, -31, None, -30, None, -29, None, -28, None, -27, None, -26, None, -25, None, -24, None, -23, None, -22, None, -21, None, -20, None, -19, None, -18, None, -17, None, -16, None, -15, None, -14, None, -13, None, -12, None, -11, None, -10, None, -9, None, -8, None, -7, None, -6, None, -5, None, -4, None, -3, None, -2, None, -1])) == [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56, -57, -58, -59, -60, -61, -62, -63, -64, -65, -66, -67, -68, -69, -70, -71, -72, -73, -74, -75, -76, -77, -78, -79, -80, -81, -82, -83, -84, -85, -86, -87, -88, -89, -90, -91, -92, -93, -94, -95, -96, -97, -98, -99, -100, 100]\n assert candidate(root = tree_node([4, 2, None, 1, 3])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, 6, 9, 11, 13, 14, 17, 22, 28, 5, 7, None, None, None, None, None, None, 18, 21, 23, 24, 26, 27, None, None, None, None, None, None, 19])) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 19, 18, 14, 21, 16, 23, 17, 24, 20, 26, 22, 27, 25, 28]\n assert candidate(root = tree_node([3, 1, 5, 0, 2, 4, 6])) == [0, 1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, 22, 28, 38, None, None, None, 14, None, 18, None, 32, None, None, None, None, 29, None, 33])) == [5, 29, 14, 10, 12, 33, 18, 15, 20, 22, 32, 25, 28, 30, 38, 35, 40]\n assert candidate(root = tree_node([8, 3, 10, 1, 5, None, 14, None, None, 4, 7, 12, 15, 11, 13])) == [1, 3, 11, 4, 13, 5, 7, 8, 10, 12, 14, 15]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().inorderTraversal", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var inorderTraversal = function(root) {", "container": null, "callable": "inorderTraversal", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 96, "task_id": "unique-binary-search-trees", "difficulty": "Medium", "problem_description": "Given an integer n, return the number of structurally unique BST's (binary search trees) which has exactly n nodes of unique values from 1 to n.\n \nExample 1:\n\n\nInput: n = 3\nOutput: 5\n\nExample 2:\n\nInput: n = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= n <= 19\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == 5\n assert candidate(n = 4) == 14\n assert candidate(n = 19) == 1767263190\n assert candidate(n = 1) == 1\n assert candidate(n = 10) == 16796\n assert candidate(n = 5) == 42\n assert candidate(n = 8) == 1430\n assert candidate(n = 15) == 9694845\n assert candidate(n = 12) == 208012\n assert candidate(n = 18) == 477638700\n assert candidate(n = 9) == 4862\n assert candidate(n = 6) == 132\n assert candidate(n = 2) == 2\n assert candidate(n = 7) == 429\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().numTrees", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numTrees = function(n) {", "container": null, "callable": "numTrees", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 97, "task_id": "interleaving-string", "difficulty": "Medium", "problem_description": "Given strings s1, s2, and s3, find whether s3 is formed by an interleaving of s1 and s2.\nAn interleaving of two strings s and t is a configuration where s and t are divided into n and m substrings respectively, such that:\n\ns = s1 + s2 + ... + sn\nt = t1 + t2 + ... + tm\n|n - m| <= 1\nThe interleaving is s1 + t1 + s2 + t2 + s3 + t3 + ... or t1 + s1 + t2 + s2 + t3 + s3 + ...\n\nNote: a + b is the concatenation of strings a and b.\n \nExample 1:\n\n\nInput: s1 = \"aabcc\", s2 = \"dbbca\", s3 = \"aadbbcbcac\"\nOutput: true\nExplanation: One way to obtain s3 is:\nSplit s1 into s1 = \"aa\" + \"bc\" + \"c\", and s2 into s2 = \"dbbc\" + \"a\".\nInterleaving the two splits, we get \"aa\" + \"dbbc\" + \"bc\" + \"a\" + \"c\" = \"aadbbcbcac\".\nSince s3 can be obtained by interleaving s1 and s2, we return true.\n\nExample 2:\n\nInput: s1 = \"aabcc\", s2 = \"dbbca\", s3 = \"aadbbbaccc\"\nOutput: false\nExplanation: Notice how it is impossible to interleave s2 with any other string to obtain s3.\n\nExample 3:\n\nInput: s1 = \"\", s2 = \"\", s3 = \"\"\nOutput: true\n\n \nConstraints:\n\n0 <= s1.length, s2.length <= 100\n0 <= s3.length <= 200\ns1, s2, and s3 consist of lowercase English letters.\n\n \nFollow up: Could you solve it using only O(s2.length) additional memory space?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s1 = \"abc\",s2 = \"abc\",s3 = \"aabbcc\") == True\n assert candidate(s1 = \"\",s2 = \"a\",s3 = \"a\") == True\n assert candidate(s1 = \"\",s2 = \"b\",s3 = \"b\") == True\n assert candidate(s1 = \"a\",s2 = \"\",s3 = \"a\") == True\n assert candidate(s1 = \"abc\",s2 = \"\",s3 = \"abc\") == True\n assert candidate(s1 = \"aab\",s2 = \"dbbc\",s3 = \"aadbbcbc\") == False\n assert candidate(s1 = \"aabcc\",s2 = \"dbbca\",s3 = \"aadbbbaccc\") == False\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"defabc\") == True\n assert candidate(s1 = \"a\",s2 = \"a\",s3 = \"aa\") == True\n assert candidate(s1 = \"aaaa\",s2 = \"bbbb\",s3 = \"abababab\") == True\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"abcdef\") == True\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"abcfde\") == False\n assert candidate(s1 = \"\",s2 = \"abc\",s3 = \"abc\") == True\n assert candidate(s1 = \"a\",s2 = \"b\",s3 = \"ba\") == True\n assert candidate(s1 = \"a\",s2 = \"a\",s3 = \"ab\") == False\n assert candidate(s1 = \"aabcc\",s2 = \"dbbca\",s3 = \"aadbbcbcac\") == True\n assert candidate(s1 = \"ab\",s2 = \"cd\",s3 = \"abcd\") == True\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"adbcef\") == True\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"aaddbbccceedeff\") == False\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"aabbccddeeff\") == True\n assert candidate(s1 = \"a\",s2 = \"b\",s3 = \"ab\") == True\n assert candidate(s1 = \"\",s2 = \"def\",s3 = \"def\") == True\n assert candidate(s1 = \"\",s2 = \"\",s3 = \"\") == True\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"cabdef\") == False\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"aadddbbbeeffcc\") == False\n assert candidate(s1 = \"\",s2 = \"abcdef\",s3 = \"abcdef\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"klmnopqrstu\",s3 = \"ackbgdenfphiojqmrstnu\") == False\n assert candidate(s1 = \"abc\",s2 = \"defghijkl\",s3 = \"adbecfghijkl\") == True\n assert candidate(s1 = \"aaa\",s2 = \"bb\",s3 = \"aaabb\") == True\n assert candidate(s1 = \"xy\",s2 = \"xxyy\",s3 = \"xxxyyy\") == True\n assert candidate(s1 = \"abcde\",s2 = \"xyz\",s3 = \"axbyczde\") == True\n assert candidate(s1 = \"abcdef\",s2 = \"ghijkl\",s3 = \"aghbciidfjkel\") == False\n assert candidate(s1 = \"abcdefgh\",s2 = \"hgfedcba\",s3 = \"ahbgcfeddaehbgcfecba\") == False\n assert candidate(s1 = \"abcd\",s2 = \"efgh\",s3 = \"aebfcgdh\") == True\n assert candidate(s1 = \"aaa\",s2 = \"bbb\",s3 = \"ababab\") == True\n assert candidate(s1 = \"mississippi\",s2 = \"pwwkew\",s3 = \"mpiswimppwisikew\") == False\n assert candidate(s1 = \"abcd\",s2 = \"efgh\",s3 = \"aebcfdgh\") == True\n assert candidate(s1 = \"aaa\",s2 = \"bbb\",s3 = \"aababbab\") == False\n assert candidate(s1 = \"a\",s2 = \"ababababab\",s3 = \"abababababa\") == True\n assert candidate(s1 = \"abcabc\",s2 = \"defdef\",s3 = \"abcdefabcdef\") == True\n assert candidate(s1 = \"zzzz\",s2 = \"zzzz\",s3 = \"zzzzzzzz\") == True\n assert candidate(s1 = \"abcdefghijklmnopqrstuvwxyz\",s2 = \"zyxwvutsrqponmlkjihgfedcba\",s3 = \"azbycxdwevfugthvisjrkqlpmqonnpmojniklhgfeidchbegaf\") == False\n assert candidate(s1 = \"aaabbb\",s2 = \"aaabbb\",s3 = \"aaabbaabbb\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"klmnopqrst\",s3 = \"akblcfdmengoqhpristj\") == False\n assert candidate(s1 = \"abcabcabc\",s2 = \"bcdbcd\",s3 = \"abcbcadbcabc\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"klmnopqrst\",s3 = \"akblcmfdgnheijopqrst\") == False\n assert candidate(s1 = \"aabb\",s2 = \"ccdd\",s3 = \"accbbd\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"klm\",s3 = \"akbclmdefghij\") == True\n assert candidate(s1 = \"abcdefg\",s2 = \"hijklmn\",s3 = \"haijbckldemfnfg\") == False\n assert candidate(s1 = \"aabb\",s2 = \"bbcc\",s3 = \"aabbccbb\") == True\n assert candidate(s1 = \"aabbaa\",s2 = \"bbccbb\",s3 = \"aabbabbbccba\") == False\n assert candidate(s1 = \"aabbccddeeff\",s2 = \"gghhiijjkkllmm\",s3 = \"agbhchdijejfkflglhlimkmjmmnnoopp\") == False\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"aaddbbeeffcc\") == True\n assert candidate(s1 = \"abcde\",s2 = \"fghij\",s3 = \"afbgchidiej\") == False\n assert candidate(s1 = \"xxxx\",s2 = \"yyyy\",s3 = \"xxyxyyxxyy\") == False\n assert candidate(s1 = \"abcdefghij\",s2 = \"klmnopqrst\",s3 = \"akbldmconepfqgrhtisj\") == False\n assert candidate(s1 = \"\",s2 = \"abcd\",s3 = \"abcd\") == True\n assert candidate(s1 = \"abcd\",s2 = \"\",s3 = \"abcd\") == True\n assert candidate(s1 = \"abcde\",s2 = \"fghij\",s3 = \"afbgchdije\") == True\n assert candidate(s1 = \"aab\",s2 = \"bc\",s3 = \"aabbcc\") == False\n assert candidate(s1 = \"xyz\",s2 = \"uvw\",s3 = \"xuzyvw\") == False\n assert candidate(s1 = \"aabb\",s2 = \"ccdd\",s3 = \"accdbdb\") == False\n assert candidate(s1 = \"abc\",s2 = \"abc\",s3 = \"aabbbc\") == False\n assert candidate(s1 = \"abcd\",s2 = \"efgh\",s3 = \"aebfcdgh\") == True\n assert candidate(s1 = \"aaaaaa\",s2 = \"bbbbbb\",s3 = \"abababababab\") == True\n assert candidate(s1 = \"aabb\",s2 = \"ccdd\",s3 = \"acbdcbad\") == False\n assert candidate(s1 = \"xyz\",s2 = \"abc\",s3 = \"xyzabc\") == True\n assert candidate(s1 = \"aaa\",s2 = \"bbb\",s3 = \"aaabbb\") == True\n assert candidate(s1 = \"abcdefg\",s2 = \"hijklmn\",s3 = \"ahbicdjekflgmn\") == True\n assert candidate(s1 = \"abc\",s2 = \"defg\",s3 = \"adbcefeg\") == False\n assert candidate(s1 = \"zzz\",s2 = \"zzz\",s3 = \"zzzzzzz\") == False\n assert candidate(s1 = \"\",s2 = \"aabbccddeeff\",s3 = \"aabbccddeeff\") == True\n assert candidate(s1 = \"abcabcabc\",s2 = \"abcabcabc\",s3 = \"aabbaabbaabbaabcabc\") == False\n assert candidate(s1 = \"\",s2 = \"abcde\",s3 = \"abcde\") == True\n assert candidate(s1 = \"abcd\",s2 = \"aabb\",s3 = \"aabaabdc\") == False\n assert candidate(s1 = \"ababab\",s2 = \"bababa\",s3 = \"babababababa\") == True\n assert candidate(s1 = \"abc\",s2 = \"\",s3 = \"acb\") == False\n assert candidate(s1 = \"abcdefgh\",s2 = \"ijklmnop\",s3 = \"aicfbjdhekgmlonp\") == False\n assert candidate(s1 = \"abcd\",s2 = \"ef\",s3 = \"aebcfed\") == False\n assert candidate(s1 = \"abcdef\",s2 = \"ghijkl\",s3 = \"agbhicjkldfe\") == False\n assert candidate(s1 = \"aabbccddeeff\",s2 = \"zzzxxx\",s3 = \"azzbzxcxzddeeff\") == False\n assert candidate(s1 = \"abcdexyz\",s2 = \"mnopqr\",s3 = \"ambonpdqcrxezy\") == False\n assert candidate(s1 = \"abcabc\",s2 = \"xyzxyz\",s3 = \"axbyczaxbycz\") == True\n assert candidate(s1 = \"aab\",s2 = \"dbb\",s3 = \"aadbb\") == False\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"addbeeffcc\") == False\n assert candidate(s1 = \"abcd\",s2 = \"abdc\",s3 = \"aabbbdcc\") == False\n assert candidate(s1 = \"\",s2 = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",s3 = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == True\n assert candidate(s1 = \"abcd\",s2 = \"efgh\",s3 = \"abcdghfe\") == False\n assert candidate(s1 = \"aab\",s2 = \"cdd\",s3 = \"aadbb\") == False\n assert candidate(s1 = \"abababab\",s2 = \"babababa\",s3 = \"abbabababaabab\") == False\n assert candidate(s1 = \"abacabadabacaba\",s2 = \"cdcdcdc\",s3 = \"acbacabaacbadabacaba\") == False\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"abcdefg\") == False\n assert candidate(s1 = \"\",s2 = \"z\",s3 = \"z\") == True\n assert candidate(s1 = \"ab\",s2 = \"cd\",s3 = \"cabd\") == True\n assert candidate(s1 = \"abcdef\",s2 = \"\",s3 = \"abcdef\") == True\n assert candidate(s1 = \"aaabbb\",s2 = \"ccdddd\",s3 = \"aaacbbbddddd\") == False\n assert candidate(s1 = \"xxyy\",s2 = \"aabb\",s3 = \"xaayybb\") == False\n assert candidate(s1 = \"ab\",s2 = \"cd\",s3 = \"cadb\") == True\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"abdecf\") == True\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"adabdbcecefef\") == False\n assert candidate(s1 = \"aa\",s2 = \"aa\",s3 = \"aaaa\") == True\n assert candidate(s1 = \"abc\",s2 = \"abc\",s3 = \"abacbc\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"klmnopqrst\",s3 = \"akblcmndfoegphiqjrst\") == False\n assert candidate(s1 = \"abcde\",s2 = \"fghij\",s3 = \"afbgchdeij\") == True\n assert candidate(s1 = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",s2 = \"\",s3 = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == True\n assert candidate(s1 = \"zzzz\",s2 = \"zzz\",s3 = \"zzzzzzz\") == True\n assert candidate(s1 = \"abcd\",s2 = \"efgh\",s3 = \"abcdefghe\") == False\n assert candidate(s1 = \"abc\",s2 = \"abcd\",s3 = \"abcabcd\") == True\n assert candidate(s1 = \"aabbccddeeff\",s2 = \"\",s3 = \"aabbccddeeff\") == True\n assert candidate(s1 = \"abcdefghijk\",s2 = \"lmnopqrstuvwxyz\",s3 = \"abcdefghijklmnoqrstuvwxyz\") == False\n assert candidate(s1 = \"abc\",s2 = \"abc\",s3 = \"abccba\") == False\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"dabcef\") == True\n assert candidate(s1 = \"abcde\",s2 = \"\",s3 = \"abcde\") == True\n assert candidate(s1 = \"abcdef\",s2 = \"ghijkl\",s3 = \"aghbidejfkfl\") == False\n assert candidate(s1 = \"z\",s2 = \"\",s3 = \"z\") == True\n assert candidate(s1 = \"zxy\",s2 = \"xzy\",s3 = \"zxzyxy\") == True\n assert candidate(s1 = \"abcdefghij\",s2 = \"klmnopqrst\",s3 = \"akblcmnodpefqgrstihj\") == False\n assert candidate(s1 = \"aab\",s2 = \"acc\",s3 = \"aaabcac\") == False\n assert candidate(s1 = \"aabbaabbaabb\",s2 = \"bbccbbccbbcc\",s3 = \"aabbaabbccbaabbccbaabbccbb\") == False\n assert candidate(s1 = \"xxxx\",s2 = \"yyyy\",s3 = \"xyxxyxyyxyyx\") == False\n assert candidate(s1 = \"aabbcc\",s2 = \"ddeeff\",s3 = \"aadbbccddeeff\") == False\n assert candidate(s1 = \"ababab\",s2 = \"bababa\",s3 = \"abababababab\") == True\n assert candidate(s1 = \"aabb\",s2 = \"ccdd\",s3 = \"acabcd\") == False\n assert candidate(s1 = \"aabb\",s2 = \"ccdd\",s3 = \"acbdad\") == False\n assert candidate(s1 = \"aaaaa\",s2 = \"bbbbb\",s3 = \"ababababab\") == True\n assert candidate(s1 = \"aabbccddeeff\",s2 = \"gg hh ii jj kk ll\",s3 = \"aaggbbccddhhffeeggiijjkkl\") == False\n assert candidate(s1 = \"abcabcabc\",s2 = \"xyzxyzxyz\",s3 = \"axbyczaxbyczaxbycz\") == True\n assert candidate(s1 = \"aabcc\",s2 = \"dbbca\",s3 = \"aadbbcbcacd\") == False\n assert candidate(s1 = \"aabb\",s2 = \"ccdd\",s3 = \"acabcdbd\") == True\n assert candidate(s1 = \"abc\",s2 = \"def\",s3 = \"dabecf\") == True\n assert candidate(s1 = \"abcde\",s2 = \"fghij\",s3 = \"abcdefghij\") == True\n assert candidate(s1 = \"abcabcabc\",s2 = \"xyzxyzxyz\",s3 = \"axbxcyzaybzcyzabc\") == False\n"}, "metadata": {"canonical_parameter_names": ["s1", "s2", "s3"], "leetcode_dataset_entry_point": "Solution().isInterleave", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isInterleave = function(s1, s2, s3) {", "container": null, "callable": "isInterleave", "parameters": [{"name": "s1", "type": "string"}, {"name": "s2", "type": "string"}, {"name": "s3", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 98, "task_id": "validate-binary-search-tree", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, determine if it is a valid binary search tree (BST).\nA valid BST is defined as follows:\n\nThe left subtree of a node contains only nodes with keys less than the node's key.\nThe right subtree of a node contains only nodes with keys greater than the node's key.\nBoth the left and right subtrees must also be binary search trees.\n\n \nExample 1:\n\n\nInput: root = [2,1,3]\nOutput: true\n\nExample 2:\n\n\nInput: root = [5,1,4,null,null,3,6]\nOutput: false\nExplanation: The root node's value is 5 but its right child's value is 4.\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 104].\n-231 <= Node.val <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, None, 1])) == False\n assert candidate(root = tree_node([5, 4, 6, None, None, 3, 7])) == False\n assert candidate(root = tree_node([0, -1])) == True\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == False\n assert candidate(root = tree_node([3, 1, 5, 0, 2, 4, 6])) == True\n assert candidate(root = tree_node([3, 1, 4, 3, 2, 6, 5])) == False\n assert candidate(root = tree_node([2, 2, 2])) == False\n assert candidate(root = tree_node([2, None, 1])) == False\n assert candidate(root = tree_node([1, 2])) == False\n assert candidate(root = tree_node([2147483647])) == True\n assert candidate(root = tree_node([1, None, 2])) == True\n assert candidate(root = tree_node([2, 1, 3])) == True\n assert candidate(root = tree_node([32, 26, 47, 19, None, None, 56, None, 27])) == False\n assert candidate(root = tree_node([1, None, 2, 3])) == False\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7])) == True\n assert candidate(root = tree_node([1])) == True\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == False\n assert candidate(root = tree_node([5, 4, 6, 3, None, None, 7])) == True\n assert candidate(root = tree_node([3, 2, 5, 1, None, None, 6, 0, None, None, 4])) == False\n assert candidate(root = tree_node([1, 0, 2, None, None, 1.5, 2.5])) == True\n assert candidate(root = tree_node([5, 3, 7, 1, 4, 6, 9, None, None, None, None, None, 10])) == False\n assert candidate(root = tree_node([8, 5, 10, None, 6, 8, 15, None, None, 7])) == False\n assert candidate(root = tree_node([9, 7, 10, None, None, 8, None, 6])) == False\n assert candidate(root = tree_node([5, 1, 5, None, None, 4, 6])) == False\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == True\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 190])) == True\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, None, None, None, None, None, None, 9])) == False\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])) == True\n assert candidate(root = tree_node([3, None, 30, 10, None, None, 15, None, 45])) == False\n assert candidate(root = tree_node([10, None, 20, 15, 30, None, None, 12, 17])) == False\n assert candidate(root = tree_node([2, 1, 3, None, None, 2])) == False\n assert candidate(root = tree_node([10, 5, 15, 1, 7, None, 20, None, None, 6, 8])) == True\n assert candidate(root = tree_node([1, 0, 2, None, None, 1.5])) == True\n assert candidate(root = tree_node([5, 1, 5, None, None, 5, 5])) == False\n assert candidate(root = tree_node([5, 3, 7, 2, 4, None, 8])) == True\n assert candidate(root = tree_node([50, 20, 60, 10, 25, 55, 70, 5, 15, 22, 30, 52, 65, 67, 80])) == False\n assert candidate(root = tree_node([2, None, 3, None, 4, None, 5, None, 6])) == True\n assert candidate(root = tree_node([8, 5, 15, 1, 7, None, 18, None, 6])) == False\n assert candidate(root = tree_node([3, 1, 5, 0, 2, 4, 6, None, None, None, 3])) == False\n assert candidate(root = tree_node([8, 5, 15, 1, 7, 10, 18, None, None, None, 8])) == False\n assert candidate(root = tree_node([32, 26, 40, 17, 27, None, 45, None, None, None, 29, 30])) == False\n assert candidate(root = tree_node([12, 7, 14, 3, 9, 13, 15, None, None, 8])) == True\n assert candidate(root = tree_node([50, 30, 80, 20, 40, 70, 90, None, None, 25, 45, 65, 75, None, None, None, None, 42])) == False\n assert candidate(root = tree_node([9, 4, 10, None, None, None, 11])) == True\n assert candidate(root = tree_node([5, 1, 6, None, None, 3, 7, None, None, None, 8])) == False\n assert candidate(root = tree_node([2147483646, 2147483647])) == False\n assert candidate(root = tree_node([2, 2, 2, 2, 2, 2, 2])) == False\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20])) == True\n assert candidate(root = tree_node([100, 50, 150, None, None, 60, 200])) == False\n assert candidate(root = tree_node([12, 7, 14, 3, 9, 13, 20, 1, 5, 8, 11, 12, 17, 16, 18])) == False\n assert candidate(root = tree_node([2, 1, 3, 0, 5, None, 4])) == False\n assert candidate(root = tree_node([5, 4, 6, None, None, 3, 7, 2, None, None, None, 4, None])) == False\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 2, None, None, None, 16])) == True\n assert candidate(root = tree_node([7, 3, 15, None, None, None, 20])) == True\n assert candidate(root = tree_node([1, 0, 2, None, None, 3, None])) == False\n assert candidate(root = tree_node([32, 26, 40, 18, 28, 36, 48, 13, 19, 27, 31, 34, 43, 49, 52, None, 14, None, None, 24, 29, None, None, 32, None, 35, 41, 44, 46, 47, 50, None, None, 51])) == False\n assert candidate(root = tree_node([2, None, 3, None, None, 4])) == True\n assert candidate(root = tree_node([5, 2, 14, None, None, 10, 20, 8, 15, 11, 19])) == False\n assert candidate(root = tree_node([10, 5, 15, 1, 8, 12, 20, None, None, 6, 9, 11, 13])) == True\n assert candidate(root = tree_node([12, 7, 14, 3, 9, 13, 18, 1, None, 8, None, 11, 15, None, 17])) == False\n assert candidate(root = tree_node([2, 1, 3, None, None, 2, 4])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == True\n assert candidate(root = tree_node([120, 70, 140, 50, 100, 130, 160, 20, 60, 80, 110, 125, 150, 180, 200])) == False\n assert candidate(root = tree_node([1, 1, None, 1])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5])) == False\n assert candidate(root = tree_node([1, 1])) == False\n assert candidate(root = tree_node([1, 0, 2])) == True\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6, 2, 2])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4])) == True\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8])) == True\n assert candidate(root = tree_node([32, 26, 40, 19, 27, None, 44, None, None, None, None, None, 42])) == False\n assert candidate(root = tree_node([50, 30, 80, 20, 40, 70, 90])) == True\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, 4])) == True\n assert candidate(root = tree_node([1, None, 1, None, 1, None, 1, None, 1])) == False\n assert candidate(root = tree_node([5, 1, 4, None, None, None, 6])) == False\n assert candidate(root = tree_node([3, 2, 4, None, None, 3, None])) == False\n assert candidate(root = tree_node([12, 5, 18, 2, 9, 15, 19, 1, 3, 7, 11, 14, 17, 20])) == False\n assert candidate(root = tree_node([5, 1, 8, None, 4, 7, 9])) == True\n assert candidate(root = tree_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == False\n assert candidate(root = tree_node([8, 5, 10, None, 6, 9, 11])) == True\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, None, 9])) == False\n assert candidate(root = tree_node([5, 1, 5, None, 7])) == False\n assert candidate(root = tree_node([2, 1, 3, 0, 2, None, 4])) == False\n assert candidate(root = tree_node([3, 1, 4, 3, 3])) == False\n assert candidate(root = tree_node([5, 2, 8, 1, 3, None, 9])) == True\n assert candidate(root = tree_node([20, 10, 30, 5, 15, None, None, None, None, 13, 18])) == True\n assert candidate(root = tree_node([10, 5, 15, None, None, 12, 20])) == True\n assert candidate(root = tree_node([3, 1, 4, None, None, 2, 6])) == False\n assert candidate(root = tree_node([2147483647, 2147483647])) == False\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180])) == True\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, None, None, None, None, None, None, None, 9])) == True\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 90])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5])) == False\n assert candidate(root = tree_node([50, 30, 80, 20, 40, 70, 90, None, None, 25, 45, 65, 75, None, None, None, None, 41])) == False\n assert candidate(root = tree_node([1, None, 3, None, 2])) == False\n assert candidate(root = tree_node([5, 4, 6, 3, None, None, 7, 2, None, None, None, None, 8])) == False\n assert candidate(root = tree_node([10, 5, 15, 1, 7, None, 18])) == True\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().isValidBST", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isValidBST = function(root) {", "container": null, "callable": "isValidBST", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 99, "task_id": "recover-binary-search-tree", "difficulty": "Medium", "problem_description": "You are given the root of a binary search tree (BST), where the values of exactly two nodes of the tree were swapped by mistake. Recover the tree without changing its structure.\n \nExample 1:\n\n\nInput: root = [1,3,null,null,2]\nOutput: [3,1,null,null,2]\nExplanation: 3 cannot be a left child of 1 because 3 > 1. Swapping 1 and 3 makes the BST valid.\n\nExample 2:\n\n\nInput: root = [3,1,4,null,null,2]\nOutput: [2,1,4,null,null,3]\nExplanation: 2 cannot be in the right subtree of 3 because 2 < 3. Swapping 2 and 3 makes the BST valid.\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [2, 1000].\n-231 <= Node.val <= 231 - 1\n\n \nFollow up: A solution using O(n) space is pretty straight-forward. Could you devise a constant O(1) space solution?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([2, 3, 1])) == None\n assert candidate(root = tree_node([3, 1, 4, None, None, 2])) == None\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == None\n assert candidate(root = tree_node([1, 3, None, None, 2])) == None\n assert candidate(root = tree_node([3, 2, 1])) == None\n assert candidate(root = tree_node([5, 3, 9, -20, 10])) == None\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == None\n assert candidate(root = tree_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == None\n assert candidate(root = tree_node([7, 3, 10, None, None, 8, 12, 1, None, None, 9, 11, 13])) == None\n assert candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, None, None, None, None, None, None, 18, 22])) == None\n assert candidate(root = tree_node([7, 3, 15, None, 4, 10, 18, 2, 5, 9, 12, 8, 16, 14, 19])) == None\n assert candidate(root = tree_node([12, 5, 18, 2, 8, 15, 25, 1, 3, 7, 10, 13, 17, 22, 27, None, None, None, None, 6, 9, None, None, None, None, 14, None, 11, 16, 19, 21, 24, 23, 26, 28, 29, 30])) == None\n assert candidate(root = tree_node([30, 15, 45, 5, 20, 35, 50, 1, 7, 10, 25, 33, 40, 48, 60])) == None\n assert candidate(root = tree_node([7, 3, 10, 1, 5, 8, 12, None, None, 4, None, 9, 11, 13, 14])) == None\n assert candidate(root = tree_node([15, 10, 20, 5, 12, 18, 25, 3, 7, None, 14, None, None, 16, None, None, None, None, None])) == None\n assert candidate(root = tree_node([60, 30, 80, 20, 40, 70, 90, 10, 25, 35, 50, 65, 75, 85, 95, 5, 15, 22, 28, 32, 45, 48, 63, 73, 82, 88, 93, 98, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([7, 3, 9, 1, 5, 8, 10, 0, 2, 4, 6, None, None, None, None, None, 11])) == None\n assert candidate(root = tree_node([5, 2, 6, 1, 4, 3, 8, None, None, None, None, 7, 9])) == None\n assert candidate(root = tree_node([8, 5, 10, 2, 7, 9, 11, 1, 3, 6, None, None, None, None, None, 4])) == None\n assert candidate(root = tree_node([8, 3, 10, 1, 5, 9, 12, None, 2, 4, 7, 11, 13])) == None\n assert candidate(root = tree_node([5, 2, 8, 1, 4, None, 10, None, None, 3, 6])) == None\n assert candidate(root = tree_node([15, 10, 20, 5, 12, 16, 25, 3, 7, 11, 13, 14, 17, 22, 30])) == None\n assert candidate(root = tree_node([12, 9, 15, 5, 11, 13, 18, 3, 6, 8, 10, 14, 16, 17, 19])) == None\n assert candidate(root = tree_node([20, 15, 30, 10, 18, 25, 35, 5, 11, 16, 19, None, None, 14])) == None\n assert candidate(root = tree_node([20, 15, 30, 10, 25, 28, 40, 5, 12, 18, 27, 35, 38, 45, 50])) == None\n assert candidate(root = tree_node([10, 15, 8, None, None, 12, 20])) == None\n assert candidate(root = tree_node([9, 4, 20, None, None, 15, 60, None, None, 10, 25, None, None, 7, 12, None, 30])) == None\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 22, 28, 32, 38, 45, None, None, 2, 8, 14, 16, 21, 24, 27, 31, 34, 37, 42, 48, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([250, 125, 375, 62, 187, 312, 437, 31, 93, 156, 221, 278, 363, 412, 492, None, None, 15, 46, 78, 138, 171, 206, 254, 341, 400, 458, 518, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, None, None, 18, 25, 35, 48, None, None, None, None, 22, None, None, None, None])) == None\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 17, 23, 35, 48, 1, 8, 11, 13, 16, 18, 21, 22, 27, 33, 42, 47, 53, None, 4, None, None, 6, 9, None, None, 14, None, 7, 10, None, None, None, None, 19, None, 24, None, 26, 28, 29, None, 31, 34, None, None, 38, None, 41, 43, None, 46, None, 49, None, 51, 52, None, 54, None, 55])) == None\n assert candidate(root = tree_node([60, 30, 90, 20, 40, 70, 100, 10, 25, 35, 45, 65, 75, 85, 105])) == None\n assert candidate(root = tree_node([5, 10, 15, 3, None, None, 20, None, None, None, 25])) == None\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, 5.5])) == None\n assert candidate(root = tree_node([8, 3, 10, 1, 5, 9, 12, None, 2, 4, 6, 7, 11, 13, 14, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 80, 110, 140, 160, 180, 5, 15, 28, 45, 65, 75, 105, 135, 155, 170, 190, None, None, None, None, 20, 35, None, 53, None, None, None, None, None, 54, None, 78, None, None, None, None, None, 115, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([30, 20, 50, 10, 25, 40, 60, None, None, 15, 27, 35, 55, 45, 65])) == None\n assert candidate(root = tree_node([7, 3, 10, 1, 5, 8, 12, None, 2, None, 4, 6, 9, 11, 13])) == None\n assert candidate(root = tree_node([9, 7, 10, 6, 8, 11, 12, 5, None, None, None, 13, 14])) == None\n assert candidate(root = tree_node([15, 10, 20, 7, 12, 16, 25, 2, 6, 11, 14, 13, 17, 21, 30])) == None\n assert candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 5, 12, None, 17, 21, 27, 26, 35])) == None\n assert candidate(root = tree_node([12, 9, 15, 6, 10, 13, 18, 2, 7, 8, 11, 14, 16, 17, 20])) == None\n assert candidate(root = tree_node([4, 2, 5, 1, 3, 6, 7, 0, None, None, None, None, None, None, 8])) == None\n assert candidate(root = tree_node([15, 10, 20, None, None, 6, 25, 4, None, 11, 17])) == None\n assert candidate(root = tree_node([60, 30, 80, 10, 40, 70, 90, 5, 25, 35, 55, 65, 85, 95, None, 1, None, 15, 28, 40, 53, 63, 75, 88, 93, 100, None, None, 11, None, 26, None, 36, 45, 54, 64, 76, 89, None, None, None, None, None, 101])) == None\n assert candidate(root = tree_node([8, 5, 10, 2, 7, None, 15, 1, None, 6, 9, 12, 18, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 200, 10, 30, 60, 80, 110, 140, 180, 220, None, 12, 28, None, 55, 85, 105, 135, 165, 195, 210, 225, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 17, None, None, 100])) == None\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 90, 110, 140, 160, 180, 5, 15, 28, 40, 65, 85, 105, 135, 155, 170, 190])) == None\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 17, 25, 35, 48, 3, 8, 14, 19, 24, 31, 47, 49, None, None, None, None, None, None, None, None, 9, None, None, 16, None, None, None, None, 23, None, None, None, None, 32, None, None, None, None, 46, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([9, 5, 12, 3, 7, 10, 15, 2, 4, 6, 8, 11, 13, 14, 17])) == None\n assert candidate(root = tree_node([30, 20, 40, 10, 25, 35, 50, 5, 15, None, None, 22, None, 27, 33, None, 45, 48, 55])) == None\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 8, 16])) == None\n assert candidate(root = tree_node([5, 3, 8, 2, 4, 6, 9, 1, None, None, None, None, None, 7, 10])) == None\n assert candidate(root = tree_node([8, 5, 12, 3, 7, 10, 15, 2, 4, 6, 9, 11, 13, 14, 16])) == None\n assert candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 5, 12, 16, 19, 21, 24, 28, 32, 3, 7, 11, 13, 17, 23, 27, 31])) == None\n assert candidate(root = tree_node([9, 5, 12, 3, 7, 11, 14, 2, 4, 6, 8, 10, 13, None, None, None, None, None, None, 1])) == None\n assert candidate(root = tree_node([22, 10, 30, 5, 15, 25, 40, 2, 7, 13, 18, 21, 35, 38, 45, 1, 3, 6, 8, 11, 14, 17, 20, 24, 28, 33, 36, 43, 41, 44, 47, 48, 4, 9, 12, 16, 19, 23, 27, 29, 32, 34, 37, 42, 46, 49, 50, 51])) == None\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == None\n assert candidate(root = tree_node([90, 60, 120, 30, 70, 100, 150, 10, 50, 65, 80, 95, 110, 140, 160, 5, 25, 45, 55, 75, 85, 92, 105, 125, 135, 155, 170, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, 8, 12, 18, 22, 28, 32, 38, None, None, 4, None, 6, None, None, None, 9, None, None, 11, None, None, 14, None, None, 16, None, None, 19, None, None, 23, None, None, 27, None, None, 31, None, None, 34, None, None, 37, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([15, 10, 20, None, 12, 17, 25, 8, None, None, 13, None, 19, 16, 23])) == None\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190, None, None, 5, 15, 30, 45, 65, 85, 95, 105, 120, 130, 145, 155, 170, 185, 195, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([8, 3, 10, 1, 5, 9, 12, None, 2, 4, 7, 11, 13, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([35, 20, 55, 10, 30, 50, 60, None, None, 25, 34, 45, 56, None, None, 27, 32, None, 33, 40, 47, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([200, 100, 300, 50, 150, 250, 350, 25, 75, 125, 175, 225, 275, 325, 375, None, None, 10, 40, 60, 90, 110, 140, 160, 190, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == None\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, None, 25, 35, 55, 65, 75, 90])) == None\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().recoverTree", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var recoverTree = function(root) {", "container": null, "callable": "recoverTree", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "void", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 100, "task_id": "same-tree", "difficulty": "Easy", "problem_description": "Given the roots of two binary trees p and q, write a function to check if they are the same or not.\nTwo binary trees are considered the same if they are structurally identical, and the nodes have the same value.\n \nExample 1:\n\n\nInput: p = [1,2,3], q = [1,2,3]\nOutput: true\n\nExample 2:\n\n\nInput: p = [1,2], q = [1,null,2]\nOutput: false\n\nExample 3:\n\n\nInput: p = [1,2,1], q = [1,1,2]\nOutput: false\n\n \nConstraints:\n\nThe number of nodes in both trees is in the range [0, 100].\n-104 <= Node.val <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(p = tree_node([1, 2, 3]),q = tree_node([1, 2, 3, 4])) == False\n assert candidate(p = tree_node([1, 2]),q = tree_node([1, None, 2])) == False\n assert candidate(p = tree_node([1, 0]),q = tree_node([1, None])) == False\n assert candidate(p = tree_node([1, None, 3]),q = tree_node([1, None, 3])) == True\n assert candidate(p = tree_node([1, 2, 3]),q = tree_node([1, 2, 3])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5]),q = tree_node([1, 2, 3, 4, 5])) == True\n assert candidate(p = tree_node([1, None, 2, None, 3]),q = tree_node([1, None, 2, None, 3])) == True\n assert candidate(p = tree_node([1, None, 2]),q = tree_node([1, 2, None])) == False\n assert candidate(p = tree_node([1, 2, 1]),q = tree_node([1, 1, 2])) == False\n assert candidate(p = tree_node([]),q = tree_node([])) == True\n assert candidate(p = tree_node([1, None, 3]),q = tree_node([1, 2, 3])) == False\n assert candidate(p = tree_node([5, 1, 4, None, None, 3, 6]),q = tree_node([5, 1, 4, None, None, 3, 6])) == True\n assert candidate(p = tree_node([1]),q = tree_node([1])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5]),q = tree_node([1, 2, 3, 4, 6])) == False\n assert candidate(p = tree_node([1, 2, None, 3]),q = tree_node([1, 2, None, 3])) == True\n assert candidate(p = tree_node([1, 2, None, 3]),q = tree_node([1, 2, None, 4])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7]),q = tree_node([1, 2, 3, 4, 5, 6, 7])) == True\n assert candidate(p = tree_node([10, 5, 15]),q = tree_node([10, 5, None, None, 15])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, None, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, None, None, 12]),q = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, None, None, 13])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, 6]),q = tree_node([1, 2, 3, None, 4, 5, None, 7])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 7, 8, 9]),q = tree_node([1, 2, 3, 4, 5, None, 7, 8, 9])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, 10, 11]),q = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, 10, 11])) == True\n assert candidate(p = tree_node([5, 1, 4, None, None, 3, 6]),q = tree_node([5, 1, 4, None, None, 2, 6])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])) == False\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7]),q = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 14])) == False\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18, None, None, 6, 9]),q = tree_node([10, 5, 15, 3, 7, None, 18, None, None, 6, 9])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 5, 6]),q = tree_node([1, 2, 3, None, 4, 5, 6])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8, None, None, 9, 10]),q = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8, None, None, 10, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18, 19]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18, 19])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 17])) == False\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18, None, None, 6, 9]),q = tree_node([10, 5, 15, 3, 7, None, 19, None, None, 6, 9])) == False\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9]),q = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == True\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8]),q = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 9])) == False\n assert candidate(p = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15]),q = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 16])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 17])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, None, None, None, 6, 7]),q = tree_node([1, 2, 3, 4, 5, None, None, None, None, 6, 8])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, None, 9]),q = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, None, 10])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7]),q = tree_node([1, 2, 3, 4, None, 6, 7])) == True\n assert candidate(p = tree_node([1, 2, 3, None, None, 4, 5, 6, 7]),q = tree_node([1, 2, 3, None, None, 4, 5, 6, None])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 7, None, 8]),q = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 7, None, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, None, 6, 7, 8]),q = tree_node([1, 2, 3, None, 4, 5, None, None, 6, 7, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, 8, 9]),q = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, 8, 10])) == False\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10]),q = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 11])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18, 19]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18, None])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, 9, None, None, 10]),q = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, 9, None, None, 10])) == True\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5]),q = tree_node([1, None, 2, None, 3, None, 4, None, 6])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8]),q = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, None, 5]),q = tree_node([1, 2, 3, None, 4, None, 5])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9, 10, 11]),q = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9, 10, 11])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, 6]),q = tree_node([1, 2, 3, None, 4, 5, None])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, None, 8, 9, 10]),q = tree_node([1, 2, 3, 4, None, 6, 7, None, 8, 9, 10])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, None, 8, 9, 10]),q = tree_node([1, 2, 3, 4, None, 6, 7, None, 8, None, 10])) == False\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, None, 8]),q = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, None, 8])) == True\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5]),q = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, None, 5]),q = tree_node([1, 2, 3, 4, None, None, 6])) == False\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9]),q = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 10])) == False\n assert candidate(p = tree_node([3, 5, 1, 6, 2, 9, 8, None, None, 7, 4]),q = tree_node([3, 5, 1, 6, 2, 9, 8, None, None, 7, 3])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, None, None, 12]),q = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, None, None, 12])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13, 15, 14])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11]),q = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 12])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, 6]),q = tree_node([1, 2, 3, None, 4, 5, 6])) == True\n assert candidate(p = tree_node([3, 5, 1, 6, 2, 9, 8, None, None, 7, 4]),q = tree_node([3, 5, 1, 6, 2, 9, 8, None, None, 7, 4])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 7, 8]),q = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 8, 7])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9, 10, 11]),q = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9, 10, 12])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 5, 6, None, 7]),q = tree_node([1, 2, 3, 4, None, 5, 6, None, 8])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 7, 8, 9]),q = tree_node([1, 2, 3, 4, None, None, 7, 8, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7]),q = tree_node([1, 2, 3, 4, None, 6])) == False\n assert candidate(p = tree_node([5, 1, 4, None, None, 3, 6]),q = tree_node([5, 1, 4, None, None, 6, 3])) == False\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18]),q = tree_node([10, 5, 15, 3, 7, None, 19])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 7]),q = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 8])) == False\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4]),q = tree_node([1, None, 2, None, 3, None, 4])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, 17]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, 17])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 10])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, None, 5]),q = tree_node([1, 2, 3, None, 4, None, 6])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, None, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == True\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6]),q = tree_node([10, 5, 15, 3, 7, None, 18, 2, None, 6])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11]),q = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, None, 6]),q = tree_node([1, 2, 3, None, 4, None, 5, None, None, 6])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 7, 8, 9]),q = tree_node([1, 2, 3, 4, 5, None, 7, 8, None])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, 6]),q = tree_node([1, 2, 3, None, 4, 6, 5])) == False\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18]),q = tree_node([10, 5, 15, 3, 7, None, 18])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13, 14, 15])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 5, None, 7, 8]),q = tree_node([1, 2, 3, None, 5, None, 7, 8])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13, 14, 16])) == False\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6]),q = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11, None, 12, 13, None, 14, 15, None, 16, 17, None, 18, 19, None, 20, 21]),q = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11, None, 12, 13, None, 14, 15, None, 16, 17, None, 18, 19, None, 20, 21])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 19])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, 17]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 7, 8]),q = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 7, 8])) == True\n assert candidate(p = tree_node([1, 2, 3, None, None, 6, 7, 8, 9]),q = tree_node([1, 2, 3, None, None, 6, 7, 8, 9])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, None, None, 9]),q = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, None, None, 9])) == True\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4, None, 5]),q = tree_node([1, None, 2, None, 3, None, 4, None, None])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8]),q = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 10, None, None, 12, 13])) == False\n assert candidate(p = tree_node([10, 5, 15, None, None, 6, 20]),q = tree_node([10, 5, 15, None, None, 6, 20])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, 9, None, None, 10]),q = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, 9, None, None, 11])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9]),q = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 4, None, 5, 6]),q = tree_node([1, 2, 3, None, 4, None, 5, 6])) == True\n assert candidate(p = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, None, 8]),q = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, None, 9])) == False\n assert candidate(p = tree_node([1, None, 2, 3]),q = tree_node([1, 2, None, 3])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7]),q = tree_node([1, 2, 3, 4, None, 6, 8])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, 16, None, 18])) == True\n assert candidate(p = tree_node([10, 5, 15, None, None, 6, 20]),q = tree_node([10, 5, 15, None, None, 7, 20])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8, None, None, 9, 10]),q = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8, None, None, 9, 11])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9]),q = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 10])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, 6]),q = tree_node([1, 2, 3, None, 4, 5, None, 6])) == True\n assert candidate(p = tree_node([1, None, 2, None, 3, None, 4]),q = tree_node([1, None, 2, None, 3, None, 5])) == False\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11, None, 12, 13, None, 14, 15, None, 16, 17, None, 18, 19, None, 20, 21]),q = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11, None, 12, 13, None, 14, 15, None, 16, 17, None, 18, 19, None, 20, 22])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11]),q = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 12])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == True\n assert candidate(p = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11]),q = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, 11])) == True\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 20])) == False\n assert candidate(p = tree_node([1, 2, 3, None, None, 6, 7, 8, 9]),q = tree_node([1, 2, 3, None, None, 6, 7, None, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None])) == True\n assert candidate(p = tree_node([1]),q = tree_node([2])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8]),q = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, 13]),q = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),q = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14])) == False\n assert candidate(p = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, None, 9]),q = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, None, 9])) == True\n"}, "metadata": {"canonical_parameter_names": ["p", "q"], "leetcode_dataset_entry_point": "Solution().isSameTree", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isSameTree = function(p, q) {", "container": null, "callable": "isSameTree", "parameters": [{"name": "p", "type": "TreeNode"}, {"name": "q", "type": "TreeNode"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 101, "task_id": "symmetric-tree", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, check whether it is a mirror of itself (i.e., symmetric around its center).\n \nExample 1:\n\n\nInput: root = [1,2,2,3,4,4,3]\nOutput: true\n\nExample 2:\n\n\nInput: root = [1,2,2,null,3,null,3]\nOutput: false\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 1000].\n-100 <= Node.val <= 100\n\n \nFollow up: Could you solve it both recursively and iteratively?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == False\n assert candidate(root = tree_node([1, 2, 3])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5])) == False\n assert candidate(root = tree_node([2, 3, 3, 4, 5, 5, 4])) == True\n assert candidate(root = tree_node([1, 2])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 8, 7, 6, 5])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 3, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 5, 3])) == False\n assert candidate(root = tree_node([1, 2, 2, None, 3, None, 3])) == False\n assert candidate(root = tree_node([1])) == True\n assert candidate(root = tree_node([1, 2, 2, 2, None, 2])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 6, 7, 8, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 10, 11, 11, 10, 12, 13, 13, 12])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, None, 4, 4])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 8, 7, 6, 5, None, None, None, None, None, None, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, 5, None, None, 6, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 6, None, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, None, None, None, 8, 9, 10, 11])) == False\n assert candidate(root = tree_node([1, 2, 3, 3, 2, 1, None, 4, None, None, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 5, None, None, None, None, 6, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, None, 4, 5, 5, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, 5, 5, None, None, 6, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, 6, 7, None, None, 8, 9])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, None, 8, None, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 5, None, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, 3, None, 4, None, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 5, None, None, 6, 6, None, 7, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, None, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, 6, None, None, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, None, None, 5, 6, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 9, 10, 11, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, None, 6, 7, 7, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, None, 6, None, 5, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 6, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, None, 3, 3, None, 4, None, None, 4, None, 5, None, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 9, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, 10, 11, 11, 10, 9, 8])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 6, 5, 7, 8, 8, 7, 9, 9, 10, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 6, None, 7, None, 8, 9])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, None, 7, 8, 8, 7, None, None, 9])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, 5, 6, None, None, 7, 8])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, 5, None, 5, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, 7, None, None, 8, 9, 9, 8])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, None, None, 11, 12, 12, 11])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, 6, 7, 8, 8, 7, 6, None, None, 9, 10, 10, 9])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 7, 8, 9, None, 9, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, None, 5, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 7, 8, None, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, 6, 7, None, 8, 9])) == False\n assert candidate(root = tree_node([1, 2, 3, 3, 2, None, 1, 4, None, None, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, 3, 3, None, 4, 4, 4, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, None, None, 5, None, None, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, None, 3, None, 5, 6, 7, 8, 9, 10, 11, 11, 10, 9, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, None, None, 5, None, None, 6, 7, None, None, 8])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, None, 3, 5, None, 6, None, 7, 8, 9, None, None, None, None, 10, None, None, 11, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 5, 5, 4])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, None, 5, None, None, None, 6, 7, 8, 8, 7, 6])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, 10, 11, None, None, 12, None, None, 13, None, None, 14])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, None, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 5, None, 5, None, 4, 6, None, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 9, 10, 11, 12])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, None, None, 5, 6, 5, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, 5, None, 6, 6, None, 7, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 5, 5, None, 6, 6, 7, 8, 8, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 5, 6, 6, 5, 7, 8, 8, 7, 9, 9, 10, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 3, 4, None, None, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 6, 7, 8, 9, 10, 11])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, None, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 7, None, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 7, 8, None, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 7, None, 6, 5, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, None, None, 5, 6, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, 7, None, 8, None, None, 9, 10, 10, 9, None, 8, None, 7, None, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 5, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, None, None, 4, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, 6, None, 5, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 8, 7, 6, 5, 9, 10, 10, 9, 11, 12, 12, 11, 13, 14, 15, 15, 14, 13])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, 7, 8, 9, 10, 11, 11, 10, 9, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, None, 4, 5, None, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 8, 7, 6, 5, 9, None, None, None, None, None, None, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, None, None, 7, 6, 5])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, 6, 5, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, None, None, None, 6, 5])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, 8, 7, 6, 5, 9, 10, 10, 9, 11, 12, 12, 11, 13, 14, 14, 13])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 5, None, None, 5, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, 4, 3, 5, None, 6, None, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, None, 6, 7, 8, 8, 7, 6, None, None, 9, 10, None, None, 10, 9])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, 5, 6, 6, 5])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, 6, None, 6, 5, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, None, 5, None, None, None, 6, None, 8, 8, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, 5, None, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 6, 5, None, 7, 7, None, 8, 8])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, 5, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, 6, 5, None, None, 7, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 7, 8, None, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, 5, 5, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, 10, 11, 12, 13, 14])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, None, None, 5, 6, 7, 8, 9, 10, None, None, 10, 9, 8, 7, 6, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, 6, 5, 7, 8, 8, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, None, None, 5, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, 3, 3, 4, None, None, 4, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, 5, None, 5, None, None, 6, 7])) == False\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().isSymmetric", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isSymmetric = function(root) {", "container": null, "callable": "isSymmetric", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 102, "task_id": "binary-tree-level-order-traversal", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, return the level order traversal of its nodes' values. (i.e., from left to right, level by level).\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: [[3],[9,20],[15,7]]\n\nExample 2:\n\nInput: root = [1]\nOutput: [[1]]\n\nExample 3:\n\nInput: root = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 2000].\n-1000 <= Node.val <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == [[3], [9, 20], [15, 7]]\n assert candidate(root = tree_node([1])) == [[1]]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [[1], [2, 3], [4, 5, 6, 7]]\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == [[0], [2, 4], [1, 3, -1], [5, 1, 6, 8]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [[1], [2], [3], [4], [5]]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19])) == [[0], [-1, -2], [-3, -4, -5, -6], [-7, -8, -9, -10, -11, -12, -13, -14], [-15, -16, -17, -18, -19]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15], [16]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]\n assert candidate(root = tree_node([3, 9, 20, 10, None, None, 15, 7, 8, 11, 16])) == [[3], [9, 20], [10, 15], [7, 8, 11, 16]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5])) == [[1], [2, 3], [4, 5]]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, None, 6, None, None, 7])) == [[1], [2, 3], [4, 5], [6], [7]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 18, 19, 21, None, None, None, None, 22, 23, 24, 25, 26, None, 27, 28, 29, 30])) == [[3], [9, 20], [15, 7, 18, 19], [21, 22, 23, 24], [25, 26, 27, 28, 29, 30]]\n assert candidate(root = tree_node([1, None, 3, 2, 4, None, 5, 6])) == [[1], [3], [2, 4], [5, 6]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, 7, 8, 9])) == [[1], [2, 3], [4, 5], [6, 7, 8, 9]]\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == [[1], [2, 2], [3, 3], [4, 4]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11], [12, 13, 14, 15]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, None, 16, 18])) == [[3], [9, 20], [15, 7], [12, 16, 18]]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4])) == [[1], [2]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 16, 8, 17, 18, 19, 20, 21, 22, 23, 24])) == [[3], [9, 20], [15, 7, 16, 8], [17, 18, 19, 20, 21, 22, 23, 24]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, 9, None, None, 10, None, 11, None, None, 12])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10], [11, 12]]\n assert candidate(root = tree_node([1, 2, 3, None, None, None, 4, 5, 6])) == [[1], [2, 3], [4], [5, 6]]\n assert candidate(root = tree_node([3, 9, 20, 8, None, 15, 7, 10, 11, None, None, 16, 17])) == [[3], [9, 20], [8, 15, 7], [10, 11, 16, 17]]\n assert candidate(root = tree_node([3, 1, 4, None, None, 2, None, 5])) == [[3], [1, 4], [2], [5]]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == [[10], [5, 15], [6, 20]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7])) == [[1], [2, 3], [4, 5], [6], [7]]\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5])) == [[1], [2], [3], [4], [5]]\n assert candidate(root = tree_node([3, 9, 20, 11, 12, 13, 14, None, None, None, None, 15, None, None, None, 16])) == [[3], [9, 20], [11, 12, 13, 14], [15], [16]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19, 20])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == [[10], [5, 15], [3, 7, 18]]\n assert candidate(root = tree_node([1, None, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16])) == [[1], [2], [3, 4], [5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16]]\n assert candidate(root = tree_node([3, 9, 20, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])) == [[3], [9, 20], [12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8])) == [[1], [2, 3], [4, 5], [6, 7, 8]]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == [[1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20]]\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])) == [[6], [2, 8], [0, 4, 7, 9], [3, 5]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, 7])) == [[1], [2, 3], [4, 5], [6], [7]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, None, None, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [[1], [2, 3], [4, 5, 6, 7]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == [[5], [4, 8], [11, 13, 4], [7, 2, 1]]\n assert candidate(root = tree_node([1, None, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [[1], [2], [3, 4], [5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20]]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, 6, 7])) == [[1], [2, 3], [4, 5], [6, 7]]\n assert candidate(root = tree_node([3, None, 20, 15, 7])) == [[3], [20], [15, 7]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 10, 8, None, None, None, None, None, 12])) == [[3], [9, 20], [15, 7, 10, 8], [12]]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [[5], [1, 4], [3, 6]]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [[1], [2, 3], [4], [5], [6], [7], [8], [9], [10]]\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1])) == [[10], [5, -3], [3, 2, 11], [3, -2, 1]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 18, 19, 21])) == [[3], [9, 20], [15, 7], [18, 19, 21]]\n assert candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4, None, None, None, None, 9, 10])) == [[3], [5, 1], [6, 2, 0, 8], [7, 4], [9, 10]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]]\n assert candidate(root = tree_node([1, None, 2, 3])) == [[1], [2], [3]]\n assert candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4])) == [[3], [5, 1], [6, 2, 0, 8], [7, 4]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, 10, 11, 12, 13])) == [[1], [2, 3], [4, 5], [6, 7, 8, 9], [10, 11, 12, 13]]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == [[0], [-1, -2], [-3, -4, -5, -6], [-7, -8, -9, -10, -11, -12, -13, -14], [-15]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, 7])) == [[1], [2, 3], [4, 5], [6, 7]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14, 15]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 10, 8, 13, 14, 15, None, None, None, None, None, None, None, None, 16])) == [[3], [9, 20], [15, 7, 10, 8], [13, 14, 15], [16]]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == [[1], [2, 2], [3, 4, 4, 3]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == [[1], [2], [3], [4], [5]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == [[1], [2, 3], [4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4])) == [[1], [2, 2], [3, 3], [4, 4]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, 7, None, None, 8, None, 9])) == [[1], [2, 3], [4, 5, 6], [7, 8], [9]]\n assert candidate(root = tree_node([0, -1, 2, -2, None, 1, None, -3, None, None, -4])) == [[0], [-1, 2], [-2, 1], [-3, -4]]\n assert candidate(root = tree_node([3, 9, 20, None, 17, 15, 7])) == [[3], [9, 20], [17, 15, 7]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8])) == [[1], [2, 3], [4, 5, 6], [7, 8]]\n assert candidate(root = tree_node([0, -1, 2, -2, None, -3, None, -4, -5])) == [[0], [-1, 2], [-2, -3], [-4, -5]]\n assert candidate(root = tree_node([3, 9, 20, 8, 10, None, 17, 1, None, None, 18, 2, 5, None, None, None, 4, 6])) == [[3], [9, 20], [8, 10, 17], [1, 18, 2, 5], [4, 6]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == [[5], [4, 8], [11, 13, 4], [7, 2, 5, 1]]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().levelOrder", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var levelOrder = function(root) {", "container": null, "callable": "levelOrder", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 103, "task_id": "binary-tree-zigzag-level-order-traversal", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, return the zigzag level order traversal of its nodes' values. (i.e., from left to right, then right to left for the next level and alternate between).\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: [[3],[20,9],[15,7]]\n\nExample 2:\n\nInput: root = [1]\nOutput: [[1]]\n\nExample 3:\n\nInput: root = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 2000].\n-100 <= Node.val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [[1], [3, 2], [4, 5, 6, 7]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [[1], [2], [3], [4], [5]]\n assert candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4])) == [[3], [1, 5], [6, 2, 0, 8], [4, 7]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == [[3], [20, 9], [15, 7]]\n assert candidate(root = tree_node([1])) == [[1]]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]\n assert candidate(root = tree_node([1, None, 2, None, None, None, None, 3, None, None, None, None, None, 4])) == [[1], [2]]\n assert candidate(root = tree_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == [[10], [8, 9], [7, 6, 5, 4], [1, 2, 3]]\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == [[1], [2, 2], [3, 3], [4, 4]]\n assert candidate(root = tree_node([1, None, 3, None, None, 2, None])) == [[1], [3]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, None, None, 6, 9])) == [[10], [15, 5], [3, 7, 18], [9, 6]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [[1], [2], [3], [4], [5], [6], [7], [8], [9]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, None, 10, 11, 12, 13, None, None, 14, 15, 16, 17, 18, 19, 20])) == [[1], [3, 2], [4, 5, 6, 7], [13, 12, 11, 10, 9, 8], [14, 15, 16, 17, 18, 19, 20]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [[1], [2], [3], [4], [5], [6], [7], [8]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, 8, None, 9, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == [[1], [3, 2], [4, 5, 6], [9, 8, 7], [10, 11, 12], [15, 14, 13], [16, 17, 18], [20, 19]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, None, None, None, 6, None, 7, None, 8, None, 9])) == [[1], [3, 2], [4, 5]]\n assert candidate(root = tree_node([1, None, 2, 3, 4, None, None, 5, 6])) == [[1], [2], [3, 4], [6, 5]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 7, 8, 9, None, 11, None, None, 14, 15])) == [[1], [3, 2], [4, 7], [11, 9, 8], [14, 15]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])) == [[1], [3, 2], [4, 5, 6, 7], [15, 14, 13, 12, 11, 10, 9, 8], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, None, 6, 8, 14, 16, 19, None, None, None, None, None, None, None, None])) == [[10], [15, 5], [3, 7, 18], [14, 8, 6, 1], [16, 19]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, 7, None, 8, None, 9])) == [[1], [3, 2], [4, 5], [6], [7], [8], [9]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, 16, None, 17, None, None, 18, None, 19])) == [[1], [3, 2], [4, 5, 6, 7], [15, 14, 13, 12, 11, 10, 9, 8], [16, 17, 18, 19]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, None, 9, None, None, 10, 11, None, None, 12, None, 13, None, 14, None, None, 15])) == [[1], [3, 2], [4, 5, 6, 7], [8], [9], [10], [11], [12], [13], [14]]\n assert candidate(root = tree_node([3, 1, 4, 3, None, 1, 5])) == [[3], [4, 1], [3, 1, 5]]\n assert candidate(root = tree_node([8, 15, 10, 7, None, 12, 3, 2, None, 11, 13, None, None, 4, None, 5])) == [[8], [10, 15], [7, 12, 3], [13, 11, 2], [4, 5]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, 9])) == [[1], [3, 2], [4, 5, 6, 7], [9, 8]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, None, 10, 11, 12, 13])) == [[1], [3, 2], [4, 5], [9, 8, 7, 6], [10, 11, 12, 13]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 10, 8, 11, 12, 13, 14, 16, 17, 18, 19])) == [[3], [20, 9], [15, 7, 10, 8], [19, 18, 17, 16, 14, 13, 12, 11]]\n assert candidate(root = tree_node([2, 1, 3, 4, None, 5, 7, None, None, None, 6, None, 8, 9, 10])) == [[2], [3, 1], [4, 5, 7], [8, 6], [9, 10]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 8, 12, None, None, None, None, None, None, 14])) == [[3], [20, 9], [15, 7, 8, 12], [14]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, None, 13, 14, None, 18, 19, 20])) == [[3], [20, 9], [15, 7], [14, 13, 12], [18, 19, 20]]\n assert candidate(root = tree_node([5, 3, 8, 2, 4, 6, 9, 1, 7, None, 10, None, None, None, None, 11, 12])) == [[5], [8, 3], [2, 4, 6, 9], [10, 7, 1], [11, 12]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8, 9, 10])) == [[1], [3, 2], [4, 5, 6], [8, 7], [9, 10]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == [[1], [3, 2], [4, 5, 6, 7], [15, 14, 13, 12, 11, 10, 9, 8], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9, None, None, 10, 11, None, None, 12, 13])) == [[1], [3, 2], [4, 5], [7, 6], [8, 9], [11, 10], [12, 13]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9])) == [[1], [3, 2], [4, 5], [7, 6], [8, 9]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [[1], [3, 2], [4, 5, 6, 7], [15, 14, 13, 12, 11, 10, 9, 8], [16, 17, 18, 19, 20]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, None, 6, None, None, 7, None, None, 8])) == [[1], [3, 2], [4, 5], [6]]\n assert candidate(root = tree_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, None, None, 180, 190])) == [[10], [30, 20], [40, 50, 60, 70], [150, 140, 130, 120, 110, 100, 90, 80], [180, 190]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [[1], [3, 2], [4, 5, 6, 7], [15, 14, 13, 12, 11, 10, 9, 8]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, None, None, 9, 10])) == [[1], [3, 2], [4, 5, 6, 7], [8], [9], [10]]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4, None, None, None, 5])) == [[1], [2]]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, None, None, None, None, None, None, 5, 5])) == [[1], [2, 2], [3, 4, 4, 3], [5, 5]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 7, 8, 9, None, 12, None, 14, None, None, 15])) == [[1], [3, 2], [4, 7], [12, 9, 8], [14, 15]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == [[10], [15, 5], [3, 7, 18], [6, 1]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, None, 9, None, 10, None, 11])) == [[1], [3, 2], [4, 5, 6, 7], [10, 9, 8], [11]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])) == [[1], [3, 2], [4, 5, 6, 7], [15, 14, 13, 12, 11, 10, 9, 8], [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 7, None, 8])) == [[1], [3, 2], [4, 5], [6], [7], [8]]\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, None, None, None, 4])) == [[1], [2]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, None, None, 16, 17, 18, 19])) == [[3], [20, 9], [15, 7]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, None, 6, None, None, 7, 8, None, None, None, None, 9])) == [[1], [3, 2], [4, 5], [6], [7, 8]]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [[5], [4, 1], [3, 6]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, None, None, None, 14, 15, None, None, 16, 17])) == [[1], [3, 2], [4, 5, 6, 7], [13, 12, 11, 10, 9, 8], [14, 15, 16, 17]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, 7, 8, 9, 10, None, None, None, None, 11, 12, 13, None, None, 14, None, 15])) == [[1], [3, 2], [4, 5], [9, 8, 7, 6], [10, 11, 12, 13], [15, 14]]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 8, None, 13, 19, None, None, None, None, 18])) == [[7], [15, 3], [9, 20], [8], [13, 19]]\n assert candidate(root = tree_node([3, 1, None, None, 2, None, 3, None, None, 4, None, 5, None, 6])) == [[3], [1], [2], [3]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, None, None, 10, None, None, 11, 12])) == [[1], [3, 2], [4, 5, 6, 7], [10, 9, 8], [11, 12]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, 10, 11, None, None, 12, 13, 14, 15, None, None, 16, 17])) == [[1], [3, 2], [4, 5, 6, 7], [11, 10, 9, 8], [12, 13, 14, 15, 16, 17]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9, None, 10])) == [[1], [3, 2], [4, 5], [7, 6], [8, 9], [10]]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == [[0], [-2, -1], [-3, -4, -5, -6], [-14, -13, -12, -11, -10, -9, -8, -7], [-15]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [[1], [2], [3], [4], [5], [6], [7]]\n assert candidate(root = tree_node([100, -50, -20, None, -10, None, None, -15])) == [[100], [-20, -50], [-10], [-15]]\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == [[0], [4, 2], [1, 3, -1], [8, 6, 1, 5]]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9, None, None, None, None, 10, 11])) == [[1], [3, 2], [4, 5], [7, 6], [8, 9]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 7, None, None, 8, None, None, 9])) == [[1], [3, 2], [4, 5], [6], [7], [8]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, None, 13, None, None, 16, 17])) == [[1], [3, 2], [4, 5, 6, 7], [13, 11, 10, 9, 8], [16, 17]]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 6, 10, None, 2, None, None, None, None, None, 9, None, 11])) == [[5], [8, 3], [1, 4, 6, 10], [9, 2], [11]]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [[1], [3, 2], [4, 5], [7, 6], [8, 9], [10]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == [[1], [3, 2], [4, 5, 6], [9, 8, 7], [10, 11, 12]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, 10, 11, 12, None, None, None, None, None, 13])) == [[1], [3, 2], [4, 5, 6, 7], [12, 11, 10, 9, 8], [13]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, None, 9, 10, None, None, 11, 12])) == [[1], [3, 2], [4, 5], [8, 7, 6], [9, 10, 11, 12]]\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, 6, None, 7, None, 8, None, 9])) == [[1], [2], [3], [4], [5, 6], [8, 7], [9]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, 9, None, None, 10, None, None, 11, 12, None, None, 13, None, None, None, None, 14])) == [[1], [3, 2], [4, 5, 6, 7], [9, 8], [10], [11], [12], [13]]\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 7, 8, None, 11, None, 14])) == [[1], [3, 2], [5, 7], [11, 8], [14]]\n assert candidate(root = tree_node([5, 4, 1, None, 1, 2, None, 2, 3, None, 4, None, 5])) == [[5], [1, 4], [1, 2], [4, 3, 2], [5]]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == [[1], [2, 2], [3, 4, 4, 3]]\n assert candidate(root = tree_node([0, -1, 2, -2, None, -3, None, -4, None, -5, None, -6, None, -7, None])) == [[0], [2, -1], [-2, -3], [-5, -4], [-6, -7]]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, None, None, 5, 5, 5, 5, None, None, None, None, None, None, None, None, None, None])) == [[1], [2, 2], [3, 3, 3, 3], [4, 4, 4, 4, 4, 4, 4, 4], [5, 5, 5, 5]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, None, 7, 8, None, None, 9, 10])) == [[1], [3, 2], [4, 5, 6], [8, 7], [9, 10]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, None, None, 6, None, 16, 20, None, None, 19])) == [[10], [15, 5], [3, 7, 18], [20, 16, 6], [19]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, 9, 10, None, None, 11, 12])) == [[1], [3, 2], [4, 5, 6, 7], [11, 10, 9, 8], [12]]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().zigzagLevelOrder", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var zigzagLevelOrder = function(root) {", "container": null, "callable": "zigzagLevelOrder", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 104, "task_id": "maximum-depth-of-binary-tree", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, return its maximum depth.\nA binary tree's maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: 3\n\nExample 2:\n\nInput: root = [1,null,2]\nOutput: 2\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 104].\n-100 <= Node.val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == 3\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 5, 5])) == 4\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 4\n assert candidate(root = tree_node([1, None, 3, 2, None, 4, 5])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5])) == 3\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, None, 8])) == 4\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4])) == 4\n assert candidate(root = tree_node([1, None, 2])) == 2\n assert candidate(root = tree_node([1, None, None, 2, None, None, 3, None, None, 4, None, None, 5])) == 1\n assert candidate(root = tree_node([0])) == 1\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == 3\n assert candidate(root = tree_node([1])) == 1\n assert candidate(root = tree_node([])) == 0\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 8, None, 6, None, 4, None, 1, None])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 10\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == 4\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 16, 8, 13, 14, 18, 19, 20, 21, 22, 23])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7])) == 5\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == 3\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 4, 4])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9])) == 4\n assert candidate(root = tree_node([1, -2, -3, 4, 5, -6, -7, 8, 9, -10, -11, -12, -13, -14, -15])) == 4\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, 16, None, 17, None, None, None, None, 18])) == 4\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == 15\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 9\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, 8, None, None, None, None, None, 9])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == 8\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14])) == 8\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 10, 11, None, 12])) == 4\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, None, None, 7, 8, 9])) == 6\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == 8\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 16, 17, 18, 19, None, None, 20, None])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])) == 5\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 8, None, 6, None, 4, None, 1, None, 2])) == 6\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6])) == 3\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 6, None, None, 6, 5])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, 16])) == 5\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, None, None, 6, 7, None, None, 8, 9])) == 5\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, None, 6, None, 7])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9, 10, 11, 12, 13])) == 5\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, None, None, None, None, 17, 20])) == 4\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 5, None, None, 4, 5])) == 5\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 8, None, 9, None, None, 10])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 8, 9, 10, None, None, 11, 12])) == 5\n assert candidate(root = tree_node([2, -1, -2, None, -3, None, -4, None, -5])) == 4\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7])) == 4\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30, None, 31, None, 32])) == 32\n assert candidate(root = tree_node([10, 9, 20, None, None, 15, 7, 12, 13, 14, 15])) == 4\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 8, 10, 11, None, 12])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, None, None, 8, None, 9])) == 6\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 5\n assert candidate(root = tree_node([3, 9, None, 15, 7, 25, 30, 35, None, None, None, 40, None, None, None, None, 45])) == 6\n assert candidate(root = tree_node([2, 1, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 6\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == 5\n assert candidate(root = tree_node([5, 4, 7, 3, None, 2, None, -1, None, 9])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, None, None, 6, 7, 8, 9])) == 5\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, 4])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])) == 6\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 8, 9])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, None, 7, None, 8])) == 6\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, None, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 9\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, None, None, 6, None, None, 7, None, None, 8, None, None, 9])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, None, None, None, 9])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, 9, None, 10, None, 11, None, 12])) == 5\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 1, None, 18, None, None, 21])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == 7\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, None, None, 9, None, None, None, None, 10])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, 7, None, 8, None, 9])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, None, None, None, None, None, None, None, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == 8\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == 15\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 16, 17, None, None, None, None, 18])) == 4\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 4, None, None, 4, 4])) == 5\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, None, None, 7, 8, 9, 10, None, None, 11, 12])) == 5\n assert candidate(root = tree_node([50, 25, 75, 10, 35, 65, 100, None, None, 30, 40, 60, 80, None, None, None, None, 90, 110])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == 20\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == 4\n assert candidate(root = tree_node([3, 9, 20, 8, 10, 15, 7, 6, None, None, None, None, 18])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32])) == 6\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == 6\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 16, 17, None, None, 18, 19])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])) == 7\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 6\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, None, None, 10, 11, None, None, 12, 13, None, None, 14, 15])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == 12\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, None, None, 5, 5])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13])) == 13\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 9\n assert candidate(root = tree_node([3, 9, 20, 15, 7, None, None, 8, None, None, None, None, 10])) == 5\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 11\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, None, 10])) == 4\n assert candidate(root = tree_node([1, None, None, None, None, None, None])) == 1\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, 9, None, None, 10, 11, 12, None, None, 13, 14, 15, None, None, None, None, None, None, 16])) == 6\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, 7, None, None, None, None, None, None, 8, 9])) == 4\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, None, None, 10, None, 11])) == 5\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == 4\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().maxDepth", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxDepth = function(root) {", "container": null, "callable": "maxDepth", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 105, "task_id": "construct-binary-tree-from-preorder-and-inorder-traversal", "difficulty": "Medium", "problem_description": "Given two integer arrays preorder and inorder where preorder is the preorder traversal of a binary tree and inorder is the inorder traversal of the same tree, construct and return the binary tree.\n \nExample 1:\n\n\nInput: preorder = [3,9,20,15,7], inorder = [9,3,15,20,7]\nOutput: [3,9,20,null,null,15,7]\n\nExample 2:\n\nInput: preorder = [-1], inorder = [-1]\nOutput: [-1]\n\n \nConstraints:\n\n1 <= preorder.length <= 3000\ninorder.length == preorder.length\n-3000 <= preorder[i], inorder[i] <= 3000\npreorder and inorder consist of unique values.\nEach value of inorder also appears in preorder.\npreorder is guaranteed to be the preorder traversal of the tree.\ninorder is guaranteed to be the inorder traversal of the tree.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(preorder = [3, 9, 20, 15, 7],inorder = [9, 3, 15, 20, 7]), tree_node([3, 9, 20, None, None, 15, 7]))\n assert is_same_tree(candidate(preorder = [1, 2, 4, 5, 3, 6, 7],inorder = [4, 2, 5, 1, 6, 3, 7]), tree_node([1, 2, 3, 4, 5, 6, 7]))\n assert is_same_tree(candidate(preorder = [-1],inorder = [-1]), tree_node([-1]))\n assert is_same_tree(candidate(preorder = [1, 2, 3],inorder = [2, 1, 3]), tree_node([1, 2, 3]))\n assert is_same_tree(candidate(preorder = [1, 2],inorder = [2, 1]), tree_node([1, 2]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 1, 4, 2, 6, 7, 12, 10, 9, 11, 15, 13, 14, 16, 18, 17, 19],inorder = [1, 3, 2, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]), tree_node([8, 5, 12, 3, 6, 10, 15, 1, 4, 7, None, 9, 11, 13, 16, None, None, 2, None, None, None, None, None, None, None, None, 14, None, 18, None, None, None, None, 17, 19]))\n assert is_same_tree(candidate(preorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]), tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15]))\n assert is_same_tree(candidate(preorder = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],inorder = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]), tree_node([1, None, 3, None, 5, None, 7, None, 9, None, 11, None, 13, None, 15, None, 17, None, 19, None, 21, None, 23, None, 25, None, 27, None, 29]))\n assert is_same_tree(candidate(preorder = [8, 3, 1, 6, 4, 7, 10, 14, 13],inorder = [1, 3, 4, 6, 7, 8, 10, 13, 14]), tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13]))\n assert is_same_tree(candidate(preorder = [20, 10, 5, 3, 2, 1, 7, 6, 15, 12, 11, 14, 18, 16, 17, 25, 22, 21, 23, 27, 26, 28, 29],inorder = [1, 2, 3, 5, 6, 7, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29]), tree_node([20, 10, 25, 5, 15, 22, 27, 3, 7, 12, 18, 21, 23, 26, 28, 2, None, 6, None, 11, 14, 16, None, None, None, None, None, None, None, None, 29, 1, None, None, None, None, None, None, None, None, 17]))\n assert is_same_tree(candidate(preorder = [150, 75, 30, 15, 25, 60, 45, 55, 90, 80, 120, 110, 130, 200, 175, 160, 180, 225, 210, 230],inorder = [15, 25, 30, 45, 55, 60, 75, 80, 90, 110, 120, 130, 150, 160, 175, 180, 200, 210, 225, 230]), tree_node([150, 75, 200, 30, 90, 175, 225, 15, 60, 80, 120, 160, 180, 210, 230, None, 25, 45, None, None, None, 110, 130, None, None, None, None, None, None, None, None, None, None, None, 55]))\n assert is_same_tree(candidate(preorder = [10, 8, 7, 9, 15, 12, 11, 13, 14, 20, 18, 17, 19, 25, 22, 23, 24, 27, 26, 28, 29],inorder = [7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29]), tree_node([10, 8, 15, 7, 9, 12, 20, None, None, None, None, 11, 13, 18, 25, None, None, None, 14, 17, 19, 22, 27, None, None, None, None, None, None, None, 23, 26, 28, None, 24, None, None, None, 29]))\n assert is_same_tree(candidate(preorder = [5, 3, 2, 1, 4, 7, 6, 8, 10, 9, 11],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]), tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, None, None, 10, None, None, 9, 11]))\n assert is_same_tree(candidate(preorder = [10, 6, 4, 3, 5, 8, 7, 9, 15, 12, 11, 13, 14],inorder = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]), tree_node([10, 6, 15, 4, 8, 12, None, 3, 5, 7, 9, 11, 13, None, None, None, None, None, None, None, None, None, None, None, 14]))\n assert is_same_tree(candidate(preorder = [15, 6, 3, 2, 5, 7, 18, 13, 20, 17, 19],inorder = [2, 3, 5, 6, 7, 15, 13, 18, 17, 19, 20]), tree_node([15, 6, 18, 3, 7, 13, 20, 2, 5, None, None, None, None, 17, None, None, None, None, None, None, 19]))\n assert is_same_tree(candidate(preorder = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14],inorder = [2, 4, 5, 3, 6, 7, 1, 10, 11, 8, 12, 13, 9, 14, 15]), tree_node([1, 3, 9, 2, 7, 8, 15, None, 5, 6, None, 11, 13, 14, None, 4, None, None, None, 10, None, 12]))\n assert is_same_tree(candidate(preorder = [50, 20, 10, 5, 1, 2, 30, 25, 22, 23, 35, 32, 31, 33, 40, 38, 39, 60, 55, 52, 51, 53, 58, 56, 57, 65, 62, 61, 63, 68, 66, 67, 69],inorder = [1, 2, 5, 10, 20, 22, 23, 25, 30, 31, 32, 33, 35, 38, 39, 40, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69]), tree_node([50, 20, 60, 10, 30, 55, 65, 5, None, 25, 35, 52, 58, 62, 68, 1, None, 22, None, 32, 40, 51, 53, 56, None, 61, 63, 66, 69, None, 2, None, 23, 31, 33, 38, None, None, None, None, None, None, 57, None, None, None, None, None, 67, None, None, None, None, None, None, None, None, None, None, None, 39]))\n assert is_same_tree(candidate(preorder = [25, 15, 10, 5, 3, 2, 4, 12, 11, 13, 30, 28, 27, 29, 35, 33, 32, 34, 37, 36, 38],inorder = [2, 3, 4, 5, 10, 12, 11, 13, 15, 30, 27, 28, 29, 25, 32, 33, 34, 35, 36, 38, 37]), tree_node([25, 15, 35, 10, 30, 33, 37, 5, 12, None, 28, 32, 34, 36, None, 3, None, None, 11, 27, 29, None, None, None, None, None, 38, 2, 4, None, 13]))\n assert is_same_tree(candidate(preorder = [10, 5, 1, 3, 7, 6, 8, 15, 12, 11, 13, 18, 17, 20, 19],inorder = [1, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19, 20]), tree_node([10, 5, 15, 1, 7, 12, 18, None, 3, 6, 8, 11, 13, 17, 20, None, None, None, None, None, None, None, None, None, None, None, None, 19]))\n assert is_same_tree(candidate(preorder = [10, 6, 2, 1, 3, 8, 5, 7, 12, 11, 13],inorder = [1, 2, 3, 6, 5, 7, 8, 10, 11, 12, 13]), tree_node([10, 6, 12, 2, 8, 11, 13, 1, 3, 5, None, None, None, None, None, None, None, None, None, None, 7]))\n assert is_same_tree(candidate(preorder = [8, 5, 9, 7, 3, 6, 2, 4, 1, 10, 11],inorder = [9, 5, 7, 8, 6, 3, 2, 4, 1, 10, 11]), tree_node([8, 5, 3, 9, 7, 6, 2, None, None, None, None, None, None, None, 4, None, 1, None, 10, None, 11]))\n assert is_same_tree(candidate(preorder = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]), tree_node([1, None, 3, 2, 5, None, None, 4, 7, None, None, 6, 9, None, None, 8, 11, None, None, 10, 13, None, None, 12, 15, None, None, 14]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 1, 4, 7, 6, 9, 12, 10, 11, 14, 13, 15],inorder = [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]), tree_node([8, 5, 9, 3, 7, None, 12, 1, 4, 6, None, 10, 14, None, None, None, None, None, None, None, 11, 13, 15]))\n assert is_same_tree(candidate(preorder = [20, 10, 5, 3, 7, 15, 13, 18, 25, 22, 27],inorder = [3, 5, 7, 10, 13, 15, 18, 20, 22, 25, 27]), tree_node([20, 10, 25, 5, 15, 22, 27, 3, 7, 13, 18]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 2, 4, 7, 6, 9, 12, 10, 11, 14, 13, 15, 17, 16, 18],inorder = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]), tree_node([8, 5, 9, 3, 7, None, 12, 2, 4, 6, None, 10, 14, None, None, None, None, None, None, None, 11, 13, 15, None, None, None, None, None, 17, 16, 18]))\n assert is_same_tree(candidate(preorder = [20, 10, 5, 1, 6, 15, 12, 18, 30, 25, 35],inorder = [1, 5, 6, 10, 12, 15, 18, 20, 25, 30, 35]), tree_node([20, 10, 30, 5, 15, 25, 35, 1, 6, 12, 18]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 1, 4, 7, 6, 9, 12, 10, 11, 13],inorder = [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]), tree_node([8, 5, 9, 3, 7, None, 12, 1, 4, 6, None, 10, 13, None, None, None, None, None, None, None, 11]))\n assert is_same_tree(candidate(preorder = [50, 30, 20, 10, 15, 40, 35, 37, 45, 60, 55, 52, 57, 70, 65, 75],inorder = [10, 15, 20, 30, 35, 37, 40, 45, 50, 52, 55, 57, 60, 65, 70, 75]), tree_node([50, 30, 60, 20, 40, 55, 70, 10, None, 35, 45, 52, 57, 65, 75, None, 15, None, 37]))\n assert is_same_tree(candidate(preorder = [7, 3, 1, 0, -1, 2, 5, 4, 6, 9, 8, 10, 11, 13, 12, 15, 14, 16, 18, 17, 20, 19, 22, 21, 23],inorder = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]), tree_node([7, 3, 9, 1, 5, 8, 10, 0, 2, 4, 6, None, None, None, 11, -1, None, None, None, None, None, None, None, None, 13, None, None, 12, 15, None, None, 14, 16, None, None, None, 18, 17, 20, None, None, 19, 22, None, None, 21, 23]))\n assert is_same_tree(candidate(preorder = [34, 23, 12, 9, 7, 8, 15, 13, 14, 26, 25, 27, 36, 35, 37, 45, 40, 42, 41, 43, 47, 46, 48],inorder = [7, 8, 9, 12, 13, 14, 15, 23, 25, 26, 27, 34, 35, 36, 37, 40, 41, 42, 43, 45, 46, 47, 48]), tree_node([34, 23, 36, 12, 26, 35, 37, 9, 15, 25, 27, None, None, None, 45, 7, None, 13, None, None, None, None, None, 40, 47, None, 8, None, 14, None, 42, 46, 48, None, None, None, None, 41, 43]))\n assert is_same_tree(candidate(preorder = [10, 5, 1, 3, 7, 6, 9, 8, 20, 15, 12, 18, 25],inorder = [1, 3, 5, 6, 7, 8, 9, 10, 12, 15, 18, 20, 25]), tree_node([10, 5, 20, 1, 7, 15, 25, None, 3, 6, 9, 12, 18, None, None, None, None, None, None, 8]))\n assert is_same_tree(candidate(preorder = [20, 10, 5, 3, 7, 15, 12, 18, 25, 22, 27],inorder = [3, 5, 7, 10, 12, 15, 18, 20, 22, 25, 27]), tree_node([20, 10, 25, 5, 15, 22, 27, 3, 7, 12, 18]))\n assert is_same_tree(candidate(preorder = [30, 15, 10, 5, 7, 25, 20, 18, 27, 40, 35, 32, 38, 50, 45, 55],inorder = [5, 7, 10, 15, 18, 20, 25, 27, 30, 32, 35, 38, 40, 45, 50, 55]), tree_node([30, 15, 40, 10, 25, 35, 50, 5, None, 20, 27, 32, 38, 45, 55, None, 7, 18]))\n assert is_same_tree(candidate(preorder = [100, 75, 60, 40, 50, 90, 80, 120, 110, 130],inorder = [40, 50, 60, 75, 80, 90, 100, 110, 120, 130]), tree_node([100, 75, 120, 60, 90, 110, 130, 40, None, 80, None, None, None, None, None, None, 50]))\n assert is_same_tree(candidate(preorder = [50, 30, 20, 10, 40, 70, 60, 90, 80, 110],inorder = [10, 20, 30, 40, 50, 60, 70, 80, 90, 110]), tree_node([50, 30, 70, 20, 40, 60, 90, 10, None, None, None, None, None, 80, 110]))\n assert is_same_tree(candidate(preorder = [20, 10, 5, 3, 1, 7, 15, 12, 9, 14, 18, 17, 25, 23, 22, 24, 30, 28, 27, 29, 32, 31],inorder = [1, 3, 5, 7, 10, 9, 12, 14, 15, 20, 22, 23, 24, 25, 17, 18, 27, 28, 29, 30, 31, 32]), tree_node([20, 10, 18, 5, 15, 17, 30, 3, 7, 12, None, 25, None, 28, 32, 1, None, None, None, 9, 14, 23, None, 27, 29, 31, None, None, None, None, None, None, None, 22, 24]))\n assert is_same_tree(candidate(preorder = [5, 3, 1, 4, 8, 6, 7, 10, 9],inorder = [1, 3, 4, 5, 6, 7, 8, 9, 10]), tree_node([5, 3, 8, 1, 4, 6, 10, None, None, None, None, None, 7, 9]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 1, 4, 7, 6, 9, 10, 11],inorder = [1, 3, 4, 5, 6, 7, 8, 9, 10, 11]), tree_node([8, 5, 9, 3, 7, None, 10, 1, 4, 6, None, None, 11]))\n assert is_same_tree(candidate(preorder = [100, 50, 25, 10, 30, 75, 60, 80, 150, 125, 175],inorder = [10, 25, 30, 50, 60, 75, 80, 100, 125, 150, 175]), tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80]))\n assert is_same_tree(candidate(preorder = [30, 15, 7, 3, 9, 22, 18, 20, 25, 40, 35, 37, 45, 50],inorder = [3, 7, 9, 15, 18, 20, 22, 25, 30, 35, 37, 40, 45, 50]), tree_node([30, 15, 40, 7, 22, 35, 45, 3, 9, 18, 25, None, 37, None, 50, None, None, None, None, None, 20]))\n assert is_same_tree(candidate(preorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]), tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 2, 4, 7, 6, 9, 11, 10, 12],inorder = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]), tree_node([8, 5, 9, 3, 7, None, 11, 2, 4, 6, None, 10, 12]))\n assert is_same_tree(candidate(preorder = [10, 5, 1, 2, 6, 3, 4, 8, 7, 9, 11, 12],inorder = [1, 2, 5, 3, 4, 6, 10, 7, 8, 9, 11, 12]), tree_node([10, 5, 8, 1, 6, 7, 9, None, 2, 3, None, None, None, None, 11, None, None, None, 4, None, 12]))\n assert is_same_tree(candidate(preorder = [5, 2, 1, 3, 4, 8, 6, 7, 9],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9]), tree_node([5, 2, 8, 1, 3, 6, 9, None, None, None, 4, None, 7]))\n assert is_same_tree(candidate(preorder = [21, 15, 10, 8, 12, 17, 16, 18, 25, 23, 24, 28, 27, 29, 30],inorder = [8, 10, 12, 15, 16, 17, 18, 21, 23, 24, 25, 27, 28, 29, 30]), tree_node([21, 15, 25, 10, 17, 23, 28, 8, 12, 16, 18, None, 24, 27, 29, None, None, None, None, None, None, None, None, None, None, None, None, None, 30]))\n assert is_same_tree(candidate(preorder = [7, 3, 1, 5, 4, 6, 10, 9, 11, 14, 12, 13, 15],inorder = [1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15]), tree_node([7, 3, 10, 1, 5, 9, 11, None, None, 4, 6, None, None, None, 14, None, None, None, None, 12, 15, None, 13]))\n assert is_same_tree(candidate(preorder = [1, 2, 3, 4, 5, 6, 7, 8, 9],inorder = [9, 8, 7, 6, 5, 4, 3, 2, 1]), tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9]))\n assert is_same_tree(candidate(preorder = [15, 5, 3, 2, 1, 4, 7, 6, 8, 10, 9, 11, 20, 18, 17, 19, 25, 23, 22, 24, 30, 28, 27, 29, 32, 31],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32]), tree_node([15, 5, 20, 3, 7, 18, 25, 2, 4, 6, 8, 17, 19, 23, 30, 1, None, None, None, None, None, None, 10, None, None, None, None, 22, 24, 28, 32, None, None, None, 9, None, None, None, None, 27, 29, 31, None, None, 11]))\n assert is_same_tree(candidate(preorder = [10, 5, 1, 7, 6, 11, 15, 12, 20, 18, 25],inorder = [1, 5, 6, 7, 10, 11, 12, 15, 18, 20, 25]), tree_node([10, 5, 11, 1, 7, None, 15, None, None, 6, None, 12, 20, None, None, None, None, 18, 25]))\n assert is_same_tree(candidate(preorder = [50, 30, 20, 10, 25, 40, 35, 45, 70, 60, 80],inorder = [10, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80]), tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45]))\n assert is_same_tree(candidate(preorder = [40, 20, 10, 5, 3, 8, 15, 13, 18, 30, 25, 28, 50, 45, 42, 47, 55, 52, 58],inorder = [3, 5, 8, 10, 13, 15, 18, 20, 25, 28, 30, 40, 42, 45, 47, 50, 52, 55, 58]), tree_node([40, 20, 50, 10, 30, 45, 55, 5, 15, 25, None, 42, 47, 52, 58, 3, 8, 13, 18, None, 28]))\n assert is_same_tree(candidate(preorder = [8, 5, 3, 1, 4, 6, 7, 12, 10, 9, 11, 14, 13, 15],inorder = [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]), tree_node([8, 5, 12, 3, 6, 10, 14, 1, 4, None, 7, 9, 11, 13, 15]))\n assert is_same_tree(candidate(preorder = [60, 30, 15, 5, 25, 45, 40, 50, 90, 80, 100, 95, 110],inorder = [5, 15, 25, 30, 40, 45, 50, 60, 80, 90, 95, 100, 110]), tree_node([60, 30, 90, 15, 45, 80, 100, 5, 25, 40, 50, None, None, 95, 110]))\n assert is_same_tree(candidate(preorder = [25, 15, 10, 5, 3, 7, 12, 20, 18, 17, 19, 30, 28, 27, 29, 32, 31],inorder = [3, 5, 7, 10, 12, 15, 17, 18, 19, 20, 25, 27, 28, 29, 30, 31, 32]), tree_node([25, 15, 30, 10, 20, 28, 32, 5, 12, 18, None, 27, 29, 31, None, 3, 7, None, None, 17, 19]))\n assert is_same_tree(candidate(preorder = [25, 15, 10, 5, 12, 20, 17, 30, 27, 32, 35],inorder = [5, 10, 12, 15, 17, 20, 25, 27, 30, 32, 35]), tree_node([25, 15, 30, 10, 20, 27, 32, 5, 12, 17, None, None, None, None, 35]))\n assert is_same_tree(candidate(preorder = [50, 20, 10, 5, 15, 40, 25, 30, 35, 70, 60, 55, 65, 80, 75, 85],inorder = [5, 10, 15, 20, 25, 30, 35, 40, 50, 55, 60, 65, 70, 75, 80, 85]), tree_node([50, 20, 70, 10, 40, 60, 80, 5, 15, 25, None, 55, 65, 75, 85, None, None, None, None, None, 30, None, None, None, None, None, None, None, None, None, 35]))\n assert is_same_tree(candidate(preorder = [7, 3, 1, 2, 5, 4, 6, 15, 9, 8, 10, 20, 18, 19, 25],inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 18, 19, 20, 25]), tree_node([7, 3, 15, 1, 5, 9, 20, None, 2, 4, 6, 8, 10, 18, 25, None, None, None, None, None, None, None, None, None, None, None, 19]))\n assert is_same_tree(candidate(preorder = [50, 25, 10, 5, 3, 7, 20, 15, 30, 27, 35, 40, 45, 55],inorder = [3, 5, 7, 10, 15, 20, 25, 27, 30, 35, 40, 45, 50, 55]), tree_node([50, 25, 55, 10, 30, None, None, 5, 20, 27, 35, 3, 7, 15, None, None, None, None, 40, None, None, None, None, None, None, None, 45]))\n assert is_same_tree(candidate(preorder = [10, 5, 1, 2, 3, 8, 6, 7, 15, 13, 12, 14, 20, 18, 17, 19, 25, 23, 22, 24, 28, 27, 26, 29],inorder = [1, 2, 3, 5, 6, 7, 8, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29]), tree_node([10, 5, 15, 1, 8, 13, 20, None, 2, 6, None, 12, 14, 18, 25, None, 3, None, 7, None, None, None, None, 17, 19, 23, 28, None, None, None, None, None, None, None, None, 22, 24, 27, 29, None, None, None, None, 26]))\n assert is_same_tree(candidate(preorder = [25, 15, 10, 4, 12, 6, 8, 20, 16, 22, 28, 27, 30, 32],inorder = [4, 10, 6, 8, 12, 15, 16, 20, 22, 25, 27, 28, 30, 32]), tree_node([25, 15, 28, 10, 20, 27, 30, 4, 12, 16, 22, None, None, None, 32, None, None, 6, None, None, None, None, None, None, None, None, 8]))\n assert is_same_tree(candidate(preorder = [10, 5, 2, 1, 3, 8, 6, 7, 15, 12, 11, 13, 20, 18, 19, 25],inorder = [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 18, 19, 20, 25]), tree_node([10, 5, 15, 2, 8, 12, 20, 1, 3, 6, None, 11, 13, 18, 25, None, None, None, None, None, 7, None, None, None, None, None, 19]))\n"}, "metadata": {"canonical_parameter_names": ["preorder", "inorder"], "leetcode_dataset_entry_point": "Solution().buildTree", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var buildTree = function(preorder, inorder) {", "container": null, "callable": "buildTree", "parameters": [{"name": "preorder", "type": "number[]"}, {"name": "inorder", "type": "number[]"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 106, "task_id": "construct-binary-tree-from-inorder-and-postorder-traversal", "difficulty": "Medium", "problem_description": "Given two integer arrays inorder and postorder where inorder is the inorder traversal of a binary tree and postorder is the postorder traversal of the same tree, construct and return the binary tree.\n \nExample 1:\n\n\nInput: inorder = [9,3,15,20,7], postorder = [9,15,7,20,3]\nOutput: [3,9,20,null,null,15,7]\n\nExample 2:\n\nInput: inorder = [-1], postorder = [-1]\nOutput: [-1]\n\n \nConstraints:\n\n1 <= inorder.length <= 3000\npostorder.length == inorder.length\n-3000 <= inorder[i], postorder[i] <= 3000\ninorder and postorder consist of unique values.\nEach value of postorder also appears in inorder.\ninorder is guaranteed to be the inorder traversal of the tree.\npostorder is guaranteed to be the postorder traversal of the tree.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(inorder = [-1],postorder = [-1]), tree_node([-1]))\n assert is_same_tree(candidate(inorder = [1, 2],postorder = [2, 1]), tree_node([1, None, 2]))\n assert is_same_tree(candidate(inorder = [3, 2, 1],postorder = [3, 2, 1]), tree_node([1, 2, None, 3]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5],postorder = [1, 2, 5, 4, 3]), tree_node([3, 2, 4, 1, None, None, 5]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4],postorder = [1, 2, 4, 3]), tree_node([3, 2, 4, 1]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7],postorder = [1, 3, 2, 5, 7, 6, 4]), tree_node([4, 2, 6, 1, 3, 5, 7]))\n assert is_same_tree(candidate(inorder = [9, 3, 15, 20, 7],postorder = [9, 15, 7, 20, 3]), tree_node([3, 9, 20, None, None, 15, 7]))\n assert is_same_tree(candidate(inorder = [4, 2, 5, 1, 6, 3, 7],postorder = [4, 5, 2, 6, 7, 3, 1]), tree_node([1, 2, 3, 4, 5, 6, 7]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],postorder = [1, 2, 4, 3, 6, 8, 10, 9, 7, 5, 12, 14, 16, 17, 15, 13, 11, 18, 20, 19]), tree_node([19, 18, 20, 11, None, None, None, 5, 13, 3, 7, 12, 15, 2, 4, 6, 9, None, None, 14, 17, 1, None, None, None, None, None, 8, 10, None, None, 16]))\n assert is_same_tree(candidate(inorder = [7, 10, 4, 3, 1, 2, 8, 11, 5, 9, 6],postorder = [7, 10, 4, 3, 11, 8, 9, 5, 6, 2, 1]), tree_node([1, 3, 2, 4, None, None, 6, 10, None, 5, None, 7, None, 8, 9, None, None, None, 11]))\n assert is_same_tree(candidate(inorder = [5, 4, 8, 7, 10, 9, 1, 3, 6, 2],postorder = [5, 8, 10, 9, 7, 4, 6, 3, 2, 1]), tree_node([1, 4, 2, 5, 7, 3, None, None, None, 8, 9, None, 6, None, None, 10]))\n assert is_same_tree(candidate(inorder = [3, 1, 4, 2, 5, 9, 6, 7, 8],postorder = [3, 4, 1, 9, 7, 8, 6, 5, 2]), tree_node([2, 1, 5, 3, 4, None, 6, None, None, None, None, 9, 8, None, None, 7]))\n assert is_same_tree(candidate(inorder = [2, 4, 5, 7, 11, 13, 15, 17, 19, 21, 23, 25],postorder = [2, 5, 4, 11, 15, 13, 7, 23, 25, 21, 19, 17]), tree_node([17, 7, 19, 4, 13, None, 21, 2, 5, 11, 15, None, 25, None, None, None, None, None, None, None, None, 23]))\n assert is_same_tree(candidate(inorder = [1, 2, 5, 3, 4, 6, 8, 7, 9, 11, 10, 12, 13, 14, 15],postorder = [1, 5, 2, 4, 3, 8, 11, 10, 12, 9, 7, 6, 14, 15, 13]), tree_node([13, 6, 15, 3, 7, 14, None, 2, 4, 8, 9, None, None, 1, 5, None, None, None, None, None, 12, None, None, None, None, 10, None, 11]))\n assert is_same_tree(candidate(inorder = [4, 2, 5, 1, 6, 9, 8, 7, 3, 11, 10],postorder = [4, 5, 2, 6, 9, 7, 8, 1, 11, 10, 3]), tree_node([3, 1, 10, 2, 8, 11, None, 4, 5, 9, 7, None, None, None, None, None, None, 6]))\n assert is_same_tree(candidate(inorder = [5, 3, 8, 1, 4, 9, 7, 2, 6, 11, 10, 12],postorder = [5, 8, 3, 9, 4, 1, 11, 12, 10, 6, 2, 7]), tree_node([7, 1, 2, 3, 4, None, 6, 5, 8, None, 9, None, 10, None, None, None, None, None, None, 11, 12]))\n assert is_same_tree(candidate(inorder = [5, 3, 7, 1, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],postorder = [5, 7, 3, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 1]), tree_node([1, 3, 29, 5, 7, 27, None, None, None, None, None, 25, None, 23, None, 21, None, 19, None, 17, None, 15, None, 13, None, 11, None, 9]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],postorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]), tree_node([20, 19, None, 18, None, 17, None, 16, None, 15, None, 14, None, 13, None, 12, None, 11, None, 10, None, 9, None, 8, None, 7, None, 6, None, 5, None, 4, None, 3, None, 2, None, 1]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12],postorder = [1, 3, 2, 5, 7, 6, 4, 9, 11, 12, 10, 8]), tree_node([8, 4, 10, 2, 6, 9, 12, 1, 3, 5, 7, None, None, 11]))\n assert is_same_tree(candidate(inorder = [16, 8, 17, 4, 18, 9, 19, 2, 20, 10, 21, 5, 22, 11, 23, 1, 24, 6, 25, 12, 26, 3, 27, 7, 28],postorder = [16, 17, 8, 18, 19, 9, 4, 20, 21, 10, 22, 11, 5, 23, 2, 24, 25, 12, 26, 6, 27, 28, 7, 3, 1]), tree_node([1, 2, 3, 4, 23, 6, 7, 8, 9, 5, None, 24, 26, 27, 28, 16, 17, 18, 19, 10, 11, None, None, 12, None, None, None, None, None, None, None, None, None, None, None, None, None, 20, 21, 22, None, 25]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9],postorder = [1, 3, 2, 5, 4, 7, 9, 8, 6]), tree_node([6, 4, 8, 2, 5, 7, 9, 1, 3]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],postorder = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14]), tree_node([14, 12, 15, 10, 13, None, None, 8, 11, None, None, 6, 9, None, None, 4, 7, None, None, 2, 5, None, None, 1, 3]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9],postorder = [1, 2, 4, 3, 6, 8, 9, 7, 5]), tree_node([5, 3, 7, 2, 4, 6, 9, 1, None, None, None, None, None, 8]))\n assert is_same_tree(candidate(inorder = [3, 1, 2, 4, 6, 5, 7],postorder = [3, 2, 1, 6, 7, 5, 4]), tree_node([4, 1, 5, 3, 2, 6, 7]))\n assert is_same_tree(candidate(inorder = [3, 9, 20, 15, 7, 10, 25, 30],postorder = [3, 15, 7, 20, 10, 30, 25, 9]), tree_node([9, 3, 25, None, None, 10, 30, 20, None, None, None, None, 7, 15]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],postorder = [1, 3, 2, 5, 4, 7, 6, 9, 11, 13, 15, 14, 12, 10, 8]), tree_node([8, 6, 10, 4, 7, 9, 12, 2, 5, None, None, None, None, 11, 14, 1, 3, None, None, None, None, 13, 15]))\n assert is_same_tree(candidate(inorder = [10, 5, 15, 3, 7, 18, 12, 20, 25],postorder = [10, 15, 5, 7, 3, 18, 25, 20, 12]), tree_node([12, 18, 20, 3, None, None, 25, 5, 7, None, None, 10, 15]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],postorder = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]), tree_node([2, 1, 4, None, None, 3, 6, None, None, 5, 8, None, None, 7, 10, None, None, 9, 12, None, None, 11, 14, None, None, 13, 16, None, None, 15, 18, None, None, 17, 20, None, None, 19]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],postorder = [1, 3, 5, 7, 9, 11, 13, 15, 14, 12, 10, 8, 6, 4, 2]), tree_node([2, 1, 4, None, None, 3, 6, None, None, 5, 8, None, None, 7, 10, None, None, 9, 12, None, None, 11, 14, None, None, 13, 15]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16],postorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]), tree_node([16, 15, None, 14, None, 13, None, 12, None, 11, None, 10, None, 9, None, 8, None, 7, None, 6, None, 5, None, 4, None, 3, None, 2, None, 1]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],postorder = [1, 3, 5, 7, 9, 10, 8, 6, 4, 2]), tree_node([2, 1, 4, None, None, 3, 6, None, None, 5, 8, None, None, 7, 10, None, None, 9]))\n assert is_same_tree(candidate(inorder = [1, 3, 2, 6, 5, 7, 4, 8, 10, 9],postorder = [1, 3, 6, 7, 5, 2, 10, 9, 8, 4]), tree_node([4, 2, 8, 3, 5, None, 9, 1, None, 6, 7, 10]))\n assert is_same_tree(candidate(inorder = [8, 5, 11, 1, 2, 6, 9, 3, 13, 7, 10],postorder = [8, 11, 5, 2, 6, 1, 9, 13, 10, 7, 3]), tree_node([3, 9, 7, 1, None, 13, 10, 5, 6, None, None, None, None, 8, 11, 2]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],postorder = [1, 3, 2, 5, 7, 6, 4, 9, 11, 13, 14, 12, 10, 8, 15]), tree_node([15, 8, None, 4, 10, 2, 6, 9, 12, 1, 3, 5, 7, None, None, 11, 14, None, None, None, None, None, None, None, None, None, None, 13]))\n assert is_same_tree(candidate(inorder = [1, 5, 3, 6, 2, 7, 4, 8],postorder = [1, 5, 6, 3, 7, 8, 4, 2]), tree_node([2, 3, 4, 5, 6, 7, 8, 1]))\n assert is_same_tree(candidate(inorder = [4, 2, 5, 1, 6, 3, 8, 10, 7, 9],postorder = [4, 5, 2, 6, 8, 10, 9, 7, 3, 1]), tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 10, 9, 8]))\n assert is_same_tree(candidate(inorder = [8, 4, 9, 2, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15],postorder = [8, 9, 4, 10, 11, 5, 2, 12, 13, 6, 14, 15, 7, 3, 1]), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(inorder = [5, 4, 6, 2, 7, 8, 3, 1, 9],postorder = [5, 6, 4, 8, 7, 3, 9, 1, 2]), tree_node([2, 4, 1, 5, 6, 3, 9, None, None, None, None, 7, None, None, None, None, 8]))\n assert is_same_tree(candidate(inorder = [16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],postorder = [16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]), tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17],postorder = [1, 3, 2, 5, 4, 7, 6, 9, 11, 13, 15, 17, 16, 14, 12, 10, 8]), tree_node([8, 6, 10, 4, 7, 9, 12, 2, 5, None, None, None, None, 11, 14, 1, 3, None, None, None, None, 13, 16, None, None, None, None, None, None, 15, 17]))\n assert is_same_tree(candidate(inorder = [1, 2, 3, 4, 5, 6, 7, 8, 9],postorder = [1, 3, 5, 7, 9, 8, 6, 4, 2]), tree_node([2, 1, 4, None, None, 3, 6, None, None, 5, 8, None, None, 7, 9]))\n assert is_same_tree(candidate(inorder = [5, 3, 7, 2, 8, 9, 4, 10, 1, 6, 11, 12],postorder = [5, 7, 3, 8, 9, 2, 10, 4, 11, 12, 6, 1]), tree_node([1, 4, 6, 2, 10, None, 12, 3, 9, None, None, 11, None, 5, 7, 8]))\n"}, "metadata": {"canonical_parameter_names": ["inorder", "postorder"], "leetcode_dataset_entry_point": "Solution().buildTree", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var buildTree = function(inorder, postorder) {", "container": null, "callable": "buildTree", "parameters": [{"name": "inorder", "type": "number[]"}, {"name": "postorder", "type": "number[]"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 107, "task_id": "binary-tree-level-order-traversal-ii", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, return the bottom-up level order traversal of its nodes' values. (i.e., from left to right, level by level from leaf to root).\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: [[15,7],[9,20],[3]]\n\nExample 2:\n\nInput: root = [1]\nOutput: [[1]]\n\nExample 3:\n\nInput: root = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 2000].\n-1000 <= Node.val <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == [[15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([1])) == [[1]]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [[4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == [[5, 1, 6, 8], [1, 3, -1], [2, 4], [0]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [[5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([3, 1, 4, None, 2])) == [[2], [1, 4], [3]]\n assert candidate(root = tree_node([3, 9, 20, 8, None, 15, 7, 4, 5, None, None, 6])) == [[4, 5, 6], [8, 15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [[10], [9], [8], [7], [6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8])) == [[7, 8], [4, 5, 6], [2, 3], [1]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == [[6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5])) == [[4, 5], [2, 3], [1]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [[12, 13, 14, 15], [8, 9, 10, 11], [4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 2, 25, 8, 6, 1, 12, 9, 4, 18, 10])) == [[8, 6, 1, 12, 9, 4, 18, 10], [15, 7, 2, 25], [9, 20], [3]]\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, None, None, 4, None])) == [[2], [1]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, 17, 18, 20, None, None, None, None, None, None, 1])) == [[1], [12, 17, 18, 20], [15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([3, 1, 4, None, 2, None, None])) == [[2], [1, 4], [3]]\n assert candidate(root = tree_node([5, None, 4, None, 3, None, 2, None, 1])) == [[1], [2], [3], [4], [5]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, None, None, 18, 25, 27])) == [[25, 27], [12, 18], [15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16])) == [[16], [15], [14], [13], [12], [11], [10], [9], [8], [7], [6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == [[6, 20], [5, 15], [10]]\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5])) == [[5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([3, 9, 20, 10, None, 15, 7, 5, 11, 18])) == [[5, 11, 18], [10, 15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 25, None, None, 22])) == [[22], [25], [15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == [[3, 7, 18], [5, 15], [10]]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 4, 4])) == [[4, 4, 4, 4], [3, 3], [2, 2], [1]]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9])) == [[-7, -8, -9], [-3, -4, -5, -6], [-1, -2], [0]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, None, 17, 18, 19, 20, 21, 22, 23])) == [[16, 17, 18, 19, 20, 21, 22, 23], [8, 9, 10, 11, 12, 13, 14, 15], [4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [[9], [8], [7], [6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180, 5, 15, 20, 35, 65, 70, 85, 105, 115, 135, 145, 155, 175, 185])) == [[5, 15, 20, 35, 65, 70, 85, 105, 115, 135, 145, 155, 175, 185], [10, 30, 60, 80, 110, 140, 160, 180], [25, 75, 125, 175], [50, 150], [100]]\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])) == [[3, 5], [0, 4, 7, 9], [2, 8], [6]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == [[7, 2, 5, 1], [11, 13, 4], [4, 8], [5]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == [[7, 2, 1], [11, 13, 4], [4, 8], [5]]\n assert candidate(root = tree_node([0, None, 1, None, 2, None, 3, None, 4])) == [[4], [3], [2], [1], [0]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 7, 8, 9, 10, 11, None, 13, None, None, 14, 15])) == [[14, 15], [8, 9, 10, 11, 13], [4, 5, 7], [2, 3], [1]]\n assert candidate(root = tree_node([3, 9, 20, 8, 10, 15, 7, None, None, None, 13, None, None, None, 17])) == [[13, 17], [8, 10, 15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])) == [[-7, -8, -9, -10], [-3, -4, -5, -6], [-1, -2], [0]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [[9], [8], [7], [6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 16, 17])) == [[16, 17], [15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [[3, 6], [1, 4], [5]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 14, 15])) == [[14, 15], [8, 9, 10, 11, 12, 13], [4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [[8], [7], [6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8, 9])) == [[9], [7, 8], [4, 5, 6], [2, 3], [1]]\n assert candidate(root = tree_node([10, -5, 15, None, -8, None, 20, -12, None, None, 18])) == [[-12, 18], [-8, 20], [-5, 15], [10]]\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180])) == [[10, 30, 60, 80, 110, 140, 160, 180], [25, 75, 125, 175], [50, 150], [100]]\n assert candidate(root = tree_node([10, None, 20, 30, 40, None, 50, None, None, 60, 70])) == [[60, 70], [50], [30, 40], [20], [10]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, 6, None, None, 3, None, None, None, 9])) == [[9], [6, 3], [7, 2, 5, 1], [11, 13, 4], [4, 8], [5]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == [[16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [8, 9, 10, 11, 12, 13, 14, 15], [4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4])) == [[7, 4], [6, 2, 0, 8], [5, 1], [3]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [[16, 17, 18, 19, 20], [8, 9, 10, 11, 12, 13, 14, 15], [4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6, 2, None, None, None, None, 7])) == [[7], [2], [3, 6], [1, 4], [5]]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, None, 2, None, None, None, 6, None, None, 11, 12])) == [[11, 12], [2, 6], [1, 4, 7, 9], [3, 8], [5]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [[8, 9, 10, 11, 12, 13, 14, 15], [4, 5, 6, 7], [2, 3], [1]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1, None, 3, None, None])) == [[3], [7, 2, 1], [11, 13, 4], [4, 8], [5]]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7])) == [[6, 7], [4, 5], [2, 3], [1]]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == [[3, 4, 4, 3], [2, 2], [1]]\n assert candidate(root = tree_node([5, 1, 4, 3, None, 6, 7])) == [[3, 6, 7], [1, 4], [5]]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6])) == [[2], [1]]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7, None, 8])) == [[8], [7], [6], [4, 5], [2, 3], [1]]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4])) == [[4, 4], [3, 3], [2, 2], [1]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [[7], [6], [5], [4], [3], [2], [1]]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == [[-15], [-7, -8, -9, -10, -11, -12, -13, -14], [-3, -4, -5, -6], [-1, -2], [0]]\n assert candidate(root = tree_node([3, 9, 20, 10, None, 15, 7, 11, None, 13, 14])) == [[11, 13, 14], [10, 15, 7], [9, 20], [3]]\n assert candidate(root = tree_node([3, 9, 20, 10, 11, 15, 7, None, None, 12, None, 16, 13, None, None, None, 14, 17, 18])) == [[14, 17, 18], [12, 16, 13], [10, 11, 15, 7], [9, 20], [3]]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().levelOrderBottom", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var levelOrderBottom = function(root) {", "container": null, "callable": "levelOrderBottom", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 108, "task_id": "convert-sorted-array-to-binary-search-tree", "difficulty": "Easy", "problem_description": "Given an integer array nums where the elements are sorted in ascending order, convert it to a height-balanced binary search tree.\n \nExample 1:\n\n\nInput: nums = [-10,-3,0,5,9]\nOutput: [0,-3,9,-10,null,5]\nExplanation: [0,-10,5,null,-3,null,9] is also accepted:\n\n\nExample 2:\n\n\nInput: nums = [1,3]\nOutput: [3,1]\nExplanation: [1,null,3] and [3,1] are both height-balanced BSTs.\n\n \nConstraints:\n\n1 <= nums.length <= 104\n-104 <= nums[i] <= 104\nnums is sorted in a strictly increasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(nums = [0]), tree_node([0]))\n assert is_same_tree(candidate(nums = [1, 3]), tree_node([1, None, 3]))\n assert is_same_tree(candidate(nums = [-10, -3, 0, 5, 9]), tree_node([0, -10, 5, None, -3, None, 9]))\n assert is_same_tree(candidate(nums = [-1, 0, 1, 2]), tree_node([0, -1, 1, None, None, None, 2]))\n assert is_same_tree(candidate(nums = [-1, -2, -3, -4, -5]), tree_node([-3, -1, -4, None, -2, None, -5]))\n assert is_same_tree(candidate(nums = [1, 2, 3, 4, 5, 6, 7]), tree_node([4, 2, 6, 1, 3, 5, 7]))\n assert is_same_tree(candidate(nums = [-1, 0, 1]), tree_node([0, -1, 1]))\n assert is_same_tree(candidate(nums = [-10, -5, 0, 5, 10, 15, 20]), tree_node([5, -5, 15, -10, 0, 10, 20]))\n assert is_same_tree(candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97]), tree_node([49, 21, 73, 9, 33, 61, 85, 1, 13, 25, 41, 53, 65, 77, 93, None, 5, None, 17, None, 29, 37, 45, None, 57, None, 69, None, 81, 89, 97]))\n assert is_same_tree(candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]), tree_node([15, 7, 23, 3, 11, 19, 27, 1, 5, 9, 13, 17, 21, 25, 29, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 31]))\n assert is_same_tree(candidate(nums = [-20, -15, -10, -5, 0, 5, 10, 15, 20]), tree_node([0, -15, 10, -20, -10, 5, 15, None, None, None, -5, None, None, None, 20]))\n assert is_same_tree(candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]), tree_node([24, 11, 37, 5, 17, 30, 43, 2, 8, 14, 20, 27, 33, 40, 46, 0, 3, 6, 9, 12, 15, 18, 22, 25, 28, 31, 35, 38, 41, 44, 48, None, 1, None, 4, None, 7, None, 10, None, 13, None, 16, None, 19, 21, 23, None, 26, None, 29, None, 32, 34, 36, None, 39, None, 42, None, 45, 47, 49]))\n assert is_same_tree(candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]), tree_node([50, 25, 75, 10, 35, 60, 90, 5, 15, 30, 40, 55, 65, 80, 95, None, None, None, 20, None, None, None, 45, None, None, None, 70, None, 85, None, 100]))\n assert is_same_tree(candidate(nums = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]), tree_node([15, 5, 24, 0, 10, 19, 29, -2, 2, 7, 12, 17, 21, 26, 31, -3, -1, 1, 3, 6, 8, 11, 13, 16, 18, 20, 22, 25, 27, 30, 32, None, None, None, None, None, None, None, 4, None, None, None, 9, None, None, None, 14, None, None, None, None, None, None, None, 23, None, None, None, 28, None, None, None, 33]))\n assert is_same_tree(candidate(nums = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]), tree_node([0, -600, 500, -900, -300, 200, 800, -1000, -800, -500, -200, 100, 300, 600, 900, None, None, None, -700, None, -400, None, -100, None, None, None, 400, None, 700, None, 1000]))\n assert is_same_tree(candidate(nums = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]), tree_node([0, -60, 50, -90, -30, 20, 80, -100, -80, -50, -20, 10, 30, 60, 90, None, None, None, -70, None, -40, None, -10, None, None, None, 40, None, 70, None, 100]))\n assert is_same_tree(candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]), tree_node([15, 7, 23, 3, 11, 19, 27, 1, 5, 9, 13, 17, 21, 25, 29, None, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]))\n assert is_same_tree(candidate(nums = [-100, -50, -25, -10, -5, 0, 5, 10, 25, 50, 100]), tree_node([0, -25, 25, -100, -10, 5, 50, None, -50, None, -5, None, 10, None, 100]))\n assert is_same_tree(candidate(nums = [-500, -250, -125, -63, -31, -15, -7, -3, -1, 0, 1, 3, 7, 15, 31, 63, 125, 250, 500]), tree_node([0, -31, 31, -250, -7, 3, 125, -500, -125, -15, -3, 1, 7, 63, 250, None, None, None, -63, None, None, None, -1, None, None, None, 15, None, None, None, 500]))\n assert is_same_tree(candidate(nums = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]), tree_node([6, 1, 11, -2, 3, 8, 14, -3, -1, 2, 4, 7, 9, 12, 15, None, None, None, 0, None, None, None, 5, None, None, None, 10, None, 13, None, 16]))\n assert is_same_tree(candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]), tree_node([49, 23, 75, 11, 35, 61, 87, 5, 17, 29, 41, 55, 67, 81, 93, 1, 7, 13, 19, 25, 31, 37, 45, 51, 57, 63, 71, 77, 83, 89, 97, None, 3, None, 9, None, 15, None, 21, None, 27, None, 33, None, 39, 43, 47, None, 53, None, 59, None, 65, 69, 73, None, 79, None, 85, None, 91, 95, 99]))\n assert is_same_tree(candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]), tree_node([19, 9, 29, 3, 13, 23, 35, 1, 5, 11, 15, 21, 25, 31, 37, None, None, None, 7, None, None, None, 17, None, None, None, 27, None, 33, None, 39]))\n assert is_same_tree(candidate(nums = [-20, -15, -10, -5, 0, 1, 3, 5, 8, 10, 13, 15, 20]), tree_node([3, -10, 10, -20, 0, 5, 15, None, -15, -5, 1, None, 8, 13, 20]))\n assert is_same_tree(candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500]), tree_node([1300, 600, 1900, 300, 900, 1600, 2200, 100, 400, 700, 1100, 1400, 1700, 2000, 2400, None, 200, None, 500, None, 800, 1000, 1200, None, 1500, None, 1800, None, 2100, 2300, 2500]))\n assert is_same_tree(candidate(nums = [-200, -190, -180, -170, -160, -150, -140, -130, -120, -110, -100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]), tree_node([0, -110, 100, -160, -60, 50, 150, -190, -140, -90, -30, 20, 70, 120, 180, -200, -180, -150, -130, -100, -80, -50, -20, 10, 30, 60, 80, 110, 130, 160, 190, None, None, None, -170, None, None, None, -120, None, None, None, -70, None, -40, None, -10, None, None, None, 40, None, None, None, 90, None, None, None, 140, None, 170, None, 200]))\n assert is_same_tree(candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60]), tree_node([30, 14, 46, 6, 22, 38, 54, 2, 10, 18, 26, 34, 42, 50, 58, None, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60]))\n assert is_same_tree(candidate(nums = [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]), tree_node([8, 2, 14, -1, 5, 11, 17, -2, 0, 3, 6, 9, 12, 15, 18, None, None, None, 1, None, 4, None, 7, None, 10, None, 13, None, 16, None, 19]))\n assert is_same_tree(candidate(nums = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625]), tree_node([169, 36, 361, 9, 81, 256, 484, 1, 16, 49, 121, 196, 289, 400, 576, None, 4, None, 25, None, 64, 100, 144, None, 225, None, 324, None, 441, 529, 625]))\n assert is_same_tree(candidate(nums = [-1000, -500, -250, -100, -50, -25, -10, -5, -2, -1, 0, 1, 2, 5, 10, 25, 50, 100, 250, 500, 1000]), tree_node([0, -50, 25, -500, -5, 2, 250, -1000, -250, -25, -2, 1, 5, 50, 500, None, None, None, -100, None, -10, None, -1, None, None, None, 10, None, 100, None, 1000]))\n assert is_same_tree(candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150]), tree_node([75, 35, 115, 15, 55, 95, 135, 5, 25, 45, 65, 85, 105, 125, 145, None, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]))\n assert is_same_tree(candidate(nums = [-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500]), tree_node([500, -100, 1000, -400, 200, 700, 1300, -500, -300, 0, 300, 600, 800, 1100, 1400, None, None, None, -200, None, 100, None, 400, None, None, None, 900, None, 1200, None, 1500]))\n assert is_same_tree(candidate(nums = [-2000, -1900, -1800, -1700, -1600, -1500, -1400, -1300, -1200, -1100, -1000, -900, -800, -700, -600, -500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]), tree_node([0, -1100, 1000, -1600, -600, 500, 1500, -1900, -1400, -900, -300, 200, 700, 1200, 1800, -2000, -1800, -1500, -1300, -1000, -800, -500, -200, 100, 300, 600, 800, 1100, 1300, 1600, 1900, None, None, None, -1700, None, None, None, -1200, None, None, None, -700, None, -400, None, -100, None, None, None, 400, None, None, None, 900, None, None, None, 1400, None, 1700, None, 2000]))\n assert is_same_tree(candidate(nums = [-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50]), tree_node([0, -30, 30, -50, -20, 10, 40, None, -40, None, -10, None, 20, None, 50]))\n assert is_same_tree(candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58]), tree_node([28, 13, 43, 4, 19, 34, 52, 1, 7, 16, 22, 31, 37, 46, 55, None, None, None, 10, None, None, None, 25, None, None, None, 40, None, 49, None, 58]))\n assert is_same_tree(candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]), tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]))\n assert is_same_tree(candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]), tree_node([19, 8, 30, 3, 13, 24, 35, 0, 5, 10, 16, 21, 27, 32, 38, -1, 1, 4, 6, 9, 11, 14, 17, 20, 22, 25, 28, 31, 33, 36, 39, None, None, None, 2, None, None, None, 7, None, None, None, 12, None, 15, None, 18, None, None, None, 23, None, 26, None, 29, None, None, None, 34, None, 37, None, 40]))\n assert is_same_tree(candidate(nums = [-99, -97, -95, -93, -91, -89, -87, -85, -83, -81, -79, -77, -75, -73, -71, -69, -67, -65, -63, -61, -59, -57, -55, -53, -51, -49, -47, -45, -43, -41, -39, -37, -35, -33, -31, -29, -27, -25, -23, -21, -19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]), tree_node([-1, -51, 49, -77, -27, 23, 75, -89, -65, -39, -15, 11, 35, 61, 87, -95, -83, -71, -59, -45, -33, -21, -9, 5, 17, 29, 41, 55, 67, 81, 93, -99, -93, -87, -81, -75, -69, -63, -55, -49, -43, -37, -31, -25, -19, -13, -5, 1, 7, 13, 19, 25, 31, 37, 45, 51, 57, 63, 71, 77, 83, 89, 97, None, -97, None, -91, None, -85, None, -79, None, -73, None, -67, None, -61, -57, -53, None, -47, None, -41, None, -35, None, -29, None, -23, None, -17, None, -11, -7, -3, None, 3, None, 9, None, 15, None, 21, None, 27, None, 33, None, 39, 43, 47, None, 53, None, 59, None, 65, 69, 73, None, 79, None, 85, None, 91, 95, 99]))\n assert is_same_tree(candidate(nums = [-15, -10, -5, 0, 5, 10, 15, 20, 25]), tree_node([5, -10, 15, -15, -5, 10, 20, None, None, None, 0, None, None, None, 25]))\n assert is_same_tree(candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]), tree_node([7, 2, 12, 0, 4, 9, 14, -1, 1, 3, 5, 8, 10, 13, 15, None, None, None, None, None, None, None, 6, None, None, None, 11, None, None, None, 16]))\n assert is_same_tree(candidate(nums = [-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), tree_node([0, -5, 5, -8, -3, 2, 7, -9, -7, -4, -2, 1, 3, 6, 8, None, None, None, -6, None, None, None, -1, None, None, None, 4, None, None, None, 9]))\n assert is_same_tree(candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125]), tree_node([65, 30, 95, 15, 45, 80, 110, 5, 20, 35, 55, 70, 85, 100, 120, None, 10, None, 25, None, 40, 50, 60, None, 75, None, 90, None, 105, 115, 125]))\n assert is_same_tree(candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]), tree_node([49, 23, 75, 10, 36, 62, 88, 4, 16, 29, 42, 55, 68, 81, 94, 1, 7, 13, 19, 26, 32, 39, 45, 52, 58, 65, 71, 78, 84, 91, 97, -1, 2, 5, 8, 11, 14, 17, 21, 24, 27, 30, 34, 37, 40, 43, 47, 50, 53, 56, 60, 63, 66, 69, 73, 76, 79, 82, 86, 89, 92, 95, 99, None, 0, None, 3, None, 6, None, 9, None, 12, None, 15, None, 18, 20, 22, None, 25, None, 28, None, 31, 33, 35, None, 38, None, 41, None, 44, 46, 48, None, 51, None, 54, None, 57, 59, 61, None, 64, None, 67, None, 70, 72, 74, None, 77, None, 80, None, 83, 85, 87, None, 90, None, 93, None, 96, 98, 100]))\n assert is_same_tree(candidate(nums = [-1000, -500, -250, -125, -62, -31, -15, -7, -3, -1, 0, 1, 3, 7, 15, 31, 62, 125, 250, 500, 1000]), tree_node([0, -62, 31, -500, -7, 3, 250, -1000, -250, -31, -3, 1, 7, 62, 500, None, None, None, -125, None, -15, None, -1, None, None, None, 15, None, 125, None, 1000]))\n assert is_same_tree(candidate(nums = [-20, -18, -16, -14, -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]), tree_node([0, -12, 10, -18, -6, 4, 16, -20, -16, -10, -4, 2, 6, 12, 18, None, None, None, -14, None, -8, None, -2, None, None, None, 8, None, 14, None, 20]))\n assert is_same_tree(candidate(nums = [-9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991, -9990, -9989, -9988, -9987, -9986, -9985]), tree_node([-9992, -9996, -9988, -9998, -9994, -9990, -9986, -9999, -9997, -9995, -9993, -9991, -9989, -9987, -9985]))\n assert is_same_tree(candidate(nums = [-100, -50, -20, -10, -5, 0, 5, 10, 20, 50, 100]), tree_node([0, -20, 20, -100, -10, 5, 50, None, -50, None, -5, None, 10, None, 100]))\n assert is_same_tree(candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]), tree_node([100, 50, 150, 20, 70, 120, 180, 10, 30, 60, 80, 110, 130, 160, 190, None, None, None, 40, None, None, None, 90, None, None, None, 140, None, 170, None, 200]))\n assert is_same_tree(candidate(nums = [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]), tree_node([9, 3, 15, 0, 6, 12, 18, -2, 1, 4, 7, 10, 13, 16, 19, None, -1, None, 2, None, 5, None, 8, None, 11, None, 14, None, 17, None, 20]))\n assert is_same_tree(candidate(nums = [-5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]), tree_node([9, 3, 15, 0, 6, 12, 18, -5, 1, 4, 7, 10, 13, 16, 19, None, None, None, 2, None, 5, None, 8, None, 11, None, 14, None, 17, None, 20]))\n assert is_same_tree(candidate(nums = [-30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50]), tree_node([10, -15, 30, -25, -5, 20, 40, -30, -20, -10, 0, 15, 25, 35, 45, None, None, None, None, None, None, None, 5, None, None, None, None, None, None, None, 50]))\n assert is_same_tree(candidate(nums = [-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]), tree_node([0, -26, 25, -39, -13, 12, 38, -45, -33, -20, -7, 6, 18, 31, 44, -48, -42, -36, -30, -23, -17, -10, -4, 3, 9, 15, 21, 28, 34, 41, 47, -50, -47, -44, -41, -38, -35, -32, -28, -25, -22, -19, -15, -12, -9, -6, -2, 1, 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 36, 39, 42, 45, 49, None, -49, None, -46, None, -43, None, -40, None, -37, None, -34, None, -31, -29, -27, None, -24, None, -21, None, -18, -16, -14, None, -11, None, -8, None, -5, -3, -1, None, 2, None, 5, None, 8, None, 11, None, 14, None, 17, None, 20, 22, 24, None, 27, None, 30, None, 33, 35, 37, None, 40, None, 43, None, 46, 48, 50]))\n assert is_same_tree(candidate(nums = [-9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991, -9990, -9989, -9988, -9987, -9986, -9985, -9984, -9983, -9982, -9981, -9980]), tree_node([-9990, -9995, -9985, -9998, -9993, -9988, -9982, -9999, -9997, -9994, -9992, -9989, -9987, -9984, -9981, None, None, None, -9996, None, None, None, -9991, None, None, None, -9986, None, -9983, None, -9980]))\n assert is_same_tree(candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250]), tree_node([130, 60, 190, 30, 90, 160, 220, 10, 40, 70, 110, 140, 170, 200, 240, None, 20, None, 50, None, 80, 100, 120, None, 150, None, 180, None, 210, 230, 250]))\n assert is_same_tree(candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]), tree_node([8, 3, 12, 1, 5, 10, 14, 0, 2, 4, 6, 9, 11, 13, 15, None, None, None, None, None, None, None, 7, None, None, None, None, None, None, None, 16]))\n assert is_same_tree(candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]), tree_node([0, -6, 5, -9, -3, 2, 8, -10, -8, -5, -2, 1, 3, 6, 9, None, None, None, -7, None, -4, None, -1, None, None, None, 4, None, 7, None, 10]))\n assert is_same_tree(candidate(nums = [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]), tree_node([14, 5, 23, 1, 9, 18, 27, -1, 3, 7, 11, 16, 20, 25, 29, -2, 0, 2, 4, 6, 8, 10, 12, 15, 17, 19, 21, 24, 26, 28, 30, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 13, None, None, None, None, None, None, None, 22, None, None, None, None, None, None, None, 31]))\n assert is_same_tree(candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]), tree_node([14, 6, 22, 2, 10, 18, 26, 0, 4, 8, 12, 16, 20, 24, 28, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 30]))\n assert is_same_tree(candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]), tree_node([25, 11, 37, 5, 17, 31, 43, 1, 7, 13, 21, 27, 33, 39, 47, None, 3, None, 9, None, 15, 19, 23, None, 29, None, 35, None, 41, 45, 49]))\n assert is_same_tree(candidate(nums = [-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]), tree_node([9, 4, 13, 2, 6, 11, 15, -1, 3, 5, 7, 10, 12, 14, 16, None, None, None, None, None, None, None, 8, None, None, None, None, None, None, None, 17]))\n assert is_same_tree(candidate(nums = [-1000, -500, -250, -125, -63, -31, -16, -8, -4, -2, -1, 0, 1, 2, 4, 8, 16, 31, 63, 125, 250, 500, 1000]), tree_node([0, -31, 31, -250, -4, 4, 250, -1000, -125, -16, -2, 1, 8, 63, 500, None, -500, None, -63, None, -8, None, -1, None, 2, None, 16, None, 125, None, 1000]))\n assert is_same_tree(candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300]), tree_node([150, 70, 230, 30, 110, 190, 270, 10, 50, 90, 130, 170, 210, 250, 290, None, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300]))\n assert is_same_tree(candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]), tree_node([10, 5, 15, 2, 7, 12, 18, 1, 3, 6, 8, 11, 13, 16, 19, None, None, None, 4, None, None, None, 9, None, None, None, 14, None, 17, None, 20]))\n assert is_same_tree(candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]), tree_node([7, -2, 16, -7, 2, 11, 21, -9, -5, 0, 4, 9, 13, 18, 23, -10, -8, -6, -4, -1, 1, 3, 5, 8, 10, 12, 14, 17, 19, 22, 24, None, None, None, None, None, None, None, -3, None, None, None, None, None, None, None, 6, None, None, None, None, None, None, None, 15, None, None, None, 20, None, None, None, 25]))\n assert is_same_tree(candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]), tree_node([5000, 2000, 8000, 1000, 3000, 6000, 9000, None, None, None, 4000, None, 7000, None, 10000]))\n assert is_same_tree(candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]), tree_node([12, 5, 19, 2, 8, 15, 22, 0, 3, 6, 10, 13, 17, 20, 24, None, 1, None, 4, None, 7, 9, 11, None, 14, 16, 18, None, 21, 23, 25]))\n assert is_same_tree(candidate(nums = [500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500, 7000, 7500, 8000, 8500, 9000, 9500, 10000]), tree_node([5000, 2500, 7500, 1000, 3500, 6000, 9000, 500, 1500, 3000, 4000, 5500, 6500, 8000, 9500, None, None, None, 2000, None, None, None, 4500, None, None, None, 7000, None, 8500, None, 10000]))\n assert is_same_tree(candidate(nums = [-50, -45, -40, -35, -30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50]), tree_node([0, -30, 25, -45, -15, 10, 40, -50, -40, -25, -10, 5, 15, 30, 45, None, None, None, -35, None, -20, None, -5, None, None, None, 20, None, 35, None, 50]))\n assert is_same_tree(candidate(nums = [-100, -50, -25, -10, -3, 0, 5, 9, 20, 50, 75, 100]), tree_node([0, -25, 20, -100, -10, 5, 75, None, -50, None, -3, None, 9, 50, 100]))\n assert is_same_tree(candidate(nums = [-15, -10, -5, -3, 0, 1, 2, 5, 6, 8, 10, 15]), tree_node([1, -5, 6, -15, -3, 2, 10, None, -10, None, 0, None, 5, 8, 15]))\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().sortedArrayToBST", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var sortedArrayToBST = function(nums) {", "container": null, "callable": "sortedArrayToBST", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 109, "task_id": "convert-sorted-list-to-binary-search-tree", "difficulty": "Medium", "problem_description": "Given the head of a singly linked list where elements are sorted in ascending order, convert it to a height-balanced binary search tree.\n \nExample 1:\n\n\nInput: head = [-10,-3,0,5,9]\nOutput: [0,-3,9,-10,null,5]\nExplanation: One possible answer is [0,-3,9,-10,null,5], which represents the shown height balanced BST.\n\nExample 2:\n\nInput: head = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in head is in the range [0, 2 * 104].\n-105 <= Node.val <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7])), tree_node([4, 2, 6, 1, 3, 5, 7]))\n assert is_same_tree(candidate(head = list_node([-1, 0, 1, 2])), tree_node([0, -1, 1, None, None, None, 2]))\n assert is_same_tree(candidate(head = list_node([-10, -5, 0, 5, 10])), tree_node([0, -10, 5, None, -5, None, 10]))\n assert is_same_tree(candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), tree_node([5, 2, 8, 0, 3, 6, 9, None, 1, None, 4, None, 7, None, 10]))\n assert is_same_tree(candidate(head = list_node([-10, -3, 0, 5, 9])), tree_node([0, -10, 5, None, -3, None, 9]))\n assert candidate(head = list_node([])) == None\n assert is_same_tree(candidate(head = list_node([1])), tree_node([1]))\n assert is_same_tree(candidate(head = list_node([1, 3])), tree_node([1, None, 3]))\n assert is_same_tree(candidate(head = list_node([-1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10])), tree_node([5, -3, -8, 1, -4, 6, 9, -1, -2, 3, 4, -6, -7, 8, -10, None, None, None, 2, None, None, None, -5, None, None, None, 7, None, -9, None, 10]))\n assert is_same_tree(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500])), tree_node([800, 400, 1200, 200, 600, 1000, 1400, 100, 300, 500, 700, 900, 1100, 1300, 1500]))\n assert is_same_tree(candidate(head = list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), tree_node([7, 0, 14, -3, 3, 10, 17, -5, -2, 1, 5, 8, 12, 15, 19, None, -4, None, -1, None, 2, 4, 6, None, 9, 11, 13, None, 16, 18, 20]))\n assert is_same_tree(candidate(head = list_node([-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])), tree_node([3, -1, 6, -3, 1, 4, 8, None, -2, 0, 2, None, 5, 7, 9]))\n assert is_same_tree(candidate(head = list_node([-200, -199, -198, -197, -196, -195, -194, -193, -192, -191, -190, -189, -188, -187, -186, -185, -184, -183, -182, -181, -180, -179, -178, -177, -176, -175, -174, -173, -172, -171, -170])), tree_node([-185, -193, -177, -197, -189, -181, -173, -199, -195, -191, -187, -183, -179, -175, -171, -200, -198, -196, -194, -192, -190, -188, -186, -184, -182, -180, -178, -176, -174, -172, -170]))\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), tree_node([15, 7, 23, 3, 11, 19, 27, 1, 5, 9, 13, 17, 21, 25, 29, None, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]))\n assert is_same_tree(candidate(head = list_node([-100, -50, -25, 0, 25, 50, 100, 150, 200, 250, 300])), tree_node([50, -25, 200, -100, 0, 100, 250, None, -50, None, 25, None, 150, None, 300]))\n assert is_same_tree(candidate(head = list_node([100000])), tree_node([100000]))\n assert is_same_tree(candidate(head = list_node([-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])), tree_node([5, 0, 9, -2, 2, 7, 11, -3, -1, 1, 3, 6, 8, 10, 12, None, None, None, None, None, None, None, 4, None, None, None, None, None, None, None, 13]))\n assert is_same_tree(candidate(head = list_node([1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000])), tree_node([10000, 5000, 15000, 2000, 7000, 12000, 18000, 1000, 3000, 6000, 8000, 11000, 13000, 16000, 19000, None, None, None, 4000, None, None, None, 9000, None, None, None, 14000, None, 17000, None, 20000]))\n assert is_same_tree(candidate(head = list_node([-2000, -1500, -1000, -500, 0, 500, 1000, 1500, 2000])), tree_node([0, -1500, 1000, -2000, -1000, 500, 1500, None, None, None, -500, None, None, None, 2000]))\n assert is_same_tree(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39])), tree_node([19, 9, 29, 3, 13, 23, 35, 1, 5, 11, 15, 21, 25, 31, 37, None, None, None, 7, None, None, None, 17, None, None, None, 27, None, 33, None, 39]))\n assert is_same_tree(candidate(head = list_node([-30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30])), tree_node([0, -20, 15, -30, -10, 5, 25, None, -25, -15, -5, None, 10, 20, 30]))\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])), tree_node([25, 12, 38, 6, 18, 31, 44, 3, 9, 15, 21, 28, 34, 41, 47, 1, 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 36, 39, 42, 45, 49, None, 2, None, 5, None, 8, None, 11, None, 14, None, 17, None, 20, 22, 24, None, 27, None, 30, None, 33, 35, 37, None, 40, None, 43, None, 46, 48, 50]))\n assert is_same_tree(candidate(head = list_node([-5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000])), tree_node([0, -3000, 3000, -5000, -2000, 1000, 4000, None, -4000, None, -1000, None, 2000, None, 5000]))\n assert is_same_tree(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120])), tree_node([60, 30, 90, 15, 45, 75, 105, 5, 20, 35, 50, 65, 80, 95, 115, None, 10, None, 25, None, 40, None, 55, None, 70, None, 85, None, 100, 110, 120]))\n assert is_same_tree(candidate(head = list_node([10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000])), tree_node([50000, 20000, 80000, 10000, 30000, 60000, 90000, None, None, None, 40000, None, 70000, None, 100000]))\n assert is_same_tree(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31])), tree_node([15, 7, 23, 3, 11, 19, 27, 1, 5, 9, 13, 17, 21, 25, 29, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 31]))\n assert is_same_tree(candidate(head = list_node([5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215, 225, 235, 245])), tree_node([125, 55, 185, 25, 85, 155, 215, 5, 35, 65, 105, 135, 165, 195, 235, None, 15, None, 45, None, 75, 95, 115, None, 145, None, 175, None, 205, 225, 245]))\n assert is_same_tree(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100])), tree_node([50, 25, 75, 10, 35, 60, 90, 5, 15, 30, 40, 55, 65, 80, 95, None, None, None, 20, None, None, None, 45, None, None, None, 70, None, 85, None, 100]))\n assert is_same_tree(candidate(head = list_node([-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100])), tree_node([20, -20, 60, -40, 0, 40, 80, -50, -30, -10, 10, 30, 50, 70, 90, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 100]))\n assert is_same_tree(candidate(head = list_node([-999, -888, -777, -666, -555, -444, -333, -222, -111, 0, 111, 222, 333, 444, 555, 666, 777, 888, 999])), tree_node([0, -555, 555, -888, -333, 222, 777, -999, -777, -444, -222, 111, 333, 666, 888, None, None, None, -666, None, None, None, -111, None, None, None, 444, None, None, None, 999]))\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), tree_node([10, 5, 15, 2, 7, 12, 18, 1, 3, 6, 8, 11, 13, 16, 19, None, None, None, 4, None, None, None, 9, None, None, None, 14, None, 17, None, 20]))\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35])), tree_node([18, 9, 27, 4, 13, 22, 31, 2, 6, 11, 15, 20, 24, 29, 33, 1, 3, 5, 7, 10, 12, 14, 16, 19, 21, 23, 25, 28, 30, 32, 34, None, None, None, None, None, None, None, 8, None, None, None, None, None, None, None, 17, None, None, None, None, None, None, None, 26, None, None, None, None, None, None, None, 35]))\n assert is_same_tree(candidate(head = list_node([-30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90])), tree_node([30, -5, 60, -20, 10, 45, 75, -30, -15, 0, 20, 35, 50, 65, 85, None, -25, None, -10, None, 5, 15, 25, None, 40, None, 55, None, 70, 80, 90]))\n assert is_same_tree(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400])), tree_node([200, 100, 300, 50, 150, 250, 350, 20, 70, 120, 170, 220, 270, 320, 380, 10, 30, 60, 80, 110, 130, 160, 180, 210, 230, 260, 280, 310, 330, 360, 390, None, None, None, 40, None, None, None, 90, None, None, None, 140, None, None, None, 190, None, None, None, 240, None, None, None, 290, None, None, None, 340, None, 370, None, 400]))\n assert is_same_tree(candidate(head = list_node([-1000, -500, -250, -100, -50, 0, 50, 100, 250, 500, 1000])), tree_node([0, -250, 250, -1000, -100, 50, 500, None, -500, None, -50, None, 100, None, 1000]))\n assert is_same_tree(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20])), tree_node([-10, -5, -15, -2, -7, -12, -18, -1, -3, -6, -8, -11, -13, -16, -19, None, None, None, -4, None, None, None, -9, None, None, None, -14, None, -17, None, -20]))\n assert is_same_tree(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49])), tree_node([25, 11, 37, 5, 17, 31, 43, 1, 7, 13, 21, 27, 33, 39, 47, None, 3, None, 9, None, 15, 19, 23, None, 29, None, 35, None, 41, 45, 49]))\n assert is_same_tree(candidate(head = list_node([-500, -400, -300, -200, -100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 200, 300, 400, 500])), tree_node([20, -70, 110, -200, -30, 60, 150, -400, -90, -50, -10, 40, 80, 130, 300, -500, -300, -100, -80, -60, -40, -20, 0, 30, 50, 70, 90, 120, 140, 200, 400, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 10, None, None, None, None, None, None, None, 100, None, None, None, None, None, None, None, 500]))\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])), tree_node([13, 6, 19, 3, 9, 16, 22, 1, 4, 7, 11, 14, 17, 20, 24, None, 2, None, 5, None, 8, 10, 12, None, 15, None, 18, None, 21, 23, 25]))\n assert is_same_tree(candidate(head = list_node([-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000])), tree_node([0, -600, 500, -900, -300, 200, 800, -1000, -800, -500, -200, 100, 300, 600, 900, None, None, None, -700, None, -400, None, -100, None, None, None, 400, None, 700, None, 1000]))\n assert is_same_tree(candidate(head = list_node([1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100])), tree_node([49, 22, 76, 10, 34, 61, 88, 4, 16, 28, 40, 55, 67, 82, 94, 1, 7, 13, 19, 25, 31, 37, 43, 52, 58, 64, 70, 79, 85, 91, 97, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 46, None, None, None, None, None, None, None, 73, None, None, None, None, None, None, None, 100]))\n assert is_same_tree(candidate(head = list_node([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])), tree_node([9, 3, 14, 0, 6, 11, 17, -1, 1, 4, 7, 10, 12, 15, 18, None, None, None, 2, None, 5, None, 8, None, None, None, 13, None, 16, None, 19]))\n assert is_same_tree(candidate(head = list_node([-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100])), tree_node([0, -60, 50, -90, -30, 20, 80, -100, -80, -50, -20, 10, 30, 60, 90, None, None, None, -70, None, -40, None, -10, None, None, None, 40, None, 70, None, 100]))\n assert is_same_tree(candidate(head = list_node([0])), tree_node([0]))\n assert is_same_tree(candidate(head = list_node([-20, -15, -10, -5, 0, 5, 10, 15, 20])), tree_node([0, -15, 10, -20, -10, 5, 15, None, None, None, -5, None, None, None, 20]))\n assert is_same_tree(candidate(head = list_node([-100000])), tree_node([-100000]))\n assert is_same_tree(candidate(head = list_node([-20, -15, -10, -5, 0, 5, 10, 15, 20])), tree_node([0, -15, 10, -20, -10, 5, 15, None, None, None, -5, None, None, None, 20]))\n assert is_same_tree(candidate(head = list_node([-500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500])), tree_node([0, -300, 300, -500, -200, 100, 400, None, -400, None, -100, None, 200, None, 500]))\n assert is_same_tree(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149])), tree_node([75, 37, 113, 17, 55, 93, 131, 7, 27, 45, 65, 83, 103, 121, 141, 3, 11, 21, 31, 41, 49, 59, 69, 79, 87, 97, 107, 117, 125, 135, 145, 1, 5, 9, 13, 19, 23, 29, 33, 39, 43, 47, 51, 57, 61, 67, 71, 77, 81, 85, 89, 95, 99, 105, 109, 115, 119, 123, 127, 133, 137, 143, 147, None, None, None, None, None, None, None, 15, None, None, None, 25, None, None, None, 35, None, None, None, None, None, None, None, 53, None, None, None, 63, None, None, None, 73, None, None, None, None, None, None, None, 91, None, None, None, 101, None, None, None, 111, None, None, None, None, None, None, None, 129, None, None, None, 139, None, None, None, 149]))\n assert is_same_tree(candidate(head = list_node([-300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000])), tree_node([800, 200, 1400, -100, 500, 1100, 1700, -300, 0, 300, 600, 900, 1200, 1500, 1900, None, -200, None, 100, None, 400, None, 700, None, 1000, None, 1300, None, 1600, 1800, 2000]))\n assert is_same_tree(candidate(head = list_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, 10])), tree_node([-5, 2, 8, -1, -3, 6, -9, None, None, None, 4, None, -7, None, 10]))\n assert is_same_tree(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250])), tree_node([130, 60, 190, 30, 90, 160, 220, 10, 40, 70, 110, 140, 170, 200, 240, None, 20, None, 50, None, 80, 100, 120, None, 150, None, 180, None, 210, 230, 250]))\n assert is_same_tree(candidate(head = list_node([-100, -50, -25, -10, 0, 10, 25, 50, 100])), tree_node([0, -50, 25, -100, -25, 10, 50, None, None, None, -10, None, None, None, 100]))\n assert is_same_tree(candidate(head = list_node([-200, -190, -180, -170, -160, -150, -140, -130, -120, -110, -100, -90, -80, -70, -60, -50, -40, -30, -20, -10])), tree_node([-110, -160, -60, -190, -140, -90, -30, -200, -180, -150, -130, -100, -80, -50, -20, None, None, None, -170, None, None, None, -120, None, None, None, -70, None, -40, None, -10]))\n assert is_same_tree(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29])), tree_node([15, 7, 23, 3, 11, 19, 27, 1, 5, 9, 13, 17, 21, 25, 29]))\n assert is_same_tree(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150])), tree_node([75, 35, 115, 15, 55, 95, 135, 5, 25, 45, 65, 85, 105, 125, 145, None, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]))\n assert is_same_tree(candidate(head = list_node([-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), tree_node([15, 7, 23, 3, 11, 19, 27, -1, 5, 9, 13, 17, 21, 25, 29, None, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]))\n assert is_same_tree(candidate(head = list_node([-99999, -88888, -77777, -66666, -55555, -44444, -33333, -22222, -11111, 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999])), tree_node([0, -55555, 55555, -88888, -33333, 22222, 77777, -99999, -77777, -44444, -22222, 11111, 33333, 66666, 88888, None, None, None, -66666, None, None, None, -11111, None, None, None, 44444, None, None, None, 99999]))\n assert is_same_tree(candidate(head = list_node([-50000, -40000, -30000, -20000, -10000, 0, 10000, 20000, 30000, 40000, 50000])), tree_node([0, -30000, 30000, -50000, -20000, 10000, 40000, None, -40000, None, -10000, None, 20000, None, 50000]))\n assert is_same_tree(candidate(head = list_node([-300, -250, -200, -150, -100, -50, 0, 50, 100, 150, 200, 250, 300])), tree_node([0, -200, 150, -300, -100, 50, 250, None, -250, -150, -50, None, 100, 200, 300]))\n assert is_same_tree(candidate(head = list_node([-500, -450, -400, -350, -300, -250, -200, -150, -100, -50, 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500])), tree_node([0, -300, 250, -450, -150, 100, 400, -500, -400, -250, -100, 50, 150, 300, 450, None, None, None, -350, None, -200, None, -50, None, None, None, 200, None, 350, None, 500]))\n assert is_same_tree(candidate(head = list_node([1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000])), tree_node([5000, 2000, 8000, 1000, 3000, 6000, 9000, None, None, None, 4000, None, 7000, None, 10000]))\n assert is_same_tree(candidate(head = list_node([1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000])), tree_node([8000, 4000, 12000, 2000, 6000, 10000, 14000, 1000, 3000, 5000, 7000, 9000, 11000, 13000, 15000]))\n assert is_same_tree(candidate(head = list_node([-100, -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100])), tree_node([0, -60, 50, -90, -30, 20, 80, -100, -80, -50, -20, 10, 30, 60, 90, None, None, None, -70, None, -40, None, -10, None, None, None, 40, None, 70, None, 100]))\n assert is_same_tree(candidate(head = list_node([-20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30])), tree_node([5, -10, 20, -20, -5, 10, 25, None, -15, None, 0, None, 15, None, 30]))\n assert is_same_tree(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99])), tree_node([49, 23, 75, 11, 35, 61, 87, 5, 17, 29, 41, 55, 67, 81, 93, 1, 7, 13, 19, 25, 31, 37, 45, 51, 57, 63, 71, 77, 83, 89, 97, None, 3, None, 9, None, 15, None, 21, None, 27, None, 33, None, 39, 43, 47, None, 53, None, 59, None, 65, 69, 73, None, 79, None, 85, None, 91, 95, 99]))\n assert is_same_tree(candidate(head = list_node([-50, -49, -48, -47, -46, -45, -44, -43, -42, -41, -40, -39, -38, -37, -36, -35, -34, -33, -32, -31, -30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])), tree_node([0, -26, 25, -39, -13, 12, 38, -45, -33, -20, -7, 6, 18, 31, 44, -48, -42, -36, -30, -23, -17, -10, -4, 3, 9, 15, 21, 28, 34, 41, 47, -50, -47, -44, -41, -38, -35, -32, -28, -25, -22, -19, -15, -12, -9, -6, -2, 1, 4, 7, 10, 13, 16, 19, 23, 26, 29, 32, 36, 39, 42, 45, 49, None, -49, None, -46, None, -43, None, -40, None, -37, None, -34, None, -31, -29, -27, None, -24, None, -21, None, -18, -16, -14, None, -11, None, -8, None, -5, -3, -1, None, 2, None, 5, None, 8, None, 11, None, 14, None, 17, None, 20, 22, 24, None, 27, None, 30, None, 33, 35, 37, None, 40, None, 43, None, 46, 48, 50]))\n assert is_same_tree(candidate(head = list_node([-20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40])), tree_node([10, -10, 25, -20, 0, 15, 35, None, -15, -5, 5, None, 20, 30, 40]))\n assert is_same_tree(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000])), tree_node([1000, 500, 1500, 200, 700, 1200, 1800, 100, 300, 600, 800, 1100, 1300, 1600, 1900, None, None, None, 400, None, None, None, 900, None, None, None, 1400, None, 1700, None, 2000]))\n assert is_same_tree(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000])), tree_node([1000, 500, 1500, 200, 700, 1200, 1800, 100, 300, 600, 800, 1100, 1300, 1600, 1900, None, None, None, 400, None, None, None, 900, None, None, None, 1400, None, 1700, None, 2000]))\n assert is_same_tree(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140])), tree_node([70, 35, 105, 15, 50, 85, 125, 5, 25, 40, 60, 75, 95, 115, 135, None, 10, 20, 30, None, 45, 55, 65, None, 80, 90, 100, 110, 120, 130, 140]))\n assert is_same_tree(candidate(head = list_node([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), tree_node([9, 3, 15, 0, 6, 12, 18, -1, 1, 4, 7, 10, 13, 16, 19, None, None, None, 2, None, 5, None, 8, None, 11, None, 14, None, 17, None, 20]))\n assert is_same_tree(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().sortedListToBST", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var sortedListToBST = function(head) {", "container": null, "callable": "sortedListToBST", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 110, "task_id": "balanced-binary-tree", "difficulty": "Easy", "problem_description": "Given a binary tree, determine if it is height-balanced.\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: true\n\nExample 2:\n\n\nInput: root = [1,2,2,3,3,null,null,4,4]\nOutput: false\n\nExample 3:\n\nInput: root = []\nOutput: true\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 5000].\n-104 <= Node.val <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, 7])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, None, None, 5, 5])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 4, 4, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3])) == False\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 4, None, None, 4, 4])) == False\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == True\n assert candidate(root = tree_node([1])) == True\n assert candidate(root = tree_node([])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5])) == True\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, 8, 9, None, None, 10, 11])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, 7, 8, 9, 10, 11, 12, None, None, 13, 14, 15])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, 7, 8, 9, 10, 11, 12])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 7, 8, None, 10, 11, 12, None, None, 15])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, None, 10])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 4, 5, 5, None, None, 6, 6])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 9, None, None, 14, None, 16, 17, 18, 19, None, None, None, None, None, None, None, None, 28])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30, None, 31, None, 32])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, None, 4, 5, 5])) == True\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, 6, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, 9, None])) == True\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, 8, 9, 10, None, None, 11, 12])) == False\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == False\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, 20, None])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, None, None, None, None, 5, 5, 5, 5, None, None, None, None])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, None, None, None, None, None, None, 21])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, 7, 8, 9, 10, None, None, 11, 12])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 4, None, 5, 6, 7, 8, 9])) == False\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 16])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, None, None, None, None, 5, None, None, None, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 4, 5, None, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, None, 8, 9])) == False\n assert candidate(root = tree_node([1, None, 3, None, None, None, 6, None, None, None, None, 12, None, None, None, 19])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4, 5, None, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, None, None, 5])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, None, 3, 4, 5, 6, 7, None, None, None, None, None, 8, 9, 10, 11])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 9, None, 11, 14, None, 16, 17, 18, 19, None, 23, None, None, None, None, None, None, 28])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, 16, 17])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 5, 5, None, None, 6, 6])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9])) == True\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, 16])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 31])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, 10, 11, 12, 13, 14, 15, 16, None, None, None, None, None, None, None, None, None, None, None, 28, 29, 30])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, 8, 9, 10, None, None, 11, 12, 13, 14])) == False\n assert candidate(root = tree_node([1, 2, None, 4, None, 7, 8, 14, 15])) == False\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, 8])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, 7, 8, 9, 10, 11, 12, 13, 14])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, None])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, None, None, 10, 11])) == True\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, 6, None, 7, None, 8, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, None, None, None, 10, 11, 12, 13, None, None, None, None, None, None, None, 14])) == False\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, 4])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, 15, 16, 17])) == True\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, None, None, None, None, None, None, None, 4])) == True\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, None])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 7, 8, None, 10, None, 14, None, 16, 17, 18, 19, None, None, None, None, None, None, None, None, 28])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, None, 4, None, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, None, None, 13, None, None, 14])) == True\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == False\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9, None, 10])) == False\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, None, None, 16])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, None, None, None, 10, 11, 12, 13, None, None, None, None, None, None, 14, 15, 16, 17, 18, 19, 20])) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17])) == True\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, None, 6, None, None, None, None, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 4, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, None, 7, None, 8, 9])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, None, 8, None, 10, 11, 12, None, None, None, 16, None, None, None, None, None, None, 25])) == False\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, None, None, 5, 5])) == False\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, None, 6])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9])) == True\n assert candidate(root = tree_node([1, 2, 2, None, 3, 3, None, 4, 4])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, None, 3, 4, 5, None, 5])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4])) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None])) == True\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7])) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, None, None, None, None, None, None, None, 5])) == False\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().isBalanced", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isBalanced = function(root) {", "container": null, "callable": "isBalanced", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 111, "task_id": "minimum-depth-of-binary-tree", "difficulty": "Easy", "problem_description": "Given a binary tree, find its minimum depth.\nThe minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node.\nNote: A leaf is a node with no children.\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: 2\n\nExample 2:\n\nInput: root = [2,null,3,null,4,null,5,null,6]\nOutput: 5\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 105].\n-1000 <= Node.val <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == 3\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == 4\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 5\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])) == 3\n assert candidate(root = tree_node([2, None, 3, None, 4, None, 5, None, 6])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5])) == 3\n assert candidate(root = tree_node([1, 2])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, 8, None, None, 9, 10])) == 2\n assert candidate(root = tree_node([0])) == 1\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == 2\n assert candidate(root = tree_node([1])) == 1\n assert candidate(root = tree_node([])) == 0\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 10\n assert candidate(root = tree_node([1, 2, 3, None, None, None, 4, None, None, 5, None, None, 6])) == 2\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7])) == 3\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == 2\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, None, None, 5, None, 6, None, 7, None, 8])) == 2\n assert candidate(root = tree_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, None, None, None, None, None, None, None, None, None, None])) == 3\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, None, 18])) == 2\n assert candidate(root = tree_node([1, None, None, 2, None, None, 3, None, None, 4, None, None, 5])) == 1\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, None, None, None, None, 8])) == 3\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == 8\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, 4, None, None, None, None, None, 5, None, None, None, None, None, 6, None, None, None, None, None, 7, None, None, None, None, None, 8, None, None, None, None, None, 9, None, None, None, None, None, 10, None, None, None, None, None, 11])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, None, None, None, None, 6])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, None, None, 6, 7, None, 8])) == 3\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 25, 28, 30, None, None, None, 29, 31])) == 3\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, 4, None, None, None, None, 5, None, None, None, None, 6, None, None, None, None, 7])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, 10, 11, 12, 13, None, None, 16, 17, 18, 19])) == 3\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4])) == 2\n assert candidate(root = tree_node([3, 9, 20, None, 1, 15, 7, None, None, 14, 6, None, 8])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, None, None, None, 7, 8, None, None, 9, None])) == 3\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, None, 5, None, None, 6, None, None, 7])) == 2\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30])) == 30\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 6\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, 4, None, None, None, None, 5])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, None, 8, 9, None, 10])) == 4\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6, None, None, 7])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, None, None, 14, None, None, None, None, 15, None, None, None, None, 16, None, None, None, None, 17, None, None, None, None, 18, None, None, None, None, 19, None, None, None, None, 20])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7])) == 4\n assert candidate(root = tree_node([1, 2, None, None, 3, None, None, None, None, 4, None, 5])) == 3\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, 16])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, None, None, None, 10, 11])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9])) == 5\n assert candidate(root = tree_node([1, None, None, 2, None, None, None, 3])) == 1\n assert candidate(root = tree_node([1, None, 2, None, None, None, None, 3, None, None, None, None, None, 4, None, None, None, None, None, 5])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 4\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, None, None, None, None, 6, None, None, None, None, None, 7, None, None, None, None, None, 8, None, None, None, None, None, 9])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 16])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, 12, None, 14])) == 3\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, None, 5, 6])) == 2\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, 9, None, None, 10])) == 3\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, None, 6, None, None, 7, None, None, 8, None, None, 9, None, None, 10])) == 6\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == 4\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, 4, None, 5, None, 6, None, 7])) == 2\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == 8\n assert candidate(root = tree_node([10, 5, 15, None, 7, None, 18, None, 8, None, 20, 16, 22])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14])) == 7\n assert candidate(root = tree_node([1, 2, None, 4, None, None, 5, None, 6, None, 7, None, 8])) == 7\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, None, None, None, None, 5, 5])) == 2\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == 7\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25])) == 13\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, None, None, 6, 7, None, None, 8, 9, None, None, 10, 11, None, None, 12, 13])) == 2\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == 2\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, 1])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 6\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 7, None, None, None, None, None, 8])) == 3\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 7, None, 9])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, None, None, None, 7, None, None, None, None, None, 8, None, None, None, None, None, 9, None, None, None, None, None, 10, None, None, None, None, None, 11, None, None, None, None, None, 12, None, None, None, None, None, 13])) == 3\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == 6\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, None, None, 16, 18, 17])) == 2\n assert candidate(root = tree_node([3, 9, None, 8, None, None, 10, None, None, None, None, 11, None, None, None, None, 12])) == 4\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == 12\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16])) == 16\n assert candidate(root = tree_node([1, None, None, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6, None, None, 7])) == 1\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, 4, None, None, None, None, None, 5, None, None, None, None, None, 6])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, 9, 10, None, None, 11])) == 4\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, 6, 7, None, None, 8, 9, None, None, 10, 11, None, 12, None, 13])) == 6\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13])) == 13\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 9\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, None, None, None, None, None, None, 14])) == 2\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 11\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, None, None, 5, 5])) == 2\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 14, 6, None, None, None, 8])) == 2\n assert candidate(root = tree_node([42])) == 1\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, 8, None, None, None, 9])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, None, 10, None, 11, None, 12])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, 10, 11, 12, 13])) == 2\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == 3\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, None, 12])) == 12\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().minDepth", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minDepth = function(root) {", "container": null, "callable": "minDepth", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 112, "task_id": "path-sum", "difficulty": "Easy", "problem_description": "Given the root of a binary tree and an integer targetSum, return true if the tree has a root-to-leaf path such that adding up all the values along the path equals targetSum.\nA leaf is a node with no children.\n \nExample 1:\n\n\nInput: root = [5,4,8,11,null,13,4,7,2,null,null,null,1], targetSum = 22\nOutput: true\nExplanation: The root-to-leaf path with the target sum is shown.\n\nExample 2:\n\n\nInput: root = [1,2,3], targetSum = 5\nOutput: false\nExplanation: There are two root-to-leaf paths in the tree:\n(1 --> 2): The sum is 3.\n(1 --> 3): The sum is 4.\nThere is no root-to-leaf path with sum = 5.\n\nExample 3:\n\nInput: root = [], targetSum = 0\nOutput: false\nExplanation: Since the tree is empty, there are no root-to-leaf paths.\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 5000].\n-1000 <= Node.val <= 1000\n-1000 <= targetSum <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([]),targetSum = 0) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7]),targetSum = 10) == True\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1]),targetSum = 3) == False\n assert candidate(root = tree_node([1, 2]),targetSum = 3) == True\n assert candidate(root = tree_node([1, 2, 3]),targetSum = 5) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1]),targetSum = 22) == True\n assert candidate(root = tree_node([1, 2]),targetSum = 1) == False\n assert candidate(root = tree_node([-2, None, -3]),targetSum = -5) == True\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5]),targetSum = 10) == False\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190]),targetSum = 400) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1]),targetSum = 26) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 30) == False\n assert candidate(root = tree_node([0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]),targetSum = 2) == True\n assert candidate(root = tree_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),targetSum = 0) == True\n assert candidate(root = tree_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),targetSum = 54) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 26) == True\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, None, 1, None, 6, 8, None, None, 11, 13]),targetSum = 22) == False\n assert candidate(root = tree_node([-1, None, -2, None, -3, None, -4, None, -5, None, -6, None, -7, None, -8]),targetSum = -16) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 27) == False\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),targetSum = 32) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 120) == False\n assert candidate(root = tree_node([0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]),targetSum = 3) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 31) == False\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),targetSum = 22) == True\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1]),targetSum = 30) == False\n assert candidate(root = tree_node([100, 50, 200, None, 150, None, 300, 125, None, None, None, 250]),targetSum = 475) == False\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15]),targetSum = -30) == False\n assert candidate(root = tree_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),targetSum = 100) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),targetSum = 93) == False\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5]),targetSum = 15) == True\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1]),targetSum = 31) == False\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 3, 4, None, None, None, None, 5, 5, 5, 5]),targetSum = 13) == False\n assert candidate(root = tree_node([100, -100, 100, -100, 100, -100, 100, -100, 100]),targetSum = 0) == True\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10]),targetSum = 10) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 22) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 45) == False\n assert candidate(root = tree_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),targetSum = 550) == False\n assert candidate(root = tree_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15]),targetSum = 3) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),targetSum = 39) == False\n assert candidate(root = tree_node([1000, -1000, 1000, -1000, 1000, -1000, 1000]),targetSum = 0) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 100) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 9) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 27) == True\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10]),targetSum = 55) == True\n assert candidate(root = tree_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),targetSum = 400) == False\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]),targetSum = 23) == False\n assert candidate(root = tree_node([1000, -1000, 1000, -1000, None, 1000, -1000, None, -1000, None, 1000]),targetSum = 0) == False\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1]),targetSum = 8) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),targetSum = 60) == False\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 80, 110, 140, 160, 190]),targetSum = 450) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 29) == False\n assert candidate(root = tree_node([0, -1, 1, None, -2, 2, None, None, -3, 3]),targetSum = -1) == False\n assert candidate(root = tree_node([-1, None, -2, -3, None, -4, None]),targetSum = -10) == True\n assert candidate(root = tree_node([-10, -5, -15, -3, -7, None, -18]),targetSum = -28) == False\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1]),targetSum = 2) == True\n assert candidate(root = tree_node([100, 50, 200, 25, 75, None, 350, 12, None, 60, 85, None, None, None, 400]),targetSum = 275) == False\n assert candidate(root = tree_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15]),targetSum = -15) == True\n assert candidate(root = tree_node([0, 1, 1, 0, 1, 0, 1, -1, -1, None, None, None, -1, None, -1, None, 1, None, -1, None, -1, None, 1, None, None, None, None, None, None, None, None]),targetSum = 2) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]),targetSum = 90) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1]),targetSum = 21) == False\n assert candidate(root = tree_node([-1, -2, -3, -4, None, -6, -7]),targetSum = -14) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 64) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),targetSum = 38) == True\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 60) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 32) == False\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]),targetSum = 28) == False\n assert candidate(root = tree_node([0, 1, 1, 0, 1, 0, None, None, 1, 0]),targetSum = 1) == True\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190]),targetSum = 250) == False\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180]),targetSum = 450) == False\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 1) == False\n assert candidate(root = tree_node([100, 98, 102, None, None, 99, 101, 97, None, 103]),targetSum = 300) == False\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7]),targetSum = 7) == False\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190]),targetSum = 500) == False\n assert candidate(root = tree_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15]),targetSum = -16) == False\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 18) == True\n"}, "metadata": {"canonical_parameter_names": ["root", "targetSum"], "leetcode_dataset_entry_point": "Solution().hasPathSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var hasPathSum = function(root, targetSum) {", "container": null, "callable": "hasPathSum", "parameters": [{"name": "root", "type": "TreeNode"}, {"name": "targetSum", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 113, "task_id": "path-sum-ii", "difficulty": "Medium", "problem_description": "Given the root of a binary tree and an integer targetSum, return all root-to-leaf paths where the sum of the node values in the path equals targetSum. Each path should be returned as a list of the node values, not node references.\nA root-to-leaf path is a path starting from the root and ending at any leaf node. A leaf is a node with no children.\n \nExample 1:\n\n\nInput: root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22\nOutput: [[5,4,11,2],[5,8,4,5]]\nExplanation: There are two paths whose sum equals targetSum:\n5 + 4 + 11 + 2 = 22\n5 + 8 + 4 + 5 = 22\n\nExample 2:\n\n\nInput: root = [1,2,3], targetSum = 5\nOutput: []\n\nExample 3:\n\nInput: root = [1,2], targetSum = 0\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 5000].\n-1000 <= Node.val <= 1000\n-1000 <= targetSum <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([0, 1, 1]),targetSum = 1) == [[0, 1], [0, 1]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 45) == []\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6]),targetSum = 21) == [[1, 2, 3, 4, 5, 6]]\n assert candidate(root = tree_node([-2, None, -3]),targetSum = -5) == [[-2, -3]]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7]),targetSum = 15) == []\n assert candidate(root = tree_node([1, 2, 3]),targetSum = 5) == []\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1, -1]),targetSum = -1) == [[1, -2, 1, -1], [1, -2, 1, -1]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 27) == [[5, 4, 11, 7]]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6]),targetSum = 15) == []\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1]),targetSum = 8) == []\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),targetSum = 22) == [[10, 5, 7]]\n assert candidate(root = tree_node([0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7]),targetSum = 15) == []\n assert candidate(root = tree_node([1, 2]),targetSum = 0) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 27) == []\n assert candidate(root = tree_node([0, 0, 0, 0, 0]),targetSum = 0) == [[0, 0, 0], [0, 0, 0], [0, 0]]\n assert candidate(root = tree_node([1]),targetSum = 1) == [[1]]\n assert candidate(root = tree_node([]),targetSum = 0) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 30) == []\n assert candidate(root = tree_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15]),targetSum = -15) == [[-1, 2, -5, -11]]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),targetSum = 25) == []\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),targetSum = 25) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 60) == []\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1]),targetSum = 2) == [[1, -2, 3]]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5]),targetSum = 15) == [[1, 2, 3, 4, 5]]\n assert candidate(root = tree_node([]),targetSum = 5) == []\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 26) == [[5, 8, 13]]\n assert candidate(root = tree_node([0, 1, 1]),targetSum = 0) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5]),targetSum = 10) == []\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 22) == [[5, 4, 11, 2], [5, 8, 4, 5]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 18) == [[5, 8, 4, 1]]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 21) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 100) == []\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1]),targetSum = 3) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7]),targetSum = 9) == []\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 190]),targetSum = 300) == []\n assert candidate(root = tree_node([8, 6, 10, 5, 7, 9, 11, 4, None, None, None, None, None, 3]),targetSum = 26) == []\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190]),targetSum = 250) == []\n assert candidate(root = tree_node([]),targetSum = 1) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7]),targetSum = 10) == [[1, 3, 6]]\n"}, "metadata": {"canonical_parameter_names": ["root", "targetSum"], "leetcode_dataset_entry_point": "Solution().pathSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var pathSum = function(root, targetSum) {", "container": null, "callable": "pathSum", "parameters": [{"name": "root", "type": "TreeNode"}, {"name": "targetSum", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 114, "task_id": "flatten-binary-tree-to-linked-list", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, flatten the tree into a \"linked list\":\n\nThe \"linked list\" should use the same TreeNode class where the right child pointer points to the next node in the list and the left child pointer is always null.\nThe \"linked list\" should be in the same order as a pre-order traversal of the binary tree.\n\n \nExample 1:\n\n\nInput: root = [1,2,5,3,4,null,6]\nOutput: [1,null,2,null,3,null,4,null,5,null,6]\n\nExample 2:\n\nInput: root = []\nOutput: []\n\nExample 3:\n\nInput: root = [0]\nOutput: [0]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 2000].\n-100 <= Node.val <= 100\n\n \nFollow up: Can you flatten the tree in-place (with O(1) extra space)?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == None\n assert candidate(root = tree_node([1, 2, 3, 4])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 7])) == None\n assert candidate(root = tree_node([1, 2])) == None\n assert candidate(root = tree_node([1, None, None, 2, None, 3, None, 4])) == None\n assert candidate(root = tree_node([1, None, 2])) == None\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == None\n assert candidate(root = tree_node([0])) == None\n assert candidate(root = tree_node([1, 2, 5, 3, 4, None, 6])) == None\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, 6])) == None\n assert candidate(root = tree_node([])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, 7, 8, 9, None, None, 10, 11, None, 12, 13, None, None, 14])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, None, 13, 14, None, None, 15, None, 16, 17, None, None, None, 18, None, None, 19, None, None, None, None, 20])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, 10, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == None\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9, None, None, 10, None, None, 11, None, None, 12])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, 7, 8, 9, 10, 11, 12, None, 13, None, 14, None, 15])) == None\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, 8, 9, None, 10, None, None, 11, 12])) == None\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6, None, None, 7, None, None, 8, None, None, 9, None, None, 10, None, None, 11, None, None, 12, None, None, 13, None, None, 14, None, None, 15, None, None, 16])) == None\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, 6, 7, 8, 9, None, None, 10, None, None, 11, None, None, 12])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, 7, None, None, None, 8, None, None, 9])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, None, None, 17, None, None, 18])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, None, 8, 9, None, None, 10, 11, None, None, 12, 13, None, None, 14, 15])) == None\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5])) == None\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, None, 6, 7])) == None\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == None\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, None, 7, None, None, None, None, 8])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30, None, 31, None, 32, None, 33, None, 34, None, 35])) == None\n assert candidate(root = tree_node([1, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, None, 5, None, None, 6, None, None, 7, None, None, 8])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, 10, None, None, 11, None, None, 12, 13, 14, None, None, 15])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, 9, 10, 11, 12, None, None, 13, 14])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, None, 7, None, 8, None, 9, None, 10])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25])) == None\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == None\n assert candidate(root = tree_node([10, 5, 15, None, 7, 13, None, None, None, 6, 8, 11, 14, None, None, None, 9])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == None\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, None, 8, 9, None, None, 10, 11])) == None\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7])) == None\n assert candidate(root = tree_node([1, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6, None, None, 7])) == None\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == None\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 18, 19, 21, 22])) == None\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == None\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == None\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9])) == None\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, 8, None, 9, None, None, 10, 11, None, None, 12, 13])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, None, 9, 10, 11, 12, None, None, None, None, 13, None, 14, None, 15, None, 16])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, 7, 8, 9, 10, None, None, 11, 12, 13, 14, None, None, 15, 16, 17, None, None, 18, 19, 20])) == None\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, None, 7, None, None, None, 8, None, None, 9, None, None, 10, None, None, 11, None, None, None, 12, None, None, 13, None, None, 14, None, None, None, 15])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, 16, 17, 18, 19, 20, None, None, None, None, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, None, 31, None, 32])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, 6, 7, None, None, None, None, 8, None])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, 16, 17, 18, 19, 20, None, 21, 22, 23, 24, None, 25, 26, 27, 28, 29, 30, None, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])) == None\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4, None, None, None, 5])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == None\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, 6, 7, None, 8, None, 9, None, 10])) == None\n assert candidate(root = tree_node([5, 3, 8, 1, 4, None, 9, None, 2, None, None, None, 6, 7])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, None, 8, 9])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, None, None, None, 8, 9])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == None\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == None\n assert candidate(root = tree_node([1, 2, None, None, 3, 4, None, None, 5, None, 6, 7, None, None, 8, 9, None, None, 10])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, None, None, 9, None, 10, 11, 12, 13, None, None, None, 14, None, None, 15])) == None\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, 7, None, None, None, None, None, 8, 9])) == None\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == None\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().flatten", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var flatten = function(root) {", "container": null, "callable": "flatten", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "void", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 115, "task_id": "distinct-subsequences", "difficulty": "Hard", "problem_description": "Given two strings s and t, return the number of distinct subsequences of s which equals t.\nThe test cases are generated so that the answer fits on a 32-bit signed integer.\n \nExample 1:\n\nInput: s = \"rabbbit\", t = \"rabbit\"\nOutput: 3\nExplanation:\nAs shown below, there are 3 ways you can generate \"rabbit\" from s.\nrabbbit\nrabbbit\nrabbbit\n\nExample 2:\n\nInput: s = \"babgbag\", t = \"bag\"\nOutput: 5\nExplanation:\nAs shown below, there are 5 ways you can generate \"bag\" from s.\nbabgbag\nbabgbag\nbabgbag\nbabgbag\nbabgbag\n \nConstraints:\n\n1 <= s.length, t.length <= 1000\ns and t consist of English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abc\",t = \"abcd\") == 0\n assert candidate(s = \"abcd\",t = \"abcd\") == 1\n assert candidate(s = \"rabbbit\",t = \"rabbit\") == 3\n assert candidate(s = \"aaa\",t = \"a\") == 3\n assert candidate(s = \"\",t = \"abc\") == 0\n assert candidate(s = \"mississippi\",t = \"isip\") == 16\n assert candidate(s = \"aaaaa\",t = \"aa\") == 10\n assert candidate(s = \"abcde\",t = \"ae\") == 1\n assert candidate(s = \"abcde\",t = \"\") == 1\n assert candidate(s = \"abcd\",t = \"ab\") == 1\n assert candidate(s = \"a\",t = \"a\") == 1\n assert candidate(s = \"abcdabcabc\",t = \"abc\") == 10\n assert candidate(s = \"babgbag\",t = \"bag\") == 5\n assert candidate(s = \"abc\",t = \"abc\") == 1\n assert candidate(s = \"pppp\",t = \"p\") == 4\n assert candidate(s = \"abab\",t = \"aba\") == 1\n assert candidate(s = \"\",t = \"\") == 1\n assert candidate(s = \"leetcodeisgood\",t = \"code\") == 1\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"acegikmoqsuwy\") == 1\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzz\",t = \"zzz\") == 1140\n assert candidate(s = \"dynamicprogramming\",t = \"dpm\") == 2\n assert candidate(s = \"ababababab\",t = \"abab\") == 35\n assert candidate(s = \"abcdabcdabcd\",t = \"abcd\") == 15\n assert candidate(s = \"abcdabcdabcdabcd\",t = \"abcd\") == 35\n assert candidate(s = \"zzzzzzzzzz\",t = \"zzzz\") == 210\n assert candidate(s = \"aaaabbbbccccdddd\",t = \"abcd\") == 256\n assert candidate(s = \"abracadabra\",t = \"abrac\") == 1\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefgabcdefg\",t = \"abcdefg\") == 330\n assert candidate(s = \"abcabcabcabcabcabcabcabc\",t = \"abcabc\") == 924\n assert candidate(s = \"ababcabcabc\",t = \"abc\") == 19\n assert candidate(s = \"abcdefghikjlmnopqrstuvwxyz\",t = \"xyz\") == 1\n assert candidate(s = \"abcabcabcabc\",t = \"abc\") == 20\n assert candidate(s = \"abcbabc\",t = \"abc\") == 5\n assert candidate(s = \"xyzxyzxyz\",t = \"xyzyx\") == 1\n assert candidate(s = \"aabbbccc\",t = \"abc\") == 18\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzz\") == 64512240\n assert candidate(s = \"xyzxyzxyzxyz\",t = \"xyz\") == 20\n assert candidate(s = \"aabbccddeeffgg\",t = \"aabbcc\") == 1\n assert candidate(s = \"abcdeabcdeabcde\",t = \"abc\") == 10\n assert candidate(s = \"xyzzxyzzxyzzxyzz\",t = \"xyz\") == 40\n assert candidate(s = \"xxyxyxyxyxyxyxyx\",t = \"xyx\") == 112\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"abc\") == 8\n assert candidate(s = \"xyxxyxyxyx\",t = \"xyx\") == 27\n assert candidate(s = \"mississippi\",t = \"issi\") == 15\n assert candidate(s = \"pneumonoultramicroscopicsilicovolcanoconiosis\",t = \"pneumo\") == 23\n assert candidate(s = \"pppppppppppp\",t = \"pppp\") == 495\n assert candidate(s = \"aaaaabaaaaabaabaaabaababab\",t = \"aab\") == 686\n assert candidate(s = \"abcdefg\",t = \"xyz\") == 0\n assert candidate(s = \"rabbbitrabbbitrabbbit\",t = \"rabbit\") == 126\n assert candidate(s = \"leetcodeleetcode\",t = \"leet\") == 12\n assert candidate(s = \"xyzxyzxyzxyz\",t = \"xyzxyz\") == 28\n assert candidate(s = \"abcdefghijk\",t = \"acegi\") == 1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"abcdefghijklmnopqrstuvwxyz\") == 67108864\n assert candidate(s = \"aabbccddeeffgg\",t = \"abcde\") == 32\n assert candidate(s = \"longerstringexample\",t = \"long\") == 3\n assert candidate(s = \"abracadabra\",t = \"abra\") == 9\n assert candidate(s = \"xxyyzzxxxyyzz\",t = \"xyxz\") == 24\n assert candidate(s = \"pppppppp\",t = \"pp\") == 28\n assert candidate(s = \"attatchmentattach\",t = \"attach\") == 32\n assert candidate(s = \"abcdefghijabcdefghij\",t = \"abcde\") == 6\n assert candidate(s = \"abcdabcdeabcdeabcd\",t = \"abcd\") == 35\n assert candidate(s = \"abcdefghij\",t = \"abcdefghijk\") == 0\n assert candidate(s = \"zzzzzzzzzz\",t = \"zz\") == 45\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzz\") == 14782231840815648\n assert candidate(s = \"ppppppppp\",t = \"ppp\") == 84\n assert candidate(s = \"abcdefghij\",t = \"j\") == 1\n assert candidate(s = \"abcdabcdabcdabcdabcd\",t = \"abcd\") == 70\n assert candidate(s = \"repeatedsequence\",t = \"seq\") == 1\n assert candidate(s = \"aaaaaaaaaaaaaab\",t = \"aaab\") == 364\n assert candidate(s = \"aabbaabbaabbaabbaabb\",t = \"aabb\") == 415\n assert candidate(s = \"mixedcharacters\",t = \"mix\") == 1\n assert candidate(s = \"abababababab\",t = \"ababab\") == 84\n assert candidate(s = \"abcabcabcabc\",t = \"abcabc\") == 28\n assert candidate(s = \"aaaaaaabbaaaaa\",t = \"aaaaaab\") == 14\n assert candidate(s = \"abcabcabc\",t = \"abc\") == 10\n assert candidate(s = \"abcdabcdabcd\",t = \"abca\") == 5\n assert candidate(s = \"babgbagbabgbagbabgbag\",t = \"bagbag\") == 329\n assert candidate(s = \"anappleperap\",t = \"ape\") == 10\n assert candidate(s = \"zzzzzzzzzz\",t = \"zzz\") == 120\n assert candidate(s = \"aaaaaaaaaa\",t = \"aaaaa\") == 252\n assert candidate(s = \"abcdefghij\",t = \"af\") == 1\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",t = \"abcabc\") == 3003\n assert candidate(s = \"complexpattern\",t = \"comp\") == 2\n assert candidate(s = \"abcdefghij\",t = \"a\") == 1\n assert candidate(s = \"aabbaabbaabbaabbaabb\",t = \"aab\") == 190\n assert candidate(s = \"abracadabraabracadabra\",t = \"abra\") == 103\n assert candidate(s = \"leetcodeleetcodeleetcode\",t = \"leet\") == 51\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmnoonnpooqqrrssttuuvvwwxxyyzz\",t = \"abcxyz\") == 64\n assert candidate(s = \"abcdefabcdefabcdef\",t = \"abcdef\") == 28\n assert candidate(s = \"abcdefghij\",t = \"acegi\") == 1\n assert candidate(s = \"pppppppppp\",t = \"pp\") == 45\n assert candidate(s = \"hellohellohello\",t = \"hellohello\") == 17\n assert candidate(s = \"abcdefghij\",t = \"aceg\") == 1\n assert candidate(s = \"aabbccddeeffgg\",t = \"abcdefg\") == 128\n assert candidate(s = \"hellohellohello\",t = \"he\") == 6\n assert candidate(s = \"thisisaverylongstringthisisaverylongstring\",t = \"thisisaverylongstring\") == 73\n assert candidate(s = \"subsequenceexample\",t = \"subseq\") == 1\n assert candidate(s = \"abracadabra\",t = \"aca\") == 6\n assert candidate(s = \"abcdeabcde\",t = \"abc\") == 4\n assert candidate(s = \"aaaaabaaaabaaaab\",t = \"aaab\") == 380\n assert candidate(s = \"abcdefghijabcdefghijabcdefghij\",t = \"abcde\") == 21\n"}, "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().numDistinct", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numDistinct = function(s, t) {", "container": null, "callable": "numDistinct", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 118, "task_id": "pascals-triangle", "difficulty": "Easy", "problem_description": "Given an integer numRows, return the first numRows of Pascal's triangle.\nIn Pascal's triangle, each number is the sum of the two numbers directly above it as shown:\n\n \nExample 1:\nInput: numRows = 5\nOutput: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]\nExample 2:\nInput: numRows = 1\nOutput: [[1]]\n\n \nConstraints:\n\n1 <= numRows <= 30\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(numRows = 10) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1]]\n assert candidate(numRows = 3) == [[1], [1, 1], [1, 2, 1]]\n assert candidate(numRows = 1) == [[1]]\n assert candidate(numRows = 5) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]\n assert candidate(numRows = 30) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1], [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1], [1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1], [1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1], [1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1], [1, 22, 231, 1540, 7315, 26334, 74613, 170544, 319770, 497420, 646646, 705432, 646646, 497420, 319770, 170544, 74613, 26334, 7315, 1540, 231, 22, 1], [1, 23, 253, 1771, 8855, 33649, 100947, 245157, 490314, 817190, 1144066, 1352078, 1352078, 1144066, 817190, 490314, 245157, 100947, 33649, 8855, 1771, 253, 23, 1], [1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1], [1, 25, 300, 2300, 12650, 53130, 177100, 480700, 1081575, 2042975, 3268760, 4457400, 5200300, 5200300, 4457400, 3268760, 2042975, 1081575, 480700, 177100, 53130, 12650, 2300, 300, 25, 1], [1, 26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, 5311735, 7726160, 9657700, 10400600, 9657700, 7726160, 5311735, 3124550, 1562275, 657800, 230230, 65780, 14950, 2600, 325, 26, 1], [1, 27, 351, 2925, 17550, 80730, 296010, 888030, 2220075, 4686825, 8436285, 13037895, 17383860, 20058300, 20058300, 17383860, 13037895, 8436285, 4686825, 2220075, 888030, 296010, 80730, 17550, 2925, 351, 27, 1], [1, 28, 378, 3276, 20475, 98280, 376740, 1184040, 3108105, 6906900, 13123110, 21474180, 30421755, 37442160, 40116600, 37442160, 30421755, 21474180, 13123110, 6906900, 3108105, 1184040, 376740, 98280, 20475, 3276, 378, 28, 1], [1, 29, 406, 3654, 23751, 118755, 475020, 1560780, 4292145, 10015005, 20030010, 34597290, 51895935, 67863915, 77558760, 77558760, 67863915, 51895935, 34597290, 20030010, 10015005, 4292145, 1560780, 475020, 118755, 23751, 3654, 406, 29, 1]]\n assert candidate(numRows = 17) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1]]\n assert candidate(numRows = 2) == [[1], [1, 1]]\n assert candidate(numRows = 16) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1]]\n assert candidate(numRows = 12) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1]]\n assert candidate(numRows = 28) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1], [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1], [1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1], [1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1], [1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1], [1, 22, 231, 1540, 7315, 26334, 74613, 170544, 319770, 497420, 646646, 705432, 646646, 497420, 319770, 170544, 74613, 26334, 7315, 1540, 231, 22, 1], [1, 23, 253, 1771, 8855, 33649, 100947, 245157, 490314, 817190, 1144066, 1352078, 1352078, 1144066, 817190, 490314, 245157, 100947, 33649, 8855, 1771, 253, 23, 1], [1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1], [1, 25, 300, 2300, 12650, 53130, 177100, 480700, 1081575, 2042975, 3268760, 4457400, 5200300, 5200300, 4457400, 3268760, 2042975, 1081575, 480700, 177100, 53130, 12650, 2300, 300, 25, 1], [1, 26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, 5311735, 7726160, 9657700, 10400600, 9657700, 7726160, 5311735, 3124550, 1562275, 657800, 230230, 65780, 14950, 2600, 325, 26, 1], [1, 27, 351, 2925, 17550, 80730, 296010, 888030, 2220075, 4686825, 8436285, 13037895, 17383860, 20058300, 20058300, 17383860, 13037895, 8436285, 4686825, 2220075, 888030, 296010, 80730, 17550, 2925, 351, 27, 1]]\n assert candidate(numRows = 7) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1]]\n assert candidate(numRows = 20) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1], [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1], [1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1]]\n assert candidate(numRows = 18) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1]]\n assert candidate(numRows = 15) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1]]\n assert candidate(numRows = 25) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1], [1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1], [1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1], [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1], [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1], [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1], [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1], [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1], [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1], [1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1], [1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1], [1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1], [1, 22, 231, 1540, 7315, 26334, 74613, 170544, 319770, 497420, 646646, 705432, 646646, 497420, 319770, 170544, 74613, 26334, 7315, 1540, 231, 22, 1], [1, 23, 253, 1771, 8855, 33649, 100947, 245157, 490314, 817190, 1144066, 1352078, 1352078, 1144066, 817190, 490314, 245157, 100947, 33649, 8855, 1771, 253, 23, 1], [1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1]]\n assert candidate(numRows = 4) == [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]\n"}, "metadata": {"canonical_parameter_names": ["numRows"], "leetcode_dataset_entry_point": "Solution().generate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var generate = function(numRows) {", "container": null, "callable": "generate", "parameters": [{"name": "numRows", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 119, "task_id": "pascals-triangle-ii", "difficulty": "Easy", "problem_description": "Given an integer rowIndex, return the rowIndexth (0-indexed) row of the Pascal's triangle.\nIn Pascal's triangle, each number is the sum of the two numbers directly above it as shown:\n\n \nExample 1:\nInput: rowIndex = 3\nOutput: [1,3,3,1]\nExample 2:\nInput: rowIndex = 0\nOutput: [1]\nExample 3:\nInput: rowIndex = 1\nOutput: [1,1]\n\n \nConstraints:\n\n0 <= rowIndex <= 33\n\n \nFollow up: Could you optimize your algorithm to use only O(rowIndex) extra space?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(rowIndex = 0) == [1]\n assert candidate(rowIndex = 10) == [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1]\n assert candidate(rowIndex = 15) == [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1]\n assert candidate(rowIndex = 1) == [1, 1]\n assert candidate(rowIndex = 3) == [1, 3, 3, 1]\n assert candidate(rowIndex = 20) == [1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970, 167960, 184756, 167960, 125970, 77520, 38760, 15504, 4845, 1140, 190, 20, 1]\n assert candidate(rowIndex = 5) == [1, 5, 10, 10, 5, 1]\n assert candidate(rowIndex = 33) == [1, 33, 528, 5456, 40920, 237336, 1107568, 4272048, 13884156, 38567100, 92561040, 193536720, 354817320, 573166440, 818809200, 1037158320, 1166803110, 1166803110, 1037158320, 818809200, 573166440, 354817320, 193536720, 92561040, 38567100, 13884156, 4272048, 1107568, 237336, 40920, 5456, 528, 33, 1]\n assert candidate(rowIndex = 11) == [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1]\n assert candidate(rowIndex = 7) == [1, 7, 21, 35, 35, 21, 7, 1]\n assert candidate(rowIndex = 8) == [1, 8, 28, 56, 70, 56, 28, 8, 1]\n assert candidate(rowIndex = 30) == [1, 30, 435, 4060, 27405, 142506, 593775, 2035800, 5852925, 14307150, 30045015, 54627300, 86493225, 119759850, 145422675, 155117520, 145422675, 119759850, 86493225, 54627300, 30045015, 14307150, 5852925, 2035800, 593775, 142506, 27405, 4060, 435, 30, 1]\n assert candidate(rowIndex = 25) == [1, 25, 300, 2300, 12650, 53130, 177100, 480700, 1081575, 2042975, 3268760, 4457400, 5200300, 5200300, 4457400, 3268760, 2042975, 1081575, 480700, 177100, 53130, 12650, 2300, 300, 25, 1]\n assert candidate(rowIndex = 16) == [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1]\n assert candidate(rowIndex = 29) == [1, 29, 406, 3654, 23751, 118755, 475020, 1560780, 4292145, 10015005, 20030010, 34597290, 51895935, 67863915, 77558760, 77558760, 67863915, 51895935, 34597290, 20030010, 10015005, 4292145, 1560780, 475020, 118755, 23751, 3654, 406, 29, 1]\n assert candidate(rowIndex = 22) == [1, 22, 231, 1540, 7315, 26334, 74613, 170544, 319770, 497420, 646646, 705432, 646646, 497420, 319770, 170544, 74613, 26334, 7315, 1540, 231, 22, 1]\n assert candidate(rowIndex = 12) == [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1]\n assert candidate(rowIndex = 28) == [1, 28, 378, 3276, 20475, 98280, 376740, 1184040, 3108105, 6906900, 13123110, 21474180, 30421755, 37442160, 40116600, 37442160, 30421755, 21474180, 13123110, 6906900, 3108105, 1184040, 376740, 98280, 20475, 3276, 378, 28, 1]\n assert candidate(rowIndex = 18) == [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1]\n assert candidate(rowIndex = 27) == [1, 27, 351, 2925, 17550, 80730, 296010, 888030, 2220075, 4686825, 8436285, 13037895, 17383860, 20058300, 20058300, 17383860, 13037895, 8436285, 4686825, 2220075, 888030, 296010, 80730, 17550, 2925, 351, 27, 1]\n"}, "metadata": {"canonical_parameter_names": ["rowIndex"], "leetcode_dataset_entry_point": "Solution().getRow", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getRow = function(rowIndex) {", "container": null, "callable": "getRow", "parameters": [{"name": "rowIndex", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 120, "task_id": "triangle", "difficulty": "Medium", "problem_description": "Given a triangle array, return the minimum path sum from top to bottom.\nFor each step, you may move to an adjacent number of the row below. More formally, if you are on index i on the current row, you may move to either index i or index i + 1 on the next row.\n \nExample 1:\n\nInput: triangle = [[2],[3,4],[6,5,7],[4,1,8,3]]\nOutput: 11\nExplanation: The triangle looks like:\n 2\n 3 4\n 6 5 7\n4 1 8 3\nThe minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above).\n\nExample 2:\n\nInput: triangle = [[-10]]\nOutput: -10\n\n \nConstraints:\n\n1 <= triangle.length <= 200\ntriangle[0].length == 1\ntriangle[i].length == triangle[i - 1].length + 1\n-104 <= triangle[i][j] <= 104\n\n \nFollow up: Could you do this using only O(n) extra space, where n is the total number of rows in the triangle?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(triangle = [[-10]]) == -10\n assert candidate(triangle = [[-1], [2, 3], [1, -1, -3], [-2, 1, -1, -2]]) == -3\n assert candidate(triangle = [[0], [1, 2], [3, 4, 5], [6, 7, 8, 9]]) == 10\n assert candidate(triangle = [[-1], [2, -2], [3, -3, 3], [-4, -4, 4, 4]]) == -10\n assert candidate(triangle = [[-1], [2, 3], [1, -1, -3]]) == -1\n assert candidate(triangle = [[2], [3, 4], [6, 5, 7], [4, 1, 8, 3]]) == 11\n assert candidate(triangle = [[0], [1, 0], [1, 1, 1], [1, 2, 3, 4]]) == 3\n assert candidate(triangle = [[0], [-1, -2], [-3, -4, -5]]) == -7\n assert candidate(triangle = [[0], [10000, -10000], [10000, 10000, 10000]]) == 0\n assert candidate(triangle = [[3], [7, 4], [2, 4, 6], [8, 5, 9, 3]]) == 16\n assert candidate(triangle = [[-1], [2, -3], [4, -5, 6], [-7, 8, -9, 10]]) == -18\n assert candidate(triangle = [[1], [2, 3], [4, 5, 6]]) == 7\n assert candidate(triangle = [[1], [2, 3], [4, 5, 6], [7, 8, 9, 10]]) == 14\n assert candidate(triangle = [[10], [20, 30], [40, 50, 60], [70, 80, 90, 100], [110, 120, 130, 140, 150]]) == 250\n assert candidate(triangle = [[5], [9, 6], [4, 6, 8], [4, 2, 6, 5], [8, 4, 9, 6, 1]]) == 23\n assert candidate(triangle = [[-10000], [10000, -10000], [10000, 10000, 10000], [10000, -10000, 10000, -10000], [10000, 10000, 10000, 10000, 10000]]) == -10000\n assert candidate(triangle = [[-1], [0, -2], [0, -1, 0], [-1, 0, -1, 0]]) == -5\n assert candidate(triangle = [[5], [9, 4], [2, 6, 7], [4, 6, 8, 4], [9, 5, 2, 1, 3]]) == 21\n assert candidate(triangle = [[1], [2, 1], [1, 2, 3], [4, 1, 2, 3], [3, 4, 1, 2, 3]]) == 6\n assert candidate(triangle = [[-1], [-2, -3], [-4, -5, -6], [-7, -8, -9, -10], [-11, -12, -13, -14, -15]]) == -35\n assert candidate(triangle = [[-1], [0, -1], [0, 0, -1], [0, 0, 0, -1], [0, 0, 0, 0, -1]]) == -5\n assert candidate(triangle = [[-1], [-1, -2], [-1, -2, -3], [-1, -2, -3, -4], [-1, -2, -3, -4, -5]]) == -15\n assert candidate(triangle = [[1], [-2, 3], [-4, 5, -6], [-7, -8, 9, 10], [-11, 12, -13, 14, -15]]) == -26\n assert candidate(triangle = [[1], [2, 1], [3, 3, 2], [4, 6, 5, 4], [5, 7, 9, 8, 5]]) == 13\n assert candidate(triangle = [[100], [90, 110], [80, 90, 100], [70, 80, 90, 100], [60, 70, 80, 90, 100]]) == 400\n assert candidate(triangle = [[1], [2, 3], [1, 1, 1], [3, 2, 1, 4], [4, 5, 2, 3, 1]]) == 7\n assert candidate(triangle = [[10000], [9999, 10001], [-10000, 10000, 10000], [10000, 10000, 10000, 10000], [0, 0, 0, 0, 0]]) == 19999\n assert candidate(triangle = [[1], [2, 2], [3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6], [7, 7, 7, 7, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 8]]) == 36\n assert candidate(triangle = [[-5], [3, -8], [6, -7, -4], [2, -6, 5, -7], [8, -4, -3, 5, -2]]) == -30\n assert candidate(triangle = [[-7], [10, -3], [-6, 1, -4], [6, -5, 8, -6], [4, 3, -6, 2, -5]]) == -25\n assert candidate(triangle = [[-10000], [10000, -10000], [0, 0, 0], [10000, 10000, -10000, -10000], [10000, -10000, 10000, -10000, 10000]]) == -40000\n assert candidate(triangle = [[-1], [-2, -2], [-3, -3, -3], [-4, -4, -4, -4], [-5, -5, -5, -5, -5], [-6, -6, -6, -6, -6, -6]]) == -21\n assert candidate(triangle = [[5], [4, 4], [3, 3, 3], [2, 2, 2, 2], [1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]]) == 15\n assert candidate(triangle = [[5], [9, 6], [4, 6, 8], [4, 2, 6, 5], [4, 4, 1, 7, 6]]) == 20\n assert candidate(triangle = [[9999], [9998, 9999], [9997, 9998, 9999], [9996, 9997, 9998, 9999]]) == 39990\n assert candidate(triangle = [[0], [0, 0], [0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 0\n assert candidate(triangle = [[7], [3, 8], [8, 1, 0], [2, 7, 4, 4], [4, 5, 2, 6, 5]]) == 17\n assert candidate(triangle = [[1], [2, 3], [4, 5, 6], [7, 8, 9, 10], [11, 12, 13, 14, 15]]) == 25\n assert candidate(triangle = [[-9999], [-9998, -9999], [-9997, -9998, -9999], [-9996, -9997, -9998, -9999]]) == -39996\n assert candidate(triangle = [[-1], [0, -1], [-1, 0, -1], [-1, -1, 0, -1]]) == -4\n assert candidate(triangle = [[-100], [100, -200], [300, -400, 500], [-600, 700, -800, 900], [1000, -1100, 1200, -1300, 1400]]) == -2800\n assert candidate(triangle = [[5], [3, 4], [1, 6, 5], [9, 4, 3, 8], [8, 9, 6, 4, 5]]) == 19\n assert candidate(triangle = [[-10], [10, -20], [20, 30, -40], [-40, 50, 60, 70], [-70, 80, -90, 100, 110]]) == -100\n assert candidate(triangle = [[1], [9, 2], [8, 7, 3], [6, 5, 4, 9], [5, 7, 8, 4, 6], [1, 5, 6, 7, 2, 3]]) == 16\n assert candidate(triangle = [[-100], [200, -300], [400, -500, 600], [-700, 800, -900, 1000], [-1100, 1200, -1300, 1400, -1500]]) == -3100\n assert candidate(triangle = [[10], [-10, 20], [-20, 30, 40], [-30, 40, 50, 60], [-40, 50, 60, 70, 80]]) == -90\n assert candidate(triangle = [[1], [2, 2], [3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6]]) == 21\n assert candidate(triangle = [[10], [5, 3], [2, 3, 4], [7, 1, 0, 2], [6, 3, 2, 5, 4]]) == 18\n assert candidate(triangle = [[-1], [3, -2], [1, -4, 7], [-8, 2, 3, -1], [1, -1, 2, -2, 3]]) == -6\n assert candidate(triangle = [[-1000], [-500, 2500], [-200, 1000, -750], [-1000, 500, -250, 1000], [-750, 1250, -375, 625, -1000]]) == -3450\n assert candidate(triangle = [[-1], [2, 3], [-4, 5, 6], [7, -8, 9, 10], [-11, 12, -13, 14, 15], [16, -17, 18, -19, 20, 21]]) == -43\n assert candidate(triangle = [[10], [9, 11], [7, 15, 12], [4, 8, 10, 13], [6, 7, 12, 7, 8]]) == 36\n assert candidate(triangle = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9]]) == 15\n assert candidate(triangle = [[1], [2, 2], [3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5, 5]]) == 15\n assert candidate(triangle = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9, -10], [-11, -12, -13, -14, -15]]) == -29\n assert candidate(triangle = [[-1000], [-500, 500], [-250, 0, 250], [-125, -50, 50, 125], [-62, -25, 0, 25, 62]]) == -1937\n assert candidate(triangle = [[0], [1, -1], [2, -2, 2], [-3, 3, -3, 3], [4, -4, 4, -4, 4]]) == -10\n assert candidate(triangle = [[0], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]) == 4\n assert candidate(triangle = [[-5000], [-4000, 4000], [-3000, -2000, 3000], [-1000, 0, 2000, -3000], [-4000, 1000, -2000, 3000, 4000]]) == -17000\n assert candidate(triangle = [[-100], [100, -200], [300, -400, 500], [1000, -1000, 1000, -1000], [2000, -2000, 2000, -2000, 2000]]) == -3700\n assert candidate(triangle = [[10000], [-10000, 10000], [-10000, -10000, -10000], [-10000, -10000, -10000, -10000]]) == -20000\n assert candidate(triangle = [[5], [7, 8], [2, 3, 4], [4, 9, 6, 1], [7, 8, 4, 5, 9]]) == 23\n assert candidate(triangle = [[9999], [10000, 9999], [10000, 10000, 9999], [10000, 10000, 10000, 9999], [10000, 10000, 10000, 10000, 9999]]) == 49995\n assert candidate(triangle = [[-5], [-2, -3], [-1, -2, -4], [3, 2, -1, -1], [-1, -2, -3, -4, -5]]) == -18\n assert candidate(triangle = [[-10], [100, -200], [300, 400, -500], [-600, 700, -800, 900]]) == -1510\n assert candidate(triangle = [[-10], [20, 30], [-10, -20, -30], [40, 50, 60, 70], [-80, -90, -100, -110, -120]]) == -60\n assert candidate(triangle = [[1], [2, 2], [3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5, 5], [6, 6, 6, 6, 6, 6], [7, 7, 7, 7, 7, 7, 7], [8, 8, 8, 8, 8, 8, 8, 8], [9, 9, 9, 9, 9, 9, 9, 9, 9]]) == 45\n assert candidate(triangle = [[-10000], [-9000, -9000], [-8000, -8000, -8000], [-7000, -7000, -7000, -7000], [-6000, -6000, -6000, -6000, -6000]]) == -40000\n assert candidate(triangle = [[100], [-50, 100], [-25, 50, -75], [20, -20, 20, -20]]) == 5\n assert candidate(triangle = [[10000], [9999, -9999], [9998, -9998, -9998], [9997, -9997, -9997, -9997]]) == -19994\n assert candidate(triangle = [[10000], [10000, 10000], [10000, 10000, 10000], [10000, 10000, 10000, 10000], [10000, 10000, 10000, 10000, 10000]]) == 50000\n assert candidate(triangle = [[100], [200, 300], [400, 500, 600], [700, 800, 900, 1000], [1100, 1200, 1300, 1400, 1500], [1600, 1700, 1800, 1900, 2000, 2100]]) == 4100\n assert candidate(triangle = [[5], [3, 8], [6, 7, 4], [2, 6, 5, 7], [8, 4, 3, 5, 2]]) == 20\n assert candidate(triangle = [[-1, 2, 3], [4, 5, -6], [7, -8, 9, 10], [11, 12, 13, -14, 15]]) == -1\n assert candidate(triangle = [[1], [2, 3], [4, 5, 6], [7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20, 21]]) == 41\n assert candidate(triangle = [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]]) == 7\n assert candidate(triangle = [[1], [1, 9999], [9999, 9999, 9999], [9999, 9999, 9999, 9999], [9999, 9999, 9999, 9999, 9999]]) == 29999\n assert candidate(triangle = [[-100], [-50, 20], [-15, -25, 30], [-5, -10, 15, 20], [10, 20, 30, -40, -50]]) == -200\n assert candidate(triangle = [[-5], [10, -4], [-6, 1, -5], [7, -8, 9, -2], [4, 3, -7, 2, -6], [1, 5, 6, 7, 2, -3]]) == -25\n assert candidate(triangle = [[0], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]) == 5\n assert candidate(triangle = [[-10000], [10000, -9999], [9998, -9997, 9996], [9995, -9994, 9993, -9992], [9991, -9990, 9989, -9988, 9987]]) == -49980\n assert candidate(triangle = [[-10000], [10000, -10000], [10000, -10000, 10000], [-10000, 10000, -10000, 10000]]) == -40000\n assert candidate(triangle = [[100], [101, 102], [103, 104, 105], [106, 107, 108, 109], [110, 111, 112, 113, 114]]) == 520\n assert candidate(triangle = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26], [27, 28, 29, 30, 31, 32, 33, 34, 35]]) == 65\n assert candidate(triangle = [[-1], [0, -2], [1, 2, -3], [0, -1, 2, 3], [-1, 0, 2, -2, 3]]) == -6\n assert candidate(triangle = [[-100], [-200, -300], [-400, -500, -600], [-700, -800, -900, -1000]]) == -2000\n assert candidate(triangle = [[10000], [-10000, 10000], [-10000, -10000, 10000], [10000, 10000, -10000, 10000]]) == -20000\n assert candidate(triangle = [[100], [-200, 300], [-400, 500, 600], [-700, 800, -900, 1000], [-1100, 1200, 1300, 1400, 1500]]) == -2300\n assert candidate(triangle = [[-1000], [1000, -1000], [500, -500, 500], [250, -250, 250, -250]]) == -2750\n assert candidate(triangle = [[-5], [-4, -6], [-3, -6, -9], [-2, -6, -9, -12], [-1, -6, -9, -12, -15]]) == -47\n assert candidate(triangle = [[-100], [-200, 150], [-50, -100, -150], [200, 300, 400, 500]]) == -150\n assert candidate(triangle = [[-1], [2, 3], [-4, -5, -6], [-7, 8, -9, 10], [-11, -12, 13, -14, 15]]) == -27\n"}, "metadata": {"canonical_parameter_names": ["triangle"], "leetcode_dataset_entry_point": "Solution().minimumTotal", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minimumTotal = function(triangle) {", "container": null, "callable": "minimumTotal", "parameters": [{"name": "triangle", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 121, "task_id": "best-time-to-buy-and-sell-stock", "difficulty": "Easy", "problem_description": "You are given an array prices where prices[i] is the price of a given stock on the ith day.\nYou want to maximize your profit by choosing a single day to buy one stock and choosing a different day in the future to sell that stock.\nReturn the maximum profit you can achieve from this transaction. If you cannot achieve any profit, return 0.\n \nExample 1:\n\nInput: prices = [7,1,5,3,6,4]\nOutput: 5\nExplanation: Buy on day 2 (price = 1) and sell on day 5 (price = 6), profit = 6-1 = 5.\nNote that buying on day 2 and selling on day 1 is not allowed because you must buy before you sell.\n\nExample 2:\n\nInput: prices = [7,6,4,3,1]\nOutput: 0\nExplanation: In this case, no transactions are done and the max profit = 0.\n\n \nConstraints:\n\n1 <= prices.length <= 105\n0 <= prices[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(prices = [10, 9, 8, 2]) == 0\n assert candidate(prices = [1]) == 0\n assert candidate(prices = [2, 1, 2, 1, 0, 1, 2]) == 2\n assert candidate(prices = [2, 1]) == 0\n assert candidate(prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 4\n assert candidate(prices = [7, 1, 5, 3, 6, 4]) == 5\n assert candidate(prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(prices = [1, 2]) == 1\n assert candidate(prices = [8, 9, 7, 9, 8, 7, 9, 10, 7, 9, 8, 10, 11, 10, 12]) == 5\n assert candidate(prices = [1, 2, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6]) == 5\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 1, 2, 3, 8, 2, 10]) == 9\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [8, 6, 7, 3, 3, 5, 1, 0, 6, 5]) == 6\n assert candidate(prices = [1, 5, 3, 8, 12, 10, 9, 15, 18, 5, 7]) == 17\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 1, 5, 3, 7, 10, 4, 8, 12, 6, 14, 2, 18, 9, 20, 1, 22, 10, 24, 5, 26, 11, 28, 12, 30, 13, 32, 14, 34, 15, 36, 16, 38, 17, 40]) == 40\n assert candidate(prices = [8, 3, 6, 2, 8, 8, 8, 4, 2, 0, 9, 5, 7, 6, 2]) == 9\n assert candidate(prices = [4, 1, 2, 3, 5, 6, 1, 2, 3, 1, 5, 6, 7, 8, 1, 2, 3, 1]) == 7\n assert candidate(prices = [897, 456, 680, 509, 535, 695, 890, 456, 509, 535, 695, 890, 456, 509, 535, 695]) == 434\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(prices = [100, 180, 260, 40, 310, 535, 695, 10, 1]) == 655\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(prices = [100, 90, 80, 50, 20, 10]) == 0\n assert candidate(prices = [1, 2, 3, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8]) == 7\n assert candidate(prices = [3, 2, 6, 5, 0, 3]) == 4\n assert candidate(prices = [100, 180, 260, 40, 310, 535, 695]) == 655\n assert candidate(prices = [1, 9, 2, 8, 3, 7, 4, 6, 5, 10]) == 9\n assert candidate(prices = [1, 9, 6, 9, 1, 7, 1, 1, 5, 9, 9, 9, 8, 9, 8, 9, 10, 9, 8, 9, 10]) == 9\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 8\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(prices = [8, 6, 4, 6, 8, 9, 3, 4, 5, 1]) == 5\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 10, 2, 8, 15]) == 14\n assert candidate(prices = [5, 2, 3, 4, 1, 6, 8, 7, 8, 9]) == 8\n assert candidate(prices = [100, 180, 260, 310, 40, 535, 695]) == 655\n assert candidate(prices = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 9\n assert candidate(prices = [10, 10, 10, 5, 5, 5, 10, 10, 15, 15]) == 10\n assert candidate(prices = [8, 5, 12, 9, 19, 1, 7, 17, 3, 18]) == 17\n assert candidate(prices = [30, 15, 50, 10, 60, 35, 100, 40, 90, 50, 120, 60, 130, 70, 140, 80, 150, 90]) == 140\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [50, 20, 30, 10, 50, 20, 30, 10, 50, 20, 30, 10, 50, 20, 30, 10, 50, 20, 30, 10, 50]) == 40\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 1\n assert candidate(prices = [8, 4, 6, 2, 3, 10, 14, 11, 13]) == 12\n assert candidate(prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 0\n assert candidate(prices = [1, 5, 3, 7, 10, 4, 8, 12, 6, 14, 2, 18, 9, 20, 1, 22, 10, 24, 5, 26, 11, 28, 12, 30, 13, 32, 14, 34, 15, 36]) == 35\n assert candidate(prices = [5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 8, 9, 2, 1, 5, 6, 3, 10]) == 9\n assert candidate(prices = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 10\n assert candidate(prices = [1, 3, 2, 5, 7, 11, 8, 12, 14, 15]) == 14\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3]) == 2\n assert candidate(prices = [10, 1, 1, 6, 9, 1, 2, 1, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [1, 5, 3, 8, 12, 7, 9, 2, 3, 15, 10]) == 14\n assert candidate(prices = [8, 6, 7, 8, 4, 9, 1, 9, 4, 5]) == 8\n assert candidate(prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [1, 2, 1, 3, 1, 2, 3, 1, 2, 3, 4]) == 3\n assert candidate(prices = [5, 2, 3, 0, 3, 1, 6, 2, 8, 3, 4]) == 8\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 10, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == 9\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [1, 5, 3, 6, 7, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1]) == 9\n assert candidate(prices = [1, 9, 1, 9, 1, 9, 1, 9, 1, 9]) == 8\n assert candidate(prices = [100, 200, 300, 100, 150, 200, 250, 100, 150, 200, 250, 300, 100, 150, 200, 250]) == 200\n assert candidate(prices = [1, 3, 2, 8, 4, 9, 3, 5, 2, 10, 1, 3, 7, 2, 4, 9, 1, 6, 3, 5]) == 9\n assert candidate(prices = [1, 9, 18, 2, 7, 21, 12, 17, 6, 19]) == 20\n assert candidate(prices = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1]) == 2\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 9\n assert candidate(prices = [5, 11, 3, 50, 60, 90, 70, 80, 65, 30, 55, 95]) == 92\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [8, 6, 4, 3, 3, 5, 10, 0, 6, 2, 9, 10, 4, 7, 1]) == 10\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5]) == 5\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [2, 2, 5, 11, 1, 3, 4, 11, 1, 2, 11, 3, 4]) == 10\n assert candidate(prices = [1, 7, 2, 9, 4, 6, 3, 8, 5, 10]) == 9\n assert candidate(prices = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(prices = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 1\n assert candidate(prices = [10, 22, 5, 75, 65, 80]) == 75\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9]) == 9\n assert candidate(prices = [1, 9, 6, 9, 2, 8, 7, 1, 9, 4, 9, 2, 3, 8, 1, 6, 5, 8, 1, 1, 5]) == 8\n assert candidate(prices = [5, 3, 6, 7, 2, 8, 1, 4, 9, 10, 1, 11]) == 10\n assert candidate(prices = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(prices = [1, 2, 3, 2, 4, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(prices = [1, 9, 6, 9, 1, 7, 1, 1, 5, 9, 9, 9, 8]) == 8\n assert candidate(prices = [1, 9, 6, 9, 1, 7, 1, 1, 5, 9, 9, 9]) == 8\n assert candidate(prices = [5, 2, 6, 1, 9, 12, 9, 12, 12, 1, 5, 3, 3, 5, 2, 8, 10, 9, 1, 2]) == 11\n assert candidate(prices = [1, 3, 2, 8, 4, 9, 3, 5, 10, 6, 2, 3, 1, 5, 20, 3, 1, 2, 3, 10]) == 19\n assert candidate(prices = [10, 7, 5, 8, 11, 9]) == 6\n assert candidate(prices = [1, 5, 3, 7, 10, 4, 8, 12, 6, 14, 2, 18, 9, 20, 1, 22, 10, 24, 5, 26, 11, 28, 12, 30, 13, 32]) == 31\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 4\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 9\n assert candidate(prices = [1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100]) == 99\n assert candidate(prices = [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]) == 3\n assert candidate(prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [5, 9, 1, 6, 2, 8, 3, 7, 4, 10]) == 9\n assert candidate(prices = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(prices = [10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1]) == 9\n assert candidate(prices = [310, 310, 275, 275, 260, 260, 260, 230, 230, 230]) == 0\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 8\n assert candidate(prices = [1, 3, 2, 4, 7, 5, 8, 11, 9, 13]) == 12\n"}, "metadata": {"canonical_parameter_names": ["prices"], "leetcode_dataset_entry_point": "Solution().maxProfit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProfit = function(prices) {", "container": null, "callable": "maxProfit", "parameters": [{"name": "prices", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 122, "task_id": "best-time-to-buy-and-sell-stock-ii", "difficulty": "Medium", "problem_description": "You are given an integer array prices where prices[i] is the price of a given stock on the ith day.\nOn each day, you may decide to buy and/or sell the stock. You can only hold at most one share of the stock at any time. However, you can buy it then immediately sell it on the same day.\nFind and return the maximum profit you can achieve.\n \nExample 1:\n\nInput: prices = [7,1,5,3,6,4]\nOutput: 7\nExplanation: Buy on day 2 (price = 1) and sell on day 3 (price = 5), profit = 5-1 = 4.\nThen buy on day 4 (price = 3) and sell on day 5 (price = 6), profit = 6-3 = 3.\nTotal profit is 4 + 3 = 7.\n\nExample 2:\n\nInput: prices = [1,2,3,4,5]\nOutput: 4\nExplanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.\nTotal profit is 4.\n\nExample 3:\n\nInput: prices = [7,6,4,3,1]\nOutput: 0\nExplanation: There is no way to make a positive profit, so we never buy the stock to achieve the maximum profit of 0.\n\n \nConstraints:\n\n1 <= prices.length <= 3 * 104\n0 <= prices[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [1, 2, 2, 3, 4, 4, 5]) == 4\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1]) == 3\n assert candidate(prices = [6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [1, 9, 6, 9, 1, 7, 1, 1, 5, 9, 9, 9]) == 25\n assert candidate(prices = [1, 2, 2, 3, 0, 4]) == 6\n assert candidate(prices = [1, 2]) == 1\n assert candidate(prices = [1]) == 0\n assert candidate(prices = [1, 3, 2, 8, 4, 9]) == 13\n assert candidate(prices = [7, 1, 5, 3, 6, 4]) == 7\n assert candidate(prices = [3, 2, 6, 5, 0, 3]) == 7\n assert candidate(prices = [1, 2, 2, 3, 4, 5]) == 4\n assert candidate(prices = [10, 9, 8, 2]) == 0\n assert candidate(prices = [1, 100]) == 99\n assert candidate(prices = [1, 9, 6, 9, 1, 7, 1, 1, 5, 9, 9, 9, 8, 9]) == 26\n assert candidate(prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 4, 5, 6]) == 7\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 8\n assert candidate(prices = [1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 2, 8, 3, 10, 2, 5, 8, 12]) == 30\n assert candidate(prices = [1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10]) == 16\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [30, 28, 25, 22, 20, 18, 15, 13, 10, 8, 5, 3, 1, 0, 2, 4, 6, 8]) == 8\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 12\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]) == 15\n assert candidate(prices = [2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15]) == 26\n assert candidate(prices = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(prices = [100, 101, 102, 98, 97, 96, 100, 105, 110, 108, 107, 109, 112, 115, 118, 120, 119, 117, 116, 115, 114, 113, 112, 111, 110, 109]) == 29\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 19\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 10, 8, 12, 15, 10, 18, 14, 20, 25, 22, 27, 30]) == 47\n assert candidate(prices = [5, 2, 4, 9, 8, 10, 3, 2, 6, 4, 8]) == 17\n assert candidate(prices = [8, 6, 4, 6, 8, 7, 4, 12, 14, 13, 11, 10, 8, 6, 4, 2, 0]) == 14\n assert candidate(prices = [1, 5, 3, 8, 12, 4, 7, 15, 10, 18, 14, 20, 25, 22, 27, 30]) == 51\n assert candidate(prices = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 48\n assert candidate(prices = [5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 8\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [5, 3, 2, 6, 7, 8, 4, 5, 6, 1, 2, 3]) == 10\n assert candidate(prices = [5, 2, 3, 7, 6, 1, 8, 4, 9]) == 17\n assert candidate(prices = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [10, 7, 5, 8, 11, 9]) == 6\n assert candidate(prices = [8, 6, 4, 2, 0, 2, 4, 6, 8, 10, 12, 14, 16]) == 16\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 0, 0, 1, 8]) == 11\n assert candidate(prices = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2]) == 10\n assert candidate(prices = [80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80]) == 0\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 10\n assert candidate(prices = [1, 3, 2, 5, 7, 8, 9, 10, 12, 11, 13, 15, 14, 16, 17]) == 19\n assert candidate(prices = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]) == 8\n assert candidate(prices = [10, 9, 8, 2, 3, 6, 8, 5, 8, 10]) == 11\n assert candidate(prices = [5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == 8\n assert candidate(prices = [5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [5, 3, 5, 10, 4, 8, 2, 6, 7, 2, 3, 1, 5, 9, 10, 3, 2, 1, 5, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 44\n assert candidate(prices = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [10, 7, 5, 8, 11, 9, 12, 10, 14, 13, 15]) == 15\n assert candidate(prices = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14]) == 26\n assert candidate(prices = [1, 2, 3, 2, 4, 5, 3, 6, 7, 5, 8, 9, 7, 10, 11, 9]) == 17\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 1\n assert candidate(prices = [7, 1, 3, 4, 6, 2, 5, 7, 8, 1, 9, 11, 13, 10]) == 23\n assert candidate(prices = [2, 1, 2, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 26\n assert candidate(prices = [1, 5, 1, 3, 1, 5, 1, 3, 1, 5]) == 16\n assert candidate(prices = [1, 2, 2, 3, 0, 1, 2, 1, 2, 3]) == 6\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 4, 5, 2, 3, 0, 4, 2, 3]) == 15\n assert candidate(prices = [1, 3, 2, 8, 4, 9, 5, 10, 6, 11, 7, 12, 8, 13, 9, 14, 10, 15, 11, 16, 12, 17, 13, 18, 14, 19, 15, 20]) == 68\n assert candidate(prices = [10, 9, 10, 8, 11, 7, 12, 6, 13, 5, 14, 4, 15, 3, 16, 2, 17, 1]) == 64\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 23\n assert candidate(prices = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 28\n assert candidate(prices = [8, 6, 4, 3, 3, 5, 7, 9, 10, 8, 11, 13, 12, 15, 17]) == 17\n assert candidate(prices = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15]) == 27\n assert candidate(prices = [1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6]) == 5\n assert candidate(prices = [1, 2, 2, 2, 3, 4, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12]) == 11\n assert candidate(prices = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80]) == 0\n assert candidate(prices = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == 9\n assert candidate(prices = [1, 2, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 14, 15]) == 16\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [10, 7, 15, 8, 12, 9, 20, 18, 25, 17]) == 30\n assert candidate(prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30]) == 30\n assert candidate(prices = [7, 2, 5, 3, 10, 1, 3, 8, 1, 9, 2, 6]) == 29\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]) == 12\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10]) == 18\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 10, 8, 6, 8, 12, 10, 8, 10, 14, 12, 10, 12, 16, 14, 12, 14, 18, 16, 14, 16]) == 39\n assert candidate(prices = [1, 5, 3, 8, 12, 10, 14, 18, 22, 20, 25, 28, 26, 30, 32, 31, 35, 38]) == 46\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 5, 8, 2, 9, 1, 5, 7, 3, 8]) == 29\n assert candidate(prices = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == 9\n assert candidate(prices = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 14\n assert candidate(prices = [8, 12, 4, 6, 10, 3, 12, 7, 9, 8]) == 21\n assert candidate(prices = [1, 3, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == 13\n assert candidate(prices = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 0\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 9\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2]) == 5\n assert candidate(prices = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15]) == 26\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 8\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 9\n assert candidate(prices = [10, 9, 8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 17\n assert candidate(prices = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 15\n assert candidate(prices = [10, 5, 10, 20, 10, 15, 10, 25, 15, 30, 20, 35, 25, 40, 30]) == 80\n assert candidate(prices = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 101]) == 1\n assert candidate(prices = [5, 3, 6, 7, 4, 3, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 21\n assert candidate(prices = [1, 3, 2, 8, 4, 9, 5, 10, 6, 11, 7, 12, 8, 13, 9, 14, 10, 15, 11, 16]) == 48\n assert candidate(prices = [2, 2, 5, 0, 1, 5, 0, 3, 1, 2, 5]) == 15\n assert candidate(prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50]) == 50\n assert candidate(prices = [10, 7, 5, 8, 11, 9]) == 6\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 8\n assert candidate(prices = [1, 3, 2, 4, 5, 7, 6, 8, 9, 11, 10, 12, 14, 13, 15]) == 18\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 10\n assert candidate(prices = [1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100]) == 990\n assert candidate(prices = [1, 2, 2, 6, 3, 5, 4, 8, 7, 9, 10, 11, 10, 12, 13, 14, 15, 16]) == 21\n assert candidate(prices = [1, 2, 3, 2, 1, 4, 5, 4, 3, 2, 1, 6, 7, 6, 5, 4, 3, 2, 1]) == 12\n assert candidate(prices = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 4\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 20, 15, 16, 14, 22, 25, 30, 35, 40]) == 46\n assert candidate(prices = [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 23\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(prices = [1, 5, 3, 9, 7, 8, 4, 10, 1, 12, 11, 13]) == 30\n assert candidate(prices = [5, 3, 5, 2, 8, 4, 9, 10, 1, 11, 13, 12, 14, 15, 13, 16, 18, 17, 20, 22]) == 39\n assert candidate(prices = [10, 7, 5, 8, 11, 9, 12, 15, 13, 17, 20, 18]) == 19\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [10, 1, 10, 1, 10, 1, 10, 1, 10, 1]) == 36\n assert candidate(prices = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16]) == 23\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 14\n"}, "metadata": {"canonical_parameter_names": ["prices"], "leetcode_dataset_entry_point": "Solution().maxProfit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProfit = function(prices) {", "container": null, "callable": "maxProfit", "parameters": [{"name": "prices", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 123, "task_id": "best-time-to-buy-and-sell-stock-iii", "difficulty": "Hard", "problem_description": "You are given an array prices where prices[i] is the price of a given stock on the ith day.\nFind the maximum profit you can achieve. You may complete at most two transactions.\nNote: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).\n \nExample 1:\n\nInput: prices = [3,3,5,0,0,3,1,4]\nOutput: 6\nExplanation: Buy on day 4 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.\nThen buy on day 7 (price = 1) and sell on day 8 (price = 4), profit = 4-1 = 3.\nExample 2:\n\nInput: prices = [1,2,3,4,5]\nOutput: 4\nExplanation: Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4.\nNote that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.\n\nExample 3:\n\nInput: prices = [7,6,4,3,1]\nOutput: 0\nExplanation: In this case, no transaction is done, i.e. max profit = 0.\n\n \nConstraints:\n\n1 <= prices.length <= 105\n0 <= prices[i] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(prices = [1, 5, 1, 5, 1, 5, 1, 5]) == 8\n assert candidate(prices = [2, 1, 4, 5, 2, 9, 7]) == 11\n assert candidate(prices = [10, 22, 5, 75, 65, 80]) == 87\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [3, 2, 6, 5, 0, 3]) == 7\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [1, 4, 2, 8, 2, 6, 7, 8, 2, 4, 5, 2, 1]) == 13\n assert candidate(prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(prices = [1, 3, 2, 8, 4, 9]) == 12\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 6\n assert candidate(prices = [1, 2]) == 1\n assert candidate(prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(prices = [3, 3, 3, 3, 3]) == 0\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 13\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 1, 2, 3, 4]) == 7\n assert candidate(prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 10\n assert candidate(prices = [10, 22, 5, 75, 65, 80, 120, 130, 110, 140, 150, 160]) == 175\n assert candidate(prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 13\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 7, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 10\n assert candidate(prices = [7, 6, 4, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]) == 6\n assert candidate(prices = [1, 3, 5, 4, 3, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == 18\n assert candidate(prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 100\n assert candidate(prices = [10, 1, 9, 1, 8, 1, 7, 1, 6, 1, 5, 1, 4, 1, 3, 1, 2, 1]) == 15\n assert candidate(prices = [5, 11, 3, 50, 60, 90, 30, 80, 100, 50, 80, 120]) == 177\n assert candidate(prices = [1, 2, 3, 4, 5, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 14\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 19\n assert candidate(prices = [31, 41, 48, 54, 37, 76, 56, 99, 1, 180]) == 247\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 24\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 2, 10]) == 12\n assert candidate(prices = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 18\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 2, 8, 10, 4]) == 13\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == 18\n assert candidate(prices = [1, 100, 2, 98, 3, 96, 4, 94, 5, 92, 6, 90, 7, 88, 8, 86, 9, 84, 10, 82]) == 195\n assert candidate(prices = [10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1]) == 18\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(prices = [2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 2\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 6, 8, 2, 5]) == 11\n assert candidate(prices = [100, 180, 260, 40, 310, 535, 695]) == 815\n assert candidate(prices = [90, 80, 70, 60, 50, 40, 30, 20, 10, 0]) == 0\n assert candidate(prices = [8, 6, 4, 3, 3, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 5\n assert candidate(prices = [5, 2, 10, 1, 3, 12, 6, 9, 1, 15]) == 25\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 2, 8, 10, 5, 6, 7, 3, 10, 4, 5, 6, 1, 10]) == 18\n assert candidate(prices = [5, 2, 4, 0, 0, 3, 5, 7, 8, 2, 8]) == 14\n assert candidate(prices = [1, 4, 3, 0, 5, 8, 3, 1, 5, 6, 4, 10, 2, 5, 12, 8, 9, 1, 10]) == 21\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 10, 8, 6, 2, 9, 5, 7, 1, 10]) == 19\n assert candidate(prices = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 3, 5, 7, 9, 11]) == 17\n assert candidate(prices = [100, 180, 260, 310, 40, 535, 695]) == 865\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9, 1, 2, 1, 3, 5, 7]) == 17\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 1, 4, 6, 8, 2, 5, 7, 8, 1]) == 14\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 10, 12, 15, 14, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 17\n assert candidate(prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 13\n assert candidate(prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 14]) == 22\n assert candidate(prices = [8, 12, 15, 7, 3, 18, 20, 15]) == 24\n assert candidate(prices = [100, 180, 260, 310, 40, 535, 695, 10, 5, 11, 3, 8, 10, 5, 11, 3, 8, 10, 5, 11]) == 865\n assert candidate(prices = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(prices = [5, 2, 3, 0, 3, 2, 5, 4, 1, 6, 7, 8, 1, 10]) == 17\n assert candidate(prices = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [5, 0, 3, 12, 6, 9, 21, 18, 13, 8, 12, 3, 20, 15, 18]) == 38\n assert candidate(prices = [90, 80, 70, 60, 50, 40, 30]) == 0\n assert candidate(prices = [10, 7, 5, 8, 11, 9, 1, 15]) == 20\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 11\n assert candidate(prices = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 18\n assert candidate(prices = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(prices = [100, 180, 260, 310, 40, 535, 695, 10, 20, 30, 100, 150]) == 865\n assert candidate(prices = [12, 14, 17, 10, 14, 13, 12, 15]) == 10\n assert candidate(prices = [3, 1, 4, 8, 7, 2, 5, 1, 3, 5, 2, 9]) == 15\n assert candidate(prices = [1, 2, 3, 2, 1, 4, 5, 4, 6, 7, 8, 9, 10, 8, 12, 15]) == 16\n assert candidate(prices = [100, 30, 15, 10, 8, 25, 80]) == 72\n assert candidate(prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 14, 13, 12, 11, 10]) == 18\n assert candidate(prices = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 0\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 2, 5, 7, 3]) == 9\n assert candidate(prices = [1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 1, 13, 1, 15, 1, 17, 1, 19, 1, 21, 1, 23, 1, 25, 1, 27]) == 50\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 1, 4, 7, 8, 10, 11, 12, 10, 13, 14, 15, 16, 17, 18, 19]) == 23\n assert candidate(prices = [30, 50, 10, 60, 40, 90, 55]) == 100\n assert candidate(prices = [8, 6, 4, 3, 3, 5, 8, 6, 4, 3, 3, 5, 8, 6, 4, 3, 3, 5, 8, 6, 4, 3, 3, 5]) == 10\n assert candidate(prices = [5, 1, 7, 8, 3, 6, 1, 2, 9, 10, 4, 5, 11, 12, 6, 7, 13, 14, 8, 9]) == 20\n assert candidate(prices = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 135\n assert candidate(prices = [1, 2, 3, 1, 4, 5, 2, 7, 8, 1, 9, 10, 1, 11, 12, 1, 13, 14]) == 24\n assert candidate(prices = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 38\n assert candidate(prices = [10, 22, 5, 75, 65, 80, 10, 90, 50, 20, 120, 15, 8, 90]) == 197\n assert candidate(prices = [7, 6, 5, 8, 3, 8, 2, 6, 5, 7, 3, 8, 5, 6, 8, 9, 1, 2, 4, 5, 6]) == 12\n assert candidate(prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 10\n assert candidate(prices = [1, 7, 4, 3, 8, 8, 6, 4, 10, 9, 3]) == 13\n assert candidate(prices = [90, 80, 70, 60, 50, 40, 30, 20, 10]) == 0\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 1, 2, 5, 1, 3, 7]) == 11\n assert candidate(prices = [10, 22, 5, 75, 65, 80]) == 87\n assert candidate(prices = [3, 8, 4, 0, 5, 6, 2, 9, 8, 1, 10]) == 18\n assert candidate(prices = [1, 3, 2, 8, 4, 9, 3, 5, 7, 1, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22]) == 29\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9]) == 17\n assert candidate(prices = [31, 41, 48, 54, 37, 44, 66, 59, 56, 78, 100]) == 86\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 10, 15, 20, 5, 25, 30, 5, 35, 40]) == 65\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4, 2, 5, 1, 4, 7, 1, 10]) == 16\n assert candidate(prices = [5, 3, 10, 1, 7, 8, 2, 9, 4]) == 15\n assert candidate(prices = [100, 30, 15, 10, 8, 25, 80, 50, 150, 40, 60, 70, 90, 120, 130, 50, 20, 100, 140, 150]) == 272\n assert candidate(prices = [1, 2, 3, 4, 5, 0, 100, 101, 102, 103]) == 107\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 1, 4, 7, 8, 10, 9, 11, 12, 8, 10, 5, 7, 3, 4, 2, 1, 5, 6, 8, 9, 10, 1]) == 21\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 2\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 190\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 8, 3, 8, 2, 6]) == 11\n assert candidate(prices = [50, 10, 5, 3, 8, 20, 30, 25, 20, 15, 10, 5, 10, 15, 20, 25, 30, 35, 40, 45]) == 67\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 14\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 21\n assert candidate(prices = [1, 2, 3, 10, 1, 2, 3, 10, 1, 2, 3, 10, 1, 2, 3, 10, 1, 2, 3, 10]) == 18\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 8, 2, 9, 10, 15, 20, 2, 18, 25]) == 42\n assert candidate(prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 13\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 20\n assert candidate(prices = [80, 70, 60, 50, 40, 30, 20, 10]) == 0\n assert candidate(prices = [100, 180, 260, 40, 310, 535, 695]) == 815\n assert candidate(prices = [5, 3, 10, 1, 4, 9, 2, 8, 0, 7, 3, 6, 1, 5, 2, 4]) == 15\n"}, "metadata": {"canonical_parameter_names": ["prices"], "leetcode_dataset_entry_point": "Solution().maxProfit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProfit = function(prices) {", "container": null, "callable": "maxProfit", "parameters": [{"name": "prices", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 124, "task_id": "binary-tree-maximum-path-sum", "difficulty": "Hard", "problem_description": "A path in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence at most once. Note that the path does not need to pass through the root.\nThe path sum of a path is the sum of the node's values in the path.\nGiven the root of a binary tree, return the maximum path sum of any non-empty path.\n \nExample 1:\n\n\nInput: root = [1,2,3]\nOutput: 6\nExplanation: The optimal path is 2 -> 1 -> 3 with a path sum of 2 + 1 + 3 = 6.\n\nExample 2:\n\n\nInput: root = [-10,9,20,null,null,15,7]\nOutput: 42\nExplanation: The optimal path is 15 -> 20 -> 7 with a path sum of 15 + 20 + 7 = 42.\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 3 * 104].\n-1000 <= Node.val <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 15\n assert candidate(root = tree_node([2, -1])) == 2\n assert candidate(root = tree_node([-3])) == -3\n assert candidate(root = tree_node([1, 2, 3])) == 6\n assert candidate(root = tree_node([1, -2, -3])) == 1\n assert candidate(root = tree_node([-2, 1])) == 1\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7])) == 42\n assert candidate(root = tree_node([1, 2])) == 3\n assert candidate(root = tree_node([1, None, 2])) == 3\n assert candidate(root = tree_node([0])) == 0\n assert candidate(root = tree_node([-1])) == -1\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == 48\n assert candidate(root = tree_node([1])) == 1\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1])) == 3\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == 48\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7, -1, -2, 1, 1, -3, -4, -5, -6])) == 43\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 55\n assert candidate(root = tree_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150])) == 440\n assert candidate(root = tree_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, None, None, None, None, None, -10])) == 16\n assert candidate(root = tree_node([50, 20, 30, 15, 25, 10, 35, -10, -5, None, None, None, None, None, None])) == 160\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == 36\n assert candidate(root = tree_node([-10, 5, 15, -5, 3, None, 7, -1, None, -2, 4, None, None, 8])) == 24\n assert candidate(root = tree_node([9, 6, -3, None, None, -6, 2, None, None, 2, 2, None, -1, -6, -6, -6])) == 16\n assert candidate(root = tree_node([50, 20, 30, 10, 40, 25, 35, 5, 15, 32, 45, 22, 28, 33, 42, 1, 9, 11, 19, 31, 37, 43, 48, 0, 4, 8, 14, 16, 18, 21, 24, 27, 29, 34, 36, 39, 41, 44, 46, 47, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == 351\n assert candidate(root = tree_node([1, None, -2, None, -3, None, -4, None, -5, None, -6, None, -7, None, -8, None, -9])) == 1\n assert candidate(root = tree_node([-1, None, -2, None, -3, None, -4, -5, None])) == -1\n assert candidate(root = tree_node([2, -5, 7, -4, None, None, 6, -3, -1, 8, 9, None, None, None, None, None, 10])) == 33\n assert candidate(root = tree_node([10, 9, -10, None, None, 15, 7, None, None, None, 1, None, None, -1, None, -5])) == 24\n assert candidate(root = tree_node([2, -1, -2, 1, -3, -4, -5, -6, -7])) == 2\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, -2, 9, 3, 1, None, None, None, None, None, None, None, -10])) == 52\n assert candidate(root = tree_node([-1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == 27\n assert candidate(root = tree_node([100, -50, -50, 40, 20, None, -60, 30, None, 10, None, -5])) == 120\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1, None, -5, 6, 8, -4, -6, None, 7, 9])) == 58\n assert candidate(root = tree_node([-1, 2, 2, None, 3, None, 3, None, 4, None, 4])) == 17\n assert candidate(root = tree_node([0, -10, 20, None, None, 15, 6, None, None, -5, 12, 11, 13, -14])) == 53\n assert candidate(root = tree_node([-10, -20, -30, -40, None, -50, -60, None, None, -70, -80, -90, None, None, -100])) == -10\n assert candidate(root = tree_node([100, 50, 200, 25, 75, 150, 300, 10, 40, 60, 90, 125, 175, 250, 350])) == 1175\n assert candidate(root = tree_node([-1, -2, -3, 1, 2, -1, -1, -2, None, -3, None, -2, -2])) == 2\n assert candidate(root = tree_node([10, 9, 20, None, None, 15, 7, 6, 12, 3, 8, 99, -100, 5, None, 4, 2, 1, None, None, None, None, None, None, None, -99])) == 159\n assert candidate(root = tree_node([100, -50, 50, -25, 25, -12, 12, -6, 6, -3, 3, -1, 1, 0, -100, 100, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == 181\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1, None, None, None, 9])) == 52\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == 44\n assert candidate(root = tree_node([1, -10, 20, 15, 10, None, -25, 6, None, None, -3, None, 4])) == 32\n assert candidate(root = tree_node([-1, -2, -3, -4, -5])) == -1\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, -1, None, -5, 6, 9])) == 50\n assert candidate(root = tree_node([1, -2, 3, 4, None, None, -6, None, -7, None, None, 8, 9])) == 10\n assert candidate(root = tree_node([-10, 5, 20, 15, 25, None, None, None, -5, 30, None])) == 75\n assert candidate(root = tree_node([10, -2, 15, 20, -5, None, 7, None, 1, None, 3, 9])) == 60\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == 101\n assert candidate(root = tree_node([2, -5, -1, None, -9, -4, None, None, -3, None, -8])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 69\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 3, 10, -1, None, -15, 9, None, None, None, -1])) == 59\n assert candidate(root = tree_node([0, -10, 20, 15, 7, -2, None, None, None, None, None, 5, 1, None, None, None, -1])) == 28\n assert candidate(root = tree_node([10, 2, 10, 8, 34, 7, 6, 1, None, None, None, None, None, 9, 8, 7])) == 71\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1, None, 5])) == 53\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1, -14, 16, 18, None, None, None, None, None, None, None, -19])) == 64\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 44\n assert candidate(root = tree_node([0, 2, 5, None, None, 6, 3, None, None, 9, None, None, 12, 15, 7])) == 50\n assert candidate(root = tree_node([0, -10, 7, 8, None, 15, None, -8, None, 5, None, 9, 6, 11, None, None, None, None, None, None, None, None, None, None, None])) == 38\n assert candidate(root = tree_node([1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1])) == 1\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, 4, 6, 8, 12, 14, 17, 19, None, 2, None, 0, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == 82\n assert candidate(root = tree_node([-1, None, 9, -6, 3, None, None, None, -2])) == 12\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30])) == 44\n assert candidate(root = tree_node([1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20])) == 48\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7, None, None, None, None, 2, None, 1, None, -1, None, None, None, -2])) == 42\n assert candidate(root = tree_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == 0\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32])) == -1\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, -1, None, -1, None, -2])) == 48\n assert candidate(root = tree_node([100, -50, 200, -75, 25, 150, 250, -100, None, 20, None, -50, None, 30, 40])) == 640\n assert candidate(root = tree_node([-1, None, -2, None, -3, None, -4, None, -5])) == -1\n assert candidate(root = tree_node([9, 4, 0, -1, -3, None, -10, None, None, -5])) == 13\n assert candidate(root = tree_node([0, -10, 5, None, None, -5, 6])) == 11\n assert candidate(root = tree_node([10, -10, 20, -20, 30, -30, 40, None, None, None, -40, None, None, -50, -60, None, None, -70, -80])) == 90\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == -1\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30, None, 31, None, 32, None, 33, None, 34, None, 35, None, 36, None, 37, None, 38, None, 39, None, 40])) == 820\n assert candidate(root = tree_node([-1, None, -2, None, -3, None, -4, None, -5, None, -6, None, -7])) == -1\n assert candidate(root = tree_node([10, 9, 20, None, None, 15, 7, 12, None, 2, 1, None, None, -5])) == 66\n assert candidate(root = tree_node([5, -4, -8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, -1, None, -5, 6, 9, -3])) == 26\n assert candidate(root = tree_node([2, -1, -2, 1, -4, -5, -6])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32])) == 119\n assert candidate(root = tree_node([2, -5, 6, None, 5, None, 7])) == 15\n assert candidate(root = tree_node([100, 50, 50, 25, 25, 25, 25, 12, 13, 14, 15, 16, 17, 18, 19])) == 284\n assert candidate(root = tree_node([3, -2, 5, -6, None, None, 4, None, None, -8, None, None, 7])) == 12\n assert candidate(root = tree_node([50, 20, 30, 10, 40, 25, 35, 5, 15, 32, 45, 23, 27, 33, 47, 1, 9, 11, 19, 31, 34, 39, 44, 46, 48])) == 325\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 45\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, None, -1, None, -9])) == 48\n assert candidate(root = tree_node([10, 9, -10, None, None, 15, 20, 1, None, -1, None, -5, None, 4, None, -6])) == 32\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1])) == 29\n assert candidate(root = tree_node([1, -2, 3, -4, None, 5, -6, 7, None, None, 8, None, 9])) == 19\n assert candidate(root = tree_node([1, -2, 3, 4, None, 5, -6, None, None, 7, -8, 9, -10, None, None, None, None, 11])) == 29\n assert candidate(root = tree_node([10, -10, 20, 15, 7, None, -5, 20, 30])) == 65\n assert candidate(root = tree_node([1, -2, -3, 4, 5, None, 6, None, None, -8, -9])) == 7\n assert candidate(root = tree_node([-10, 5, 9, None, -3, None, -8, None, -2, None, 7, -5, None, -1, None, 6, None, None, None, None, None, None, 8])) == 9\n assert candidate(root = tree_node([9, 6, -3, None, None, -6, 2, None, None, 2, None, -6, -6, -6])) == 16\n assert candidate(root = tree_node([100, -50, -50, None, -100, -100, None, -50, -100, None, -150, -150])) == 100\n assert candidate(root = tree_node([10, 9, 20, None, None, 15, 7, None, None, 30, 40, None, 50])) == 127\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().maxPathSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxPathSum = function(root) {", "container": null, "callable": "maxPathSum", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 125, "task_id": "valid-palindrome", "difficulty": "Easy", "problem_description": "A phrase is a palindrome if, after converting all uppercase letters into lowercase letters and removing all non-alphanumeric characters, it reads the same forward and backward. Alphanumeric characters include letters and numbers.\nGiven a string s, return true if it is a palindrome, or false otherwise.\n \nExample 1:\n\nInput: s = \"A man, a plan, a canal: Panama\"\nOutput: true\nExplanation: \"amanaplanacanalpanama\" is a palindrome.\n\nExample 2:\n\nInput: s = \"race a car\"\nOutput: false\nExplanation: \"raceacar\" is not a palindrome.\n\nExample 3:\n\nInput: s = \" \"\nOutput: true\nExplanation: s is an empty string \"\" after removing non-alphanumeric characters.\nSince an empty string reads the same forward and backward, it is a palindrome.\n\n \nConstraints:\n\n1 <= s.length <= 2 * 105\ns consists only of printable ASCII characters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"race a car\") == False\n assert candidate(s = \" \") == True\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().isPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPalindrome = function(s) {", "container": null, "callable": "isPalindrome", "parameters": [{"name": "s", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 127, "task_id": "word-ladder", "difficulty": "Hard", "problem_description": "A transformation sequence from word beginWord to word endWord using a dictionary wordList is a sequence of words beginWord -> s1 -> s2 -> ... -> sk such that:\n\nEvery adjacent pair of words differs by a single letter.\nEvery si for 1 <= i <= k is in wordList. Note that beginWord does not need to be in wordList.\nsk == endWord\n\nGiven two words, beginWord and endWord, and a dictionary wordList, return the number of words in the shortest transformation sequence from beginWord to endWord, or 0 if no such sequence exists.\n \nExample 1:\n\nInput: beginWord = \"hit\", endWord = \"cog\", wordList = [\"hot\",\"dot\",\"dog\",\"lot\",\"log\",\"cog\"]\nOutput: 5\nExplanation: One shortest transformation sequence is \"hit\" -> \"hot\" -> \"dot\" -> \"dog\" -> cog\", which is 5 words long.\n\nExample 2:\n\nInput: beginWord = \"hit\", endWord = \"cog\", wordList = [\"hot\",\"dot\",\"dog\",\"lot\",\"log\"]\nOutput: 0\nExplanation: The endWord \"cog\" is not in wordList, therefore there is no valid transformation sequence.\n\n \nConstraints:\n\n1 <= beginWord.length <= 10\nendWord.length == beginWord.length\n1 <= wordList.length <= 5000\nwordList[i].length == beginWord.length\nbeginWord, endWord, and wordList[i] consist of lowercase English letters.\nbeginWord != endWord\nAll the words in wordList are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(beginWord = \"leet\",endWord = \"code\",wordList = ['lest', 'leet', 'lose', 'code', 'lode', 'robe', 'home', 'dote', 'cake']) == 0\n assert candidate(beginWord = \"talk\",endWord = \"tell\",wordList = ['talk', 'tell', 'tall', 'toll', 'toll']) == 3\n assert candidate(beginWord = \"talk\",endWord = \"walk\",wordList = ['talk', 'walk', 'tall', 'tale', 'tali', 'wali', 'wali', 'wale', 'wall', 'walk']) == 2\n assert candidate(beginWord = \"leet\",endWord = \"code\",wordList = ['lest', 'leet', 'lose', 'code', 'lode', 'robe', 'lost']) == 6\n assert candidate(beginWord = \"red\",endWord = \"tax\",wordList = ['ted', 'tex', 'red', 'tax', 'tad', 'den', 'rex', 'pee']) == 4\n assert candidate(beginWord = \"cat\",endWord = \"dog\",wordList = ['bat', 'rat', 'hat', 'hot', 'dot', 'dog']) == 5\n assert candidate(beginWord = \"hit\",endWord = \"cog\",wordList = ['hot', 'dot', 'dog', 'lot', 'log']) == 0\n assert candidate(beginWord = \"hit\",endWord = \"cog\",wordList = ['hot', 'dot', 'dog', 'lot', 'log', 'cog']) == 5\n assert candidate(beginWord = \"abcf\",endWord = \"aefh\",wordList = ['abcf', 'aefg', 'aefh', 'aegh', 'cefh', 'cefh', 'aegh', 'cefg', 'abcf', 'abef']) == 0\n assert candidate(beginWord = \"machine\",endWord = \"natural\",wordList = ['machene', 'machenr', 'machrne', 'machren', 'machenl', 'machenm', 'machene', 'machrne', 'machren', 'machenl', 'machenm', 'machane', 'machrne', 'machren', 'machenl', 'machenm', 'machenl', 'machene', 'machrne', 'machren', 'machenl', 'machenm', 'nachenl', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'nachene', 'nachrne', 'nachren', 'nachenl', 'nachenm', 'natural']) == 0\n assert candidate(beginWord = \"listen\",endWord = \"silent\",wordList = ['lisen', 'litesn', 'litens', 'listne', 'listen', 'siltne', 'silent', 'linset', 'lintes', 'sleint', 'ltsine', 'lintse', 'lisnet', 'lsitne', 'lnties', 'lintes', 'lintes', 'linsat', 'slient', 'lsinte', 'linset']) == 0\n assert candidate(beginWord = \"algorithm\",endWord = \"rhythm\",wordList = ['alorhythm', 'alohrhythm', 'alohrhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'alorhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm', 'rhythm']) == 0\n assert candidate(beginWord = \"physics\",endWord = \"chemist\",wordList = ['phyiscs', 'phyisic', 'phyisct', 'phyisci', 'phyicsi', 'physics', 'physisi', 'physcii', 'physici', 'phyiscs', 'phyiscs', 'phyiscs', 'phyiscs', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'physcis', 'chemics', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist', 'chemist']) == 0\n"}, "metadata": {"canonical_parameter_names": ["beginWord", "endWord", "wordList"], "leetcode_dataset_entry_point": "Solution().ladderLength", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var ladderLength = function(beginWord, endWord, wordList) {", "container": null, "callable": "ladderLength", "parameters": [{"name": "beginWord", "type": "string"}, {"name": "endWord", "type": "string"}, {"name": "wordList", "type": "string[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 128, "task_id": "longest-consecutive-sequence", "difficulty": "Medium", "problem_description": "Given an unsorted array of integers nums, return the length of the longest consecutive elements sequence.\nYou must write an algorithm that runs in O(n) time.\n \nExample 1:\n\nInput: nums = [100,4,200,1,3,2]\nOutput: 4\nExplanation: The longest consecutive elements sequence is [1, 2, 3, 4]. Therefore its length is 4.\n\nExample 2:\n\nInput: nums = [0,3,7,2,5,8,4,6,0,1]\nOutput: 9\n\nExample 3:\n\nInput: nums = [1,0,1,2]\nOutput: 3\n\n \nConstraints:\n\n0 <= nums.length <= 105\n-109 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-1, -2, -3, -4]) == 4\n assert candidate(nums = [10, 5, 12, 3, 9, 7, 8, 11]) == 6\n assert candidate(nums = [1, 9, 3, 10, 4, 20, 2]) == 4\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(nums = [10, 5, 12, 3, 14, 7, 16, 20, 18, 11, 9, 8, 13, 6, 4, 19, 15, 17, 2, 1]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [10, 5, 12, 3, 7, 8, 9, 2, 1, 0]) == 4\n assert candidate(nums = [1000000000, -1000000000, 500000000, -500000000]) == 1\n assert candidate(nums = [-1, -2, -3, -4, -5]) == 5\n assert candidate(nums = [0, 0, 0, 0, 0]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5]) == 5\n assert candidate(nums = [10, 5, 12, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8]) == 12\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 10\n assert candidate(nums = [100, 4, 200, 1, 3, 2]) == 4\n assert candidate(nums = []) == 0\n assert candidate(nums = [0, 3, 7, 2, 5, 8, 4, 6, 0, 1]) == 9\n assert candidate(nums = [5, 4, 3, 2, 1]) == 5\n assert candidate(nums = [1, 2, 0, 1]) == 3\n assert candidate(nums = [1, 0, 1, 2]) == 3\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 10\n assert candidate(nums = [1000000000, -1000000000, 0]) == 1\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5]) == 5\n assert candidate(nums = [5]) == 1\n assert candidate(nums = [-1, 0, 1]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 50\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110]) == 11\n assert candidate(nums = [-10, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 9\n assert candidate(nums = [500000000, 500000001, 500000002, 500000003, 500000004, 500000005, 500000006, 500000007, 500000008, 500000009]) == 10\n assert candidate(nums = [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64]) == 15\n assert candidate(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 20, 12, 19, 13, 18, 14, 17, 15, 16, 21, 30, 22, 29, 23, 28, 24, 27, 25, 26]) == 30\n assert candidate(nums = [100, 200, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [1000000000, -1000000000, 1000000001, -1000000001, 0, 1, -1, 2, -2]) == 5\n assert candidate(nums = [999999999, 1000000000, 1000000001, 1000000002, 1000000003]) == 5\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 31, 32]) == 3\n assert candidate(nums = [10, 5, 0, 5, 3, 15, 10, 5, 3, 6, 7, 100, 200, 300, 400, 500, 600, 700, 800, 900]) == 3\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000]) == 1\n assert candidate(nums = [-10, -5, -3, -1, -2, 0, -8, -9, -7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 14\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19]) == 3\n assert candidate(nums = [100, 200, 300, 400, 500, 101, 102, 103, 104, 105]) == 6\n assert candidate(nums = [5, 1, 3, 2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 14\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 10\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 30\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]) == 1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 10\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 1\n assert candidate(nums = [-1000000000, -999999999, -999999998, -999999997, -999999996, -999999995, -999999994, -999999993, -999999992, -999999991]) == 10\n assert candidate(nums = [10, 5, 0, -5, -10, -15, -20, -25, -30]) == 1\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 21\n assert candidate(nums = [1000000000, 1000000001, 999999999, 999999998, 999999997]) == 5\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105]) == 6\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004]) == 5\n assert candidate(nums = [1000000000, 1000000002, 1000000001, 1000000003, 1000000004, 1000000005, 1000000006, 1000000007, 1000000008, 1000000009]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 101, 201, 301, 401, 501, 601, 701, 801, 901, 1001]) == 2\n assert candidate(nums = [10, 15, 1, 3, 2, 8, 7, 4, 12, 14, 11, 6, 9, 5]) == 12\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20]) == 6\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009]) == 10\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25]) == 7\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384]) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 1\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 11\n assert candidate(nums = [10, 5, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 10\n assert candidate(nums = [1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 31\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 11, 12, 13, 14, 15, 16, 17, 8, 6, 4, 1, 0]) == 19\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 12\n assert candidate(nums = [100, 200, 300, 400, 500, 101, 201, 301, 401, 501]) == 2\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30]) == 30\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 31\n assert candidate(nums = [1000000000, 999999999, 1000000001, 1000000002, 1000000003, 1000000004]) == 6\n assert candidate(nums = [5, 3, 8, 1, 2, 7, 4, 6, 9, 0, 11, 12, 13, 14, 15]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 25\n assert candidate(nums = [5, 100, 50, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == 11\n assert candidate(nums = [50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 100, 101, 102, 103, 104, 200, 201, 202, 203, 204]) == 5\n assert candidate(nums = [1000000000, 999999999, 1000000001, 1000000002, 1000000003]) == 5\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98]) == 1\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 10\n assert candidate(nums = [-5, -3, -4, -2, -1, 0, 1, 2, 3, 4, 5]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 30\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]) == 1\n assert candidate(nums = [5, 3, 8, 9, 11, 12, 13, 14, 10]) == 7\n assert candidate(nums = [10, 5, 15, 3, 8, 2, 20, 25, 18, 7, 6, 11, 12, 13, 14, 16, 17, 19, 4, 9]) == 19\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 1\n assert candidate(nums = [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 1\n assert candidate(nums = [5, 3, 1, 2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 15\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 31\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 11\n assert candidate(nums = [5, 2, 9, 1, 5, 6, 7, 3, 8, 4, 10, 11, 12, 13, 14]) == 14\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 21\n assert candidate(nums = [42, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]) == 13\n assert candidate(nums = [5, 3, 8, 6, 2, 7, 4, 1, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 20\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005, 1000000006, 1000000007, 1000000008, 1000000009, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 21\n assert candidate(nums = [5, 1, 9, 11, 7, 3, 8, 4, 2, 10, 6, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 5\n assert candidate(nums = [1000000000, -1000000000, 2147483647, -2147483648, 0]) == 1\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005]) == 6\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 11\n assert candidate(nums = [10, 5, 0, -5, -10, 15, 20, 25, 30, 35, 40]) == 1\n assert candidate(nums = [1000000000, -1000000000, 500000000, 500000001, 500000002, -1000000001]) == 3\n assert candidate(nums = [500000000, 500000001, 500000002, 500000003, 500000004, 500000005, 500000006, 500000007, 500000008, 500000009]) == 10\n assert candidate(nums = [-10, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 10, 11, 12]) == 9\n assert candidate(nums = [5, 3, 8, 4, 7, 6, 9, 1, 2, 0]) == 10\n assert candidate(nums = [10, 5, 9, 1, 11, 8, 6, 7, 3, 4, 2]) == 11\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 20\n assert candidate(nums = [-1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5]) == 11\n assert candidate(nums = [10, 5, 9, 1, 11, 5, 7, 8, 2, 12, 3, 6, 4]) == 12\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 501, 502, 503, 504, 505]) == 6\n assert candidate(nums = [5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 10\n assert candidate(nums = [10, 5, 9, 1, 11, 13, 8, 2, 4, 6, 7, 3]) == 11\n assert candidate(nums = [-1, -2, -3, 0, 1, 2, 3, 4, 5]) == 9\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005, 1000000006, 1000000007, 1000000008, 1000000009]) == 10\n assert candidate(nums = [10, 5, 0, 5, 3, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]) == 1\n assert candidate(nums = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980]) == 21\n assert candidate(nums = [-1, -2, -3, -4, 0, 1, 2, 3, 4, 5]) == 10\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 1\n assert candidate(nums = [5, 3, 8, 9, 11, 1, 7, 10, 12, 6, 2, 4]) == 12\n assert candidate(nums = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 20]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110]) == 11\n assert candidate(nums = [200, 199, 198, 197, 196, 195, 194, 193, 192, 191, 190]) == 11\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1, 3, 5, 2, 4, 6, 8, 7, 10, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 21\n assert candidate(nums = [500000000, 500000001, 500000002, 500000003, 500000004, 500000005, 500000006, 500000007, 500000008, 500000009, 500000010]) == 11\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24]) == 5\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().longestConsecutive", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestConsecutive = function(nums) {", "container": null, "callable": "longestConsecutive", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 129, "task_id": "sum-root-to-leaf-numbers", "difficulty": "Medium", "problem_description": "You are given the root of a binary tree containing digits from 0 to 9 only.\nEach root-to-leaf path in the tree represents a number.\n\nFor example, the root-to-leaf path 1 -> 2 -> 3 represents the number 123.\n\nReturn the total sum of all root-to-leaf numbers. Test cases are generated so that the answer will fit in a 32-bit integer.\nA leaf node is a node with no children.\n \nExample 1:\n\n\nInput: root = [1,2,3]\nOutput: 25\nExplanation:\nThe root-to-leaf path 1->2 represents the number 12.\nThe root-to-leaf path 1->3 represents the number 13.\nTherefore, sum = 12 + 13 = 25.\n\nExample 2:\n\n\nInput: root = [4,9,0,5,1]\nOutput: 1026\nExplanation:\nThe root-to-leaf path 4->9->5 represents the number 495.\nThe root-to-leaf path 4->9->1 represents the number 491.\nThe root-to-leaf path 4->0 represents the number 40.\nTherefore, sum = 495 + 491 + 40 = 1026.\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 1000].\n0 <= Node.val <= 9\nThe depth of the tree will not exceed 10.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == 522\n assert candidate(root = tree_node([9, 3, 20, None, None, 15, 7])) == 2315\n assert candidate(root = tree_node([1, 2, 3])) == 25\n assert candidate(root = tree_node([1, 0, 0])) == 20\n assert candidate(root = tree_node([1, 0])) == 10\n assert candidate(root = tree_node([5, 2, 8, 3, 5, 4, 9, 0, None, None, 6])) == 11659\n assert candidate(root = tree_node([1, 0, 1])) == 21\n assert candidate(root = tree_node([1, 0, 1, 0, 1, 0, 1])) == 422\n assert candidate(root = tree_node([4, 9, 0, 5, 1])) == 1026\n assert candidate(root = tree_node([1, None, 2])) == 12\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, 8, 1, None, None, None, 7, 9])) == 17231\n assert candidate(root = tree_node([0])) == 0\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8])) == 2220\n assert candidate(root = tree_node([4, 3, None, 1, 2])) == 863\n assert candidate(root = tree_node([2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6])) == 19350\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1])) == 22655\n assert candidate(root = tree_node([3, 1, 5, None, 2, 4, 6, 7, 8, 9])) == 10160\n assert candidate(root = tree_node([8, None, 5, None, 3, None, 1])) == 8531\n assert candidate(root = tree_node([2, 3, 5, 6, 4, None, 9, 8, 7, 1, 0, None, None, None, None, None, None, 5])) == 30749\n assert candidate(root = tree_node([9, 4, 0, 9, 8, 6, 0, 1, 3, 8, 9, 0, 6, 7, 9])) == 74103\n assert candidate(root = tree_node([5, 5, 5, 5, 5, None, 5, 5, None, 5, 5, 5, 5, None, None, 5])) == 77775\n assert candidate(root = tree_node([1, 3, None, None, 5, 2, None, None, 8, 6, 9])) == 270575\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None])) == 123456789\n assert candidate(root = tree_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0])) == 157777\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 123456789\n assert candidate(root = tree_node([5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == 43076\n assert candidate(root = tree_node([1, 9, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0])) == 123485\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == 541795\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, 9, None, None, 0, 1])) == 27594\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5])) == 10472\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, None, None, None, None, None, None, None, None, None])) == 31520\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5])) == 78398\n assert candidate(root = tree_node([6, 0, 8, None, 7, 1, 3, None, None, 2, 5, None, None, None, 4])) == 76229\n assert candidate(root = tree_node([1, 9, 8, 7, 6, 5, 4, 3, 2, 1, None, None, 0, 9, 8, 7, 6, 5, 4, 3])) == 104082\n assert candidate(root = tree_node([2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 23456789\n assert candidate(root = tree_node([5, 9, 6, 7, 4, 0, 2, None, None, 8, 1, None, None, 3, 9])) == 24298\n assert candidate(root = tree_node([1, 9, 8, 2, 8, 7, 9, 4, 4, 6, 8, 3, 0, 7, 9, None, None, None, None, None, 4, None, None, None, None, 0, None, 3, None, None, 2, None, 1, None, 9])) == 431324\n assert candidate(root = tree_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])) == 1499985\n assert candidate(root = tree_node([1, None, 3, None, 5, None, 7, None, 9, None, 11, None, 13, None, 15, None, 17, None, 19])) == 1358024689\n assert candidate(root = tree_node([8, 15, 7, 1, None, 10, 2, 8, None, None, 5, None, 10, None, 9])) == 112724\n assert candidate(root = tree_node([6, 7, 8, 2, 7, 1, 3, 9, None, 1, 4, None, None, None, 5])) == 27790\n assert candidate(root = tree_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])) == 8444\n assert candidate(root = tree_node([7, 0, 8, None, 2, 3, None, 9])) == 7812\n assert candidate(root = tree_node([5, 9, 1, None, 3, None, None, None, 2])) == 5983\n assert candidate(root = tree_node([7, 5, 6, 0, 1, 2, 8, 4, None, 3, None, None, None, None, None, 9])) == 84092\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, None, None, None, None, None, None, 9])) == 120287\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 69405\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 0])) == 1234567890\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])) == 31520\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, None, 1, 2, None, 3, 4, None, 5, 6, None, 7, 8, None, 9, 0, None, 1])) == 104580\n assert candidate(root = tree_node([1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0])) == 150745\n assert candidate(root = tree_node([7, 6, 7, 4, 3, 6, 7, 8, 7, 4, 7, 8, 7, 3, 7])) == 61651\n assert candidate(root = tree_node([7, 3, 6, 1, 5, 8, 2, 0, 9, None, None, None, None, None, None])) == 16894\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0])) == 69195\n assert candidate(root = tree_node([3, 9, 8, 4, 0, 1, 2, None, None, None, 5, None, None, 6, 7])) == 12333\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5])) == 131357\n assert candidate(root = tree_node([7, 1, 4, 6, 9, None, 3, None, None, None, 5])) == 8654\n assert candidate(root = tree_node([2, 3, 5, 4, 1, 6, 8, 7, None, 9, None, None, None, 0, None])) == 7502\n assert candidate(root = tree_node([5, 3, 6, 2, 4, 8, 9, 1, 7, None, None, 0, None, None, 0, 0, None, None, 0, 0])) == 169504\n assert candidate(root = tree_node([5, 3, 2, 8, 9, 7, 1, 4, 6, None, None, None, None, None, None])) == 12357\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 1, None, 2, None, 3, None, 4, None, 5])) == 565898\n assert candidate(root = tree_node([9, 4, 5, 1, 6, 7, 2, None, None, None, None, 8, 3, 0, None])) == 30558\n assert candidate(root = tree_node([5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5])) == 43996\n assert candidate(root = tree_node([6, 7, 8, 0, 1, 2, 3, 4, 5, None, None, None, None, None, None, 9])) == 75790\n assert candidate(root = tree_node([4, 9, 0, 5, 1, 0, 0, None, None, 3, 2, 0, 0])) == 18720\n assert candidate(root = tree_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29])) == 12176\n assert candidate(root = tree_node([2, 3, 5, 1, 9, 4, 6, 7, 8, 0, 2, 5, 8, 9, 3])) == 19642\n assert candidate(root = tree_node([1, 0, 2, 3, 4, 5, 6, 7, 8, 9])) == 3375\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 25, 26, 30, 31, 32, 33, 34, 35])) == 217394\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 2, 5, 10, 11, 12, 13, 14, 15])) == 216394\n assert candidate(root = tree_node([7, 3, 4, 1, 5, 8, 2, 9, 6, None, None, 0, None, None, 0, None, None, 0, None, None, 0])) == 163434\n assert candidate(root = tree_node([8, 5, 9, 7, 3, None, 1, None, 6, 2, 4])) == 26533\n assert candidate(root = tree_node([6, 7, 8, 9, 0, 1, 2, 3, 4, 5, None, None, None, None, None, None, None, None, None])) == 21655\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, None, None, None, None, None, None, None, None, None])) == 475\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0])) == 195765\n assert candidate(root = tree_node([3, 1, 8, None, 4, 2, 7, None, None, None, 5])) == 4526\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5])) == 19397\n assert candidate(root = tree_node([0, 1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 123456789\n assert candidate(root = tree_node([6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0])) == 54282\n assert candidate(root = tree_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, None, 9, 8, 7, 6])) == 68543\n assert candidate(root = tree_node([7, 3, 8, None, None, 1, 4, 6, 2, None, None, 5, 9])) == 165003\n assert candidate(root = tree_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])) == 79992\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4])) == 1594\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])) == 93345\n assert candidate(root = tree_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])) == 1599984\n assert candidate(root = tree_node([1, 9, None, 2, 8, None, 7, None, 3, 6, None, 4, 5, None, None, None, None])) == 58945\n assert candidate(root = tree_node([6, 7, 8, 2, 7, 1, 3, 9, None, 1, 4, None, 5, None, None, None, None, None, 5])) == 88716\n assert candidate(root = tree_node([1, None, 9, 2, None, 8, 4, None, None, None, 5, None, None, 6, 3])) == 21173\n assert candidate(root = tree_node([1, 0, 1, None, 1, 0, 1, None, None, None, 1])) == 1313\n assert candidate(root = tree_node([3, 0, 1, None, None, 0, 2, 1, 4, None, None, 6, 9, None, None, 8, None, None, None, None, None])) == 344633\n assert candidate(root = tree_node([1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 9])) == 105550\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])) == 475\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == 23308\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().sumNumbers", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var sumNumbers = function(root) {", "container": null, "callable": "sumNumbers", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 131, "task_id": "palindrome-partitioning", "difficulty": "Medium", "problem_description": "Given a string s, partition s such that every substring of the partition is a palindrome. Return all possible palindrome partitioning of s.\n \nExample 1:\nInput: s = \"aab\"\nOutput: [[\"a\",\"a\",\"b\"],[\"aa\",\"b\"]]\nExample 2:\nInput: s = \"a\"\nOutput: [[\"a\"]]\n\n \nConstraints:\n\n1 <= s.length <= 16\ns contains only lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"madam\") == [['m', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm'], ['madam']]\n assert candidate(s = \"deified\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'd'], ['deified']]\n assert candidate(s = \"repaper\") == [['r', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'pap', 'e', 'r'], ['r', 'epape', 'r'], ['repaper']]\n assert candidate(s = \"aaab\") == [['a', 'a', 'a', 'b'], ['a', 'aa', 'b'], ['aa', 'a', 'b'], ['aaa', 'b']]\n assert candidate(s = \"aabbaa\") == [['a', 'a', 'b', 'b', 'a', 'a'], ['a', 'a', 'b', 'b', 'aa'], ['a', 'a', 'bb', 'a', 'a'], ['a', 'a', 'bb', 'aa'], ['a', 'abba', 'a'], ['aa', 'b', 'b', 'a', 'a'], ['aa', 'b', 'b', 'aa'], ['aa', 'bb', 'a', 'a'], ['aa', 'bb', 'aa'], ['aabbaa']]\n assert candidate(s = \"abcdedcba\") == [['a', 'b', 'c', 'd', 'e', 'd', 'c', 'b', 'a'], ['a', 'b', 'c', 'ded', 'c', 'b', 'a'], ['a', 'b', 'cdedc', 'b', 'a'], ['a', 'bcdedcb', 'a'], ['abcdedcba']]\n assert candidate(s = \"refer\") == [['r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r'], ['refer']]\n assert candidate(s = \"kayak\") == [['k', 'a', 'y', 'a', 'k'], ['k', 'aya', 'k'], ['kayak']]\n assert candidate(s = \"a\") == [['a']]\n assert candidate(s = \"\") == [[]]\n assert candidate(s = \"aabaa\") == [['a', 'a', 'b', 'a', 'a'], ['a', 'a', 'b', 'aa'], ['a', 'aba', 'a'], ['aa', 'b', 'a', 'a'], ['aa', 'b', 'aa'], ['aabaa']]\n assert candidate(s = \"noonnoon\") == [['n', 'o', 'o', 'n', 'n', 'o', 'o', 'n'], ['n', 'o', 'o', 'n', 'n', 'oo', 'n'], ['n', 'o', 'o', 'n', 'noon'], ['n', 'o', 'o', 'nn', 'o', 'o', 'n'], ['n', 'o', 'o', 'nn', 'oo', 'n'], ['n', 'o', 'onno', 'o', 'n'], ['n', 'oo', 'n', 'n', 'o', 'o', 'n'], ['n', 'oo', 'n', 'n', 'oo', 'n'], ['n', 'oo', 'n', 'noon'], ['n', 'oo', 'nn', 'o', 'o', 'n'], ['n', 'oo', 'nn', 'oo', 'n'], ['n', 'oonnoo', 'n'], ['noon', 'n', 'o', 'o', 'n'], ['noon', 'n', 'oo', 'n'], ['noon', 'noon'], ['noonnoon']]\n assert candidate(s = \"civic\") == [['c', 'i', 'v', 'i', 'c'], ['c', 'ivi', 'c'], ['civic']]\n assert candidate(s = \"rotor\") == [['r', 'o', 't', 'o', 'r'], ['r', 'oto', 'r'], ['rotor']]\n assert candidate(s = \"racecar\") == [['r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'a', 'cec', 'a', 'r'], ['r', 'aceca', 'r'], ['racecar']]\n assert candidate(s = \"abcb\") == [['a', 'b', 'c', 'b'], ['a', 'bcb']]\n assert candidate(s = \"aabb\") == [['a', 'a', 'b', 'b'], ['a', 'a', 'bb'], ['aa', 'b', 'b'], ['aa', 'bb']]\n assert candidate(s = \"abba\") == [['a', 'b', 'b', 'a'], ['a', 'bb', 'a'], ['abba']]\n assert candidate(s = \"noon\") == [['n', 'o', 'o', 'n'], ['n', 'oo', 'n'], ['noon']]\n assert candidate(s = \"banana\") == [['b', 'a', 'n', 'a', 'n', 'a'], ['b', 'a', 'n', 'ana'], ['b', 'a', 'nan', 'a'], ['b', 'ana', 'n', 'a'], ['b', 'anana']]\n assert candidate(s = \"deeee\") == [['d', 'e', 'e', 'e', 'e'], ['d', 'e', 'e', 'ee'], ['d', 'e', 'ee', 'e'], ['d', 'e', 'eee'], ['d', 'ee', 'e', 'e'], ['d', 'ee', 'ee'], ['d', 'eee', 'e'], ['d', 'eeee']]\n assert candidate(s = \"abc\") == [['a', 'b', 'c']]\n assert candidate(s = \"ababa\") == [['a', 'b', 'a', 'b', 'a'], ['a', 'b', 'aba'], ['a', 'bab', 'a'], ['aba', 'b', 'a'], ['ababa']]\n assert candidate(s = \"aabaaa\") == [['a', 'a', 'b', 'a', 'a', 'a'], ['a', 'a', 'b', 'a', 'aa'], ['a', 'a', 'b', 'aa', 'a'], ['a', 'a', 'b', 'aaa'], ['a', 'aba', 'a', 'a'], ['a', 'aba', 'aa'], ['aa', 'b', 'a', 'a', 'a'], ['aa', 'b', 'a', 'aa'], ['aa', 'b', 'aa', 'a'], ['aa', 'b', 'aaa'], ['aabaa', 'a']]\n assert candidate(s = \"aaaa\") == [['a', 'a', 'a', 'a'], ['a', 'a', 'aa'], ['a', 'aa', 'a'], ['a', 'aaa'], ['aa', 'a', 'a'], ['aa', 'aa'], ['aaa', 'a'], ['aaaa']]\n assert candidate(s = \"aab\") == [['a', 'a', 'b'], ['aa', 'b']]\n assert candidate(s = \"redder\") == [['r', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'dd', 'e', 'r'], ['r', 'edde', 'r'], ['redder']]\n assert candidate(s = \"ababab\") == [['a', 'b', 'a', 'b', 'a', 'b'], ['a', 'b', 'a', 'bab'], ['a', 'b', 'aba', 'b'], ['a', 'bab', 'a', 'b'], ['a', 'babab'], ['aba', 'b', 'a', 'b'], ['aba', 'bab'], ['ababa', 'b']]\n assert candidate(s = \"level\") == [['l', 'e', 'v', 'e', 'l'], ['l', 'eve', 'l'], ['level']]\n assert candidate(s = \"bb\") == [['b', 'b'], ['bb']]\n assert candidate(s = \"abcdefg\") == [['a', 'b', 'c', 'd', 'e', 'f', 'g']]\n assert candidate(s = \"babad\") == [['b', 'a', 'b', 'a', 'd'], ['b', 'aba', 'd'], ['bab', 'a', 'd']]\n assert candidate(s = \"noonlevelrotorredder\") == [['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'redder'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'redder'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'redder'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'redder'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'redder'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'rotor', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'rotor', 'redder'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'redder'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'r', 'redder'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'r', 'oto', 'rr', 'edde', 'r'], ['n', 'o', 'o', 'n', 'level', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['n', 'o', 'o', 'n', 'level', 'rotor', 'r', 'edde', 'r'], ['n', 'o', 'o', 'n', 'level', 'rotor', 'redder'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'redder'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'redder'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'rotor', 'redder'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'redder'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'r', 'redder'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'rotor', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'rotor', 'redder'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'r', 'redder'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'r', 'redder'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'r', 'oto', 'rr', 'edde', 'r'], ['n', 'oo', 'n', 'level', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['n', 'oo', 'n', 'level', 'rotor', 'r', 'edde', 'r'], ['n', 'oo', 'n', 'level', 'rotor', 'redder'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r', 'redder'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r', 'redder'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'rr', 'edde', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'rotor', 'r', 'edde', 'r'], ['noon', 'l', 'e', 'v', 'e', 'l', 'rotor', 'redder'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r', 'redder'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'r', 'redder'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'r', 'oto', 'rr', 'edde', 'r'], ['noon', 'l', 'eve', 'l', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'l', 'eve', 'l', 'rotor', 'r', 'edde', 'r'], ['noon', 'l', 'eve', 'l', 'rotor', 'redder'], ['noon', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'level', 'r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['noon', 'level', 'r', 'o', 't', 'o', 'r', 'redder'], ['noon', 'level', 'r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['noon', 'level', 'r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['noon', 'level', 'r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['noon', 'level', 'r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'level', 'r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'level', 'r', 'oto', 'r', 'r', 'edde', 'r'], ['noon', 'level', 'r', 'oto', 'r', 'redder'], ['noon', 'level', 'r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['noon', 'level', 'r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['noon', 'level', 'r', 'oto', 'rr', 'edde', 'r'], ['noon', 'level', 'rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['noon', 'level', 'rotor', 'r', 'e', 'dd', 'e', 'r'], ['noon', 'level', 'rotor', 'r', 'edde', 'r'], ['noon', 'level', 'rotor', 'redder']]\n assert candidate(s = \"repaperrepaper\") == [['r', 'e', 'p', 'a', 'p', 'e', 'r', 'r', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'p', 'a', 'p', 'e', 'r', 'r', 'e', 'pap', 'e', 'r'], ['r', 'e', 'p', 'a', 'p', 'e', 'r', 'r', 'epape', 'r'], ['r', 'e', 'p', 'a', 'p', 'e', 'r', 'repaper'], ['r', 'e', 'p', 'a', 'p', 'e', 'rr', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'p', 'a', 'p', 'e', 'rr', 'e', 'pap', 'e', 'r'], ['r', 'e', 'p', 'a', 'p', 'e', 'rr', 'epape', 'r'], ['r', 'e', 'p', 'a', 'p', 'erre', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'p', 'a', 'p', 'erre', 'pap', 'e', 'r'], ['r', 'e', 'p', 'a', 'perrep', 'a', 'p', 'e', 'r'], ['r', 'e', 'p', 'aperrepa', 'p', 'e', 'r'], ['r', 'e', 'pap', 'e', 'r', 'r', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'pap', 'e', 'r', 'r', 'e', 'pap', 'e', 'r'], ['r', 'e', 'pap', 'e', 'r', 'r', 'epape', 'r'], ['r', 'e', 'pap', 'e', 'r', 'repaper'], ['r', 'e', 'pap', 'e', 'rr', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'pap', 'e', 'rr', 'e', 'pap', 'e', 'r'], ['r', 'e', 'pap', 'e', 'rr', 'epape', 'r'], ['r', 'e', 'pap', 'erre', 'p', 'a', 'p', 'e', 'r'], ['r', 'e', 'pap', 'erre', 'pap', 'e', 'r'], ['r', 'e', 'paperrepap', 'e', 'r'], ['r', 'epape', 'r', 'r', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'epape', 'r', 'r', 'e', 'pap', 'e', 'r'], ['r', 'epape', 'r', 'r', 'epape', 'r'], ['r', 'epape', 'r', 'repaper'], ['r', 'epape', 'rr', 'e', 'p', 'a', 'p', 'e', 'r'], ['r', 'epape', 'rr', 'e', 'pap', 'e', 'r'], ['r', 'epape', 'rr', 'epape', 'r'], ['r', 'epaperrepape', 'r'], ['repaper', 'r', 'e', 'p', 'a', 'p', 'e', 'r'], ['repaper', 'r', 'e', 'pap', 'e', 'r'], ['repaper', 'r', 'epape', 'r'], ['repaper', 'repaper'], ['repaperrepaper']]\n assert candidate(s = \"referrefer\") == [['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r'], ['r', 'e', 'f', 'e', 'r', 'refer'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'efe', 'r'], ['r', 'e', 'f', 'erre', 'f', 'e', 'r'], ['r', 'e', 'ferref', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r', 'r', 'efe', 'r'], ['r', 'efe', 'r', 'refer'], ['r', 'efe', 'rr', 'e', 'f', 'e', 'r'], ['r', 'efe', 'rr', 'efe', 'r'], ['r', 'eferrefe', 'r'], ['refer', 'r', 'e', 'f', 'e', 'r'], ['refer', 'r', 'efe', 'r'], ['refer', 'refer'], ['referrefer']]\n assert candidate(s = \"rotorrotor\") == [['r', 'o', 't', 'o', 'r', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'oto', 'r'], ['r', 'o', 't', 'o', 'r', 'rotor'], ['r', 'o', 't', 'o', 'rr', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'rr', 'oto', 'r'], ['r', 'o', 't', 'orro', 't', 'o', 'r'], ['r', 'o', 'torrot', 'o', 'r'], ['r', 'oto', 'r', 'r', 'o', 't', 'o', 'r'], ['r', 'oto', 'r', 'r', 'oto', 'r'], ['r', 'oto', 'r', 'rotor'], ['r', 'oto', 'rr', 'o', 't', 'o', 'r'], ['r', 'oto', 'rr', 'oto', 'r'], ['r', 'otorroto', 'r'], ['rotor', 'r', 'o', 't', 'o', 'r'], ['rotor', 'r', 'oto', 'r'], ['rotor', 'rotor'], ['rotorrotor']]\n assert candidate(s = \"zzzz\") == [['z', 'z', 'z', 'z'], ['z', 'z', 'zz'], ['z', 'zz', 'z'], ['z', 'zzz'], ['zz', 'z', 'z'], ['zz', 'zz'], ['zzz', 'z'], ['zzzz']]\n assert candidate(s = \"rotorlevelrotor\") == [['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'rotor'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'r', 'oto', 'r'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'rotor'], ['r', 'o', 't', 'o', 'r', 'level', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'level', 'r', 'oto', 'r'], ['r', 'o', 't', 'o', 'r', 'level', 'rotor'], ['r', 'o', 't', 'o', 'rlevelr', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'rlevelr', 'oto', 'r'], ['r', 'o', 't', 'orlevelro', 't', 'o', 'r'], ['r', 'o', 'torlevelrot', 'o', 'r'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'rotor'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'r', 'oto', 'r'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'rotor'], ['r', 'oto', 'r', 'level', 'r', 'o', 't', 'o', 'r'], ['r', 'oto', 'r', 'level', 'r', 'oto', 'r'], ['r', 'oto', 'r', 'level', 'rotor'], ['r', 'oto', 'rlevelr', 'o', 't', 'o', 'r'], ['r', 'oto', 'rlevelr', 'oto', 'r'], ['r', 'otorlevelroto', 'r'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'r', 'o', 't', 'o', 'r'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'r', 'oto', 'r'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'rotor'], ['rotor', 'l', 'eve', 'l', 'r', 'o', 't', 'o', 'r'], ['rotor', 'l', 'eve', 'l', 'r', 'oto', 'r'], ['rotor', 'l', 'eve', 'l', 'rotor'], ['rotor', 'level', 'r', 'o', 't', 'o', 'r'], ['rotor', 'level', 'r', 'oto', 'r'], ['rotor', 'level', 'rotor'], ['rotorlevelrotor']]\n assert candidate(s = \"levelmadam\") == [['l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['l', 'e', 'v', 'e', 'l', 'madam'], ['l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['l', 'eve', 'l', 'm', 'ada', 'm'], ['l', 'eve', 'l', 'madam'], ['level', 'm', 'a', 'd', 'a', 'm'], ['level', 'm', 'ada', 'm'], ['level', 'madam']]\n assert candidate(s = \"abcbbbabc\") == [['a', 'b', 'c', 'b', 'b', 'b', 'a', 'b', 'c'], ['a', 'b', 'c', 'b', 'b', 'bab', 'c'], ['a', 'b', 'c', 'b', 'bb', 'a', 'b', 'c'], ['a', 'b', 'c', 'bb', 'b', 'a', 'b', 'c'], ['a', 'b', 'c', 'bb', 'bab', 'c'], ['a', 'b', 'c', 'bbb', 'a', 'b', 'c'], ['a', 'bcb', 'b', 'b', 'a', 'b', 'c'], ['a', 'bcb', 'b', 'bab', 'c'], ['a', 'bcb', 'bb', 'a', 'b', 'c']]\n assert candidate(s = \"tattarrattat\") == [['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'atta', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'atta', 't'], ['t', 'a', 't', 't', 'arra', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'arra', 't', 'tat'], ['t', 'a', 't', 't', 'arra', 'tt', 'a', 't'], ['t', 'a', 't', 'tarrat', 't', 'a', 't'], ['t', 'a', 't', 'tarrat', 'tat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 'tat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'atta', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 'tat'], ['t', 'a', 'tt', 'a', 'rr', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'atta', 't'], ['t', 'a', 'tt', 'arra', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'arra', 't', 'tat'], ['t', 'a', 'tt', 'arra', 'tt', 'a', 't'], ['t', 'a', 'ttarratt', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 't', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 'tat'], ['t', 'atta', 'r', 'r', 'a', 'tt', 'a', 't'], ['t', 'atta', 'r', 'r', 'atta', 't'], ['t', 'atta', 'rr', 'a', 't', 't', 'a', 't'], ['t', 'atta', 'rr', 'a', 't', 'tat'], ['t', 'atta', 'rr', 'a', 'tt', 'a', 't'], ['t', 'atta', 'rr', 'atta', 't'], ['t', 'attarratta', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 'tat'], ['tat', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'atta', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 't', 'a', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 'tat'], ['tat', 't', 'a', 'rr', 'a', 'tt', 'a', 't'], ['tat', 't', 'a', 'rr', 'atta', 't'], ['tat', 't', 'arra', 't', 't', 'a', 't'], ['tat', 't', 'arra', 't', 'tat'], ['tat', 't', 'arra', 'tt', 'a', 't'], ['tat', 'tarrat', 't', 'a', 't'], ['tat', 'tarrat', 'tat'], ['tattarrattat']]\n assert candidate(s = \"deifiedcivicdeified\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'deified'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c', 'deified'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'civic', 'd', 'eifie', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'civic', 'deified'], ['d', 'e', 'i', 'f', 'i', 'e', 'dcivicd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'dcivicd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'dcivicd', 'eifie', 'd'], ['d', 'e', 'i', 'f', 'i', 'edcivicde', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'edcivicde', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'iedcivicdei', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'fiedcivicdeif', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c', 'deified'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c', 'deified'], ['d', 'e', 'ifi', 'e', 'd', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'civic', 'd', 'eifie', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'civic', 'deified'], ['d', 'e', 'ifi', 'e', 'dcivicd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'dcivicd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'dcivicd', 'eifie', 'd'], ['d', 'e', 'ifi', 'edcivicde', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'edcivicde', 'ifi', 'e', 'd'], ['d', 'e', 'ifiedcivicdeifi', 'e', 'd'], ['d', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['d', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c', 'deified'], ['d', 'eifie', 'd', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'eifie', 'd', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'd', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['d', 'eifie', 'd', 'c', 'ivi', 'c', 'deified'], ['d', 'eifie', 'd', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'eifie', 'd', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'd', 'civic', 'd', 'eifie', 'd'], ['d', 'eifie', 'd', 'civic', 'deified'], ['d', 'eifie', 'dcivicd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'eifie', 'dcivicd', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'dcivicd', 'eifie', 'd'], ['d', 'eifiedcivicdeifie', 'd'], ['deified', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['deified', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['deified', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['deified', 'c', 'i', 'v', 'i', 'c', 'deified'], ['deified', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['deified', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['deified', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['deified', 'c', 'ivi', 'c', 'deified'], ['deified', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['deified', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['deified', 'civic', 'd', 'eifie', 'd'], ['deified', 'civic', 'deified'], ['deifiedcivicdeified']]\n assert candidate(s = \"aaaabaaaa\") == [['a', 'a', 'a', 'a', 'b', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'b', 'a', 'a', 'aa'], ['a', 'a', 'a', 'a', 'b', 'a', 'aa', 'a'], ['a', 'a', 'a', 'a', 'b', 'a', 'aaa'], ['a', 'a', 'a', 'a', 'b', 'aa', 'a', 'a'], ['a', 'a', 'a', 'a', 'b', 'aa', 'aa'], ['a', 'a', 'a', 'a', 'b', 'aaa', 'a'], ['a', 'a', 'a', 'a', 'b', 'aaaa'], ['a', 'a', 'a', 'aba', 'a', 'a', 'a'], ['a', 'a', 'a', 'aba', 'a', 'aa'], ['a', 'a', 'a', 'aba', 'aa', 'a'], ['a', 'a', 'a', 'aba', 'aaa'], ['a', 'a', 'aa', 'b', 'a', 'a', 'a', 'a'], ['a', 'a', 'aa', 'b', 'a', 'a', 'aa'], ['a', 'a', 'aa', 'b', 'a', 'aa', 'a'], ['a', 'a', 'aa', 'b', 'a', 'aaa'], ['a', 'a', 'aa', 'b', 'aa', 'a', 'a'], ['a', 'a', 'aa', 'b', 'aa', 'aa'], ['a', 'a', 'aa', 'b', 'aaa', 'a'], ['a', 'a', 'aa', 'b', 'aaaa'], ['a', 'a', 'aabaa', 'a', 'a'], ['a', 'a', 'aabaa', 'aa'], ['a', 'aa', 'a', 'b', 'a', 'a', 'a', 'a'], ['a', 'aa', 'a', 'b', 'a', 'a', 'aa'], ['a', 'aa', 'a', 'b', 'a', 'aa', 'a'], ['a', 'aa', 'a', 'b', 'a', 'aaa'], ['a', 'aa', 'a', 'b', 'aa', 'a', 'a'], ['a', 'aa', 'a', 'b', 'aa', 'aa'], ['a', 'aa', 'a', 'b', 'aaa', 'a'], ['a', 'aa', 'a', 'b', 'aaaa'], ['a', 'aa', 'aba', 'a', 'a', 'a'], ['a', 'aa', 'aba', 'a', 'aa'], ['a', 'aa', 'aba', 'aa', 'a'], ['a', 'aa', 'aba', 'aaa'], ['a', 'aaa', 'b', 'a', 'a', 'a', 'a'], ['a', 'aaa', 'b', 'a', 'a', 'aa'], ['a', 'aaa', 'b', 'a', 'aa', 'a'], ['a', 'aaa', 'b', 'a', 'aaa'], ['a', 'aaa', 'b', 'aa', 'a', 'a'], ['a', 'aaa', 'b', 'aa', 'aa'], ['a', 'aaa', 'b', 'aaa', 'a'], ['a', 'aaa', 'b', 'aaaa'], ['a', 'aaabaaa', 'a'], ['aa', 'a', 'a', 'b', 'a', 'a', 'a', 'a'], ['aa', 'a', 'a', 'b', 'a', 'a', 'aa'], ['aa', 'a', 'a', 'b', 'a', 'aa', 'a'], ['aa', 'a', 'a', 'b', 'a', 'aaa'], ['aa', 'a', 'a', 'b', 'aa', 'a', 'a'], ['aa', 'a', 'a', 'b', 'aa', 'aa'], ['aa', 'a', 'a', 'b', 'aaa', 'a'], ['aa', 'a', 'a', 'b', 'aaaa'], ['aa', 'a', 'aba', 'a', 'a', 'a'], ['aa', 'a', 'aba', 'a', 'aa'], ['aa', 'a', 'aba', 'aa', 'a'], ['aa', 'a', 'aba', 'aaa'], ['aa', 'aa', 'b', 'a', 'a', 'a', 'a'], ['aa', 'aa', 'b', 'a', 'a', 'aa'], ['aa', 'aa', 'b', 'a', 'aa', 'a'], ['aa', 'aa', 'b', 'a', 'aaa'], ['aa', 'aa', 'b', 'aa', 'a', 'a'], ['aa', 'aa', 'b', 'aa', 'aa'], ['aa', 'aa', 'b', 'aaa', 'a'], ['aa', 'aa', 'b', 'aaaa'], ['aa', 'aabaa', 'a', 'a'], ['aa', 'aabaa', 'aa'], ['aaa', 'a', 'b', 'a', 'a', 'a', 'a'], ['aaa', 'a', 'b', 'a', 'a', 'aa'], ['aaa', 'a', 'b', 'a', 'aa', 'a'], ['aaa', 'a', 'b', 'a', 'aaa'], ['aaa', 'a', 'b', 'aa', 'a', 'a'], ['aaa', 'a', 'b', 'aa', 'aa'], ['aaa', 'a', 'b', 'aaa', 'a'], ['aaa', 'a', 'b', 'aaaa'], ['aaa', 'aba', 'a', 'a', 'a'], ['aaa', 'aba', 'a', 'aa'], ['aaa', 'aba', 'aa', 'a'], ['aaa', 'aba', 'aaa'], ['aaaa', 'b', 'a', 'a', 'a', 'a'], ['aaaa', 'b', 'a', 'a', 'aa'], ['aaaa', 'b', 'a', 'aa', 'a'], ['aaaa', 'b', 'a', 'aaa'], ['aaaa', 'b', 'aa', 'a', 'a'], ['aaaa', 'b', 'aa', 'aa'], ['aaaa', 'b', 'aaa', 'a'], ['aaaa', 'b', 'aaaa'], ['aaaabaaaa']]\n assert candidate(s = \"noonabccba\") == [['n', 'o', 'o', 'n', 'a', 'b', 'c', 'c', 'b', 'a'], ['n', 'o', 'o', 'n', 'a', 'b', 'cc', 'b', 'a'], ['n', 'o', 'o', 'n', 'a', 'bccb', 'a'], ['n', 'o', 'o', 'n', 'abccba'], ['n', 'oo', 'n', 'a', 'b', 'c', 'c', 'b', 'a'], ['n', 'oo', 'n', 'a', 'b', 'cc', 'b', 'a'], ['n', 'oo', 'n', 'a', 'bccb', 'a'], ['n', 'oo', 'n', 'abccba'], ['noon', 'a', 'b', 'c', 'c', 'b', 'a'], ['noon', 'a', 'b', 'cc', 'b', 'a'], ['noon', 'a', 'bccb', 'a'], ['noon', 'abccba']]\n assert candidate(s = \"madamadam\") == [['m', 'a', 'd', 'a', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'madam'], ['m', 'a', 'd', 'ama', 'd', 'a', 'm'], ['m', 'a', 'damad', 'a', 'm'], ['m', 'ada', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'ada', 'm'], ['m', 'ada', 'madam'], ['m', 'adamada', 'm'], ['madam', 'a', 'd', 'a', 'm'], ['madam', 'ada', 'm'], ['madamadam']]\n assert candidate(s = \"racecarrace\") == [['r', 'a', 'c', 'e', 'c', 'a', 'r', 'r', 'a', 'c', 'e'], ['r', 'a', 'c', 'e', 'c', 'a', 'rr', 'a', 'c', 'e'], ['r', 'a', 'c', 'e', 'c', 'arra', 'c', 'e'], ['r', 'a', 'c', 'e', 'carrac', 'e'], ['r', 'a', 'c', 'ecarrace'], ['r', 'a', 'cec', 'a', 'r', 'r', 'a', 'c', 'e'], ['r', 'a', 'cec', 'a', 'rr', 'a', 'c', 'e'], ['r', 'a', 'cec', 'arra', 'c', 'e'], ['r', 'aceca', 'r', 'r', 'a', 'c', 'e'], ['r', 'aceca', 'rr', 'a', 'c', 'e'], ['racecar', 'r', 'a', 'c', 'e']]\n assert candidate(s = \"rotorlevel\") == [['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l'], ['r', 'o', 't', 'o', 'r', 'level'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l'], ['r', 'oto', 'r', 'l', 'eve', 'l'], ['r', 'oto', 'r', 'level'], ['rotor', 'l', 'e', 'v', 'e', 'l'], ['rotor', 'l', 'eve', 'l'], ['rotor', 'level']]\n assert candidate(s = \"abccbaabccba\") == [['a', 'b', 'c', 'c', 'b', 'a', 'a', 'b', 'c', 'c', 'b', 'a'], ['a', 'b', 'c', 'c', 'b', 'a', 'a', 'b', 'cc', 'b', 'a'], ['a', 'b', 'c', 'c', 'b', 'a', 'a', 'bccb', 'a'], ['a', 'b', 'c', 'c', 'b', 'a', 'abccba'], ['a', 'b', 'c', 'c', 'b', 'aa', 'b', 'c', 'c', 'b', 'a'], ['a', 'b', 'c', 'c', 'b', 'aa', 'b', 'cc', 'b', 'a'], ['a', 'b', 'c', 'c', 'b', 'aa', 'bccb', 'a'], ['a', 'b', 'c', 'c', 'baab', 'c', 'c', 'b', 'a'], ['a', 'b', 'c', 'c', 'baab', 'cc', 'b', 'a'], ['a', 'b', 'c', 'cbaabc', 'c', 'b', 'a'], ['a', 'b', 'cc', 'b', 'a', 'a', 'b', 'c', 'c', 'b', 'a'], ['a', 'b', 'cc', 'b', 'a', 'a', 'b', 'cc', 'b', 'a'], ['a', 'b', 'cc', 'b', 'a', 'a', 'bccb', 'a'], ['a', 'b', 'cc', 'b', 'a', 'abccba'], ['a', 'b', 'cc', 'b', 'aa', 'b', 'c', 'c', 'b', 'a'], ['a', 'b', 'cc', 'b', 'aa', 'b', 'cc', 'b', 'a'], ['a', 'b', 'cc', 'b', 'aa', 'bccb', 'a'], ['a', 'b', 'cc', 'baab', 'c', 'c', 'b', 'a'], ['a', 'b', 'cc', 'baab', 'cc', 'b', 'a'], ['a', 'b', 'ccbaabcc', 'b', 'a'], ['a', 'bccb', 'a', 'a', 'b', 'c', 'c', 'b', 'a'], ['a', 'bccb', 'a', 'a', 'b', 'cc', 'b', 'a'], ['a', 'bccb', 'a', 'a', 'bccb', 'a'], ['a', 'bccb', 'a', 'abccba'], ['a', 'bccb', 'aa', 'b', 'c', 'c', 'b', 'a'], ['a', 'bccb', 'aa', 'b', 'cc', 'b', 'a'], ['a', 'bccb', 'aa', 'bccb', 'a'], ['a', 'bccbaabccb', 'a'], ['abccba', 'a', 'b', 'c', 'c', 'b', 'a'], ['abccba', 'a', 'b', 'cc', 'b', 'a'], ['abccba', 'a', 'bccb', 'a'], ['abccba', 'abccba'], ['abccbaabccba']]\n assert candidate(s = \"madamatoyotademadam\") == [['m', 'a', 'd', 'a', 'm', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'madam'], ['m', 'a', 'd', 'a', 'm', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'madam'], ['m', 'a', 'd', 'a', 'm', 'a', 'toyot', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'a', 'toyot', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'a', 'toyot', 'a', 'd', 'e', 'madam'], ['m', 'a', 'd', 'a', 'm', 'atoyota', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'atoyota', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'atoyota', 'd', 'e', 'madam'], ['m', 'a', 'd', 'ama', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'ama', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'ama', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'madam'], ['m', 'a', 'd', 'ama', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'ama', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'ama', 't', 'oyo', 't', 'a', 'd', 'e', 'madam'], ['m', 'a', 'd', 'ama', 'toyot', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'ama', 'toyot', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'a', 'd', 'ama', 'toyot', 'a', 'd', 'e', 'madam'], ['m', 'ada', 'm', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'madam'], ['m', 'ada', 'm', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'madam'], ['m', 'ada', 'm', 'a', 'toyot', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'a', 'toyot', 'a', 'd', 'e', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'a', 'toyot', 'a', 'd', 'e', 'madam'], ['m', 'ada', 'm', 'atoyota', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'atoyota', 'd', 'e', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'atoyota', 'd', 'e', 'madam'], ['madam', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['madam', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['madam', 'a', 't', 'o', 'y', 'o', 't', 'a', 'd', 'e', 'madam'], ['madam', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['madam', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'm', 'ada', 'm'], ['madam', 'a', 't', 'oyo', 't', 'a', 'd', 'e', 'madam'], ['madam', 'a', 'toyot', 'a', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['madam', 'a', 'toyot', 'a', 'd', 'e', 'm', 'ada', 'm'], ['madam', 'a', 'toyot', 'a', 'd', 'e', 'madam'], ['madam', 'atoyota', 'd', 'e', 'm', 'a', 'd', 'a', 'm'], ['madam', 'atoyota', 'd', 'e', 'm', 'ada', 'm'], ['madam', 'atoyota', 'd', 'e', 'madam']]\n assert candidate(s = \"levelnooncivicdeified\") == [['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'deified'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'deified'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'civic', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n', 'civic', 'deified'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'deified'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'deified'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'civic', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n', 'civic', 'deified'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'deified'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'c', 'ivi', 'c', 'deified'], ['l', 'e', 'v', 'e', 'l', 'noon', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'civic', 'd', 'eifie', 'd'], ['l', 'e', 'v', 'e', 'l', 'noon', 'civic', 'deified'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'deified'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'deified'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'civic', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'n', 'o', 'o', 'n', 'civic', 'deified'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'deified'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'deified'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'civic', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'n', 'oo', 'n', 'civic', 'deified'], ['l', 'eve', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'noon', 'c', 'i', 'v', 'i', 'c', 'deified'], ['l', 'eve', 'l', 'noon', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'noon', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'noon', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'noon', 'c', 'ivi', 'c', 'deified'], ['l', 'eve', 'l', 'noon', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['l', 'eve', 'l', 'noon', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['l', 'eve', 'l', 'noon', 'civic', 'd', 'eifie', 'd'], ['l', 'eve', 'l', 'noon', 'civic', 'deified'], ['level', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['level', 'n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'deified'], ['level', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['level', 'n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'deified'], ['level', 'n', 'o', 'o', 'n', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'n', 'o', 'o', 'n', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'n', 'o', 'o', 'n', 'civic', 'd', 'eifie', 'd'], ['level', 'n', 'o', 'o', 'n', 'civic', 'deified'], ['level', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['level', 'n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'deified'], ['level', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['level', 'n', 'oo', 'n', 'c', 'ivi', 'c', 'deified'], ['level', 'n', 'oo', 'n', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'n', 'oo', 'n', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'n', 'oo', 'n', 'civic', 'd', 'eifie', 'd'], ['level', 'n', 'oo', 'n', 'civic', 'deified'], ['level', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'noon', 'c', 'i', 'v', 'i', 'c', 'd', 'eifie', 'd'], ['level', 'noon', 'c', 'i', 'v', 'i', 'c', 'deified'], ['level', 'noon', 'c', 'ivi', 'c', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'noon', 'c', 'ivi', 'c', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'noon', 'c', 'ivi', 'c', 'd', 'eifie', 'd'], ['level', 'noon', 'c', 'ivi', 'c', 'deified'], ['level', 'noon', 'civic', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['level', 'noon', 'civic', 'd', 'e', 'ifi', 'e', 'd'], ['level', 'noon', 'civic', 'd', 'eifie', 'd'], ['level', 'noon', 'civic', 'deified']]\n assert candidate(s = \"nooncivicrotor\") == [['n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'r', 'o', 't', 'o', 'r'], ['n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'r', 'oto', 'r'], ['n', 'o', 'o', 'n', 'c', 'i', 'v', 'i', 'c', 'rotor'], ['n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'r', 'o', 't', 'o', 'r'], ['n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'r', 'oto', 'r'], ['n', 'o', 'o', 'n', 'c', 'ivi', 'c', 'rotor'], ['n', 'o', 'o', 'n', 'civic', 'r', 'o', 't', 'o', 'r'], ['n', 'o', 'o', 'n', 'civic', 'r', 'oto', 'r'], ['n', 'o', 'o', 'n', 'civic', 'rotor'], ['n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'r', 'o', 't', 'o', 'r'], ['n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'r', 'oto', 'r'], ['n', 'oo', 'n', 'c', 'i', 'v', 'i', 'c', 'rotor'], ['n', 'oo', 'n', 'c', 'ivi', 'c', 'r', 'o', 't', 'o', 'r'], ['n', 'oo', 'n', 'c', 'ivi', 'c', 'r', 'oto', 'r'], ['n', 'oo', 'n', 'c', 'ivi', 'c', 'rotor'], ['n', 'oo', 'n', 'civic', 'r', 'o', 't', 'o', 'r'], ['n', 'oo', 'n', 'civic', 'r', 'oto', 'r'], ['n', 'oo', 'n', 'civic', 'rotor'], ['noon', 'c', 'i', 'v', 'i', 'c', 'r', 'o', 't', 'o', 'r'], ['noon', 'c', 'i', 'v', 'i', 'c', 'r', 'oto', 'r'], ['noon', 'c', 'i', 'v', 'i', 'c', 'rotor'], ['noon', 'c', 'ivi', 'c', 'r', 'o', 't', 'o', 'r'], ['noon', 'c', 'ivi', 'c', 'r', 'oto', 'r'], ['noon', 'c', 'ivi', 'c', 'rotor'], ['noon', 'civic', 'r', 'o', 't', 'o', 'r'], ['noon', 'civic', 'r', 'oto', 'r'], ['noon', 'civic', 'rotor']]\n assert candidate(s = \"aabbccddeee\") == [['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'e', 'e'], ['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'ee'], ['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'ee', 'e'], ['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'eee'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'e', 'e', 'e'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'e', 'ee'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'ee', 'e'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'eee'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'e', 'e', 'e'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'e', 'ee'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'ee', 'e'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'eee'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'e', 'e', 'e'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'e', 'ee'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'ee', 'e'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'eee'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'e', 'e', 'e'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'e', 'ee'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'ee', 'e'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'eee'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'e', 'e', 'e'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'e', 'ee'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'ee', 'e'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'eee'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'e', 'e', 'e'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'e', 'ee'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'ee', 'e'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'eee'], ['a', 'a', 'bb', 'cc', 'dd', 'e', 'e', 'e'], ['a', 'a', 'bb', 'cc', 'dd', 'e', 'ee'], ['a', 'a', 'bb', 'cc', 'dd', 'ee', 'e'], ['a', 'a', 'bb', 'cc', 'dd', 'eee'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'e', 'e'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'ee'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'ee', 'e'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'eee'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'e', 'e', 'e'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'e', 'ee'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'ee', 'e'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'eee'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'e', 'e', 'e'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'e', 'ee'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'ee', 'e'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'eee'], ['aa', 'b', 'b', 'cc', 'dd', 'e', 'e', 'e'], ['aa', 'b', 'b', 'cc', 'dd', 'e', 'ee'], ['aa', 'b', 'b', 'cc', 'dd', 'ee', 'e'], ['aa', 'b', 'b', 'cc', 'dd', 'eee'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'e', 'e', 'e'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'e', 'ee'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'ee', 'e'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'eee'], ['aa', 'bb', 'c', 'c', 'dd', 'e', 'e', 'e'], ['aa', 'bb', 'c', 'c', 'dd', 'e', 'ee'], ['aa', 'bb', 'c', 'c', 'dd', 'ee', 'e'], ['aa', 'bb', 'c', 'c', 'dd', 'eee'], ['aa', 'bb', 'cc', 'd', 'd', 'e', 'e', 'e'], ['aa', 'bb', 'cc', 'd', 'd', 'e', 'ee'], ['aa', 'bb', 'cc', 'd', 'd', 'ee', 'e'], ['aa', 'bb', 'cc', 'd', 'd', 'eee'], ['aa', 'bb', 'cc', 'dd', 'e', 'e', 'e'], ['aa', 'bb', 'cc', 'dd', 'e', 'ee'], ['aa', 'bb', 'cc', 'dd', 'ee', 'e'], ['aa', 'bb', 'cc', 'dd', 'eee']]\n assert candidate(s = \"madamracecar\") == [['m', 'a', 'd', 'a', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['m', 'a', 'd', 'a', 'm', 'r', 'a', 'cec', 'a', 'r'], ['m', 'a', 'd', 'a', 'm', 'r', 'aceca', 'r'], ['m', 'a', 'd', 'a', 'm', 'racecar'], ['m', 'ada', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['m', 'ada', 'm', 'r', 'a', 'cec', 'a', 'r'], ['m', 'ada', 'm', 'r', 'aceca', 'r'], ['m', 'ada', 'm', 'racecar'], ['madam', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['madam', 'r', 'a', 'cec', 'a', 'r'], ['madam', 'r', 'aceca', 'r'], ['madam', 'racecar']]\n assert candidate(s = \"levelrefer\") == [['l', 'e', 'v', 'e', 'l', 'r', 'e', 'f', 'e', 'r'], ['l', 'e', 'v', 'e', 'l', 'r', 'efe', 'r'], ['l', 'e', 'v', 'e', 'l', 'refer'], ['l', 'eve', 'l', 'r', 'e', 'f', 'e', 'r'], ['l', 'eve', 'l', 'r', 'efe', 'r'], ['l', 'eve', 'l', 'refer'], ['level', 'r', 'e', 'f', 'e', 'r'], ['level', 'r', 'efe', 'r'], ['level', 'refer']]\n assert candidate(s = \"xyxzxyzxzxyx\") == [['x', 'y', 'x', 'z', 'x', 'y', 'z', 'x', 'z', 'x', 'y', 'x'], ['x', 'y', 'x', 'z', 'x', 'y', 'z', 'x', 'z', 'xyx'], ['x', 'y', 'x', 'z', 'x', 'y', 'z', 'xzx', 'y', 'x'], ['x', 'y', 'x', 'z', 'x', 'y', 'zxz', 'x', 'y', 'x'], ['x', 'y', 'x', 'z', 'x', 'y', 'zxz', 'xyx'], ['x', 'y', 'xzx', 'y', 'z', 'x', 'z', 'x', 'y', 'x'], ['x', 'y', 'xzx', 'y', 'z', 'x', 'z', 'xyx'], ['x', 'y', 'xzx', 'y', 'z', 'xzx', 'y', 'x'], ['x', 'y', 'xzx', 'y', 'zxz', 'x', 'y', 'x'], ['x', 'y', 'xzx', 'y', 'zxz', 'xyx'], ['x', 'yxzxy', 'z', 'x', 'z', 'x', 'y', 'x'], ['x', 'yxzxy', 'z', 'x', 'z', 'xyx'], ['x', 'yxzxy', 'z', 'xzx', 'y', 'x'], ['x', 'yxzxy', 'zxz', 'x', 'y', 'x'], ['x', 'yxzxy', 'zxz', 'xyx'], ['xyx', 'z', 'x', 'y', 'z', 'x', 'z', 'x', 'y', 'x'], ['xyx', 'z', 'x', 'y', 'z', 'x', 'z', 'xyx'], ['xyx', 'z', 'x', 'y', 'z', 'xzx', 'y', 'x'], ['xyx', 'z', 'x', 'y', 'zxz', 'x', 'y', 'x'], ['xyx', 'z', 'x', 'y', 'zxz', 'xyx']]\n assert candidate(s = \"refercivic\") == [['r', 'e', 'f', 'e', 'r', 'c', 'i', 'v', 'i', 'c'], ['r', 'e', 'f', 'e', 'r', 'c', 'ivi', 'c'], ['r', 'e', 'f', 'e', 'r', 'civic'], ['r', 'efe', 'r', 'c', 'i', 'v', 'i', 'c'], ['r', 'efe', 'r', 'c', 'ivi', 'c'], ['r', 'efe', 'r', 'civic'], ['refer', 'c', 'i', 'v', 'i', 'c'], ['refer', 'c', 'ivi', 'c'], ['refer', 'civic']]\n assert candidate(s = \"noonlevelmadam\") == [['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'madam'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'madam'], ['n', 'o', 'o', 'n', 'level', 'm', 'a', 'd', 'a', 'm'], ['n', 'o', 'o', 'n', 'level', 'm', 'ada', 'm'], ['n', 'o', 'o', 'n', 'level', 'madam'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'madam'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'madam'], ['n', 'oo', 'n', 'level', 'm', 'a', 'd', 'a', 'm'], ['n', 'oo', 'n', 'level', 'm', 'ada', 'm'], ['n', 'oo', 'n', 'level', 'madam'], ['noon', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['noon', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['noon', 'l', 'e', 'v', 'e', 'l', 'madam'], ['noon', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['noon', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['noon', 'l', 'eve', 'l', 'madam'], ['noon', 'level', 'm', 'a', 'd', 'a', 'm'], ['noon', 'level', 'm', 'ada', 'm'], ['noon', 'level', 'madam']]\n assert candidate(s = \"abacabacabac\") == [['a', 'b', 'a', 'c', 'a', 'b', 'a', 'c', 'a', 'b', 'a', 'c'], ['a', 'b', 'a', 'c', 'a', 'b', 'a', 'c', 'aba', 'c'], ['a', 'b', 'a', 'c', 'a', 'b', 'a', 'cabac'], ['a', 'b', 'a', 'c', 'a', 'b', 'aca', 'b', 'a', 'c'], ['a', 'b', 'a', 'c', 'a', 'bacab', 'a', 'c'], ['a', 'b', 'a', 'c', 'aba', 'c', 'a', 'b', 'a', 'c'], ['a', 'b', 'a', 'c', 'aba', 'c', 'aba', 'c'], ['a', 'b', 'a', 'c', 'aba', 'cabac'], ['a', 'b', 'a', 'c', 'abacaba', 'c'], ['a', 'b', 'a', 'cabac', 'a', 'b', 'a', 'c'], ['a', 'b', 'a', 'cabac', 'aba', 'c'], ['a', 'b', 'a', 'cabacabac'], ['a', 'b', 'aca', 'b', 'a', 'c', 'a', 'b', 'a', 'c'], ['a', 'b', 'aca', 'b', 'a', 'c', 'aba', 'c'], ['a', 'b', 'aca', 'b', 'a', 'cabac'], ['a', 'b', 'aca', 'b', 'aca', 'b', 'a', 'c'], ['a', 'b', 'aca', 'bacab', 'a', 'c'], ['a', 'b', 'acabaca', 'b', 'a', 'c'], ['a', 'bacab', 'a', 'c', 'a', 'b', 'a', 'c'], ['a', 'bacab', 'a', 'c', 'aba', 'c'], ['a', 'bacab', 'a', 'cabac'], ['a', 'bacab', 'aca', 'b', 'a', 'c'], ['a', 'bacabacab', 'a', 'c'], ['aba', 'c', 'a', 'b', 'a', 'c', 'a', 'b', 'a', 'c'], ['aba', 'c', 'a', 'b', 'a', 'c', 'aba', 'c'], ['aba', 'c', 'a', 'b', 'a', 'cabac'], ['aba', 'c', 'a', 'b', 'aca', 'b', 'a', 'c'], ['aba', 'c', 'a', 'bacab', 'a', 'c'], ['aba', 'c', 'aba', 'c', 'a', 'b', 'a', 'c'], ['aba', 'c', 'aba', 'c', 'aba', 'c'], ['aba', 'c', 'aba', 'cabac'], ['aba', 'c', 'abacaba', 'c'], ['aba', 'cabac', 'a', 'b', 'a', 'c'], ['aba', 'cabac', 'aba', 'c'], ['aba', 'cabacabac'], ['abacaba', 'c', 'a', 'b', 'a', 'c'], ['abacaba', 'c', 'aba', 'c'], ['abacaba', 'cabac'], ['abacabacaba', 'c']]\n assert candidate(s = \"madaminnakayak\") == [['m', 'a', 'd', 'a', 'm', 'i', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['m', 'a', 'd', 'a', 'm', 'i', 'n', 'n', 'a', 'k', 'aya', 'k'], ['m', 'a', 'd', 'a', 'm', 'i', 'n', 'n', 'a', 'kayak'], ['m', 'a', 'd', 'a', 'm', 'i', 'n', 'n', 'aka', 'y', 'a', 'k'], ['m', 'a', 'd', 'a', 'm', 'i', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['m', 'a', 'd', 'a', 'm', 'i', 'nn', 'a', 'k', 'aya', 'k'], ['m', 'a', 'd', 'a', 'm', 'i', 'nn', 'a', 'kayak'], ['m', 'a', 'd', 'a', 'm', 'i', 'nn', 'aka', 'y', 'a', 'k'], ['m', 'ada', 'm', 'i', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['m', 'ada', 'm', 'i', 'n', 'n', 'a', 'k', 'aya', 'k'], ['m', 'ada', 'm', 'i', 'n', 'n', 'a', 'kayak'], ['m', 'ada', 'm', 'i', 'n', 'n', 'aka', 'y', 'a', 'k'], ['m', 'ada', 'm', 'i', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['m', 'ada', 'm', 'i', 'nn', 'a', 'k', 'aya', 'k'], ['m', 'ada', 'm', 'i', 'nn', 'a', 'kayak'], ['m', 'ada', 'm', 'i', 'nn', 'aka', 'y', 'a', 'k'], ['madam', 'i', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['madam', 'i', 'n', 'n', 'a', 'k', 'aya', 'k'], ['madam', 'i', 'n', 'n', 'a', 'kayak'], ['madam', 'i', 'n', 'n', 'aka', 'y', 'a', 'k'], ['madam', 'i', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['madam', 'i', 'nn', 'a', 'k', 'aya', 'k'], ['madam', 'i', 'nn', 'a', 'kayak'], ['madam', 'i', 'nn', 'aka', 'y', 'a', 'k']]\n assert candidate(s = \"atoyotaatoyota\") == [['a', 't', 'o', 'y', 'o', 't', 'a', 'a', 't', 'o', 'y', 'o', 't', 'a'], ['a', 't', 'o', 'y', 'o', 't', 'a', 'a', 't', 'oyo', 't', 'a'], ['a', 't', 'o', 'y', 'o', 't', 'a', 'a', 'toyot', 'a'], ['a', 't', 'o', 'y', 'o', 't', 'a', 'atoyota'], ['a', 't', 'o', 'y', 'o', 't', 'aa', 't', 'o', 'y', 'o', 't', 'a'], ['a', 't', 'o', 'y', 'o', 't', 'aa', 't', 'oyo', 't', 'a'], ['a', 't', 'o', 'y', 'o', 't', 'aa', 'toyot', 'a'], ['a', 't', 'o', 'y', 'o', 'taat', 'o', 'y', 'o', 't', 'a'], ['a', 't', 'o', 'y', 'o', 'taat', 'oyo', 't', 'a'], ['a', 't', 'o', 'y', 'otaato', 'y', 'o', 't', 'a'], ['a', 't', 'o', 'yotaatoy', 'o', 't', 'a'], ['a', 't', 'oyo', 't', 'a', 'a', 't', 'o', 'y', 'o', 't', 'a'], ['a', 't', 'oyo', 't', 'a', 'a', 't', 'oyo', 't', 'a'], ['a', 't', 'oyo', 't', 'a', 'a', 'toyot', 'a'], ['a', 't', 'oyo', 't', 'a', 'atoyota'], ['a', 't', 'oyo', 't', 'aa', 't', 'o', 'y', 'o', 't', 'a'], ['a', 't', 'oyo', 't', 'aa', 't', 'oyo', 't', 'a'], ['a', 't', 'oyo', 't', 'aa', 'toyot', 'a'], ['a', 't', 'oyo', 'taat', 'o', 'y', 'o', 't', 'a'], ['a', 't', 'oyo', 'taat', 'oyo', 't', 'a'], ['a', 't', 'oyotaatoyo', 't', 'a'], ['a', 'toyot', 'a', 'a', 't', 'o', 'y', 'o', 't', 'a'], ['a', 'toyot', 'a', 'a', 't', 'oyo', 't', 'a'], ['a', 'toyot', 'a', 'a', 'toyot', 'a'], ['a', 'toyot', 'a', 'atoyota'], ['a', 'toyot', 'aa', 't', 'o', 'y', 'o', 't', 'a'], ['a', 'toyot', 'aa', 't', 'oyo', 't', 'a'], ['a', 'toyot', 'aa', 'toyot', 'a'], ['a', 'toyotaatoyot', 'a'], ['atoyota', 'a', 't', 'o', 'y', 'o', 't', 'a'], ['atoyota', 'a', 't', 'oyo', 't', 'a'], ['atoyota', 'a', 'toyot', 'a'], ['atoyota', 'atoyota'], ['atoyotaatoyota']]\n assert candidate(s = \"madammadam\") == [['m', 'a', 'd', 'a', 'm', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'madam'], ['m', 'a', 'd', 'a', 'mm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'mm', 'ada', 'm'], ['m', 'a', 'd', 'amma', 'd', 'a', 'm'], ['m', 'a', 'dammad', 'a', 'm'], ['m', 'ada', 'm', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'madam'], ['m', 'ada', 'mm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'mm', 'ada', 'm'], ['m', 'adammada', 'm'], ['madam', 'm', 'a', 'd', 'a', 'm'], ['madam', 'm', 'ada', 'm'], ['madam', 'madam'], ['madammadam']]\n assert candidate(s = \"madamlevelmadam\") == [['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'madam'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'madam'], ['m', 'a', 'd', 'a', 'm', 'level', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'level', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'level', 'madam'], ['m', 'a', 'd', 'a', 'mlevelm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'mlevelm', 'ada', 'm'], ['m', 'a', 'd', 'amlevelma', 'd', 'a', 'm'], ['m', 'a', 'damlevelmad', 'a', 'm'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'madam'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'madam'], ['m', 'ada', 'm', 'level', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'level', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'level', 'madam'], ['m', 'ada', 'mlevelm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'mlevelm', 'ada', 'm'], ['m', 'adamlevelmada', 'm'], ['madam', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['madam', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['madam', 'l', 'e', 'v', 'e', 'l', 'madam'], ['madam', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['madam', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['madam', 'l', 'eve', 'l', 'madam'], ['madam', 'level', 'm', 'a', 'd', 'a', 'm'], ['madam', 'level', 'm', 'ada', 'm'], ['madam', 'level', 'madam'], ['madamlevelmadam']]\n assert candidate(s = \"refermadamracecar\") == [['r', 'e', 'f', 'e', 'r', 'm', 'a', 'd', 'a', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'e', 'f', 'e', 'r', 'm', 'a', 'd', 'a', 'm', 'r', 'a', 'cec', 'a', 'r'], ['r', 'e', 'f', 'e', 'r', 'm', 'a', 'd', 'a', 'm', 'r', 'aceca', 'r'], ['r', 'e', 'f', 'e', 'r', 'm', 'a', 'd', 'a', 'm', 'racecar'], ['r', 'e', 'f', 'e', 'r', 'm', 'ada', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'e', 'f', 'e', 'r', 'm', 'ada', 'm', 'r', 'a', 'cec', 'a', 'r'], ['r', 'e', 'f', 'e', 'r', 'm', 'ada', 'm', 'r', 'aceca', 'r'], ['r', 'e', 'f', 'e', 'r', 'm', 'ada', 'm', 'racecar'], ['r', 'e', 'f', 'e', 'r', 'madam', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'e', 'f', 'e', 'r', 'madam', 'r', 'a', 'cec', 'a', 'r'], ['r', 'e', 'f', 'e', 'r', 'madam', 'r', 'aceca', 'r'], ['r', 'e', 'f', 'e', 'r', 'madam', 'racecar'], ['r', 'e', 'f', 'e', 'rmadamr', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'e', 'f', 'e', 'rmadamr', 'a', 'cec', 'a', 'r'], ['r', 'e', 'f', 'e', 'rmadamr', 'aceca', 'r'], ['r', 'efe', 'r', 'm', 'a', 'd', 'a', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'efe', 'r', 'm', 'a', 'd', 'a', 'm', 'r', 'a', 'cec', 'a', 'r'], ['r', 'efe', 'r', 'm', 'a', 'd', 'a', 'm', 'r', 'aceca', 'r'], ['r', 'efe', 'r', 'm', 'a', 'd', 'a', 'm', 'racecar'], ['r', 'efe', 'r', 'm', 'ada', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'efe', 'r', 'm', 'ada', 'm', 'r', 'a', 'cec', 'a', 'r'], ['r', 'efe', 'r', 'm', 'ada', 'm', 'r', 'aceca', 'r'], ['r', 'efe', 'r', 'm', 'ada', 'm', 'racecar'], ['r', 'efe', 'r', 'madam', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'efe', 'r', 'madam', 'r', 'a', 'cec', 'a', 'r'], ['r', 'efe', 'r', 'madam', 'r', 'aceca', 'r'], ['r', 'efe', 'r', 'madam', 'racecar'], ['r', 'efe', 'rmadamr', 'a', 'c', 'e', 'c', 'a', 'r'], ['r', 'efe', 'rmadamr', 'a', 'cec', 'a', 'r'], ['r', 'efe', 'rmadamr', 'aceca', 'r'], ['refer', 'm', 'a', 'd', 'a', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['refer', 'm', 'a', 'd', 'a', 'm', 'r', 'a', 'cec', 'a', 'r'], ['refer', 'm', 'a', 'd', 'a', 'm', 'r', 'aceca', 'r'], ['refer', 'm', 'a', 'd', 'a', 'm', 'racecar'], ['refer', 'm', 'ada', 'm', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['refer', 'm', 'ada', 'm', 'r', 'a', 'cec', 'a', 'r'], ['refer', 'm', 'ada', 'm', 'r', 'aceca', 'r'], ['refer', 'm', 'ada', 'm', 'racecar'], ['refer', 'madam', 'r', 'a', 'c', 'e', 'c', 'a', 'r'], ['refer', 'madam', 'r', 'a', 'cec', 'a', 'r'], ['refer', 'madam', 'r', 'aceca', 'r'], ['refer', 'madam', 'racecar']]\n assert candidate(s = \"xyxyxyxyxy\") == [['x', 'y', 'x', 'y', 'x', 'y', 'x', 'y', 'x', 'y'], ['x', 'y', 'x', 'y', 'x', 'y', 'x', 'yxy'], ['x', 'y', 'x', 'y', 'x', 'y', 'xyx', 'y'], ['x', 'y', 'x', 'y', 'x', 'yxy', 'x', 'y'], ['x', 'y', 'x', 'y', 'x', 'yxyxy'], ['x', 'y', 'x', 'y', 'xyx', 'y', 'x', 'y'], ['x', 'y', 'x', 'y', 'xyx', 'yxy'], ['x', 'y', 'x', 'y', 'xyxyx', 'y'], ['x', 'y', 'x', 'yxy', 'x', 'y', 'x', 'y'], ['x', 'y', 'x', 'yxy', 'x', 'yxy'], ['x', 'y', 'x', 'yxy', 'xyx', 'y'], ['x', 'y', 'x', 'yxyxy', 'x', 'y'], ['x', 'y', 'x', 'yxyxyxy'], ['x', 'y', 'xyx', 'y', 'x', 'y', 'x', 'y'], ['x', 'y', 'xyx', 'y', 'x', 'yxy'], ['x', 'y', 'xyx', 'y', 'xyx', 'y'], ['x', 'y', 'xyx', 'yxy', 'x', 'y'], ['x', 'y', 'xyx', 'yxyxy'], ['x', 'y', 'xyxyx', 'y', 'x', 'y'], ['x', 'y', 'xyxyx', 'yxy'], ['x', 'y', 'xyxyxyx', 'y'], ['x', 'yxy', 'x', 'y', 'x', 'y', 'x', 'y'], ['x', 'yxy', 'x', 'y', 'x', 'yxy'], ['x', 'yxy', 'x', 'y', 'xyx', 'y'], ['x', 'yxy', 'x', 'yxy', 'x', 'y'], ['x', 'yxy', 'x', 'yxyxy'], ['x', 'yxy', 'xyx', 'y', 'x', 'y'], ['x', 'yxy', 'xyx', 'yxy'], ['x', 'yxy', 'xyxyx', 'y'], ['x', 'yxyxy', 'x', 'y', 'x', 'y'], ['x', 'yxyxy', 'x', 'yxy'], ['x', 'yxyxy', 'xyx', 'y'], ['x', 'yxyxyxy', 'x', 'y'], ['x', 'yxyxyxyxy'], ['xyx', 'y', 'x', 'y', 'x', 'y', 'x', 'y'], ['xyx', 'y', 'x', 'y', 'x', 'yxy'], ['xyx', 'y', 'x', 'y', 'xyx', 'y'], ['xyx', 'y', 'x', 'yxy', 'x', 'y'], ['xyx', 'y', 'x', 'yxyxy'], ['xyx', 'y', 'xyx', 'y', 'x', 'y'], ['xyx', 'y', 'xyx', 'yxy'], ['xyx', 'y', 'xyxyx', 'y'], ['xyx', 'yxy', 'x', 'y', 'x', 'y'], ['xyx', 'yxy', 'x', 'yxy'], ['xyx', 'yxy', 'xyx', 'y'], ['xyx', 'yxyxy', 'x', 'y'], ['xyx', 'yxyxyxy'], ['xyxyx', 'y', 'x', 'y', 'x', 'y'], ['xyxyx', 'y', 'x', 'yxy'], ['xyxyx', 'y', 'xyx', 'y'], ['xyxyx', 'yxy', 'x', 'y'], ['xyxyx', 'yxyxy'], ['xyxyxyx', 'y', 'x', 'y'], ['xyxyxyx', 'yxy'], ['xyxyxyxyx', 'y']]\n assert candidate(s = \"stepsonnodenoses\") == [['s', 't', 'e', 'p', 's', 'o', 'n', 'n', 'o', 'd', 'e', 'n', 'o', 's', 'e', 's'], ['s', 't', 'e', 'p', 's', 'o', 'n', 'n', 'o', 'd', 'e', 'n', 'o', 'ses'], ['s', 't', 'e', 'p', 's', 'o', 'nn', 'o', 'd', 'e', 'n', 'o', 's', 'e', 's'], ['s', 't', 'e', 'p', 's', 'o', 'nn', 'o', 'd', 'e', 'n', 'o', 'ses'], ['s', 't', 'e', 'p', 's', 'onno', 'd', 'e', 'n', 'o', 's', 'e', 's'], ['s', 't', 'e', 'p', 's', 'onno', 'd', 'e', 'n', 'o', 'ses']]\n assert candidate(s = \"racecaranakayak\") == [['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'a', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'ana', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'ana', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'ana', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'a', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'a', 'kayak'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'ana', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'ana', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'a', 'r', 'ana', 'kayak'], ['r', 'a', 'cec', 'ara', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'ara', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'ara', 'n', 'a', 'kayak'], ['r', 'a', 'cec', 'ara', 'n', 'aka', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'a', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'a', 'n', 'a', 'k', 'aya', 'k'], ['r', 'aceca', 'r', 'a', 'n', 'a', 'kayak'], ['r', 'aceca', 'r', 'a', 'n', 'aka', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'ana', 'k', 'a', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'ana', 'k', 'aya', 'k'], ['r', 'aceca', 'r', 'ana', 'kayak'], ['racecar', 'a', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['racecar', 'a', 'n', 'a', 'k', 'aya', 'k'], ['racecar', 'a', 'n', 'a', 'kayak'], ['racecar', 'a', 'n', 'aka', 'y', 'a', 'k'], ['racecar', 'ana', 'k', 'a', 'y', 'a', 'k'], ['racecar', 'ana', 'k', 'aya', 'k'], ['racecar', 'ana', 'kayak']]\n assert candidate(s = \"abcbaaabcb\") == [['a', 'b', 'c', 'b', 'a', 'a', 'a', 'b', 'c', 'b'], ['a', 'b', 'c', 'b', 'a', 'a', 'a', 'bcb'], ['a', 'b', 'c', 'b', 'a', 'aa', 'b', 'c', 'b'], ['a', 'b', 'c', 'b', 'a', 'aa', 'bcb'], ['a', 'b', 'c', 'b', 'aa', 'a', 'b', 'c', 'b'], ['a', 'b', 'c', 'b', 'aa', 'a', 'bcb'], ['a', 'b', 'c', 'b', 'aaa', 'b', 'c', 'b'], ['a', 'b', 'c', 'b', 'aaa', 'bcb'], ['a', 'b', 'c', 'baaab', 'c', 'b'], ['a', 'b', 'cbaaabc', 'b'], ['a', 'bcb', 'a', 'a', 'a', 'b', 'c', 'b'], ['a', 'bcb', 'a', 'a', 'a', 'bcb'], ['a', 'bcb', 'a', 'aa', 'b', 'c', 'b'], ['a', 'bcb', 'a', 'aa', 'bcb'], ['a', 'bcb', 'aa', 'a', 'b', 'c', 'b'], ['a', 'bcb', 'aa', 'a', 'bcb'], ['a', 'bcb', 'aaa', 'b', 'c', 'b'], ['a', 'bcb', 'aaa', 'bcb'], ['a', 'bcbaaabcb'], ['abcba', 'a', 'a', 'b', 'c', 'b'], ['abcba', 'a', 'a', 'bcb'], ['abcba', 'aa', 'b', 'c', 'b'], ['abcba', 'aa', 'bcb']]\n assert candidate(s = \"levelannakayak\") == [['l', 'e', 'v', 'e', 'l', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['l', 'e', 'v', 'e', 'l', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['l', 'e', 'v', 'e', 'l', 'a', 'n', 'n', 'a', 'kayak'], ['l', 'e', 'v', 'e', 'l', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['l', 'e', 'v', 'e', 'l', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['l', 'e', 'v', 'e', 'l', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['l', 'e', 'v', 'e', 'l', 'a', 'nn', 'a', 'kayak'], ['l', 'e', 'v', 'e', 'l', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['l', 'e', 'v', 'e', 'l', 'anna', 'k', 'a', 'y', 'a', 'k'], ['l', 'e', 'v', 'e', 'l', 'anna', 'k', 'aya', 'k'], ['l', 'e', 'v', 'e', 'l', 'anna', 'kayak'], ['l', 'eve', 'l', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['l', 'eve', 'l', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['l', 'eve', 'l', 'a', 'n', 'n', 'a', 'kayak'], ['l', 'eve', 'l', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['l', 'eve', 'l', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['l', 'eve', 'l', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['l', 'eve', 'l', 'a', 'nn', 'a', 'kayak'], ['l', 'eve', 'l', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['l', 'eve', 'l', 'anna', 'k', 'a', 'y', 'a', 'k'], ['l', 'eve', 'l', 'anna', 'k', 'aya', 'k'], ['l', 'eve', 'l', 'anna', 'kayak'], ['level', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['level', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['level', 'a', 'n', 'n', 'a', 'kayak'], ['level', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['level', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['level', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['level', 'a', 'nn', 'a', 'kayak'], ['level', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['level', 'anna', 'k', 'a', 'y', 'a', 'k'], ['level', 'anna', 'k', 'aya', 'k'], ['level', 'anna', 'kayak']]\n assert candidate(s = \"noonabac\") == [['n', 'o', 'o', 'n', 'a', 'b', 'a', 'c'], ['n', 'o', 'o', 'n', 'aba', 'c'], ['n', 'oo', 'n', 'a', 'b', 'a', 'c'], ['n', 'oo', 'n', 'aba', 'c'], ['noon', 'a', 'b', 'a', 'c'], ['noon', 'aba', 'c']]\n assert candidate(s = \"aabbaba\") == [['a', 'a', 'b', 'b', 'a', 'b', 'a'], ['a', 'a', 'b', 'b', 'aba'], ['a', 'a', 'b', 'bab', 'a'], ['a', 'a', 'bb', 'a', 'b', 'a'], ['a', 'a', 'bb', 'aba'], ['a', 'abba', 'b', 'a'], ['aa', 'b', 'b', 'a', 'b', 'a'], ['aa', 'b', 'b', 'aba'], ['aa', 'b', 'bab', 'a'], ['aa', 'bb', 'a', 'b', 'a'], ['aa', 'bb', 'aba']]\n assert candidate(s = \"abcbaabcba\") == [['a', 'b', 'c', 'b', 'a', 'a', 'b', 'c', 'b', 'a'], ['a', 'b', 'c', 'b', 'a', 'a', 'bcb', 'a'], ['a', 'b', 'c', 'b', 'a', 'abcba'], ['a', 'b', 'c', 'b', 'aa', 'b', 'c', 'b', 'a'], ['a', 'b', 'c', 'b', 'aa', 'bcb', 'a'], ['a', 'b', 'c', 'baab', 'c', 'b', 'a'], ['a', 'b', 'cbaabc', 'b', 'a'], ['a', 'bcb', 'a', 'a', 'b', 'c', 'b', 'a'], ['a', 'bcb', 'a', 'a', 'bcb', 'a'], ['a', 'bcb', 'a', 'abcba'], ['a', 'bcb', 'aa', 'b', 'c', 'b', 'a'], ['a', 'bcb', 'aa', 'bcb', 'a'], ['a', 'bcbaabcb', 'a'], ['abcba', 'a', 'b', 'c', 'b', 'a'], ['abcba', 'a', 'bcb', 'a'], ['abcba', 'abcba'], ['abcbaabcba']]\n assert candidate(s = \"deifiedcivic\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'civic'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'civic'], ['d', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c'], ['d', 'eifie', 'd', 'c', 'ivi', 'c'], ['d', 'eifie', 'd', 'civic'], ['deified', 'c', 'i', 'v', 'i', 'c'], ['deified', 'c', 'ivi', 'c'], ['deified', 'civic']]\n assert candidate(s = \"kayaksapakayak\") == [['k', 'a', 'y', 'a', 'k', 's', 'a', 'p', 'a', 'k', 'a', 'y', 'a', 'k'], ['k', 'a', 'y', 'a', 'k', 's', 'a', 'p', 'a', 'k', 'aya', 'k'], ['k', 'a', 'y', 'a', 'k', 's', 'a', 'p', 'a', 'kayak'], ['k', 'a', 'y', 'a', 'k', 's', 'a', 'p', 'aka', 'y', 'a', 'k'], ['k', 'a', 'y', 'a', 'k', 's', 'apa', 'k', 'a', 'y', 'a', 'k'], ['k', 'a', 'y', 'a', 'k', 's', 'apa', 'k', 'aya', 'k'], ['k', 'a', 'y', 'a', 'k', 's', 'apa', 'kayak'], ['k', 'aya', 'k', 's', 'a', 'p', 'a', 'k', 'a', 'y', 'a', 'k'], ['k', 'aya', 'k', 's', 'a', 'p', 'a', 'k', 'aya', 'k'], ['k', 'aya', 'k', 's', 'a', 'p', 'a', 'kayak'], ['k', 'aya', 'k', 's', 'a', 'p', 'aka', 'y', 'a', 'k'], ['k', 'aya', 'k', 's', 'apa', 'k', 'a', 'y', 'a', 'k'], ['k', 'aya', 'k', 's', 'apa', 'k', 'aya', 'k'], ['k', 'aya', 'k', 's', 'apa', 'kayak'], ['kayak', 's', 'a', 'p', 'a', 'k', 'a', 'y', 'a', 'k'], ['kayak', 's', 'a', 'p', 'a', 'k', 'aya', 'k'], ['kayak', 's', 'a', 'p', 'a', 'kayak'], ['kayak', 's', 'a', 'p', 'aka', 'y', 'a', 'k'], ['kayak', 's', 'apa', 'k', 'a', 'y', 'a', 'k'], ['kayak', 's', 'apa', 'k', 'aya', 'k'], ['kayak', 's', 'apa', 'kayak']]\n assert candidate(s = \"repaperlevel\") == [['r', 'e', 'p', 'a', 'p', 'e', 'r', 'l', 'e', 'v', 'e', 'l'], ['r', 'e', 'p', 'a', 'p', 'e', 'r', 'l', 'eve', 'l'], ['r', 'e', 'p', 'a', 'p', 'e', 'r', 'level'], ['r', 'e', 'pap', 'e', 'r', 'l', 'e', 'v', 'e', 'l'], ['r', 'e', 'pap', 'e', 'r', 'l', 'eve', 'l'], ['r', 'e', 'pap', 'e', 'r', 'level'], ['r', 'epape', 'r', 'l', 'e', 'v', 'e', 'l'], ['r', 'epape', 'r', 'l', 'eve', 'l'], ['r', 'epape', 'r', 'level'], ['repaper', 'l', 'e', 'v', 'e', 'l'], ['repaper', 'l', 'eve', 'l'], ['repaper', 'level']]\n assert candidate(s = \"wasitacaroracatisaw\") == [['w', 'a', 's', 'i', 't', 'a', 'c', 'a', 'r', 'o', 'r', 'a', 'c', 'a', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'a', 'c', 'a', 'r', 'o', 'r', 'aca', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'a', 'c', 'a', 'ror', 'a', 'c', 'a', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'a', 'c', 'a', 'ror', 'aca', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'a', 'c', 'arora', 'c', 'a', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'a', 'carorac', 'a', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'aca', 'r', 'o', 'r', 'a', 'c', 'a', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'aca', 'r', 'o', 'r', 'aca', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'aca', 'ror', 'a', 'c', 'a', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'aca', 'ror', 'aca', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 't', 'acaroraca', 't', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'i', 'tacaroracat', 'i', 's', 'a', 'w'], ['w', 'a', 's', 'itacaroracati', 's', 'a', 'w'], ['w', 'a', 'sitacaroracatis', 'a', 'w'], ['w', 'asitacaroracatisa', 'w'], ['wasitacaroracatisaw']]\n assert candidate(s = \"levellevel\") == [['l', 'e', 'v', 'e', 'l', 'l', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'l', 'l', 'eve', 'l'], ['l', 'e', 'v', 'e', 'l', 'level'], ['l', 'e', 'v', 'e', 'll', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'll', 'eve', 'l'], ['l', 'e', 'v', 'elle', 'v', 'e', 'l'], ['l', 'e', 'vellev', 'e', 'l'], ['l', 'eve', 'l', 'l', 'e', 'v', 'e', 'l'], ['l', 'eve', 'l', 'l', 'eve', 'l'], ['l', 'eve', 'l', 'level'], ['l', 'eve', 'll', 'e', 'v', 'e', 'l'], ['l', 'eve', 'll', 'eve', 'l'], ['l', 'evelleve', 'l'], ['level', 'l', 'e', 'v', 'e', 'l'], ['level', 'l', 'eve', 'l'], ['level', 'level'], ['levellevel']]\n assert candidate(s = \"aibohphobia\") == [['a', 'i', 'b', 'o', 'h', 'p', 'h', 'o', 'b', 'i', 'a'], ['a', 'i', 'b', 'o', 'hph', 'o', 'b', 'i', 'a'], ['a', 'i', 'b', 'ohpho', 'b', 'i', 'a'], ['a', 'i', 'bohphob', 'i', 'a'], ['a', 'ibohphobi', 'a'], ['aibohphobia']]\n assert candidate(s = \"referredder\") == [['r', 'e', 'f', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'edde', 'r'], ['r', 'e', 'f', 'e', 'r', 'redder'], ['r', 'e', 'f', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'edde', 'r'], ['r', 'e', 'f', 'erre', 'd', 'd', 'e', 'r'], ['r', 'e', 'f', 'erre', 'dd', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'efe', 'r', 'r', 'edde', 'r'], ['r', 'efe', 'r', 'redder'], ['r', 'efe', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'efe', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'efe', 'rr', 'edde', 'r'], ['refer', 'r', 'e', 'd', 'd', 'e', 'r'], ['refer', 'r', 'e', 'dd', 'e', 'r'], ['refer', 'r', 'edde', 'r'], ['refer', 'redder']]\n assert candidate(s = \"stats\") == [['s', 't', 'a', 't', 's'], ['s', 'tat', 's'], ['stats']]\n assert candidate(s = \"detartratedetartatra\") == [['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd', 'e', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd', 'e', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd', 'e', 't', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd', 'e', 't', 'artatra'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'ede', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'ede', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'ede', 't', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'ede', 't', 'artatra'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 'tedet', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 'tedet', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 'tedet', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 'tedet', 'artatra'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'atedeta', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'atedeta', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'r', 'atedeta', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'ratedetar', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 't', 'ratedetar', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'r', 'tratedetart', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd', 'e', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd', 'e', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd', 'e', 't', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd', 'e', 't', 'artatra'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'ede', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'ede', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'ede', 't', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'ede', 't', 'artatra'], ['d', 'e', 't', 'a', 'rtr', 'a', 'tedet', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 'tedet', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 'tedet', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'a', 'rtr', 'a', 'tedet', 'artatra'], ['d', 'e', 't', 'a', 'rtr', 'atedeta', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'atedeta', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'a', 'rtr', 'atedeta', 'rtatr', 'a'], ['d', 'e', 't', 'artra', 't', 'e', 'd', 'e', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'artra', 't', 'e', 'd', 'e', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'artra', 't', 'e', 'd', 'e', 't', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'artra', 't', 'e', 'd', 'e', 't', 'artatra'], ['d', 'e', 't', 'artra', 't', 'ede', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'artra', 't', 'ede', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'artra', 't', 'ede', 't', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'artra', 't', 'ede', 't', 'artatra'], ['d', 'e', 't', 'artra', 'tedet', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 't', 'artra', 'tedet', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 't', 'artra', 'tedet', 'a', 'rtatr', 'a'], ['d', 'e', 't', 'artra', 'tedet', 'artatra'], ['d', 'e', 'tartrat', 'e', 'd', 'e', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 'tartrat', 'e', 'd', 'e', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 'tartrat', 'e', 'd', 'e', 't', 'a', 'rtatr', 'a'], ['d', 'e', 'tartrat', 'e', 'd', 'e', 't', 'artatra'], ['d', 'e', 'tartrat', 'ede', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'e', 'tartrat', 'ede', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'e', 'tartrat', 'ede', 't', 'a', 'rtatr', 'a'], ['d', 'e', 'tartrat', 'ede', 't', 'artatra'], ['d', 'etartrate', 'd', 'e', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['d', 'etartrate', 'd', 'e', 't', 'a', 'r', 'tat', 'r', 'a'], ['d', 'etartrate', 'd', 'e', 't', 'a', 'rtatr', 'a'], ['d', 'etartrate', 'd', 'e', 't', 'artatra'], ['detartrated', 'e', 't', 'a', 'r', 't', 'a', 't', 'r', 'a'], ['detartrated', 'e', 't', 'a', 'r', 'tat', 'r', 'a'], ['detartrated', 'e', 't', 'a', 'rtatr', 'a'], ['detartrated', 'e', 't', 'artatra']]\n assert candidate(s = \"referreferrefer\") == [['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r', 'refer'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'rr', 'efe', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'erre', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'e', 'ferref', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r', 'r', 'efe', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r', 'refer'], ['r', 'e', 'f', 'e', 'r', 'r', 'efe', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'efe', 'rr', 'efe', 'r'], ['r', 'e', 'f', 'e', 'r', 'r', 'eferrefe', 'r'], ['r', 'e', 'f', 'e', 'r', 'refer', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'r', 'refer', 'r', 'efe', 'r'], ['r', 'e', 'f', 'e', 'r', 'refer', 'refer'], ['r', 'e', 'f', 'e', 'r', 'referrefer'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r', 'r', 'efe', 'r'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r', 'refer'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'rr', 'efe', 'r'], ['r', 'e', 'f', 'e', 'rr', 'e', 'f', 'erre', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'e', 'ferref', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'efe', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'efe', 'r', 'r', 'efe', 'r'], ['r', 'e', 'f', 'e', 'rr', 'efe', 'r', 'refer'], ['r', 'e', 'f', 'e', 'rr', 'efe', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rr', 'efe', 'rr', 'efe', 'r'], ['r', 'e', 'f', 'e', 'rr', 'eferrefe', 'r'], ['r', 'e', 'f', 'e', 'rreferr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'e', 'rreferr', 'efe', 'r'], ['r', 'e', 'f', 'erre', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'erre', 'f', 'e', 'r', 'r', 'efe', 'r'], ['r', 'e', 'f', 'erre', 'f', 'e', 'r', 'refer'], ['r', 'e', 'f', 'erre', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'f', 'erre', 'f', 'e', 'rr', 'efe', 'r'], ['r', 'e', 'f', 'erre', 'f', 'erre', 'f', 'e', 'r'], ['r', 'e', 'f', 'erre', 'ferref', 'e', 'r'], ['r', 'e', 'f', 'erreferre', 'f', 'e', 'r'], ['r', 'e', 'ferref', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'e', 'ferref', 'e', 'r', 'r', 'efe', 'r'], ['r', 'e', 'ferref', 'e', 'r', 'refer'], ['r', 'e', 'ferref', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'e', 'ferref', 'e', 'rr', 'efe', 'r'], ['r', 'e', 'ferref', 'erre', 'f', 'e', 'r'], ['r', 'e', 'ferreferref', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r'], ['r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r', 'refer'], ['r', 'efe', 'r', 'r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'f', 'e', 'rr', 'efe', 'r'], ['r', 'efe', 'r', 'r', 'e', 'f', 'erre', 'f', 'e', 'r'], ['r', 'efe', 'r', 'r', 'e', 'ferref', 'e', 'r'], ['r', 'efe', 'r', 'r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r', 'r', 'efe', 'r', 'r', 'efe', 'r'], ['r', 'efe', 'r', 'r', 'efe', 'r', 'refer'], ['r', 'efe', 'r', 'r', 'efe', 'rr', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r', 'r', 'efe', 'rr', 'efe', 'r'], ['r', 'efe', 'r', 'r', 'eferrefe', 'r'], ['r', 'efe', 'r', 'refer', 'r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'r', 'refer', 'r', 'efe', 'r'], ['r', 'efe', 'r', 'refer', 'refer'], ['r', 'efe', 'r', 'referrefer'], ['r', 'efe', 'rr', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'rr', 'e', 'f', 'e', 'r', 'r', 'efe', 'r'], ['r', 'efe', 'rr', 'e', 'f', 'e', 'r', 'refer'], ['r', 'efe', 'rr', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['r', 'efe', 'rr', 'e', 'f', 'e', 'rr', 'efe', 'r'], ['r', 'efe', 'rr', 'e', 'f', 'erre', 'f', 'e', 'r'], ['r', 'efe', 'rr', 'e', 'ferref', 'e', 'r'], ['r', 'efe', 'rr', 'efe', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'efe', 'rr', 'efe', 'r', 'r', 'efe', 'r'], ['r', 'efe', 'rr', 'efe', 'r', 'refer'], ['r', 'efe', 'rr', 'efe', 'rr', 'e', 'f', 'e', 'r'], ['r', 'efe', 'rr', 'efe', 'rr', 'efe', 'r'], ['r', 'efe', 'rr', 'eferrefe', 'r'], ['r', 'efe', 'rreferr', 'e', 'f', 'e', 'r'], ['r', 'efe', 'rreferr', 'efe', 'r'], ['r', 'eferrefe', 'r', 'r', 'e', 'f', 'e', 'r'], ['r', 'eferrefe', 'r', 'r', 'efe', 'r'], ['r', 'eferrefe', 'r', 'refer'], ['r', 'eferrefe', 'rr', 'e', 'f', 'e', 'r'], ['r', 'eferrefe', 'rr', 'efe', 'r'], ['r', 'eferreferrefe', 'r'], ['refer', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'f', 'e', 'r'], ['refer', 'r', 'e', 'f', 'e', 'r', 'r', 'efe', 'r'], ['refer', 'r', 'e', 'f', 'e', 'r', 'refer'], ['refer', 'r', 'e', 'f', 'e', 'rr', 'e', 'f', 'e', 'r'], ['refer', 'r', 'e', 'f', 'e', 'rr', 'efe', 'r'], ['refer', 'r', 'e', 'f', 'erre', 'f', 'e', 'r'], ['refer', 'r', 'e', 'ferref', 'e', 'r'], ['refer', 'r', 'efe', 'r', 'r', 'e', 'f', 'e', 'r'], ['refer', 'r', 'efe', 'r', 'r', 'efe', 'r'], ['refer', 'r', 'efe', 'r', 'refer'], ['refer', 'r', 'efe', 'rr', 'e', 'f', 'e', 'r'], ['refer', 'r', 'efe', 'rr', 'efe', 'r'], ['refer', 'r', 'eferrefe', 'r'], ['refer', 'refer', 'r', 'e', 'f', 'e', 'r'], ['refer', 'refer', 'r', 'efe', 'r'], ['refer', 'refer', 'refer'], ['refer', 'referrefer'], ['referrefer', 'r', 'e', 'f', 'e', 'r'], ['referrefer', 'r', 'efe', 'r'], ['referrefer', 'refer'], ['referreferrefer']]\n assert candidate(s = \"rotorarotor\") == [['r', 'o', 't', 'o', 'r', 'a', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'a', 'r', 'oto', 'r'], ['r', 'o', 't', 'o', 'r', 'a', 'rotor'], ['r', 'o', 't', 'o', 'rar', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'o', 'rar', 'oto', 'r'], ['r', 'o', 't', 'oraro', 't', 'o', 'r'], ['r', 'o', 'torarot', 'o', 'r'], ['r', 'oto', 'r', 'a', 'r', 'o', 't', 'o', 'r'], ['r', 'oto', 'r', 'a', 'r', 'oto', 'r'], ['r', 'oto', 'r', 'a', 'rotor'], ['r', 'oto', 'rar', 'o', 't', 'o', 'r'], ['r', 'oto', 'rar', 'oto', 'r'], ['r', 'otoraroto', 'r'], ['rotor', 'a', 'r', 'o', 't', 'o', 'r'], ['rotor', 'a', 'r', 'oto', 'r'], ['rotor', 'a', 'rotor'], ['rotorarotor']]\n assert candidate(s = \"aaaaa\") == [['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'aa'], ['a', 'a', 'aa', 'a'], ['a', 'a', 'aaa'], ['a', 'aa', 'a', 'a'], ['a', 'aa', 'aa'], ['a', 'aaa', 'a'], ['a', 'aaaa'], ['aa', 'a', 'a', 'a'], ['aa', 'a', 'aa'], ['aa', 'aa', 'a'], ['aa', 'aaa'], ['aaa', 'a', 'a'], ['aaa', 'aa'], ['aaaa', 'a'], ['aaaaa']]\n assert candidate(s = \"redderredder\") == [['r', 'e', 'd', 'd', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'd', 'd', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'e', 'd', 'd', 'e', 'r', 'r', 'edde', 'r'], ['r', 'e', 'd', 'd', 'e', 'r', 'redder'], ['r', 'e', 'd', 'd', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'd', 'd', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'e', 'd', 'd', 'e', 'rr', 'edde', 'r'], ['r', 'e', 'd', 'd', 'erre', 'd', 'd', 'e', 'r'], ['r', 'e', 'd', 'd', 'erre', 'dd', 'e', 'r'], ['r', 'e', 'd', 'derred', 'd', 'e', 'r'], ['r', 'e', 'dd', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'dd', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'e', 'dd', 'e', 'r', 'r', 'edde', 'r'], ['r', 'e', 'dd', 'e', 'r', 'redder'], ['r', 'e', 'dd', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'e', 'dd', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'e', 'dd', 'e', 'rr', 'edde', 'r'], ['r', 'e', 'dd', 'erre', 'd', 'd', 'e', 'r'], ['r', 'e', 'dd', 'erre', 'dd', 'e', 'r'], ['r', 'e', 'dderredd', 'e', 'r'], ['r', 'edde', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'edde', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'edde', 'r', 'r', 'edde', 'r'], ['r', 'edde', 'r', 'redder'], ['r', 'edde', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'edde', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'edde', 'rr', 'edde', 'r'], ['r', 'edderredde', 'r'], ['redder', 'r', 'e', 'd', 'd', 'e', 'r'], ['redder', 'r', 'e', 'dd', 'e', 'r'], ['redder', 'r', 'edde', 'r'], ['redder', 'redder'], ['redderredder']]\n assert candidate(s = \"racecarabc\") == [['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'b', 'c'], ['r', 'a', 'c', 'e', 'c', 'ara', 'b', 'c'], ['r', 'a', 'cec', 'a', 'r', 'a', 'b', 'c'], ['r', 'a', 'cec', 'ara', 'b', 'c'], ['r', 'aceca', 'r', 'a', 'b', 'c'], ['racecar', 'a', 'b', 'c']]\n assert candidate(s = \"civiclevelmadamrotor\") == [['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'madam', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'madam', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'e', 'v', 'e', 'l', 'madam', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'm', 'ada', 'm', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'madam', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'madam', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'l', 'eve', 'l', 'madam', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'level', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'level', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'level', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'level', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'level', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'level', 'm', 'ada', 'm', 'rotor'], ['c', 'i', 'v', 'i', 'c', 'level', 'madam', 'r', 'o', 't', 'o', 'r'], ['c', 'i', 'v', 'i', 'c', 'level', 'madam', 'r', 'oto', 'r'], ['c', 'i', 'v', 'i', 'c', 'level', 'madam', 'rotor'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'rotor'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'madam', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'madam', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'l', 'e', 'v', 'e', 'l', 'madam', 'rotor'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'm', 'ada', 'm', 'rotor'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'madam', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'madam', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'l', 'eve', 'l', 'madam', 'rotor'], ['c', 'ivi', 'c', 'level', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'level', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'level', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['c', 'ivi', 'c', 'level', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'level', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'level', 'm', 'ada', 'm', 'rotor'], ['c', 'ivi', 'c', 'level', 'madam', 'r', 'o', 't', 'o', 'r'], ['c', 'ivi', 'c', 'level', 'madam', 'r', 'oto', 'r'], ['c', 'ivi', 'c', 'level', 'madam', 'rotor'], ['civic', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['civic', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['civic', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['civic', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['civic', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['civic', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm', 'rotor'], ['civic', 'l', 'e', 'v', 'e', 'l', 'madam', 'r', 'o', 't', 'o', 'r'], ['civic', 'l', 'e', 'v', 'e', 'l', 'madam', 'r', 'oto', 'r'], ['civic', 'l', 'e', 'v', 'e', 'l', 'madam', 'rotor'], ['civic', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['civic', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['civic', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['civic', 'l', 'eve', 'l', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['civic', 'l', 'eve', 'l', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['civic', 'l', 'eve', 'l', 'm', 'ada', 'm', 'rotor'], ['civic', 'l', 'eve', 'l', 'madam', 'r', 'o', 't', 'o', 'r'], ['civic', 'l', 'eve', 'l', 'madam', 'r', 'oto', 'r'], ['civic', 'l', 'eve', 'l', 'madam', 'rotor'], ['civic', 'level', 'm', 'a', 'd', 'a', 'm', 'r', 'o', 't', 'o', 'r'], ['civic', 'level', 'm', 'a', 'd', 'a', 'm', 'r', 'oto', 'r'], ['civic', 'level', 'm', 'a', 'd', 'a', 'm', 'rotor'], ['civic', 'level', 'm', 'ada', 'm', 'r', 'o', 't', 'o', 'r'], ['civic', 'level', 'm', 'ada', 'm', 'r', 'oto', 'r'], ['civic', 'level', 'm', 'ada', 'm', 'rotor'], ['civic', 'level', 'madam', 'r', 'o', 't', 'o', 'r'], ['civic', 'level', 'madam', 'r', 'oto', 'r'], ['civic', 'level', 'madam', 'rotor']]\n assert candidate(s = \"madamleveldeified\") == [['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'd', 'eifie', 'd'], ['m', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'deified'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'd', 'eifie', 'd'], ['m', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'deified'], ['m', 'a', 'd', 'a', 'm', 'level', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['m', 'a', 'd', 'a', 'm', 'level', 'd', 'e', 'ifi', 'e', 'd'], ['m', 'a', 'd', 'a', 'm', 'level', 'd', 'eifie', 'd'], ['m', 'a', 'd', 'a', 'm', 'level', 'deified'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'd', 'eifie', 'd'], ['m', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'deified'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'd', 'eifie', 'd'], ['m', 'ada', 'm', 'l', 'eve', 'l', 'deified'], ['m', 'ada', 'm', 'level', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['m', 'ada', 'm', 'level', 'd', 'e', 'ifi', 'e', 'd'], ['m', 'ada', 'm', 'level', 'd', 'eifie', 'd'], ['m', 'ada', 'm', 'level', 'deified'], ['madam', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['madam', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['madam', 'l', 'e', 'v', 'e', 'l', 'd', 'eifie', 'd'], ['madam', 'l', 'e', 'v', 'e', 'l', 'deified'], ['madam', 'l', 'eve', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['madam', 'l', 'eve', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['madam', 'l', 'eve', 'l', 'd', 'eifie', 'd'], ['madam', 'l', 'eve', 'l', 'deified'], ['madam', 'level', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['madam', 'level', 'd', 'e', 'ifi', 'e', 'd'], ['madam', 'level', 'd', 'eifie', 'd'], ['madam', 'level', 'deified']]\n assert candidate(s = \"abcbabcba\") == [['a', 'b', 'c', 'b', 'a', 'b', 'c', 'b', 'a'], ['a', 'b', 'c', 'b', 'a', 'bcb', 'a'], ['a', 'b', 'c', 'b', 'abcba'], ['a', 'b', 'c', 'bab', 'c', 'b', 'a'], ['a', 'b', 'cbabc', 'b', 'a'], ['a', 'bcb', 'a', 'b', 'c', 'b', 'a'], ['a', 'bcb', 'a', 'bcb', 'a'], ['a', 'bcb', 'abcba'], ['a', 'bcbabcb', 'a'], ['abcba', 'b', 'c', 'b', 'a'], ['abcba', 'bcb', 'a'], ['abcbabcba']]\n assert candidate(s = \"deifiedrotor\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'o', 't', 'o', 'r'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'oto', 'r'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'rotor'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'o', 't', 'o', 'r'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'oto', 'r'], ['d', 'e', 'ifi', 'e', 'd', 'rotor'], ['d', 'eifie', 'd', 'r', 'o', 't', 'o', 'r'], ['d', 'eifie', 'd', 'r', 'oto', 'r'], ['d', 'eifie', 'd', 'rotor'], ['deified', 'r', 'o', 't', 'o', 'r'], ['deified', 'r', 'oto', 'r'], ['deified', 'rotor']]\n assert candidate(s = \"noonracecarrace\") == [['n', 'o', 'o', 'n', 'r', 'a', 'c', 'e', 'c', 'a', 'r', 'r', 'a', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'a', 'c', 'e', 'c', 'a', 'rr', 'a', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'a', 'c', 'e', 'c', 'arra', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'a', 'c', 'e', 'carrac', 'e'], ['n', 'o', 'o', 'n', 'r', 'a', 'c', 'ecarrace'], ['n', 'o', 'o', 'n', 'r', 'a', 'cec', 'a', 'r', 'r', 'a', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'a', 'cec', 'a', 'rr', 'a', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'a', 'cec', 'arra', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'aceca', 'r', 'r', 'a', 'c', 'e'], ['n', 'o', 'o', 'n', 'r', 'aceca', 'rr', 'a', 'c', 'e'], ['n', 'o', 'o', 'n', 'racecar', 'r', 'a', 'c', 'e'], ['n', 'oo', 'n', 'r', 'a', 'c', 'e', 'c', 'a', 'r', 'r', 'a', 'c', 'e'], ['n', 'oo', 'n', 'r', 'a', 'c', 'e', 'c', 'a', 'rr', 'a', 'c', 'e'], ['n', 'oo', 'n', 'r', 'a', 'c', 'e', 'c', 'arra', 'c', 'e'], ['n', 'oo', 'n', 'r', 'a', 'c', 'e', 'carrac', 'e'], ['n', 'oo', 'n', 'r', 'a', 'c', 'ecarrace'], ['n', 'oo', 'n', 'r', 'a', 'cec', 'a', 'r', 'r', 'a', 'c', 'e'], ['n', 'oo', 'n', 'r', 'a', 'cec', 'a', 'rr', 'a', 'c', 'e'], ['n', 'oo', 'n', 'r', 'a', 'cec', 'arra', 'c', 'e'], ['n', 'oo', 'n', 'r', 'aceca', 'r', 'r', 'a', 'c', 'e'], ['n', 'oo', 'n', 'r', 'aceca', 'rr', 'a', 'c', 'e'], ['n', 'oo', 'n', 'racecar', 'r', 'a', 'c', 'e'], ['noon', 'r', 'a', 'c', 'e', 'c', 'a', 'r', 'r', 'a', 'c', 'e'], ['noon', 'r', 'a', 'c', 'e', 'c', 'a', 'rr', 'a', 'c', 'e'], ['noon', 'r', 'a', 'c', 'e', 'c', 'arra', 'c', 'e'], ['noon', 'r', 'a', 'c', 'e', 'carrac', 'e'], ['noon', 'r', 'a', 'c', 'ecarrace'], ['noon', 'r', 'a', 'cec', 'a', 'r', 'r', 'a', 'c', 'e'], ['noon', 'r', 'a', 'cec', 'a', 'rr', 'a', 'c', 'e'], ['noon', 'r', 'a', 'cec', 'arra', 'c', 'e'], ['noon', 'r', 'aceca', 'r', 'r', 'a', 'c', 'e'], ['noon', 'r', 'aceca', 'rr', 'a', 'c', 'e'], ['noon', 'racecar', 'r', 'a', 'c', 'e']]\n assert candidate(s = \"civiccivic\") == [['c', 'i', 'v', 'i', 'c', 'c', 'i', 'v', 'i', 'c'], ['c', 'i', 'v', 'i', 'c', 'c', 'ivi', 'c'], ['c', 'i', 'v', 'i', 'c', 'civic'], ['c', 'i', 'v', 'i', 'cc', 'i', 'v', 'i', 'c'], ['c', 'i', 'v', 'i', 'cc', 'ivi', 'c'], ['c', 'i', 'v', 'icci', 'v', 'i', 'c'], ['c', 'i', 'vicciv', 'i', 'c'], ['c', 'ivi', 'c', 'c', 'i', 'v', 'i', 'c'], ['c', 'ivi', 'c', 'c', 'ivi', 'c'], ['c', 'ivi', 'c', 'civic'], ['c', 'ivi', 'cc', 'i', 'v', 'i', 'c'], ['c', 'ivi', 'cc', 'ivi', 'c'], ['c', 'iviccivi', 'c'], ['civic', 'c', 'i', 'v', 'i', 'c'], ['civic', 'c', 'ivi', 'c'], ['civic', 'civic'], ['civiccivic']]\n assert candidate(s = \"detartrated\") == [['d', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['d', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['d', 'e', 't', 'artra', 't', 'e', 'd'], ['d', 'e', 'tartrat', 'e', 'd'], ['d', 'etartrate', 'd'], ['detartrated']]\n assert candidate(s = \"abccbaabba\") == [['a', 'b', 'c', 'c', 'b', 'a', 'a', 'b', 'b', 'a'], ['a', 'b', 'c', 'c', 'b', 'a', 'a', 'bb', 'a'], ['a', 'b', 'c', 'c', 'b', 'a', 'abba'], ['a', 'b', 'c', 'c', 'b', 'aa', 'b', 'b', 'a'], ['a', 'b', 'c', 'c', 'b', 'aa', 'bb', 'a'], ['a', 'b', 'c', 'c', 'baab', 'b', 'a'], ['a', 'b', 'cc', 'b', 'a', 'a', 'b', 'b', 'a'], ['a', 'b', 'cc', 'b', 'a', 'a', 'bb', 'a'], ['a', 'b', 'cc', 'b', 'a', 'abba'], ['a', 'b', 'cc', 'b', 'aa', 'b', 'b', 'a'], ['a', 'b', 'cc', 'b', 'aa', 'bb', 'a'], ['a', 'b', 'cc', 'baab', 'b', 'a'], ['a', 'bccb', 'a', 'a', 'b', 'b', 'a'], ['a', 'bccb', 'a', 'a', 'bb', 'a'], ['a', 'bccb', 'a', 'abba'], ['a', 'bccb', 'aa', 'b', 'b', 'a'], ['a', 'bccb', 'aa', 'bb', 'a'], ['abccba', 'a', 'b', 'b', 'a'], ['abccba', 'a', 'bb', 'a'], ['abccba', 'abba']]\n assert candidate(s = \"abccba\") == [['a', 'b', 'c', 'c', 'b', 'a'], ['a', 'b', 'cc', 'b', 'a'], ['a', 'bccb', 'a'], ['abccba']]\n assert candidate(s = \"aaabaaa\") == [['a', 'a', 'a', 'b', 'a', 'a', 'a'], ['a', 'a', 'a', 'b', 'a', 'aa'], ['a', 'a', 'a', 'b', 'aa', 'a'], ['a', 'a', 'a', 'b', 'aaa'], ['a', 'a', 'aba', 'a', 'a'], ['a', 'a', 'aba', 'aa'], ['a', 'aa', 'b', 'a', 'a', 'a'], ['a', 'aa', 'b', 'a', 'aa'], ['a', 'aa', 'b', 'aa', 'a'], ['a', 'aa', 'b', 'aaa'], ['a', 'aabaa', 'a'], ['aa', 'a', 'b', 'a', 'a', 'a'], ['aa', 'a', 'b', 'a', 'aa'], ['aa', 'a', 'b', 'aa', 'a'], ['aa', 'a', 'b', 'aaa'], ['aa', 'aba', 'a', 'a'], ['aa', 'aba', 'aa'], ['aaa', 'b', 'a', 'a', 'a'], ['aaa', 'b', 'a', 'aa'], ['aaa', 'b', 'aa', 'a'], ['aaa', 'b', 'aaa'], ['aaabaaa']]\n assert candidate(s = \"aabbccddeeff\") == [['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'e', 'f', 'f'], ['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'e', 'ff'], ['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'ee', 'f', 'f'], ['a', 'a', 'b', 'b', 'c', 'c', 'd', 'd', 'ee', 'ff'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'e', 'e', 'f', 'f'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'e', 'e', 'ff'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'ee', 'f', 'f'], ['a', 'a', 'b', 'b', 'c', 'c', 'dd', 'ee', 'ff'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'e', 'e', 'f', 'f'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'e', 'e', 'ff'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'ee', 'f', 'f'], ['a', 'a', 'b', 'b', 'cc', 'd', 'd', 'ee', 'ff'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'e', 'e', 'f', 'f'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'e', 'e', 'ff'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'ee', 'f', 'f'], ['a', 'a', 'b', 'b', 'cc', 'dd', 'ee', 'ff'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'e', 'e', 'f', 'f'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'e', 'e', 'ff'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'ee', 'f', 'f'], ['a', 'a', 'bb', 'c', 'c', 'd', 'd', 'ee', 'ff'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'e', 'e', 'f', 'f'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'e', 'e', 'ff'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'ee', 'f', 'f'], ['a', 'a', 'bb', 'c', 'c', 'dd', 'ee', 'ff'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'e', 'e', 'f', 'f'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'e', 'e', 'ff'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'ee', 'f', 'f'], ['a', 'a', 'bb', 'cc', 'd', 'd', 'ee', 'ff'], ['a', 'a', 'bb', 'cc', 'dd', 'e', 'e', 'f', 'f'], ['a', 'a', 'bb', 'cc', 'dd', 'e', 'e', 'ff'], ['a', 'a', 'bb', 'cc', 'dd', 'ee', 'f', 'f'], ['a', 'a', 'bb', 'cc', 'dd', 'ee', 'ff'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'e', 'f', 'f'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'e', 'e', 'ff'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'ee', 'f', 'f'], ['aa', 'b', 'b', 'c', 'c', 'd', 'd', 'ee', 'ff'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'e', 'e', 'f', 'f'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'e', 'e', 'ff'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'ee', 'f', 'f'], ['aa', 'b', 'b', 'c', 'c', 'dd', 'ee', 'ff'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'e', 'e', 'f', 'f'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'e', 'e', 'ff'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'ee', 'f', 'f'], ['aa', 'b', 'b', 'cc', 'd', 'd', 'ee', 'ff'], ['aa', 'b', 'b', 'cc', 'dd', 'e', 'e', 'f', 'f'], ['aa', 'b', 'b', 'cc', 'dd', 'e', 'e', 'ff'], ['aa', 'b', 'b', 'cc', 'dd', 'ee', 'f', 'f'], ['aa', 'b', 'b', 'cc', 'dd', 'ee', 'ff'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'e', 'e', 'f', 'f'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'e', 'e', 'ff'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'ee', 'f', 'f'], ['aa', 'bb', 'c', 'c', 'd', 'd', 'ee', 'ff'], ['aa', 'bb', 'c', 'c', 'dd', 'e', 'e', 'f', 'f'], ['aa', 'bb', 'c', 'c', 'dd', 'e', 'e', 'ff'], ['aa', 'bb', 'c', 'c', 'dd', 'ee', 'f', 'f'], ['aa', 'bb', 'c', 'c', 'dd', 'ee', 'ff'], ['aa', 'bb', 'cc', 'd', 'd', 'e', 'e', 'f', 'f'], ['aa', 'bb', 'cc', 'd', 'd', 'e', 'e', 'ff'], ['aa', 'bb', 'cc', 'd', 'd', 'ee', 'f', 'f'], ['aa', 'bb', 'cc', 'd', 'd', 'ee', 'ff'], ['aa', 'bb', 'cc', 'dd', 'e', 'e', 'f', 'f'], ['aa', 'bb', 'cc', 'dd', 'e', 'e', 'ff'], ['aa', 'bb', 'cc', 'dd', 'ee', 'f', 'f'], ['aa', 'bb', 'cc', 'dd', 'ee', 'ff']]\n assert candidate(s = \"xyzyzyzyx\") == [['x', 'y', 'z', 'y', 'z', 'y', 'z', 'y', 'x'], ['x', 'y', 'z', 'y', 'z', 'yzy', 'x'], ['x', 'y', 'z', 'y', 'zyz', 'y', 'x'], ['x', 'y', 'z', 'yzy', 'z', 'y', 'x'], ['x', 'y', 'z', 'yzyzy', 'x'], ['x', 'y', 'zyz', 'y', 'z', 'y', 'x'], ['x', 'y', 'zyz', 'yzy', 'x'], ['x', 'y', 'zyzyz', 'y', 'x'], ['x', 'yzy', 'z', 'y', 'z', 'y', 'x'], ['x', 'yzy', 'z', 'yzy', 'x'], ['x', 'yzy', 'zyz', 'y', 'x'], ['x', 'yzyzy', 'z', 'y', 'x'], ['x', 'yzyzyzy', 'x'], ['xyzyzyzyx']]\n assert candidate(s = \"madamimadam\") == [['m', 'a', 'd', 'a', 'm', 'i', 'm', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'm', 'i', 'm', 'ada', 'm'], ['m', 'a', 'd', 'a', 'm', 'i', 'madam'], ['m', 'a', 'd', 'a', 'mim', 'a', 'd', 'a', 'm'], ['m', 'a', 'd', 'a', 'mim', 'ada', 'm'], ['m', 'a', 'd', 'amima', 'd', 'a', 'm'], ['m', 'a', 'damimad', 'a', 'm'], ['m', 'ada', 'm', 'i', 'm', 'a', 'd', 'a', 'm'], ['m', 'ada', 'm', 'i', 'm', 'ada', 'm'], ['m', 'ada', 'm', 'i', 'madam'], ['m', 'ada', 'mim', 'a', 'd', 'a', 'm'], ['m', 'ada', 'mim', 'ada', 'm'], ['m', 'adamimada', 'm'], ['madam', 'i', 'm', 'a', 'd', 'a', 'm'], ['madam', 'i', 'm', 'ada', 'm'], ['madam', 'i', 'madam'], ['madamimadam']]\n assert candidate(s = \"xyzyzyzyzyz\") == [['x', 'y', 'z', 'y', 'z', 'y', 'z', 'y', 'z', 'y', 'z'], ['x', 'y', 'z', 'y', 'z', 'y', 'z', 'y', 'zyz'], ['x', 'y', 'z', 'y', 'z', 'y', 'z', 'yzy', 'z'], ['x', 'y', 'z', 'y', 'z', 'y', 'zyz', 'y', 'z'], ['x', 'y', 'z', 'y', 'z', 'y', 'zyzyz'], ['x', 'y', 'z', 'y', 'z', 'yzy', 'z', 'y', 'z'], ['x', 'y', 'z', 'y', 'z', 'yzy', 'zyz'], ['x', 'y', 'z', 'y', 'z', 'yzyzy', 'z'], ['x', 'y', 'z', 'y', 'zyz', 'y', 'z', 'y', 'z'], ['x', 'y', 'z', 'y', 'zyz', 'y', 'zyz'], ['x', 'y', 'z', 'y', 'zyz', 'yzy', 'z'], ['x', 'y', 'z', 'y', 'zyzyz', 'y', 'z'], ['x', 'y', 'z', 'y', 'zyzyzyz'], ['x', 'y', 'z', 'yzy', 'z', 'y', 'z', 'y', 'z'], ['x', 'y', 'z', 'yzy', 'z', 'y', 'zyz'], ['x', 'y', 'z', 'yzy', 'z', 'yzy', 'z'], ['x', 'y', 'z', 'yzy', 'zyz', 'y', 'z'], ['x', 'y', 'z', 'yzy', 'zyzyz'], ['x', 'y', 'z', 'yzyzy', 'z', 'y', 'z'], ['x', 'y', 'z', 'yzyzy', 'zyz'], ['x', 'y', 'z', 'yzyzyzy', 'z'], ['x', 'y', 'zyz', 'y', 'z', 'y', 'z', 'y', 'z'], ['x', 'y', 'zyz', 'y', 'z', 'y', 'zyz'], ['x', 'y', 'zyz', 'y', 'z', 'yzy', 'z'], ['x', 'y', 'zyz', 'y', 'zyz', 'y', 'z'], ['x', 'y', 'zyz', 'y', 'zyzyz'], ['x', 'y', 'zyz', 'yzy', 'z', 'y', 'z'], ['x', 'y', 'zyz', 'yzy', 'zyz'], ['x', 'y', 'zyz', 'yzyzy', 'z'], ['x', 'y', 'zyzyz', 'y', 'z', 'y', 'z'], ['x', 'y', 'zyzyz', 'y', 'zyz'], ['x', 'y', 'zyzyz', 'yzy', 'z'], ['x', 'y', 'zyzyzyz', 'y', 'z'], ['x', 'y', 'zyzyzyzyz'], ['x', 'yzy', 'z', 'y', 'z', 'y', 'z', 'y', 'z'], ['x', 'yzy', 'z', 'y', 'z', 'y', 'zyz'], ['x', 'yzy', 'z', 'y', 'z', 'yzy', 'z'], ['x', 'yzy', 'z', 'y', 'zyz', 'y', 'z'], ['x', 'yzy', 'z', 'y', 'zyzyz'], ['x', 'yzy', 'z', 'yzy', 'z', 'y', 'z'], ['x', 'yzy', 'z', 'yzy', 'zyz'], ['x', 'yzy', 'z', 'yzyzy', 'z'], ['x', 'yzy', 'zyz', 'y', 'z', 'y', 'z'], ['x', 'yzy', 'zyz', 'y', 'zyz'], ['x', 'yzy', 'zyz', 'yzy', 'z'], ['x', 'yzy', 'zyzyz', 'y', 'z'], ['x', 'yzy', 'zyzyzyz'], ['x', 'yzyzy', 'z', 'y', 'z', 'y', 'z'], ['x', 'yzyzy', 'z', 'y', 'zyz'], ['x', 'yzyzy', 'z', 'yzy', 'z'], ['x', 'yzyzy', 'zyz', 'y', 'z'], ['x', 'yzyzy', 'zyzyz'], ['x', 'yzyzyzy', 'z', 'y', 'z'], ['x', 'yzyzyzy', 'zyz'], ['x', 'yzyzyzyzy', 'z']]\n assert candidate(s = \"rotatorrotor\") == [['r', 'o', 't', 'a', 't', 'o', 'r', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'a', 't', 'o', 'r', 'r', 'oto', 'r'], ['r', 'o', 't', 'a', 't', 'o', 'r', 'rotor'], ['r', 'o', 't', 'a', 't', 'o', 'rr', 'o', 't', 'o', 'r'], ['r', 'o', 't', 'a', 't', 'o', 'rr', 'oto', 'r'], ['r', 'o', 't', 'a', 't', 'orro', 't', 'o', 'r'], ['r', 'o', 't', 'a', 'torrot', 'o', 'r'], ['r', 'o', 'tat', 'o', 'r', 'r', 'o', 't', 'o', 'r'], ['r', 'o', 'tat', 'o', 'r', 'r', 'oto', 'r'], ['r', 'o', 'tat', 'o', 'r', 'rotor'], ['r', 'o', 'tat', 'o', 'rr', 'o', 't', 'o', 'r'], ['r', 'o', 'tat', 'o', 'rr', 'oto', 'r'], ['r', 'o', 'tat', 'orro', 't', 'o', 'r'], ['r', 'otato', 'r', 'r', 'o', 't', 'o', 'r'], ['r', 'otato', 'r', 'r', 'oto', 'r'], ['r', 'otato', 'r', 'rotor'], ['r', 'otato', 'rr', 'o', 't', 'o', 'r'], ['r', 'otato', 'rr', 'oto', 'r'], ['rotator', 'r', 'o', 't', 'o', 'r'], ['rotator', 'r', 'oto', 'r'], ['rotator', 'rotor']]\n assert candidate(s = \"racecarannakayak\") == [['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'n', 'a', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'nn', 'a', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'anna', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'anna', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'anna', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'n', 'a', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'ara', 'n', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'nn', 'a', 'k', 'aya', 'k'], ['r', 'a', 'c', 'e', 'c', 'ara', 'nn', 'a', 'kayak'], ['r', 'a', 'c', 'e', 'c', 'ara', 'nn', 'aka', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'n', 'a', 'kayak'], ['r', 'a', 'cec', 'a', 'r', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'a', 'r', 'a', 'nn', 'a', 'kayak'], ['r', 'a', 'cec', 'a', 'r', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'anna', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'a', 'r', 'anna', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'a', 'r', 'anna', 'kayak'], ['r', 'a', 'cec', 'ara', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'ara', 'n', 'n', 'a', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'ara', 'n', 'n', 'a', 'kayak'], ['r', 'a', 'cec', 'ara', 'n', 'n', 'aka', 'y', 'a', 'k'], ['r', 'a', 'cec', 'ara', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'a', 'cec', 'ara', 'nn', 'a', 'k', 'aya', 'k'], ['r', 'a', 'cec', 'ara', 'nn', 'a', 'kayak'], ['r', 'a', 'cec', 'ara', 'nn', 'aka', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['r', 'aceca', 'r', 'a', 'n', 'n', 'a', 'kayak'], ['r', 'aceca', 'r', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['r', 'aceca', 'r', 'a', 'nn', 'a', 'kayak'], ['r', 'aceca', 'r', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'anna', 'k', 'a', 'y', 'a', 'k'], ['r', 'aceca', 'r', 'anna', 'k', 'aya', 'k'], ['r', 'aceca', 'r', 'anna', 'kayak'], ['racecar', 'a', 'n', 'n', 'a', 'k', 'a', 'y', 'a', 'k'], ['racecar', 'a', 'n', 'n', 'a', 'k', 'aya', 'k'], ['racecar', 'a', 'n', 'n', 'a', 'kayak'], ['racecar', 'a', 'n', 'n', 'aka', 'y', 'a', 'k'], ['racecar', 'a', 'nn', 'a', 'k', 'a', 'y', 'a', 'k'], ['racecar', 'a', 'nn', 'a', 'k', 'aya', 'k'], ['racecar', 'a', 'nn', 'a', 'kayak'], ['racecar', 'a', 'nn', 'aka', 'y', 'a', 'k'], ['racecar', 'anna', 'k', 'a', 'y', 'a', 'k'], ['racecar', 'anna', 'k', 'aya', 'k'], ['racecar', 'anna', 'kayak']]\n assert candidate(s = \"amanaplanacanalpanama\") == [['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'anacana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'anacana', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'l', 'anacana', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'lanacanal', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'p', 'lanacanal', 'p', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'p', 'lanacanal', 'p', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'planacanalp', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'a', 'planacanalp', 'a', 'n', 'ama'], ['a', 'm', 'a', 'n', 'a', 'planacanalp', 'ana', 'm', 'a'], ['a', 'm', 'a', 'n', 'aplanacanalpa', 'n', 'a', 'm', 'a'], ['a', 'm', 'a', 'n', 'aplanacanalpa', 'n', 'ama'], ['a', 'm', 'a', 'naplanacanalpan', 'a', 'm', 'a'], ['a', 'm', 'a', 'naplanacanalpan', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'anacana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'l', 'anacana', 'l', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'l', 'anacana', 'l', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'p', 'lanacanal', 'p', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'p', 'lanacanal', 'p', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'p', 'lanacanal', 'p', 'ana', 'm', 'a'], ['a', 'm', 'ana', 'planacanalp', 'a', 'n', 'a', 'm', 'a'], ['a', 'm', 'ana', 'planacanalp', 'a', 'n', 'ama'], ['a', 'm', 'ana', 'planacanalp', 'ana', 'm', 'a'], ['a', 'm', 'anaplanacanalpana', 'm', 'a'], ['a', 'manaplanacanalpanam', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'a', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'a', 'c', 'ana', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'a', 'n', 'aca', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'a', 'nacan', 'a', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'ana', 'c', 'a', 'n', 'a', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'ana', 'c', 'ana', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'anacana', 'l', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'l', 'anacana', 'l', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'l', 'anacana', 'l', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'p', 'lanacanal', 'p', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'p', 'lanacanal', 'p', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'p', 'lanacanal', 'p', 'ana', 'm', 'a'], ['ama', 'n', 'a', 'planacanalp', 'a', 'n', 'a', 'm', 'a'], ['ama', 'n', 'a', 'planacanalp', 'a', 'n', 'ama'], ['ama', 'n', 'a', 'planacanalp', 'ana', 'm', 'a'], ['ama', 'n', 'aplanacanalpa', 'n', 'a', 'm', 'a'], ['ama', 'n', 'aplanacanalpa', 'n', 'ama'], ['ama', 'naplanacanalpan', 'a', 'm', 'a'], ['ama', 'naplanacanalpan', 'ama'], ['amanaplanacanalpanama']]\n assert candidate(s = \"tattarrattattat\") == [['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 't', 'atta', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 'tat', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 'tat', 'tat'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 't', 'tattat'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 'tt', 'atta', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'a', 'ttatt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'atta', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'atta', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'atta', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'r', 'r', 'attatta', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 't', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 't', 'atta', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 'tat', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 'tat', 'tat'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 't', 'tattat'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 'tt', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 'tt', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 'tt', 'atta', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'a', 'ttatt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'atta', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'atta', 't', 'tat'], ['t', 'a', 't', 't', 'a', 'rr', 'atta', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'a', 'rr', 'attatta', 't'], ['t', 'a', 't', 't', 'arra', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'arra', 't', 't', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'arra', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'arra', 't', 't', 'atta', 't'], ['t', 'a', 't', 't', 'arra', 't', 'tat', 't', 'a', 't'], ['t', 'a', 't', 't', 'arra', 't', 'tat', 'tat'], ['t', 'a', 't', 't', 'arra', 't', 'tattat'], ['t', 'a', 't', 't', 'arra', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 't', 'arra', 'tt', 'a', 't', 'tat'], ['t', 'a', 't', 't', 'arra', 'tt', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 't', 'arra', 'tt', 'atta', 't'], ['t', 'a', 't', 't', 'arra', 'ttatt', 'a', 't'], ['t', 'a', 't', 'tarrat', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 't', 'tarrat', 't', 'a', 't', 'tat'], ['t', 'a', 't', 'tarrat', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 't', 'tarrat', 't', 'atta', 't'], ['t', 'a', 't', 'tarrat', 'tat', 't', 'a', 't'], ['t', 'a', 't', 'tarrat', 'tat', 'tat'], ['t', 'a', 't', 'tarrat', 'tattat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 't', 'a', 't', 'tat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 't', 'atta', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 'tat', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 'tat', 'tat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 't', 'tattat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 'tt', 'a', 't', 'tat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 'tt', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 'tt', 'atta', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'a', 'ttatt', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'atta', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'atta', 't', 'tat'], ['t', 'a', 'tt', 'a', 'r', 'r', 'atta', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'r', 'r', 'attatta', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 't', 'a', 't', 'tat'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 't', 'atta', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 'tat', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 'tat', 'tat'], ['t', 'a', 'tt', 'a', 'rr', 'a', 't', 'tattat'], ['t', 'a', 'tt', 'a', 'rr', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 'tt', 'a', 't', 'tat'], ['t', 'a', 'tt', 'a', 'rr', 'a', 'tt', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 'tt', 'atta', 't'], ['t', 'a', 'tt', 'a', 'rr', 'a', 'ttatt', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'atta', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'atta', 't', 'tat'], ['t', 'a', 'tt', 'a', 'rr', 'atta', 'tt', 'a', 't'], ['t', 'a', 'tt', 'a', 'rr', 'attatta', 't'], ['t', 'a', 'tt', 'arra', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'arra', 't', 't', 'a', 't', 'tat'], ['t', 'a', 'tt', 'arra', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'arra', 't', 't', 'atta', 't'], ['t', 'a', 'tt', 'arra', 't', 'tat', 't', 'a', 't'], ['t', 'a', 'tt', 'arra', 't', 'tat', 'tat'], ['t', 'a', 'tt', 'arra', 't', 'tattat'], ['t', 'a', 'tt', 'arra', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'a', 'tt', 'arra', 'tt', 'a', 't', 'tat'], ['t', 'a', 'tt', 'arra', 'tt', 'a', 'tt', 'a', 't'], ['t', 'a', 'tt', 'arra', 'tt', 'atta', 't'], ['t', 'a', 'tt', 'arra', 'ttatt', 'a', 't'], ['t', 'a', 'ttarratt', 'a', 't', 't', 'a', 't'], ['t', 'a', 'ttarratt', 'a', 't', 'tat'], ['t', 'a', 'ttarratt', 'a', 'tt', 'a', 't'], ['t', 'a', 'ttarratt', 'atta', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 't', 'a', 't', 'tat'], ['t', 'atta', 'r', 'r', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 't', 'atta', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 'tat', 't', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 't', 'tat', 'tat'], ['t', 'atta', 'r', 'r', 'a', 't', 'tattat'], ['t', 'atta', 'r', 'r', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 'tt', 'a', 't', 'tat'], ['t', 'atta', 'r', 'r', 'a', 'tt', 'a', 'tt', 'a', 't'], ['t', 'atta', 'r', 'r', 'a', 'tt', 'atta', 't'], ['t', 'atta', 'r', 'r', 'a', 'ttatt', 'a', 't'], ['t', 'atta', 'r', 'r', 'atta', 't', 't', 'a', 't'], ['t', 'atta', 'r', 'r', 'atta', 't', 'tat'], ['t', 'atta', 'r', 'r', 'atta', 'tt', 'a', 't'], ['t', 'atta', 'r', 'r', 'attatta', 't'], ['t', 'atta', 'rr', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['t', 'atta', 'rr', 'a', 't', 't', 'a', 't', 'tat'], ['t', 'atta', 'rr', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['t', 'atta', 'rr', 'a', 't', 't', 'atta', 't'], ['t', 'atta', 'rr', 'a', 't', 'tat', 't', 'a', 't'], ['t', 'atta', 'rr', 'a', 't', 'tat', 'tat'], ['t', 'atta', 'rr', 'a', 't', 'tattat'], ['t', 'atta', 'rr', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['t', 'atta', 'rr', 'a', 'tt', 'a', 't', 'tat'], ['t', 'atta', 'rr', 'a', 'tt', 'a', 'tt', 'a', 't'], ['t', 'atta', 'rr', 'a', 'tt', 'atta', 't'], ['t', 'atta', 'rr', 'a', 'ttatt', 'a', 't'], ['t', 'atta', 'rr', 'atta', 't', 't', 'a', 't'], ['t', 'atta', 'rr', 'atta', 't', 'tat'], ['t', 'atta', 'rr', 'atta', 'tt', 'a', 't'], ['t', 'atta', 'rr', 'attatta', 't'], ['t', 'attarratta', 't', 't', 'a', 't'], ['t', 'attarratta', 't', 'tat'], ['t', 'attarratta', 'tt', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 't', 'tat'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 't', 'atta', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 'tat', 't', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 'tat', 'tat'], ['tat', 't', 'a', 'r', 'r', 'a', 't', 'tattat'], ['tat', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 't', 'tat'], ['tat', 't', 'a', 'r', 'r', 'a', 'tt', 'a', 'tt', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 'tt', 'atta', 't'], ['tat', 't', 'a', 'r', 'r', 'a', 'ttatt', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'atta', 't', 't', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'atta', 't', 'tat'], ['tat', 't', 'a', 'r', 'r', 'atta', 'tt', 'a', 't'], ['tat', 't', 'a', 'r', 'r', 'attatta', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 't', 'a', 't', 't', 'a', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 't', 'a', 't', 'tat'], ['tat', 't', 'a', 'rr', 'a', 't', 't', 'a', 'tt', 'a', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 't', 'atta', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 'tat', 't', 'a', 't'], ['tat', 't', 'a', 'rr', 'a', 't', 'tat', 'tat'], ['tat', 't', 'a', 'rr', 'a', 't', 'tattat'], ['tat', 't', 'a', 'rr', 'a', 'tt', 'a', 't', 't', 'a', 't'], ['tat', 't', 'a', 'rr', 'a', 'tt', 'a', 't', 'tat'], ['tat', 't', 'a', 'rr', 'a', 'tt', 'a', 'tt', 'a', 't'], ['tat', 't', 'a', 'rr', 'a', 'tt', 'atta', 't'], ['tat', 't', 'a', 'rr', 'a', 'ttatt', 'a', 't'], ['tat', 't', 'a', 'rr', 'atta', 't', 't', 'a', 't'], ['tat', 't', 'a', 'rr', 'atta', 't', 'tat'], ['tat', 't', 'a', 'rr', 'atta', 'tt', 'a', 't'], ['tat', 't', 'a', 'rr', 'attatta', 't'], ['tat', 't', 'arra', 't', 't', 'a', 't', 't', 'a', 't'], ['tat', 't', 'arra', 't', 't', 'a', 't', 'tat'], ['tat', 't', 'arra', 't', 't', 'a', 'tt', 'a', 't'], ['tat', 't', 'arra', 't', 't', 'atta', 't'], ['tat', 't', 'arra', 't', 'tat', 't', 'a', 't'], ['tat', 't', 'arra', 't', 'tat', 'tat'], ['tat', 't', 'arra', 't', 'tattat'], ['tat', 't', 'arra', 'tt', 'a', 't', 't', 'a', 't'], ['tat', 't', 'arra', 'tt', 'a', 't', 'tat'], ['tat', 't', 'arra', 'tt', 'a', 'tt', 'a', 't'], ['tat', 't', 'arra', 'tt', 'atta', 't'], ['tat', 't', 'arra', 'ttatt', 'a', 't'], ['tat', 'tarrat', 't', 'a', 't', 't', 'a', 't'], ['tat', 'tarrat', 't', 'a', 't', 'tat'], ['tat', 'tarrat', 't', 'a', 'tt', 'a', 't'], ['tat', 'tarrat', 't', 'atta', 't'], ['tat', 'tarrat', 'tat', 't', 'a', 't'], ['tat', 'tarrat', 'tat', 'tat'], ['tat', 'tarrat', 'tattat'], ['tattarrattat', 't', 'a', 't'], ['tattarrattat', 'tat']]\n assert candidate(s = \"rotorreferredder\") == [['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'edde', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'r', 'redder'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'e', 'rr', 'edde', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'erre', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'f', 'erre', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'r', 'r', 'edde', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'r', 'redder'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'efe', 'rr', 'edde', 'r'], ['r', 'o', 't', 'o', 'r', 'refer', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'refer', 'r', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'refer', 'r', 'edde', 'r'], ['r', 'o', 't', 'o', 'r', 'refer', 'redder'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'r', 'r', 'edde', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'r', 'redder'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'e', 'rr', 'edde', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'erre', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'f', 'erre', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'efe', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'efe', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'efe', 'r', 'r', 'edde', 'r'], ['r', 'o', 't', 'o', 'rr', 'efe', 'r', 'redder'], ['r', 'o', 't', 'o', 'rr', 'efe', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'efe', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'efe', 'rr', 'edde', 'r'], ['r', 'o', 't', 'o', 'rreferr', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rreferr', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rreferr', 'edde', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'r', 'r', 'edde', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'r', 'redder'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'e', 'rr', 'edde', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'erre', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'e', 'f', 'erre', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'efe', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'efe', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'efe', 'r', 'r', 'edde', 'r'], ['r', 'oto', 'r', 'r', 'efe', 'r', 'redder'], ['r', 'oto', 'r', 'r', 'efe', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'efe', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'efe', 'rr', 'edde', 'r'], ['r', 'oto', 'r', 'refer', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'refer', 'r', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'refer', 'r', 'edde', 'r'], ['r', 'oto', 'r', 'refer', 'redder'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'r', 'r', 'edde', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'r', 'redder'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'e', 'rr', 'edde', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'erre', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rr', 'e', 'f', 'erre', 'dd', 'e', 'r'], ['r', 'oto', 'rr', 'efe', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rr', 'efe', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'rr', 'efe', 'r', 'r', 'edde', 'r'], ['r', 'oto', 'rr', 'efe', 'r', 'redder'], ['r', 'oto', 'rr', 'efe', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rr', 'efe', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'rr', 'efe', 'rr', 'edde', 'r'], ['r', 'oto', 'rreferr', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rreferr', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'rreferr', 'edde', 'r'], ['rotor', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['rotor', 'r', 'e', 'f', 'e', 'r', 'r', 'e', 'dd', 'e', 'r'], ['rotor', 'r', 'e', 'f', 'e', 'r', 'r', 'edde', 'r'], ['rotor', 'r', 'e', 'f', 'e', 'r', 'redder'], ['rotor', 'r', 'e', 'f', 'e', 'rr', 'e', 'd', 'd', 'e', 'r'], ['rotor', 'r', 'e', 'f', 'e', 'rr', 'e', 'dd', 'e', 'r'], ['rotor', 'r', 'e', 'f', 'e', 'rr', 'edde', 'r'], ['rotor', 'r', 'e', 'f', 'erre', 'd', 'd', 'e', 'r'], ['rotor', 'r', 'e', 'f', 'erre', 'dd', 'e', 'r'], ['rotor', 'r', 'efe', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['rotor', 'r', 'efe', 'r', 'r', 'e', 'dd', 'e', 'r'], ['rotor', 'r', 'efe', 'r', 'r', 'edde', 'r'], ['rotor', 'r', 'efe', 'r', 'redder'], ['rotor', 'r', 'efe', 'rr', 'e', 'd', 'd', 'e', 'r'], ['rotor', 'r', 'efe', 'rr', 'e', 'dd', 'e', 'r'], ['rotor', 'r', 'efe', 'rr', 'edde', 'r'], ['rotor', 'refer', 'r', 'e', 'd', 'd', 'e', 'r'], ['rotor', 'refer', 'r', 'e', 'dd', 'e', 'r'], ['rotor', 'refer', 'r', 'edde', 'r'], ['rotor', 'refer', 'redder']]\n assert candidate(s = \"rotorleveldeified\") == [['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'eifie', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'deified'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'eifie', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'deified'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'eifie', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'deified'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'eifie', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'deified'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'eifie', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'deified'], ['r', 'oto', 'r', 'level', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'oto', 'r', 'level', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'oto', 'r', 'level', 'd', 'eifie', 'd'], ['r', 'oto', 'r', 'level', 'deified'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'eifie', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'deified'], ['rotor', 'l', 'eve', 'l', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['rotor', 'l', 'eve', 'l', 'd', 'e', 'ifi', 'e', 'd'], ['rotor', 'l', 'eve', 'l', 'd', 'eifie', 'd'], ['rotor', 'l', 'eve', 'l', 'deified'], ['rotor', 'level', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['rotor', 'level', 'd', 'e', 'ifi', 'e', 'd'], ['rotor', 'level', 'd', 'eifie', 'd'], ['rotor', 'level', 'deified']]\n assert candidate(s = \"deifiedmadam\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd', 'm', 'a', 'd', 'a', 'm'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'm', 'ada', 'm'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'madam'], ['d', 'e', 'ifi', 'e', 'd', 'm', 'a', 'd', 'a', 'm'], ['d', 'e', 'ifi', 'e', 'd', 'm', 'ada', 'm'], ['d', 'e', 'ifi', 'e', 'd', 'madam'], ['d', 'eifie', 'd', 'm', 'a', 'd', 'a', 'm'], ['d', 'eifie', 'd', 'm', 'ada', 'm'], ['d', 'eifie', 'd', 'madam'], ['deified', 'm', 'a', 'd', 'a', 'm'], ['deified', 'm', 'ada', 'm'], ['deified', 'madam']]\n assert candidate(s = \"noonhighnoon\") == [['n', 'o', 'o', 'n', 'h', 'i', 'g', 'h', 'n', 'o', 'o', 'n'], ['n', 'o', 'o', 'n', 'h', 'i', 'g', 'h', 'n', 'oo', 'n'], ['n', 'o', 'o', 'n', 'h', 'i', 'g', 'h', 'noon'], ['n', 'oo', 'n', 'h', 'i', 'g', 'h', 'n', 'o', 'o', 'n'], ['n', 'oo', 'n', 'h', 'i', 'g', 'h', 'n', 'oo', 'n'], ['n', 'oo', 'n', 'h', 'i', 'g', 'h', 'noon'], ['noon', 'h', 'i', 'g', 'h', 'n', 'o', 'o', 'n'], ['noon', 'h', 'i', 'g', 'h', 'n', 'oo', 'n'], ['noon', 'h', 'i', 'g', 'h', 'noon']]\n assert candidate(s = \"rotorleveldetartrated\") == [['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'tartrat', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'etartrate', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'detartrated'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'e', 'tartrat', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'd', 'etartrate', 'd'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'detartrated'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'e', 'tartrat', 'e', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'd', 'etartrate', 'd'], ['r', 'o', 't', 'o', 'r', 'level', 'detartrated'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'tartrat', 'e', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'd', 'etartrate', 'd'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'detartrated'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'e', 'tartrat', 'e', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'd', 'etartrate', 'd'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'detartrated'], ['r', 'oto', 'r', 'level', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['r', 'oto', 'r', 'level', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['r', 'oto', 'r', 'level', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['r', 'oto', 'r', 'level', 'd', 'e', 'tartrat', 'e', 'd'], ['r', 'oto', 'r', 'level', 'd', 'etartrate', 'd'], ['r', 'oto', 'r', 'level', 'detartrated'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'e', 'tartrat', 'e', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'd', 'etartrate', 'd'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'detartrated'], ['rotor', 'l', 'eve', 'l', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['rotor', 'l', 'eve', 'l', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['rotor', 'l', 'eve', 'l', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['rotor', 'l', 'eve', 'l', 'd', 'e', 'tartrat', 'e', 'd'], ['rotor', 'l', 'eve', 'l', 'd', 'etartrate', 'd'], ['rotor', 'l', 'eve', 'l', 'detartrated'], ['rotor', 'level', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'e', 'd'], ['rotor', 'level', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'e', 'd'], ['rotor', 'level', 'd', 'e', 't', 'artra', 't', 'e', 'd'], ['rotor', 'level', 'd', 'e', 'tartrat', 'e', 'd'], ['rotor', 'level', 'd', 'etartrate', 'd'], ['rotor', 'level', 'detartrated']]\n assert candidate(s = \"aabbababa\") == [['a', 'a', 'b', 'b', 'a', 'b', 'a', 'b', 'a'], ['a', 'a', 'b', 'b', 'a', 'b', 'aba'], ['a', 'a', 'b', 'b', 'a', 'bab', 'a'], ['a', 'a', 'b', 'b', 'aba', 'b', 'a'], ['a', 'a', 'b', 'b', 'ababa'], ['a', 'a', 'b', 'bab', 'a', 'b', 'a'], ['a', 'a', 'b', 'bab', 'aba'], ['a', 'a', 'b', 'babab', 'a'], ['a', 'a', 'bb', 'a', 'b', 'a', 'b', 'a'], ['a', 'a', 'bb', 'a', 'b', 'aba'], ['a', 'a', 'bb', 'a', 'bab', 'a'], ['a', 'a', 'bb', 'aba', 'b', 'a'], ['a', 'a', 'bb', 'ababa'], ['a', 'abba', 'b', 'a', 'b', 'a'], ['a', 'abba', 'b', 'aba'], ['a', 'abba', 'bab', 'a'], ['aa', 'b', 'b', 'a', 'b', 'a', 'b', 'a'], ['aa', 'b', 'b', 'a', 'b', 'aba'], ['aa', 'b', 'b', 'a', 'bab', 'a'], ['aa', 'b', 'b', 'aba', 'b', 'a'], ['aa', 'b', 'b', 'ababa'], ['aa', 'b', 'bab', 'a', 'b', 'a'], ['aa', 'b', 'bab', 'aba'], ['aa', 'b', 'babab', 'a'], ['aa', 'bb', 'a', 'b', 'a', 'b', 'a'], ['aa', 'bb', 'a', 'b', 'aba'], ['aa', 'bb', 'a', 'bab', 'a'], ['aa', 'bb', 'aba', 'b', 'a'], ['aa', 'bb', 'ababa']]\n assert candidate(s = \"noonlevelnoon\") == [['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n'], ['n', 'o', 'o', 'n', 'l', 'e', 'v', 'e', 'l', 'noon'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'n', 'o', 'o', 'n'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'n', 'oo', 'n'], ['n', 'o', 'o', 'n', 'l', 'eve', 'l', 'noon'], ['n', 'o', 'o', 'n', 'level', 'n', 'o', 'o', 'n'], ['n', 'o', 'o', 'n', 'level', 'n', 'oo', 'n'], ['n', 'o', 'o', 'n', 'level', 'noon'], ['n', 'o', 'o', 'nleveln', 'o', 'o', 'n'], ['n', 'o', 'o', 'nleveln', 'oo', 'n'], ['n', 'o', 'onlevelno', 'o', 'n'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n'], ['n', 'oo', 'n', 'l', 'e', 'v', 'e', 'l', 'noon'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'n', 'o', 'o', 'n'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'n', 'oo', 'n'], ['n', 'oo', 'n', 'l', 'eve', 'l', 'noon'], ['n', 'oo', 'n', 'level', 'n', 'o', 'o', 'n'], ['n', 'oo', 'n', 'level', 'n', 'oo', 'n'], ['n', 'oo', 'n', 'level', 'noon'], ['n', 'oo', 'nleveln', 'o', 'o', 'n'], ['n', 'oo', 'nleveln', 'oo', 'n'], ['n', 'oonlevelnoo', 'n'], ['noon', 'l', 'e', 'v', 'e', 'l', 'n', 'o', 'o', 'n'], ['noon', 'l', 'e', 'v', 'e', 'l', 'n', 'oo', 'n'], ['noon', 'l', 'e', 'v', 'e', 'l', 'noon'], ['noon', 'l', 'eve', 'l', 'n', 'o', 'o', 'n'], ['noon', 'l', 'eve', 'l', 'n', 'oo', 'n'], ['noon', 'l', 'eve', 'l', 'noon'], ['noon', 'level', 'n', 'o', 'o', 'n'], ['noon', 'level', 'n', 'oo', 'n'], ['noon', 'level', 'noon'], ['noonlevelnoon']]\n assert candidate(s = \"abacdfgdcaba\") == [['a', 'b', 'a', 'c', 'd', 'f', 'g', 'd', 'c', 'a', 'b', 'a'], ['a', 'b', 'a', 'c', 'd', 'f', 'g', 'd', 'c', 'aba'], ['aba', 'c', 'd', 'f', 'g', 'd', 'c', 'a', 'b', 'a'], ['aba', 'c', 'd', 'f', 'g', 'd', 'c', 'aba']]\n assert candidate(s = \"rotormadamlevelcivic\") == [['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'civic'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'civic'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'level', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'level', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'a', 'd', 'a', 'm', 'level', 'civic'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'civic'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'l', 'eve', 'l', 'civic'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'level', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'level', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'm', 'ada', 'm', 'level', 'civic'], ['r', 'o', 't', 'o', 'r', 'madam', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'madam', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'madam', 'l', 'e', 'v', 'e', 'l', 'civic'], ['r', 'o', 't', 'o', 'r', 'madam', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'madam', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'madam', 'l', 'eve', 'l', 'civic'], ['r', 'o', 't', 'o', 'r', 'madam', 'level', 'c', 'i', 'v', 'i', 'c'], ['r', 'o', 't', 'o', 'r', 'madam', 'level', 'c', 'ivi', 'c'], ['r', 'o', 't', 'o', 'r', 'madam', 'level', 'civic'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'civic'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'civic'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'level', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'level', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'm', 'a', 'd', 'a', 'm', 'level', 'civic'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'civic'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'l', 'eve', 'l', 'civic'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'level', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'level', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'm', 'ada', 'm', 'level', 'civic'], ['r', 'oto', 'r', 'madam', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'madam', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'madam', 'l', 'e', 'v', 'e', 'l', 'civic'], ['r', 'oto', 'r', 'madam', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'madam', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'madam', 'l', 'eve', 'l', 'civic'], ['r', 'oto', 'r', 'madam', 'level', 'c', 'i', 'v', 'i', 'c'], ['r', 'oto', 'r', 'madam', 'level', 'c', 'ivi', 'c'], ['r', 'oto', 'r', 'madam', 'level', 'civic'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'l', 'e', 'v', 'e', 'l', 'civic'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'l', 'eve', 'l', 'civic'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'level', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'level', 'c', 'ivi', 'c'], ['rotor', 'm', 'a', 'd', 'a', 'm', 'level', 'civic'], ['rotor', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['rotor', 'm', 'ada', 'm', 'l', 'e', 'v', 'e', 'l', 'civic'], ['rotor', 'm', 'ada', 'm', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'm', 'ada', 'm', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['rotor', 'm', 'ada', 'm', 'l', 'eve', 'l', 'civic'], ['rotor', 'm', 'ada', 'm', 'level', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'm', 'ada', 'm', 'level', 'c', 'ivi', 'c'], ['rotor', 'm', 'ada', 'm', 'level', 'civic'], ['rotor', 'madam', 'l', 'e', 'v', 'e', 'l', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'madam', 'l', 'e', 'v', 'e', 'l', 'c', 'ivi', 'c'], ['rotor', 'madam', 'l', 'e', 'v', 'e', 'l', 'civic'], ['rotor', 'madam', 'l', 'eve', 'l', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'madam', 'l', 'eve', 'l', 'c', 'ivi', 'c'], ['rotor', 'madam', 'l', 'eve', 'l', 'civic'], ['rotor', 'madam', 'level', 'c', 'i', 'v', 'i', 'c'], ['rotor', 'madam', 'level', 'c', 'ivi', 'c'], ['rotor', 'madam', 'level', 'civic']]\n assert candidate(s = \"abbaabba\") == [['a', 'b', 'b', 'a', 'a', 'b', 'b', 'a'], ['a', 'b', 'b', 'a', 'a', 'bb', 'a'], ['a', 'b', 'b', 'a', 'abba'], ['a', 'b', 'b', 'aa', 'b', 'b', 'a'], ['a', 'b', 'b', 'aa', 'bb', 'a'], ['a', 'b', 'baab', 'b', 'a'], ['a', 'bb', 'a', 'a', 'b', 'b', 'a'], ['a', 'bb', 'a', 'a', 'bb', 'a'], ['a', 'bb', 'a', 'abba'], ['a', 'bb', 'aa', 'b', 'b', 'a'], ['a', 'bb', 'aa', 'bb', 'a'], ['a', 'bbaabb', 'a'], ['abba', 'a', 'b', 'b', 'a'], ['abba', 'a', 'bb', 'a'], ['abba', 'abba'], ['abbaabba']]\n assert candidate(s = \"deifieddeified\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'd', 'eifie', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'deified'], ['d', 'e', 'i', 'f', 'i', 'e', 'dd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'dd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'e', 'dd', 'eifie', 'd'], ['d', 'e', 'i', 'f', 'i', 'edde', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'f', 'i', 'edde', 'ifi', 'e', 'd'], ['d', 'e', 'i', 'f', 'ieddei', 'f', 'i', 'e', 'd'], ['d', 'e', 'i', 'fieddeif', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'd', 'eifie', 'd'], ['d', 'e', 'ifi', 'e', 'd', 'deified'], ['d', 'e', 'ifi', 'e', 'dd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'dd', 'e', 'ifi', 'e', 'd'], ['d', 'e', 'ifi', 'e', 'dd', 'eifie', 'd'], ['d', 'e', 'ifi', 'edde', 'i', 'f', 'i', 'e', 'd'], ['d', 'e', 'ifi', 'edde', 'ifi', 'e', 'd'], ['d', 'e', 'ifieddeifi', 'e', 'd'], ['d', 'eifie', 'd', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'eifie', 'd', 'd', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'd', 'd', 'eifie', 'd'], ['d', 'eifie', 'd', 'deified'], ['d', 'eifie', 'dd', 'e', 'i', 'f', 'i', 'e', 'd'], ['d', 'eifie', 'dd', 'e', 'ifi', 'e', 'd'], ['d', 'eifie', 'dd', 'eifie', 'd'], ['d', 'eifieddeifie', 'd'], ['deified', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['deified', 'd', 'e', 'ifi', 'e', 'd'], ['deified', 'd', 'eifie', 'd'], ['deified', 'deified'], ['deifieddeified']]\n assert candidate(s = \"wowzowwow\") == [['w', 'o', 'w', 'z', 'o', 'w', 'w', 'o', 'w'], ['w', 'o', 'w', 'z', 'o', 'w', 'wow'], ['w', 'o', 'w', 'z', 'o', 'ww', 'o', 'w'], ['w', 'o', 'w', 'z', 'owwo', 'w'], ['wow', 'z', 'o', 'w', 'w', 'o', 'w'], ['wow', 'z', 'o', 'w', 'wow'], ['wow', 'z', 'o', 'ww', 'o', 'w'], ['wow', 'z', 'owwo', 'w']]\n assert candidate(s = \"levelonevenolevel\") == [['l', 'e', 'v', 'e', 'l', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'l', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'l', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'l', 'eve', 'l'], ['l', 'e', 'v', 'e', 'l', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'level'], ['l', 'e', 'v', 'e', 'l', 'o', 'n', 'eve', 'n', 'o', 'l', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'l', 'o', 'n', 'eve', 'n', 'o', 'l', 'eve', 'l'], ['l', 'e', 'v', 'e', 'l', 'o', 'n', 'eve', 'n', 'o', 'level'], ['l', 'e', 'v', 'e', 'l', 'o', 'neven', 'o', 'l', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'l', 'o', 'neven', 'o', 'l', 'eve', 'l'], ['l', 'e', 'v', 'e', 'l', 'o', 'neven', 'o', 'level'], ['l', 'e', 'v', 'e', 'l', 'oneveno', 'l', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'l', 'oneveno', 'l', 'eve', 'l'], ['l', 'e', 'v', 'e', 'l', 'oneveno', 'level'], ['l', 'e', 'v', 'e', 'lonevenol', 'e', 'v', 'e', 'l'], ['l', 'e', 'v', 'e', 'lonevenol', 'eve', 'l'], ['l', 'e', 'v', 'elonevenole', 'v', 'e', 'l'], ['l', 'e', 'velonevenolev', 'e', 'l'], ['l', 'eve', 'l', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'l', 'e', 'v', 'e', 'l'], ['l', 'eve', 'l', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'l', 'eve', 'l'], ['l', 'eve', 'l', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'level'], ['l', 'eve', 'l', 'o', 'n', 'eve', 'n', 'o', 'l', 'e', 'v', 'e', 'l'], ['l', 'eve', 'l', 'o', 'n', 'eve', 'n', 'o', 'l', 'eve', 'l'], ['l', 'eve', 'l', 'o', 'n', 'eve', 'n', 'o', 'level'], ['l', 'eve', 'l', 'o', 'neven', 'o', 'l', 'e', 'v', 'e', 'l'], ['l', 'eve', 'l', 'o', 'neven', 'o', 'l', 'eve', 'l'], ['l', 'eve', 'l', 'o', 'neven', 'o', 'level'], ['l', 'eve', 'l', 'oneveno', 'l', 'e', 'v', 'e', 'l'], ['l', 'eve', 'l', 'oneveno', 'l', 'eve', 'l'], ['l', 'eve', 'l', 'oneveno', 'level'], ['l', 'eve', 'lonevenol', 'e', 'v', 'e', 'l'], ['l', 'eve', 'lonevenol', 'eve', 'l'], ['l', 'evelonevenoleve', 'l'], ['level', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'l', 'e', 'v', 'e', 'l'], ['level', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'l', 'eve', 'l'], ['level', 'o', 'n', 'e', 'v', 'e', 'n', 'o', 'level'], ['level', 'o', 'n', 'eve', 'n', 'o', 'l', 'e', 'v', 'e', 'l'], ['level', 'o', 'n', 'eve', 'n', 'o', 'l', 'eve', 'l'], ['level', 'o', 'n', 'eve', 'n', 'o', 'level'], ['level', 'o', 'neven', 'o', 'l', 'e', 'v', 'e', 'l'], ['level', 'o', 'neven', 'o', 'l', 'eve', 'l'], ['level', 'o', 'neven', 'o', 'level'], ['level', 'oneveno', 'l', 'e', 'v', 'e', 'l'], ['level', 'oneveno', 'l', 'eve', 'l'], ['level', 'oneveno', 'level'], ['levelonevenolevel']]\n assert candidate(s = \"kayaklevelmadam\") == [['k', 'a', 'y', 'a', 'k', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['k', 'a', 'y', 'a', 'k', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['k', 'a', 'y', 'a', 'k', 'l', 'e', 'v', 'e', 'l', 'madam'], ['k', 'a', 'y', 'a', 'k', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['k', 'a', 'y', 'a', 'k', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['k', 'a', 'y', 'a', 'k', 'l', 'eve', 'l', 'madam'], ['k', 'a', 'y', 'a', 'k', 'level', 'm', 'a', 'd', 'a', 'm'], ['k', 'a', 'y', 'a', 'k', 'level', 'm', 'ada', 'm'], ['k', 'a', 'y', 'a', 'k', 'level', 'madam'], ['k', 'aya', 'k', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['k', 'aya', 'k', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['k', 'aya', 'k', 'l', 'e', 'v', 'e', 'l', 'madam'], ['k', 'aya', 'k', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['k', 'aya', 'k', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['k', 'aya', 'k', 'l', 'eve', 'l', 'madam'], ['k', 'aya', 'k', 'level', 'm', 'a', 'd', 'a', 'm'], ['k', 'aya', 'k', 'level', 'm', 'ada', 'm'], ['k', 'aya', 'k', 'level', 'madam'], ['kayak', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['kayak', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['kayak', 'l', 'e', 'v', 'e', 'l', 'madam'], ['kayak', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['kayak', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['kayak', 'l', 'eve', 'l', 'madam'], ['kayak', 'level', 'm', 'a', 'd', 'a', 'm'], ['kayak', 'level', 'm', 'ada', 'm'], ['kayak', 'level', 'madam']]\n assert candidate(s = \"ababababa\") == [['a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a'], ['a', 'b', 'a', 'b', 'a', 'b', 'aba'], ['a', 'b', 'a', 'b', 'a', 'bab', 'a'], ['a', 'b', 'a', 'b', 'aba', 'b', 'a'], ['a', 'b', 'a', 'b', 'ababa'], ['a', 'b', 'a', 'bab', 'a', 'b', 'a'], ['a', 'b', 'a', 'bab', 'aba'], ['a', 'b', 'a', 'babab', 'a'], ['a', 'b', 'aba', 'b', 'a', 'b', 'a'], ['a', 'b', 'aba', 'b', 'aba'], ['a', 'b', 'aba', 'bab', 'a'], ['a', 'b', 'ababa', 'b', 'a'], ['a', 'b', 'abababa'], ['a', 'bab', 'a', 'b', 'a', 'b', 'a'], ['a', 'bab', 'a', 'b', 'aba'], ['a', 'bab', 'a', 'bab', 'a'], ['a', 'bab', 'aba', 'b', 'a'], ['a', 'bab', 'ababa'], ['a', 'babab', 'a', 'b', 'a'], ['a', 'babab', 'aba'], ['a', 'bababab', 'a'], ['aba', 'b', 'a', 'b', 'a', 'b', 'a'], ['aba', 'b', 'a', 'b', 'aba'], ['aba', 'b', 'a', 'bab', 'a'], ['aba', 'b', 'aba', 'b', 'a'], ['aba', 'b', 'ababa'], ['aba', 'bab', 'a', 'b', 'a'], ['aba', 'bab', 'aba'], ['aba', 'babab', 'a'], ['ababa', 'b', 'a', 'b', 'a'], ['ababa', 'b', 'aba'], ['ababa', 'bab', 'a'], ['abababa', 'b', 'a'], ['ababababa']]\n assert candidate(s = \"racecardeifiedcivic\") == [['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'civic'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'e', 'ifi', 'e', 'd', 'civic'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'eifie', 'd', 'c', 'ivi', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'd', 'eifie', 'd', 'civic'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'deified', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'deified', 'c', 'ivi', 'c'], ['r', 'a', 'c', 'e', 'c', 'a', 'r', 'deified', 'civic'], ['r', 'a', 'cec', 'a', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'cec', 'a', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c'], ['r', 'a', 'cec', 'a', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'civic'], ['r', 'a', 'cec', 'a', 'r', 'd', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'cec', 'a', 'r', 'd', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c'], ['r', 'a', 'cec', 'a', 'r', 'd', 'e', 'ifi', 'e', 'd', 'civic'], ['r', 'a', 'cec', 'a', 'r', 'd', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'cec', 'a', 'r', 'd', 'eifie', 'd', 'c', 'ivi', 'c'], ['r', 'a', 'cec', 'a', 'r', 'd', 'eifie', 'd', 'civic'], ['r', 'a', 'cec', 'a', 'r', 'deified', 'c', 'i', 'v', 'i', 'c'], ['r', 'a', 'cec', 'a', 'r', 'deified', 'c', 'ivi', 'c'], ['r', 'a', 'cec', 'a', 'r', 'deified', 'civic'], ['r', 'aceca', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'aceca', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c'], ['r', 'aceca', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'civic'], ['r', 'aceca', 'r', 'd', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'aceca', 'r', 'd', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c'], ['r', 'aceca', 'r', 'd', 'e', 'ifi', 'e', 'd', 'civic'], ['r', 'aceca', 'r', 'd', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c'], ['r', 'aceca', 'r', 'd', 'eifie', 'd', 'c', 'ivi', 'c'], ['r', 'aceca', 'r', 'd', 'eifie', 'd', 'civic'], ['r', 'aceca', 'r', 'deified', 'c', 'i', 'v', 'i', 'c'], ['r', 'aceca', 'r', 'deified', 'c', 'ivi', 'c'], ['r', 'aceca', 'r', 'deified', 'civic'], ['racecar', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['racecar', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'c', 'ivi', 'c'], ['racecar', 'd', 'e', 'i', 'f', 'i', 'e', 'd', 'civic'], ['racecar', 'd', 'e', 'ifi', 'e', 'd', 'c', 'i', 'v', 'i', 'c'], ['racecar', 'd', 'e', 'ifi', 'e', 'd', 'c', 'ivi', 'c'], ['racecar', 'd', 'e', 'ifi', 'e', 'd', 'civic'], ['racecar', 'd', 'eifie', 'd', 'c', 'i', 'v', 'i', 'c'], ['racecar', 'd', 'eifie', 'd', 'c', 'ivi', 'c'], ['racecar', 'd', 'eifie', 'd', 'civic'], ['racecar', 'deified', 'c', 'i', 'v', 'i', 'c'], ['racecar', 'deified', 'c', 'ivi', 'c'], ['racecar', 'deified', 'civic']]\n assert candidate(s = \"xyxzyx\") == [['x', 'y', 'x', 'z', 'y', 'x'], ['xyx', 'z', 'y', 'x']]\n assert candidate(s = \"rotordetartratoredor\") == [['r', 'o', 't', 'o', 'r', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'd', 'e', 't', 'artra', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'o', 't', 'o', 'r', 'd', 'e', 'tartrat', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'oto', 'r', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'oto', 'r', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'oto', 'r', 'd', 'e', 't', 'artra', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['r', 'oto', 'r', 'd', 'e', 'tartrat', 'o', 'r', 'e', 'd', 'o', 'r'], ['rotor', 'd', 'e', 't', 'a', 'r', 't', 'r', 'a', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['rotor', 'd', 'e', 't', 'a', 'rtr', 'a', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['rotor', 'd', 'e', 't', 'artra', 't', 'o', 'r', 'e', 'd', 'o', 'r'], ['rotor', 'd', 'e', 'tartrat', 'o', 'r', 'e', 'd', 'o', 'r']]\n assert candidate(s = \"steponnopest\") == [['s', 't', 'e', 'p', 'o', 'n', 'n', 'o', 'p', 'e', 's', 't'], ['s', 't', 'e', 'p', 'o', 'nn', 'o', 'p', 'e', 's', 't'], ['s', 't', 'e', 'p', 'onno', 'p', 'e', 's', 't'], ['s', 't', 'e', 'ponnop', 'e', 's', 't'], ['s', 't', 'eponnope', 's', 't']]\n assert candidate(s = \"mississippi\") == [['m', 'i', 's', 's', 'i', 's', 's', 'i', 'p', 'p', 'i'], ['m', 'i', 's', 's', 'i', 's', 's', 'i', 'pp', 'i'], ['m', 'i', 's', 's', 'i', 's', 's', 'ippi'], ['m', 'i', 's', 's', 'i', 'ss', 'i', 'p', 'p', 'i'], ['m', 'i', 's', 's', 'i', 'ss', 'i', 'pp', 'i'], ['m', 'i', 's', 's', 'i', 'ss', 'ippi'], ['m', 'i', 's', 's', 'issi', 'p', 'p', 'i'], ['m', 'i', 's', 's', 'issi', 'pp', 'i'], ['m', 'i', 's', 'sis', 's', 'i', 'p', 'p', 'i'], ['m', 'i', 's', 'sis', 's', 'i', 'pp', 'i'], ['m', 'i', 's', 'sis', 's', 'ippi'], ['m', 'i', 'ss', 'i', 's', 's', 'i', 'p', 'p', 'i'], ['m', 'i', 'ss', 'i', 's', 's', 'i', 'pp', 'i'], ['m', 'i', 'ss', 'i', 's', 's', 'ippi'], ['m', 'i', 'ss', 'i', 'ss', 'i', 'p', 'p', 'i'], ['m', 'i', 'ss', 'i', 'ss', 'i', 'pp', 'i'], ['m', 'i', 'ss', 'i', 'ss', 'ippi'], ['m', 'i', 'ss', 'issi', 'p', 'p', 'i'], ['m', 'i', 'ss', 'issi', 'pp', 'i'], ['m', 'i', 'ssiss', 'i', 'p', 'p', 'i'], ['m', 'i', 'ssiss', 'i', 'pp', 'i'], ['m', 'i', 'ssiss', 'ippi'], ['m', 'issi', 's', 's', 'i', 'p', 'p', 'i'], ['m', 'issi', 's', 's', 'i', 'pp', 'i'], ['m', 'issi', 's', 's', 'ippi'], ['m', 'issi', 'ss', 'i', 'p', 'p', 'i'], ['m', 'issi', 'ss', 'i', 'pp', 'i'], ['m', 'issi', 'ss', 'ippi'], ['m', 'ississi', 'p', 'p', 'i'], ['m', 'ississi', 'pp', 'i']]\n assert candidate(s = \"redividerdeified\") == [['r', 'e', 'd', 'i', 'v', 'i', 'd', 'e', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'e', 'd', 'i', 'v', 'i', 'd', 'e', 'r', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'e', 'd', 'i', 'v', 'i', 'd', 'e', 'r', 'd', 'eifie', 'd'], ['r', 'e', 'd', 'i', 'v', 'i', 'd', 'e', 'r', 'deified'], ['r', 'e', 'd', 'ivi', 'd', 'e', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'e', 'd', 'ivi', 'd', 'e', 'r', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'e', 'd', 'ivi', 'd', 'e', 'r', 'd', 'eifie', 'd'], ['r', 'e', 'd', 'ivi', 'd', 'e', 'r', 'deified'], ['r', 'e', 'divid', 'e', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'e', 'divid', 'e', 'r', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'e', 'divid', 'e', 'r', 'd', 'eifie', 'd'], ['r', 'e', 'divid', 'e', 'r', 'deified'], ['r', 'edivide', 'r', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['r', 'edivide', 'r', 'd', 'e', 'ifi', 'e', 'd'], ['r', 'edivide', 'r', 'd', 'eifie', 'd'], ['r', 'edivide', 'r', 'deified'], ['redivider', 'd', 'e', 'i', 'f', 'i', 'e', 'd'], ['redivider', 'd', 'e', 'ifi', 'e', 'd'], ['redivider', 'd', 'eifie', 'd'], ['redivider', 'deified']]\n assert candidate(s = \"referencereference\") == [['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e', 'r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e', 'r', 'e', 'f', 'ere', 'n', 'c', 'e'], ['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e', 'r', 'efe', 'r', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e', 'refer', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'ere', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'ere', 'f', 'ere', 'n', 'c', 'e'], ['r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'erefere', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'e', 'r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'e', 'r', 'e', 'f', 'ere', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'e', 'r', 'efe', 'r', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'e', 'refer', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'ere', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'ere', 'f', 'ere', 'n', 'c', 'e'], ['r', 'e', 'f', 'ere', 'n', 'c', 'erefere', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'e', 'r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'e', 'r', 'e', 'f', 'ere', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'e', 'r', 'efe', 'r', 'e', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'e', 'refer', 'e', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'ere', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'ere', 'f', 'ere', 'n', 'c', 'e'], ['r', 'efe', 'r', 'e', 'n', 'c', 'erefere', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'e', 'r', 'e', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'e', 'r', 'e', 'f', 'ere', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'e', 'r', 'efe', 'r', 'e', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'e', 'refer', 'e', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'ere', 'f', 'e', 'r', 'e', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'ere', 'f', 'ere', 'n', 'c', 'e'], ['refer', 'e', 'n', 'c', 'erefere', 'n', 'c', 'e']]\n assert candidate(s = \"rotorlevelmadam\") == [['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['r', 'o', 't', 'o', 'r', 'l', 'e', 'v', 'e', 'l', 'madam'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['r', 'o', 't', 'o', 'r', 'l', 'eve', 'l', 'madam'], ['r', 'o', 't', 'o', 'r', 'level', 'm', 'a', 'd', 'a', 'm'], ['r', 'o', 't', 'o', 'r', 'level', 'm', 'ada', 'm'], ['r', 'o', 't', 'o', 'r', 'level', 'madam'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['r', 'oto', 'r', 'l', 'e', 'v', 'e', 'l', 'madam'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['r', 'oto', 'r', 'l', 'eve', 'l', 'madam'], ['r', 'oto', 'r', 'level', 'm', 'a', 'd', 'a', 'm'], ['r', 'oto', 'r', 'level', 'm', 'ada', 'm'], ['r', 'oto', 'r', 'level', 'madam'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'm', 'a', 'd', 'a', 'm'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'm', 'ada', 'm'], ['rotor', 'l', 'e', 'v', 'e', 'l', 'madam'], ['rotor', 'l', 'eve', 'l', 'm', 'a', 'd', 'a', 'm'], ['rotor', 'l', 'eve', 'l', 'm', 'ada', 'm'], ['rotor', 'l', 'eve', 'l', 'madam'], ['rotor', 'level', 'm', 'a', 'd', 'a', 'm'], ['rotor', 'level', 'm', 'ada', 'm'], ['rotor', 'level', 'madam']]\n assert candidate(s = \"rotorredder\") == [['r', 'o', 't', 'o', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'r', 'r', 'edde', 'r'], ['r', 'o', 't', 'o', 'r', 'redder'], ['r', 'o', 't', 'o', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'o', 't', 'o', 'rr', 'edde', 'r'], ['r', 'oto', 'r', 'r', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'r', 'r', 'edde', 'r'], ['r', 'oto', 'r', 'redder'], ['r', 'oto', 'rr', 'e', 'd', 'd', 'e', 'r'], ['r', 'oto', 'rr', 'e', 'dd', 'e', 'r'], ['r', 'oto', 'rr', 'edde', 'r'], ['rotor', 'r', 'e', 'd', 'd', 'e', 'r'], ['rotor', 'r', 'e', 'dd', 'e', 'r'], ['rotor', 'r', 'edde', 'r'], ['rotor', 'redder']]\n assert candidate(s = \"deifiedrotorcivic\") == [['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'o', 't', 'o', 'r', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'o', 't', 'o', 'r', 'c', 'ivi', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'o', 't', 'o', 'r', 'civic'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'oto', 'r', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'oto', 'r', 'c', 'ivi', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'r', 'oto', 'r', 'civic'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'rotor', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'rotor', 'c', 'ivi', 'c'], ['d', 'e', 'i', 'f', 'i', 'e', 'd', 'rotor', 'civic'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'o', 't', 'o', 'r', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'o', 't', 'o', 'r', 'c', 'ivi', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'o', 't', 'o', 'r', 'civic'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'oto', 'r', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'oto', 'r', 'c', 'ivi', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'r', 'oto', 'r', 'civic'], ['d', 'e', 'ifi', 'e', 'd', 'rotor', 'c', 'i', 'v', 'i', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'rotor', 'c', 'ivi', 'c'], ['d', 'e', 'ifi', 'e', 'd', 'rotor', 'civic'], ['d', 'eifie', 'd', 'r', 'o', 't', 'o', 'r', 'c', 'i', 'v', 'i', 'c'], ['d', 'eifie', 'd', 'r', 'o', 't', 'o', 'r', 'c', 'ivi', 'c'], ['d', 'eifie', 'd', 'r', 'o', 't', 'o', 'r', 'civic'], ['d', 'eifie', 'd', 'r', 'oto', 'r', 'c', 'i', 'v', 'i', 'c'], ['d', 'eifie', 'd', 'r', 'oto', 'r', 'c', 'ivi', 'c'], ['d', 'eifie', 'd', 'r', 'oto', 'r', 'civic'], ['d', 'eifie', 'd', 'rotor', 'c', 'i', 'v', 'i', 'c'], ['d', 'eifie', 'd', 'rotor', 'c', 'ivi', 'c'], ['d', 'eifie', 'd', 'rotor', 'civic'], ['deified', 'r', 'o', 't', 'o', 'r', 'c', 'i', 'v', 'i', 'c'], ['deified', 'r', 'o', 't', 'o', 'r', 'c', 'ivi', 'c'], ['deified', 'r', 'o', 't', 'o', 'r', 'civic'], ['deified', 'r', 'oto', 'r', 'c', 'i', 'v', 'i', 'c'], ['deified', 'r', 'oto', 'r', 'c', 'ivi', 'c'], ['deified', 'r', 'oto', 'r', 'civic'], ['deified', 'rotor', 'c', 'i', 'v', 'i', 'c'], ['deified', 'rotor', 'c', 'ivi', 'c'], ['deified', 'rotor', 'civic']]\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().partition", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var partition = function(s) {", "container": null, "callable": "partition", "parameters": [{"name": "s", "type": "string"}], "return_type": "string[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 132, "task_id": "palindrome-partitioning-ii", "difficulty": "Hard", "problem_description": "Given a string s, partition s such that every substring of the partition is a palindrome.\nReturn the minimum cuts needed for a palindrome partitioning of s.\n \nExample 1:\n\nInput: s = \"aab\"\nOutput: 1\nExplanation: The palindrome partitioning [\"aa\",\"b\"] could be produced using 1 cut.\n\nExample 2:\n\nInput: s = \"a\"\nOutput: 0\n\nExample 3:\n\nInput: s = \"ab\"\nOutput: 1\n\n \nConstraints:\n\n1 <= s.length <= 2000\ns consists of lowercase English letters only.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcba\") == 0\n assert candidate(s = \"aabbaa\") == 0\n assert candidate(s = \"abcdcba\") == 0\n assert candidate(s = \"abababab\") == 1\n assert candidate(s = \"a\") == 0\n assert candidate(s = \"ab\") == 1\n assert candidate(s = \"noonnoon\") == 0\n assert candidate(s = \"aabaa\") == 0\n assert candidate(s = \"aabb\") == 1\n assert candidate(s = \"racecar\") == 0\n assert candidate(s = \"abba\") == 0\n assert candidate(s = \"abcdabcdabcd\") == 11\n assert candidate(s = \"abc\") == 2\n assert candidate(s = \"abcd\") == 3\n assert candidate(s = \"abccba\") == 0\n assert candidate(s = \"aab\") == 1\n assert candidate(s = \"abcbm\") == 2\n assert candidate(s = \"aabbcc\") == 2\n assert candidate(s = \"mississippi\") == 3\n assert candidate(s = \"leet\") == 2\n assert candidate(s = \"abcdefg\") == 6\n assert candidate(s = \"ababcbabcba\") == 2\n assert candidate(s = \"abacdcbaabcdeedcba\") == 4\n assert candidate(s = \"abacdfgdcabaedcba\") == 12\n assert candidate(s = \"aabcbabcbabcba\") == 1\n assert candidate(s = \"abaaabaaabaaab\") == 1\n assert candidate(s = \"abcabcabcabc\") == 11\n assert candidate(s = \"abcdeedcbaeedcba\") == 5\n assert candidate(s = \"acbbccaaa\") == 3\n assert candidate(s = \"aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbb\") == 1\n assert candidate(s = \"aabaaabaaabaaa\") == 1\n assert candidate(s = \"abacdbacabcbaabcbaabcba\") == 6\n assert candidate(s = \"aabbababaabbaabb\") == 4\n assert candidate(s = \"abacdbacabcbaab\") == 5\n assert candidate(s = \"abacba\") == 3\n assert candidate(s = \"aaaaabaaaabaaabaaa\") == 2\n assert candidate(s = \"abacdbacabcbaabcbaabcbaabcbaabcba\") == 6\n assert candidate(s = \"abacdcbaabcdeedcbaabcdeedcba\") == 4\n assert candidate(s = \"aaaabaaaaa\") == 1\n assert candidate(s = \"noonmoonnoon\") == 3\n assert candidate(s = \"abccbaabccba\") == 0\n assert candidate(s = \"abacabacaba\") == 0\n assert candidate(s = \"aaaaabbbbb\") == 1\n assert candidate(s = \"abbbabbabbbabbabbbabbabbbabbbabbb\") == 1\n assert candidate(s = \"abbaabbabbabba\") == 1\n assert candidate(s = \"noonnoonnoonnoon\") == 0\n assert candidate(s = \"abcdcbe\") == 2\n assert candidate(s = \"ababbbababbbaba\") == 0\n assert candidate(s = \"abacaba\") == 0\n assert candidate(s = \"madamracecar\") == 1\n assert candidate(s = \"abcbac\") == 1\n assert candidate(s = \"abcdedcbafedcbabcd\") == 3\n assert candidate(s = \"aaaabaaa\") == 1\n assert candidate(s = \"aabbaabbaabbaabb\") == 1\n assert candidate(s = \"abbbabbabbbabbabbbabbabbb\") == 1\n assert candidate(s = \"abcbaababcba\") == 3\n assert candidate(s = \"abbabbaabbabba\") == 0\n assert candidate(s = \"abacabadabacabadabacabadabacaba\") == 0\n assert candidate(s = \"abab\") == 1\n assert candidate(s = \"abcdcbaefghfeabcdcba\") == 7\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 0\n assert candidate(s = \"racecarabcba\") == 1\n assert candidate(s = \"xyzyxzyxyzyx\") == 3\n assert candidate(s = \"aabbccddeeeffffggg\") == 6\n assert candidate(s = \"levelup\") == 2\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == 0\n assert candidate(s = \"abababababababab\") == 1\n assert candidate(s = \"abcdeedcba\") == 0\n assert candidate(s = \"ababababababab\") == 1\n assert candidate(s = \"noon\") == 0\n assert candidate(s = \"aaaaaa\") == 0\n assert candidate(s = \"xyxzyzyxzyxzyx\") == 9\n assert candidate(s = \"abababababab\") == 1\n assert candidate(s = \"deeee\") == 1\n assert candidate(s = \"abcbaabcba\") == 0\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == 0\n assert candidate(s = \"xyzyxzyzyxzyx\") == 6\n assert candidate(s = \"abcdeedcbaabcdeedcbaabcdeedcbaabcdeedcba\") == 0\n assert candidate(s = \"zyxxyzyxyzyx\") == 2\n assert candidate(s = \"abcdabcdabcdabcd\") == 15\n assert candidate(s = \"level\") == 0\n assert candidate(s = \"bananaabananabana\") == 4\n assert candidate(s = \"abcdefghiijihgfedcba\") == 17\n assert candidate(s = \"aabaabaaa\") == 1\n assert candidate(s = \"abacdbacabcbaabcbaabcbaabcbaab\") == 5\n assert candidate(s = \"abcdabcdabcdabcdabcd\") == 19\n assert candidate(s = \"madam\") == 0\n assert candidate(s = \"abbbba\") == 0\n assert candidate(s = \"aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbaaaaaaaaaaaaaaaaaa\") == 0\n assert candidate(s = \"ababababcba\") == 2\n assert candidate(s = \"rotorcarcarecat\") == 10\n assert candidate(s = \"abacabadabacaba\") == 0\n assert candidate(s = \"abababa\") == 0\n assert candidate(s = \"aabbccddeeefffggg\") == 6\n assert candidate(s = \"ababbabaababbabaababbab\") == 1\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzz\") == 0\n assert candidate(s = \"abacdbacabcbaabcbaabcbaabcba\") == 6\n assert candidate(s = \"abbabbabb\") == 1\n assert candidate(s = \"abbbabbbbabb\") == 2\n assert candidate(s = \"abcbabcba\") == 0\n assert candidate(s = \"banana\") == 1\n assert candidate(s = \"abcbddcba\") == 5\n assert candidate(s = \"abcbaeabcdedcba\") == 2\n assert candidate(s = \"abcbabcbabcba\") == 0\n assert candidate(s = \"bcbabbc\") == 3\n assert candidate(s = \"ababababababababababababab\") == 1\n assert candidate(s = \"anana\") == 0\n assert candidate(s = \"aababababababababababababababababababababababababababababababababababababab\") == 1\n assert candidate(s = \"aabbccddeeffgg\") == 6\n assert candidate(s = \"abbacdcba\") == 3\n assert candidate(s = \"aabbccddeeff\") == 5\n assert candidate(s = \"abaca\") == 2\n assert candidate(s = \"abacdbacaba\") == 4\n assert candidate(s = \"madamimadam\") == 0\n assert candidate(s = \"abcdefghij\") == 9\n assert candidate(s = \"abcbaabcbaabcbaabcbaabcbaabcba\") == 0\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 25\n assert candidate(s = \"aabbabba\") == 1\n assert candidate(s = \"bananaabananabananaabananabanana\") == 6\n assert candidate(s = \"aabbccddeeefffgggbbb\") == 7\n assert candidate(s = \"abacdbacabcbaabcbaab\") == 5\n assert candidate(s = \"racecarannakayak\") == 2\n assert candidate(s = \"amanaplanacanalpanama\") == 0\n assert candidate(s = \"aaaaaaaaaaaaaaaaaab\") == 1\n assert candidate(s = \"noonracecar\") == 1\n assert candidate(s = \"noonnoonnoon\") == 0\n assert candidate(s = \"abacdbacabcba\") == 6\n assert candidate(s = \"noonmoonnoonnoonnoonnoonnoon\") == 3\n assert candidate(s = \"abcdedcba\") == 0\n assert candidate(s = \"abcdeedcbabacdcba\") == 5\n assert candidate(s = \"mamad\") == 2\n assert candidate(s = \"aaaaaaaaaabbbbbbbbbccccccccc\") == 2\n assert candidate(s = \"abcdefgfedcbamnoponmabcdedcba\") == 2\n assert candidate(s = \"noonhighnoon\") == 5\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == 0\n assert candidate(s = \"racecarlevelmadamracecar\") == 3\n assert candidate(s = \"abacdfgdcaba\") == 7\n assert candidate(s = \"aabaaabbaabbaabb\") == 2\n assert candidate(s = \"abcdabcabcde\") == 11\n assert candidate(s = \"ababababab\") == 1\n assert candidate(s = \"abcdedcbaabcdedcbaabcdedcba\") == 0\n assert candidate(s = \"abacdbacabcbaabcba\") == 6\n assert candidate(s = \"rotor\") == 0\n assert candidate(s = \"abcadacbdb\") == 3\n assert candidate(s = \"xyzzazxzyx\") == 6\n assert candidate(s = \"aabba\") == 1\n assert candidate(s = \"abcabcabcabcabcabcabcabc\") == 23\n assert candidate(s = \"ababbbababbbababb\") == 1\n assert candidate(s = \"aabbccddeeefff\") == 5\n assert candidate(s = \"abacdbacabcbaabcbaabcbaab\") == 5\n assert candidate(s = \"abcdcbabcdcbabcdcbabcdcb\") == 1\n assert candidate(s = \"aabbccddeeefffggghhhhiiiii\") == 8\n assert candidate(s = \"abcabcabcabcabc\") == 14\n assert candidate(s = \"abacdcaba\") == 0\n assert candidate(s = \"aaaaabbbbbccccc\") == 2\n assert candidate(s = \"aabbababab\") == 2\n assert candidate(s = \"xyxzyzyx\") == 3\n assert candidate(s = \"abbab\") == 1\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().minCut", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minCut = function(s) {", "container": null, "callable": "minCut", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 134, "task_id": "gas-station", "difficulty": "Medium", "problem_description": "There are n gas stations along a circular route, where the amount of gas at the ith station is gas[i].\nYou have a car with an unlimited gas tank and it costs cost[i] of gas to travel from the ith station to its next (i + 1)th station. You begin the journey with an empty tank at one of the gas stations.\nGiven two integer arrays gas and cost, return the starting gas station's index if you can travel around the circuit once in the clockwise direction, otherwise return -1. If there exists a solution, it is guaranteed to be unique.\n \nExample 1:\n\nInput: gas = [1,2,3,4,5], cost = [3,4,5,1,2]\nOutput: 3\nExplanation:\nStart at station 3 (index 3) and fill up with 4 unit of gas. Your tank = 0 + 4 = 4\nTravel to station 4. Your tank = 4 - 1 + 5 = 8\nTravel to station 0. Your tank = 8 - 2 + 1 = 7\nTravel to station 1. Your tank = 7 - 3 + 2 = 6\nTravel to station 2. Your tank = 6 - 4 + 3 = 5\nTravel to station 3. The cost is 5. Your gas is just enough to travel back to station 3.\nTherefore, return 3 as the starting index.\n\nExample 2:\n\nInput: gas = [2,3,4], cost = [3,4,3]\nOutput: -1\nExplanation:\nYou can't start at station 0 or 1, as there is not enough gas to travel to the next station.\nLet's start at station 2 and fill up with 4 unit of gas. Your tank = 0 + 4 = 4\nTravel to station 0. Your tank = 4 - 3 + 2 = 3\nTravel to station 1. Your tank = 3 - 3 + 3 = 3\nYou cannot travel back to station 2, as it requires 4 unit of gas but you only have 3.\nTherefore, you can't travel around the circuit once no matter where you start.\n\n \nConstraints:\n\nn == gas.length == cost.length\n1 <= n <= 105\n0 <= gas[i], cost[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(gas = [1, 2, 3, 4, 5],cost = [3, 4, 5, 1, 2]) == 3\n assert candidate(gas = [1, 1, 1, 1],cost = [1, 1, 1, 1]) == 3\n assert candidate(gas = [1, 1, 1, 1, 1],cost = [1, 1, 1, 1, 1]) == 4\n assert candidate(gas = [5, 1, 2, 3, 4],cost = [4, 5, 1, 2, 3]) == 2\n assert candidate(gas = [1, 2, 3, 4, 5],cost = [5, 4, 3, 2, 1]) == 3\n assert candidate(gas = [2, 3, 4],cost = [3, 4, 3]) == -1\n assert candidate(gas = [5, 8, 2, 8],cost = [6, 5, 6, 6]) == 3\n assert candidate(gas = [0, 0, 0, 0, 0],cost = [0, 0, 0, 0, 0]) == 4\n assert candidate(gas = [10, 20, 30, 40, 50],cost = [15, 25, 35, 45, 55]) == -1\n assert candidate(gas = [3, 1, 1],cost = [1, 2, 2]) == 0\n assert candidate(gas = [10, 1, 2, 3, 4],cost = [3, 4, 5, 1, 2]) == 4\n assert candidate(gas = [3, 3, 4],cost = [3, 4, 4]) == -1\n assert candidate(gas = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100],cost = [101, 99, 101, 99, 101, 99, 101, 99, 101, 99]) == 9\n assert candidate(gas = [100, 50, 20, 5, 10],cost = [10, 20, 50, 100, 5]) == 4\n assert candidate(gas = [20, 20, 20, 20, 20, 20, 20, 20, 20, 20],cost = [19, 19, 19, 19, 19, 19, 19, 19, 19, 20]) == 9\n assert candidate(gas = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],cost = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == 9\n assert candidate(gas = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],cost = [2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == -1\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 1\n assert candidate(gas = [100, 50, 25, 75, 200, 300],cost = [200, 150, 200, 20, 100, 50]) == 3\n assert candidate(gas = [50, 60, 70, 80, 90, 100, 110, 120, 130, 140],cost = [100, 110, 120, 130, 140, 150, 160, 170, 180, 190]) == -1\n assert candidate(gas = [10, 20, 30, 40, 50],cost = [50, 10, 20, 30, 40]) == 1\n assert candidate(gas = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],cost = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == -1\n assert candidate(gas = [6, 5, 4, 3, 2, 1],cost = [1, 2, 3, 4, 5, 6]) == 0\n assert candidate(gas = [10, 30, 20, 10, 5, 40, 10, 30, 20, 10],cost = [15, 25, 10, 15, 10, 30, 10, 20, 15, 15]) == 7\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [1, 2, 3, 4, 5, 6, 7, 8, 10, 1]) == 9\n assert candidate(gas = [5, 8, 2, 8, 4],cost = [6, 5, 6, 6, 8]) == -1\n assert candidate(gas = [3, 3, 4, 4, 1, 1, 2, 2],cost = [3, 3, 3, 3, 2, 2, 2, 2]) == 7\n assert candidate(gas = [1, 10, 10, 10, 1],cost = [10, 1, 1, 1, 10]) == 2\n assert candidate(gas = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],cost = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 9\n assert candidate(gas = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],cost = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 19\n assert candidate(gas = [3, 3, 4, 4, 5, 5, 6, 6, 7, 7],cost = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 9\n assert candidate(gas = [100, 200, 300, 400, 500],cost = [500, 100, 200, 300, 400]) == 1\n assert candidate(gas = [30, 25, 20, 15, 10, 5, 0],cost = [5, 10, 15, 20, 25, 30, 1]) == -1\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],cost = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(gas = [10, 20, 30, 40, 50],cost = [9, 19, 29, 39, 49]) == 4\n assert candidate(gas = [10, 20, 30, 40, 50],cost = [5, 10, 15, 20, 25]) == 4\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],cost = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(gas = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],cost = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 0\n assert candidate(gas = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],cost = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 5\n assert candidate(gas = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],cost = [90, 80, 70, 60, 50, 40, 30, 20, 10, 150]) == -1\n assert candidate(gas = [2, 3, 4, 5, 1, 6],cost = [3, 4, 5, 1, 6, 2]) == 5\n assert candidate(gas = [15, 20, 5, 20, 15, 20, 15, 20, 15, 20],cost = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 9\n assert candidate(gas = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5],cost = [5, 3, 5, 3, 9, 2, 6, 5, 3, 5, 3]) == -1\n assert candidate(gas = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100],cost = [99, 99, 99, 99, 99, 99, 99, 99, 99, 100]) == 9\n assert candidate(gas = [10, 0, 10, 0, 10],cost = [0, 10, 0, 10, 0]) == 4\n assert candidate(gas = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],cost = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 100]) == -1\n assert candidate(gas = [10, 20, 30, 40, 50],cost = [40, 30, 20, 10, 5]) == 4\n assert candidate(gas = [15, 10, 10, 10, 10],cost = [10, 10, 10, 15, 10]) == 4\n assert candidate(gas = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],cost = [4, 4, 4, 4, 4, 4, 4, 4, 4, 5]) == 9\n assert candidate(gas = [8, 6, 7, 4, 5],cost = [5, 6, 7, 3, 4]) == 4\n assert candidate(gas = [5, 8, 2, 8, 4, 7, 6, 6, 1, 4],cost = [4, 4, 5, 7, 1, 5, 4, 4, 5, 4]) == 9\n assert candidate(gas = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],cost = [150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 8\n assert candidate(gas = [1, 1, 1, 1, 1],cost = [2, 2, 2, 2, 2]) == -1\n assert candidate(gas = [10, 20, 30, 10, 5, 15],cost = [20, 15, 10, 5, 15, 10]) == 2\n assert candidate(gas = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],cost = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 9\n assert candidate(gas = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],cost = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(gas = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],cost = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 0\n assert candidate(gas = [3, 3, 4, 5, 1, 2],cost = [4, 1, 5, 1, 2, 3]) == 3\n assert candidate(gas = [20, 30, 10, 40, 50, 60],cost = [50, 10, 60, 10, 20, 30]) == 4\n assert candidate(gas = [3, 5, 7, 2, 8, 10, 6, 4, 12, 9],cost = [4, 4, 8, 5, 5, 6, 7, 8, 3, 2]) == 9\n assert candidate(gas = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],cost = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20]) == -1\n assert candidate(gas = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],cost = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 19\n assert candidate(gas = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20],cost = [11, 9, 11, 9, 11, 9, 11, 9, 11, 9]) == 9\n assert candidate(gas = [5, 5, 5, 5, 5, 5, 5],cost = [6, 6, 6, 6, 6, 6, 6]) == -1\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],cost = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4]) == 11\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [1, 1, 1, 1, 1, 1, 1, 1, 1, 20]) == 7\n assert candidate(gas = [2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [10, 2, 3, 4, 5, 6, 7, 8, 9]) == 1\n assert candidate(gas = [2, 2, 2, 2, 2],cost = [1, 1, 1, 1, 1]) == 4\n assert candidate(gas = [4, 3, 2, 1, 5, 6, 7],cost = [5, 4, 3, 2, 6, 7, 1]) == 6\n assert candidate(gas = [2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [3, 4, 5, 6, 7, 8, 9, 10, 2]) == 8\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 5\n assert candidate(gas = [30, 20, 10, 40, 50, 20, 10, 60, 70, 80],cost = [20, 30, 40, 50, 60, 70, 80, 90, 10, 10]) == -1\n assert candidate(gas = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500],cost = [400, 450, 500, 50, 100, 150, 200, 250, 300, 350]) == 3\n assert candidate(gas = [100, 20, 10, 15, 5],cost = [70, 15, 10, 10, 5]) == 4\n assert candidate(gas = [1, 6, 3, 4, 5, 2, 8],cost = [2, 5, 4, 3, 6, 1, 5]) == 6\n assert candidate(gas = [1, 6, 3, 4, 5, 6, 7, 8, 9, 10],cost = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 7\n assert candidate(gas = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],cost = [110, 9, 19, 29, 39, 49, 59, 69, 79, 89]) == -1\n assert candidate(gas = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],cost = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 9\n assert candidate(gas = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1],cost = [0, 0, 0, 0, 0, 0, 0, 0, 1, 0]) == 9\n assert candidate(gas = [2, 5, 7, 3, 8, 4, 6],cost = [6, 2, 4, 8, 7, 3, 5]) == 1\n assert candidate(gas = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15],cost = [14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14]) == 19\n assert candidate(gas = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],cost = [2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == -1\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],cost = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 5\n assert candidate(gas = [3, 2, 6, 5, 10, 1],cost = [6, 5, 4, 3, 1, 2]) == 4\n assert candidate(gas = [20, 20, 20, 20, 20],cost = [15, 15, 15, 15, 15]) == 4\n assert candidate(gas = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],cost = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 9\n assert candidate(gas = [2, 4, 5, 3, 1],cost = [3, 4, 3, 2, 2]) == 2\n assert candidate(gas = [3, 2, 6, 5, 4],cost = [2, 3, 4, 5, 3]) == 4\n assert candidate(gas = [20, 30, 10, 40, 50],cost = [35, 15, 25, 20, 40]) == 3\n assert candidate(gas = [8, 1, 3, 5, 2, 6, 7],cost = [7, 2, 5, 4, 1, 3, 6]) == 5\n assert candidate(gas = [50, 30, 10, 20, 40],cost = [30, 40, 15, 25, 30]) == 4\n assert candidate(gas = [5, 5, 5, 5, 5],cost = [4, 4, 4, 4, 4]) == 4\n assert candidate(gas = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],cost = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1]) == 14\n assert candidate(gas = [2, 3, 6, 5, 1, 3, 4],cost = [3, 4, 3, 1, 2, 4, 3]) == 3\n assert candidate(gas = [1, 3, 5, 7, 9],cost = [9, 7, 5, 3, 1]) == 3\n assert candidate(gas = [1000, 1000, 1000, 1000, 1000],cost = [999, 999, 999, 999, 5000]) == -1\n"}, "metadata": {"canonical_parameter_names": ["gas", "cost"], "leetcode_dataset_entry_point": "Solution().canCompleteCircuit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canCompleteCircuit = function(gas, cost) {", "container": null, "callable": "canCompleteCircuit", "parameters": [{"name": "gas", "type": "number[]"}, {"name": "cost", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 135, "task_id": "candy", "difficulty": "Hard", "problem_description": "There are n children standing in a line. Each child is assigned a rating value given in the integer array ratings.\nYou are giving candies to these children subjected to the following requirements:\n\nEach child must have at least one candy.\nChildren with a higher rating get more candies than their neighbors.\n\nReturn the minimum number of candies you need to have to distribute the candies to the children.\n \nExample 1:\n\nInput: ratings = [1,0,2]\nOutput: 5\nExplanation: You can allocate to the first, second and third child with 2, 1, 2 candies respectively.\n\nExample 2:\n\nInput: ratings = [1,2,2]\nOutput: 4\nExplanation: You can allocate to the first, second and third child with 1, 2, 1 candies respectively.\nThe third child gets 1 candy because it satisfies the above two conditions.\n\n \nConstraints:\n\nn == ratings.length\n1 <= n <= 2 * 104\n0 <= ratings[i] <= 2 * 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(ratings = [50, 40, 30, 20, 10]) == 15\n assert candidate(ratings = [1]) == 1\n assert candidate(ratings = [1, 3, 4, 5, 2]) == 11\n assert candidate(ratings = [1, 1, 1, 1]) == 4\n assert candidate(ratings = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 24\n assert candidate(ratings = [5, 4, 3, 2, 1]) == 15\n assert candidate(ratings = [10, 20, 30, 40, 50, 45, 35, 25, 15, 5]) == 31\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 66\n assert candidate(ratings = [1, 3, 2, 2, 3, 1]) == 8\n assert candidate(ratings = [1, 3, 4, 3, 2]) == 9\n assert candidate(ratings = [1, 6, 10, 8, 7, 3, 2]) == 18\n assert candidate(ratings = [10, 20, 30, 40, 50]) == 15\n assert candidate(ratings = [1, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 22\n assert candidate(ratings = [1, 1, 1, 1, 1]) == 5\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 55\n assert candidate(ratings = [1, 3, 2, 4, 5, 6]) == 13\n assert candidate(ratings = [1, 2, 2]) == 4\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(ratings = [1, 3, 2, 2, 1]) == 7\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 100\n assert candidate(ratings = [10, 20, 15, 10, 15, 20, 10]) == 13\n assert candidate(ratings = [1, 2, 3, 4, 5]) == 15\n assert candidate(ratings = [1, 0, 2]) == 5\n assert candidate(ratings = [1, 2, 3, 4, 5, 4, 3, 2, 1, 0]) == 31\n assert candidate(ratings = [1, 2, 2, 3, 3, 4, 5, 5, 6]) == 15\n assert candidate(ratings = [1, 6, 10, 8, 7, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 123\n assert candidate(ratings = [1, 2, 2, 2, 1, 2, 3, 2, 1]) == 15\n assert candidate(ratings = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6]) == 16\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 66\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 109\n assert candidate(ratings = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 19\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 55\n assert candidate(ratings = [1, 2, 2, 3, 2, 2, 3, 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 2]) == 26\n assert candidate(ratings = [10, 10, 10, 10, 10]) == 5\n assert candidate(ratings = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 8]) == 31\n assert candidate(ratings = [1, 2, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 48\n assert candidate(ratings = [1, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 84\n assert candidate(ratings = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 15\n assert candidate(ratings = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 259\n assert candidate(ratings = [1, 2, 2, 2, 1]) == 7\n assert candidate(ratings = [1, 3, 2, 2, 3, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 47\n assert candidate(ratings = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 33\n assert candidate(ratings = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10]) == 28\n assert candidate(ratings = [1, 3, 2, 2, 3, 1, 2, 3, 4, 3, 2, 1]) == 23\n assert candidate(ratings = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 124\n assert candidate(ratings = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(ratings = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == 45\n assert candidate(ratings = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == 60\n assert candidate(ratings = [1, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 57\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 100\n assert candidate(ratings = [3, 3, 3, 3, 3, 2, 1, 1, 2, 3, 3, 3, 3, 3, 4, 5, 4, 3, 2, 1]) == 37\n assert candidate(ratings = [10, 20, 10, 50, 20, 30, 10]) == 10\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 154\n assert candidate(ratings = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 210\n assert candidate(ratings = [5, 3, 8, 6, 7, 2, 4, 1]) == 12\n assert candidate(ratings = [1, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4]) == 66\n assert candidate(ratings = [1, 2, 2, 3, 3, 3, 2, 1]) == 13\n assert candidate(ratings = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 20\n assert candidate(ratings = [20, 19, 20, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 193\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10]) == 41\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 110\n assert candidate(ratings = [1, 2, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3]) == 90\n assert candidate(ratings = [5, 2, 3, 1, 4, 6, 1]) == 12\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == 69\n assert candidate(ratings = [1, 2, 2, 3, 3, 4, 4, 3, 2, 1, 1, 2, 3, 3, 4, 4]) == 29\n assert candidate(ratings = [3, 3, 3, 2, 1, 2, 3, 3, 3]) == 15\n assert candidate(ratings = [1, 2, 3, 4, 3, 2, 3, 4, 5, 6, 7]) == 33\n assert candidate(ratings = [5, 3, 8, 6, 7, 2, 4, 1]) == 12\n assert candidate(ratings = [1, 3, 2, 2, 3, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 43\n assert candidate(ratings = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 46\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 210\n assert candidate(ratings = [3, 2, 1, 4, 3, 5, 4, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 66\n assert candidate(ratings = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14]) == 22\n assert candidate(ratings = [1, 2, 2, 3, 3, 3, 2, 1, 2, 3, 4, 4, 3, 2, 1]) == 32\n assert candidate(ratings = [5, 4, 3, 2, 1, 2, 3, 4, 5]) == 29\n assert candidate(ratings = [1, 2, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == 28\n assert candidate(ratings = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 49\n assert candidate(ratings = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 109\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 225\n assert candidate(ratings = [1, 1, 1, 1, 1, 1, 1, 1, 1]) == 9\n assert candidate(ratings = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 21\n assert candidate(ratings = [7, 3, 5, 4, 6, 5, 4, 3, 5, 6, 7]) == 25\n assert candidate(ratings = [1, 3, 2, 2, 3, 1, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 72\n assert candidate(ratings = [5, 3, 8, 6, 7, 9, 2]) == 12\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 400\n assert candidate(ratings = [1, 2, 2, 2, 3, 4, 4, 3, 2, 1]) == 20\n assert candidate(ratings = [1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1]) == 38\n assert candidate(ratings = [10, 20, 15, 10, 5, 10, 20, 30, 25, 20, 15, 10, 5]) == 37\n assert candidate(ratings = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10]) == 28\n assert candidate(ratings = [1, 2, 3, 4, 3, 2, 3, 4, 5, 6, 5, 4, 5, 6, 7, 8, 7, 6, 7, 8, 9]) == 56\n assert candidate(ratings = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3]) == 38\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 36\n assert candidate(ratings = [3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 41\n assert candidate(ratings = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 106\n assert candidate(ratings = [1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4]) == 34\n assert candidate(ratings = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5]) == 16\n assert candidate(ratings = [1, 3, 2, 3, 1, 5, 2, 4, 1]) == 13\n assert candidate(ratings = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 21\n assert candidate(ratings = [5, 3, 4, 2, 1, 6, 7, 8, 9, 1]) == 24\n assert candidate(ratings = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6]) == 15\n assert candidate(ratings = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 10\n assert candidate(ratings = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == 56\n assert candidate(ratings = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == 60\n assert candidate(ratings = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == 26\n assert candidate(ratings = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3]) == 29\n assert candidate(ratings = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 29\n assert candidate(ratings = [5, 3, 1, 2, 5, 4, 3, 2, 1]) == 23\n assert candidate(ratings = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 48\n assert candidate(ratings = [1, 2, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 207\n assert candidate(ratings = [3, 2, 1, 4, 5, 6, 5, 4, 3, 2, 1]) == 32\n assert candidate(ratings = [1, 2, 3, 4, 5, 4, 3, 2, 1]) == 25\n assert candidate(ratings = [1, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == 12\n"}, "metadata": {"canonical_parameter_names": ["ratings"], "leetcode_dataset_entry_point": "Solution().candy", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var candy = function(ratings) {", "container": null, "callable": "candy", "parameters": [{"name": "ratings", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 136, "task_id": "single-number", "difficulty": "Easy", "problem_description": "Given a non-empty array of integers nums, every element appears twice except for one. Find that single one.\nYou must implement a solution with a linear runtime complexity and use only constant extra space.\n \nExample 1:\n\nInput: nums = [2,2,1]\nOutput: 1\n\nExample 2:\n\nInput: nums = [4,1,2,1,2]\nOutput: 4\n\nExample 3:\n\nInput: nums = [1]\nOutput: 1\n\n \nConstraints:\n\n1 <= nums.length <= 3 * 104\n-3 * 104 <= nums[i] <= 3 * 104\nEach element in the array appears twice except for one element which appears only once.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-1, 2, -1, -2, 2]) == -2\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [10, 1, 10, 2, 2]) == 1\n assert candidate(nums = [3, 3, 7, 7, 10]) == 10\n assert candidate(nums = [10, 10, 20, 20, 30]) == 30\n assert candidate(nums = [3, 3, 5, 7, 5, 7, 9]) == 9\n assert candidate(nums = [-1, -1, -2]) == -2\n assert candidate(nums = [100000, 100000, 50000]) == 50000\n assert candidate(nums = [5, 7, 5, 7, 9]) == 9\n assert candidate(nums = [3, 3, 2, 2, 5]) == 5\n assert candidate(nums = [2147483647, -2147483648, -2147483648, 2147483647, 0]) == 0\n assert candidate(nums = [0, 1, 0, 1, 2]) == 2\n assert candidate(nums = [100000, 100000, -100000]) == -100000\n assert candidate(nums = [100000, -100000, 100000]) == -100000\n assert candidate(nums = [0, 1, 0, 1, 99]) == 99\n assert candidate(nums = [2, 2, 1]) == 1\n assert candidate(nums = [4, 1, 2, 1, 2]) == 4\n assert candidate(nums = [100, 100, 200, 200, 300, 300, 400, 400, 500, 500, 600]) == 600\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == 21\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 1\n assert candidate(nums = [-1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8]) == -8\n assert candidate(nums = [100, 100, 200, 200, 300, 300, 400, 400, 500, 500, 600, 600, 700, 700, 800, 800, 900, 900, 1000, 1000, 1]) == 1\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15]) == 14\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 100]) == 100\n assert candidate(nums = [123, 123, 456, 456, 789, 789, 101, 101, 202, 202, 303, 303, 404]) == 404\n assert candidate(nums = [10, 20, 10, 30, 30, 50, 50]) == 20\n assert candidate(nums = [12345, 12345, 67890, 67890, 24680, 55555, 24680, 77777, 77777, 99999, 99999]) == 55555\n assert candidate(nums = [123456, 123456, 789012, 789012, 345678, 345678, 901234]) == 901234\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 10\n assert candidate(nums = [-10000, 10000, -10000, 20000, 20000, 30000, 30000]) == 10000\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20]) == 0\n assert candidate(nums = [100000, 100000, 200000, 200000, 300000, 300000, 400000]) == 400000\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 4\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16]) == 17\n assert candidate(nums = [10000, -10000, 10000, -10000, 20000, -20000, 20000, -20000, 30000]) == 30000\n assert candidate(nums = [-1000, 500, -1000, 500, 10000, 9999, 10000, 9999, 8888]) == 8888\n assert candidate(nums = [1000, 2000, 1000, 3000, 4000, 3000, 5000, 6000, 5000, 7000, 8000, 6000, 7000, 8000, 9000]) == 11096\n assert candidate(nums = [100, 100, 200, 200, 300, 300, 400, 400, 500, 500, 600, 600, 700, 700, 800, 800, 900, 900, 1000, 1000, 1100]) == 1100\n assert candidate(nums = [5, 7, 5, 7, 9, 10, 11, 11, 10, 12, 12, 13, 13, 14, 14, 15, 15]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8]) == 9\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21]) == 21\n assert candidate(nums = [-1, -2, -3, -4, -5, -1, -2, -3, -4, -5, 100000]) == 100000\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 20\n assert candidate(nums = [99999, 99999, 88888, 88888, 77777, 77777]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 0\n assert candidate(nums = [100000, 100000, -50000, -50000, 23456, 23456, 78901]) == 78901\n assert candidate(nums = [10000, 10000, 5000, 5000, 7, 7, 3, 3, 2]) == 2\n assert candidate(nums = [-1000, 1000, -1000, 2000, 2000, 3000, 3000, 4000]) == 3144\n assert candidate(nums = [-100, -100, -50, -50, 1, 1, 2, 2, 3, 3, 4]) == 4\n assert candidate(nums = [-1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7]) == -7\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13]) == 13\n assert candidate(nums = [5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == 10\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11]) == 11\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 1\n assert candidate(nums = [999, 999, 888, 888, 777, 777, 666, 666, 555, 555, 444, 444, 333, 333, 222, 222, 111, 111, 101]) == 101\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 15\n assert candidate(nums = [1000, 1000, 2000, 2000, 3000, 3000, 4000, 4000, 5000, 5000, 6000, 6000, 7000, 7000, 8000, 8000, 9000, 9000, 10000, 10000, 10001]) == 10001\n assert candidate(nums = [98765, 87654, 76543, 65432, 54321, 43210, 32109, 21098, 10987, 98765, 87654, 76543, 65432, 54321, 43210, 32109, 21098, 10987, 9876, 8765, 7654, 6543, 5432, 4321, 3210, 2109, 1098, 987, 876, 765, 654, 543, 432, 321, 210, 109, 98, 87, 76, 65, 54, 43, 32, 21, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1898\n assert candidate(nums = [9999, -9999, 8888, -8888, 7777, -7777, 6666, -6666, 5555]) == 5567\n assert candidate(nums = [0, 0, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7]) == 7\n assert candidate(nums = [3, 3, 7, 7, 5, 5, 2, 2, 8, 8, 4, 4, 6, 6, 9, 9, 1, 1, 11, 11, 10]) == 10\n assert candidate(nums = [-10000, -10000, -9999, -9999, -9998, -9998, 0]) == 0\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == 1\n assert candidate(nums = [-10000, -10000, 0, 0, 5000, 5000, 7000, 8000, 8000]) == 7000\n assert candidate(nums = [12345, -12345, 12345, -12345, 6789]) == 6789\n assert candidate(nums = [-30000, -30000, -20000, -20000, -10000, -10000, 0, 0, 10000]) == 10000\n assert candidate(nums = [100000, -100000, 100000, 200000, -200000, 200000, 300000, -300000, 300000, 400000]) == -768\n assert candidate(nums = [123, 456, 789, 123, 456, 789, 101112, -101112, -101112, 131415, 131415]) == 101112\n assert candidate(nums = [23456, 23456, 78901, 22222, 22222, 11111, 11111, 33333, 33333, 44444, 44444, 55555, 55555, 66666, 66666, 77777]) == 7140\n assert candidate(nums = [-1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -10]) == -10\n assert candidate(nums = [100000, 100000, 200000, 300000, 200000, 300000, 400000]) == 400000\n assert candidate(nums = [10, 20, 10, 20, 30, 40, 50, 40, 50, 60, 70, 60, 70]) == 30\n assert candidate(nums = [1, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == 8\n assert candidate(nums = [100000, 100000, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == 10\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50, 60]) == 60\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 2\n assert candidate(nums = [100000, -100000, 100000, -100000, 1]) == 1\n assert candidate(nums = [10, 20, 10, 2, 2, 30, 30]) == 20\n assert candidate(nums = [12345, -12345, 6789, -6789, 11111]) == 11111\n assert candidate(nums = [1234, 1234, 5678, 5678, 91011, 91011, 121314]) == 121314\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == 10\n assert candidate(nums = [100, 200, 300, 400, 500, 100, 200, 300, 400]) == 500\n assert candidate(nums = [-1, -1, -2, -2, -3, -3, -4, -4, -5]) == -5\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7]) == 7\n assert candidate(nums = [10, 10, 20, 20, 30, 30, 40, 40, 50, 50, 60, 60, 70, 70, 80, 80, 90, 90, 100, 100, 110]) == 110\n assert candidate(nums = [1000, 1000, 2000, 2000, 3000, 3000, 4000, 4000, 5000, 5000, 6000, 6000, 7000, 7000, 8000, 8000, 9000, 9000, 9999]) == 9999\n assert candidate(nums = [100000, 200000, 300000, 100000, 200000]) == 300000\n assert candidate(nums = [100000, 100000, 20000, 20000, 3000, 3000, 40]) == 40\n assert candidate(nums = [5, 7, 7, 5, 3, 9, 3, 8, 8, 6, 6]) == 9\n assert candidate(nums = [-30000, -30000, -29999, -29999, -29998, -29998, 0, 0, 1, 1, 2, 2, 3, 3]) == 0\n assert candidate(nums = [7, 7, 8, 8, 9, 9, 10, 10, 11]) == 11\n assert candidate(nums = [1000, 1000, 2000, 2000, 3000, 3000, 4000, 4000, 5000, 5000, 6000, 6000, 7000, 7000, 8000, 8000, 9000, 9000, 10000]) == 10000\n assert candidate(nums = [100, 200, 300, 100, 200, 300, 400]) == 400\n assert candidate(nums = [10, 20, 10, 20, 30, 30, 40]) == 40\n assert candidate(nums = [5, 7, 5, 7, 8, 8, 9, 10, 9, 10, 11]) == 11\n assert candidate(nums = [-1000, -1000, -2000, -2000, -3000, -3000, -4000, -4000, -5000, -5000, -6000]) == -6000\n assert candidate(nums = [1000, 2000, 3000, 1000, 4000, 2000, 5000, 3000, 4000]) == 5000\n assert candidate(nums = [9999, 8888, 7777, 6666, 5555, 4444, 3333, 2222, 1111, 0, 0, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888]) == 9999\n assert candidate(nums = [98765, 98765, 87654, 87654, 76543, 76543, 65432, 65432, 54321, 54321, 12345]) == 12345\n assert candidate(nums = [-1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -9]) == -9\n assert candidate(nums = [12345, 12345, 67890, 67890, -1, -1, -2, -2, -3, -3, 5]) == 5\n assert candidate(nums = [-100, -200, -100, -300, -200, -400, -300]) == -400\n assert candidate(nums = [12345, 67890, 12345, 67890, -11111, -22222, -11111, -33333, -22222, -33333, 44444]) == 44444\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6]) == 6\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().singleNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var singleNumber = function(nums) {", "container": null, "callable": "singleNumber", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 137, "task_id": "single-number-ii", "difficulty": "Medium", "problem_description": "Given an integer array nums where every element appears three times except for one, which appears exactly once. Find the single element and return it.\nYou must implement a solution with a linear runtime complexity and use only constant extra space.\n \nExample 1:\nInput: nums = [2,2,3,2]\nOutput: 3\nExample 2:\nInput: nums = [0,1,0,1,0,1,99]\nOutput: 99\n\n \nConstraints:\n\n1 <= nums.length <= 3 * 104\n-231 <= nums[i] <= 231 - 1\nEach element in nums appears exactly three times except for one element which appears once.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 7]) == 7\n assert candidate(nums = [-1, -1, -1, 100]) == 100\n assert candidate(nums = [-2, -2, -2, 1]) == 1\n assert candidate(nums = [1000000, 1000000, 1000000, 2000000]) == 2000000\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3]) == 3\n assert candidate(nums = [7, 7, 7, 10]) == 10\n assert candidate(nums = [4, 4, 4, 9]) == 9\n assert candidate(nums = [4, 1, 4, 4]) == 1\n assert candidate(nums = [1, 1, 1, 2]) == 2\n assert candidate(nums = [2, 2, 3, 2]) == 3\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 99]) == 99\n assert candidate(nums = [10, 10, 3, 10]) == 3\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3]) == 3\n assert candidate(nums = [-2, -2, -2, 3]) == 3\n assert candidate(nums = [1, 1, 1, 2, 3, 3, 3]) == 2\n assert candidate(nums = [-1, -1, -1, 2, 2, 2, 3]) == 3\n assert candidate(nums = [5, 5, 5, 100, 100, 100, -1]) == -1\n assert candidate(nums = [5, 5, 5, 3, 3, 3, 7, 7, 7, 9, 9, 9, 11]) == 11\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4]) == 4\n assert candidate(nums = [3, 3, 3, 10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40, 40, 50, 50, 50, 60]) == 60\n assert candidate(nums = [-1000000, -1000000, -1000000, 999999, 999999, 999999, 888888]) == 888888\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6]) == 6\n assert candidate(nums = [123456789, 123456789, 123456789, 987654321]) == 987654321\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 3\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8]) == 8\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 4]) == 4\n assert candidate(nums = [123456789, 123456789, 123456789, -987654321]) == -987654321\n assert candidate(nums = [0, 0, 0, 100, 100, 100, 200, 200, 200, 300, 300, 300, 400, 400, 400, 500]) == 500\n assert candidate(nums = [1, 1, 1, 1000000000, 2, 2, 2]) == 1000000000\n assert candidate(nums = [7, 7, 7, 8, 8, 8, 9, 9, 9, 10]) == 10\n assert candidate(nums = [-1, -2, -3, -1, -1, -2, -2, -3, -3, 0]) == 0\n assert candidate(nums = [-1, -1, -1, -2, -2, -2, -3, -3, -3, 5]) == 5\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 2000000000, 2000000000, 2000000000, 3000000000]) == -1294967296\n assert candidate(nums = [-2, -2, -2, 0, 0, 0, 1, 1, 1, 100, 100, 100, 99]) == 99\n assert candidate(nums = [-10, -10, -10, -20, -20, -20, -30]) == -30\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 4, 4, 4, 4, 4, 4]) == 4\n assert candidate(nums = [1000, 1000, 1000, 2000, 2000, 2000, 3000, 3000, 3000, 4000, 4000, 4000, 5000]) == 5000\n assert candidate(nums = [123, 123, 123, 456, 456, 456, 789, 789, 789, 101112, 101112, 101112, 131415]) == 131415\n assert candidate(nums = [-3, -3, -3, -5, -5, -5, -7, -7, -7, 1]) == 1\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10]) == 11\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4]) == 4\n assert candidate(nums = [2147483647, 2147483647, 2147483647, 0, 0, 0, -1]) == -1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11]) == 11\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8]) == 8\n assert candidate(nums = [4, 4, 4, 5, 5, 5, 6, 6, 6, 7]) == 7\n assert candidate(nums = [-2147483648, -2147483648, -2147483648, 0, 0, 0, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1000000000, 1000000000, 1000000000, 2]) == 2\n assert candidate(nums = [-1000000, -1000000, -1000000, 500000, 500000, 500000, 600000]) == 600000\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 3\n assert candidate(nums = [-100, -100, -100, -200, -200, -200, -300, -300, -300, 0]) == 0\n assert candidate(nums = [1000000, 1000000, 1000000, 2000000, 2000000, 2000000, 3000000, 3000000, 3000000, 4000000]) == 4000000\n assert candidate(nums = [1000000000, 1000000000, 1000000000, -1000000000, -1000000000, -1000000000, 123456789]) == 123456789\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8]) == 9\n assert candidate(nums = [-1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3]) == 3\n assert candidate(nums = [3, 3, 3, 1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]) == 0\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000001, 1000000001, 1000000001, 1000000002]) == 1000000002\n assert candidate(nums = [1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 5]) == 7\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5]) == 5\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 2147483647, 2147483647, 2147483647, -1]) == -1\n assert candidate(nums = [500000000, 500000000, 500000000, -500000000, -500000000, -500000000, 0]) == 0\n assert candidate(nums = [5, 5, 5, 7, 8, 8, 8, 9, 9, 9, 7, 7]) == 0\n assert candidate(nums = [-2147483648, -2147483648, -2147483648, 2147483647]) == 2147483647\n assert candidate(nums = [-5, -5, -5, -6, -6, -6, 7, 7, 7, 8]) == 8\n assert candidate(nums = [-2147483648, -2147483648, -2147483648, 0, 0, 0, 42]) == 42\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5]) == 5\n assert candidate(nums = [9, 9, 9, 8, 8, 8, 7, 7, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1]) == 1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, -3, -3, -3, 4]) == 4\n assert candidate(nums = [5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11]) == 11\n assert candidate(nums = [100, 100, 100, 200, 200, 200, 300, 300, 300, 400, 400, 400, 500]) == 500\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5]) == 5\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7]) == 7\n assert candidate(nums = [10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40, 40, 50]) == 50\n assert candidate(nums = [999999999, 999999999, 999999999, -999999999]) == -999999999\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10]) == 10\n assert candidate(nums = [7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11]) == 11\n assert candidate(nums = [10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40, 40, 50, 50, 50, 60, 60, 60, 70, 70, 70, 80, 80, 80, 90, 90, 90, 100]) == 100\n assert candidate(nums = [10, 20, 30, 10, 10, 20, 20, 30, 30, 40]) == 40\n assert candidate(nums = [999999999, 999999999, 999999999, 888888888, 888888888, 888888888, 777777777]) == 777777777\n assert candidate(nums = [5, 5, 5, 7, 7, 7, 9, 9, 9, 11, 11, 11, 13]) == 13\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9]) == 9\n assert candidate(nums = [15, 15, 15, 20, 20, 20, 25, 25, 25, 30, 30, 30, 35, 35, 35, 40]) == 40\n assert candidate(nums = [1000000000, 1000000000, 1000000000, -1000000000]) == -1000000000\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7]) == 7\n assert candidate(nums = [999999999, 999999999, 999999999, 1000000000, 1000000000, 1000000000, 1]) == 1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10]) == 10\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7]) == 7\n assert candidate(nums = [-100, -100, -100, -200, -200, -200, -300, -300, -300, -400, -400, -400, -500]) == -500\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10]) == 13\n assert candidate(nums = [-2, -2, -2, 0, 0, 0, 10, 10, 10, 20]) == 20\n assert candidate(nums = [30, 30, 30, 40, 40, 40, 50, 50, 50, 60, 60, 60, 70, 70, 70, 80, 80, 80, 90, 90, 90, 100]) == 100\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 5, 6, 5, 6, 5, 6, 7]) == 7\n assert candidate(nums = [-2147483648, -2147483648, -2147483648, 0, 1, 1, 1]) == 0\n assert candidate(nums = [-2147483648, -2147483648, -2147483648, 0, 0, 0, 2147483647]) == 2147483647\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5]) == 5\n assert candidate(nums = [7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21]) == 21\n assert candidate(nums = [2147483647, 2147483647, 2147483647, -2147483648, -2147483648, -2147483648, 1]) == 1\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 2147483647]) == 2147483647\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().singleNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var singleNumber = function(nums) {", "container": null, "callable": "singleNumber", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 139, "task_id": "word-break", "difficulty": "Medium", "problem_description": "Given a string s and a dictionary of strings wordDict, return true if s can be segmented into a space-separated sequence of one or more dictionary words.\nNote that the same word in the dictionary may be reused multiple times in the segmentation.\n \nExample 1:\n\nInput: s = \"leetcode\", wordDict = [\"leet\",\"code\"]\nOutput: true\nExplanation: Return true because \"leetcode\" can be segmented as \"leet code\".\n\nExample 2:\n\nInput: s = \"applepenapple\", wordDict = [\"apple\",\"pen\"]\nOutput: true\nExplanation: Return true because \"applepenapple\" can be segmented as \"apple pen apple\".\nNote that you are allowed to reuse a dictionary word.\n\nExample 3:\n\nInput: s = \"catsandog\", wordDict = [\"cats\",\"dog\",\"sand\",\"and\",\"cat\"]\nOutput: false\n\n \nConstraints:\n\n1 <= s.length <= 300\n1 <= wordDict.length <= 1000\n1 <= wordDict[i].length <= 20\ns and wordDict[i] consist of only lowercase English letters.\nAll the strings of wordDict are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"cars\",wordDict = ['car', 'ca', 'rs']) == True\n assert candidate(s = \"goals\",wordDict = ['go', 'goal', 'goals']) == True\n assert candidate(s = \"pineapplepenapple\",wordDict = ['apple', 'pen', 'applepen', 'pine', 'pineapple']) == True\n assert candidate(s = \"leetcode\",wordDict = ['leet', 'code']) == True\n assert candidate(s = \"applepenapple\",wordDict = ['apple', 'pen']) == True\n assert candidate(s = \"catsandog\",wordDict = ['cats', 'dog', 'sand', 'and', 'cat']) == False\n assert candidate(s = \"abcd\",wordDict = ['a', 'abc', 'b', 'cd']) == True\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragi', 'listic', 'expi', 'ali', 'docious']) == True\n assert candidate(s = \"skyscraper\",wordDict = ['sky', 'sc', 'raper', 'scra', 'per']) == True\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'wordbreak', 'breakproblem', 'wordbreakproblem', 'wordbreakpro', 'blem', 'wordprob', 'lem', 'wordb', 'reak', 'breakpro', 'brea', 'kprob', 'wordbre', 'akprob', 'wordbreakp', 'rob', 'reakp', 'reakpro', 'wordbre', 'reakproblem']) == True\n assert candidate(s = \"cascadingsubstrings\",wordDict = ['cascade', 'sub', 'strings', 'cascade', 'ing', 'substring']) == False\n assert candidate(s = \"breaktheglassceiling\",wordDict = ['break', 'the', 'glass', 'ceiling', 'breaks', 'theglass', 'ceiling']) == True\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",wordDict = ['a', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog']) == True\n assert candidate(s = \"abcdabcdabcd\",wordDict = ['a', 'ab', 'abc', 'abcd']) == True\n assert candidate(s = \"abcd\",wordDict = ['a', 'b', 'c', 'd', 'abc', 'bc', 'abcd', 'cd']) == True\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'pro', 'gram', 'wordbreak', 'breakprob']) == True\n assert candidate(s = \"aaaaaaaaaaaaaab\",wordDict = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == False\n assert candidate(s = \"interviewquestionsarehard\",wordDict = ['interview', 'questions', 'are', 'hard', 'inter', 'view', 'quest', 'ions', 'ques', 'tionsare', 'arehard']) == True\n assert candidate(s = \"mississippi\",wordDict = ['mis', 'is', 'sip', 'i', 'pi', 'p', 'mississipp', 'missis', 'miss', 'issi', 'ippi', 'ssippi', 'ssipp', 'ssip', 'ssips', 'ssip', 'issipi', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips', 'issip', 'issipp', 'issip', 'issips']) == True\n assert candidate(s = \"complexwordbreakproblem\",wordDict = ['complex', 'word', 'break', 'problem', 'wordbreak', 'breakprob', 'lem', 'prob', 'lemp', 'complexword']) == True\n assert candidate(s = \"mississippi\",wordDict = ['mis', 'issi', 'ppi', 'issip', 'ippi', 'missis', 'sip', 'pi', 'ssippi', 'is', 'ip', 'sipi', 'issipp', 'ippi', 'ippi', 'mississi', 'ppis', 'ippii', 'missi', 'mississipp', 'i', 'p', 'issippip', 'issiippi', 'mississippi']) == True\n assert candidate(s = \"abracadabra\",wordDict = ['abra', 'cad', 'abra', 'cadabra', 'ra', 'dab', 'ra', 'cadabra']) == True\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragilistic', 'expiali', 'docious', 'superca', 'li', 'fragi', 'listicex', 'piali', 'do']) == True\n assert candidate(s = \"abrakadabra\",wordDict = ['abra', 'kadabra', 'abra', 'ka', 'da', 'bra']) == True\n assert candidate(s = \"aabbccddeeff\",wordDict = ['aa', 'bb', 'cc', 'dd', 'ee', 'ff', 'abc', 'def', 'ef', 'fe', 'efg', 'gh', 'abcdefgh']) == True\n assert candidate(s = \"helplineshorthelpline\",wordDict = ['help', 'line', 'short', 'helpline']) == True\n assert candidate(s = \"leetleetcodeleet\",wordDict = ['leet', 'code', 'leetcode']) == True\n assert candidate(s = \"racecar\",wordDict = ['race', 'car', 'racec', 'arc', 'cec', 'er', 'c', 'ra', 'ec', 'ce']) == True\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab\",wordDict = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'ba']) == False\n assert candidate(s = \"mississippi\",wordDict = ['mis', 'sis', 'ip', 'is']) == False\n assert candidate(s = \"aaaaaaa\",wordDict = ['aa', 'aaa']) == True\n assert candidate(s = \"mississippi\",wordDict = ['mis', 'is', 'ip', 'i', 'ssip']) == False\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragilistic', 'expiali', 'docious', 'superfragilisticexpialidocious']) == True\n assert candidate(s = \"banana\",wordDict = ['ba', 'na', 'nan', 'ban', 'nana', 'an']) == True\n assert candidate(s = \"thisisatest\",wordDict = ['this', 'is', 'a', 'test', 'thisis', 'isatest']) == True\n assert candidate(s = \"abcdefgh\",wordDict = ['a', 'abc', 'abcd', 'efg', 'h']) == True\n assert candidate(s = \"abcdabcdeabcdabcde\",wordDict = ['abc', 'abcd', 'abcde', 'de', 'abcdabcde']) == True\n assert candidate(s = \"ababcabcabcabab\",wordDict = ['ab', 'abc', 'ababc', 'ababcabc', 'ababcabcabc', 'abab']) == True\n assert candidate(s = \"ababababab\",wordDict = ['ab', 'aba', 'bab', 'baba']) == True\n assert candidate(s = \"aaaaaaa\",wordDict = ['aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa']) == True\n assert candidate(s = \"dynamicprogramming\",wordDict = ['dynamic', 'programming', 'dyna', 'mic', 'prog', 'gram', 'ming']) == True\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",wordDict = ['a', 'quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog', 'aquick', 'brownfox', 'jump', 'sover', 'thelazy', 'zydog', 'quickbr', 'ownfo', 'xjump', 'soverth']) == True\n assert candidate(s = \"thisisaverylongstringthatisdifficulttobreak\",wordDict = ['this', 'is', 'a', 'very', 'long', 'string', 'that', 'is', 'difficult', 'to', 'break', 'avery', 'longstring', 'isdifficult']) == True\n assert candidate(s = \"aabbccddeeff\",wordDict = ['aa', 'bb', 'cc', 'dd', 'ee', 'ff', 'abc', 'def', 'ef', 'cd', 'ab', 'de', 'fe', 'bc', 'dc', 'ad', 'da', 'fb', 'bf', 'ba', 'ac', 'ca', 'ea', 'ae', 'be', 'eb']) == True\n assert candidate(s = \"programmingisfun\",wordDict = ['pro', 'gram', 'ming', 'is', 'fun', 'grammi', 'ngis', 'funny', 'progr', 'amming', 'isfun', 'ogramming', 'grammi', 'ngisfu', 'n']) == True\n assert candidate(s = \"mississippi\",wordDict = ['missi', 'pi', 'ssippi', 'issipi', 'ippi']) == True\n assert candidate(s = \"abcdefghij\",wordDict = ['a', 'ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij']) == True\n assert candidate(s = \"abcdefghijk\",wordDict = ['abc', 'def', 'ghi', 'jkl']) == False\n assert candidate(s = \"thefastbrownfoxjumpedoverthelazydog\",wordDict = ['the', 'fast', 'brown', 'fox', 'jumped', 'over', 'lazy', 'dog']) == True\n assert candidate(s = \"solutionsarefun\",wordDict = ['solution', 'solutions', 'are', 'fun', 'solu', 'tions', 'sol', 'u', 'n']) == True\n assert candidate(s = \"thelongestword\",wordDict = ['the', 'long', 'longest', 'word', 'lon', 'gest', 'longes', 'estword', 'longestwo', 'longestwo', 'longes', 'gestwo', 'est', 'wordwo', 'rdwo', 'rdo', 'wo', 'o']) == True\n assert candidate(s = \"bcbcbc\",wordDict = ['b', 'c', 'bc', 'cb']) == True\n assert candidate(s = \"programming\",wordDict = ['pro', 'gram', 'ming', 'gramm', 'ing', 'program']) == True\n assert candidate(s = \"xyzzyzyxzyzyzyzyxzyz\",wordDict = ['xyz', 'zyz', 'zx', 'zyxzy', 'zyzyz', 'zyzyzy']) == False\n assert candidate(s = \"theskyisblue\",wordDict = ['the', 'sky', 'is', 'blue', 'thesky', 'isblue', 'theskyisblue', 'theblue', 'theskyblue', 'blueis', 'isblue', 'blueisblue', 'theskyis']) == True\n assert candidate(s = \"mississippi\",wordDict = ['miss', 'issi', 'ssippi', 'ppi', 'ipi', 'i']) == True\n assert candidate(s = \"sheisbeautiful\",wordDict = ['she', 'is', 'beau', 'tiful', 'beauti', 'ful', 'be', 'auti', 'ful', 'ti', 'ful', 'shi', 'bea', 'autiful', 'sheis']) == True\n assert candidate(s = \"exampleexampleexampleexample\",wordDict = ['ex', 'ample', 'example', 'pleexam', 'ampleex']) == True\n assert candidate(s = \"abcdefgh\",wordDict = ['ab', 'abc', 'cd', 'efgh', 'abcd']) == True\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",wordDict = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yz', 'mnopqr', 'stuvwx', 'yzab', 'cdefghijklmnop', 'qrstuvwxyza', 'bcdefghijklmnopq', 'rstuvwxyzabcde']) == True\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragilistic', 'expiali', 'docious', 'superfragilistic']) == True\n assert candidate(s = \"ababababab\",wordDict = ['a', 'ab', 'aba', 'ababa']) == True\n assert candidate(s = \"thisisaverylongwordthatcanbebrokenintomultiplesubwords\",wordDict = ['this', 'is', 'a', 'very', 'long', 'word', 'that', 'can', 'be', 'broken', 'into', 'multiple', 'sub', 'words', 'averylong', 'bebroken']) == True\n assert candidate(s = \"interview\",wordDict = ['in', 'ter', 'view', 'int', 'ent', 'rview', 'terview', 'erview']) == True\n assert candidate(s = \"abcdefghij\",wordDict = ['ab', 'abc', 'cd', 'efg', 'hij', 'abcdefghij']) == True\n assert candidate(s = \"thisisatutorial\",wordDict = ['this', 'is', 'a', 'tu', 'torial', 'tuto', 'rial', 'ial', 'al']) == True\n assert candidate(s = \"abcdabcde\",wordDict = ['ab', 'cd', 'ef', 'de', 'abcde', 'abcd']) == True\n assert candidate(s = \"mississippi\",wordDict = ['mis', 'is', 'is', 'ppi', 'issi', 'ippi', 'pp', 'miss', 'mis', 'ippi']) == True\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab\",wordDict = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa']) == False\n assert candidate(s = \"findingthesolutionisfun\",wordDict = ['find', 'finding', 'the', 'solution', 'is', 'fun', 'solutions', 'funny']) == True\n assert candidate(s = \"thelongestword\",wordDict = ['the', 'long', 'longest', 'word', 'longestword', 'oneword', 'endword', 'word', 'one']) == True\n assert candidate(s = \"abcd\",wordDict = ['a', 'ab', 'abc', 'abcd', 'abcde']) == True\n assert candidate(s = \"xxyzzyyx\",wordDict = ['xy', 'xyz', 'zy', 'zyx', 'yx', 'xx', 'zz', 'zyxzyx']) == False\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragi', 'listic', 'expi', 'ali', 'docious', 'supercalifragilisticexpialidoci']) == True\n assert candidate(s = \"thelongestword\",wordDict = ['the', 'long', 'est', 'word', 'longest', 'estword', 'ongestwor', 'ngestwo', 'gestw', 'estwo', 'stwo', 'two', 'thelo', 'hello', 'world']) == True\n assert candidate(s = \"programmingisawesome\",wordDict = ['pro', 'gram', 'ming', 'is', 'awe', 'some', 'awesome', 'awe', 'so', 'me']) == True\n assert candidate(s = \"thecodecanbeanything\",wordDict = ['the', 'code', 'can', 'be', 'anything', 'any', 'thing']) == True\n assert candidate(s = \"a\",wordDict = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == True\n assert candidate(s = \"abcdabcd\",wordDict = ['ab', 'abcd', 'cd']) == True\n assert candidate(s = \"thisisaverylongstringthatshouldnotmatch\",wordDict = ['this', 'is', 'very', 'long', 'string', 'that', 'should', 'not', 'match']) == False\n assert candidate(s = \"programmingproblemsolver\",wordDict = ['pro', 'gram', 'ming', 'problem', 'problemsolver', 'solver']) == True\n assert candidate(s = \"aaaaaaa\",wordDict = ['aaa', 'aaaa', 'aa']) == True\n assert candidate(s = \"skilfullyskilled\",wordDict = ['skill', 'ful', 'ly', 'ski', 'lly', 'ed']) == False\n assert candidate(s = \"internationalization\",wordDict = ['inter', 'national', 'ization', 'inter', 'nationalization']) == True\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab\",wordDict = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == False\n assert candidate(s = \"abracadabra\",wordDict = ['abra', 'cad', 'bra', 'a', 'ab', 'rac']) == True\n assert candidate(s = \"complexstringwithwords\",wordDict = ['complex', 'string', 'with', 'words', 'complexstring', 'stringwith', 'withwords']) == True\n"}, "metadata": {"canonical_parameter_names": ["s", "wordDict"], "leetcode_dataset_entry_point": "Solution().wordBreak", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var wordBreak = function(s, wordDict) {", "container": null, "callable": "wordBreak", "parameters": [{"name": "s", "type": "string"}, {"name": "wordDict", "type": "string[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 140, "task_id": "word-break-ii", "difficulty": "Hard", "problem_description": "Given a string s and a dictionary of strings wordDict, add spaces in s to construct a sentence where each word is a valid dictionary word. Return all such possible sentences in any order.\nNote that the same word in the dictionary may be reused multiple times in the segmentation.\n \nExample 1:\n\nInput: s = \"catsanddog\", wordDict = [\"cat\",\"cats\",\"and\",\"sand\",\"dog\"]\nOutput: [\"cats and dog\",\"cat sand dog\"]\n\nExample 2:\n\nInput: s = \"pineapplepenapple\", wordDict = [\"apple\",\"pen\",\"applepen\",\"pine\",\"pineapple\"]\nOutput: [\"pine apple pen apple\",\"pineapple pen apple\",\"pine applepen apple\"]\nExplanation: Note that you are allowed to reuse a dictionary word.\n\nExample 3:\n\nInput: s = \"catsandog\", wordDict = [\"cats\",\"dog\",\"sand\",\"and\",\"cat\"]\nOutput: []\n\n \nConstraints:\n\n1 <= s.length <= 20\n1 <= wordDict.length <= 1000\n1 <= wordDict[i].length <= 10\ns and wordDict[i] consist of only lowercase English letters.\nAll the strings of wordDict are unique.\nInput is generated in a way that the length of the answer doesn't exceed 105.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aaaaaaa\",wordDict = ['aa', 'aaa']) == ['aa aa aaa', 'aa aaa aa', 'aaa aa aa']\n assert candidate(s = \"pineapplepenapple\",wordDict = ['apple', 'pen', 'applepen', 'pine', 'pineapple']) == ['pine apple pen apple', 'pine applepen apple', 'pineapple pen apple']\n assert candidate(s = \"a\",wordDict = ['a']) == ['a']\n assert candidate(s = \"catsanddog\",wordDict = ['cat', 'cats', 'and', 'sand', 'dog']) == ['cat sand dog', 'cats and dog']\n assert candidate(s = \"catsandog\",wordDict = ['cats', 'dog', 'sand', 'and', 'cat']) == []\n assert candidate(s = \"abcd\",wordDict = ['a', 'abc', 'b', 'cd']) == ['a b cd']\n assert candidate(s = \"leetcodeleet\",wordDict = ['leet', 'code']) == ['leet code leet']\n assert candidate(s = \"nevergonnagiveyouup\",wordDict = ['never', 'gonna', 'give', 'you', 'up', 'nevergonna', 'gonnagive', 'onnagive', 'nnagive', 'nagive', 'agive', 'giveu', 'giveyo', 'giveyou', 'giveyoup', 'giveyoupu', 'giveyoupup', 'youpup', 'oupup', 'pupup', 'upup', 'pup', 'up']) == ['never gonna give you up', 'never gonna giveyou up', 'never gonnagive you up', 'nevergonna give you up', 'nevergonna giveyou up']\n assert candidate(s = \"thisproblemisverydifficult\",wordDict = ['this', 'problem', 'is', 'very', 'difficult', 'difficul', 'icult']) == ['this problem is very difficult']\n assert candidate(s = \"exampleofquestion\",wordDict = ['example', 'of', 'question', 'ex', 'ample', 'que', 'stion', 'exam', 'ple', 'quest', 'uest', 'ion']) == ['ex ample of que stion', 'ex ample of quest ion', 'ex ample of question', 'exam ple of que stion', 'exam ple of quest ion', 'exam ple of question', 'example of que stion', 'example of quest ion', 'example of question']\n assert candidate(s = \"amazingrace\",wordDict = ['amazing', 'race', 'amaz', 'ing', 'zing', 'ace', 'rac']) == ['amaz ing race', 'amazing race']\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'wordbreak', 'breakprob', 'lem', 'pro', 'b', 'reak', 'prob', 'lem', 'wordbreakprob']) == ['word b reak pro b lem', 'word b reak prob lem', 'word b reak problem', 'word break pro b lem', 'word break prob lem', 'word break problem', 'word breakprob lem', 'wordbreak pro b lem', 'wordbreak prob lem', 'wordbreak problem', 'wordbreakprob lem']\n assert candidate(s = \"skyscraper\",wordDict = ['sky', 'scraper', 'sky', 'scrap', 'er']) == ['sky scrap er', 'sky scraper']\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'wordbreak', 'prob', 'lem']) == ['word break prob lem', 'word break problem', 'wordbreak prob lem', 'wordbreak problem']\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefgabcdefg\",wordDict = ['abc', 'defg', 'abcd', 'efgabc', 'abcdefg', 'fgabcde', 'abcde', 'bcdefg', 'def', 'abcfg']) == ['abc defg abc defg abc defg abc defg abc defg', 'abc defg abc defg abc defg abc defg abcdefg', 'abc defg abc defg abc defg abcd efgabc defg', 'abc defg abc defg abc defg abcdefg abc defg', 'abc defg abc defg abc defg abcdefg abcdefg', 'abc defg abc defg abcd efgabc defg abc defg', 'abc defg abc defg abcd efgabc defg abcdefg', 'abc defg abc defg abcdefg abc defg abc defg', 'abc defg abc defg abcdefg abc defg abcdefg', 'abc defg abc defg abcdefg abcd efgabc defg', 'abc defg abc defg abcdefg abcdefg abc defg', 'abc defg abc defg abcdefg abcdefg abcdefg', 'abc defg abcd efgabc defg abc defg abc defg', 'abc defg abcd efgabc defg abc defg abcdefg', 'abc defg abcd efgabc defg abcd efgabc defg', 'abc defg abcd efgabc defg abcdefg abc defg', 'abc defg abcd efgabc defg abcdefg abcdefg', 'abc defg abcdefg abc defg abc defg abc defg', 'abc defg abcdefg abc defg abc defg abcdefg', 'abc defg abcdefg abc defg abcd efgabc defg', 'abc defg abcdefg abc defg abcdefg abc defg', 'abc defg abcdefg abc defg abcdefg abcdefg', 'abc defg abcdefg abcd efgabc defg abc defg', 'abc defg abcdefg abcd efgabc defg abcdefg', 'abc defg abcdefg abcdefg abc defg abc defg', 'abc defg abcdefg abcdefg abc defg abcdefg', 'abc defg abcdefg abcdefg abcd efgabc defg', 'abc defg abcdefg abcdefg abcdefg abc defg', 'abc defg abcdefg abcdefg abcdefg abcdefg', 'abcd efgabc defg abc defg abc defg abc defg', 'abcd efgabc defg abc defg abc defg abcdefg', 'abcd efgabc defg abc defg abcd efgabc defg', 'abcd efgabc defg abc defg abcdefg abc defg', 'abcd efgabc defg abc defg abcdefg abcdefg', 'abcd efgabc defg abcd efgabc defg abc defg', 'abcd efgabc defg abcd efgabc defg abcdefg', 'abcd efgabc defg abcdefg abc defg abc defg', 'abcd efgabc defg abcdefg abc defg abcdefg', 'abcd efgabc defg abcdefg abcd efgabc defg', 'abcd efgabc defg abcdefg abcdefg abc defg', 'abcd efgabc defg abcdefg abcdefg abcdefg', 'abcdefg abc defg abc defg abc defg abc defg', 'abcdefg abc defg abc defg abc defg abcdefg', 'abcdefg abc defg abc defg abcd efgabc defg', 'abcdefg abc defg abc defg abcdefg abc defg', 'abcdefg abc defg abc defg abcdefg abcdefg', 'abcdefg abc defg abcd efgabc defg abc defg', 'abcdefg abc defg abcd efgabc defg abcdefg', 'abcdefg abc defg abcdefg abc defg abc defg', 'abcdefg abc defg abcdefg abc defg abcdefg', 'abcdefg abc defg abcdefg abcd efgabc defg', 'abcdefg abc defg abcdefg abcdefg abc defg', 'abcdefg abc defg abcdefg abcdefg abcdefg', 'abcdefg abcd efgabc defg abc defg abc defg', 'abcdefg abcd efgabc defg abc defg abcdefg', 'abcdefg abcd efgabc defg abcd efgabc defg', 'abcdefg abcd efgabc defg abcdefg abc defg', 'abcdefg abcd efgabc defg abcdefg abcdefg', 'abcdefg abcdefg abc defg abc defg abc defg', 'abcdefg abcdefg abc defg abc defg abcdefg', 'abcdefg abcdefg abc defg abcd efgabc defg', 'abcdefg abcdefg abc defg abcdefg abc defg', 'abcdefg abcdefg abc defg abcdefg abcdefg', 'abcdefg abcdefg abcd efgabc defg abc defg', 'abcdefg abcdefg abcd efgabc defg abcdefg', 'abcdefg abcdefg abcdefg abc defg abc defg', 'abcdefg abcdefg abcdefg abc defg abcdefg', 'abcdefg abcdefg abcdefg abcd efgabc defg', 'abcdefg abcdefg abcdefg abcdefg abc defg', 'abcdefg abcdefg abcdefg abcdefg abcdefg']\n assert candidate(s = \"anagramproblem\",wordDict = ['anagram', 'anagramprob', 'gram', 'prob', 'lem', 'problem', 'ana', 'gramprob', 'anag', 'ramprob', 'rampro', 'an', 'grampro', 'gramprob']) == ['ana gram prob lem', 'ana gram problem', 'ana gramprob lem', 'anag ramprob lem', 'anagram prob lem', 'anagram problem', 'anagramprob lem']\n assert candidate(s = \"amazingrace\",wordDict = ['amazing', 'race', 'amazingr', 'acer', 'age', 'maze', 'rang', 'racer', 'ace', 'zing']) == ['amazing race', 'amazingr ace']\n assert candidate(s = \"thisproblemiswaytoolongtobreakdownintosmallervariables\",wordDict = ['this', 'problem', 'is', 'way', 'too', 'long', 'to', 'be', 'broken', 'down', 'into', 'smaller', 'variables', 'break', 'down', 'small']) == ['this problem is way too long to break down into smaller variables']\n assert candidate(s = \"mississippi\",wordDict = ['mis', 'is', 'sip', 'issi', 'ppi', 'ippi', 'pi', 'pippi', 'miss', 'sipi']) == ['miss is sip pi', 'miss issi ppi']\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",wordDict = ['quick', 'brown', 'fox', 'jumps', 'over', 'the', 'lazy', 'dog', 'quickbrown', 'brownfox', 'jumpsover', 'overthe', 'the', 'lazydog']) == ['quick brown fox jumps over the lazy dog', 'quick brown fox jumps over the lazydog', 'quick brown fox jumps overthe lazy dog', 'quick brown fox jumps overthe lazydog', 'quick brown fox jumpsover the lazy dog', 'quick brown fox jumpsover the lazydog', 'quick brownfox jumps over the lazy dog', 'quick brownfox jumps over the lazydog', 'quick brownfox jumps overthe lazy dog', 'quick brownfox jumps overthe lazydog', 'quick brownfox jumpsover the lazy dog', 'quick brownfox jumpsover the lazydog', 'quickbrown fox jumps over the lazy dog', 'quickbrown fox jumps over the lazydog', 'quickbrown fox jumps overthe lazy dog', 'quickbrown fox jumps overthe lazydog', 'quickbrown fox jumpsover the lazy dog', 'quickbrown fox jumpsover the lazydog']\n assert candidate(s = \"abcd\",wordDict = ['a', 'ab', 'abc', 'abcd', 'b', 'bc', 'bcd', 'c', 'cd', 'd']) == ['a b c d', 'a b cd', 'a bc d', 'a bcd', 'ab c d', 'ab cd', 'abc d', 'abcd']\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'breakproblem', 'problem', 'wordbreak', 'breakpro', 'lem']) == ['word break problem', 'word breakproblem', 'wordbreak problem']\n assert candidate(s = \"amazingprogramminglanguage\",wordDict = ['amazing', 'programming', 'language', 'pro', 'gram', 'ming', 'amaz', 'ing', 'za', 'zing']) == ['amaz ing pro gram ming language', 'amaz ing programming language', 'amazing pro gram ming language', 'amazing programming language']\n assert candidate(s = \"programmingisfun\",wordDict = ['programming', 'is', 'fun', 'pro', 'gram', 'ming', 'gramming', 'isfun', 'progra']) == ['pro gram ming is fun', 'pro gram ming isfun', 'pro gramming is fun', 'pro gramming isfun', 'programming is fun', 'programming isfun']\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragi', 'listic', 'expi', 'ali', 'docious', 'supercal', 'ifragilisticexpi', 'alidocious', 'frag', 'listicexpialido', 'cious']) == ['super cali fragi listic expi ali docious', 'super cali fragi listic expi alidocious', 'super cali fragi listicexpialido cious', 'supercal ifragilisticexpi ali docious', 'supercal ifragilisticexpi alidocious']\n assert candidate(s = \"optimization\",wordDict = ['opt', 'im', 'iza', 'tio', 'n', 'on', 'optim', 'optimiz', 'optimiza', 'ization']) == ['opt im iza tio n', 'opt im ization', 'optim iza tio n', 'optim ization', 'optimiza tio n']\n assert candidate(s = \"theprogramminglanguage\",wordDict = ['the', 'pro', 'gram', 'ming', 'lan', 'guage']) == ['the pro gram ming lan guage']\n assert candidate(s = \"thisisatest\",wordDict = ['this', 'is', 'a', 'test', 'thisis', 'ate', 'st']) == ['this is a test', 'this is ate st', 'thisis a test', 'thisis ate st']\n assert candidate(s = \"backtrackingalgorithm\",wordDict = ['back', 'tracking', 'algorithm', 'backtrack', 'ingalgo', 'rithm', 'backtracki', 'ngalgor', 'thmalgo', 'rithmal', 'backtrac', 'kingalg', 'thm', 'algo', 'thmalgo', 'backtrackin', 'backtrackinga', 'backtrackingal', 'backtrackingalg', 'backtrackingalgo']) == ['back tracking algo rithm', 'back tracking algorithm', 'backtrack ingalgo rithm', 'backtrackingalgo rithm']\n assert candidate(s = \"thepinkquickbrownfoxjumpsoverthelazydog\",wordDict = ['the', 'pink', 'quick', 'brown', 'fox', 'jumps', 'over', 'lazy', 'dog', 'pinkquick', 'brownfox', 'overthe', 'lazydog']) == ['the pink quick brown fox jumps over the lazy dog', 'the pink quick brown fox jumps over the lazydog', 'the pink quick brown fox jumps overthe lazy dog', 'the pink quick brown fox jumps overthe lazydog', 'the pink quick brownfox jumps over the lazy dog', 'the pink quick brownfox jumps over the lazydog', 'the pink quick brownfox jumps overthe lazy dog', 'the pink quick brownfox jumps overthe lazydog', 'the pinkquick brown fox jumps over the lazy dog', 'the pinkquick brown fox jumps over the lazydog', 'the pinkquick brown fox jumps overthe lazy dog', 'the pinkquick brown fox jumps overthe lazydog', 'the pinkquick brownfox jumps over the lazy dog', 'the pinkquick brownfox jumps over the lazydog', 'the pinkquick brownfox jumps overthe lazy dog', 'the pinkquick brownfox jumps overthe lazydog']\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",wordDict = ['the', 'quick', 'brown', 'fox', 'jumps', 'over', 'lazy', 'dog', 'quickbrown', 'brownfox', 'foxjump', 'jumpsover', 'overthe', 'thelazy']) == ['the quick brown fox jumps over the lazy dog', 'the quick brown fox jumps over thelazy dog', 'the quick brown fox jumps overthe lazy dog', 'the quick brown fox jumpsover the lazy dog', 'the quick brown fox jumpsover thelazy dog', 'the quick brownfox jumps over the lazy dog', 'the quick brownfox jumps over thelazy dog', 'the quick brownfox jumps overthe lazy dog', 'the quick brownfox jumpsover the lazy dog', 'the quick brownfox jumpsover thelazy dog', 'the quickbrown fox jumps over the lazy dog', 'the quickbrown fox jumps over thelazy dog', 'the quickbrown fox jumps overthe lazy dog', 'the quickbrown fox jumpsover the lazy dog', 'the quickbrown fox jumpsover thelazy dog']\n assert candidate(s = \"sololeveltwo\",wordDict = ['sol', 'olev', 'el', 'elv', 'ello', 'lev', 'leve', 'vel', 'velt', 'velto', 'veltwo', 'o', 'l', 'v', 't', 'w', 'two', 'to', 'level', 'levelt', 'levelto', 'leveltwo']) == ['sol o lev el t w o', 'sol o lev el two', 'sol o leve l t w o', 'sol o leve l two', 'sol o level t w o', 'sol o level two', 'sol o levelt w o', 'sol o leveltwo', 'sol olev el t w o', 'sol olev el two']\n assert candidate(s = \"thisisjustasillywordtobreak\",wordDict = ['this', 'is', 'just', 'a', 'silly', 'word', 'to', 'break', 'sillyword', 'wordtobreak']) == ['this is just a silly word to break', 'this is just a silly wordtobreak', 'this is just a sillyword to break']\n assert candidate(s = \"thisisaverylongsentencethatweneedtosplit\",wordDict = ['this', 'is', 'a', 'very', 'long', 'sentence', 'that', 'we', 'need', 'to', 'split', 'verylong', 'sentencewe', 'needtos', 'tosplit', 'thisisavery']) == ['this is a very long sentence that we need to split', 'this is a very long sentence that we need tosplit', 'this is a verylong sentence that we need to split', 'this is a verylong sentence that we need tosplit', 'thisisavery long sentence that we need to split', 'thisisavery long sentence that we need tosplit']\n assert candidate(s = \"solvetheproblem\",wordDict = ['solve', 'the', 'problem', 'sol', 've', 'prob', 'lem', 'othe', 'probem', 'solvethe', 'heproblem']) == ['sol ve the prob lem', 'sol ve the problem', 'solve the prob lem', 'solve the problem', 'solvethe prob lem', 'solvethe problem']\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragilistic', 'expiali', 'docious', 'frag', 'ilisti', 'c', 'ex', 'piali', 'doc', 'io', 'us', 'superca', 'li', 'frag', 'listic', 'expi', 'ali', 'do', 'cious']) == ['super c ali frag ilisti c ex piali do c io us', 'super c ali frag ilisti c ex piali do cious', 'super c ali frag ilisti c ex piali doc io us', 'super c ali frag ilisti c ex piali docious', 'super c ali frag ilisti c expi ali do c io us', 'super c ali frag ilisti c expi ali do cious', 'super c ali frag ilisti c expi ali doc io us', 'super c ali frag ilisti c expi ali docious', 'super c ali frag ilisti c expiali do c io us', 'super c ali frag ilisti c expiali do cious', 'super c ali frag ilisti c expiali doc io us', 'super c ali frag ilisti c expiali docious', 'super c ali fragilistic ex piali do c io us', 'super c ali fragilistic ex piali do cious', 'super c ali fragilistic ex piali doc io us', 'super c ali fragilistic ex piali docious', 'super c ali fragilistic expi ali do c io us', 'super c ali fragilistic expi ali do cious', 'super c ali fragilistic expi ali doc io us', 'super c ali fragilistic expi ali docious', 'super c ali fragilistic expiali do c io us', 'super c ali fragilistic expiali do cious', 'super c ali fragilistic expiali doc io us', 'super c ali fragilistic expiali docious', 'super cali frag ilisti c ex piali do c io us', 'super cali frag ilisti c ex piali do cious', 'super cali frag ilisti c ex piali doc io us', 'super cali frag ilisti c ex piali docious', 'super cali frag ilisti c expi ali do c io us', 'super cali frag ilisti c expi ali do cious', 'super cali frag ilisti c expi ali doc io us', 'super cali frag ilisti c expi ali docious', 'super cali frag ilisti c expiali do c io us', 'super cali frag ilisti c expiali do cious', 'super cali frag ilisti c expiali doc io us', 'super cali frag ilisti c expiali docious', 'super cali fragilistic ex piali do c io us', 'super cali fragilistic ex piali do cious', 'super cali fragilistic ex piali doc io us', 'super cali fragilistic ex piali docious', 'super cali fragilistic expi ali do c io us', 'super cali fragilistic expi ali do cious', 'super cali fragilistic expi ali doc io us', 'super cali fragilistic expi ali docious', 'super cali fragilistic expiali do c io us', 'super cali fragilistic expiali do cious', 'super cali fragilistic expiali doc io us', 'super cali fragilistic expiali docious', 'superca li frag ilisti c ex piali do c io us', 'superca li frag ilisti c ex piali do cious', 'superca li frag ilisti c ex piali doc io us', 'superca li frag ilisti c ex piali docious', 'superca li frag ilisti c expi ali do c io us', 'superca li frag ilisti c expi ali do cious', 'superca li frag ilisti c expi ali doc io us', 'superca li frag ilisti c expi ali docious', 'superca li frag ilisti c expiali do c io us', 'superca li frag ilisti c expiali do cious', 'superca li frag ilisti c expiali doc io us', 'superca li frag ilisti c expiali docious', 'superca li fragilistic ex piali do c io us', 'superca li fragilistic ex piali do cious', 'superca li fragilistic ex piali doc io us', 'superca li fragilistic ex piali docious', 'superca li fragilistic expi ali do c io us', 'superca li fragilistic expi ali do cious', 'superca li fragilistic expi ali doc io us', 'superca li fragilistic expi ali docious', 'superca li fragilistic expiali do c io us', 'superca li fragilistic expiali do cious', 'superca li fragilistic expiali doc io us', 'superca li fragilistic expiali docious']\n assert candidate(s = \"leetcode\",wordDict = ['leet', 'code', 'le', 'et', 'code', 'cod', 'leetco']) == ['le et code', 'leet code']\n assert candidate(s = \"thelongestwordisinthisdictionary\",wordDict = ['the', 'longest', 'word', 'is', 'in', 'this', 'dictionary']) == ['the longest word is in this dictionary']\n assert candidate(s = \"backtracking\",wordDict = ['back', 'track', 'ing', 'backtrack', 'backtracking', 'tra', 'ck', 'bac', 'king']) == ['back tra ck ing', 'back track ing', 'backtrack ing', 'backtracking']\n assert candidate(s = \"thethreefishes\",wordDict = ['the', 'three', 'threefish', 'fish', 'fishes']) == ['the three fishes']\n assert candidate(s = \"abcd\",wordDict = ['a', 'b', 'c', 'd', 'ab', 'bc', 'cd', 'abcd']) == ['a b c d', 'a b cd', 'a bc d', 'ab c d', 'ab cd', 'abcd']\n assert candidate(s = \"canadaday\",wordDict = ['can', 'ada', 'day', 'canada', 'anada', 'aday']) == ['can ada day', 'canada day']\n assert candidate(s = \"ambiguityindictionary\",wordDict = ['ambi', 'biguity', 'in', 'dictionary', 'ambigui', 'tity', 'uity', 'amb', 'uityin', 'ityinden', 'uityindict', 'uityindicti', 'uityindiction', 'uityindictiona', 'uityindictionar', 'uityindictionary']) == []\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'wordbreak', 'pro', 'blem', 'wordbreakpro', 'breakpro', 'lemproblem']) == ['word break pro blem', 'word break problem', 'word breakpro blem', 'wordbreak pro blem', 'wordbreak problem', 'wordbreakpro blem']\n assert candidate(s = \"optimizethiscode\",wordDict = ['optimize', 'this', 'code', 'opt', 'imize', 'thisco', 'deopt', 'mizethis', 'ethiscode', 'optimizethis', 'opti', 'mize', 'thisc']) == ['opt imize this code', 'opti mize this code', 'opti mizethis code', 'optimize this code', 'optimizethis code']\n assert candidate(s = \"abababababababababababababab\",wordDict = ['aba', 'abab', 'ababa', 'bab', 'babab', 'bababa']) == ['aba bab aba bab aba bab aba bab abab', 'aba bab aba bab aba bab abab aba bab', 'aba bab aba bab aba bab ababa babab', 'aba bab aba bab aba babab aba babab', 'aba bab aba bab aba babab abab abab', 'aba bab aba bab aba babab ababa bab', 'aba bab aba bab aba bababa bab abab', 'aba bab aba bab abab aba bab aba bab', 'aba bab aba bab abab aba babab abab', 'aba bab aba bab abab aba bababa bab', 'aba bab aba bab abab abab aba babab', 'aba bab aba bab abab abab abab abab', 'aba bab aba bab abab abab ababa bab', 'aba bab aba bab abab ababa bab abab', 'aba bab aba bab ababa bab aba babab', 'aba bab aba bab ababa bab abab abab', 'aba bab aba bab ababa bab ababa bab', 'aba bab aba bab ababa babab aba bab', 'aba bab aba bab ababa bababa babab', 'aba bab aba babab aba bab aba babab', 'aba bab aba babab aba bab abab abab', 'aba bab aba babab aba bab ababa bab', 'aba bab aba babab aba babab aba bab', 'aba bab aba babab aba bababa babab', 'aba bab aba babab abab aba bab abab', 'aba bab aba babab abab abab aba bab', 'aba bab aba babab abab ababa babab', 'aba bab aba babab ababa bab aba bab', 'aba bab aba babab ababa babab abab', 'aba bab aba babab ababa bababa bab', 'aba bab aba bababa bab aba bab abab', 'aba bab aba bababa bab abab aba bab', 'aba bab aba bababa bab ababa babab', 'aba bab aba bababa babab aba babab', 'aba bab aba bababa babab abab abab', 'aba bab aba bababa babab ababa bab', 'aba bab aba bababa bababa bab abab', 'aba bab abab aba bab aba bab aba bab', 'aba bab abab aba bab aba babab abab', 'aba bab abab aba bab aba bababa bab', 'aba bab abab aba bab abab aba babab', 'aba bab abab aba bab abab abab abab', 'aba bab abab aba bab abab ababa bab', 'aba bab abab aba bab ababa bab abab', 'aba bab abab aba babab aba bab abab', 'aba bab abab aba babab abab aba bab', 'aba bab abab aba babab ababa babab', 'aba bab abab aba bababa bab aba bab', 'aba bab abab aba bababa babab abab', 'aba bab abab aba bababa bababa bab', 'aba bab abab abab aba bab aba babab', 'aba bab abab abab aba bab abab abab', 'aba bab abab abab aba bab ababa bab', 'aba bab abab abab aba babab aba bab', 'aba bab abab abab aba bababa babab', 'aba bab abab abab abab aba bab abab', 'aba bab abab abab abab abab aba bab', 'aba bab abab abab abab ababa babab', 'aba bab abab abab ababa bab aba bab', 'aba bab abab abab ababa babab abab', 'aba bab abab abab ababa bababa bab', 'aba bab abab ababa bab aba bab abab', 'aba bab abab ababa bab abab aba bab', 'aba bab abab ababa bab ababa babab', 'aba bab abab ababa babab aba babab', 'aba bab abab ababa babab abab abab', 'aba bab abab ababa babab ababa bab', 'aba bab abab ababa bababa bab abab', 'aba bab ababa bab aba bab aba babab', 'aba bab ababa bab aba bab abab abab', 'aba bab ababa bab aba bab ababa bab', 'aba bab ababa bab aba babab aba bab', 'aba bab ababa bab aba bababa babab', 'aba bab ababa bab abab aba bab abab', 'aba bab ababa bab abab abab aba bab', 'aba bab ababa bab abab ababa babab', 'aba bab ababa bab ababa bab aba bab', 'aba bab ababa bab ababa babab abab', 'aba bab ababa bab ababa bababa bab', 'aba bab ababa babab aba bab aba bab', 'aba bab ababa babab aba babab abab', 'aba bab ababa babab aba bababa bab', 'aba bab ababa babab abab aba babab', 'aba bab ababa babab abab abab abab', 'aba bab ababa babab abab ababa bab', 'aba bab ababa babab ababa bab abab', 'aba bab ababa bababa bab aba babab', 'aba bab ababa bababa bab abab abab', 'aba bab ababa bababa bab ababa bab', 'aba bab ababa bababa babab aba bab', 'aba bab ababa bababa bababa babab', 'aba babab aba bab aba bab aba babab', 'aba babab aba bab aba bab abab abab', 'aba babab aba bab aba bab ababa bab', 'aba babab aba bab aba babab aba bab', 'aba babab aba bab aba bababa babab', 'aba babab aba bab abab aba bab abab', 'aba babab aba bab abab abab aba bab', 'aba babab aba bab abab ababa babab', 'aba babab aba bab ababa bab aba bab', 'aba babab aba bab ababa babab abab', 'aba babab aba bab ababa bababa bab', 'aba babab aba babab aba bab aba bab', 'aba babab aba babab aba babab abab', 'aba babab aba babab aba bababa bab', 'aba babab aba babab abab aba babab', 'aba babab aba babab abab abab abab', 'aba babab aba babab abab ababa bab', 'aba babab aba babab ababa bab abab', 'aba babab aba bababa bab aba babab', 'aba babab aba bababa bab abab abab', 'aba babab aba bababa bab ababa bab', 'aba babab aba bababa babab aba bab', 'aba babab aba bababa bababa babab', 'aba babab abab aba bab aba bab abab', 'aba babab abab aba bab abab aba bab', 'aba babab abab aba bab ababa babab', 'aba babab abab aba babab aba babab', 'aba babab abab aba babab abab abab', 'aba babab abab aba babab ababa bab', 'aba babab abab aba bababa bab abab', 'aba babab abab abab aba bab aba bab', 'aba babab abab abab aba babab abab', 'aba babab abab abab aba bababa bab', 'aba babab abab abab abab aba babab', 'aba babab abab abab abab abab abab', 'aba babab abab abab abab ababa bab', 'aba babab abab abab ababa bab abab', 'aba babab abab ababa bab aba babab', 'aba babab abab ababa bab abab abab', 'aba babab abab ababa bab ababa bab', 'aba babab abab ababa babab aba bab', 'aba babab abab ababa bababa babab', 'aba babab ababa bab aba bab aba bab', 'aba babab ababa bab aba babab abab', 'aba babab ababa bab aba bababa bab', 'aba babab ababa bab abab aba babab', 'aba babab ababa bab abab abab abab', 'aba babab ababa bab abab ababa bab', 'aba babab ababa bab ababa bab abab', 'aba babab ababa babab aba bab abab', 'aba babab ababa babab abab aba bab', 'aba babab ababa babab ababa babab', 'aba babab ababa bababa bab aba bab', 'aba babab ababa bababa babab abab', 'aba babab ababa bababa bababa bab', 'aba bababa bab aba bab aba bab abab', 'aba bababa bab aba bab abab aba bab', 'aba bababa bab aba bab ababa babab', 'aba bababa bab aba babab aba babab', 'aba bababa bab aba babab abab abab', 'aba bababa bab aba babab ababa bab', 'aba bababa bab aba bababa bab abab', 'aba bababa bab abab aba bab aba bab', 'aba bababa bab abab aba babab abab', 'aba bababa bab abab aba bababa bab', 'aba bababa bab abab abab aba babab', 'aba bababa bab abab abab abab abab', 'aba bababa bab abab abab ababa bab', 'aba bababa bab abab ababa bab abab', 'aba bababa bab ababa bab aba babab', 'aba bababa bab ababa bab abab abab', 'aba bababa bab ababa bab ababa bab', 'aba bababa bab ababa babab aba bab', 'aba bababa bab ababa bababa babab', 'aba bababa babab aba bab aba babab', 'aba bababa babab aba bab abab abab', 'aba bababa babab aba bab ababa bab', 'aba bababa babab aba babab aba bab', 'aba bababa babab aba bababa babab', 'aba bababa babab abab aba bab abab', 'aba bababa babab abab abab aba bab', 'aba bababa babab abab ababa babab', 'aba bababa babab ababa bab aba bab', 'aba bababa babab ababa babab abab', 'aba bababa babab ababa bababa bab', 'aba bababa bababa bab aba bab abab', 'aba bababa bababa bab abab aba bab', 'aba bababa bababa bab ababa babab', 'aba bababa bababa babab aba babab', 'aba bababa bababa babab abab abab', 'aba bababa bababa babab ababa bab', 'aba bababa bababa bababa bab abab', 'abab aba bab aba bab aba bab aba bab', 'abab aba bab aba bab aba babab abab', 'abab aba bab aba bab aba bababa bab', 'abab aba bab aba bab abab aba babab', 'abab aba bab aba bab abab abab abab', 'abab aba bab aba bab abab ababa bab', 'abab aba bab aba bab ababa bab abab', 'abab aba bab aba babab aba bab abab', 'abab aba bab aba babab abab aba bab', 'abab aba bab aba babab ababa babab', 'abab aba bab aba bababa bab aba bab', 'abab aba bab aba bababa babab abab', 'abab aba bab aba bababa bababa bab', 'abab aba bab abab aba bab aba babab', 'abab aba bab abab aba bab abab abab', 'abab aba bab abab aba bab ababa bab', 'abab aba bab abab aba babab aba bab', 'abab aba bab abab aba bababa babab', 'abab aba bab abab abab aba bab abab', 'abab aba bab abab abab abab aba bab', 'abab aba bab abab abab ababa babab', 'abab aba bab abab ababa bab aba bab', 'abab aba bab abab ababa babab abab', 'abab aba bab abab ababa bababa bab', 'abab aba bab ababa bab aba bab abab', 'abab aba bab ababa bab abab aba bab', 'abab aba bab ababa bab ababa babab', 'abab aba bab ababa babab aba babab', 'abab aba bab ababa babab abab abab', 'abab aba bab ababa babab ababa bab', 'abab aba bab ababa bababa bab abab', 'abab aba babab aba bab aba bab abab', 'abab aba babab aba bab abab aba bab', 'abab aba babab aba bab ababa babab', 'abab aba babab aba babab aba babab', 'abab aba babab aba babab abab abab', 'abab aba babab aba babab ababa bab', 'abab aba babab aba bababa bab abab', 'abab aba babab abab aba bab aba bab', 'abab aba babab abab aba babab abab', 'abab aba babab abab aba bababa bab', 'abab aba babab abab abab aba babab', 'abab aba babab abab abab abab abab', 'abab aba babab abab abab ababa bab', 'abab aba babab abab ababa bab abab', 'abab aba babab ababa bab aba babab', 'abab aba babab ababa bab abab abab', 'abab aba babab ababa bab ababa bab', 'abab aba babab ababa babab aba bab', 'abab aba babab ababa bababa babab', 'abab aba bababa bab aba bab aba bab', 'abab aba bababa bab aba babab abab', 'abab aba bababa bab aba bababa bab', 'abab aba bababa bab abab aba babab', 'abab aba bababa bab abab abab abab', 'abab aba bababa bab abab ababa bab', 'abab aba bababa bab ababa bab abab', 'abab aba bababa babab aba bab abab', 'abab aba bababa babab abab aba bab', 'abab aba bababa babab ababa babab', 'abab aba bababa bababa bab aba bab', 'abab aba bababa bababa babab abab', 'abab aba bababa bababa bababa bab', 'abab abab aba bab aba bab aba babab', 'abab abab aba bab aba bab abab abab', 'abab abab aba bab aba bab ababa bab', 'abab abab aba bab aba babab aba bab', 'abab abab aba bab aba bababa babab', 'abab abab aba bab abab aba bab abab', 'abab abab aba bab abab abab aba bab', 'abab abab aba bab abab ababa babab', 'abab abab aba bab ababa bab aba bab', 'abab abab aba bab ababa babab abab', 'abab abab aba bab ababa bababa bab', 'abab abab aba babab aba bab aba bab', 'abab abab aba babab aba babab abab', 'abab abab aba babab aba bababa bab', 'abab abab aba babab abab aba babab', 'abab abab aba babab abab abab abab', 'abab abab aba babab abab ababa bab', 'abab abab aba babab ababa bab abab', 'abab abab aba bababa bab aba babab', 'abab abab aba bababa bab abab abab', 'abab abab aba bababa bab ababa bab', 'abab abab aba bababa babab aba bab', 'abab abab aba bababa bababa babab', 'abab abab abab aba bab aba bab abab', 'abab abab abab aba bab abab aba bab', 'abab abab abab aba bab ababa babab', 'abab abab abab aba babab aba babab', 'abab abab abab aba babab abab abab', 'abab abab abab aba babab ababa bab', 'abab abab abab aba bababa bab abab', 'abab abab abab abab aba bab aba bab', 'abab abab abab abab aba babab abab', 'abab abab abab abab aba bababa bab', 'abab abab abab abab abab aba babab', 'abab abab abab abab abab abab abab', 'abab abab abab abab abab ababa bab', 'abab abab abab abab ababa bab abab', 'abab abab abab ababa bab aba babab', 'abab abab abab ababa bab abab abab', 'abab abab abab ababa bab ababa bab', 'abab abab abab ababa babab aba bab', 'abab abab abab ababa bababa babab', 'abab abab ababa bab aba bab aba bab', 'abab abab ababa bab aba babab abab', 'abab abab ababa bab aba bababa bab', 'abab abab ababa bab abab aba babab', 'abab abab ababa bab abab abab abab', 'abab abab ababa bab abab ababa bab', 'abab abab ababa bab ababa bab abab', 'abab abab ababa babab aba bab abab', 'abab abab ababa babab abab aba bab', 'abab abab ababa babab ababa babab', 'abab abab ababa bababa bab aba bab', 'abab abab ababa bababa babab abab', 'abab abab ababa bababa bababa bab', 'abab ababa bab aba bab aba bab abab', 'abab ababa bab aba bab abab aba bab', 'abab ababa bab aba bab ababa babab', 'abab ababa bab aba babab aba babab', 'abab ababa bab aba babab abab abab', 'abab ababa bab aba babab ababa bab', 'abab ababa bab aba bababa bab abab', 'abab ababa bab abab aba bab aba bab', 'abab ababa bab abab aba babab abab', 'abab ababa bab abab aba bababa bab', 'abab ababa bab abab abab aba babab', 'abab ababa bab abab abab abab abab', 'abab ababa bab abab abab ababa bab', 'abab ababa bab abab ababa bab abab', 'abab ababa bab ababa bab aba babab', 'abab ababa bab ababa bab abab abab', 'abab ababa bab ababa bab ababa bab', 'abab ababa bab ababa babab aba bab', 'abab ababa bab ababa bababa babab', 'abab ababa babab aba bab aba babab', 'abab ababa babab aba bab abab abab', 'abab ababa babab aba bab ababa bab', 'abab ababa babab aba babab aba bab', 'abab ababa babab aba bababa babab', 'abab ababa babab abab aba bab abab', 'abab ababa babab abab abab aba bab', 'abab ababa babab abab ababa babab', 'abab ababa babab ababa bab aba bab', 'abab ababa babab ababa babab abab', 'abab ababa babab ababa bababa bab', 'abab ababa bababa bab aba bab abab', 'abab ababa bababa bab abab aba bab', 'abab ababa bababa bab ababa babab', 'abab ababa bababa babab aba babab', 'abab ababa bababa babab abab abab', 'abab ababa bababa babab ababa bab', 'abab ababa bababa bababa bab abab', 'ababa bab aba bab aba bab aba babab', 'ababa bab aba bab aba bab abab abab', 'ababa bab aba bab aba bab ababa bab', 'ababa bab aba bab aba babab aba bab', 'ababa bab aba bab aba bababa babab', 'ababa bab aba bab abab aba bab abab', 'ababa bab aba bab abab abab aba bab', 'ababa bab aba bab abab ababa babab', 'ababa bab aba bab ababa bab aba bab', 'ababa bab aba bab ababa babab abab', 'ababa bab aba bab ababa bababa bab', 'ababa bab aba babab aba bab aba bab', 'ababa bab aba babab aba babab abab', 'ababa bab aba babab aba bababa bab', 'ababa bab aba babab abab aba babab', 'ababa bab aba babab abab abab abab', 'ababa bab aba babab abab ababa bab', 'ababa bab aba babab ababa bab abab', 'ababa bab aba bababa bab aba babab', 'ababa bab aba bababa bab abab abab', 'ababa bab aba bababa bab ababa bab', 'ababa bab aba bababa babab aba bab', 'ababa bab aba bababa bababa babab', 'ababa bab abab aba bab aba bab abab', 'ababa bab abab aba bab abab aba bab', 'ababa bab abab aba bab ababa babab', 'ababa bab abab aba babab aba babab', 'ababa bab abab aba babab abab abab', 'ababa bab abab aba babab ababa bab', 'ababa bab abab aba bababa bab abab', 'ababa bab abab abab aba bab aba bab', 'ababa bab abab abab aba babab abab', 'ababa bab abab abab aba bababa bab', 'ababa bab abab abab abab aba babab', 'ababa bab abab abab abab abab abab', 'ababa bab abab abab abab ababa bab', 'ababa bab abab abab ababa bab abab', 'ababa bab abab ababa bab aba babab', 'ababa bab abab ababa bab abab abab', 'ababa bab abab ababa bab ababa bab', 'ababa bab abab ababa babab aba bab', 'ababa bab abab ababa bababa babab', 'ababa bab ababa bab aba bab aba bab', 'ababa bab ababa bab aba babab abab', 'ababa bab ababa bab aba bababa bab', 'ababa bab ababa bab abab aba babab', 'ababa bab ababa bab abab abab abab', 'ababa bab ababa bab abab ababa bab', 'ababa bab ababa bab ababa bab abab', 'ababa bab ababa babab aba bab abab', 'ababa bab ababa babab abab aba bab', 'ababa bab ababa babab ababa babab', 'ababa bab ababa bababa bab aba bab', 'ababa bab ababa bababa babab abab', 'ababa bab ababa bababa bababa bab', 'ababa babab aba bab aba bab aba bab', 'ababa babab aba bab aba babab abab', 'ababa babab aba bab aba bababa bab', 'ababa babab aba bab abab aba babab', 'ababa babab aba bab abab abab abab', 'ababa babab aba bab abab ababa bab', 'ababa babab aba bab ababa bab abab', 'ababa babab aba babab aba bab abab', 'ababa babab aba babab abab aba bab', 'ababa babab aba babab ababa babab', 'ababa babab aba bababa bab aba bab', 'ababa babab aba bababa babab abab', 'ababa babab aba bababa bababa bab', 'ababa babab abab aba bab aba babab', 'ababa babab abab aba bab abab abab', 'ababa babab abab aba bab ababa bab', 'ababa babab abab aba babab aba bab', 'ababa babab abab aba bababa babab', 'ababa babab abab abab aba bab abab', 'ababa babab abab abab abab aba bab', 'ababa babab abab abab ababa babab', 'ababa babab abab ababa bab aba bab', 'ababa babab abab ababa babab abab', 'ababa babab abab ababa bababa bab', 'ababa babab ababa bab aba bab abab', 'ababa babab ababa bab abab aba bab', 'ababa babab ababa bab ababa babab', 'ababa babab ababa babab aba babab', 'ababa babab ababa babab abab abab', 'ababa babab ababa babab ababa bab', 'ababa babab ababa bababa bab abab', 'ababa bababa bab aba bab aba babab', 'ababa bababa bab aba bab abab abab', 'ababa bababa bab aba bab ababa bab', 'ababa bababa bab aba babab aba bab', 'ababa bababa bab aba bababa babab', 'ababa bababa bab abab aba bab abab', 'ababa bababa bab abab abab aba bab', 'ababa bababa bab abab ababa babab', 'ababa bababa bab ababa bab aba bab', 'ababa bababa bab ababa babab abab', 'ababa bababa bab ababa bababa bab', 'ababa bababa babab aba bab aba bab', 'ababa bababa babab aba babab abab', 'ababa bababa babab aba bababa bab', 'ababa bababa babab abab aba babab', 'ababa bababa babab abab abab abab', 'ababa bababa babab abab ababa bab', 'ababa bababa babab ababa bab abab', 'ababa bababa bababa bab aba babab', 'ababa bababa bababa bab abab abab', 'ababa bababa bababa bab ababa bab', 'ababa bababa bababa babab aba bab', 'ababa bababa bababa bababa babab']\n assert candidate(s = \"abcdefgh\",wordDict = ['ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh']) == ['abcdefgh']\n assert candidate(s = \"elephant\",wordDict = ['ele', 'phant', 'lephant', 'el', 'phant', 'le', 'pha', 'nt', 'e', 'phantom', 'pha']) == ['e le pha nt', 'e le phant', 'e lephant', 'el e pha nt', 'el e phant', 'ele pha nt', 'ele phant']\n assert candidate(s = \"thelongwordthatshouldbreakdown\",wordDict = ['the', 'long', 'word', 'that', 'should', 'break', 'down', 'thelon', 'breakdo', 'wordtha', 'thatshoul', 'ouldbreak']) == ['the long word that should break down']\n assert candidate(s = \"thisisaverylongstringthatcanbebrokenintomultiplewordswithdictionary\",wordDict = ['this', 'is', 'a', 'very', 'long', 'string', 'that', 'can', 'be', 'broken', 'into', 'multiple', 'words', 'with', 'dictionary']) == ['this is a very long string that can be broken into multiple words with dictionary']\n assert candidate(s = \"solvetheproblem\",wordDict = ['solve', 'the', 'problem', 'solvethe', 'solvepro', 'prob', 'lem', 'prob', 'lempro', 'solvethepro', 'solvetheprob', 'solvetheproblem', 'sol', 'vel', 'ethe', 'prob', 'pro', 'lem', 'lempro', 'solvethepro', 'solvetheprob', 'solvetheproblem']) == ['solve the prob lem', 'solve the problem', 'solvethe prob lem', 'solvethe problem', 'solvetheprob lem', 'solvetheproblem']\n assert candidate(s = \"aquickbrownfox\",wordDict = ['a', 'quick', 'brown', 'fox', 'quickbrown', 'brownfox']) == ['a quick brown fox', 'a quick brownfox', 'a quickbrown fox']\n assert candidate(s = \"thisisatoyproblem\",wordDict = ['this', 'is', 'atoy', 'problem', 'isato', 'oyprob', 'lem', 'toy', 'prob', 'em', 'l', 'em', 'thisisato', 'oy', 'prob']) == ['this is atoy prob l em', 'this is atoy prob lem', 'this is atoy problem']\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",wordDict = ['the', 'quick', 'brown', 'fox', 'jumps', 'over', 'lazy', 'dog', 'thequick', 'brownfox', 'jumpsover', 'thelazy']) == ['the quick brown fox jumps over the lazy dog', 'the quick brown fox jumps over thelazy dog', 'the quick brown fox jumpsover the lazy dog', 'the quick brown fox jumpsover thelazy dog', 'the quick brownfox jumps over the lazy dog', 'the quick brownfox jumps over thelazy dog', 'the quick brownfox jumpsover the lazy dog', 'the quick brownfox jumpsover thelazy dog', 'thequick brown fox jumps over the lazy dog', 'thequick brown fox jumps over thelazy dog', 'thequick brown fox jumpsover the lazy dog', 'thequick brown fox jumpsover thelazy dog', 'thequick brownfox jumps over the lazy dog', 'thequick brownfox jumps over thelazy dog', 'thequick brownfox jumpsover the lazy dog', 'thequick brownfox jumpsover thelazy dog']\n assert candidate(s = \"abcd\",wordDict = ['a', 'b', 'c', 'd', 'ab', 'bc', 'cd', 'abcd', 'abc', 'bcd', 'ab', 'bc', 'a', 'd', 'abcd']) == ['a b c d', 'a b cd', 'a bc d', 'a bcd', 'ab c d', 'ab cd', 'abc d', 'abcd']\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'wordbreak', 'pro', 'blem']) == ['word break pro blem', 'word break problem', 'wordbreak pro blem', 'wordbreak problem']\n assert candidate(s = \"wordbreakproblem\",wordDict = ['word', 'break', 'problem', 'wordbreak', 'breakprob', 'lem', 'prob', 'lempro', 'breakpro', 'wordbreakpro', 'wordbreakprob', 'wordbreakproblem']) == ['word break prob lem', 'word break problem', 'word breakprob lem', 'wordbreak prob lem', 'wordbreak problem', 'wordbreakprob lem', 'wordbreakproblem']\n assert candidate(s = \"supercalifragilisticexpialidocious\",wordDict = ['super', 'cali', 'fragilistic', 'expiali', 'docious', 'cal', 'frag', 'ilis', 'tic', 'exp', 'expi', 'ali', 'do', 'cious']) == ['super cali frag ilis tic expi ali do cious', 'super cali frag ilis tic expi ali docious', 'super cali frag ilis tic expiali do cious', 'super cali frag ilis tic expiali docious', 'super cali fragilistic expi ali do cious', 'super cali fragilistic expi ali docious', 'super cali fragilistic expiali do cious', 'super cali fragilistic expiali docious']\n assert candidate(s = \"solvetheproblemrecursively\",wordDict = ['solve', 'the', 'problem', 'recursively', 'solvethe', 'problemre', 'cursivelysolve', 'solvetheproblem', 'theproblemis', 'solvetheproble', 'problemrecursively', 'theisproblem']) == ['solve the problem recursively', 'solve the problemrecursively', 'solvethe problem recursively', 'solvethe problemrecursively', 'solvetheproblem recursively']\n"}, "metadata": {"canonical_parameter_names": ["s", "wordDict"], "leetcode_dataset_entry_point": "Solution().wordBreak", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var wordBreak = function(s, wordDict) {", "container": null, "callable": "wordBreak", "parameters": [{"name": "s", "type": "string"}, {"name": "wordDict", "type": "string[]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 144, "task_id": "binary-tree-preorder-traversal", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, return the preorder traversal of its nodes' values.\n \nExample 1:\n\nInput: root = [1,null,2,3]\nOutput: [1,2,3]\nExplanation:\n\n\nExample 2:\n\nInput: root = [1,2,3,4,5,null,8,null,null,6,7,9]\nOutput: [1,2,4,5,6,7,3,8,9]\nExplanation:\n\n\nExample 3:\n\nInput: root = []\nOutput: []\n\nExample 4:\n\nInput: root = [1]\nOutput: [1]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 100].\n-100 <= Node.val <= 100\n\n \nFollow up: Recursive solution is trivial, could you do it iteratively?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5])) == [1, 2, 4, 3, 5]\n assert candidate(root = tree_node([1, None, None])) == [1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 8, None, None, 6, 7, 9])) == [1, 2, 4, 5, 6, 7, 3, 8, 9]\n assert candidate(root = tree_node([1, None, 3, None, 2])) == [1, 3, 2]\n assert candidate(root = tree_node([1, 2])) == [1, 2]\n assert candidate(root = tree_node([1, None, 2])) == [1, 2]\n assert candidate(root = tree_node([1, None, 2, 3])) == [1, 2, 3]\n assert candidate(root = tree_node([1])) == [1]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == [10, 5, 15, 6, 20]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 9])) == [10, 5, 3, 1, 7, 6, 9, 15, 18]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == [10, 5, 3, 7, 15, 18]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12])) == [1, 2, 4, 6, 8, 10, 12, 3, 5, 7, 9, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, None, None, None, None, 5, 6])) == [1, 2, 4, 3]\n assert candidate(root = tree_node([100, -50, 50, -100, 0, 49, 99, -150, None, -75, -25, -1, None, 5, None, None, 25, 75, 98, 100])) == [100, -50, -100, -150, 25, 0, -75, 75, 98, -25, 100, 50, 49, -1, 99, 5]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15])) == [8, 4, 2, 1, 3, 6, 5, 7, 12, 10, 9, 11, 14, 13, 15]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, None, 6, 7, None, None, 8, None, 9])) == [1, 2, 4, 6, 8, 7, 9, 3, 5]\n assert candidate(root = tree_node([3, None, 5, 4, 6, None, 7])) == [3, 5, 4, 7, 6]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [1, 2, 4, 8, 13, 9, 14, 5, 10, 15, 3, 6, 11, 7, 12]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, 6, None, 7, 8, None, 9, 10, None, 11])) == [1, 2, 3, 4, 5, 6, 7, 9, 11, 8, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, None, None, 6, 7, None, None, None, None, 8, 9])) == [1, 2, 4, 5, 6, 7, 3]\n assert candidate(root = tree_node([10, None, 20, None, 30, None, 40, 50, 60])) == [10, 20, 30, 40, 50, 60]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, 4, 6, 9, 11, 20])) == [10, 5, 3, 1, 4, 7, 6, 9, 15, 18, 11, 20]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20])) == [7, 3, 15, 9, 20]\n assert candidate(root = tree_node([8, 5, 12, 4, 6, 10, 14, 2, None, None, None, None, 11, None, 13])) == [8, 5, 4, 2, 6, 12, 10, 11, 14, 13]\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, None, None, None, 6, None, 7])) == [1, 2, 4, 3, 5, 6, 7]\n assert candidate(root = tree_node([1, None, 2, None, None, None, None, 3, None, 4, None, 5])) == [1, 2]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, 4])) == [1, 2]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 9, None, None, 12, None, None, None, None, None, 20])) == [10, 5, 3, 1, 12, 20, 7, 6, 9, 15, 18]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 4, 6, 8, 3, 5, 7, 9]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, None, None, 12, None, 22, 28])) == [20, 10, 5, 15, 12, 30, 25, 22, 28, 35]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 4, 6, 8, 10, 3, 5, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, None, None, 6, 7])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [1, 2, 4, 8, 16, 17, 9, 18, 19, 5, 10, 20, 11, 3, 6, 12, 13, 7, 14, 15]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, 10, 11, None, None, 12, None, None, 13, None, None, 14, None, None, 15])) == [1, 2, 4, 5, 8, 12, 15, 9, 13, 3, 6, 10, 11, 14, 7]\n assert candidate(root = tree_node([3, 1, 4, None, 2, None, None, None, None, 5])) == [3, 1, 2, 4]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [1, 2, 4, 8, 9, 5, 10, 11, 3, 6, 12, 13, 7, 14, 15]\n assert candidate(root = tree_node([100, -50, 200, -200, -100, 150, 300, -300, -150, -75, -25, 25, 75, 125, 175, 225, 275])) == [100, -50, -200, -300, 225, 275, -150, -100, -75, -25, 200, 150, 25, 75, 300, 125, 175]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == [10, 5, 3, 1, 7, 6, 15, 18]\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, None, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 4, 6, 8, 3, 5, 7, 9]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([5, 4, 7, 3, 8, 6, 9, 2, 11, 12, 13, 14, 15, 16, 17])) == [5, 4, 3, 2, 11, 8, 12, 13, 7, 6, 14, 15, 9, 16, 17]\n assert candidate(root = tree_node([3, 1, 2, None, None, None, 4, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(root = tree_node([0, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8])) == [0, -1, -2, -4, 5, 3, -5, 6, 2, -3, -6, 7, 4, -7, 8]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, 0, 2, 6, None, None, None, None, None, None, 10])) == [5, 3, 1, 0, 10, 2, 4, 6, 8, 7, 9]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, 4, None, 5, None, 6, None, 7])) == [1, 2]\n assert candidate(root = tree_node([-1, -2, None, -3, -4, -5])) == [-1, -2, -3, -5, -4]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == [1, 2, 4, 8, 9, 16, 17, 5, 10, 18, 19, 11, 20, 21, 3, 6, 12, 22, 23, 13, 24, 25, 7, 14, 15]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 15, 25, 35, 45, 55, 65, 75, 85])) == [50, 30, 20, 15, 25, 40, 35, 45, 70, 60, 55, 65, 80, 75, 85]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19, 20, None, 21, 22, 23, None, 24, 25, 26])) == [1, 2, 4, 8, 9, 16, 17, 5, 10, 18, 19, 11, 20, 3, 6, 12, 21, 22, 13, 23, 7, 14, 24, 25, 15, 26]\n assert candidate(root = tree_node([0, -1, 2, -2, None, 3, None, None, None, None, None, None, 4])) == [0, -1, -2, 2, 3]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [5, 1, 4, 3, 6]\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, 5, None, 6, 7, None, 8, 9, None, 10, None, 11, 12])) == [1, 2, 3, 4, 6, 8, 11, 9, 12, 5, 7, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, 8, 9])) == [1, 2, 4, 7, 5, 3, 6, 8, 9]\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [0, 1, 3, 7, 15, 16, 8, 17, 18, 4, 9, 19, 20, 10, 2, 5, 11, 12, 6, 13, 14]\n assert candidate(root = tree_node([2, 1, 3, None, None, 4, 5])) == [2, 1, 3, 4, 5]\n assert candidate(root = tree_node([100, -50, 150, -200, 0, 120, 200, -300, -100, -60, 90, 110, 160, 180, 220])) == [100, -50, -200, -300, -100, 0, -60, 90, 150, 120, 110, 160, 200, 180, 220]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, 1])) == [5, 3, 2, 1, 4, 6, 7]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6])) == [10, 5, 3, 1, 7, 6, 15, 13, 18]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, None, None, None, None, None, 10, 11])) == [1, 2, 4, 8, 10, 11, 9, 5, 3, 6, 7]\n assert candidate(root = tree_node([3, 1, 4, None, 2])) == [3, 1, 2, 4]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, None, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 4, 6, 8, 10, 3, 5, 7, 9]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, 4, None, 5])) == [1, 2]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, None, None, 6, 7, 8, 9, 10, 11])) == [1, 2, 4, 5, 6, 8, 9, 7, 10, 11, 3]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(root = tree_node([5, 4, 6, 2, 5, None, None, 1, None, 3])) == [5, 4, 2, 1, 5, 3, 6]\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 15, 25, None, None, 55, None, None, 75, 65, 85])) == [50, 30, 20, 15, 65, 85, 25, 40, 70, 60, 55, 80, 75]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4, None, None, None, None, 5])) == [1, 2]\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, 4, None, 5])) == [1, 2]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, None, None, None, None, None, None, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == [1, 2, 4, 8, 10, 13, 19, 20, 14, 21, 22, 9, 11, 15, 23, 24, 16, 25, 12, 17, 18, 5, 3, 6, 7]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, None, None, 6, None, 7])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([5, None, 10, None, 15, None, 20, None, 25])) == [5, 10, 15, 20, 25]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().preorderTraversal", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var preorderTraversal = function(root) {", "container": null, "callable": "preorderTraversal", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 145, "task_id": "binary-tree-postorder-traversal", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, return the postorder traversal of its nodes' values.\n \nExample 1:\n\nInput: root = [1,null,2,3]\nOutput: [3,2,1]\nExplanation:\n\n\nExample 2:\n\nInput: root = [1,2,3,4,5,null,8,null,null,6,7,9]\nOutput: [4,6,7,5,2,9,8,3,1]\nExplanation:\n\n\nExample 3:\n\nInput: root = []\nOutput: []\n\nExample 4:\n\nInput: root = [1]\nOutput: [1]\n\n \nConstraints:\n\nThe number of the nodes in the tree is in the range [0, 100].\n-100 <= Node.val <= 100\n\n \nFollow up: Recursive solution is trivial, could you do it iteratively?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([2, None, 1])) == [1, 2]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 8, None, None, 6, 7, 9])) == [4, 6, 7, 5, 2, 9, 8, 3, 1]\n assert candidate(root = tree_node([1, 2])) == [2, 1]\n assert candidate(root = tree_node([1, None, 2, 3])) == [3, 2, 1]\n assert candidate(root = tree_node([3, 1, 2])) == [1, 2, 3]\n assert candidate(root = tree_node([1])) == [1]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, 4, None, None, 5])) == [2, 1]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, None, 4])) == [2, 1]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == [5, 6, 20, 15, 10]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 9])) == [1, 3, 6, 9, 7, 5, 18, 15, 10]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == [3, 7, 5, 18, 15, 10]\n assert candidate(root = tree_node([1, None, 2, 3, 4])) == [3, 4, 2, 1]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, None, 5, None, None, None, 6])) == [5, 4, 3, 2, 1]\n assert candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13])) == [1, 4, 7, 6, 3, 13, 14, 10, 8]\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])) == [0, 3, 5, 4, 2, 7, 9, 8, 6]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15])) == [1, 3, 2, 5, 7, 6, 4, 9, 11, 10, 13, 15, 14, 12, 8]\n assert candidate(root = tree_node([9, 7, 20, 5, 8, None, None, 2, None, None, 11])) == [2, 5, 11, 8, 7, 20, 9]\n assert candidate(root = tree_node([1, 2, None, 3, None, None, 4, None, 5])) == [5, 4, 3, 2, 1]\n assert candidate(root = tree_node([5, 4, 6, 3, None, None, 7, 2, None, 1])) == [2, 3, 4, 1, 7, 6, 5]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9])) == [2, 4, 6, 8, 9, 7, 5, 3, 1]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, None, None, None, None, 5])) == [2, 4, 3, 1]\n assert candidate(root = tree_node([3, 1, 2, None, None, 4, 5])) == [1, 4, 5, 2, 3]\n assert candidate(root = tree_node([2, 1, 3, None, None, 4, None, None, None, 5])) == [1, 4, 3, 2]\n assert candidate(root = tree_node([8, 5, 1, 7, 10, 12])) == [7, 10, 5, 12, 1, 8]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, None, None, None, 6, None, 7, None, None, 8, None, None, 9, None, None, 10])) == [3, 5, 4, 2, 1]\n assert candidate(root = tree_node([5, 1, 6, None, 2, None, None, 3, 4])) == [3, 4, 2, 1, 6, 5]\n assert candidate(root = tree_node([9, 4, 13, 2, 6, 11, 16, 1, 3, 5, 7, 8, 10, 12, 14, 15])) == [15, 1, 3, 2, 5, 7, 6, 4, 8, 10, 11, 12, 14, 16, 13, 9]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6, None, None, 7, None, None, 8, None, None, 9, None, None, 10])) == [2, 1]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20])) == [3, 9, 20, 15, 7]\n assert candidate(root = tree_node([22, 11, 33, 5, 17, 27, 41, 2, 6, 14, 19, 25, 31, 37, 45, 1, 3, 4, 7, 10, 13, 16, 18, 21, 24, 26, 29, 32, 36, 38, 40, 43, 44, 46, 47])) == [43, 44, 1, 46, 47, 3, 2, 4, 7, 6, 5, 10, 13, 14, 16, 18, 19, 17, 11, 21, 24, 25, 26, 29, 31, 27, 32, 36, 37, 38, 40, 45, 41, 33, 22]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20, None, None, None, 30])) == [5, 6, 30, 20, 15, 10]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, None, 4, None, None, None, None, 5])) == [3, 2, 1]\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, None, 9, 10])) == [1, 2, 4, 3, 6, 9, 10, 8, 7, 5]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, None, 6, 7, None, None, None, None, 8, None, None, None, None, 9])) == [6, 7, 5, 3, 4, 2, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, 9, None, None, 10, 11, None, None, None, None, None, None, 12, 13, None, None, 14, 15, None, None, None, None, 16])) == [8, 4, 9, 5, 2, 6, 10, 12, 14, 15, 13, 11, 7, 3, 1]\n assert candidate(root = tree_node([7, 3, 15, None, None, None, 20])) == [3, 20, 15, 7]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [10, 8, 6, 4, 2, 9, 7, 5, 3, 1]\n assert candidate(root = tree_node([5, 4, 6, 3, 8, 7, 9])) == [3, 8, 4, 7, 9, 6, 5]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, None, None, 6, 7])) == [2, 4, 5, 3, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6])) == [4, 2, 5, 6, 3, 1]\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, None, 18, None, None, None, None, 22])) == [5, 10, 18, 20, 15, 30, 22, 40, 35, 25]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9])) == [8, 6, 4, 2, 9, 7, 5, 3, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [16, 17, 8, 18, 19, 9, 4, 20, 10, 11, 5, 2, 12, 13, 6, 14, 15, 7, 3, 1]\n assert candidate(root = tree_node([5, 3, 8, 1, None, None, 10, None, 2, None, None, 11])) == [11, 2, 1, 3, 10, 8, 5]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [8, 9, 4, 10, 11, 5, 2, 12, 13, 6, 14, 15, 7, 3, 1]\n assert candidate(root = tree_node([5, 3, 8, 2, 4, 6, 9, 1, 7, None, None, None, None, None, 10])) == [1, 7, 2, 4, 3, 6, 10, 9, 8, 5]\n assert candidate(root = tree_node([14, 9, 21, 7, 11, 17, 25, 5, 8, 10, 12, 15, 18, 23, 27, 3, 6, None, None, None, None, None, None, None, 13, None, None, None, 16, None, 19, None, 22, None, 26, None, 24, None, None, None, None, 20, None, None, None, None, None, 28])) == [28, 20, 22, 3, 26, 6, 5, 8, 7, 10, 12, 11, 9, 24, 13, 15, 18, 17, 16, 23, 19, 27, 25, 21, 14]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == [5, 4, 3, 2, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, 9, None, None, 10])) == [10, 7, 4, 8, 9, 5, 2, 6, 3, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [4, 5, 2, 6, 7, 3, 1]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [5, 4, 3, 2, 1]\n assert candidate(root = tree_node([17, 8, 26, 4, 13, 22, 31, 2, 6, 11, 15, 19, 24, 28, 34, 1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 32, 33, 35])) == [33, 35, 1, 3, 2, 5, 7, 6, 4, 9, 10, 11, 12, 14, 15, 13, 8, 16, 18, 19, 20, 23, 24, 22, 25, 27, 28, 29, 32, 34, 31, 26, 17]\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, 4])) == [2, 1]\n assert candidate(root = tree_node([15, 7, 23, 3, 11, 19, 27, 1, 5, 9, 13, 17, 21, 25, 29, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 31])) == [2, 4, 1, 6, 8, 5, 3, 10, 12, 9, 14, 16, 13, 11, 7, 18, 20, 17, 22, 24, 21, 19, 26, 28, 25, 30, 31, 29, 27, 23, 15]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4])) == [4, 3, 2, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, 16, None, 17, None, 18, None, 19])) == [16, 8, 17, 9, 4, 18, 10, 19, 11, 5, 2, 12, 13, 6, 14, 15, 7, 3, 1]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, None, 2, None, None, None, None, None, 10])) == [2, 1, 4, 3, 7, 10, 9, 8, 5]\n assert candidate(root = tree_node([7, 3, 15, None, None, None, 9])) == [3, 9, 15, 7]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5])) == [5, 3, 4, 2, 1]\n assert candidate(root = tree_node([25, 15, 30, 10, 20, 28, 35, 5, 12, 17, 22, 27, 33, 32, 36])) == [5, 12, 10, 17, 22, 20, 15, 27, 33, 28, 32, 36, 35, 30, 25]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 10, None, 2, 6, 9, 11])) == [2, 1, 6, 9, 4, 3, 11, 7, 10, 8, 5]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [7, 6, 5, 4, 3, 2, 1]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [1, 3, 6, 4, 5]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, None, 5])) == [5, 4, 3, 2, 1]\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 6, 7, None, 8, None, 9])) == [9, 7, 5, 2, 8, 6, 3, 1]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8, None, None, None, None, 9])) == [1, 3, 9, 6, 8, 7, 5, 18, 15, 10]\n assert candidate(root = tree_node([11, 7, 19, 3, 9, 13, 21, 1, 5, None, 8, None, 12, 17, None, None, None, None, None, 14, 16, 18, 20, 22, 23])) == [1, 5, 3, 14, 16, 8, 9, 7, 18, 20, 12, 13, 22, 23, 17, 21, 19, 11]\n assert candidate(root = tree_node([1, None, None, None, 2])) == [1]\n assert candidate(root = tree_node([1, None, None])) == [1]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, 4])) == [2, 1]\n assert candidate(root = tree_node([16, 8, 24, 4, 12, 20, 28, 2, 6, 10, 14, 18, 22, 26, 30, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31])) == [1, 3, 2, 5, 7, 6, 4, 9, 11, 10, 13, 15, 14, 12, 8, 17, 19, 18, 21, 23, 22, 20, 25, 27, 26, 29, 31, 30, 28, 24, 16]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 10, 0, 2, 6, 9, None, None, None, None, None, 11])) == [11, 0, 2, 1, 6, 9, 4, 3, 7, 10, 8, 5]\n assert candidate(root = tree_node([2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [7, 6, 5, 4, 3, 2]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == [6, 5, 4, 3, 2, 1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, None, 10, None, None, 11, None, None, 12, None, None, 13, None, None, 14])) == [8, 14, 12, 9, 4, 5, 2, 13, 10, 6, 11, 7, 3, 1]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, 4])) == [2, 1]\n assert candidate(root = tree_node([30, 25, 35, 20, 27, 32, 40, 18, None, None, 23, None, None, None, None, None, 45])) == [45, 18, 20, 23, 27, 25, 32, 40, 35, 30]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, 6])) == [5, 3, 6, 4, 2, 1]\n assert candidate(root = tree_node([30, 15, 45, 7, 22, 37, 52, 3, 11, 18, 26, 32, 41, 50, 57, 1, 2, 5, 6, 8, 9, 10, 12, 13, 16, 17, 19, 20, 23, 24, 25, 27, 28, 30, 31, 33, 35, 36, 39, 40, 42, 43, 44, 46, 47, 48, 49, 51, 53, 54, 55, 56, 58, 59])) == [27, 28, 1, 30, 31, 2, 3, 33, 35, 5, 36, 39, 6, 11, 7, 40, 42, 8, 43, 44, 9, 18, 46, 47, 10, 48, 49, 12, 26, 22, 15, 51, 53, 13, 54, 55, 16, 32, 56, 58, 17, 59, 19, 41, 37, 20, 23, 50, 24, 25, 57, 52, 45, 30]\n assert candidate(root = tree_node([7, 3, 15, 1, 5, 9, 20, None, None, 2, 6, None, None, 8, 12, None, 18])) == [1, 18, 2, 6, 5, 3, 9, 8, 12, 20, 15, 7]\n assert candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 5, 12, None, 17, 21, 24, 28, 35])) == [5, 12, 10, 17, 18, 15, 21, 24, 22, 28, 35, 30, 25, 20]\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7])) == [1, 3, 2, 5, 7, 6, 4]\n assert candidate(root = tree_node([3, 1, 2, 4, None, 5, 6, 7, None, 8, 9])) == [7, 4, 1, 8, 9, 5, 6, 2, 3]\n assert candidate(root = tree_node([3, 1, 2, 4])) == [4, 1, 2, 3]\n assert candidate(root = tree_node([8, 5, 12, 4, 6, 11, 13, 2, None, None, None, None, None, None, 14])) == [2, 4, 6, 5, 11, 14, 13, 12, 8]\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 17, 22, 28, 33, 38, 45, 3, 7, 9, 11, 14, 16, 18, 21, 23, 27, 29, 32, 36, 37, 39, 41, 44, 46])) == [44, 46, 3, 7, 5, 9, 11, 12, 10, 14, 16, 17, 18, 21, 22, 20, 15, 23, 27, 28, 29, 32, 33, 30, 36, 37, 38, 39, 41, 45, 40, 35, 25]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, None, 7, 8])) == [4, 7, 8, 5, 2, 6, 3, 1]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().postorderTraversal", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var postorderTraversal = function(root) {", "container": null, "callable": "postorderTraversal", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 147, "task_id": "insertion-sort-list", "difficulty": "Medium", "problem_description": "Given the head of a singly linked list, sort the list using insertion sort, and return the sorted list's head.\nThe steps of the insertion sort algorithm:\n\nInsertion sort iterates, consuming one input element each repetition and growing a sorted output list.\nAt each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list and inserts it there.\nIt repeats until no input elements remain.\n\nThe following is a graphical example of the insertion sort algorithm. The partially sorted list (black) initially contains only the first element in the list. One element (red) is removed from the input data and inserted in-place into the sorted list with each iteration.\n\n \nExample 1:\n\n\nInput: head = [4,2,1,3]\nOutput: [1,2,3,4]\n\nExample 2:\n\n\nInput: head = [-1,5,3,4,0]\nOutput: [-1,0,3,4,5]\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [1, 5000].\n-5000 <= Node.val <= 5000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0])), list_node([0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([10, -1, 0, 5, 3, 2, -5])), list_node([-5, -1, 0, 2, 3, 5, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([5, 2, 4, 6, 1, 3])), list_node([1, 2, 3, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([3, 1, 2, 1, 3, 1, 2])), list_node([1, 1, 1, 2, 2, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1000, 500, 250, 125, 62, 31, 15, 7, 3, 1])), list_node([1, 3, 7, 15, 31, 62, 125, 250, 500, 1000]))\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1000, 999, 998, 997, 996, 995, 994, 993, 992, 991])), list_node([991, 992, 993, 994, 995, 996, 997, 998, 999, 1000]))\n assert is_same_list(candidate(head = list_node([-1, 5, 3, 4, 0])), list_node([-1, 0, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([0, -1, -2, -3, -4])), list_node([-4, -3, -2, -1, 0]))\n assert is_same_list(candidate(head = list_node([-5000, 5000, -5000, 5000, 0])), list_node([-5000, -5000, 0, 5000, 5000]))\n assert is_same_list(candidate(head = list_node([4, 2, 1, 3])), list_node([1, 2, 3, 4]))\n assert is_same_list(candidate(head = list_node([100, 50, 25, 12, 6, 3, 1])), list_node([1, 3, 6, 12, 25, 50, 100]))\n assert is_same_list(candidate(head = list_node([4, 4, 4, 4, 4])), list_node([4, 4, 4, 4, 4]))\n assert is_same_list(candidate(head = list_node([5, 1, 4, 2, 3])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-5000, 5000, -4999, 4999])), list_node([-5000, -4999, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 2500, 0, -2500, 1250, -1250, 625, -625, 312, -312])), list_node([-5000, -2500, -1250, -625, -312, 0, 312, 625, 1250, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 0, 2500, -2500, 4000, -4000, 1000, -1000])), list_node([-5000, -4000, -2500, -1000, 0, 1000, 2500, 4000, 5000]))\n assert is_same_list(candidate(head = list_node([7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140])), list_node([7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140]))\n assert is_same_list(candidate(head = list_node([34, 22, 10, 19, 17, 26, 31, 44, 54, 20])), list_node([10, 17, 19, 20, 22, 26, 31, 34, 44, 54]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([23, 5, 67, 2, 34, 89, 12, 56, 3, 78])), list_node([2, 3, 5, 12, 23, 34, 56, 67, 78, 89]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 4999, -4999, 4998, -4998, 4997, -4997, 4996, -4996, 4995, -4995, 4994, -4994])), list_node([-5000, -4999, -4998, -4997, -4996, -4995, -4994, 4994, 4995, 4996, 4997, 4998, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([0, -1, -2, -3, -4, -5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5])), list_node([-5, -5, -4, -4, -3, -3, -2, -2, -1, -1, 0, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 2500, -2500, 1250, -1250])), list_node([-5000, -2500, -1250, 1250, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5])), list_node([1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5])), list_node([1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 4, 3, 2, 1, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5])), list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5])), list_node([-5, -4, -3, -2, -1, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([3, 1, 2, 5, 4, 6, 7, 8, 10, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 150, 250, 350, 450, 550])), list_node([100, 150, 200, 250, 300, 350, 400, 450, 500, 550]))\n assert is_same_list(candidate(head = list_node([2, 3, 5, 4, 1, 7, 6, 9, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991, -4990, -4989, -4988, -4987, -4986, -4985, -4984, -4983, -4982, -4981])), list_node([-5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991, -4990, -4989, -4988, -4987, -4986, -4985, -4984, -4983, -4982, -4981]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 3, 7, 9, 3, 3, 7, 2, 0, 7, 8, 1, 6, 4, 2, 1, 6, 1, 9, 9, 9, 4, 5, 3, 0, 7, 7, 2, 7])), list_node([0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 2, 1, 4, 5, 4, 3, 2, 1, 6, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7]))\n assert is_same_list(candidate(head = list_node([9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990])), list_node([9990, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 9999]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 2, 1, 3, 2, 1, 2, 1, 3, 2, 1, 2, 3, 2, 1, 3, 2, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 10, 20, 30, 40, 50, 60, 70, 80, 90, 1])), list_node([1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]))\n assert is_same_list(candidate(head = list_node([100, 50, 25, 12, 6, 3, 1, 0, -1, -2, -5, -10, -25, -50, -100])), list_node([-100, -50, -25, -10, -5, -2, -1, 0, 1, 3, 6, 12, 25, 50, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5]))\n assert is_same_list(candidate(head = list_node([5, 3, 8, 6, 2, 7, 4, 1, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([100, 200, 150, 175, 160, 180, 190, 140, 130, 120])), list_node([100, 120, 130, 140, 150, 160, 175, 180, 190, 200]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10, -10, 20, -20, 30, -30, 40, -40, 50, -50])), list_node([-50, -40, -30, -20, -10, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([0, 5000, -5000, 2500, -2500, 1250, -1250, 625, -625, 312, -312, 156, -156, 78, -78, 39, -39, 19, -19, 9, -9, 4, -4, 2, -2, 1, -1])), list_node([-5000, -2500, -1250, -625, -312, -156, -78, -39, -19, -9, -4, -2, -1, 0, 1, 2, 4, 9, 19, 39, 78, 156, 312, 625, 1250, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000])), list_node([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20])), list_node([-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5])), list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 2, 4, 6, 7, 8, 10, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([3, -1, 4, 1, 5, 9, -2, 6, 5, 3, 5])), list_node([-2, -1, 1, 3, 3, 4, 5, 5, 5, 6, 9]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 2500, -2500, 1250, -1250, 625, -625, 312, -312, 156, -156, 78, -78, 39, -39])), list_node([-5000, -2500, -1250, -625, -312, -156, -78, -39, 39, 78, 156, 312, 625, 1250, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([3, 1, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([5, 3, 4, 2, 6, 1, 7, 9, 8, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 11, -11, 12, -12, 13, -13, 14, -14, 15, -15])), list_node([-15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 50, 150, 250, 350, 450])), list_node([50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1, 2, 3, 4, 5])), list_node([1, 2, 3, 4, 5, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]))\n assert is_same_list(candidate(head = list_node([4, 1, 7, 3, 2, 6, 5, 8, 0, 9])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([-10, -20, 5, 3, -15, 7, 0])), list_node([-20, -15, -10, 0, 3, 5, 7]))\n assert is_same_list(candidate(head = list_node([5, 3, 8, 6, 2, 7, 4, 1, 10, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([23, 45, 12, 33, 5, 67, 4, 89, 21])), list_node([4, 5, 12, 21, 23, 33, 45, 67, 89]))\n assert is_same_list(candidate(head = list_node([10, 3, 1, 9, 2, 5, 8, 7, 6, 4])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25])), list_node([-25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 0, 2500, -2500, 1250, -1250, 625, -625, 312, -312])), list_node([-5000, -2500, -1250, -625, -312, 0, 312, 625, 1250, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])), list_node([-15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5])), list_node([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75])), list_node([75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]))\n assert is_same_list(candidate(head = list_node([-5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991, -4990, -4989, -4988, -4987, -4986, -4985])), list_node([-5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991, -4990, -4989, -4988, -4987, -4986, -4985]))\n assert is_same_list(candidate(head = list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981])), list_node([4981, 4982, 4983, 4984, 4985, 4986, 4987, 4988, 4989, 4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([3, 1, 2, 1, 3, 1, 2, 1, 3])), list_node([1, 1, 1, 1, 2, 2, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([2000, 1000, 500, 250, 125, 62, 31, 15, 7, 3, 1, -1, -3, -7, -15, -31, -62, -125, -250, -500, -1000, -2000])), list_node([-2000, -1000, -500, -250, -125, -62, -31, -15, -7, -3, -1, 1, 3, 7, 15, 31, 62, 125, 250, 500, 1000, 2000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1])), list_node([1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([3, 1, 2, 5, 4, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21])), list_node([1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]))\n assert is_same_list(candidate(head = list_node([100, 101, 99, 98, 102, 103, 97, 96, 104, 105])), list_node([96, 97, 98, 99, 100, 101, 102, 103, 104, 105]))\n assert is_same_list(candidate(head = list_node([5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985])), list_node([4985, 4986, 4987, 4988, 4989, 4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([5, 3, 1, 4, 2, 6, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 2500, -2500, 1250, -1250, 625, -625, 312, -312])), list_node([-5000, -2500, -1250, -625, -312, 312, 625, 1250, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5])), list_node([-5, -4, -3, -2, -1, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([-100, -200, -150, -175, -160, -180, -190, -140, -130, -120])), list_node([-200, -190, -180, -175, -160, -150, -140, -130, -120, -100]))\n assert is_same_list(candidate(head = list_node([5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981, 4980])), list_node([4980, 4981, 4982, 4983, 4984, 4985, 4986, 4987, 4988, 4989, 4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().insertionSortList", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var insertionSortList = function(head) {", "container": null, "callable": "insertionSortList", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 148, "task_id": "sort-list", "difficulty": "Medium", "problem_description": "Given the head of a linked list, return the list after sorting it in ascending order.\n \nExample 1:\n\n\nInput: head = [4,2,1,3]\nOutput: [1,2,3,4]\n\nExample 2:\n\n\nInput: head = [-1,5,3,4,0]\nOutput: [-1,0,3,4,5]\n\nExample 3:\n\nInput: head = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 5 * 104].\n-105 <= Node.val <= 105\n\n \nFollow up: Can you sort the linked list in O(n logn) time and O(1) memory (i.e. constant space)?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5])), list_node([-5, -4, -3, -2, -1, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0])), list_node([0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-1, 5, 3, 4, 0])), list_node([-1, 0, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0]))\n assert candidate(head = list_node([])) == None\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([100000, -100000, 0, 50000, -50000])), list_node([-100000, -50000, 0, 50000, 100000]))\n assert is_same_list(candidate(head = list_node([10, -10, 20, -20, 30, -30])), list_node([-30, -20, -10, 10, 20, 30]))\n assert is_same_list(candidate(head = list_node([-100000, 100000, -100000, 100000])), list_node([-100000, -100000, 100000, 100000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([100000, -100000, 0])), list_node([-100000, 0, 100000]))\n assert is_same_list(candidate(head = list_node([4, 2, 1, 3])), list_node([1, 2, 3, 4]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([5])), list_node([5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10])), list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([25000, 25001, 25002, 25003, 25004, 25005, 25006, 25007, 25008, 25009, 25010, 25011, 25012, 25013, 25014])), list_node([25000, 25001, 25002, 25003, 25004, 25005, 25006, 25007, 25008, 25009, 25010, 25011, 25012, 25013, 25014]))\n assert is_same_list(candidate(head = list_node([1000, 500, 250, 125, 62, 31, 15, 7, 3, 1])), list_node([1, 3, 7, 15, 31, 62, 125, 250, 500, 1000]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 3, 7, 2, 8, 6, 4, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([5, 3, 1, 4, 2, 7, 6, 9, 8, 10, 0, -1, -2, -3, -4, -5])), list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 950, 850, 750, 650, 550, 450, 350, 250, 150, 50])), list_node([50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000]))\n assert is_same_list(candidate(head = list_node([50000, -50000, 100000, -100000, 150000, -150000, 200000, -200000, 250000, -250000, 300000, -300000])), list_node([-300000, -250000, -200000, -150000, -100000, -50000, 50000, 100000, 150000, 200000, 250000, 300000]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([100000, 90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000, 0, -10000, -20000, -30000, -40000, -50000, -60000, -70000, -80000, -90000])), list_node([-90000, -80000, -70000, -60000, -50000, -40000, -30000, -20000, -10000, 0, 10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 2, 8, 3, 7, 4, 6, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([5, 1, 4, 2, 8, 3, 7, 6, 9, 10, 11, 12, 13, 14, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1000000, 100000, 10000, 1000, 100, 10, 1, 0, -1, -10, -100, -1000, -10000, -100000, -1000000])), list_node([-1000000, -100000, -10000, -1000, -100, -10, -1, 0, 1, 10, 100, 1000, 10000, 100000, 1000000]))\n assert is_same_list(candidate(head = list_node([5, 1, 4, 2, 8, 5, 1, 4, 2, 8])), list_node([1, 1, 2, 2, 4, 4, 5, 5, 8, 8]))\n assert is_same_list(candidate(head = list_node([-99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991, -99990])), list_node([-99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991, -99990]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 10, 100, 1000, 10000, 100000, -1, -10, -100, -1000, -10000, -100000])), list_node([-100000, -10000, -1000, -100, -10, -1, 1, 10, 100, 1000, 10000, 100000]))\n assert is_same_list(candidate(head = list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991, -99990])), list_node([-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991, -99990]))\n assert is_same_list(candidate(head = list_node([100000, 50000, 25000, 12500, 6250, 3125, 1562, 781, 390, 195, 97, 48, 24, 12, 6, 3, 1, -1, -3, -6, -12, -24, -48, -97, -195, -390, -781, -1562, -3125, -6250, -12500, -25000, -50000, -100000])), list_node([-100000, -50000, -25000, -12500, -6250, -3125, -1562, -781, -390, -195, -97, -48, -24, -12, -6, -3, -1, 1, 3, 6, 12, 24, 48, 97, 195, 390, 781, 1562, 3125, 6250, 12500, 25000, 50000, 100000]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([-100000, 100000, -99999, 99999, -99998, 99998, -99997, 99997, -99996, 99996, -99995, 99995])), list_node([-100000, -99999, -99998, -99997, -99996, -99995, 99995, 99996, 99997, 99998, 99999, 100000]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000])), list_node([100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 1, 2, 3, 4, 5])), list_node([1, 2, 3, 4, 5, 10, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 0, -1, 2, -2, 3, -3, 4, -4, 5])), list_node([-4, -3, -2, -1, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 0, -100, -200, -300, -400, -500, -600, -700, -800, -900, -1000])), list_node([-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]))\n assert is_same_list(candidate(head = list_node([1, 9, 2, 8, 3, 7, 4, 6, 5, 0])), list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990])), list_node([99990, 99991, 99992, 99993, 99994, 99995, 99996, 99997, 99998, 99999, 100000]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([5, 1, 9, 3, 7, 2, 8, 6, 4, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([50000, 50001, 50002, 50003, 50004, 49999, 49998, 49997, 49996, 49995])), list_node([49995, 49996, 49997, 49998, 49999, 50000, 50001, 50002, 50003, 50004]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9])), list_node([-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-1, 0, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([-50000, -40000, -30000, -20000, -10000, 0, 10000, 20000, 30000, 40000, 50000])), list_node([-50000, -40000, -30000, -20000, -10000, 0, 10000, 20000, 30000, 40000, 50000]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([23, 8, 45, 78, 1, 3, 89, 4, 2, 67, 43, 90, 12, 34, 56, 78, 9, 10, 21, 11, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 34, 43, 45, 56, 67, 78, 78, 89, 90]))\n assert is_same_list(candidate(head = list_node([100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]))\n assert is_same_list(candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9])), list_node([-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991])), list_node([-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991]))\n assert is_same_list(candidate(head = list_node([5, 2, 9, 1, 5, 6, 3, 8, 4, 7, 1, 5, 6, 3, 8, 4, 7])), list_node([1, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -15])), list_node([-15, -14, -12, -10, -8, -6, -4, -2, 1, 3, 5, 7, 9, 11, 13, 15]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 5, 4, 7, 6, 9, 8, 10, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 1, 20, 2, 30, 3, 40, 4, 50, 5, 60, 6, 70, 7, 80, 8, 90, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8])), list_node([-8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]))\n assert is_same_list(candidate(head = list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 20, 12, 19, 13, 18, 14, 17, 15, 16])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991])), list_node([99991, 99992, 99993, 99994, 99995, 99996, 99997, 99998, 99999, 100000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10000, 1000, 100, 10, 1, 0, -1, -10, -100, -1000, -10000])), list_node([-10000, -1000, -100, -10, -1, 0, 1, 10, 100, 1000, 10000]))\n assert is_same_list(candidate(head = list_node([10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981])), list_node([9981, 9982, 9983, 9984, 9985, 9986, 9987, 9988, 9989, 9990, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 9999, 10000]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991])), list_node([99991, 99992, 99993, 99994, 99995, 99996, 99997, 99998, 99999, 100000]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5])), list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991])), list_node([-100000, -99999, -99998, -99997, -99996, -99995, -99994, -99993, -99992, -99991]))\n assert is_same_list(candidate(head = list_node([2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 25])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5])), list_node([-5, -5, -5, -5, -5, -5, -5, -5, -5, -5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([5, -5, 10, -10, 15, -15, 20, -20, 25, -25, 30, -30])), list_node([-30, -25, -20, -15, -10, -5, 5, 10, 15, 20, 25, 30]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 5, 9, 13, 17, 2, 6, 10, 14, 18, 3, 7, 11, 15, 19, 4, 8, 12, 16, 20])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([9, 3, 7, 1, 5, 13, 11, 2, 6, 12, 8, 4, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().sortList", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var sortList = function(head) {", "container": null, "callable": "sortList", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 149, "task_id": "max-points-on-a-line", "difficulty": "Hard", "problem_description": "Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane, return the maximum number of points that lie on the same straight line.\n \nExample 1:\n\n\nInput: points = [[1,1],[2,2],[3,3]]\nOutput: 3\n\nExample 2:\n\n\nInput: points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]\nOutput: 4\n\n \nConstraints:\n\n1 <= points.length <= 300\npoints[i].length == 2\n-104 <= xi, yi <= 104\nAll the points are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5]]) == 6\n assert candidate(points = [[0, 0], [1, 1], [0, 1], [1, 0]]) == 2\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]]) == 6\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4]]) == 4\n assert candidate(points = [[1, 1], [2, 2], [2, 3], [3, 2], [3, 3]]) == 3\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 4], [4, 5], [5, 6], [7, 8]]) == 4\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 5\n assert candidate(points = [[-4, -4], [-8, -582], [-5, -26], [0, 3], [-1, 1], [0, -7], [1, -1], [5, 5], [-8, -6722], [-6, -576], [-6, -3608]]) == 2\n assert candidate(points = [[-1, -1], [2, 2], [3, 3]]) == 3\n assert candidate(points = [[1, 1], [1, 1], [1, 1]]) == 3\n assert candidate(points = [[1, 1], [3, 2], [5, 3], [4, 1], [2, 3], [1, 4]]) == 4\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 6\n assert candidate(points = [[1, 1]]) == 1\n assert candidate(points = [[1, 1], [2, 2], [3, 3]]) == 3\n assert candidate(points = [[0, 0], [1, 65536], [65536, 0], [65536, 65536], [0, 65536]]) == 3\n assert candidate(points = [[0, 0], [1, 1], [1, -1], [2, 2], [2, -2], [3, 3], [3, -3], [4, 4], [4, -4], [5, 5], [5, -5], [6, 6], [6, -6], [7, 7], [7, -7], [8, 8], [8, -8], [9, 9], [9, -9], [10, 10], [10, -10]]) == 11\n assert candidate(points = [[0, 0], [1, 65536], [65536, 1], [233, 233], [65536, 233], [233, 65536], [0, 1], [1, 0], [1, 2], [2, 1], [65535, 65535]]) == 3\n assert candidate(points = [[1, 1], [1, 1], [1, 1], [2, 2], [2, 2], [2, 2], [3, 3], [3, 3], [3, 3], [4, 4], [4, 4], [4, 4]]) == 12\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 5], [5, 7], [6, 9], [7, 11], [8, 13], [9, 15]]) == 7\n assert candidate(points = [[1, 1], [1, 6], [2, 2], [2, 7], [3, 3], [3, 8], [4, 4], [4, 9], [5, 5], [5, 10]]) == 5\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15], [1, 15], [2, 14], [3, 13], [4, 12], [5, 11], [6, 10], [7, 9], [8, 8], [9, 7], [10, 6], [11, 5], [12, 4], [13, 3], [14, 2], [15, 1]]) == 16\n assert candidate(points = [[-10000, -10000], [10000, 10000], [5000, 5000], [0, 0], [-5000, -5000]]) == 5\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15]]) == 15\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [5, 1], [6, 2], [7, 3], [8, 4], [9, 5], [1, 6], [2, 7], [3, 8], [4, 9]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 9\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0]]) == 10\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4]]) == 5\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [2, 1], [3, 2], [4, 3], [3, 1], [4, 2], [5, 3]]) == 3\n assert candidate(points = [[-10, -10], [0, 0], [10, 10], [20, 20], [30, 30], [40, 40], [50, 50]]) == 7\n assert candidate(points = [[-1, -2], [0, -1], [1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6]]) == 9\n assert candidate(points = [[1, 1], [2, 2], [3, 4], [5, 5], [6, 6], [7, 8], [9, 9], [10, 10], [11, 12], [13, 13], [14, 14], [15, 16], [17, 17], [18, 18], [19, 20], [21, 21], [22, 22], [23, 24], [25, 25], [26, 26], [27, 28]]) == 14\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9]]) == 5\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 6\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 5], [5, 8], [6, 11], [7, 14], [8, 17]]) == 5\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 1], [2, 2], [3, 3], [4, 4]]) == 5\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8]]) == 9\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]]) == 3\n assert candidate(points = [[1, 1], [1, 2], [2, 1], [2, 2], [3, 1], [3, 2], [4, 1], [4, 2], [5, 1], [5, 2], [6, 1], [6, 2]]) == 6\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [2, 2], [2, 4], [2, 6], [2, 8], [3, 3], [3, 6], [3, 9], [3, 12]]) == 4\n assert candidate(points = [[-10000, -10000], [10000, 10000], [5000, 5000], [-5000, -5000], [0, 0], [2500, 2500], [-2500, -2500], [7500, 7500], [-7500, -7500], [10000, -10000], [-10000, 10000]]) == 9\n assert candidate(points = [[1, 1], [1, 6], [2, 2], [2, 5], [3, 3], [3, 4], [4, 4], [4, 3], [5, 5], [5, 2], [6, 6], [6, 1]]) == 6\n assert candidate(points = [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]) == 10\n assert candidate(points = [[1, 1], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2]]) == 5\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 7\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11], [1, 12], [1, 13], [1, 14], [1, 15], [1, 16], [1, 17], [1, 18], [1, 19], [1, 20]]) == 20\n assert candidate(points = [[0, 0], [1, 1], [2, 3], [3, 6], [4, 10], [5, 15], [6, 21], [7, 28], [8, 36], [9, 45]]) == 2\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [2, 2], [3, 3], [4, 4], [5, 5]]) == 5\n assert candidate(points = [[-1, -1], [-2, -2], [-3, -3], [-4, -4], [-5, -5], [-6, -6], [-7, -7], [-8, -8], [-9, -9]]) == 9\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5]]) == 7\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 8\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [2, 1], [3, 1], [4, 1], [5, 1], [2, 2], [3, 2], [4, 2], [5, 2]]) == 5\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [5, 1], [6, 2], [7, 3], [8, 4], [9, 5]]) == 10\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [1, 0], [1, 1], [1, 2], [1, 3], [2, 0], [2, 1], [2, 2], [2, 3]]) == 4\n assert candidate(points = [[0, 0], [1, 1], [-1, -1], [2, 2], [-2, -2], [3, 3], [-3, -3], [4, 4], [-4, -4], [5, 5], [-5, -5]]) == 11\n assert candidate(points = [[1, 1], [2, 1], [1, 2], [2, 2], [3, 3], [3, 4], [4, 3], [4, 4], [5, 5], [5, 6]]) == 5\n assert candidate(points = [[10, 10], [20, 20], [30, 30], [40, 40], [50, 50], [60, 60], [70, 70], [80, 80], [90, 90]]) == 9\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16]]) == 15\n assert candidate(points = [[1, 1], [2, 3], [3, 5], [4, 7], [5, 9], [6, 11], [7, 13], [8, 15], [9, 17], [10, 19]]) == 10\n assert candidate(points = [[-100, 100], [0, 0], [100, -100], [50, 50], [75, 25], [25, 75], [0, 100], [100, 0]]) == 5\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 3], [2, 6], [3, 9], [4, 12], [5, 15]]) == 5\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9], [0, 10]]) == 11\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15], [16, 16], [17, 17], [18, 18], [19, 19], [20, 20]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]) == 7\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0]]) == 11\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 6], [2, 5], [3, 4], [4, 3], [5, 2], [6, 1], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 6\n assert candidate(points = [[1, 1], [2, 3], [3, 2], [4, 6], [5, 5], [6, 4], [7, 7], [8, 9], [9, 8]]) == 3\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [1, 9], [2, 8], [3, 7], [4, 6], [5, 5], [6, 4], [7, 3], [8, 2], [9, 1]]) == 10\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [2, 2], [2, 3], [2, 4], [3, 3], [3, 4], [4, 4]]) == 4\n assert candidate(points = [[1, 1], [1, 1], [1, 1], [1, 1], [2, 2], [2, 2], [2, 2], [2, 2], [3, 3], [3, 3]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10]]) == 8\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9]]) == 9\n assert candidate(points = [[1, 1], [1, 3], [1, 5], [1, 7], [1, 9], [2, 2], [2, 4], [2, 6], [2, 8], [2, 10]]) == 5\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [-4, 4], [-5, 5], [-6, 6], [-7, 7], [-8, 8], [-9, 9], [-10, 10]]) == 10\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12], [7, 14], [8, 16], [9, 18], [10, 20]]) == 10\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [2, 1], [2, 2], [2, 3], [2, 4], [3, 1], [3, 2], [3, 3], [3, 4]]) == 4\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 9\n assert candidate(points = [[0, 0], [1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12], [7, 14], [8, 16], [9, 18]]) == 10\n assert candidate(points = [[-5, -5], [0, 0], [5, 5], [10, 10], [15, 15], [20, 20], [25, 25], [30, 30], [35, 35], [40, 40]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12], [7, 14], [8, 16], [9, 18], [10, 20]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 5\n assert candidate(points = [[-10000, 10000], [10000, -10000], [0, 0], [5000, 5000], [-5000, -5000], [2000, 2000], [-2000, -2000], [3000, 3000], [-3000, -3000]]) == 7\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21]]) == 17\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == 10\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [0, 1], [1, 1], [2, 1], [0, 2], [1, 2], [2, 2]]) == 3\n assert candidate(points = [[-1000, -1000], [-1000, -999], [-1000, -998], [-1000, -997], [-1000, -996], [-1000, -995], [-1000, -994], [-1000, -993], [-1000, -992], [-1000, -991], [-1000, -990]]) == 11\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [1, 2], [2, 3]]) == 4\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 11\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [-4, 4], [-5, 5], [-6, 6], [-7, 7], [-8, 8], [-9, 9]]) == 9\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12]]) == 6\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0], [20, 0]]) == 21\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10]]) == 10\n assert candidate(points = [[1, 1], [1, 1], [1, 2], [1, 3], [2, 2], [2, 3], [3, 3], [3, 4], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == 14\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9]]) == 5\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 10\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]) == 6\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [0, 1], [1, 2], [2, 3], [3, 4]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [0, 1], [1, 1], [2, 1], [3, 1], [4, 1]]) == 5\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 6], [5, 5], [6, 8], [7, 7], [8, 10], [9, 9], [10, 12]]) == 6\n assert candidate(points = [[1, 1], [1, 1], [2, 2], [2, 2], [3, 3], [3, 3], [4, 4], [4, 4], [5, 5], [5, 5], [6, 6], [6, 6]]) == 12\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15], [16, 16], [17, 17], [18, 18], [19, 19]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 8\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 12]]) == 6\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [1, 0], [1, 1], [1, 2], [1, 3], [2, 0], [2, 1], [2, 2], [2, 3], [3, 0], [3, 1], [3, 2], [3, 3]]) == 4\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [5, 5], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11]]) == 10\n"}, "metadata": {"canonical_parameter_names": ["points"], "leetcode_dataset_entry_point": "Solution().maxPoints", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxPoints = function(points) {", "container": null, "callable": "maxPoints", "parameters": [{"name": "points", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 150, "task_id": "evaluate-reverse-polish-notation", "difficulty": "Medium", "problem_description": "You are given an array of strings tokens that represents an arithmetic expression in a Reverse Polish Notation.\nEvaluate the expression. Return an integer that represents the value of the expression.\nNote that:\n\nThe valid operators are '+', '-', '*', and '/'.\nEach operand may be an integer or another expression.\nThe division between two integers always truncates toward zero.\nThere will not be any division by zero.\nThe input represents a valid arithmetic expression in a reverse polish notation.\nThe answer and all the intermediate calculations can be represented in a 32-bit integer.\n\n \nExample 1:\n\nInput: tokens = [\"2\",\"1\",\"+\",\"3\",\"*\"]\nOutput: 9\nExplanation: ((2 + 1) * 3) = 9\n\nExample 2:\n\nInput: tokens = [\"4\",\"13\",\"5\",\"/\",\"+\"]\nOutput: 6\nExplanation: (4 + (13 / 5)) = 6\n\nExample 3:\n\nInput: tokens = [\"10\",\"6\",\"9\",\"3\",\"+\",\"-11\",\"*\",\"/\",\"*\",\"17\",\"+\",\"5\",\"+\"]\nOutput: 22\nExplanation: ((10 * (6 / ((9 + 3) * -11))) + 17) + 5\n= ((10 * (6 / (12 * -11))) + 17) + 5\n= ((10 * (6 / -132)) + 17) + 5\n= ((10 * 0) + 17) + 5\n= (0 + 17) + 5\n= 17 + 5\n= 22\n\n \nConstraints:\n\n1 <= tokens.length <= 104\ntokens[i] is either an operator: \"+\", \"-\", \"*\", or \"/\", or an integer in the range [-200, 200].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(tokens = ['4', '13', '5', '/', '+']) == 6\n assert candidate(tokens = ['2', '1', '+', '3', '*']) == 9\n assert candidate(tokens = ['10', '6', '9', '3', '+', '-11', '*', '/', '*', '17', '+', '5', '+']) == 22\n assert candidate(tokens = ['20', '5', '/', '2', '+', '10', '3', '/', '-', '3', '4', '*', '+', '2', '-', '1', '*']) == 13\n assert candidate(tokens = ['100', '50', '/', '3', '-', '2', '*', '4', '1', '+', '/', '5', '-', '2', '*']) == -10\n assert candidate(tokens = ['-10', '-3', '/', '2', '*']) == 6\n assert candidate(tokens = ['20', '5', '*']) == 100\n assert candidate(tokens = ['3', '-4', '+', '2', '*', '5', '/', '10', '+']) == 10\n assert candidate(tokens = ['8', '4', '+', '3', '*', '2', '/', '7', '-', '1', '+', '5', '*']) == 60\n assert candidate(tokens = ['17', '5', '+', '3', '8', '*', '-', '10', '2', '/', '+']) == 3\n assert candidate(tokens = ['10', '-5', '*', '2', '-', '3', '*']) == -156\n assert candidate(tokens = ['100', '50', '-', '20', '*', '2', '/', '3', '+', '5', '-', '6', '*', '7', '/', '8', '+', '9', '-']) == 425\n assert candidate(tokens = ['100', '50', '/', '20', '10', '/', '*', '30', '2', '*', '+']) == 64\n assert candidate(tokens = ['100', '-50', '/', '20', '-10', '/', '*']) == 4\n assert candidate(tokens = ['1', '2', '+', '3', '4', '+', '*', '5', '6', '+', '7', '8', '+', '*', '9', '10', '+', '*']) == 21\n assert candidate(tokens = ['8', '4', '*', '6', '2', '/', '-', '5', '+', '3', '2', '*']) == 34\n assert candidate(tokens = ['-10', '-5', '/', '2', '*', '-1', '+']) == 3\n assert candidate(tokens = ['8', '12', '+', '3', '/', '4', '*', '5', '2', '/', '-', '7', '+', '2', '*']) == 58\n assert candidate(tokens = ['1', '2', '+', '3', '4', '+', '*']) == 21\n assert candidate(tokens = ['3', '8', '2', '/', '+', '4', '*', '10', '5', '/', '-', '2', '*']) == 52\n assert candidate(tokens = ['20', '5', '+', '3', '*', '2', '-', '8', '/', '4', '*']) == 36\n assert candidate(tokens = ['5', '2', '/', '1', '+', '4', '*']) == 12\n assert candidate(tokens = ['7', '3', '+', '2', '*', '5', '-']) == 15\n assert candidate(tokens = ['8', '2', '/', '3', '4', '+', '*', '1', '5', '-', '*']) == -112\n assert candidate(tokens = ['20', '10', '/', '5', '*']) == 10\n assert candidate(tokens = ['1', '3', '2', '*', '+', '5', '-', '1', '2', '+', '/']) == 0\n assert candidate(tokens = ['10', '5', '2', '/', '+', '3', '-14', '*', '8', '/']) == 12\n assert candidate(tokens = ['-1', '3', '*', -1, '2', '+', '*', '4', '1', '-']) == -3\n assert candidate(tokens = ['10', '5', '+', '20', '-', '2', '/', '15', '*', '3', '-', '10', '/', '2', '+', '1', '-', '7', '*', '3', '/', '2', '*']) == -8\n assert candidate(tokens = ['12', '-3', '*', '4', '/', '8', '+', '2', '-', '5', '*', '-2', '/']) == 7\n assert candidate(tokens = ['5', '8', '4', '/', '+']) == 7\n assert candidate(tokens = ['10', '4', '2', '+', '*']) == 60\n assert candidate(tokens = ['10', '3', '5', '/', '2', '*', '+', '8', '3', '2', '*', '-', '4', '*', '2', '/', '+']) == 14\n assert candidate(tokens = ['12', '3', '*']) == 36\n assert candidate(tokens = ['17', '5', '+', '3', '*', '2', '-', '1', '+', '4', '/', '2', '*', '3', '+', '1', '-', '9', '/', '3', '*', '-11', '+', '-2', '*', '-3', '+', '17', '/', '5', '-', '7', '+', '-4', '*']) == -8\n assert candidate(tokens = ['18', '4', '-']) == 14\n assert candidate(tokens = ['10', '20', '+', '30', '*', '40', '+', '50', '*', '60', '-']) == 46940\n assert candidate(tokens = ['10', '-5', '*', '2', '+', '20', '-10', '/', '*', '3', '+', '2', '*']) == 198\n assert candidate(tokens = ['10', '20', '30', '40', '+', '*']) == 10\n assert candidate(tokens = ['8', '3', '-', '2', '1', '/', '*']) == 10\n assert candidate(tokens = ['9', '3', '+', '6', '2', '/', '-', '11', '*', '7', '/', '2', '+']) == 16\n assert candidate(tokens = ['1', '2', '3', '4', '+', '*', '5', '/']) == 1\n assert candidate(tokens = ['1', '2', '3', '+', '4', '/', '+', '5', '-', '6', '*']) == -18\n assert candidate(tokens = ['1', '1', '+', '1', '1', '+', '1', '1', '+', '1', '1', '+', '1', '1', '+']) == 2\n assert candidate(tokens = ['-7', '3', '/', '2', '-3', '*']) == -2\n assert candidate(tokens = ['9', '3', '+', '6', '2', '/', '*']) == 36\n assert candidate(tokens = ['9', '3', '-', '4', '/', '8', '2', '*', '+', '6', '1', '-', '*', '3', '+', '5', '-', '11', '/']) == 7\n assert candidate(tokens = ['7', '-8', '*', '2', '/', '3', '+', '1', '-', '5', '11', '+', '2', '/', '*', '4', '-']) == -212\n assert candidate(tokens = ['100', '50', '+', '25', '-', '10', '*', '5', '/']) == 250\n assert candidate(tokens = ['7', '-3', '*', '2', '1', '+', '*', '5', '-', '3', '+', '2', '*']) == -130\n assert candidate(tokens = ['10', '3', '/', '5', '+', '-3', '*', '7', '2', '/', '+', '8', '-', '2', '*', '3', '+', '6', '-', '4', '/', '9', '+', '11', '-', '13', '*', '15', '/', '17', '+', '19', '-']) == -16\n assert candidate(tokens = ['5', '8', '4', '2', '+', '*']) == 5\n assert candidate(tokens = ['5', '3', '+', '2', '*', '8', '4', '/', '-']) == 14\n assert candidate(tokens = ['-1', '-2', '*']) == 2\n assert candidate(tokens = ['15', '7', '1', '1', '+', '-', '3', '/', '2', '1', '1', '+', '+', '-']) == 15\n assert candidate(tokens = ['20', '4', '/', '5', '2', '*', '+']) == 15\n assert candidate(tokens = ['8', '4', '+', '2', '/', '3', '*', '1', '+', '6', '-']) == 13\n assert candidate(tokens = ['9', '3', '/', '2', '1', '+', '*']) == 9\n assert candidate(tokens = ['18', '7', '+', '3', '-', '1', '*', '2', '+', '5', '/', '9', '+', '1', '+', '-11', '*', '13', '-', '5', '+', '9', '+', '15', '+', '1', '-', '7', '*', '8', '+', '-3', '-', '2', '-']) == -964\n assert candidate(tokens = ['10', '-5', '+', '20', '-10', '/', '2', '*']) == 5\n assert candidate(tokens = ['5', '-2', '*']) == -10\n assert candidate(tokens = ['10', '20', '5', '/', '2', '*']) == 10\n assert candidate(tokens = ['13', '7', '2', '+', '/']) == 1\n assert candidate(tokens = ['-1', '-1', '*', '-2', '-', '2', '*', '-3', '/', '4', '-']) == -6\n assert candidate(tokens = ['1', '3', '-']) == -2\n assert candidate(tokens = ['15', '11', '+']) == 26\n assert candidate(tokens = ['10', '20', '+', '30', '40', '+', '50', '60', '+', '70', '80', '+', '90', '*']) == 30\n assert candidate(tokens = ['6', '3', '1', '+', '*', '4', '/']) == 6\n assert candidate(tokens = ['15', '7', '1', '1', '+', '-', '/', '3', '*', '2', '1', '1', '+', '+', '-']) == 5\n assert candidate(tokens = ['100', '50', '+', '20', '*', '4', '/', '2', '+', '8', '-', '3', '*']) == 2232\n assert candidate(tokens = ['1', '2', '+', '3', '4', '+', '*', '5', '6', '+', '*', '7', '8', '+', '*', '9', '10', '+', '*']) == 65835\n assert candidate(tokens = ['100', '50', '-']) == 50\n assert candidate(tokens = ['100', '200', '+', '50', '-', '2', '/', '3', '*', '10', '+']) == 385\n assert candidate(tokens = ['5', '3', '+', '7', '4', '-', '*']) == 24\n assert candidate(tokens = ['1', '2', '+', '3', '*', '4', '+', '5', '*', '6', '+', '7', '*', '8', '+', '9', '+', '10', '+', '11', '+', '12', '+', '13', '+', '14', '+', '15', '+', '16', '+', '17', '+', '18', '+', '19', '+']) == 659\n assert candidate(tokens = ['100', '50', '/', '20', '*', '10', '-', '5', '+', '2', '*', '3', '/', '1', '+', '4', '-']) == 20\n assert candidate(tokens = ['18', '5', '+', '12', '-', '3', '/', '2', '*', '4', '-']) == 2\n assert candidate(tokens = ['8', '3', '2', '*', '1', '-', '2', '/']) == 8\n assert candidate(tokens = ['-11', '-12', '-', '13', '-14', '-', '*']) == 27\n assert candidate(tokens = ['20', '5', '2', '/', '*']) == 40\n assert candidate(tokens = ['0', '3', '/', '5', '+']) == 5\n assert candidate(tokens = ['3', '-4', '*', '2', '/', '5', '-']) == -11\n assert candidate(tokens = ['1', '2', '3', '+', '*']) == 5\n assert candidate(tokens = ['100', '50', '2', '*', '-', '30', '20', '+', '/', '10', '+']) == 10\n assert candidate(tokens = ['7', '-3', '*', '11', '5', '-', '/', '2', '2', '+', '*']) == -12\n assert candidate(tokens = ['7', '-3', '*', '2', '1', '+', '-', '15', '5', '/', '+']) == -21\n assert candidate(tokens = ['2', '3', '4', '5', '+', '*', '6', '/']) == 2\n assert candidate(tokens = ['10', '6', '9', '3', '+', '-11', '*']) == 10\n assert candidate(tokens = ['7', '-3', '*']) == -21\n assert candidate(tokens = ['10', '5', '-', '3', '*', '4', '+', '2', '/']) == 9\n assert candidate(tokens = ['7', '-3', '*', '2', '+', '15', '5', '/', '*']) == -57\n assert candidate(tokens = ['15', '-3', '/', '7', '+', '2', '*', '10', '-', '5', '*']) == -30\n assert candidate(tokens = ['100', '50', '/', '25', '*', '5', '+', '3', '-', '2', '*']) == 104\n assert candidate(tokens = ['7', '-8', '*', '5', '+', '3', '-12', '/', '4', '*']) == -51\n assert candidate(tokens = ['7', '8', '3', '*', '+', '2', '/', '4', '-', '10', '5', '*', '+']) == 61\n assert candidate(tokens = ['5', '2', '/', '10', '2', '/', '-', '3', '*', '7', '+', '-1', '*']) == 2\n assert candidate(tokens = ['5', '2', '/', '-1', '*', '3', '-']) == -5\n"}, "metadata": {"canonical_parameter_names": ["tokens"], "leetcode_dataset_entry_point": "Solution().evalRPN", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var evalRPN = function(tokens) {", "container": null, "callable": "evalRPN", "parameters": [{"name": "tokens", "type": "string[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 151, "task_id": "reverse-words-in-a-string", "difficulty": "Medium", "problem_description": "Given an input string s, reverse the order of the words.\nA word is defined as a sequence of non-space characters. The words in s will be separated by at least one space.\nReturn a string of the words in reverse order concatenated by a single space.\nNote that s may contain leading or trailing spaces or multiple spaces between two words. The returned string should only have a single space separating the words. Do not include any extra spaces.\n \nExample 1:\n\nInput: s = \"the sky is blue\"\nOutput: \"blue is sky the\"\n\nExample 2:\n\nInput: s = \" hello world \"\nOutput: \"world hello\"\nExplanation: Your reversed string should not contain leading or trailing spaces.\n\nExample 3:\n\nInput: s = \"a good example\"\nOutput: \"example good a\"\nExplanation: You need to reduce multiple spaces between two words to a single space in the reversed string.\n\n \nConstraints:\n\n1 <= s.length <= 104\ns contains English letters (upper-case and lower-case), digits, and spaces ' '.\nThere is at least one word in s.\n\n \nFollow-up: If the string data type is mutable in your language, can you solve it in-place with O(1) extra space?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"the sky is blue\") == \"blue is sky the\"\n assert candidate(s = \"  hello world  \") == \"world hello\"\n assert candidate(s = \"a good   example\") == \"example good a\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().reverseWords", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverseWords = function(s) {", "container": null, "callable": "reverseWords", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 152, "task_id": "maximum-product-subarray", "difficulty": "Medium", "problem_description": "Given an integer array nums, find a subarray that has the largest product, and return the product.\nThe test cases are generated so that the answer will fit in a 32-bit integer.\n \nExample 1:\n\nInput: nums = [2,3,-2,4]\nOutput: 6\nExplanation: [2,3] has the largest product 6.\n\nExample 2:\n\nInput: nums = [-2,0,-1]\nOutput: 0\nExplanation: The result cannot be 2, because [-2,-1] is not a subarray.\n\n \nConstraints:\n\n1 <= nums.length <= 2 * 104\n-10 <= nums[i] <= 10\nThe product of any subarray of nums is guaranteed to fit in a 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [2, -5, -2, -4, 3]) == 24\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [-2, 3, -4]) == 24\n assert candidate(nums = [10, -20, 0, 5, 1]) == 10\n assert candidate(nums = [3, -1, 4]) == 4\n assert candidate(nums = [-1, -2, -3, 0]) == 6\n assert candidate(nums = [0, 2]) == 2\n assert candidate(nums = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10]) == 3628800\n assert candidate(nums = [2, 3, -2, 4]) == 6\n assert candidate(nums = [1, 2, -1, 4]) == 4\n assert candidate(nums = [0, 2, 0]) == 2\n assert candidate(nums = [-1, -2, -3, -4]) == 24\n assert candidate(nums = [-1]) == -1\n assert candidate(nums = [-2, 0, -1]) == 0\n assert candidate(nums = [-2, 3, -4, 5, 7, -8, 2, 3]) == 20160\n assert candidate(nums = [1, 2, 3, 4, 5]) == 120\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 3628800\n assert candidate(nums = [0, 2, 3, -2, 4, -1, 5]) == 240\n assert candidate(nums = [-10, 0, 10, 20, 30, -40, 50, 60, -70, 80]) == 4032000000000\n assert candidate(nums = [-1, 0, -1, 0, -1, 0, -1, 0, -1, 0]) == 0\n assert candidate(nums = [2, 3, -2, 4, -1, 5, 6]) == 1440\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50]) == 2880000000000\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1]) == 1\n assert candidate(nums = [-2, -3, 7, -4, 0, 5, -8, 3, 6]) == 84\n assert candidate(nums = [5, 0, 5, -1, 0, 5, -1, 0, 5, -1]) == 5\n assert candidate(nums = [0, 2, -3, 4, -5, 6]) == 720\n assert candidate(nums = [0, 2, -3, 4, -5, 6]) == 720\n assert candidate(nums = [2, 3, 0, -1, 4, 5, 0, -2, 3, 0]) == 20\n assert candidate(nums = [2, 3, 0, -1, -2, 4, 0, 5, 6, 0, -7, 8, -9]) == 504\n assert candidate(nums = [1, 0, -1, 0, 1, -1, 0, 1, 0]) == 1\n assert candidate(nums = [5, 6, -3, 4, 0, 2, 3, -2, 4]) == 30\n assert candidate(nums = [10, -10, 10, -10, 10, -10]) == 100000\n assert candidate(nums = [5, 6, -3, 4, 0, -1, 2, -5]) == 30\n assert candidate(nums = [0, 2, 3, -2, 4, -1, 5, 6]) == 1440\n assert candidate(nums = [2, -5, 3, 1, -4, 2]) == 240\n assert candidate(nums = [5, 3, -1, 2, 0, -6, -2, 0, 5, 3, -1, 2, 0, -6, -2]) == 15\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [-2, -3, 0, -2, -40, 0, -10]) == 80\n assert candidate(nums = [0, 2, -3, 4, -1, 2, 1, -5, 4]) == 160\n assert candidate(nums = [10, -2, -3, 5, -10, 0, 9, 6]) == 300\n assert candidate(nums = [100, -100, 50, -50, 25, -25, 10, -10, 5, -5]) == 7812500000000\n assert candidate(nums = [-2, 0, -1, 0, 1, 2, -3]) == 2\n assert candidate(nums = [5, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1814400\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5]) == 2880\n assert candidate(nums = [-1, -2, 0, 1, -3, 4, -5, 6, -7, 8, -9, 10]) == 1814400\n assert candidate(nums = [1, 0, -1, 0, 1, 0, -1, 0, 1]) == 1\n assert candidate(nums = [10, -10, 10, -10, 10, -10, 10]) == 100000\n assert candidate(nums = [-10, 0, 0, 0, 0, 0, 0, 0, 0, -10]) == 0\n assert candidate(nums = [-10, 0, 10, 0, -10, 0, 10, 0, -10, 0]) == 10\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 3628800\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [-3, -1, 0, 2, 4, -2, 0, -1]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 3628800\n assert candidate(nums = [3, -1, 4, 1, 5, -9, 2, 6, 5, 3, 5]) == 486000\n assert candidate(nums = [5, 3, -2, 5, -1, 5, -1, 0, 5]) == 750\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == 1\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10]) == 1814400\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 120\n assert candidate(nums = [-10, 0, 5, 2, -3, -2, 4, 5, 0, -1, 2]) == 1200\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10]) == 1814400\n assert candidate(nums = [3, -1, 4, 1, 5, -9, 2, 6, -5, 3, 5]) == 162000\n assert candidate(nums = [0, 2, -3, 4, -1, 0, 5, -2]) == 24\n assert candidate(nums = [2, -5, -2, -4, 3]) == 24\n assert candidate(nums = [-10, 9, -10, 10, -1, -100]) == 900000\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 3628800\n assert candidate(nums = [3, -1, 4, -1, 5, -9, 2, 6, -5, 3, 5]) == 486000\n assert candidate(nums = [1, 0, -1, 0, -2, 0, 1, 0, -1, 0, -2, 0]) == 1\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1]) == 1\n assert candidate(nums = [100, -100, 100, -100, 100, -100, 100, -100, 100, -100]) == 1000000000000000000\n assert candidate(nums = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10]) == 3628800\n assert candidate(nums = [10, -10, 0, 10, -10, 0, 10]) == 10\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9]) == 362880\n assert candidate(nums = [0, 2, -3, -4, 5, 0, 1]) == 120\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == 1\n assert candidate(nums = [-10, -10, -10, -10, -10]) == 10000\n assert candidate(nums = [-2, 3, -4, 5, -6, 7, -8, 9, -10, 11]) == 19958400\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 3628800\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == 1\n assert candidate(nums = [1, 2, 3, -4, -5, -6, 7, 8, 9, 10, -11]) == 39916800\n assert candidate(nums = [10, -10, 10, -10, 10]) == 100000\n assert candidate(nums = [5, -3, 1, -2, 0, 4, -2, 3, -1]) == 30\n assert candidate(nums = [10, -10, 10, -10, 10, -10]) == 100000\n assert candidate(nums = [-10, -20, 0, -5, -7, 0, 2, -1]) == 200\n assert candidate(nums = [1, 2, 3, 0, -1, -2, -3, -4, 5, 6]) == 720\n assert candidate(nums = [1, 2, 3, 0, -1, -2, -3, 0, 4, 5, 6, 0, -7, -8, -9, 0, 10, 11, 12]) == 1320\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8]) == 40320\n assert candidate(nums = [10, -10, 10, -10, 10, -10, 10, -10]) == 100000000\n assert candidate(nums = [2, 0, 1, 0, 2, 3, -2, 4, -1, 5]) == 240\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().maxProduct", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProduct = function(nums) {", "container": null, "callable": "maxProduct", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 153, "task_id": "find-minimum-in-rotated-sorted-array", "difficulty": "Medium", "problem_description": "Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array nums = [0,1,2,4,5,6,7] might become:\n\n[4,5,6,7,0,1,2] if it was rotated 4 times.\n[0,1,2,4,5,6,7] if it was rotated 7 times.\n\nNotice that rotating an array [a[0], a[1], a[2], ..., a[n-1]] 1 time results in the array [a[n-1], a[0], a[1], a[2], ..., a[n-2]].\nGiven the sorted rotated array nums of unique elements, return the minimum element of this array.\nYou must write an algorithm that runs in O(log n) time.\n \nExample 1:\n\nInput: nums = [3,4,5,1,2]\nOutput: 1\nExplanation: The original array was [1,2,3,4,5] rotated 3 times.\n\nExample 2:\n\nInput: nums = [4,5,6,7,0,1,2]\nOutput: 0\nExplanation: The original array was [0,1,2,4,5,6,7] and it was rotated 4 times.\n\nExample 3:\n\nInput: nums = [11,13,15,17]\nOutput: 11\nExplanation: The original array was [11,13,15,17] and it was rotated 4 times. \n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 5000\n-5000 <= nums[i] <= 5000\nAll the integers of nums are unique.\nnums is sorted and rotated between 1 and n times.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2]) == 0\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 1, 0]) == 1\n assert candidate(nums = [1, 3, 2]) == 1\n assert candidate(nums = [10, 15, 1, 3, 8]) == 1\n assert candidate(nums = [11, 13, 15, 17]) == 11\n assert candidate(nums = [7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 6]) == 1\n assert candidate(nums = [10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 1\n assert candidate(nums = [2, 1, 3]) == 2\n assert candidate(nums = [5, 1, 2, 3, 4]) == 1\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 1]) == 1\n assert candidate(nums = [3, 1, 2]) == 1\n assert candidate(nums = [2, 1]) == 1\n assert candidate(nums = [3, 4, 5, 1, 2]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]) == 1\n assert candidate(nums = [2, 3, 1]) == 1\n assert candidate(nums = [6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [59, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57]) == 1\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, -1000, -900, -800, -700, -600, -500, -400, -300, -200, -100]) == -1000\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 0\n assert candidate(nums = [3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 3030, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) == 0\n assert candidate(nums = [40, 50, 60, 70, 80, 90, 100, 0, 10, 20, 30]) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == 0\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1]) == 0\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 1, 2, 3]) == 1\n assert candidate(nums = [0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 1\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]) == 1\n assert candidate(nums = [15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 0\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == -10\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 0, 1]) == 0\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2]) == 1\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [-5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991, -4990, -4989, -4988, -4987, -4986, -4985, -4984, -4983, -4982, -4981, -4980, -4979, -4978, -4977, -4976, -4975, -4974, -4973, -4972, -4971, -4970, -4969, -4968, -4967, -4966, -4965, -4964, -4963, -4962, -4961, -4960, -4959, -4958, -4957, -4956, -4955, -4954, -4953, -4952, -4951, -4950, -4949, -4948, -4947, -4946, -4945, -4944, -4943, -4942, -4941, -4940, -4939, -4938, -4937, -4936, -4935, -4934, -4933, -4932, -4931, -4930, -4929, -4928, -4927, -4926, -4925, -4924, -4923, -4922, -4921, -4920, -4919, -4918, -4917, -4916, -4915, -4914, -4913, -4912, -4911, -4910, -4909, -4908, -4907, -4906, -4905, -4904, -4903, -4902, -4901, -4900, -4899, -4898, -4897, -4896, -4895, -4894, -4893, -4892, -4891, -4890, -4889, -4888, -4887, -4886, -4885, -4884, -4883, -4882, -4881, -4880, -4879, -4878, -4877, -4876, -4875, -4874, -4873, -4872, -4871, -4870, -4869, -4868, -4867, -4866, -4865, -4864, -4863, -4862, -4861, -4860, -4859, -4858, -4857, -4856, -4855, -4854, -4853, -4852, -4851, -4850, -4849, -4848, -4847, -4846, -4845, -4844, -4843, -4842, -4841, -4840, -4839, -4838, -4837, -4836, -4835, -4834, -4833, -4832, -4831, -4830, -4829, -4828, -4827, -4826, -4825, -4824, -4823, -4822, -4821, -4820, -4819, -4818, -4817, -4816, -4815, -4814, -4813, -4812, -4811, -4810, -4809, -4808, -4807, -4806, -4805, -4804, -4803, -4802, -4801, 5000]) == -5000\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 1, 2]) == 1\n assert candidate(nums = [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) == 0\n assert candidate(nums = [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) == 0\n assert candidate(nums = [5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991, -4990, -4989, -4988, -4987, -4986, -4985, -4984, -4983, -4982, -4981, -4980, -4979, -4978, -4977, -4976, -4975, -4974, -4973, -4972, -4971, -4970, -4969, -4968, -4967, -4966, -4965, -4964, -4963, -4962, -4961, -4960, -4959, -4958, -4957, -4956, -4955, -4954, -4953, -4952, -4951, -4950, -4949, -4948, -4947, -4946, -4945, -4944, -4943, -4942, -4941, -4940, -4939, -4938, -4937, -4936, -4935, -4934, -4933, -4932, -4931, -4930, -4929, -4928, -4927, -4926, -4925, -4924, -4923, -4922, -4921, -4920, -4919, -4918, -4917, -4916, -4915, -4914, -4913, -4912, -4911, -4910, -4909, -4908, -4907, -4906, -4905, -4904, -4903, -4902, -4901, -4900, -4899, -4898, -4897, -4896, -4895, -4894, -4893, -4892, -4891, -4890, -4889, -4888, -4887, -4886, -4885, -4884, -4883, -4882, -4881, -4880, -4879, -4878, -4877, -4876, -4875, -4874, -4873, -4872, -4871, -4870, -4869, -4868, -4867, -4866, -4865, -4864, -4863, -4862, -4861, -4860, -4859, -4858, -4857, -4856, -4855, -4854, -4853, -4852, -4851, -4850, -4849, -4848, -4847, -4846, -4845, -4844, -4843, -4842, -4841, -4840, -4839, -4838, -4837, -4836, -4835, -4834, -4833, -4832, -4831, -4830, -4829, -4828, -4827, -4826, -4825, -4824, -4823, -4822, -4821, -4820, -4819, -4818, -4817, -4816, -4815, -4814, -4813, -4812, -4811, -4810, -4809, -4808, -4807, -4806, -4805, -4804, -4803, -4802, -4801, -4800]) == -4999\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4]) == 1\n assert candidate(nums = [1, 0]) == 0\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0]) == 0\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 1, 2]) == 1\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [5000, -5000, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == -5000\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 0\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 1\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0]) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 3030]) == 0\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 0\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]) == 0\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1, 2]) == 1\n assert candidate(nums = [0, 1]) == 0\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3]) == 0\n assert candidate(nums = [999, -999, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == -999\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == -10\n assert candidate(nums = [5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981, 4980, 4979, 4978, 4977, 4976, 4975, 4974, 4973, 4972, 4971, 4970, 4969, 4968, 4967, 4966, 4965, 4964, 4963, 4962, 4961, 4960, 4959, 4958, 4957, 4956, 4955, 4954, 4953, 4952, 4951, 4950, 4949, 4948, 4947, 4946, 4945, 4944, 4943, 4942, 4941, 4940, 4939, 4938, 4937, 4936, 4935, 4934, 4933, 4932, 4931, 4930, 4929, 4928, 4927, 4926, 4925, 4924, 4923, 4922, 4921, 4920, 4919, 4918, 4917, 4916, 4915, 4914, 4913, 4912, 4911, 4910, 4909, 4908, 4907, 4906, 4905, 4904, 4903, 4902, 4901, 4900, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 4999\n assert candidate(nums = [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == 0\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0]) == 0\n assert candidate(nums = [1, -5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991]) == -5000\n assert candidate(nums = [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0]) == 0\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 0, 1]) == 0\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 0\n assert candidate(nums = [20, 21, 22, 23, 24, 25, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 0\n assert candidate(nums = [-2, -1, 0, 1, 2]) == -2\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [5000, -4999, -4998, -4997, -4996, -4995, -4994, -4993, -4992, -4991]) == -4999\n assert candidate(nums = [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) == 0\n assert candidate(nums = [-5000]) == -5000\n assert candidate(nums = [99, 100, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0]) == 0\n assert candidate(nums = [3, 8, 9, 1, 2, 3, 4, 5, 6, 7]) == 3\n assert candidate(nums = [999, -999, -500, -250, -100, -50, -25, -10, -5, -1, 0, 1, 5, 10, 25, 50, 100, 250, 500]) == -999\n assert candidate(nums = [4999, -4999, 4998, -4998, 4997, -4997, 4996, -4996, 4995, -4995, 4994, -4994, 4993, -4993, 4992, -4992, 4991, -4991, 4990, -4990, 4989, -4989, 4988, -4988, 4987, -4987, 4986, -4986, 4985, -4985, 4984, -4984, 4983, -4983, 4982, -4982, 4981, -4981, 4980, -4980, 4979, -4979, 4978, -4978, 4977, -4977, 4976, -4976, 4975, -4975, 4974, -4974, 4973, -4973, 4972, -4972, 4971, -4971, 4970, -4970, 4969, -4969, 4968, -4968, 4967, -4967, 4966, -4966, 4965, -4965, 4964, -4964, 4963, -4963, 4962, -4962, 4961, -4961, 4960, -4960, 4959, -4959, 4958, -4958, 4957, -4957, 4956, -4956, 4955, -4955, 4954, -4954, 4953, -4953, 4952, -4952, 4951, -4951, 4950, -4950, 4949, -4949, 4948, -4948, 4947, -4947, 4946, -4946, 4945, -4945, 4944, -4944, 4943, -4943, 4942, -4942, 4941, -4941, 4940, -4940, 4939, -4939, 4938, -4938, 4937, -4937, 4936, -4936, 4935, -4935, 4934, -4934, 4933, -4933, 4932, -4932, 4931, -4931, 4930, -4930, 4929, -4929, 4928, -4928, 4927, -4927, 4926, -4926, 4925, -4925, 4924, -4924, 4923, -4923, 4922, -4922, 4921, -4921, 4920, -4920, 4919, -4919, 4918, -4918, 4917, -4917, 4916, -4916, 4915, -4915, 4914, -4914, 4913, -4913, 4912, -4912, 4911, -4911, 4910, -4910, 4909, -4909, 4908, -4908, 4907, -4907, 4906, -4906, 4905, -4905, 4904, -4904, 4903, -4903, 4902, -4902, 4901, -4901, 4900, -4900, 4899, -4899, 4898, -4898, 4897, -4897, 4896, -4896, 4895, -4895, 4894, -4894, 4893, -4893, 4892, -4892, 4891, -4891, 4890, -4890, 4889, -4889, 4888, -4888, 4887, -4887, 4886, -4886, 4885, -4885, 4884, -4884, 4883, -4883, 4882, -4882, 4881, -4881, 4880, -4880, 4879, -4879, 4878, -4878, 4877, -4877, 4876, -4876, 4875, -4875, 4874, -4874, 4873, -4873, 4872, -4872, 4871, -4871, 4870, -4870, 4869, -4869, 4868, -4868, 4867, -4867, 4866, -4866, 4865, -4865, 4864, -4864, 4863, -4863, 4862, -4862, 4861, -4861, 4860, -4860, 4859, -4859, 4858, -4858, 4857, -4857, 4856, -4856, 4855, -4855, 4854, -4854, 4853, -4853, 4852, -4852, 4851, -4851, 4850, -4850, 4849, -4849, 4848, -4848, 4847, -4847, 4846, -4846, 4845, -4845, 4844, -4844, 4843, -4843, 4842, -4842, 4841, -4841, 4840, -4840, 4839, -4839, 4838, -4838, 4837, -4837, 4836, -4836, 4835, -4835, 4834, -4834, 4833, -4833, 4832, -4832, 4831, -4831, 4830, -4830, 4829, -4829, 4828, -4828, 4827, -4827, 4826, -4826, 4825, -4825, 4824, -4824, 4823, -4823, 4822, -4822, 4821, -4821, 4820, -4820, 4819, -4819, 4818, -4818, 4817, -4817, 4816, -4816, 4815, -4815, 4814, -4814, 4813, -4813, 4812, -4812, 4811, -4811, 4810, -4810, 4809, -4809, 4808, -4808, 4807, -4807, 4806, -4806, 4805, -4805, 4804, -4804, 4803, -4803, 4802, -4802, 4801, -4801, 4800, -4800]) == -4999\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3]) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == 1\n assert candidate(nums = [40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]) == 0\n assert candidate(nums = [5000]) == 5000\n assert candidate(nums = [1000, 2000, 3000, 4000, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == -1\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20]) == -1\n assert candidate(nums = [20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 0]) == 10\n assert candidate(nums = [5000, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 0\n assert candidate(nums = [20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 1\n assert candidate(nums = [15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 0\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findMin", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMin = function(nums) {", "container": null, "callable": "findMin", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 154, "task_id": "find-minimum-in-rotated-sorted-array-ii", "difficulty": "Hard", "problem_description": "Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array nums = [0,1,4,4,5,6,7] might become:\n\n[4,5,6,7,0,1,4] if it was rotated 4 times.\n[0,1,4,4,5,6,7] if it was rotated 7 times.\n\nNotice that rotating an array [a[0], a[1], a[2], ..., a[n-1]] 1 time results in the array [a[n-1], a[0], a[1], a[2], ..., a[n-2]].\nGiven the sorted rotated array nums that may contain duplicates, return the minimum element of this array.\nYou must decrease the overall operation steps as much as possible.\n \nExample 1:\nInput: nums = [1,3,5]\nOutput: 1\nExample 2:\nInput: nums = [2,2,2,0,1]\nOutput: 0\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 5000\n-5000 <= nums[i] <= 5000\nnums is sorted and rotated between 1 and n times.\n\n \nFollow up: This problem is similar to Find Minimum in Rotated Sorted Array, but nums may contain duplicates. Would this affect the runtime complexity? How and why?\n \n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4]) == 0\n assert candidate(nums = [1, 3, 5]) == 1\n assert candidate(nums = [2, 2, 2, 0, 1]) == 0\n assert candidate(nums = [5, 1, 2, 3, 4]) == 1\n assert candidate(nums = [3, 4, 5, 1, 2]) == 1\n assert candidate(nums = [15, 17, 11, 13]) == 11\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]) == 0\n assert candidate(nums = [0, 1, 4, 4, 5, 6, 7]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 3]) == 1\n assert candidate(nums = [4, 4, 5, 6, 7, 0, 1, 2, 3]) == 0\n assert candidate(nums = [11, 13, 15, 17]) == 11\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2]) == 0\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4]) == 1\n assert candidate(nums = [4, 4, 4, 4, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [10, 1, 10, 10, 10]) == 1\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 4]) == 0\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 0, 1]) == 0\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2]) == 2\n assert candidate(nums = [100, 200, 300, 400, 500, 1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [104, 105, 106, 107, 108, 109, 0, 100, 101, 102, 103]) == 0\n assert candidate(nums = [0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3]) == 0\n assert candidate(nums = [7, 8, 9, 10, 1, 2, 3, 4, 5, 6]) == 1\n assert candidate(nums = [3, 4, 5, 1, 2, 2, 2, 2, 2]) == 1\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 0\n assert candidate(nums = [6, 7, 1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [6, 7, 0, 1, 2, 4, 5]) == 0\n assert candidate(nums = [108, 109, 0, 100, 101, 102, 103, 104, 105, 106, 107]) == 0\n assert candidate(nums = [106, 107, 108, 109, 0, 100, 101, 102, 103, 104, 105]) == 0\n assert candidate(nums = [2, 5, 6, 0, 0, 1, 2]) == 0\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2]) == 0\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 1]) == 0\n assert candidate(nums = [11, 13, 15, 17, 19, 2, 5, 7]) == 2\n assert candidate(nums = [8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 0]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 0, 1, 2, 2, 3]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 1, 1]) == 1\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 0\n assert candidate(nums = [11, 13, 15, 17, 19, 1, 3, 5, 7]) == 1\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == 1\n assert candidate(nums = [2, 3, 4, 5, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]) == 0\n assert candidate(nums = [5, 6, 7, 0, 1, 2, 3]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 1]) == 0\n assert candidate(nums = [103, 104, 105, 106, 107, 108, 109, 0, 100, 101, 102]) == 0\n assert candidate(nums = [1, 0, 1, 1, 1, 1]) == 0\n assert candidate(nums = [6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5]) == 0\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 1]) == 1\n assert candidate(nums = [3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == 0\n assert candidate(nums = [7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6]) == 0\n assert candidate(nums = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [4, 4, 4, 4, 4, 0, 1, 2, 3]) == 0\n assert candidate(nums = [1, 2, 2, 2, 0, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 0]) == 0\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [109, 0, 100, 101, 102, 103, 104, 105, 106, 107, 108]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [5, 5, 5, 5, 5, 1, 2, 3, 4]) == 1\n assert candidate(nums = [4, 5, 6, 7, 0, 1, 2]) == 0\n assert candidate(nums = [100, 101, 102, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 0\n assert candidate(nums = [15, 17, 19, 0, 1, 3, 5, 7, 9, 11, 13]) == 0\n assert candidate(nums = [2, 2, 2, 2, 1, 2, 2, 2]) == 1\n assert candidate(nums = [2, 0, 1, 1, 1, 2, 2]) == 0\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 1, 2]) == 1\n assert candidate(nums = [107, 108, 109, 0, 100, 101, 102, 103, 104, 105, 106]) == 0\n assert candidate(nums = [2, 2, 2, 0, 1, 2]) == 0\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]) == 0\n assert candidate(nums = [105, 106, 107, 108, 109, 0, 100, 101, 102, 103, 104]) == 0\n assert candidate(nums = [2, 2, 2, 0, 1, 1, 2]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1]) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 0, 0, 0]) == 0\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1]) == 0\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4]) == 0\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3]) == 0\n assert candidate(nums = [101, 102, 103, 104, 105, 106, 107, 108, 109, 0, 100]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 1, 3, 3, 3]) == 1\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 0, 5]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 0\n assert candidate(nums = [4, 4, 4, 4, 0, 1, 4]) == 0\n assert candidate(nums = [1, 2, 0, 1, 1, 1]) == 0\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 1]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1]) == 0\n assert candidate(nums = [6, 7, 1, 2, 2, 2, 2, 2, 2]) == 1\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 0\n assert candidate(nums = [11, 13, 15, 17, 19, 0, 1, 3, 5, 7, 9]) == 0\n assert candidate(nums = [102, 103, 104, 105, 106, 107, 108, 109, 0, 100, 101]) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 5, 10]) == 5\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 0]) == 0\n assert candidate(nums = [2, 2, 0, 2, 2, 2, 2, 2, 2, 2]) == 0\n assert candidate(nums = [3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 6, 6, 6, 0, 1, 2]) == 0\n assert candidate(nums = [0, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2]) == 1\n assert candidate(nums = [2, 2, 2, 0, 1, 2, 2, 2, 2, 2]) == 0\n assert candidate(nums = [1, 1, 0, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]) == 0\n assert candidate(nums = [11, 13, 15, 17, 19, 21, 2, 3, 5, 7, 9]) == 2\n assert candidate(nums = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15]) == 0\n assert candidate(nums = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [4, 5, 1, 2, 3]) == 1\n assert candidate(nums = [0, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 3, 3]) == 1\n assert candidate(nums = [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 0\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findMin", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMin = function(nums) {", "container": null, "callable": "findMin", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 162, "task_id": "find-peak-element", "difficulty": "Medium", "problem_description": "A peak element is an element that is strictly greater than its neighbors.\nGiven a 0-indexed integer array nums, find a peak element, and return its index. If the array contains multiple peaks, return the index to any of the peaks.\nYou may imagine that nums[-1] = nums[n] = -∞. In other words, an element is always considered to be strictly greater than a neighbor that is outside the array.\nYou must write an algorithm that runs in O(log n) time.\n \nExample 1:\n\nInput: nums = [1,2,3,1]\nOutput: 2\nExplanation: 3 is a peak element and your function should return the index number 2.\nExample 2:\n\nInput: nums = [1,2,1,3,5,6,4]\nOutput: 5\nExplanation: Your function can return either index number 1 where the peak element is 2, or index number 5 where the peak element is 6.\n \nConstraints:\n\n1 <= nums.length <= 1000\n-231 <= nums[i] <= 231 - 1\nnums[i] != nums[i + 1] for all valid i.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 3, 1]) == 2\n assert candidate(nums = [1, 2, 2, 3, 1]) == 3\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [2, 1]) == 0\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(nums = [6, 5, 4, 3, 2, 3, 2]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 4\n assert candidate(nums = [1, 3, 20, 4, 1, 0]) == 2\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1]) == 3\n assert candidate(nums = [1, 3, 2]) == 1\n assert candidate(nums = [10, 20, 15, 2, 23, 90, 67]) == 5\n assert candidate(nums = [5, 4, 3, 2, 1]) == 0\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1]) == 5\n assert candidate(nums = [1, 2]) == 1\n assert candidate(nums = [1, 3, 2, 1]) == 1\n assert candidate(nums = [1, 2, 1, 3, 5, 6, 4]) == 5\n assert candidate(nums = [1, 3, 2, 1, 3, 5, 4, 6, 5, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 11\n assert candidate(nums = [1, 2, 3, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 19\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 11\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1]) == 9\n assert candidate(nums = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10]) == 5\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 17\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 4\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14]) == 13\n assert candidate(nums = [5, 1, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 29\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 12\n assert candidate(nums = [1, 10, 8, 9, 10, 6, 7, 8, 9, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 33\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 6\n assert candidate(nums = [1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1]) == 10\n assert candidate(nums = [1, 3, 5, 4, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 12\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == 14\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 15\n assert candidate(nums = [5, 1, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == 2\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 19\n assert candidate(nums = [1, 3, 20, 4, 1, 0, -5, 2, 23, 1, 2, 1]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 17\n assert candidate(nums = [1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 23\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3]) == 9\n assert candidate(nums = [1, 10, 8, 6, 7, 9, 5, 3, 4, 2, 1]) == 1\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 0\n assert candidate(nums = [1, 2, 1, 3, 5, 6, 4, 7, 8, 9, 0]) == 5\n assert candidate(nums = [5, 1, 4, 3, 2, 1, 0]) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 18, 17, 16, 15, 14]) == 9\n assert candidate(nums = [1, 10, 8, 9, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]) == 9\n assert candidate(nums = [1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 5\n assert candidate(nums = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20]) == 31\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == 49\n assert candidate(nums = [1, 100, 2, 3, 4, 5, 6, 7, 8, 9]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 39\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 13\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 14, 12, 10, 8, 6, 4, 2]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 29\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9]) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 14\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == 39\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4]) == 5\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 3, 2, 1]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == 29\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3]) == 8\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 9\n assert candidate(nums = [1, 3, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28]) == 20\n assert candidate(nums = [5, 1, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == 17\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 13\n assert candidate(nums = [1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 24\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [5, 1, 4, 3, 2]) == 2\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findPeakElement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findPeakElement = function(nums) {", "container": null, "callable": "findPeakElement", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 164, "task_id": "maximum-gap", "difficulty": "Medium", "problem_description": "Given an integer array nums, return the maximum difference between two successive elements in its sorted form. If the array contains less than two elements, return 0.\nYou must write an algorithm that runs in linear time and uses linear extra space.\n \nExample 1:\n\nInput: nums = [3,6,9,1]\nOutput: 3\nExplanation: The sorted form of the array is [1,3,6,9], either (3,6) or (6,9) has the maximum difference 3.\n\nExample 2:\n\nInput: nums = [10]\nOutput: 0\nExplanation: The array contains less than 2 elements, therefore return 0.\n\n \nConstraints:\n\n1 <= nums.length <= 105\n0 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1000000000]) == 999999999\n assert candidate(nums = [8, 10, 58, 59, 9, 29, 90, 1, 7, 2, 45]) == 31\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [10]) == 0\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [1000000000]) == 0\n assert candidate(nums = [5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [0, 999999999]) == 999999999\n assert candidate(nums = [1, 3, 6, 9, 12, 15, 18, 21, 24, 27]) == 3\n assert candidate(nums = [0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [5, 5, 5, 5]) == 0\n assert candidate(nums = [9, 3, 1, 10]) == 6\n assert candidate(nums = [100, 100, 100, 100]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, 3, 100, 10000, 100000]) == 90000\n assert candidate(nums = [1, 3, 100, 1000000000]) == 999999900\n assert candidate(nums = [5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 3, 100, 10000]) == 9900\n assert candidate(nums = [3, 6, 9, 1]) == 3\n assert candidate(nums = [100, 300, 200, 400]) == 100\n assert candidate(nums = [5, 3, 8, 4, 9, 2, 1, 7, 6, 10]) == 1\n assert candidate(nums = [8, 15, 1, 17, 3, 19, 2, 11, 7]) == 4\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996]) == 1\n assert candidate(nums = [100000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, 900000]) == 100000\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500]) == 100\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 100\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 100\n assert candidate(nums = [999999999, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 999999979\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 1\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 1000000000, 1, 1000000000, 1]) == 999999999\n assert candidate(nums = [8, 1, 5, 3, 7, 10, 2, 6, 4, 9]) == 1\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 2\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992]) == 999999982\n assert candidate(nums = [1, 1000000000, 2, 999999999, 3, 999999998, 4, 999999997]) == 999999993\n assert candidate(nums = [5, 3, 8, 6, 2, 7, 4, 1]) == 1\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == 1\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]) == 1\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000]) == 100000000\n assert candidate(nums = [123456789, 234567890, 345678901, 456789012, 567890123, 678901234, 789012345, 890123456, 901234567]) == 111111101\n assert candidate(nums = [3, 6, 9, 1, 15, 10, 20, 5, 8]) == 5\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97]) == 4\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 100\n assert candidate(nums = [1000000000, 0, 500000000, 250000000, 750000000]) == 250000000\n assert candidate(nums = [999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010]) == 1\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 900000000\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 1\n assert candidate(nums = [5, 3, 8, 6, 2, 7, 4, 1, 9]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 2\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 1\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990]) == 1\n assert candidate(nums = [1, 3, 6, 9, 12, 15, 18, 21, 24, 27]) == 3\n assert candidate(nums = [2147483647, 100, 200, 300, 400, 500, 600, 700, 800, 900]) == 2147482747\n assert candidate(nums = [123456789, 987654321, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666, 777777777, 888888888]) == 111111111\n assert candidate(nums = [9, 3, 5, 1, 7, 8, 2, 6, 4]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4]) == 1\n assert candidate(nums = [987654321, 123456789, 876543210, 234567891, 765432109, 345678912, 654321098, 456789123, 543210987, 111111111]) == 111111111\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125]) == 500000000\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]) == 10\n assert candidate(nums = [1, 1000000000, 2, 999999998, 3, 999999997]) == 999999994\n assert candidate(nums = [5, 3, 1, 4, 2, 8, 6, 7, 9, 0]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384]) == 8192\n assert candidate(nums = [1, 1000000000, 2, 999999999, 3, 888888888, 4]) == 888888884\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 1\n assert candidate(nums = [1000000000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 999999970\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4]) == 1\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(nums = [5, 3, 1, 9, 7, 2, 8, 6, 4, 0]) == 1\n assert candidate(nums = [10, 1, 2, 9, 3, 8, 4, 7, 5, 6]) == 1\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 900000000\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 1\n assert candidate(nums = [1, 1000000000, 2, 999999998, 3]) == 999999995\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 10\n assert candidate(nums = [999999999, 0, 999999998, 1, 999999997, 2]) == 999999995\n assert candidate(nums = [500000000, 400000000, 300000000, 200000000, 100000000, 0, 600000000, 700000000, 800000000, 900000000]) == 100000000\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 10\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 1\n assert candidate(nums = [10, 100, 1000, 10000, 100000, 1000000]) == 900000\n assert candidate(nums = [1, 1000000000, 2, 999999998, 3, 999999997]) == 999999994\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250]) == 10\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]) == 3\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992]) == 1\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 0\n assert candidate(nums = [50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]) == 10\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000, 600000000, 700000000, 800000000, 900000000, 1000000000]) == 100000000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 1\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000]) == 100000000\n assert candidate(nums = [1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 900000000\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995]) == 1\n assert candidate(nums = [1, 1000000000, 1, 1000000000, 1, 1000000000, 1, 1000000000, 1, 1000000000]) == 999999999\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 10\n assert candidate(nums = [500000000, 250000000, 750000000, 125000000, 375000000]) == 250000000\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990]) == 1\n assert candidate(nums = [9, 3, 7, 1, 5, 11, 13, 17, 19, 23]) == 4\n assert candidate(nums = [25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27]) == 1\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 1\n assert candidate(nums = [500000000, 500000001, 500000002, 500000003, 500000004, 500000005, 500000006, 500000007, 500000008, 500000009]) == 1\n assert candidate(nums = [123456789, 234567891, 345678912, 456789123, 567891234, 678912345, 789123456, 891234567, 912345678, 123456789]) == 111111102\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 2\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 10\n assert candidate(nums = [500, 250, 750, 1000, 0, 125, 375, 625, 875, 925, 975, 1025]) == 125\n assert candidate(nums = [1000000000, 100000000, 10000000, 1000000, 100000, 10000, 1000, 100, 10, 1]) == 900000000\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 1\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995]) == 1\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3]) == 2\n assert candidate(nums = [1, 3, 100, 999999999, 2]) == 999999899\n assert candidate(nums = [1000000000, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 999999991\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000]) == 90000\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 10\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 1\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105]) == 14\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 100\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 10\n assert candidate(nums = [1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 8000000, 9000000, 10000000]) == 1000000\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995]) == 1\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 0, 999999999]) == 899999999\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().maximumGap", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maximumGap = function(nums) {", "container": null, "callable": "maximumGap", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 165, "task_id": "compare-version-numbers", "difficulty": "Medium", "problem_description": "Given two version strings, version1 and version2, compare them. A version string consists of revisions separated by dots '.'. The value of the revision is its integer conversion ignoring leading zeros.\nTo compare version strings, compare their revision values in left-to-right order. If one of the version strings has fewer revisions, treat the missing revision values as 0.\nReturn the following:\n\nIf version1 < version2, return -1.\nIf version1 > version2, return 1.\nOtherwise, return 0.\n\n \nExample 1:\n\nInput: version1 = \"1.2\", version2 = \"1.10\"\nOutput: -1\nExplanation:\nversion1's second revision is \"2\" and version2's second revision is \"10\": 2 < 10, so version1 < version2.\n\nExample 2:\n\nInput: version1 = \"1.01\", version2 = \"1.001\"\nOutput: 0\nExplanation:\nIgnoring leading zeroes, both \"01\" and \"001\" represent the same integer \"1\".\n\nExample 3:\n\nInput: version1 = \"1.0\", version2 = \"1.0.0.0\"\nOutput: 0\nExplanation:\nversion1 has less revisions, which means every missing revision are treated as \"0\".\n\n \nConstraints:\n\n1 <= version1.length, version2.length <= 500\nversion1 and version2 only contain digits and '.'.\nversion1 and version2 are valid version numbers.\nAll the given revisions in version1 and version2 can be stored in a 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(version1 = \"0\",version2 = \"0.0.0\") == 0\n assert candidate(version1 = \"1.1.1.1\",version2 = \"1.1.1.1\") == 0\n assert candidate(version1 = \"1.2.3.4\",version2 = \"1.2.3\") == 1\n assert candidate(version1 = \"1.1.1.1\",version2 = \"1.1.1\") == 1\n assert candidate(version1 = \"1.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"5.0000\",version2 = \"5.00000\") == 0\n assert candidate(version1 = \"0.0.1\",version2 = \"0.0.2\") == -1\n assert candidate(version1 = \"5.5.5.5\",version2 = \"5.5.5\") == 1\n assert candidate(version1 = \"5.12\",version2 = \"5.10.0\") == 1\n assert candidate(version1 = \"1.2.3\",version2 = \"1.2.3\") == 0\n assert candidate(version1 = \"1.2\",version2 = \"1.10\") == -1\n assert candidate(version1 = \"1.0.0.1\",version2 = \"1\") == 1\n assert candidate(version1 = \"2.0\",version2 = \"1.9\") == 1\n assert candidate(version1 = \"1.01\",version2 = \"1.001\") == 0\n assert candidate(version1 = \"0.1\",version2 = \"1.1\") == -1\n assert candidate(version1 = \"1.10.0\",version2 = \"1.1\") == 1\n assert candidate(version1 = \"1.0\",version2 = \"1.0.0.0\") == 0\n assert candidate(version1 = \"0.1\",version2 = \"0.0.1\") == 1\n assert candidate(version1 = \"1.1.1\",version2 = \"1.1.1\") == 0\n assert candidate(version1 = \"10.0.0\",version2 = \"10\") == 0\n assert candidate(version1 = \"10.5.2\",version2 = \"10.5.2\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0\",version2 = \"1.0\") == 0\n assert candidate(version1 = \"1\",version2 = \"1.0\") == 0\n assert candidate(version1 = \"1.0.1\",version2 = \"1\") == 1\n assert candidate(version1 = \"7.5.2.4\",version2 = \"7.5.3\") == -1\n assert candidate(version1 = \"1.2.3\",version2 = \"1.2.4\") == -1\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9\",version2 = \"1.2.3.4.5.6.7.8.9.0.0.0\") == 0\n assert candidate(version1 = \"123456789.987654321\",version2 = \"123456789.987654321.0\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0.0\",version2 = \"1.0.0.0.0.0.0.0.0.0\") == 0\n assert candidate(version1 = \"1.2.3.4.5\",version2 = \"1.2.3.4.6\") == -1\n assert candidate(version1 = \"1.23.456.7890\",version2 = \"1.23.456.7890.0\") == 0\n assert candidate(version1 = \"1.0.0.1\",version2 = \"1.0\") == 1\n assert candidate(version1 = \"001.002.003\",version2 = \"1.2.3\") == 0\n assert candidate(version1 = \"99999.99999.99999.99999\",version2 = \"100000.0.0.0\") == -1\n assert candidate(version1 = \"1.001.0001.00001\",version2 = \"1.1.1.1\") == 0\n assert candidate(version1 = \"1000000000\",version2 = \"1\") == 1\n assert candidate(version1 = \"1.2.3\",version2 = \"1.2.3.0\") == 0\n assert candidate(version1 = \"1.999999999.999999999\",version2 = \"2\") == -1\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"0.0.0.0.0.0.0.0\",version2 = \"0\") == 0\n assert candidate(version1 = \"1.001.00001.000000001\",version2 = \"1.1.1.1\") == 0\n assert candidate(version1 = \"3.14159.26535\",version2 = \"3.14159.26535.0\") == 0\n assert candidate(version1 = \"1.0.0\",version2 = \"1.0\") == 0\n assert candidate(version1 = \"1.1.1.1.1\",version2 = \"1.1.1.1.2\") == -1\n assert candidate(version1 = \"1.2\",version2 = \"1.02\") == 0\n assert candidate(version1 = \"1.000001\",version2 = \"1.00001\") == 0\n assert candidate(version1 = \"1.0.10.0.0\",version2 = \"1.0.10\") == 0\n assert candidate(version1 = \"1.2.3\",version2 = \"1.2.0.3\") == 1\n assert candidate(version1 = \"999999999\",version2 = \"1000000000\") == -1\n assert candidate(version1 = \"99999.99999.99999\",version2 = \"100000\") == -1\n assert candidate(version1 = \"1.000000000.000000000\",version2 = \"1.0\") == 0\n assert candidate(version1 = \"1.0.10\",version2 = \"1.0.1\") == 1\n assert candidate(version1 = \"1000.1000.1000\",version2 = \"1000.1000\") == 1\n assert candidate(version1 = \"100000.99999.88888\",version2 = \"100000.99999.88889\") == -1\n assert candidate(version1 = \"0.1.2.3.4.5.6.7.8.9\",version2 = \"0.1.2.3.4.5.6.7.8.10\") == -1\n assert candidate(version1 = \"1.010.0010\",version2 = \"1.10.10\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.10\",version2 = \"1.2.3.4.5.6.7.8.9\") == 1\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9\",version2 = \"1.2.3.4.5.6.7.8.9\") == 0\n assert candidate(version1 = \"1.1.1.1.1.1.1.1.1.1\",version2 = \"1.1.1.1.1.1.1.1.1.1\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"1.0.1\",version2 = \"1.1.0\") == -1\n assert candidate(version1 = \"1.010.001\",version2 = \"1.10.1\") == 0\n assert candidate(version1 = \"2.0.0.0\",version2 = \"1.9.9.9\") == 1\n assert candidate(version1 = \"1.2.3.4.5.6\",version2 = \"1.2.3.4.5.6.0\") == 0\n assert candidate(version1 = \"5.5.5\",version2 = \"5.05.005\") == 0\n assert candidate(version1 = \"0.0.0.0.0.1\",version2 = \"0.0.0.0.0.0\") == 1\n assert candidate(version1 = \"1.1.1.1.1.1.1.1.1.1\",version2 = \"1.1.1.1.1.1.1.1.1.1.0\") == 0\n assert candidate(version1 = \"1.2.3.4.5\",version2 = \"1.2.3.4.5.6\") == -1\n assert candidate(version1 = \"2.0\",version2 = \"2.0.0.0.0.0\") == 0\n assert candidate(version1 = \"9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9\",version2 = \"9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.9.0\") == 0\n assert candidate(version1 = \"2.5.0.0.0\",version2 = \"2.5\") == 0\n assert candidate(version1 = \"1.0.0\",version2 = \"1.0.0.0\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.10\",version2 = \"1.2.3.4.5.6.7.8.9.9\") == 1\n assert candidate(version1 = \"0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0\",version2 = \"0\") == 0\n assert candidate(version1 = \"0.0.0.0.0\",version2 = \"0\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9\",version2 = \"1.2.3.4.5.6.7.8.9.0\") == 0\n assert candidate(version1 = \"2.0.0\",version2 = \"2\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9\",version2 = \"1.2.3.4.5.6.7.8.10\") == -1\n assert candidate(version1 = \"1.2.3.4\",version2 = \"1.2.3.4.0.0\") == 0\n assert candidate(version1 = \"10.0.0.0\",version2 = \"10\") == 0\n assert candidate(version1 = \"9.8.7.6.5.4.3.2.1\",version2 = \"9.8.7.6.5.4.3.2.0\") == 1\n assert candidate(version1 = \"1.0.0\",version2 = \"1.0.0.0.0.0\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.10\",version2 = \"1.2.3.4.5.6.7.8.9.10.0.0\") == 0\n assert candidate(version1 = \"1.10.100.1000\",version2 = \"1.10.100.1000.0\") == 0\n assert candidate(version1 = \"1.001.002.003\",version2 = \"1.1.2.3\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0.0.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.10.11\",version2 = \"1.2.3.4.5.6.7.8.9.10\") == 1\n assert candidate(version1 = \"1.0.0.0.0.0.0\",version2 = \"1.0.0.0.0\") == 0\n assert candidate(version1 = \"1.2.3.0.0.0.0\",version2 = \"1.2.3\") == 0\n assert candidate(version1 = \"1.0.0.0.1\",version2 = \"1\") == 1\n assert candidate(version1 = \"1.2.3.4.5\",version2 = \"1.2.3.4.5.0.0\") == 0\n assert candidate(version1 = \"1.1.1.1.1.1.1.1.1.1\",version2 = \"1.1.1.1.1.1.1.1.1.2\") == -1\n assert candidate(version1 = \"1.2.0.0.0\",version2 = \"1.2\") == 0\n assert candidate(version1 = \"1.2.3.4.5\",version2 = \"1.2.3.4\") == 1\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.10\",version2 = \"1.2.3.4.5.6.7.8.9.11\") == -1\n assert candidate(version1 = \"1.000000001\",version2 = \"1.1\") == 0\n assert candidate(version1 = \"1.200.300.400\",version2 = \"1.200.300.400.000.000\") == 0\n assert candidate(version1 = \"9.9.9.9\",version2 = \"9.9.9.9.0\") == 0\n assert candidate(version1 = \"2.3.4.5.6\",version2 = \"2.3.4.5.0\") == 1\n assert candidate(version1 = \"1.002.003\",version2 = \"1.2.3\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.0\",version2 = \"1.2.3.4.5.6.7.8.9\") == 0\n assert candidate(version1 = \"1.20.3.4\",version2 = \"1.20.3.5\") == -1\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0\",version2 = \"1.0.0\") == 0\n assert candidate(version1 = \"1.2.3.4.5.6.7.8.9.10.11.12.13.14.15\",version2 = \"1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.0\") == 0\n assert candidate(version1 = \"0.0.0.0.0.0.0.0.0.0\",version2 = \"0\") == 0\n assert candidate(version1 = \"1.100.100\",version2 = \"1.99.99\") == 1\n assert candidate(version1 = \"1.000000000.000000000.000000000.000000000\",version2 = \"1.0.0.0\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.1\",version2 = \"1\") == 1\n assert candidate(version1 = \"1.20.3\",version2 = \"1.19.99\") == 1\n assert candidate(version1 = \"1.0.0.0.0.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"1.2.3.4\",version2 = \"1.2.3.4.5\") == -1\n assert candidate(version1 = \"123456789.987654321\",version2 = \"123456789.987654320\") == 1\n assert candidate(version1 = \"1000000000.1000000000\",version2 = \"1000000000.1000000000.0\") == 0\n assert candidate(version1 = \"1.0.0.0.0.0.0.0\",version2 = \"1\") == 0\n assert candidate(version1 = \"0001.0002.0003\",version2 = \"1.2.3\") == 0\n assert candidate(version1 = \"1.00001.00002\",version2 = \"1.1.2\") == 0\n assert candidate(version1 = \"999999999.999999999.999999999\",version2 = \"1000000000\") == -1\n assert candidate(version1 = \"1.0.0.0.0\",version2 = \"1\") == 0\n"}, "metadata": {"canonical_parameter_names": ["version1", "version2"], "leetcode_dataset_entry_point": "Solution().compareVersion", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var compareVersion = function(version1, version2) {", "container": null, "callable": "compareVersion", "parameters": [{"name": "version1", "type": "string"}, {"name": "version2", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 166, "task_id": "fraction-to-recurring-decimal", "difficulty": "Medium", "problem_description": "Given two integers representing the numerator and denominator of a fraction, return the fraction in string format.\nIf the fractional part is repeating, enclose the repeating part in parentheses.\nIf multiple answers are possible, return any of them.\nIt is guaranteed that the length of the answer string is less than 104 for all the given inputs.\n \nExample 1:\n\nInput: numerator = 1, denominator = 2\nOutput: \"0.5\"\n\nExample 2:\n\nInput: numerator = 2, denominator = 1\nOutput: \"2\"\n\nExample 3:\n\nInput: numerator = 4, denominator = 333\nOutput: \"0.(012)\"\n\n \nConstraints:\n\n-231 <= numerator, denominator <= 231 - 1\ndenominator != 0\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(numerator = 7,denominator = -3) == \"-2.(3)\"\n assert candidate(numerator = 1,denominator = 6) == \"0.1(6)\"\n assert candidate(numerator = 4,denominator = 333) == \"0.(012)\"\n assert candidate(numerator = 22,denominator = 7) == \"3.(142857)\"\n assert candidate(numerator = -1,denominator = 1) == \"-1\"\n assert candidate(numerator = -1,denominator = 2) == \"-0.5\"\n assert candidate(numerator = 5,denominator = 2) == \"2.5\"\n assert candidate(numerator = 7,denominator = 6) == \"1.1(6)\"\n assert candidate(numerator = 1,denominator = 13) == \"0.(076923)\"\n assert candidate(numerator = 1,denominator = -2) == \"-0.5\"\n assert candidate(numerator = -1,denominator = -2) == \"0.5\"\n assert candidate(numerator = 2,denominator = 1) == \"2\"\n assert candidate(numerator = 11,denominator = 6) == \"1.8(3)\"\n assert candidate(numerator = 1,denominator = 2) == \"0.5\"\n assert candidate(numerator = 0,denominator = 1) == \"0\"\n assert candidate(numerator = -1,denominator = -1) == \"1\"\n assert candidate(numerator = 1,denominator = -1) == \"-1\"\n assert candidate(numerator = -50,denominator = 8) == \"-6.25\"\n assert candidate(numerator = -2147483648,denominator = 1) == \"-2147483648\"\n assert candidate(numerator = 1,denominator = 17) == \"0.(0588235294117647)\"\n assert candidate(numerator = 1,denominator = 3) == \"0.(3)\"\n assert candidate(numerator = 2,denominator = 3) == \"0.(6)\"\n assert candidate(numerator = 1,denominator = 7) == \"0.(142857)\"\n assert candidate(numerator = 1,denominator = 666) == \"0.0(015)\"\n assert candidate(numerator = 1,denominator = 997) == \"0.(0010030090270812437311935807422266800401203610832497492477432296890672016048144433299899699097291875626880641925777331995987963891675025075225677031093279839518555667)\"\n assert candidate(numerator = -2147483648,denominator = 2) == \"-1073741824\"\n assert candidate(numerator = 1000,denominator = 777) == \"1.(287001)\"\n assert candidate(numerator = 2147483647,denominator = 3) == \"715827882.(3)\"\n assert candidate(numerator = 7,denominator = 12) == \"0.58(3)\"\n assert candidate(numerator = 1,denominator = 999) == \"0.(001)\"\n assert candidate(numerator = 5,denominator = 20) == \"0.25\"\n assert candidate(numerator = 22,denominator = 3) == \"7.(3)\"\n assert candidate(numerator = 789,denominator = 321) == \"2.(45794392523364485981308411214953271028037383177570093)\"\n assert candidate(numerator = 111,denominator = 400) == \"0.2775\"\n assert candidate(numerator = -21,denominator = 6) == \"-3.5\"\n assert candidate(numerator = 29,denominator = 37) == \"0.(783)\"\n assert candidate(numerator = 1,denominator = 1000000000) == \"0.000000001\"\n assert candidate(numerator = 1,denominator = 10001) == \"0.(00009999)\"\n assert candidate(numerator = 1234567890,denominator = 100000000) == \"12.3456789\"\n assert candidate(numerator = 100,denominator = 999) == \"0.(100)\"\n assert candidate(numerator = 10,denominator = 16) == \"0.625\"\n assert candidate(numerator = 100,denominator = 101) == \"0.(9900)\"\n assert candidate(numerator = 111111111,denominator = 333333333) == \"0.(3)\"\n assert candidate(numerator = 123,denominator = 456) == \"0.269(736842105263157894)\"\n assert candidate(numerator = 500,denominator = 22) == \"22.(72)\"\n assert candidate(numerator = 1,denominator = 199) == \"0.(005025125628140703517587939698492462311557788944723618090452261306532663316582914572864321608040201)\"\n assert candidate(numerator = 1,denominator = 333) == \"0.(003)\"\n assert candidate(numerator = 1,denominator = 1001) == \"0.(000999)\"\n assert candidate(numerator = 1,denominator = 99) == \"0.(01)\"\n assert candidate(numerator = 123456,denominator = 111111) == \"1.(111105)\"\n assert candidate(numerator = 5,denominator = 22) == \"0.2(27)\"\n assert candidate(numerator = 1,denominator = 1000) == \"0.001\"\n assert candidate(numerator = 77,denominator = 22) == \"3.5\"\n assert candidate(numerator = -22,denominator = 7) == \"-3.(142857)\"\n assert candidate(numerator = 10,denominator = -3) == \"-3.(3)\"\n assert candidate(numerator = 1,denominator = 1111111111) == \"0.(0000000009)\"\n assert candidate(numerator = -1,denominator = -6) == \"0.1(6)\"\n assert candidate(numerator = 99,denominator = 77) == \"1.(285714)\"\n assert candidate(numerator = 1,denominator = 33333) == \"0.(00003)\"\n assert candidate(numerator = 111,denominator = 990) == \"0.1(12)\"\n assert candidate(numerator = -2,denominator = -3) == \"0.(6)\"\n assert candidate(numerator = 50,denominator = 22) == \"2.(27)\"\n assert candidate(numerator = 1,denominator = 100000) == \"0.00001\"\n assert candidate(numerator = 123456,denominator = 789012) == \"0.(156469103131511307812808930662651518608082006357317759425712)\"\n assert candidate(numerator = 5,denominator = 12) == \"0.41(6)\"\n assert candidate(numerator = 100,denominator = 777) == \"0.(128700)\"\n assert candidate(numerator = 123456,denominator = 987654) == \"0.(124999240624753203044790989557071606048271965688388848726375836072146723447685120497664161740852565777083877552260204484566457484098682332071757923321325079430650814961514862492330310007350752388994526423221087546853452727372136395944328681906821619717026408033582610914348547163277828065294121220589396691553924755025545383302249573231111300111172536131074242599128844716874532984223219872546458577599037719687258898359141966721139184370234920326349106063459470624327952906584694640025758008371352720689634224131122842614923849850251201331640432783140654520712719231633750280968841314873427333863883505762139372695296125971240940653305712324356505415864260155884550662478965305663724340710410730883487537133449568371109720610659198464239500877837785297280221616072025223408197607664222490872309533500598387694476000704700229027574433961691037549587203615841175148381923224125047840640548208178167657904488818958866161631502530238322327454756422795837408647157810326288356043715714207607117472313178501783013079479250830756519995868998657424563662983190469536902599493344835337071484548232478175555407055507293039870237957827336293884295512396041528713496831886470363102868008432102740433390640851958276886439988092996130223742322716254882782836904421993937148029573109611260623659702689403374056096568231384675200019440006318002053350667338966885164237678377245472604778596553043879739260915259797459434174316106652734662138765195098688407073732298962997162974077966575339136985219520196344063811820738841740123565540158800551610179273308263825185743185366535244123954340285160592677192620087601528470496752911444696219526271346038187462410925283550717153983075044499389462301575248011955603885571262810660413464634376006172202005965651938836880121986039645462884775437552017204405591431817215340594985693370350345363862243255229057949443833569245910004920751599244269754387670175992807197662339240260253084582252489232059000419175136231919275373764496473461353874940009355503040538488175008656877813485289382719049383691049699591152367124519315468777527352696389626326628556154280750141243795904233668875942384681275021414381959674136894094490580709438730567587434465916201422765462398775279601965870638907957645086234653026262233535225898948417158235576426562338632760055647018085280877716285257792708782630354354865165331178732633088105753634369931170227630323979855293452970372215370969995565248558705781579379013298179321908279620190876562034882661336864934481103706358704566578984138169844905199594189868111707136304819299066272196538463875000759375246796955209010442928393951728034311611151273624163927853276552314879502335838259147434222916122447739795515433542515901317667928242076678674920569349185038485137507669689992649247611005473576778912453146547272627863604055671318093178380282973591966417389085651452836722171934705878779410603308446075244974454616697750426768888699888827463868925757400871155283125467015776780127453541422400962280312741101640858033278860815629765079673650893936540529375672047093415305359974241991628647279310365775868877157385076150149748798668359567216859345479287280768366249719031158685126572666136116494237860627304703874028759059346694287675643494584135739844115449337521034694336275659289589269116512462866550431628890279389340801535760499122162214702719778383927974776591802392335777509127690466499401612305523999295299770972425566038308962450412796384158824851618076775874952159359451791821832342095511181041133838368497469761677672545243577204162591352842189673711643956284285792392882527686821498216986920520749169243480004131001342575436337016809530463097400506655164662928515451767521824444592944492706960129762042172663706115704487603958471286503168113529636897131991567897259566609359148041723113560011907003869776257677283745117217163095578006062851970426890388739376340297310596625943903431768615324799980559993681997946649332661033114835762321622754527395221403446956120260739084740202540565825683893347265337861234804901311592926267701037002837025922033424660863014780479803655936188179261158259876434459841199448389820726691736174814256814633464755876045659714839407322807379912398471529503247088555303780473728653961812537589074716449282846016924955500610537698424751988044396114428737189339586535365623993827797994034348061163119878013960354537115224562447982795594408568182784659405014306629649654636137756744770942050556166430754089995079248400755730245612329824007192802337660759739746915417747510767940999580824863768080724626235503526538646125059990644496959461511824991343122186514710617280950616308950300408847632875480684531222472647303610373673371443845719249858756204095766331124057615318724978585618040325863105905509419290561269432412565534083798577234537601224720398034129361092042354913765346973737766464774101051582841764423573437661367239944352981914719122283714742207291217369645645134834668821267366911894246365630068829772369676020144706547029627784629030004434751441294218420620986701820678091720379809123437965117338663135065518896293641295433421015861830155094800405810131888292863695180700933727803461536)\"\n assert candidate(numerator = -5,denominator = 2) == \"-2.5\"\n assert candidate(numerator = 100,denominator = 77) == \"1.(298701)\"\n assert candidate(numerator = 1,denominator = 27) == \"0.(037)\"\n assert candidate(numerator = 100,denominator = 99) == \"1.(01)\"\n assert candidate(numerator = -1,denominator = -333) == \"0.(003)\"\n assert candidate(numerator = -1,denominator = 3) == \"-0.(3)\"\n assert candidate(numerator = 1,denominator = -2147483648) == \"-0.0000000004656612873077392578125\"\n assert candidate(numerator = 100,denominator = 33) == \"3.(03)\"\n assert candidate(numerator = 10,denominator = 3) == \"3.(3)\"\n assert candidate(numerator = 111,denominator = 999) == \"0.(1)\"\n assert candidate(numerator = 4,denominator = 11) == \"0.(36)\"\n assert candidate(numerator = 2147483647,denominator = 1) == \"2147483647\"\n assert candidate(numerator = 100,denominator = -3) == \"-33.(3)\"\n assert candidate(numerator = 1,denominator = 3333) == \"0.(0003)\"\n assert candidate(numerator = 1,denominator = 10007) == \"0.(0000999300489657239932047566703307684620765464175077445787948436094733686419506345558109323473568502048566003797341860697511741780753472569201558908763865294293994204057159988008394124113120815429199560307784550814429899070650544618766863195762965923853302688118317177975417207954431897671629859098630958329169581293094833616468472069551314080143899270510642550214849605276306585390226841211152193464574797641650844408913760367742580193864294993504546817227940441690816428500049965024482861996602378335165384231038273208753872289397421804736684320975317277905466173678425102428300189867093034875587089037673628460077945438193264714699710202857999400419706205656040771459978015389227540721494953532527230938343159788148296192665134405915858898770860397721594883581492954931547916458479064654741680823423603477565704007194963525532127510742480263815329269511342060557609673228739882082542220445688018387129009693214749675227340861397022084540821425002498251224143099830118916758269211551913660437693614469871090236834216048765863895273308683921255121415009493354651743779354451883681423003897271909663235734985510142899970020985310282802038572998900769461377036074747676626361546917157989407414809633256720295792944938543019886079744179074647746577395822923953232737084041171180173878285200359748176276606375537124013190766463475567103027880483661436994104127111022284400919356450484660737483761367043069851104227041071250124912561207154991505945837913460577595683021884680723493554511841710802438293194763665434196062756070750474667732587188967722594184071150194863595483161786749275507144998501049265514140101928649945038473068851803737383831318077345857899470370740481662836014789647246927150994303987208953732387328869791146197661636854202058559008693914260017987408813830318776856200659538323173778355151394024183071849705206355551114220045967822524233036874188068352153492555211352053562506245628060357749575297291895673028879784151094234036174677725592085540121914659738183271709803137803537523733386629359448386129709203557509743179774158089337463775357249925052463275707005096432497251923653442590186869191565903867292894973518537024083141800739482362346357549715199360447686619366443489557309883081842710102927950434695713000899370440691515938842810032976916158688917757569701209153592485260317777555711002298391126211651843709403417607674627760567602678125312281403017887478764864594783651443989207554711701808733886279604277006095732986909163585490156890176876186669331467972419306485460177875487158988707904466873188767862496252623163785350254821624862596182672129509343459578295193364644748675926851204157090036974118117317877485759968022384330968322174477865494154092135505146397521734785650044968522034575796942140501648845807934445887878485060457679624263015888877785550114919556310582592185470170880383731388028380133906265614070150894373938243229739182572199460377735585090436694313980213850304786649345458179274507844508843809333466573398620965324273008893774357949435395223343659438393124812631158189267512741081243129809133606475467172978914759668232237433796342560207854501848705905865893874287998401119216548416108723893274707704606775257319876086739282502248426101728789847107025082442290396722294393924253022883981213150794443889277505745977815529129609273508544019186569401419006695313280703507544718696912161486959128609973018886779254521834715699010692515239332467272908963725392225442190466673328669931048266213650444688717897471769761167182971919656240631557909463375637054062156490456680323773358648945737983411611871689817128010392725092435295293294693714399920055960827420805436194663735385230338762865993804336964125112421305086439492355351254122114519836114719696212651144199060657539722194463875287298890776456480463675427200959328470070950334765664035175377235934845608074347956430498650944338962726091735784950534625761966623363645448186269611272109523333666433496552413310682522234435894873588488058359148595982812031577895473168781852703107824522834016188667932447286899170580593584490856400519636254621764764664734685719996002798041371040271809733186769261516938143299690216848206255621065254321974617767562706105725991805735984810632557209953032876986109723193764364944538822824023183771360047966423503547516738283201758768861796742280403717397821524932547216948136304586789247526731288098331168182272409313480563605476166683321674827620665534126111721794743679424402917957429799140601578894773658439092635155391226141700809433396622364344958529029679224542820025981812731088238233236734285999800139902068552013590486659338463075846907164984510842410312781053262716098730888378135305286299590286799240531627860497651643849305486159688218247226941141201159188568002398321175177375836914160087938443089837114020185869891076246627360847406815229339462376336564404916558409113620465674028180273808334166083741381033276706305586089737183971220145897871489957030078944738682921954631757769561307085040471669831118217247926451483961227141001299090636554411911661836714299990006995103427600679524332966923153792345358249225542120515639052663135804936544418906765264314979514339962026581393024882582192465274307984410912361347057060057959428400119916058758868791845708004396922154491855701009293494553812331368042370340761466973118816828220245827920455681023283701409013690416708304187069051663835315279304486859198561007294893574497851503947236934146097731587888478065354252023583491555910862396322574198061357050064954531827720595583091835714999500349755171380033976216648346157689617267912461277106025781952633156790246827220945338263215748975716998101329069651244129109623263715399220545618067352853002897971420005995802937943439592285400219846107724592785050464674727690616568402118517038073348655940841411012291396022784051164185070450684520835415209353452583191765763965224342959928050364744678724892575197361846707304886579394423903267712601179174577795543119816128709903067852503247726591386029779154591785749975017487758569001698810832417307884480863395623063855301289097631657839512341361047266913160787448785849905066453482562206455481163185769961027280903367642650144898571000299790146897171979614270010992305386229639252523233736384530828420105925851903667432797042070550614569801139202558209253522534226041770760467672629159588288198261217147996402518237233936244628759868092335365244328969721195163385630058958728889777155990806435495153392625162386329569301488957729589287498750874387928450084940541620865394224043169781153192765064454881582891975617068052363345658039372439292495253322674128110322774058159288498051364045168382132507244928550014989507344858598980713500549615269311481962626161686819226541421005296292595183371639852103527530728490056960127910462676126711302088538023383631457979414409913060857399820125911861696812231437993404616768262216448486059758169281502947936444488857799540321774757669631258119316478465074447886479464374937543719396422504247027081043269711202158489057659638253222744079144598780853402618167282901968621964624762666133706405516138702907964424902568202258419106625362246427500749475367242929949035675027480763465574098131308084340961327071050264814629759168581992605176376536424502848006395523133806335565104426901169181572898970720495653042869991006295593084840611571899670230838413110822424302987908464075147396822224442889977016088737883481562905965823923253722394323973218746877185969821125212351354052163485560107924452882981912661137203957229939042670130908364145098431098231238133306685320275806935145398221245128410112920955331268112321375037473768362146497451783751374038173278704906565404217048066353552513240731487958429099630258818826821225142400319776156690316778255221345058459078644948536024782652143499550314779654242030578594983511541920655541121215149395423203757369841111222144498850804436894174078145298291196162686119716198660937343859298491056260617567702608174278005396222644149095633056860197861496952133506545418207254921554911561906665334266013790346757269911062256420505646047766563405616068751873688418107324872589187568701908663935245328270210852403317677625662036574397921454981512940941341061257120015988807834515838912761067252922953932247426801239132607174977515738982712101528929749175577096032777056060757469771160187868492055561107224942540221844708703907264914559808134305985809933046867192964924552813030878385130408713900269811132207454781652843009893074847606675327270910362746077745578095333266713300689517337863495553112821025282302388328170280803437593684420905366243629459378435095433196762266413510542620165883881283101828719896072749075647047067053062856000799440391725791945638053362646147696612371340061956630358748875786949135605076446487458778854801638852803037873488558009393424602778055361247127011092235435195363245727990406715299290496652343359648246227640651543919256520435695013490556610372739082642150494653742380333766363545518137303887278904766663335665034475866893174777655641051264115119416408514040171879684221045268312181472968921754771659838113320675527131008294194064155091435994803637453782352353352653142800039972019586289597281902668132307384830618567003097831517937443789347456780253822324372938942740081942640151893674427900469671230138902768062356350554611771759768162286399520335764964524832617167982412311382032577195962826021784750674527830518636954132107524732687119016688318177275906865194363945238333166783251723793344658738882782052563205755970820425702008593984211052263415609073648446087738582991905666033776356550414709703207754571799740181872689117617667632657140001998600979314479864095133406615369241530928350154891575896872189467372839012691116218646947137004097132007594683721395023483561506945138403117817527730588587988408114319976016788248226241630858399120615569101628859798141301089237533726391525931847706605376236634355950834415908863795343259718197261916658339162586189667232936944139102628160287798541021285100429699210552613170780453682422304386929149595283301688817827520735485160387728589987009093634455880883381632857)\"\n assert candidate(numerator = 999,denominator = 77) == \"12.(974025)\"\n"}, "metadata": {"canonical_parameter_names": ["numerator", "denominator"], "leetcode_dataset_entry_point": "Solution().fractionToDecimal", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var fractionToDecimal = function(numerator, denominator) {", "container": null, "callable": "fractionToDecimal", "parameters": [{"name": "numerator", "type": "number"}, {"name": "denominator", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 167, "task_id": "two-sum-ii-input-array-is-sorted", "difficulty": "Medium", "problem_description": "Given a 1-indexed array of integers numbers that is already sorted in non-decreasing order, find two numbers such that they add up to a specific target number. Let these two numbers be numbers[index1] and numbers[index2] where 1 <= index1 < index2 <= numbers.length.\nReturn the indices of the two numbers, index1 and index2, added by one as an integer array [index1, index2] of length 2.\nThe tests are generated such that there is exactly one solution. You may not use the same element twice.\nYour solution must use only constant extra space.\n \nExample 1:\n\nInput: numbers = [2,7,11,15], target = 9\nOutput: [1,2]\nExplanation: The sum of 2 and 7 is 9. Therefore, index1 = 1, index2 = 2. We return [1, 2].\n\nExample 2:\n\nInput: numbers = [2,3,4], target = 6\nOutput: [1,3]\nExplanation: The sum of 2 and 4 is 6. Therefore index1 = 1, index2 = 3. We return [1, 3].\n\nExample 3:\n\nInput: numbers = [-1,0], target = -1\nOutput: [1,2]\nExplanation: The sum of -1 and 0 is -1. Therefore index1 = 1, index2 = 2. We return [1, 2].\n\n \nConstraints:\n\n2 <= numbers.length <= 3 * 104\n-1000 <= numbers[i] <= 1000\nnumbers is sorted in non-decreasing order.\n-1000 <= target <= 1000\nThe tests are generated such that there is exactly one solution.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(numbers = [-3, -2, -1, 0, 0, 1, 2, 3],target = 0) == [1, 8]\n assert candidate(numbers = [-10, -5, 0, 5, 10],target = 0) == [1, 5]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9],target = 17) == [8, 9]\n assert candidate(numbers = [-10, -5, -3, 3, 5, 6, 7, 8, 9],target = 0) == [2, 5]\n assert candidate(numbers = [5, 25, 75],target = 100) == [2, 3]\n assert candidate(numbers = [-10, -5, -2, -1, 0, 1, 2, 5, 10],target = 0) == [1, 9]\n assert candidate(numbers = [-10, -5, -3, -1, 0, 2, 3, 5, 6, 9],target = -8) == [1, 6]\n assert candidate(numbers = [1, 2, 3, 4, 4, 9, 56, 90],target = 8) == [4, 5]\n assert candidate(numbers = [1, 3, 5, 7, 9],target = 10) == [1, 5]\n assert candidate(numbers = [-1000, -500, 0, 500, 1000],target = 0) == [1, 5]\n assert candidate(numbers = [-1, 0],target = -1) == [1, 2]\n assert candidate(numbers = [2, 3, 4],target = 6) == [1, 3]\n assert candidate(numbers = [2, 7, 11, 15],target = 9) == [1, 2]\n assert candidate(numbers = [-50, -25, 0, 25, 50, 75, 100],target = 25) == [1, 6]\n assert candidate(numbers = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40],target = 65) == [9, 14]\n assert candidate(numbers = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110],target = 219) == [10, 11]\n assert candidate(numbers = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],target = 1) == [1, 11]\n assert candidate(numbers = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],target = 768) == [9, 10]\n assert candidate(numbers = [-500, -450, -400, -350, -300, -250, -200, -150, -100, -50, 0],target = -250) == [6, 11]\n assert candidate(numbers = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 40) == [6, 15]\n assert candidate(numbers = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 51) == [9, 12]\n assert candidate(numbers = [-999, -500, -100, 0, 100, 500, 999],target = 500) == [4, 6]\n assert candidate(numbers = [-3, -2, -1, 0, 1, 2, 3],target = 0) == [1, 7]\n assert candidate(numbers = [-10, -5, 0, 3, 7, 9, 11],target = 2) == [2, 5]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 13) == [1, 12]\n assert candidate(numbers = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],target = 70) == [15, 20]\n assert candidate(numbers = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = 0) == [1, 11]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 29) == [14, 15]\n assert candidate(numbers = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],target = 1) == [2, 11]\n assert candidate(numbers = [-10, -5, 0, 3, 7, 9, 11, 15],target = 8) == None\n assert candidate(numbers = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],target = 108) == [25, 30]\n assert candidate(numbers = [-10, -5, 0, 5, 10, 15],target = 5) == [1, 6]\n assert candidate(numbers = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987],target = 1597) == [14, 15]\n assert candidate(numbers = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100],target = -1800) == [1, 3]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 38) == [18, 20]\n assert candidate(numbers = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 1500) == [5, 10]\n assert candidate(numbers = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == [1, 2]\n assert candidate(numbers = [-50, -20, -10, 0, 10, 20, 30, 40, 50],target = 0) == [1, 9]\n assert candidate(numbers = [-499, -333, -222, -111, 0, 111, 222, 333, 499, 666, 888, 1111, 1333, 1666, 1999],target = 1000) == [2, 13]\n assert candidate(numbers = [1, 1, 2, 2, 3, 4, 5],target = 4) == [1, 5]\n assert candidate(numbers = [1, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9],target = 8) == [1, 13]\n assert candidate(numbers = [-10, -5, 0, 5, 10],target = 0) == [1, 5]\n assert candidate(numbers = [-1000, -999, -998, -997, -996, -995, -994, -993, -992, -991],target = -1981) == None\n assert candidate(numbers = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120],target = 210) == None\n assert candidate(numbers = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 5, 6, 7],target = 5) == [1, 12]\n assert candidate(numbers = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],target = 1) == [1, 15]\n assert candidate(numbers = [-1000, -500, -250, -125, -62, -31, -15, -7, -3, -1, 0, 1, 3, 7, 15, 31, 62, 125, 250, 500, 1000],target = -1562) == None\n assert candidate(numbers = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 30) == [5, 10]\n assert candidate(numbers = [1, 1, 1, 1, 1, 1, 1, 1, 1, 9],target = 10) == [1, 10]\n assert candidate(numbers = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31],target = 58) == [14, 16]\n assert candidate(numbers = [1, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 38) == [9, 10]\n assert candidate(numbers = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2],target = 3) == [1, 15]\n assert candidate(numbers = [-10, -5, -1, 0, 2, 5, 8, 12],target = -3) == [2, 5]\n assert candidate(numbers = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 58) == None\n assert candidate(numbers = [-50, -25, -10, -5, 0, 5, 10, 25, 50],target = 0) == [1, 9]\n assert candidate(numbers = [-1000, -999, -998, -997, -996],target = -1998) == [1, 3]\n assert candidate(numbers = [-50, -25, 0, 25, 50],target = 25) == [2, 5]\n assert candidate(numbers = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75],target = 130) == [11, 15]\n assert candidate(numbers = [3, 3, 3, 3, 3],target = 6) == [1, 2]\n assert candidate(numbers = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == [1, 2]\n assert candidate(numbers = [995, 996, 997, 998, 999, 1000],target = 1995) == [1, 6]\n assert candidate(numbers = [-100, -90, -80, -70, -60, -50, -40, -30, -20, -10],target = -80) == [4, 10]\n assert candidate(numbers = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 120) == [3, 19]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],target = 28) == [13, 15]\n assert candidate(numbers = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2],target = 3) == [1, 21]\n assert candidate(numbers = [-500, -250, -100, -50, -25, -10, -5, 0, 5, 10, 25, 50, 100, 250, 500],target = 0) == [1, 15]\n assert candidate(numbers = [500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511],target = 1011) == [1, 12]\n assert candidate(numbers = [100, 150, 200, 250, 300, 350, 400, 450, 500],target = 750) == [4, 9]\n assert candidate(numbers = [-999, -998, -997, -996, -995, -994, -993, -992, -991, -990, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999],target = 0) == [1, 20]\n assert candidate(numbers = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 10],target = 15) == [1, 15]\n assert candidate(numbers = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = -500) == [1, 16]\n assert candidate(numbers = [-100, -50, -25, -10, -5, 0, 5, 10, 25, 50, 100],target = 0) == [1, 11]\n assert candidate(numbers = [100, 150, 200, 250, 300, 350, 400, 450, 500],target = 800) == [5, 9]\n assert candidate(numbers = [-100, -50, -25, 0, 25, 50, 100, 150, 200, 250, 300],target = 200) == [1, 11]\n assert candidate(numbers = [-50, -20, -10, -5, 0, 5, 10, 20, 50],target = 0) == [1, 9]\n assert candidate(numbers = [-1000, -900, -800, -700, -600, -500, -400, -300, -200, -100, 0, 100, 200, 300, 400],target = -500) == [2, 15]\n assert candidate(numbers = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987],target = 1094) == None\n assert candidate(numbers = [-10, -5, 0, 3, 8, 12, 15],target = 5) == [1, 7]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 39) == [19, 20]\n assert candidate(numbers = [-5, 0, 2, 3, 7, 11],target = 5) == [3, 4]\n assert candidate(numbers = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 190) == [17, 19]\n assert candidate(numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 18) == [8, 10]\n assert candidate(numbers = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67],target = 94) == [14, 17]\n assert candidate(numbers = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 8) == [1, 11]\n assert candidate(numbers = [-100, -50, -10, 0, 50, 100, 150],target = 0) == [1, 6]\n assert candidate(numbers = [1, 3, 6, 8, 12, 14, 16, 18, 20, 23, 26, 28, 30, 32, 35, 37, 40, 42, 45, 47],target = 87) == [17, 20]\n assert candidate(numbers = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 7) == [1, 10]\n assert candidate(numbers = [-100, -50, -10, 0, 10, 50, 100],target = 0) == [1, 7]\n assert candidate(numbers = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],target = 768) == [9, 10]\n"}, "metadata": {"canonical_parameter_names": ["numbers", "target"], "leetcode_dataset_entry_point": "Solution().twoSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var twoSum = function(numbers, target) {", "container": null, "callable": "twoSum", "parameters": [{"name": "numbers", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 168, "task_id": "excel-sheet-column-title", "difficulty": "Easy", "problem_description": "Given an integer columnNumber, return its corresponding column title as it appears in an Excel sheet.\nFor example:\n\nA -> 1\nB -> 2\nC -> 3\n...\nZ -> 26\nAA -> 27\nAB -> 28 \n...\n\n \nExample 1:\n\nInput: columnNumber = 1\nOutput: \"A\"\n\nExample 2:\n\nInput: columnNumber = 28\nOutput: \"AB\"\n\nExample 3:\n\nInput: columnNumber = 701\nOutput: \"ZY\"\n\n \nConstraints:\n\n1 <= columnNumber <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(columnNumber = 1) == \"A\"\n assert candidate(columnNumber = 28) == \"AB\"\n assert candidate(columnNumber = 1045) == \"ANE\"\n assert candidate(columnNumber = 2147483647) == \"FXSHRXW\"\n assert candidate(columnNumber = 456976) == \"YYYZ\"\n assert candidate(columnNumber = 52) == \"AZ\"\n assert candidate(columnNumber = 701) == \"ZY\"\n assert candidate(columnNumber = 1048576) == \"BGQCV\"\n assert candidate(columnNumber = 26) == \"Z\"\n assert candidate(columnNumber = 134217728) == \"KGRJXH\"\n assert candidate(columnNumber = 702) == \"ZZ\"\n assert candidate(columnNumber = 1047) == \"ANG\"\n assert candidate(columnNumber = 1046527) == \"BGNCA\"\n assert candidate(columnNumber = 351) == \"MM\"\n assert candidate(columnNumber = 27) == \"AA\"\n assert candidate(columnNumber = 4194304) == \"IDPOJ\"\n assert candidate(columnNumber = 466527) == \"ZNCI\"\n assert candidate(columnNumber = 1048575) == \"BGQCU\"\n assert candidate(columnNumber = 703) == \"AAA\"\n assert candidate(columnNumber = 1234567) == \"BRFGI\"\n assert candidate(columnNumber = 2702) == \"CYX\"\n assert candidate(columnNumber = 16384) == \"XFD\"\n assert candidate(columnNumber = 1000) == \"ALL\"\n assert candidate(columnNumber = 1379) == \"BAA\"\n assert candidate(columnNumber = 123456) == \"FZPH\"\n assert candidate(columnNumber = 4095) == \"FAM\"\n assert candidate(columnNumber = 676) == \"YZ\"\n assert candidate(columnNumber = 10000000) == \"UVXWJ\"\n assert candidate(columnNumber = 14776336) == \"AFHRLP\"\n assert candidate(columnNumber = 1378) == \"AZZ\"\n assert candidate(columnNumber = 140625) == \"GYZQ\"\n assert candidate(columnNumber = 728) == \"AAZ\"\n assert candidate(columnNumber = 2704) == \"CYZ\"\n assert candidate(columnNumber = 18278) == \"ZZZ\"\n assert candidate(columnNumber = 234567890) == \"SSGWWX\"\n assert candidate(columnNumber = 255) == \"IU\"\n assert candidate(columnNumber = 99999999) == \"HJUNYU\"\n assert candidate(columnNumber = 11829215) == \"YVZUU\"\n"}, "metadata": {"canonical_parameter_names": ["columnNumber"], "leetcode_dataset_entry_point": "Solution().convertToTitle", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var convertToTitle = function(columnNumber) {", "container": null, "callable": "convertToTitle", "parameters": [{"name": "columnNumber", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 169, "task_id": "majority-element", "difficulty": "Easy", "problem_description": "Given an array nums of size n, return the majority element.\nThe majority element is the element that appears more than ⌊n / 2⌋ times. You may assume that the majority element always exists in the array.\n \nExample 1:\nInput: nums = [3,2,3]\nOutput: 3\nExample 2:\nInput: nums = [2,2,1,1,1,2,2]\nOutput: 2\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 5 * 104\n-109 <= nums[i] <= 109\n\n \nFollow-up: Could you solve the problem in linear time and in O(1) space?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 2, 2, 2, 2, 2]) == 2\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 3]) == 1\n assert candidate(nums = [2, 2, 1, 1, 1, 2, 2]) == 2\n assert candidate(nums = [-1, 100, -1, -1, -1, -1, 1, 1, 1, 1]) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 4, 4, 4]) == 4\n assert candidate(nums = [4, 4, 4, 4, 2, 2, 3]) == 4\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1, 1, 1, 1, 1]) == 1000000000\n assert candidate(nums = [5, 5, 4, 5, 5, 6, 5, 5]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1000000000, -1000000000, 1000000000, 1000000000, 1000000000]) == 1000000000\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3]) == 3\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 0, 0, 0]) == 7\n assert candidate(nums = [-1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, 1, 1, 1, 1, 1]) == -1000000000\n assert candidate(nums = [1, 1, 2, 2, 1, 1, 1]) == 1\n assert candidate(nums = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == 8\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [3, 2, 3]) == 3\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [4, 4, 4, 4, 4, 4, 5, 5, 5, 5]) == 4\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8]) == 7\n assert candidate(nums = [4, 4, 4, 4, 1, 2, 3]) == 4\n assert candidate(nums = [100, 200, 100, 300, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 100\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == 9\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 0\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1, 2, 3]) == 1000000000\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1, 1, 1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 7\n assert candidate(nums = [1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 1]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-1, -1, -1, -1, -1, 1, 2, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-1, 100, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == -1\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 500000000, 500000000, 500000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 1000000000\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 10, 10, 10, 10, 10]) == 10\n assert candidate(nums = [5, 4, 3, 2, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7]) == 7\n assert candidate(nums = [2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().majorityElement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var majorityElement = function(nums) {", "container": null, "callable": "majorityElement", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 171, "task_id": "excel-sheet-column-number", "difficulty": "Easy", "problem_description": "Given a string columnTitle that represents the column title as appears in an Excel sheet, return its corresponding column number.\nFor example:\n\nA -> 1\nB -> 2\nC -> 3\n...\nZ -> 26\nAA -> 27\nAB -> 28 \n...\n\n \nExample 1:\n\nInput: columnTitle = \"A\"\nOutput: 1\n\nExample 2:\n\nInput: columnTitle = \"AB\"\nOutput: 28\n\nExample 3:\n\nInput: columnTitle = \"ZY\"\nOutput: 701\n\n \nConstraints:\n\n1 <= columnTitle.length <= 7\ncolumnTitle consists only of uppercase English letters.\ncolumnTitle is in the range [\"A\", \"FXSHRXW\"].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(columnTitle = \"MAD\") == 8818\n assert candidate(columnTitle = \"AAA\") == 703\n assert candidate(columnTitle = \"ZY\") == 701\n assert candidate(columnTitle = \"AC\") == 29\n assert candidate(columnTitle = \"Z\") == 26\n assert candidate(columnTitle = \"ZYZ\") == 18252\n assert candidate(columnTitle = \"FXSHRXW\") == 2147483647\n assert candidate(columnTitle = \"ZAB\") == 17604\n assert candidate(columnTitle = \"BZ\") == 78\n assert candidate(columnTitle = \"M\") == 13\n assert candidate(columnTitle = \"ABC\") == 731\n assert candidate(columnTitle = \"ZZZ\") == 18278\n assert candidate(columnTitle = \"AB\") == 28\n assert candidate(columnTitle = \"A\") == 1\n assert candidate(columnTitle = \"XYZ\") == 16900\n assert candidate(columnTitle = \"ZYZY\") == 474577\n assert candidate(columnTitle = \"AAN\") == 716\n assert candidate(columnTitle = \"ACB\") == 756\n assert candidate(columnTitle = \"AAI\") == 711\n assert candidate(columnTitle = \"AAD\") == 706\n assert candidate(columnTitle = \"FXSHRXV\") == 2147483646\n assert candidate(columnTitle = \"ASDFGH\") == 20638470\n assert candidate(columnTitle = \"SS\") == 513\n assert candidate(columnTitle = \"GH\") == 190\n assert candidate(columnTitle = \"AAR\") == 720\n assert candidate(columnTitle = \"ALIBABA\") == 455640953\n assert candidate(columnTitle = \"PQ\") == 433\n assert candidate(columnTitle = \"AAE\") == 707\n assert candidate(columnTitle = \"UU\") == 567\n assert candidate(columnTitle = \"LO\") == 327\n assert candidate(columnTitle = \"RT\") == 488\n assert candidate(columnTitle = \"QWJH\") == 314608\n assert candidate(columnTitle = \"EEEEE\") == 2376275\n assert candidate(columnTitle = \"AAB\") == 704\n assert candidate(columnTitle = \"WORLD\") == 10786572\n assert candidate(columnTitle = \"IK\") == 245\n assert candidate(columnTitle = \"COLUMN\") == 42724228\n assert candidate(columnTitle = \"AZZ\") == 1378\n assert candidate(columnTitle = \"II\") == 243\n assert candidate(columnTitle = \"BAA\") == 1379\n assert candidate(columnTitle = \"AAM\") == 715\n assert candidate(columnTitle = \"DDDDD\") == 1901020\n assert candidate(columnTitle = \"TUVW\") == 366311\n assert candidate(columnTitle = \"ABB\") == 730\n assert candidate(columnTitle = \"BB\") == 54\n assert candidate(columnTitle = \"MZZ\") == 9490\n assert candidate(columnTitle = \"AZY\") == 1377\n assert candidate(columnTitle = \"VV\") == 594\n assert candidate(columnTitle = \"TRE\") == 13993\n assert candidate(columnTitle = \"AAQ\") == 719\n assert candidate(columnTitle = \"MN\") == 352\n assert candidate(columnTitle = \"TY\") == 545\n assert candidate(columnTitle = \"HJKL\") == 147666\n assert candidate(columnTitle = \"ADZ\") == 806\n assert candidate(columnTitle = \"AAAA\") == 18279\n assert candidate(columnTitle = \"CB\") == 80\n assert candidate(columnTitle = \"LL\") == 324\n assert candidate(columnTitle = \"NO\") == 379\n assert candidate(columnTitle = \"ABCDEFG\") == 334123303\n assert candidate(columnTitle = \"BCD\") == 1434\n assert candidate(columnTitle = \"STUVWX\") == 235270254\n assert candidate(columnTitle = \"PO\") == 431\n assert candidate(columnTitle = \"CVBNM\") == 1759329\n assert candidate(columnTitle = \"ALGORITHM\") == 307557815253\n assert candidate(columnTitle = \"QWERTY\") == 212594433\n assert candidate(columnTitle = \"ZXCVBN\") == 319950866\n assert candidate(columnTitle = \"QRSTU\") == 8098345\n assert candidate(columnTitle = \"ALPHABET\") == 11932576390\n assert candidate(columnTitle = \"UVWX\") == 384590\n assert candidate(columnTitle = \"DF\") == 110\n assert candidate(columnTitle = \"WW\") == 621\n assert candidate(columnTitle = \"CC\") == 81\n assert candidate(columnTitle = \"AAO\") == 717\n assert candidate(columnTitle = \"GG\") == 189\n assert candidate(columnTitle = \"QWEN\") == 314484\n assert candidate(columnTitle = \"SD\") == 498\n assert candidate(columnTitle = \"QWJRTYUP\") == 143773244150\n assert candidate(columnTitle = \"WZYZ\") == 422500\n assert candidate(columnTitle = \"MNBVCXZ\") == 4183547654\n assert candidate(columnTitle = \"FXSH\") == 122182\n assert candidate(columnTitle = \"PQRST\") == 7623090\n assert candidate(columnTitle = \"AAU\") == 723\n assert candidate(columnTitle = \"UI\") == 555\n assert candidate(columnTitle = \"NUMBER\") == 176165748\n assert candidate(columnTitle = \"MM\") == 351\n assert candidate(columnTitle = \"BAC\") == 1381\n assert candidate(columnTitle = \"FF\") == 162\n assert candidate(columnTitle = \"WX\") == 622\n assert candidate(columnTitle = \"FXSHRXU\") == 2147483645\n assert candidate(columnTitle = \"YUIOP\") == 11799986\n assert candidate(columnTitle = \"MATH\") == 229692\n assert candidate(columnTitle = \"MIX\") == 9046\n assert candidate(columnTitle = \"LM\") == 325\n assert candidate(columnTitle = \"XY\") == 649\n assert candidate(columnTitle = \"BBZ\") == 1430\n assert candidate(columnTitle = \"AAF\") == 708\n assert candidate(columnTitle = \"IO\") == 249\n assert candidate(columnTitle = \"TU\") == 541\n assert candidate(columnTitle = \"AEZ\") == 832\n assert candidate(columnTitle = \"ER\") == 148\n assert candidate(columnTitle = \"ZZ\") == 702\n assert candidate(columnTitle = \"OL\") == 402\n assert candidate(columnTitle = \"AAV\") == 724\n assert candidate(columnTitle = \"AFZ\") == 858\n assert candidate(columnTitle = \"AAT\") == 722\n assert candidate(columnTitle = \"FGHTY\") == 2870841\n assert candidate(columnTitle = \"QQ\") == 459\n assert candidate(columnTitle = \"MID\") == 9026\n assert candidate(columnTitle = \"DEF\") == 2840\n assert candidate(columnTitle = \"ST\") == 514\n assert candidate(columnTitle = \"ZXCVBNM\") == 8318722529\n assert candidate(columnTitle = \"ACZ\") == 780\n assert candidate(columnTitle = \"ABZ\") == 754\n assert candidate(columnTitle = \"RS\") == 487\n assert candidate(columnTitle = \"QQQQQ\") == 8079335\n assert candidate(columnTitle = \"AS\") == 45\n assert candidate(columnTitle = \"LETTERS\") == 3775891099\n assert candidate(columnTitle = \"XYZZY\") == 11425101\n assert candidate(columnTitle = \"CODING\") == 42575527\n assert candidate(columnTitle = \"AXX\") == 1324\n assert candidate(columnTitle = \"FG\") == 163\n assert candidate(columnTitle = \"AAH\") == 710\n assert candidate(columnTitle = \"QW\") == 465\n assert candidate(columnTitle = \"XYZZ\") == 439426\n assert candidate(columnTitle = \"MIXED\") == 6115230\n assert candidate(columnTitle = \"AGZ\") == 884\n assert candidate(columnTitle = \"AAL\") == 714\n assert candidate(columnTitle = \"UY\") == 571\n assert candidate(columnTitle = \"TR\") == 538\n assert candidate(columnTitle = \"UV\") == 568\n assert candidate(columnTitle = \"AXY\") == 1325\n assert candidate(columnTitle = \"UPPERCASE\") == 4518887657679\n assert candidate(columnTitle = \"AAK\") == 713\n assert candidate(columnTitle = \"VBN\") == 14938\n assert candidate(columnTitle = \"ZZZZ\") == 475254\n assert candidate(columnTitle = \"HJ\") == 218\n assert candidate(columnTitle = \"PROGRAMMING\") == 2359598803856431\n assert candidate(columnTitle = \"ZYXWVUT\") == 8340231686\n assert candidate(columnTitle = \"CAT\") == 2074\n assert candidate(columnTitle = \"BNM\") == 1729\n assert candidate(columnTitle = \"ZZZZZ\") == 12356630\n assert candidate(columnTitle = \"XYZXYZ\") == 297051300\n assert candidate(columnTitle = \"STUVWXYZ\") == 159042692380\n assert candidate(columnTitle = \"SHEET\") == 8826682\n assert candidate(columnTitle = \"OP\") == 406\n assert candidate(columnTitle = \"BBA\") == 1405\n assert candidate(columnTitle = \"NN\") == 378\n assert candidate(columnTitle = \"EE\") == 135\n assert candidate(columnTitle = \"ZZZZZZ\") == 321272406\n assert candidate(columnTitle = \"MNO\") == 9167\n assert candidate(columnTitle = \"QR\") == 460\n assert candidate(columnTitle = \"AAJ\") == 712\n assert candidate(columnTitle = \"AAX\") == 726\n assert candidate(columnTitle = \"QQQQ\") == 310743\n assert candidate(columnTitle = \"HH\") == 216\n assert candidate(columnTitle = \"AZX\") == 1376\n assert candidate(columnTitle = \"AAZ\") == 728\n assert candidate(columnTitle = \"AAG\") == 709\n assert candidate(columnTitle = \"TITLE\") == 9311541\n assert candidate(columnTitle = \"BN\") == 66\n assert candidate(columnTitle = \"TT\") == 540\n assert candidate(columnTitle = \"LEETCODE\") == 97994910369\n assert candidate(columnTitle = \"ABCD\") == 19010\n assert candidate(columnTitle = \"ASDFGHJKL\") == 362741755778\n assert candidate(columnTitle = \"AXZ\") == 1326\n assert candidate(columnTitle = \"PYTHON\") == 201883748\n assert candidate(columnTitle = \"AAS\") == 721\n assert candidate(columnTitle = \"AAC\") == 705\n assert candidate(columnTitle = \"AA\") == 27\n assert candidate(columnTitle = \"OO\") == 405\n assert candidate(columnTitle = \"EXCEL\") == 2708874\n assert candidate(columnTitle = \"HELLO\") == 3752127\n assert candidate(columnTitle = \"GHJKL\") == 3346498\n assert candidate(columnTitle = \"AXB\") == 1302\n assert candidate(columnTitle = \"YY\") == 675\n assert candidate(columnTitle = \"TUVWX\") == 9524110\n assert candidate(columnTitle = \"DD\") == 108\n assert candidate(columnTitle = \"XX\") == 648\n assert candidate(columnTitle = \"JK\") == 271\n assert candidate(columnTitle = \"KL\") == 298\n assert candidate(columnTitle = \"RR\") == 486\n assert candidate(columnTitle = \"CA\") == 79\n assert candidate(columnTitle = \"JKLMNOPQR\") == 2180488677476\n assert candidate(columnTitle = \"SPREADSHEET\") == 2772846287758970\n assert candidate(columnTitle = \"JJ\") == 270\n assert candidate(columnTitle = \"DA\") == 105\n assert candidate(columnTitle = \"PP\") == 432\n assert candidate(columnTitle = \"CVB\") == 2602\n assert candidate(columnTitle = \"OPQR\") == 274916\n assert candidate(columnTitle = \"CODE\") == 62977\n assert candidate(columnTitle = \"AAP\") == 718\n assert candidate(columnTitle = \"TREND\") == 9459636\n assert candidate(columnTitle = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\") == 256094574536617744129141650397448476\n assert candidate(columnTitle = \"BEE\") == 1487\n assert candidate(columnTitle = \"VW\") == 595\n assert candidate(columnTitle = \"LMNO\") == 220079\n assert candidate(columnTitle = \"AAW\") == 725\n assert candidate(columnTitle = \"ZZZZZZZ\") == 8353082582\n assert candidate(columnTitle = \"ABCDEF\") == 12850896\n assert candidate(columnTitle = \"YZ\") == 676\n assert candidate(columnTitle = \"KK\") == 297\n"}, "metadata": {"canonical_parameter_names": ["columnTitle"], "leetcode_dataset_entry_point": "Solution().titleToNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var titleToNumber = function(columnTitle) {", "container": null, "callable": "titleToNumber", "parameters": [{"name": "columnTitle", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 172, "task_id": "factorial-trailing-zeroes", "difficulty": "Medium", "problem_description": "Given an integer n, return the number of trailing zeroes in n!.\nNote that n! = n * (n - 1) * (n - 2) * ... * 3 * 2 * 1.\n \nExample 1:\n\nInput: n = 3\nOutput: 0\nExplanation: 3! = 6, no trailing zero.\n\nExample 2:\n\nInput: n = 5\nOutput: 1\nExplanation: 5! = 120, one trailing zero.\n\nExample 3:\n\nInput: n = 0\nOutput: 0\n\n \nConstraints:\n\n0 <= n <= 104\n\n \nFollow up: Could you write a solution that works in logarithmic time complexity?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 3) == 0\n assert candidate(n = 10000) == 2499\n assert candidate(n = 25) == 6\n assert candidate(n = 100) == 24\n assert candidate(n = 1000) == 249\n assert candidate(n = 10) == 2\n assert candidate(n = 5) == 1\n assert candidate(n = 625) == 156\n assert candidate(n = 15000) == 3748\n assert candidate(n = 1875) == 468\n assert candidate(n = 4000) == 999\n assert candidate(n = 29) == 6\n assert candidate(n = 2345) == 583\n assert candidate(n = 99999) == 24994\n assert candidate(n = 49) == 10\n assert candidate(n = 125) == 31\n assert candidate(n = 62499) == 15618\n assert candidate(n = 4096) == 1021\n assert candidate(n = 2000) == 499\n assert candidate(n = 7500) == 1874\n assert candidate(n = 50000) == 12499\n assert candidate(n = 50) == 12\n assert candidate(n = 2304) == 573\n assert candidate(n = 30) == 7\n assert candidate(n = 4) == 0\n assert candidate(n = 99) == 22\n assert candidate(n = 31249) == 7806\n assert candidate(n = 15625) == 3906\n assert candidate(n = 31250) == 7812\n assert candidate(n = 2050) == 511\n assert candidate(n = 1024) == 253\n assert candidate(n = 250) == 62\n assert candidate(n = 100000) == 24999\n assert candidate(n = 15624) == 3900\n assert candidate(n = 20000) == 4999\n assert candidate(n = 2048) == 509\n assert candidate(n = 8192) == 2045\n assert candidate(n = 375) == 93\n assert candidate(n = 999) == 246\n assert candidate(n = 8000) == 1998\n assert candidate(n = 62500) == 15624\n assert candidate(n = 18) == 3\n assert candidate(n = 5000) == 1249\n assert candidate(n = 9999) == 2495\n assert candidate(n = 20) == 4\n assert candidate(n = 149) == 35\n assert candidate(n = 19) == 3\n assert candidate(n = 249) == 59\n assert candidate(n = 1250) == 312\n assert candidate(n = 24) == 4\n assert candidate(n = 7654) == 1911\n assert candidate(n = 150) == 37\n assert candidate(n = 8750) == 2186\n assert candidate(n = 15) == 3\n assert candidate(n = 2500) == 624\n assert candidate(n = 4999) == 1245\n assert candidate(n = 200) == 49\n assert candidate(n = 14) == 2\n assert candidate(n = 1234) == 305\n assert candidate(n = 9) == 1\n assert candidate(n = 3125) == 781\n assert candidate(n = 9876) == 2467\n assert candidate(n = 7812) == 1950\n assert candidate(n = 124) == 28\n assert candidate(n = 1249) == 308\n assert candidate(n = 499) == 121\n assert candidate(n = 199) == 47\n assert candidate(n = 1) == 0\n assert candidate(n = 500) == 124\n assert candidate(n = 180) == 44\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().trailingZeroes", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var trailingZeroes = function(n) {", "container": null, "callable": "trailingZeroes", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 174, "task_id": "dungeon-game", "difficulty": "Hard", "problem_description": "The demons had captured the princess and imprisoned her in the bottom-right corner of a dungeon. The dungeon consists of m x n rooms laid out in a 2D grid. Our valiant knight was initially positioned in the top-left room and must fight his way through dungeon to rescue the princess.\nThe knight has an initial health point represented by a positive integer. If at any point his health point drops to 0 or below, he dies immediately.\nSome of the rooms are guarded by demons (represented by negative integers), so the knight loses health upon entering these rooms; other rooms are either empty (represented as 0) or contain magic orbs that increase the knight's health (represented by positive integers).\nTo reach the princess as quickly as possible, the knight decides to move only rightward or downward in each step.\nReturn the knight's minimum initial health so that he can rescue the princess.\nNote that any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.\n \nExample 1:\n\n\nInput: dungeon = [[-2,-3,3],[-5,-10,1],[10,30,-5]]\nOutput: 7\nExplanation: The initial health of the knight must be at least 7 if he follows the optimal path: RIGHT-> RIGHT -> DOWN -> DOWN.\n\nExample 2:\n\nInput: dungeon = [[0]]\nOutput: 1\n\n \nConstraints:\n\nm == dungeon.length\nn == dungeon[i].length\n1 <= m, n <= 200\n-1000 <= dungeon[i][j] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(dungeon = [[1, -3, 3], [0, -2, 0], [-3, -3, -3]]) == 3\n assert candidate(dungeon = [[-5, -4, -6], [-6, -5, -8], [3, 3, 1]]) == 12\n assert candidate(dungeon = [[-2, -3, 3], [-5, -10, 1], [10, 30, -5]]) == 7\n assert candidate(dungeon = [[0, 0, 0], [0, 0, 0], [0, 0, 0]]) == 1\n assert candidate(dungeon = [[1, 6, 7, -6, 5, 3], [4, -8, -5, 5, -9, 3], [-3, 1, -2, 6, -6, 2], [-8, -6, -3, -8, -9, -5], [-5, -8, -8, -1, 5, -9]]) == 1\n assert candidate(dungeon = [[-2, -1], [-1, 10]]) == 4\n assert candidate(dungeon = [[0]]) == 1\n assert candidate(dungeon = [[100, 50, -50], [10, -10, -10], [10, 10, -10]]) == 1\n assert candidate(dungeon = [[-1, -2, -6, -3], [-2, -3, -3, -5], [-1, -3, -5, -7], [-8, -8, -3, -4]]) == 20\n assert candidate(dungeon = [[-2, -1, 1], [-1, -2, -2], [-3, 3, 1]]) == 5\n assert candidate(dungeon = [[-3, 5, -10], [0, 0, -3], [3, 1, -2]]) == 4\n assert candidate(dungeon = [[-10, -50, 20], [-30, -10, 10], [10, 30, -5]]) == 41\n assert candidate(dungeon = [[-1, -1, -1], [-1, -1, -1], [-1, -1, 100]]) == 5\n assert candidate(dungeon = [[1, -1, 1, -1, 1], [1, -1, 1, -1, 1], [-1, 1, -1, 1, -1], [1, -1, 1, -1, 1], [-1, 1, -1, 1, -1]]) == 1\n assert candidate(dungeon = [[-2, -3, 3, -5], [-5, -10, 1, 20], [10, 30, -5, 15], [-10, -20, 5, 30]]) == 6\n assert candidate(dungeon = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) == 1\n assert candidate(dungeon = [[10, -15, 20, -25, 30], [-35, 40, -45, 50, -55], [60, -65, 70, -75, 80], [-85, 90, -95, 100, -105], [110, -115, 120, -125, 130]]) == 21\n assert candidate(dungeon = [[-10, -20, -30, 40], [-50, -60, 70, -80], [90, -100, 110, -120], [-130, 140, -150, 160]]) == 61\n assert candidate(dungeon = [[-10, 20, -30, 40, -50, 60], [-20, 30, -40, 50, -60, 70], [30, -40, 50, -60, 70, -80], [40, -50, 60, -70, 80, -90]]) == 11\n assert candidate(dungeon = [[0, -10, 20, -30, 40], [10, -20, 30, -40, 50], [-10, 20, -30, 40, -50], [20, -30, 40, -50, 60], [-30, 40, -50, 60, -70]]) == 11\n assert candidate(dungeon = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == 1\n assert candidate(dungeon = [[1, -1, 1, -1, 1], [-1, 1, -1, 1, -1], [1, -1, 1, -1, 1], [-1, 1, -1, 1, -1], [1, -1, 1, -1, 1]]) == 1\n assert candidate(dungeon = [[-1, -2, -3], [-2, -3, -4], [-3, -4, -5], [-4, -5, -6], [-5, -6, -7]]) == 29\n assert candidate(dungeon = [[-1, -3, -5, -7, -9], [-2, -4, -6, -8, -10], [-3, -6, -9, -12, -15], [-4, -8, -12, -16, -20], [-5, -10, -15, -20, -25]]) == 86\n assert candidate(dungeon = [[-20, -20, -20, -20], [20, 20, 20, 20], [-10, -10, -10, -10], [10, 10, 10, 10]]) == 21\n assert candidate(dungeon = [[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]]) == 2\n assert candidate(dungeon = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 1\n assert candidate(dungeon = [[-5, 0, 5, -10, 10], [-2, 3, -4, 5, -6], [0, 1, -2, 3, -4], [5, -6, 7, -8, 9], [10, -11, 12, -13, 14]]) == 6\n assert candidate(dungeon = [[-100, -200, 300], [400, -500, 100], [-200, 100, -300], [50, 100, -100]]) == 101\n assert candidate(dungeon = [[-1, 2, -3, 4, -5], [5, -4, 3, -2, 1], [-1, 2, -3, 4, -5], [5, -4, 3, -2, 1], [-1, 2, -3, 4, -5]]) == 2\n assert candidate(dungeon = [[-10, -20, -30], [10, 20, 30], [-10, -20, -30], [10, 20, 30], [-10, -20, -30]]) == 11\n assert candidate(dungeon = [[-30, -20, -10], [0, 10, 20], [10, 20, 30], [-10, -20, -30]]) == 31\n assert candidate(dungeon = [[-1, 2, -3, 4], [-5, 6, -7, 8], [-9, 10, -11, 12], [-13, 14, -15, 16]]) == 2\n assert candidate(dungeon = [[1000, -1000, 1000], [-1000, 1000, -1000], [1000, -1000, 1000]]) == 1\n assert candidate(dungeon = [[-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1]]) == 10\n assert candidate(dungeon = [[-5, -5, -5, -5], [-5, 0, 0, -5], [-5, 0, 0, -5], [-5, -5, -5, -5]]) == 21\n assert candidate(dungeon = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == 1\n assert candidate(dungeon = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]) == 1\n assert candidate(dungeon = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1]]) == 1\n assert candidate(dungeon = [[100, -100, 100, -100], [100, -100, 100, -100], [100, -100, 100, -100], [100, -100, 100, -100]]) == 1\n assert candidate(dungeon = [[1000, -1000, 1000, -1000], [1000, 1000, -1000, 1000], [-1000, 1000, 1000, -1000], [-1000, -1000, 1000, 1000]]) == 1\n assert candidate(dungeon = [[-1000, 1000, -1000, 1000], [-1000, 1000, -1000, 1000], [1000, -1000, 1000, -1000], [1000, -1000, 1000, -1000]]) == 1001\n assert candidate(dungeon = [[-500, 500, -500, 500], [500, -500, 500, -500], [-500, 500, -500, 500], [500, -500, 500, -1]]) == 501\n assert candidate(dungeon = [[-50, -10, -20, -15], [20, 30, -10, 10], [-5, 15, 20, -20], [10, -10, 30, -30]]) == 51\n assert candidate(dungeon = [[-20, -30, 40, 10], [-15, -25, 35, 5], [-10, -5, 25, -5], [5, 10, -15, 20]]) == 46\n assert candidate(dungeon = [[-20, -30, 10, 50], [-50, -10, 20, 30], [-10, 5, -100, 10], [100, 10, -5, 20]]) == 51\n assert candidate(dungeon = [[1, -2, 3, -4, 5], [6, -7, 8, -9, 10], [-11, 12, -13, 14, -15], [16, -17, 18, -19, 20], [21, -22, 23, -24, 25]]) == 2\n assert candidate(dungeon = [[10, -10, 20, -20, 30], [-30, 40, -50, 60, -70], [80, -90, 100, -110, 120], [-130, 140, -150, 160, -170]]) == 31\n assert candidate(dungeon = [[100, -100, 200, -200], [-200, 300, -300, 400], [400, -400, 500, -500], [-500, 600, -600, 700]]) == 1\n assert candidate(dungeon = [[-1, -2, -3, -4, -5], [10, 9, 8, 7, 6], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == 2\n assert candidate(dungeon = [[-10, -20, -30, -40, -50], [-9, -18, -27, -36, -45], [-8, -16, -24, -32, -40], [-7, -14, -21, -28, -35], [-6, -12, -18, -24, -30]]) == 125\n assert candidate(dungeon = [[-1, -2, -3, -4, -5, 6, 7, 8, 9, 10], [-10, -9, -8, -7, -6, 5, 4, 3, 2, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4], [-4, -3, -2, -1, 0, 1, 2, 3, 4, 5], [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6], [-2, -1, 0, 1, 2, 3, 4, 5, 6, 7], [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]]) == 12\n assert candidate(dungeon = [[-20, -30, 40, 50], [-10, -20, -10, 10], [30, 10, -20, -30], [50, 50, 50, -5]]) == 31\n assert candidate(dungeon = [[-20, -30, 30, -50], [10, 20, -40, 60], [-30, -40, 20, -10], [50, 10, -20, -60]]) == 41\n assert candidate(dungeon = [[1, -3, 2, 4, -1], [2, -2, 3, -2, -2], [1, -1, -2, -3, 3], [-1, 3, -2, -3, 4]]) == 1\n assert candidate(dungeon = [[0, -10, 5, 0, 0], [-5, 0, 0, -10, -1], [0, 0, 10, 0, -20], [0, 10, -20, 0, 10], [-10, -20, 0, 10, 0]]) == 6\n assert candidate(dungeon = [[-2, -1, -6], [-1, 10, -1], [-2, -3, -4], [1, 2, -5]]) == 4\n assert candidate(dungeon = [[1000, -1000, 1000], [-1000, 1000, -1000], [1000, -1000, 1000], [-1000, 1000, -1000], [1000, -1000, 1000]]) == 1\n assert candidate(dungeon = [[10, -10, 20, -20], [5, -5, 10, -10], [0, 0, 0, 0], [-5, 5, -15, 15]]) == 1\n assert candidate(dungeon = [[-5, -4, -3, -2, -1, 0, 1, 2, 3, 4], [4, 3, 2, 1, 0, -1, -2, -3, -4, -5], [5, 4, 3, 2, 1, 0, -1, -2, -3, -4], [4, 3, 2, 1, 0, -1, -2, -3, -4, -5], [3, 2, 1, 0, -1, -2, -3, -4, -5, -4], [2, 1, 0, -1, -2, -3, -4, -5, -4, -3], [1, 0, -1, -2, -3, -4, -5, -4, -3, -2], [0, -1, -2, -3, -4, -5, -4, -3, -2, -1]]) == 12\n assert candidate(dungeon = [[-1, -2, -3, -4, -5], [5, 4, 3, 2, 1], [1, 0, 1, 0, 1], [0, 1, 0, 1, 0], [-5, -4, -3, -2, -1]]) == 2\n assert candidate(dungeon = [[-10, -20, -30, -40], [-30, -40, -50, -60], [-40, -50, -60, -70], [-50, -60, -70, -80]]) == 311\n assert candidate(dungeon = [[-2, -3, -2, -5], [-3, -2, -2, -5], [-2, -2, -2, -5], [-5, -5, -5, -20]]) == 37\n assert candidate(dungeon = [[1, 2, 3, 4], [2, 3, 4, 5], [3, 4, 5, 6], [4, 5, 6, 7]]) == 1\n assert candidate(dungeon = [[-50, -50, -50, -50], [-50, -50, -50, -50], [-50, -50, -50, -50], [-50, -50, -50, 100]]) == 301\n assert candidate(dungeon = [[-1, 100, 200, -300], [100, -200, -300, 400], [200, -300, 400, -500], [300, 400, -500, 600]]) == 2\n assert candidate(dungeon = [[-1, -2, -3, -4], [-2, -3, -4, -5], [-3, -4, -5, -6], [-4, -5, -6, -7]]) == 29\n assert candidate(dungeon = [[-20, -15, -10, -5], [-10, -5, 0, 5], [0, 5, 10, 15], [5, 10, 15, 20]]) == 31\n assert candidate(dungeon = [[10, -15, 10], [-10, 20, -10], [10, -5, 20], [-15, 10, -20]]) == 1\n assert candidate(dungeon = [[-5, 10, 15, -20], [-10, 20, -15, 25], [5, -10, 30, -35], [-15, 25, -20, 30]]) == 6\n assert candidate(dungeon = [[1, -1, 1, -1], [-1, 1, -1, 1], [1, -1, 1, -1], [-1, 1, -1, 1]]) == 1\n assert candidate(dungeon = [[-1000, 1000, -1000, 1000], [-1000, 1000, -1000, 1000], [-1000, 1000, -1000, 1000], [-1000, 1000, -1000, 1000]]) == 1001\n assert candidate(dungeon = [[-1, 2, -3, 4, -5], [6, -7, 8, -9, 10], [-11, 12, -13, 14, -15], [16, -17, 18, -19, 20], [-21, 22, -23, 24, -25]]) == 6\n assert candidate(dungeon = [[-100, -200, 300], [-400, -500, 600], [700, 800, -900]]) == 301\n assert candidate(dungeon = [[-10, -20, -30, -40], [-40, -50, -60, -70], [-70, -80, -90, -100], [100, 100, 100, 100]]) == 121\n assert candidate(dungeon = [[-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, 1000]]) == 7\n assert candidate(dungeon = [[-5, -10, 15, -20, 25], [-30, 35, -40, 45, -50], [-60, 65, -70, 75, -80], [-90, 95, -100, 105, -110], [120, -125, 130, -135, 140]]) == 16\n assert candidate(dungeon = [[-20, -30, 30, -10], [10, -5, -50, 20], [0, 20, -30, 10], [-10, 50, -10, 20]]) == 21\n assert candidate(dungeon = [[-100, 100, -50, 50], [-200, 200, -150, 150], [100, -100, 50, -50], [-50, 50, -25, 25]]) == 101\n assert candidate(dungeon = [[100, -100, 0, -100], [100, -100, 0, 100], [0, 100, -100, 0], [-100, 0, 100, -100]]) == 1\n assert candidate(dungeon = [[10, -30, 20, -40, 50], [30, -10, -50, 10, 0], [0, 20, 30, -20, -10], [-10, 10, 20, -30, 40], [-50, 40, -30, 20, 10]]) == 1\n assert candidate(dungeon = [[-2, -3, 4, 1], [-3, -2, 1, -1], [3, -4, 2, -4], [4, 2, -4, 3]]) == 6\n assert candidate(dungeon = [[-1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1]]) == 2\n assert candidate(dungeon = [[-2, -3, 3, -4], [3, -5, -10, 1], [10, 30, -5, 20], [10, 10, -10, -20]]) == 3\n assert candidate(dungeon = [[0, -5, 10, -10, 20], [-5, 10, -5, 0, 5], [10, -5, 0, 5, -10], [0, 5, -10, 15, -5]]) == 6\n assert candidate(dungeon = [[-20, 10, -30, 40], [-10, -5, 5, -15], [20, -20, 10, -10], [-30, 20, -10, 5]]) == 21\n assert candidate(dungeon = [[-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, 10]]) == 7\n assert candidate(dungeon = [[-1, -2, -3, -4, -5], [-5, -6, -7, -8, -9], [-9, -10, -11, -12, -13], [-13, -14, -15, -16, -17], [-17, -18, -19, -20, 100]]) == 55\n assert candidate(dungeon = [[-1, -1, -10], [-5, -5, -5], [-2, -1, 10]]) == 9\n assert candidate(dungeon = [[-5, -10, 100], [-50, -100, 200], [-100, -200, 300], [-200, -300, 400]]) == 16\n assert candidate(dungeon = [[-1, -3, -5, -7], [-9, -11, -13, -15], [-17, -19, -21, -23], [-25, -27, -29, -31]]) == 86\n assert candidate(dungeon = [[-10, -20, -30], [10, 20, 30], [-10, -20, -30], [10, 20, 30], [-10, -20, 100]]) == 11\n assert candidate(dungeon = [[-2, -3, 3, -5], [1, 2, -4, 6], [-3, -4, 2, -1], [5, 1, -2, -6]]) == 5\n assert candidate(dungeon = [[10, -10, 0, 10], [-10, 10, -10, 10], [0, -10, 10, -10], [10, -10, 10, 0]]) == 1\n assert candidate(dungeon = [[-20, -30, 10, 50], [-10, -40, 20, 10], [30, -10, -20, 40], [-50, 10, 5, -15]]) == 31\n assert candidate(dungeon = [[-2, -3, 3, -4], [5, -6, 7, -8], [-9, 10, -11, 12], [13, -14, 15, -16]]) == 6\n assert candidate(dungeon = [[1, -1, -1, 1], [-1, -2, -1, 1], [-1, -2, -1, -1], [1, 1, -1, -1]]) == 2\n assert candidate(dungeon = [[-1, -2, -3, -4], [-2, -3, -4, -5], [-3, -4, -5, -6], [-4, -5, -6, -7]]) == 29\n"}, "metadata": {"canonical_parameter_names": ["dungeon"], "leetcode_dataset_entry_point": "Solution().calculateMinimumHP", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var calculateMinimumHP = function(dungeon) {", "container": null, "callable": "calculateMinimumHP", "parameters": [{"name": "dungeon", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 179, "task_id": "largest-number", "difficulty": "Medium", "problem_description": "Given a list of non-negative integers nums, arrange them such that they form the largest number and return it.\nSince the result may be very large, so you need to return a string instead of an integer.\n \nExample 1:\n\nInput: nums = [10,2]\nOutput: \"210\"\n\nExample 2:\n\nInput: nums = [3,30,34,5,9]\nOutput: \"9534330\"\n\n \nConstraints:\n\n1 <= nums.length <= 100\n0 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 0]) == \"0\"\n assert candidate(nums = [1]) == \"1\"\n assert candidate(nums = [3, 30, 34, 5, 9]) == \"9534330\"\n assert candidate(nums = [10, 2]) == \"210\"\n assert candidate(nums = [111311, 1113]) == \"1113111311\"\n assert candidate(nums = [10, 100, 1000]) == \"101001000\"\n assert candidate(nums = [9, 99, 999, 9999]) == \"9999999999\"\n assert candidate(nums = [3, 30, 34, 5, 9, 10]) == \"953433010\"\n assert candidate(nums = [10, 20, 30, 40, 50]) == \"5040302010\"\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == \"9876543210\"\n assert candidate(nums = [34323, 3432]) == \"343234323\"\n assert candidate(nums = [121, 12]) == \"12121\"\n assert candidate(nums = [100, 10, 1]) == \"110100\"\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000]) == \"1101001000100001000001000000\"\n assert candidate(nums = [12, 121, 1212, 12121]) == \"12121212121121\"\n assert candidate(nums = [12345, 1234, 123, 12, 1]) == \"123451234123121\"\n assert candidate(nums = [233, 23, 2]) == \"233232\"\n assert candidate(nums = [11, 111, 1111, 11111]) == \"11111111111111\"\n assert candidate(nums = [123, 12, 121, 1212, 1]) == \"1231212121211\"\n assert candidate(nums = [12, 121, 12121, 1212]) == \"12121212121121\"\n assert candidate(nums = [33, 3, 333, 3333]) == \"3333333333\"\n assert candidate(nums = [82, 828, 8282, 82828]) == \"82882828828282\"\n assert candidate(nums = [233, 23, 2333]) == \"233323323\"\n assert candidate(nums = [99, 98, 97, 96, 95, 94, 93, 92, 91, 90]) == \"99989796959493929190\"\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == \"9876543210\"\n assert candidate(nums = [30, 3, 34, 5, 9, 31]) == \"953433130\"\n assert candidate(nums = [56, 565, 5656, 56565]) == \"56565656565565\"\n assert candidate(nums = [21, 212, 2121]) == \"212212121\"\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000]) == \"110100100010000100000\"\n assert candidate(nums = [12, 121, 1211]) == \"121211211\"\n assert candidate(nums = [34323, 3432, 343, 34]) == \"34343343234323\"\n assert candidate(nums = [830, 8308]) == \"8308830\"\n assert candidate(nums = [1000000, 10000, 100, 1]) == \"1100100001000000\"\n assert candidate(nums = [987, 98, 9, 9876]) == \"9989879876\"\n assert candidate(nums = [3, 30, 34, 5, 9, 300, 303]) == \"9534330330300\"\n assert candidate(nums = [830, 83, 83083]) == \"8383083830\"\n assert candidate(nums = [0, 0, 0, 1]) == \"1000\"\n assert candidate(nums = [999, 99, 9, 100, 10]) == \"99999910100\"\n assert candidate(nums = [10, 100, 1000, 10000, 100000]) == \"10100100010000100000\"\n assert candidate(nums = [12, 21, 121, 122, 212, 211]) == \"2122121112212121\"\n assert candidate(nums = [90, 900, 9000, 90000, 900000, 9000000, 90000000]) == \"90900900090000900000900000090000000\"\n assert candidate(nums = [34323, 3432]) == \"343234323\"\n assert candidate(nums = [1000, 100, 10, 1]) == \"1101001000\"\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]) == \"1000000000\"\n assert candidate(nums = [45, 454, 4545, 45454]) == \"45454545454454\"\n assert candidate(nums = [839, 8399, 83998, 83983]) == \"83998839983983983\"\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == \"0\"\n assert candidate(nums = [789, 7897, 78978, 789789, 7897897, 78978978]) == \"789789789789789787897897789787897\"\n assert candidate(nums = [33, 333, 3333, 33333]) == \"33333333333333\"\n assert candidate(nums = [830, 83, 834, 835, 832]) == \"83835834832830\"\n assert candidate(nums = [55, 555, 5, 5555, 55555]) == \"555555555555555\"\n assert candidate(nums = [0, 0, 0, 0, 1]) == \"10000\"\n assert candidate(nums = [11, 111, 1111, 11111, 111111, 1111111]) == \"111111111111111111111111111\"\n assert candidate(nums = [101, 10, 1, 100]) == \"110110100\"\n assert candidate(nums = [2, 22, 222, 2222, 22222, 222222, 2222222, 22222222]) == \"222222222222222222222222222222222222\"\n assert candidate(nums = [987, 98, 9, 999, 99, 998, 9989]) == \"999999998999898987\"\n assert candidate(nums = [12, 121, 1213, 12131]) == \"12131213112121\"\n assert candidate(nums = [111311, 1113, 11113, 11131, 111]) == \"11131113111131111113111\"\n assert candidate(nums = [1111111111, 111111111, 11111111, 1111111, 111111, 11111, 1111, 111, 11, 1]) == \"1111111111111111111111111111111111111111111111111111111\"\n assert candidate(nums = [100, 1000, 10, 1]) == \"1101001000\"\n assert candidate(nums = [5, 55, 555, 5555, 55555]) == \"555555555555555\"\n assert candidate(nums = [7, 77, 777, 7777, 77777]) == \"777777777777777\"\n assert candidate(nums = [987654321, 98765432, 9876543, 987654, 98765, 9876, 987, 98, 9]) == \"998987987698765987654987654398765432987654321\"\n assert candidate(nums = [0, 0, 0, 1]) == \"1000\"\n assert candidate(nums = [9, 99, 999, 9999, 99999, 999999]) == \"999999999999999999999\"\n assert candidate(nums = [12, 121, 12121, 1212, 1]) == \"121212121211211\"\n assert candidate(nums = [7, 77, 777, 7777]) == \"7777777777\"\n assert candidate(nums = [21, 212, 2121, 211]) == \"212212121211\"\n assert candidate(nums = [9999, 999, 99, 9]) == \"9999999999\"\n assert candidate(nums = [34, 343, 3434]) == \"343434343\"\n assert candidate(nums = [7, 70, 707, 77, 700]) == \"77770770700\"\n assert candidate(nums = [123, 1234, 12345, 123456]) == \"123456123451234123\"\n assert candidate(nums = [999, 9999, 99999]) == \"999999999999\"\n assert candidate(nums = [1111, 111, 11, 1]) == \"1111111111\"\n assert candidate(nums = [1, 34, 3, 98, 9, 76, 45, 6]) == \"998766453431\"\n assert candidate(nums = [9, 98, 989, 9898]) == \"9989989898\"\n assert candidate(nums = [99, 9, 999, 9999]) == \"9999999999\"\n assert candidate(nums = [300, 30, 3]) == \"330300\"\n assert candidate(nums = [987, 98, 9]) == \"998987\"\n assert candidate(nums = [8, 89, 898, 8989, 89898, 898989]) == \"898989898989898988988\"\n assert candidate(nums = [10, 101, 1011, 10111]) == \"10111101110110\"\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0]) == \"9876543210\"\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == \"98765432110\"\n assert candidate(nums = [345, 3453, 34534]) == \"345345343453\"\n assert candidate(nums = [555, 55, 5]) == \"555555\"\n assert candidate(nums = [12, 121]) == \"12121\"\n assert candidate(nums = [7, 77, 777, 7777, 77777]) == \"777777777777777\"\n assert candidate(nums = [0, 4, 44, 444, 4444]) == \"44444444440\"\n assert candidate(nums = [111, 11, 1111, 11111, 1]) == \"111111111111111\"\n assert candidate(nums = [90, 909, 9090]) == \"909909090\"\n assert candidate(nums = [1000, 10, 100, 1]) == \"1101001000\"\n assert candidate(nums = [67, 676, 6767, 67676, 676767, 6767676]) == \"676767676767676767667676676\"\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == \"98765432110\"\n assert candidate(nums = [7, 77, 777, 7777, 77777, 777777, 7777777]) == \"7777777777777777777777777777\"\n assert candidate(nums = [830, 8308, 830830, 83083]) == \"830883083830830830\"\n assert candidate(nums = [1000, 100, 10, 1]) == \"1101001000\"\n assert candidate(nums = [1, 20, 23, 4, 2]) == \"4232201\"\n assert candidate(nums = [78, 787, 7878, 78787]) == \"78787878787787\"\n assert candidate(nums = [21, 212, 2121, 21212]) == \"21221212212121\"\n assert candidate(nums = [111311, 1113, 11, 11131111, 11111113, 11113111]) == \"111311131111131111111131111111111311\"\n assert candidate(nums = [5, 50, 500, 5000, 50000, 500000, 5000000, 50000000]) == \"550500500050000500000500000050000000\"\n assert candidate(nums = [123, 234, 345, 456, 567, 678, 789, 890]) == \"890789678567456345234123\"\n assert candidate(nums = [824, 82, 8]) == \"882824\"\n assert candidate(nums = [3, 30, 34, 5, 9, 300, 303, 33, 333]) == \"953433333330330300\"\n assert candidate(nums = [79, 798, 797, 7987]) == \"798798779797\"\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == \"908070605040302010100\"\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == \"1101001000100001000001000000100000001000000001000000000\"\n assert candidate(nums = [1, 10, 101, 1011, 10111]) == \"110111101110110\"\n assert candidate(nums = [88, 888, 8888, 88888, 888888, 8888888, 88888888]) == \"88888888888888888888888888888888888\"\n assert candidate(nums = [83, 838, 8383, 83838]) == \"83883838838383\"\n assert candidate(nums = [20, 200, 2000, 20000]) == \"20200200020000\"\n assert candidate(nums = [999999999, 99999999, 9999999, 999999, 99999, 9999, 999, 99, 9, 0]) == \"9999999999999999999999999999999999999999999990\"\n assert candidate(nums = [30, 303, 3003, 3]) == \"3303303003\"\n assert candidate(nums = [30033, 300, 3, 3003]) == \"3300333003300\"\n assert candidate(nums = [100, 1000, 10000, 100000, 1]) == \"1100100010000100000\"\n assert candidate(nums = [56, 565, 566]) == \"56656565\"\n assert candidate(nums = [6, 66, 666, 6666, 66666, 666666, 6666666, 66666666, 666666666, 6666666666]) == \"6666666666666666666666666666666666666666666666666666666\"\n assert candidate(nums = [111, 11, 1]) == \"111111\"\n assert candidate(nums = [123, 1231, 12312, 12, 121, 1212]) == \"123123121231121212121\"\n assert candidate(nums = [12, 121, 1211, 12111]) == \"12121121112111\"\n assert candidate(nums = [432, 4324, 43, 43243, 4]) == \"443432443243432\"\n assert candidate(nums = [111, 11, 1, 1111]) == \"1111111111\"\n assert candidate(nums = [33, 330, 3330, 333]) == \"333333330330\"\n assert candidate(nums = [824, 8247]) == \"8248247\"\n assert candidate(nums = [9, 99, 999, 9999]) == \"9999999999\"\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 0]) == \"1110000\"\n assert candidate(nums = [1, 20, 23, 4, 25]) == \"42523201\"\n assert candidate(nums = [0, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == \"8642018161412100\"\n assert candidate(nums = [21, 212, 2121, 21212]) == \"21221212212121\"\n assert candidate(nums = [4, 44, 444, 4444, 44444, 444444, 4444444, 44444444]) == \"444444444444444444444444444444444444\"\n assert candidate(nums = [111311, 1113, 11, 1111, 1]) == \"11131113111111111\"\n assert candidate(nums = [100, 10, 1, 101, 110, 111, 11, 1001]) == \"111111110101101001100\"\n assert candidate(nums = [1, 34, 3, 98, 9, 76, 45, 67]) == \"9987667453431\"\n assert candidate(nums = [54, 546, 548, 60]) == \"6054854654\"\n assert candidate(nums = [33, 333, 3333, 33333, 3]) == \"333333333333333\"\n assert candidate(nums = [1000000000, 100000000, 10000000, 1000000, 100000, 10000, 1000, 100, 10, 1]) == \"1101001000100001000001000000100000001000000001000000000\"\n assert candidate(nums = [10, 100, 1000, 10000]) == \"10100100010000\"\n assert candidate(nums = [999999999, 99999999, 9999999, 999999, 99999, 9999, 999, 99, 9, 1]) == \"9999999999999999999999999999999999999999999991\"\n assert candidate(nums = [66, 666, 6666, 66666, 666666, 6666666, 66666666]) == \"66666666666666666666666666666666666\"\n assert candidate(nums = [1, 10, 100, 1000, 10000]) == \"110100100010000\"\n assert candidate(nums = [824, 938, 1399, 5607, 6973, 5703, 9609, 4398, 6828, 5662, 6699, 10, 7896, 8626, 3462, 2000, 7988, 626, 6670, 4224, 2996]) == \"9609938862682479887896697368286699667062657035662560743984224346229962000139910\"\n assert candidate(nums = [233, 322, 32]) == \"32322233\"\n assert candidate(nums = [32, 323, 3232, 32323]) == \"32332323323232\"\n assert candidate(nums = [647, 64, 646, 6476]) == \"647664764664\"\n assert candidate(nums = [111, 11, 1]) == \"111111\"\n assert candidate(nums = [1, 20, 200, 2000, 20000]) == \"202002000200001\"\n assert candidate(nums = [12, 121, 1211, 12111, 121111, 1]) == \"121211211121111211111\"\n assert candidate(nums = [333, 33, 3]) == \"333333\"\n assert candidate(nums = [824, 8247]) == \"8248247\"\n assert candidate(nums = [35, 353, 3535, 35353, 353535, 3535353, 35353535]) == \"35353535353535353535353535335353353\"\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().largestNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var largestNumber = function(nums) {", "container": null, "callable": "largestNumber", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 187, "task_id": "repeated-dna-sequences", "difficulty": "Medium", "problem_description": "The DNA sequence is composed of a series of nucleotides abbreviated as 'A', 'C', 'G', and 'T'.\n\nFor example, \"ACGAATTCCG\" is a DNA sequence.\n\nWhen studying DNA, it is useful to identify repeated sequences within the DNA.\nGiven a string s that represents a DNA sequence, return all the 10-letter-long sequences (substrings) that occur more than once in a DNA molecule. You may return the answer in any order.\n \nExample 1:\nInput: s = \"AAAAACCCCCAAAAACCCCCCAAAAAGGGTTT\"\nOutput: [\"AAAAACCCCC\",\"CCCCCAAAAA\"]\nExample 2:\nInput: s = \"AAAAAAAAAAAAA\"\nOutput: [\"AAAAAAAAAA\"]\n\n \nConstraints:\n\n1 <= s.length <= 105\ns[i] is either 'A', 'C', 'G', or 'T'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"ACGACGACGACGACGACG\") == ['ACGACGACGA', 'CGACGACGAC', 'GACGACGACG']\n assert candidate(s = \"AAAAAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"AAAAACCCCCAAAAACCCCCCAAAAAGGGTTT\") == ['AAAAACCCCC', 'CCCCCAAAAA']\n assert candidate(s = \"CGTTGCGTTGCGTTGCGTTG\") == ['CGTTGCGTTG', 'GTTGCGTTGC', 'TTGCGTTGCG', 'TGCGTTGCGT', 'GCGTTGCGTT']\n assert candidate(s = \"AAAAAAAAAATTTTTTTTTTAAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"CGCGCGCGCGCGCGCGCGCG\") == ['CGCGCGCGCG', 'GCGCGCGCGC']\n assert candidate(s = \"ACGTTTACGTTTACGTTT\") == ['ACGTTTACGT', 'CGTTTACGTT', 'GTTTACGTTT']\n assert candidate(s = \"ACGACGACGACGACGACGACGACGACG\") == ['ACGACGACGA', 'CGACGACGAC', 'GACGACGACG']\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT\") == ['TTTTTTTTTT']\n assert candidate(s = \"ACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"ACGACGACGACGACGACGACGACGACGACG\") == ['ACGACGACGA', 'CGACGACGAC', 'GACGACGACG']\n assert candidate(s = \"AAAAAAAAAAAACCCCCCCCCC\") == ['AAAAAAAAAA']\n assert candidate(s = \"GGGGGGGGGGGGGGGGGGGG\") == ['GGGGGGGGGG']\n assert candidate(s = \"ACGTCGTCGTCGTCGT\") == ['CGTCGTCGTC', 'GTCGTCGTCG', 'TCGTCGTCGT']\n assert candidate(s = \"AAAAAAAAAAACCCCCCCCCCAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"TTTTTTTTTTAAAAAAAAAA\") == []\n assert candidate(s = \"TTAGGGTTAGGGTTAGGG\") == ['TTAGGGTTAG', 'TAGGGTTAGG', 'AGGGTTAGGG']\n assert candidate(s = \"AAAAAAAAAAAGGGGGGGGGGG\") == ['AAAAAAAAAA', 'GGGGGGGGGG']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACG\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"ACGACGACGACGACGACGACGACGACGACGACGACGACGACG\") == ['ACGACGACGA', 'CGACGACGAC', 'GACGACGACG']\n assert candidate(s = \"AAAAAAAAAAACCCCCCCAAAAAAAAAACCCCCCCCCCCC\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'CCCCCCCCCC']\n assert candidate(s = \"TTAGGGTACCTAGGGTACCTAGGGTACC\") == ['TAGGGTACCT', 'AGGGTACCTA', 'GGGTACCTAG', 'GGTACCTAGG', 'GTACCTAGGG', 'TACCTAGGGT', 'ACCTAGGGTA', 'CCTAGGGTAC', 'CTAGGGTACC']\n assert candidate(s = \"ATATATATATATATATATATATATATATATATATATATATATATATATATATATATATATAT\") == ['ATATATATAT', 'TATATATATA']\n assert candidate(s = \"CCAGTTACCGGGTAAAGGGCCCTAAAGGGCCCTAAAGGGCCCTAAAGGGCCC\") == ['TAAAGGGCCC', 'AAAGGGCCCT', 'AAGGGCCCTA', 'AGGGCCCTAA', 'GGGCCCTAAA', 'GGCCCTAAAG', 'GCCCTAAAGG', 'CCCTAAAGGG', 'CCTAAAGGGC', 'CTAAAGGGCC']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTA\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"GCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTA\") == ['GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA', 'AGCTAGCTAG']\n assert candidate(s = \"ACGTACGTACGTACGTACGTTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"TTACGTACGTACGTACGTACGTACGTACGTAC\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"GTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCAGTCA\") == ['GTCAGTCAGT', 'TCAGTCAGTC', 'CAGTCAGTCA', 'AGTCAGTCAG']\n assert candidate(s = \"AAAAACCCCCAAAAAAAAAAAAACCCCCAAAA\") == ['AAAAAAAAAA', 'AAAAACCCCC', 'AAAACCCCCA', 'AAACCCCCAA', 'AACCCCCAAA', 'ACCCCCAAAA']\n assert candidate(s = \"AAAAAAAAAAACCCCCCCCCCAAAAAAAAAAAACCCCCCCCCCAGGGGGGGGGG\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCC', 'CCCCCCCCCA']\n assert candidate(s = \"AGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCT\") == ['AGCTAGCTAG', 'GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA']\n assert candidate(s = \"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\") == ['GGGGGGGGGG']\n assert candidate(s = \"ACCTGACCTGACCTGACCTGACCTGACCTGACCTGACCTG\") == ['ACCTGACCTG', 'CCTGACCTGA', 'CTGACCTGAC', 'TGACCTGACC', 'GACCTGACCT']\n assert candidate(s = \"GACGTGACGTGACGTGACGTGACGTGACGTGACGTGACG\") == ['GACGTGACGT', 'ACGTGACGTG', 'CGTGACGTGA', 'GTGACGTGAC', 'TGACGTGACG']\n assert candidate(s = \"AACCGGTTAACCGGTTAACCGGTTAACCGGTTAACCGGTT\") == ['AACCGGTTAA', 'ACCGGTTAAC', 'CCGGTTAACC', 'CGGTTAACCG', 'GGTTAACCGG', 'GTTAACCGGT', 'TTAACCGGTT', 'TAACCGGTTA']\n assert candidate(s = \"GAAAAAAAAATTTTTTTTTTAAAAAAAAAA\") == []\n assert candidate(s = \"AGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCT\") == ['AGCTAGCTAG', 'GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA']\n assert candidate(s = \"AGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTA\") == ['AGCTAGCTAG', 'GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA']\n assert candidate(s = \"AAAAAGGGGGAAAAAGGGGGCCCCCATTTTTT\") == ['AAAAAGGGGG']\n assert candidate(s = \"TTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTT\") == ['TTTACGTTTA', 'TTACGTTTAC', 'TACGTTTACG', 'ACGTTTACGT', 'CGTTTACGTT', 'GTTTACGTTT']\n assert candidate(s = \"GGGGGGGGGGTTGGGGGGGGTTGGGGGGGGTTGGGGGG\") == ['GGGGGGGGTT', 'GGGGGGGTTG', 'GGGGGGTTGG', 'GGGGGTTGGG', 'GGGGTTGGGG', 'GGGTTGGGGG', 'GGTTGGGGGG', 'GTTGGGGGGG', 'TTGGGGGGGG', 'TGGGGGGGGT']\n assert candidate(s = \"ACGACGACGACGACGACGACGACGACGACGACG\") == ['ACGACGACGA', 'CGACGACGAC', 'GACGACGACG']\n assert candidate(s = \"AAAAAAAAAAGGGGGGGGGGAAAAAAAAAAGGGG\") == ['AAAAAAAAAA', 'AAAAAAAAAG', 'AAAAAAAAGG', 'AAAAAAAGGG', 'AAAAAAGGGG']\n assert candidate(s = \"CCCCCCCCCCGGCCCCCCCCCCGGCCCCCCCCCCGG\") == ['CCCCCCCCCC', 'CCCCCCCCCG', 'CCCCCCCCGG', 'CCCCCCCGGC', 'CCCCCCGGCC', 'CCCCCGGCCC', 'CCCCGGCCCC', 'CCCGGCCCCC', 'CCGGCCCCCC', 'CGGCCCCCCC', 'GGCCCCCCCC', 'GCCCCCCCCC']\n assert candidate(s = \"ATATATATATACGTACGTACGTACGTACGTACGT\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"GATACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTAC\") == ['TACAGTACAG', 'ACAGTACAGT', 'CAGTACAGTA', 'AGTACAGTAC', 'GTACAGTACA']\n assert candidate(s = \"TCGATCGATCGATCGATCGATCGATCGATCGA\") == ['TCGATCGATC', 'CGATCGATCG', 'GATCGATCGA', 'ATCGATCGAT']\n assert candidate(s = \"ACGTACGTTACGTACGTTACGTACGTTACGTACGTTACGTACGTT\") == ['ACGTACGTTA', 'CGTACGTTAC', 'GTACGTTACG', 'TACGTTACGT', 'ACGTTACGTA', 'CGTTACGTAC', 'GTTACGTACG', 'TTACGTACGT', 'TACGTACGTT']\n assert candidate(s = \"ACCGGTTTAAACCGGTTTAAACCGGTTTAA\") == ['ACCGGTTTAA', 'CCGGTTTAAA', 'CGGTTTAAAC', 'GGTTTAAACC', 'GTTTAAACCG', 'TTTAAACCGG', 'TTAAACCGGT', 'TAAACCGGTT', 'AAACCGGTTT', 'AACCGGTTTA']\n assert candidate(s = \"TTTTAAAAATTTTTAAAAATTTTTAAAAATTTTTAAAAATTTTTAAAAATTTTTAAAAA\") == ['TTTTAAAAAT', 'TTTAAAAATT', 'TTAAAAATTT', 'TAAAAATTTT', 'AAAAATTTTT', 'AAAATTTTTA', 'AAATTTTTAA', 'AATTTTTAAA', 'ATTTTTAAAA', 'TTTTTAAAAA']\n assert candidate(s = \"ACCGGTTTAAACCGGTTTAAACCGGTTTAAACCGGTTTAAACCGGTTTA\") == ['ACCGGTTTAA', 'CCGGTTTAAA', 'CGGTTTAAAC', 'GGTTTAAACC', 'GTTTAAACCG', 'TTTAAACCGG', 'TTAAACCGGT', 'TAAACCGGTT', 'AAACCGGTTT', 'AACCGGTTTA']\n assert candidate(s = \"ACGCGTACGCGTACGCGTACGCGTACGCGTACGCGT\") == ['ACGCGTACGC', 'CGCGTACGCG', 'GCGTACGCGT', 'CGTACGCGTA', 'GTACGCGTAC', 'TACGCGTACG']\n assert candidate(s = \"GAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGA\") == ['GAGAGAGAGA', 'AGAGAGAGAG']\n assert candidate(s = \"ACACACACACACACACACACACACACACACAC\") == ['ACACACACAC', 'CACACACACA']\n assert candidate(s = \"CGATCGATCGATCGATCGATCGATCGATCGATCGATCGATCGAT\") == ['CGATCGATCG', 'GATCGATCGA', 'ATCGATCGAT', 'TCGATCGATC']\n assert candidate(s = \"AAACCGGGTTAAACCGGGTTAAACCGGGTT\") == ['AAACCGGGTT', 'AACCGGGTTA', 'ACCGGGTTAA', 'CCGGGTTAAA', 'CGGGTTAAAC', 'GGGTTAAACC', 'GGTTAAACCG', 'GTTAAACCGG', 'TTAAACCGGG', 'TAAACCGGGT']\n assert candidate(s = \"TTTTTTTTTTCCTTTTTTTTCCTTTTTTTTCCTTTTTT\") == ['TTTTTTTTCC', 'TTTTTTTCCT', 'TTTTTTCCTT', 'TTTTTCCTTT', 'TTTTCCTTTT', 'TTTCCTTTTT', 'TTCCTTTTTT', 'TCCTTTTTTT', 'CCTTTTTTTT', 'CTTTTTTTTC']\n assert candidate(s = \"ACACACACACACACACACACACACACACACACACACACAC\") == ['ACACACACAC', 'CACACACACA']\n assert candidate(s = \"ATATATATATATATATATATATATATATATATAT\") == ['ATATATATAT', 'TATATATATA']\n assert candidate(s = \"TATATAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"TGCCTGCCTGCCTGCCTGCCTGCC\") == ['TGCCTGCCTG', 'GCCTGCCTGC', 'CCTGCCTGCC', 'CTGCCTGCCT']\n assert candidate(s = \"CGTACGTAACGTACGTAACGTACGTAACGTAC\") == ['CGTACGTAAC', 'GTACGTAACG', 'TACGTAACGT', 'ACGTAACGTA', 'CGTAACGTAC', 'GTAACGTACG', 'TAACGTACGT', 'AACGTACGTA', 'ACGTACGTAA']\n assert candidate(s = \"ACCGGTTTAAACCGGTTTAAACCGGTTTAAACCGGTTTAAACCGGTTTAA\") == ['ACCGGTTTAA', 'CCGGTTTAAA', 'CGGTTTAAAC', 'GGTTTAAACC', 'GTTTAAACCG', 'TTTAAACCGG', 'TTAAACCGGT', 'TAAACCGGTT', 'AAACCGGTTT', 'AACCGGTTTA']\n assert candidate(s = \"ACGTACGTACGTACGTATATATATACGTACGTAC\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"AAAAAAAAAAACCCCCCCCCGGGGGGGGGGTTTTTTTTTTAAAAAAAAAAACCCCCCCCCGGGGGGGGGGTTTTTTTTTT\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCG', 'CCCCCCCCGG', 'CCCCCCCGGG', 'CCCCCCGGGG', 'CCCCCGGGGG', 'CCCCGGGGGG', 'CCCGGGGGGG', 'CCGGGGGGGG', 'CGGGGGGGGG', 'GGGGGGGGGG', 'GGGGGGGGGT', 'GGGGGGGGTT', 'GGGGGGGTTT', 'GGGGGGTTTT', 'GGGGGTTTTT', 'GGGGTTTTTT', 'GGGTTTTTTT', 'GGTTTTTTTT', 'GTTTTTTTTT', 'TTTTTTTTTT']\n assert candidate(s = \"ATATATATATATATATATATATATATATATAT\") == ['ATATATATAT', 'TATATATATA']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"ATCGATCGATCGATCGATCGATCGATCGATCGATCG\") == ['ATCGATCGAT', 'TCGATCGATC', 'CGATCGATCG', 'GATCGATCGA']\n assert candidate(s = \"AAAAAAAAAAAGGGGGGGGGGGGGGGGGGGGGGG\") == ['AAAAAAAAAA', 'GGGGGGGGGG']\n assert candidate(s = \"AAAAAAAAAACAAAAAAAAAACAAAAAAAAAACAAAAAAA\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACA', 'AAAAAAACAA', 'AAAAAACAAA', 'AAAAACAAAA', 'AAAACAAAAA', 'AAACAAAAAA', 'AACAAAAAAA', 'ACAAAAAAAA', 'CAAAAAAAAA']\n assert candidate(s = \"AAAAAAAAAAACAAAAAAAAAAACAAAAAAAAAAAC\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACA', 'AAAAAAACAA', 'AAAAAACAAA', 'AAAAACAAAA', 'AAAACAAAAA', 'AAACAAAAAA', 'AACAAAAAAA', 'ACAAAAAAAA', 'CAAAAAAAAA']\n assert candidate(s = \"AGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCT\") == ['AGCTAGCTAG', 'GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA']\n assert candidate(s = \"CCCGGGCCCGGGCCCGGGCCCGGGCCCGGGCCCGGGCCCGGG\") == ['CCCGGGCCCG', 'CCGGGCCCGG', 'CGGGCCCGGG', 'GGGCCCGGGC', 'GGCCCGGGCC', 'GCCCGGGCCC']\n assert candidate(s = \"GCTGCTGCTGCTGCTGCTGCTGCTGCTGCTGCTGCTGCTGCTG\") == ['GCTGCTGCTG', 'CTGCTGCTGC', 'TGCTGCTGCT']\n assert candidate(s = \"ATATATATATATATATATATATATATAT\") == ['ATATATATAT', 'TATATATATA']\n assert candidate(s = \"ACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTT\") == ['ACGTTTACGT', 'CGTTTACGTT', 'GTTTACGTTT', 'TTTACGTTTA', 'TTACGTTTAC', 'TACGTTTACG']\n assert candidate(s = \"GGGGGGGGGGAAAAAAAAAACCCCCCCCCCGGGGGGGGGGAAAAAAAAAACCCCCCCCCCGGGGGGGGGG\") == ['GGGGGGGGGG', 'GGGGGGGGGA', 'GGGGGGGGAA', 'GGGGGGGAAA', 'GGGGGGAAAA', 'GGGGGAAAAA', 'GGGGAAAAAA', 'GGGAAAAAAA', 'GGAAAAAAAA', 'GAAAAAAAAA', 'AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCC', 'CCCCCCCCCG', 'CCCCCCCCGG', 'CCCCCCCGGG', 'CCCCCCGGGG', 'CCCCCGGGGG', 'CCCCGGGGGG', 'CCCGGGGGGG', 'CCGGGGGGGG', 'CGGGGGGGGG']\n assert candidate(s = \"TTTTACCGGGAAAAACCGGGAAAAACCGGGAAAA\") == ['ACCGGGAAAA', 'CCGGGAAAAA', 'CGGGAAAAAC', 'GGGAAAAACC', 'GGAAAAACCG', 'GAAAAACCGG', 'AAAAACCGGG', 'AAAACCGGGA', 'AAACCGGGAA', 'AACCGGGAAA']\n assert candidate(s = \"TACGTACGTACGTACGTACGTACGTACGTACG\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"AGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTACAGTAC\") == ['AGTACAGTAC', 'GTACAGTACA', 'TACAGTACAG', 'ACAGTACAGT', 'CAGTACAGTA']\n assert candidate(s = \"GCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTA\") == ['GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA', 'AGCTAGCTAG']\n assert candidate(s = \"TTTTTTTTTTAAAAAAAAAAAATTTTTTTTTTAAAAAAAAAAAATTTTT\") == ['AAAAAAAAAA', 'TTTTTTTTTT', 'TTTTTTTTTA', 'TTTTTTTTAA', 'TTTTTTTAAA', 'TTTTTTAAAA', 'TTTTTAAAAA', 'TTTTAAAAAA', 'TTTAAAAAAA', 'TTAAAAAAAA', 'TAAAAAAAAA', 'AAAAAAAAAT', 'AAAAAAAATT', 'AAAAAAATTT', 'AAAAAATTTT', 'AAAAATTTTT']\n assert candidate(s = \"CCCCGGGGAAGGGGCCCCGGGGAAGGGGCCCCGGGGAAGGGGCCCCGGGGAAGGGG\") == ['CCCCGGGGAA', 'CCCGGGGAAG', 'CCGGGGAAGG', 'CGGGGAAGGG', 'GGGGAAGGGG', 'GGGAAGGGGC', 'GGAAGGGGCC', 'GAAGGGGCCC', 'AAGGGGCCCC', 'AGGGGCCCCG', 'GGGGCCCCGG', 'GGGCCCCGGG', 'GGCCCCGGGG', 'GCCCCGGGGA']\n assert candidate(s = \"AAAAAAAAAAAAAAACCCCCCCCCCCCCCCCCCCCCCC\") == ['AAAAAAAAAA', 'CCCCCCCCCC']\n assert candidate(s = \"AAAAAAAAAAAACCCCCCCCCCAAAAAAAAAAAACCCCCCCCCC\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCC']\n assert candidate(s = \"AAAAAAAAAAAACCCCCCCCCCGGGGGGGGGGTTTTTTTTTTAAAAAAAAAAAACCCCCCCCCCGGGGGGGGGGTTTTTTTTTT\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCC', 'CCCCCCCCCG', 'CCCCCCCCGG', 'CCCCCCCGGG', 'CCCCCCGGGG', 'CCCCCGGGGG', 'CCCCGGGGGG', 'CCCGGGGGGG', 'CCGGGGGGGG', 'CGGGGGGGGG', 'GGGGGGGGGG', 'GGGGGGGGGT', 'GGGGGGGGTT', 'GGGGGGGTTT', 'GGGGGGTTTT', 'GGGGGTTTTT', 'GGGGTTTTTT', 'GGGTTTTTTT', 'GGTTTTTTTT', 'GTTTTTTTTT', 'TTTTTTTTTT']\n assert candidate(s = \"AGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCT\") == ['AGCTAGCTAG', 'GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA']\n assert candidate(s = \"ACGTACGTTTTACGTTTTACGTTTTACGTTTT\") == ['TACGTTTTAC', 'ACGTTTTACG', 'CGTTTTACGT', 'GTTTTACGTT', 'TTTTACGTTT', 'TTTACGTTTT', 'TTACGTTTTA']\n assert candidate(s = \"GAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGAGA\") == ['GAGAGAGAGA', 'AGAGAGAGAG']\n assert candidate(s = \"ACGTCGTTTTTACGTCGTTTTTACGTCGTTTTTACGTCGTTTTT\") == ['ACGTCGTTTT', 'CGTCGTTTTT', 'GTCGTTTTTA', 'TCGTTTTTAC', 'CGTTTTTACG', 'GTTTTTACGT', 'TTTTTACGTC', 'TTTTACGTCG', 'TTTACGTCGT', 'TTACGTCGTT', 'TACGTCGTTT']\n assert candidate(s = \"ACGTACGTACGTATATATATACGTACGTACGTAT\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'ACGTACGTAT']\n assert candidate(s = \"TACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\") == ['AAAAAAAAAA']\n assert candidate(s = \"TTTACCGGAAAACCGGAAAACCGGAAAACCGGAAAACCGG\") == ['ACCGGAAAAC', 'CCGGAAAACC', 'CGGAAAACCG', 'GGAAAACCGG', 'GAAAACCGGA', 'AAAACCGGAA', 'AAACCGGAAA', 'AACCGGAAAA']\n assert candidate(s = \"AGAGAGAGAGAGAGAGAGAGAGAGAGAGAGAG\") == ['AGAGAGAGAG', 'GAGAGAGAGA']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"AAAAAAAAAAAACCCCCCCCCCAAAAAAAAAACCCCCCCCCC\") == ['AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCC']\n assert candidate(s = \"TACGTACGTACGTACGTACGTACGTACGTACGTACGTACG\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"AAAAACCCCCAAAAACCCCCAAAAACCCCCAAAAACCCCC\") == ['AAAAACCCCC', 'AAAACCCCCA', 'AAACCCCCAA', 'AACCCCCAAA', 'ACCCCCAAAA', 'CCCCCAAAAA', 'CCCCAAAAAC', 'CCCAAAAACC', 'CCAAAAACCC', 'CAAAAACCCC']\n assert candidate(s = \"AAAAAAAAAAAAGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\") == ['AAAAAAAAAA', 'GGGGGGGGGG']\n assert candidate(s = \"ACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTT\") == ['ACGTTTACGT', 'CGTTTACGTT', 'GTTTACGTTT', 'TTTACGTTTA', 'TTACGTTTAC', 'TACGTTTACG']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"ACGTTTACGTTTACGTTTACGTTTACGTTTACGTTT\") == ['ACGTTTACGT', 'CGTTTACGTT', 'GTTTACGTTT', 'TTTACGTTTA', 'TTACGTTTAC', 'TACGTTTACG']\n assert candidate(s = \"TTTTTTTTTTGGGGGGGGGGTTTTTTTTTTGGGGGGGGGG\") == ['TTTTTTTTTT', 'TTTTTTTTTG', 'TTTTTTTTGG', 'TTTTTTTGGG', 'TTTTTTGGGG', 'TTTTTGGGGG', 'TTTTGGGGGG', 'TTTGGGGGGG', 'TTGGGGGGGG', 'TGGGGGGGGG', 'GGGGGGGGGG']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"GCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTA\") == ['GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA', 'AGCTAGCTAG']\n assert candidate(s = \"CGTACGTACGTACGTACGTACGTACGTACGTACGTAC\") == ['CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA', 'ACGTACGTAC']\n assert candidate(s = \"TATATATATATATATATATATATATATATATATATATATATATA\") == ['TATATATATA', 'ATATATATAT']\n assert candidate(s = \"GTACGTACGTACGTACGTACGTACGTACGTACGTACG\") == ['GTACGTACGT', 'TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG']\n assert candidate(s = \"TGACGTGACGTGACGTGACGTGACGTGACGTGACGTGAC\") == ['TGACGTGACG', 'GACGTGACGT', 'ACGTGACGTG', 'CGTGACGTGA', 'GTGACGTGAC']\n assert candidate(s = \"TACGTACGTACGTACGTACGTACGTACGTACGTAC\") == ['TACGTACGTA', 'ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTAC\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n assert candidate(s = \"TTTTTTTTTTGGGGGGGGGGAAAAAAAAAATTTTTTTTTTGGGGGGGGGG\") == ['TTTTTTTTTT', 'TTTTTTTTTG', 'TTTTTTTTGG', 'TTTTTTTGGG', 'TTTTTTGGGG', 'TTTTTGGGGG', 'TTTTGGGGGG', 'TTTGGGGGGG', 'TTGGGGGGGG', 'TGGGGGGGGG', 'GGGGGGGGGG']\n assert candidate(s = \"AAAAAAAAAAAAACCCCCCCCCCCCCCCGGGGGGGGGGGGGG\") == ['AAAAAAAAAA', 'CCCCCCCCCC', 'GGGGGGGGGG']\n assert candidate(s = \"ACGGTACGGTACGGTACGGTACGGTACGGTACGGTACGGT\") == ['ACGGTACGGT', 'CGGTACGGTA', 'GGTACGGTAC', 'GTACGGTACG', 'TACGGTACGG']\n assert candidate(s = \"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\") == ['GGGGGGGGGG']\n assert candidate(s = \"AGACGTAGACGTAGACGTAGACGTAGACGTAGACGTAG\") == ['AGACGTAGAC', 'GACGTAGACG', 'ACGTAGACGT', 'CGTAGACGTA', 'GTAGACGTAG', 'TAGACGTAGA']\n assert candidate(s = \"TTTTTTTTTTAAAAAAAAAACCCCCCCCCCGGGGGGGGGGTTTTTTTTTTAAAAAAAAAACCCCCCCCCCGGGGGGGGGG\") == ['TTTTTTTTTT', 'TTTTTTTTTA', 'TTTTTTTTAA', 'TTTTTTTAAA', 'TTTTTTAAAA', 'TTTTTAAAAA', 'TTTTAAAAAA', 'TTTAAAAAAA', 'TTAAAAAAAA', 'TAAAAAAAAA', 'AAAAAAAAAA', 'AAAAAAAAAC', 'AAAAAAAACC', 'AAAAAAACCC', 'AAAAAACCCC', 'AAAAACCCCC', 'AAAACCCCCC', 'AAACCCCCCC', 'AACCCCCCCC', 'ACCCCCCCCC', 'CCCCCCCCCC', 'CCCCCCCCCG', 'CCCCCCCCGG', 'CCCCCCCGGG', 'CCCCCCGGGG', 'CCCCCGGGGG', 'CCCCGGGGGG', 'CCCGGGGGGG', 'CCGGGGGGGG', 'CGGGGGGGGG', 'GGGGGGGGGG']\n assert candidate(s = \"ACGGTGACGGTGACGGTGACGGTGACGGTGACGGTG\") == ['ACGGTGACGG', 'CGGTGACGGT', 'GGTGACGGTG', 'GTGACGGTGA', 'TGACGGTGAC', 'GACGGTGACG']\n assert candidate(s = \"AAAAAAAAAAGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\") == ['GGGGGGGGGG']\n assert candidate(s = \"ACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACGACG\") == ['ACGACGACGA', 'CGACGACGAC', 'GACGACGACG']\n assert candidate(s = \"GCGCGCGCGCGCGCGCGCGCGCGCGCGCGCGC\") == ['GCGCGCGCGC', 'CGCGCGCGCG']\n assert candidate(s = \"ACGTTTACGTTTACGTTTACGTTTACGTTTACGTTTACGTTT\") == ['ACGTTTACGT', 'CGTTTACGTT', 'GTTTACGTTT', 'TTTACGTTTA', 'TTACGTTTAC', 'TACGTTTACG']\n assert candidate(s = \"ACGAATTCCGACGAATTCCGACGAATTCCGACGAATTCCG\") == ['ACGAATTCCG', 'CGAATTCCGA', 'GAATTCCGAC', 'AATTCCGACG', 'ATTCCGACGA', 'TTCCGACGAA', 'TCCGACGAAT', 'CCGACGAATT', 'CGACGAATTC', 'GACGAATTCC']\n assert candidate(s = \"GATTACAAGATTACAAGATTACAAGATTACAAGATTAC\") == ['GATTACAAGA', 'ATTACAAGAT', 'TTACAAGATT', 'TACAAGATTA', 'ACAAGATTAC', 'CAAGATTACA', 'AAGATTACAA', 'AGATTACAAG']\n assert candidate(s = \"GCTAGCTAGCTAGCTAGCTAGCTAGCTAGCTA\") == ['GCTAGCTAGC', 'CTAGCTAGCT', 'TAGCTAGCTA', 'AGCTAGCTAG']\n assert candidate(s = \"ACGACGTTTTACGACGTTTTACGACGTTTT\") == ['ACGACGTTTT', 'CGACGTTTTA', 'GACGTTTTAC', 'ACGTTTTACG', 'CGTTTTACGA', 'GTTTTACGAC', 'TTTTACGACG', 'TTTACGACGT', 'TTACGACGTT', 'TACGACGTTT']\n assert candidate(s = \"CCGGTTTAAAACCGGTTTAAAACCGGTTTAAAACCGGTTTAAA\") == ['CCGGTTTAAA', 'CGGTTTAAAA', 'GGTTTAAAAC', 'GTTTAAAACC', 'TTTAAAACCG', 'TTAAAACCGG', 'TAAAACCGGT', 'AAAACCGGTT', 'AAACCGGTTT', 'AACCGGTTTA', 'ACCGGTTTAA']\n assert candidate(s = \"AAGGTTCCGGTTCCTTAAAGGTTCCGGTTCCT\") == ['AAGGTTCCGG', 'AGGTTCCGGT', 'GGTTCCGGTT', 'GTTCCGGTTC', 'TTCCGGTTCC', 'TCCGGTTCCT']\n assert candidate(s = \"ACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTACGTT\") == ['ACGTACGTAC', 'CGTACGTACG', 'GTACGTACGT', 'TACGTACGTA']\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().findRepeatedDnaSequences", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findRepeatedDnaSequences = function(s) {", "container": null, "callable": "findRepeatedDnaSequences", "parameters": [{"name": "s", "type": "string"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 188, "task_id": "best-time-to-buy-and-sell-stock-iv", "difficulty": "Hard", "problem_description": "You are given an integer array prices where prices[i] is the price of a given stock on the ith day, and an integer k.\nFind the maximum profit you can achieve. You may complete at most k transactions: i.e. you may buy at most k times and sell at most k times.\nNote: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).\n \nExample 1:\n\nInput: k = 2, prices = [2,4,1]\nOutput: 2\nExplanation: Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.\n\nExample 2:\n\nInput: k = 2, prices = [3,2,6,5,0,3]\nOutput: 7\nExplanation: Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.\n\n \nConstraints:\n\n1 <= k <= 100\n1 <= prices.length <= 1000\n0 <= prices[i] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(k = 2,prices = [10, 22, 5, 75, 65, 80]) == 87\n assert candidate(k = 5,prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(k = 2,prices = [2, 4, 1]) == 2\n assert candidate(k = 1,prices = [7, 1, 5, 3, 6, 4]) == 5\n assert candidate(k = 1,prices = [3, 3, 3, 3, 3]) == 0\n assert candidate(k = 1,prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(k = 100,prices = [10, 22, 5, 75, 65, 80]) == 97\n assert candidate(k = 5,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 15\n assert candidate(k = 1,prices = [1]) == 0\n assert candidate(k = 10,prices = [30, 80, 60, 90, 50, 120, 30, 10, 50, 60]) == 200\n assert candidate(k = 0,prices = [1, 2, 3, 4, 5]) == 0\n assert candidate(k = 2,prices = [3, 2, 6, 5, 0, 3]) == 7\n assert candidate(k = 3,prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 8\n assert candidate(k = 2,prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 9\n assert candidate(k = 0,prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(k = 3,prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(k = 1,prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 4\n assert candidate(k = 4,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 15\n assert candidate(k = 3,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 15\n assert candidate(k = 10,prices = [8, 6, 4, 5, 3, 8, 9, 10, 11, 12, 13, 14, 15]) == 13\n assert candidate(k = 5,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9]) == 24\n assert candidate(k = 5,prices = [7, 6, 4, 3, 1, 2, 3, 5, 6, 8, 10, 1, 2, 2, 4, 5, 7, 8, 8, 9, 10]) == 18\n assert candidate(k = 1,prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(k = 5,prices = [12, 14, 17, 10, 14, 13, 12, 15]) == 12\n assert candidate(k = 4,prices = [30, 80, 50, 90, 100, 150]) == 150\n assert candidate(k = 5,prices = [10, 22, 5, 75, 65, 80, 120, 130, 70, 50, 60, 100, 180]) == 277\n assert candidate(k = 50,prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 27\n assert candidate(k = 2,prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(k = 3,prices = [12, 14, 17, 10, 14, 13, 12, 15]) == 12\n assert candidate(k = 10,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 32\n assert candidate(k = 6,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(k = 3,prices = [3, 3, 5, 0, 0, 3, 1, 4, 7, 8, 9, 10]) == 14\n assert candidate(k = 5,prices = [10, 22, 5, 75, 65, 80]) == 97\n assert candidate(k = 3,prices = [5, 2, 4, 0, 0, 3, 1, 4, 3, 6, 5, 0, 3, 8, 6, 8, 10, 1, 2, 3, 4, 5]) == 20\n assert candidate(k = 4,prices = [8, 5, 12, 19, 21, 10]) == 16\n assert candidate(k = 3,prices = [7, 6, 4, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(k = 3,prices = [1, 2, 2, 4, 5, 7, 8, 8, 9, 10]) == 9\n assert candidate(k = 5,prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(k = 3,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(k = 5,prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 14\n assert candidate(k = 3,prices = [1, 3, 2, 8, 4, 9, 10, 11, 10, 9, 10, 11, 10, 9, 10, 11, 10, 9]) == 16\n assert candidate(k = 2,prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(k = 10,prices = [2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1]) == 5\n assert candidate(k = 4,prices = [10, 22, 5, 75, 65, 80]) == 97\n assert candidate(k = 5,prices = [31, 31, 27, 39, 59, 91, 92, 58, 84, 100]) == 107\n assert candidate(k = 3,prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 0\n assert candidate(k = 1,prices = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 0\n assert candidate(k = 10,prices = [8, 9, 8, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9]) == 8\n assert candidate(k = 4,prices = [1, 2, 2, 4, 5, 7, 8, 8, 9, 10, 1, 2, 2, 4, 5, 7, 8, 8, 9, 10]) == 18\n assert candidate(k = 5,prices = [30, 10, 20, 40, 50, 15, 35, 60, 70, 25, 45, 80, 90]) == 160\n assert candidate(k = 5,prices = [10, 22, 5, 75, 65, 80, 90, 100, 110, 120, 130, 140, 150]) == 167\n assert candidate(k = 2,prices = [3, 3, 5, 0, 0, 3, 1, 4, 7, 11, 10, 13, 12, 9, 15, 18, 17, 20, 22, 21]) == 26\n assert candidate(k = 3,prices = [90, 80, 70, 60, 50, 40, 30, 20, 10, 0]) == 0\n assert candidate(k = 4,prices = [7, 6, 4, 3, 1, 2, 5, 6, 4, 3, 1, 2]) == 6\n assert candidate(k = 4,prices = [30, 25, 20, 15, 10, 5]) == 0\n assert candidate(k = 2,prices = [3, 2, 1, 4, 3, 5, 3, 6, 4, 7, 8, 10, 6, 12, 14, 8, 15, 16, 18, 20]) == 25\n assert candidate(k = 6,prices = [8, 1, 9, 5, 7, 4, 3, 6, 0, 9, 2, 6, 10, 14]) == 34\n assert candidate(k = 4,prices = [10, 1, 1, 10, 3, 5, 10, 9, 1, 3, 5, 6, 8, 9, 0, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 34\n assert candidate(k = 4,prices = [3, 5, 0, 0, 3, 1, 4, 7, 9, 8, 5, 3, 2, 10, 12, 14, 16, 18, 20, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 31\n assert candidate(k = 4,prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2]) == 16\n assert candidate(k = 5,prices = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(k = 4,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(k = 20,prices = [5, 2, 8, 3, 10, 4, 12, 5, 14, 6, 16, 7, 18, 8, 20, 9, 22, 10, 24, 11]) == 90\n assert candidate(k = 5,prices = [1, 3, 2, 8, 4, 9, 5, 11, 6, 10, 7, 12, 8, 13, 9, 14, 10, 15, 11, 16]) == 32\n assert candidate(k = 2,prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(k = 2,prices = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(k = 1,prices = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]) == 0\n assert candidate(k = 4,prices = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23]) == 22\n assert candidate(k = 1,prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(k = 3,prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(k = 10,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(k = 2,prices = [3, 2, 6, 5, 0, 3, 1, 4, 7, 8, 5]) == 12\n assert candidate(k = 2,prices = [1, 3, 2, 8, 4, 9]) == 12\n assert candidate(k = 1,prices = [100, 180, 260, 310, 40, 535, 695]) == 655\n assert candidate(k = 5,prices = [3, 3, 5, 0, 0, 3, 1, 4, 7, 9, 8, 5, 3, 2, 10]) == 21\n assert candidate(k = 2,prices = [1, 2, 3, 2, 4, 5, 6, 4, 7, 8, 9, 7, 10, 11, 12, 10, 13, 14, 15, 13, 16, 17, 18, 16, 19, 20, 21, 19]) == 22\n assert candidate(k = 10,prices = [100, 300, 200, 400, 500, 800, 300, 600, 500, 700]) == 1300\n assert candidate(k = 2,prices = [100, 180, 260, 310, 40, 535, 695]) == 865\n assert candidate(k = 3,prices = [3, 3, 5, 0, 0, 3, 1, 4, 7, 8, 2]) == 12\n assert candidate(k = 2,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9, 1, 2, 3, 5]) == 17\n assert candidate(k = 3,prices = [8, 3, 6, 2, 8, 8, 8, 4, 2, 0, 1, 2, 5, 1, 0, 3, 6, 1, 1, 9]) == 20\n assert candidate(k = 4,prices = [3, 3, 5, 0, 0, 3, 1, 4, 7, 8, 5]) == 12\n assert candidate(k = 3,prices = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]) == 4\n assert candidate(k = 100,prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 52\n assert candidate(k = 2,prices = [5, 4, 3, 2, 1]) == 0\n assert candidate(k = 100,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(k = 3,prices = [5, 2, 3, 0, 3, 5, 6, 8, 1, 9]) == 17\n assert candidate(k = 3,prices = [1, 3, 2, 8, 4, 9, 5, 10, 11, 15, 13, 14, 16, 17]) == 24\n assert candidate(k = 5,prices = [50, 30, 20, 40, 90, 100, 40, 80, 60, 50, 70, 120, 150, 130, 170]) == 260\n assert candidate(k = 3,prices = [10, 22, 5, 75, 65, 80]) == 97\n assert candidate(k = 4,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0, 9]) == 24\n assert candidate(k = 3,prices = [3, 3, 5, 0, 0, 3, 1, 4, 7, 11, 10, 13, 12, 9]) == 17\n assert candidate(k = 1,prices = [1, 2, 4, 2, 5, 7, 2, 4, 9, 0]) == 8\n assert candidate(k = 100,prices = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3]) == 68\n assert candidate(k = 7,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(k = 10,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(k = 5,prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n"}, "metadata": {"canonical_parameter_names": ["k", "prices"], "leetcode_dataset_entry_point": "Solution().maxProfit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProfit = function(k, prices) {", "container": null, "callable": "maxProfit", "parameters": [{"name": "k", "type": "number"}, {"name": "prices", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 190, "task_id": "reverse-bits", "difficulty": "Easy", "problem_description": "Reverse bits of a given 32 bits unsigned integer.\nNote:\n\nNote that in some languages, such as Java, there is no unsigned integer type. In this case, both input and output will be given as a signed integer type. They should not affect your implementation, as the integer's internal binary representation is the same, whether it is signed or unsigned.\nIn Java, the compiler represents the signed integers using 2's complement notation. Therefore, in Example 2 above, the input represents the signed integer -3 and the output represents the signed integer -1073741825.\n\n \nExample 1:\n\nInput: n = 00000010100101000001111010011100\nOutput: 964176192 (00111001011110000010100101000000)\nExplanation: The input binary string 00000010100101000001111010011100 represents the unsigned integer 43261596, so return 964176192 which its binary representation is 00111001011110000010100101000000.\n\nExample 2:\n\nInput: n = 11111111111111111111111111111101\nOutput: 3221225471 (10111111111111111111111111111111)\nExplanation: The input binary string 11111111111111111111111111111101 represents the unsigned integer 4294967293, so return 3221225471 which its binary representation is 10111111111111111111111111111111.\n\n \nConstraints:\n\nThe input must be a binary string of length 32\n\n \nFollow up: If this function is called many times, how would you optimize it?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 11111111111111111111111111111111) == 3817748707\n assert candidate(n = 0) == 0\n assert candidate(n = 10000000000000000000000000000000) == 1\n assert candidate(n = 2147483648) == 1\n assert candidate(n = 43261596) == 964176192\n assert candidate(n = 4294967293) == 3221225471\n assert candidate(n = 1) == 2147483648\n assert candidate(n = 11111111111111111111111111111101) == 3180214499\n assert candidate(n = 10100101001010010100101001010010) == 1524246408\n assert candidate(n = 11110000111100001111000011110000) == 242192076\n assert candidate(n = 11110000000011111111000000001111) == 3928946530\n assert candidate(n = 11111111111111110000000000000000) == 57352\n assert candidate(n = 11011011011011011011011011011011) == 3280443572\n assert candidate(n = 10011100100001011011100110000110) == 2012287233\n assert candidate(n = 11100000111000001110000011100000) == 117259735\n assert candidate(n = 11100001111000011110000111100001) == 2248527424\n assert candidate(n = 10010010010010010010010010010010) == 1501692052\n assert candidate(n = 10101010101010100101010101010101) == 2910733234\n assert candidate(n = 10101010101010101010101010101010) == 1221553761\n assert candidate(n = 11111111000000001111111100000000) == 15193787\n assert candidate(n = 11110000000000000000000000000000) == 14\n assert candidate(n = 10001000100010001000100010001000) == 373324907\n assert candidate(n = 11001100110011001100110011001100) == 815197725\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().reverseBits", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverseBits = function(n) {", "container": null, "callable": "reverseBits", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 191, "task_id": "number-of-1-bits", "difficulty": "Easy", "problem_description": "Given a positive integer n, write a function that returns the number of set bits in its binary representation (also known as the Hamming weight).\n \nExample 1:\n\nInput: n = 11\nOutput: 3\nExplanation:\nThe input binary string 1011 has a total of three set bits.\n\nExample 2:\n\nInput: n = 128\nOutput: 1\nExplanation:\nThe input binary string 10000000 has a total of one set bit.\n\nExample 3:\n\nInput: n = 2147483645\nOutput: 30\nExplanation:\nThe input binary string 1111111111111111111111111111101 has a total of thirty set bits.\n\n \nConstraints:\n\n1 <= n <= 231 - 1\n\n \nFollow up: If this function is called many times, how would you optimize it?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 4095) == 12\n assert candidate(n = 11) == 3\n assert candidate(n = 15) == 4\n assert candidate(n = 2147483647) == 31\n assert candidate(n = 32) == 1\n assert candidate(n = 1023) == 10\n assert candidate(n = 2147483645) == 30\n assert candidate(n = 1) == 1\n assert candidate(n = 65535) == 16\n assert candidate(n = 128) == 1\n assert candidate(n = 3) == 2\n assert candidate(n = 1099511627776) == 1\n assert candidate(n = 2147483646) == 30\n assert candidate(n = 239) == 7\n assert candidate(n = 53) == 4\n assert candidate(n = 262143) == 18\n assert candidate(n = 43) == 4\n assert candidate(n = 268435456) == 1\n assert candidate(n = 2047) == 11\n assert candidate(n = 5) == 2\n assert candidate(n = 549755813888) == 1\n assert candidate(n = 103) == 5\n assert candidate(n = 37) == 3\n assert candidate(n = 223) == 7\n assert candidate(n = 211) == 5\n assert candidate(n = 73) == 3\n assert candidate(n = 1022) == 9\n assert candidate(n = 33554432) == 1\n assert candidate(n = 251) == 7\n assert candidate(n = 181) == 5\n assert candidate(n = 8) == 1\n assert candidate(n = 193) == 3\n assert candidate(n = 131) == 3\n assert candidate(n = 2048) == 1\n assert candidate(n = 241) == 5\n assert candidate(n = 263) == 4\n assert candidate(n = 8191) == 13\n assert candidate(n = 1000000000) == 13\n assert candidate(n = 32768) == 1\n assert candidate(n = 1048575) == 20\n assert candidate(n = 500000000) == 13\n assert candidate(n = 313) == 5\n assert candidate(n = 167) == 5\n assert candidate(n = 97) == 3\n assert candidate(n = 317) == 6\n assert candidate(n = 107374182) == 14\n assert candidate(n = 271) == 5\n assert candidate(n = 8589934591) == 33\n assert candidate(n = 21) == 3\n assert candidate(n = 107) == 5\n assert candidate(n = 163) == 4\n assert candidate(n = 524288) == 1\n assert candidate(n = 524287) == 19\n assert candidate(n = 28) == 3\n assert candidate(n = 268435455) == 28\n assert candidate(n = 137) == 3\n assert candidate(n = 4) == 1\n assert candidate(n = 134217728) == 1\n assert candidate(n = 257) == 2\n assert candidate(n = 1073741823) == 30\n assert candidate(n = 1610612735) == 30\n assert candidate(n = 16777215) == 24\n assert candidate(n = 101) == 4\n assert candidate(n = 68719476735) == 36\n assert candidate(n = 2199023255551) == 41\n assert candidate(n = 89) == 4\n assert candidate(n = 256) == 1\n assert candidate(n = 1099511627775) == 40\n assert candidate(n = 71) == 4\n assert candidate(n = 151) == 5\n assert candidate(n = 293) == 4\n assert candidate(n = 41) == 3\n assert candidate(n = 9) == 2\n assert candidate(n = 83) == 4\n assert candidate(n = 123456789) == 16\n assert candidate(n = 283) == 5\n assert candidate(n = 8388608) == 1\n assert candidate(n = 79) == 5\n assert candidate(n = 63) == 6\n assert candidate(n = 269) == 4\n assert candidate(n = 61) == 5\n assert candidate(n = 999999999) == 21\n assert candidate(n = 49) == 3\n assert candidate(n = 227) == 5\n assert candidate(n = 47) == 5\n assert candidate(n = 4096) == 1\n assert candidate(n = 113) == 4\n assert candidate(n = 233) == 5\n assert candidate(n = 32767) == 15\n assert candidate(n = 511) == 9\n assert candidate(n = 4294967295) == 32\n assert candidate(n = 1879048192) == 3\n assert candidate(n = 4194303) == 22\n assert candidate(n = 191) == 7\n assert candidate(n = 16) == 1\n assert candidate(n = 4026531840) == 4\n assert candidate(n = 17179869183) == 34\n assert candidate(n = 311) == 6\n assert candidate(n = 179) == 5\n assert candidate(n = 2) == 1\n assert candidate(n = 3221225471) == 31\n assert candidate(n = 2147483644) == 29\n assert candidate(n = 34359738367) == 35\n assert candidate(n = 255) == 8\n assert candidate(n = 127) == 7\n assert candidate(n = 987654321) == 17\n assert candidate(n = 307) == 5\n assert candidate(n = 14) == 3\n assert candidate(n = 26) == 3\n assert candidate(n = 281) == 4\n assert candidate(n = 536870911) == 29\n assert candidate(n = 33554431) == 25\n assert candidate(n = 13) == 3\n assert candidate(n = 277) == 4\n assert candidate(n = 197) == 4\n assert candidate(n = 157) == 5\n assert candidate(n = 16383) == 14\n assert candidate(n = 59) == 5\n assert candidate(n = 173) == 5\n assert candidate(n = 67) == 3\n assert candidate(n = 134217727) == 27\n assert candidate(n = 64) == 1\n assert candidate(n = 8388607) == 23\n assert candidate(n = 254) == 7\n assert candidate(n = 4094) == 11\n assert candidate(n = 1024) == 1\n assert candidate(n = 1073741824) == 1\n assert candidate(n = 22) == 3\n assert candidate(n = 149) == 4\n assert candidate(n = 19) == 3\n assert candidate(n = 1599999999) == 23\n assert candidate(n = 139) == 4\n assert candidate(n = 109) == 5\n assert candidate(n = 31) == 5\n assert candidate(n = 229) == 5\n assert candidate(n = 199) == 5\n assert candidate(n = 7) == 3\n assert candidate(n = 25) == 3\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().hammingWeight", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var hammingWeight = function(n) {", "container": null, "callable": "hammingWeight", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 198, "task_id": "house-robber", "difficulty": "Medium", "problem_description": "You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security systems connected and it will automatically contact the police if two adjacent houses were broken into on the same night.\nGiven an integer array nums representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.\n \nExample 1:\n\nInput: nums = [1,2,3,1]\nOutput: 4\nExplanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).\nTotal amount you can rob = 1 + 3 = 4.\n\nExample 2:\n\nInput: nums = [2,7,9,3,1]\nOutput: 12\nExplanation: Rob house 1 (money = 2), rob house 3 (money = 9) and rob house 5 (money = 1).\nTotal amount you can rob = 2 + 9 + 1 = 12.\n\n \nConstraints:\n\n1 <= nums.length <= 100\n0 <= nums[i] <= 400\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [1, 2, 3, 1]) == 4\n assert candidate(nums = [2, 1, 1, 2]) == 4\n assert candidate(nums = [5, 2, 6, 3, 4, 1]) == 15\n assert candidate(nums = [5, 2, 6, 3, 1, 8, 9, 4, 7]) == 28\n assert candidate(nums = [1, 2]) == 2\n assert candidate(nums = [10, 2, 3, 8, 10, 1]) == 23\n assert candidate(nums = [0]) == 0\n assert candidate(nums = [3, 2, 5, 10, 7]) == 15\n assert candidate(nums = [5, 10, 5, 10]) == 20\n assert candidate(nums = [1, 3, 1, 3, 100]) == 103\n assert candidate(nums = [10, 20, 30, 40, 50]) == 90\n assert candidate(nums = [0, 0, 0, 0]) == 0\n assert candidate(nums = [50, 10, 100, 10, 5]) == 155\n assert candidate(nums = [3, 5, 100, 1, 1, 1, 1, 1, 100, 1, 1, 1, 1]) == 207\n assert candidate(nums = [2, 7, 9, 3, 1]) == 12\n assert candidate(nums = [3, 10, 3, 1, 2, 1]) == 12\n assert candidate(nums = [300, 400, 500, 100, 200, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500]) == 6500\n assert candidate(nums = [299, 399, 199, 299, 399, 199, 299, 399, 199, 299, 399, 199, 299, 399, 199, 299, 399, 199, 299, 399]) == 3090\n assert candidate(nums = [10, 5, 15, 20, 25, 30, 35, 40]) == 100\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 136\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 3000\n assert candidate(nums = [400, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 400\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 30\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]) == 27\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 11000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 42\n assert candidate(nums = [399, 0, 399, 0, 399, 0, 399, 0, 399, 0, 399, 0, 399, 0, 399, 0, 399]) == 3591\n assert candidate(nums = [100, 0, 100, 0, 100, 0, 100, 0, 100]) == 500\n assert candidate(nums = [4, 1, 2, 7, 5, 3, 9, 2, 8, 6, 4, 10, 1, 2, 5, 3, 7, 8, 6, 9]) == 60\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [200, 100, 150, 50, 300, 100, 400, 200, 350, 150]) == 1400\n assert candidate(nums = [300, 200, 100, 50, 25, 10, 5, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 458\n assert candidate(nums = [400, 399, 398, 397, 396, 395, 394, 393, 392, 391]) == 1980\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 240\n assert candidate(nums = [400, 0, 400, 0, 400, 0, 400, 0, 400, 0]) == 2000\n assert candidate(nums = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 100\n assert candidate(nums = [10, 1, 20, 3, 40, 5, 60, 7, 80]) == 210\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 64\n assert candidate(nums = [10, 5, 1, 2, 12, 4, 5, 6, 1, 2]) == 31\n assert candidate(nums = [100, 1, 1, 100, 1, 1, 100, 1, 1, 100]) == 400\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 420\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 400]) == 400\n assert candidate(nums = [1, 3, 1, 1, 3, 1, 1, 3, 1, 1]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 16\n assert candidate(nums = [400, 300, 200, 100, 0, 0, 0, 0, 0, 0]) == 600\n assert candidate(nums = [100, 0, 50, 0, 200, 0, 300, 0, 400, 0]) == 1050\n assert candidate(nums = [300, 200, 100, 400, 300, 500, 400, 600, 500, 700]) == 2500\n assert candidate(nums = [150, 100, 120, 200, 180, 170, 160, 250, 300, 290]) == 1060\n assert candidate(nums = [300, 0, 400, 0, 300, 0]) == 1000\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 400]) == 435\n assert candidate(nums = [400, 300, 200, 100, 50, 40]) == 650\n assert candidate(nums = [300, 0, 0, 300, 0, 0, 300, 0, 0, 300]) == 1200\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 55\n assert candidate(nums = [2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1]) == 14\n assert candidate(nums = [1, 3, 1, 5, 2, 2, 1, 3, 4]) == 14\n assert candidate(nums = [3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3]) == 21\n assert candidate(nums = [100, 200, 300, 400, 500, 600]) == 1200\n assert candidate(nums = [1, 3, 1, 3, 100, 1, 1, 1, 1, 1]) == 105\n assert candidate(nums = [400, 0, 400, 0, 400, 0, 400, 0, 400, 0, 400, 0, 400, 0, 400, 0, 400, 0, 400, 0]) == 4000\n assert candidate(nums = [5, 4, 3, 2, 1, 0, 9, 8, 7, 6]) == 25\n assert candidate(nums = [4, 2, 3, 6, 3, 8, 5, 10, 7]) == 28\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55]) == 175\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 110\n assert candidate(nums = [399, 1, 399, 1, 399, 1, 399, 1, 399, 1]) == 1995\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [3, 10, 3, 1, 2, 9, 5, 4, 6, 8, 1, 7]) == 39\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 30\n assert candidate(nums = [10, 5, 15, 20, 25, 30, 35, 40, 45, 50]) == 150\n assert candidate(nums = [100, 0, 100, 0, 100, 0, 100]) == 400\n assert candidate(nums = [3, 2, 5, 10, 7, 8, 5, 1, 100, 2, 5, 8, 5, 1, 100]) == 231\n assert candidate(nums = [1, 2, 3, 1, 1, 2, 3, 1, 1, 2]) == 10\n assert candidate(nums = [10, 5, 10, 5, 10, 5, 10, 5, 10, 5]) == 50\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 128\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 5\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 300\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3]) == 30\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 60\n assert candidate(nums = [200, 100, 200, 200, 100, 300, 150, 250, 200, 100]) == 1050\n assert candidate(nums = [300, 1, 1, 300, 1, 1, 300, 1, 1, 300, 1, 1, 300, 1, 1, 300, 1, 1, 300, 1]) == 2100\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 30\n assert candidate(nums = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]) == 7\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3]) == 18\n assert candidate(nums = [300, 100, 200, 150, 250, 125, 350]) == 1100\n assert candidate(nums = [100, 1, 200, 3, 400, 5]) == 700\n assert candidate(nums = [0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [150, 200, 50, 100, 100, 50, 200, 150, 100, 100, 50, 200, 150]) == 800\n assert candidate(nums = [100, 200, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 260\n assert candidate(nums = [300, 200, 100, 0, 50, 10, 20, 30, 40, 5]) == 510\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80, 70]) == 235\n assert candidate(nums = [50, 1, 50, 1, 50, 1, 50, 1, 50, 1]) == 250\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [300, 200, 100, 400, 300, 500, 200]) == 1200\n assert candidate(nums = [300, 200, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 400\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [50, 100, 200, 50, 100, 200, 50, 100, 200, 50]) == 650\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 50\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1]) == 18\n assert candidate(nums = [50, 10, 40, 70, 30, 60, 20, 80, 100, 90]) == 350\n assert candidate(nums = [31, 41, 59, 26, 53, 58, 97, 93, 23, 84, 62, 64, 33, 83, 27, 95, 8, 41, 32, 9]) == 617\n assert candidate(nums = [400, 300, 200, 100, 0, 100, 200, 300, 400]) == 1200\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 90\n assert candidate(nums = [4, 1, 2, 7, 5, 3, 1, 1, 1, 2, 3, 4, 5]) == 23\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 20\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 66\n assert candidate(nums = [3, 7, 5, 1, 9, 2, 6, 4]) == 23\n assert candidate(nums = [400, 399, 398, 397, 396, 395, 394, 393, 392, 391]) == 1980\n assert candidate(nums = [4, 1, 2, 7, 5, 3, 1, 1, 1, 1]) == 16\n assert candidate(nums = [10, 15, 10, 5, 10, 15, 10, 5, 10, 15]) == 55\n assert candidate(nums = [10, 5, 10, 5, 15, 20]) == 40\n assert candidate(nums = [2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2]) == 10\n assert candidate(nums = [10, 0, 0, 0, 0, 10, 0, 0, 0, 0, 10]) == 30\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 3000\n assert candidate(nums = [3, 5, 100, 1, 1, 1, 1, 1, 100, 1, 1, 5, 3]) == 210\n assert candidate(nums = [8, 2, 8, 10, 6, 5, 1, 9, 3, 7, 4, 2, 5]) == 44\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().rob", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var rob = function(nums) {", "container": null, "callable": "rob", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 199, "task_id": "binary-tree-right-side-view", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, imagine yourself standing on the right side of it, return the values of the nodes you can see ordered from top to bottom.\n \nExample 1:\n\nInput: root = [1,2,3,null,5,null,4]\nOutput: [1,3,4]\nExplanation:\n\n\nExample 2:\n\nInput: root = [1,2,3,4,null,null,null,5]\nOutput: [1,3,4,5]\nExplanation:\n\n\nExample 3:\n\nInput: root = [1,null,3]\nOutput: [1,3]\n\nExample 4:\n\nInput: root = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 100].\n-100 <= Node.val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, None, 3])) == [1, 3]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, None, 5])) == [1, 3, 4, 5]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 4])) == [1, 3, 4]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, None, None, None, 5, None, None, None, 6, None, None, None, 7, None, None, None, 8, None, None, None, 9, None, None, None, 10])) == [1, 3, 4]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7])) == [1, 3, 5, 6, 7]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 9])) == [10, 15, 18, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, 6, None, 7, 8, 9, None, None, 10, 11, 12, None, None, 13, None, None, 14])) == [1, 3, 5, 7, 9, 12, 14]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, None, 9, 2, None, None, None, None, 10])) == [5, 8, 9, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9])) == [1, 3, 7, 9]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 4, None, 6, None, 7, None, 8, None, 9])) == [1, 3, 4, 7, 9]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 14, 15])) == [1, 3, 7, 13, 15]\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, 6, None, None, None, None, 7, None, 8, 9])) == [1, 2, 3, 4, 6]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, 16])) == [1, 3, 7, 15, 16]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, 8, 9, None, 10, None, None, 11, None, 12])) == [1, 3, 6, 10, 12]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])) == [1, 3, 7, 15, 31]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, 10, 11, None, None, None, None, 12, 13, 14, 15])) == [1, 3, 7, 11, 15]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8])) == [1, 3, 6, 8]\n assert candidate(root = tree_node([1, 2, 3, None, None, None, 4, None, None, 5, None, None, 6, None, None, 7])) == [1, 3, 4]\n assert candidate(root = tree_node([100, -50, 50, -75, -25, 25, 75, -100, 0, 0, 100])) == [100, 50, 75, 100]\n assert candidate(root = tree_node([1, None, 2, 3, 4, 5, 6, None, None, 7, 8, 9, 10, None, None, 11, 12, 13, 14, 15])) == [1, 2, 4, 6, 10, 15]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == [3, 20, 7]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, None, 7, None, 8, None, 9])) == [1, 3, 5, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, None, 6, 7, 8, 9])) == [1, 3, 5, 6, 8, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 3, 5, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, 7, None, 8, None, 9, None, 10])) == [1, 3, 5, 8, 10]\n assert candidate(root = tree_node([1, 2, 3, None, 5, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == [1, 3, 6, 8, 10, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, None, None, None, None, 6, 7, 8, 9, 10, 11])) == [1, 3, 5]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7])) == [1, 3, 5, 7]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [1, 3, 7, 15, 20]\n assert candidate(root = tree_node([1, 2, None, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8])) == [1, 2, 4, 7, 8]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [1, 3, 7, 15]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [1, 3, 7]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, 7, None, None, None, None, None, 8, 9])) == [1, 3, 6, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, 8, 9, None, 10, None, None, 11])) == [1, 3, 6, 10, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, 8, None, None, None, 9])) == [1, 3, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, None, 5, 6, None, 7, None, 8, 9])) == [1, 3, 6, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, 10, 11, 12, 13, None, None, None, None, 14])) == [1, 3, 7, 13, 14]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, None, None, 5, 6])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 9])) == [1, 3, 7, 8]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, 10, None, None, None, None, 11, 12, None, None, 13, None, 14])) == [1, 3, 5, 9, 12, 14]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, 6])) == [1, 2, 4, 6]\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 4, 6, 7])) == [1, 3, 4, 7]\n assert candidate(root = tree_node([1, 2, None, 4, None, 6, 7, None, None, None, 8])) == [1, 2, 4, 7, 8]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, 6, 7, 8, None, 9, None, 10, 11])) == [1, 3, 5, 8, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, None, 11, 12, 13, 14, 15])) == [1, 3, 7, 14, 15]\n assert candidate(root = tree_node([1, None, 2, None, None, None, None, 3, None, None, None, 4, None, None, None, 5])) == [1, 2]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [5, 4, 6]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, None, 6, 7, None, 8, 9, None, None, None, None, 10])) == [1, 2, 4, 5, 7, 9, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, None, 7, 8, None, None, 9, 10, None, None, 11, 12])) == [1, 3, 6, 8, 10, 12]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, None, 5, 6, None, None, 7, 8, None, None, 9, 10, None, None, 11, 12])) == [1, 2, 4, 6, 8, 10, 12]\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 7, 8, 9, 10, None, None, 11, 12])) == [1, 3, 6, 10, 12]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, 4])) == [1, 2]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, None, None, 6, 7, None, None, 8, 9])) == [1, 3, 5]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 3, 5, 7, 9]\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == [0, 4, -1, 8]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, 6, None, 7, 8, 9, 10, None, None, 11, 12])) == [1, 3, 5, 8, 12]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == [1, 2, 3, 4, 5, 6]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, 7, 8, 9, None, None, None, 10])) == [1, 3, 6, 9, 10]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, 6, 7, None, None, 8, None, 9, 10])) == [1, 2, 4, 7, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, 9, 10, None, 11])) == [1, 3, 6, 10, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, None, 13, None, None, 14])) == [1, 3, 7, 13, 14]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, 16])) == [1, 3, 7, 15, 16]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9, None, None, 10, 11])) == [1, 3, 5, 7, 9, 11]\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 7, 8, None, None, 9, 10])) == [1, 3, 6, 8, 10]\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, 6, 7, 8, 9, 10, 11, 12, 13])) == [1, 3, 5, 9, 13]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [1, 3, 5, 7, 8]\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, None, 6, None, None, None, 7])) == [1, 2, 4, 5, 6]\n assert candidate(root = tree_node([-10, -5, -15, -3, -8, -20, -18, -1, -4, None, -9, None, None, -6, -7])) == [-10, -15, -18, -7]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, 7, 8, None, 9, 10, None, 11])) == [1, 3, 6, 10, 11]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, None, 8, None, None, None, 9])) == [1, 3, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, 10, 11, 12, 13, 14])) == [1, 3, 7, 14]\n assert candidate(root = tree_node([1, 2, 3, None, 5, 6, None, 7, 8])) == [1, 3, 6, 8]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, None, None, 6, None, 7, None, 8, None, 9])) == [1, 3, 5, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7])) == [1, 3, 5, 7]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, None, None, 7, 8])) == [1, 3, 6, 8]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, None, 8, 9, None, None, None, 10, 11])) == [1, 3, 7, 9, 11]\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, None, None, 6, None, None, 7])) == [1, 3, 5]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, None, None, 17, None, 18, None, None, 19, None, None, 20])) == [1, 3, 7, 15, 20]\n assert candidate(root = tree_node([1, 2, None, 3, 4, 5, None, 6, 7, None, None, 8, None, None, 9, None, 10])) == [1, 2, 4, 7, 9, 10]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, 8, 9, None, None, 10])) == [1, 3, 5, 8, 10]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().rightSideView", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var rightSideView = function(root) {", "container": null, "callable": "rightSideView", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 200, "task_id": "number-of-islands", "difficulty": "Medium", "problem_description": "Given an m x n 2D binary grid grid which represents a map of '1's (land) and '0's (water), return the number of islands.\nAn island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.\n \nExample 1:\n\nInput: grid = [\n [\"1\",\"1\",\"1\",\"1\",\"0\"],\n [\"1\",\"1\",\"0\",\"1\",\"0\"],\n [\"1\",\"1\",\"0\",\"0\",\"0\"],\n [\"0\",\"0\",\"0\",\"0\",\"0\"]\n]\nOutput: 1\n\nExample 2:\n\nInput: grid = [\n [\"1\",\"1\",\"0\",\"0\",\"0\"],\n [\"1\",\"1\",\"0\",\"0\",\"0\"],\n [\"0\",\"0\",\"1\",\"0\",\"0\"],\n [\"0\",\"0\",\"0\",\"1\",\"1\"]\n]\nOutput: 3\n\n \nConstraints:\n\nm == grid.length\nn == grid[i].length\n1 <= m, n <= 300\ngrid[i][j] is '0' or '1'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(grid = [['1', '1', '1', '1', '0'], ['1', '1', '0', '1', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '0', '0', '0']]) == 1\n assert candidate(grid = [['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0']]) == 0\n assert candidate(grid = [['1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '1', '0', '0'], ['0', '0', '0', '1', '1']]) == 3\n assert candidate(grid = [['1', '1', '1'], ['0', '0', '0'], ['1', '1', '1']]) == 2\n assert candidate(grid = [['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0']]) == 10\n assert candidate(grid = [['1', '1', '1', '0', '0', '0'], ['0', '0', '0', '1', '1', '0'], ['1', '0', '1', '0', '0', '1'], ['0', '1', '0', '1', '0', '1'], ['0', '0', '1', '1', '1', '0']]) == 7\n assert candidate(grid = [['1', '0', '0', '0', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '1', '1', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '1', '1', '0'], ['0', '0', '0', '0', '0', '0', '0', '1', '1', '0'], ['0', '1', '1', '0', '0', '1', '1', '0', '0', '1']]) == 6\n assert candidate(grid = [['1', '0', '0', '1', '0', '0', '1', '0', '0', '1'], ['0', '1', '1', '0', '1', '1', '0', '1', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '1', '0', '1', '1', '0', '1', '1', '0'], ['1', '0', '0', '1', '0', '0', '1', '0', '0', '1']]) == 28\n assert candidate(grid = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '1', '1', '1', '0', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '0', '1']]) == 1\n assert candidate(grid = [['1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0']]) == 18\n assert candidate(grid = [['1', '1', '0', '0', '0', '0', '0'], ['0', '1', '0', '0', '1', '1', '0'], ['0', '0', '1', '1', '0', '0', '1'], ['0', '0', '0', '0', '1', '1', '0'], ['1', '0', '1', '0', '1', '0', '1'], ['1', '1', '0', '0', '1', '0', '1']]) == 8\n assert candidate(grid = [['1', '1', '0', '0', '0', '0', '1'], ['1', '1', '0', '0', '1', '0', '1'], ['0', '0', '0', '0', '1', '0', '1'], ['0', '0', '1', '1', '1', '0', '0'], ['0', '0', '0', '0', '0', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '1', '0', '0', '1'], ['1', '0', '0', '1', '0', '0', '1'], ['1', '1', '1', '1', '0', '0', '1'], ['0', '0', '0', '0', '1', '1', '1'], ['0', '0', '1', '0', '1', '1', '0'], ['0', '0', '0', '0', '1', '1', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '1', '0', '0', '0', '1', '1', '1'], ['1', '1', '0', '1', '0', '0', '0', '1', '0', '1'], ['1', '1', '0', '0', '0', '0', '0', '0', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1', '0', '0', '0', '0', '0'], ['1', '0', '0', '0', '1', '0', '0', '0', '1', '1'], ['1', '0', '0', '1', '0', '0', '0', '1', '0', '1']]) == 6\n assert candidate(grid = [['1', '1', '1', '0', '0', '1', '1'], ['1', '0', '1', '0', '0', '1', '0'], ['1', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '1', '1', '0', '0'], ['0', '0', '0', '1', '1', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '0', '0', '1'], ['1', '0', '0', '1', '1'], ['0', '0', '1', '0', '0'], ['1', '1', '0', '0', '1']]) == 5\n assert candidate(grid = [['1', '1', '1', '0', '0'], ['0', '0', '0', '0', '0'], ['1', '1', '1', '0', '0'], ['0', '0', '0', '1', '1']]) == 3\n assert candidate(grid = [['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1']]) == 10\n assert candidate(grid = [['1', '1', '1', '0', '0', '0', '1', '0', '0', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '1', '0'], ['0', '1', '1', '0', '1', '1', '0', '0', '0', '1', '1'], ['0', '0', '0', '1', '0', '1', '0', '1', '0', '1', '1'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '0', '1'], ['0', '1', '1', '0', '1', '0', '1', '1', '0', '1', '0'], ['1', '0', '1', '1', '1', '1', '1', '0', '1', '1', '0'], ['0', '1', '1', '1', '0', '0', '0', '1', '0', '0', '0'], ['1', '0', '1', '1', '0', '0', '0', '0', '1', '1', '0'], ['1', '1', '0', '0', '1', '1', '1', '0', '0', '1', '1']]) == 14\n assert candidate(grid = [['1', '0', '1', '1', '1', '0', '1', '1', '0', '0'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '1', '0', '1', '0', '1', '1', '1', '0'], ['0', '0', '0', '0', '0', '0', '1', '0', '1', '1'], ['1', '1', '1', '0', '1', '0', '0', '0', '0', '0'], ['1', '1', '1', '0', '0', '1', '0', '0', '1', '0']]) == 10\n assert candidate(grid = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '0', '1'], ['1', '0', '1', '0', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(grid = [['1', '1', '1', '1', '0', '0', '0'], ['0', '0', '0', '1', '0', '0', '0'], ['1', '1', '0', '1', '0', '1', '1'], ['1', '1', '0', '1', '0', '1', '1'], ['0', '0', '0', '0', '0', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 2\n assert candidate(grid = [['1', '1', '1', '1', '1', '0', '0', '0', '0'], ['1', '0', '0', '1', '1', '0', '0', '0', '0'], ['1', '0', '0', '0', '0', '0', '1', '1', '0'], ['0', '0', '0', '0', '0', '0', '1', '1', '0'], ['0', '1', '1', '0', '0', '0', '0', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '1', '1', '1', '1', '0', '0'], ['0', '0', '0', '0', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '1', '1', '0', '0', '0', '0']]) == 5\n assert candidate(grid = [['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '1', '1', '1', '1', '0', '1', '1', '1', '1', '0', '1', '1', '1', '0'], ['0', '1', '0', '0', '1', '0', '1', '0', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '0', '1', '0', '1', '0', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '1', '1', '1', '0', '1', '1', '1', '1', '0', '1', '1', '1', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '0', '0', '0', '1', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '1', '0', '0'], ['1', '1', '1', '0', '0', '0', '1', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '1', '0', '0'], ['1', '1', '1', '0', '0', '0', '1', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '1', '0', '0'], ['0', '0', '0', '1', '1', '0', '0', '0', '0', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '1', '1', '0', '0', '0', '0', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '1', '1', '1', '1', '0', '0', '0', '0', '0', '0', '0', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '1', '1', '1', '1', '0', '0', '0', '0', '0', '0', '0', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 9\n assert candidate(grid = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 2\n assert candidate(grid = [['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1']]) == 42\n assert candidate(grid = [['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1']]) == 25\n assert candidate(grid = [['1', '1', '1', '0', '0'], ['0', '1', '0', '1', '1'], ['1', '0', '1', '1', '0'], ['0', '0', '0', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '0', '0', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '1', '1', '1', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '0', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '1', '1', '0', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 2\n assert candidate(grid = [['1', '1', '1', '0', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '1', '1', '0', '1', '1', '1', '0', '1'], ['0', '1', '0', '0', '1', '0', '0', '1', '0'], ['1', '0', '1', '1', '1', '1', '1', '0', '1']]) == 6\n assert candidate(grid = [['1', '1', '1', '0', '1', '1', '0', '0', '0', '0'], ['1', '0', '1', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '0', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '0', '1', '1', '0', '1', '1', '0'], ['0', '0', '0', '0', '0', '0', '0', '1', '1', '0']]) == 4\n assert candidate(grid = [['1', '0', '0', '0', '0', '0', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '1', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '1', '1', '1', '0', '0', '0', '0', '0'], ['0', '0', '1', '0', '1', '0', '0', '0', '0', '0'], ['0', '0', '1', '1', '1', '0', '0', '0', '0', '0']]) == 4\n assert candidate(grid = [['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '1', '1', '0', '1', '1', '0', '1', '1', '0'], ['0', '1', '1', '0', '1', '1', '0', '1', '1', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '1', '1', '0', '1', '1', '0', '1'], ['1', '1', '0', '1', '1', '0', '1', '1', '0', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 7\n assert candidate(grid = [['1', '1', '0', '0', '1', '0', '0', '1', '1'], ['0', '1', '0', '0', '0', '0', '0', '1', '1'], ['1', '1', '0', '0', '1', '1', '1', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1']]) == 9\n assert candidate(grid = [['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '1', '1', '1', '0', '1', '1', '1', '0', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '0'], ['0', '1', '1', '1', '0', '1', '1', '1', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '0', '0', '0', '0', '0', '1', '1'], ['1', '0', '1', '0', '0', '0', '0', '0', '1', '1'], ['1', '1', '1', '0', '0', '0', '0', '0', '1', '1']]) == 4\n assert candidate(grid = [['1', '1', '1', '1', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '1', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 1\n assert candidate(grid = [['1', '1', '1', '0', '1', '1', '1', '0', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '0', '1', '1', '1', '0', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '1', '0', '1', '1', '1', '0', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 9\n assert candidate(grid = [['1', '1', '1', '0', '0', '0', '1', '1', '1'], ['1', '0', '1', '0', '0', '0', '1', '0', '1'], ['1', '1', '1', '0', '0', '0', '1', '1', '1'], ['0', '0', '0', '1', '1', '1', '0', '0', '0'], ['1', '1', '1', '1', '0', '1', '1', '1', '1']]) == 3\n assert candidate(grid = [['1', '1', '1', '0', '0', '0', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '1', '0'], ['0', '1', '1', '0', '1', '1', '0', '0', '0', '1', '1'], ['0', '0', '0', '1', '0', '1', '0', '1', '0', '1', '1'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '0', '1'], ['0', '1', '1', '0', '1', '0', '1', '1', '0', '1', '0']]) == 10\n assert candidate(grid = [['1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0'], ['1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0', '1', '1', '0', '0']]) == 15\n assert candidate(grid = [['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '1', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1']]) == 2\n assert candidate(grid = [['1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0', '1', '1', '0', '0', '0', '1', '1', '0', '0', '0'], ['0', '0', '0', '1', '0', '0', '0', '1', '0', '0', '0', '0', '0', '1', '0'], ['0', '0', '0', '1', '0', '0', '0', '1', '0', '0', '0', '0', '0', '1', '0'], ['0', '0', '0', '0', '1', '1', '1', '0', '1', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '0', '1', '1', '1', '0', '1', '1', '1', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '1', '1', '1', '1']]) == 9\n assert candidate(grid = [['1', '0', '0', '1', '1'], ['1', '0', '0', '1', '0'], ['0', '0', '0', '0', '0'], ['1', '1', '0', '0', '1']]) == 4\n assert candidate(grid = [['1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '1', '1', '1'], ['1', '1', '1', '0', '0'], ['0', '0', '0', '1', '1']]) == 3\n assert candidate(grid = [['1', '0', '0', '0', '0', '0', '1', '0', '0', '0', '0', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 54\n assert candidate(grid = [['1', '0', '0', '0', '1', '1', '1', '1'], ['1', '1', '0', '0', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0', '0', '0'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1']]) == 18\n assert candidate(grid = [['1', '1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '1', '1', '1', '1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '1', '1', '1', '1', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '1', '1', '1', '1', '1', '1', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '1', '1', '1', '1', '1', '1', '0', '0', '0', '0', '0', '0', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '1', '0'], ['1', '0', '0', '1', '0'], ['1', '0', '0', '0', '0'], ['0', '1', '1', '1', '0']]) == 2\n assert candidate(grid = [['0', '1', '0', '0', '0', '0', '0', '0', '0', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0']]) == 26\n assert candidate(grid = [['1', '1', '1', '0', '1', '1'], ['1', '0', '0', '0', '1', '0'], ['1', '0', '1', '0', '0', '1'], ['0', '0', '0', '0', '0', '0'], ['1', '1', '0', '1', '1', '1']]) == 6\n assert candidate(grid = [['1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 2\n assert candidate(grid = [['1', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '1', '0', '0', '0', '1', '1'], ['0', '0', '0', '0', '1', '1', '1', '1', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0']]) == 2\n assert candidate(grid = [['0', '0', '1', '0', '0', '1', '0', '0', '1', '0'], ['0', '0', '1', '0', '0', '1', '0', '0', '1', '0'], ['0', '0', '1', '0', '0', '1', '0', '0', '1', '0'], ['0', '0', '1', '0', '0', '1', '0', '0', '1', '0'], ['0', '0', '1', '0', '0', '1', '0', '0', '1', '0']]) == 3\n assert candidate(grid = [['1', '1', '1', '1', '1', '0', '0', '0', '0', '0'], ['1', '0', '0', '0', '1', '0', '0', '0', '0', '0'], ['1', '0', '0', '0', '1', '0', '0', '0', '0', '0'], ['1', '0', '0', '0', '1', '0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1', '0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '1', '0', '0', '1', '1'], ['0', '0', '0', '0', '0', '1', '1', '1', '1', '1']]) == 2\n assert candidate(grid = [['1', '1', '1', '0', '0'], ['1', '0', '0', '1', '0'], ['1', '0', '0', '1', '0'], ['0', '1', '1', '0', '0'], ['0', '0', '0', '0', '1']]) == 4\n assert candidate(grid = [['1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1', '0', '1']]) == 32\n"}, "metadata": {"canonical_parameter_names": ["grid"], "leetcode_dataset_entry_point": "Solution().numIslands", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numIslands = function(grid) {", "container": null, "callable": "numIslands", "parameters": [{"name": "grid", "type": "character[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 201, "task_id": "bitwise-and-of-numbers-range", "difficulty": "Medium", "problem_description": "Given two integers left and right that represent the range [left, right], return the bitwise AND of all numbers in this range, inclusive.\n \nExample 1:\n\nInput: left = 5, right = 7\nOutput: 4\n\nExample 2:\n\nInput: left = 0, right = 0\nOutput: 0\n\nExample 3:\n\nInput: left = 1, right = 2147483647\nOutput: 0\n\n \nConstraints:\n\n0 <= left <= right <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(left = 5,right = 7) == 4\n assert candidate(left = 100,right = 105) == 96\n assert candidate(left = 16,right = 31) == 16\n assert candidate(left = 123456,right = 654321) == 0\n assert candidate(left = 8,right = 12) == 8\n assert candidate(left = 0,right = 0) == 0\n assert candidate(left = 33,right = 35) == 32\n assert candidate(left = 1,right = 1) == 1\n assert candidate(left = 1,right = 2147483647) == 0\n assert candidate(left = 8,right = 8) == 8\n assert candidate(left = 10,right = 15) == 8\n assert candidate(left = 100,right = 200) == 0\n assert candidate(left = 4194304,right = 4194305) == 4194304\n assert candidate(left = 1000000,right = 1000010) == 1000000\n assert candidate(left = 4095,right = 8191) == 0\n assert candidate(left = 8388608,right = 8388608) == 8388608\n assert candidate(left = 134217728,right = 134217729) == 134217728\n assert candidate(left = 536870912,right = 536870913) == 536870912\n assert candidate(left = 32768,right = 32769) == 32768\n assert candidate(left = 32,right = 33) == 32\n assert candidate(left = 1024,right = 2047) == 1024\n assert candidate(left = 1,right = 1073741824) == 0\n assert candidate(left = 16777215,right = 16777216) == 0\n assert candidate(left = 1000000000,right = 1000000100) == 1000000000\n assert candidate(left = 512,right = 1023) == 512\n assert candidate(left = 100000000,right = 200000000) == 0\n assert candidate(left = 65536,right = 131071) == 65536\n assert candidate(left = 123456,right = 123458) == 123456\n assert candidate(left = 1,right = 3) == 0\n assert candidate(left = 1024,right = 1025) == 1024\n assert candidate(left = 131072,right = 131073) == 131072\n assert candidate(left = 1073741824,right = 1073741825) == 1073741824\n assert candidate(left = 536870912,right = 1073741823) == 536870912\n assert candidate(left = 1,right = 10) == 0\n assert candidate(left = 16384,right = 32767) == 16384\n assert candidate(left = 512,right = 513) == 512\n assert candidate(left = 32768,right = 65535) == 32768\n assert candidate(left = 16384,right = 16385) == 16384\n assert candidate(left = 67108864,right = 67108865) == 67108864\n assert candidate(left = 256,right = 257) == 256\n assert candidate(left = 64,right = 65) == 64\n assert candidate(left = 262144,right = 262145) == 262144\n assert candidate(left = 2097152,right = 2097153) == 2097152\n assert candidate(left = 16,right = 17) == 16\n assert candidate(left = 536870912,right = 536870919) == 536870912\n assert candidate(left = 16777216,right = 33554431) == 16777216\n assert candidate(left = 2048,right = 2049) == 2048\n assert candidate(left = 512,right = 768) == 512\n assert candidate(left = 2147483644,right = 2147483647) == 2147483644\n assert candidate(left = 1000000,right = 1000100) == 999936\n assert candidate(left = 500000000,right = 500000100) == 500000000\n assert candidate(left = 4096,right = 4096) == 4096\n assert candidate(left = 1048576,right = 1048577) == 1048576\n assert candidate(left = 33554432,right = 33554433) == 33554432\n assert candidate(left = 1073741824,right = 2147483647) == 1073741824\n assert candidate(left = 4,right = 7) == 4\n assert candidate(left = 2147483646,right = 2147483647) == 2147483646\n assert candidate(left = 1,right = 1000) == 0\n assert candidate(left = 16777216,right = 16777217) == 16777216\n assert candidate(left = 268435456,right = 268435457) == 268435456\n assert candidate(left = 32,right = 63) == 32\n assert candidate(left = 524288,right = 524289) == 524288\n assert candidate(left = 256,right = 511) == 256\n assert candidate(left = 1023,right = 1024) == 0\n assert candidate(left = 8192,right = 8193) == 8192\n assert candidate(left = 2147483645,right = 2147483647) == 2147483644\n assert candidate(left = 512,right = 1024) == 0\n assert candidate(left = 268435456,right = 268435460) == 268435456\n assert candidate(left = 1073741824,right = 1073741827) == 1073741824\n assert candidate(left = 130,right = 135) == 128\n assert candidate(left = 8388608,right = 8388609) == 8388608\n assert candidate(left = 134217728,right = 268435455) == 134217728\n assert candidate(left = 1024,right = 2048) == 0\n assert candidate(left = 50,right = 100) == 0\n assert candidate(left = 33554432,right = 67108863) == 33554432\n assert candidate(left = 100000,right = 100099) == 99840\n assert candidate(left = 1048576,right = 2097151) == 1048576\n assert candidate(left = 268435456,right = 536870911) == 268435456\n assert candidate(left = 4096,right = 4097) == 4096\n assert candidate(left = 16777215,right = 16777219) == 0\n assert candidate(left = 16777215,right = 16777215) == 16777215\n assert candidate(left = 123456,right = 123479) == 123456\n assert candidate(left = 33554431,right = 33554432) == 0\n assert candidate(left = 65536,right = 65537) == 65536\n assert candidate(left = 8,right = 15) == 8\n assert candidate(left = 8191,right = 8192) == 0\n assert candidate(left = 1048576,right = 1049087) == 1048576\n assert candidate(left = 1048576,right = 1048580) == 1048576\n assert candidate(left = 500000000,right = 1000000000) == 0\n assert candidate(left = 2,right = 3) == 2\n assert candidate(left = 1023,right = 2047) == 0\n assert candidate(left = 128,right = 128) == 128\n assert candidate(left = 123456,right = 123500) == 123456\n assert candidate(left = 128,right = 255) == 128\n assert candidate(left = 1,right = 1000000000) == 0\n assert candidate(left = 128,right = 129) == 128\n assert candidate(left = 16777216,right = 16777232) == 16777216\n"}, "metadata": {"canonical_parameter_names": ["left", "right"], "leetcode_dataset_entry_point": "Solution().rangeBitwiseAnd", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var rangeBitwiseAnd = function(left, right) {", "container": null, "callable": "rangeBitwiseAnd", "parameters": [{"name": "left", "type": "number"}, {"name": "right", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 202, "task_id": "happy-number", "difficulty": "Easy", "problem_description": "Write an algorithm to determine if a number n is happy.\nA happy number is a number defined by the following process:\n\nStarting with any positive integer, replace the number by the sum of the squares of its digits.\nRepeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1.\nThose numbers for which this process ends in 1 are happy.\n\nReturn true if n is a happy number, and false if not.\n \nExample 1:\n\nInput: n = 19\nOutput: true\nExplanation:\n12 + 92 = 82\n82 + 22 = 68\n62 + 82 = 100\n12 + 02 + 02 = 1\n\nExample 2:\n\nInput: n = 2\nOutput: false\n\n \nConstraints:\n\n1 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 100) == True\n assert candidate(n = 4) == False\n assert candidate(n = 20) == False\n assert candidate(n = 2) == False\n assert candidate(n = 1111111) == True\n assert candidate(n = 19) == True\n assert candidate(n = 1) == True\n assert candidate(n = 1000000000) == True\n assert candidate(n = 7) == True\n assert candidate(n = 489) == False\n assert candidate(n = 789789789) == False\n assert candidate(n = 130) == True\n assert candidate(n = 49) == True\n assert candidate(n = 2147483647) == False\n assert candidate(n = 32442) == True\n assert candidate(n = 324) == False\n assert candidate(n = 203) == True\n assert candidate(n = 82) == True\n assert candidate(n = 70) == True\n assert candidate(n = 2736895) == False\n assert candidate(n = 1000) == True\n assert candidate(n = 44) == True\n assert candidate(n = 190) == True\n assert candidate(n = 58) == False\n assert candidate(n = 28) == True\n assert candidate(n = 289) == False\n assert candidate(n = 444444444) == False\n assert candidate(n = 14659) == False\n assert candidate(n = 6892) == False\n assert candidate(n = 3249671058) == False\n assert candidate(n = 145) == False\n assert candidate(n = 14657) == False\n assert candidate(n = 10000) == True\n assert candidate(n = 23) == True\n assert candidate(n = 784) == True\n assert candidate(n = 133) == True\n assert candidate(n = 999) == False\n assert candidate(n = 89) == False\n assert candidate(n = 9474) == False\n assert candidate(n = 111111111) == False\n assert candidate(n = 404) == True\n assert candidate(n = 442) == False\n assert candidate(n = 987654321) == False\n assert candidate(n = 1234567890) == False\n assert candidate(n = 139) == True\n assert candidate(n = 1000000007) == False\n assert candidate(n = 13441) == False\n assert candidate(n = 200) == False\n assert candidate(n = 8989898989) == False\n assert candidate(n = 3249) == False\n assert candidate(n = 123456789) == False\n assert candidate(n = 370) == False\n assert candidate(n = 789999) == False\n assert candidate(n = 1111111111) == True\n assert candidate(n = 100000000) == True\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().isHappy", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isHappy = function(n) {", "container": null, "callable": "isHappy", "parameters": [{"name": "n", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 203, "task_id": "remove-linked-list-elements", "difficulty": "Easy", "problem_description": "Given the head of a linked list and an integer val, remove all the nodes of the linked list that has Node.val == val, and return the new head.\n \nExample 1:\n\n\nInput: head = [1,2,6,3,4,5,6], val = 6\nOutput: [1,2,3,4,5]\n\nExample 2:\n\nInput: head = [], val = 1\nOutput: []\n\nExample 3:\n\nInput: head = [7,7,7,7], val = 7\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [0, 104].\n1 <= Node.val <= 50\n0 <= val <= 50\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([1, 2, 6, 3, 4, 5, 6]),val = 6), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50]),val = 10), list_node([20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([50, 20, 30, 20, 10]),val = 20), list_node([50, 30, 10]))\n assert candidate(head = list_node([1, 1, 1, 1, 1]),val = 1) == None\n assert is_same_list(candidate(head = list_node([50, 40, 30, 20, 10]),val = 50), list_node([40, 30, 20, 10]))\n assert candidate(head = list_node([7, 7, 7, 7]),val = 7) == None\n assert is_same_list(candidate(head = list_node([5, 1, 2, 3, 5, 4, 5]),val = 5), list_node([1, 2, 3, 4]))\n assert is_same_list(candidate(head = list_node([5, 1, 5, 2, 5, 3, 5]),val = 5), list_node([1, 2, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),val = 3), list_node([1, 2, 4, 5]))\n assert candidate(head = list_node([]),val = 1) == None\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 3]),val = 1), list_node([2, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5]),val = 6), list_node([1, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),val = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31]),val = 35), list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 34, 33, 32, 31]))\n assert is_same_list(candidate(head = list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21]),val = 45), list_node([50, 49, 48, 47, 46, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),val = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20]))\n assert candidate(head = list_node([42, 42, 42, 42, 42, 42]),val = 42) == None\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]),val = 20), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 22, 24, 26, 28, 30]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3]),val = 2), list_node([1, 1, 1, 1, 3, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 2, 4, 2, 5, 2, 6]),val = 2), list_node([1, 3, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 1, 3, 3, 3, 2, 2, 1]),val = 2), list_node([1, 1, 3, 3, 3, 1]))\n assert is_same_list(candidate(head = list_node([50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 50]),val = 50), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 10, 20, 30]),val = 20), list_node([10, 30, 40, 50, 10, 30]))\n assert is_same_list(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50]),val = 5), list_node([10, 15, 20, 25, 30, 35, 40, 45, 50, 10, 15, 20, 25, 30, 35, 40, 45, 50]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),val = 8), list_node([10, 9, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),val = 11), list_node([1, 3, 5, 7, 9, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50]),val = 2), list_node([4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),val = 20), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),val = 13), list_node([1, 3, 5, 7, 9, 11, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7]),val = 2), list_node([1, 3, 4, 5, 6, 7]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 2, 1, 2, 3, 2, 1, 2]),val = 2), list_node([1, 3, 1, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),val = 5), list_node([1, 2, 3, 4, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),val = 9), list_node([10, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),val = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50]),val = 10), list_node([20, 30, 40, 50, 60, 70, 80, 90, 100, 20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),val = 70), list_node([10, 20, 30, 40, 50, 60, 80, 90, 100]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]),val = 14), list_node([2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 26, 28, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 1, 3, 1, 4, 1, 5]),val = 1), list_node([2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),val = 1), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),val = 7), list_node([1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22]),val = 22), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6]),val = 3), list_node([1, 2, 4, 5, 6, 1, 2, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([3, 5, 2, 3, 7, 3, 8, 3, 3]),val = 3), list_node([5, 2, 7, 8]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),val = 2), list_node([1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 2, 4, 2, 5, 2, 6, 2]),val = 2), list_node([1, 3, 4, 5, 6]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]),val = 10), list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]))\n assert is_same_list(candidate(head = list_node([3, 2, 1, 4, 5, 6, 3, 7, 8, 9, 3]),val = 3), list_node([2, 1, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]),val = 5), list_node([3, 1, 4, 1, 9, 2, 6, 3]))\n assert is_same_list(candidate(head = list_node([3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1]),val = 3), list_node([2, 1, 2, 1, 2, 1, 2, 1]))\n assert is_same_list(candidate(head = list_node([15, 16, 15, 17, 15, 18, 15, 19, 15, 20]),val = 15), list_node([16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),val = 25), list_node([30, 29, 28, 27, 26, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([34, 33, 32, 31, 30, 29, 28, 27, 26, 25]),val = 27), list_node([34, 33, 32, 31, 30, 29, 28, 26, 25]))\n assert is_same_list(candidate(head = list_node([2, 2, 2, 1, 1, 1, 3, 3, 3]),val = 2), list_node([1, 1, 1, 3, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),val = 19), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20]))\n assert is_same_list(candidate(head = list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41]),val = 47), list_node([50, 49, 48, 46, 45, 44, 43, 42, 41]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 1]),val = 1), list_node([2, 2, 3, 3, 2, 2, 2, 2]))\n assert candidate(head = list_node([4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]),val = 4) == None\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),val = 1), list_node([3, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 1, 2, 1, 2, 1, 2, 1, 2]),val = 1), list_node([2, 2, 2, 2, 2]))\n assert candidate(head = list_node([42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]),val = 42) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]),val = 3), list_node([1, 2, 4, 2, 1, 2, 4, 2, 1]))\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),val = 1) == None\n assert is_same_list(candidate(head = list_node([1, 2, 3, 1, 2, 3, 1, 2, 3, 1]),val = 1), list_node([2, 3, 2, 3, 2, 3]))\n assert candidate(head = list_node([42, 42, 42, 42, 42, 42, 42, 42, 42, 42]),val = 42) == None\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]),val = 18), list_node([2, 4, 6, 8, 10, 12, 14, 16, 20]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]),val = 19), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]))\n assert is_same_list(candidate(head = list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31]),val = 31), list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 10, 40, 10, 50]),val = 10), list_node([20, 30, 40, 50]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]),val = 16), list_node([2, 4, 6, 8, 10, 12, 14, 18, 20]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),val = 1), list_node([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),val = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),val = 7), list_node([1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]),val = 21), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([3, 3, 3, 2, 2, 1, 1, 1, 2, 2, 2]),val = 2), list_node([3, 3, 3, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]),val = 2), list_node([1, 1, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]),val = 4), list_node([1, 2, 2, 3, 3, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]),val = 2), list_node([1, 1, 1, 3, 3, 3, 4, 4, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),val = 10), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2]),val = 1), list_node([2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]),val = 2), list_node([1, 1, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]),val = 13), list_node([1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]))\n assert is_same_list(candidate(head = list_node([42, 17, 22, 17, 35, 17, 5, 17]),val = 17), list_node([42, 22, 35, 5]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 50]),val = 50), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]),val = 13), list_node([1, 3, 5, 7, 9, 11, 15, 17, 19, 21]))\n assert candidate(head = list_node([25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25]),val = 25) == None\n assert is_same_list(candidate(head = list_node([1, 3, 2, 6, 5, 4, 6, 7, 8, 6, 9]),val = 6), list_node([1, 3, 2, 5, 4, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),val = 10), list_node([5, 6, 7, 8, 9, 11, 12, 13, 14, 15]))\n assert candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),val = 5) == None\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]),val = 1), list_node([2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),val = 20), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5]),val = 1), list_node([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 2, 3, 4, 5]))\n assert is_same_list(candidate(head = list_node([5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 5, 10]),val = 5), list_node([1, 2, 3, 4, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),val = 3), list_node([1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50]),val = 26), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50]))\n assert is_same_list(candidate(head = list_node([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]),val = 3), list_node([1, 4, 1, 5, 9, 2, 6, 5, 5]))\n assert is_same_list(candidate(head = list_node([2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]),val = 3), list_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3]),val = 3), list_node([1, 2, 4, 5, 6, 7, 8, 9]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 3, 2, 1, 3, 2, 1]),val = 3), list_node([1, 2, 4, 2, 1, 2, 1]))\n assert is_same_list(candidate(head = list_node([10, 20, 10, 30, 10, 40]),val = 10), list_node([20, 30, 40]))\n assert is_same_list(candidate(head = list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40]),val = 45), list_node([50, 49, 48, 47, 46, 44, 43, 42, 41, 40]))\n assert candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),val = 5) == None\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20]),val = 20), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18]))\n assert is_same_list(candidate(head = list_node([50, 49, 48, 47, 46, 45, 44, 43, 42, 41]),val = 45), list_node([50, 49, 48, 47, 46, 44, 43, 42, 41]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]),val = 50), list_node([10, 20, 30, 40, 60, 70, 80, 90, 100]))\n assert is_same_list(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]),val = 50), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]),val = 3), list_node([1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 40, 30, 20, 10]),val = 30), list_node([10, 20, 40, 50, 40, 20, 10]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),val = 3), list_node([10, 9, 8, 7, 6, 5, 4, 2, 1]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]),val = 10), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),val = 2), list_node([3]))\n assert is_same_list(candidate(head = list_node([49, 48, 47, 46, 45, 44, 43, 42, 41, 40]),val = 45), list_node([49, 48, 47, 46, 44, 43, 42, 41, 40]))\n assert candidate(head = list_node([1]),val = 1) == None\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4]),val = 10), list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),val = 15), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]))\n assert is_same_list(candidate(head = list_node([42, 23, 42, 23, 42, 23, 42, 23, 42]),val = 42), list_node([23, 23, 23, 23]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]),val = 30), list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40]))\n"}, "metadata": {"canonical_parameter_names": ["head", "val"], "leetcode_dataset_entry_point": "Solution().removeElements", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeElements = function(head, val) {", "container": null, "callable": "removeElements", "parameters": [{"name": "head", "type": "ListNode"}, {"name": "val", "type": "number"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 204, "task_id": "count-primes", "difficulty": "Medium", "problem_description": "Given an integer n, return the number of prime numbers that are strictly less than n.\n \nExample 1:\n\nInput: n = 10\nOutput: 4\nExplanation: There are 4 prime numbers less than 10, they are 2, 3, 5, 7.\n\nExample 2:\n\nInput: n = 0\nOutput: 0\n\nExample 3:\n\nInput: n = 1\nOutput: 0\n\n \nConstraints:\n\n0 <= n <= 5 * 106\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 5000000) == 348513\n assert candidate(n = 1000) == 168\n assert candidate(n = 100) == 25\n assert candidate(n = 30) == 10\n assert candidate(n = 1500000) == 114155\n assert candidate(n = 1000000) == 78498\n assert candidate(n = 20) == 8\n assert candidate(n = 2) == 0\n assert candidate(n = 1) == 0\n assert candidate(n = 50) == 15\n assert candidate(n = 10) == 4\n assert candidate(n = 5) == 2\n assert candidate(n = 3) == 1\n assert candidate(n = 4999999) == 348512\n assert candidate(n = 10000) == 1229\n assert candidate(n = 17) == 6\n assert candidate(n = 7890123) == 532888\n assert candidate(n = 2000000) == 148933\n assert candidate(n = 4000000) == 283146\n assert candidate(n = 3141592) == 226277\n assert candidate(n = 499979) == 41537\n assert candidate(n = 10000000) == 664579\n assert candidate(n = 5000001) == 348513\n assert candidate(n = 18) == 7\n assert candidate(n = 5000) == 669\n assert candidate(n = 999983) == 78497\n assert candidate(n = 3000000) == 216816\n assert candidate(n = 789654) == 63183\n assert candidate(n = 31337) == 3378\n assert candidate(n = 104729) == 9999\n assert candidate(n = 500000) == 41538\n assert candidate(n = 1234567) == 95360\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countPrimes", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countPrimes = function(n) {", "container": null, "callable": "countPrimes", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 205, "task_id": "isomorphic-strings", "difficulty": "Easy", "problem_description": "Given two strings s and t, determine if they are isomorphic.\nTwo strings s and t are isomorphic if the characters in s can be replaced to get t.\nAll occurrences of a character must be replaced with another character while preserving the order of characters. No two characters may map to the same character, but a character may map to itself.\n \nExample 1:\n\nInput: s = \"egg\", t = \"add\"\nOutput: true\nExplanation:\nThe strings s and t can be made identical by:\n\nMapping 'e' to 'a'.\nMapping 'g' to 'd'.\n\n\nExample 2:\n\nInput: s = \"foo\", t = \"bar\"\nOutput: false\nExplanation:\nThe strings s and t can not be made identical as 'o' needs to be mapped to both 'a' and 'r'.\n\nExample 3:\n\nInput: s = \"paper\", t = \"title\"\nOutput: true\n\n \nConstraints:\n\n1 <= s.length <= 5 * 104\nt.length == s.length\ns and t consist of any valid ascii character.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"hello\",t = \"world\") == False\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(s = \"paper\",t = \"title\") == True\n assert candidate(s = \"#a@C\",t = \"%b$D\") == True\n assert candidate(s = \"1234567890\",t = \"0987654321\") == True\n assert candidate(s = \"aaaa\",t = \"bbbb\") == True\n assert candidate(s = \"123\",t = \"456\") == True\n assert candidate(s = \"13\",t = \"42\") == True\n assert candidate(s = \"egg\",t = \"add\") == True\n assert candidate(s = \"test\",t = \"tets\") == False\n assert candidate(s = \"foo\",t = \"bar\") == False\n assert candidate(s = \"badc\",t = \"baba\") == False\n assert candidate(s = \"abba\",t = \"abba\") == True\n assert candidate(s = \"a\",t = \"a\") == True\n assert candidate(s = \"abcd\",t = \"dcba\") == True\n assert candidate(s = \"ab\",t = \"aa\") == False\n assert candidate(s = \"abcdefghijabcdefghij\",t = \"zyxwvutsrqzyxwvutsrq\") == True\n assert candidate(s = \"testcase\",t = \"tattldce\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzz\") == False\n assert candidate(s = \"thisisatest\",t = \"qdpdqpdafqd\") == False\n assert candidate(s = \"123456\",t = \"654321\") == True\n assert candidate(s = \"hello world\",t = \"uifsf ftuqi\") == False\n assert candidate(s = \"aba\",t = \"cdc\") == True\n assert candidate(s = \"xyzzzzzzzzzyxzzzzzzzxy\",t = \"yxqqqqqqqqqyxqqqqqqqyx\") == False\n assert candidate(s = \"aabbccddeeff\",t = \"zzyyxxwwvvuuzz\") == True\n assert candidate(s = \"aabb\",t = \"cccc\") == False\n assert candidate(s = \"abracadabra\",t = \"xyxzyzyxzyx\") == False\n assert candidate(s = \"aaaaa\",t = \"bbbbb\") == True\n assert candidate(s = \"abcdeabcde\",t = \"fghijfghij\") == True\n assert candidate(s = \"abcdefg\",t = \"gfedcba\") == True\n assert candidate(s = \"a\",t = \"z\") == True\n assert candidate(s = \"abacaba\",t = \"xyzxzyx\") == False\n assert candidate(s = \"abccbaabc\",t = \"xyzyxzyxzyx\") == False\n assert candidate(s = \"abcdabcdabcd\",t = \"wxyzwxyzwxyz\") == True\n assert candidate(s = \"mississippi\",t = \"bbccddeffgg\") == False\n assert candidate(s = \"aabbccddeeff\",t = \"zzzzyyxxwwvvuuzz\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggeeffddeebbaa\") == False\n assert candidate(s = \"abcde\",t = \"edcba\") == True\n assert candidate(s = \"ababab\",t = \"xyzxyz\") == False\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == False\n assert candidate(s = \"ababababab\",t = \"cdcdcdcdcd\") == True\n assert candidate(s = \"randomstring\",t = \"stringrandom\") == False\n assert candidate(s = \"mississippi\",t = \"hhlllppppss\") == False\n assert candidate(s = \"aabbccddeeffgg\",t = \"zzxxccvvnngghh\") == True\n assert candidate(s = \"repeatedcharacters\",t = \"substitutedletters\") == False\n assert candidate(s = \"aabbcc\",t = \"ddeeff\") == True\n assert candidate(s = \"abcdefghijkabcdefghijkabcdefghijkabcdefghijk\",t = \"abcdefghijkabcdefghijkabcdefghijkabcdefghijk\") == True\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"bcdefghijklmnopqrstuvwxyza\") == True\n assert candidate(s = \"longlongstringwithvariouscharacters\",t = \"shortshort\") == False\n assert candidate(s = \"sos\",t = \"non\") == True\n assert candidate(s = \"rat\",t = \"car\") == True\n assert candidate(s = \"elephant\",t = \"mouse\") == False\n assert candidate(s = \"abc\",t = \"zyx\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzxxwwvvuuttssrrqqppoonnmmllkkjjiihhggeeffddccbbaa\") == True\n assert candidate(s = \"isomorphic\",t = \"esomoprphc\") == False\n assert candidate(s = \"aaabbbccc\",t = \"xxxyyyzzz\") == True\n assert candidate(s = \"abcdefghij\",t = \"jihgfedcba\") == True\n assert candidate(s = \"aaaaaa\",t = \"bbbbbb\") == True\n assert candidate(s = \"mississippi\",t = \"bbcccb\") == False\n assert candidate(s = \"xyxxyxyxyx\",t = \"xyxyyxyxyx\") == False\n assert candidate(s = \"aaaabbbbccccdddd\",t = \"ddddccccbbbbaaaa\") == True\n assert candidate(s = \"sameexample\",t = \"gnatgnatgnat\") == False\n assert candidate(s = \"twosky\",t = \"threesky\") == False\n assert candidate(s = \"abcabcabc\",t = \"xyzxyzxyz\") == True\n assert candidate(s = \"hellohello\",t = \"worldworld\") == False\n assert candidate(s = \"12345\",t = \"54321\") == True\n assert candidate(s = \"aabbccddeeffgghhii\",t = \"zzxxyywwvvuuttrrqqpp\") == True\n assert candidate(s = \"123123123\",t = \"abcabcabc\") == True\n assert candidate(s = \"racecar\",t = \"level\") == False\n assert candidate(s = \"racecar\",t = \"madam\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == True\n assert candidate(s = \"abacabadabacaba\",t = \"xyxyxyxyxyxyxyxy\") == False\n assert candidate(s = \"abcdeffedcba\",t = \"gfedcbaabcdefg\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggeeffdccbbbaa\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzzzyyyxxwwvvuuttrrsqqppoonnmmllkkjjiihhggffeeddccbbaa\") == False\n assert candidate(s = \"1234567890\",t = \"!@#$%^&*()\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzxxwvuttssrrqqponmlkjihgfedcbbaa\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhhgggffeeeeddccbbbaa\") == False\n assert candidate(s = \"xyzzxyzz\",t = \"abccabcc\") == True\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyz\") == True\n assert candidate(s = \"thisisatest\",t = \"abccbaabcab\") == False\n assert candidate(s = \"abcdabcdabcdabcd\",t = \"dcbaabcdabcdabcd\") == False\n assert candidate(s = \"anagram\",t = \"nagaram\") == False\n assert candidate(s = \"aaaaabbbbbccccc\",t = \"bbbbbcccccaaaaa\") == True\n assert candidate(s = \"abcdabcd\",t = \"wxyzwxyz\") == True\n assert candidate(s = \"twowords\",t = \"twooorld\") == False\n assert candidate(s = \"abbabbbbabaabababbaaabbbabbbaaa\",t = \"xyzxxzzxzyzyzyzyzyzyzyzyzyzyzyzyzyz\") == False\n assert candidate(s = \"aaabbbcccdddeeefffggghhhh\",t = \"mmmnnnoooqqrssstttuuuvvvvv\") == False\n assert candidate(s = \"mississippi\",t = \"bbjjjjbbbrrr\") == False\n assert candidate(s = \"abab\",t = \"baba\") == True\n assert candidate(s = \"thisisatest\",t = \"thisisatest\") == True\n assert candidate(s = \"unique\",t = \"unique\") == True\n assert candidate(s = \"abcabcabcabc\",t = \"defgdefgdefgdefg\") == False\n assert candidate(s = \"isomorphic\",t = \"homomorphi\") == False\n assert candidate(s = \"aaaaabbbbbaaaa\",t = \"cccceeeedddd\") == False\n assert candidate(s = \"xxxxx\",t = \"yyyyy\") == True\n assert candidate(s = \"abcabcabcabc\",t = \"xyzxyzxyzxyz\") == True\n assert candidate(s = \"abcabcabc\",t = \"xyzxyzyxzy\") == False\n assert candidate(s = \"isomorphic\",t = \"homomorphic\") == False\n assert candidate(s = \"sabcsabc\",t = \"tabctabc\") == True\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\",t = \"mlkjihgfdsapoiuytrewqzxcvbnm\") == False\n assert candidate(s = \"thisisatest\",t = \"thatistest\") == False\n assert candidate(s = \"!@#$%^&*()\",t = \"()&*^%$#@!\") == True\n assert candidate(s = \"racecar\",t = \"kayyak\") == False\n assert candidate(s = \"!@#$%^&*()\",t = \")(*&^%$#@!\") == True\n assert candidate(s = \"sphinxofblackquartzjumps\",t = \"zpmxkbvhnckgyusldqpj\") == False\n assert candidate(s = \"1122334455\",t = \"1122334455\") == True\n assert candidate(s = \"ab\",t = \"zy\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == True\n assert candidate(s = \"aaaaaa\",t = \"zzzzzz\") == True\n assert candidate(s = \"noon\",t = \"moon\") == False\n assert candidate(s = \"aaaaabbbbccccddddd\",t = \"bbbbbccccdddddfffff\") == False\n assert candidate(s = \"special$chars!@#\",t = \"normal%^&*()\") == False\n assert candidate(s = \"abcabcabcabc\",t = \"defdefdefdef\") == True\n assert candidate(s = \"mississippi\",t = \"bbnnnnoooppp\") == False\n assert candidate(s = \"teest\",t = \"beest\") == False\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(s = \"!@#$%^\",t = \"^%$#@!\") == True\n assert candidate(s = \"unique\",t = \"mapped\") == False\n assert candidate(s = \"mississippi\",t = \"eeffgghhiiii\") == False\n assert candidate(s = \"xyxxyxyxyx\",t = \"zvzvzvzvzv\") == False\n assert candidate(s = \"abacabadabacaba\",t = \"xyxzyxzyzxzyxzy\") == False\n assert candidate(s = \"aabbccddeeffgghhiijj\",t = \"zzxxccvvnnooppmmqqllkk\") == True\n assert candidate(s = \"abababab\",t = \"cdcdcdcd\") == True\n assert candidate(s = \"xyxzyzyx\",t = \"qpqpqpqp\") == False\n assert candidate(s = \"abcdefghijabcdefghij\",t = \"klmnopqrstklmnopqrst\") == True\n assert candidate(s = \"aabbccddeeff\",t = \"zzxxyywwvvuutt\") == True\n assert candidate(s = \"elephant\",t = \"zuluqaak\") == False\n assert candidate(s = \"mississippi\",t = \"lllssssiiip\") == False\n assert candidate(s = \"thisproblemisfun\",t = \"thatquestionistame\") == False\n assert candidate(s = \"abcdefghij\",t = \"abcdefghij\") == True\n"}, "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().isIsomorphic", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isIsomorphic = function(s, t) {", "container": null, "callable": "isIsomorphic", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 206, "task_id": "reverse-linked-list", "difficulty": "Easy", "problem_description": "Given the head of a singly linked list, reverse the list, and return the reversed list.\n \nExample 1:\n\n\nInput: head = [1,2,3,4,5]\nOutput: [5,4,3,2,1]\n\nExample 2:\n\n\nInput: head = [1,2]\nOutput: [2,1]\n\nExample 3:\n\nInput: head = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the list is the range [0, 5000].\n-5000 <= Node.val <= 5000\n\n \nFollow up: A linked list can be reversed either iteratively or recursively. Could you implement both?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([5000, -5000, 0, 1000, -1000])), list_node([-1000, 1000, 0, -5000, 5000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([5, 4, 3, 2, 1]))\n assert candidate(head = list_node([])) == None\n assert is_same_list(candidate(head = list_node([1, 2])), list_node([2, 1]))\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5])), list_node([-5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([3])), list_node([3]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([-1000, 0, 1000])), list_node([1000, 0, -1000]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 5000, -5000])), list_node([-5000, 5000, -5000, 5000]))\n assert is_same_list(candidate(head = list_node([100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5])), list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21])), list_node([21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([-5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000])), list_node([5000, 4000, 3000, 2000, 1000, 0, -1000, -2000, -3000, -4000, -5000]))\n assert is_same_list(candidate(head = list_node([-5000, -2500, 0, 2500, 5000])), list_node([5000, 2500, 0, -2500, -5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25])), list_node([25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20])), list_node([-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([-5000])), list_node([-5000]))\n assert is_same_list(candidate(head = list_node([5000, 2500, 0, -2500, -5000, 5000, 2500, 0, -2500, -5000])), list_node([-5000, -2500, 0, 2500, 5000, -5000, -2500, 0, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10])), list_node([10, 10, 10, 9, 9, 9, 8, 8, 8, 7, 7, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39])), list_node([39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000])), list_node([1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([-5000, 5000, -5000, 5000, -5000, 5000])), list_node([5000, -5000, 5000, -5000, 5000, -5000]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, -2, 3, -4, 5, -6, 7, -8, 9, -10])), list_node([-10, 9, -8, 7, -6, 5, -4, 3, -2, 1]))\n assert is_same_list(candidate(head = list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([-1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10])), list_node([10, -10, 9, -9, 8, -8, 7, -7, 6, -6, 5, -5, 4, -4, 3, -3, 2, -2, 1, -1]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991])), list_node([4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5])), list_node([-5, 5, -4, 4, -3, 3, -2, 2, -1, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000])), list_node([-5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21])), list_node([21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([5000])), list_node([5000]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49])), list_node([49, 47, 45, 43, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([1000, 900, 800, 700, 600, 500, 400, 300, 200, 100])), list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]))\n assert is_same_list(candidate(head = list_node([21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]))\n assert is_same_list(candidate(head = list_node([5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100])), list_node([100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5]))\n assert is_same_list(candidate(head = list_node([1000, 2000, 3000, 4000, 5000, 4000, 3000, 2000, 1000])), list_node([1000, 2000, 3000, 4000, 5000, 4000, 3000, 2000, 1000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])), list_node([25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([-10, 9, -8, 7, -6, 5, -4, 3, -2, 1])), list_node([1, -2, 3, -4, 5, -6, 7, -8, 9, -10]))\n assert is_same_list(candidate(head = list_node([2, 2, 2, 1, 1, 1, 3, 3, 3, 4, 4, 4])), list_node([4, 4, 4, 3, 3, 3, 1, 1, 1, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([-1])), list_node([-1]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40])), list_node([40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]))\n assert is_same_list(candidate(head = list_node([25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15])), list_node([15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981, 4980, 4979, 4978, 4977, 4976, 4975, 4974, 4973, 4972, 4971, 4970])), list_node([4970, 4971, 4972, 4973, 4974, 4975, 4976, 4977, 4978, 4979, 4980, 4981, 4982, 4983, 4984, 4985, 4986, 4987, 4988, 4989, 4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5000]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150])), list_node([150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]))\n assert is_same_list(candidate(head = list_node([1000, 2000, 3000, 4000, 5000, -1000, -2000, -3000, -4000, -5000])), list_node([-5000, -4000, -3000, -2000, -1000, 5000, 4000, 3000, 2000, 1000]))\n assert is_same_list(candidate(head = list_node([1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0])), list_node([0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500])), list_node([1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([-5000, 5000, -4000, 4000, -3000, 3000, -2000, 2000, -1000, 1000])), list_node([1000, -1000, 2000, -2000, 3000, -3000, 4000, -4000, 5000, -5000]))\n assert is_same_list(candidate(head = list_node([0, 10, 0, 20, 0, 30, 0, 40, 0, 50, 0, 60, 0, 70, 0, 80, 0, 90, 0, 100, 0])), list_node([0, 100, 0, 90, 0, 80, 0, 70, 0, 60, 0, 50, 0, 40, 0, 30, 0, 20, 0, 10, 0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39])), list_node([39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5])), list_node([5, 5, 4, 4, 3, 3, 2, 2, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 10])), list_node([10, 8, 6, 4, 2, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([-5000, 5000, -4999, 4999, -4998, 4998, -4997, 4997, -4996, 4996])), list_node([4996, -4996, 4997, -4997, 4998, -4998, 4999, -4999, 5000, -5000]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 6, 5, 7, 9, 8, 10])), list_node([10, 8, 9, 7, 5, 6, 4, 2, 3, 1]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10])), list_node([-10, 10, -9, 9, -8, 8, -7, 7, -6, 6, -5, 5, -4, 4, -3, 3, -2, 2, -1, 1]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 2, 2, 1, 1])), list_node([1, 1, 2, 2, 3, 3, 2, 2, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([5000, 4000, 3000, 2000, 1000, 0, -1000, -2000, -3000, -4000, -5000])), list_node([-5000, -4000, -3000, -2000, -1000, 0, 1000, 2000, 3000, 4000, 5000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 2, 1])), list_node([1, 2, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000])), list_node([1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]))\n assert is_same_list(candidate(head = list_node([5, -5, 10, -10, 15, -15, 20, -20, 25, -25, 30, -30, 35, -35, 40, -40])), list_node([-40, 40, -35, 35, -30, 30, -25, 25, -20, 20, -15, 15, -10, 10, -5, 5]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000])), list_node([2000, 1900, 1800, 1700, 1600, 1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]))\n assert is_same_list(candidate(head = list_node([1000, -1000, 2000, -2000, 3000, -3000, 4000, -4000, 5000, -5000])), list_node([-5000, 5000, -4000, 4000, -3000, 3000, -2000, 2000, -1000, 1000]))\n assert is_same_list(candidate(head = list_node([5000, 2500, 0, -2500, -5000])), list_node([-5000, -2500, 0, 2500, 5000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([1000, 900, 800, 700, 600, 500, 400, 300, 200, 100])), list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5])), list_node([5, 5, 4, 4, 3, 3, 2, 2, 1, 1]))\n assert is_same_list(candidate(head = list_node([20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_list(candidate(head = list_node([500, 400, 300, 200, 100, 50, 25, 12, 6, 3, 1, 0, -1, -3, -6, -12, -25, -50, -100, -200, -300, -400, -500])), list_node([-500, -400, -300, -200, -100, -50, -25, -12, -6, -3, -1, 0, 1, 3, 6, 12, 25, 50, 100, 200, 300, 400, 500]))\n assert is_same_list(candidate(head = list_node([-1, -1, -1, -1, -1, -1, -1, -1, -1, -1])), list_node([-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]))\n assert is_same_list(candidate(head = list_node([49, 47, 45, 43, 41, 39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]))\n assert is_same_list(candidate(head = list_node([-5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000])), list_node([5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000, 5000, -5000]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]))\n assert is_same_list(candidate(head = list_node([1, -1, 2, -2, 3, -3, 4, -4, 5, -5])), list_node([-5, 5, -4, 4, -3, 3, -2, 2, -1, 1]))\n assert is_same_list(candidate(head = list_node([21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 4, 3, 2, 1])), list_node([1, 2, 3, 4, 5, 4, 3, 2, 1]))\n assert is_same_list(candidate(head = list_node([5000, -5000, 4000, -4000, 3000, -3000, 2000, -2000, 1000, -1000, 0])), list_node([0, -1000, 1000, -2000, 2000, -3000, 3000, -4000, 4000, -5000, 5000]))\n assert is_same_list(candidate(head = list_node([5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5])), list_node([-5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().reverseList", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverseList = function(head) {", "container": null, "callable": "reverseList", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 207, "task_id": "course-schedule", "difficulty": "Medium", "problem_description": "There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.\n\nFor example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.\n\nReturn true if you can finish all courses. Otherwise, return false.\n \nExample 1:\n\nInput: numCourses = 2, prerequisites = [[1,0]]\nOutput: true\nExplanation: There are a total of 2 courses to take. \nTo take course 1 you should have finished course 0. So it is possible.\n\nExample 2:\n\nInput: numCourses = 2, prerequisites = [[1,0],[0,1]]\nOutput: false\nExplanation: There are a total of 2 courses to take. \nTo take course 1 you should have finished course 0, and to take course 0 you should also have finished course 1. So it is impossible.\n\n \nConstraints:\n\n1 <= numCourses <= 2000\n0 <= prerequisites.length <= 5000\nprerequisites[i].length == 2\n0 <= ai, bi < numCourses\nAll the pairs prerequisites[i] are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(numCourses = 2,prerequisites = [[1, 0], [0, 1]]) == False\n assert candidate(numCourses = 5,prerequisites = [[1, 4], [2, 4], [3, 1], [3, 2]]) == True\n assert candidate(numCourses = 4,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2]]) == True\n assert candidate(numCourses = 3,prerequisites = [[1, 0], [2, 1]]) == True\n assert candidate(numCourses = 1,prerequisites = []) == True\n assert candidate(numCourses = 2,prerequisites = [[1, 0]]) == True\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [7, 4], [8, 5], [8, 6], [9, 7], [10, 7], [11, 8], [12, 8], [13, 9], [14, 10], [14, 11], [14, 12], [15, 13], [16, 13], [17, 14], [18, 15], [18, 16], [19, 17], [19, 18]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 4], [6, 4], [7, 5], [8, 5], [9, 6], [9, 7]]) == True\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 3], [5, 4], [6, 5], [7, 6], [8, 7], [8, 5]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 1], [5, 2], [6, 3]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 3], [5, 3], [6, 4], [6, 5]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [5, 2], [6, 3], [7, 3], [8, 4], [8, 5], [9, 6], [9, 7]]) == True\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [4, 8]]) == False\n assert candidate(numCourses = 6,prerequisites = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 0]]) == False\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [7, 4], [8, 5]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 2], [5, 4], [6, 4], [7, 5], [7, 6]]) == True\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [11, 5], [7, 9], [8, 10]]) == True\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10], [12, 11], [13, 12], [14, 13], [15, 14], [16, 15], [17, 16], [18, 17], [19, 18], [0, 19]]) == False\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [5, 4], [6, 5]]) == True\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [0, 8]]) == False\n assert candidate(numCourses = 13,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 1], [7, 1], [8, 2], [9, 2], [10, 3], [11, 3], [12, 4], [12, 5], [12, 6], [12, 7]]) == True\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 3], [6, 4], [7, 4], [8, 5], [9, 5], [10, 6], [11, 6], [12, 7], [12, 8], [13, 9], [13, 10], [14, 11], [14, 12]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [4, 6], [5, 7]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [0, 9]]) == False\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [5, 3]]) == True\n assert candidate(numCourses = 10,prerequisites = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 7], [5, 8], [6, 8], [7, 9], [8, 9]]) == True\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10], [12, 11], [13, 12], [14, 13]]) == True\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 4]]) == True\n assert candidate(numCourses = 10,prerequisites = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 0]]) == False\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4]]) == True\n assert candidate(numCourses = 11,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [7, 4], [8, 5], [9, 6], [10, 7], [10, 8]]) == True\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [5, 4]]) == True\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [0, 5]]) == False\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [5, 6]]) == True\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [7, 4], [8, 5], [8, 6], [9, 7], [10, 7], [11, 8], [12, 8], [13, 9], [14, 10], [14, 11], [14, 12]]) == True\n assert candidate(numCourses = 5,prerequisites = [[1, 0], [2, 1], [3, 4], [4, 3]]) == False\n assert candidate(numCourses = 20,prerequisites = [[0, 1], [0, 2], [0, 3], [0, 4], [1, 5], [1, 6], [2, 7], [2, 8], [3, 9], [3, 10], [4, 11], [4, 12], [5, 13], [5, 14], [6, 15], [6, 16], [7, 17], [8, 18], [9, 19], [10, 19], [11, 19], [12, 19], [13, 19], [14, 19], [15, 19], [16, 19], [17, 19], [18, 19]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [5, 0]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [6, 5]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [4, 3], [5, 2], [5, 3], [6, 4], [6, 5], [7, 6]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [4, 6], [5, 6]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [7, 5], [8, 6], [9, 7], [8, 9]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [0, 6]]) == False\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 6], [13, 7], [14, 8], [14, 9]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [5, 6]]) == True\n assert candidate(numCourses = 7,prerequisites = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 4], [3, 5], [4, 5], [5, 6]]) == True\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [7, 4], [8, 5], [8, 6]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 0], [4, 1], [5, 2], [6, 3], [7, 3]]) == True\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [5, 2], [6, 3], [7, 3], [8, 4], [8, 5], [9, 6], [9, 7], [10, 8], [11, 8]]) == True\n assert candidate(numCourses = 10,prerequisites = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 0], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9]]) == False\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [0, 7]]) == False\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [6, 7]]) == False\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [7, 4], [8, 5], [9, 6], [9, 7]]) == True\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 1], [3, 0], [4, 3], [5, 3]]) == True\n assert candidate(numCourses = 10,prerequisites = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [0, 9], [9, 1]]) == False\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [1, 9]]) == False\n assert candidate(numCourses = 15,prerequisites = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 4], [3, 5], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [9, 5]]) == True\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [7, 5], [7, 6]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 3], [5, 4], [6, 5]]) == True\n assert candidate(numCourses = 10,prerequisites = [[0, 1], [1, 2], [2, 0], [3, 4], [4, 5], [5, 3], [6, 7], [7, 8], [8, 9], [9, 6]]) == False\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 6], [1, 7], [6, 4], [7, 0], [0, 5]]) == True\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [11, 5], [12, 5], [13, 6], [14, 7], [14, 8], [14, 9]]) == True\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 1], [5, 2], [6, 3], [7, 3], [8, 4], [9, 5]]) == True\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 2], [5, 4], [5, 3]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 3], [5, 4], [6, 5]]) == True\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [6, 3]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 0], [7, 6]]) == True\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 3], [6, 4], [7, 4], [8, 5], [9, 5], [10, 6], [11, 6], [12, 7], [12, 8], [13, 9], [13, 10], [14, 11], [14, 12], [15, 13], [16, 13], [17, 14], [18, 14], [19, 15], [19, 16]]) == True\n assert candidate(numCourses = 11,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [7, 4], [8, 5], [8, 6], [9, 7], [10, 7]]) == True\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [10, 5], [11, 6], [11, 7]]) == True\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [0, 8], [8, 0]]) == False\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [7, 5], [8, 6], [9, 7], [0, 8]]) == False\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [11, 5], [12, 5], [13, 6], [14, 7], [15, 7], [16, 8], [17, 8], [18, 9], [19, 9], [15, 12], [16, 13], [17, 14], [18, 15], [19, 16]]) == True\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [7, 4], [7, 5]]) == True\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 1], [3, 0], [4, 1], [5, 2], [6, 3], [7, 4], [8, 5], [9, 6], [10, 7], [11, 8], [12, 9], [13, 10], [14, 11], [14, 12]]) == True\n assert candidate(numCourses = 7,prerequisites = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 0]]) == False\n"}, "metadata": {"canonical_parameter_names": ["numCourses", "prerequisites"], "leetcode_dataset_entry_point": "Solution().canFinish", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canFinish = function(numCourses, prerequisites) {", "container": null, "callable": "canFinish", "parameters": [{"name": "numCourses", "type": "number"}, {"name": "prerequisites", "type": "number[][]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 209, "task_id": "minimum-size-subarray-sum", "difficulty": "Medium", "problem_description": "Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.\n \nExample 1:\n\nInput: target = 7, nums = [2,3,1,2,4,3]\nOutput: 2\nExplanation: The subarray [4,3] has the minimal length under the problem constraint.\n\nExample 2:\n\nInput: target = 4, nums = [1,4,4]\nOutput: 1\n\nExample 3:\n\nInput: target = 11, nums = [1,1,1,1,1,1,1,1]\nOutput: 0\n\n \nConstraints:\n\n1 <= target <= 109\n1 <= nums.length <= 105\n1 <= nums[i] <= 104\n\n \nFollow up: If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log(n)).", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(target = 8,nums = [1, 2, 3, 4, 5]) == 2\n assert candidate(target = 9,nums = [4, 3, 3, 2, 1]) == 3\n assert candidate(target = 11,nums = [1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(target = 100,nums = [10, 20, 30, 40, 50]) == 3\n assert candidate(target = 8,nums = [2, 2, 2, 2, 2, 2, 2, 2]) == 4\n assert candidate(target = 8,nums = [3, 4, 3, 1, 1, 1, 1, 1]) == 3\n assert candidate(target = 7,nums = [2, 3, 1, 2, 4, 3]) == 2\n assert candidate(target = 4,nums = [1, 4, 4]) == 1\n assert candidate(target = 3,nums = [1, 1, 1]) == 3\n assert candidate(target = 15,nums = [5, 5, 5, 5, 5]) == 3\n assert candidate(target = 5,nums = [2, 3, 1, 1, 1, 1, 1]) == 2\n assert candidate(target = 15,nums = [5, 1, 3, 5, 10, 7, 4, 9, 2, 8]) == 2\n assert candidate(target = 10,nums = [5, 1, 3, 5, 10, 7, 4, 9, 2, 8]) == 1\n assert candidate(target = 8,nums = [2, 3, 4, 2, 3, 4, 2, 3, 4]) == 3\n assert candidate(target = 3,nums = [1, 1, 1, 1, 1, 1, 1, 1]) == 3\n assert candidate(target = 3,nums = [1, 1, 1, 1, 1]) == 3\n assert candidate(target = 15,nums = [1, 2, 3, 4, 5]) == 5\n assert candidate(target = 6,nums = [1, 2, 3, 4, 5]) == 2\n assert candidate(target = 50,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 50\n assert candidate(target = 1,nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991]) == 1\n assert candidate(target = 15,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 1\n assert candidate(target = 3,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 3\n assert candidate(target = 100,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 6\n assert candidate(target = 1000,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 0\n assert candidate(target = 20,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 3\n assert candidate(target = 5,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 5\n assert candidate(target = 55,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 3\n assert candidate(target = 250,nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 50\n assert candidate(target = 20,nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 10\n assert candidate(target = 100,nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(target = 25,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 25\n assert candidate(target = 50,nums = [10, 2, 3, 8, 5, 10, 2, 1, 3, 5, 7, 8]) == 10\n assert candidate(target = 500,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 0\n assert candidate(target = 25,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 2\n assert candidate(target = 18,nums = [1, 2, 3, 4, 5, 6, 7]) == 3\n assert candidate(target = 99,nums = [50, 25, 20, 5, 10, 10, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 4\n assert candidate(target = 25,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5]) == 5\n assert candidate(target = 150,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 4\n assert candidate(target = 1000,nums = [100, 200, 300, 400, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 100, 200, 300, 400, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50]) == 4\n assert candidate(target = 15,nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == 5\n assert candidate(target = 200,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 8\n assert candidate(target = 100,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 4\n assert candidate(target = 25,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 4\n assert candidate(target = 30,nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 10\n assert candidate(target = 5,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(target = 10,nums = [100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(target = 120,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51]) == 3\n assert candidate(target = 42,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42]) == 1\n assert candidate(target = 23,nums = [2, 3, 1, 2, 4, 3, 5, 6, 7, 8, 9, 10]) == 3\n assert candidate(target = 100,nums = [10, 20, 30, 40, 50, 60, 70, 80, 90]) == 2\n assert candidate(target = 100,nums = [50, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]) == 4\n assert candidate(target = 12,nums = [2, 3, 1, 2, 4, 3, 5]) == 3\n assert candidate(target = 200,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(target = 5,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(target = 100,nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(target = 100000,nums = [10000, 20000, 30000, 40000, 1000, 2000, 3000, 4000, 5000, 1000, 2000, 3000, 4000, 5000, 1000, 2000, 3000, 4000, 5000, 1000, 2000, 3000, 4000, 5000, 1000, 2000, 3000, 4000, 5000]) == 4\n assert candidate(target = 7,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 7\n assert candidate(target = 50,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 4\n assert candidate(target = 120,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 5\n assert candidate(target = 25,nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25]) == 1\n assert candidate(target = 500,nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(target = 5,nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 3\n assert candidate(target = 50,nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 50\n assert candidate(target = 7,nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 5\n assert candidate(target = 500,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 12\n assert candidate(target = 100,nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 1\n assert candidate(target = 45,nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 6\n assert candidate(target = 20,nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 4\n assert candidate(target = 20,nums = [5, 1, 3, 5, 2, 1, 4]) == 7\n assert candidate(target = 1000,nums = [250, 250, 250, 250]) == 4\n assert candidate(target = 40,nums = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 3\n assert candidate(target = 30,nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 6\n assert candidate(target = 120,nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50]) == 3\n"}, "metadata": {"canonical_parameter_names": ["target", "nums"], "leetcode_dataset_entry_point": "Solution().minSubArrayLen", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minSubArrayLen = function(target, nums) {", "container": null, "callable": "minSubArrayLen", "parameters": [{"name": "target", "type": "number"}, {"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 210, "task_id": "course-schedule-ii", "difficulty": "Medium", "problem_description": "There are a total of numCourses courses you have to take, labeled from 0 to numCourses - 1. You are given an array prerequisites where prerequisites[i] = [ai, bi] indicates that you must take course bi first if you want to take course ai.\n\nFor example, the pair [0, 1], indicates that to take course 0 you have to first take course 1.\n\nReturn the ordering of courses you should take to finish all courses. If there are many valid answers, return any of them. If it is impossible to finish all courses, return an empty array.\n \nExample 1:\n\nInput: numCourses = 2, prerequisites = [[1,0]]\nOutput: [0,1]\nExplanation: There are a total of 2 courses to take. To take course 1 you should have finished course 0. So the correct course order is [0,1].\n\nExample 2:\n\nInput: numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]\nOutput: [0,2,1,3]\nExplanation: There are a total of 4 courses to take. To take course 3 you should have finished both courses 1 and 2. Both courses 1 and 2 should be taken after you finished course 0.\nSo one correct course order is [0,1,2,3]. Another correct ordering is [0,2,1,3].\n\nExample 3:\n\nInput: numCourses = 1, prerequisites = []\nOutput: [0]\n\n \nConstraints:\n\n1 <= numCourses <= 2000\n0 <= prerequisites.length <= numCourses * (numCourses - 1)\nprerequisites[i].length == 2\n0 <= ai, bi < numCourses\nai != bi\nAll the pairs [ai, bi] are distinct.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(numCourses = 4,prerequisites = [[1, 0], [2, 0], [3, 1]]) == [0, 1, 2, 3]\n assert candidate(numCourses = 7,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]]) == [0, 1, 2, 3, 4, 5, 6]\n assert candidate(numCourses = 5,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 3]]) == [0, 1, 2, 3, 4]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [2, 1]]) == [0, 4, 5, 1, 2, 3]\n assert candidate(numCourses = 3,prerequisites = [[0, 1], [1, 2], [2, 0]]) == []\n assert candidate(numCourses = 3,prerequisites = [[1, 0], [1, 2], [0, 1]]) == []\n assert candidate(numCourses = 3,prerequisites = [[0, 1], [0, 2], [1, 2]]) == [2, 1, 0]\n assert candidate(numCourses = 3,prerequisites = [[1, 0], [0, 1]]) == []\n assert candidate(numCourses = 5,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2]]) == [0, 4, 1, 2, 3]\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 2], [5, 3], [6, 3], [7, 4], [7, 5]]) == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(numCourses = 5,prerequisites = [[1, 4], [2, 4], [3, 1], [3, 2]]) == [0, 4, 1, 2, 3]\n assert candidate(numCourses = 4,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2]]) == [0, 1, 2, 3]\n assert candidate(numCourses = 3,prerequisites = [[1, 0], [2, 1]]) == [0, 1, 2]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 3], [5, 4]]) == [0, 1, 2, 3, 4, 5]\n assert candidate(numCourses = 1,prerequisites = []) == [0]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [5, 4]]) == [0, 1, 2, 3, 4, 5]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [5, 3]]) == [0, 1, 2, 3, 4, 5]\n assert candidate(numCourses = 2,prerequisites = [[1, 0]]) == [0, 1]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [2, 0], [3, 2], [4, 2], [5, 3], [5, 4], [6, 5], [7, 6], [8, 6]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [10, 5], [11, 6], [11, 7], [11, 8], [11, 9]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 11,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 1], [6, 1], [7, 2], [8, 2], [9, 3], [10, 3]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(numCourses = 11,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [9, 5], [10, 9]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [7, 4], [7, 5], [8, 6], [8, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 5], [14, 6], [15, 6], [16, 7], [17, 7], [18, 8], [19, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [10, 5], [11, 6], [11, 7], [12, 8], [12, 9], [13, 10], [13, 11], [14, 12], [14, 13], [15, 14], [16, 14], [17, 15], [17, 16], [18, 17], [19, 18]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [5, 2], [6, 3], [7, 3], [8, 4], [8, 5], [9, 6], [9, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [7, 5], [8, 6], [9, 7], [10, 8], [11, 9], [12, 10], [13, 11], [14, 12], [15, 13], [16, 14], [17, 15], [18, 16], [19, 17], [18, 19]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 18]\n assert candidate(numCourses = 11,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [8, 4], [9, 5], [9, 6], [10, 7], [10, 8], [10, 9]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 1], [5, 2], [5, 3], [6, 1], [6, 2], [6, 3], [7, 4], [7, 5], [7, 6], [8, 4], [8, 5], [8, 6]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [4, 3], [5, 4], [6, 4], [7, 5], [8, 6], [9, 7], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [0, 8]]) == []\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [11, 5], [12, 5], [13, 6], [13, 7], [14, 8], [14, 9], [14, 10], [14, 11]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 14,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 1], [6, 2], [7, 3], [8, 4], [9, 5], [10, 6], [11, 7], [12, 8], [13, 9], [13, 10], [13, 11], [13, 12]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 1], [4, 3], [5, 2], [5, 3], [6, 3], [6, 4], [7, 3], [7, 4], [7, 5], [8, 4], [8, 5], [8, 6], [9, 4], [9, 5], [9, 6], [9, 7], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [11, 4], [11, 5], [11, 6], [11, 7], [11, 8], [11, 9], [12, 5], [12, 6], [12, 7], [12, 8], [12, 9], [12, 10], [12, 11], [13, 6], [13, 7], [13, 8], [13, 9], [13, 10], [13, 11], [13, 12], [14, 7], [14, 8], [14, 9], [14, 10], [14, 11], [14, 12], [14, 13], [15, 8], [15, 9], [15, 10], [15, 11], [15, 12], [15, 13], [15, 14], [16, 9], [16, 10], [16, 11], [16, 12], [16, 13], [16, 14], [16, 15], [17, 10], [17, 11], [17, 12], [17, 13], [17, 14], [17, 15], [17, 16], [18, 11], [18, 12], [18, 13], [18, 14], [18, 15], [18, 16], [18, 17], [19, 12], [19, 13], [19, 14], [19, 15], [19, 16], [19, 17], [19, 18]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [0, 9]]) == []\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 5], [8, 5], [9, 7], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 6], [13, 7], [14, 8], [14, 9], [14, 10], [14, 11], [14, 12], [14, 13]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 4]]) == [0, 1, 2, 3, 4, 5]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 5], [11, 6], [10, 11]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [11, 5], [12, 5], [13, 6], [14, 6], [15, 7], [16, 7], [17, 8], [18, 8], [19, 9], [19, 10], [19, 11], [19, 12], [19, 13], [19, 14], [19, 15], [19, 16], [19, 17], [19, 18]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10], [12, 11], [13, 12], [14, 13]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [4, 3], [5, 4], [6, 4], [7, 5], [7, 6], [8, 5], [8, 6], [8, 7], [9, 7], [10, 7], [10, 8], [11, 7], [11, 8], [11, 9], [11, 10], [12, 7], [12, 8], [12, 9], [12, 10], [12, 11], [13, 9], [13, 10], [13, 11], [13, 12], [14, 11], [14, 12], [14, 13]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4]]) == [0, 1, 2, 3, 4, 5]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 1], [6, 2], [7, 3], [7, 4], [8, 5], [8, 6], [9, 7], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10], [0, 11]]) == []\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 5], [14, 6], [15, 6], [16, 7], [17, 7], [18, 8], [19, 8], [19, 16]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [10, 9], [11, 10]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 1], [5, 2], [5, 3], [6, 4], [6, 5], [7, 6]]) == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [1, 2], [2, 0], [3, 1], [3, 2], [4, 3], [5, 3], [6, 4], [6, 5], [7, 6], [8, 7], [9, 7], [9, 8]]) == [0, 2, 1, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 18,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 1], [5, 3], [6, 2], [6, 4], [7, 3], [7, 4], [8, 5], [8, 6], [9, 5], [9, 6], [10, 7], [10, 8], [11, 7], [11, 8], [12, 9], [12, 10], [13, 10], [13, 11], [14, 12], [14, 13], [15, 13], [16, 14], [16, 15], [17, 15], [17, 16]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]\n assert candidate(numCourses = 5,prerequisites = [[1, 0], [2, 1], [3, 1], [3, 2], [4, 2], [4, 3]]) == [0, 1, 2, 3, 4]\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [7, 4], [7, 5], [7, 6]]) == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 4], [9, 5], [9, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 3], [6, 3], [7, 4], [8, 4], [9, 7], [10, 7], [11, 8], [11, 9]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 4], [9, 6], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [5, 2], [6, 3], [7, 3], [8, 4], [9, 4], [10, 5], [11, 5], [12, 6], [13, 7], [14, 7], [13, 14]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 13]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [10, 5], [11, 6], [11, 7], [11, 8], [11, 9], [11, 10]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [9, 4], [9, 5], [9, 6], [9, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 3], [6, 3], [7, 4], [8, 5], [9, 5], [10, 6], [11, 6], [12, 7], [13, 8], [14, 9], [14, 10], [14, 11], [14, 12], [14, 13]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [10, 5], [11, 6], [11, 7], [10, 8], [10, 9], [10, 11]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [9, 5], [10, 6], [10, 7], [11, 8], [11, 9], [11, 10]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [7, 4], [8, 5], [9, 6], [7, 8]]) == [0, 1, 2, 3, 4, 5, 6, 8, 9, 7]\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 1], [5, 2], [5, 3], [6, 4], [7, 5], [7, 6]]) == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 5], [14, 6], [15, 6], [16, 7], [17, 7], [18, 8], [19, 8], [19, 9], [18, 10], [17, 11], [16, 12], [15, 13], [14, 14], [13, 15], [12, 16], [11, 17], [10, 18], [9, 19], [8, 19]]) == []\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [5, 9]]) == []\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [9, 5], [10, 6], [10, 7], [11, 8], [11, 9], [12, 10], [13, 10], [14, 11], [14, 12], [14, 13]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [5, 6], [7, 8], [9, 7]]) == [0, 1, 2, 3, 4, 6, 8, 5, 7, 9]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 5], [14, 6], [14, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [2, 1], [3, 0], [3, 1], [3, 2], [4, 0], [4, 1], [4, 2], [4, 3], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [7, 6], [8, 0], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [9, 0], [9, 1], [9, 2], [9, 3], [9, 4], [9, 5], [9, 6], [9, 7], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 8,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [7, 5]]) == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(numCourses = 13,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 2], [5, 3], [6, 4], [7, 5], [8, 6], [9, 7], [10, 8], [11, 9], [12, 10], [12, 11]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [2, 0], [3, 2], [3, 1], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 12,prerequisites = [[1, 0], [2, 1], [3, 1], [4, 2], [5, 2], [6, 3], [7, 3], [8, 6], [9, 7], [10, 8], [10, 9], [11, 10]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(numCourses = 6,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 1], [5, 2], [5, 3], [5, 4]]) == [0, 1, 2, 3, 4, 5]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [4, 3], [5, 1], [5, 2], [5, 3], [6, 4], [7, 4], [8, 5], [9, 5], [10, 5], [11, 6], [12, 7], [13, 8], [14, 9], [14, 10], [14, 11], [14, 12], [14, 13]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [8, 3]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 20,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 1], [6, 1], [7, 1], [8, 2], [9, 2], [10, 2], [11, 3], [12, 3], [13, 4], [14, 4], [15, 5], [16, 5], [17, 6], [18, 6], [19, 7], [19, 8], [19, 9], [19, 10], [19, 11], [19, 12], [19, 13], [19, 14], [19, 15], [19, 16], [19, 17], [19, 18]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 2], [6, 3], [7, 3], [8, 4], [8, 5], [8, 6], [8, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 13,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [9, 5], [10, 6], [10, 7], [11, 8], [11, 9], [12, 10], [12, 11]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4], [10, 4], [11, 5], [12, 5], [13, 6], [14, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [4, 2], [5, 2], [6, 3], [7, 3], [8, 4], [8, 5], [9, 6], [9, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 15,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [10, 4], [11, 4], [12, 5], [13, 5], [14, 6], [13, 7], [12, 8], [11, 9], [10, 10], [9, 11], [8, 12], [7, 13], [6, 14]]) == []\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 1], [5, 2], [6, 3], [6, 4], [7, 5], [8, 6], [9, 7], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 2], [5, 3], [6, 3], [7, 4], [7, 5], [8, 6], [9, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 11,prerequisites = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(numCourses = 16,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 1], [5, 2], [6, 1], [6, 3], [7, 1], [7, 4], [8, 2], [8, 3], [8, 4], [9, 2], [9, 3], [9, 4], [10, 3], [10, 4], [11, 4], [12, 5], [12, 6], [12, 7], [12, 8], [13, 5], [13, 6], [13, 7], [13, 8], [13, 9], [14, 6], [14, 7], [14, 8], [14, 9], [14, 10], [14, 11], [15, 7], [15, 8], [15, 9], [15, 10], [15, 11], [15, 12], [15, 13], [15, 14]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [3, 2], [4, 3], [5, 3], [6, 4], [6, 5], [7, 6], [8, 6], [9, 7], [9, 8]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(numCourses = 9,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 3], [8, 4], [8, 5], [8, 6], [8, 7]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 0], [4, 1], [5, 1], [6, 2], [7, 2], [8, 3], [9, 3], [4, 6], [5, 7], [8, 4], [8, 5], [9, 8]]) == [0, 1, 2, 3, 6, 7, 4, 5, 8, 9]\n assert candidate(numCourses = 10,prerequisites = [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 4], [9, 5], [9, 6]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"}, "metadata": {"canonical_parameter_names": ["numCourses", "prerequisites"], "leetcode_dataset_entry_point": "Solution().findOrder", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findOrder = function(numCourses, prerequisites) {", "container": null, "callable": "findOrder", "parameters": [{"name": "numCourses", "type": "number"}, {"name": "prerequisites", "type": "number[][]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 212, "task_id": "word-search-ii", "difficulty": "Hard", "problem_description": "Given an m x n board of characters and a list of strings words, return all words on the board.\nEach word must be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once in a word.\n \nExample 1:\n\n\nInput: board = [[\"o\",\"a\",\"a\",\"n\"],[\"e\",\"t\",\"a\",\"e\"],[\"i\",\"h\",\"k\",\"r\"],[\"i\",\"f\",\"l\",\"v\"]], words = [\"oath\",\"pea\",\"eat\",\"rain\"]\nOutput: [\"eat\",\"oath\"]\n\nExample 2:\n\n\nInput: board = [[\"a\",\"b\"],[\"c\",\"d\"]], words = [\"abcb\"]\nOutput: []\n\n \nConstraints:\n\nm == board.length\nn == board[i].length\n1 <= m, n <= 12\nboard[i][j] is a lowercase English letter.\n1 <= words.length <= 3 * 104\n1 <= words[i].length <= 10\nwords[i] consists of lowercase English letters.\nAll the strings of words are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = [['o', 'a', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain']) == ['oath', 'eat']\n assert candidate(board = [['a', 'a']],words = ['a']) == ['a']\n assert candidate(board = [['o', 'a', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain']) == ['oath', 'eat']\n assert candidate(board = [['a'], ['a']],words = ['a']) == ['a']\n assert candidate(board = [['a', 'b'], ['c', 'd']],words = ['abcb']) == []\n assert candidate(board = [['a', 'a']],words = ['aaa']) == []\n assert candidate(board = [['a']],words = ['a']) == ['a']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']],words = ['abc', 'cfi', 'beh', 'defi', 'ghi']) == ['abc', 'beh', 'cfi', 'defi', 'ghi']\n assert candidate(board = [['a', 'b'], ['c', 'd']],words = ['abcb']) == []\n assert candidate(board = [['a', 'b'], ['c', 'f']],words = ['ab', 'cf', 'bf', 'ca']) == ['ab', 'bf', 'ca', 'cf']\n assert candidate(board = [['a', 'b', 'c'], ['a', 'e', 'd'], ['a', 'f', 'g']],words = ['abcdefg', 'gfedcba', 'abcd', 'dcba']) == ['abcd', 'abcdefg', 'dcba', 'gfedcba']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaaa', 'aaaab', 'aaaba']) == ['aaaaa']\n assert candidate(board = [['a', 'b', 'c', 'd', 'e'], ['f', 'g', 'h', 'i', 'j'], ['k', 'l', 'm', 'n', 'o'], ['p', 'q', 'r', 's', 't'], ['u', 'v', 'w', 'x', 'y']],words = ['abcdefg', 'hijklmn', 'opqrstu', 'vwxyz', 'abgmvxz', 'abcdefghi', 'pqrstuvwy']) == []\n assert candidate(board = [['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a']],words = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaaaaaaaaaaaaaaaaaaaa']) == ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaaaaaaaaaaaaaaaaaaaa']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaaaaaaaa', 'aaaaaaaaaab', 'aaaaaaaaaac', 'aaaaaaaaaad']) == ['aaaaaaaaaa']\n assert candidate(board = [['a', 'b', 'c'], ['a', 'b', 'c'], ['a', 'b', 'c']],words = ['abc', 'bca', 'cab', 'cba', 'bac', 'acb', 'aabc', 'abca', 'bcab', 'cbac']) == ['abc', 'aabc', 'cba']\n assert candidate(board = [['o', 'a', 'b', 'n'], ['o', 't', 'a', 'e'], ['a', 'h', 'k', 'r'], ['a', 'f', 'l', 'v']],words = ['oath', 'path', 'parent', 'enact']) == ['oath']\n assert candidate(board = [['p', 'e', 'a', 'f'], ['t', 'h', 'o', 'w'], ['o', 'r', 'a', 'g'], ['n', 'l', 'e', 'd']],words = ['pear', 'flow', 'tow', 'orange', 'lead']) == []\n assert candidate(board = [['z', 'a', 'b', 'c'], ['z', 'e', 'f', 'g'], ['z', 'h', 'i', 'j'], ['z', 'k', 'l', 'm']],words = ['zafe', 'zjih', 'zmkl', 'zabc', 'zefg', 'zihj', 'zkjg', 'zlif', 'zzzz']) == ['zabc', 'zzzz', 'zefg']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']],words = ['abc', 'def', 'ghi', 'bfg', 'hce', 'dih']) == ['abc', 'def', 'ghi']\n assert candidate(board = [['a', 'b', 'c', 'd', 'e'], ['f', 'g', 'h', 'i', 'j'], ['k', 'l', 'm', 'n', 'o'], ['p', 'q', 'r', 's', 't'], ['u', 'v', 'w', 'x', 'y']],words = ['abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy', 'ajgtw', 'bsmr']) == ['abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy']\n assert candidate(board = [['a', 'b', 'c', 'd'], ['e', 'f', 'g', 'h'], ['i', 'j', 'k', 'l'], ['m', 'n', 'o', 'p'], ['q', 'r', 's', 't']],words = ['abcdefghijlkmnoprst', 'bcegikmnort', 'afgknprt']) == []\n assert candidate(board = [['c', 'c', 'c', 'c'], ['c', 'c', 'c', 'c'], ['c', 'c', 'c', 'c'], ['c', 'c', 'c', 'c']],words = ['cccc', 'cccccc', 'cccccccc']) == ['cccc', 'cccccc', 'cccccccc']\n assert candidate(board = [['p', 'z', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain', 'zeta', 'pani']) == ['eat']\n assert candidate(board = [['x', 'y', 'x'], ['y', 'x', 'y'], ['x', 'y', 'x']],words = ['xyx', 'yxy', 'xyy', 'yxx']) == ['xyx', 'yxy']\n assert candidate(board = [['o', 'a', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain', 'oathk', 'vli', 'hek', 'tae', 'rat', 'iate', 'tier', 'neif', 'heat']) == ['oath', 'oathk', 'tae', 'eat']\n assert candidate(board = [['z', 'y', 'x'], ['w', 'v', 'u'], ['t', 's', 'r'], ['q', 'p', 'o'], ['n', 'm', 'l'], ['k', 'j', 'i'], ['h', 'g', 'f'], ['e', 'd', 'c'], ['b', 'a', 'a']],words = ['zyx', 'wvu', 'tsr', 'qpo', 'nml', 'kji', 'hgf', 'edc', 'baa', 'zyxwvutsrqponmlkjihgfedcba']) == ['zyx', 'wvu', 'tsr', 'qpo', 'nml', 'kji', 'hgf', 'edc', 'baa']\n assert candidate(board = [['s', 'e', 'e', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['seen', 'seat', 'heat', 'pear', 'rate', 'feat']) == ['seen']\n assert candidate(board = [['a', 'b', 'c', 'd', 'e'], ['f', 'g', 'h', 'i', 'j'], ['k', 'l', 'm', 'n', 'o'], ['p', 'q', 'r', 's', 't'], ['u', 'v', 'w', 'x', 'y']],words = ['cat', 'dog', 'bat', 'rat', 'mat']) == []\n assert candidate(board = [['o', 'a', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain', 'oate', 'hoaf']) == ['oath', 'oate', 'eat']\n assert candidate(board = [['p', 'e', 'r', 'f'], ['e', 't', 'e', 'r'], ['r', 'e', 'd', 'o'], ['f', 'o', 'x', 'o']],words = ['perfect', 'robot', 'redo', 'fire', 'fore']) == ['redo']\n assert candidate(board = [['s', 'e', 'e', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['seen', 'tear', 'heap', 'inter', 'neat', 'kite']) == ['seen', 'neat']\n assert candidate(board = [['a', 'b', 'c', 'd'], ['e', 'f', 'g', 'h'], ['i', 'j', 'k', 'l'], ['m', 'n', 'o', 'p']],words = ['abcf', 'bceg', 'cfil', 'ghjo', 'klon', 'mnop']) == ['mnop']\n assert candidate(board = [['s', 'e', 'e', 'n'], ['e', 't', 'e', 'e'], ['e', 'e', 's', 'n'], ['n', 's', 't', 'e']],words = ['seen', 'nees', 'tees', 'test', 'east']) == ['seen', 'nees', 'test']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']],words = ['abc', 'bfg', 'chi', 'def', 'geh']) == ['abc', 'def']\n assert candidate(board = [['a']],words = ['a']) == ['a']\n assert candidate(board = [['x', 'y', 'x', 'y'], ['y', 'x', 'y', 'x'], ['x', 'y', 'x', 'y'], ['y', 'x', 'y', 'x']],words = ['xyxy', 'yxyx', 'xyyx', 'yxyy', 'xxyx', 'yxx', 'xyx']) == ['xyx', 'xyxy', 'yxyx']\n assert candidate(board = [['a', 'b', 'c', 'e'], ['z', 'f', 'c', 's'], ['a', 'd', 'e', 'e']],words = ['abcced', 'see', 'abce']) == ['abce', 'abcced', 'see']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i'], ['j', 'k', 'l'], ['m', 'n', 'o']],words = ['abc', 'def', 'ghi', 'jkl', 'mno', 'adg', 'beh', 'cfi', 'amk', 'bnl', 'co']) == ['abc', 'adg', 'beh', 'cfi', 'def', 'ghi', 'jkl', 'mno']\n assert candidate(board = [['o', 'a', 'b', 'n'], ['o', 't', 'a', 'e'], ['a', 'h', 'k', 'r'], ['a', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain', 'oathf', 'oat', 'ate']) == ['oat', 'oath', 'oathf', 'eat']\n assert candidate(board = [['x', 'x', 'x', 'x'], ['x', 'x', 'x', 'x'], ['x', 'x', 'x', 'x'], ['x', 'x', 'x', 'x']],words = ['xxxx', 'xxxy', 'xyxx', 'xxyx']) == ['xxxx']\n assert candidate(board = [['a', 'b', 'c'], ['a', 'e', 'd'], ['a', 'f', 'g']],words = ['abcdefg', 'bed', 'fad', 'gfedcba']) == ['abcdefg', 'bed', 'gfedcba']\n assert candidate(board = [['a', 'b', 'c', 'd'], ['e', 'f', 'g', 'h'], ['i', 'j', 'k', 'l'], ['m', 'n', 'o', 'p']],words = ['abcdefgh', 'ponmlkjihgfedcba', 'abcd', 'efgh', 'ijkl', 'mnop', 'mnopijkl']) == ['abcd', 'efgh', 'ijkl', 'mnop']\n assert candidate(board = [['a', 'b', 'c', 'd', 'e'], ['f', 'g', 'h', 'i', 'j'], ['k', 'l', 'm', 'n', 'o'], ['p', 'q', 'r', 's', 't'], ['u', 'v', 'w', 'x', 'y']],words = ['abcdefghij', 'klmnopqrstu', 'vwxyz', 'zutrqponmlk', 'ytxwvusrqponmlkjihgfedcba']) == []\n assert candidate(board = [['a', 'z', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['zath', 'zeat', 'kait', 'lain']) == []\n assert candidate(board = [['z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z']],words = ['zzz', 'zzzz', 'zzzzz']) == ['zzz', 'zzzz', 'zzzzz']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaaaaaaaaaaa', 'aaaaaaaab']) == ['aaaaaaaaaaaaa']\n assert candidate(board = [['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a']],words = ['aaaaa', 'aaaaaa', 'aaaaaaaa']) == ['aaaaa', 'aaaaaa', 'aaaaaaaa']\n assert candidate(board = [['o', 'a', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['oath', 'pea', 'eat', 'rain', 'kite', 'pear', 'lane']) == ['oath', 'eat']\n assert candidate(board = [['a', 'b', 'c'], ['a', 'e', 'd'], ['a', 'f', 'g']],words = ['abcdefg', 'gfedcba', 'abcd', 'efg']) == ['abcd', 'abcdefg', 'efg', 'gfedcba']\n assert candidate(board = [['a', 'b', 'c', 'e'], ['s', 'f', 'c', 's'], ['a', 'd', 'e', 'e']],words = ['abcced', 'see', 'abcb']) == ['abcced', 'see']\n assert candidate(board = [['x', 'y', 'z'], ['x', 'y', 'z'], ['x', 'y', 'z']],words = ['xyz', 'zyx', 'yy', 'zzz', 'xzy']) == ['xyz', 'yy', 'zzz', 'zyx']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']],words = ['abc', 'bcd', 'cde', 'efg', 'fgh', 'ghi', 'adg', 'beh', 'cfi']) == ['abc', 'adg', 'beh', 'cfi', 'ghi']\n assert candidate(board = [['a', 'b', 'c', 'd', 'e', 'f'], ['g', 'h', 'i', 'j', 'k', 'l'], ['m', 'n', 'o', 'p', 'q', 'r'], ['s', 't', 'u', 'v', 'w', 'x'], ['y', 'z', 'a', 'b', 'c', 'd']],words = ['abcdefghij', 'mnopqrstuv', 'wxyzabcd']) == []\n assert candidate(board = [['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a', 'a']],words = ['aaaaa', 'aaaaaa', 'aaaaaaaa', 'aaaaaaa']) == ['aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa']\n assert candidate(board = [['z', 'z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z', 'z']],words = ['zzzzz', 'zzzzzz', 'zzzzzzz']) == ['zzzzz', 'zzzzzz', 'zzzzzzz']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']],words = ['abc', 'def', 'ghi', 'bce', 'dfi', 'hcg', 'bdf', 'cei', 'adg']) == ['abc', 'adg', 'def', 'ghi']\n assert candidate(board = [['x', 'y', 'z'], ['w', 'v', 'u'], ['t', 's', 'r'], ['q', 'p', 'o']],words = ['xyz', 'uvw', 'rst', 'qpo', 'xuw', 'ytv', 'zsr', 'wpo']) == ['xyz', 'uvw', 'rst', 'qpo']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaaa', 'aaa', 'aa', 'a']) == ['a', 'aa', 'aaa', 'aaaaa']\n assert candidate(board = [['w', 'o', 'r', 'l'], ['o', 'n', 'k', 'n'], ['r', 'l', 'd', 't'], ['d', 't', 'a', 'e']],words = ['world', 'note', 'rate', 'tare']) == ['world']\n assert candidate(board = [['x', 'y', 'x', 'y', 'x'], ['y', 'x', 'y', 'x', 'y'], ['x', 'y', 'x', 'y', 'x'], ['y', 'x', 'y', 'x', 'y'], ['x', 'y', 'x', 'y', 'x']],words = ['xyxyx', 'yxyxy', 'xyyxy']) == ['xyxyx', 'yxyxy']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaaaaaaaa', 'aaaaaaaab', 'aaaaaaaac']) == ['aaaaaaaaaa']\n assert candidate(board = [['c', 'a', 't'], ['a', 't', 'c'], ['t', 'c', 'a']],words = ['cat', 'act', 'tat', 'tac', 'att', 'tat', 'cta']) == ['cat', 'tat', 'tac', 'cta', 'act']\n assert candidate(board = [['s', 'e', 'e', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v']],words = ['seen', 'seat', 'near', 'tree']) == ['seen']\n assert candidate(board = [['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a', 'a']],words = ['aaaaa', 'aaaaab', 'aaaaac', 'aaaaad']) == ['aaaaa']\n assert candidate(board = [['p', 'e', 'a'], ['a', 'o', 't'], ['t', 'h', 't'], ['a', 'i', 'p']],words = ['peacht', 'poth', 'tophat', 'peat']) == ['peat']\n assert candidate(board = [['a', 'b', 'c'], ['a', 'e', 'd'], ['a', 'f', 'g']],words = ['abc', 'bce', 'cda', 'gfa']) == ['abc', 'gfa']\n assert candidate(board = [['m', 'y', 'b', 'a', 'b', 'y'], ['x', 'x', 'x', 'x', 'x', 'x'], ['x', 'o', 'a', 'a', 'a', 'x'], ['x', 'x', 'x', 'x', 'x', 'x'], ['m', 'y', 'b', 'a', 'b', 'y']],words = ['baby', 'my', 'by', 'ma']) == ['my', 'baby', 'by']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaa', 'aaa', 'aa', 'a', 'aaaaaaaaaaaaaaaa']) == ['a', 'aa', 'aaa', 'aaaa', 'aaaaaaaaaaaaaaaa']\n assert candidate(board = [['a', 'b', 'c'], ['b', 'c', 'd'], ['c', 'd', 'e']],words = ['abc', 'bcd', 'cde', 'abcd', 'bcde', 'ab', 'cd', 'de']) == ['ab', 'abc', 'abcd', 'bcd', 'bcde', 'cd', 'cde', 'de']\n assert candidate(board = [['x', 'y', 'z', 'w'], ['x', 'y', 'z', 'w'], ['x', 'y', 'z', 'w'], ['x', 'y', 'z', 'w']],words = ['xyzz', 'xwyz', 'wxzy', 'zywx', 'zwxy', 'zyxw', 'yxwz', 'wyxz']) == ['xyzz']\n assert candidate(board = [['z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z'], ['z', 'z', 'z', 'z']],words = ['zzzzzzzzzz', 'zzzzzzzzzza', 'zzzzzzzzzzb', 'zzzzzzzzzzc']) == ['zzzzzzzzzz']\n assert candidate(board = [['d', 'o', 'g'], ['d', 'o', 'g'], ['d', 'o', 'g']],words = ['dog', 'god', 'dogo', 'dogod', 'dogodu']) == ['dog', 'god']\n assert candidate(board = [['p', 'q', 'r', 's'], ['t', 'u', 'v', 'w'], ['x', 'y', 'z', 'a'], ['b', 'c', 'd', 'e']],words = ['pqrs', 'tuvw', 'xyzab', 'pqru', 'rtxy', 'styz', 'uvwz']) == ['pqrs', 'tuvw']\n assert candidate(board = [['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a'], ['a', 'a', 'a', 'a']],words = ['aaaaaaaaaaaaa', 'aaaabaaa', 'aaaaabaa']) == ['aaaaaaaaaaaaa']\n assert candidate(board = [['h', 'o', 'l', 'a'], ['o', 'n', 'k', 'n'], ['r', 'l', 'd', 't'], ['d', 't', 'a', 'e']],words = ['hola', 'note', 'rode', 'taen']) == ['hola']\n assert candidate(board = [['x', 'y', 'z'], ['u', 'v', 'w'], ['p', 'q', 'r']],words = ['xyz', 'uvw', 'pqr', 'yzw', 'zwp', 'vyu']) == ['xyz', 'yzw', 'uvw', 'pqr']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i'], ['j', 'k', 'l'], ['m', 'n', 'o']],words = ['abc', 'def', 'ghi', 'jkl', 'mno', 'adgjm', 'behkn', 'cfilor', 'aeim', 'bfjn', 'cgko', 'ahko', 'bdil', 'cehn', 'aflo', 'bgkn', 'chim']) == ['abc', 'adgjm', 'behkn', 'def', 'ghi', 'jkl', 'mno']\n assert candidate(board = [['m', 'a', 'r', 't'], ['a', 't', 'e', 'n'], ['r', 'e', 't', 'a'], ['t', 'a', 'n', 'e']],words = ['mart', 'rate', 'tane', 'tart', 'ten', 'mate', 'ment', 'taen', 'meta', 'atma']) == ['mart', 'mate', 'rate', 'tart', 'ten', 'tane', 'taen']\n assert candidate(board = [['a', 'b', 'c'], ['a', 'e', 'd'], ['e', 'f', 'g']],words = ['abc', 'bce', 'fed', 'def']) == ['abc', 'def', 'fed']\n assert candidate(board = [['o', 'a', 'a', 'n'], ['e', 't', 'a', 'e'], ['i', 'h', 'k', 'r'], ['i', 'f', 'l', 'v'], ['g', 'h', 'i', 'j']],words = ['oath', 'pea', 'eat', 'rain', 'ghij', 'gfedcba', 'nihao']) == ['oath', 'eat', 'ghij']\n assert candidate(board = [['a', 'b', 'c'], ['d', 'e', 'f'], ['g', 'h', 'i']],words = ['abc', 'bfg', 'cfi', 'adh', 'beh', 'cei', 'aeg']) == ['abc', 'beh', 'cfi']\n assert candidate(board = [['p', 'e', 'a'], ['e', 'r', 'a'], ['a', 'n', 'a'], ['n', 'l', 'a']],words = ['pear', 'peal', 'pale', 'pan', 'lane', 'paler', 'panel', 'paren', 'pare', 'parel', 'parer']) == []\n"}, "metadata": {"canonical_parameter_names": ["board", "words"], "leetcode_dataset_entry_point": "Solution().findWords", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findWords = function(board, words) {", "container": null, "callable": "findWords", "parameters": [{"name": "board", "type": "character[][]"}, {"name": "words", "type": "string[]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 213, "task_id": "house-robber-ii", "difficulty": "Medium", "problem_description": "You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed. All houses at this place are arranged in a circle. That means the first house is the neighbor of the last one. Meanwhile, adjacent houses have a security system connected, and it will automatically contact the police if two adjacent houses were broken into on the same night.\nGiven an integer array nums representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police.\n \nExample 1:\n\nInput: nums = [2,3,2]\nOutput: 3\nExplanation: You cannot rob house 1 (money = 2) and then rob house 3 (money = 2), because they are adjacent houses.\n\nExample 2:\n\nInput: nums = [1,2,3,1]\nOutput: 4\nExplanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).\nTotal amount you can rob = 1 + 3 = 4.\n\nExample 3:\n\nInput: nums = [1,2,3]\nOutput: 3\n\n \nConstraints:\n\n1 <= nums.length <= 100\n0 <= nums[i] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 3, 1]) == 4\n assert candidate(nums = [1, 0, 1, 0, 1]) == 2\n assert candidate(nums = [5, 1, 2, 4, 7, 8]) == 14\n assert candidate(nums = [5, 3, 1, 1, 1]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 30\n assert candidate(nums = [10, 20, 30, 40, 50]) == 80\n assert candidate(nums = [300, 3, 140, 20, 10, 5, 5, 200]) == 455\n assert candidate(nums = [5, 5, 5, 5, 5]) == 10\n assert candidate(nums = [4, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 25\n assert candidate(nums = [1, 2, 3, 4, 5]) == 8\n assert candidate(nums = [2, 7, 9, 3, 1]) == 11\n assert candidate(nums = [1000]) == 1000\n assert candidate(nums = [2, 3, 2]) == 3\n assert candidate(nums = [2, 1, 1, 2]) == 3\n assert candidate(nums = [3, 6, 4, 2, 5, 7, 8]) == 19\n assert candidate(nums = [1, 1, 1, 1, 1]) == 2\n assert candidate(nums = [0]) == 0\n assert candidate(nums = [200, 3, 140, 20, 10]) == 340\n assert candidate(nums = [5, 5, 10, 100, 10, 5, 5]) == 110\n assert candidate(nums = [300, 3, 100, 4]) == 400\n assert candidate(nums = [5, 1, 1, 5]) == 6\n assert candidate(nums = [1, 2]) == 2\n assert candidate(nums = [1, 2, 3]) == 3\n assert candidate(nums = [10, 2, 3, 4, 5, 6]) == 18\n assert candidate(nums = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]) == 7000\n assert candidate(nums = [200, 300, 150, 100, 250, 300, 200, 100, 50, 400, 350, 250]) == 1450\n assert candidate(nums = [100, 0, 100, 0, 100, 0, 100, 0, 100, 0]) == 500\n assert candidate(nums = [50, 100, 150, 200, 250, 300]) == 600\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 110\n assert candidate(nums = [500, 400, 300, 200, 100, 0, 100, 200, 300, 400, 500, 0, 500, 400, 300, 200, 100, 0, 100, 200, 300, 400, 500]) == 3300\n assert candidate(nums = [200, 100, 50, 150, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100, 50, 150, 200, 300, 400, 500]) == 4050\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 2550\n assert candidate(nums = [10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1, 1, 10, 1]) == 70\n assert candidate(nums = [1, 10, 100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 10, 1]) == 3020\n assert candidate(nums = [90, 200, 200, 100, 400, 90, 200, 200, 100, 400, 90, 200, 200, 100, 400]) == 1800\n assert candidate(nums = [2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]) == 24\n assert candidate(nums = [1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1]) == 5000\n assert candidate(nums = [5, 10, 3, 12, 8, 6, 11, 7, 14, 9]) == 47\n assert candidate(nums = [5, 2, 6, 2, 5, 2, 6, 2, 5, 2, 6, 2, 5, 2, 6]) == 39\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 63\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == 12\n assert candidate(nums = [100, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 100, 100]) == 208\n assert candidate(nums = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]) == 3000\n assert candidate(nums = [25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 168\n assert candidate(nums = [100, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 100]) == 109\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 240\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 35\n assert candidate(nums = [2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]) == 84\n assert candidate(nums = [100, 0, 0, 0, 0, 0, 0, 0, 0, 100, 100, 0, 0, 0, 0, 0, 0, 0, 0, 100]) == 200\n assert candidate(nums = [500, 100, 500, 100, 500, 100, 500, 100, 500, 100, 500, 100, 500]) == 3000\n assert candidate(nums = [123, 456, 789, 101, 202, 303, 404, 505, 606, 707, 808, 909]) == 3213\n assert candidate(nums = [200, 1, 100, 1, 100, 1, 200, 1, 100, 1, 100, 1]) == 800\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == 500\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 63\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1000, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1000\n assert candidate(nums = [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == 19\n assert candidate(nums = [800, 200, 100, 300, 600, 400, 500, 700, 50, 90]) == 2200\n assert candidate(nums = [999, 0, 999, 0, 999, 0, 999, 0, 999, 0]) == 4995\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 50\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 200\n assert candidate(nums = [50, 1, 1, 50, 1, 1, 50, 1, 1, 50, 1, 1]) == 200\n assert candidate(nums = [5, 100, 5, 100, 5, 100, 5, 100, 5, 100, 5, 100, 5, 100, 5, 100]) == 800\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 100]) == 2500\n assert candidate(nums = [200, 3, 140, 20, 10, 5, 5, 200, 150, 250, 350, 450]) == 1050\n assert candidate(nums = [1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0]) == 10000\n assert candidate(nums = [5, 10, 5, 10, 5, 10, 5]) == 30\n assert candidate(nums = [5, 1, 2, 9, 1, 5, 1, 2, 9, 1, 5, 1, 2, 9, 1, 5, 1, 2, 9, 1]) == 56\n assert candidate(nums = [10, 2, 3, 4, 1, 5, 6, 7, 8, 9, 10]) == 35\n assert candidate(nums = [9, 4, 1, 7, 3, 2, 5, 6, 8, 0, 12, 15]) == 41\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 110\n assert candidate(nums = [2, 3, 5, 6, 7, 8, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 44\n assert candidate(nums = [1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100]) == 1000\n assert candidate(nums = [10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1, 10, 1, 1, 1]) == 44\n assert candidate(nums = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985]) == 6951\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50]) == 140\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 50\n assert candidate(nums = [100, 0, 100, 0, 100, 0, 100]) == 300\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 190\n assert candidate(nums = [50, 1, 1, 50, 1, 1, 50, 1, 1, 50]) == 151\n assert candidate(nums = [50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1, 50, 1]) == 500\n assert candidate(nums = [50, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 640\n assert candidate(nums = [1000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 1000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 168\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 300\n assert candidate(nums = [1, 3, 1, 3, 100, 1, 3, 1, 3, 1, 3, 100]) == 209\n assert candidate(nums = [10, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == 24\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3]) == 30\n assert candidate(nums = [10, 2, 5, 3, 7, 9, 8, 10, 2, 5]) == 34\n assert candidate(nums = [200, 300, 200, 300, 200, 300, 200, 300, 200, 300, 200, 300, 200, 300, 200, 300, 200, 300, 200, 300]) == 3000\n assert candidate(nums = [50, 100, 50, 100, 50, 100, 50]) == 300\n assert candidate(nums = [100, 100, 0, 100, 0, 100, 0, 100, 0, 100]) == 500\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 50]) == 5050\n assert candidate(nums = [250, 200, 150, 100, 50, 0, 50, 100, 150, 200, 250, 0, 250, 200, 150, 100, 50, 0, 50, 100, 150, 200, 250]) == 1650\n assert candidate(nums = [1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0]) == 8000\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 110\n assert candidate(nums = [20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20, 1, 20]) == 200\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 630\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 500\n assert candidate(nums = [50, 1, 50, 1, 50, 1, 50, 1, 50, 1]) == 250\n assert candidate(nums = [1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000]) == 10000\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 300\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0]) == 800\n assert candidate(nums = [9, 3, 5, 7, 1, 3, 5, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 47\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 60\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 650\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [50, 100, 200, 300, 100, 50]) == 450\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250]) == 1680\n assert candidate(nums = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980, 979, 978, 977, 976, 975]) == 11856\n assert candidate(nums = [100, 0, 0, 100, 0, 0, 100, 0, 0, 100]) == 300\n assert candidate(nums = [2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]) == 30\n assert candidate(nums = [5, 2, 3, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 52\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 300\n assert candidate(nums = [999, 1, 999, 1, 999, 1, 999, 1]) == 3996\n assert candidate(nums = [200, 1, 200, 1, 200, 1, 200, 1, 200, 1, 200, 1, 200, 1, 200, 1, 200, 1, 200, 1]) == 2000\n assert candidate(nums = [999, 1, 999, 1, 999, 1, 999, 1, 999, 1, 999, 1, 999, 1, 999, 1, 999, 1, 999, 1]) == 9990\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 90\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 85\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 3000\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 100\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().rob", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var rob = function(nums) {", "container": null, "callable": "rob", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 214, "task_id": "shortest-palindrome", "difficulty": "Hard", "problem_description": "You are given a string s. You can convert s to a palindrome by adding characters in front of it.\nReturn the shortest palindrome you can find by performing this transformation.\n \nExample 1:\nInput: s = \"aacecaaa\"\nOutput: \"aaacecaaa\"\nExample 2:\nInput: s = \"abcd\"\nOutput: \"dcbabcd\"\n\n \nConstraints:\n\n0 <= s.length <= 5 * 104\ns consists of lowercase English letters only.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcba\") == \"abcba\"\n assert candidate(s = \"madam\") == \"madam\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == \"zyxwvutsrqponmlkjihgfedcbabcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"abac\") == \"cabac\"\n assert candidate(s = \"zxcvbnm\") == \"mnbvcxzxcvbnm\"\n assert candidate(s = \"aabbaa\") == \"aabbaa\"\n assert candidate(s = \"abcdcba\") == \"abcdcba\"\n assert candidate(s = \"aaaaa\") == \"aaaaa\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"abcabcabc\") == \"cbacbacbabcabcabc\"\n assert candidate(s = \"step\") == \"petstep\"\n assert candidate(s = \"abacdfgdcaba\") == \"abacdgfdcabacdfgdcaba\"\n assert candidate(s = \"ab\") == \"bab\"\n assert candidate(s = \"\") == \"\"\n assert candidate(s = \"abcde\") == \"edcbabcde\"\n assert candidate(s = \"abcabc\") == \"cbacbabcabc\"\n assert candidate(s = \"rotor\") == \"rotor\"\n assert candidate(s = \"aabb\") == \"bbaabb\"\n assert candidate(s = \"racecar\") == \"racecar\"\n assert candidate(s = \"aacecaaa\") == \"aaacecaaa\"\n assert candidate(s = \"aabba\") == \"abbaabba\"\n assert candidate(s = \"abba\") == \"abba\"\n assert candidate(s = \"race\") == \"ecarace\"\n assert candidate(s = \"noon\") == \"noon\"\n assert candidate(s = \"banana\") == \"ananabanana\"\n assert candidate(s = \"deeee\") == \"eeeedeeee\"\n assert candidate(s = \"zzazzacca\") == \"accazzazzacca\"\n assert candidate(s = \"abcd\") == \"dcbabcd\"\n assert candidate(s = \"aba\") == \"aba\"\n assert candidate(s = \"abbacd\") == \"dcabbacd\"\n assert candidate(s = \"level\") == \"level\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == \"abcdefghijklmnopqrstuvwxyzyxwvutsrqponmlkjihgfedcba\"\n assert candidate(s = \"aabbaab\") == \"baabbaab\"\n assert candidate(s = \"aabbaca\") == \"acabbaabbaca\"\n assert candidate(s = \"aabbccddeeeffgg\") == \"ggffeeeddccbbaabbccddeeeffgg\"\n assert candidate(s = \"noonappo\") == \"oppanoonappo\"\n assert candidate(s = \"abacabadabacabadabacaba\") == \"abacabadabacabadabacaba\"\n assert candidate(s = \"repaperrepaper\") == \"repaperrepaper\"\n assert candidate(s = \"xyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyx\") == \"xyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyx\"\n assert candidate(s = \"abracadabra\") == \"arbadacarbabracadabra\"\n assert candidate(s = \"rotorrotor\") == \"rotorrotor\"\n assert candidate(s = \"zzzz\") == \"zzzz\"\n assert candidate(s = \"abbaa\") == \"aabbaa\"\n assert candidate(s = \"zazazz\") == \"zzazazz\"\n assert candidate(s = \"aaaabaaaa\") == \"aaaabaaaa\"\n assert candidate(s = \"noonnoon\") == \"noonnoon\"\n assert candidate(s = \"aabbccddeeefffgg\") == \"ggfffeeeddccbbaabbccddeeefffgg\"\n assert candidate(s = \"repaid\") == \"diaperepaid\"\n assert candidate(s = \"algorithm\") == \"mhtiroglalgorithm\"\n assert candidate(s = \"ananabanana\") == \"ananabanana\"\n assert candidate(s = \"hello\") == \"ollehello\"\n assert candidate(s = \"abcdecba\") == \"abcedcbabcdecba\"\n assert candidate(s = \"redder\") == \"redder\"\n assert candidate(s = \"qwertyuiop\") == \"poiuytrewqwertyuiop\"\n assert candidate(s = \"noonnoonnoonnoon\") == \"noonnoonnoonnoon\"\n assert candidate(s = \"deeeeffffgggggggggggggggggggggggggggggggg\") == \"ggggggggggggggggggggggggggggggggffffeeeedeeeeffffgggggggggggggggggggggggggggggggg\"\n assert candidate(s = \"abcdabc\") == \"cbadcbabcdabc\"\n assert candidate(s = \"mississippimississippi\") == \"ippississimippississimississippimississippi\"\n assert candidate(s = \"aabbccddeee\") == \"eeeddccbbaabbccddeee\"\n assert candidate(s = \"xyzzyx\") == \"xyzzyx\"\n assert candidate(s = \"abcdefghihgfedcbabc\") == \"cbabcdefghihgfedcbabc\"\n assert candidate(s = \"abca\") == \"acbabca\"\n assert candidate(s = \"bba\") == \"abba\"\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"abbae\") == \"eabbae\"\n assert candidate(s = \"repaperandmorepaperrepaperandmorepaper\") == \"repaperomdnarepaperrepaperomdnarepaperandmorepaperrepaperandmorepaper\"\n assert candidate(s = \"algorhythmhmorthygrola\") == \"alorgyhtromhmhtyhroglalgorhythmhmorthygrola\"\n assert candidate(s = \"palindrome\") == \"emordnilapalindrome\"\n assert candidate(s = \"abacaxi\") == \"ixacabacaxi\"\n assert candidate(s = \"kayak\") == \"kayak\"\n assert candidate(s = \"abab\") == \"babab\"\n assert candidate(s = \"aabbccddeeefffhhh\") == \"hhhfffeeeddccbbaabbccddeeefffhhh\"\n assert candidate(s = \"aabbbaaa\") == \"aaabbbaaa\"\n assert candidate(s = \"xyxz\") == \"zxyxz\"\n assert candidate(s = \"abcdefghihgfedcbabcd\") == \"dcbabcdefghihgfedcbabcd\"\n assert candidate(s = \"aabbccddeeefffggghhh\") == \"hhhgggfffeeeddccbbaabbccddeeefffggghhh\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\") == \"mnbvcxzlkjhgfdsapoiuytrewqwertyuiopasdfghjklzxcvbnm\"\n assert candidate(s = \"levelup\") == \"pulevelup\"\n assert candidate(s = \"raceacar\") == \"racaecaraceacar\"\n assert candidate(s = \"levelupandnevergiveup\") == \"puevigrevendnapulevelupandnevergiveup\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz\") == \"zzzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz\"\n assert candidate(s = \"abcdeedcba\") == \"abcdeedcba\"\n assert candidate(s = \"leveler\") == \"releveler\"\n assert candidate(s = \"xyzzyxw\") == \"wxyzzyxw\"\n assert candidate(s = \"abcbae\") == \"eabcbae\"\n assert candidate(s = \"aabbccddeeeff\") == \"ffeeeddccbbaabbccddeeeff\"\n assert candidate(s = \"abcdeffedcba\") == \"abcdeffedcba\"\n assert candidate(s = \"deeeeffffgggg\") == \"ggggffffeeeedeeeeffffgggg\"\n assert candidate(s = \"levellevel\") == \"levellevel\"\n assert candidate(s = \"aabbccddeeefffhhhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiiihhhfffeeeddccbbaabbccddeeefffhhhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\") == \"zyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"aabcd\") == \"dcbaabcd\"\n assert candidate(s = \"abcdefedcba\") == \"abcdefedcba\"\n assert candidate(s = \"thisisnotapalindrome\") == \"emordnilapatonsisihthisisnotapalindrome\"\n assert candidate(s = \"amanaplanacanalsofpnmala\") == \"alamnpfoslanacanalpanamanaplanacanalsofpnmala\"\n assert candidate(s = \"xyzzzzzzzzzzzzzzzzzyx\") == \"xyzzzzzzzzzzzzzzzzzyx\"\n assert candidate(s = \"aeroplaneeplanar\") == \"ranalpeenalporeaeroplaneeplanar\"\n assert candidate(s = \"aaaaabbaaaaa\") == \"aaaaabbaaaaa\"\n assert candidate(s = \"abcdefghijk\") == \"kjihgfedcbabcdefghijk\"\n assert candidate(s = \"abababab\") == \"babababab\"\n assert candidate(s = \"abcdefghihgfedcbaa\") == \"aabcdefghihgfedcbaa\"\n assert candidate(s = \"abacabadabacaba\") == \"abacabadabacaba\"\n assert candidate(s = \"abababa\") == \"abababa\"\n assert candidate(s = \"bananaananab\") == \"bananaananab\"\n assert candidate(s = \"ananabananabana\") == \"anabananabananabana\"\n assert candidate(s = \"rotator\") == \"rotator\"\n assert candidate(s = \"redderredder\") == \"redderredder\"\n assert candidate(s = \"aabbccddeeefffgghhiiijjjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjjiiihhggfffeeeddccbbaabbccddeeefffgghhiiijjjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"xyzabcxyzabc\") == \"cbazyxcbazyxyzabcxyzabc\"\n assert candidate(s = \"world\") == \"dlroworld\"\n assert candidate(s = \"abcbabcba\") == \"abcbabcba\"\n assert candidate(s = \"abcbad\") == \"dabcbad\"\n assert candidate(s = \"aabbccddeeefffhhhiijj\") == \"jjiihhhfffeeeddccbbaabbccddeeefffhhhiijj\"\n assert candidate(s = \"abcdefgh\") == \"hgfedcbabcdefgh\"\n assert candidate(s = \"civiccivic\") == \"civiccivic\"\n assert candidate(s = \"detartrated\") == \"detartrated\"\n assert candidate(s = \"racecarcar\") == \"racracecarcar\"\n assert candidate(s = \"aaabaaa\") == \"aaabaaa\"\n assert candidate(s = \"aabbccddeeff\") == \"ffeeddccbbaabbccddeeff\"\n assert candidate(s = \"reviver\") == \"reviver\"\n assert candidate(s = \"madamimadam\") == \"madamimadam\"\n assert candidate(s = \"aabbccddeeefffhhhiiijjkkll\") == \"llkkjjiiihhhfffeeeddccbbaabbccddeeefffhhhiiijjkkll\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"amanaplanacanalpanama\") == \"amanaplanacanalpanama\"\n assert candidate(s = \"abcdabcba\") == \"abcbadcbabcdabcba\"\n assert candidate(s = \"abcdefg\") == \"gfedcbabcdefg\"\n assert candidate(s = \"aaaabbbbccccdddd\") == \"ddddccccbbbbaaaabbbbccccdddd\"\n assert candidate(s = \"racecarracecar\") == \"racecarracecar\"\n assert candidate(s = \"abbaab\") == \"baabbaab\"\n assert candidate(s = \"deified\") == \"deified\"\n assert candidate(s = \"repaper\") == \"repaper\"\n assert candidate(s = \"abbaabbaabba\") == \"abbaabbaabba\"\n assert candidate(s = \"abcdef\") == \"fedcbabcdef\"\n assert candidate(s = \"zzzzy\") == \"yzzzzy\"\n assert candidate(s = \"abcdedcba\") == \"abcdedcba\"\n assert candidate(s = \"xyzzzzzzzyx\") == \"xyzzzzzzzyx\"\n assert candidate(s = \"bbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\") == \"mnbvcxzlkjhgfdsapoiuytrewqmnbvcxzlkjhgfdsapoiuytrewqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\"\n assert candidate(s = \"repaperandmorepaper\") == \"repaperomdnarepaperandmorepaper\"\n assert candidate(s = \"deifieddeified\") == \"deifieddeified\"\n assert candidate(s = \"abcddcba\") == \"abcddcba\"\n assert candidate(s = \"civic\") == \"civic\"\n assert candidate(s = \"aaaaabaaa\") == \"aaabaaaaabaaa\"\n assert candidate(s = \"abcdefghihgfedcba\") == \"abcdefghihgfedcba\"\n assert candidate(s = \"amanaplanacanalsofpnmalamalamalamalamal\") == \"lamalamalamalamalamnpfoslanacanalpanamanaplanacanalsofpnmalamalamalamalamal\"\n assert candidate(s = \"ababababa\") == \"ababababa\"\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\") == \"godyzalehtrevospmujxofnworbkciuqaquickbrownfoxjumpsoverthelazydog\"\n assert candidate(s = \"reviled\") == \"delivereviled\"\n assert candidate(s = \"levelupandnevergiveuplevelupandnevergiveup\") == \"puevigrevendnapulevelpuevigrevendnapulevelupandnevergiveuplevelupandnevergiveup\"\n assert candidate(s = \"amandaplanacanalpanama\") == \"amanaplanacanalpadnamandaplanacanalpanama\"\n assert candidate(s = \"aabbcc\") == \"ccbbaabbcc\"\n assert candidate(s = \"mississippi\") == \"ippississimississippi\"\n assert candidate(s = \"aeroplane\") == \"enalporeaeroplane\"\n assert candidate(s = \"deed\") == \"deed\"\n assert candidate(s = \"xyxzyzyx\") == \"xyzyzxyxzyzyx\"\n assert candidate(s = \"xyzabc\") == \"cbazyxyzabc\"\n assert candidate(s = \"refer\") == \"refer\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().shortestPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var shortestPalindrome = function(s) {", "container": null, "callable": "shortestPalindrome", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 215, "task_id": "kth-largest-element-in-an-array", "difficulty": "Medium", "problem_description": "Given an integer array nums and an integer k, return the kth largest element in the array.\nNote that it is the kth largest element in the sorted order, not the kth distinct element.\nCan you solve it without sorting?\n \nExample 1:\nInput: nums = [3,2,1,5,6,4], k = 2\nOutput: 5\nExample 2:\nInput: nums = [3,2,3,1,2,4,5,5,6], k = 4\nOutput: 4\n\n \nConstraints:\n\n1 <= k <= nums.length <= 105\n-104 <= nums[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1],k = 5) == 3\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1],k = 3) == 5\n assert candidate(nums = [10000, -10000, 0],k = 2) == 0\n assert candidate(nums = [3, 2, 1, 5, 6, 4],k = 2) == 5\n assert candidate(nums = [-1, -2, -3, -4, -5],k = 2) == -2\n assert candidate(nums = [1],k = 1) == 1\n assert candidate(nums = [3, 2, 3, 1, 2, 4, 5, 5, 6],k = 4) == 4\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981],k = 10) == 9991\n assert candidate(nums = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981],k = 15) == 986\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 20) == 1\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 20) == 1\n assert candidate(nums = [-10000, -9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991],k = 3) == -9993\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],k = 10) == 600\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 20) == 6\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 1) == 100\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10],k = 25) == 4\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],k = 15) == 60\n assert candidate(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 18) == 3\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],k = 10) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 15) == 6\n assert candidate(nums = [9, 1, 8, 2, 7, 3, 6, 4, 5],k = 3) == 7\n assert candidate(nums = [-10000, -10000, -10000, -10000, -10000, -10000, -10000, -10000, -10000, -10000],k = 10) == -10000\n assert candidate(nums = [-10000, 10000, -9999, 9999, -9998, 9998, -9997, 9997, -9996, 9996],k = 5) == 9996\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15],k = 7) == -7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 20) == 11\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],k = 25) == 26\n assert candidate(nums = [9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990],k = 5) == 9995\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 1) == 20\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 5) == 60\n assert candidate(nums = [2, 2, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1],k = 5) == 7\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6],k = 10) == 5\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == 0\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981],k = 15) == 9986\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 10) == -10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 19) == 2\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 15) == 5\n assert candidate(nums = [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000],k = 1) == 10000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == 11\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 5) == -5\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 7) == 27\n assert candidate(nums = [-10000, -9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991, -9990, -9989, -9988, -9987, -9986, -9985, -9984, -9983, -9982, -9981],k = 15) == -9995\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 7) == -7\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],k = 10) == 22\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 17) == 14\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 1) == 5\n assert candidate(nums = [1, 10000, 2, 9999, 3, 9998, 4, 9997, 5, 9996, 6, 9995, 7, 9994, 8, 9993, 9, 9992, 10, 9991],k = 7) == 9994\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],k = 10) == 60\n assert candidate(nums = [25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 18) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20) == 1\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100],k = 12) == -10\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990],k = 10) == 9991\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 14) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 25) == 6\n assert candidate(nums = [10000, 5000, 0, -5000, -10000, 10000, 5000, 0, -5000, -10000, 10000, 5000, 0, -5000, -10000],k = 8) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 15) == 11\n assert candidate(nums = [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000],k = 15) == 10000\n assert candidate(nums = [-10000, -9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991, -9990],k = 8) == -9997\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 10) == -9\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 1) == 1\n assert candidate(nums = [20, 20, 19, 19, 18, 18, 17, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11],k = 18) == 12\n assert candidate(nums = [104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85],k = 15) == 90\n assert candidate(nums = [9, 3, 7, 6, 2, 5, 8, 4, 1, 10],k = 3) == 8\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5],k = 10) == 0\n assert candidate(nums = [1, 3, 2, 6, 4, 5, 8, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 12) == 14\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6],k = 7) == 5\n assert candidate(nums = [50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 30) == 21\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 5) == 5\n assert candidate(nums = [100, 90, 90, 80, 80, 70, 70, 60, 60, 50, 50, 40, 40, 30, 30, 20, 20, 10, 10, 0, 0, -10, -10, -20, -20, -30, -30, -40, -40],k = 18) == 10\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 3) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 8) == 8\n assert candidate(nums = [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000],k = 5) == 10000\n assert candidate(nums = [5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 19) == 1\n assert candidate(nums = [9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981, 9980],k = 10) == 9990\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],k = 20) == 0\n assert candidate(nums = [-10000, -9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991, -9990, -9989, -9988, -9987, -9986, -9985, -9984, -9983, -9982, -9981],k = 10) == -9990\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 3) == 5\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 25) == 5\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 10) == 5\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().findKthLargest", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findKthLargest = function(nums, k) {", "container": null, "callable": "findKthLargest", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 216, "task_id": "combination-sum-iii", "difficulty": "Medium", "problem_description": "Find all valid combinations of k numbers that sum up to n such that the following conditions are true:\n\nOnly numbers 1 through 9 are used.\nEach number is used at most once.\n\nReturn a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order.\n \nExample 1:\n\nInput: k = 3, n = 7\nOutput: [[1,2,4]]\nExplanation:\n1 + 2 + 4 = 7\nThere are no other valid combinations.\nExample 2:\n\nInput: k = 3, n = 9\nOutput: [[1,2,6],[1,3,5],[2,3,4]]\nExplanation:\n1 + 2 + 6 = 9\n1 + 3 + 5 = 9\n2 + 3 + 4 = 9\nThere are no other valid combinations.\n\nExample 3:\n\nInput: k = 4, n = 1\nOutput: []\nExplanation: There are no valid combinations.\nUsing 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 > 1, there are no valid combination.\n\n \nConstraints:\n\n2 <= k <= 9\n1 <= n <= 60\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(k = 7,n = 28) == [[1, 2, 3, 4, 5, 6, 7]]\n assert candidate(k = 5,n = 25) == [[1, 2, 5, 8, 9], [1, 2, 6, 7, 9], [1, 3, 4, 8, 9], [1, 3, 5, 7, 9], [1, 3, 6, 7, 8], [1, 4, 5, 6, 9], [1, 4, 5, 7, 8], [2, 3, 4, 7, 9], [2, 3, 5, 6, 9], [2, 3, 5, 7, 8], [2, 4, 5, 6, 8], [3, 4, 5, 6, 7]]\n assert candidate(k = 5,n = 20) == [[1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 4, 5, 8], [1, 2, 4, 6, 7], [1, 3, 4, 5, 7], [2, 3, 4, 5, 6]]\n assert candidate(k = 7,n = 56) == []\n assert candidate(k = 4,n = 1) == []\n assert candidate(k = 2,n = 15) == [[6, 9], [7, 8]]\n assert candidate(k = 9,n = 45) == [[1, 2, 3, 4, 5, 6, 7, 8, 9]]\n assert candidate(k = 8,n = 84) == []\n assert candidate(k = 3,n = 18) == [[1, 8, 9], [2, 7, 9], [3, 6, 9], [3, 7, 8], [4, 5, 9], [4, 6, 8], [5, 6, 7]]\n assert candidate(k = 3,n = 9) == [[1, 2, 6], [1, 3, 5], [2, 3, 4]]\n assert candidate(k = 7,n = 63) == []\n assert candidate(k = 4,n = 28) == [[4, 7, 8, 9], [5, 6, 8, 9]]\n assert candidate(k = 3,n = 7) == [[1, 2, 4]]\n assert candidate(k = 3,n = 23) == [[6, 8, 9]]\n assert candidate(k = 8,n = 36) == [[1, 2, 3, 4, 5, 6, 7, 8]]\n assert candidate(k = 6,n = 45) == []\n assert candidate(k = 2,n = 18) == []\n assert candidate(k = 5,n = 15) == [[1, 2, 3, 4, 5]]\n assert candidate(k = 8,n = 60) == []\n assert candidate(k = 2,n = 5) == [[1, 4], [2, 3]]\n assert candidate(k = 9,n = 90) == []\n assert candidate(k = 4,n = 17) == [[1, 2, 5, 9], [1, 2, 6, 8], [1, 3, 4, 9], [1, 3, 5, 8], [1, 3, 6, 7], [1, 4, 5, 7], [2, 3, 4, 8], [2, 3, 5, 7], [2, 4, 5, 6]]\n assert candidate(k = 8,n = 72) == []\n assert candidate(k = 3,n = 20) == [[3, 8, 9], [4, 7, 9], [5, 6, 9], [5, 7, 8]]\n assert candidate(k = 7,n = 35) == [[1, 2, 3, 5, 7, 8, 9], [1, 2, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 8]]\n assert candidate(k = 5,n = 23) == [[1, 2, 3, 8, 9], [1, 2, 4, 7, 9], [1, 2, 5, 6, 9], [1, 2, 5, 7, 8], [1, 3, 4, 6, 9], [1, 3, 4, 7, 8], [1, 3, 5, 6, 8], [1, 4, 5, 6, 7], [2, 3, 4, 5, 9], [2, 3, 4, 6, 8], [2, 3, 5, 6, 7]]\n assert candidate(k = 6,n = 25) == [[1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 5, 6, 8], [1, 2, 4, 5, 6, 7]]\n assert candidate(k = 7,n = 21) == []\n assert candidate(k = 7,n = 40) == [[1, 4, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 9]]\n assert candidate(k = 6,n = 30) == [[1, 2, 3, 7, 8, 9], [1, 2, 4, 6, 8, 9], [1, 2, 5, 6, 7, 9], [1, 3, 4, 5, 8, 9], [1, 3, 4, 6, 7, 9], [1, 3, 5, 6, 7, 8], [2, 3, 4, 5, 7, 9], [2, 3, 4, 6, 7, 8]]\n assert candidate(k = 6,n = 35) == [[1, 4, 6, 7, 8, 9], [2, 3, 6, 7, 8, 9], [2, 4, 5, 7, 8, 9], [3, 4, 5, 6, 8, 9]]\n assert candidate(k = 5,n = 33) == [[3, 6, 7, 8, 9], [4, 5, 7, 8, 9]]\n assert candidate(k = 4,n = 14) == [[1, 2, 3, 8], [1, 2, 4, 7], [1, 2, 5, 6], [1, 3, 4, 6], [2, 3, 4, 5]]\n assert candidate(k = 7,n = 29) == [[1, 2, 3, 4, 5, 6, 8]]\n assert candidate(k = 6,n = 42) == []\n assert candidate(k = 5,n = 18) == [[1, 2, 3, 4, 8], [1, 2, 3, 5, 7], [1, 2, 4, 5, 6]]\n assert candidate(k = 4,n = 22) == [[1, 4, 8, 9], [1, 5, 7, 9], [1, 6, 7, 8], [2, 3, 8, 9], [2, 4, 7, 9], [2, 5, 6, 9], [2, 5, 7, 8], [3, 4, 6, 9], [3, 4, 7, 8], [3, 5, 6, 8], [4, 5, 6, 7]]\n assert candidate(k = 6,n = 24) == [[1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 6, 8], [1, 2, 3, 5, 6, 7]]\n assert candidate(k = 7,n = 42) == [[3, 4, 5, 6, 7, 8, 9]]\n assert candidate(k = 4,n = 10) == [[1, 2, 3, 4]]\n assert candidate(k = 5,n = 17) == [[1, 2, 3, 4, 7], [1, 2, 3, 5, 6]]\n assert candidate(k = 3,n = 10) == [[1, 2, 7], [1, 3, 6], [1, 4, 5], [2, 3, 5]]\n assert candidate(k = 3,n = 17) == [[1, 7, 9], [2, 6, 9], [2, 7, 8], [3, 5, 9], [3, 6, 8], [4, 5, 8], [4, 6, 7]]\n assert candidate(k = 4,n = 20) == [[1, 2, 8, 9], [1, 3, 7, 9], [1, 4, 6, 9], [1, 4, 7, 8], [1, 5, 6, 8], [2, 3, 6, 9], [2, 3, 7, 8], [2, 4, 5, 9], [2, 4, 6, 8], [2, 5, 6, 7], [3, 4, 5, 8], [3, 4, 6, 7]]\n assert candidate(k = 5,n = 30) == [[1, 5, 7, 8, 9], [2, 4, 7, 8, 9], [2, 5, 6, 8, 9], [3, 4, 6, 8, 9], [3, 5, 6, 7, 9], [4, 5, 6, 7, 8]]\n assert candidate(k = 5,n = 10) == []\n assert candidate(k = 6,n = 39) == [[4, 5, 6, 7, 8, 9]]\n assert candidate(k = 4,n = 30) == [[6, 7, 8, 9]]\n assert candidate(k = 4,n = 15) == [[1, 2, 3, 9], [1, 2, 4, 8], [1, 2, 5, 7], [1, 3, 4, 7], [1, 3, 5, 6], [2, 3, 4, 6]]\n assert candidate(k = 6,n = 40) == []\n assert candidate(k = 4,n = 23) == [[1, 5, 8, 9], [1, 6, 7, 9], [2, 4, 8, 9], [2, 5, 7, 9], [2, 6, 7, 8], [3, 4, 7, 9], [3, 5, 6, 9], [3, 5, 7, 8], [4, 5, 6, 8]]\n assert candidate(k = 4,n = 25) == [[1, 7, 8, 9], [2, 6, 8, 9], [3, 5, 8, 9], [3, 6, 7, 9], [4, 5, 7, 9], [4, 6, 7, 8]]\n assert candidate(k = 8,n = 81) == []\n assert candidate(k = 5,n = 35) == [[5, 6, 7, 8, 9]]\n assert candidate(k = 2,n = 16) == [[7, 9]]\n assert candidate(k = 6,n = 55) == []\n assert candidate(k = 8,n = 30) == []\n assert candidate(k = 6,n = 18) == []\n assert candidate(k = 3,n = 15) == [[1, 5, 9], [1, 6, 8], [2, 4, 9], [2, 5, 8], [2, 6, 7], [3, 4, 8], [3, 5, 7], [4, 5, 6]]\n assert candidate(k = 4,n = 12) == [[1, 2, 3, 6], [1, 2, 4, 5]]\n assert candidate(k = 7,n = 49) == []\n assert candidate(k = 7,n = 30) == [[1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 7, 8]]\n"}, "metadata": {"canonical_parameter_names": ["k", "n"], "leetcode_dataset_entry_point": "Solution().combinationSum3", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var combinationSum3 = function(k, n) {", "container": null, "callable": "combinationSum3", "parameters": [{"name": "k", "type": "number"}, {"name": "n", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 217, "task_id": "contains-duplicate", "difficulty": "Easy", "problem_description": "Given an integer array nums, return true if any value appears at least twice in the array, and return false if every element is distinct.\n \nExample 1:\n\nInput: nums = [1,2,3,1]\nOutput: true\nExplanation:\nThe element 1 occurs at the indices 0 and 3.\n\nExample 2:\n\nInput: nums = [1,2,3,4]\nOutput: false\nExplanation:\nAll elements are distinct.\n\nExample 3:\n\nInput: nums = [1,1,1,3,3,4,3,2,4,2]\nOutput: true\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-109 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1]) == False\n assert candidate(nums = [1, 2, 3, 1]) == True\n assert candidate(nums = [1, 1, 1, 3, 3, 4, 3, 2, 4, 2]) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(nums = [1, 2, 3, 4]) == False\n assert candidate(nums = [1, 2]) == False\n assert candidate(nums = [5, 7, 8, 9, 5]) == True\n assert candidate(nums = [0]) == False\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000]) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0]) == True\n assert candidate(nums = [-1, 0, 1, 2]) == False\n assert candidate(nums = [-1, 0, 1, 2, 3, -1]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == True\n assert candidate(nums = [5, 7, 8, 9, 10, 1]) == False\n assert candidate(nums = [1000000000, -1000000000, 1000000000]) == True\n assert candidate(nums = [-1, 0, 1, 2, -1]) == True\n assert candidate(nums = [-2147483648, -2147483647, 2147483647, 2147483646, 0, 0, 1, -1, 2, -2]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == True\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000, 600000000, 700000000, 800000000, 900000000, 100000000]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20]) == True\n assert candidate(nums = [1000000000, -1000000000, 2000000000, -2000000000, 1000000000]) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 1000000000]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == False\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1]) == True\n assert candidate(nums = [987654321, 987654322, 987654323, 987654321]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50]) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50]) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100]) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100]) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30]) == True\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 0]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -1]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 100]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 1]) == True\n assert candidate(nums = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [999999999, -999999999, 999999998, -999999998, 999999997, -999999997, 999999996, -999999996, 999999995, -999999995, 999999999]) == True\n assert candidate(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0]) == True\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 1]) == True\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 5]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20]) == True\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 0]) == True\n assert candidate(nums = [-2147483648, 2147483647, 0, -1, 1, -2147483648]) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 0]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 0]) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1]) == True\n assert candidate(nums = [1000000000, -1000000000, 500000000, 500000000]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 1]) == True\n assert candidate(nums = [999999999, -999999999, 999999999, -999999999, 999999999, -999999999, 999999999, -999999999, 999999999, -999999999]) == True\n assert candidate(nums = [987654321, 987654322, 987654323, 987654324, 987654325, 987654321]) == True\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999990]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1]) == True\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1]) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 0]) == True\n assert candidate(nums = [-999999999, -999999998, -999999997, -999999996, -999999995, -999999994, -999999993, -999999992, -999999991, -999999990, -999999999]) == True\n assert candidate(nums = [-1000000000, -999999999, -999999998, -999999997, -999999996, -999999995, -999999994, -999999993, -999999992, -999999991, -999999990, -999999989, -999999988, -999999987, -999999986, -999999985, -999999984, -999999983, -999999982, -999999981, -999999980, -999999979, -999999978, -999999977, -999999976, -999999975, -999999974, -999999973, -999999972, -999999971, -999999970, -999999969, -999999968, -999999967, -999999966, -999999965, -999999964, -999999963, -999999962, -999999961, -999999960, -999999959, -999999958, -999999957, -999999956, -999999955, -999999954, -999999953, -999999952, -999999951, -999999950, -999999949, -999999948, -999999947, -999999946, -999999945, -999999944, -999999943, -999999942, -999999941, -999999940, -999999939, -999999938, -999999937, -999999936, -999999935, -999999934, -999999933, -999999932, -999999931, -999999930, -999999929, -999999928, -999999927, -999999926, -999999925, -999999924, -999999923, -999999922, -999999921, -999999920, -999999919, -999999918, -999999917, -999999916, -999999915, -999999914, -999999913, -999999912, -999999911, -999999910, -999999909, -999999908, -999999907, -999999906, -999999905, -999999904, -999999903, -999999902, -999999901, -999999900, -1000000000]) == True\n assert candidate(nums = [987654321, 876543210, 765432109, 654321098, 543210987, 432109876, 321098765, 210987654, 109876543, 987654321]) == True\n assert candidate(nums = [-1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, 9]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9]) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 1]) == True\n assert candidate(nums = [5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 11, 11]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == False\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999999]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, 500000000, -500000000, 500000000]) == True\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000, 600000000, 700000000, 800000000, 900000000, 100000000]) == True\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().containsDuplicate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var containsDuplicate = function(nums) {", "container": null, "callable": "containsDuplicate", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 218, "task_id": "the-skyline-problem", "difficulty": "Hard", "problem_description": "A city's skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return the skyline formed by these buildings collectively.\nThe geometric information of each building is given in the array buildings where buildings[i] = [lefti, righti, heighti]:\n\nlefti is the x coordinate of the left edge of the ith building.\nrighti is the x coordinate of the right edge of the ith building.\nheighti is the height of the ith building.\n\nYou may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0.\nThe skyline should be represented as a list of \"key points\" sorted by their x-coordinate in the form [[x1,y1],[x2,y2],...]. Each key point is the left endpoint of some horizontal segment in the skyline except the last point in the list, which always has a y-coordinate 0 and is used to mark the skyline's termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline's contour.\nNote: There must be no consecutive horizontal lines of equal height in the output skyline. For instance, [...,[2 3],[4 5],[7 5],[11 5],[12 7],...] is not acceptable; the three lines of height 5 should be merged into one in the final output as such: [...,[2 3],[4 5],[12 7],...]\n \nExample 1:\n\n\nInput: buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]\nOutput: [[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]\nExplanation:\nFigure A shows the buildings of the input.\nFigure B shows the skyline formed by those buildings. The red points in figure B represent the key points in the output list.\n\nExample 2:\n\nInput: buildings = [[0,2,3],[2,5,3]]\nOutput: [[0,3],[5,0]]\n\n \nConstraints:\n\n1 <= buildings.length <= 104\n0 <= lefti < righti <= 231 - 1\n1 <= heighti <= 231 - 1\nbuildings is sorted by lefti in non-decreasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(buildings = [[0, 5, 7], [5, 10, 3], [5, 10, 12], [10, 15, 15], [15, 20, 10], [15, 20, 10], [20, 25, 10]]) == [[0, 7], [5, 12], [10, 15], [15, 10], [25, 0]]\n assert candidate(buildings = [[1, 2, 1], [1, 2, 2], [1, 2, 3]]) == [[1, 3], [2, 0]]\n assert candidate(buildings = [[0, 3, 3], [1, 5, 3], [2, 4, 3]]) == [[0, 3], [5, 0]]\n assert candidate(buildings = [[1, 1000000000, 1]]) == [[1, 1], [1000000000, 0]]\n assert candidate(buildings = [[0, 5, 7], [5, 10, 3], [5, 8, 12], [10, 15, 5]]) == [[0, 7], [5, 12], [8, 3], [10, 5], [15, 0]]\n assert candidate(buildings = [[0, 1, 3], [1, 2, 3], [2, 3, 3]]) == [[0, 3], [3, 0]]\n assert candidate(buildings = [[1, 5, 3], [1, 5, 3], [1, 5, 3]]) == [[1, 3], [5, 0]]\n assert candidate(buildings = [[1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4], [5, 6, 5]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 0]]\n assert candidate(buildings = [[1, 4, 10], [2, 3, 15]]) == [[1, 10], [2, 15], [3, 10], [4, 0]]\n assert candidate(buildings = [[1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 0]]\n assert candidate(buildings = [[2, 9, 10], [3, 7, 15], [5, 12, 12], [15, 20, 10], [19, 24, 8]]) == [[2, 10], [3, 15], [7, 12], [12, 0], [15, 10], [20, 8], [24, 0]]\n assert candidate(buildings = [[0, 2, 3], [2, 5, 3]]) == [[0, 3], [5, 0]]\n assert candidate(buildings = [[1, 5, 20], [2, 6, 30], [3, 7, 20], [4, 8, 10], [5, 9, 5]]) == [[1, 20], [2, 30], [6, 20], [7, 10], [8, 5], [9, 0]]\n assert candidate(buildings = [[10, 20, 50], [15, 30, 40], [25, 40, 60], [35, 50, 55], [45, 60, 45], [55, 70, 65], [65, 80, 50]]) == [[10, 50], [20, 40], [25, 60], [40, 55], [50, 45], [55, 65], [70, 50], [80, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 10, 20], [3, 10, 30], [4, 10, 40], [5, 10, 50], [6, 10, 60], [7, 10, 70], [8, 10, 80], [9, 10, 90]]) == [[1, 10], [2, 20], [3, 30], [4, 40], [5, 50], [6, 60], [7, 70], [8, 80], [9, 90], [10, 0]]\n assert candidate(buildings = [[1, 2, 10], [2, 3, 10], [3, 4, 10], [4, 5, 10], [5, 6, 10], [6, 7, 10], [7, 8, 10]]) == [[1, 10], [8, 0]]\n assert candidate(buildings = [[1, 10, 100], [5, 15, 200], [10, 20, 150], [15, 25, 100], [20, 30, 50]]) == [[1, 100], [5, 200], [15, 150], [20, 100], [25, 50], [30, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 9, 9], [3, 8, 8], [4, 7, 7], [5, 6, 6], [6, 5, 5], [7, 4, 4], [8, 3, 3], [9, 2, 2], [10, 1, 1]]) == [[1, 10], [10, 0]]\n assert candidate(buildings = [[1, 100, 1], [2, 99, 2], [3, 98, 3], [4, 97, 4], [5, 96, 5], [6, 95, 6], [7, 94, 7], [8, 93, 8], [9, 92, 9], [10, 91, 10]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [91, 9], [92, 8], [93, 7], [94, 6], [95, 5], [96, 4], [97, 3], [98, 2], [99, 1], [100, 0]]\n assert candidate(buildings = [[1, 10, 100], [5, 15, 50], [10, 20, 20], [15, 25, 10], [20, 30, 5]]) == [[1, 100], [10, 50], [15, 20], [20, 10], [25, 5], [30, 0]]\n assert candidate(buildings = [[1, 15, 10], [3, 7, 15], [5, 10, 12], [8, 20, 8], [12, 25, 10]]) == [[1, 10], [3, 15], [7, 12], [10, 10], [25, 0]]\n assert candidate(buildings = [[1, 100, 10], [10, 90, 15], [20, 80, 12], [30, 70, 14], [40, 60, 10], [50, 50, 20], [60, 40, 15], [70, 30, 10]]) == [[1, 10], [10, 15], [90, 10], [100, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 5, 15], [3, 7, 12], [4, 9, 14], [5, 11, 10], [6, 12, 15], [7, 13, 10]]) == [[1, 10], [2, 15], [5, 14], [6, 15], [12, 10], [13, 0]]\n assert candidate(buildings = [[1, 1000000000, 10], [200000000, 800000000, 15], [300000000, 700000000, 12], [400000000, 600000000, 8], [500000000, 550000000, 9], [600000000, 650000000, 10]]) == [[1, 10], [200000000, 15], [800000000, 10], [1000000000, 0]]\n assert candidate(buildings = [[1, 5, 1], [5, 10, 2], [10, 15, 3], [15, 20, 4], [20, 25, 5], [25, 30, 6]]) == [[1, 1], [5, 2], [10, 3], [15, 4], [20, 5], [25, 6], [30, 0]]\n assert candidate(buildings = [[1, 2, 10], [2, 3, 15], [3, 4, 12], [4, 5, 8], [5, 6, 9], [6, 7, 10], [7, 8, 8], [8, 9, 9], [9, 10, 10]]) == [[1, 10], [2, 15], [3, 12], [4, 8], [5, 9], [6, 10], [7, 8], [8, 9], [9, 10], [10, 0]]\n assert candidate(buildings = [[1, 3, 50], [3, 6, 20], [6, 9, 70], [9, 12, 30], [12, 15, 60]]) == [[1, 50], [3, 20], [6, 70], [9, 30], [12, 60], [15, 0]]\n assert candidate(buildings = [[1, 100, 1], [10, 90, 2], [20, 80, 3], [30, 70, 4], [40, 60, 5], [50, 50, 6], [60, 40, 7], [70, 30, 8], [80, 20, 9], [90, 10, 10]]) == [[1, 1], [10, 2], [20, 3], [30, 4], [40, 5], [60, 4], [70, 3], [80, 2], [90, 1], [100, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 9, 15], [3, 8, 12], [4, 7, 14], [5, 6, 10], [6, 5, 15], [7, 4, 10]]) == [[1, 10], [2, 15], [9, 10], [10, 0]]\n assert candidate(buildings = [[1, 3, 10], [2, 6, 15], [3, 5, 20], [4, 7, 15], [5, 8, 10], [6, 9, 5]]) == [[1, 10], [2, 15], [3, 20], [5, 15], [7, 10], [8, 5], [9, 0]]\n assert candidate(buildings = [[1, 100, 100], [10, 90, 90], [20, 80, 80], [30, 70, 70], [40, 60, 60], [50, 50, 50], [60, 40, 40], [70, 30, 30], [80, 20, 20], [90, 10, 10]]) == [[1, 100], [100, 0]]\n assert candidate(buildings = [[1, 10, 5], [2, 8, 4], [3, 7, 3], [4, 6, 2], [5, 5, 1]]) == [[1, 5], [10, 0]]\n assert candidate(buildings = [[1, 2, 1], [1, 3, 2], [1, 4, 3], [1, 5, 4], [1, 6, 5], [1, 7, 6], [1, 8, 7], [1, 9, 8], [1, 10, 9]]) == [[1, 9], [10, 0]]\n assert candidate(buildings = [[1, 2, 1], [3, 4, 2], [5, 6, 3], [7, 8, 4], [9, 10, 5], [11, 12, 6], [13, 14, 7], [15, 16, 8], [17, 18, 9], [19, 20, 10], [21, 22, 11]]) == [[1, 1], [2, 0], [3, 2], [4, 0], [5, 3], [6, 0], [7, 4], [8, 0], [9, 5], [10, 0], [11, 6], [12, 0], [13, 7], [14, 0], [15, 8], [16, 0], [17, 9], [18, 0], [19, 10], [20, 0], [21, 11], [22, 0]]\n assert candidate(buildings = [[1, 5, 10], [2, 3, 15], [3, 4, 10], [4, 6, 15], [5, 7, 10], [6, 8, 15], [7, 9, 10]]) == [[1, 10], [2, 15], [3, 10], [4, 15], [8, 10], [9, 0]]\n assert candidate(buildings = [[1, 100, 10], [20, 80, 15], [30, 70, 12], [40, 60, 8], [50, 55, 9], [60, 65, 10]]) == [[1, 10], [20, 15], [80, 10], [100, 0]]\n assert candidate(buildings = [[1, 10, 100], [10, 20, 90], [20, 30, 80], [30, 40, 70], [40, 50, 60], [50, 60, 50], [60, 70, 40], [70, 80, 30], [80, 90, 20], [90, 100, 10]]) == [[1, 100], [10, 90], [20, 80], [30, 70], [40, 60], [50, 50], [60, 40], [70, 30], [80, 20], [90, 10], [100, 0]]\n assert candidate(buildings = [[0, 2, 3], [2, 4, 3], [4, 6, 3], [6, 8, 3], [8, 10, 3]]) == [[0, 3], [10, 0]]\n assert candidate(buildings = [[1, 10, 10], [10, 20, 20], [20, 30, 30], [30, 40, 40], [40, 50, 50], [50, 60, 60], [60, 70, 70], [70, 80, 80], [80, 90, 90], [90, 100, 100]]) == [[1, 10], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [100, 0]]\n assert candidate(buildings = [[0, 10, 10], [1, 3, 20], [5, 7, 15], [6, 9, 25], [8, 12, 5]]) == [[0, 10], [1, 20], [3, 10], [5, 15], [6, 25], [9, 10], [10, 5], [12, 0]]\n assert candidate(buildings = [[1, 2000000000, 1000000000], [200000000, 300000000, 2000000000], [500000000, 800000000, 1200000000], [600000000, 1200000000, 1400000000], [1500000000, 2000000000, 1000000000], [1900000000, 2400000000, 800000000]]) == [[1, 1000000000], [200000000, 2000000000], [300000000, 1000000000], [500000000, 1200000000], [600000000, 1400000000], [1200000000, 1000000000], [2000000000, 800000000], [2400000000, 0]]\n assert candidate(buildings = [[1, 10, 5], [2, 9, 8], [3, 8, 7], [4, 7, 6], [5, 6, 10]]) == [[1, 5], [2, 8], [5, 10], [6, 8], [9, 5], [10, 0]]\n assert candidate(buildings = [[0, 10, 10], [5, 15, 15], [10, 20, 12], [15, 25, 8], [20, 30, 9]]) == [[0, 10], [5, 15], [15, 12], [20, 9], [30, 0]]\n assert candidate(buildings = [[1, 50, 10], [5, 45, 20], [10, 40, 30], [15, 35, 40], [20, 30, 50], [25, 25, 60], [30, 20, 50], [35, 15, 40], [40, 10, 30], [45, 5, 20], [50, 1, 10]]) == [[1, 10], [5, 20], [10, 30], [15, 40], [20, 50], [30, 40], [35, 30], [40, 20], [45, 10], [50, 0]]\n assert candidate(buildings = [[1, 3, 10], [2, 5, 15], [3, 7, 12], [4, 8, 8], [5, 9, 9], [6, 10, 10]]) == [[1, 10], [2, 15], [5, 12], [7, 10], [10, 0]]\n assert candidate(buildings = [[1, 3, 10], [1, 3, 15], [1, 3, 12], [1, 3, 8], [1, 3, 9], [1, 3, 10]]) == [[1, 15], [3, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 9, 15], [3, 8, 20], [4, 7, 25], [5, 6, 30]]) == [[1, 10], [2, 15], [3, 20], [4, 25], [5, 30], [6, 25], [7, 20], [8, 15], [9, 10], [10, 0]]\n assert candidate(buildings = [[0, 5, 10], [5, 15, 15], [10, 20, 10], [15, 25, 8], [20, 25, 12]]) == [[0, 10], [5, 15], [15, 10], [20, 12], [25, 0]]\n assert candidate(buildings = [[10, 15, 100], [15, 20, 200], [20, 25, 300], [25, 30, 400], [30, 35, 500], [35, 40, 600], [40, 45, 700], [45, 50, 800], [50, 55, 900]]) == [[10, 100], [15, 200], [20, 300], [25, 400], [30, 500], [35, 600], [40, 700], [45, 800], [50, 900], [55, 0]]\n assert candidate(buildings = [[1, 100, 10], [2, 99, 20], [3, 98, 30], [4, 97, 40], [5, 96, 50]]) == [[1, 10], [2, 20], [3, 30], [4, 40], [5, 50], [96, 40], [97, 30], [98, 20], [99, 10], [100, 0]]\n assert candidate(buildings = [[1, 3, 10], [2, 5, 20], [3, 6, 15], [4, 7, 30], [5, 8, 25]]) == [[1, 10], [2, 20], [4, 30], [7, 25], [8, 0]]\n assert candidate(buildings = [[1, 10, 10], [5, 15, 15], [10, 20, 20], [15, 25, 10], [20, 30, 5], [25, 35, 3]]) == [[1, 10], [5, 15], [10, 20], [20, 10], [25, 5], [30, 3], [35, 0]]\n assert candidate(buildings = [[1, 3, 300], [2, 4, 200], [3, 5, 100], [4, 6, 50], [5, 7, 25], [6, 8, 12], [7, 9, 5]]) == [[1, 300], [3, 200], [4, 100], [5, 50], [6, 25], [7, 12], [8, 5], [9, 0]]\n assert candidate(buildings = [[1, 100, 50], [25, 75, 75], [50, 100, 100], [75, 125, 25], [100, 150, 50]]) == [[1, 50], [25, 75], [50, 100], [100, 50], [150, 0]]\n assert candidate(buildings = [[1, 4, 10], [2, 3, 15], [3, 6, 12], [4, 7, 14], [5, 8, 10], [6, 9, 15], [7, 10, 10]]) == [[1, 10], [2, 15], [3, 12], [4, 14], [6, 15], [9, 10], [10, 0]]\n assert candidate(buildings = [[1, 4, 10], [2, 6, 15], [3, 5, 9], [4, 7, 12], [5, 8, 8], [6, 9, 10]]) == [[1, 10], [2, 15], [6, 12], [7, 10], [9, 0]]\n assert candidate(buildings = [[1, 5, 3], [1, 5, 4], [1, 5, 5], [1, 5, 6], [1, 5, 7]]) == [[1, 7], [5, 0]]\n assert candidate(buildings = [[1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 6], [5, 6, 7], [6, 7, 8], [7, 8, 9], [8, 9, 10]]) == [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 0]]\n assert candidate(buildings = [[0, 2, 3], [1, 3, 5], [2, 5, 2], [3, 7, 4], [4, 6, 6], [5, 8, 1], [6, 9, 3], [7, 10, 5]]) == [[0, 3], [1, 5], [3, 4], [4, 6], [6, 4], [7, 5], [10, 0]]\n assert candidate(buildings = [[1, 10, 100], [2, 9, 90], [3, 8, 80], [4, 7, 70], [5, 6, 60], [6, 5, 50], [7, 4, 40], [8, 3, 30], [9, 2, 20], [10, 1, 10]]) == [[1, 100], [10, 0]]\n assert candidate(buildings = [[1, 5, 10], [1, 5, 15], [1, 5, 20], [2, 4, 25], [2, 4, 30], [2, 4, 35], [3, 3, 40], [3, 3, 45], [3, 3, 50], [4, 2, 55], [4, 2, 60]]) == [[1, 20], [2, 35], [4, 20], [5, 0]]\n assert candidate(buildings = [[1, 5, 10], [2, 4, 15], [3, 8, 12], [4, 7, 8], [5, 6, 9]]) == [[1, 10], [2, 15], [4, 12], [8, 0]]\n assert candidate(buildings = [[1, 10, 100], [1, 5, 50], [1, 3, 30], [3, 7, 70], [5, 9, 90], [7, 11, 50]]) == [[1, 100], [10, 50], [11, 0]]\n assert candidate(buildings = [[1, 20, 10], [3, 10, 15], [5, 8, 12], [6, 12, 14], [15, 20, 10], [19, 24, 8]]) == [[1, 10], [3, 15], [10, 14], [12, 10], [20, 8], [24, 0]]\n assert candidate(buildings = [[1, 20, 10], [5, 15, 20], [10, 25, 30], [15, 35, 40], [20, 45, 50], [25, 55, 60], [30, 65, 70], [35, 75, 80]]) == [[1, 10], [5, 20], [10, 30], [15, 40], [20, 50], [25, 60], [30, 70], [35, 80], [75, 0]]\n assert candidate(buildings = [[1, 5, 10], [1, 5, 20], [1, 5, 30], [2, 4, 40], [2, 4, 50], [3, 3, 60]]) == [[1, 30], [2, 50], [4, 30], [5, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 9, 15], [3, 8, 20], [4, 7, 25], [5, 6, 30], [6, 5, 25], [7, 4, 20], [8, 3, 15], [9, 2, 10]]) == [[1, 10], [2, 15], [3, 20], [4, 25], [5, 30], [6, 25], [7, 20], [8, 15], [9, 10], [10, 0]]\n assert candidate(buildings = [[1, 10, 5], [2, 8, 7], [3, 6, 9], [4, 5, 12], [5, 7, 10]]) == [[1, 5], [2, 7], [3, 9], [4, 12], [5, 10], [7, 7], [8, 5], [10, 0]]\n assert candidate(buildings = [[1, 3, 30], [3, 5, 20], [5, 7, 30], [7, 9, 20], [9, 11, 30]]) == [[1, 30], [3, 20], [5, 30], [7, 20], [9, 30], [11, 0]]\n assert candidate(buildings = [[1, 2, 1000000000], [2, 3, 999999999], [3, 4, 999999998], [4, 5, 999999997]]) == [[1, 1000000000], [2, 999999999], [3, 999999998], [4, 999999997], [5, 0]]\n assert candidate(buildings = [[1, 1000000000, 100], [500000000, 1500000000, 200], [1000000000, 2000000000, 300]]) == [[1, 100], [500000000, 200], [1000000000, 300], [2000000000, 0]]\n assert candidate(buildings = [[1, 5, 10], [3, 8, 15], [7, 12, 20], [10, 15, 10], [13, 18, 15]]) == [[1, 10], [3, 15], [7, 20], [12, 10], [13, 15], [18, 0]]\n assert candidate(buildings = [[1, 2, 3], [2, 3, 6], [3, 4, 9], [4, 5, 12], [5, 6, 15], [6, 7, 18], [7, 8, 21], [8, 9, 24], [9, 10, 27]]) == [[1, 3], [2, 6], [3, 9], [4, 12], [5, 15], [6, 18], [7, 21], [8, 24], [9, 27], [10, 0]]\n assert candidate(buildings = [[1, 2, 1], [2, 3, 2], [3, 4, 3], [4, 5, 4], [5, 6, 5], [6, 7, 6], [7, 8, 7], [8, 9, 8]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 0]]\n assert candidate(buildings = [[1, 4, 10], [1, 4, 20], [2, 3, 30], [2, 3, 40], [3, 4, 50]]) == [[1, 20], [2, 40], [3, 50], [4, 0]]\n assert candidate(buildings = [[1, 5, 5], [1, 5, 3], [1, 5, 10], [2, 4, 15], [2, 4, 20], [2, 4, 5], [3, 3, 25]]) == [[1, 10], [2, 20], [4, 10], [5, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 9, 20], [3, 8, 30], [4, 7, 40], [5, 6, 50], [6, 5, 60]]) == [[1, 10], [2, 20], [3, 30], [4, 40], [5, 50], [6, 40], [7, 30], [8, 20], [9, 10], [10, 0]]\n assert candidate(buildings = [[1, 10, 5], [2, 6, 7], [3, 15, 8], [4, 12, 12], [5, 9, 10], [6, 14, 9], [7, 13, 11], [8, 11, 13]]) == [[1, 5], [2, 7], [3, 8], [4, 12], [8, 13], [11, 12], [12, 11], [13, 9], [14, 8], [15, 0]]\n assert candidate(buildings = [[1, 5, 1], [2, 4, 2], [3, 6, 3], [4, 7, 4], [5, 8, 5], [6, 9, 6], [7, 10, 7], [8, 11, 8], [9, 12, 9], [10, 13, 10]]) == [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [13, 0]]\n assert candidate(buildings = [[10, 20, 10], [15, 25, 20], [20, 30, 15], [25, 35, 25], [30, 40, 10], [35, 45, 5]]) == [[10, 10], [15, 20], [25, 25], [35, 10], [40, 5], [45, 0]]\n assert candidate(buildings = [[1, 20, 10], [5, 15, 20], [10, 25, 30], [15, 30, 40], [20, 35, 50], [25, 40, 60], [30, 45, 70], [35, 50, 80], [40, 55, 90]]) == [[1, 10], [5, 20], [10, 30], [15, 40], [20, 50], [25, 60], [30, 70], [35, 80], [40, 90], [55, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 5, 15], [3, 7, 20], [5, 15, 10], [10, 20, 8]]) == [[1, 10], [2, 15], [3, 20], [7, 10], [15, 8], [20, 0]]\n assert candidate(buildings = [[1, 2, 100], [2, 3, 90], [3, 4, 80], [4, 5, 70], [5, 6, 60], [6, 7, 50], [7, 8, 40], [8, 9, 30], [9, 10, 20], [10, 11, 10]]) == [[1, 100], [2, 90], [3, 80], [4, 70], [5, 60], [6, 50], [7, 40], [8, 30], [9, 20], [10, 10], [11, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 8, 15], [3, 7, 12], [4, 9, 20], [5, 6, 25], [7, 11, 30], [9, 12, 20]]) == [[1, 10], [2, 15], [4, 20], [5, 25], [6, 20], [7, 30], [11, 20], [12, 0]]\n assert candidate(buildings = [[1, 2, 10], [2, 3, 10], [3, 4, 10], [4, 5, 10], [5, 6, 10], [6, 7, 10], [7, 8, 10], [8, 9, 10]]) == [[1, 10], [9, 0]]\n assert candidate(buildings = [[1, 10, 100], [5, 15, 150], [10, 20, 100], [15, 25, 200], [20, 30, 150]]) == [[1, 100], [5, 150], [15, 200], [25, 150], [30, 0]]\n assert candidate(buildings = [[1, 3, 5], [2, 4, 10], [3, 5, 15], [4, 6, 20], [5, 7, 25], [6, 8, 30]]) == [[1, 5], [2, 10], [3, 15], [4, 20], [5, 25], [6, 30], [8, 0]]\n assert candidate(buildings = [[1, 10, 10], [2, 3, 15], [3, 7, 12], [8, 15, 8], [12, 20, 10]]) == [[1, 10], [2, 15], [3, 12], [7, 10], [10, 8], [12, 10], [20, 0]]\n assert candidate(buildings = [[1, 3, 10], [4, 7, 20], [8, 10, 15], [12, 14, 30], [16, 19, 25]]) == [[1, 10], [3, 0], [4, 20], [7, 0], [8, 15], [10, 0], [12, 30], [14, 0], [16, 25], [19, 0]]\n assert candidate(buildings = [[1, 2, 10], [2, 3, 20], [3, 4, 30], [4, 5, 40], [5, 6, 50], [6, 7, 60], [7, 8, 70], [8, 9, 80], [9, 10, 90], [10, 11, 100], [11, 12, 110], [12, 13, 120]]) == [[1, 10], [2, 20], [3, 30], [4, 40], [5, 50], [6, 60], [7, 70], [8, 80], [9, 90], [10, 100], [11, 110], [12, 120], [13, 0]]\n assert candidate(buildings = [[10, 20, 5], [15, 30, 10], [25, 40, 20], [35, 50, 25], [45, 60, 15], [55, 70, 10]]) == [[10, 5], [15, 10], [25, 20], [35, 25], [50, 15], [60, 10], [70, 0]]\n assert candidate(buildings = [[1, 10, 100], [2, 9, 150], [3, 8, 200], [4, 7, 250], [5, 6, 300], [6, 5, 350], [7, 4, 400], [8, 3, 450], [9, 2, 500], [10, 1, 550]]) == [[1, 100], [2, 150], [3, 200], [4, 250], [5, 300], [6, 250], [7, 200], [8, 150], [9, 100], [10, 0]]\n assert candidate(buildings = [[1, 5, 10], [2, 4, 20], [3, 3, 30], [4, 5, 40], [5, 6, 50], [6, 7, 60], [7, 8, 70], [8, 9, 80], [9, 10, 90], [10, 11, 100]]) == [[1, 10], [2, 20], [4, 40], [5, 50], [6, 60], [7, 70], [8, 80], [9, 90], [10, 100], [11, 0]]\n assert candidate(buildings = [[1, 3, 10], [2, 5, 15], [3, 6, 20], [4, 7, 25], [5, 8, 30], [6, 9, 35], [7, 10, 40]]) == [[1, 10], [2, 15], [3, 20], [4, 25], [5, 30], [6, 35], [7, 40], [10, 0]]\n assert candidate(buildings = [[10, 20, 100], [15, 30, 80], [20, 40, 60], [25, 50, 40], [30, 60, 20]]) == [[10, 100], [20, 80], [30, 60], [40, 40], [50, 20], [60, 0]]\n assert candidate(buildings = [[1, 2, 300], [2, 4, 200], [4, 5, 100], [5, 7, 50], [7, 9, 25], [9, 10, 10], [10, 12, 5], [12, 14, 3], [14, 16, 2], [16, 18, 1], [18, 20, 0]]) == [[1, 300], [2, 200], [4, 100], [5, 50], [7, 25], [9, 10], [10, 5], [12, 3], [14, 2], [16, 1], [18, 0]]\n assert candidate(buildings = [[1, 2, 10], [2, 3, 15], [3, 4, 10], [4, 5, 20], [5, 6, 25], [6, 7, 20], [7, 8, 15], [8, 9, 10]]) == [[1, 10], [2, 15], [3, 10], [4, 20], [5, 25], [6, 20], [7, 15], [8, 10], [9, 0]]\n assert candidate(buildings = [[1, 4, 100], [2, 6, 200], [3, 9, 150], [4, 12, 100], [5, 14, 50], [6, 16, 25], [7, 18, 10], [8, 20, 5], [9, 22, 3], [10, 24, 2], [11, 26, 1], [12, 28, 0]]) == [[1, 100], [2, 200], [6, 150], [9, 100], [12, 50], [14, 25], [16, 10], [18, 5], [20, 3], [22, 2], [24, 1], [26, 0]]\n assert candidate(buildings = [[1, 10, 5], [2, 5, 7], [3, 8, 4], [6, 12, 8], [9, 15, 10], [13, 20, 6]]) == [[1, 5], [2, 7], [5, 5], [6, 8], [9, 10], [15, 6], [20, 0]]\n assert candidate(buildings = [[1, 15, 10], [2, 14, 20], [3, 13, 30], [4, 12, 40], [5, 11, 50], [6, 10, 60], [7, 9, 70], [8, 8, 80]]) == [[1, 10], [2, 20], [3, 30], [4, 40], [5, 50], [6, 60], [7, 70], [9, 60], [10, 50], [11, 40], [12, 30], [13, 20], [14, 10], [15, 0]]\n assert candidate(buildings = [[1, 3, 10], [2, 4, 15], [3, 5, 20], [4, 6, 25], [5, 7, 30], [6, 8, 35], [7, 9, 40], [8, 10, 45], [9, 11, 50]]) == [[1, 10], [2, 15], [3, 20], [4, 25], [5, 30], [6, 35], [7, 40], [8, 45], [9, 50], [11, 0]]\n"}, "metadata": {"canonical_parameter_names": ["buildings"], "leetcode_dataset_entry_point": "Solution().getSkyline", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getSkyline = function(buildings) {", "container": null, "callable": "getSkyline", "parameters": [{"name": "buildings", "type": "number[][]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 219, "task_id": "contains-duplicate-ii", "difficulty": "Easy", "problem_description": "Given an integer array nums and an integer k, return true if there are two distinct indices i and j in the array such that nums[i] == nums[j] and abs(i - j) <= k.\n \nExample 1:\n\nInput: nums = [1,2,3,1], k = 3\nOutput: true\n\nExample 2:\n\nInput: nums = [1,0,1,1], k = 1\nOutput: true\n\nExample 3:\n\nInput: nums = [1,2,3,1,2,3], k = 2\nOutput: false\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-109 <= nums[i] <= 109\n0 <= k <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 8) == False\n assert candidate(nums = [1, 0, 1, 1],k = 1) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 9],k = 1) == True\n assert candidate(nums = [1, 2, 2, 1],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5],k = 4) == False\n assert candidate(nums = [1, 2, 3, 4, 5],k = 5) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 9) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 18) == True\n assert candidate(nums = [9, 9],k = 1) == True\n assert candidate(nums = [9, 1, 2, 3, 9],k = 4) == True\n assert candidate(nums = [1],k = 0) == False\n assert candidate(nums = [1, 2, 3, 1],k = 3) == True\n assert candidate(nums = [999999999, 999999999, 1, 1],k = 2) == True\n assert candidate(nums = [999999999, -999999999, 999999999],k = 2) == True\n assert candidate(nums = [1, 2, 2],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 8) == False\n assert candidate(nums = [1, 1],k = 0) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 20) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3],k = 2) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 0) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 1) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 3) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2],k = 1) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 7) == False\n assert candidate(nums = [1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0],k = 1) == False\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999999],k = 9) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 1) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 1) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 50],k = 49) == True\n assert candidate(nums = [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1],k = 20) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5],k = 49) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 10) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 9) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 20) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 1) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1],k = 10) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1],k = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30],k = 29) == True\n assert candidate(nums = [1000000000, 1000000000, 1, 2, 3],k = 1) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 20) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1],k = 14) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 9) == True\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4],k = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 8) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 17) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 0) == False\n assert candidate(nums = [1000000000, 999999999, 1000000000, 999999999, 1000000000, 999999999],k = 2) == True\n assert candidate(nums = [1000000000, 1000000000],k = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5],k = 4) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1],k = 29) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 10],k = 9) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 9) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1],k = 49) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1],k = 10) == True\n assert candidate(nums = [-1000000000, -2000000000, -1000000000, -3000000000, -2000000000],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 100000) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 18) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 8) == False\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005, 1000000006, 1000000007, 1000000008, 1000000009, 1000000000],k = 10) == True\n assert candidate(nums = [10, 1, 2, 10, 3, 4, 5, 10, 6, 7, 8, 9, 10],k = 8) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1],k = 24) == False\n assert candidate(nums = [1, 0, 1, 1, 0, 1, 0, 1],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 19) == False\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20],k = 20) == True\n assert candidate(nums = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1],k = 1) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 5) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1],k = 5) == False\n assert candidate(nums = [1000000000, 2000000000, 1000000000, 3000000000, 2000000000],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1],k = 20) == True\n assert candidate(nums = [1000000000, 2000000000, 1000000000],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1],k = 10) == True\n assert candidate(nums = [1, 0, 1, 1, 0, 1, 0, 1, 0, 1],k = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 19) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 10) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1],k = 30) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == False\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5],k = 10) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1],k = 39) == False\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1],k = 2) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],k = 2) == True\n assert candidate(nums = [1, 0, 1, 1, 0, 1],k = 2) == True\n assert candidate(nums = [5, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0],k = 5) == False\n assert candidate(nums = [1000000000, 1000000001, 1000000000, 1000000001, 1000000000],k = 2) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],k = 1) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50],k = 4) == False\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 1],k = 20) == True\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999999],k = 9) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5],k = 10) == True\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().containsNearbyDuplicate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var containsNearbyDuplicate = function(nums, k) {", "container": null, "callable": "containsNearbyDuplicate", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 220, "task_id": "contains-duplicate-iii", "difficulty": "Hard", "problem_description": "You are given an integer array nums and two integers indexDiff and valueDiff.\nFind a pair of indices (i, j) such that:\n\ni != j,\nabs(i - j) <= indexDiff.\nabs(nums[i] - nums[j]) <= valueDiff, and\n\nReturn true if such pair exists or false otherwise.\n \nExample 1:\n\nInput: nums = [1,2,3,1], indexDiff = 3, valueDiff = 0\nOutput: true\nExplanation: We can choose (i, j) = (0, 3).\nWe satisfy the three conditions:\ni != j --> 0 != 3\nabs(i - j) <= indexDiff --> abs(0 - 3) <= 3\nabs(nums[i] - nums[j]) <= valueDiff --> abs(1 - 1) <= 0\n\nExample 2:\n\nInput: nums = [1,5,9,1,5,9], indexDiff = 2, valueDiff = 3\nOutput: false\nExplanation: After trying all the possible pairs (i, j), we cannot satisfy the three conditions, so we return false.\n\n \nConstraints:\n\n2 <= nums.length <= 105\n-109 <= nums[i] <= 109\n1 <= indexDiff <= nums.length\n0 <= valueDiff <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, 1, 3, 1, 3],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 1, 4, 1, 3],indexDiff = 5,valueDiff = 2) == True\n assert candidate(nums = [10, 10, 10, 10, 10, 10],indexDiff = 3,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [8, 7, 15, 1, 6, 1, 9, 15],indexDiff = 1,valueDiff = 3) == True\n assert candidate(nums = [2, 1, 2, 3, 1, 5],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 1],indexDiff = 3,valueDiff = 0) == True\n assert candidate(nums = [2147483647, -2147483647],indexDiff = 1,valueDiff = 2147483647) == False\n assert candidate(nums = [1, 5, 9, 1, 5, 9],indexDiff = 2,valueDiff = 3) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 5,valueDiff = 5) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 1, 0, 1],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 4,valueDiff = 2) == True\n assert candidate(nums = [10, 10, 10, 10],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [-1, 2147483647],indexDiff = 1,valueDiff = 2147483647) == False\n assert candidate(nums = [4, 1, 2],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90],indexDiff = 2,valueDiff = 20) == True\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],indexDiff = 5,valueDiff = 5) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000],indexDiff = 3,valueDiff = 0) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000],indexDiff = 4,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 8,valueDiff = 4) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 1,valueDiff = 0) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],indexDiff = 10,valueDiff = 10) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],indexDiff = 5,valueDiff = 10) == True\n assert candidate(nums = [1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 8000000, 9000000, 10000000],indexDiff = 9,valueDiff = 3000000) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 3,valueDiff = 0) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 8,valueDiff = 1) == True\n assert candidate(nums = [-1000000000, 1000000000, -999999999, 999999999, -1000000001, 1000000001],indexDiff = 5,valueDiff = 1) == True\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5],indexDiff = 5,valueDiff = 4) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],indexDiff = 1,valueDiff = 19) == True\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],indexDiff = 5,valueDiff = 10) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],indexDiff = 10,valueDiff = 10) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],indexDiff = 3,valueDiff = 2000000000) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],indexDiff = 10,valueDiff = 0) == False\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119],indexDiff = 10,valueDiff = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 1) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],indexDiff = 4,valueDiff = 25) == True\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],indexDiff = 10,valueDiff = 5) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],indexDiff = 7,valueDiff = 5) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],indexDiff = 3,valueDiff = 2000000000) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 2,valueDiff = 5) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],indexDiff = 19,valueDiff = 10) == True\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10],indexDiff = 2,valueDiff = 9) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 10,valueDiff = 9) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],indexDiff = 20,valueDiff = 0) == False\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 4,valueDiff = 1) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],indexDiff = 10000,valueDiff = 0) == True\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 7,valueDiff = 3) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004],indexDiff = 3,valueDiff = 1) == True\n assert candidate(nums = [0, 1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000],indexDiff = 10,valueDiff = 1000000000) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],indexDiff = 5,valueDiff = 50) == False\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10],indexDiff = 2,valueDiff = 8) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],indexDiff = 5,valueDiff = 0) == True\n assert candidate(nums = [1, 5, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69],indexDiff = 6,valueDiff = 5) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],indexDiff = 5,valueDiff = 150) == True\n assert candidate(nums = [1000000000, 999999999, 1000000001, 999999998, 1000000002],indexDiff = 4,valueDiff = 2) == True\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 7,valueDiff = 4) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],indexDiff = 15,valueDiff = 5) == True\n assert candidate(nums = [0, 1000000000, -1000000000, 1000000000, 0, -1000000000, 1000000000, 0, -1000000000, 1000000000],indexDiff = 4,valueDiff = 500000000) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 20,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 5,valueDiff = 5) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 25,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 5,valueDiff = 4) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 4,valueDiff = 2) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 10,valueDiff = 0) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [-1000000000, 1000000000, -1000000000, 1000000000, 0],indexDiff = 4,valueDiff = 2000000000) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95],indexDiff = 10,valueDiff = 5) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [1, 3, 1, 5, 9, 10, 7, 6, 4, 2],indexDiff = 5,valueDiff = 3) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],indexDiff = 5,valueDiff = 100) == True\n assert candidate(nums = [1, 1000000000, 2, 1000000001, 3, 1000000002, 4, 1000000003],indexDiff = 7,valueDiff = 999999999) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 10,valueDiff = 0) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],indexDiff = 12,valueDiff = 5) == True\n assert candidate(nums = [2147483647, -2147483648, 2147483646, -2147483647],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 5, 6, 7, 8, 9],indexDiff = 4,valueDiff = 3) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],indexDiff = 15,valueDiff = 10) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],indexDiff = 10,valueDiff = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 5,valueDiff = 4) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],indexDiff = 10,valueDiff = 15) == True\n assert candidate(nums = [10, 1, 9, 2, 8, 3, 7, 4, 6, 5],indexDiff = 3,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],indexDiff = 19,valueDiff = 1) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 0) == False\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 5,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 20,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 1) == True\n assert candidate(nums = [0, 1000000000, 0, 1000000000, 0],indexDiff = 2,valueDiff = 1000000000) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [1, 1000000000, 1, 1000000000, 1, 1000000000, 1, 1000000000],indexDiff = 6,valueDiff = 999999999) == True\n assert candidate(nums = [1000, 100, 10, 1, 0, 1, 10, 100, 1000, 10000],indexDiff = 9,valueDiff = 9900) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 2) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 5,valueDiff = 0) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [1, 3, 6, 8, 12, 15, 20, 22, 25, 28, 30],indexDiff = 4,valueDiff = 3) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 5,valueDiff = 4) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],indexDiff = 10,valueDiff = 0) == True\n assert candidate(nums = [1, 1000000000, -1000000000, 2, 1000000000, -1000000000],indexDiff = 5,valueDiff = 1999999999) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000],indexDiff = 10,valueDiff = 999999999) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 100,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 0) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 4,valueDiff = 4) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 6,valueDiff = 4) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 10,valueDiff = 9) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],indexDiff = 5,valueDiff = 0) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],indexDiff = 10,valueDiff = 15) == True\n assert candidate(nums = [-1000000000, -999999999, -999999998, -999999997, -999999996, -999999995, -999999994, -999999993, -999999992, -999999991],indexDiff = 10,valueDiff = 0) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],indexDiff = 5,valueDiff = 5) == True\n assert candidate(nums = [-1, 2147483647, -2147483648, 2147483647, -1, 2147483647, -2147483648, 2147483647, -1, 2147483647],indexDiff = 3,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 0) == True\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10],indexDiff = 3,valueDiff = 9) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 3,valueDiff = 1) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 4,valueDiff = 3) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 10,valueDiff = 0) == True\n assert candidate(nums = [8, 7, 15, 1, 6, 1, 9, 15],indexDiff = 2,valueDiff = 3) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 4,valueDiff = 1) == True\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [2, 1, 2, 1],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [2147483647, -1, 2147483647, -1],indexDiff = 1,valueDiff = 2147483647) == False\n assert candidate(nums = [1],indexDiff = 1,valueDiff = 1) == False\n assert candidate(nums = [10, 100, 1000, 10, 100, 1000],indexDiff = 2,valueDiff = 899) == True\n assert candidate(nums = [1, 0, 1, 1],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 5,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 5,valueDiff = 10) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],indexDiff = 1,valueDiff = 0) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 5,valueDiff = 0) == False\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],indexDiff = 10,valueDiff = 0) == True\n assert candidate(nums = [-1, -1, -1, -3, -2, 0, -4, -2, -2, -2, -2, -2, -2, -2, -2],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 8,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 1, 2],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14],indexDiff = 1,valueDiff = 1) == False\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 5,valueDiff = 4) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],indexDiff = 2,valueDiff = 1000000000) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1, 1, 10, 9, 8, 7, 9, 3, 1],indexDiff = 2,valueDiff = 3) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1, 1, 10, 23],indexDiff = 4,valueDiff = 1) == True\n assert candidate(nums = [8, 2, 23, 4, 25, 36, 7, 45, 8, 9, 45],indexDiff = 2,valueDiff = 5) == True\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 1,valueDiff = 0) == False\n assert candidate(nums = [8, 2, 4, 2, 0, 2, 0, 4, 2, 2],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [5, 4, 3, 2, 1],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],indexDiff = 3,valueDiff = 15) == True\n assert candidate(nums = [2147483647, -2147483647],indexDiff = 1,valueDiff = 4294967294) == True\n assert candidate(nums = [0, 1, 1, 1],indexDiff = 1,valueDiff = 2) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],indexDiff = 2,valueDiff = 1999999999) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],indexDiff = 8,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1, 1, 10, 9],indexDiff = 1,valueDiff = 2) == True\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648],indexDiff = 1,valueDiff = 4294967295) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],indexDiff = 7,valueDiff = 2) == True\n assert candidate(nums = [10, 10, 10, 10, 10],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 1, 2, 5, 5, 1, 2, 5],indexDiff = 2,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 4,valueDiff = 4) == True\n assert candidate(nums = [1, 5, 9, 1, 5, 9],indexDiff = 2,valueDiff = 3) == False\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],indexDiff = 2,valueDiff = 1999999999) == True\n assert candidate(nums = [10, 100, 1000, 10000],indexDiff = 3,valueDiff = 5000) == True\n assert candidate(nums = [8, 2, 2, 2, 5, 3, 9, 8, 2, 8],indexDiff = 4,valueDiff = 2) == True\n assert candidate(nums = [1, 0, 1, 1],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 1,valueDiff = 0) == False\n assert candidate(nums = [0, 10, 20, 30, 40, 50],indexDiff = 3,valueDiff = 10) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],indexDiff = 4,valueDiff = 2) == True\n assert candidate(nums = [0, 0, 0, 0, 0],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 9,valueDiff = 9) == True\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [1, 2, 3, 1],indexDiff = 3,valueDiff = 0) == True\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [0, 2147483647],indexDiff = 1,valueDiff = 2147483647) == True\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 4,valueDiff = 2) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [7, 1, 3, 6, 5, 10, 12, 8],indexDiff = 5,valueDiff = 8) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1],indexDiff = 1,valueDiff = 2) == True\n assert candidate(nums = [7, 1, 3, 6, 5, 10, 12, 8],indexDiff = 5,valueDiff = 2) == True\n assert candidate(nums = [999999999, 999999999, 999999999, 999999999],indexDiff = 3,valueDiff = 0) == True\n assert candidate(nums = [1, 2],indexDiff = 0,valueDiff = 1) == False\n assert candidate(nums = [1, 2, 1, 2, 1, 2],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [8, 2, 4, 5, 0, 1, 7, 9],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 3, 1, 3, 1, 3],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [1, 0, 1, 1],indexDiff = 1,valueDiff = 2) == True\n assert candidate(nums = [10, 100, 10, 1000, 100, 10],indexDiff = 1,valueDiff = 90) == True\n assert candidate(nums = [10, 100, 1000, 10000, 100000],indexDiff = 4,valueDiff = 90000) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1, 1, 10, 6, 11, 7, 10, 3, 4, 7, 13, 1, 3, 15, 5],indexDiff = 2,valueDiff = 3) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 1,valueDiff = 0) == False\n assert candidate(nums = [2, 0, -2, 2],indexDiff = 2,valueDiff = 1) == False\n assert candidate(nums = [2, 1, 2, 1],indexDiff = 1,valueDiff = 0) == False\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1],indexDiff = 1,valueDiff = 1) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 11,valueDiff = 0) == True\n assert candidate(nums = [1, 3, 1, 2],indexDiff = 3,valueDiff = 1) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 4,valueDiff = 3) == True\n assert candidate(nums = [1, 2, 3, 4, 5],indexDiff = 4,valueDiff = 3) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],indexDiff = 10,valueDiff = 9) == True\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 21],indexDiff = 2,valueDiff = 1) == True\n assert candidate(nums = [-1, 2147483647, -1, 2147483647],indexDiff = 1,valueDiff = 2147483647) == False\n assert candidate(nums = [8, 7, 15, 1, 6, 1, 9, 15],indexDiff = 1,valueDiff = 3) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],indexDiff = 5,valueDiff = 4) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],indexDiff = 2,valueDiff = 2000000000) == True\n assert candidate(nums = [1000000000, 1000000000],indexDiff = 0,valueDiff = 0) == False\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000],indexDiff = 7,valueDiff = 9999999) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],indexDiff = 3,valueDiff = 0) == True\n assert candidate(nums = [8, 2, 4, 5, 0, 1, 9, 3],indexDiff = 3,valueDiff = 2) == True\n assert candidate(nums = [1, 5, 9, 1, 5, 9],indexDiff = 2,valueDiff = 2) == False\n assert candidate(nums = [-1, 2147483647],indexDiff = 1,valueDiff = 2147483647) == False\n assert candidate(nums = [8, 2, 4, 2, 0, 14, 1, 13],indexDiff = 5,valueDiff = 3) == True\n assert candidate(nums = [10, 10, 10, 10, 10, 10],indexDiff = 1,valueDiff = 0) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2],indexDiff = 1,valueDiff = 1) == True\n assert candidate(nums = [0, 21233, 15334453, 123345],indexDiff = 3,valueDiff = 3) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 5,valueDiff = 3) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],indexDiff = 2,valueDiff = 0) == True\n assert candidate(nums = [10, 100, 1000, 10000, 100000],indexDiff = 5,valueDiff = 90000) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 5,valueDiff = 1) == True\n assert candidate(nums = [8, 2, 4, 5, 0, 7, 9],indexDiff = 1,valueDiff = 2) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],indexDiff = 5,valueDiff = 2) == True\n assert candidate(nums = [8, 2, 4, 5, 0, 1, 9, 3],indexDiff = 2,valueDiff = 3) == True\n assert candidate(nums = [1, 2],indexDiff = 1,valueDiff = 0) == False\n"}, "metadata": {"canonical_parameter_names": ["nums", "indexDiff", "valueDiff"], "leetcode_dataset_entry_point": "Solution().containsNearbyAlmostDuplicate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var containsNearbyAlmostDuplicate = function(nums, indexDiff, valueDiff) {", "container": null, "callable": "containsNearbyAlmostDuplicate", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "indexDiff", "type": "number"}, {"name": "valueDiff", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 221, "task_id": "maximal-square", "difficulty": "Medium", "problem_description": "Given an m x n binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.\n \nExample 1:\n\n\nInput: matrix = [[\"1\",\"0\",\"1\",\"0\",\"0\"],[\"1\",\"0\",\"1\",\"1\",\"1\"],[\"1\",\"1\",\"1\",\"1\",\"1\"],[\"1\",\"0\",\"0\",\"1\",\"0\"]]\nOutput: 4\n\nExample 2:\n\n\nInput: matrix = [[\"0\",\"1\"],[\"1\",\"0\"]]\nOutput: 1\n\nExample 3:\n\nInput: matrix = [[\"0\"]]\nOutput: 0\n\n \nConstraints:\n\nm == matrix.length\nn == matrix[i].length\n1 <= m, n <= 300\nmatrix[i][j] is '0' or '1'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [['0', '1'], ['1', '0']]) == 1\n assert candidate(matrix = [['1', '0', '1'], ['1', '1', '0'], ['1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1'], ['1', '1']]) == 4\n assert candidate(matrix = [['0']]) == 0\n assert candidate(matrix = [['1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0']]) == 4\n assert candidate(matrix = [['1', '0', '1', '0', '0'], ['1', '0', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '1', '0']]) == 4\n assert candidate(matrix = [['1', '0', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '0', '1', '1', '0'], ['1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1'], ['1', '1', '1', '1', '0']]) == 9\n assert candidate(matrix = [['1', '0', '1', '1', '1'], ['1', '0', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '0', '1', '0']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '0', '0', '1'], ['1', '1', '0', '1', '1'], ['0', '1', '1', '1', '1'], ['0', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 25\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '0', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 16\n assert candidate(matrix = [['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '1', '1', '0', '0'], ['1', '1', '1', '0', '0'], ['1', '1', '1', '0', '0'], ['0', '0', '0', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1', '0', '0', '0'], ['1', '1', '1', '1', '1', '0', '0', '1'], ['0', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1', '1', '1']]) == 25\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1']]) == 25\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '0', '1', '1', '1', '0', '1'], ['1', '0', '0', '1', '0', '1', '0', '1'], ['1', '0', '0', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '0']]) == 16\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '1', '0', '1'], ['1', '0', '1', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['0', '0', '0', '0', '0'], ['0', '1', '1', '1', '0'], ['0', '1', '1', '1', '0'], ['0', '1', '1', '1', '0'], ['0', '0', '0', '0', '0']]) == 9\n assert candidate(matrix = [['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1'], ['1', '0', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '0', '1', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1'], ['1', '0', '1'], ['1', '1', '1'], ['1', '1', '1'], ['1', '0', '1'], ['1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '0', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['0', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '0', '0', '0', '1'], ['1', '0', '1', '0', '1'], ['1', '0', '0', '0', '1'], ['1', '1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '0', '0'], ['1', '1', '0', '0', '0', '0'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1']]) == 16\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1']]) == 64\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0'], ['0', '0', '0', '0', '0']]) == 0\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '0'], ['0', '1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '0'], ['0', '0', '0', '0', '0'], ['1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '0'], ['1', '1', '1', '0', '0'], ['1', '1', '0', '0', '0'], ['1', '0', '0', '0', '0'], ['0', '0', '0', '0', '0']]) == 4\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '0', '0', '0'], ['1', '1', '1', '0', '1', '1'], ['1', '1', '1', '0', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '0', '0', '0', '1', '0', '1'], ['1', '0', '1', '0', '1', '1', '1', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '1', '0', '1'], ['1', '0', '1', '0', '1', '0', '1', '1', '0', '1'], ['1', '0', '1', '1', '1', '1', '1', '1', '0', '1'], ['1', '0', '0', '0', '0', '0', '0', '0', '0', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '1', '1', '1'], ['0', '0', '1', '1', '1'], ['0', '0', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '0', '0', '0', '0', '0'], ['0', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '0', '0']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '0', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '0', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '0', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '0', '0']]) == 16\n assert candidate(matrix = [['1', '1', '0', '0', '1'], ['1', '1', '0', '0', '1'], ['0', '0', '1', '1', '0'], ['0', '0', '1', '1', '0'], ['1', '0', '0', '1', '0']]) == 4\n assert candidate(matrix = [['1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1'], ['1', '1', '1', '1', '1'], ['1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 36\n assert candidate(matrix = [['1', '1', '1', '0', '1', '1'], ['1', '1', '1', '0', '1', '1'], ['1', '1', '1', '0', '1', '1'], ['0', '0', '0', '0', '0', '0'], ['1', '1', '1', '0', '1', '1'], ['1', '1', '1', '0', '1', '1']]) == 9\n assert candidate(matrix = [['0', '0', '0', '0', '0'], ['0', '1', '1', '1', '0'], ['0', '1', '0', '1', '0'], ['0', '1', '1', '1', '0'], ['0', '0', '0', '0', '0']]) == 1\n assert candidate(matrix = [['1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0', '1', '0']]) == 1\n assert candidate(matrix = [['1', '0', '0', '1', '0'], ['0', '1', '1', '0', '1'], ['0', '1', '1', '0', '1'], ['1', '0', '0', '1', '0'], ['0', '1', '1', '0', '1']]) == 4\n assert candidate(matrix = [['1', '1', '1'], ['1', '0', '1'], ['1', '1', '1'], ['1', '0', '1'], ['1', '1', '1']]) == 1\n assert candidate(matrix = [['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1'], ['0', '1', '0', '1', '0'], ['1', '0', '1', '0', '1']]) == 1\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '0', '0', '1', '1'], ['1', '1', '0', '0', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '0', '1', '1', '1', '1', '0', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 81\n assert candidate(matrix = [['1', '1', '1', '1', '0'], ['1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1'], ['0', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '0', '1', '1'], ['1', '1', '0', '1', '0', '1', '1'], ['1', '1', '0', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1']]) == 100\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['0', '0', '0', '0', '1', '1'], ['0', '0', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 9\n assert candidate(matrix = [['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '0', '0', '1', '1'], ['1', '1', '1', '1', '1', '1'], ['1', '1', '1', '1', '1', '1']]) == 4\n assert candidate(matrix = [['1', '1', '0', '0', '0'], ['1', '1', '0', '0', '0'], ['0', '0', '1', '1', '1'], ['0', '0', '1', '1', '1'], ['0', '0', '1', '1', '1']]) == 9\n assert candidate(matrix = [['0', '0', '0', '0', '0', '0'], ['0', '1', '1', '1', '1', '0'], ['0', '1', '0', '0', '1', '0'], ['0', '1', '0', '1', '1', '0'], ['0', '1', '1', '1', '1', '0'], ['0', '0', '0', '0', '0', '0']]) == 4\n assert candidate(matrix = [['1', '1', '1', '1'], ['1', '0', '0', '1'], ['1', '0', '0', '1'], ['1', '1', '1', '1']]) == 1\n assert candidate(matrix = [['1', '1', '0', '1'], ['1', '1', '0', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['1', '1', '1', '1'], ['0', '0', '0', '0']]) == 9\n assert candidate(matrix = [['1', '1', '1', '0', '0'], ['1', '1', '1', '0', '0'], ['1', '1', '1', '0', '0'], ['0', '0', '0', '1', '1'], ['0', '0', '0', '1', '1']]) == 9\n assert candidate(matrix = [['0', '0', '0', '0'], ['0', '1', '1', '0'], ['0', '1', '1', '0'], ['0', '0', '0', '0']]) == 4\n"}, "metadata": {"canonical_parameter_names": ["matrix"], "leetcode_dataset_entry_point": "Solution().maximalSquare", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maximalSquare = function(matrix) {", "container": null, "callable": "maximalSquare", "parameters": [{"name": "matrix", "type": "character[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 222, "task_id": "count-complete-tree-nodes", "difficulty": "Easy", "problem_description": "Given the root of a complete binary tree, return the number of the nodes in the tree.\nAccording to Wikipedia, every level, except possibly the last, is completely filled in a complete binary tree, and all nodes in the last level are as far left as possible. It can have between 1 and 2h nodes inclusive at the last level h.\nDesign an algorithm that runs in less than O(n) time complexity.\n \nExample 1:\n\n\nInput: root = [1,2,3,4,5,6]\nOutput: 6\n\nExample 2:\n\nInput: root = []\nOutput: 0\n\nExample 3:\n\nInput: root = [1]\nOutput: 1\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 5 * 104].\n0 <= Node.val <= 5 * 104\nThe tree is guaranteed to be complete.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == 7\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 15\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 7])) == 6\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6])) == 6\n assert candidate(root = tree_node([1])) == 1\n assert candidate(root = tree_node([])) == 0\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 16, 17])) == 15\n assert candidate(root = tree_node([1, 2, 3, None, None, 6, 7])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 16, 17, None, None, 19, 20, 21, 22, None, None, None, None, 23, 24, 25, 26, None, None, 27, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 28])) == 25\n assert candidate(root = tree_node([1, 2, 3, 4])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34])) == 34\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32])) == 32\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48])) == 48\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64])) == 64\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33])) == 33\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == 25\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])) == 13\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])) == 50\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27])) == 27\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38])) == 38\n assert candidate(root = tree_node([1, 2])) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8])) == 8\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 16, None, 18])) == 15\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])) == 11\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 7, 8, 9, 10, 11, 12, 13, 14, None])) == 13\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])) == 100\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28])) == 28\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])) == 40\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) == 10\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17])) == 17\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 16, 17, None, None, 19, 20, 21, 22, None, None, 23, 24])) == 21\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37])) == 37\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35])) == 35\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 8, 9, 10, 11])) == 9\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18])) == 18\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])) == 23\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])) == 19\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39])) == 39\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])) == 14\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63])) == 63\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, None, None, None, None, 35])) == 32\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == 15\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == 7\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16])) == 16\n assert candidate(root = tree_node([1, 2, 3])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36])) == 36\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == 30\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 20\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24])) == 24\n assert candidate(root = tree_node([1, 2, 3, 4, 5])) == 5\n assert candidate(root = tree_node([1, 2, 3, None, 5, 6, 7])) == 6\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, 16, 17, None, None, 19, 20, None, None, None, None, 21])) == 18\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])) == 12\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])) == 31\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21])) == 21\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22])) == 22\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26])) == 26\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29])) == 29\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9])) == 9\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().countNodes", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countNodes = function(root) {", "container": null, "callable": "countNodes", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 223, "task_id": "rectangle-area", "difficulty": "Medium", "problem_description": "Given the coordinates of two rectilinear rectangles in a 2D plane, return the total area covered by the two rectangles.\nThe first rectangle is defined by its bottom-left corner (ax1, ay1) and its top-right corner (ax2, ay2).\nThe second rectangle is defined by its bottom-left corner (bx1, by1) and its top-right corner (bx2, by2).\n \nExample 1:\n\n\nInput: ax1 = -3, ay1 = 0, ax2 = 3, ay2 = 4, bx1 = 0, by1 = -1, bx2 = 9, by2 = 2\nOutput: 45\n\nExample 2:\n\nInput: ax1 = -2, ay1 = -2, ax2 = 2, ay2 = 2, bx1 = -2, by1 = -2, bx2 = 2, by2 = 2\nOutput: 16\n\n \nConstraints:\n\n-104 <= ax1 <= ax2 <= 104\n-104 <= ay1 <= ay2 <= 104\n-104 <= bx1 <= bx2 <= 104\n-104 <= by1 <= by2 <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(ax1 = -2,ay1 = -2,ax2 = 2,ay2 = 2,bx1 = -2,by1 = -2,bx2 = 2,by2 = 2) == 16\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 3,ay2 = 3,bx1 = 2,by1 = 2,bx2 = 4,by2 = 4) == 7\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 5,ay2 = 5,bx1 = 5,by1 = 5,bx2 = 10,by2 = 10) == 50\n assert candidate(ax1 = -3,ay1 = 0,ax2 = 3,ay2 = 4,bx1 = 0,by1 = -1,bx2 = 9,by2 = 2) == 45\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 0,ay2 = 0,bx1 = -3,by1 = -3,bx2 = 3,by2 = 3) == 52\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 0,ay2 = 0,bx1 = -3,by1 = -3,bx2 = -1,by2 = -1) == 25\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 4,ay2 = 5,bx1 = 2,by1 = 2,bx2 = 5,by2 = 6) == 18\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 1,ay2 = 1,bx1 = 2,by1 = 2,bx2 = 3,by2 = 3) == 2\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 5,ay2 = 5,bx1 = 3,by1 = 3,bx2 = 7,by2 = 7) == 28\n assert candidate(ax1 = -1,ay1 = -1,ax2 = 1,ay2 = 1,bx1 = 0,by1 = 0,bx2 = 2,by2 = 2) == 7\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 3,ay2 = 3,bx1 = 4,by1 = 4,bx2 = 6,by2 = 6) == 8\n assert candidate(ax1 = -20,ay1 = -20,ax2 = 20,ay2 = 20,bx1 = 15,by1 = 15,bx2 = 25,by2 = 25) == 1675\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 5,ay2 = 5,bx1 = -5,by1 = -5,bx2 = -4,by2 = -4) == 100\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 4,ay2 = 4,bx1 = 2,by1 = 2,bx2 = 5,by2 = 5) == 14\n assert candidate(ax1 = -1,ay1 = -1,ax2 = 1,ay2 = 1,bx1 = 1,by1 = 1,bx2 = 3,by2 = 3) == 8\n assert candidate(ax1 = 5,ay1 = 5,ax2 = 15,ay2 = 15,bx1 = 10,by1 = 10,bx2 = 20,by2 = 20) == 175\n assert candidate(ax1 = -100,ay1 = 100,ax2 = 0,ay2 = 200,bx1 = -50,by1 = 150,bx2 = 50,by2 = 250) == 17500\n assert candidate(ax1 = -100,ay1 = -100,ax2 = -50,ay2 = -50,bx1 = 50,by1 = 50,bx2 = 100,by2 = 100) == 5000\n assert candidate(ax1 = -20,ay1 = -20,ax2 = 0,ay2 = 0,bx1 = -5,by1 = -5,bx2 = 5,by2 = 5) == 475\n assert candidate(ax1 = 500,ay1 = 500,ax2 = 600,ay2 = 600,bx1 = 550,by1 = 550,bx2 = 700,by2 = 700) == 30000\n assert candidate(ax1 = -5000,ay1 = -5000,ax2 = 5000,ay2 = 5000,bx1 = 0,by1 = 0,bx2 = 1,by2 = 1) == 100000000\n assert candidate(ax1 = -3,ay1 = -3,ax2 = 3,ay2 = 3,bx1 = -1,by1 = -1,bx2 = 1,by2 = 1) == 36\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 10,ay2 = 10,bx1 = 5,by1 = 5,bx2 = 15,by2 = 15) == 156\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = -20,by1 = -20,bx2 = -15,by2 = -15) == 425\n assert candidate(ax1 = 20,ay1 = 20,ax2 = 40,ay2 = 60,bx1 = 30,by1 = 40,bx2 = 50,by2 = 80) == 1400\n assert candidate(ax1 = -2,ay1 = 2,ax2 = 2,ay2 = 6,bx1 = 1,by1 = 4,bx2 = 3,by2 = 8) == 22\n assert candidate(ax1 = -800,ay1 = -800,ax2 = -700,ay2 = -700,bx1 = -750,by1 = -750,bx2 = -650,by2 = -650) == 17500\n assert candidate(ax1 = -1,ay1 = -1,ax2 = 1,ay2 = 1,bx1 = 1,by1 = 1,bx2 = 2,by2 = 2) == 5\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 10000,ay2 = 10000,bx1 = 5000,by1 = 5000,bx2 = 15000,by2 = 15000) == 175000000\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 1,ay2 = 1,bx1 = -5000,by1 = -5000,bx2 = 5000,by2 = 5000) == 100000000\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = 11,by1 = 11,bx2 = 20,by2 = 20) == 481\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = -5,by1 = -5,bx2 = 5,by2 = 5) == 400\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 5,ay2 = 5,bx1 = 5,by1 = 0,bx2 = 10,by2 = 5) == 50\n assert candidate(ax1 = -10000,ay1 = -10000,ax2 = 10000,ay2 = 10000,bx1 = -5000,by1 = -5000,bx2 = 5000,by2 = 5000) == 400000000\n assert candidate(ax1 = -200,ay1 = -200,ax2 = -100,ay2 = -100,bx1 = -150,by1 = -150,bx2 = -50,by2 = -50) == 17500\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 10,ay2 = 10,bx1 = 1,by1 = 1,bx2 = 9,by2 = 9) == 100\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 10000,ay2 = 10000,bx1 = 1,by1 = 1,bx2 = 9999,by2 = 9999) == 100000000\n assert candidate(ax1 = -100,ay1 = -100,ax2 = 100,ay2 = 100,bx1 = 0,by1 = 0,bx2 = 50,by2 = 50) == 40000\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = 5,by1 = 5,bx2 = 15,by2 = 15) == 475\n assert candidate(ax1 = -20,ay1 = -20,ax2 = 5,ay2 = 5,bx1 = -15,by1 = -15,bx2 = 0,by2 = 0) == 625\n assert candidate(ax1 = -10000,ay1 = -10000,ax2 = 10000,ay2 = 10000,bx1 = 5000,by1 = 5000,bx2 = 15000,by2 = 15000) == 475000000\n assert candidate(ax1 = -1000,ay1 = -1000,ax2 = 1000,ay2 = 1000,bx1 = -500,by1 = -500,bx2 = 500,by2 = 500) == 4000000\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 5,ay2 = 5,bx1 = -5,by1 = -5,bx2 = 15,by2 = 15) == 525\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = 10,by1 = 10,bx2 = 20,by2 = 20) == 500\n assert candidate(ax1 = 10,ay1 = 20,ax2 = 30,ay2 = 40,bx1 = 25,by1 = 30,bx2 = 45,by2 = 50) == 750\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 1,ay2 = 1,bx1 = 1,by1 = 1,bx2 = 2,by2 = 2) == 2\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 1,ay2 = 1,bx1 = -1,by1 = -1,bx2 = 0,by2 = 0) == 2\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 5,ay2 = 5,bx1 = -5,by1 = -5,bx2 = 5,by2 = 5) == 100\n assert candidate(ax1 = -80,ay1 = -80,ax2 = -60,ay2 = -40,bx1 = -70,by1 = -70,bx2 = -50,by2 = -50) == 1000\n assert candidate(ax1 = -2,ay1 = -2,ax2 = 2,ay2 = 2,bx1 = -1,by1 = -1,bx2 = 1,by2 = 1) == 16\n assert candidate(ax1 = -50,ay1 = -50,ax2 = 50,ay2 = 50,bx1 = -30,by1 = -30,bx2 = 30,by2 = 30) == 10000\n assert candidate(ax1 = -500,ay1 = -500,ax2 = 500,ay2 = 500,bx1 = -300,by1 = -300,bx2 = 300,by2 = 300) == 1000000\n assert candidate(ax1 = 1,ay1 = 1,ax2 = 5,ay2 = 5,bx1 = 2,by1 = 2,bx2 = 6,by2 = 6) == 23\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 5,ay2 = 5,bx1 = 5,by1 = -5,bx2 = 15,by2 = 5) == 200\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = 0,by1 = -5,bx2 = 5,by2 = 5) == 400\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 10,ay2 = 10,bx1 = 5,by1 = 5,bx2 = 15,by2 = 15) == 175\n assert candidate(ax1 = -100,ay1 = -100,ax2 = 100,ay2 = 100,bx1 = -50,by1 = -50,bx2 = 50,by2 = 50) == 40000\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 0,ay2 = 0,bx1 = -5,by1 = -5,bx2 = 5,by2 = 5) == 175\n assert candidate(ax1 = -20,ay1 = -20,ax2 = -10,ay2 = -10,bx1 = -15,by1 = -15,bx2 = -5,by2 = -5) == 175\n assert candidate(ax1 = -50,ay1 = -50,ax2 = 50,ay2 = 50,bx1 = -60,by1 = -60,bx2 = 60,by2 = 60) == 14400\n assert candidate(ax1 = -1000,ay1 = -1000,ax2 = -500,ay2 = -500,bx1 = -750,by1 = -750,bx2 = -250,by2 = -250) == 437500\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 0,ay2 = 0,bx1 = 0,by1 = 0,bx2 = 10,by2 = 10) == 200\n assert candidate(ax1 = -500,ay1 = -500,ax2 = -200,ay2 = -200,bx1 = -400,by1 = -400,bx2 = -100,by2 = -100) == 140000\n assert candidate(ax1 = -100,ay1 = -100,ax2 = -50,ay2 = -50,bx1 = -75,by1 = -75,bx2 = -25,by2 = -25) == 4375\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = 5,by1 = -5,bx2 = 15,by2 = 5) == 450\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 10,ay2 = 20,bx1 = 5,by1 = 5,bx2 = 15,by2 = 15) == 250\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 0,ay2 = 0,bx1 = 0,by1 = 0,bx2 = 0,by2 = 0) == 0\n assert candidate(ax1 = -10,ay1 = -10,ax2 = 10,ay2 = 10,bx1 = 10,by1 = -10,bx2 = 20,by2 = 10) == 600\n assert candidate(ax1 = 10,ay1 = 10,ax2 = 20,ay2 = 20,bx1 = 15,by1 = 15,bx2 = 25,by2 = 25) == 175\n assert candidate(ax1 = -50,ay1 = -50,ax2 = 50,ay2 = 50,bx1 = -25,by1 = -25,bx2 = 25,by2 = 25) == 10000\n assert candidate(ax1 = 200,ay1 = 200,ax2 = 300,ay2 = 300,bx1 = 100,by1 = 100,bx2 = 250,by2 = 250) == 30000\n assert candidate(ax1 = 0,ay1 = 0,ax2 = 100,ay2 = 100,bx1 = 90,by1 = 90,bx2 = 200,by2 = 200) == 22000\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 5,ay2 = 5,bx1 = 6,by1 = 6,bx2 = 10,by2 = 10) == 116\n assert candidate(ax1 = 100,ay1 = 100,ax2 = 200,ay2 = 200,bx1 = 150,by1 = 150,bx2 = 250,by2 = 250) == 17500\n assert candidate(ax1 = -5,ay1 = -5,ax2 = 5,ay2 = 5,bx1 = 6,by1 = 6,bx2 = 11,by2 = 11) == 125\n assert candidate(ax1 = -1000,ay1 = -1000,ax2 = -900,ay2 = -900,bx1 = -950,by1 = -950,bx2 = -850,by2 = -850) == 17500\n"}, "metadata": {"canonical_parameter_names": ["ax1", "ay1", "ax2", "ay2", "bx1", "by1", "bx2", "by2"], "leetcode_dataset_entry_point": "Solution().computeArea", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var computeArea = function(ax1, ay1, ax2, ay2, bx1, by1, bx2, by2) {", "container": null, "callable": "computeArea", "parameters": [{"name": "ax1", "type": "number"}, {"name": "ay1", "type": "number"}, {"name": "ax2", "type": "number"}, {"name": "ay2", "type": "number"}, {"name": "bx1", "type": "number"}, {"name": "by1", "type": "number"}, {"name": "bx2", "type": "number"}, {"name": "by2", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 224, "task_id": "basic-calculator", "difficulty": "Hard", "problem_description": "Given a string s representing a valid expression, implement a basic calculator to evaluate it, and return the result of the evaluation.\nNote: You are not allowed to use any built-in function which evaluates strings as mathematical expressions, such as eval().\n \nExample 1:\n\nInput: s = \"1 + 1\"\nOutput: 2\n\nExample 2:\n\nInput: s = \" 2-1 + 2 \"\nOutput: 3\n\nExample 3:\n\nInput: s = \"(1+(4+5+2)-3)+(6+8)\"\nOutput: 23\n\n \nConstraints:\n\n1 <= s.length <= 3 * 105\ns consists of digits, '+', '-', '(', ')', and ' '.\ns represents a valid expression.\n'+' is not used as a unary operation (i.e., \"+1\" and \"+(2 + 3)\" is invalid).\n'-' could be used as a unary operation (i.e., \"-1\" and \"-(2 + 3)\" is valid).\nThere will be no two consecutive operators in the input.\nEvery number and running calculation will fit in a signed 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"30 - (5 + (10 - 15) + 20)\") == 10\n assert candidate(s = \"2147483647\") == 2147483647\n assert candidate(s = \"-2147483647\") == -2147483647\n assert candidate(s = \"- (3 + (2 - 1))\") == -4\n assert candidate(s = \"1 + (2 + 3) + (4 + (5 + 6))\") == 21\n assert candidate(s = \"5 - (3 - (1 + 2))\") == 5\n assert candidate(s = \"(1-2+(3-(4-5)))\") == 3\n assert candidate(s = \" 2-1 + 2 \") == 3\n assert candidate(s = \"(1+(4+5+2)-3)+(6+8)\") == 23\n assert candidate(s = \"- (3 + (2 - 1) )\") == -4\n assert candidate(s = \"100 * 2 + 12\") == 114\n assert candidate(s = \"(1+(2+(3+(4+(5+(6+(7+(8+(9+(10)))))))))\") == 55\n assert candidate(s = \"((100 - 50) + (25 - 10))\") == 65\n assert candidate(s = \"10 + 2 * 6\") == 18\n assert candidate(s = \"10 + 20 - 5\") == 25\n assert candidate(s = \"- (5 - (- (1 + 1)))\") == -7\n assert candidate(s = \"-1 + (2 - (-3 + 4))\") == 0\n assert candidate(s = \"10 + (2 - 6)\") == 6\n assert candidate(s = \"-1 + (3-5)\") == -3\n assert candidate(s = \"10 - (-5 + 3)\") == 12\n assert candidate(s = \"(123 + (456 - 789))\") == -210\n assert candidate(s = \"(10 - (5 + 3))\") == 2\n assert candidate(s = \"(1 + (2 + (3 + (4 + 5))))\") == 15\n assert candidate(s = \"10 - (2 - (3 - 4))\") == 7\n assert candidate(s = \"100 * ( 2 + 12 )\") == 114\n assert candidate(s = \"10 + (2 - 3)\") == 9\n assert candidate(s = \"(5 + 15) - (10 + 20)\") == -10\n assert candidate(s = \"(123 + 456) - 789\") == -210\n assert candidate(s = \"1 - (2 - (3 - (4 - (5 - (6 - (7 - (8 - 9)))))))\") == 5\n assert candidate(s = \"- (5 + 10 + (15 - 20))\") == -10\n assert candidate(s = \"1 - (-1)\") == 2\n assert candidate(s = \"((1 + 3) + (5 + 7))\") == 16\n assert candidate(s = \"1 + 1\") == 2\n assert candidate(s = \"(1 + ((2 + 3) * (4 / 2)))\") == 12\n assert candidate(s = \"(100 - (50 + (25 - (12 + (6 - (3 + (1 - 1)))))))\") == 40\n assert candidate(s = \"100 / ((5 + (5 - (5 + (5 - 5)))) * 2)\") == 103\n assert candidate(s = \"10 - (5 - (3 - (2 - (1 - 0))))\") == 7\n assert candidate(s = \"-1 + (2 - (3 + (4 - (5 + (6 - (7 + (8 - 9)))))))\") == -1\n assert candidate(s = \"5 + (8 * 3 + 9 + (3 * 5))\") == 33\n assert candidate(s = \"((10 + 20) * (30 / 5)) - (40 + (50 - 60))\") == 35\n assert candidate(s = \"(1 + 2) * (3 + 4) * (5 + 6) * (7 + 8)\") == 36\n assert candidate(s = \"1 + (2 + (3 + (4 + (5 + (6 + (7 + (8 + (9 + 10))))))))\") == 55\n assert candidate(s = \"100 - (50 + ((25 * 2) - (10 + 5)))\") == 38\n assert candidate(s = \"(3 + (2 * 2) - (1 + 3) + (4 - (5 + 6)))\") == -4\n assert candidate(s = \"(1 - (2 - (3 - (4 - (5 - (6 - (7 - 8)))))))\") == -4\n assert candidate(s = \"(1 + (2 - (3 + (4 - (5 + 6)))))\") == 7\n assert candidate(s = \"(((((1 + 2) + 3) + 4) + 5) + 6)\") == 21\n assert candidate(s = \"10 + 20 * (30 + 40 / 5) + 5 * (6 + 7 * (8 + 9))\") == 140\n assert candidate(s = \"(10 + 20) - (30 - 40) + (50 * 60) / (70 - 80)\") == 140\n assert candidate(s = \"123 + (456 - 789) * (10 - 5)\") == -215\n assert candidate(s = \"3 * (5 + 2 * (2 + 3)) + 4 * (2 + (3 - 1))\") == 23\n assert candidate(s = \"((5 - 3) * (6 + 2) - (4 + 1) * (3 - 8)) + 10\") == -6\n assert candidate(s = \"((1 + 2) * (3 + (4 * (5 + 6))))\") == 21\n assert candidate(s = \"( 10 - ( 20 - ( 30 - ( 40 - ( 50 - 60 ) ) ) ) )\") == -30\n assert candidate(s = \"(1 + (2 + (3 + (4 + (5 + 6)))))\") == 21\n assert candidate(s = \"((1 + 2) * (3 - 4) + (5 * 6) - 7)\") == 6\n assert candidate(s = \"1 + (2 * (2 + 2) - (3 - 4) * (3 + (2 - 1)))\") == 4\n assert candidate(s = \"(9 + (8 + (7 + (6 + (5 + (4 + (3 + (2 + 1))))))))\") == 45\n assert candidate(s = \"10 - (20 + (30 - (40 + (50 - 60))))\") == -10\n assert candidate(s = \"(9 - (8 + 7 - (6 + 5 - 4))) * (3 + (2 - (1 + 0 - (-1))))\") == -2\n assert candidate(s = \"100 - (25 + 3 * (4 + 5))\") == 63\n assert candidate(s = \"100 - (50 + (25 - (10 + (5 - (2 + (1 - (0 + 1)))))))\") == 38\n assert candidate(s = \"(1 + (2 + (3 + (4 + (5 + (6 + (7 + (8 + 9))))))))\") == 45\n assert candidate(s = \"100 + ((-200 + (300 - (400 + (500 - (600 + (700 - (800 + (900 - 1000))))))))\") == -200\n assert candidate(s = \"(100 - (50 - (25 - (10 - (5 - 1)))))\") == 69\n assert candidate(s = \"5 + 3 * (10 - 2) / 4 - 1\") == 11\n assert candidate(s = \"1 + 2 * (3 + (4 * (5 + (6 * (7 + 8)))))\") == 36\n assert candidate(s = \"(9 + (8 - (7 + (6 - (5 + (4 - (3 + (2 - 1))))))))\") == 9\n assert candidate(s = \"( 1 + 2 ) * ( 3 + 4 ) - ( 5 + 6 ) * ( 7 + 8 )\") == 14\n assert candidate(s = \"(100 - 50) + ((25 * 2) - (10 + 5))\") == 62\n assert candidate(s = \"10 - (20 - (30 - (40 - 50)))\") == 30\n assert candidate(s = \"5 + ((1 + (2 * 2) + (3 * (4 + 5))) * 6)\") == 28\n assert candidate(s = \"(((((1 + 2) * 3) + 4) - 5) * 6) - 7\") == -8\n assert candidate(s = \"((2 + 3) * (5 - 1) + 7)\") == 16\n assert candidate(s = \"((10 + 2) - (5 + 3) * (2 - 8)) + 4\") == 2\n assert candidate(s = \"((1 + (2 + (3 + (4 + (5 + (6 + (7 + (8 + (9 + 0)))))))))\") == 45\n assert candidate(s = \"(((10 - 2) * 3) / 2) + (((4 + 5) * 6) / 3)\") == 21\n assert candidate(s = \"(1 - (2 + (3 - (4 + (5 - (6 + (7 - (8 + 9))))))))\") == 9\n assert candidate(s = \"(1 + (2 * (2 + 3) - 4) + 5)\") == 9\n assert candidate(s = \"((1 + 2) * (3 + 4) - 5) * 2\") == 3\n assert candidate(s = \"((10 + 20) - (30 + 40)) + (50 + (60 - (70 + (80 - (90 + (100 - (110 + (120 - 130))))))))\") == 10\n assert candidate(s = \"((1 + 2) * (3 + 4)) - ((5 + 6) * (7 + 8))\") == -16\n assert candidate(s = \"(2 + 6 * (25 - (3 + 3) * 2 ) ) + 5\") == 34\n assert candidate(s = \"(1 + (4 + (5 + (2 - 3)) - 3)) + (6 + 8)\") == 20\n assert candidate(s = \"((22 + (2 * (3 + 5))) - (7 + 3))\") == 22\n assert candidate(s = \"(1 + (2 - 3) * (4 + 5) - 6)\") == -15\n assert candidate(s = \"(1 + (2 - (3 + (4 - (5 + (6 - (7 + (8 - 9))))))))\") == 1\n assert candidate(s = \"(1 + 2) * (3 + 4) - (5 + 6) * (7 + 8) + (9 * 10)\") == 33\n assert candidate(s = \"1 - (2 + (3 - (4 - (5 - 6))))\") == 1\n assert candidate(s = \"(1 + (2 + (3 + (4 + (5 + (6 + (7 + 8)))))))\") == 36\n assert candidate(s = \"(1 + 2) + (3 + 4) + (5 + 6) + (7 + 8) + (9 + 10)\") == 55\n assert candidate(s = \"30 - (10 + 20) + (5 * (2 + 3))\") == 10\n assert candidate(s = \"(123 - (45 + (67 - (89 + 10))) + 21)\") == 131\n assert candidate(s = \"- ( - ( - ( - ( - 1 ) ) ) )\") == -1\n assert candidate(s = \"- (3 + (4 - 5))\") == -2\n assert candidate(s = \"(((((1 + 2) * 3) - 4) + 5) * (6 - (7 + 8)))\") == -2\n assert candidate(s = \"3 * (2 + (1 - 5) * (3 + 7)) - 2\") == -11\n assert candidate(s = \"( ( 1 + 2 ) * ( 3 + 4 ) ) - ( ( 5 + 6 ) * ( 7 + 8 ) )\") == -16\n assert candidate(s = \"(3 * (4 - (5 + 2)) / (1 - 2))\") == -1\n assert candidate(s = \"((((-1 + 2) - 3) + 4) - 5)\") == -3\n assert candidate(s = \"(12 - (4 + 3) * (2 - 1)) + 7\") == 13\n assert candidate(s = \"( 123 + ( 456 - ( 789 + ( 12 - 34 ) ) ) )\") == -188\n assert candidate(s = \"10 + 20 * (30 - 20 / 2) + 5\") == 43\n assert candidate(s = \"((2 + 3) * (4 + 5) - 6) + 7 * (8 - 9)\") == 14\n assert candidate(s = \"(1 + (2 * (2 + 3)) - (4 * (5 - 6))) + (7 * (8 - (9 + 1)))\") == 10\n assert candidate(s = \"(((1 + 2) * 3) + ((4 + 5) * 6) + ((7 + 8) * 9))\") == 45\n assert candidate(s = \"(10 + 20) - (30 + 40) + (50 - 60)\") == -50\n assert candidate(s = \"(5 + (10 + (15 + (20 + (25 + (30 + (35 + (40 + (45 + 50)))))))))\") == 275\n assert candidate(s = \"10 - 2 * (6 / (3 + 1))\") == -2\n assert candidate(s = \"(10 + 2) * 6 - (3 + (4 - 5))\") == 16\n assert candidate(s = \"100 + ( 50 - ( 25 * ( 4 + 1 ) ) ) + ( 10 - ( 2 * 3 ) )\") == 125\n assert candidate(s = \"((2 + 3) * (4 + 5)) - (6 * (7 + 8))\") == -7\n assert candidate(s = \"100 - ((99 - (98 - (97 - (96 - (95 - (94 - (93 - (92 - (91 - 90)))))))))\") == 5\n assert candidate(s = \"((3 + 5) - (2 * (8 / 4)) + 1)\") == -5\n assert candidate(s = \"(123 - (456 + 789) + (101 - 202))\") == -1223\n assert candidate(s = \"100 - ( 3 * ( 2 + 4 ) ) + 5\") == 96\n assert candidate(s = \"-1 + (-2 + (-3 * (-4 - (-5))))\") == -7\n assert candidate(s = \"- ( 2 + 3 ) + ( 4 - 5 )\") == -6\n assert candidate(s = \"(100 - (50 + (25 - (10 + (5 - 2)))))\") == 38\n assert candidate(s = \"(10 + 2 * 6) / ((5 - 3) * 2)\") == 18\n assert candidate(s = \"10 + (2 * (6 / 3))\") == 21\n assert candidate(s = \"5 * (3 + (2 * (2 + (1 + (0 - (-1))))))\") == 14\n assert candidate(s = \"1 - (2 + 3) * (4 - 5) + (6 / 3)\") == 4\n assert candidate(s = \"1 - (2 + (3 * (4 + (5 * (6 + (7 * (8 + (9 * (10 + 11)))))))))\") == -64\n assert candidate(s = \"(100 - 50) - ((25 * 2) - (10 + 5))\") == 38\n assert candidate(s = \"1 + (2 + (3 + (4 + (5 + 6))))\") == 21\n assert candidate(s = \"((22 + (2 * 3)) * (4 + 3))\") == 34\n assert candidate(s = \"(10 + 20) - ((30 + 40) - (50 + (60 - (70 + (80 - (90 + (100 - 110)))))))\") == 0\n assert candidate(s = \"(8 - (4 + (1 - 3) + (2 - (5 + 7))))\") == 16\n assert candidate(s = \"100 - (25 * (2 + 3))\") == 70\n assert candidate(s = \"-((1 + 2) + (3 + 4)) + ((5 + 6) + (7 + 8))\") == 16\n assert candidate(s = \"(100 + 200 + (300 + (400 + (500 + (600 + (700 + (800 + 900)))))))\") == 4500\n assert candidate(s = \"10 - (9 - (8 - (7 - (6 - (5 - (4 - (3 - (2 - 1))))))))\") == 5\n assert candidate(s = \"100 + (200 * (300 + 400) - 500)\") == 500\n assert candidate(s = \"1 - (-2 - (-3 - (-4)))\") == 4\n assert candidate(s = \"10 + 20 - 30 + (40 - 50)\") == -10\n assert candidate(s = \"((1 + 2) * (3 - 4)) + (5 + 6)\") == 13\n assert candidate(s = \"12 - (4 * (2 + 3)) + 15\") == 18\n assert candidate(s = \"3 + 5 / 2\") == 10\n assert candidate(s = \"1 + (2 * (2 + 2) - (3 - 4) * 3)\") == 5\n assert candidate(s = \"(5 + 3) * (7 - (2 + 3))\") == 10\n assert candidate(s = \"10 + 2 * (6 / (3 + 1)) - (8 - 4) * (2 + 1)\") == 15\n assert candidate(s = \"2 * ((3 + 4) * (5 - 6) + 7) - 8\") == 7\n assert candidate(s = \"(1 + (2 * (2 + (3 * (4 + (5 * (6 + 7)))))))\") == 30\n assert candidate(s = \"123 + (456 - (789 + (101 - 202) ) )\") == -109\n assert candidate(s = \"3 + (2 * (2 + (2 * (2 + (2 * 2)))))\") == 15\n assert candidate(s = \"-1 + (-2 + (-3 + (-4 + (-5))))\") == -15\n assert candidate(s = \"(((1 + 2) * (3 + 4)) - 5) * (6 + 7)\") == -8\n assert candidate(s = \"(3 + (2 * (2 + 1)))\") == 8\n assert candidate(s = \"20 * ((1 + 2) * (3 + 4) - (5 * 6)) / 10\") == 29\n assert candidate(s = \"((100 - (50 + (25 - (10 + (5 - (2 + (1 - 0))))))) + (10 - 5))\") == 42\n assert candidate(s = \"(5 - 3) * (10 - (4 + 2) * (3 - 1))\") == -4\n assert candidate(s = \"(1 + 2) * 3 - 4 * (5 + 6)\") == -9\n assert candidate(s = \"(1 - (2 + (3 - (4 + (5 - 6)))))\") == -1\n assert candidate(s = \"(1 - (2 - (3 - (4 - (5 - (6 - (7 - (8 - 9)))))))\") == 5\n assert candidate(s = \"(3 - 4) * (5 - (6 - (7 - (8 - (9 - 10)))))\") == 2\n assert candidate(s = \"(10 + ((20 + 30) - (40 + (50 - (60 + (70 - 80))))))\") == 20\n assert candidate(s = \"(((1 + 2) * (3 + 4)) - (5 + 6)) * (7 - (8 + 9))\") == -11\n assert candidate(s = \"(1 + (2 * (3 + (4 * (5 + (6 * (7 + (8 * (9 + 10))))))))\") == 55\n assert candidate(s = \"1 + (2 - (3 + (4 - (5 + (6 - (7 + (8 - 9)))))))\") == 1\n assert candidate(s = \"(3 * (5 - (2 + 1)) + 4) - (6 * (8 - (7 + 1)))\") == 3\n assert candidate(s = \"((1 + 2) * (3 + 4) - (5 + 6)) * (7 + 8) - (9 + 10)\") == -5\n assert candidate(s = \"(1 + 2) * (3 - 4) * (5 + 6) * (7 - 8)\") == -10\n assert candidate(s = \"1 + 2 - 3 * (4 - 5) / (6 - 7) + 8\") == 10\n assert candidate(s = \"(1 + (2 * 3)) - (4 + (5 * 6))\") == -9\n assert candidate(s = \"(((3 + 2) * (4 + 5)) - (6 + (7 * 8) - 9)) + 10\") == 12\n assert candidate(s = \"(100 - (50 + 25 - (10 * 2 + 5)) + 15)\") == 57\n assert candidate(s = \"1000 + (2000 - (3000 - (4000 - (5000 - (6000 - (7000 - 8000))))))\") == 6000\n assert candidate(s = \"( ( ( 1 + 2 ) * 3 ) - ( 4 + 5 ) )\") == -3\n assert candidate(s = \"(1 + (2 * (3 + (4 * (5 + 6))))) - (7 + (8 * (9 + 10)))\") == -13\n assert candidate(s = \"((1 + 2) * (3 + 4) - (5 * 6))\") == -1\n assert candidate(s = \"(10 - 5) + (3 * 2) + (8 / 4)\") == 22\n assert candidate(s = \"3 + 5 * ( 2 - 8 )\") == 2\n assert candidate(s = \"(3 - (5 - (7 - (9 - (11 - (13 - (15 - 17))))))\") == -8\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().calculate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var calculate = function(s) {", "container": null, "callable": "calculate", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 226, "task_id": "invert-binary-tree", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, invert the tree, and return its root.\n \nExample 1:\n\n\nInput: root = [4,2,7,1,3,6,9]\nOutput: [4,7,2,9,6,3,1]\n\nExample 2:\n\n\nInput: root = [2,1,3]\nOutput: [2,3,1]\n\nExample 3:\n\nInput: root = []\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 100].\n-100 <= Node.val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 6, 9])), tree_node([4, 7, 2, 9, 6, 3, 1]))\n assert is_same_tree(candidate(root = tree_node([2, 1, 3])), tree_node([2, 3, 1]))\n assert candidate(root = tree_node([])) == None\n assert is_same_tree(candidate(root = tree_node([3, 1, 4, None, 2])), tree_node([3, 4, 1, None, None, 2]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])), tree_node([1, 2, None, 3, None, 4, None, 5]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, None, 7, 8, None, 10, 11, 12])), tree_node([1, 3, 2, 7, None, 5, 4, None, 12, 11, 10, None, 8]))\n assert is_same_tree(candidate(root = tree_node([50, 20, 70, 10, 30, 60, 80, 5, 15, 25, 35, 55, 65, 75, 85])), tree_node([50, 70, 20, 80, 60, 30, 10, 85, 75, 65, 55, 35, 25, 15, 5]))\n assert is_same_tree(candidate(root = tree_node([3, 1, 4, 3, None, 1, 5])), tree_node([3, 4, 1, 5, 1, None, 3]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])), tree_node([1, 2, None, 3, None, 4, None, 5, None, 6]))\n assert is_same_tree(candidate(root = tree_node([8, 5, 9, 3, 7, 12, 15, 1, 4, 6, 10, 13, 17])), tree_node([8, 9, 5, 15, 12, 7, 3, None, None, 17, 13, 10, 6, 4, 1]))\n assert is_same_tree(candidate(root = tree_node([5, 15, 1, None, 30, 20, None])), tree_node([5, 1, 15, None, 20, 30]))\n assert is_same_tree(candidate(root = tree_node([8, 15, 3, 7, 19, 1, 2])), tree_node([8, 3, 15, 2, 1, 19, 7]))\n assert is_same_tree(candidate(root = tree_node([6, 3, 8, 1, 4, 7, 9, None, None, 2, 5])), tree_node([6, 8, 3, 9, 7, 4, 1, None, None, None, None, 5, 2]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37])), tree_node([20, 30, 10, 35, 25, 15, 5, 37, 33, 27, 23, 17, 13, 7, 3]))\n assert is_same_tree(candidate(root = tree_node([1, 2])), tree_node([1, None, 2]))\n assert is_same_tree(candidate(root = tree_node([10, None, 20, None, 30, None, 40])), tree_node([10, 20, None, 30, None, 40]))\n assert is_same_tree(candidate(root = tree_node([3, 9, 20, None, None, 15, 7])), tree_node([3, 20, 9, 7, 15]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, 1, 5, 9, 20, None, None, None, 6, None, 18])), tree_node([7, 15, 3, 20, 9, 5, 1, None, None, 18, None, 6]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, None, None, 6, 20])), tree_node([10, 15, 5, 20, 6]))\n assert is_same_tree(candidate(root = tree_node([1, 3, 2, 5, 4])), tree_node([1, 2, 3, None, None, 4, 5]))\n assert is_same_tree(candidate(root = tree_node([8, 5, 9, 2, 7, None, None, None, 3, None, 4])), tree_node([8, 9, 5, None, None, 7, 2, 4, None, 3]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, None, 4, None, 5])), tree_node([1, 3, 2, 5, None, 4]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19, 20])), tree_node([1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 10, 9, 8, None, None, None, None, None, None, None, None, None, 20, 19, 18, 17, 16]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])), tree_node([10, 15, 5, 18, None, 7, 3]))\n assert is_same_tree(candidate(root = tree_node([-10, -5, -15, -3, -8, None, -20])), tree_node([-10, -15, -5, -20, None, -8, -3]))\n assert is_same_tree(candidate(root = tree_node([1, 3, 2, None, 6, 5, 4, None, None, None, None, None, 7])), tree_node([1, 2, 3, 4, 5, 6, None, 7]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1])), tree_node([5, 7, 3, 8, 6, 4, 2, None, None, None, None, None, None, None, 1]))\n assert is_same_tree(candidate(root = tree_node([100, -50, -20, -60, -80, -30, -10])), tree_node([100, -20, -50, -10, -30, -80, -60]))\n assert is_same_tree(candidate(root = tree_node([5, 1, 8, None, None, 6, 9])), tree_node([5, 8, 1, 9, 6]))\n assert is_same_tree(candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7])), tree_node([-1, -3, -2, -7, -6, -5, -4]))\n assert is_same_tree(candidate(root = tree_node([7, -3, 9, -5, -4, 8, -10, None, None, None, -9, -8, -6])), tree_node([7, 9, -3, -10, 8, -4, -5, None, None, -6, -8, -9]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 8, None, 9, None, 10])), tree_node([1, 3, 2, 5, None, None, 4, None, 8, None, 6, None, 10, None, 9]))\n assert is_same_tree(candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])), tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9]))\n assert is_same_tree(candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])), tree_node([6, 8, 2, 9, 7, 4, 0, None, None, None, None, 5, 3]))\n assert is_same_tree(candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])), tree_node([5, 8, 4, 4, 13, None, 11, 1, 5, None, None, 2, 7]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, None, None, 4])), tree_node([1, 2]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])), tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7]))\n assert is_same_tree(candidate(root = tree_node([8, 5, 10, None, None, 6, 12, None, None, 7, 9])), tree_node([8, 10, 5, 12, 6, None, None, 9, 7]))\n assert is_same_tree(candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, 3, 5, None, None, None, None, None, None])), tree_node([6, 8, 2, 9, 7, 4, 0, None, None, None, None, None, 5, 3]))\n assert is_same_tree(candidate(root = tree_node([5, 4, 7, 3, None, 6, 9])), tree_node([5, 7, 4, 9, 6, None, 3]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 18, None, 30, None, 16, 22, 27, None, None, 19])), tree_node([20, 25, 15, 30, None, 18, 10, None, None, 27, 22, 16, None, None, None, None, None, None, 19]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, None, 10, None, None, 11, 12, None, None, 13, None, 14, 15])), tree_node([1, 3, 2, 7, 6, 5, 4, 12, 11, None, None, 10, None, 9, 8, None, None, None, None, 15, 14, None, 13]))\n assert is_same_tree(candidate(root = tree_node([5, 1, 4, None, None, 3, 6])), tree_node([5, 4, 1, 6, 3]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])), tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8]))\n assert is_same_tree(candidate(root = tree_node([1, 3, 2, None, None, 5, 4])), tree_node([1, 2, 3, 4, 5]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, 7, 8, None, None, None, None, 9])), tree_node([1, 3, 2, None, 6, 5, 4, None, None, None, None, 8, 7, None, None, None, 9]))\n assert is_same_tree(candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])), tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8]))\n assert is_same_tree(candidate(root = tree_node([100, -100, 50, 25, 75, -25, -50])), tree_node([100, 50, -100, -50, -25, 75, 25]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, None, None, 2, 6])), tree_node([5, 8, 3, 9, 7, 4, 1, None, None, None, None, 6, 2]))\n assert is_same_tree(candidate(root = tree_node([0, 0, 0, 0, 0, None, None, 0, 0])), tree_node([0, 0, 0, None, None, 0, 0, None, None, 0, 0]))\n assert is_same_tree(candidate(root = tree_node([5, 4, 7, 3, None, 2, None, -1])), tree_node([5, 7, 4, None, 2, None, 3, None, None, None, -1]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, None, None, None, None, 14])), tree_node([1, 3, 2, 7, 6, 5, 4, None, None, 13, 12, 11, 10, 9, 8, None, None, None, None, None, None, None, None, 14]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), tree_node([1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 10, 9, 8, None, None, None, None, None, None, None, None, None, None, None, 20, 19, 18, 17, 16]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])), tree_node([1, 2]))\n assert is_same_tree(candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4])), tree_node([3, 1, 5, 8, 0, 2, 6, None, None, None, None, 4, 7]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9])), tree_node([1, 3, 2, 5, 4, None, None, 7, 6, None, None, 9, 8]))\n assert is_same_tree(candidate(root = tree_node([2, None, 3, None, 4, None, 5, None, 6])), tree_node([2, 3, None, 4, None, 5, None, 6]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), tree_node([1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 10, 9, 8]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, None, 3, None])), tree_node([1, 2]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])), tree_node([1, 2, 2, 3, 4, 4, 3]))\n assert is_same_tree(candidate(root = tree_node([100, -50, 150, 25, 75, 125, 175, 15, 35, 65, 85, 115, 145, 165, 185])), tree_node([100, 150, -50, 175, 125, 75, 25, 185, 165, 145, 115, 85, 65, 35, 15]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])), tree_node([1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 10, 9, 8, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16]))\n assert is_same_tree(candidate(root = tree_node([8, 5, 1, 7, 10, 12])), tree_node([8, 1, 5, None, 12, 10, 7]))\n assert is_same_tree(candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])), tree_node([1, None, 2, None, 3, None, 4, None, 5]))\n assert is_same_tree(candidate(root = tree_node([1, 3, None, None, 2])), tree_node([1, None, 3, 2]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), tree_node([1, 2, None, 4, 3, 8, 7, 6, 5, None, 15, 14, 13, 12, 11, 10, 9, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 30, 29]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, None, None, 7, 8, None, None, 14])), tree_node([1, 3, 2, 7, None, None, 4, 14, None, None, 8]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8])), tree_node([1, 3, 2, 6, None, 5, 4, 8, None, None, None, None, 7]))\n assert is_same_tree(candidate(root = tree_node([10, None, 20, None, None, 15, 25])), tree_node([10, 20]))\n assert is_same_tree(candidate(root = tree_node([5, 1, None, None, 4, 3, None, None, 2])), tree_node([5, None, 1, 4, None, None, 3, 2]))\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().invertTree", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var invertTree = function(root) {", "container": null, "callable": "invertTree", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 227, "task_id": "basic-calculator-ii", "difficulty": "Medium", "problem_description": "Given a string s which represents an expression, evaluate this expression and return its value. \nThe integer division should truncate toward zero.\nYou may assume that the given expression is always valid. All intermediate results will be in the range of [-231, 231 - 1].\nNote: You are not allowed to use any built-in function which evaluates strings as mathematical expressions, such as eval().\n \nExample 1:\nInput: s = \"3+2*2\"\nOutput: 7\nExample 2:\nInput: s = \" 3/2 \"\nOutput: 1\nExample 3:\nInput: s = \" 3+5 / 2 \"\nOutput: 5\n\n \nConstraints:\n\n1 <= s.length <= 3 * 105\ns consists of integers and operators ('+', '-', '*', '/') separated by some number of spaces.\ns represents a valid expression.\nAll the integers in the expression are non-negative integers in the range [0, 231 - 1].\nThe answer is guaranteed to fit in a 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"2 - 3 + 4\") == 3\n assert candidate(s = \" 1000000000 - 500000000 + 250000000\") == 750000000\n assert candidate(s = \"30 + 2 * 6 / (3 - 1)\") == 33\n assert candidate(s = \"100 * ( 2 + 12 ) / 14\") == 200\n assert candidate(s = \"1 + 1 * 1 + 1\") == 3\n assert candidate(s = \"2*3+4/5\") == 6\n assert candidate(s = \"3 + 5 / ( 2 + 3 )\") == 8\n assert candidate(s = \"0 + 0\") == 0\n assert candidate(s = \"100*2+12\") == 212\n assert candidate(s = \"2147483647 + 1 - 1\") == 2147483647\n assert candidate(s = \"100000 + 100000 - 50000 * 2 + 25000 * 4 / 5\") == 120000\n assert candidate(s = \"100 * 2 + 12\") == 212\n assert candidate(s = \" 200 - 3 * 50 + 25\") == 75\n assert candidate(s = \"10 + 2 * 6\") == 22\n assert candidate(s = \"3+2*2\") == 7\n assert candidate(s = \" 30 + 2 * 6 - 12 / 3 \") == 38\n assert candidate(s = \"100*(2+12)/14\") == 200\n assert candidate(s = \" 3+5 / 2 \") == 5\n assert candidate(s = \"1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10\") == 3628800\n assert candidate(s = \"100 * 2 / 25\") == 8\n assert candidate(s = \" 0 + 0 * 1 / 1\") == 0\n assert candidate(s = \" 3/2 \") == 1\n assert candidate(s = \"3 + 5 - ( 2 + 3 )\") == 9\n assert candidate(s = \"2147483647 - 2147483646\") == 1\n assert candidate(s = \"3+5 / 2 * 3\") == 9\n assert candidate(s = \"3 + 2 * 2 + 1 - 5 / 2\") == 6\n assert candidate(s = \"10 * 5 + 3\") == 53\n assert candidate(s = \"3+5-2*3/4\") == 7\n assert candidate(s = \"3 + 5 / 2 + 3\") == 8\n assert candidate(s = \"1000 / 10 / 10\") == 10\n assert candidate(s = \"3 + 5 / 2 - 8 * 3 + 4 / 2\") == -17\n assert candidate(s = \"1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1\") == 10\n assert candidate(s = \" 30 / 3 + 10 * 2 - 5\") == 25\n assert candidate(s = \"100*(2+12)\") == 212\n assert candidate(s = \"100 * ( 2 + 12 )\") == 212\n assert candidate(s = \" 1 + 2 * 3 / 4 + 5 * 6 - 7\") == 25\n assert candidate(s = \"( 2 + 6 ) * 3 + 8\") == 28\n assert candidate(s = \"(2 + 6 * 3 + 5 - (3 * 14 / 7 + 2) * 5) + 3\") == 32\n assert candidate(s = \"2147483647 / 1\") == 2147483647\n assert candidate(s = \"1 - 1 + 1\") == 1\n assert candidate(s = \"2*3+4/5*6-7+8\") == 7\n assert candidate(s = \"10 + 2 - 5\") == 7\n assert candidate(s = \" 30 /3 + 10 * 2 \") == 30\n assert candidate(s = \"2 * 3 + 4 / 5\") == 6\n assert candidate(s = \"3 + 2 * 2 + 1\") == 8\n assert candidate(s = \"10+2*6\") == 22\n assert candidate(s = \"3 + ( 2 * 2 )\") == 7\n assert candidate(s = \"123 + 456 * 789 / 100 - 987\") == 2733\n assert candidate(s = \"1000 - 500 * 2 + 250 / 5\") == 50\n assert candidate(s = \" 100000 - 50000 * 2 + 25000 / 5000 * 20000\") == 100000\n assert candidate(s = \"987654 * 321 / 123 - 456789 + 987654\") == 3108401\n assert candidate(s = \" 1 + 2 - 3 * (4 / 5) + 6 - 7 * 8 / 9\") == 1\n assert candidate(s = \" 8 * 5 / 4 + 3 - 1\") == 12\n assert candidate(s = \" 2000 / 10 + 50 * 2 - 300 \") == 0\n assert candidate(s = \" 1234 + 567 * 89 - 101112 / 1314\") == 51621\n assert candidate(s = \" (123 + 456) * 789 - 101112 / (13 * 14) \") == 251029\n assert candidate(s = \"1 * 2 + 3 * 4 + 5 * 6 + 7 * 8 + 9 * 10\") == 190\n assert candidate(s = \"100 / 10 - 90 * 0 + 80 / 8\") == 20\n assert candidate(s = \" 1000000 - 500000 + 250000 * 2 - 125000 \") == 875000\n assert candidate(s = \"1000 - 500 * 2 / 5 + 300 / 3\") == 900\n assert candidate(s = \" 1000 + 2000 - (3000 / 4000 + 5000 - 6000 * (7000 / 8000))\") == 2750\n assert candidate(s = \" 200 * 5 + 300 / 100 - 10 \") == 993\n assert candidate(s = \"123 + 456 * 789 - 101112 / 1314\") == 359831\n assert candidate(s = \" 5 + 4 - 3 * 2 + 1 / 1\") == 4\n assert candidate(s = \" ( 100 + 200 ) * ( 300 - 100 ) / 50\") == 60098\n assert candidate(s = \"7 * 8 * 9 / 6 + 5 - 3 * 2\") == 83\n assert candidate(s = \"300 + 200 * 5 / 10 - 25\") == 375\n assert candidate(s = \"100 * 200 / 500 + 200 - 100\") == 140\n assert candidate(s = \"100000 / 100 - 99999 * 0 + 1\") == 1001\n assert candidate(s = \" 42 * (5 - 3) / 2 + 8 \") == 217\n assert candidate(s = \" 23 + 56 * 99 / 77 - 44 \") == 51\n assert candidate(s = \"100 * 2 + 12 / 3 - 5\") == 199\n assert candidate(s = \" 123 + 456 - 789 * 0 / 1 + 1000 \") == 1579\n assert candidate(s = \"33 + 22 * 11 - 44 / 11 + 55\") == 326\n assert candidate(s = \"3 * 3 * 3 * 3 * 3 - 3 * 3 * 3 + 3\") == 219\n assert candidate(s = \"2147483647 - 2147483646 + 1\") == 2\n assert candidate(s = \"10 + 2 * 6 / ( 1 - 2 ) * 3\") == 16\n assert candidate(s = \"999999 + 1 - 999999 * 0 + 999999 / 1\") == 1999999\n assert candidate(s = \"12 + 34 * 56 / 78 - 90 + 12\") == -42\n assert candidate(s = \" 2 * (3 + 4 * (5 - 6 / 2)) + 7\") == 30\n assert candidate(s = \"2 + 3 * 5 / 2 - 8 / 4 + 6\") == 13\n assert candidate(s = \"5 * 5 * 5 * 5 * 5 / 5 + 5 - 5\") == 625\n assert candidate(s = \"3 * 3 + 3 / 3 * 3 - 3\") == 9\n assert candidate(s = \" 100 - 25 * 2 + 50 / 5 - 10\") == 50\n assert candidate(s = \" 2 * 3 + ( 2 * ( 1 + 4 ) / 2 ) - 5 \") == 5\n assert candidate(s = \"333333 + 222222 * 1 - 111111 / 1\") == 444444\n assert candidate(s = \"2222 + 1111 * 2 - 3333 / 11 + 4444\") == 8585\n assert candidate(s = \" 1000 - 500 * 2 + 250 / 50 * 20\") == 100\n assert candidate(s = \" 99 * 100 - 99 * 99 + 99 * 98\") == 9801\n assert candidate(s = \"10 / 2 + 15 * 3 - 7 * (5 - 3) + 20\") == 32\n assert candidate(s = \"10000 / 1000 + 200 * 2 - 500\") == -90\n assert candidate(s = \" 33333 + 22222 - 11111 + 44444 * 55555 / 66666\") == 81480\n assert candidate(s = \"1000 * 2 / 25 + 100 - 50\") == 130\n assert candidate(s = \"123456789 + 987654321 * 1 - 123456789 / 1\") == 987654321\n assert candidate(s = \"100 * 2 + 3 * 5 / 15 - 10\") == 191\n assert candidate(s = \" 2 * ( 3 + 4 * ( 5 - 6 ) / 7 ) - 8 \") == 18\n assert candidate(s = \"1000 * 5 / 25 + 20 - 40\") == 180\n assert candidate(s = \" 200 + 50 / 5 - 30 * 2 + 10\") == 160\n assert candidate(s = \"32 / 2 * 2 + 1 - 1\") == 32\n assert candidate(s = \" 987654321 - 123456789 + 98765 * 43210 / 54321\") == 864276095\n assert candidate(s = \" 1234 + 5678 * 90 / 100 - 12345 / 5 \") == 3875\n assert candidate(s = \" 3 + 8 * 10 / 5 - 2 \") == 17\n assert candidate(s = \" 7 + 3 * ( 10 / 2 ) - 5\") == 17\n assert candidate(s = \" 100 * 2 / 5 + 3 * (20 - 15) \") == 85\n assert candidate(s = \" 10 * 20 - 5 * 4 + 3 * 2 - 1 / 1 + 8 * 2\") == 201\n assert candidate(s = \" 8 * ( 4 / 2 ) + 12 - 6\") == 22\n assert candidate(s = \" 99 + 99 * 99 / 99 - 99 \") == 99\n assert candidate(s = \"100 - 50 + 25 - 12 + 6 - 3 + 1\") == 67\n assert candidate(s = \"1000 * 2 + 300 - 50 / 2\") == 2275\n assert candidate(s = \"100 + 200 * (300 - 150 / 50) - 400\") == 59697\n assert candidate(s = \"333 * 111 + 222 * 444 / 666 - 777 + 888\") == 37222\n assert candidate(s = \"7 + 3 * (10 / 2) - 1\") == 21\n assert candidate(s = \"2 * 3 + 4 * 5 - 6 / 2 + 7\") == 30\n assert candidate(s = \"(1 + 2) * 3 / 4 + 5 - 6\") == 1\n assert candidate(s = \" 123 + 456 * 789 / 321 \") == 1243\n assert candidate(s = \"3 + 5 * 2 / 2 - 1\") == 7\n assert candidate(s = \" 1000 + 2000 * 3000 - 4000 / 5000 + 6000 - 7000 * 8000 / 9000 \") == 6000778\n assert candidate(s = \" 1000 + 2000 - 3000 * (4000 / 5000) + 6000 - 7000 * (8000 / 9000)\") == 378\n assert candidate(s = \"10 * 10 - 9 * 9 + 8 * 8 - 7 * 7 + 6 * 6\") == 70\n assert candidate(s = \" 1000 * 2000 - 3000 + 4000 / 5000 * 6000\") == 1997000\n assert candidate(s = \" 2147483647 + 1 * 2 - 3 / 4\") == 2147483649\n assert candidate(s = \" (10 + (20 + (30 + (40 + (50 + (60 + (70 + (80 + (90 + 100)))))))) \") == 550\n assert candidate(s = \" 100 + 200 - 300 * 400 / 500 + 600 * 700 / 800\") == 585\n assert candidate(s = \" 4 + 5 * 6 / 3 - 7 + 8 * 2\") == 23\n assert candidate(s = \" 1 + 2 * ( 3 + 4 ) / 2 - 1 \") == 8\n assert candidate(s = \" 1234 + 5678 - 91011 * 121314 / 151617\") == -65909\n assert candidate(s = \" 999 + 1 * 1000 - 500 / 2 \") == 1749\n assert candidate(s = \" 100 * 2 + 3 - 4 / 2 \") == 201\n assert candidate(s = \" 0 + 0 * 0 - 0 / 1\") == 0\n assert candidate(s = \" 7 + 14 / 7 - 3 + 6 * 2\") == 18\n assert candidate(s = \"0 * 1 + 2 - 3 / 4 * 5\") == 2\n assert candidate(s = \" 123 + 456 * 789 / 101 - 234\") == 3451\n assert candidate(s = \" 12345 + 67890 - 54321 / 1234 * 5678 \") == -169597\n assert candidate(s = \" 123 + 456 - 789 * 1011 / 1213\") == -78\n assert candidate(s = \" 3 * 5 / 15 + 10 - 7 \") == 4\n assert candidate(s = \" 100 - 50 + 25 * 4 / 2 \") == 100\n assert candidate(s = \"10 + 20 * (30 / 10) - 5\") == 65\n assert candidate(s = \" 99999 + 88888 - 77777 * 66666 / 55555\") == 95555\n assert candidate(s = \" 100 + 200 * (300 / 50) - 600 + 700 * 800 / 900 \") == 1322\n assert candidate(s = \"999999 / 3 + 999999 / 3 - 999999 / 3\") == 333333\n assert candidate(s = \" 1000 / ( 500 / 250 ) - 250 + 125 * ( 500 / 250 )\") == 0\n assert candidate(s = \" 2 * 3 + 4 * 5 - 6 / 3 + 8\") == 32\n assert candidate(s = \"987654 * 321 / 1000 + 123456 - 789012 / 3\") == 177488\n assert candidate(s = \" 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 \") == 3628800\n assert candidate(s = \" 42 * 2 - 5 / 1 + 3 \") == 82\n assert candidate(s = \" 2 * ( 3 + 5 ) * 4\") == 26\n assert candidate(s = \"30 / 5 * 2 - 1 + 4 * 8 - 3\") == 40\n assert candidate(s = \" 1 + (2 + (3 + (4 + (5 + 6))))\") == 21\n assert candidate(s = \" 123456789 + 987654321 - 111111111 * 222222222 / 333333333\") == 1037037036\n assert candidate(s = \"123 + 456 * 789 / 101 - 234\") == 3451\n assert candidate(s = \"1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10\") == 55\n assert candidate(s = \" 1000 / ( 25 / 5 ) + 50 - 20\") == 38\n assert candidate(s = \" 5 + 3 * (2 - 8) + 4 / 2\") == 5\n assert candidate(s = \"987654321 - 123456789 + 111111111 * 222222222 / 333333333 \") == 938271606\n assert candidate(s = \" 8 / 3 + 4 * ( 5 - 3 ) / 2 \") == 21\n assert candidate(s = \" 5 * 6 + 20 / 4 - 8\") == 27\n assert candidate(s = \" 3 + 8 * ( 4 - 2 ) / 2\") == 34\n assert candidate(s = \" 5 + 3 * ( 20 / 4 ) \") == 20\n assert candidate(s = \"1000000 + 500000 * 2 - 250000 / 5 + 125000\") == 2075000\n assert candidate(s = \"2 + 3 * 4 - 5 / 2 + 6 * 7 - 8 / 4\") == 52\n assert candidate(s = \" 1000 - 500 + 250 * 2 - 125 \") == 875\n assert candidate(s = \"0 * 0 + 0 / 1 + 100 - 50\") == 50\n assert candidate(s = \" 10 + 20 + 30 + 40 + 50 - ( 10 * 5 )\") == 100\n assert candidate(s = \" 7 * 8 - 3 + 2 * 4 \") == 61\n assert candidate(s = \"9 * 3 + 2 - 1 / 1 + 8 * 2\") == 44\n assert candidate(s = \"50 * 50 - 50 / 50 + 50 * 50 - 50 / 50\") == 4998\n assert candidate(s = \" 3 + (2 * (2 + (2 * (2 + 2))))\") == 13\n assert candidate(s = \"100 * 2 + 12 / 3 - 50\") == 154\n assert candidate(s = \"3 + 33 + 333 + 3333 + 33333 + 333333 + 3333333 + 33333333 + 333333333\") == 370370367\n assert candidate(s = \"1 + 2 * 3 + 4 / 2 - 5\") == 4\n assert candidate(s = \" 3 + 5 * ( 2 + 8 ) / 4 - 2 \") == 13\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().calculate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var calculate = function(s) {", "container": null, "callable": "calculate", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 228, "task_id": "summary-ranges", "difficulty": "Easy", "problem_description": "You are given a sorted unique integer array nums.\nA range [a,b] is the set of all integers from a to b (inclusive).\nReturn the smallest sorted list of ranges that cover all the numbers in the array exactly. That is, each element of nums is covered by exactly one of the ranges, and there is no integer x such that x is in one of the ranges but not in nums.\nEach range [a,b] in the list should be output as:\n\n\"a->b\" if a != b\n\"a\" if a == b\n\n \nExample 1:\n\nInput: nums = [0,1,2,4,5,7]\nOutput: [\"0->2\",\"4->5\",\"7\"]\nExplanation: The ranges are:\n[0,2] --> \"0->2\"\n[4,5] --> \"4->5\"\n[7,7] --> \"7\"\n\nExample 2:\n\nInput: nums = [0,2,3,4,6,8,9]\nOutput: [\"0\",\"2->4\",\"6\",\"8->9\"]\nExplanation: The ranges are:\n[0,0] --> \"0\"\n[2,4] --> \"2->4\"\n[6,6] --> \"6\"\n[8,9] --> \"8->9\"\n\n \nConstraints:\n\n0 <= nums.length <= 20\n-231 <= nums[i] <= 231 - 1\nAll the values of nums are unique.\nnums is sorted in ascending order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 1, 2, 3, 4, 5]) == ['0->5']\n assert candidate(nums = [-1, 0, 1, 2, 3, 5, 6, 7, 8, 10]) == ['-1->3', '5->8', '10']\n assert candidate(nums = [-2147483648, -2147483647, -2147483646]) == ['-2147483648->-2147483646']\n assert candidate(nums = [1, 3, 5, 7, 9]) == ['1', '3', '5', '7', '9']\n assert candidate(nums = [5, 6, 7, 9, 10, 11, 13, 14, 15, 16]) == ['5->7', '9->11', '13->16']\n assert candidate(nums = [1]) == ['1']\n assert candidate(nums = [-2, -1, 0, 1, 3, 4, 6, 8]) == ['-2->1', '3->4', '6', '8']\n assert candidate(nums = [-2147483648, -2147483647, 0, 2147483646, 2147483647]) == ['-2147483648->-2147483647', '0', '2147483646->2147483647']\n assert candidate(nums = [1, 2, 3, 6, 8, 9, 10, 12, 13, 14]) == ['1->3', '6', '8->10', '12->14']\n assert candidate(nums = [0, 1, 2, 4, 5, 7]) == ['0->2', '4->5', '7']\n assert candidate(nums = [-1, -2, -3, -4, -5]) == ['-1', '-2', '-3', '-4', '-5']\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == ['0', '2', '4', '6', '8', '10', '12', '14', '16', '18', '20']\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == ['1', '3', '5', '7', '9', '11', '13', '15', '17', '19']\n assert candidate(nums = [-1, 0, 1, 2, 3]) == ['-1->3']\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 9, 10, 11, 13]) == ['1->3', '5->7', '9->11', '13']\n assert candidate(nums = [5, 6, 7, 20, 21, 22, 23]) == ['5->7', '20->23']\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == ['-10->-1']\n assert candidate(nums = []) == []\n assert candidate(nums = [2147483646, 2147483647]) == ['2147483646->2147483647']\n assert candidate(nums = [0]) == ['0']\n assert candidate(nums = [0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == ['0->1', '3', '5', '7', '9', '11', '13', '15', '17', '19']\n assert candidate(nums = [-2147483648, -2147483647, 2147483647]) == ['-2147483648->-2147483647', '2147483647']\n assert candidate(nums = [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17]) == ['1->5', '7->11', '13->17']\n assert candidate(nums = [0, 2, 3, 4, 6, 8, 9]) == ['0', '2->4', '6', '8->9']\n assert candidate(nums = [10, 11, 12, 15, 20, 21, 22, 23, 24, 30]) == ['10->12', '15', '20->24', '30']\n assert candidate(nums = [10, 11, 12, 15, 16, 17, 20, 21, 22, 23]) == ['10->12', '15->17', '20->23']\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31]) == ['1', '4', '7', '10', '13', '16', '19', '22', '25', '28', '31']\n assert candidate(nums = [-2147483648, -2147483647, -2147483646, 0, 2147483646, 2147483647]) == ['-2147483648->-2147483646', '0', '2147483646->2147483647']\n assert candidate(nums = [1, 2, 3]) == ['1->3']\n assert candidate(nums = [-1, 0, 1, 2, 4, 5, 7]) == ['-1->2', '4->5', '7']\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109]) == ['100->109']\n assert candidate(nums = [0, 2, 4, 6, 8]) == ['0', '2', '4', '6', '8']\n assert candidate(nums = [5]) == ['5']\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == ['1->15']\n assert candidate(nums = [10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35]) == ['10->12', '14->16', '18->20', '22->24', '26->28', '30->32', '34->35']\n assert candidate(nums = [1, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28]) == ['1', '4->6', '8->9', '11->13', '15->17', '19->21', '23->25', '27->28']\n assert candidate(nums = [50, 51, 52, 54, 55, 57, 58, 59, 61, 63, 64, 65, 67, 68, 70, 71, 72, 74, 75, 76]) == ['50->52', '54->55', '57->59', '61', '63->65', '67->68', '70->72', '74->76']\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == ['1', '3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31']\n assert candidate(nums = [-10, -9, -8, -5, -4, -3, -1, 0, 1, 2, 4, 5, 6, 8, 9, 10]) == ['-10->-8', '-5->-3', '-1->2', '4->6', '8->10']\n assert candidate(nums = [-1, -2, -3, -5, -7, -8, -9, -11, -12, -13, -14, -16, -17, -18, -20]) == ['-1', '-2', '-3', '-5', '-7', '-8', '-9', '-11', '-12', '-13', '-14', '-16', '-17', '-18', '-20']\n assert candidate(nums = [1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29]) == ['1->2', '4->5', '7->8', '10->11', '13->14', '16->17', '19->20', '22->23', '25->26', '28->29']\n assert candidate(nums = [0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25]) == ['0->3', '5->7', '9->11', '13->15', '17->18', '20->22', '24->25']\n assert candidate(nums = [-50, -49, -48, -46, -45, -44, -42, -41, -40, -38, -37, -36, -34, -33, -32, -30, -29, -28, -26, -25, -24]) == ['-50->-48', '-46->-44', '-42->-40', '-38->-36', '-34->-32', '-30->-28', '-26->-24']\n assert candidate(nums = [0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29]) == ['0->3', '5->7', '9->11', '13->15', '17->19', '21->23', '25->27', '29']\n assert candidate(nums = [100, 101, 102, 104, 105, 107, 108, 109, 111, 112, 113, 114, 116, 117, 118, 119, 120]) == ['100->102', '104->105', '107->109', '111->114', '116->120']\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == ['1', '3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31', '33', '35', '37', '39']\n assert candidate(nums = [100, 101, 102, 104, 105, 106, 108, 109, 110, 112, 113, 114, 115, 116]) == ['100->102', '104->106', '108->110', '112->116']\n assert candidate(nums = [1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31]) == ['1->2', '4->5', '7->8', '10->11', '13->14', '16->17', '19->20', '22->23', '25->26', '28->29', '31']\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == ['1->30']\n assert candidate(nums = [-5, -3, -1, 2, 5, 7, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48]) == ['-5', '-3', '-1', '2', '5', '7', '9', '12', '15', '18', '21', '24', '27', '30', '33', '36', '39', '42', '45', '48']\n assert candidate(nums = [1, 4, 5, 6, 10, 11, 12, 15, 16, 17, 20, 21, 22, 23, 25, 26, 27, 28]) == ['1', '4->6', '10->12', '15->17', '20->23', '25->28']\n assert candidate(nums = [1, 2, 3, 10, 11, 12, 20, 21, 22, 30, 31, 32, 40, 41, 42, 50, 51, 52, 60, 61, 62, 70, 71, 72]) == ['1->3', '10->12', '20->22', '30->32', '40->42', '50->52', '60->62', '70->72']\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22]) == ['1->3', '5->7', '9->12', '14->16', '18->20', '22']\n assert candidate(nums = [-1000, -999, -998, -996, -995, -993, -992, -991, -989, -988, -987, -985, -984, -983, -981, -980, -979, -977, -976, -975]) == ['-1000->-998', '-996->-995', '-993->-991', '-989->-987', '-985->-983', '-981->-979', '-977->-975']\n assert candidate(nums = [-2, -1, 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26]) == ['-2->-1', '1->2', '4->5', '7->8', '10->11', '13->14', '16->17', '19->20', '22->23', '25->26']\n assert candidate(nums = [1000, 1001, 1002, 1004, 1005, 1007, 1008, 1009, 1011, 1012, 1013, 1015, 1016, 1017, 1019, 1020, 1021]) == ['1000->1002', '1004->1005', '1007->1009', '1011->1013', '1015->1017', '1019->1021']\n assert candidate(nums = [-10, -9, -8, -7, -5, -4, -3, -1, 0, 1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21]) == ['-10->-7', '-5->-3', '-1->1', '3->5', '7->9', '11->13', '15->17', '19->21']\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == ['1', '3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31', '33', '35', '37', '39', '41', '43', '45', '47', '49']\n assert candidate(nums = [1, 2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 18, 20]) == ['1->3', '5->6', '8->9', '11->13', '15->18', '20']\n assert candidate(nums = [-10, -9, -8, -6, -5, -3, -2, -1, 0, 1, 3, 4, 5, 7, 8, 10, 11, 12]) == ['-10->-8', '-6->-5', '-3->1', '3->5', '7->8', '10->12']\n assert candidate(nums = [100, 101, 102, 104, 105, 106, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119]) == ['100->102', '104->106', '108->111', '113->119']\n assert candidate(nums = [-10, -9, -8, -6, -5, -4, -2, -1, 0, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30]) == ['-10->-8', '-6->-4', '-2->0', '2->3', '5->6', '8->9', '11->12', '14->15', '17->18', '20->21', '23->24', '26->27', '29->30']\n assert candidate(nums = [-2147483648, -2147483647, -2147483646, -2147483645, -2147483644]) == ['-2147483648->-2147483644']\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 10, 11, 12, 15, 16, 17, 18, 20]) == ['1->3', '5->7', '10->12', '15->18', '20']\n assert candidate(nums = [-10, -9, -8, -6, -5, -4, -2, -1, 0, 1, 2, 4, 5, 6, 8, 9, 10]) == ['-10->-8', '-6->-4', '-2->2', '4->6', '8->10']\n assert candidate(nums = [42]) == ['42']\n assert candidate(nums = [1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37]) == ['1->5', '7->9', '11->12', '14->16', '18->20', '22->23', '25->27', '29->32', '34->37']\n assert candidate(nums = [10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42]) == ['10->12', '15->17', '20->22', '25->27', '30->32', '35->37', '40->42']\n assert candidate(nums = [-10, -9, -8, -6, -5, -4, -2, -1, 0, 1, 2, 3, 5, 6, 7, 8, 10]) == ['-10->-8', '-6->-4', '-2->3', '5->8', '10']\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == ['1', '3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29']\n assert candidate(nums = [1, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30]) == ['1', '4->6', '8->10', '12->14', '16->18', '20->22', '24->26', '28->30']\n assert candidate(nums = [10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38]) == ['10->11', '13->14', '16->17', '19->20', '22->23', '25->26', '28->29', '31->32', '34->35', '37->38']\n assert candidate(nums = [0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28]) == ['0->1', '3->4', '6->7', '9->10', '12->13', '15->16', '18->19', '21->22', '24->25', '27->28']\n assert candidate(nums = [1000, 1001, 1002, 1004, 1005, 1006, 1008, 1009, 1010, 1011, 1013, 1014, 1015, 1016, 1017, 1018, 1019]) == ['1000->1002', '1004->1006', '1008->1011', '1013->1019']\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 15, 16, 18, 19, 20, 21, 23]) == ['1->3', '5->8', '10->12', '15->16', '18->21', '23']\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == ['0->20']\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 200, 201, 202, 300]) == ['100->105', '200->202', '300']\n assert candidate(nums = [100, 101, 104, 105, 106, 110, 111, 112, 113, 114, 115]) == ['100->101', '104->106', '110->115']\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == ['1->6', '8', '10', '12', '14', '16', '18', '20', '22', '24', '26', '28', '30', '32', '34', '36', '38', '40']\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58]) == ['1', '4', '7', '10', '13', '16', '19', '22', '25', '28', '31', '34', '37', '40', '43', '46', '49', '52', '55', '58']\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 27, 28]) == ['1->3', '5->7', '9->11', '13', '15->17', '19', '21->23', '25', '27->28']\n assert candidate(nums = [-10, -9, -8, -6, -5, -3, -2, -1, 0, 1, 2, 3, 5, 6, 7, 9, 10, 11]) == ['-10->-8', '-6->-5', '-3->3', '5->7', '9->11']\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == ['0->19']\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == ['1->20']\n assert candidate(nums = [3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 19, 21, 22, 23, 25, 27, 28, 29]) == ['3->5', '7->9', '11->13', '15', '17->19', '21->23', '25', '27->29']\n assert candidate(nums = [1, 2, 3, 8, 9, 10, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25]) == ['1->3', '8->10', '12->15', '20->25']\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946]) == ['1->3', '5', '8', '13', '21', '34', '55', '89', '144', '233', '377', '610', '987', '1597', '2584', '4181', '6765', '10946']\n assert candidate(nums = [1, 2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25]) == ['1->3', '5->6', '8->9', '11->13', '15->18', '20->23', '25']\n assert candidate(nums = [1, 2, 3, 5, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20]) == ['1->3', '5', '7->8', '10->13', '15->18', '20']\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == ['1->10', '12->30']\n assert candidate(nums = [-5, -3, -2, -1, 1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15]) == ['-5', '-3->-1', '1->4', '6->8', '10->15']\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19]) == ['-5->0', '2->4', '6->8', '10->12', '14->16', '18->19']\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51]) == ['1->3', '5->7', '9->11', '13->15', '17->19', '21->23', '25->27', '29->31', '33->35', '37->39', '41->43', '45->47', '49->51']\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000004, 1000000005, 1000000006, 1000000008]) == ['1000000000->1000000002', '1000000004->1000000006', '1000000008']\n assert candidate(nums = [1000, 1001, 1003, 1004, 1006, 1007, 1008, 1010, 1012, 1013, 1014, 1016, 1017, 1019, 1020, 1021, 1023, 1025, 1026, 1027]) == ['1000->1001', '1003->1004', '1006->1008', '1010', '1012->1014', '1016->1017', '1019->1021', '1023', '1025->1027']\n assert candidate(nums = [-10, -8, -7, -5, -4, -3, 0, 1, 2, 3, 8, 9, 10, 12, 14, 15, 16, 17, 20, 21]) == ['-10', '-8->-7', '-5->-3', '0->3', '8->10', '12', '14->17', '20->21']\n assert candidate(nums = [1, 2, 3, 10, 11, 12, 20, 21, 22, 30, 31, 32, 40, 41, 42, 50, 51, 52, 60, 61]) == ['1->3', '10->12', '20->22', '30->32', '40->42', '50->52', '60->61']\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768]) == ['1->2', '4', '8', '16', '32', '64', '128', '256', '512', '1024', '2048', '4096', '8192', '16384', '32768']\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43]) == ['5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31', '33', '35', '37', '39', '41', '43']\n assert candidate(nums = [1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 26]) == ['1->5', '7->10', '12->15', '17->20', '22->24', '26']\n assert candidate(nums = [1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29]) == ['1->2', '4->5', '7->8', '10->11', '13->14', '16->17', '19->20', '22->23', '25->26', '28->29']\n assert candidate(nums = [-1, 0, 1, 3, 4, 5, 7, 8, 9, 11, 13, 14, 15, 17, 18, 19, 21, 22, 24, 25]) == ['-1->1', '3->5', '7->9', '11', '13->15', '17->19', '21->22', '24->25']\n assert candidate(nums = [100, 101, 102, 105, 106, 107, 108, 110, 111, 112, 113, 114, 116, 117, 118, 119]) == ['100->102', '105->108', '110->114', '116->119']\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == ['10->30']\n assert candidate(nums = [1, 2, 3, 4, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 39]) == ['1->4', '6->8', '10->11', '13->15', '17->19', '21->23', '25->27', '29->31', '33->35', '37->39']\n assert candidate(nums = [0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30]) == ['0->2', '4->6', '8->10', '12->14', '16->18', '20->22', '24->26', '28->30']\n assert candidate(nums = [100, 101, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116, 117, 118, 120, 121, 122, 124, 126, 127]) == ['100->102', '104->106', '108', '110->112', '114', '116->118', '120->122', '124', '126->127']\n assert candidate(nums = [1, 2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35]) == ['1->3', '5->6', '8->9', '11->13', '15->18', '20->22', '24->26', '28->30', '32->35']\n assert candidate(nums = [-10, -9, -8, -6, -5, -3, -2, -1, 0, 1, 2, 3, 5, 6, 7, 8]) == ['-10->-8', '-6->-5', '-3->3', '5->8']\n assert candidate(nums = [0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == ['0->1', '3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31', '33', '35', '37', '39']\n assert candidate(nums = [100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 112, 113, 115, 116, 117, 118, 119]) == ['100->103', '105->107', '109->113', '115->119']\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20]) == ['-1', '-2', '-3', '-4', '-5', '-6', '-7', '-8', '-9', '-10', '-11', '-12', '-13', '-14', '-15', '-16', '-17', '-18', '-19', '-20']\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33]) == ['1', '3', '5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31', '33']\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41]) == ['5', '7', '9', '11', '13', '15', '17', '19', '21', '23', '25', '27', '29', '31', '33', '35', '37', '39', '41']\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49]) == ['1->49']\n assert candidate(nums = [100, 101, 102, 104, 105, 107, 108, 109, 110, 111, 112, 113]) == ['100->102', '104->105', '107->113']\n assert candidate(nums = [1000, 1001, 1002, 1004, 1005, 1006, 1008, 1009, 1010, 1011, 1012]) == ['1000->1002', '1004->1006', '1008->1012']\n assert candidate(nums = [1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 19, 20]) == ['1->3', '5', '7->9', '11->13', '15', '17->20']\n assert candidate(nums = [0, 1, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24]) == ['0->1', '3->5', '7->10', '12->15', '17->21', '23->24']\n assert candidate(nums = [-1, -2, -3, -5, -6, -7, -9, -10, -11, -13, -14, -15, -17, -18, -19, -21, -22, -23, -25, -26, -27]) == ['-1', '-2', '-3', '-5', '-6', '-7', '-9', '-10', '-11', '-13', '-14', '-15', '-17', '-18', '-19', '-21', '-22', '-23', '-25', '-26', '-27']\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().summaryRanges", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var summaryRanges = function(nums) {", "container": null, "callable": "summaryRanges", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 229, "task_id": "majority-element-ii", "difficulty": "Medium", "problem_description": "Given an integer array of size n, find all elements that appear more than ⌊ n/3 ⌋ times.\n \nExample 1:\n\nInput: nums = [3,2,3]\nOutput: [3]\n\nExample 2:\n\nInput: nums = [1]\nOutput: [1]\n\nExample 3:\n\nInput: nums = [1,2]\nOutput: [1,2]\n\n \nConstraints:\n\n1 <= nums.length <= 5 * 104\n-109 <= nums[i] <= 109\n\n \nFollow up: Could you solve the problem in linear time and in O(1) space?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [3, 2, 3]) == [3]\n assert candidate(nums = [1]) == [1]\n assert candidate(nums = [1, 2]) == [2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1]) == []\n assert candidate(nums = [3, 3, 4, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [3]\n assert candidate(nums = [1, 1, 1, 3, 3, 2, 2, 2]) == [2, 1]\n assert candidate(nums = [2, 2, 1, 1, 1, 2, 2]) == [2, 1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == []\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 2, 3, 4, 5, 6, 7, 8, 9]) == [10]\n assert candidate(nums = [2, 2, 1, 3]) == [2]\n assert candidate(nums = [4, 1, 2, 3, 4, 2, 3, 4, 5, 6, 7, 8, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == [4]\n assert candidate(nums = [-1, -2, -3, -1, -1, -1, 0]) == [-1]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1]) == [1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [5, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == []\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == [2, 1]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == [1000000000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4]) == []\n assert candidate(nums = [10, 20, 10, 10, 30, 20, 10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]) == [20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == []\n assert candidate(nums = [10, 20, 10, 10, 30, 10, 40, 10, 50, 10, 60, 10, 70, 10, 80, 10, 90, 10, 10, 10, 10, 10]) == [10]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == []\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000]) == [1000000000, -1000000000]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == []\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == [6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5]) == []\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == []\n assert candidate(nums = [10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30, 10, 20, 30]) == []\n assert candidate(nums = [10, 10, 20, 20, 30, 30, 40, 40, 50, 50, 60, 60, 70, 70, 80, 80, 90, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == []\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == [9]\n assert candidate(nums = [-1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3, -1, -2, -3]) == []\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == []\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == []\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42]) == [42]\n assert candidate(nums = [100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200]) == [100, 200]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [10, 20, 10, 10, 30, 10, 40, 10, 10, 50, 60, 10, 10, 70, 10, 10, 80, 10, 10, 90, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == [10]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [100, 200, 300, 100, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200, 100, 200]) == [100, 200]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, -1000000000, -1000000000, -1000000000, -1000000000]) == [1000000000, -1000000000]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums = [9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3]) == [9, 3]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == []\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [-1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -2, -3, -4, -1, -1, -1, -1]) == [-1]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2]) == [2, 1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30, 30, 10, 10, 20, 20, 30]) == [10, 20]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9]) == []\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == []\n assert candidate(nums = [5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == []\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [7]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30]) == []\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == []\n assert candidate(nums = [999999999, -999999999, 0, 999999999, -999999999, 0, 999999999, -999999999, 0, 999999999, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums = [-1, -1, -1, -1, -1, -2, -2, -3, -3, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4]) == [-4]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == []\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [2]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == []\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == []\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().majorityElement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var majorityElement = function(nums) {", "container": null, "callable": "majorityElement", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 230, "task_id": "kth-smallest-element-in-a-bst", "difficulty": "Medium", "problem_description": "Given the root of a binary search tree, and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.\n \nExample 1:\n\n\nInput: root = [3,1,4,null,2], k = 1\nOutput: 1\n\nExample 2:\n\n\nInput: root = [5,3,6,2,4,null,null,1], k = 3\nOutput: 3\n\n \nConstraints:\n\nThe number of nodes in the tree is n.\n1 <= k <= n <= 104\n0 <= Node.val <= 104\n\n \nFollow up: If the BST is modified often (i.e., we can do insert and delete operations) and you need to find the kth smallest frequently, how would you optimize?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, None, 1]),k = 3) == 3\n assert candidate(root = tree_node([3, 1, 4, None, 2]),k = 1) == 1\n assert candidate(root = tree_node([3, 2, 4, 1]),k = 2) == 2\n assert candidate(root = tree_node([1]),k = 1) == 1\n assert candidate(root = tree_node([5, 1, 7, None, 2, None, 8, None, 3]),k = 4) == 5\n assert candidate(root = tree_node([3, 1, 4, None, 2, None, None, None, None, None]),k = 2) == 2\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),k = 4) == 10\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]),k = 15) == 15\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, 4, 6, 8, 11, 13, 17, 19]),k = 5) == 6\n assert candidate(root = tree_node([50, 25, 75, 10, 30, 60, 80, 5, 15, 27, 35, 55, 65, 70, 90, 1, None, 8, 12, 20, 28, 32, 38, 40, 52, 58, 62, 68, 72, 78, 85, 95]),k = 15) == 38\n assert candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13, 17, 11, 15]),k = 7) == 7\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, 8, 10, 11, 19]),k = 4) == 9\n assert candidate(root = tree_node([60, 30, 90, 20, 40, 70, 100, 15, 25, 35, 45, 65, 80, 95, 110]),k = 17) == None\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, 7, 12, 18, 23, 27, 32, 37]),k = 10) == 25\n assert candidate(root = tree_node([7, 3, 9, 2, 5, 8, 10, 1, 4, 6, None, None, None, None, None, None, None]),k = 5) == 6\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1]),k = 8) == 8\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 13, 17, 23, 27, 32, 37]),k = 10) == 25\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, None, 22]),k = 5) == 20\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1]),k = 1) == 1\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]),k = 7) == 7\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6]),k = 4) == 6\n assert candidate(root = tree_node([20, 15, 25, 10, 18, None, 30, 5, 13, None, None, None, None, 17, 19]),k = 10) == 30\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180]),k = 15) == 180\n assert candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, 1, None, 6, None, None, None, None, None, None, 3]),k = 6) == 7\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 42, 48, 55]),k = 18) == None\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 22, 28, 32, 38, 42]),k = 18) == None\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 22, 35, 42, 48, 55]),k = 7) == 22\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 17, 22, 28, 32, 38, 45, 2, 7, 11, 14, 18, 21, 26, 29, 31, 33, 36, 42, 44, 47, None, None, None, 9, None, 13, None, 16, None, None, 23, None, None, None, None, None, None, None, None, None, None, 39, None, None, None, None, None, None, None, None, 41, 43, None, 46, None, None, 48, None, None, 49]),k = 22) == 22\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 22, 28, 32, 38, 45]),k = 15) == 45\n assert candidate(root = tree_node([20, 10, 30, 5, 15, None, None, 3, 7, 12, 18]),k = 8) == 20\n assert candidate(root = tree_node([50, 20, 80, 10, 30, 70, 90, 5, 15, 25, 35, 60, 75, 85, 95]),k = 10) == 70\n assert candidate(root = tree_node([30, 10, 50, 5, 20, 40, 60, 1, 7, 15, 25, 35, 45, 55, 65]),k = 20) == None\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20]),k = 3) == 9\n assert candidate(root = tree_node([60, 40, 80, 30, 50, 70, 90, 20, 35, 45, 55, 65, 75, 85, 95]),k = 22) == None\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, 4, 6, 8, None, None, None, None, 11, 14, 16, None, None, 13, 17, 19]),k = 7) == 5\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6]),k = 5) == 7\n assert candidate(root = tree_node([10, 5, 15, None, None, 12, 20, 11, None, None, 13, 14, 16, None, None, None, 18, 19, 21]),k = 4) == 18\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 17, 22, 27, 32, 37, 1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31, 33, 36, 38, 4, 9, 14, 19, 24, 29, 34, 39]),k = 20) == 15\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, 8, None, None, None, None, 25]),k = 6) == 15\n assert candidate(root = tree_node([50, 25, 75, 15, 35, 60, 85, 10, 20, 30, 40, 55, 65, 80, 90]),k = 12) == 75\n assert candidate(root = tree_node([15, 10, 20, 5, 12, 18, 25, None, 7, 11, 14, 16, 19, 22, 27]),k = 8) == 16\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190]),k = 15) == 190\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, 18, 28, 32, 38, 45]),k = 15) == None\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 18, 22, 28, 32, 38, 1, None, 6, None, 11, 13, None, 17, 19, None, 21, 23, None, 27, 29, None, 31, 33, None, 37, 39]),k = 10) == 39\n assert candidate(root = tree_node([60, 30, 90, 20, 40, 70, 110, 10, 25, 35, 50, 65, 85, 100, 120]),k = 9) == 65\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, None, 12, 18, 22, 28, None, None, None, None, 14]),k = 10) == 25\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, 8, None, None, None, None, 22]),k = 12) == None\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 45, 48, 55]),k = 7) == 25\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 85, 110, 140, 160, 185, 5, 15, 35, 45, 55, 70, 80, 90, 105, 115, 130, 135, 155, 170, 190, 3, 7, 13, 17, 20, 30, 43, 47, 53, 65, 72, 87, 88, 95, 103, 108, 112, 127, 132, 138, 148, 157, 165, 168, 172, 182, 187, 192, 197, 2, 4, 6, 8, 11, 12, 14, 16, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 44, 46, 48, 49, 51, 52, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 89, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102, 104, 106, 107, 109, 111, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 128, 129, 131, 133, 134, 136, 137, 139, 141, 142, 143, 144, 145, 146, 147, 149, 150, 151, 152, 153, 154, 156, 158, 159, 161, 162, 163, 164, 166, 167, 169, 171, 173, 174, 175, 176, 177, 178, 179, 180, 181, 183, 184, 186, 188, 189, 191, 193, 194, 195, 196, 198, 199, 200]),k = 150) == 66\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, 18, 28, 32, None, None, None, None, None, None, 13, None, 16, None, None, 27, 29, 31, 33, None, None, None, None, None, 34]),k = 18) == 35\n assert candidate(root = tree_node([75, 50, 100, 25, 60, 85, 125, 15, 35, 55, 65, 90, 110, 130, 150]),k = 13) == 130\n assert candidate(root = tree_node([4, 2, 5, 1, 3]),k = 2) == 2\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 90, 110, 140, 160, 180]),k = 20) == None\n assert candidate(root = tree_node([55, 30, 80, 15, 40, 70, 90, 10, 20, 35, 45, 65, 75, 85, 95]),k = 9) == 65\n assert candidate(root = tree_node([50, 25, 75, 12, 37, 62, 87, 6, 18, 31, 43, 56, 70, 81, 93, 3, 9, 15, 21, 28, 34, 40, 47, 53, 59, 65, 68, 73, 79, 84, 89, 91, 96]),k = 25) == 68\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 22, 28, 32, 38, 45]),k = 18) == None\n assert candidate(root = tree_node([7, 3, 9, 1, 5, None, 10, None, 2, 4, 6, 8, None, None, None, None, None, None, None]),k = 8) == 9\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 90, 110, 140, 160, 180]),k = 15) == 180\n assert candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13]),k = 7) == 10\n assert candidate(root = tree_node([1, 2, None, None, 3, None, 4, None, 5, None, 6, None, 7]),k = 7) == 1\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]),k = 13) == 13\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 17, 25, 35, 47, 55, 60]),k = 20) == None\n assert candidate(root = tree_node([2, 1, 3, None, None, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]),k = 7) == 12\n assert candidate(root = tree_node([15, 10, 20, 8, 12, None, 25, 7, 9, 11, 13, 22, 30]),k = 15) == None\n assert candidate(root = tree_node([8, 3, 10, None, 6, 9, 14, None, 7, 8, 11, 12, 15]),k = 7) == 11\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 90, 110, 140, 160, 190]),k = 10) == 125\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37]),k = 25) == None\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15]),k = 10) == 10\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, 7, 12, 18, 22, 28, 32, 40]),k = 15) == 40\n assert candidate(root = tree_node([37, 23, 49, 10, 30, 44, 55, 5, 15, 25, 33, 41, 47, 52, 60]),k = 9) == 41\n assert candidate(root = tree_node([50, 25, 75, 10, 40, 60, 90, 5, 15, 35, 45, 55, 65, 85, 100, 3, 7, 13, 17, 32, 37, 43, 47, 52, 57, 62, 67, 80, 87, 95, 105, None, None, 8, 12, 16, 18, 33, 36, 41, 44, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 78, 83, 86, 92, 98, None, None, 6, None, 9, None, None, 11, None, None, 14, None, None, 19, None, 24, None, 27, None, None, 30, None, 34, None, None, 38, None, 42, None, None, 45, None, None, 50, None, None, 54, None, None, 59, None, None, 64, None, None, 69, None, None, 74, None, None, 79, None, None, 82, None, None, 84, None, None, 89, None, None, 91, None, None, 93, None, None, 96, None, None, 99, None, None, 102, None, None, 104]),k = 30) == 35\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7, 0]),k = 3) == 2\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 48, 2, None, 11, 14, 16, 19, 22, 28, 33, 38, 47, 52, None, 8, None, None, None, 13, None, 17, None, None, 21, 23, None, 27, None, None, 32, 36, None, None, 41, None, 46, 51, 55, None, None, None, 53, 54, None, 56]),k = 12) == 56\n assert candidate(root = tree_node([9, 5, 13, 2, 7, 11, 15, 1, 3, 6, 8, 10, 12, 14, 16]),k = 12) == 13\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5]),k = 5) == 5\n assert candidate(root = tree_node([100, 75, 125, 50, 85, 110, 140, 30, 60, 80, 90, 105, 120, 135, 150]),k = 28) == None\n assert candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, 1, None, 6]),k = 4) == 6\n assert candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, None, None, 6, 8]),k = 4) == 7\n"}, "metadata": {"canonical_parameter_names": ["root", "k"], "leetcode_dataset_entry_point": "Solution().kthSmallest", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var kthSmallest = function(root, k) {", "container": null, "callable": "kthSmallest", "parameters": [{"name": "root", "type": "TreeNode"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 231, "task_id": "power-of-two", "difficulty": "Easy", "problem_description": "Given an integer n, return true if it is a power of two. Otherwise, return false.\nAn integer n is a power of two, if there exists an integer x such that n == 2x.\n \nExample 1:\n\nInput: n = 1\nOutput: true\nExplanation: 20 = 1\n\nExample 2:\n\nInput: n = 16\nOutput: true\nExplanation: 24 = 16\n\nExample 3:\n\nInput: n = 3\nOutput: false\n\n \nConstraints:\n\n-231 <= n <= 231 - 1\n\n \nFollow up: Could you solve it without loops/recursion?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == False\n assert candidate(n = 2097152) == True\n assert candidate(n = -16) == False\n assert candidate(n = 67108864) == True\n assert candidate(n = 4096) == True\n assert candidate(n = 2147483647) == False\n assert candidate(n = 536870912) == True\n assert candidate(n = 524288) == True\n assert candidate(n = 268435456) == True\n assert candidate(n = 16384) == True\n assert candidate(n = 16777216) == True\n assert candidate(n = -1) == False\n assert candidate(n = 4) == True\n assert candidate(n = 64) == True\n assert candidate(n = 16) == True\n assert candidate(n = 134217728) == True\n assert candidate(n = 4194304) == True\n assert candidate(n = 2) == True\n assert candidate(n = 33554432) == True\n assert candidate(n = 1024) == True\n assert candidate(n = 128) == True\n assert candidate(n = 0) == False\n assert candidate(n = 1073741824) == True\n assert candidate(n = 8) == True\n assert candidate(n = 1048576) == True\n assert candidate(n = 8192) == True\n assert candidate(n = 2048) == True\n assert candidate(n = 2147483648) == True\n assert candidate(n = 65536) == True\n assert candidate(n = 256) == True\n assert candidate(n = 32) == True\n assert candidate(n = 262144) == True\n assert candidate(n = 131072) == True\n assert candidate(n = 32768) == True\n assert candidate(n = 512) == True\n assert candidate(n = 1) == True\n assert candidate(n = 8388608) == True\n assert candidate(n = 262143) == False\n assert candidate(n = 2047) == False\n assert candidate(n = 5) == False\n assert candidate(n = 23) == False\n assert candidate(n = -2147483648) == False\n assert candidate(n = 9223372036854775808) == True\n assert candidate(n = 8191) == False\n assert candidate(n = 27) == False\n assert candidate(n = 1000000000) == False\n assert candidate(n = 24) == False\n assert candidate(n = -4) == False\n assert candidate(n = 11) == False\n assert candidate(n = 4294967296) == True\n assert candidate(n = 1048575) == False\n assert candidate(n = 29) == False\n assert candidate(n = 131071) == False\n assert candidate(n = -128) == False\n assert candidate(n = 21) == False\n assert candidate(n = -2) == False\n assert candidate(n = 524287) == False\n assert candidate(n = 268435455) == False\n assert candidate(n = 28) == False\n assert candidate(n = 2147483649) == False\n assert candidate(n = 17) == False\n assert candidate(n = 1073741823) == False\n assert candidate(n = 16777215) == False\n assert candidate(n = 9) == False\n assert candidate(n = -8) == False\n assert candidate(n = 6) == False\n assert candidate(n = 10) == False\n assert candidate(n = 63) == False\n assert candidate(n = 67108863) == False\n assert candidate(n = 32767) == False\n assert candidate(n = 511) == False\n assert candidate(n = 4194303) == False\n assert candidate(n = 30) == False\n assert candidate(n = 1152921504606846976) == True\n assert candidate(n = 255) == False\n assert candidate(n = 18) == False\n assert candidate(n = 4611686018427387904) == True\n assert candidate(n = 1023) == False\n assert candidate(n = 127) == False\n assert candidate(n = 15) == False\n assert candidate(n = 14) == False\n assert candidate(n = 26) == False\n assert candidate(n = 536870911) == False\n assert candidate(n = 1000000) == False\n assert candidate(n = 33554431) == False\n assert candidate(n = 18446744073709551616) == True\n assert candidate(n = 12) == False\n assert candidate(n = 16383) == False\n assert candidate(n = 2305843009213693952) == True\n assert candidate(n = 134217727) == False\n assert candidate(n = 8388607) == False\n assert candidate(n = 2097151) == False\n assert candidate(n = 18014398509481984) == True\n assert candidate(n = 4095) == False\n assert candidate(n = 18014398509481983) == False\n assert candidate(n = 22) == False\n assert candidate(n = -32) == False\n assert candidate(n = -64) == False\n assert candidate(n = 19) == False\n assert candidate(n = 65535) == False\n assert candidate(n = 31) == False\n assert candidate(n = 7) == False\n assert candidate(n = 25) == False\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().isPowerOfTwo", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPowerOfTwo = function(n) {", "container": null, "callable": "isPowerOfTwo", "parameters": [{"name": "n", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 233, "task_id": "number-of-digit-one", "difficulty": "Hard", "problem_description": "Given an integer n, count the total number of digit 1 appearing in all non-negative integers less than or equal to n.\n \nExample 1:\n\nInput: n = 13\nOutput: 6\n\nExample 2:\n\nInput: n = 0\nOutput: 0\n\n \nConstraints:\n\n0 <= n <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 987654321) == 891632373\n assert candidate(n = 100000) == 50001\n assert candidate(n = 999999999) == 900000000\n assert candidate(n = 999) == 300\n assert candidate(n = 1000000) == 600001\n assert candidate(n = 501) == 201\n assert candidate(n = 9999) == 4000\n assert candidate(n = 100) == 21\n assert candidate(n = 1000000000) == 900000001\n assert candidate(n = 1000) == 301\n assert candidate(n = 55) == 16\n assert candidate(n = 50000000) == 45000000\n assert candidate(n = 13) == 6\n assert candidate(n = 99999) == 50000\n assert candidate(n = 210) == 142\n assert candidate(n = 1010) == 313\n assert candidate(n = 500000005) == 500000001\n assert candidate(n = 12345) == 8121\n assert candidate(n = 50123) == 30057\n assert candidate(n = 2147483647) == 2971027783\n assert candidate(n = 909090909) == 826446281\n assert candidate(n = 202020202) == 262218141\n assert candidate(n = 111) == 36\n assert candidate(n = 213456789) == 273589849\n assert candidate(n = 111000111) == 99600372\n assert candidate(n = 2000000000) == 2800000000\n assert candidate(n = 123000000) == 129800001\n assert candidate(n = 56789) == 33059\n assert candidate(n = 110) == 33\n assert candidate(n = 3000000000) == 3700000000\n assert candidate(n = 807060504) == 745234201\n assert candidate(n = 300) == 160\n assert candidate(n = 10001) == 4003\n assert candidate(n = 100100100) == 80150223\n assert candidate(n = 10999) == 5300\n assert candidate(n = 99) == 20\n assert candidate(n = 876543210) == 803978042\n assert candidate(n = 1001) == 303\n assert candidate(n = 808080808) == 745842261\n assert candidate(n = 5001) == 2501\n assert candidate(n = 1101101101) == 1082954833\n assert candidate(n = 101010101) == 81624329\n assert candidate(n = 200000000) == 260000000\n assert candidate(n = 303030303) == 342822161\n assert candidate(n = 800000000) == 740000000\n assert candidate(n = 101) == 23\n assert candidate(n = 10000000) == 7000001\n assert candidate(n = 10000000000) == 10000000001\n assert candidate(n = 432109876) == 453263855\n assert candidate(n = 2020) == 1612\n assert candidate(n = 10101) == 4125\n assert candidate(n = 600000000) == 580000000\n assert candidate(n = 1023) == 337\n assert candidate(n = 555555555) == 549382716\n assert candidate(n = 1000000001) == 900000003\n assert candidate(n = 50001) == 30001\n assert candidate(n = 111111111) == 100000008\n assert candidate(n = 1010101010) == 917253346\n assert candidate(n = 888888888) == 812345679\n assert candidate(n = 50005) == 30001\n assert candidate(n = 654321098) == 628668419\n assert candidate(n = 700000000) == 660000000\n assert candidate(n = 200) == 140\n assert candidate(n = 98765) == 49657\n assert candidate(n = 500000000) == 500000000\n assert candidate(n = 400000000) == 420000000\n assert candidate(n = 100100) == 50122\n assert candidate(n = 123456789) == 130589849\n assert candidate(n = 1999999999) == 2800000000\n assert candidate(n = 100001) == 50003\n assert candidate(n = 199) == 140\n assert candidate(n = 1111111111) == 1111111120\n assert candidate(n = 800000008) == 740000001\n assert candidate(n = 100010001) == 80014005\n assert candidate(n = 100000000) == 80000001\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countDigitOne", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countDigitOne = function(n) {", "container": null, "callable": "countDigitOne", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 234, "task_id": "palindrome-linked-list", "difficulty": "Easy", "problem_description": "Given the head of a singly linked list, return true if it is a palindrome or false otherwise.\n \nExample 1:\n\n\nInput: head = [1,2,2,1]\nOutput: true\n\nExample 2:\n\n\nInput: head = [1,2]\nOutput: false\n\n \nConstraints:\n\nThe number of nodes in the list is in the range [1, 105].\n0 <= Node.val <= 9\n\n \nFollow up: Could you do it in O(n) time and O(1) space?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(head = list_node([1, 0, 0, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([9, 8, 7, 8, 9])) == True\n assert candidate(head = list_node([1, 2, 3, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5])) == False\n assert candidate(head = list_node([1, 2, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 2, 1])) == True\n assert candidate(head = list_node([1, 2])) == False\n assert candidate(head = list_node([1])) == True\n assert candidate(head = list_node([1, 0, 1])) == True\n assert candidate(head = list_node([1, 1])) == True\n assert candidate(head = list_node([1, 1, 1, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6])) == False\n assert candidate(head = list_node([1, 1, 2, 2, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([2, 4, 6, 8, 10, 8, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == False\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2])) == False\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1])) == False\n assert candidate(head = list_node([9, 8, 7, 6, 5, 6, 7, 8, 9])) == True\n assert candidate(head = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9])) == True\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 3, 2, 4, 2, 3, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])) == True\n assert candidate(head = list_node([1, 2, 2, 3, 2, 2, 1])) == True\n assert candidate(head = list_node([9, 9, 8, 7, 6, 7, 8, 9, 9])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 0, 2, 0, 1, 0, 2, 0, 1])) == True\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 2, 3, 3, 2, 2, 1])) == True\n assert candidate(head = list_node([9, 9, 9, 9, 9, 9, 9])) == True\n assert candidate(head = list_node([1, 0, 2, 4, 2, 0, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 0, 2, 0, 1])) == True\n assert candidate(head = list_node([1, 0, 1, 0, 1, 0, 1, 0, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 2, 1, 1, 2, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 0, 1, 0, 1, 0, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 3, 2, 1, 0])) == False\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == False\n assert candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5])) == True\n assert candidate(head = list_node([1, 0, 2, 4, 5, 4, 2, 0, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 4, 3, 2, 1, 0])) == False\n assert candidate(head = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])) == True\n assert candidate(head = list_node([1, 2, 3, 2, 1, 0, 1, 0, 1])) == False\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5])) == False\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0])) == False\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == True\n assert candidate(head = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == True\n assert candidate(head = list_node([0, 0, 0, 0, 0, 0, 0])) == True\n assert candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0])) == True\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 3, 5, 7, 9, 7, 5, 3, 1, 0, 0, 0, 0, 1, 3, 5, 7, 9, 7, 5, 3, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 2, 1, 2, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 3, 3, 7, 7, 7, 3, 3, 1])) == True\n assert candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == True\n assert candidate(head = list_node([1, 2, 3, 3, 2, 1, 1])) == False\n assert candidate(head = list_node([9, 8, 7, 6, 7, 8, 9])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 2, 1, 2, 1])) == False\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 1, 2, 1, 1])) == True\n assert candidate(head = list_node([1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1])) == True\n assert candidate(head = list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0])) == False\n assert candidate(head = list_node([1, 2, 3, 3, 2, 1, 2, 3, 3, 2, 1])) == True\n assert candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])) == True\n assert candidate(head = list_node([1, 3, 5, 7, 5, 3, 1])) == True\n assert candidate(head = list_node([1, 1, 2, 2, 3, 3, 2, 2, 1, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])) == True\n assert candidate(head = list_node([5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1])) == False\n assert candidate(head = list_node([1, 1, 2, 1, 1, 2, 1, 1])) == True\n assert candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5])) == True\n assert candidate(head = list_node([1, 3, 2, 3, 1])) == True\n assert candidate(head = list_node([1, 2, 2, 3, 3, 3, 2, 2, 1])) == True\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().isPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPalindrome = function(head) {", "container": null, "callable": "isPalindrome", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 238, "task_id": "product-of-array-except-self", "difficulty": "Medium", "problem_description": "Given an integer array nums, return an array answer such that answer[i] is equal to the product of all the elements of nums except nums[i].\nThe product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.\nYou must write an algorithm that runs in O(n) time and without using the division operation.\n \nExample 1:\nInput: nums = [1,2,3,4]\nOutput: [24,12,8,6]\nExample 2:\nInput: nums = [-1,1,0,-3,3]\nOutput: [0,0,9,0,0]\n\n \nConstraints:\n\n2 <= nums.length <= 105\n-30 <= nums[i] <= 30\nThe input is generated such that answer[i] is guaranteed to fit in a 32-bit integer.\n\n \nFollow up: Can you solve the problem in O(1) extra space complexity? (The output array does not count as extra space for space complexity analysis.)\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 3, 0, 2, 1]) == [0, 0, 30, 0, 0]\n assert candidate(nums = [1, 0, -1, 2, -2]) == [0, 4, 0, 0, 0]\n assert candidate(nums = [1, -1, 2, -2, 3, -3]) == [-36, 36, -18, 18, -12, 12]\n assert candidate(nums = [5, 3, 2, 4, 1]) == [24, 40, 60, 30, 120]\n assert candidate(nums = [1, 2, 3, 4]) == [24, 12, 8, 6]\n assert candidate(nums = [-1, 1, 0, -3, 3]) == [0, 0, 9, 0, 0]\n assert candidate(nums = [2, -3, 4, -5]) == [60, -40, 30, -24]\n assert candidate(nums = [0, 0, 0, 0]) == [0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5]) == [125, 125, 125, 125]\n assert candidate(nums = [1, 0, 2, 3]) == [0, 6, 0, 0]\n assert candidate(nums = [1, 0, 3, 4]) == [0, 12, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [-30, -29, -28, -27, -26, -25, -24, -23, -22, -21]) == [-3634245014400, -3759563808000, -3893833944000, -4038050016000, -4193359632000, -4361094017280, -4542806268000, -4740319584000, -4955788656000, -5191778592000]\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [304888344611713860501504000000, 315777214062132212662272000000, 327472666434803776094208000000, 340067768989988536713216000000, 353670479749588078181744640000, 368406749739154248105984000000, 384424434510421824110592000000, 401898272442713725206528000000, 421036285416176283549696000000, 442088099686985097727180800000, 465355894407352734449664000000, 491208999652205664141312000000, 520103646690570703208448000000, 552610124608731372158976000000, 589450799582646796969574400000, 631554428124264425324544000000, 680135537979977073426432000000, 736813499478308496211968000000, 803796544885427450413056000000, 884176199373970195454361600000, 982417999304411328282624000000, 1105220249217462744317952000000, 1263108856248528850649088000000, 1473626998956616992423936000000, 1768352398747940390908723200000, 2210440498434925488635904000000, 2947253997913233984847872000000, 4420880996869850977271808000000, 8841761993739701954543616000000]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [3628800, 1814400, 1209600, 907200, 725760, 604800, 518400, 453600, 403200, 362880]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17]) == [255255, 170170, 102102, 72930, 46410, 39270, 30030]\n assert candidate(nums = [100, -100, 200, -200, 300, -300]) == [-360000000000, 360000000000, -180000000000, 180000000000, -120000000000, 120000000000]\n assert candidate(nums = [29, -29, 14, -14, 7, -7, 3.5, -3.5, 1.75, -1.75]) == [-10448701.8125, 10448701.8125, -21643739.46875, 21643739.46875, -43287478.9375, 43287478.9375, -86574957.875, 86574957.875, -173149915.75, 173149915.75]\n assert candidate(nums = [10, 20, 30, 40, 50]) == [1200000, 600000, 400000, 300000, 240000]\n assert candidate(nums = [29, 29, 29, 29, 29, 29, 29, 29, 29, 29]) == [14507145975869, 14507145975869, 14507145975869, 14507145975869, 14507145975869, 14507145975869, 14507145975869, 14507145975869, 14507145975869, 14507145975869]\n assert candidate(nums = [15, 20, 25, 30, 35, 40, 45, 50]) == [47250000000, 35437500000, 28350000000, 23625000000, 20250000000, 17718750000, 15750000000, 14175000000]\n assert candidate(nums = [10, 20, 0, 30, 40]) == [0, 0, 240000, 0, 0]\n assert candidate(nums = [1000, -1000, 500, -500, 250, -250, 125, -125, 62, -62]) == [-938476562500000000000, 938476562500000000000, -1876953125000000000000, 1876953125000000000000, -3753906250000000000000, 3753906250000000000000, -7507812500000000000000, 7507812500000000000000, -15136718750000000000000, 15136718750000000000000]\n assert candidate(nums = [30, -20, 10, -5, 4, -2, 1]) == [-8000, 12000, -24000, 48000, -60000, 120000, -240000]\n assert candidate(nums = [29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8841761993739701954543616000000]\n assert candidate(nums = [2, -3, 5, 7, 0, -1, 4]) == [0, 0, 0, 0, 840, 0, 0]\n assert candidate(nums = [29, -29, 14, -14, 7, -7, 3, -3, 1, -1]) == [-2506644, 2506644, -5192334, 5192334, -10384668, 10384668, -24230892, 24230892, -72692676, 72692676]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [10, -20, 30, -40, 50]) == [1200000, -600000, 400000, -300000, 240000]\n assert candidate(nums = [-1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10]) == [-13168189440000, 13168189440000, -6584094720000, 6584094720000, -4389396480000, 4389396480000, -3292047360000, 3292047360000, -2633637888000, 2633637888000, -2194698240000, 2194698240000, -1881169920000, 1881169920000, -1646023680000, 1646023680000, -1463132160000, 1463132160000, -1316818944000, 1316818944000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [265252859812191058636308480000000, 132626429906095529318154240000000, 88417619937397019545436160000000, 66313214953047764659077120000000, 53050571962438211727261696000000, 44208809968698509772718080000000, 37893265687455865519472640000000, 33156607476523882329538560000000, 29472539979132339848478720000000, 26525285981219105863630848000000, 24113896346562823512391680000000, 22104404984349254886359040000000, 20404066139399312202792960000000, 18946632843727932759736320000000, 17683523987479403909087232000000, 16578303738261941164769280000000, 15603109400717121096253440000000, 14736269989566169924239360000000, 13960676832220582033489920000000, 13262642990609552931815424000000, 12631088562485288506490880000000, 12056948173281411756195840000000, 11532733035312654723317760000000, 11052202492174627443179520000000, 10610114392487642345452339200000, 10202033069699656101396480000000, 9824179993044113282826240000000, 9473316421863966379868160000000, 9146650338351415815045120000000, 8841761993739701954543616000000]\n assert candidate(nums = [0, 0, 0, 1]) == [0, 0, 0, 0]\n assert candidate(nums = [-29, 29, -29, 29, -29, 29, -29, 29, -29, 29]) == [14507145975869, -14507145975869, 14507145975869, -14507145975869, 14507145975869, -14507145975869, 14507145975869, -14507145975869, 14507145975869, -14507145975869]\n assert candidate(nums = [100, 50, 25, 12, 6, 3, 1, -1, -2, -3]) == [-1620000, -3240000, -6480000, -13500000, -27000000, -54000000, -162000000, 162000000, 81000000, 54000000]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [2, 5, 1, 9, 3, 6, 8, 7]) == [45360, 18144, 90720, 10080, 30240, 15120, 11340, 12960]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [1307674368000, 653837184000, 435891456000, 326918592000, 261534873600, 217945728000, 186810624000, 163459296000, 145297152000, 130767436800, 118879488000, 108972864000, 100590336000, 93405312000, 87178291200]\n assert candidate(nums = [-1000000000, 1, -2, 3, -4]) == [24, -24000000000, 12000000000, -8000000000, 6000000000]\n assert candidate(nums = [-30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70359079638545882374689246780656119576032161719910400000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 1]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [1000000000, -1000000000, 500000000, -500000000, 250000000]) == [62500000000000000000000000000000000, -62500000000000000000000000000000000, 125000000000000000000000000000000000, -125000000000000000000000000000000000, 250000000000000000000000000000000000]\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20]) == [2432902008176640000, -1216451004088320000, 810967336058880000, -608225502044160000, 486580401635328000, -405483668029440000, 347557429739520000, -304112751022080000, 270322445352960000, -243290200817664000, 221172909834240000, -202741834014720000, 187146308321280000, -173778714869760000, 162193467211776000, -152056375511040000, 143111882833920000, -135161222676480000, 128047474114560000, -121645100408832000]\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50]) == [-14400000000000, 14400000000000, -7200000000000, 7200000000000, -4800000000000, 4800000000000, -3600000000000, 3600000000000, -2880000000000, 2880000000000]\n assert candidate(nums = [2, 3, 0, 5, 6, 0, 7]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [-30, 29, -28, 27, -26, 25, -24, 23, -22, 21, -20, 19, -18, 17, -16, 15, -14, 13, -12, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1, -1]) == [-8841761993739701954543616000000, 9146650338351415815045120000000, -9473316421863966379868160000000, 9824179993044113282826240000000, -10202033069699656101396480000000, 10610114392487642345452339200000, -11052202492174627443179520000000, 11532733035312654723317760000000, -12056948173281411756195840000000, 12631088562485288506490880000000, -13262642990609552931815424000000, 13960676832220582033489920000000, -14736269989566169924239360000000, 15603109400717121096253440000000, -16578303738261941164769280000000, 17683523987479403909087232000000, -18946632843727932759736320000000, 20404066139399312202792960000000, -22104404984349254886359040000000, 24113896346562823512391680000000, -26525285981219105863630848000000, 29472539979132339848478720000000, -33156607476523882329538560000000, 37893265687455865519472640000000, -44208809968698509772718080000000, 53050571962438211727261696000000, -66313214953047764659077120000000, 88417619937397019545436160000000, -132626429906095529318154240000000, 265252859812191058636308480000000, -265252859812191058636308480000000]\n assert candidate(nums = [30, -30, 30, -30, 30, -30, 30, -30, 30, -30, 30, -30, 30, -30, 30, -30, 30, -30, 30, -30]) == [11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000, 11622614670000000000000000000, -11622614670000000000000000000]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == [536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 536870912, 1073741824]\n assert candidate(nums = [1000000000, 1000000000, -1, 1, -1, 1, -1, 1, -1, 1]) == [1000000000, 1000000000, -1000000000000000000, 1000000000000000000, -1000000000000000000, 1000000000000000000, -1000000000000000000, 1000000000000000000, -1000000000000000000, 1000000000000000000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [2432902008176640000, 1216451004088320000, 810967336058880000, 608225502044160000, 486580401635328000, 405483668029440000, 347557429739520000, 304112751022080000, 270322445352960000, 243290200817664000, 221172909834240000, 202741834014720000, 187146308321280000, 173778714869760000, 162193467211776000, 152056375511040000, 143111882833920000, 135161222676480000, 128047474114560000, 121645100408832000]\n assert candidate(nums = [25, -25, 25, -25, 25, -25, 25, -25, 25, -25]) == [-3814697265625, 3814697265625, -3814697265625, 3814697265625, -3814697265625, 3814697265625, -3814697265625, 3814697265625, -3814697265625, 3814697265625]\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50]) == [-14400000000000, 14400000000000, -7200000000000, 7200000000000, -4800000000000, 4800000000000, -3600000000000, 3600000000000, -2880000000000, 2880000000000]\n assert candidate(nums = [15, 20, 30, 0, 0, 40, 50, 60]) == [0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-10, 9, 0, 5, -2, 3, -1, 8]) == [0, 0, -21600, 0, 0, 0, 0, 0]\n assert candidate(nums = [100, -100, 50, -50, 25, -25]) == [-156250000, 156250000, -312500000, 312500000, -625000000, 625000000]\n assert candidate(nums = [29, 28, 27, 26, 25, 24, 23, 22, 21, 20]) == [2506375872000, 2595889296000, 2692033344000, 2795573088000, 2907396011520, 3028537512000, 3160213056000, 3303859104000, 3461185728000, 3634245014400]\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [8841761993739701954543616000000, 9146650338351415815045120000000, 9473316421863966379868160000000, 9824179993044113282826240000000, 10202033069699656101396480000000, 10610114392487642345452339200000, 11052202492174627443179520000000, 11532733035312654723317760000000, 12056948173281411756195840000000, 12631088562485288506490880000000, 13262642990609552931815424000000, 13960676832220582033489920000000, 14736269989566169924239360000000, 15603109400717121096253440000000, 16578303738261941164769280000000, 17683523987479403909087232000000, 18946632843727932759736320000000, 20404066139399312202792960000000, 22104404984349254886359040000000, 24113896346562823512391680000000, 26525285981219105863630848000000, 29472539979132339848478720000000, 33156607476523882329538560000000, 37893265687455865519472640000000, 44208809968698509772718080000000, 53050571962438211727261696000000, 66313214953047764659077120000000, 88417619937397019545436160000000, 132626429906095529318154240000000, 265252859812191058636308480000000]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [265252859812191058636308480000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [15, 10, 20, 5, 3, 8, 6, 12, 4, 7]) == [48384000, 72576000, 36288000, 145152000, 241920000, 90720000, 120960000, 60480000, 181440000, 103680000]\n assert candidate(nums = [-10, 10, -10, 10, -10]) == [10000, -10000, 10000, -10000, 10000]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == [3628800000000000, 1814400000000000, 1209600000000000, 907200000000000, 725760000000000, 604800000000000, 518400000000000, 453600000000000, 403200000000000, 362880000000000]\n assert candidate(nums = [-1, -2, -3, -4, -5]) == [120, 60, 40, 30, 24]\n assert candidate(nums = [1, 2, 3, 4, 5, 0, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 604800, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 0, 0, 0, 3, 4, 5]) == [0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [2, 3, -5, 7, 11, -13, 17]) == [255255, 170170, -102102, 72930, 46410, -39270, 30030]\n assert candidate(nums = [2, -3, 4, -5, 6, -7]) == [-2520, 1680, -1260, 1008, -840, 720]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [3628800, 1814400, 1209600, 907200, 725760, 604800, 518400, 453600, 403200, 362880]\n assert candidate(nums = [-30, 29, -28, 27, -26, 25, -24, 23, -22, 21, -20, 19, -18, 17, -16, 15, -14, 13, -12, 11, -10, 9, -8, 7, -6, 5, -4, 3, -2, 1]) == [8841761993739701954543616000000, -9146650338351415815045120000000, 9473316421863966379868160000000, -9824179993044113282826240000000, 10202033069699656101396480000000, -10610114392487642345452339200000, 11052202492174627443179520000000, -11532733035312654723317760000000, 12056948173281411756195840000000, -12631088562485288506490880000000, 13262642990609552931815424000000, -13960676832220582033489920000000, 14736269989566169924239360000000, -15603109400717121096253440000000, 16578303738261941164769280000000, -17683523987479403909087232000000, 18946632843727932759736320000000, -20404066139399312202792960000000, 22104404984349254886359040000000, -24113896346562823512391680000000, 26525285981219105863630848000000, -29472539979132339848478720000000, 33156607476523882329538560000000, -37893265687455865519472640000000, 44208809968698509772718080000000, -53050571962438211727261696000000, 66313214953047764659077120000000, -88417619937397019545436160000000, 132626429906095529318154240000000, -265252859812191058636308480000000]\n assert candidate(nums = [-10, -20, -30, -40, -50]) == [1200000, 600000, 400000, 300000, 240000]\n assert candidate(nums = [-2, -4, -6, -8, -10, -12, -14, -16, -18, -20]) == [-1857945600, -928972800, -619315200, -464486400, -371589120, -309657600, -265420800, -232243200, -206438400, -185794560]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6]) == [-720, -360, -240, -180, -144, -120]\n assert candidate(nums = [0, 0, 0, 1, 2, 3]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-2, -3, -4, -5, -6]) == [360, 240, 180, 144, 120]\n assert candidate(nums = [1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1]\n assert candidate(nums = [0, 0, 0, 0, 0, 1]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1000000000, 1, 2, 3, 4]) == [24, 24000000000, 12000000000, 8000000000, 6000000000]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683, 19683]\n assert candidate(nums = [1, 2, 0, 4, 5, 0, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [7, -2, 5, 0, -3, 1]) == [0, 0, 0, 210, 0, 0]\n assert candidate(nums = [1, 2, 0, 4, 5, 0, 7, 8, 9]) == [0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-3628800, -1814400, -1209600, -907200, -725760, -604800, -518400, -453600, -403200, -362880]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [2, 3, -1, 0, 5, 6, -7, 8, -9, 10]) == [0, 0, 0, -907200, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == [-14400, 14400, -7200, 7200, -4800, 4800, -3600, 3600, -2880, 2880]\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == [1857945600, 928972800, 619315200, 464486400, 371589120, 309657600, 265420800, 232243200, 206438400, 185794560]\n assert candidate(nums = [7, 1, 2, 3, 4, 5]) == [120, 840, 420, 280, 210, 168]\n assert candidate(nums = [-30, -29, -28, -27, -26, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70359079638545882374689246780656119576032161719910400000000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21]) == [3634245014400, 3759563808000, 3893833944000, 4038050016000, 4193359632000, 4361094017280, 4542806268000, 4740319584000, 4955788656000, 5191778592000]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 0, 3, 4, 0, 5]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-3628800, -1814400, -1209600, -907200, -725760, -604800, -518400, -453600, -403200, -362880]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == [3234846615, 2156564410, 1293938646, 924241890, 588153930, 497668710, 380570190, 340510170, 281291010, 223092870]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().productExceptSelf", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var productExceptSelf = function(nums) {", "container": null, "callable": "productExceptSelf", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 239, "task_id": "sliding-window-maximum", "difficulty": "Hard", "problem_description": "You are given an array of integers nums, there is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position.\nReturn the max sliding window.\n \nExample 1:\n\nInput: nums = [1,3,-1,-3,5,3,6,7], k = 3\nOutput: [3,3,5,5,6,7]\nExplanation: \nWindow position Max\n--------------- -----\n[1 3 -1] -3 5 3 6 7 3\n 1 [3 -1 -3] 5 3 6 7 3\n 1 3 [-1 -3 5] 3 6 7 5\n 1 3 -1 [-3 5 3] 6 7 5\n 1 3 -1 -3 [5 3 6] 7 6\n 1 3 -1 -3 5 [3 6 7] 7\n\nExample 2:\n\nInput: nums = [1], k = 1\nOutput: [1]\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-104 <= nums[i] <= 104\n1 <= k <= nums.length\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7],k = 3) == [3, 3, 5, 5, 6, 7]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5],k = 5) == [5, 5, 5, 5, 5]\n assert candidate(nums = [4, -2],k = 2) == [4]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 4) == [9, 8, 7, 6, 5, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 2) == [2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [1],k = 1) == [1]\n assert candidate(nums = [1, 3, 1, 2, 0, 5],k = 3) == [3, 3, 2, 5]\n assert candidate(nums = [7, 2, 4],k = 2) == [7, 4]\n assert candidate(nums = [9, 11],k = 2) == [11]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 4, 2, 3, 1, 5, 6, 7, 8, 9, 10],k = 4) == [4, 5, 6, 6, 6, 6, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 3) == [100, 90, 80, 70, 60, 50, 40, 30]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == [3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 5) == [100, 90, 80, 70, 60, 50]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 4) == [-1, -2, -3, -4, -5, -6, -7]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 15) == [1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == [5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 25) == [1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 2) == [10, 10, 10, 10, 10, 10, 10, 10, 10]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7, 1, 2, 4, 5, 6],k = 4) == [3, 5, 5, 6, 7, 7, 7, 7, 5, 6]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11],k = 6) == [5, 6, 6, 7, 8, 8, 9, 10, 10, 11]\n assert candidate(nums = [5, 3, 5, 2, 8, 1, 9, 6, 4, 7],k = 5) == [8, 8, 9, 9, 9, 9]\n assert candidate(nums = [5, 3, 4, 4, 1, 5, 3, 6, 9, 5, 12, 2, 8, 7],k = 5) == [5, 5, 5, 6, 9, 9, 12, 12, 12, 12]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 10) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 3) == [3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 7) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [5, 3, 4, 2, 1, 8, 7, 6, 9, 10, 11],k = 5) == [5, 8, 8, 8, 9, 10, 11]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 6) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 2) == [10, 9, 8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1],k = 2) == [2, 3, 4, 5, 5, 4, 3, 2]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 3) == [0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5]\n assert candidate(nums = [2, 1, 3, 5, 4, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5],k = 5) == [5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 5]\n assert candidate(nums = [1, -1, 3, -3, 5, -5, 6, -6, 7, -7],k = 5) == [5, 5, 6, 6, 7, 7]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],k = 5) == [-6, -5, -4, -3, -2, -1]\n assert candidate(nums = [5, 3, 8, 1, 9, 2, 7, 4, 6, 0],k = 3) == [8, 8, 9, 9, 9, 7, 7, 6]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5],k = 10) == [10, 9, 8, 7, 6, 5]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3],k = 4) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [10, -5, 3, 8, 2, -9, 15, 11, 1],k = 4) == [10, 8, 8, 15, 15, 15]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4],k = 4) == [4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 3, 3, 4]\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 12],k = 4) == [11, 11, 10, 12]\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1],k = 5) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 9, 6, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [11, 11, 10, 10, 12, 12, 12, 12, 12, 11, 10, 9, 8, 7, 6, 5]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 3) == [5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 4) == [10, 9, 8, 7, 6, 5, 4]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90],k = 2) == [100, 99, 98, 97, 96, 95, 94, 93, 92, 91]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 5) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [9, 11, 8, 5, 7, 10, 6],k = 4) == [11, 11, 10, 10]\n assert candidate(nums = [10, 14, 13, 7, 10, 6, 5, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1],k = 4) == [14, 14, 13, 10, 10, 9, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20) == [20]\n assert candidate(nums = [1, 3, 2, 1, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 8, 7, 6, 5]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 2) == [3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [-7, -8, 7, 5, 7, 1, 6, 0, 1, 2, -7, -8, -2, -2, 0, 5, 0, 1, 2, -1, -4, -2, -1, -2, 4, 1, -5, 0, -7, -1, 10, 1, -6, 5, -8, 9, 10, 3, -4, -5, -9, -9, -3, -9, -8, -7, 7, -1, -7, -6, -6, 7, 0, 1, 4, 5, -5, -5, 2, -7, 9, 7, 9, 8, -9, -2, -5, -8, 2, -8, -6, -6, -6, 0, 1, 4, -8, -5, -6, -6, 6, -8, -8, -5, -6, -6, -7, -7, 7, -8, -6, -4, -6, -5, -8, -9, -6, -9, -7, -7, -8, -6, -7, -7, 7, -8, -5, -5, -5, 7, -7, 7, -7, -8, -6, -4, -6, -5, -8, -9, -6, -9, -7, -7, -8, -6, -7, -7, 7, -8, -5, -5, -5, 7, -7, 7, -7, -8, -6, -4, -6, -5],k = 25) == [7, 7, 7, 7, 7, 6, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 6) == [3, 3, 3, 3, 3]\n assert candidate(nums = [8, 5, 10, 7, 9, 4, 15, 12, 90, 13],k = 3) == [10, 10, 10, 9, 15, 15, 90, 90]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 6) == [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1],k = 8) == [25, 23, 21, 19, 17, 15]\n assert candidate(nums = [10000, -10000, 5000, -5000, 2500, -2500, 1250, -1250, 625, -625, 312, -312, 156, -156, 78, -78, 39, -39, 19, -19, 9, -9, 4, -4, 2, -2, 1, -1],k = 5) == [10000, 5000, 5000, 2500, 2500, 1250, 1250, 625, 625, 312, 312, 156, 156, 78, 78, 39, 39, 19, 19, 9, 9, 4, 4, 2]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 3) == [1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 4) == [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 7) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3],k = 3) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [5, 3, 8, 7, 6, 5, 4, 3, 2, 1],k = 3) == [8, 8, 8, 7, 6, 5, 4, 3]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7, 8, 1, 2, 3, 4, 5],k = 4) == [3, 5, 5, 6, 7, 8, 8, 8, 8, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5],k = 3) == [3, 4, 5, 5, 5, 4, 3, 2, 3, 4, 5, 5, 5, 4, 3, 2, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3],k = 5) == [4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 3]\n assert candidate(nums = [3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3],k = 4) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25],k = 7) == [13, 15, 17, 19, 21, 23, 25]\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],k = 3) == [-10, -20, -30, -40, -50, -60, -70, -80]\n assert candidate(nums = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3],k = 2) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [3, 2, 2, 3, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],k = 6) == [5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(nums = [5, 3, 8, 2, 1, 4, 7, 6, 9],k = 4) == [8, 8, 8, 7, 7, 9]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 4) == [40, 50, 60, 70, 80, 90, 100]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 5) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1],k = 4) == [3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 5, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7) == [7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [5, 3, 4, 2, 1, 6, 7, 8, 9, 10],k = 4) == [5, 4, 6, 7, 8, 9, 10]\n assert candidate(nums = [10000, -10000, 10000, -10000, 10000, -10000, 10000, -10000, 10000],k = 3) == [10000, 10000, 10000, 10000, 10000, 10000, 10000]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5],k = 2) == [1, 2, 2, 3, 3, 4, 4, 5, 5]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 3) == [-1, -2, -3, -4, -5, -6, -7, -8]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5],k = 3) == [5, 4, 3, 2, 3, 4, 5]\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18],k = 3) == [10, 9, 5, 7, 101, 101]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 7) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 12) == [20, 19, 18, 17, 16, 15, 14, 13, 12]\n assert candidate(nums = [5, 3, 4, 2, 6, 1, 8, 9, 7],k = 4) == [5, 6, 6, 8, 9, 9]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [9, 11, 8, 9, 10, 1, 7, 3, 8, 9],k = 4) == [11, 11, 10, 10, 10, 8, 9]\n assert candidate(nums = [9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == [14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [1]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [10, 9, 8, 7, 6, 5]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 7) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1],k = 5) == [5, 5, 5, 5, 5, 4, 3, 4, 5, 5, 5, 5, 5]\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1],k = 3) == [5, 4, 3, 2, 3, 4, 5, 5, 5, 4, 3]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 3) == [9, 8, 7, 6, 5, 4, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 2) == [2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 10, 5, 6],k = 4) == [11, 11, 10, 10, 10, 10]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 5) == [100, 90, 80, 70, 60, 50]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 6) == [6, 7, 8, 9, 10]\n assert candidate(nums = [5, 2, 2, 4, 1, 6, 1, 3, 2, 5, 2, 2, 4, 6, 1, 6, 3, 3, 5, 2, 1, 1, 4, 6, 3, 2, 1, 1, 5, 6, 1, 3, 5, 6, 3, 5, 6, 3, 6, 5, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10) == [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 8) == [15, 14, 13, 12, 11, 10, 9, 8]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 10) == [0]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1]\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().maxSlidingWindow", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxSlidingWindow = function(nums, k) {", "container": null, "callable": "maxSlidingWindow", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 240, "task_id": "search-a-2d-matrix-ii", "difficulty": "Medium", "problem_description": "Write an efficient algorithm that searches for a value target in an m x n integer matrix matrix. This matrix has the following properties:\n\nIntegers in each row are sorted in ascending from left to right.\nIntegers in each column are sorted in ascending from top to bottom.\n\n \nExample 1:\n\n\nInput: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5\nOutput: true\n\nExample 2:\n\n\nInput: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20\nOutput: false\n\n \nConstraints:\n\nm == matrix.length\nn == matrix[i].length\n1 <= n, m <= 300\n-109 <= matrix[i][j] <= 109\nAll the integers in each row are sorted in ascending order.\nAll the integers in each column are sorted in ascending order.\n-109 <= target <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [5, 6, 7, 8, 9], [15, 16, 17, 18, 19], [25, 26, 27, 28, 29], [35, 36, 37, 38, 39]],target = 0) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 20) == False\n assert candidate(matrix = [[-10, -5, -3, -1, -1], [0, 1, 1, 2, 2], [3, 3, 4, 4, 5], [6, 7, 8, 8, 9], [10, 10, 12, 13, 15]],target = 8) == True\n assert candidate(matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]],target = 3) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 5) == True\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19], [20, 21, 22, 23, 24]],target = 0) == False\n assert candidate(matrix = [[-10, -8, -6, -4, -3], [-9, -7, -5, -3, -1], [-4, -2, 0, 2, 4], [-3, 1, 3, 5, 7], [2, 4, 6, 8, 10]],target = 0) == True\n assert candidate(matrix = [[1, 3, 5, 7], [2, 4, 6, 8], [0, 11, 16, 20], [13, 14, 17, 18]],target = 14) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 15) == True\n assert candidate(matrix = [[-10, -8, -6, -4, -2], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],target = -5) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 13) == True\n assert candidate(matrix = [[-10, -8, -5, -3, -1], [0, 2, 3, 5, 7], [8, 9, 10, 12, 13], [15, 17, 18, 20, 21], [23, 25, 26, 27, 29]],target = 14) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [4, 6, 8, 10, 12, 14, 16, 18, 20, 22]],target = 100) == False\n assert candidate(matrix = [[1, 3, 5], [2, 6, 9], [4, 11, 16], [7, 12, 18], [8, 13, 19], [10, 14, 20], [15, 17, 21]],target = 17) == True\n assert candidate(matrix = [[1000000000, 1000000001, 1000000002], [1000000003, 1000000004, 1000000005], [1000000006, 1000000007, 1000000008]],target = 1000000004) == True\n assert candidate(matrix = [[1, 10, 20, 30, 40, 50, 60, 70, 80, 90], [11, 21, 31, 41, 51, 61, 71, 81, 91, 100], [22, 32, 42, 52, 62, 72, 82, 92, 102, 110], [33, 43, 53, 63, 73, 83, 93, 103, 113, 120], [44, 54, 64, 74, 84, 94, 104, 114, 124, 130]],target = 2) == False\n assert candidate(matrix = [[-100, -90, -80, -70, -60, -50, -40, -30, -20, -10], [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], [20, 30, 40, 50, 60, 70, 80, 90, 100, 110], [30, 40, 50, 60, 70, 80, 90, 100, 110, 120], [40, 50, 60, 70, 80, 90, 100, 110, 120, 130], [50, 60, 70, 80, 90, 100, 110, 120, 130, 140], [60, 70, 80, 90, 100, 110, 120, 130, 140, 150], [70, 80, 90, 100, 110, 120, 130, 140, 150, 160], [80, 90, 100, 110, 120, 130, 140, 150, 160, 170], [90, 100, 110, 120, 130, 140, 150, 160, 170, 180]],target = 125) == False\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [50, 51, 52, 53, 54, 55, 56, 57, 58, 59], [60, 61, 62, 63, 64, 65, 66, 67, 68, 69], [70, 71, 72, 73, 74, 75, 76, 77, 78, 79]],target = 37) == True\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],target = -15) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [4, 6, 8, 10, 12, 14, 16, 18, 20, 22], [5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [6, 8, 10, 12, 14, 16, 18, 20, 22, 24], [7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [8, 10, 12, 14, 16, 18, 20, 22, 24, 26], [9, 11, 13, 15, 17, 19, 21, 23, 25, 27], [10, 12, 14, 16, 18, 20, 22, 24, 26, 28]],target = 16) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],target = 55) == True\n assert candidate(matrix = [[-1000000000, -900000000, -800000000, -700000000, -600000000], [-500000000, -400000000, -300000000, -200000000, -1000000000], [0, 1000000000, 2000000000, 3000000000, 4000000000], [5000000000, 6000000000, 7000000000, 8000000000, 9000000000]],target = 0) == True\n assert candidate(matrix = [[-100, -90, -80, -70, -60, -50], [-90, -80, -70, -60, -50, -40], [-80, -70, -60, -50, -40, -30], [-70, -60, -50, -40, -30, -20], [-60, -50, -40, -30, -20, -10], [-50, -40, -30, -20, -10, 0]],target = -65) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15, 18], [2, 5, 8, 12, 19, 22], [3, 6, 9, 16, 22, 24], [10, 13, 14, 17, 24, 26], [18, 21, 23, 26, 30, 35], [20, 24, 27, 29, 33, 40]],target = 27) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 50) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 25) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 23, 25, 27, 29]],target = 25) == True\n assert candidate(matrix = [[-1000000000, -999999999, -999999998], [-999999997, -999999996, -999999995], [-999999994, -999999993, -999999992]],target = -999999995) == True\n assert candidate(matrix = [[-1000000000, -999999999, -999999998, -999999997], [-999999996, -999999995, -999999994, -999999993], [-999999992, -999999991, -999999990, -999999989], [-999999988, -999999987, -999999986, -999999985]],target = -999999993) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 23, 25, 27, 29]],target = 15) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 19], [2, 5, 8, 12, 19, 23], [3, 6, 9, 16, 22, 26], [10, 13, 14, 17, 24, 28], [18, 21, 23, 26, 30, 34], [29, 33, 35, 39, 43, 47]],target = 34) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60]],target = 33) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 20], [2, 5, 8, 12, 19, 25], [3, 6, 9, 16, 22, 30], [10, 13, 14, 17, 24, 35], [18, 21, 23, 26, 30, 40], [22, 27, 31, 37, 41, 45]],target = 37) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -89) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5], [-4, -3, -2, -1, 0, 1], [2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13], [14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25]],target = -5) == True\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, -1, 4, 9], [-8, -3, 1, 6, 11], [-7, -2, 2, 7, 12], [-6, -1, 3, 8, 13]],target = 13) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 19], [2, 5, 8, 12, 16, 20], [3, 6, 9, 13, 17, 21], [10, 14, 18, 22, 26, 24], [18, 22, 26, 30, 34, 32], [27, 31, 35, 39, 43, 41]],target = 35) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -93) == True\n assert candidate(matrix = [[5]],target = 5) == True\n assert candidate(matrix = [[1000000000, 2000000000, 3000000000, 4000000000, 5000000000], [1500000000, 2500000000, 3500000000, 4500000000, 5500000000], [2000000000, 3000000000, 4000000000, 5000000000, 6000000000], [2500000000, 3500000000, 4500000000, 5500000000, 6500000000], [3000000000, 4000000000, 5000000000, 6000000000, 7000000000]],target = 4500000000) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [10, 11, 13, 15, 17], [18, 19, 20, 21, 22], [25, 26, 27, 28, 29], [30, 31, 32, 33, 34]],target = 25) == True\n assert candidate(matrix = [[1000000000]],target = 1000000000) == True\n assert candidate(matrix = [[1, 10, 20, 30, 40, 50, 60, 70, 80, 90], [11, 21, 31, 41, 51, 61, 71, 81, 91, 100], [22, 32, 42, 52, 62, 72, 82, 92, 102, 110], [33, 43, 53, 63, 73, 83, 93, 103, 113, 120], [44, 54, 64, 74, 84, 94, 104, 114, 124, 130]],target = 114) == True\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],target = -13) == False\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],target = 10) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11], [2, 4, 6, 8, 10, 12], [13, 15, 17, 19, 21, 23], [24, 26, 28, 30, 32, 34], [35, 37, 39, 41, 43, 45], [46, 48, 50, 52, 54, 56]],target = 29) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 22, 23, 24, 25]],target = 0) == False\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, -1, 4, 9], [-8, -3, 1, 6, 11], [-7, -2, 2, 7, 12], [-6, -1, 3, 8, 13]],target = 14) == False\n assert candidate(matrix = [[-10, -8, -6, -4, -2, 0], [1, 3, 5, 7, 9, 11], [2, 4, 6, 8, 10, 12], [3, 5, 7, 9, 11, 13], [4, 6, 8, 10, 12, 14], [5, 7, 9, 11, 13, 15]],target = 7) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13], [2, 4, 6, 8, 10, 12, 14], [3, 5, 7, 9, 11, 13, 15], [4, 6, 8, 10, 12, 14, 16], [5, 7, 9, 11, 13, 15, 17], [6, 8, 10, 12, 14, 16, 18]],target = 17) == True\n assert candidate(matrix = [[5, 10, 15, 20, 25, 30, 35, 40, 45, 50], [6, 11, 16, 21, 26, 31, 36, 41, 46, 51], [7, 12, 17, 22, 27, 32, 37, 42, 47, 52], [8, 13, 18, 23, 28, 33, 38, 43, 48, 53], [9, 14, 19, 24, 29, 34, 39, 44, 49, 54]],target = 38) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]],target = 37) == True\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, -1, 4, 9], [-8, -3, 1, 6, 11], [-7, -2, 2, 7, 12], [-6, -1, 3, 8, 13]],target = -10) == True\n assert candidate(matrix = [[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9], [-8, -6, -4, -2, 0, 2, 4, 6, 8, 10], [-7, -5, -3, -1, 1, 3, 5, 7, 9, 11], [-6, -4, -2, 0, 2, 4, 6, 8, 10, 12], [-5, -3, -1, 1, 3, 5, 7, 9, 11, 13], [-4, -2, 0, 2, 4, 6, 8, 10, 12, 14], [-3, -1, 1, 3, 5, 7, 9, 11, 13, 15], [-2, 0, 2, 4, 6, 8, 10, 12, 14, 16], [-1, 1, 3, 5, 7, 9, 11, 13, 15, 17], [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]],target = 15) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15, 20], [2, 5, 8, 12, 19, 25], [3, 6, 9, 16, 22, 30], [10, 13, 14, 17, 24, 35], [18, 21, 23, 26, 30, 40], [27, 32, 33, 36, 39, 45]],target = 23) == True\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]],target = 1) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [3, 5, 7, 9, 11], [4, 6, 8, 10, 12], [5, 7, 9, 11, 13]],target = 7) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = -3) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 22, 23, 24, 25]],target = 13) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],target = 26) == False\n assert candidate(matrix = [[3, 6, 9, 12, 15], [6, 9, 12, 15, 18], [9, 12, 15, 18, 21], [12, 15, 18, 21, 24], [15, 18, 21, 24, 27]],target = 13) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [22, 24, 26, 28, 30, 32, 34, 36, 38, 40], [41, 43, 45, 47, 49, 51, 53, 55, 57, 59], [42, 44, 46, 48, 50, 52, 54, 56, 58, 60], [61, 63, 65, 67, 69, 71, 73, 75, 77, 79], [62, 64, 66, 68, 70, 72, 74, 76, 78, 80], [81, 83, 85, 87, 89, 91, 93, 95, 97, 99], [82, 84, 86, 88, 90, 92, 94, 96, 98, 100]],target = 64) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = -5) == True\n assert candidate(matrix = [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]],target = 5) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]],target = 5) == True\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],target = 7) == True\n assert candidate(matrix = [[-10, -5, -1, 3, 7, 9], [0, 0, 1, 4, 6, 8], [1, 2, 2, 5, 8, 9], [2, 3, 4, 6, 9, 10], [5, 6, 7, 8, 10, 11], [6, 7, 8, 10, 11, 12]],target = 13) == False\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4], [-3, -2, -1, 0, 1, 2, 3], [4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23, 24]],target = -5) == True\n assert candidate(matrix = [[-1, 3, 5, 7, 9, 11, 13, 15], [2, 4, 6, 8, 10, 12, 14, 16], [17, 19, 21, 23, 25, 27, 29, 31], [33, 35, 37, 39, 41, 43, 45, 47], [49, 51, 53, 55, 57, 59, 61, 63]],target = 30) == False\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13], [2, 4, 6, 8, 10, 12, 14], [15, 17, 19, 21, 23, 25, 27], [29, 31, 33, 35, 37, 39, 41], [43, 45, 47, 49, 51, 53, 55]],target = 30) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15, 19], [2, 5, 8, 12, 19, 23], [3, 6, 9, 16, 22, 25], [10, 13, 14, 17, 24, 26], [18, 21, 23, 26, 30, 35], [27, 32, 33, 34, 36, 37]],target = 14) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30], [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31], [4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32]],target = 17) == True\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40]],target = 25) == True\n assert candidate(matrix = [[-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1]],target = -1) == True\n assert candidate(matrix = [[5]],target = 10) == False\n assert candidate(matrix = [[-1000000000, -900000000, -800000000], [-700000000, -600000000, -500000000], [-400000000, -300000000, -200000000], [-100000000, 0, 100000000], [200000000, 300000000, 400000000], [500000000, 600000000, 700000000], [800000000, 900000000, 1000000000]],target = -500000000) == True\n assert candidate(matrix = [[-10, -5, 0, 5, 10, 15], [1, 6, 11, 16, 21, 26], [2, 7, 12, 17, 22, 27], [3, 8, 13, 18, 23, 28], [4, 9, 14, 19, 24, 29], [5, 10, 15, 20, 25, 30]],target = 3) == True\n assert candidate(matrix = [[1]],target = 1) == True\n assert candidate(matrix = [[-100, -99, -98, -97, -96], [-95, -94, -93, -92, -91], [-90, -89, -88, -87, -86], [-85, -84, -83, -82, -81], [-80, -79, -78, -77, -76]],target = -90) == True\n assert candidate(matrix = [[-1000000000, -500000000, -100000000, -50000000, -10000000], [-5000000, -2500000, -1000000, -500000, -100000], [-50000, -25000, -10000, -5000, -1000], [-500, -250, -100, -50, -10], [-5, -2, -1, -1, 0]],target = -2500) == False\n assert candidate(matrix = [[1, 10, 19, 28, 37, 46], [2, 11, 20, 29, 38, 47], [3, 12, 21, 30, 39, 48], [4, 13, 22, 31, 40, 49], [5, 14, 23, 32, 41, 50], [6, 15, 24, 33, 42, 51]],target = 100) == False\n assert candidate(matrix = [[-9, -8, -7, -6, -5, -4, -3, -2, -1, 0], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]],target = 7) == True\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 22, 23, 24, 25]],target = 25) == True\n assert candidate(matrix = [[1, 10, 20, 30], [2, 11, 21, 31], [3, 12, 22, 32], [4, 13, 23, 33], [5, 14, 24, 34]],target = 15) == False\n assert candidate(matrix = [[1, 5, 9, 13, 17, 21, 25, 29, 33, 37], [2, 6, 10, 14, 18, 22, 26, 30, 34, 38], [3, 7, 11, 15, 19, 23, 27, 31, 35, 39], [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]],target = 38) == True\n assert candidate(matrix = [[1]],target = 0) == False\n assert candidate(matrix = [[1, 10, 20, 30, 40], [2, 12, 22, 32, 42], [3, 13, 23, 33, 43], [4, 14, 24, 34, 44], [5, 15, 25, 35, 45]],target = 28) == False\n assert candidate(matrix = [[-1, 0, 1], [0, 1, 2], [1, 2, 3]],target = 0) == True\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]],target = 2) == False\n assert candidate(matrix = [[10, 20, 30, 40, 50], [60, 70, 80, 90, 100], [110, 120, 130, 140, 150], [160, 170, 180, 190, 200], [210, 220, 230, 240, 250]],target = 155) == False\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 31) == False\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],target = 55) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 1) == True\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],target = 30) == True\n assert candidate(matrix = [[100, 101, 102, 103, 104, 105], [106, 107, 108, 109, 110, 111], [112, 113, 114, 115, 116, 117], [118, 119, 120, 121, 122, 123], [124, 125, 126, 127, 128, 129], [130, 131, 132, 133, 134, 135]],target = 122) == True\n"}, "metadata": {"canonical_parameter_names": ["matrix", "target"], "leetcode_dataset_entry_point": "Solution().searchMatrix", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var searchMatrix = function(matrix, target) {", "container": null, "callable": "searchMatrix", "parameters": [{"name": "matrix", "type": "number[][]"}, {"name": "target", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 241, "task_id": "different-ways-to-add-parentheses", "difficulty": "Medium", "problem_description": "Given a string expression of numbers and operators, return all possible results from computing all the different possible ways to group numbers and operators. You may return the answer in any order.\nThe test cases are generated such that the output values fit in a 32-bit integer and the number of different results does not exceed 104.\n \nExample 1:\n\nInput: expression = \"2-1-1\"\nOutput: [0,2]\nExplanation:\n((2-1)-1) = 0 \n(2-(1-1)) = 2\n\nExample 2:\n\nInput: expression = \"2*3-4*5\"\nOutput: [-34,-14,-10,-10,10]\nExplanation:\n(2*(3-(4*5))) = -34 \n((2*3)-(4*5)) = -14 \n((2*(3-4))*5) = -10 \n(2*((3-4)*5)) = -10 \n(((2*3)-4)*5) = 10\n\n \nConstraints:\n\n1 <= expression.length <= 20\nexpression consists of digits and the operator '+', '-', and '*'.\nAll the integer values in the input expression are in the range [0, 99].\nThe integer values in the input expression do not have a leading '-' or '+' denoting the sign.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(expression = \"4*5-2*3\") == [-4, 36, 14, 36, 54]\n assert candidate(expression = \"9-3*2+1\") == [0, 2, 18, 4, 13]\n assert candidate(expression = \"3+5/2*3\") == []\n assert candidate(expression = \"1+1+1+1\") == [4, 4, 4, 4, 4]\n assert candidate(expression = \"9*8+7*6-5*4+3*2-1\") == [-1755, -2385, -1755, -2385, -3645, -999, -1125, -1755, -999, -2637, -3897, -1125, -3897, -2385, 513, 639, 513, 639, 891, -621, -495, 513, 639, -1755, -999, 513, -621, 513, -2763, -4023, -1251, -4023, -2511, 639, 891, -495, 639, -3645, -2133, 891, -1377, 891, 135, 45, 135, 45, -135, 243, 225, 135, 243, 9, -171, 225, -171, 45, 513, 639, 513, 639, 891, 2403, 3069, 2403, 3069, 4401, -783, -765, 351, 369, 297, 315, 351, 369, 1431, 1449, -1755, -999, 513, -621, 513, 135, 243, 513, 2403, -783, 351, 297, 351, 1431, -2709, -3969, -1197, -3969, -2457, 693, 945, -441, 693, -3591, -2079, 945, -1323, 945, -9, -189, 207, -189, 27, 693, 945, 3393, 4725, -765, 369, 315, 369, 1449, -3591, -2079, 945, -1323, 945, 189, 405, 945, 4725, -1647, 621, 513, 621, 2781, -3915, -5265, -3915, -5265, -7965, -2295, -2565, -3915, -2295, -5805, -8505, -2565, -8505, -5265, 945, 1215, 945, 1215, 1755, -1485, -1215, 945, 1215, -3915, -2295, 945, -1485, 945, -6075, -8775, -2835, -8775, -5535, 1215, 1755, -1215, 1215, -7965, -4725, 1755, -3105, 1755, 135, 45, 135, 45, -135, 243, 225, 135, 243, 9, -171, 225, -171, 45, 495, 405, 495, 405, 225, 603, 585, 495, 603, 369, 189, 585, 189, 405, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 5355, 6885, 5355, 6885, 9945, -783, -765, 351, 369, 297, 315, 351, 369, 1431, 1449, -1863, -1845, 567, 585, 297, 315, 657, 675, 567, 585, 1647, 1665, 567, 585, 1647, 1665, 3087, 3105, -1755, -999, 513, -621, 513, 135, 243, 513, 2403, -783, 351, 297, 351, 1431, -3915, -2295, 945, -1485, 945, 135, 243, 495, 603, 945, 2835, 945, 2835, 5355, -783, 351, 297, 351, 1431, -1863, 567, 297, 657, 567, 1647, 567, 1647, 3087, -2709, -3969, -1197, -3969, -2457, 693, 945, -441, 693, -3591, -2079, 945, -1323, 945, -9, -189, 207, -189, 27, 693, 945, 3393, 4725, -765, 369, 315, 369, 1449, -3591, -2079, 945, -1323, 945, 189, 405, 945, 4725, -1647, 621, 513, 621, 2781, -5949, -8649, -2709, -8649, -5409, 1341, 1881, -1089, 1341, -7839, -4599, 1881, -2979, 1881, -9, -189, 207, -189, 27, 351, 171, 567, 171, 387, 1341, 1881, 4041, 5661, 1341, 1881, 4041, 5661, 7641, 10701, -765, 369, 315, 369, 1449, -1845, 585, 315, 675, 585, 1665, 585, 1665, 3105, -3519, -2007, 1017, -1251, 1017, 261, 477, 1017, 4797, -1575, 693, 585, 693, 2853, -7839, -4599, 1881, -2979, 1881, 261, 477, 981, 1197, 1881, 5661, 1881, 5661, 10701, -1575, 693, 585, 693, 2853, -3735, 1125, 585, 1305, 1125, 3285, 1125, 3285, 6165, -131, -201, -131, -201, -341, -47, -61, -131, -47, -229, -369, -61, -369, -201, 121, 135, 121, 135, 163, -5, 9, 121, 135, -131, -47, 121, -5, 121, -243, -383, -75, -383, -215, 135, 163, 9, 135, -341, -173, 163, -89, 163, 79, 69, 79, 69, 49, 91, 89, 79, 91, 65, 45, 89, 45, 69, 121, 135, 121, 135, 163, 331, 405, 331, 405, 553, -23, -21, 103, 105, 97, 99, 103, 105, 223, 225, -131, -47, 121, -5, 121, 79, 91, 121, 331, -23, 103, 97, 103, 223, -237, -377, -69, -377, -209, 141, 169, 15, 141, -335, -167, 169, -83, 169, 63, 43, 87, 43, 67, 141, 169, 441, 589, -21, 105, 99, 105, 225, -335, -167, 169, -83, 169, 85, 109, 169, 589, -119, 133, 121, 133, 373, -3915, -5265, -3915, -5265, -7965, -2295, -2565, -3915, -2295, -5805, -8505, -2565, -8505, -5265, 945, 1215, 945, 1215, 1755, -1485, -1215, 945, 1215, -3915, -2295, 945, -1485, 945, -6075, -8775, -2835, -8775, -5535, 1215, 1755, -1215, 1215, -7965, -4725, 1755, -3105, 1755, -2291, -3081, -2291, -3081, -4661, -1343, -1501, -2291, -1343, -3397, -4977, -1501, -4977, -3081, 553, 711, 553, 711, 1027, -869, -711, 553, 711, -2291, -1343, 553, -869, 553, -3555, -5135, -1659, -5135, -3239, 711, 1027, -711, 711, -4661, -2765, 1027, -1817, 1027, 415, 405, 415, 405, 385, 427, 425, 415, 427, 401, 381, 425, 381, 405, 775, 765, 775, 765, 745, 787, 785, 775, 787, 761, 741, 785, 741, 765, 79, 69, 79, 69, 49, 91, 89, 79, 91, 65, 45, 89, 45, 69, 775, 765, 775, 765, 745, 787, 785, 775, 787, 761, 741, 785, 741, 765, 439, 429, 439, 429, 409, 451, 449, 439, 451, 425, 405, 449, 405, 429, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 945, 1215, 945, 1215, 1755, 2835, 3645, 2835, 3645, 5265, 5355, 6885, 5355, 6885, 9945, 553, 711, 553, 711, 1027, 763, 981, 763, 981, 1417, 945, 1215, 945, 1215, 1755, 553, 711, 553, 711, 1027, 3115, 4005, 3115, 4005, 5785, 5635, 7245, 5635, 7245, 10465, 763, 981, 763, 981, 1417, 5635, 7245, 5635, 7245, 10465, 3283, 4221, 3283, 4221, 6097, -807, -805, 327, 329, 273, 275, 327, 329, 1407, 1409, -1887, -1885, 543, 545, 273, 275, 633, 635, 543, 545, 1623, 1625, 543, 545, 1623, 1625, 3063, 3065, -23, -21, 103, 105, 97, 99, 103, 105, 223, 225, -1887, -1885, 543, 545, -1103, -1101, 319, 321, 433, 435, 793, 795, 97, 99, 793, 795, 457, 459, 543, 545, 1623, 1625, 543, 545, 1623, 1625, 3063, 3065, 319, 321, 439, 441, 543, 545, 319, 321, 1783, 1785, 3223, 3225, 439, 441, 3223, 3225, 1879, 1881, -1755, -999, 513, -621, 513, 135, 243, 513, 2403, -783, 351, 297, 351, 1431, -3915, -2295, 945, -1485, 945, 135, 243, 495, 603, 945, 2835, 945, 2835, 5355, -783, 351, 297, 351, 1431, -1863, 567, 297, 657, 567, 1647, 567, 1647, 3087, -131, -47, 121, -5, 121, 79, 91, 121, 331, -23, 103, 97, 103, 223, -3915, -2295, 945, -1485, 945, -2291, -1343, 553, -869, 553, 415, 427, 775, 787, 79, 91, 775, 787, 439, 451, 945, 2835, 945, 2835, 5355, 553, 763, 945, 553, 3115, 5635, 763, 5635, 3283, -807, 327, 273, 327, 1407, -1887, 543, 273, 633, 543, 1623, 543, 1623, 3063, -23, 103, 97, 103, 223, -1887, 543, -1103, 319, 433, 793, 97, 793, 457, 543, 1623, 543, 1623, 3063, 319, 439, 543, 319, 1783, 3223, 439, 3223, 1879, -2701, -3961, -1189, -3961, -2449, 701, 953, -433, 701, -3583, -2071, 953, -1315, 953, -1, -181, 215, -181, 35, 701, 953, 3401, 4733, -757, 377, 323, 377, 1457, -3583, -2071, 953, -1315, 953, 197, 413, 953, 4733, -1639, 629, 521, 629, 2789, -5941, -8641, -2701, -8641, -5401, 1349, 1889, -1081, 1349, -7831, -4591, 1889, -2971, 1889, -1, -181, 215, -181, 35, 359, 179, 575, 179, 395, 1349, 1889, 4049, 5669, 1349, 1889, 4049, 5669, 7649, 10709, -757, 377, 323, 377, 1457, -1837, 593, 323, 683, 593, 1673, 593, 1673, 3113, -3511, -1999, 1025, -1243, 1025, 269, 485, 1025, 4805, -1567, 701, 593, 701, 2861, -7831, -4591, 1889, -2971, 1889, 269, 485, 989, 1205, 1889, 5669, 1889, 5669, 10709, -1567, 701, 593, 701, 2861, -3727, 1133, 593, 1313, 1133, 3293, 1133, 3293, 6173, -237, -377, -69, -377, -209, 141, 169, 15, 141, -335, -167, 169, -83, 169, 63, 43, 87, 43, 67, 141, 169, 441, 589, -21, 105, 99, 105, 225, -335, -167, 169, -83, 169, 85, 109, 169, 589, -119, 133, 121, 133, 373, -5941, -8641, -2701, -8641, -5401, 1349, 1889, -1081, 1349, -7831, -4591, 1889, -2971, 1889, -3477, -5057, -1581, -5057, -3161, 789, 1105, -633, 789, -4583, -2687, 1105, -1739, 1105, 399, 379, 423, 379, 403, 759, 739, 783, 739, 763, 63, 43, 87, 43, 67, 759, 739, 783, 739, 763, 423, 403, 447, 403, 427, 1349, 1889, 4049, 5669, 1349, 1889, 4049, 5669, 7649, 10709, 789, 1105, 1089, 1525, 1349, 1889, 789, 1105, 4449, 6229, 8049, 11269, 1089, 1525, 8049, 11269, 4689, 6565, -805, 329, 275, 329, 1409, -1885, 545, 275, 635, 545, 1625, 545, 1625, 3065, -21, 105, 99, 105, 225, -1885, 545, -1101, 321, 435, 795, 99, 795, 459, 545, 1625, 545, 1625, 3065, 321, 441, 545, 321, 1785, 3225, 441, 3225, 1881, -3511, -1999, 1025, -1243, 1025, 269, 485, 1025, 4805, -1567, 701, 593, 701, 2861, -7831, -4591, 1889, -2971, 1889, 269, 485, 989, 1205, 1889, 5669, 1889, 5669, 10709, -1567, 701, 593, 701, 2861, -3727, 1133, 593, 1313, 1133, 3293, 1133, 3293, 6173, -263, -95, 241, -11, 241, 157, 181, 241, 661, -47, 205, 193, 205, 445, -7831, -4591, 1889, -2971, 1889, -4583, -2687, 1105, -1739, 1105, 829, 853, 1549, 1573, 157, 181, 1549, 1573, 877, 901, 1889, 5669, 1889, 5669, 10709, 1105, 1525, 1889, 1105, 6229, 11269, 1525, 11269, 6565, -1615, 653, 545, 653, 2813, -3775, 1085, 545, 1265, 1085, 3245, 1085, 3245, 6125, -47, 205, 193, 205, 445, -3775, 1085, -2207, 637, 865, 1585, 193, 1585, 913, 1085, 3245, 1085, 3245, 6125, 637, 877, 1085, 637, 3565, 6445, 877, 6445, 3757]\n assert candidate(expression = \"10+5-3*2\") == [9, 14, 9, 24, 24]\n assert candidate(expression = \"3+5*2\") == [13, 16]\n assert candidate(expression = \"2*3-4*5\") == [-34, -10, -14, -10, 10]\n assert candidate(expression = \"2*3+4*5\") == [46, 70, 26, 70, 50]\n assert candidate(expression = \"10+5-2*3\") == [9, 19, 9, 39, 39]\n assert candidate(expression = \"1+2*3\") == [7, 9]\n assert candidate(expression = \"4+2*3-5\") == [0, 5, -12, 5, 13]\n assert candidate(expression = \"1+2\") == [3]\n assert candidate(expression = \"9-3/3+2\") == []\n assert candidate(expression = \"2-1-1\") == [2, 0]\n assert candidate(expression = \"3-2*2+1\") == [-3, -2, 3, 0, 3]\n assert candidate(expression = \"1*2-3*4+5\") == [-25, -15, -9, -5, 1, -25, -15, -9, -9, -5, 1, -5, 1, 1]\n assert candidate(expression = \"8+2-1*3\") == [7, 11, 7, 27, 27]\n assert candidate(expression = \"100+200-50*2\") == [200, 400, 200, 500, 500]\n assert candidate(expression = \"3*4+2*5\") == [42, 90, 22, 90, 70]\n assert candidate(expression = \"1+2*3-4/2\") == []\n assert candidate(expression = \"1+2-3\") == [0, 0]\n assert candidate(expression = \"1+2*3-4\") == [-1, 3, -3, 3, 5]\n assert candidate(expression = \"3+2*2\") == [7, 10]\n assert candidate(expression = \"10+5-3*2+4\") == [-3, 5, 22, 13, 18, -3, 5, 72, 72, 13, 18, 13, 28, 28]\n assert candidate(expression = \"1*1*1*1\") == [1, 1, 1, 1, 1]\n assert candidate(expression = \"1*2-3+4*5\") == [-21, -33, 19, -25, 15, -21, -33, 19, 19, -25, 15, -25, 15, 15]\n assert candidate(expression = \"9*8-7+6-5*4\") == [135, -27, 135, -216, -216, -117, 45, -225, -117, 0, 0, 72, -360, 72, 79, 61, 79, 40, 40, -5, 13, 51, 69, -65, 43, 39, -5, 51, 0, 0, 72, -360, 72, 256, 256, 40, 264, -200, 232, 216, 40, 264]\n assert candidate(expression = \"1*2+3*4+5\") == [29, 19, 45, 19, 25, 29, 19, 45, 45, 19, 25, 19, 25, 25]\n assert candidate(expression = \"3+5*2-8\") == [-27, 5, -48, 5, 8]\n assert candidate(expression = \"1+2+3\") == [6, 6]\n assert candidate(expression = \"6/2+3-1\") == []\n assert candidate(expression = \"7*8-2+3\") == [21, 63, 51, 45, 57]\n assert candidate(expression = \"2+3*4-5+6\") == [-19, 17, 3, 5, 15, -35, 25, 3, 9, 5, 15, 1, 15, 21]\n assert candidate(expression = \"11*11+22-33*4+55-66/2\") == []\n assert candidate(expression = \"9+8-7*6+5-4*3+2-1\") == [52, 52, 31, 73, 31, -53, -53, 17, -53, 87, 45, -53, 17, -53, 52, 52, 31, 73, 31, -179, -179, -179, -179, 17, -53, 17, -137, -137, 87, 45, -53, 17, -53, 87, 45, -221, -221, 17, -53, 17, -137, -137, -14, -14, -17, -11, -17, -29, -29, -19, -29, -9, -15, -29, -19, -29, -44, -44, -47, -41, -47, -14, -14, -17, -11, -17, -179, -179, -179, -179, -155, -155, -275, -275, -155, -155, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, 81, 39, -59, 11, -59, 81, 39, -227, -227, 11, -59, 11, -143, -143, -9, -15, -29, -19, -29, -39, -45, -9, -15, -227, -227, -197, -347, -197, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, 4, 4, 7, 1, 7, 19, 19, 9, 19, -1, 5, 19, 9, 19, 4, 4, 7, 1, 7, 37, 37, 37, 37, 9, 19, 9, 31, 31, -1, 5, 19, 9, 19, -1, 5, 43, 43, 9, 19, 9, 31, 31, -36, -36, -33, -39, -33, -21, -21, -31, -21, -41, -35, -21, -31, -21, 4, 4, 7, 1, 7, 19, 19, 9, 19, -1, 5, 19, 9, 19, -76, -76, -73, -79, -73, -46, -46, -43, -49, -43, 4, 4, 7, 1, 7, -36, -36, -33, -39, -33, 4, 4, 7, 1, 7, -155, -155, -155, -155, -131, -131, -251, -251, -131, -131, 37, 37, 37, 37, -123, -123, 37, 37, -283, -283, -163, -163, 37, 37, -123, -123, 37, 37, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 79, 37, -61, 9, -61, 79, 37, -229, -229, 9, -61, 9, -145, -145, -11, -17, -31, -21, -31, -41, -47, -11, -17, -229, -229, -199, -349, -199, 21, -49, 21, -133, -133, -21, -31, -51, -21, -133, -133, -115, -205, -115, -1, 5, 19, 9, 19, -1, 5, 43, 43, 9, 19, 9, 31, 31, -41, -35, -21, -31, -21, -1, 5, 19, 9, 19, -81, -75, -51, -45, -1, 5, -41, -35, -1, 5, -197, -197, -167, -317, -167, 43, 43, -157, 43, -357, -207, 43, -157, 43, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 52, 52, 31, 73, 31, -53, -53, 17, -53, 87, 45, -53, 17, -53, 52, 52, 31, 73, 31, -179, -179, -179, -179, 17, -53, 17, -137, -137, 87, 45, -53, 17, -53, 87, 45, -221, -221, 17, -53, 17, -137, -137, -14, -14, -17, -11, -17, -29, -29, -19, -29, -9, -15, -29, -19, -29, -44, -44, -47, -41, -47, -14, -14, -17, -11, -17, -179, -179, -179, -179, -155, -155, -275, -275, -155, -155, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, 81, 39, -59, 11, -59, 81, 39, -227, -227, 11, -59, 11, -143, -143, -9, -15, -29, -19, -29, -39, -45, -9, -15, -227, -227, -197, -347, -197, 23, -47, 23, -131, -131, -19, -29, -49, -19, -131, -131, -113, -203, -113, -50, -50, -20, -80, -20, 100, 100, 0, 100, -100, -40, 100, 0, 100, -50, -50, -20, -80, -20, 280, 280, 280, 280, 0, 100, 0, 220, 220, -100, -40, 100, 0, 100, -100, -40, 340, 340, 0, 100, 0, 220, 220, -50, -50, -20, -80, -20, 100, 100, 0, 100, -100, -40, 100, 0, 100, -50, -50, -20, -80, -20, 280, 280, 280, 280, 0, 100, 0, 220, 220, -100, -40, 100, 0, 100, -100, -40, 340, 340, 0, 100, 0, 220, 220, -36, -36, -33, -39, -33, -21, -21, -31, -21, -41, -35, -21, -31, -21, 4, 4, 7, 1, 7, 19, 19, 9, 19, -1, 5, 19, 9, 19, -36, -36, -33, -39, -33, -21, -21, -31, -21, -41, -35, -21, -31, -21, 49, 49, 52, 46, 52, 64, 64, 54, 64, 44, 50, 64, 54, 64, 49, 49, 52, 46, 52, 64, 64, 54, 64, 44, 50, 64, 54, 64, -76, -76, -73, -79, -73, -46, -46, -43, -49, -43, 4, 4, 7, 1, 7, -36, -36, -33, -39, -33, 4, 4, 7, 1, 7, -76, -76, -73, -79, -73, -46, -46, -43, -49, -43, 94, 94, 97, 91, 97, 94, 94, 97, 91, 97, -36, -36, -33, -39, -33, 4, 4, 7, 1, 7, -36, -36, -33, -39, -33, 49, 49, 52, 46, 52, 49, 49, 52, 46, 52, -128, -128, -128, -128, -104, -104, -224, -224, -104, -104, 64, 64, 64, 64, -96, -96, 64, 64, -256, -256, -136, -136, 64, 64, -96, -96, 64, 64, -128, -128, -128, -128, -104, -104, -224, -224, -104, -104, 280, 280, 280, 280, 280, 280, 280, 280, -96, -96, 64, 64, -96, -96, 244, 244, 244, 244, -256, -256, -136, -136, 64, 64, -96, -96, 64, 64, -256, -256, -136, -136, 424, 424, 424, 424, -96, -96, 64, 64, -96, -96, 244, 244, 244, 244, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, -9, 91, -9, 211, 211, -9, 91, -9, 211, 211, -31, -21, 9, 19, -31, -21, 54, 64, 54, 64, -71, -41, 9, -31, 9, -71, -41, 99, 99, -31, 9, -31, 54, 54, -95, -95, -77, -167, -77, 49, 49, -71, 49, -191, -101, 49, -71, 49, -95, -95, -77, -167, -77, 211, 211, 211, 211, -71, 49, -71, 184, 184, -191, -101, 49, -71, 49, -191, -101, 319, 319, -71, 49, -71, 184, 184, 79, 37, -61, 9, -61, 79, 37, -229, -229, 9, -61, 9, -145, -145, -11, -17, -31, -21, -31, -41, -47, -11, -17, -229, -229, -199, -349, -199, 21, -49, 21, -133, -133, -21, -31, -51, -21, -133, -133, -115, -205, -115, -1, 5, 19, 9, 19, -1, 5, 43, 43, 9, 19, 9, 31, 31, -41, -35, -21, -31, -21, -1, 5, 19, 9, 19, -81, -75, -51, -45, -1, 5, -41, -35, -1, 5, -197, -197, -167, -317, -167, 43, 43, -157, 43, -357, -207, 43, -157, 43, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 79, 37, -61, 9, -61, 79, 37, -229, -229, 9, -61, 9, -145, -145, -11, -17, -31, -21, -31, -41, -47, -11, -17, -229, -229, -199, -349, -199, 21, -49, 21, -133, -133, -21, -31, -51, -21, -133, -133, -115, -205, -115, -91, -31, 109, 9, 109, -91, -31, 349, 349, 9, 109, 9, 229, 229, -91, -31, 109, 9, 109, -91, -31, 349, 349, 9, 109, 9, 229, 229, -41, -35, -21, -31, -21, -1, 5, 19, 9, 19, -41, -35, -21, -31, -21, 44, 50, 64, 54, 64, 44, 50, 64, 54, 64, -81, -75, -51, -45, -1, 5, -41, -35, -1, 5, -81, -75, -51, -45, 89, 95, 89, 95, -41, -35, -1, 5, -41, -35, 44, 50, 44, 50, -161, -161, -131, -281, -131, 79, 79, -121, 79, -321, -171, 79, -121, 79, -161, -161, -131, -281, -131, 349, 349, 349, 349, -121, 79, -121, 304, 304, -321, -171, 79, -121, 79, -321, -171, 529, 529, -121, 79, -121, 304, 304, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, 9, 19, 9, 31, 31, -31, -21, 9, 19, -71, -41, 9, -31, 9, -113, -113, -95, -185, -95, 31, 31, -89, 31, -209, -119, 31, -89, 31, 25, -45, 25, -129, -129, -17, -27, -47, -17, -129, -129, -111, -201, -111, -9, 91, -9, 211, 211, -9, 91, -9, 211, 211, -31, -21, 9, 19, -31, -21, 54, 64, 54, 64, -71, -41, 9, -31, 9, -71, -41, 99, 99, -31, 9, -31, 54, 54, -95, -95, -77, -167, -77, 49, 49, -71, 49, -191, -101, 49, -71, 49, -95, -95, -77, -167, -77, 211, 211, 211, 211, -71, 49, -71, 184, 184, -191, -101, 49, -71, 49, -191, -101, 319, 319, -71, 49, -71, 184, 184]\n assert candidate(expression = \"5*3+8-2*4+9*2\") == [-165, -205, -75, -205, -115, 675, 795, 105, 225, -165, -75, 795, 105, 345, -165, -205, -75, -205, -115, 990, 1170, 990, 1170, 105, 225, 105, 270, 270, -150, -60, 810, 120, 360, -150, -60, 1170, 1170, 120, 360, 120, 450, 450, -21, -29, -3, -29, -11, 147, 171, 33, 57, -21, -3, 171, 33, 81, 11, 3, 29, 3, 21, -21, -29, -3, -29, -11, 990, 1170, 990, 1170, 462, 546, 1166, 1378, 462, 546, 33, 153, 33, 198, 198, 33, 57, 65, 33, 198, 198, 102, 230, 102, -150, -60, 810, 120, 360, -150, -60, 1170, 1170, 120, 360, 120, 450, 450, -6, 12, 186, 48, 96, 58, 76, -6, 12, 1170, 1170, 546, 1378, 546, 48, 288, 48, 378, 378, 48, 96, 112, 48, 378, 378, 186, 442, 186]\n assert candidate(expression = \"33+33-33*33/33\") == []\n assert candidate(expression = \"9-8+7-6+5-4\") == [1, 1, -1, 9, -1, 1, 1, -1, -1, 9, -1, 9, -1, -1, 1, 1, 3, -7, 3, -13, -13, 1, 1, 1, 1, 3, -11, 3, 1, -9, 1, -9, -9, -7, 3, -21, -7, 1, 1, 3, -11, 3]\n assert candidate(expression = \"3*3-10/2+4*2-1\") == []\n assert candidate(expression = \"100-99+98-97+96-95+94-93\") == [0, 0, 2, -186, 2, 0, 0, 2, 2, -186, 2, -186, 2, 2, 0, 0, -2, 186, -2, 192, 192, 0, 0, 0, 0, -2, 190, -2, 0, 188, 0, 188, 188, 186, -2, 378, 186, 0, 0, -2, 190, -2, 0, 0, 2, -186, 2, 0, 0, 2, 2, -186, 2, -186, 2, 2, 0, 0, -2, 186, -2, 0, 0, -2, 186, -2, 192, 192, 0, 0, 192, 192, 0, 0, 0, 0, 0, 0, -2, 190, -2, 0, 0, -2, -2, 190, -2, 190, -2, -2, 0, 188, 0, 188, 188, 186, -2, 378, 186, 0, 0, -2, 190, -2, 0, 188, 0, 188, 188, 186, -2, 186, -2, 378, 186, 378, 186, 186, 0, 0, -2, 190, -2, 0, 0, -2, -2, 190, -2, 190, -2, -2, 2, 2, 0, 188, 0, 2, 2, 0, 0, 188, 0, 188, 0, 0, 2, 2, 4, -184, 4, -190, -190, 2, 2, 2, 2, 4, -188, 4, 2, -186, 2, -186, -186, -184, 4, -376, -184, 2, 2, 4, -188, 4, -194, -194, -196, -8, -196, -194, -194, -196, -196, -8, -196, -8, -196, -196, 2, 2, 0, 188, 0, 2, 2, 0, 0, 188, 0, 188, 0, 0, 0, 0, 2, -186, 2, 0, 0, 2, -186, 2, 2, 2, 4, -184, 4, -194, -194, -192, -380, -192, 2, 2, 4, -184, 4, 0, 0, -192, -192, 0, 0, -192, -192, -192, -192, -190, -190, 2, 2, -386, -386, -190, -190, 0, 0, 0, 0, 2, 2, -194, -194, 2, 2, 2, 2, 0, 192, 0, 2, 2, 0, 0, 192, 0, 192, 0, 0, 2, 2, 4, -188, 4, -194, -194, 2, 2, 2, 2, 4, -192, 4, 2, -190, 2, -190, -190, -188, 4, -384, -188, 2, 2, 4, -192, 4, -186, 2, -186, 2, 2, 0, -188, 192, 0, -186, -186, -188, 4, -188, -186, 2, -186, 2, 2, 0, -188, 0, -188, 192, 0, 192, 0, 0, -186, -186, -188, 4, -188, -186, -186, -188, -188, 4, -188, 4, -188, -188, 2, -186, 2, -186, -186, -184, 4, -376, -184, 2, 2, 4, -188, 4, -194, -382, -194, -382, -382, 2, -186, 2, -186, -186, -186, 2, -186, 2, -184, 4, -380, -192, -184, 4, -186, -378, -186, -378, -378, -376, -184, -572, -376, -186, -186, -184, -380, -184, 2, 2, 0, 192, 0, 2, 2, 0, 0, 192, 0, 192, 0, 0, 2, 2, 4, -188, 4, -194, -194, 2, 2, 2, 2, 4, -192, 4, 2, -190, 2, -190, -190, -188, 4, -384, -188, 2, 2, 4, -192, 4]\n assert candidate(expression = \"15+25*3-45/5+6*7\") == []\n assert candidate(expression = \"5+4+3+2+1+0\") == [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15]\n assert candidate(expression = \"33-5*6+7*8-9/3+2\") == []\n assert candidate(expression = \"12*3+4-5/2+6-7*8\") == []\n assert candidate(expression = \"5*6-7*8+9*10-11*12\") == [38180, 3530, 1220, 3530, -33430, 72620, 7170, 1220, -1300, 450, -36510, 7170, -36510, -66750, 5240, 290, -40, 290, -4990, 72620, 7170, 39680, 3930, -2740, -5260, -40, -5260, -2560, 450, -36510, 7170, -36510, -66750, -2790, -8070, 7170, 3930, -40470, -70710, -8070, -70710, -38310, 5450, 500, 170, 500, -4780, 10370, 1020, 170, -190, 60, -5220, 1020, -5220, -9540, -5740, -790, -460, -790, 4490, -5530, -580, -250, -580, 4700, 68930, 6780, 35990, 3540, 10370, 1020, 25010, 2460, -610, -60, -4060, -6580, -1360, -6580, -3880, -1150, -1510, -460, -250, -6310, -3610, -1510, -2710, -610, 780, -36180, 7500, -36180, -66420, -2460, -7740, 7500, 4260, -40140, -70380, -7740, -70380, -37980, 60, -5220, 1020, -5220, -9540, -3540, 1740, -1020, 4260, 6780, 3540, 1020, 2460, -60, -41460, -71700, -9060, -71700, -39300, -6540, -10860, 1740, 4260, -68460, -36060, -10860, -25260, -60, 7660, 730, 268, 730, -6662, 14548, 1458, 268, -236, 114, -7278, 1458, -7278, -13326, 1072, 82, 16, 82, -974, 14548, 1458, 7960, 810, -524, -1028, 16, -1028, -488, 114, -7278, 1458, -7278, -13326, -534, -1590, 1458, 810, -8070, -14118, -1590, -14118, -7638, 5450, 500, 170, 500, -4780, 10370, 1020, 170, -190, 60, -5220, 1020, -5220, -9540, -25070, -2300, -782, -2300, 21988, -47702, -4692, -782, 874, -276, 24012, -4692, 24012, 43884, -1348, -358, -292, -358, 698, -1138, -148, -82, -148, 908, -1124, -134, -68, -134, 922, -1138, -148, -82, -148, 908, -914, 76, 142, 76, 1132, 68930, 6780, 35990, 3540, 10370, 1020, 25010, 2460, -610, -60, 10858, 1068, 4270, 420, 10370, 1020, -47702, -4692, 29402, 2892, 3782, 372, 2074, 204, 3782, 372, -23546, -2316, -3532, -6052, -832, -6052, -3352, -622, -982, 68, 278, -5782, -3082, -982, -2182, -82, -788, -1292, -248, -1292, -752, -622, -982, 2122, 3778, -292, -82, -68, -82, 142, -5782, -3082, -982, -2182, -82, -1022, -482, -982, 3778, -2542, -442, -302, -442, 1798, 780, -36180, 7500, -36180, -66420, -2460, -7740, 7500, 4260, -40140, -70380, -7740, -70380, -37980, 60, -5220, 1020, -5220, -9540, -3540, 1740, -1020, 4260, 6780, 3540, 1020, 2460, -60, -41460, -71700, -9060, -71700, -39300, -6540, -10860, 1740, 4260, -68460, -36060, -10860, -25260, -60, 444, -6948, 1788, -6948, -12996, -204, -1260, 1788, 1140, -7740, -13788, -1260, -13788, -7308, 60, -5220, 1020, -5220, -9540, -276, 24012, -4692, 24012, 43884, -3108, -2052, -588, 468, -420, 636, -588, 468, 2100, 3156, 6780, 3540, 1020, 2460, -60, 1068, 420, 1020, -4692, 2892, 372, 204, 372, -2316, -40932, -71172, -8532, -71172, -38772, -6012, -10332, 2268, 4788, -67932, -35532, -10332, -24732, 468, -8004, -14052, -1524, -14052, -7572, -6012, -10332, 26916, 46788, -2052, 468, 636, 468, 3156, -67932, -35532, -10332, -24732, 468, -10812, -4332, -10332, 46788, -29052, -3852, -2172, -3852, 23028]\n assert candidate(expression = \"10+20-30*40/50\") == []\n assert candidate(expression = \"100-50*2+30/5-20*3\") == []\n assert candidate(expression = \"10+5*2-3*2+1\") == [-25, -15, -5, -5, 5, 11, 13, -5, 31, -9, 1, 15, 1, 25, -105, -75, -45, -45, -15, 11, 13, 21, 23, 15, 51, -45, 51, 81, -9, 1, 15, 1, 25, -59, -29, 15, 25, 11, 35, -29, 35, 55]\n assert candidate(expression = \"7+8*3-2/1+6\") == []\n assert candidate(expression = \"99-9*9+8*8-7*7+6*6\") == [21114, 38754, 5562, 38754, 23202, -3078, -5598, 378, -3078, 35874, 20322, -5598, 15138, -5598, 2151, 4356, 207, 4356, 2412, -3078, -5598, -22041, -39996, 2646, -810, -441, -810, -3897, 35874, 20322, -5598, 15138, -5598, 1476, -468, -5598, -39996, 17406, -3330, -1116, -3330, -21852, 44928, 82413, 11880, 82413, 49365, -6480, -11835, 864, -6480, 76293, 43245, -11835, 32229, -11835, 2151, 4356, 207, 4356, 2412, 1584, 3789, -360, 3789, 1845, -6480, -11835, -25443, -46233, -6480, -11835, -25443, -46233, -49824, -90459, 2646, -810, -441, -810, -3897, 6048, -1296, -441, -1008, -1296, -4383, -1296, -4383, -8352, 35469, 19917, -6003, 14733, -6003, 1071, -873, -6003, -40401, 17001, -3735, -1521, -3735, -22257, 76293, 43245, -11835, 32229, -11835, 1071, -873, -2331, -4275, -11835, -46233, -11835, -46233, -90459, 17001, -3735, -1521, -3735, -22257, 37413, -6651, -1521, -4923, -6651, -25173, -6651, -25173, -48987, 2362, 4322, 634, 4322, 2594, -326, -606, 58, -326, 4002, 2274, -606, 1698, -606, 255, 500, 39, 500, 284, -326, -606, -2433, -4428, 310, -74, -33, -74, -417, 4002, 2274, -606, 1698, -606, 180, -36, -606, -4428, 1950, -354, -108, -354, -2412, 44928, 82413, 11880, 82413, 49365, -6480, -11835, 864, -6480, 76293, 43245, -11835, 32229, -11835, 26176, 47981, 6952, 47981, 28757, -3728, -6843, 544, -3728, 44421, 25197, -6843, 18789, -6843, -257, -12, -473, -12, -228, -824, -579, -1040, -579, -795, 255, 500, 39, 500, 284, -824, -579, -1040, -579, -795, -312, -67, -528, -67, -283, -6480, -11835, -25443, -46233, -6480, -11835, -25443, -46233, -49824, -90459, -3728, -6843, -5835, -10665, -6480, -11835, -3728, -6843, -27851, -50601, -52232, -94827, -5835, -10665, -52232, -94827, -30216, -54891, 2934, -522, -153, -522, -3609, 6336, -1008, -153, -720, -1008, -4095, -1008, -4095, -8064, 310, -74, -33, -74, -417, 6336, -1008, 3712, -560, -545, -1112, -33, -1112, -600, -1008, -4095, -1008, -4095, -8064, -560, -903, -1008, -560, -4487, -8456, -903, -8456, -4872, 35469, 19917, -6003, 14733, -6003, 1071, -873, -6003, -40401, 17001, -3735, -1521, -3735, -22257, 76293, 43245, -11835, 32229, -11835, 1071, -873, -2331, -4275, -11835, -46233, -11835, -46233, -90459, 17001, -3735, -1521, -3735, -22257, 37413, -6651, -1521, -4923, -6651, -25173, -6651, -25173, -48987, 3597, 1869, -1011, 1293, -1011, -225, -441, -1011, -4833, 1545, -759, -513, -759, -2817, 76293, 43245, -11835, 32229, -11835, 44421, 25197, -6843, 18789, -6843, -3297, -3513, -6699, -6915, -225, -441, -6699, -6915, -3627, -3843, -11835, -46233, -11835, -46233, -90459, -6843, -10665, -11835, -6843, -50601, -94827, -10665, -94827, -54891, 17289, -3447, -1233, -3447, -21969, 37701, -6363, -1233, -4635, -6363, -24885, -6363, -24885, -48699, 1545, -759, -513, -759, -2817, 37701, -6363, 21957, -3675, -3585, -6987, -513, -6987, -3915, -6363, -24885, -6363, -24885, -48699, -3675, -5733, -6363, -3675, -27237, -51051, -5733, -51051, -29547, -210150, -386550, -54630, -386550, -231030, 31770, 56970, -2790, 31770, -357750, -202230, 56970, -150390, 56970, -20520, -42570, -1080, -42570, -23130, 31770, 56970, 221400, 400950, -25470, 9090, 5400, 9090, 39960, -357750, -202230, 56970, -150390, 56970, -13770, 5670, 56970, 400950, -173070, 34290, 12150, 34290, 219510, -448290, -823140, -117810, -823140, -492660, 65790, 119340, -7650, 65790, -761940, -431460, 119340, -321300, 119340, -20520, -42570, -1080, -42570, -23130, -14850, -36900, 4590, -36900, -17460, 65790, 119340, 255420, 463320, 65790, 119340, 255420, 463320, 499230, 905580, -25470, 9090, 5400, 9090, 39960, -59490, 13950, 5400, 11070, 13950, 44820, 13950, 44820, 84510, -353700, -198180, 61020, -146340, 61020, -9720, 9720, 61020, 405000, -169020, 38340, 16200, 38340, 223560, -761940, -431460, 119340, -321300, 119340, -9720, 9720, 24300, 43740, 119340, 463320, 119340, 463320, 905580, -169020, 38340, 16200, 38340, 223560, -373140, 67500, 16200, 50220, 67500, 252720, 67500, 252720, 490860, -2326, -4286, -598, -4286, -2558, 362, 642, -22, 362, -3966, -2238, 642, -1662, 642, -219, -464, -3, -464, -248, 362, 642, 2469, 4464, -274, 110, 69, 110, 453, -3966, -2238, 642, -1662, 642, -144, 72, 642, 4464, -1914, 390, 144, 390, 2448, -1534, -3494, 194, -3494, -1766, 1154, 1434, 770, 1154, -3174, -1446, 1434, -870, 1434, 573, 328, 789, 328, 544, 1154, 1434, 3261, 5256, 518, 902, 861, 902, 1245, -3174, -1446, 1434, -870, 1434, 648, 864, 1434, 5256, -1122, 1182, 936, 1182, 3240, 15822, 29052, 4158, 29052, 17388, -2322, -4212, 270, -2322, 26892, 15228, -4212, 11340, -4212, -2930, -5380, -770, -5380, -3220, 430, 780, -50, 430, -4980, -2820, 780, -2100, 780, -448290, -823140, -117810, -823140, -492660, 65790, 119340, -7650, 65790, -761940, -431460, 119340, -321300, 119340, -7618, -13988, -2002, -13988, -8372, 1118, 2028, -130, 1118, -12948, -7332, 2028, -5460, 2028, -239674, -440084, -62986, -440084, -263396, 35174, 63804, -4090, 35174, -407364, -230676, 63804, -171780, 63804, -859, -1104, -643, -1104, -888, -1426, -1671, -1210, -1671, -1455, -347, -592, -131, -592, -376, -1426, -1671, -1210, -1671, -1455, -914, -1159, -698, -1159, -943, 6269, 6024, 6485, 6024, 6240, 11939, 11694, 12155, 11694, 11910, -219, -464, -3, -464, -248, 573, 328, 789, 328, 544, -733, -978, -517, -978, -762, -221, -466, -5, -466, -250, 11939, 11694, 12155, 11694, 11910, -93, -338, 123, -338, -122, 6243, 5998, 6459, 5998, 6214, -2322, -4212, -21285, -38610, -2322, -4212, -21285, -38610, -45666, -82836, 430, 780, -1677, -3042, -2322, -4212, 430, 780, -23693, -42978, -48074, -87204, -1677, -3042, -48074, -87204, -26058, -47268, 65790, 119340, 255420, 463320, 65790, 119340, 255420, 463320, 499230, 905580, 1118, 2028, 3225, 5850, 35174, 63804, 37281, 67626, -2322, -4212, 430, 780, 65790, 119340, 1118, 2028, 35174, 63804, -24295, -44070, -48676, -88296, -2279, -4134, -48676, -88296, -26660, -48360, 282209, 511914, 526019, 954174, 3225, 5850, 37281, 67626, -18877, -34242, 3139, 5694, 526019, 954174, 8643, 15678, 281091, 509886, 3006, -450, -81, -450, -3537, 6408, -936, -81, -648, -936, -4023, -936, -4023, -7992, 382, -2, 39, -2, -345, 6408, -936, 3784, -488, -473, -1040, 39, -1040, -528, -936, -4023, -936, -4023, -7992, -488, -831, -936, -488, -4415, -8384, -831, -8384, -4800, -28674, 5886, 2196, 5886, 36756, -62694, 10746, 2196, 7866, 10746, 41616, 10746, 41616, 81306, -274, 110, 69, 110, 453, 518, 902, 861, 902, 1245, 2250, -342, -374, 106, -62694, 10746, -1030, 218, -33502, 5762, -571, -1138, -59, -1138, -626, 6557, 12227, 69, 861, -445, 67, 12227, 195, 6531, -342, -3429, -342, -3429, -7398, 106, -237, -342, 106, -3821, -7790, -237, -7790, -4206, 10746, 41616, 10746, 41616, 81306, 218, 561, 5762, 6105, -342, 106, 10746, 218, 5762, -3919, -7888, -335, -7888, -4304, 45977, 85667, 561, 6105, -3037, 547, 85667, 1443, 45795, 35964, 20412, -5508, 15228, -5508, 1566, -378, -5508, -39906, 17496, -3240, -1026, -3240, -21762, 76788, 43740, -11340, 32724, -11340, 1566, -378, -1836, -3780, -11340, -45738, -11340, -45738, -89964, 17496, -3240, -1026, -3240, -21762, 37908, -6156, -1026, -4428, -6156, -24678, -6156, -24678, -48492, 4092, 2364, -516, 1788, -516, 270, 54, -516, -4338, 2040, -264, -18, -264, -2322, 76788, 43740, -11340, 32724, -11340, 44916, 25692, -6348, 19284, -6348, -2802, -3018, -6204, -6420, 270, 54, -6204, -6420, -3132, -3348, -11340, -45738, -11340, -45738, -89964, -6348, -10170, -11340, -6348, -50106, -94332, -10170, -94332, -54396, 17784, -2952, -738, -2952, -21474, 38196, -5868, -738, -4140, -5868, -24390, -5868, -24390, -48204, 2040, -264, -18, -264, -2322, 38196, -5868, 22452, -3180, -3090, -6492, -18, -6492, -3420, -5868, -24390, -5868, -24390, -48204, -3180, -5238, -5868, -3180, -26742, -50556, -5238, -50556, -29052, -353700, -198180, 61020, -146340, 61020, -9720, 9720, 61020, 405000, -169020, 38340, 16200, 38340, 223560, -761940, -431460, 119340, -321300, 119340, -9720, 9720, 24300, 43740, 119340, 463320, 119340, 463320, 905580, -169020, 38340, 16200, 38340, 223560, -373140, 67500, 16200, 50220, 67500, 252720, 67500, 252720, 490860, -3876, -2148, 732, -1572, 732, -54, 162, 732, 4554, -1824, 480, 234, 480, 2538, 876, 2604, 5484, 3180, 5484, 4698, 4914, 5484, 9306, 2928, 5232, 4986, 5232, 7290, 26892, 15228, -4212, 11340, -4212, -4980, -2820, 780, -2100, 780, -761940, -431460, 119340, -321300, 119340, -12948, -7332, 2028, -5460, 2028, -407364, -230676, 63804, -171780, 63804, -3894, -3678, -7296, -7080, -822, -606, -7296, -7080, -4224, -4008, 38874, 39090, 72894, 73110, -54, 162, 4698, 4914, -3138, -2922, -66, 150, 72894, 73110, 702, 918, 38718, 38934, -4212, -38610, -4212, -38610, -82836, 780, -3042, -4212, 780, -42978, -87204, -3042, -87204, -47268, 119340, 463320, 119340, 463320, 905580, 2028, 5850, 63804, 67626, -4212, 780, 119340, 2028, 63804, -44070, -88296, -4134, -88296, -48360, 511914, 954174, 5850, 67626, -34242, 5694, 954174, 15678, 509886, 17856, -2880, -666, -2880, -21402, 38268, -5796, -666, -4068, -5796, -24318, -5796, -24318, -48132, 2112, -192, 54, -192, -2250, 38268, -5796, 22524, -3108, -3018, -6420, 54, -6420, -3348, -5796, -24318, -5796, -24318, -48132, -3108, -5166, -5796, -3108, -26670, -50484, -5166, -50484, -28980, -172224, 35136, 12996, 35136, 220356, -376344, 64296, 12996, 47016, 64296, 249516, 64296, 249516, 487656, -1824, 480, 234, 480, 2538, 2928, 5232, 4986, 5232, 7290, 13320, -2232, -2424, 456, -376344, 64296, -6360, 1128, -201192, 34392, -3606, -7008, -534, -7008, -3936, 39162, 73182, 234, 4986, -2850, 222, 73182, 990, 39006, -2232, -20754, -2232, -20754, -44568, 456, -1602, -2232, 456, -23106, -46920, -1602, -46920, -25416, 64296, 249516, 64296, 249516, 487656, 1128, 3186, 34392, 36450, -2232, 456, 64296, 1128, 34392, -23694, -47508, -2190, -47508, -26004, 275682, 513822, 3186, 36450, -18402, 3102, 513822, 8478, 274590]\n assert candidate(expression = \"10*9-8/2+3*7\") == []\n assert candidate(expression = \"3*5-2*3+4\") == [-27, -15, 63, 9, 39, 1, 5, 63, 91, 1, 31, 13, 31, 43]\n assert candidate(expression = \"10+5*2-3*4\") == [-40, -10, 8, -10, 38, -150, -60, 8, 18, 20, 68, -60, 68, 108]\n assert candidate(expression = \"1+2+3+4+5+6\") == [21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21]\n assert candidate(expression = \"25/5-4/4+3/3-2/2+1/1\") == []\n assert candidate(expression = \"8*9-7+6*5-4\") == [-32, -192, -32, -192, -416, 64, 224, -32, 64, -256, -480, 224, -192, 288, 59, 39, 59, 39, 11, 22, 42, 71, 91, -32, 64, 59, 22, 71, -228, -452, 252, -164, 316, 31, 3, 42, 91, -164, 316, 291, 106, 351]\n assert candidate(expression = \"15/3+2*6-4/2+3*5\") == []\n assert candidate(expression = \"8*3+2*4-1+9\") == [-72, 216, 8, 144, 152, -240, 480, 8, 80, 144, 152, 192, 152, 224, 12, 48, 22, 39, 40, -240, 480, -156, 312, 78, 150, 22, 150, 94, 81, 89, 129, 89, 161, 39, 40, 129, 87, 96, 168, 40, 168, 112]\n assert candidate(expression = \"99-77*5+33/3-22*8+11\") == []\n assert candidate(expression = \"3*2+2-1*2+1\") == [3, 3, 15, 9, 15, 3, 3, 27, 27, 9, 15, 9, 21, 21, 5, 5, 9, 7, 9, 9, 9, 5, 5, 27, 27, 21, 33, 21, 7, 13, 7, 19, 19, 7, 9, 11, 7, 19, 19, 15, 23, 15]\n assert candidate(expression = \"10-2/2+3*3\") == []\n assert candidate(expression = \"30-20*5+10/5+8*2-4*1\") == []\n assert candidate(expression = \"3+5*3-2*4+6/2-1\") == []\n assert candidate(expression = \"2*3*4+5*6-7*8/2\") == []\n assert candidate(expression = \"9*2+10-3*4+5-1+8\") == [108, -324, 108, -324, -324, 36, -108, -54, 36, -180, -180, -108, -198, -108, 18, 1026, 18, 1026, 1026, -36, 108, 234, 378, -216, -126, 504, -36, 234, -36, -36, 36, -54, 36, 594, 594, 108, 378, -72, 18, 648, 108, 378, 108, -324, 108, -324, -324, 36, -108, -54, 36, -180, -180, -108, -198, -108, 0, 1296, 0, 1296, 1296, 0, 1296, 0, 1296, 1296, -36, 108, 234, 378, -36, 108, 288, 432, 288, 432, -216, -126, 504, -36, 234, -216, -126, 648, 648, -36, 234, -36, 288, 288, -36, -36, 36, -54, 36, 594, 594, 108, 378, -72, 18, 648, 108, 378, -36, -36, 36, -54, 36, 720, 720, 720, 720, 108, 378, 108, 432, 432, -72, 18, 648, 108, 378, -72, 18, 792, 792, 108, 378, 108, 432, 432, 28, -20, 28, -20, -20, 20, 4, 10, 20, -4, -4, 4, -6, 4, 18, 130, 18, 130, 130, 12, 28, 42, 58, -8, 2, 72, 12, 42, 12, 12, 20, 10, 20, 82, 82, 28, 58, 8, 18, 88, 28, 58, 108, 60, 108, 60, 60, 100, 84, 90, 100, 76, 76, 84, 74, 84, 28, -20, 28, -20, -20, 20, 4, 10, 20, -4, -4, 4, -6, 4, 0, 1296, 0, 1296, 1296, 0, 1296, 0, 1296, 1296, 0, 400, 0, 400, 400, 0, 1680, 0, 1680, 1680, 0, 400, 0, 400, 400, -4, 12, 266, 282, -4, 12, 320, 336, 320, 336, 12, 28, 42, 58, 92, 108, 12, 28, 320, 336, 320, 336, 96, 112, 416, 432, 96, 112, -144, -54, 576, 36, 306, -144, -54, 720, 720, 36, 306, 36, 360, 360, -8, 2, 72, 12, 42, 72, 82, -8, 2, 720, 720, 216, 936, 216, -4, 266, -4, 320, 320, 12, 42, 92, 12, 320, 320, 96, 416, 96, -100, -100, -28, -118, -28, 530, 530, 44, 314, -136, -46, 584, 44, 314, -100, -100, -28, -118, -28, 656, 656, 656, 656, 44, 314, 44, 368, 368, -136, -46, 584, 44, 314, -136, -46, 728, 728, 44, 314, 44, 368, 368, 12, 12, 20, 10, 20, 82, 82, 28, 58, 8, 18, 88, 28, 58, 92, 92, 100, 90, 100, 12, 12, 20, 10, 20, 656, 656, 656, 656, 208, 208, 848, 848, 208, 208, 12, 282, 12, 336, 336, 28, 58, 108, 28, 336, 336, 112, 432, 112, -128, -38, 592, 52, 322, -128, -38, 736, 736, 52, 322, 52, 376, 376, 8, 18, 88, 28, 58, 88, 98, 8, 18, 736, 736, 232, 952, 232, 12, 282, 12, 336, 336, 28, 58, 108, 28, 336, 336, 112, 432, 112]\n assert candidate(expression = \"3+2*2+1-5*3+4\") == [-61, -29, -49, -13, -9, -61, -29, -25, -25, -13, -9, -13, -1, -1, -27, -11, -21, -3, -1, -26, -10, -27, -11, -25, -25, 3, 10, 3, -17, -13, -17, -5, -5, -3, -1, -2, -3, -5, -5, 7, 10, 7, -160, -80, -130, -40, -30, -160, -80, -70, -70, -40, -30, -40, -10, -10, -27, -11, -21, -3, -1, -24, -8, -18, 0, 2, -26, -10, -27, -11, -20, -4, -27, -11, -24, -8, -7, -7, 21, 28, 21, -70, -70, 21, 42, 28, 21, 70, 21, 42, -17, -13, -17, -5, -5, -3, -1, -2, -3, -5, -5, 7, 10, 7, -56, -46, -56, -26, -26, -3, -1, 0, 2, -2, -3, 4, -3, 0, 1, 1, 13, 16, 13, -26, -26, 13, 22, 16, 13, 34, 13, 22]\n assert candidate(expression = \"3*3-2*2+1*1-0*0+1\") == [-9, -3, -9, -15, -9, -9, -3, -9, -9, -15, -9, -15, -9, -9, -9, 9, -9, -27, -9, -9, -3, -9, -3, -9, -9, -9, -9, -9, -15, -9, -15, -9, -9, -15, 3, -15, -15, 3, 3, 3, 3, 3, -6, -3, -6, -9, -6, -6, -3, -6, -6, -9, -6, -9, -6, -6, -9, 9, -9, -27, -9, -6, 9, -6, -21, -6, -9, -6, -9, -6, -6, -3, -9, -6, -6, -3, -9, -9, -9, -9, -9, -6, -6, -9, -6, -9, -9, -6, -9, -6, -12, -6, -12, -6, -6, -12, 6, -12, -12, 6, 6, 6, 6, 6, -9, -6, -9, -6, -6, -12, 6, -9, 6, -12, -12, -9, -12, -9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 9, 6, 9, 12, 9, 9, 6, 9, 9, 12, 9, 12, 9, 9, 9, 0, 9, 18, 9, 9, 6, 9, 6, 9, 9, 9, 9, 9, 12, 9, 12, 9, 9, 12, 3, 12, 12, 3, 3, 3, 3, 3, 0, -3, 0, 3, 0, 0, -3, 0, 0, 3, 0, 3, 0, 0, 9, 6, 9, 12, 9, 9, 6, 9, 9, 12, 9, 12, 9, 9, -9, 0, -9, -18, -9, -6, 0, -6, -12, -6, 9, 0, 9, 18, 9, 0, 0, 0, 0, 0, 9, 0, 9, 18, 9, -9, -12, -9, -12, -6, -9, -9, -12, -6, -9, 9, 6, 9, 6, 0, -3, 9, 6, -9, -12, -6, -9, 9, 6, 0, -3, 9, 6, -9, -9, -9, -9, -9, -6, -6, -9, -6, -9, -9, -6, -9, -6, 9, 9, 9, 9, 9, 0, 0, 9, 9, -9, -6, 9, 0, 9, -9, -9, -6, -9, -6, 9, 9, 0, 9, -9, -6, 9, 0, 9, -6, 0, -6, 0, 0, -6, 12, -6, -6, 12, 12, 12, 12, 12, -3, 0, -3, 0, 0, -6, 12, -3, 12, -6, -6, -3, -6, -3, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 9, 12, 9, 9, 12, 3, 12, 12, 3, 3, 3, 3, 3, 3, 0, 3, 0, 0, 12, 9, 12, 9, 9, -6, 3, -3, 3, 12, 3, 3, 3, 12, 3, -6, -6, -3, -6, -3, 12, 12, 3, 12, -6, -3, 12, 3, 12, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 1, 3, 3, 5, 3, 3, 1, 3, 1, 3, 3, 3, 9, 3, -3, 3, 3, 5, 3, 5, 3, 3, 3, 3, 3, 1, 3, 1, 3, 3, 1, 7, 1, 1, 7, 7, 7, 7, 7, 4, 5, 4, 3, 4, 4, 5, 4, 4, 3, 4, 3, 4, 4, 3, 9, 3, -3, 3, 4, 9, 4, -1, 4, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 3, 3, 3, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 2, 4, 2, 4, 4, 2, 8, 2, 2, 8, 8, 8, 8, 8, 3, 4, 3, 4, 4, 2, 8, 3, 8, 2, 2, 3, 2, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 6, 9, 12, 9, 9, 6, 9, 9, 12, 9, 12, 9, 9, 9, 0, 9, 18, 9, 9, 6, 9, 6, 9, 9, 9, 9, 9, 12, 9, 12, 9, 9, 12, 3, 12, 12, 3, 3, 3, 3, 3, 21, 14, 21, 28, 21, 21, 14, 21, 21, 28, 21, 28, 21, 21, 21, 0, 21, 42, 21, 21, 14, 21, 14, 21, 21, 21, 21, 21, 28, 21, 28, 21, 21, 28, 7, 28, 28, 7, 7, 7, 7, 7, -2, -3, -2, -1, -2, -2, -3, -2, -2, -1, -2, -1, -2, -2, 7, 6, 7, 8, 7, 7, 6, 7, 7, 8, 7, 8, 7, 7, 6, 5, 6, 7, 6, 6, 5, 6, 6, 7, 6, 7, 6, 6, 7, 6, 7, 8, 7, 7, 6, 7, 7, 8, 7, 8, 7, 7, 15, 14, 15, 16, 15, 15, 14, 15, 15, 16, 15, 16, 15, 15, -9, 0, -9, -18, -9, -6, 0, -6, -12, -6, 9, 0, 9, 18, 9, 0, 0, 0, 0, 0, 9, 0, 9, 18, 9, 3, 0, 3, 6, 3, 4, 0, 4, 8, 4, 9, 0, 9, 18, 9, 21, 0, 21, 42, 21, -2, 0, -2, -4, -2, 7, 0, 7, 14, 7, 6, 0, 6, 12, 6, 7, 0, 7, 14, 7, 15, 0, 15, 30, 15, -9, -10, -9, -10, -6, -7, -9, -10, -6, -7, 9, 8, 9, 8, 0, -1, 9, 8, -9, -10, -6, -7, 9, 8, 0, -1, 9, 8, 3, 2, 3, 2, 4, 3, 3, 2, 4, 3, 9, 8, 9, 8, 21, 20, 21, 20, -2, -3, 7, 6, 6, 5, 7, 6, 15, 14, -9, -10, -6, -7, 9, 8, 0, -1, 9, 8, 3, 2, 4, 3, 9, 8, 21, 20, -2, -3, 7, 6, 6, 5, 7, 6, 15, 14, -9, -9, -9, -9, -9, -6, -6, -9, -6, -9, -9, -6, -9, -6, 9, 9, 9, 9, 9, 0, 0, 9, 9, -9, -6, 9, 0, 9, -9, -9, -6, -9, -6, 9, 9, 0, 9, -9, -6, 9, 0, 9, 3, 3, 3, 3, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 9, 9, 9, 9, 9, 21, 21, 21, 21, 21, -2, -2, 7, 7, 6, 6, 7, 7, 15, 15, -9, -6, 9, 0, 9, 3, 4, 9, 21, -2, 7, 6, 7, 15, -9, -9, -6, -9, -6, 9, 9, 0, 9, -9, -6, 9, 0, 9, 3, 3, 4, 3, 4, 9, 9, 21, 21, -2, 7, 6, 7, 15, -9, -6, 9, 0, 9, 3, 4, 9, 21, -2, 7, 6, 7, 15, -8, -2, -8, -2, -2, -8, 10, -8, -8, 10, 10, 10, 10, 10, -5, -2, -5, -2, -2, -8, 10, -5, 10, -8, -8, -5, -8, -5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 10, 7, 7, 10, 1, 10, 10, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 10, 7, 10, 7, 7, -8, 1, -5, 1, 10, 1, 1, 1, 10, 1, -8, -8, -5, -8, -5, 10, 10, 1, 10, -8, -5, 10, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 6, 4, 6, 6, 4, 10, 4, 4, 10, 10, 10, 10, 10, 5, 6, 5, 6, 6, 4, 10, 5, 10, 4, 4, 5, 4, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 7, 10, 7, 7, 10, 1, 10, 10, 1, 1, 1, 1, 1, 22, 15, 22, 15, 15, 22, 1, 22, 22, 1, 1, 1, 1, 1, -1, -2, -1, -2, -2, 8, 7, 8, 7, 7, 7, 6, 7, 6, 6, 8, 7, 8, 7, 7, 16, 15, 16, 15, 15, -8, 1, -5, 1, 10, 1, 1, 1, 10, 1, 4, 1, 5, 1, 10, 1, 22, 1, -1, 1, 8, 1, 7, 1, 8, 1, 16, 1, -8, -8, -5, -8, -5, 10, 10, 1, 10, -8, -5, 10, 1, 10, 4, 4, 5, 4, 5, 10, 10, 22, 22, -1, 8, 7, 8, 16, -8, -5, 10, 1, 10, 4, 5, 10, 22, -1, 8, 7, 8, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(expression = \"10*2-5*3+1\") == [-180, -140, -120, -120, -80, 0, 4, -120, 60, -129, -89, 6, -89, 46]\n assert candidate(expression = \"3*3*3-2*2*2+1*1*1\") == [-81, -81, -81, -81, -81, -63, -63, -81, -63, -81, -81, -63, -81, -63, -81, -81, -81, -81, -81, -54, -54, -54, -54, -81, -63, -81, -54, -54, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, -36, -36, -36, -36, 45, 45, -9, -9, 45, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -9, -9, -9, -9, -3, -3, -9, -3, -9, -9, -3, -9, -3, -9, -9, -9, -9, -9, 0, 0, 0, 0, -9, -3, -9, 0, 0, -9, -9, -3, -9, -3, -9, -9, 0, 0, -9, -3, -9, 0, 0, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, 126, 126, 126, 126, 126, 105, 105, 126, 105, 126, 126, 105, 126, 105, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, 45, 45, 45, 45, 45, 54, 54, 54, 54, 54, 126, 126, 126, 126, 126, -42, -42, -42, -42, 39, 39, -15, -15, 39, 39, 6, 6, 6, 6, 39, 39, 87, 87, -15, -15, 39, 39, 33, 33, 39, 39, 87, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -9, -3, -9, -3, -9, -9, 0, 0, -9, -3, -9, 0, 0, 54, 54, 45, 54, 45, 126, 126, 105, 126, 105, -27, -27, 54, 54, 45, 45, 54, 54, 126, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -81, -81, -81, -81, -63, -63, -81, -63, -81, -81, -63, -81, -63, -81, -81, -81, -81, -81, -54, -54, -54, -54, -81, -63, -81, -54, -54, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, -36, -36, -36, -36, 45, 45, -9, -9, 45, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 15, 15, 15, 15, 17, 17, 15, 17, 15, 15, 17, 15, 17, 15, 15, 15, 15, 15, 18, 18, 18, 18, 15, 17, 15, 18, 18, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 15, 15, 15, 15, 15, 17, 17, 15, 17, 15, 15, 17, 15, 17, 15, 15, 15, 15, 15, 18, 18, 18, 18, 15, 17, 15, 18, 18, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, 126, 126, 126, 126, 126, 105, 105, 126, 105, 126, 126, 105, 126, 105, 54, 54, 54, 54, 54, 45, 45, 54, 45, 54, 54, 45, 54, 45, 150, 150, 150, 150, 150, 125, 125, 150, 125, 150, 150, 125, 150, 125, 150, 150, 150, 150, 150, 125, 125, 150, 125, 150, 150, 125, 150, 125, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, 45, 45, 45, 45, 45, 54, 54, 54, 54, 54, 126, 126, 126, 126, 126, -27, -27, -27, -27, -27, 54, 54, 54, 54, 54, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 54, 54, 54, 54, 54, 126, 126, 126, 126, 126, 54, 54, 54, 54, 54, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, -44, -44, -44, -44, 37, 37, -17, -17, 37, 37, 4, 4, 4, 4, 37, 37, 85, 85, -17, -17, 37, 37, 31, 31, 37, 37, 85, 85, -44, -44, -44, -44, 37, 37, -17, -17, 37, 37, 20, 20, 20, 20, 20, 20, 20, 20, 37, 37, 85, 85, 37, 37, 101, 101, 101, 101, -17, -17, 37, 37, 31, 31, 37, 37, 85, 85, -17, -17, 37, 37, 47, 47, 47, 47, 37, 37, 85, 85, 37, 37, 101, 101, 101, 101, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 17, 15, 18, 18, 15, 17, 15, 18, 18, 54, 45, 126, 105, 54, 45, 150, 125, 150, 125, -27, 54, 45, 54, 126, -27, 54, 69, 69, 54, 126, 54, 150, 150, -44, -44, 37, -17, 37, 4, 4, 37, 85, -17, 37, 31, 37, 85, -44, -44, 37, -17, 37, 20, 20, 20, 20, 37, 85, 37, 101, 101, -17, 37, 31, 37, 85, -17, 37, 47, 47, 37, 85, 37, 101, 101, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -9, -3, -9, -3, -9, -9, 0, 0, -9, -3, -9, 0, 0, 54, 54, 45, 54, 45, 126, 126, 105, 126, 105, -27, -27, 54, 54, 45, 45, 54, 54, 126, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -81, -63, -81, -63, -81, -81, -54, -54, -81, -63, -81, -54, -54, 54, 54, 45, 54, 45, -27, -27, 54, 54, -36, -36, 45, -9, 45, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 15, 15, 17, 15, 17, 15, 15, 18, 18, 15, 17, 15, 18, 18, 54, 54, 45, 54, 45, 126, 126, 105, 126, 105, 54, 54, 45, 54, 45, 150, 150, 125, 150, 125, 150, 150, 125, 150, 125, -27, -27, 54, 54, 45, 45, 54, 54, 126, 126, -27, -27, 54, 54, 69, 69, 69, 69, 54, 54, 126, 126, 54, 54, 150, 150, 150, 150, -44, -44, 37, -17, 37, 4, 4, 37, 85, -17, 37, 31, 37, 85, -44, -44, 37, -17, 37, 20, 20, 20, 20, 37, 85, 37, 101, 101, -17, 37, 31, 37, 85, -17, 37, 47, 47, 37, 85, 37, 101, 101, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, -9, -3, -9, 0, 0, 54, 45, 126, 105, -27, 54, 45, 54, 126, -42, -42, 39, -15, 39, 6, 6, 39, 87, -15, 39, 33, 39, 87, -81, -63, -81, -54, -54, 54, 45, -27, 54, -36, -36, 45, -9, 45, 15, 17, 15, 18, 18, 15, 17, 15, 18, 18, 54, 45, 126, 105, 54, 45, 150, 125, 150, 125, -27, 54, 45, 54, 126, -27, 54, 69, 69, 54, 126, 54, 150, 150, -44, -44, 37, -17, 37, 4, 4, 37, 85, -17, 37, 31, 37, 85, -44, -44, 37, -17, 37, 20, 20, 20, 20, 37, 85, 37, 101, 101, -17, 37, 31, 37, 85, -17, 37, 47, 47, 37, 85, 37, 101, 101]\n assert candidate(expression = \"4+4+4+4+4+4+4+4+4+4\") == [40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 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40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40]\n assert candidate(expression = \"12+11-10*9+8*7-6*5+4-3\") == [2253, 2253, 1853, 3453, 1853, -547, -547, 1693, -547, 3933, 2333, -547, 1693, -547, -267, -267, -317, -117, -317, -547, -547, -3067, -3067, 1763, -477, -337, -477, -2577, 3723, 2123, -757, 1483, -757, -57, -257, -757, -4537, 1763, -477, -337, -477, -2577, 4953, 4953, 4103, 7503, 4103, -997, -997, 3763, -997, 8523, 5123, -997, 3763, -997, -267, -267, -317, -117, -317, -807, -807, -857, -657, -857, -997, -997, -3517, -3517, -997, -997, -3517, -3517, -6757, -6757, 1763, -477, -337, -477, -2577, 3923, -837, -337, -877, -837, -2937, -837, -2937, -5637, 3723, 2123, -757, 1483, -757, -57, -257, -757, -4537, 1763, -477, -337, -477, -2577, 8043, 4643, -1477, 3283, -1477, -57, -257, -597, -797, -1477, -5257, -1477, -5257, -10117, 1763, -477, -337, -477, -2577, 3923, -837, -337, -877, -837, -2937, -837, -2937, -5637, 165, 165, 125, 285, 125, -115, -115, 109, -115, 333, 173, -115, 109, -115, -87, -87, -92, -72, -92, -115, -115, -367, -367, 116, -108, -94, -108, -318, 312, 152, -136, 88, -136, -66, -86, -136, -514, 116, -108, -94, -108, -318, 4953, 4953, 4103, 7503, 4103, -997, -997, 3763, -997, 8523, 5123, -997, 3763, -997, 2865, 2865, 2375, 4335, 2375, -565, -565, 2179, -565, 4923, 2963, -565, 2179, -565, -591, -591, -596, -576, -596, -1131, -1131, -1136, -1116, -1136, -87, -87, -92, -72, -92, -1131, -1131, -1136, -1116, -1136, -627, -627, -632, -612, -632, -997, -997, -3517, -3517, -997, -997, -3517, -3517, -6757, -6757, -565, -565, -817, -817, -997, -997, -565, -565, -3841, -3841, -7081, -7081, -817, -817, -7081, -7081, -4057, -4057, 1772, -468, -328, -468, -2568, 3932, -828, -328, -868, -828, -2928, -828, -2928, -5628, 116, -108, -94, -108, -318, 3932, -828, 2276, -468, -598, -1138, -94, -1138, -634, -828, -2928, -828, -2928, -5628, -468, -678, -828, -468, -3198, -5898, -678, -5898, -3378, 3696, 2096, -784, 1456, -784, -84, -284, -784, -4564, 1736, -504, -364, -504, -2604, 8016, 4616, -1504, 3256, -1504, -84, -284, -624, -824, -1504, -5284, -1504, -5284, -10144, 1736, 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366, 690, 690, -162, 62, 48, 62, 272, -378, 98, 48, 102, 98, 308, 98, 308, 578, -358, -198, 90, -134, 90, 20, 40, 90, 468, -162, 62, 48, 62, 272, -790, -450, 162, -314, 162, 20, 40, 74, 94, 162, 540, 162, 540, 1026, -162, 62, 48, 62, 272, -378, 98, 48, 102, 98, 308, 98, 308, 578, -299, -299, -259, -419, -259, -19, -19, -243, -19, -467, -307, -19, -243, -19, -47, -47, -42, -62, -42, -19, -19, 233, 233, -250, -26, -40, -26, 184, -446, -286, 2, -222, 2, -68, -48, 2, 380, -250, -26, -40, -26, 184, -211, -211, -171, -331, -171, 69, 69, -155, 69, -379, -219, 69, -155, 69, 41, 41, 46, 26, 46, 69, 69, 321, 321, -162, 62, 48, 62, 272, -358, -198, 90, -134, 90, 20, 40, 90, 468, -162, 62, 48, 62, 272, 4623, 4623, 3828, 7008, 3828, -942, -942, 3510, -942, 7962, 4782, -942, 3510, -942, 2535, 2535, 2100, 3840, 2100, -510, -510, 1926, -510, 4362, 2622, -510, 1926, -510, -481, -481, -396, -736, -396, 114, 114, -362, 114, -838, -498, 114, -362, 114, 2071, 2071, 1716, 3136, 1716, -414, -414, 1574, -414, 3562, 2142, -414, 1574, -414, -481, -481, -396, -736, -396, 114, 114, -362, 114, -838, -498, 114, -362, 114, -663, -663, -658, -678, -658, -1203, -1203, -1198, -1218, -1198, -159, -159, -154, -174, -154, -1203, -1203, -1198, -1218, -1198, -699, -699, -694, -714, -694, 41, 41, 46, 26, 46, 95, 95, 100, 80, 100, -47, -47, -42, -62, -42, 41, 41, 46, 26, 46, -1137, -1137, -1132, -1152, -1132, -633, -633, -628, -648, -628, 95, 95, 100, 80, 100, -521, -521, -516, -536, -516, 95, 95, 100, 80, 100, -942, -942, -3462, -3462, -942, -942, -3462, -3462, -6702, -6702, -510, -510, -762, -762, -942, -942, -510, -510, -3786, -3786, -7026, -7026, -762, -762, -7026, -7026, -4002, -4002, 114, 114, 366, 366, 114, 114, 366, 366, 690, 690, -414, -414, -162, -162, 114, 114, 366, 366, -942, -942, -510, -510, 114, 114, -414, -414, 114, 114, -3858, -3858, -7098, -7098, -834, -834, -7098, -7098, -4074, -4074, 366, 366, 690, 690, -162, -162, 366, 366, -6702, -6702, -3678, -3678, 690, 690, -3006, -3006, 690, 690, 1774, -466, -326, -466, -2566, 3934, -826, -326, -866, -826, -2926, -826, -2926, -5626, 118, -106, -92, -106, -316, 3934, -826, 2278, -466, -596, -1136, -92, -1136, -632, -826, -2926, -826, -2926, -5626, -466, -676, -826, -466, -3196, -5896, -676, -5896, -3376, -162, 62, 48, 62, 272, -378, 98, 48, 102, 98, 308, 98, 308, 578, -250, -26, -40, -26, 184, -162, 62, 48, 62, 272, 3670, -782, 2014, -422, -378, 98, 1646, -342, -378, 98, -656, -1196, -152, -1196, -692, 48, 102, -40, 48, -1130, -626, 102, -514, 102, -782, -2882, -782, -2882, -5582, -422, -632, -782, -422, -3152, -5852, -632, -5852, -3332, 98, 308, 98, 308, 578, -342, -132, 98, 308, -782, -422, 98, -342, 98, -3212, -5912, -692, -5912, -3392, 308, 578, -132, 308, -5582, -3062, 578, -2502, 578, 3690, 2090, -790, 1450, -790, -90, -290, -790, -4570, 1730, -510, -370, -510, -2610, 8010, 4610, -1510, 3250, -1510, -90, -290, -630, -830, -1510, -5290, -1510, -5290, -10150, 1730, -510, -370, -510, -2610, 3890, -870, -370, -910, -870, -2970, -870, -2970, -5670, 306, 146, -142, 82, -142, -72, -92, -142, -520, 110, -114, -100, -114, -324, 8010, 4610, -1510, 3250, -1510, 4626, 2666, -862, 1882, -862, -576, -596, -1116, -1136, -72, -92, -1116, -1136, -612, -632, -1510, -5290, -1510, -5290, -10150, -862, -1240, -1510, -862, -5776, -10636, -1240, -10636, -6100, 1766, -474, -334, -474, -2574, 3926, -834, -334, -874, -834, -2934, -834, -2934, -5634, 110, -114, -100, -114, -324, 3926, -834, 2270, -474, -604, -1144, -100, -1144, -640, -834, -2934, -834, -2934, -5634, -474, -684, -834, -474, -3204, -5904, -684, -5904, -3384, -358, -198, 90, -134, 90, 20, 40, 90, 468, -162, 62, 48, 62, 272, -790, -450, 162, -314, 162, 20, 40, 74, 94, 162, 540, 162, 540, 1026, -162, 62, 48, 62, 272, -378, 98, 48, 102, 98, 308, 98, 308, 578, -446, -286, 2, -222, 2, -68, -48, 2, 380, -250, -26, -40, -26, 184, -358, -198, 90, -134, 90, 20, 40, 90, 468, -162, 62, 48, 62, 272, 7482, 4302, -1422, 3030, -1422, 4098, 2358, -774, 1662, -774, -790, -450, 162, -314, 162, 3346, 1926, -630, 1358, -630, -790, -450, 162, -314, 162, -684, -664, -1224, -1204, -180, -160, -1224, -1204, -720, -700, 20, 40, 74, 94, -68, -48, 20, 40, -1158, -1138, -654, -634, 74, 94, -542, -522, 74, 94, -1422, -5202, -1422, -5202, -10062, -774, -1152, -1422, -774, -5688, -10548, -1152, -10548, -6012, 162, 540, 162, 540, 1026, -630, -252, 162, 540, -1422, -774, 162, -630, 162, -5796, -10656, -1260, -10656, -6120, 540, 1026, -252, 540, -10062, -5526, 1026, -4518, 1026, 1774, -466, -326, -466, -2566, 3934, -826, -326, -866, -826, -2926, -826, -2926, -5626, 118, -106, -92, -106, -316, 3934, -826, 2278, -466, -596, -1136, -92, -1136, -632, -826, -2926, -826, -2926, -5626, -466, -676, -826, -466, -3196, -5896, -676, -5896, -3376, -162, 62, 48, 62, 272, -378, 98, 48, 102, 98, 308, 98, 308, 578, -250, -26, -40, -26, 184, -162, 62, 48, 62, 272, 3670, -782, 2014, -422, -378, 98, 1646, -342, -378, 98, -656, -1196, -152, -1196, -692, 48, 102, -40, 48, -1130, -626, 102, -514, 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-5290, -1510, -5290, -10150, -862, -1240, -1510, -862, -5776, -10636, -1240, -10636, -6100, 1766, -474, -334, -474, -2574, 3926, -834, -334, -874, -834, -2934, -834, -2934, -5634, 110, -114, -100, -114, -324, 3926, -834, 2270, -474, -604, -1144, -100, -1144, -640, -834, -2934, -834, -2934, -5634, -474, -684, -834, -474, -3204, -5904, -684, -5904, -3384, -4774, -2694, 1050, -1862, 1050, 140, 400, 1050, 5964, -2226, 686, 504, 686, 3416, -10390, -5970, 1986, -4202, 1986, 140, 400, 842, 1102, 1986, 6900, 1986, 6900, 13218, -2226, 686, 504, 686, 3416, -5034, 1154, 504, 1206, 1154, 3884, 1154, 3884, 7394, -4774, -2694, 1050, -1862, 1050, 140, 400, 1050, 5964, -2226, 686, 504, 686, 3416, -10390, -5970, 1986, -4202, 1986, 140, 400, 842, 1102, 1986, 6900, 1986, 6900, 13218, -2226, 686, 504, 686, 3416, -5034, 1154, 504, 1206, 1154, 3884, 1154, 3884, 7394, -446, -286, 2, -222, 2, -68, -48, 2, 380, -250, -26, -40, -26, 184, -358, -198, 90, -134, 90, 20, 40, 90, 468, -162, 62, 48, 62, 272, -446, -286, 2, -222, 2, -68, -48, 2, 380, -250, -26, -40, -26, 184, -262, -102, 186, -38, 186, 116, 136, 186, 564, -66, 158, 144, 158, 368, -262, -102, 186, -38, 186, 116, 136, 186, 564, -66, 158, 144, 158, 368, 6906, 3966, -1326, 2790, -1326, 3522, 2022, -678, 1422, -678, -1366, -786, 258, -554, 258, 2770, 1590, -534, 1118, -534, -1366, -786, 258, -554, 258, 6906, 3966, -1326, 2790, -1326, 3522, 2022, -678, 1422, -678, -10390, -5970, 1986, -4202, 1986, -10390, -5970, 1986, -4202, 1986, 2770, 1590, -534, 1118, -534, -1366, -786, 258, -554, 258, 2770, 1590, -534, 1118, -534, -5878, -3378, 1122, -2378, 1122, -5878, -3378, 1122, -2378, 1122, -684, -664, -1224, -1204, -180, -160, -1224, -1204, -720, -700, 20, 40, 74, 94, -68, -48, 20, 40, -1158, -1138, -654, -634, 74, 94, -542, -522, 74, 94, -684, -664, -1224, -1204, -180, -160, -1224, -1204, -720, -700, 788, 808, 1490, 1510, 788, 808, 1490, 1510, -68, -48, 20, 40, -68, -48, 116, 136, 116, 136, -1086, -1066, -582, -562, 146, 166, -470, -450, 146, 166, -1086, -1066, -582, -562, 1490, 1510, 1490, 1510, -470, -450, 146, 166, -470, -450, 818, 838, 818, 838, -1326, -5106, -1326, -5106, -9966, -678, -1056, -1326, -678, -5592, -10452, -1056, -10452, -5916, 258, 636, 258, 636, 1122, -534, -156, 258, 636, -1326, -678, 258, -534, 258, -5700, -10560, -1164, -10560, -6024, 636, 1122, -156, 636, -9966, -5430, 1122, -4422, 1122, -1326, -5106, -1326, -5106, -9966, -678, -1056, -1326, -678, -5592, -10452, -1056, -10452, -5916, 1986, 6900, 1986, 6900, 13218, 1986, 6900, 1986, 6900, 13218, -534, -156, 258, 636, -534, -156, 1122, 1500, 1122, 1500, -1326, -678, 258, -534, 258, -1326, -678, 1986, 1986, -534, 258, -534, 1122, 1122, -5700, -10560, -1164, -10560, -6024, 636, 1122, -156, 636, -9966, -5430, 1122, -4422, 1122, -5700, -10560, -1164, -10560, -6024, 7548, 13866, 7548, 13866, -156, 636, -156, 1500, 1500, -9318, -4782, 1770, -3774, 1770, -9318, -4782, 13866, 13866, -3774, 1770, -3774, 7818, 7818, 1774, -466, -326, -466, -2566, 3934, -826, -326, -866, -826, -2926, -826, -2926, -5626, 118, -106, -92, -106, -316, 3934, -826, 2278, -466, -596, -1136, -92, -1136, -632, -826, -2926, -826, -2926, -5626, -466, -676, -826, -466, -3196, -5896, -676, -5896, -3376, -162, 62, 48, 62, 272, -378, 98, 48, 102, 98, 308, 98, 308, 578, -250, -26, -40, -26, 184, -162, 62, 48, 62, 272, 3670, -782, 2014, -422, -378, 98, 1646, -342, -378, 98, -656, -1196, -152, -1196, -692, 48, 102, -40, 48, -1130, -626, 102, -514, 102, -782, -2882, -782, -2882, -5582, -422, -632, -782, -422, -3152, -5852, -632, -5852, -3332, 98, 308, 98, 308, 578, -342, -132, 98, 308, -782, -422, 98, -342, 98, -3212, -5912, -692, -5912, -3392, 308, 578, -132, 308, -5582, -3062, 578, -2502, 578, 1774, -466, -326, -466, -2566, 3934, -826, -326, -866, -826, -2926, -826, -2926, -5626, 118, -106, -92, -106, -316, 3934, -826, 2278, -466, -596, -1136, -92, -1136, -632, -826, -2926, -826, -2926, -5626, -466, -676, -826, -466, -3196, -5896, -676, -5896, -3376, -2274, 638, 456, 638, 3368, -5082, 1106, 456, 1158, 1106, 3836, 1106, 3836, 7346, -2274, 638, 456, 638, 3368, -5082, 1106, 456, 1158, 1106, 3836, 1106, 3836, 7346, -250, -26, -40, -26, 184, -162, 62, 48, 62, 272, -250, -26, -40, -26, 184, -66, 158, 144, 158, 368, -66, 158, 144, 158, 368, 3382, -734, 1726, -374, -666, 146, 1358, -294, -666, 146, 3382, -734, 1726, -374, -5082, 1106, -5082, 1106, 1358, -294, -666, 146, 1358, -294, -2874, 626, -2874, 626, -656, -1196, -152, -1196, -692, 48, 102, -40, 48, -1130, -626, 102, -514, 102, -656, -1196, -152, -1196, -692, 816, 1518, 816, 1518, -40, 48, -40, 144, 144, -1058, -554, 174, -442, 174, -1058, -554, 1518, 1518, -442, 174, -442, 846, 846, -734, -2834, -734, -2834, -5534, -374, -584, -734, -374, -3104, -5804, -584, -5804, -3284, 146, 356, 146, 356, 626, -294, -84, 146, 356, -734, -374, 146, -294, 146, -3164, -5864, -644, -5864, -3344, 356, 626, -84, 356, -5534, -3014, 626, -2454, 626, -734, -2834, -734, -2834, -5534, -374, -584, -734, -374, -3104, -5804, -584, -5804, -3284, 1106, 3836, 1106, 3836, 7346, 1106, 3836, 1106, 3836, 7346, -294, -84, 146, 356, -294, -84, 626, 836, 626, 836, -734, -374, 146, -294, 146, -734, -374, 1106, 1106, -294, 146, -294, 626, 626, -3164, -5864, -644, -5864, -3344, 356, 626, -84, 356, -5534, -3014, 626, -2454, 626, -3164, -5864, -644, -5864, -3344, 4196, 7706, 4196, 7706, -84, 356, -84, 836, 836, -5174, -2654, 986, -2094, 986, -5174, -2654, 7706, 7706, -2094, 986, -2094, 4346, 4346]\n assert candidate(expression = \"10-9-8-7-6-5-4-3-2-1\") == [5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, 1, -1, 3, 1, 5, 5, 7, -3, -1, 3, 9, 1, 3, -5, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, 5, 7, 3, 5, 1, 15, 17, 13, 15, 11, 9, 7, 1, -1, 11, 9, 9, 7, 19, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 11, 15, 9, 11, 5, 7, 3, 17, 13, 9, 1, 11, 9, 19, 7, 13, 5, 7, -1, 15, 9, 7, 17, 13, 5, 15, 13, 23, -1, -3, 1, -1, 3, -5, -3, -1, -7, -3, 1, -5, -3, -9, 3, 5, 1, 3, -1, -1, -3, 7, 5, 1, -5, 3, 1, 9, -1, 3, -3, -1, -7, 5, 1, -1, 7, 3, -3, 5, 3, 11, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, -7, -5, -9, -7, -11, -3, -5, -7, -1, -5, -9, -3, -5, 1, 1, -1, 3, 1, 5, 11, 9, 13, 11, 15, -1, -3, 1, -1, 3, 1, -1, 3, 1, 5, -11, -13, -9, -11, -7, 5, 7, -3, -1, 7, 9, 5, 7, 15, 17, -5, -3, 3, 5, 5, 7, -7, -5, -3, -1, 7, 9, -5, -3, -3, -1, -15, -13, 3, 9, 1, 3, -5, 11, 5, 3, 13, 9, 1, 11, 9, 19, -1, -7, 1, -1, 7, 3, 9, -9, -3, 1, 11, -1, 1, -11, 3, -5, 5, 3, 13, -7, 1, 3, -9, -5, 5, -7, -5, -17, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 9, 13, 7, 9, 3, 5, 1, 15, 11, 7, -1, 9, 7, 17, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, -3, 1, -5, -3, -9, 3, -1, -3, 5, 1, -5, 3, 1, 9, 5, 1, 7, 5, 11, -7, -11, -5, -7, -1, -1, 3, 9, 13, -3, 1, -1, 3, -13, -9, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -3, -9, -1, -3, 5, 1, 7, -11, -5, -1, 9, -3, -1, -13, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 13, 11, 15, 13, 17, 9, 11, 13, 7, 11, 15, 9, 11, 5, 17, 19, 15, 17, 13, 13, 11, 21, 19, 15, 9, 17, 15, 23, 13, 17, 11, 13, 7, 19, 15, 13, 21, 17, 11, 19, 17, 25, 7, 9, 5, 7, 3, 11, 9, 7, 13, 9, 5, 11, 9, 15, 13, 11, 15, 13, 17, 3, 1, 5, 3, 7, 9, 11, 17, 19, 7, 9, 9, 11, -1, 1, 13, 7, 15, 13, 21, 5, 11, 13, 3, 7, 15, 5, 7, -3, 11, 15, 9, 11, 5, 17, 13, 11, 19, 15, 9, 17, 15, 23, 7, 3, 9, 7, 13, 11, 15, 1, 5, 9, 17, 7, 9, -1, 11, 5, 13, 11, 19, 3, 9, 11, 1, 5, 13, 3, 5, -5, 5, 7, 3, 5, 1, 9, 7, 5, 11, 7, 3, 9, 7, 13, 1, -1, 3, 1, 5, 5, 7, -3, -1, 3, 9, 1, 3, -5, 5, 1, 7, 5, 11, -1, 3, 5, -3, 1, 7, -1, 1, -7, 19, 21, 17, 19, 15, 23, 21, 19, 25, 21, 17, 23, 21, 27, 15, 13, 17, 15, 19, 19, 21, 11, 13, 17, 23, 15, 17, 9, 19, 15, 21, 19, 25, 13, 17, 19, 11, 15, 21, 13, 15, 7, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, -1, -3, 1, -1, 3, -5, -3, -1, -7, -3, 1, -5, -3, -9, 13, 11, 15, 13, 17, 9, 11, 13, 7, 11, 15, 9, 11, 5, 11, 9, 13, 11, 15, 7, 9, 11, 5, 9, 13, 7, 9, 3, 25, 23, 27, 25, 29, 21, 23, 25, 19, 23, 27, 21, 23, 17, 5, 7, 3, 5, 1, 15, 17, 13, 15, 11, 3, 5, 1, 3, -1, 5, 7, 3, 5, 1, -7, -5, -9, -7, -11, 17, 19, 15, 17, 13, 7, 9, 5, 7, 3, 5, 7, 3, 5, 1, 19, 21, 17, 19, 15, 15, 17, 13, 15, 11, 3, 5, 1, 3, -1, 17, 19, 15, 17, 13, 15, 17, 13, 15, 11, 29, 31, 27, 29, 25, 9, 7, 1, -1, 11, 9, 9, 7, 19, 17, -1, -3, 7, 5, 9, 7, -3, -5, 1, -1, 11, 9, -1, -3, 1, -1, -11, -13, 13, 11, 21, 19, 11, 9, 13, 11, 3, 1, 9, 7, 1, -1, 23, 21, 15, 13, 11, 9, -1, -3, 13, 11, 11, 9, 25, 23, 9, 7, 19, 17, 7, 5, 9, 7, -3, -5, 21, 19, 11, 9, 9, 7, 23, 21, 19, 17, 7, 5, 21, 19, 19, 17, 33, 31, 5, 11, 3, 5, -3, 13, 7, 5, 15, 11, 3, 13, 11, 21, 1, -5, 3, 1, 9, 5, 11, -7, -1, 3, 13, 1, 3, -9, 5, -3, 7, 5, 15, -5, 3, 5, -7, -3, 7, -5, -3, -15, 15, 9, 17, 15, 23, 7, 13, 15, 5, 9, 17, 7, 9, -1, 5, 11, 3, 5, -3, 19, 25, 17, 19, 11, 13, 7, 1, -5, 15, 9, 13, 7, 27, 21, 5, 15, 3, 5, -7, 17, 7, 5, 19, 15, 3, 17, 15, 29, 11, 3, 13, 11, 21, 1, 9, 11, -1, 3, 13, 1, 3, -9, 15, 23, 13, 15, 5, 11, 3, 25, 17, 13, 1, 15, 13, 27, 11, 21, 9, 11, -1, 23, 13, 11, 25, 21, 9, 23, 21, 35, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 11, 15, 9, 11, 5, 7, 3, 17, 13, 9, 1, 11, 9, 19, 7, 13, 5, 7, -1, 15, 9, 7, 17, 13, 5, 15, 13, 23, -1, 3, -3, -1, -7, 5, 1, -1, 7, 3, -3, 5, 3, 11, 7, 3, 9, 7, 13, -5, -9, -3, -5, 1, 1, 5, 11, 15, -1, 3, 1, 5, -11, -7, 7, -1, 9, 7, 17, -3, 5, 7, -5, -1, 9, -3, -1, -13, 3, 9, 1, 3, -5, 11, 5, 3, 13, 9, 1, 11, 9, 19, -1, -7, 1, -1, 7, 3, 9, -9, -3, 1, 11, -1, 1, -11, 3, -5, 5, 3, 13, -7, 1, 3, -9, -5, 5, -7, -5, -17, 13, 17, 11, 13, 7, 19, 15, 13, 21, 17, 11, 19, 17, 25, 9, 5, 11, 9, 15, 13, 17, 3, 7, 11, 19, 9, 11, 1, 13, 7, 15, 13, 21, 5, 11, 13, 3, 7, 15, 5, 7, -3, 7, 3, 9, 7, 13, 1, 5, 7, -1, 3, 9, 1, 3, -5, 21, 17, 23, 21, 27, 15, 19, 21, 13, 17, 23, 15, 17, 9, 11, 15, 9, 11, 5, -1, 3, -3, -1, -7, 13, 17, 11, 13, 7, 11, 15, 9, 11, 5, 25, 29, 23, 25, 19, 7, 3, 17, 13, 5, 1, 7, 3, -5, -9, 19, 15, 9, 5, 7, 3, 21, 17, 17, 13, 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-3, -15, -1, -3, 11, -17, -5, -3, -19, -15, -1, -17, -15, -31, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -3, -9, -1, -3, 5, 1, 7, -11, -5, -1, 9, -3, -1, -13, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 11, 5, 13, 11, 19, 3, 9, 11, 1, 5, 13, 3, 5, -5, 1, 7, -1, 1, -7, 15, 21, 13, 15, 7, 9, 3, -3, -9, 11, 5, 9, 3, 23, 17, 1, 11, -1, 1, -11, 13, 3, 1, 15, 11, -1, 13, 11, 25, 7, -1, 9, 7, 17, -3, 5, 7, -5, -1, 9, -3, -1, -13, 11, 19, 9, 11, 1, 7, -1, 21, 13, 9, -3, 11, 9, 23, 7, 17, 5, 7, -5, 19, 9, 7, 21, 17, 5, 19, 17, 31, -5, -11, -3, -5, 3, -13, -7, -5, -15, -11, -3, -13, -11, -21, -1, 5, -3, -1, -9, -5, -11, 7, 1, -3, -13, -1, -3, 9, -5, 3, -7, -5, -15, 5, -3, -5, 7, 3, -7, 5, 3, 15, 1, 7, -1, 1, -7, 9, 3, 1, 11, 7, -1, 9, 7, 17, -15, -9, -17, -15, -23, -7, -13, -15, -5, -9, -17, -7, -9, 1, -3, -9, -1, -3, 5, 11, 5, 13, 11, 19, -5, -11, -3, -5, 3, -3, -9, -1, -3, 5, -19, -25, -17, -19, -11, 1, 7, -11, -5, 3, 9, 1, 7, 15, 21, -13, -7, -1, 5, 1, 7, -15, -9, -11, -5, 3, 9, -13, -7, -11, -5, -27, -21, -1, 9, -3, -1, -13, 11, 1, -1, 13, 9, -3, 11, 9, 23, -5, -15, -3, -5, 7, -1, 9, -17, -7, -3, 11, -5, -3, -19, -1, -13, 1, -1, 13, -15, -3, -1, -17, -13, 1, -15, -13, -29, 1, -7, 3, 1, 11, -9, -1, 1, -11, -7, 3, -9, -7, -19, 5, 13, 3, 5, -5, 1, -7, 15, 7, 3, -9, 5, 3, 17, 1, 11, -1, 1, -11, 13, 3, 1, 15, 11, -1, 13, 11, 25, -11, -3, -13, -11, -21, -1, -9, -11, 1, -3, -13, -1, -3, 9, 1, -7, 3, 1, 11, -15, -23, -13, -15, -5, -9, -1, 5, 13, -11, -3, -9, -1, -25, -17, 1, -11, 3, 1, 15, -13, -1, 1, -15, -11, 3, -13, -11, -27, -7, 3, -9, -7, -19, 5, -5, -7, 7, 3, -9, 5, 3, 17, -11, -21, -9, -11, 1, -7, 3, -23, -13, -9, 5, -11, -9, -25, -7, -19, -5, -7, 7, -21, -9, -7, -23, -19, -5, -21, -19, -35]\n assert candidate(expression = \"100-25*4+30/6\") == []\n assert candidate(expression = \"9-8+7-6*5+4-3*2+1\") == [-6, 6, 42, 18, 42, -6, 6, 102, 102, 18, 42, 18, 72, 72, 19, 21, 27, 23, 27, 39, 41, 19, 21, 102, 102, 87, 147, 87, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, 1, -1, -7, -3, -7, 1, -1, -17, -17, -3, -7, -3, -12, -12, 29, 27, 21, 25, 21, 1, -1, -7, -3, -7, 57, 55, 37, 35, 1, -1, 29, 27, 1, -1, 88, 88, 73, 133, 73, -17, -17, 67, -17, 151, 91, -17, 67, -17, 11, 35, 11, 65, 65, 21, 25, 41, 21, 65, 65, 55, 95, 55, -3, -7, -3, -12, -12, 25, 21, -3, -7, 53, 33, -3, 25, -3, 58, 58, 48, 88, 48, -12, -12, 44, -12, 100, 60, -12, 44, -12, -6, 6, 42, 18, 42, -6, 6, 102, 102, 18, 42, 18, 72, 72, 19, 21, 27, 23, 27, 39, 41, 19, 21, 102, 102, 87, 147, 87, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, 9, -9, -63, -27, -63, 9, -9, -153, -153, -27, -63, -27, -108, -108, 9, -9, -63, -27, -63, 9, -9, -153, -153, -27, -63, -27, -108, -108, 29, 27, 21, 25, 21, 1, -1, -7, -3, -7, 29, 27, 21, 25, 21, -31, -33, -39, -35, -39, -31, -33, -39, -35, -39, 57, 55, 37, 35, 1, -1, 29, 27, 1, -1, 57, 55, 37, 35, -63, -65, -63, -65, 29, 27, 1, -1, 29, 27, -31, -33, -31, -33, 72, 72, 57, 117, 57, -33, -33, 51, -33, 135, 75, -33, 51, -33, 72, 72, 57, 117, 57, -153, -153, -153, -153, 51, -33, 51, -129, -129, 135, 75, -33, 51, -33, 135, 75, -225, -225, 51, -33, 51, -129, -129, 11, 35, 11, 65, 65, 21, 25, 41, 21, 65, 65, 55, 95, 55, -3, -7, -3, -12, -12, 25, 21, -3, -7, 53, 33, -3, 25, -3, 58, 58, 48, 88, 48, -12, -12, 44, -12, 100, 60, -12, 44, -12, 11, 35, 11, 65, 65, 21, 25, 41, 21, 65, 65, 55, 95, 55, -19, -55, -19, -100, -100, -19, -55, -19, -100, -100, 25, 21, -3, -7, 25, 21, -35, -39, -35, -39, 53, 33, -3, 25, -3, 53, 33, -67, -67, 25, -3, 25, -35, -35, 50, 50, 40, 80, 40, -20, -20, 36, -20, 92, 52, -20, 36, -20, 50, 50, 40, 80, 40, -100, -100, -100, -100, 36, -20, 36, -84, -84, 92, 52, -20, 36, -20, 92, 52, -148, -148, 36, -20, 36, -84, -84, 8, -4, -40, -16, -40, 8, -4, -100, -100, -16, -40, -16, -70, -70, -17, -19, -25, -21, -25, -37, -39, -17, -19, -100, -100, -85, -145, -85, -11, -35, -11, -65, -65, -21, -25, -41, -21, -65, -65, -55, -95, -55, 1, 3, 9, 5, 9, 1, 3, 19, 19, 5, 9, 5, 14, 14, -27, -25, -19, -23, -19, 1, 3, 9, 5, 9, -55, -53, -35, -33, 1, 3, -27, -25, 1, 3, -86, -86, -71, -131, -71, 19, 19, -65, 19, -149, -89, 19, -65, 19, -9, -33, -9, -63, -63, -19, -23, -39, -19, -63, -63, -53, -93, -53, 5, 9, 5, 14, 14, -23, -19, 5, 9, -51, -31, 5, -23, 5, -56, -56, -46, -86, -46, 14, 14, -42, 14, -98, -58, 14, -42, 14, -6, -18, -54, -30, -54, -6, -18, -114, -114, -30, -54, -30, -84, -84, -31, -33, -39, -35, -39, -51, -53, -31, -33, -114, -114, -99, -159, -99, -25, -49, -25, -79, -79, -35, -39, -55, -35, -79, -79, -69, -109, -69, 8, -4, -40, -16, -40, 8, -4, -100, -100, -16, -40, -16, -70, -70, -17, -19, -25, -21, -25, -37, -39, -17, -19, -100, -100, -85, -145, -85, -11, -35, -11, -65, -65, -21, -25, -41, -21, -65, -65, -55, -95, -55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 16, 8, 16, 0, 4, 36, 36, 8, 16, 8, 26, 26, 0, -24, -96, -48, -96, 0, -24, -216, -216, -48, -96, -48, -156, -156, 0, 4, 16, 8, 16, 0, 4, 36, 36, 8, 16, 8, 26, 26, 19, 21, 27, 23, 27, -9, -7, -1, -5, -1, 19, 21, 27, 23, 27, -41, -39, -33, -37, -33, -41, -39, -33, -37, -33, -27, -25, -19, -23, -19, 1, 3, 9, 5, 9, -41, -39, -33, -37, -33, -27, -25, -19, -23, -19, -5, -3, 3, -1, 3, -5, -3, 3, -1, 3, 5, 7, 13, 9, 13, -65, -63, -57, -61, -57, 5, 7, 13, 9, 13, 39, 41, 19, 21, -17, -15, 11, 13, -17, -15, 39, 41, 19, 21, -81, -79, -81, -79, 11, 13, -17, -15, 11, 13, -49, -47, -49, -47, -55, -53, -35, -33, 1, 3, -27, -25, 1, 3, -69, -67, -49, -47, -55, -53, -35, -33, -9, -7, -9, -7, 9, 11, -117, -115, 9, 11, 19, 21, -9, -7, 19, 21, -41, -39, -41, -39, -27, -25, 1, 3, -41, -39, -27, -25, -5, -3, -5, -3, 5, 7, -65, -63, 5, 7, 90, 90, 75, 135, 75, -15, -15, 69, -15, 153, 93, -15, 69, -15, 90, 90, 75, 135, 75, -135, -135, -135, -135, 69, -15, 69, -111, -111, 153, 93, -15, 69, -15, 153, 93, -207, -207, 69, -15, 69, -111, -111, -84, -84, -69, -129, -69, 21, 21, -63, 21, -147, -87, 21, -63, 21, -126, -126, -111, -171, -111, -84, -84, -69, -129, -69, 0, 0, 0, 0, 36, 36, -216, -216, 36, 36, 75, -9, 75, -105, -105, -63, 21, -105, -63, 3, 3, 33, -177, 33, 135, 75, -33, 51, -33, 135, 75, -225, -225, 51, -33, 51, -129, -129, -147, -87, 21, -63, 21, -189, -129, -147, -87, -9, -9, 45, -333, 45, 75, -9, 75, -105, -105, -63, 21, -105, -63, 3, 3, 33, -177, 33, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, -1, -5, -1, -10, -10, 27, 23, -1, -5, 55, 35, -1, 27, -1, 60, 60, 50, 90, 50, -10, -10, 46, -10, 102, 62, -10, 46, -10, 13, 37, 13, 67, 67, 23, 27, 43, 23, 67, 67, 57, 97, 57, -17, -53, -17, -98, -98, -17, -53, -17, -98, -98, 27, 23, -1, -5, 27, 23, -33, -37, -33, -37, 55, 35, -1, 27, -1, 55, 35, -65, -65, 27, -1, 27, -33, -33, 52, 52, 42, 82, 42, -18, -18, 38, -18, 94, 54, -18, 38, -18, 52, 52, 42, 82, 42, -98, -98, -98, -98, 38, -18, 38, -82, -82, 94, 54, -18, 38, -18, 94, 54, -146, -146, 38, -18, 38, -82, -82, -9, -33, -9, -63, -63, -19, -23, -39, -19, -63, -63, -53, -93, -53, 5, 9, 5, 14, 14, -23, -19, 5, 9, -51, -31, 5, -23, 5, -56, -56, -46, -86, -46, 14, 14, -42, 14, -98, -58, 14, -42, 14, -23, -47, -23, -77, -77, -33, -37, -53, -33, -77, -77, -67, -107, -67, -9, -33, -9, -63, -63, -19, -23, -39, -19, -63, -63, -53, -93, -53, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 15, 7, 25, 25, -35, -83, -35, -143, -143, 7, 15, 7, 25, 25, 23, 27, -5, -1, 23, 27, -37, -33, -37, -33, -23, -19, 5, 9, -37, -33, -23, -19, -1, 3, -1, 3, 9, 13, -61, -57, 9, 13, 43, 23, -13, 15, -13, 43, 23, -77, -77, 15, -13, 15, -45, -45, -51, -31, 5, -23, 5, -65, -45, -51, -31, -5, -5, 13, -113, 13, 23, -5, 23, -37, -37, -23, 5, -37, -23, -1, -1, 9, -61, 9, 61, 61, 51, 91, 51, -9, -9, 47, -9, 103, 63, -9, 47, -9, 61, 61, 51, 91, 51, -89, -89, -89, -89, 47, -9, 47, -73, -73, 103, 63, -9, 47, -9, 103, 63, -137, -137, 47, -9, 47, -73, -73, -55, -55, -45, -85, -45, 15, 15, -41, 15, -97, -57, 15, -41, 15, -83, -83, -73, -113, -73, -55, -55, -45, -85, -45, 1, 1, 1, 1, 25, 25, -143, -143, 25, 25, 51, -5, 51, -69, -69, -41, 15, -69, -41, 3, 3, 23, -117, 23, 91, 51, -21, 35, -21, 91, 51, -149, -149, 35, -21, 35, -85, -85, -97, -57, 15, -41, 15, -125, -85, -97, -57, -5, -5, 31, -221, 31, 51, -5, 51, -69, -69, -41, 15, -69, -41, 3, 3, 23, -117, 23]\n assert candidate(expression = \"10+5*2-3/1\") == []\n assert candidate(expression = \"33-22*1+44/4-55*6+77\") == []\n assert candidate(expression = \"8*3+9-4/2+5-7\") == []\n assert candidate(expression = \"1*2*3*4*5*6*7*8-9\") == [-5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, 40302, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, 40266, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, -5040, 40104, 40104, 40104, 40104, 40104, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 39240, 39240, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, 33840, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, -5040, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311, 40311]\n assert candidate(expression = \"100-50+25*5-12*2\") == [525, 400, -51, 400, -176, 1525, 1150, -51, -251, 350, -226, 1150, -226, -626, -425, -300, 151, -300, 276, -475, -350, -1425, -1050, -99, -299, 151, 101, 351, 450, -126, 1250, -126, -526, -250, 326, -350, -1050, -174, -574, 326, 226, 726]\n assert candidate(expression = \"15/3+2*4-8/2\") == []\n assert candidate(expression = \"15+25*35-45*55/65\") == []\n assert candidate(expression = \"4*4-3*3+2*2-1*1\") == [-44, -44, -56, -44, -56, -44, -44, -56, -92, -44, -56, -44, -56, -92, -28, -28, -32, -28, -32, -44, -44, -28, -28, -64, -100, -32, -100, -68, -44, -56, -44, -56, -92, -28, -32, -44, -28, -64, -100, -32, -100, -68, 20, 20, 24, 20, 24, 20, 20, 24, 36, 20, 24, 20, 24, 36, -12, -12, -8, -12, -8, 20, 20, 24, 20, 24, -44, -44, -28, -28, 20, 20, -12, -12, 20, 20, -72, -108, -40, -108, -76, 24, 36, -8, 24, -92, -60, 36, -28, 36, -44, -56, -44, -56, -92, -28, -32, -44, -28, -64, -100, -32, -100, -68, 20, 24, 20, 24, 36, -12, -8, 20, 24, -44, -28, 20, -12, 20, -72, -108, -40, -108, -76, 24, 36, -8, 24, -92, -60, 36, -28, 36, 1, 1, -2, 1, -2, 1, 1, -2, -11, 1, -2, 1, -2, -11, 5, 5, 4, 5, 4, 1, 1, 5, 5, -4, -13, 4, -13, -5, 1, -2, 1, -2, -11, 5, 4, 1, 5, -4, -13, 4, -13, -5, 20, 20, 24, 20, 24, 20, 20, 24, 36, 20, 24, 20, 24, 36, 65, 65, 78, 65, 78, 65, 65, 78, 117, 65, 78, 65, 78, 117, -18, -18, -17, -18, -17, 14, 14, 15, 14, 15, 9, 9, 10, 9, 10, 14, 14, 15, 14, 15, 41, 41, 42, 41, 42, -44, -44, -28, -28, 20, 20, -12, -12, 20, 20, 1, 1, 5, 5, 20, 20, 65, 65, -18, -18, 14, 14, 9, 9, 14, 14, 41, 41, -69, -105, -37, -105, -73, 27, 39, -5, 27, -89, -57, 39, -25, 39, -6, -15, 2, -15, -7, 27, 39, 90, 129, -17, 15, 10, 15, 42, -89, -57, 39, -25, 39, 1, 9, 39, 129, -37, 27, 17, 27, 81, -44, -56, -44, -56, -92, -28, -32, -44, -28, -64, -100, -32, -100, -68, 20, 24, 20, 24, 36, -12, -8, 20, 24, -44, -28, 20, -12, 20, -72, -108, -40, -108, -76, 24, 36, -8, 24, -92, -60, 36, -28, 36, 1, -2, 1, -2, -11, 5, 4, 1, 5, -4, -13, 4, -13, -5, 20, 24, 20, 24, 36, 65, 78, 65, 78, 117, -18, -17, 14, 15, 9, 10, 14, 15, 41, 42, -44, -28, 20, -12, 20, 1, 5, 20, 65, -18, 14, 9, 14, 41, -69, -105, -37, -105, -73, 27, 39, -5, 27, -89, -57, 39, -25, 39, -6, -15, 2, -15, -7, 27, 39, 90, 129, -17, 15, 10, 15, 42, -89, -57, 39, -25, 39, 1, 9, 39, 129, -37, 27, 17, 27, 81]\n assert candidate(expression = \"3*2-1+4*5-6*7+8*9\") == [5631, 9663, 1311, 9663, 5343, 951, 1623, -417, -777, 9183, 4863, 1623, 3135, -105, 1365, 2373, 285, 2373, 1293, 951, 1623, -3315, -5667, 231, -129, -147, -129, -507, 9183, 4863, 1623, 3135, -105, 1893, 813, 1623, -5667, 3783, 543, 381, 543, -2859, 7041, 12081, 1641, 12081, 6681, 1191, 2031, -519, -969, 11481, 6081, 2031, 3921, -129, 1365, 2373, 285, 2373, 1293, 1353, 2361, 273, 2361, 1281, 717, 1221, -3549, -6069, 1191, 2031, -3549, -6069, -4497, -7689, 231, -129, -147, -129, -507, 345, -105, -147, -159, -147, -525, -105, -525, -609, 9159, 4839, 1599, 3111, -129, 1869, 789, 1599, -5691, 3759, 519, 357, 519, -2883, 11481, 6081, 2031, 3921, -129, 1869, 789, 1761, 681, 1221, -6069, 2031, -6069, -7689, 3759, 519, 357, 519, -2883, 4785, 735, 357, 249, 357, -3045, 735, -3045, -3801, -5625, -9657, -1305, -9657, -5337, -945, -1617, 423, 783, -9177, -4857, -1617, -3129, 111, -1359, -2367, -279, -2367, -1287, -945, -1617, 3321, 5673, -225, 135, 153, 135, 513, -9177, -4857, -1617, -3129, 111, -1887, -807, -1617, 5673, -3777, -537, -375, -537, 2865, 4221, 7245, 981, 7245, 4005, 711, 1215, -315, -585, 6885, 3645, 1215, 2349, -81, -7035, -12075, -1635, -12075, -6675, -1185, -2025, 525, 975, -11475, -6075, -2025, -3915, 135, -1479, -2487, -399, -2487, -1407, -1491, -2499, -411, -2499, -1419, -1359, -2367, -279, -2367, -1287, -1467, -2475, -387, -2475, -1395, -1347, -2355, -267, -2355, -1275, 1185, 2025, -3081, -5265, 1659, 2835, -3081, -5265, -4029, -6885, -711, -1215, 3555, 6075, 711, 1215, -1185, -2025, -5925, -10125, -6873, -11745, 3555, 6075, -4977, -8505, 4503, 7695, 663, 303, 285, 303, -75, 777, 327, 285, 273, 285, -93, 327, -93, -177, -225, 135, 153, 135, 513, 549, 279, -339, 111, 33, 21, 153, 45, 165, 321, -57, 363, -57, -141, 153, 531, 279, 111, -309, -393, 531, -225, 615, 9207, 4887, 1647, 3159, -81, 1917, 837, 1647, -5643, 3807, 567, 405, 567, -2835, 11529, 6129, 2079, 3969, -81, 1917, 837, 1809, 729, 1269, -6021, 2079, -6021, -7641, 3807, 567, 405, 567, -2835, 4833, 783, 405, 297, 405, -2997, 783, -2997, -3753, -9153, -4833, -1593, -3105, 135, -1863, -783, -1593, 5697, -3753, -513, -351, -513, 2889, 6885, 3645, 1215, 2349, -81, -11475, -6075, -2025, -3915, 135, -2943, -1863, -3051, -1971, -1863, -783, -2835, -1755, -1755, -675, 2025, -5265, 2835, -5265, -6885, -1215, 6075, 1215, -2025, -10125, -11745, 6075, -8505, 7695, 4239, 999, 837, 999, -2403, 5265, 1215, 837, 729, 837, -2565, 1215, -2565, -3321, -3753, -513, -351, -513, 2889, 3213, 783, -4779, -729, -1431, -1539, -351, -1323, -243, 1161, -2241, 1539, -2241, -2997, -351, 3051, 783, -729, -4509, -5265, 3051, -3753, 3807, 1881, 3225, 441, 3225, 1785, 321, 545, -135, -255, 3065, 1625, 545, 1049, -31, 459, 795, 99, 795, 435, 321, 545, -1101, -1885, 81, -39, -45, -39, -165, 3065, 1625, 545, 1049, -31, 635, 275, 545, -1885, 1265, 185, 131, 185, -949, 2351, 4031, 551, 4031, 2231, 401, 681, -169, -319, 3831, 2031, 681, 1311, -39, 459, 795, 99, 795, 435, 455, 791, 95, 791, 431, 243, 411, -1179, -2019, 401, 681, -1179, -2019, -1495, -2559, 81, -39, -45, -39, -165, 119, -31, -45, -49, -45, -171, -31, -171, -199, 3057, 1617, 537, 1041, -39, 627, 267, 537, -1893, 1257, 177, 123, 177, -957, 3831, 2031, 681, 1311, -39, 627, 267, 591, 231, 411, -2019, 681, -2019, -2559, 1257, 177, 123, 177, -957, 1599, 249, 123, 87, 123, -1011, 249, -1011, -1263, -1873, -3217, -433, -3217, -1777, -313, -537, 143, 263, -3057, -1617, -537, -1041, 39, -451, -787, -91, -787, -427, -313, -537, 1109, 1893, -73, 47, 53, 47, 173, -3057, -1617, -537, -1041, 39, -627, -267, -537, 1893, -1257, -177, -123, -177, 957, -1871, -3215, -431, -3215, -1775, -311, -535, 145, 265, -3055, -1615, -535, -1039, 41, -449, -785, -89, -785, -425, -311, -535, 1111, 1895, -71, 49, 55, 49, 175, -3055, -1615, -535, -1039, 41, -625, -265, -535, 1895, -1255, -175, -121, -175, 959, 4221, 7245, 981, 7245, 4005, 711, 1215, -315, -585, 6885, 3645, 1215, 2349, -81, -7035, -12075, -1635, -12075, -6675, -1185, -2025, 525, 975, -11475, -6075, -2025, -3915, 135, -469, -805, -109, -805, -445, -79, -135, 35, 65, -765, -405, -135, -261, 9, -3283, -5635, -763, -5635, -3115, -553, -945, 245, 455, -5355, -2835, -945, -1827, 63, -4221, -7245, -981, -7245, -4005, -711, -1215, 315, 585, -6885, -3645, -1215, -2349, 81, -531, -867, -171, -867, -507, -543, -879, -183, -879, -519, -411, -747, -51, -747, -387, -519, -855, -159, -855, -495, -399, -735, -39, -735, -375, -489, -825, -129, -825, -465, -493, -829, -133, -829, -469, -451, -787, -91, -787, -427, -449, -785, -89, -785, -425, -519, -855, -159, -855, -495, -399, -735, -39, -735, -375, -469, -805, -109, -805, -445, -439, -775, -79, -775, -415, -429, -765, -69, -765, -405, 1185, 2025, -3081, -5265, 1659, 2835, -3081, -5265, -4029, -6885, -711, -1215, 3555, 6075, 711, 1215, -1185, -2025, -5925, -10125, -6873, -11745, 3555, 6075, -4977, -8505, 4503, 7695, 711, 1215, -711, -1215, 869, 1485, -711, -1215, -1027, -1755, -79, -135, 1343, 2295, 79, 135, 1501, 2565, 711, 1215, -1185, -2025, -79, -135, -553, -945, -711, -1215, -4977, -8505, -5925, -10125, 4503, 7695, -4029, -6885, 5451, 9315, -1659, -2835, -1975, -3375, 1343, 2295, 1501, 2565, -4029, -6885, 5451, 9315, -79, -135, 2291, 3915, 3081, 5265, 519, 159, 141, 159, -219, 633, 183, 141, 129, 141, -237, 183, -237, -321, -369, -9, 9, -9, 369, 405, 135, -483, -33, -111, -123, 9, -99, 21, 177, -201, 219, -201, -285, 9, 387, 135, -33, -453, -537, 387, -369, 471, 225, 105, 99, 105, -21, 263, 113, 99, 95, 99, -27, 113, -27, -55, -73, 47, 53, 47, 173, -71, 49, 55, 49, 175, 405, 135, -483, -33, 35, 65, -187, 23, -261, 9, -27, -39, 93, -15, 105, 15, 11, 53, 55, -15, 105, 35, 65, 75, 177, -201, 219, -201, -285, 9, 387, 135, -33, -453, -537, 387, -369, 471, 135, 9, 149, 9, -19, 65, 191, 79, 205, 135, -33, 65, 23, 9, -369, -453, 471, -285, 555, -75, -103, 191, 205, -285, 555, 65, 275, 345, 9207, 4887, 1647, 3159, -81, 1917, 837, 1647, -5643, 3807, 567, 405, 567, -2835, 11529, 6129, 2079, 3969, -81, 1917, 837, 1809, 729, 1269, -6021, 2079, -6021, -7641, 3807, 567, 405, 567, -2835, 4833, 783, 405, 297, 405, -2997, 783, -2997, -3753, -9153, -4833, -1593, -3105, 135, -1863, -783, -1593, 5697, -3753, -513, -351, -513, 2889, 6885, 3645, 1215, 2349, -81, -11475, -6075, -2025, -3915, 135, -2943, -1863, -3051, -1971, -1863, -783, -2835, -1755, -1755, -675, 2025, -5265, 2835, -5265, -6885, -1215, 6075, 1215, -2025, -10125, -11745, 6075, -8505, 7695, 4239, 999, 837, 999, -2403, 5265, 1215, 837, 729, 837, -2565, 1215, -2565, -3321, -3753, -513, -351, -513, 2889, 3213, 783, -4779, -729, -1431, -1539, -351, -1323, -243, 1161, -2241, 1539, -2241, -2997, -351, 3051, 783, -729, -4509, -5265, 3051, -3753, 3807, 3105, 1665, 585, 1089, 9, 675, 315, 585, -1845, 1305, 225, 171, 225, -909, 3879, 2079, 729, 1359, 9, 675, 315, 639, 279, 459, -1971, 729, -1971, -2511, 1305, 225, 171, 225, -909, 1647, 297, 171, 135, 171, -963, 297, -963, -1215, -3033, -1593, -513, -1017, 63, -603, -243, -513, 1917, -1233, -153, -99, -153, 981, -3015, -1575, -495, -999, 81, -585, -225, -495, 1935, -1215, -135, -81, -135, 999, 6885, 3645, 1215, 2349, -81, -11475, -6075, -2025, -3915, 135, -765, -405, -135, -261, 9, -5355, -2835, -945, -1827, 63, -6885, -3645, -1215, -2349, 81, -1323, -963, -1431, -1071, -243, 117, -1215, -855, -135, 225, -945, -585, -981, -621, -603, -243, -585, -225, -1215, -855, -135, 225, -765, -405, -495, -135, -405, -45, 2025, -5265, 2835, -5265, -6885, -1215, 6075, 1215, -2025, -10125, -11745, 6075, -8505, 7695, 1215, -1215, 1485, -1215, -1755, -135, 2295, 135, 2565, 1215, -2025, -135, -945, -1215, -8505, -10125, 7695, -6885, 9315, -2835, -3375, 2295, 2565, -6885, 9315, -135, 3915, 5265, 4095, 855, 693, 855, -2547, 5121, 1071, 693, 585, 693, -2709, 1071, -2709, -3465, -3897, -657, -495, -657, 2745, 3069, 639, -4923, -873, -1575, -1683, -495, -1467, -387, 1017, -2385, 1395, -2385, -3141, -495, 2907, 639, -873, -4653, -5409, 2907, -3897, 3663, 1449, 369, 315, 369, -765, 1791, 441, 315, 279, 315, -819, 441, -819, -1071, -1233, -153, -99, -153, 981, -1215, -135, -81, -135, 999, 3069, 639, -4923, -873, -261, 9, -2259, -369, -2925, -495, -819, -927, 261, -711, 369, -441, -477, -99, -81, -711, 369, -261, 9, 99, 1017, -2385, 1395, -2385, -3141, -495, 2907, 639, -873, -4653, -5409, 2907, -3897, 3663, 639, -495, 765, -495, -747, 9, 1143, 135, 1269, 639, -873, 9, -369, -495, -3897, -4653, 3663, -3141, 4419, -1251, -1503, 1143, 1269, -3141, 4419, 9, 1899, 2529]\n assert candidate(expression = \"3*3*3*3-2*2*2\") == [-135, -135, 108, -54, 108, 9, 9, 108, 252, -54, 108, 90, 108, 252, -135, -135, 108, -54, 108, 57, 57, 57, 57, 108, 252, 108, 300, 300, -54, 108, 90, 108, 252, -54, 108, 138, 138, 108, 252, 108, 300, 300, -135, -135, 108, -54, 108, 9, 9, 108, 252, -54, 108, 90, 108, 252, -135, -135, 108, -54, 108, -135, -135, 108, -54, 108, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 108, 252, 108, 300, 300, 108, 252, 108, 108, 316, 316, 316, 316, 316, -54, 108, 90, 108, 252, -54, 108, 138, 138, 108, 252, 108, 300, 300, -54, 108, 90, 108, 252, -54, 108, -54, 108, 154, 154, 154, 154, 154, 108, 252, 108, 300, 300, 108, 252, 108, 108, 316, 316, 316, 316, 316]\n assert candidate(expression = \"7+6*5-4/2\") == []\n assert candidate(expression = \"1+2+3+4+5+6+7+8\") == [36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36]\n assert candidate(expression = \"9*9-8/2+7-6*5+4\") == []\n assert candidate(expression = \"50+25-10*2+5\") == [5, 50, 155, 60, 85, 5, 50, 455, 455, 60, 85, 60, 135, 135]\n assert candidate(expression = \"5*5-4*4+3*3-2*2+1*1\") == [125, 125, 65, 125, 65, -235, -235, -55, -235, 125, 65, -235, -55, -235, -115, -115, -135, -115, -135, -235, -235, -475, -475, -15, -195, -175, -195, -355, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 445, 305, 445, 305, -395, -395, 25, -395, 445, 305, -395, 25, -395, -115, -115, -135, -115, -135, -275, -275, -295, -275, -295, -395, -395, -635, -635, -395, -395, -635, -635, -1115, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -10, -25, -10, -25, -100, -100, -55, -100, -10, -25, -100, -55, -100, -70, -70, -75, -70, -75, -100, -100, -160, -160, -45, -90, -85, -90, -130, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 445, 305, 445, 305, -395, -395, 25, -395, 445, 305, -395, 25, -395, 310, 310, 215, 310, 215, -260, -260, 25, -260, 310, 215, -260, 25, -260, -205, -205, -210, -205, -210, -365, -365, -370, -365, -370, -70, -70, -75, -70, -75, -365, -365, -370, -365, -370, -230, -230, -235, -230, -235, -395, -395, -635, -635, -395, -395, -635, -635, -1115, -1115, -260, -260, -320, -320, -395, -395, -260, -260, -725, -725, -1205, -1205, -320, -320, -1205, -1205, -800, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, 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75, 50, 90, 75, 115, 75, 115, 195, -100, -100, -85, -100, -85, -10, -10, -55, -10, -100, -85, -10, -55, -10, -40, -40, -35, -40, -35, -10, -10, 50, 50, -65, -20, -25, -20, 20, -100, -85, -10, -55, -10, -40, -35, -10, 50, -65, -20, -25, -20, 20, -25, -25, -10, -25, -10, 65, 65, 20, 65, -25, -10, 65, 20, 65, 35, 35, 40, 35, 40, 65, 65, 125, 125, 10, 55, 50, 55, 95, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, 345, 345, 230, 345, 230, -345, -345, 0, -345, 345, 230, -345, 0, -345, 210, 210, 140, 210, 140, -210, -210, 0, -210, 210, 140, -210, 0, -210, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, 120, 120, 80, 120, 80, -120, -120, 0, -120, 120, 80, -120, 0, -120, -105, -105, -70, -105, -70, 105, 105, 0, 105, -105, -70, 105, 0, 105, -265, -265, -260, -265, -260, -425, -425, -420, -425, -420, -130, -130, -125, -130, -125, -425, -425, -420, -425, -420, -290, -290, -285, -290, -285, 35, 35, 40, 35, 40, 75, 75, 80, 75, 80, -40, -40, -35, -40, -35, 35, 35, 40, 35, 40, -375, -375, -370, -375, -370, -240, -240, -235, -240, -235, 75, 75, 80, 75, 80, -150, -150, -145, -150, -145, 75, 75, 80, 75, 80, -345, -345, -585, -585, -345, -345, -585, -585, -1065, -1065, -210, -210, -270, -270, -345, -345, -210, -210, -675, -675, -1155, -1155, -270, -270, -1155, -1155, -750, -750, 105, 105, 165, 165, 105, 105, 165, 165, 285, 285, -120, -120, -60, -60, 105, 105, 165, 165, -345, -345, -210, -210, 105, 105, -120, -120, 105, 105, -735, -735, -1215, -1215, -330, -330, -1215, -1215, -810, -810, 165, 165, 285, 285, -60, -60, 165, 165, -1065, -1065, -660, -660, 285, 285, -390, -390, 285, 285, 10, -170, -150, -170, -330, 170, -250, -150, -310, -250, -410, -250, -410, -730, -35, -80, -75, -80, -120, 170, -250, 125, -160, -210, -370, -75, -370, -235, -250, -410, -250, -410, -730, -160, -200, -250, -160, -470, -790, -200, -790, -520, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -65, -20, -25, -20, 20, 10, 55, 50, 55, 95, 120, -225, 75, -135, -30, 75, 45, -75, -30, 75, -250, -410, -115, -410, -275, 50, 90, -25, 50, -360, -225, 90, -135, 90, -225, -385, -225, -385, -705, -135, -175, -225, -135, -445, -765, -175, -765, -495, 75, 115, 75, 115, 195, -75, -35, 75, 115, -225, -135, 75, -75, 75, -485, -805, -215, -805, -535, 115, 195, -35, 115, -705, -435, 195, -255, 195, 125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 305, -395, 25, -395, 310, 215, -260, 25, -260, -205, -210, -365, -370, -70, -75, -365, -370, -230, -235, -395, -635, -395, -635, -1115, -260, -320, -395, -260, -725, -1205, -320, -1205, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, 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-156, -69, -46, 69, 0, 69, -36, -24, 36, 0, 36, -69, -46, 69, 0, 69, -261, -174, 261, 0, 261, -241, -240, -401, -400, -106, -105, -401, -400, -266, -265, 59, 60, 99, 100, -16, -15, 59, 60, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -33, -32, -65, -64, -6, -5, -65, -64, -38, -37, 59, 60, 99, 100, 267, 268, 435, 436, -52, -51, 23, 24, 12, 13, 23, 24, 87, 88, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -15, -14, 12, 13, 99, 100, 435, 436, -162, -161, 63, 64, 30, 31, 63, 64, 255, 256, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, -9, -57, -9, -57, -153, 18, 6, -9, 18, -75, -171, 6, -171, -90, 105, 165, 105, 165, 285, 441, 693, 441, 693, 1197, -156, -144, 69, 81, 36, 48, 69, 81, 261, 273, -345, -210, 105, -120, 105, -9, 18, 105, 441, -156, 69, 36, 69, 261, -711, -1191, -306, -1191, -786, 189, 309, -36, 189, -1041, -636, 309, -366, 309, -87, -183, -6, -183, -102, 189, 309, 813, 1317, -144, 81, 48, 81, 273, -1041, -636, 309, -366, 309, -33, 48, 309, 1317, -474, 201, 102, 201, 777, 6, -174, -154, -174, -334, 166, -254, -154, -314, -254, -414, -254, -414, -734, -39, -84, -79, -84, -124, 166, -254, 121, -164, -214, -374, -79, -374, -239, -254, -414, -254, -414, -734, -164, -204, -254, -164, -474, -794, -204, -794, -524, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, -69, -24, -29, -24, 16, 6, 51, 46, 51, 91, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, -254, -414, -119, -414, -279, 46, 86, -29, 46, -364, -229, 86, -139, 86, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, 22, -14, -10, -14, -46, 54, -30, -10, -42, -30, -62, -30, -62, -126, 13, 4, 5, 4, -4, 54, -30, 45, -12, -22, -54, 5, -54, -27, -30, -62, -30, -62, -126, -12, -20, -30, -12, -74, -138, -20, -138, -84, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, 22, 211, 190, 211, 379, -146, 295, 190, 358, 295, 463, 295, 463, 799, -57, -48, -49, -48, -40, 18, 27, 26, 27, 35, 7, 16, 15, 16, 24, 18, 27, 26, 27, 35, 82, 91, 90, 91, 99, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, 4, -5, -5, 13, -34, 71, -146, 295, 53, -103, -22, 47, -11, 25, -22, 47, -86, 175, -238, -398, -103, -398, -263, 62, 102, -13, 62, -348, -213, 102, -123, 102, -30, -62, -3, -62, -35, 62, 102, 270, 438, -49, 26, 15, 26, 90, -348, -213, 102, -123, 102, -12, 15, 102, 438, -159, 66, 33, 66, 258, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, -5, -37, -5, -37, -101, 13, 5, -5, 13, -49, -113, 5, -113, -59, 71, 111, 71, 111, 191, 295, 463, 295, 463, 799, -103, -95, 47, 55, 25, 33, 47, 55, 175, 183, -229, -139, 71, -79, 71, -5, 13, 71, 295, -103, 47, 25, 47, 175, -473, -793, -203, -793, -523, 127, 207, -23, 127, -693, -423, 207, -243, 207, -57, -121, -3, -121, -67, 127, 207, 543, 879, -95, 55, 33, 55, 183, -693, -423, 207, -243, 207, -21, 33, 207, 879, -315, 135, 69, 135, 519]\n assert candidate(expression = \"1+2-3*4/5+6-7*8/9+10\") == []\n assert candidate(expression = \"4+3*2-1+5*6/3\") == []\n assert candidate(expression = \"10-5+3-2+1*2*3-4*5\") == [-30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -100, -28, -40, -28, 32, -66, -18, -100, -28, -10, -10, 0, -6, 0, 2, 22, 2, 22, 22, -28, 32, -18, -28, 22, 22, 72, 42, 72, 38, 14, 18, 14, -6, 38, 14, 18, 18, 14, -6, 14, -6, -6, 5, 5, 5, 5, 5, 73, 25, 33, 25, -15, -12, 0, -46, -10, 56, 20, 5, 5, 73, 25, 30, 30, 40, 34, 40, 18, 18, 25, 13, 28, 34, 16, 25, 13, -10, 10, -10, 10, 10, -40, 20, -30, -40, 10, 10, 60, 30, 60, 10, -10, 10, -10, -10, 5, 5, 25, -15, 0, -10, 20, 5, 25, 50, 50, 100, 70, 100, -10, -10, 25, -35, 40, 70, -20, 25, -35, -30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -100, -28, -40, -28, 32, -66, -18, -100, -28, -10, -10, 0, -6, 0, 2, 22, 2, 22, 22, -28, 32, -18, -28, 22, 22, 72, 42, 72, 38, 14, 18, 14, -6, 38, 14, 18, 18, 14, -6, 14, -6, -6, 38, 14, 18, 14, -6, 38, 14, 18, 18, 14, -6, 14, -6, -6, 180, 60, 80, 60, -40, 248, 80, 108, 80, -60, 180, 60, 80, 60, -40, 248, 80, 108, 80, -60, 248, 80, 108, 80, -60, 78, 30, 44, 20, 146, 50, 95, 35, 163, 55, 78, 30, 44, 20, 146, 50, 146, 50, 180, 60, 248, 80, 180, 60, 248, 80, 248, 80, 30, 30, 40, 34, 40, 18, 18, 25, 13, 28, 34, 16, 25, 13, 30, 30, 40, 34, 40, 18, 18, 18, 18, 0, -12, 0, -12, -12, 18, 24, 6, 15, 3, 18, 24, 6, 6, 0, -12, 0, -12, -12, -30, -10, -30, -10, -10, -60, 0, -50, -60, -10, -10, 40, 10, 40, -10, -30, -10, -30, -30, -15, -15, 5, -35, -20, -30, 0, -15, 5, 30, 30, 80, 50, 80, -30, -30, 5, -55, 20, 50, -40, 5, -55, -30, -10, -30, -10, -10, -60, 0, -50, -60, -10, -10, 40, 10, 40, -10, -30, -10, -30, -30, -10, -30, -10, -30, -30, 60, -40, 80, -60, 60, -40, 80, -60, 80, -60, 30, 20, 50, 35, 55, 30, 20, 50, 50, 60, 80, 60, 80, 80, 30, 30, 80, 50, 80, -30, -30, 5, -55, 20, 50, -40, 5, -55, 30, 30, 80, 50, 80, -30, -30, -30, -30, -120, -180, -120, -180, -180, -30, 0, -90, -45, -105, -30, 0, -90, -90, -120, -180, -120, -180, -180, 40, 16, 20, 16, -4, 40, 16, 20, 20, 16, -4, 16, -4, -4, 110, 38, 50, 38, -22, 76, 28, 110, 38, 20, 20, 10, 16, 10, 8, -12, 8, -12, -12, 38, -22, 28, 38, -12, -12, -62, -32, -62, -28, -4, -8, -4, 16, -28, -4, -8, -8, -4, 16, -4, 16, 16, 5, 5, 5, 5, 5, -63, -15, -23, -15, 25, 22, 10, 56, 20, -46, -10, 5, 5, -63, -15, -20, -20, -30, -24, -30, -8, -8, -15, -3, -18, -24, -6, -15, -3, 20, 0, 20, 0, 0, 50, -10, 40, 50, 0, 0, -50, -20, -50, 0, 20, 0, 20, 20, 5, 5, -15, 25, 10, 20, -10, 5, -15, -40, -40, -90, -60, -90, 20, 20, -15, 45, -30, -60, 30, -15, 45, 34, 10, 14, 10, -10, 34, 10, 14, 14, 10, -10, 10, -10, -10, 104, 32, 44, 32, -28, 70, 22, 104, 32, 14, 14, 4, 10, 4, 2, -18, 2, -18, -18, 32, -28, 22, 32, -18, -18, -68, -38, -68, 40, 16, 20, 16, -4, 40, 16, 20, 20, 16, -4, 16, -4, -4, 110, 38, 50, 38, -22, 76, 28, 110, 38, 20, 20, 10, 16, 10, 8, -12, 8, -12, -12, 38, -22, 28, 38, -12, -12, -62, -32, -62, -30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -30, -6, -10, -6, 14, -30, -6, -10, -10, -6, 14, -6, 14, 14, -28, -4, -8, -4, 16, -28, -4, -8, -8, -4, 16, -4, 16, 16, -34, -10, -14, -10, 10, -34, -10, -14, -14, -10, 10, -10, 10, 10, -28, -4, -8, -4, 16, -28, -4, -8, -8, -4, 16, -4, 16, 16, -170, -50, -70, -50, 50, -102, -30, -42, -30, 30, -170, -50, -70, -50, 50, -102, -30, -42, -30, 30, -102, -30, -42, -30, 30, -170, -50, -70, -50, 50, -238, -70, -98, -70, 70, 34, 10, 14, 10, -10, -170, -50, -70, -50, 50, -170, -50, -70, -50, 50, -170, -50, -70, -50, 50, -238, -70, -98, -70, 70, -34, -10, -14, -10, 10, -238, -70, -98, -70, 70, -102, -30, -136, -40, -34, -10, -85, -25, -17, -5, -102, -30, -136, -40, -34, -10, -34, -10, 0, 0, 68, 20, 0, 0, 68, 20, 68, 20, -68, -20, -34, -10, -136, -40, -85, -25, -153, -45, 34, 10, 68, 20, -68, -20, -34, -10, -102, -30, -102, -30, -136, -40, -34, -10, -136, -40, -170, -50, -102, -30, -170, -50, -102, -30, -102, -30, -170, -50, -238, -70, 34, 10, -170, -50, -170, -50, -170, -50, -238, -70, -34, -10, -238, -70, -10, -10, 0, -6, 0, -22, -22, -15, -27, -12, -6, -24, -15, -27, -10, -10, 0, -6, 0, -22, -22, -22, -22, -40, -52, -40, -52, -52, -22, -16, -34, -25, -37, -22, -16, -34, -34, -40, -52, -40, -52, -52, -20, -20, -30, -24, -30, -8, -8, -15, -3, -18, -24, -6, -15, -3, -26, -26, -36, -30, -36, -20, -20, -30, -24, -30, -10, -10, -10, -10, -8, -8, -14, -14, -8, -8, 10, -2, 10, -2, -2, 10, 22, -26, 10, 10, 10, 22, -14, 22, -2, 4, -14, -5, -17, -2, 4, -14, -14, -20, -32, -20, -32, -32, -8, -14, 4, -5, 7, -26, -32, -8, -14, -2, -2, 4, -14, 4, 10, -2, 10, -2, -2, 10, 22, -26, 10, 10, 10, 22, -14, 22, 10, 30, 10, 30, 30, -20, 40, -10, -20, 30, 30, 80, 50, 80, 30, 10, 30, 10, 10, 25, 25, 45, 5, 20, 10, 40, 25, 45, 70, 70, 120, 90, 120, 10, 10, 45, -15, 60, 90, 0, 45, -15, 10, 30, 10, 30, 30, -20, 40, -10, -20, 30, 30, 80, 50, 80, 30, 10, 30, 10, 10, 30, 10, 30, 10, 10, 100, 0, 120, -20, 100, 0, 120, -20, 120, -20, 70, 60, 90, 75, 95, 70, 60, 90, 90, 100, 120, 100, 120, 120, 70, 70, 120, 90, 120, 10, 10, 45, -15, 60, 90, 0, 45, -15, 70, 70, 120, 90, 120, 10, 10, 10, 10, -80, -140, -80, -140, -140, 10, 40, -50, -5, -65, 10, 40, -50, -50, -80, -140, -80, -140, -140, 40, 20, 40, 20, 20, 70, 10, 60, 70, 20, 20, -30, 0, -30, 20, 40, 20, 40, 40, 25, 25, 5, 45, 30, 40, 10, 25, 5, -20, -20, -70, -40, -70, 40, 40, 5, 65, -10, -40, 50, 5, 65, 10, -10, 10, -10, -10, 40, -20, 30, 40, -10, -10, -60, -30, -60, 40, 20, 40, 20, 20, 70, 10, 60, 70, 20, 20, -30, 0, -30, 10, 30, 10, 30, 30, 10, 30, 10, 30, 30, 20, 40, 20, 40, 40, -10, 10, -10, 10, 10, 20, 40, 20, 40, 40, -50, 50, -30, 30, -50, 50, -30, 30, -30, 30, -50, 50, -70, 70, 10, -10, -50, 50, -50, 50, -50, 50, -70, 70, -10, 10, -70, 70, -30, -40, -10, -25, -5, -30, -40, -10, -10, 0, 20, 0, 20, 20, -20, -10, -40, -25, -45, 10, 20, -20, -10, -30, -30, -40, -10, -40, -50, -30, -50, -30, -30, -50, -70, 10, -50, -50, -50, -70, -10, -70, 30, 30, 80, 50, 80, -30, -30, 5, -55, 20, 50, -40, 5, -55, 30, 30, 80, 50, 80, -30, -30, -30, -30, -120, -180, -120, -180, -180, -30, 0, -90, -45, -105, -30, 0, -90, -90, -120, -180, -120, -180, -180, -20, -20, -70, -40, -70, 40, 40, 5, 65, -10, -40, 50, 5, 65, -50, -50, -100, -70, -100, -20, -20, -70, -40, -70, 30, 30, 30, 30, 40, 40, 10, 10, 40, 40, 130, 70, 130, 70, 70, 130, 190, -50, 130, 130, 130, 190, 10, 190, 70, 100, 10, 55, -5, 70, 100, 10, 10, -20, -80, -20, -80, -80, 40, 10, 100, 55, 115, -50, -80, 40, 10, 70, 70, 100, 10, 100, 130, 70, 130, 70, 70, 130, 190, -50, 130, 130, 130, 190, 10, 190]\n assert candidate(expression = \"3*7-2+5*8-4/2+6\") == []\n assert candidate(expression = \"1*2+3-4*5+6*7-8*9+10\") == [3465, 1785, 441, 1305, -39, 425, 145, 441, -2599, 1505, 161, 65, 161, -1279, 6385, 3305, 841, 2425, -39, 425, 145, 305, 25, 81, -2959, 841, -2959, -5239, 1505, 161, 65, 161, -1279, 2825, 361, 65, -55, 1, -1439, 361, -1439, -2519, 855, 435, 99, 315, -21, 95, 25, 99, -661, 365, 29, 5, 29, -331, 6385, 3305, 841, 2425, -39, 3775, 1955, 499, 1435, -21, -31, -101, -151, -221, 95, 25, -151, -221, -25, -95, 81, -2959, 841, -2959, -5239, -261, -1021, 841, 499, -3415, -5695, -1021, -5695, -3301, 1535, 191, 95, 191, -1249, 2855, 391, 95, -25, 31, -1409, 391, -1409, -2489, 365, 29, 5, 29, -331, 2855, 391, 1685, 229, -121, -241, 5, -241, -115, 31, -1409, 391, -1409, -2489, -131, -491, 391, 229, -1625, -2705, -491, -2705, -1571, 867, 447, 111, 327, -9, 107, 37, 111, -649, 377, 41, 17, 41, -319, 1597, 827, 211, 607, -9, 107, 37, 77, 7, 21, -739, 211, -739, -1309, 377, 41, 17, 41, -319, 707, 91, 17, -13, 1, -359, 91, -359, -629, -885, -465, -129, -345, -9, -125, -55, -129, 631, -395, -59, -35, -59, 301, -873, 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-3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, -3629, -5909, -1235, -5909, -3515, 741, 1311, 741, 1311, 361, 589, 361, 741, 741, -5339, -2945, -1349, -1349, 247, -5339, -2945, 1311, 1311, -1349, 247, -1349, 1311, 1311, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, 57, -703, 247, -703, -1273, -399, 361, -171, 589, 817, 475, 247, 247, 19, -3629, -5909, -1235, -5909, -3515, -1007, -1577, 361, 589, -5567, -3173, -1577, -1577, 19, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, 171, -2869, 931, -2869, -5149, -171, -931, 931, 589, -3325, -5605, -931, -5605, -3211, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -19, 741, -209, 741, 1311, -399, 361, -171, 589, -399, 361, -19, 741, -19, 741, -399, 361, -171, 589, -399, 361, -399, 361, -19, 741, -19, 741, -19, 741, -19, 741, -19, 741, 741, 399, 171, 171, -57, 741, 399, -209, -209, 171, -57, 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321, -395, -59, -35, -59, 301, -383, -47, -23, -47, 313, -395, -59, -35, -59, 301, -395, -59, -35, -59, 301, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, -375, -39, -15, -39, 321, 2545, 361, 1375, 199, 595, 91, 595, 91, -185, -17, 2545, 361, 1375, 199, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, -705, -89, -705, -89, 2545, 361, 1375, 199, 595, 91, 595, 91, -185, -17, 2545, 361, 1375, 199, 2545, 361, 1375, 199, -705, -89, -705, -89, -705, -89, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, -705, -89, -705, -89, 595, 91, -185, -17, 595, 91, 595, 91, -705, -89, -705, -89, -705, -89, -705, -89, -705, -89, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, -245, -365, -119, -365, -239, -15, 15, -15, 15, -35, -23, -35, -15, -15, -335, -209, -125, -125, -41, -335, -209, 15, 15, -125, -41, -125, 15, 15, -245, -365, -119, -365, -239, -107, -137, -35, -23, -347, -221, -137, -137, -53, -245, -365, 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631, 181, 289, 181, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 37, -323, 127, -323, -593, -179, 181, -71, 289, 397, 235, 127, 127, 19, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 91, -1349, 451, -1349, -2429, -71, -431, 451, 289, -1565, -2645, -431, -2645, -1511, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, 1, 361, -89, 361, 631, -179, 181, -71, 289, -179, 181, 1, 361, 1, 361, -179, 181, -71, 289, -179, 181, -179, 181, 1, 361, 1, 361, 1, 361, 1, 361, 1, 361, 361, 199, 91, 91, -17, 361, 199, -89, -89, 91, -17, 91, -89, -89, 361, 199, 91, 91, -17, 361, 199, 361, 199, -89, -89, -89, -89, -89, 91, -17, 91, -89, -89, 91, -17, 91, 91, -89, -89, -89, -89, -89, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 181, 289, 181, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, -1709, -2789, -575, -2789, -1655, -467, -737, 181, 289, -2627, -1493, -737, -737, 19, -1709, -2789, -575, -2789, -1655, -1709, -2789, -575, -2789, -1655, 361, 631, 361, 631, 361, 631, 361, 631, 361, 631, 181, 289, 181, 361, 361, 181, 289, 181, 181, 361, 361, 361, 361, 361, -2519, -1385, -629, -629, 127, -2519, -1385, 631, 631, -629, 127, -629, 631, 631, -2519, -1385, -629, -629, 127, -2519, -1385, -2519, -1385, 631, 631, 631, 631, 631, -629, 127, -629, 631, 631, -629, 127, -629, -629, 631, 631, 631, 631, 631]\n assert candidate(expression = \"10+2*6/3-8\") == []\n assert candidate(expression = \"1*2*3+4*5*6-7*8*9\") == [-19914, -19914, -2874, -17994, -2874, -3786, -3786, -2874, 13254, -17994, -2874, -1866, -2874, 13254, -19914, -19914, -2874, -17994, -2874, -762, -762, -762, -762, -2874, 13254, -2874, 16278, 16278, -17994, -2874, -1866, -2874, 13254, -17994, -2874, 1158, 1158, -2874, 13254, -2874, 16278, 16278, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -762, -762, -762, -762, -588, -588, -732, -732, -588, -588, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -9954, -9954, -1434, -8994, -1434, -1890, -1890, -1434, 6630, -8994, -1434, -930, -1434, 6630, -9954, -9954, -1434, -8994, -1434, -378, -378, -378, -378, -1434, 6630, -1434, 8142, 8142, -8994, -1434, -930, -1434, 6630, -8994, -1434, 582, 582, -1434, 6630, -1434, 8142, 8142, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -12948, -12948, -1872, -11700, -1872, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -258, -258, -258, -258, -84, -84, -228, -228, -84, -84, -378, -378, -378, -378, -84, -84, -204, -204, -228, -228, -84, -84, -348, -348, -84, -84, -204, -204, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -20700, -3312, -31500, -5040, -11700, -1872, -31500, -5040, -22500, -3600, 1710, 1710, 3276, 1980, 3276, 630, 630, 3276, 2196, 1980, 3276, 900, 3276, 2196, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -19914, -19914, -2874, -17994, -2874, -3786, -3786, -2874, 13254, -17994, -2874, -1866, -2874, 13254, -19914, -19914, -2874, -17994, -2874, -762, -762, -762, -762, -2874, 13254, -2874, 16278, 16278, -17994, -2874, -1866, -2874, 13254, -17994, -2874, 1158, 1158, -2874, 13254, -2874, 16278, 16278, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -762, -762, -762, -762, -588, -588, -732, -732, -588, -588, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -9954, -9954, -1434, -8994, -1434, -1890, -1890, -1434, 6630, -8994, -1434, -930, -1434, 6630, -9954, -9954, -1434, -8994, -1434, -378, -378, -378, -378, -1434, 6630, -1434, 8142, 8142, -8994, -1434, -930, -1434, 6630, -8994, -1434, 582, 582, -1434, 6630, -1434, 8142, 8142, -9954, -9954, -1434, -8994, -1434, -1890, -1890, -1434, 6630, -8994, -1434, -930, -1434, 6630, -9954, -9954, -1434, -8994, -1434, -378, -378, -378, -378, -1434, 6630, -1434, 8142, 8142, -8994, -1434, -930, -1434, 6630, -8994, -1434, 582, 582, -1434, 6630, -1434, 8142, 8142, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -34860, -34860, -5040, -31500, -5040, -6636, -6636, -5040, 23184, -31500, -5040, -3276, -5040, 23184, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -24900, -24900, -3600, -22500, -3600, -4740, -4740, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -12948, -12948, -1872, -11700, -1872, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -22908, -22908, -3312, -20700, -3312, -34860, -34860, -5040, -31500, -5040, -12948, -12948, -1872, -11700, -1872, -12948, -12948, -1872, -11700, -1872, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -34860, -34860, -5040, -31500, -5040, -24900, -24900, -3600, -22500, -3600, -24900, -24900, -3600, -22500, -3600, -258, -258, -258, -258, -84, -84, -228, -228, -84, -84, -378, -378, -378, -378, -84, -84, -204, -204, -228, -228, -84, -84, -348, -348, -84, -84, -204, -204, -258, -258, -258, -258, -84, -84, -228, -228, -84, -84, -378, -378, -378, -378, -378, -378, -378, -378, -84, -84, -204, -204, -84, -84, -204, -204, -204, -204, -228, -228, -84, -84, -348, -348, -84, -84, -204, -204, -228, -228, -84, -84, -348, -348, -348, -348, -84, -84, -204, -204, -84, -84, -204, -204, -204, -204, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -5040, 23184, -3600, 16560, -3600, 16560, -3312, -5040, -1872, -5040, -3600, -3312, -5040, -1872, -1872, -5040, -3600, -5040, -3600, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 8568, 8568, 29736, 21096, 29736, 21096, 21096, 19368, 29736, 10728, 29736, 21096, 19368, 29736, 10728, 10728, 29736, 21096, 29736, 21096, 21096, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -20700, -3312, -31500, -5040, -11700, -1872, -31500, -5040, -22500, -3600, 1710, 1710, 3276, 1980, 3276, 630, 630, 3276, 2196, 1980, 3276, 900, 3276, 2196, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -17946, -2826, -1818, -2826, 13302, -17946, -2826, 1206, 1206, -2826, 13302, -2826, 16326, 16326, -31500, -5040, -3276, -5040, 23184, -20700, -3312, -31500, -5040, 1206, 1206, 2772, 1476, 2772, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -8946, -1386, -882, -1386, 6678, -8946, -1386, 630, 630, -1386, 6678, -1386, 8190, 8190, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -31500, -5040, -3276, -5040, 23184, -22500, -3600, -2340, -3600, 16560, -22500, -3600, -2340, -3600, 16560, -20700, -3312, -31500, -5040, -11700, -1872, -31500, -5040, -22500, -3600, -20700, -3312, -31500, -5040, -11700, -1872, -11700, -1872, -31500, -5040, -22500, -3600, -31500, -5040, -22500, -3600, -22500, -3600, 1710, 1710, 3276, 1980, 3276, 630, 630, 3276, 2196, 1980, 3276, 900, 3276, 2196, 1710, 1710, 3276, 1980, 3276, 630, 630, 630, 630, 3276, 2196, 3276, 2196, 2196, 1980, 3276, 900, 3276, 2196, 1980, 3276, 900, 900, 3276, 2196, 3276, 2196, 2196, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -3312, -5040, -1872, -5040, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, -2448, 13680, -2448, 16704, 16704, -5040, 23184, -3312, -5040, 16704, 16704, 29232, 18864, 29232, -1008, 7056, -1008, 8568, 8568, -1008, 7056, -1008, 8568, 8568, -5040, 23184, -3600, 16560, -5040, 23184, -3600, 16560, -3600, 16560, -3312, -5040, -1872, -5040, -3600, -3312, -5040, -1872, -1872, -5040, -3600, -5040, -3600, -3600, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 29736, 21096, 19368, 29736, 10728, 29736, 21096, 17208, 17208, 29736, 19368, 29736, 8568, 8568, 8568, 8568, 29736, 21096, 29736, 21096, 21096, 19368, 29736, 10728, 29736, 21096, 19368, 29736, 10728, 10728, 29736, 21096, 29736, 21096, 21096]\n assert candidate(expression = \"1*2+3*4-5*6+7*8-9*10\") == [8534, 974, 434, 974, -7126, 16004, 1964, 434, -196, 164, -7936, 1964, -7936, -14236, 1646, 134, 26, 134, -1486, 16004, 1964, 9116, 1124, -646, -1276, 26, -1276, -604, 164, -7936, 1964, -7936, -14236, -676, -2296, 1964, 1124, -9016, -15316, -2296, -15316, -8596, 1706, 194, 86, 194, -1426, 3200, 392, 86, -40, 32, -1588, 392, -1588, -2848, -1798, -286, -178, -286, 1334, -1738, -226, -118, -226, 1394, 15008, 1832, 8120, 992, 3200, 392, 4676, 572, -244, -28, -1186, -1816, -514, -1816, -1144, -454, -580, -178, -118, -1732, -1060, -580, -724, -244, 272, -7828, 2072, -7828, -14128, -568, -2188, 2072, 1232, -8908, -15208, -2188, -15208, -8488, 32, -1588, 392, -1588, -2848, -988, 632, -388, 1232, 1832, 992, 392, 572, -28, -9448, -15748, -2728, -15748, -9028, -2128, -3388, 632, 1232, -14908, -8188, -3388, -4828, -28, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 1706, 194, 86, 194, -1426, 3200, 392, 86, -40, 32, -1588, 392, -1588, -2848, -3974, -446, -194, -446, 3334, -7460, -908, -194, 100, -68, 3712, -908, 3712, 6652, -650, -146, -110, -146, 394, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -590, -86, -50, -86, 454, -530, -26, 10, -26, 514, 15008, 1832, 8120, 992, 3200, 392, 4676, 572, -244, -28, 4348, 532, 2052, 252, 3200, 392, -7460, -908, 5824, 712, 904, 112, 904, 112, 904, 112, -4016, -488, -1006, -1636, -334, -1636, -964, -274, -400, 2, 62, -1552, -880, -400, -544, -64, -386, -596, -162, -596, -372, -274, -400, 346, 640, -110, -50, -50, -50, 10, -1552, -880, -400, -544, -64, -512, -288, -400, 640, -656, -176, -176, -176, 304, 272, -7828, 2072, -7828, -14128, -568, -2188, 2072, 1232, -8908, -15208, -2188, -15208, -8488, 32, -1588, 392, -1588, -2848, -988, 632, -388, 1232, 1832, 992, 392, 572, -28, -9448, -15748, -2728, -15748, -9028, -2128, -3388, 632, 1232, -14908, -8188, -3388, -4828, -28, 172, -2528, 772, -2528, -4628, -108, -648, 772, 492, -2888, -4988, -648, -4988, -2748, 32, -1588, 392, -1588, -2848, -68, 3712, -908, 3712, 6652, -848, -308, -248, 292, -248, 292, -248, 292, 352, 892, 1832, 992, 392, 572, -28, 532, 252, 392, -908, 712, 112, 112, 112, -488, -9268, -15568, -2548, -15568, -8848, -1948, -3208, 812, 1412, -14728, -8008, -3208, -4648, 152, -3068, -5168, -828, -5168, -2928, -1948, -3208, 4252, 7192, -308, 292, 292, 292, 892, -14728, -8008, -3208, -4648, 152, -4328, -2088, -3208, 7192, -5768, -968, -968, -968, 3832, 14220, 1620, 720, 1620, -11880, 26670, 3270, 720, -330, 270, -13230, 3270, -13230, -23730, 2740, 220, 40, 220, -2480, 26670, 3270, 15190, 1870, -1080, -2130, 40, -2130, -1010, 270, -13230, 3270, -13230, -23730, -1130, -3830, 3270, 1870, -15030, -25530, -3830, -25530, -14330, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -3000, -480, -300, -480, 2220, -2900, -380, -200, -380, 2320, 25010, 3050, 13530, 1650, 5330, 650, 7790, 950, -410, -50, -1980, -3030, -860, -3030, -1910, -760, -970, -300, -200, -2890, -1770, -970, -1210, -410, 450, -13050, 3450, -13050, -23550, -950, -3650, 3450, 2050, -14850, -25350, -3650, -25350, -14150, 50, -2650, 650, -2650, -4750, -1650, 1050, -650, 2050, 3050, 1650, 650, 950, -50, -15750, -26250, -4550, -26250, -15050, -3550, -5650, 1050, 2050, -24850, -13650, -5650, -8050, -50, 2854, 334, 154, 334, -2366, 5344, 664, 154, -56, 64, -2636, 664, -2636, -4736, 558, 54, 18, 54, -486, 5344, 664, 3048, 384, -206, -416, 18, -416, -192, 64, -2636, 664, -2636, -4736, -216, -756, 664, 384, -2996, -5096, -756, -5096, -2856, 2860, 340, 160, 340, -2360, 5350, 670, 160, -50, 70, -2630, 670, -2630, -4730, 564, 60, 24, 60, -480, 5350, 670, 3054, 390, -200, -410, 24, -410, -186, 70, -2630, 670, -2630, -4730, -210, -750, 670, 390, -2990, -5090, -750, -5090, -2850, 568, 64, 28, 64, -476, 1066, 130, 28, -14, 10, -530, 130, -530, -950, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, 2840, 320, 140, 320, -2380, 5330, 650, 140, -70, 50, -2650, 650, -2650, -4750, -5112, -576, -252, -576, 4284, -9594, -1170, -252, 126, -90, 4770, -1170, 4770, 8550, -8520, -960, -420, -960, 7140, -15990, -1950, -420, 210, -150, 7950, -1950, 7950, 14250, -650, -146, -110, -146, 394, 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-14710, -7990, -3190, -4630, 170, -4310, -2070, -3190, 7210, -5750, -950, -950, -950, 3850, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -15390, -25890, -4190, -25890, -14690, -3190, -5290, 1410, 2410, -24490, -13290, -5290, -7690, 310, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -3050, -5150, -810, -5150, -2910, -2990, -5090, -750, -5090, -2850, -2990, -5090, -750, -5090, -2850, -710, -1130, 5490, 9270, -3190, -5290, 5490, 9270, 9210, 15510, -710, -1130, 5490, 9270, -3190, -5290, -3190, -5290, 5490, 9270, 9210, 15510, 5490, 9270, 9210, 15510, 9210, 15510, -290, 310, 310, 310, 910, -830, 170, 310, 370, 410, 1010, 170, 1010, 1370, -290, 310, 310, 310, 910, -830, 170, -830, 170, 310, 370, 310, 370, 370, 410, 1010, 170, 1010, 1370, 410, 1010, 170, 170, 1010, 1370, 1010, 1370, 1370, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, -14570, -7850, -3050, -4490, 310, -4170, -1930, -3050, 7350, -5610, -810, -810, -810, 3990, -24490, -13290, -5290, -7690, 310, -24490, -13290, -5290, -7690, 310, -4170, -1930, -3690, -1450, -4170, -1930, -3690, -1450, -3690, -1450, -1130, 9270, -5290, 9270, 15510, -1130, 9270, -5290, -5290, 9270, 15510, 9270, 15510, 15510, -5610, -810, -810, -810, 3990, -9930, -1930, -810, -330, -10, 4790, -1930, 4790, 7670, -5610, -810, -810, -810, 3990, -9930, -1930, -9930, -1930, -810, -330, -810, -330, -330, -10, 4790, -1930, 4790, 7670, -10, 4790, -1930, -1930, 4790, 7670, 4790, 7670, 7670]\n assert candidate(expression = \"55+33*2-11/1+44-66\") == []\n assert candidate(expression = \"12*5+3-6/2*4\") == []\n assert candidate(expression = \"2*3-4+5*6-7+8*9-10\") == [-72, 628, -212, 628, 1188, 88, -612, -92, 68, 828, 1388, -612, 908, -532, -64, 76, -92, 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-200, -312, -100, -240, -72, -240, -352, 60, -80, 88, -80, -192, -70, -210, -42, -210, -322, 50, -90, 78, -90, -202, -8, 132, -64, 76, 8, 148, -64, 76, -104, 36, -28, 112, 28, 168, -4, 136, -24, 116, -92, 48, -132, 8, 28, 168, -102, 38, 18, 158, -88, 72, 32, 8, 64, -168, 120, 32, 72, 8, 64, -8, 64, 104, 92, -68, -28, -4, -60, -108, 84, 72, -56, 92, 132, -28, 102, -18, -24, 32, -40, 32, 72, -4, -60, -28, -8, 60, 100, -60, 70, -50, 708, 1268, -732, 788, -652, 76, 188, -156, -212, 788, -652, -292, -76, -580, 1300, 2308, -1292, 1444, -1148, 76, 188, 36, 148, -156, -212, -140, -212, -252, 724, -716, -356, -140, -644, 1444, -1148, -356, -716, -140, -644, 4, -644, -1004, -752, -1312, 688, -832, 608, -120, -232, 112, 168, -832, 608, 248, 32, 536, 856, 1528, -872, 952, -776, -604, -1052, 548, -668, 484, -240, -352, -280, -392, -120, -232, -250, -362, -130, -242, 132, 76, 148, 76, 36, 112, 168, 136, 116, 48, 8, 168, 38, 158, 772, -668, -308, -92, -596, 1492, -1100, -308, -668, -92, -596, 52, -596, -956, -848, 592, 232, 16, 520, 952, -776, -668, 484, -848, -1208, 232, -938, 142, 196, -308, 340, -308, -668, 16, 520, 232, 52, -560, -920, 520, -650, 430, -33, 317, -103, 317, 597, 47, -303, -43, 37, 417, 697, -303, 457, -263, -29, 41, -43, 41, 97, 15, -55, -13, -83, -43, 37, 17, 5, 33, 377, 657, -343, 417, -303, 61, 117, -55, -83, 417, -303, -123, -15, -267, -57, 573, -183, 573, 1077, 87, -543, -75, 69, 753, 1257, -543, 825, -471, -29, 41, -43, 41, 97, -49, 21, -63, 21, 77, 15, -55, -13, -83, 23, -47, -13, -83, -33, -103, -35, 45, 25, 13, 41, -75, 69, 25, 45, 13, 41, 5, 41, 61, 377, 657, -343, 417, -303, 61, 117, -55, -83, 417, -303, -123, -15, -267, 673, 1177, -623, 745, -551, 61, 117, 41, 97, -55, -83, -47, -83, -103, 385, -335, -155, -47, -299, 745, -551, -155, -335, -47, -299, 25, -299, -479, 33, -317, 103, -317, -597, -47, 303, 43, -37, -417, -697, 303, -457, 263, 29, -41, 43, -41, -97, -15, 55, 13, 83, 43, -37, -17, -5, -33, -377, -657, 343, -417, 303, -61, -117, 55, 83, -417, 303, 123, 15, 267, 37, -313, 107, -313, -593, -43, 307, 47, -33, -413, -693, 307, -453, 267, 33, -37, 47, -37, -93, -11, 59, 17, 87, 47, -33, -13, -1, -29, -373, -653, 347, -413, 307, -57, -113, 59, 87, -413, 307, 127, 19, 271, -84, 756, -252, 756, 1428, 108, -732, -108, 84, 996, 1668, -732, 1092, -636, 56, -504, 168, -504, -952, -72, 488, 72, -56, -664, -1112, 488, -728, 424, -21, 189, -63, 189, 357, 27, -183, -27, 21, 249, 417, -183, 273, -159, 21, -189, 63, -189, -357, -27, 183, 27, -21, -249, -417, 183, -273, 159, 49, -441, 147, -441, -833, -63, 427, 63, -49, -581, -973, 427, -637, 371, -61, -131, -47, -131, -187, -101, -171, -87, -171, -227, 59, -11, 73, -11, -67, -71, -141, -57, -141, -197, 49, -21, 63, -21, -77, -27, -97, -13, -97, -153, -47, -117, -33, -117, -173, 29, -41, 43, -41, -97, 33, -37, 47, -37, -93, -71, -141, -57, -141, -197, 49, -21, 63, -21, -77, -17, -87, -3, -87, -143, 19, -51, 33, -51, -107, 43, -27, 57, -27, -83, 0, 70, -56, 14, 16, 86, -56, 14, -96, -26, -20, 50, 36, 106, 4, 74, -16, 54, -84, -14, -124, -54, 36, 106, -94, -24, 26, 96, -1, 69, -29, 41, 7, 77, -29, 41, -49, 21, -15, 55, 13, 83, -11, 59, 17, 87, 4, 74, -16, 54, -5, 65, -11, 59, -15, 55, -77, -7, -117, -47, 43, 113, -87, -17, 33, 103, -43, 27, -63, 7, 13, 83, 17, 87, -87, -17, 33, 103, -33, 37, 3, 73, 27, 97, -88, 72, 32, 8, 64, -168, 120, 32, 72, 8, 64, -8, 64, 104, 92, -68, -28, -4, -60, -108, 84, 72, -56, 92, 132, -28, 102, -18, -24, 32, -40, 32, 72, -4, -60, -28, -8, 60, 100, -60, 70, -50, -47, 33, 13, 1, 29, -87, 57, 13, 33, 1, 29, -7, 29, 49, 47, -33, -13, -1, -29, 43, -37, -17, -5, -33, -108, 84, 72, -56, -27, 21, 27, -21, 63, -49, 77, 117, -43, 87, -33, 43, 63, -13, -17, 87, -33, 33, -3, -27, -16, 40, -32, 40, 80, 4, -52, -20, 0, 68, 108, -52, 78, -42, -15, 13, -23, 13, 33, -1, -29, -5, -33, -20, 0, -11, -5, -1, 61, 101, -59, 71, -49, 27, 47, -29, -33, 71, -49, 17, -19, -43, 718, 1278, -722, 798, -642, 86, 198, -146, -202, 798, -642, -282, -66, -570, 1310, 2318, -1282, 1454, -1138, 86, 198, 46, 158, -146, -202, -130, -202, -242, 734, -706, -346, -130, -634, 1454, -1138, -346, -706, -130, -634, 14, -634, -994, -742, -1302, 698, -822, 618, -110, -222, 122, 178, -822, 618, 258, 42, 546, 866, 1538, -862, 962, -766, -594, -1042, 558, -658, 494, -230, -342, -270, -382, -110, -222, -240, -352, -120, -232, 142, 86, 158, 86, 46, 122, 178, 146, 126, 58, 18, 178, 48, 168, 782, -658, -298, -82, -586, 1502, -1090, -298, -658, -82, -586, 62, -586, -946, -838, 602, 242, 26, 530, 962, -766, -658, 494, -838, -1198, 242, -928, 152, 206, -298, 350, -298, -658, 26, 530, 242, 62, -550, -910, 530, -640, 440, 357, 637, -363, 397, -323, 41, 97, -75, -103, 397, -323, -143, -35, -287, 653, 1157, -643, 725, -571, 41, 97, 21, 77, -75, -103, -67, -103, -123, 365, -355, -175, -67, -319, 725, -571, -175, -355, -67, -319, 5, -319, -499, -377, -657, 343, -417, 303, -61, -117, 55, 83, -417, 303, 123, 15, 267, -373, -653, 347, -413, 307, -57, -113, 59, 87, -413, 307, 127, 19, 271, 866, 1538, -862, 962, -766, -594, -1042, 558, -658, 494, 209, 377, -223, 233, -199, -229, -397, 203, -253, 179, -521, -913, 487, -577, 431, -151, -207, -191, -247, -31, -87, -161, -217, -41, -97, -117, -173, -137, -193, -61, -117, -57, -113, -161, -217, -41, -97, -107, -163, -71, -127, -47, -103, 70, 14, 86, 14, -26, 50, 106, 74, 54, -14, -54, 106, -24, 96, 69, 41, 77, 41, 21, 55, 83, 59, 87, 74, 54, 65, 59, 55, -7, -47, 113, -17, 103, 27, 7, 83, 87, -17, 103, 37, 73, 97, 782, -658, -298, -82, -586, 1502, -1090, -298, -658, -82, -586, 62, -586, -946, -838, 602, 242, 26, 530, 962, -766, -658, 494, -838, -1198, 242, -928, 152, 206, -298, 350, -298, -658, 26, 530, 242, 62, -550, -910, 530, -640, 440, 413, -307, -127, -19, -271, 773, -523, -127, -307, -19, -271, 53, -271, -451, -433, 287, 107, -1, 251, -397, 323, 143, 35, 287, 962, -766, -658, 494, 233, -199, -253, 179, -577, 431, -703, -1063, 377, -793, 287, -397, -577, 107, 143, -793, 287, -307, 17, 233, 134, -370, 278, -370, -730, -46, 458, 170, -10, -622, -982, 458, -712, 368, 125, -127, 197, -127, -307, -1, 251, 35, 287, 170, -10, 89, 35, -1, -559, -919, 521, -649, 431, -253, -433, 251, 287, -649, 431, -163, 161, 377]\n assert candidate(expression = \"9*8-7*6+5*4-3*2\") == [324, -936, -1188, -936, -2448, 1458, -1314, -1188, -2322, -1314, -2826, -1314, -2826, -5094, -216, -396, -432, -396, -612, 1458, -1314, 918, -774, -1512, -2646, -432, -2646, -1566, -1314, -2826, -1314, -2826, -5094, -774, -990, -1314, -774, -3150, -5418, -990, -5418, -3258, -36, 144, 180, 144, 360, -198, 198, 180, 342, 198, 414, 198, 414, 738, -396, -216, -180, -216, 0, -36, 144, 180, 144, 360, 1242, -1242, 702, -702, -198, 198, 522, -522, -198, 198, -1620, -2754, -540, -2754, -1674, 180, 342, -180, 180, -2538, -1458, 342, -1098, 342, -1242, -2754, -1242, -2754, -5022, -702, -918, -1242, -702, -3078, -5346, -918, -5346, -3186, 198, 414, 198, 414, 738, -522, -306, 198, 414, -1242, -702, 198, -522, 198, -3186, -5454, -1026, -5454, -3294, 414, 738, -306, 414, -5022, -2862, 738, -2142, 738, 100, -40, -68, -40, -208, 226, -82, -68, -194, -82, -250, -82, -250, -502, 40, 20, 16, 20, -4, 226, -82, 166, -22, -104, -230, 16, -230, -110, -82, -250, -82, -250, -502, -22, -46, -82, -22, -286, -538, -46, -538, -298, -36, 144, 180, 144, 360, -198, 198, 180, 342, 198, 414, 198, 414, 738, -260, 1040, 1300, 1040, 2600, -1430, 1430, 1300, 2470, 1430, 2990, 1430, 2990, 5330, -316, -296, -292, -296, -272, 44, 64, 68, 64, 88, 20, 40, 44, 40, 64, 44, 64, 68, 64, 88, 380, 400, 404, 400, 424, 1242, -1242, 702, -702, -198, 198, 522, -522, -198, 198, 10, -10, -50, 50, -198, 198, -1430, 1430, 602, -602, -118, 118, -70, 70, -118, 118, -790, 790, -1572, -2706, -492, -2706, -1626, 228, 390, -132, 228, -2490, -1410, 390, -1050, 390, -116, -242, 4, -242, -122, 228, 390, 1684, 2854, -292, 68, 44, 68, 404, -2490, -1410, 390, -1050, 390, -26, 94, 390, 2854, -1210, 230, 134, 230, 1574, -1242, -2754, -1242, -2754, -5022, -702, -918, -1242, -702, -3078, -5346, -918, -5346, -3186, 198, 414, 198, 414, 738, -522, -306, 198, 414, -1242, -702, 198, -522, 198, -3186, -5454, -1026, -5454, -3294, 414, 738, -306, 414, -5022, -2862, 738, -2142, 738, -10, -178, -10, -178, -430, 50, 26, -10, 50, -214, -466, 26, -466, -226, 198, 414, 198, 414, 738, 1430, 2990, 1430, 2990, 5330, -602, -578, 118, 142, 70, 94, 118, 142, 790, 814, -1242, -702, 198, -522, 198, -10, 50, 198, 1430, -602, 118, 70, 118, 790, -3138, -5406, -978, -5406, -3246, 462, 786, -258, 462, -4974, -2814, 786, -2094, 786, -226, -478, 14, -478, -238, 462, 786, 3374, 5714, -578, 142, 94, 142, 814, -4974, -2814, 786, -2094, 786, -46, 194, 786, 5714, -2414, 466, 274, 466, 3154]\n assert candidate(expression = \"7*8-9+2*3-1+4\") == [21, -91, -14, -63, -70, 210, -406, -14, -140, -63, -70, -126, -70, -196, -35, 77, 0, 49, 56, 42, -126, -14, 42, -84, -210, 0, -98, -14, -7, -14, -70, -14, -140, 49, 56, -14, 42, -28, -154, 56, -42, 42, 51, 35, 46, 39, 38, 78, -10, 46, 28, 39, 38, 30, 38, 20, -11, 5, -6, 1, 2, 43, 59, 48, 55, 56, 42, -126, -14, 42, -90, 270, 10, -30, -98, 294, -54, -180, 30, -68, 16, 36, 18, -6, 48, -68, 16, 130, -20, 142, -31, -38, -94, -38, -164, 25, 32, -38, 18, -52, -178, 32, -66, 18, 47, 46, 38, 46, 28, 1, 2, 55, 56, -38, 18, 94, -6, 102, -46, -172, 38, -60, 24, 44, 26, 2, 56, -60, 24, 138, -12, 150]\n assert candidate(expression = \"20+19-18*17/16+15\") == []\n assert candidate(expression = \"20*3+5-4*7+6-8*1\") == [-240, -240, -240, -240, -240, -360, -360, -720, -360, -240, -240, -360, -720, -360, 160, 160, 160, 160, 160, -440, -440, 160, 160, -1040, -680, 160, -440, 160, -240, -240, -360, -720, -360, 160, 160, -440, 160, -1040, -680, 160, -440, 160, -240, -240, -240, -240, -240, -360, -360, -720, -360, -240, -240, -360, -720, -360, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, -440, -440, 160, 160, -440, -440, 520, 520, 520, 520, -1040, -680, 160, -440, 160, -1040, -680, 880, 880, -440, 160, -440, 520, 520, -240, -240, -360, -720, -360, 160, 160, -440, 160, -1040, -680, 160, -440, 160, -240, -240, -360, -720, -360, 400, 400, 400, 400, -440, 160, -440, 520, 520, -1040, -680, 160, -440, 160, -1040, -680, 880, 880, -440, 160, -440, 520, 520, 45, 45, 45, 45, 45, 39, 39, 21, 39, 45, 45, 39, 21, 39, 65, 65, 65, 65, 65, 35, 35, 65, 65, 5, 23, 65, 35, 65, 45, 45, 39, 21, 39, 65, 65, 35, 65, 5, 23, 65, 35, 65, 140, 140, 140, 140, 140, 134, 134, 116, 134, 140, 140, 134, 116, 134, 45, 45, 45, 45, 45, 39, 39, 21, 39, 45, 45, 39, 21, 39, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 305, 305, 305, 305, 305, 780, 780, 780, 780, 780, 305, 305, 305, 305, 305, -402, -402, 198, 198, -402, -402, 558, 558, 558, 558, 35, 35, 65, 65, 130, 130, 35, 35, 558, 558, 558, 558, 425, 425, 1090, 1090, 425, 425, -888, -528, 312, -288, 312, -888, -528, 1032, 1032, -288, 312, -288, 672, 672, 5, 23, 65, 35, 65, 100, 118, 5, 23, 1032, 1032, 785, 2020, 785, -402, 198, -402, 558, 558, 35, 65, 130, 35, 558, 558, 425, 1090, 425, -240, -240, -360, -720, -360, 160, 160, -440, 160, -1040, -680, 160, -440, 160, -240, -240, -360, -720, -360, 400, 400, 400, 400, -440, 160, -440, 520, 520, -1040, -680, 160, -440, 160, -1040, -680, 880, 880, -440, 160, -440, 520, 520, 45, 45, 39, 21, 39, 65, 65, 35, 65, 5, 23, 65, 35, 65, 140, 140, 134, 116, 134, 45, 45, 39, 21, 39, 400, 400, 400, 400, 305, 305, 780, 780, 305, 305, -402, 198, -402, 558, 558, 35, 65, 130, 35, 558, 558, 425, 1090, 425, -888, -528, 312, -288, 312, -888, -528, 1032, 1032, -288, 312, -288, 672, 672, 5, 23, 65, 35, 65, 100, 118, 5, 23, 1032, 1032, 785, 2020, 785, -402, 198, -402, 558, 558, 35, 65, 130, 35, 558, 558, 425, 1090, 425]\n assert candidate(expression = \"7-2*3+1*4-5\") == [3, 3, 15, 3, -15, 2, 2, 15, 14, -2, -20, 2, -20, -16, 10, 10, -20, 10, 55, 0, 0, 14, 14, 1, 0, -20, -2, -16, -12, -30, -8, -30, -26, 30, 75, 0, 14, -9, -5, 75, 3, 59]\n assert candidate(expression = \"9+8*7-6+5*4-3+2*1\") == [57, 57, -103, 57, -103, -103, -103, -39, -135, 57, -103, -103, -39, -135, 153, 153, -199, 153, -199, -103, -103, -247, -247, -39, -135, -39, -135, -279, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, -23, 137, -23, 137, 137, 137, 73, 169, -23, 137, 137, 73, 169, 41, 41, -87, 41, -87, -39, -39, 153, -39, 153, -183, -183, -327, -327, 137, 137, -159, -159, 161, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, 137, 137, 73, 169, 41, -87, -39, 153, -183, -327, 137, -159, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 64, 64, 44, 64, 44, 44, 44, 52, 40, 64, 44, 44, 52, 40, 76, 76, 32, 76, 32, 44, 44, 26, 26, 52, 40, 52, 40, 22, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 12, 12, 32, 12, 32, 32, 32, 24, 36, 12, 32, 32, 24, 36, 54, 54, 74, 54, 74, 74, 74, 66, 78, 54, 74, 74, 66, 78, 41, 41, -87, 41, -87, -39, -39, 153, -39, 153, -36, -36, 144, -36, 144, -4, -4, 48, -4, 48, -46, -46, 174, -46, 174, -148, -148, -292, -292, 172, 172, -124, -124, 196, 196, 34, 34, 16, 16, 32, 32, 74, 74, -124, -124, 196, 196, 184, 184, 56, 56, 224, 224, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, 137, 137, 73, 169, 41, -87, -39, 153, -183, -327, 137, -159, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 41, -87, -39, 153, -36, 144, -4, 48, -46, 174, -148, -292, 172, -124, 196, 34, 16, 32, 74, -124, 196, 184, 56, 224, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, 102, 102, -238, 102, -238, -238, -238, -102, -306, 102, -238, -238, -102, -306, 306, 306, -442, 306, -442, -238, -238, -544, -544, -102, -306, -102, -306, -612, 102, -238, -238, -102, -306, 306, -442, -238, -544, -102, -306, -102, -306, -612, -68, -68, 272, -68, 272, 272, 272, 136, 340, -68, 272, 272, 136, 340, 68, 68, -204, 68, -204, -102, -102, 306, -102, 306, -408, -408, -714, -714, 272, 272, -357, -357, 323, 323, -34, -238, -34, -238, -544, 136, 340, -34, 136, -340, -646, 340, -289, 391, 102, -238, -238, -102, -306, 306, -442, -238, -544, -102, -306, -102, -306, -612, -68, 272, 272, 136, 340, 68, -204, -102, 306, -408, -714, 272, -357, 323, -34, -238, -34, -238, -544, 136, 340, -34, 136, -340, -646, 340, -289, 391, 64, 64, 44, 64, 44, 44, 44, 52, 40, 64, 44, 44, 52, 40, 76, 76, 32, 76, 32, 44, 44, 26, 26, 52, 40, 52, 40, 22, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 118, 118, 98, 118, 98, 98, 98, 106, 94, 118, 98, 98, 106, 94, 130, 130, 86, 130, 86, 98, 98, 80, 80, 106, 94, 106, 94, 76, 118, 98, 98, 106, 94, 130, 86, 98, 80, 106, 94, 106, 94, 76, 12, 12, 32, 12, 32, 32, 32, 24, 36, 12, 32, 32, 24, 36, 54, 54, 74, 54, 74, 74, 74, 66, 78, 54, 74, 74, 66, 78, 12, 12, 32, 12, 32, 32, 32, 24, 36, 12, 32, 32, 24, 36, 54, 54, 74, 54, 74, 74, 74, 66, 78, 54, 74, 74, 66, 78, 108, 108, 128, 108, 128, 128, 128, 120, 132, 108, 128, 128, 120, 132, 23, 23, -69, 23, -69, -57, -57, 171, -57, 171, -54, -54, 162, -54, 162, -22, -22, 66, -22, 66, -64, -64, 192, -64, 192, 68, 68, -204, 68, -204, -102, -102, 306, -102, 306, -54, -54, 162, -54, 162, -108, -108, 324, -108, 324, -22, -22, 66, -22, 66, -64, -64, 192, -64, 192, -22, -22, 66, -22, 66, -64, -64, 192, -64, 192, -118, -118, 354, -118, 354, -148, -148, -292, -292, 172, 172, -124, -124, 196, 196, 34, 34, 16, 16, 32, 32, 74, 74, -124, -124, 196, 196, 184, 184, 56, 56, 224, 224, -328, -328, -634, -634, 352, 352, -277, -277, 403, 403, 34, 34, 16, 16, 88, 88, 70, 70, 32, 32, 74, 74, 32, 32, 74, 74, 128, 128, -97, -97, 223, 223, 211, 211, 83, 83, 251, 251, -277, -277, 403, 403, 211, 211, 427, 427, 83, 83, 251, 251, 83, 83, 251, 251, 467, 467, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -66, -270, -66, -270, -576, 104, 308, -66, 104, -372, -678, 308, -321, 359, 56, 44, 56, 44, 26, 110, 98, 110, 98, 80, 24, 36, 66, 78, 24, 36, 66, 78, 120, 132, -21, 59, 56, 24, 66, -66, 104, 56, 110, 24, 66, 24, 66, 120, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -324, -630, 356, -273, 407, 38, 20, 92, 74, 36, 78, 36, 78, 132, -93, 227, 215, 87, 255, -273, 407, 215, 431, 87, 255, 87, 255, 471, 57, -103, -103, -39, -135, 153, -199, -103, -247, -39, -135, -39, -135, -279, -23, 137, 137, 73, 169, 41, -87, -39, 153, -183, -327, 137, -159, 161, -7, -103, -7, -103, -247, 73, 169, -7, 73, -151, -295, 169, -127, 193, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 41, -87, -39, 153, -36, 144, -4, 48, -46, 174, -148, -292, 172, -124, 196, 34, 16, 32, 74, -124, 196, 184, 56, 224, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, 102, -238, -238, -102, -306, 306, -442, -238, -544, -102, -306, -102, -306, -612, -68, 272, 272, 136, 340, 68, -204, -102, 306, -408, -714, 272, -357, 323, -34, -238, -34, -238, -544, 136, 340, -34, 136, -340, -646, 340, -289, 391, 64, 44, 44, 52, 40, 76, 32, 44, 26, 52, 40, 52, 40, 22, 118, 98, 98, 106, 94, 130, 86, 98, 80, 106, 94, 106, 94, 76, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 12, 32, 32, 24, 36, 54, 74, 74, 66, 78, 108, 128, 128, 120, 132, 23, -69, -57, 171, -54, 162, -22, 66, -64, 192, 68, -204, -102, 306, -54, 162, -108, 324, -22, 66, -64, 192, -22, 66, -64, 192, -118, 354, -148, -292, 172, -124, 196, 34, 16, 32, 74, -124, 196, 184, 56, 224, -328, -634, 352, -277, 403, 34, 16, 88, 70, 32, 74, 32, 74, 128, -97, 223, 211, 83, 251, -277, 403, 211, 427, 83, 251, 83, 251, 467, -21, -117, -21, -117, -261, 59, 155, -21, 59, -165, -309, 155, -141, 179, 56, 44, 56, 44, 26, 24, 36, 66, 78, -21, 59, 56, 24, 66, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -66, -270, -66, -270, -576, 104, 308, -66, 104, -372, -678, 308, -321, 359, 56, 44, 56, 44, 26, 110, 98, 110, 98, 80, 24, 36, 66, 78, 24, 36, 66, 78, 120, 132, -21, 59, 56, 24, 66, -66, 104, 56, 110, 24, 66, 24, 66, 120, -144, -288, 176, -120, 200, 38, 20, 36, 78, -120, 200, 188, 60, 228, -324, -630, 356, -273, 407, 38, 20, 92, 74, 36, 78, 36, 78, 132, -93, 227, 215, 87, 255, -273, 407, 215, 431, 87, 255, 87, 255, 471]\n assert candidate(expression = \"7*6-5*4+3*2-1*0\") == [-308, -98, -308, -98, -98, -448, 42, -308, -448, 42, 42, 42, 42, 42, -140, -98, -140, -98, -98, -448, 42, -280, 42, -308, -448, -140, -448, -280, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 70, 28, 70, 28, 28, 98, 0, 70, 98, 0, 0, 0, 0, 0, -56, -98, -56, -98, -98, 70, 28, 70, 28, 28, -406, 0, -238, 0, 98, 0, -154, 0, 98, 0, -308, -448, -140, -448, -280, 70, 98, -56, 70, -406, -238, 98, -154, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 22, -8, 22, 22, -28, 42, -8, -28, 42, 42, 42, 42, 42, 16, 22, 16, 22, 22, -28, 42, -4, 42, -8, -28, 16, -28, -4, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 70, 28, 70, 28, 28, 98, 0, 70, 98, 0, 0, 0, 0, 0, 370, 148, 370, 148, 148, 518, 0, 370, 518, 0, 0, 0, 0, 0, -92, -98, -92, -98, -98, 34, 28, 34, 28, 28, 28, 22, 28, 22, 22, 34, 28, 34, 28, 28, 154, 148, 154, 148, 148, -406, 0, -238, 0, 98, 0, -154, 0, 98, 0, 14, 0, 38, 0, 98, 0, 518, 0, -190, 0, 62, 0, 50, 0, 62, 0, 302, 0, -308, -448, -140, -448, -280, 70, 98, -56, 70, -406, -238, 98, -154, 98, -8, -28, 16, -28, -4, 70, 98, 370, 518, -92, 34, 28, 34, 154, -406, -238, 98, -154, 98, 14, 38, 98, 518, -190, 62, 50, 62, 302, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(expression = \"11+11*11-11*11+11*11-11*11\") == [145211, -1199, -1199, -1199, -147609, 292952, 132, -1199, -14509, -14509, -160919, 132, -160919, -307329, 12111, -1199, -1199, -1199, -14509, 292952, 132, 159852, 132, -14509, -27819, -1199, -27819, -14509, -14509, -160919, 132, -160919, -307329, -14509, -27819, 132, 132, -174229, -320639, -27819, -320639, -174229, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -14509, -1199, -1199, -1199, 12111, -13299, 11, 11, 11, 13321, 279521, 11, 146421, 11, 11, 11, 119801, 11, -13299, 11, -17171, -30481, -3861, -30481, -17171, -1320, -1320, -1199, 11, -29271, -15961, -1320, -13299, 11, -13299, -159709, 1342, -159709, -306119, -13299, -26609, 1342, 1342, -173019, -319429, -26609, -319429, -173019, 11, 11, 11, 11, 11, -13299, 11, 11, 13321, 11, 11, 11, 11, 11, -175681, -322091, -29271, -322091, -175681, -1320, -1320, 11, 13321, -308781, -162371, -1320, -133089, 13321, 13321, 11, 11, 11, -13299, 26752, 132, 11, -1199, -1199, -14509, 132, -14509, -27819, 1221, 11, 11, 11, -1199, 26752, 132, 14652, 132, -1199, -2409, 11, -2409, -1199, -1199, -14509, 132, -14509, -27819, -1199, -2409, 132, 132, -15719, -29029, -2409, -29029, -15719, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -131879, 1221, 1221, 1221, 134321, -266189, 11, 1221, 13321, 13321, 146421, 11, 146421, 279521, -2409, -1199, -1199, -1199, 11, -1199, 11, 11, 11, 1221, -1199, 11, 11, 11, 1221, -1199, 11, 11, 11, 1221, 11, 1221, 1221, 1221, 2431, 279521, 11, 146421, 11, 11, 11, 119801, 11, -13299, 11, 13321, 11, 1221, 11, 11, 11, -266189, 11, 131901, 11, -1199, 11, -1199, 11, -1199, 11, -134299, 11, -15961, -29271, -2651, -29271, -15961, -110, -110, 11, 1221, -28061, -14751, -110, -12089, 1221, -1441, -2651, -231, -2651, -1441, -110, -110, 14410, 26510, -1199, 11, 11, 11, 1221, -28061, -14751, -110, -12089, 1221, -1441, -231, -110, 26510, -13299, 11, 11, 11, 13321, -13299, -159709, 1342, -159709, -306119, -13299, -26609, 1342, 1342, -173019, -319429, -26609, -319429, -173019, 11, 11, 11, 11, 11, -13299, 11, 11, 13321, 11, 11, 11, 11, 11, -175681, -322091, -29271, -322091, -175681, -1320, -1320, 11, 13321, -308781, -162371, -1320, -133089, 13321, 11, -13299, 1342, -13299, -26609, 11, -1199, 1342, 1342, -14509, -27819, -1199, -27819, -14509, 11, 11, 11, 11, 11, 13321, 146421, 11, 146421, 279521, -13299, -12089, 11, 1221, 11, 1221, 11, 1221, 13321, 14531, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -174471, -320881, -28061, -320881, -174471, -110, -110, 1221, 14531, -307571, -161161, -110, -131879, 14531, -14751, -28061, -1441, -28061, -14751, -110, -110, 159610, 292710, -12089, 1221, 1221, 1221, 14531, -307571, -161161, -110, -131879, 14531, -14751, -1441, -110, 292710, -145189, 1221, 1221, 1221, 147631, 290400, -2420, -2420, -2420, -295240, 585882, 242, -2420, -29040, -29040, -321860, 242, -321860, -614680, 24200, -2420, -2420, -2420, -29040, 585882, 242, 319682, 242, -29040, -55660, -2420, -55660, -29040, -29040, -321860, 242, -321860, -614680, -29040, -55660, 242, 242, -348480, -641300, -55660, -641300, -348480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29040, -2420, -2420, -2420, 24200, -26620, 0, 0, 0, 26620, 559020, 0, 292820, 0, 0, 0, 239580, 0, -26620, 0, -34364, -60984, -7744, -60984, -34364, -2662, -2662, -2420, 0, -58564, -31944, -2662, -26620, 0, -26620, -319440, 2662, -319440, -612260, -26620, -53240, 2662, 2662, -346060, -638880, -53240, -638880, -346060, 0, 0, 0, 0, 0, -26620, 0, 0, 26620, 0, 0, 0, 0, 0, -351384, -644204, -58564, -644204, -351384, -2662, -2662, 0, 26620, -617584, -324764, -2662, -266200, 26620, 13321, 11, 11, 11, -13299, 26752, 132, 11, -1199, -1199, -14509, 132, -14509, -27819, 1221, 11, 11, 11, -1199, 26752, 132, 14652, 132, -1199, -2409, 11, -2409, -1199, -1199, -14509, 132, -14509, -27819, -1199, -2409, 132, 132, -15719, -29029, -2409, -29029, -15719, 13431, 121, 121, 121, -13189, 26862, 242, 121, -1089, -1089, -14399, 242, -14399, -27709, 1331, 121, 121, 121, -1089, 26862, 242, 14762, 242, -1089, -2299, 121, -2299, -1089, -1089, -14399, 242, -14399, -27709, -1089, -2299, 242, 242, -15609, -28919, -2299, -28919, -15609, -13189, 121, 121, 121, 13431, -26620, 0, 121, 1331, 1331, 14641, 0, 14641, 27951, -145079, 1331, 1331, 1331, 147741, -292820, 0, 1331, 14641, 14641, 161051, 0, 161051, 307461, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -145079, 1331, 1331, 1331, 147741, -292820, 0, 1331, 14641, 14641, 161051, 0, 161051, 307461, -276969, 2541, 2541, 2541, 282051, -559020, 0, 2541, 27951, 27951, 307461, 0, 307461, 586971, -2409, -1199, -1199, -1199, 11, -1199, 11, 11, 11, 1221, -1199, 11, 11, 11, 1221, -1199, 11, 11, 11, 1221, 11, 1221, 1221, 1221, 2431, -3630, -2420, -2420, -2420, -1210, -1210, 0, 0, 0, 1210, -1199, 11, 11, 11, 1221, -1089, 121, 121, 121, 1331, -1089, 121, 121, 121, 1331, 121, 1331, 1331, 1331, 2541, -1210, 0, 0, 0, 1210, 121, 1331, 1331, 1331, 2541, 1331, 2541, 2541, 2541, 3751, 278300, 0, 145200, 0, -1210, 0, 118580, 0, -14520, 0, 12100, 0, 0, 0, -1210, 0, -267410, 0, 130680, 0, -2420, 0, -2420, 0, -2420, 0, -135520, 0, 559020, 0, 292820, 0, 0, 0, 239580, 0, -26620, 0, 12100, 0, 0, 0, 0, 0, -12100, 0, -26620, 0, -292820, 0, 0, 0, -292820, 0, -559020, 0, 130680, 0, -2420, 0, -2420, 0, -2420, 0, -135520, 0, 264990, 0, -1210, 0, -2420, 0, -14520, 0, -14520, 0, -147620, 0, -1210, 0, -147620, 0, -280720, 0, -15961, -29271, -2651, -29271, -15961, -110, -110, 11, 1221, -28061, -14751, -110, -12089, 1221, -1441, -2651, -231, -2651, -1441, -110, -110, 14410, 26510, -1199, 11, 11, 11, 1221, -28061, -14751, -110, -12089, 1221, -1441, -231, -110, 26510, -13299, 11, 11, 11, 13321, -31823, -58443, -5203, -58443, -31823, -121, -121, 121, 2541, -56023, -29403, -121, -24079, 2541, -1441, -2651, -231, -2651, -1441, -1331, -2541, -121, -2541, -1331, 1331, 2541, 15851, 29161, -121, -121, 15851, 29161, 30371, 55781, -1199, 11, 11, 11, 1221, -2420, 0, 11, 121, 121, 1331, 0, 1331, 2541, -27951, -14641, 0, -11979, 1331, -1331, -121, 0, 26620, -13189, 121, 121, 121, 13431, -56023, -29403, -121, -24079, 2541, -1331, -121, -121, 1089, 2541, 29161, -121, 29161, 55781, -13189, 121, 121, 121, 13431, -26620, 0, 121, 1331, 1331, 14641, 0, 14641, 27951, -13189, -159599, 1452, -159599, -306009, -13189, -26499, 1452, 1452, -172909, -319319, -26499, -319319, -172909, 121, 121, 121, 121, 121, -13189, 121, 121, 13431, 121, 121, 121, 121, 121, -175571, -321981, -29161, -321981, -175571, -1210, -1210, 121, 13431, -308671, -162261, -1210, -132979, 13431, 121, -13189, 1452, -13189, -26499, 121, -1089, 1452, 1452, -14399, -27709, -1089, -27709, -14399, 121, 121, 121, 121, 121, 13431, 146531, 121, 146531, 279631, -13189, -11979, 121, 1331, 121, 1331, 121, 1331, 13431, 14641, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, -174361, -320771, -27951, -320771, -174361, 0, 0, 1331, 14641, -307461, -161051, 0, -131769, 14641, -14641, -27951, -1331, -27951, -14641, 0, 0, 159720, 292820, -11979, 1331, 1331, 1331, 14641, -307461, -161051, 0, -131769, 14641, -14641, -1331, 0, 292820, -145079, 1331, 1331, 1331, 147741, -26620, -319440, 2662, -319440, -612260, -26620, -53240, 2662, 2662, -346060, -638880, -53240, -638880, -346060, 0, 0, 0, 0, 0, -26620, 0, 0, 26620, 0, 0, 0, 0, 0, -351384, -644204, -58564, -644204, -351384, -2662, -2662, 0, 26620, -617584, -324764, -2662, -266200, 26620, 121, -13189, 1452, -13189, -26499, 121, -1089, 1452, 1452, -14399, -27709, -1089, -27709, -14399, 1331, -11979, 2662, -11979, -25289, 1331, 121, 2662, 2662, -13189, -26499, 121, -26499, -13189, 1331, 14641, 0, 14641, 27951, 14641, 161051, 0, 161051, 307461, 0, 0, 0, 0, 0, 14641, 161051, 0, 161051, 307461, 27951, 307461, 0, 307461, 586971, -13189, -11979, 121, 1331, 121, 1331, 121, 1331, 13431, 14641, -26620, -25410, 0, 1210, 121, 1331, 1331, 2541, 1331, 2541, 14641, 15851, 0, 1210, 14641, 15851, 27951, 29161, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -174361, -320771, -27951, -320771, -174361, 0, 0, 1331, 14641, -307461, -161051, 0, -131769, 14641, -14641, -27951, -1331, -27951, -14641, 0, 0, 159720, 292820, -11979, 1331, 1331, 1331, 14641, -307461, -161051, 0, -131769, 14641, -14641, -1331, 0, 292820, -145079, 1331, 1331, 1331, 147741, -348843, -641663, -56023, -641663, -348843, -121, -121, 2541, 29161, -615043, -322223, -121, -263659, 29161, -14641, -27951, -1331, -27951, -14641, -13431, -26741, -121, -26741, -13431, 15851, 29161, 175571, 321981, -121, -121, 175571, 321981, 335291, 614801, -11979, 1331, 1331, 1331, 14641, -25410, 1210, 1331, 2541, 2541, 15851, 1210, 15851, 29161, -306251, -159841, 1210, -130559, 15851, -13431, -121, 1210, 294030, -143869, 2541, 2541, 2541, 148951, -615043, -322223, -121, -263659, 29161, -13431, -121, -121, 13189, 29161, 321981, -121, 321981, 614801, -143869, 2541, 2541, 2541, 148951, -291610, 1210, 2541, 15851, 15851, 162261, 1210, 162261, 308671]\n assert candidate(expression = \"99-98+97-96+95-94\") == [1, 1, -1, 189, -1, 1, 1, -1, -1, 189, -1, 189, -1, -1, 1, 1, 3, -187, 3, -193, -193, 1, 1, 1, 1, 3, -191, 3, 1, -189, 1, -189, -189, -187, 3, -381, -187, 1, 1, 3, -191, 3]\n assert candidate(expression = \"1*1*1*1*1*1*1*1*1*1\") == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(expression = \"11+12*13-14/7+15\") == []\n assert candidate(expression = \"9*8*7-6*5+4*3-2*1\") == [-3384, -3384, -5976, -3384, -5976, -3384, -3384, -5976, -10296, -3384, -5976, -3384, -5976, -10296, -1944, -1944, -2376, -1944, -2376, -3384, -3384, -1944, -1944, -6696, -11016, -2376, -11016, -6696, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 648, 1080, 648, 1080, 648, 648, 1080, 1800, 648, 1080, 648, 1080, 1800, -1368, -1368, -936, -1368, -936, 648, 648, 1080, 648, 1080, -3384, -3384, -1944, -1944, 648, 648, -1368, -1368, 648, 648, -6984, -11304, -2664, 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-10154, -5834, 1942, -4106, 1942, 400, 340, 460, 340, 400, 400, 340, 460, 340, 400, 1222, 1942, 7648, 12148, 1222, 1942, 8464, 13444, 8464, 13444, -1646, 370, 244, 370, 2260, -1646, 370, 484, 484, 370, 2260, 370, 2500, 2500, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -10154, -5834, 1942, -4106, 1942, 1348, 1408, 1348, 1408, 1942, 12148, 1942, 13444, 13444, -4958, 1090, 712, 1090, 6760, -4958, 1090, 1432, 1432, 1090, 6760, 1090, 7480, 7480, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 18, -306, 18, -306, -846, 198, 144, 18, 198, -396, -936, 144, -936, -396, 648, 1080, 648, 1080, 1800, 4050, 6750, 4050, 6750, 11250, -1620, -1566, 396, 450, 270, 324, 396, 450, 2286, 2340, -3384, -1944, 648, -1368, 648, 18, 198, 648, 4050, -1620, 396, 270, 396, 2286, -6858, -11178, -2538, -11178, -6858, 1206, 1926, -810, 1206, -10170, -5850, 1926, -4122, 1926, -432, -972, 108, -972, -432, 1206, 1926, 7632, 12132, -1566, 450, 324, 450, 2340, -10170, -5850, 1926, -4122, 1926, 36, 576, 1926, 12132, -4878, 1170, 792, 1170, 6840, -3384, -5976, -3384, -5976, -10296, -1944, -2376, -3384, -1944, -6696, -11016, -2376, -11016, -6696, 648, 1080, 648, 1080, 1800, -1368, -936, 648, 1080, -3384, -1944, 648, -1368, 648, -6984, -11304, -2664, -11304, -6984, 1080, 1800, -936, 1080, -10296, -5976, 1800, -4248, 1800, 450, 414, 450, 414, 354, 470, 464, 450, 470, 404, 344, 464, 344, 404, 450, 414, 450, 414, 354, 470, 464, 450, 470, 404, 344, 464, 344, 404, 648, 1080, 648, 1080, 1800, 4050, 6750, 4050, 6750, 11250, 648, 1080, 648, 1080, 1800, 4482, 7470, 4482, 7470, 12450, 4482, 7470, 4482, 7470, 12450, -1652, -1646, 364, 370, 238, 244, 364, 370, 2254, 2260, -1652, -1646, 364, 370, 478, 484, 478, 484, 364, 370, 2254, 2260, 364, 370, 2494, 2500, 2494, 2500, -3384, -1944, 648, -1368, 648, 18, 198, 648, 4050, -1620, 396, 270, 396, 2286, -3384, -1944, 648, -1368, 648, 450, 470, 450, 470, 648, 4050, 648, 4482, 4482, -1652, 364, 238, 364, 2254, -1652, 364, 478, 478, 364, 2254, 364, 2494, 2494, -6842, -11162, -2522, -11162, -6842, 1222, 1942, -794, 1222, -10154, -5834, 1942, -4106, 1942, -416, -956, 124, -956, -416, 1222, 1942, 7648, 12148, -1550, 466, 340, 466, 2356, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -6842, -11162, -2522, -11162, -6842, 1222, 1942, -794, 1222, -10154, -5834, 1942, -4106, 1942, 400, 340, 460, 340, 400, 400, 340, 460, 340, 400, 1222, 1942, 7648, 12148, 1222, 1942, 8464, 13444, 8464, 13444, -1646, 370, 244, 370, 2260, -1646, 370, 484, 484, 370, 2260, 370, 2500, 2500, -10154, -5834, 1942, -4106, 1942, 52, 592, 1942, 12148, -4862, 1186, 808, 1186, 6856, -10154, -5834, 1942, -4106, 1942, 1348, 1408, 1348, 1408, 1942, 12148, 1942, 13444, 13444, -4958, 1090, 712, 1090, 6760, -4958, 1090, 1432, 1432, 1090, 6760, 1090, 7480, 7480]\n assert candidate(expression = \"6*3+4-2*5/1+7\") == []\n assert candidate(expression = \"1*2*3*4*5-6*7+8\") == [-2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -60, 20, -60, 20, -360, 1260, -360, 1620, 1620, -872, -152, -116, -152, 604, -872, -152, 52, 52, -152, 604, -152, 772, 772, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, -360, 1260, -360, 1620, 1620, -360, 1260, -360, -360, 1710, 1710, 1710, 1710, 1710, -880, -160, -124, -160, 596, -880, -160, 44, 44, -160, 596, -160, 764, 764, -880, -160, -124, -160, 596, -880, -160, -880, -160, 86, 86, 86, 86, 86, -160, 596, -160, 764, 764, -160, 596, -160, -160, 806, 806, 806, 806, 806, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -60, 20, -60, 20, -360, 1260, -360, 1620, 1620, -872, -152, -116, -152, 604, -872, -152, 52, 52, -152, 604, -152, 772, 772, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -420, -180, -360, 1260, -840, -120, -84, -120, 636, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, -2040, -1080, -360, -696, 24, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, 30, 70, -360, 1260, -360, 1620, 1620, -360, 1260, -360, -360, 1710, 1710, 1710, 1710, 1710, -360, 1260, -360, 1620, 1620, -360, 1260, -360, 1260, -360, -360, -360, -360, -360, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, 1710, -880, -160, -124, -160, 596, -880, -160, 44, 44, -160, 596, -160, 764, 764, -880, -160, -124, -160, 596, -880, -160, -880, -160, 86, 86, 86, 86, 86, -160, 596, -160, 764, 764, -160, 596, -160, -160, 806, 806, 806, 806, 806, -880, -160, -124, -160, 596, -880, -160, 44, 44, -160, 596, -160, 764, 764, -880, -160, -124, -160, 596, -880, -160, -124, -160, 596, -880, -160, -880, -160, -880, -160, -880, -160, -880, -160, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, 86, -160, 596, -160, 764, 764, -160, 596, -160, -160, 806, 806, 806, 806, 806, -160, 596, -160, 764, 764, -160, 596, -160, 596, -160, -160, -160, -160, -160, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806, 806]\n assert candidate(expression = \"3+3*3-3*3+3*3-3*3\") == [147, -15, -15, -15, -177, 336, 12, -15, -69, -69, -231, 12, -231, -393, 39, -15, -15, -15, -69, 336, 12, 228, 12, -69, -123, -15, -123, -69, -69, -231, 12, -231, -393, -69, -123, 12, 12, -285, -447, -123, -447, -285, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -69, -15, -15, -15, 39, -51, 3, 3, 3, 57, 273, 3, 165, 3, 3, 3, 57, 3, -51, 3, -123, -177, -69, -177, -123, -24, -24, -15, 3, -159, -105, -24, -51, 3, -51, -213, 30, -213, -375, -51, -105, 30, 30, -267, -429, -105, -429, -267, 3, 3, 3, 3, 3, -51, 3, 3, 57, 3, 3, 3, 3, 3, -321, -483, -159, -483, -321, -24, -24, 3, 57, -429, -267, -24, -105, 57, 57, 3, 3, 3, -51, 120, 12, 3, -15, -15, -69, 12, -69, -123, 21, 3, 3, 3, -15, 120, 12, 84, 12, -15, -33, 3, -33, -15, -15, -69, 12, -69, -123, -15, -33, 12, 12, -87, -141, -33, -141, -87, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -87, 21, 21, 21, 129, -213, 3, 21, 57, 57, 165, 3, 165, 273, -33, -15, -15, -15, 3, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, 3, 21, 21, 21, 39, 273, 3, 165, 3, 3, 3, 57, 3, -51, 3, 57, 3, 21, 3, 3, 3, -213, 3, 93, 3, -15, 3, -15, 3, -15, 3, -123, 3, -105, -159, -51, -159, -105, -6, -6, 3, 21, -141, -87, -6, -33, 21, -33, -51, -15, -51, -33, -6, -6, 66, 102, -15, 3, 3, 3, 21, -141, -87, -6, -33, 21, -33, -15, -6, 102, -51, 3, 3, 3, 57, -51, -213, 30, -213, -375, -51, -105, 30, 30, -267, -429, -105, -429, -267, 3, 3, 3, 3, 3, -51, 3, 3, 57, 3, 3, 3, 3, 3, -321, -483, -159, -483, -321, -24, -24, 3, 57, -429, -267, -24, -105, 57, 3, -51, 30, -51, -105, 3, -15, 30, 30, -69, -123, -15, -123, -69, 3, 3, 3, 3, 3, 57, 165, 3, 165, 273, -51, -33, 3, 21, 3, 21, 3, 21, 57, 75, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -303, -465, -141, -465, -303, -6, -6, 21, 75, -411, -249, -6, -87, 75, -87, -141, -33, -141, -87, -6, -6, 210, 318, -33, 21, 21, 21, 75, -411, -249, -6, -87, 75, -87, -33, -6, 318, -141, 21, 21, 21, 183, 288, -36, -36, -36, -360, 666, 18, -36, -144, -144, -468, 18, -468, -792, 72, -36, -36, -36, -144, 666, 18, 450, 18, -144, -252, -36, -252, -144, -144, -468, 18, -468, -792, -144, -252, 18, 18, -576, -900, -252, -900, -576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, -36, -36, -36, 72, -108, 0, 0, 0, 108, 540, 0, 324, 0, 0, 0, 108, 0, -108, 0, -252, -360, -144, -360, -252, -54, -54, -36, 0, -324, -216, -54, -108, 0, -108, -432, 54, -432, -756, -108, -216, 54, 54, -540, -864, -216, -864, -540, 0, 0, 0, 0, 0, -108, 0, 0, 108, 0, 0, 0, 0, 0, -648, -972, -324, -972, -648, -54, -54, 0, 108, -864, -540, -54, -216, 108, 57, 3, 3, 3, -51, 120, 12, 3, -15, -15, -69, 12, -69, -123, 21, 3, 3, 3, -15, 120, 12, 84, 12, -15, -33, 3, -33, -15, -15, -69, 12, -69, -123, -15, -33, 12, 12, -87, -141, -33, -141, -87, 63, 9, 9, 9, -45, 126, 18, 9, -9, -9, -63, 18, -63, -117, 27, 9, 9, 9, -9, 126, 18, 90, 18, -9, -27, 9, -27, -9, -9, -63, 18, -63, -117, -9, -27, 18, 18, -81, -135, -27, -135, -81, -45, 9, 9, 9, 63, -108, 0, 9, 27, 27, 81, 0, 81, 135, -135, 27, 27, 27, 189, -324, 0, 27, 81, 81, 243, 0, 243, 405, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -135, 27, 27, 27, 189, -324, 0, 27, 81, 81, 243, 0, 243, 405, -225, 45, 45, 45, 315, -540, 0, 45, 135, 135, 405, 0, 405, 675, -33, -15, -15, -15, 3, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, -15, 3, 3, 3, 21, 3, 21, 21, 21, 39, -54, -36, -36, -36, -18, -18, 0, 0, 0, 18, -15, 3, 3, 3, 21, -9, 9, 9, 9, 27, -9, 9, 9, 9, 27, 9, 27, 27, 27, 45, -18, 0, 0, 0, 18, 9, 27, 27, 27, 45, 27, 45, 45, 45, 63, 252, 0, 144, 0, -18, 0, 36, 0, -72, 0, 36, 0, 0, 0, -18, 0, -234, 0, 72, 0, -36, 0, -36, 0, -36, 0, -144, 0, 540, 0, 324, 0, 0, 0, 108, 0, -108, 0, 36, 0, 0, 0, 0, 0, -36, 0, -108, 0, -324, 0, 0, 0, -324, 0, -540, 0, 72, 0, -36, 0, -36, 0, -36, 0, -144, 0, 198, 0, -18, 0, -36, 0, -72, 0, -72, 0, -180, 0, -18, 0, -180, 0, -288, 0, -105, -159, -51, -159, -105, -6, -6, 3, 21, -141, -87, -6, -33, 21, -33, -51, -15, -51, -33, -6, -6, 66, 102, -15, 3, 3, 3, 21, -141, -87, -6, -33, 21, -33, -15, -6, 102, -51, 3, 3, 3, 57, -207, -315, -99, -315, -207, -9, -9, 9, 45, -279, -171, -9, -63, 45, -33, -51, -15, -51, -33, -27, -45, -9, -45, -27, 27, 45, 99, 153, -9, -9, 99, 153, 171, 261, -15, 3, 3, 3, 21, -36, 0, 3, 9, 9, 27, 0, 27, 45, -135, -81, 0, -27, 27, -27, -9, 0, 108, -45, 9, 9, 9, 63, -279, -171, -9, -63, 45, -27, -9, -9, 9, 45, 153, -9, 153, 261, -45, 9, 9, 9, 63, -108, 0, 9, 27, 27, 81, 0, 81, 135, -45, -207, 36, -207, -369, -45, -99, 36, 36, -261, -423, -99, -423, -261, 9, 9, 9, 9, 9, -45, 9, 9, 63, 9, 9, 9, 9, 9, -315, -477, -153, -477, -315, -18, -18, 9, 63, -423, -261, -18, -99, 63, 9, -45, 36, -45, -99, 9, -9, 36, 36, -63, -117, -9, -117, -63, 9, 9, 9, 9, 9, 63, 171, 9, 171, 279, -45, -27, 9, 27, 9, 27, 9, 27, 63, 81, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -297, -459, -135, -459, -297, 0, 0, 27, 81, -405, -243, 0, -81, 81, -81, -135, -27, -135, -81, 0, 0, 216, 324, -27, 27, 27, 27, 81, -405, -243, 0, -81, 81, -81, -27, 0, 324, -135, 27, 27, 27, 189, -108, -432, 54, -432, -756, -108, -216, 54, 54, -540, -864, -216, -864, -540, 0, 0, 0, 0, 0, -108, 0, 0, 108, 0, 0, 0, 0, 0, -648, -972, -324, -972, -648, -54, -54, 0, 108, -864, -540, -54, -216, 108, 9, -45, 36, -45, -99, 9, -9, 36, 36, -63, -117, -9, -117, -63, 27, -27, 54, -27, -81, 27, 9, 54, 54, -45, -99, 9, -99, -45, 27, 81, 0, 81, 135, 81, 243, 0, 243, 405, 0, 0, 0, 0, 0, 81, 243, 0, 243, 405, 135, 405, 0, 405, 675, -45, -27, 9, 27, 9, 27, 9, 27, 63, 81, -108, -90, 0, 18, 9, 27, 27, 45, 27, 45, 81, 99, 0, 18, 81, 99, 135, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -297, -459, -135, -459, -297, 0, 0, 27, 81, -405, -243, 0, -81, 81, -81, -135, -27, -135, -81, 0, 0, 216, 324, -27, 27, 27, 27, 81, -405, -243, 0, -81, 81, -81, -27, 0, 324, -135, 27, 27, 27, 189, -603, -927, -279, -927, -603, -9, -9, 45, 153, -819, -495, -9, -171, 153, -81, -135, -27, -135, -81, -63, -117, -9, -117, -63, 99, 153, 315, 477, -9, -9, 315, 477, 531, 801, -27, 27, 27, 27, 81, -90, 18, 27, 45, 45, 99, 18, 99, 153, -387, -225, 18, -63, 99, -63, -9, 18, 342, -117, 45, 45, 45, 207, -819, -495, -9, -171, 153, -63, -9, -9, 45, 153, 477, -9, 477, 801, -117, 45, 45, 45, 207, -306, 18, 45, 99, 99, 261, 18, 261, 423]\n assert candidate(expression = \"1+2+3*4-5*6+7-8*9\") == [900, 60, 900, -660, -660, 120, -48, 36, 120, -660, -660, -768, -1524, -768, 180, 12, 180, -132, -132, -270, -102, -210, -42, -396, -312, -252, -270, -210, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 180, 12, 180, -132, -132, -410, -18, -410, 318, 318, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, -114, -114, -150, -402, -150, -132, -132, 318, 318, -708, -168, -168, -168, 372, -1716, -960, -420, -582, -42, -546, -294, -420, 750, -708, -168, -168, -168, 372, 1496, 96, 1496, -1104, -1104, 196, -84, 56, 196, -1104, -1104, -1284, -2544, -1284, 296, 16, 296, -224, -224, -454, -174, -354, -74, -664, -524, -424, -454, -354, -944, -944, -1124, -2384, -1124, -224, -224, -1214, -314, -3104, -1844, -944, -1214, -314, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 316, 36, 316, -204, -204, 56, 0, 28, 56, -204, -204, -240, -492, -240, 60, 4, 60, -44, -44, -530, -26, -530, 406, 406, 296, 16, 296, -224, -224, -530, -26, -530, 406, 406, -884, -44, -884, 676, 676, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -194, -138, -94, -38, -80, -24, -74, -18, -70, -14, -10, 46, -94, -38, -10, 46, 26, 82, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -376, -236, -136, -166, -66, -122, -94, -116, -88, -84, 46, -136, 46, 124, -140, -80, -80, -80, -20, -194, -94, -80, -74, -70, -10, -94, -10, 26, -548, -548, -656, -1412, -656, -116, -116, -710, -170, -1844, -1088, -548, -710, -170, -98, -98, -134, -386, -134, -116, -116, 334, 334, -692, -152, -152, -152, 388, -1700, -944, -404, -566, -26, -530, -278, -404, 766, -692, -152, -152, -152, 388, -944, -944, -1124, -2384, -1124, -224, -224, -1214, -314, -3104, -1844, -944, -1214, -314, -98, -98, -134, -386, -134, -44, -44, -80, -332, -80, -44, -44, 406, 406, -224, -224, 406, 406, 676, 676, -692, -152, -152, -152, 388, -1178, -278, -152, -98, -62, 478, -278, 478, 802, -1700, -944, -404, -566, -26, -530, -278, -404, 766, -692, -152, -152, -152, 388, -2816, -1556, -656, -926, -26, -530, -278, -476, -224, -188, 982, -656, 982, 1684, -692, -152, -152, -152, 388, -1178, -278, -152, -98, -62, 478, -278, 478, 802, 900, 60, 900, -660, -660, 120, -48, 36, 120, -660, -660, -768, -1524, -768, 180, 12, 180, -132, -132, -270, -102, -210, -42, -396, -312, -252, -270, -210, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 180, 12, 180, -132, -132, -410, -18, -410, 318, 318, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -564, -564, -672, -1428, -672, -132, -132, -726, -186, -1860, -1104, -564, -726, -186, -114, -114, -150, -402, -150, -132, -132, 318, 318, -708, -168, -168, -168, 372, -1716, -960, -420, -582, -42, -546, -294, -420, 750, -708, -168, -168, -168, 372, 1794, 114, 1794, -1326, -1326, 234, -102, 66, 234, -1326, -1326, -1542, -3054, -1542, 354, 18, 354, -270, -270, -546, -210, -426, -90, -798, -630, -510, -546, -426, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, 1794, 114, 1794, -1326, -1326, 234, -102, 66, 234, -1326, -1326, -1542, -3054, -1542, 354, 18, 354, -270, -270, -546, -210, -426, -90, -798, -630, -510, -546, -426, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 316, 36, 316, -204, -204, 56, 0, 28, 56, -204, -204, -240, -492, -240, 310, 30, 310, -210, -210, 50, -6, 22, 50, -210, -210, -246, -498, -246, 319, 39, 319, -201, -201, 59, 3, 31, 59, -201, -201, -237, -489, -237, 319, 39, 319, -201, -201, 59, 3, 31, 59, -201, -201, -237, -489, -237, 0, 0, 0, 0, 0, -590, -30, -590, 450, 450, 236, 12, 236, -180, -180, -590, -30, -590, 450, 450, -944, -48, -944, 720, 720, 0, 0, 0, 0, 0, -590, -30, -590, 450, 450, 354, 18, 354, -270, -270, 354, 18, 354, -270, -270, -590, -30, -590, 450, 450, -944, -48, -944, 720, 720, -590, -30, -590, 450, 450, -1121, -57, -1121, 855, 855, -1121, -57, -1121, 855, 855, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -194, -138, -94, -38, -80, -24, -74, -18, -70, -14, -10, 46, -94, -38, -10, 46, 26, 82, -140, -84, -80, -24, -80, -24, -80, -24, -20, 36, -221, -165, -101, -45, -221, -165, -101, -45, -80, -24, -74, -18, -80, -24, -71, -15, -71, -15, -65, -9, -5, 51, -89, -33, -5, 51, 31, 87, -65, -9, -5, 51, -101, -45, -101, -45, -5, 51, 31, 87, -5, 51, 49, 105, 49, 105, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -376, -236, -136, -166, -66, -122, -94, -116, -88, -84, 46, -136, 46, 124, -140, -80, -80, -80, -20, -194, -94, -80, -74, -70, -10, -94, -10, 26, -252, -168, -108, -126, -66, -122, -94, -108, 22, -140, -80, -80, -80, -20, -438, -270, -150, -186, -66, -438, -270, -150, -186, -66, -122, -94, -116, -88, -122, -94, -113, -85, -113, -85, -72, 58, -124, 58, 136, -72, 58, -150, -150, 58, 136, 58, 175, 175, -140, -80, -80, -80, -20, -194, -94, -80, -74, -70, -10, -94, -10, 26, -140, -80, -80, -80, -20, -221, -101, -221, -101, -80, -74, -80, -71, -71, -65, -5, -89, -5, 31, -65, -5, -101, -101, -5, 31, -5, 49, 49, -540, -540, -648, -1404, -648, -108, -108, -702, -162, -1836, -1080, -540, -702, -162, -90, -90, -126, -378, -126, -108, -108, 342, 342, -684, -144, -144, -144, 396, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -936, -936, -1116, -2376, -1116, -216, -216, -1206, -306, -3096, -1836, -936, -1206, -306, -90, -90, -126, -378, -126, -36, -36, -72, -324, -72, -36, -36, 414, 414, -216, -216, 414, 414, 684, 684, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -2808, -1548, -648, -918, -18, -522, -270, -468, -216, -180, 990, -648, 990, 1692, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -540, -540, -648, -1404, -648, -108, -108, -702, -162, -1836, -1080, -540, -702, -162, -90, -90, -126, -378, -126, -108, -108, 342, 342, -684, -144, -144, -144, 396, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, -1134, -1134, -1350, -2862, -1350, -270, -270, -1458, -378, -3726, -2214, -1134, -1458, -378, -90, -90, -126, -378, -126, -36, -36, -72, -324, -72, -90, -90, -126, -378, -126, -9, -9, -45, -297, -45, -9, -9, -45, -297, -45, 0, 0, 450, 450, -180, -180, 450, 450, 720, 720, 0, 0, 450, 450, -270, -270, -270, -270, 450, 450, 720, 720, 450, 450, 855, 855, 855, 855, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -684, -144, -144, -144, 396, -1413, -333, -1413, -333, -144, -90, -144, -63, -63, -9, 531, -225, 531, 855, -9, 531, -333, -333, 531, 855, 531, 1017, 1017, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -2808, -1548, -648, -918, -18, -522, -270, -468, -216, -180, 990, -648, 990, 1692, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -1692, -936, -396, -558, -18, -522, -270, -396, 774, -684, -144, -144, -144, 396, -3366, -1854, -774, -1098, -18, -3366, -1854, -774, -1098, -18, -522, -270, -468, -216, -522, -270, -441, -189, -441, -189, -72, 1098, -540, 1098, 1800, -72, 1098, -774, -774, 1098, 1800, 1098, 2151, 2151, -684, -144, -144, -144, 396, -1170, -270, -144, -90, -54, 486, -270, 486, 810, -684, -144, -144, -144, 396, -1413, -333, -1413, -333, -144, -90, -144, -63, -63, -9, 531, -225, 531, 855, -9, 531, -333, -333, 531, 855, 531, 1017, 1017]\n assert candidate(expression = \"10+5*2-3/1+8\") == []\n assert candidate(expression = \"1*2*3*4*5\") == [120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120]\n assert candidate(expression = \"6*7+8-9*10+11-12\") == [-396, -396, -444, -972, -444, -12, -12, -456, -24, -1116, -588, -156, -456, -24, -396, -396, -444, -972, -444, 324, 324, 324, 324, -456, -24, -456, 354, 354, -1116, -588, -156, -456, -24, -1116, -588, 684, 684, -456, -24, -456, 354, 354, -31, -31, -39, -127, -39, 33, 33, -41, 31, -151, -63, 9, -41, 31, 9, 9, 1, -87, 1, -31, -31, -39, -127, -39, 324, 324, 324, 324, 369, 369, 729, 729, 369, 369, -451, -19, -451, 359, 359, -41, 31, -1, -41, 359, 359, 409, 809, 409, -1056, -528, -96, -396, 36, -1056, -528, 744, 744, -396, 36, -396, 414, 414, -151, -63, 9, -41, 31, -111, -23, -151, -63, 744, 744, 849, 1689, 849, -451, -19, -451, 359, 359, -41, 31, -1, -41, 359, 359, 409, 809, 409]\n assert candidate(expression = \"66-44*3+22/1-55*7+88\") == []\n assert candidate(expression = \"6/2+3*4-5\") == []\n assert candidate(expression = \"8*3+4-2*9+5-1\") == [-152, -152, -120, -160, -120, 232, 232, -56, 200, -176, -136, 240, -56, 200, -152, -152, -120, -160, -120, 520, 520, 520, 520, -56, 200, -56, 392, 392, -176, -136, 240, -56, 200, -176, -136, 552, 552, -56, 200, -56, 392, 392, 2, 2, 6, 1, 6, 50, 50, 14, 46, -1, 4, 51, 14, 46, 30, 30, 34, 29, 34, 2, 2, 6, 1, 6, 520, 520, 520, 520, 338, 338, 702, 702, 338, 338, -84, 172, -84, 364, 364, 14, 46, 42, 14, 364, 364, 238, 490, 238, -169, -129, 247, -49, 207, -169, -129, 559, 559, -49, 207, -49, 399, 399, -1, 4, 51, 14, 46, 27, 32, -1, 4, 559, 559, 363, 755, 363, -84, 172, -84, 364, 364, 14, 46, 42, 14, 364, 364, 238, 490, 238]\n assert candidate(expression = \"77+55*2-33/3+22*8-11\") == []\n assert candidate(expression = \"2*2*2*2-1+1*1*1\") == [0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 8, 8, 8, 8, 8, 12, 12, 16, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 10, 10, 14, 14, 10, 10, 16, 16, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 12, 12, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 8, 8, 8, 8, 8, 12, 12, 16, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 0, 0, 0, 0, 0, 16, 16, 0, 16, 0, 0, 16, 0, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 9, 9, 13, 13, 9, 9, 15, 15, 15, 15, 9, 9, 13, 13, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 0, 16, 14, 14, 14, 14, 14, 9, 13, 9, 15, 15, 9, 13, 9, 9, 16, 16, 16, 16, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 12, 12, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 0, 16, 0, 16, 8, 8, 12, 16, 0, 16, 8, 12, 16, 0, 0, 16, 0, 16, 0, 0, 16, 0, 16, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 9, 13, 9, 15, 15, 9, 13, 9, 9, 16, 16, 16, 16, 16, 0, 16, 8, 12, 16, 0, 16, 12, 12, 10, 14, 10, 16, 16, 0, 16, 8, 12, 16, 0, 16, 0, 16, 14, 14, 14, 14, 14, 9, 13, 9, 15, 15, 9, 13, 9, 9, 16, 16, 16, 16, 16]\n assert candidate(expression = \"100-50*2+25*4/2\") == []\n assert candidate(expression = \"5*5*5-3*3*3+2*2*2\") == [-2350, -2350, -4375, -3025, -4375, -1150, -1150, -4375, -3175, -3025, -4375, -1825, -4375, -3175, -2350, -2350, -4375, -3025, -4375, -750, -750, -750, -750, -4375, -3175, -4375, -2775, -2775, -3025, -4375, -1825, -4375, -3175, -3025, -4375, -1425, -1425, -4375, -3175, -4375, -2775, -2775, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, -350, -350, -350, -350, 650, 650, -100, -100, 650, 650, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -370, -370, -775, -505, -775, -130, -130, -775, -535, -505, -775, -265, -775, -535, -370, -370, -775, -505, -775, -50, -50, -50, -50, -775, -535, -775, -455, -455, -505, -775, -265, -775, -535, -505, -775, -185, -185, -775, -535, -775, -455, -455, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, 3630, 3630, 6600, 4620, 6600, 1870, 1870, 6600, 4840, 4620, 6600, 2860, 6600, 4840, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, 880, 880, 1600, 1120, 1600, 1650, 1650, 3000, 2100, 3000, 3630, 3630, 6600, 4620, 6600, -510, -510, -510, -510, 490, 490, -260, -260, 490, 490, 30, 30, 30, 30, 490, 490, 1030, 1030, -260, -260, 490, 490, 280, 280, 490, 490, 1030, 1030, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -380, -650, -140, -650, -410, -380, -650, -60, -60, -650, -410, -650, -330, -330, 2100, 3000, 1300, 3000, 2200, 4620, 6600, 2860, 6600, 4840, -1400, -2000, 2100, 3000, 1120, 1600, 2100, 3000, 4620, 6600, -1060, -1060, 940, -560, 940, 20, 20, 940, 2020, -560, 940, 520, 940, 2020, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -2350, -2350, -4375, -3025, -4375, -1150, -1150, -4375, -3175, -3025, -4375, -1825, -4375, -3175, -2350, -2350, -4375, -3025, -4375, -750, -750, -750, -750, -4375, -3175, -4375, -2775, -2775, -3025, -4375, -1825, -4375, -3175, -3025, -4375, -1425, -1425, -4375, -3175, -4375, -2775, -2775, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, -350, -350, -350, -350, 650, 650, -100, -100, 650, 650, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 26, 26, -55, -1, -55, 74, 74, -55, -7, -1, -55, 47, -55, -7, 26, 26, -55, -1, -55, 90, 90, 90, 90, -55, -7, -55, 9, 9, -1, -55, 47, -55, -7, -1, -55, 63, 63, -55, -7, -55, 9, 9, 26, 26, -55, -1, -55, 74, 74, -55, -7, -1, -55, 47, -55, -7, 26, 26, -55, -1, -55, 90, 90, 90, 90, -55, -7, -55, 9, 9, -1, -55, 47, -55, -7, -1, -55, 63, 63, -55, -7, -55, 9, 9, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, 3630, 3630, 6600, 4620, 6600, 1870, 1870, 6600, 4840, 4620, 6600, 2860, 6600, 4840, 1650, 1650, 3000, 2100, 3000, 850, 850, 3000, 2200, 2100, 3000, 1300, 3000, 2200, 4026, 4026, 7320, 5124, 7320, 2074, 2074, 7320, 5368, 5124, 7320, 3172, 7320, 5368, 4026, 4026, 7320, 5124, 7320, 2074, 2074, 7320, 5368, 5124, 7320, 3172, 7320, 5368, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, 880, 880, 1600, 1120, 1600, 1650, 1650, 3000, 2100, 3000, 3630, 3630, 6600, 4620, 6600, -1100, -1100, -2000, -1400, -2000, 1650, 1650, 3000, 2100, 3000, 1276, 1276, 2320, 1624, 2320, 1276, 1276, 2320, 1624, 2320, 1650, 1650, 3000, 2100, 3000, 3630, 3630, 6600, 4620, 6600, 1650, 1650, 3000, 2100, 3000, 4026, 4026, 7320, 5124, 7320, 4026, 4026, 7320, 5124, 7320, -542, -542, -542, -542, 458, 458, -292, -292, 458, 458, -2, -2, -2, -2, 458, 458, 998, 998, -292, -292, 458, 458, 248, 248, 458, 458, 998, 998, -542, -542, -542, -542, 458, 458, -292, -292, 458, 458, 106, 106, 106, 106, 106, 106, 106, 106, 458, 458, 998, 998, 458, 458, 1106, 1106, 1106, 1106, -292, -292, 458, 458, 248, 248, 458, 458, 998, 998, -292, -292, 458, 458, 356, 356, 356, 356, 458, 458, 998, 998, 458, 458, 1106, 1106, 1106, 1106, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 320, 368, 320, 384, 384, 320, 368, 320, 384, 384, 3000, 2200, 6600, 4840, 3000, 2200, 7320, 5368, 7320, 5368, -2000, 3000, 1600, 3000, 6600, -2000, 3000, 2320, 2320, 3000, 6600, 3000, 7320, 7320, -2192, -2192, 1808, -1192, 1808, -32, -32, 1808, 3968, -1192, 1808, 968, 1808, 3968, -2192, -2192, 1808, -1192, 1808, 400, 400, 400, 400, 1808, 3968, 1808, 4400, 4400, -1192, 1808, 968, 1808, 3968, -1192, 1808, 1400, 1400, 1808, 3968, 1808, 4400, 4400, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -380, -650, -140, -650, -410, -380, -650, -60, -60, -650, -410, -650, -330, -330, 2100, 3000, 1300, 3000, 2200, 4620, 6600, 2860, 6600, 4840, -1400, -2000, 2100, 3000, 1120, 1600, 2100, 3000, 4620, 6600, -1060, -1060, 940, -560, 940, 20, 20, 940, 2020, -560, 940, 520, 940, 2020, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -2900, -4250, -1700, -4250, -3050, -2900, -4250, -1300, -1300, -4250, -3050, -4250, -2650, -2650, 2100, 3000, 1300, 3000, 2200, -1400, -2000, 2100, 3000, -900, -900, 1100, -400, 1100, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 124, 70, 172, 70, 118, 124, 70, 188, 188, 70, 118, 70, 134, 134, 124, 70, 172, 70, 118, 124, 70, 188, 188, 70, 118, 70, 134, 134, 2100, 3000, 1300, 3000, 2200, 4620, 6600, 2860, 6600, 4840, 2100, 3000, 1300, 3000, 2200, 5124, 7320, 3172, 7320, 5368, 5124, 7320, 3172, 7320, 5368, -1400, -2000, 2100, 3000, 1120, 1600, 2100, 3000, 4620, 6600, -1400, -2000, 2100, 3000, 1624, 2320, 1624, 2320, 2100, 3000, 4620, 6600, 2100, 3000, 5124, 7320, 5124, 7320, -1092, -1092, 908, -592, 908, -12, -12, 908, 1988, -592, 908, 488, 908, 1988, -1092, -1092, 908, -592, 908, 204, 204, 204, 204, 908, 1988, 908, 2204, 2204, -592, 908, 488, 908, 1988, -592, 908, 704, 704, 908, 1988, 908, 2204, 2204, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, -400, -160, -400, -80, -80, 3000, 2200, 6600, 4840, -2000, 3000, 1600, 3000, 6600, -2160, -2160, 1840, -1160, 1840, 0, 0, 1840, 4000, -1160, 1840, 1000, 1840, 4000, -4000, -2800, -4000, -2400, -2400, 3000, 2200, -2000, 3000, -2000, -2000, 2000, -1000, 2000, 320, 368, 320, 384, 384, 320, 368, 320, 384, 384, 3000, 2200, 6600, 4840, 3000, 2200, 7320, 5368, 7320, 5368, -2000, 3000, 1600, 3000, 6600, -2000, 3000, 2320, 2320, 3000, 6600, 3000, 7320, 7320, -2192, -2192, 1808, -1192, 1808, -32, -32, 1808, 3968, -1192, 1808, 968, 1808, 3968, -2192, -2192, 1808, -1192, 1808, 400, 400, 400, 400, 1808, 3968, 1808, 4400, 4400, -1192, 1808, 968, 1808, 3968, -1192, 1808, 1400, 1400, 1808, 3968, 1808, 4400, 4400]\n assert candidate(expression = \"5+3*2-8/4+6\") == []\n assert candidate(expression = \"7-3+2*5-8/4\") == []\n assert candidate(expression = \"8*3-2*4+6/2-1\") == []\n assert candidate(expression = \"7-3*2+4*5-6/2\") == []\n assert candidate(expression = \"5*3+10-2*8+4\") == [-55, -35, 495, 5, 355, -55, -35, 660, 660, 5, 355, 5, 460, 460, 1, 5, 111, 13, 83, 41, 45, 1, 5, 660, 660, 276, 756, 276, -11, 339, -11, 444, 444, 13, 83, 53, 13, 444, 444, 188, 508, 188]\n assert candidate(expression = \"9*8-7*6+5*4-3*2+1\") == [1269, 639, -1251, 9, -1251, -999, -1125, -1251, -3519, 261, -999, -1251, -999, -2511, 3537, 2151, -2007, 765, -2007, -999, -1125, -2133, -2259, -2007, -4275, -2007, -4275, -7677, 261, -999, -1251, -999, -2511, 1395, -1377, -1251, -2385, -1377, -2889, -1377, -2889, -5157, -81, -171, -441, -261, -441, -405, -423, -441, -765, -225, -405, -441, -405, -621, 3537, 2151, -2007, 765, -2007, 2187, 1341, -1197, 495, -1197, -1485, -1503, -2619, -2637, -405, -423, -2619, -2637, -1539, -1557, -2007, -4275, -2007, -4275, -7677, -1197, -1521, -2007, -1197, -4761, -8163, -1521, -8163, -4923, 315, -945, -1197, -945, -2457, 1449, -1323, -1197, -2331, -1323, -2835, -1323, -2835, -5103, -225, -405, -441, -405, -621, 1449, -1323, 909, -783, -1521, -2655, -441, -2655, -1575, -1323, -2835, -1323, -2835, -5103, -783, -999, -1323, -783, -3159, -5427, -999, -5427, -3267, -171, -81, 189, 9, 189, 153, 171, 189, 513, -27, 153, 189, 153, 369, -495, -297, 297, -99, 297, 153, 171, 315, 333, 297, 621, 297, 621, 1107, -27, 153, 189, 153, 369, -189, 207, 189, 351, 207, 423, 207, 423, 747, -531, -441, -171, -351, -171, -207, -189, -171, 153, -387, -207, -171, -207, 9, -171, -81, 189, 9, 189, 153, 171, 189, 513, -27, 153, 189, 153, 369, 3105, 1863, -1863, 621, -1863, 1755, 1053, -1053, 351, -1053, -495, -297, 297, -99, 297, 1305, 783, -783, 261, -783, -495, -297, 297, -99, 297, -1647, -1629, -2781, -2763, -567, -549, -2781, -2763, -1701, -1683, 153, 171, 315, 333, -207, -189, 153, 171, -2565, -2547, -1485, -1467, 315, 333, -1125, -1107, 315, 333, -1863, -4131, -1863, -4131, -7533, -1053, -1377, -1863, -1053, -4617, -8019, -1377, -8019, -4779, 297, 621, 297, 621, 1107, -783, -459, 297, 621, -1863, -1053, 297, -783, 297, -4779, -8181, -1539, -8181, -4941, 621, 1107, -459, 621, -7533, -4293, 1107, -3213, 1107, 333, -927, -1179, -927, -2439, 1467, -1305, -1179, -2313, -1305, -2817, -1305, -2817, -5085, -207, -387, -423, -387, -603, 1467, -1305, 927, -765, -1503, -2637, -423, -2637, -1557, -1305, -2817, -1305, -2817, -5085, -765, -981, -1305, -765, -3141, -5409, -981, -5409, -3249, -27, 153, 189, 153, 369, -189, 207, 189, 351, 207, 423, 207, 423, 747, -387, -207, -171, -207, 9, -27, 153, 189, 153, 369, 1251, -1233, 711, -693, -189, 207, 531, -513, -189, 207, -1611, -2745, -531, -2745, -1665, 189, 351, -171, 189, -2529, -1449, 351, -1089, 351, -1233, -2745, -1233, -2745, -5013, -693, -909, -1233, -693, -3069, -5337, -909, -5337, -3177, 207, 423, 207, 423, 747, -513, -297, 207, 423, -1233, -693, 207, -513, 207, -3177, -5445, -1017, -5445, -3285, 423, 747, -297, 423, -5013, -2853, 747, -2133, 747, 205, 135, -75, 65, -75, -47, -61, -75, -327, 93, -47, -75, -47, -215, 457, 303, -159, 149, -159, -47, -61, -173, -187, -159, -411, -159, -411, -789, 93, -47, -75, -47, -215, 219, -89, -75, -201, -89, -257, -89, -257, -509, 55, 45, 15, 35, 15, 19, 17, 15, -21, 39, 19, 15, 19, -5, 457, 303, -159, 149, -159, 307, 213, -69, 119, -69, -101, -103, -227, -229, 19, 17, -227, -229, -107, -109, -159, -411, -159, -411, -789, -69, -105, -159, -69, -465, -843, -105, -843, -483, 99, -41, -69, -41, -209, 225, -83, -69, -195, -83, -251, -83, -251, -503, 39, 19, 15, 19, -5, 225, -83, 165, -23, -105, -231, 15, -231, -111, -83, -251, -83, -251, -503, -23, -47, -83, -23, -287, -539, -47, -539, -299, -171, -81, 189, 9, 189, 153, 171, 189, 513, -27, 153, 189, 153, 369, -495, -297, 297, -99, 297, 153, 171, 315, 333, 297, 621, 297, 621, 1107, -27, 153, 189, 153, 369, -189, 207, 189, 351, 207, 423, 207, 423, 747, -1235, -585, 1365, 65, 1365, 1105, 1235, 1365, 3705, -195, 1105, 1365, 1105, 2665, -3575, -2145, 2145, -715, 2145, 1105, 1235, 2275, 2405, 2145, 4485, 2145, 4485, 7995, -195, 1105, 1365, 1105, 2665, -1365, 1495, 1365, 2535, 1495, 3055, 1495, 3055, 5395, -331, -321, -291, -311, -291, -295, -293, -291, -255, -315, -295, -291, -295, -271, 29, 39, 69, 49, 69, 65, 67, 69, 105, 45, 65, 69, 65, 89, 5, 15, 45, 25, 45, 41, 43, 45, 81, 21, 41, 45, 41, 65, 29, 39, 69, 49, 69, 65, 67, 69, 105, 45, 65, 69, 65, 89, 365, 375, 405, 385, 405, 401, 403, 405, 441, 381, 401, 405, 401, 425, 3105, 1863, -1863, 621, -1863, 1755, 1053, -1053, 351, -1053, -495, -297, 297, -99, 297, 1305, 783, -783, 261, -783, -495, -297, 297, -99, 297, 25, 15, -15, 5, -15, -125, -75, 75, -25, 75, -495, -297, 297, -99, 297, -3575, -2145, 2145, -715, 2145, 1505, 903, -903, 301, -903, -295, -177, 177, -59, 177, -175, -105, 105, -35, 105, -295, -177, 177, -59, 177, -1975, -1185, 1185, -395, 1185, -1575, -1573, -2709, -2707, -495, -493, -2709, -2707, -1629, -1627, 225, 227, 387, 389, -135, -133, 225, 227, -2493, -2491, -1413, -1411, 387, 389, -1053, -1051, 387, 389, -119, -117, -245, -243, 1, 3, -245, -243, -125, -123, 225, 227, 387, 389, 1681, 1683, 2851, 2853, -295, -293, 65, 67, 41, 43, 65, 67, 401, 403, -2493, -2491, -1413, -1411, 387, 389, -1053, -1051, 387, 389, -29, -27, 91, 93, 387, 389, 2851, 2853, -1213, -1211, 227, 229, 131, 133, 227, 229, 1571, 1573, -1863, -4131, -1863, -4131, -7533, -1053, -1377, -1863, -1053, -4617, -8019, -1377, -8019, -4779, 297, 621, 297, 621, 1107, -783, -459, 297, 621, -1863, -1053, 297, -783, 297, -4779, -8181, -1539, -8181, -4941, 621, 1107, -459, 621, -7533, -4293, 1107, -3213, 1107, -15, -267, -15, -267, -645, 75, 39, -15, 75, -321, -699, 39, -699, -339, 297, 621, 297, 621, 1107, 2145, 4485, 2145, 4485, 7995, -903, -867, 177, 213, 105, 141, 177, 213, 1185, 1221, -1863, -1053, 297, -783, 297, -15, 75, 297, 2145, -903, 177, 105, 177, 1185, -4707, -8109, -1467, -8109, -4869, 693, 1179, -387, 693, -7461, -4221, 1179, -3141, 1179, -339, -717, 21, -717, -357, 693, 1179, 5061, 8571, -867, 213, 141, 213, 1221, -7461, -4221, 1179, -3141, 1179, -69, 291, 1179, 8571, -3621, 699, 411, 699, 4731, 325, -935, -1187, -935, -2447, 1459, -1313, -1187, -2321, -1313, -2825, -1313, -2825, -5093, -215, -395, -431, -395, -611, 1459, -1313, 919, -773, -1511, -2645, -431, -2645, -1565, -1313, -2825, -1313, -2825, -5093, -773, -989, -1313, -773, -3149, -5417, -989, -5417, -3257, -35, 145, 181, 145, 361, -197, 199, 181, 343, 199, 415, 199, 415, 739, -395, -215, -179, -215, 1, -35, 145, 181, 145, 361, 1243, -1241, 703, -701, -197, 199, 523, -521, -197, 199, -1619, -2753, -539, -2753, -1673, 181, 343, -179, 181, -2537, -1457, 343, -1097, 343, -1241, -2753, -1241, -2753, -5021, -701, -917, -1241, -701, -3077, -5345, -917, -5345, -3185, 199, 415, 199, 415, 739, -521, -305, 199, 415, -1241, -701, 199, -521, 199, -3185, -5453, -1025, -5453, -3293, 415, 739, -305, 415, -5021, -2861, 739, -2141, 739, 101, -39, -67, -39, -207, 227, -81, -67, -193, -81, -249, -81, -249, -501, 41, 21, 17, 21, -3, 227, -81, 167, -21, -103, -229, 17, -229, -109, -81, -249, -81, -249, -501, -21, -45, -81, -21, -285, -537, -45, -537, -297, -35, 145, 181, 145, 361, -197, 199, 181, 343, 199, 415, 199, 415, 739, -259, 1041, 1301, 1041, 2601, -1429, 1431, 1301, 2471, 1431, 2991, 1431, 2991, 5331, -315, -295, -291, -295, -271, 45, 65, 69, 65, 89, 21, 41, 45, 41, 65, 45, 65, 69, 65, 89, 381, 401, 405, 401, 425, 1243, -1241, 703, -701, -197, 199, 523, -521, -197, 199, 11, -9, -49, 51, -197, 199, -1429, 1431, 603, -601, -117, 119, -69, 71, -117, 119, -789, 791, -1571, -2705, -491, -2705, -1625, 229, 391, -131, 229, -2489, -1409, 391, -1049, 391, -115, -241, 5, -241, -121, 229, 391, 1685, 2855, -291, 69, 45, 69, 405, -2489, -1409, 391, -1049, 391, -25, 95, 391, 2855, -1209, 231, 135, 231, 1575, -1241, -2753, -1241, -2753, -5021, -701, -917, -1241, -701, -3077, -5345, -917, -5345, -3185, 199, 415, 199, 415, 739, -521, -305, 199, 415, -1241, -701, 199, -521, 199, -3185, -5453, -1025, -5453, -3293, 415, 739, -305, 415, -5021, -2861, 739, -2141, 739, -9, -177, -9, -177, -429, 51, 27, -9, 51, -213, -465, 27, -465, -225, 199, 415, 199, 415, 739, 1431, 2991, 1431, 2991, 5331, -601, -577, 119, 143, 71, 95, 119, 143, 791, 815, -1241, -701, 199, -521, 199, -9, 51, 199, 1431, -601, 119, 71, 119, 791, -3137, -5405, -977, -5405, -3245, 463, 787, -257, 463, -4973, -2813, 787, -2093, 787, -225, -477, 15, -477, -237, 463, 787, 3375, 5715, -577, 143, 95, 143, 815, -4973, -2813, 787, -2093, 787, -45, 195, 787, 5715, -2413, 467, 275, 467, 3155]\n assert candidate(expression = \"5+5+5+5+5+5+5+5+5+5\") == [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 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50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]\n assert candidate(expression = \"99*98-97*96+95*94-93*92\") == [7718843484, -84842406, -4503708, -84842406, -7808189598, 15520781628, -168734214, -4503708, -90239292, -168734214, -7892081406, -168734214, -7892081406, -15779755134, 78672924, -1777446, -949212, -1777446, -81399582, 15520781628, -168734214, 7880611068, -85669254, -85819932, -171555516, -949212, -171555516, -86684796, -168734214, -7892081406, -168734214, -7892081406, -15779755134, -85669254, -165291390, -168734214, -85669254, -7973397630, -15861071358, -165291390, -15861071358, -8052965118, -79575606, 874764, 46530, 874764, 80496900, -160007958, 1739628, 46530, 930402, 1739628, 81361764, 1739628, 81361764, 162677988, -80497296, -46926, -875160, -46926, 79575210, -79575606, 874764, 46530, 874764, 80496900, 15438673602, -167851332, 7798503042, -84786372, -160007958, 1739628, 7639332822, -83055852, -160007958, 1739628, -87514020, -173249604, -2643300, -173249604, -88378884, 46530, 930402, -875160, 46530, -172347318, -87476598, 930402, -85708458, 930402, -167851332, -7891198524, -167851332, -7891198524, -15778872252, -84786372, -164408508, -167851332, -84786372, -7972514748, -15860188476, -164408508, -15860188476, -8052082236, 1739628, 81361764, 1739628, 81361764, 162677988, -83055852, -3433716, 1739628, 81361764, -167851332, -84786372, 1739628, -83055852, 1739628, -7974208836, -15861882564, -166102596, -15861882564, -8053776324, 81361764, 162677988, -3433716, 81361764, -15778872252, -7970766012, 162677988, -7808097132, 162677988, 77977720, -847390, -35888, -847390, -78860998, 156785176, -1694782, -35888, -901904, -1694782, -79708390, -1694782, -79708390, -159381862, 804280, -8350, 16, -8350, -812614, 156785176, -1694782, 79611736, -855742, -857264, -1723280, 16, -1723280, -866000, -1694782, -79708390, -1694782, -79708390, -159381862, -855742, -1660006, -1694782, -855742, -80529766, -160203238, -1660006, -160203238, -81333478, -79575606, 874764, 46530, 874764, 80496900, -160007958, 1739628, 46530, 930402, 1739628, 81361764, 1739628, 81361764, 162677988, -7720441370, 84869780, 4514350, 84869780, 7809825500, -15524004410, 168779060, 4514350, 90267790, 168779060, 7893734780, 168779060, 7893734780, 15783051260, -1716076, -903446, -911812, -903446, -99182, -794386, 18244, 9878, 18244, 822508, -803500, 9130, 764, 9130, 813394, -794386, 18244, 9878, 18244, 822508, 118190, 930820, 922454, 930820, 1735084, 15438673602, -167851332, 7798503042, -84786372, -160007958, 1739628, 7639332822, -83055852, -160007958, 1739628, 74677150, -811900, -2496290, 27140, -160007958, 1739628, -15524004410, 168779060, 7718114042, -83912372, -81226738, 883108, -4104070, 44620, -81226738, 883108, -7803444850, 84840100, -86675532, -172411116, -1804812, -172411116, -87540396, 885018, 1768890, -36672, 885018, -171508830, -86638110, 1768890, -84869970, 1768890, -874376, -1740392, -17096, -1740392, -883112, 885018, 1768890, 86686174, 172439614, -911812, 9878, 764, 9878, 922454, -171508830, -86638110, 1768890, -84869970, 1768890, -838106, 19174, 1768890, 172439614, -85745110, 893750, 37034, 893750, 86675894, -167851332, -7891198524, -167851332, -7891198524, -15778872252, -84786372, -164408508, -167851332, -84786372, -7972514748, -15860188476, -164408508, -15860188476, -8052082236, 1739628, 81361764, 1739628, 81361764, 162677988, -83055852, -3433716, 1739628, 81361764, -167851332, -84786372, 1739628, -83055852, 1739628, -7974208836, -15861882564, -166102596, -15861882564, -8053776324, 81361764, 162677988, -3433716, 81361764, -15778872252, -7970766012, 162677988, -7808097132, 162677988, -811900, -78825508, -811900, -78825508, -158498980, 27140, -777124, -811900, 27140, -79646884, -159320356, -777124, -159320356, -80450596, 1739628, 81361764, 1739628, 81361764, 162677988, 168779060, 7893734780, 168779060, 7893734780, 15783051260, -83912372, -83108108, 883108, 1687372, 44620, 848884, 883108, 1687372, 84840100, 85644364, -167851332, -84786372, 1739628, -83055852, 1739628, -811900, 27140, 1739628, 168779060, -83912372, 883108, 44620, 883108, 84840100, -7973370348, -15861044076, -165264108, -15861044076, -8052937836, 82200252, 163516476, -2595228, 82200252, -15778033764, -7969927524, 163516476, -7807258644, 163516476, -79663996, -159337468, -794236, -159337468, -80467708, 82200252, 163516476, 7975906604, 15865223084, -83108108, 1687372, 848884, 1687372, 85644364, -15778033764, -7969927524, 163516476, -7807258644, 163516476, -76327156, 2542604, 163516476, 15865223084, -7887771524, 83003596, 4185724, 83003596, 7974960844]\n assert candidate(expression = \"9*8+7*6-5*4+3*2\") == [-2700, -3960, -1188, -3960, -2448, 702, 954, -432, 702, -3582, -2070, 954, -1314, 954, 0, -180, 216, -180, 36, 702, 954, 3402, 4734, -756, 378, 324, 378, 1458, -3582, -2070, 954, -1314, 954, 198, 414, 954, 4734, -1638, 630, 522, 630, 2790, -5940, -8640, -2700, -8640, -5400, 1350, 1890, -1080, 1350, -7830, -4590, 1890, -2970, 1890, 0, -180, 216, -180, 36, 360, 180, 576, 180, 396, 1350, 1890, 4050, 5670, 1350, 1890, 4050, 5670, 7650, 10710, -756, 378, 324, 378, 1458, -1836, 594, 324, 684, 594, 1674, 594, 1674, 3114, -3510, -1998, 1026, -1242, 1026, 270, 486, 1026, 4806, -1566, 702, 594, 702, 2862, -7830, -4590, 1890, -2970, 1890, 270, 486, 990, 1206, 1890, 5670, 1890, 5670, 10710, -1566, 702, 594, 702, 2862, -3726, 1134, 594, 1314, 1134, 3294, 1134, 3294, 6174, -236, -376, -68, -376, -208, 142, 170, 16, 142, -334, -166, 170, -82, 170, 64, 44, 88, 44, 68, 142, 170, 442, 590, -20, 106, 100, 106, 226, -334, -166, 170, -82, 170, 86, 110, 170, 590, -118, 134, 122, 134, 374, -5940, -8640, -2700, -8640, -5400, 1350, 1890, -1080, 1350, -7830, -4590, 1890, -2970, 1890, -3476, -5056, -1580, -5056, -3160, 790, 1106, -632, 790, -4582, -2686, 1106, -1738, 1106, 400, 380, 424, 380, 404, 760, 740, 784, 740, 764, 64, 44, 88, 44, 68, 760, 740, 784, 740, 764, 424, 404, 448, 404, 428, 1350, 1890, 4050, 5670, 1350, 1890, 4050, 5670, 7650, 10710, 790, 1106, 1090, 1526, 1350, 1890, 790, 1106, 4450, 6230, 8050, 11270, 1090, 1526, 8050, 11270, 4690, 6566, -804, 330, 276, 330, 1410, -1884, 546, 276, 636, 546, 1626, 546, 1626, 3066, -20, 106, 100, 106, 226, -1884, 546, -1100, 322, 436, 796, 100, 796, 460, 546, 1626, 546, 1626, 3066, 322, 442, 546, 322, 1786, 3226, 442, 3226, 1882, -3510, -1998, 1026, -1242, 1026, 270, 486, 1026, 4806, -1566, 702, 594, 702, 2862, -7830, -4590, 1890, -2970, 1890, 270, 486, 990, 1206, 1890, 5670, 1890, 5670, 10710, -1566, 702, 594, 702, 2862, -3726, 1134, 594, 1314, 1134, 3294, 1134, 3294, 6174, -262, -94, 242, -10, 242, 158, 182, 242, 662, -46, 206, 194, 206, 446, -7830, -4590, 1890, -2970, 1890, -4582, -2686, 1106, -1738, 1106, 830, 854, 1550, 1574, 158, 182, 1550, 1574, 878, 902, 1890, 5670, 1890, 5670, 10710, 1106, 1526, 1890, 1106, 6230, 11270, 1526, 11270, 6566, -1614, 654, 546, 654, 2814, -3774, 1086, 546, 1266, 1086, 3246, 1086, 3246, 6126, -46, 206, 194, 206, 446, -3774, 1086, -2206, 638, 866, 1586, 194, 1586, 914, 1086, 3246, 1086, 3246, 6126, 638, 878, 1086, 638, 3566, 6446, 878, 6446, 3758]\n assert candidate(expression = \"10*9-8*7+6*5-4*3\") == [2890, -1910, -1910, -1910, -6710, 7370, -3030, -1910, -4150, -3030, -7830, -3030, -7830, -14550, -50, -650, -650, -650, -1250, 7370, -3030, 4430, -1770, -2750, -4990, -650, -4990, -2890, -3030, -7830, -3030, -7830, -14550, -1770, -2370, -3030, -1770, -8670, -15390, -2370, -15390, -9090, -350, 250, 250, 250, 850, -910, 390, 250, 530, 390, 990, 390, 990, 1830, -890, -290, -290, -290, 310, -350, 250, 250, 250, 850, 6650, -2850, 3710, -1590, -910, 390, 2870, -1230, -910, 390, -2990, -5230, -890, -5230, -3130, 250, 530, -290, 250, -4870, -2770, 530, -2170, 530, -2850, -7650, -2850, -7650, -14370, -1590, -2190, -2850, -1590, -8490, -15210, -2190, -15210, -8910, 390, 990, 390, 990, 1830, -1230, -630, 390, 990, -2850, -1590, 390, -1230, 390, -8730, -15450, -2430, -15450, -9150, 990, 1830, -630, 990, -14370, -8070, 1830, -6270, 1830, 370, -110, -110, -110, -590, 818, -222, -110, -334, -222, -702, -222, -702, -1374, 76, 16, 16, 16, -44, 818, -222, 524, -96, -194, -418, 16, -418, -208, -222, -702, -222, -702, -1374, -96, -156, -222, -96, -786, -1458, -156, -1458, -828, -350, 250, 250, 250, 850, -910, 390, 250, 530, 390, 990, 390, 990, 1830, -2870, 2050, 2050, 2050, 6970, -7462, 3198, 2050, 4346, 3198, 8118, 3198, 8118, 15006, -512, -452, -452, -452, -392, 28, 88, 88, 88, 148, -8, 52, 52, 52, 112, 28, 88, 88, 88, 148, 532, 592, 592, 592, 652, 6650, -2850, 3710, -1590, -910, 390, 2870, -1230, -910, 390, 98, -42, -196, 84, -910, 390, -7462, 3198, 3248, -1392, -532, 228, -280, 120, -532, 228, -4060, 1740, -2882, -5122, -782, -5122, -3022, 358, 638, -182, 358, -4762, -2662, 638, -2062, 638, -218, -442, -8, -442, -232, 358, 638, 3022, 5318, -452, 88, 52, 88, 592, -4762, -2662, 638, -2062, 638, -82, 128, 638, 5318, -2332, 368, 188, 368, 2888, -2850, -7650, -2850, -7650, -14370, -1590, -2190, -2850, -1590, -8490, -15210, -2190, -15210, -8910, 390, 990, 390, 990, 1830, -1230, -630, 390, 990, -2850, -1590, 390, -1230, 390, -8730, -15450, -2430, -15450, -9150, 990, 1830, -630, 990, -14370, -8070, 1830, -6270, 1830, -42, -522, -42, -522, -1194, 84, 24, -42, 84, -606, -1278, 24, -1278, -648, 390, 990, 390, 990, 1830, 3198, 8118, 3198, 8118, 15006, -1392, -1332, 228, 288, 120, 180, 228, 288, 1740, 1800, -2850, -1590, 390, -1230, 390, -42, 84, 390, 3198, -1392, 228, 120, 228, 1740, -8622, -15342, -2322, -15342, -9042, 1098, 1938, -522, 1098, -14262, -7962, 1938, -6162, 1938, -630, -1302, 0, -1302, -672, 1098, 1938, 9090, 15978, -1332, 288, 180, 288, 1800, -14262, -7962, 1938, -6162, 1938, -222, 408, 1938, 15978, -6972, 1128, 588, 1128, 8688]\n assert candidate(expression = \"12+34-56*78/9\") == []\n assert candidate(expression = \"15-5*3+2-8/4+9*2\") == []\n assert candidate(expression = \"9*8-7+6*5-4*3+2\") == [819, 495, -261, 279, -261, -81, -135, -261, -1161, 369, -171, -171, -171, -711, 1827, 1125, -513, 657, -513, -81, -135, -333, -387, -513, -1413, -513, -1413, -2673, 369, -171, -171, -171, -711, 873, -297, -171, -423, -297, -837, -297, -837, -1593, -801, -477, 279, -261, 279, 99, 153, 279, 1179, -351, 189, 189, 189, 729, 675, 405, -225, 225, -225, -945, -567, 315, -315, 315, -441, -387, -693, -639, 99, 153, -405, -351, 135, 189, -225, -1125, -225, -1125, -2385, 315, 1215, -225, 315, -1485, -2745, 1215, -1305, 1395, 405, -135, -135, -135, -675, 909, -261, -135, -387, -261, -801, -261, -801, -1557, -351, 189, 189, 189, 729, 333, -117, -423, 207, -351, -603, 189, -315, 225, -117, -657, -117, -657, -1413, 207, 747, -117, 207, -873, -1629, 747, -765, 855, 155, 119, 35, 95, 35, 55, 49, 35, -65, 105, 45, 45, 45, -15, 267, 189, 7, 137, 7, 55, 49, 27, 21, 7, -93, 7, -93, -233, 105, 45, 45, 45, -15, 161, 31, 45, 17, 31, -29, 31, -29, -113, -81, -45, 39, -21, 39, 19, 25, 39, 139, -31, 29, 29, 29, 89, -25, 11, 95, 35, 95, 75, 81, 95, 195, 25, 85, 85, 85, 145, 675, 405, -225, 225, -225, -945, -567, 315, -315, 315, -885, -531, 295, -295, 295, -225, -135, 75, -75, 75, -1065, -639, 355, -355, 355, -281, -275, -533, -527, 259, 265, -245, -239, 295, 301, 15, 21, -13, -7, 19, 25, 75, 81, -245, -239, 295, 301, 275, 281, 55, 61, 335, 341, -225, -1125, -225, -1125, -2385, 315, 1215, -225, 315, -1485, -2745, 1215, -1305, 1395, 295, 195, 295, 195, 55, 75, 175, 355, 455, -225, 315, 295, 75, 355, -1325, -2585, 1375, -1145, 1555, 155, 15, 175, 455, -1145, 1555, 1455, 355, 1755, 389, -151, -151, -151, -691, 893, -277, -151, -403, -277, -817, -277, -817, -1573, -367, 173, 173, 173, 713, 317, -133, -439, 191, -367, -619, 173, -331, 209, -133, -673, -133, -673, -1429, 191, 731, -133, 191, -889, -1645, 731, -781, 839, 109, 49, 49, 49, -11, 165, 35, 49, 21, 35, -25, 35, -25, -109, -31, 29, 29, 29, 89, 25, 85, 85, 85, 145, 317, -133, -439, 191, -411, 179, -103, 47, -495, 215, -271, -523, 269, -235, 305, 25, -3, 29, 85, -235, 305, 285, 65, 345, -133, -673, -133, -673, -1429, 191, 731, -133, 191, -889, -1645, 731, -781, 839, 179, 119, 179, 119, 35, 47, 107, 215, 275, -133, 191, 179, 47, 215, -793, -1549, 827, -685, 935, 95, 11, 107, 275, -685, 935, 875, 215, 1055]\n assert candidate(expression = \"55+44*3-22/2+11*9-88\") == []\n assert candidate(expression = \"8*9-2*3+5*2\") == [-136, -184, -56, -184, -104, 728, 896, 104, 248, -112, -32, 896, 128, 416, 46, 40, 56, 40, 50, 728, 896, 910, 1120, 34, 178, 76, 178, 220, -112, -32, 896, 128, 416, 112, 122, 896, 1120, 58, 346, 142, 346, 430]\n assert candidate(expression = \"44-22*3+55/5-66*7+88\") == []\n assert candidate(expression = \"9*3-4*2+1/1-5\") == []\n assert candidate(expression = \"9*3+2*8-4*5+6/3\") == []\n assert candidate(expression = \"8*7-6*5+4*3-2*1\") == [-376, -376, -664, -376, -664, -376, -376, -664, -1144, -376, -664, -376, -664, -1144, -216, -216, -264, -216, -264, -376, -376, -216, -216, -744, -1224, -264, -1224, -744, -376, -664, -376, -664, -1144, -216, -264, -376, -216, -744, -1224, -264, -1224, -744, 72, 72, 120, 72, 120, 72, 72, 120, 200, 72, 120, 72, 120, 200, -152, -152, -104, -152, -104, 72, 72, 120, 72, 120, -376, -376, -216, -216, 72, 72, -152, -152, 72, 72, -776, -1256, -296, -1256, -776, 120, 200, -104, 120, -1144, -664, 200, -472, 200, -376, -664, -376, -664, -1144, -216, -264, -376, -216, -744, -1224, -264, -1224, -744, 72, 120, 72, 120, 200, -152, -104, 72, 120, -376, -216, 72, -152, 72, -776, -1256, -296, -1256, -776, 120, 200, -104, 120, -1144, -664, 200, -472, 200, 2, 2, -34, 2, -34, 2, 2, -34, -94, 2, -34, 2, -34, -94, 22, 22, 16, 22, 16, 2, 2, 22, 22, -44, -104, 16, -104, -44, 2, -34, 2, -34, -94, 22, 16, 2, 22, -44, -104, 16, -104, -44, 72, 72, 120, 72, 120, 72, 72, 120, 200, 72, 120, 72, 120, 200, 450, 450, 750, 450, 750, 450, 450, 750, 1250, 450, 750, 450, 750, 1250, -180, -180, -174, -180, -174, 44, 44, 50, 44, 50, 30, 30, 36, 30, 36, 44, 44, 50, 44, 50, 254, 254, 260, 254, 260, -376, -376, -216, -216, 72, 72, -152, -152, 72, 72, 2, 2, 22, 22, 72, 72, 450, 450, -180, -180, 44, 44, 30, 30, 44, 44, 254, 254, -762, -1242, -282, -1242, -762, 134, 214, -90, 134, -1130, -650, 214, -458, 214, -48, -108, 12, -108, -48, 134, 214, 848, 1348, -174, 50, 36, 50, 260, -1130, -650, 214, -458, 214, 4, 64, 214, 1348, -542, 130, 88, 130, 760, -376, -664, -376, -664, -1144, -216, -264, -376, -216, -744, -1224, -264, -1224, -744, 72, 120, 72, 120, 200, -152, -104, 72, 120, -376, -216, 72, -152, 72, -776, -1256, -296, -1256, -776, 120, 200, -104, 120, -1144, -664, 200, -472, 200, 2, -34, 2, -34, -94, 22, 16, 2, 22, -44, -104, 16, -104, -44, 72, 120, 72, 120, 200, 450, 750, 450, 750, 1250, -180, -174, 44, 50, 30, 36, 44, 50, 254, 260, -376, -216, 72, -152, 72, 2, 22, 72, 450, -180, 44, 30, 44, 254, -762, -1242, -282, -1242, -762, 134, 214, -90, 134, -1130, -650, 214, -458, 214, -48, -108, 12, -108, -48, 134, 214, 848, 1348, -174, 50, 36, 50, 260, -1130, -650, 214, -458, 214, 4, 64, 214, 1348, -542, 130, 88, 130, 760]\n assert candidate(expression = \"3+3*3-3+3*3-3+3\") == [30, -24, -6, -6, -24, 66, -42, -6, -24, -6, -24, 3, -24, -42, -24, 30, 12, 12, 30, 30, -24, -24, 30, -42, -60, 12, -42, 12, 12, -6, 21, -6, -24, 12, 30, 12, 12, -24, -42, 30, -24, 30, 18, 0, 6, 6, 0, 30, -6, 6, 0, 6, 0, 9, 0, -6, -6, 12, 6, 6, 12, 0, 18, 12, 12, 18, 30, -24, -24, 30, -6, 12, -6, 12, -24, 30, -30, -48, 24, -30, 24, -6, -12, 6, 12, -30, 24, 6, 6, 24, 6, -12, 15, -12, -30, 6, 24, 6, 6, -30, -48, 24, -30, 24, 12, 6, 15, 6, 0, 6, 12, 12, 18, 6, 6, 6, 6, 6, -24, -42, 30, -24, 30, 0, -6, 12, 18, -24, 30, 12, 12, 30, 54, -54, -18, -18, -54, 126, -90, -18, -54, -18, -54, 0, -54, -90, -54, 54, 18, 18, 54, 54, -54, -54, 54, -90, -126, 18, -90, 18, 18, -18, 36, -18, -54, 18, 54, 18, 18, -54, -90, 54, -54, 54, 18, 0, 6, 6, 0, 30, -6, 6, 0, 6, 0, 9, 0, -6, 24, 6, 12, 12, 6, 36, 0, 12, 6, 12, 6, 15, 6, 0, -6, 12, 6, 6, 12, 0, 18, 12, 12, 18, -9, 9, 3, 3, 9, 0, 18, 12, 12, 18, 6, 24, 18, 18, 24, 18, -18, -36, 36, -18, 18, -18, 18, -36, 36, 54, -54, -54, 54, -18, 18, -36, 36, -18, 18, -36, 36, -9, 9, -36, 36, -54, 54, -30, -48, 24, -30, 24, -6, -12, 6, 12, -30, 24, 6, 6, 24, -60, -96, 48, -60, 48, -6, -12, 0, -6, 6, 12, 3, 12, 18, -24, 30, 12, 12, 30, -60, 48, 12, 30, 12, 30, 3, 30, 48, 6, -12, 15, -12, -30, 6, 24, 6, 6, -30, -48, 24, -30, 24, 12, 6, 15, 6, 0, 6, 12, 12, 18, 6, 6, 6, 6, 6, -24, -42, 30, -24, 30, 0, -6, 12, 18, -24, 30, 12, 12, 30, 3, -33, 21, -33, -69, 3, 39, 3, 3, -69, -105, 39, -69, 39, 12, 6, 15, 6, 0, 18, 12, 21, 12, 6, 6, 12, 12, 18, 3, 9, 12, 18, 18, 24, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, -24, -42, 30, -24, 30, 0, -6, 12, 18, -24, 30, 12, 12, 30, -54, -90, 54, -54, 54, 0, -6, 6, 0, 12, 18, 9, 18, 24, -18, 36, 18, 18, 36, -54, 54, 18, 36, 18, 36, 9, 36, 54]\n assert candidate(expression = \"5*6-7+8-9*10+11\") == [900, 460, 100, 350, -10, 900, 460, -600, -600, 350, -10, 350, -325, -325, -910, -470, -110, -360, 0, -990, -550, -910, -470, 0, 0, -210, -1890, -210, 460, 100, 460, -215, -215, -360, 0, -440, -360, 55, 55, -45, -845, -45, 204, 116, 44, 94, 22, 204, 116, -96, -96, 94, 22, 94, -41, -41, -186, -98, -26, -76, -4, -158, -70, 2, -48, 24, -234, -146, -154, -66, -174, -86, -186, -98, -158, -70, 0, 0, -210, -1890, -210, 504, 504, -126, 462, -1134, 546, 126, -126, 462, 416, 56, 416, -259, -259, -404, -44, -484, -404, 11, 11, -89, -889, -89, 116, 44, 116, -19, -19, -76, -4, -48, 24, -124, -44, -64, -76, -48, 11, 11, -89, -889, -89, 251, 251, -49, 231, -529, 271, 71, -49, 231]\n assert candidate(expression = \"22*9-88+77/7-66*5+44\") == []\n assert candidate(expression = \"5*5-4*4+3*3-2*2+1\") == [125, 65, -235, -55, -235, -115, -135, -235, -475, -15, -195, -175, -195, -355, 445, 305, -395, 25, -395, -115, -135, -275, -295, -395, -635, -395, -635, -1115, -15, -195, -175, -195, -355, 145, -275, -175, -335, -275, -435, -275, -435, -755, -10, -25, -100, -55, -100, -70, -75, -100, -160, -45, -90, -85, -90, -130, 445, 305, -395, 25, -395, 310, 215, -260, 25, -260, -205, -210, -365, -370, -70, -75, -365, -370, -230, -235, -395, -635, -395, -635, -1115, -260, -320, -395, -260, -725, -1205, -320, -1205, -800, 0, -180, -160, -180, -340, 160, -260, -160, -320, -260, -420, -260, -420, -740, -45, -90, -85, -90, -130, 160, -260, 115, -170, -220, -380, -85, -380, -245, -260, -420, -260, -420, -740, -170, -210, -260, -170, -480, -800, -210, -800, -530, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -100, -85, -10, -55, -10, -40, -35, -10, 50, -65, -20, -25, -20, 20, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, -265, -260, -425, -420, -130, -125, -425, -420, -290, -285, 35, 40, 75, 80, -40, -35, 35, 40, -375, -370, -240, -235, 75, 80, -150, -145, 75, 80, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, 10, -170, -150, -170, -330, 170, -250, -150, -310, -250, -410, -250, -410, -730, -35, -80, -75, -80, -120, 170, -250, 125, -160, -210, -370, -75, -370, -235, -250, -410, -250, -410, -730, -160, -200, -250, -160, -470, -790, -200, -790, -520, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -65, -20, -25, -20, 20, 10, 55, 50, 55, 95, 120, -225, 75, -135, -30, 75, 45, -75, -30, 75, -250, -410, -115, -410, -275, 50, 90, -25, 50, -360, -225, 90, -135, 90, -225, -385, -225, -385, -705, -135, -175, -225, -135, -445, -765, -175, -765, -495, 75, 115, 75, 115, 195, -75, -35, 75, 115, -225, -135, 75, -75, 75, -485, -805, -215, -805, -535, 115, 195, -35, 115, -705, -435, 195, -255, 195, 45, 33, -27, 9, -27, -3, -7, -27, -75, 17, -19, -15, -19, -51, 109, 81, -59, 25, -59, -3, -7, -35, -39, -59, -107, -59, -107, -203, 17, -19, -15, -19, -51, 49, -35, -15, -47, -35, -67, -35, -67, -131, 18, 15, 0, 9, 0, 6, 5, 0, -12, 11, 2, 3, 2, -6, 109, 81, -59, 25, -59, 82, 63, -32, 25, -32, -21, -22, -53, -54, 6, 5, -53, -54, -26, -27, -59, -107, -59, -107, -203, -32, -44, -59, -32, -125, -221, -44, -221, -140, 20, -16, -12, -16, -48, 52, -32, -12, -44, -32, -64, -32, -64, -128, 11, 2, 3, 2, -6, 52, -32, 43, -14, -24, -56, 3, -56, -29, -32, -64, -32, -64, -128, -14, -22, -32, -14, -76, -140, -22, -140, -86, -25, -10, 65, 20, 65, 35, 40, 65, 125, 10, 55, 50, 55, 95, -105, -70, 105, 0, 105, 35, 40, 75, 80, 105, 165, 105, 165, 285, 10, 55, 50, 55, 95, -30, 75, 50, 90, 75, 115, 75, 115, 195, -105, -42, 273, 84, 273, 147, 168, 273, 525, 42, 231, 210, 231, 399, -441, -294, 441, 0, 441, 147, 168, 315, 336, 441, 693, 441, 693, 1197, 42, 231, 210, 231, 399, -126, 315, 210, 378, 315, 483, 315, 483, 819, -64, -61, -46, -55, -46, -52, -51, -46, -34, -57, -48, -49, -48, -40, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 0, 3, 18, 9, 18, 12, 13, 18, 30, 7, 16, 15, 16, 24, 11, 14, 29, 20, 29, 23, 24, 29, 41, 18, 27, 26, 27, 35, 75, 78, 93, 84, 93, 87, 88, 93, 105, 82, 91, 90, 91, 99, 345, 230, -345, 0, -345, 210, 140, -210, 0, -210, -105, -70, 105, 0, 105, 120, 80, -120, 0, -120, -105, -70, 105, 0, 105, 9, 6, -9, 0, -9, -18, -12, 18, 0, 18, -105, -70, 105, 0, 105, -441, -294, 441, 0, 441, 156, 104, -156, 0, -156, -69, -46, 69, 0, 69, -36, -24, 36, 0, 36, -69, -46, 69, 0, 69, -261, -174, 261, 0, 261, -241, -240, -401, -400, -106, -105, -401, -400, -266, -265, 59, 60, 99, 100, -16, -15, 59, 60, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -33, -32, -65, -64, -6, -5, -65, -64, -38, -37, 59, 60, 99, 100, 267, 268, 435, 436, -52, -51, 23, 24, 12, 13, 23, 24, 87, 88, -351, -350, -216, -215, 99, 100, -126, -125, 99, 100, -15, -14, 12, 13, 99, 100, 435, 436, -162, -161, 63, 64, 30, 31, 63, 64, 255, 256, -345, -585, -345, -585, -1065, -210, -270, -345, -210, -675, -1155, -270, -1155, -750, 105, 165, 105, 165, 285, -120, -60, 105, 165, -345, -210, 105, -120, 105, -735, -1215, -330, -1215, -810, 165, 285, -60, 165, -1065, -660, 285, -390, 285, -9, -57, -9, -57, -153, 18, 6, -9, 18, -75, -171, 6, -171, -90, 105, 165, 105, 165, 285, 441, 693, 441, 693, 1197, -156, -144, 69, 81, 36, 48, 69, 81, 261, 273, -345, -210, 105, -120, 105, -9, 18, 105, 441, -156, 69, 36, 69, 261, -711, -1191, -306, -1191, -786, 189, 309, -36, 189, -1041, -636, 309, -366, 309, -87, -183, -6, -183, -102, 189, 309, 813, 1317, -144, 81, 48, 81, 273, -1041, -636, 309, -366, 309, -33, 48, 309, 1317, -474, 201, 102, 201, 777, 6, -174, -154, -174, -334, 166, -254, -154, -314, -254, -414, -254, -414, -734, -39, -84, -79, -84, -124, 166, -254, 121, -164, -214, -374, -79, -374, -239, -254, -414, -254, -414, -734, -164, -204, -254, -164, -474, -794, -204, -794, -524, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, -69, -24, -29, -24, 16, 6, 51, 46, 51, 91, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, -254, -414, -119, -414, -279, 46, 86, -29, 46, -364, -229, 86, -139, 86, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, 22, -14, -10, -14, -46, 54, -30, -10, -42, -30, -62, -30, -62, -126, 13, 4, 5, 4, -4, 54, -30, 45, -12, -22, -54, 5, -54, -27, -30, -62, -30, -62, -126, -12, -20, -30, -12, -74, -138, -20, -138, -84, 6, 51, 46, 51, 91, -34, 71, 46, 86, 71, 111, 71, 111, 191, 22, 211, 190, 211, 379, -146, 295, 190, 358, 295, 463, 295, 463, 799, -57, -48, -49, -48, -40, 18, 27, 26, 27, 35, 7, 16, 15, 16, 24, 18, 27, 26, 27, 35, 82, 91, 90, 91, 99, 116, -229, 71, -139, -34, 71, 41, -79, -34, 71, 4, -5, -5, 13, -34, 71, -146, 295, 53, -103, -22, 47, -11, 25, -22, 47, -86, 175, -238, -398, -103, -398, -263, 62, 102, -13, 62, -348, -213, 102, -123, 102, -30, -62, -3, -62, -35, 62, 102, 270, 438, -49, 26, 15, 26, 90, -348, -213, 102, -123, 102, -12, 15, 102, 438, -159, 66, 33, 66, 258, -229, -389, -229, -389, -709, -139, -179, -229, -139, -449, -769, -179, -769, -499, 71, 111, 71, 111, 191, -79, -39, 71, 111, -229, -139, 71, -79, 71, -489, -809, -219, -809, -539, 111, 191, -39, 111, -709, -439, 191, -259, 191, -5, -37, -5, -37, -101, 13, 5, -5, 13, -49, -113, 5, -113, -59, 71, 111, 71, 111, 191, 295, 463, 295, 463, 799, -103, -95, 47, 55, 25, 33, 47, 55, 175, 183, -229, -139, 71, -79, 71, -5, 13, 71, 295, -103, 47, 25, 47, 175, -473, -793, -203, -793, -523, 127, 207, -23, 127, -693, -423, 207, -243, 207, -57, -121, -3, -121, -67, 127, 207, 543, 879, -95, 55, 33, 55, 183, -693, -423, 207, -243, 207, -21, 33, 207, 879, -315, 135, 69, 135, 519]\n assert candidate(expression = \"10*2-5*3+2-8/4+9*2\") == []\n assert candidate(expression = \"7-6+5*4-3\") == [-4, -16, -4, -16, -34, 6, 18, -4, 6, -22, -40, 18, -19, 21]\n assert candidate(expression = \"12-8*2+4/1+6*2-5\") == []\n assert candidate(expression = \"7+3*2-5/1+8\") == []\n assert candidate(expression = \"100-50*2+25/5+15*3-5*2\") == []\n assert candidate(expression = \"8-6*2+4/2+3*3-1\") == []\n assert candidate(expression = \"10-5*2+3*2-1\") == [-15, -25, -15, -25, -35, -3, -5, -15, -3, -29, -39, -5, -39, -15, 25, 35, 25, 35, 45, 3, 5, 13, 15, -15, -3, 25, 3, 13, -31, -41, -7, -41, -17, 39, 49, 5, 15, -31, -7, 49, 5, 25]\n assert candidate(expression = \"5-3*2+4*3\") == [-37, -49, -13, -49, -25, 28, 36, 11, 16, -39, -15, 36, 9, 24]\n assert candidate(expression = \"3-2*2+1+4*5\") == [-43, -51, -43, -67, -67, -22, -26, -23, -22, -67, -67, -42, -47, -42, 23, 27, 23, 35, 35, 20, 24, 23, 27, 17, 18, 23, 20, 23, -55, -55, -30, -35, -30, 35, 35, 20, 35, 5, 10, 35, 20, 35]\n assert candidate(expression = \"1+2+3+4+5+6+7+8+9+0\") == [45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 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45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45]\n assert candidate(expression = \"18*2-5*3+6/2-4*3\") == []\n assert candidate(expression = \"9+8*7+6-5*4+3-2*1+0\") == [-87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -55, -55, -55, -55, -55, -151, -151, -55, -55, -87, -87, -55, -151, -55, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, 105, -39, -39, -39, -39, -39, 105, 105, 105, 105, 105, -183, -183, -87, -87, 105, 105, -39, -39, 105, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, -39, -39, 105, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -87, -55, -55, -55, -55, -55, -151, -151, -55, -55, -87, -87, -55, -151, -55, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, -39, -39, -39, -39, -39, 105, 105, 105, 105, 105, -39, -39, -39, -39, -39, 273, 273, 273, 273, 273, 273, 273, 273, 273, 273, -183, -183, -87, -87, 105, 105, -39, -39, 105, 105, -183, -183, -87, -87, 441, 441, 441, 441, -39, -39, 105, 105, -39, -39, 273, 273, 273, 273, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 105, 105, 105, 105, 105, -39, -39, 105, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -87, -87, -87, -55, -55, -151, -55, -87, -87, -55, -151, -55, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, -39, -39, 105, 105, -39, -39, 273, 273, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 70, 70, 70, 70, 70, 52, 52, 70, 70, 34, 46, 70, 52, 70, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 88, 92, 92, 92, 92, 92, 80, 80, 92, 92, 88, 88, 92, 80, 92, 88, 88, 88, 88, 88, 92, 92, 80, 92, 88, 88, 92, 80, 92, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 50, 50, 50, 50, 50, 38, 38, 50, 50, 46, 46, 50, 38, 50, 46, 46, 46, 46, 46, 50, 50, 38, 50, 46, 46, 50, 38, 50, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 329, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 504, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, 294, -46, -46, -46, -46, -46, 98, 98, 98, 98, 98, -46, -46, -46, -46, -46, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 52, 52, 52, 52, 52, 70, 70, 70, 70, 70, 94, 94, 94, 94, 94, 52, 52, 52, 52, 52, 266, 266, 266, 266, 266, 266, 266, 266, 266, 266, 238, 238, 238, 238, 238, 406, 406, 406, 406, 406, 238, 238, 238, 238, 238, -169, -169, -73, -73, 119, 119, -25, -25, 119, 119, -169, -169, -73, -73, 455, 455, 455, 455, -25, -25, 119, 119, -25, -25, 287, 287, 287, 287, 34, 34, 46, 46, 70, 70, 52, 52, 70, 70, 76, 76, 88, 88, 34, 34, 46, 46, 455, 455, 455, 455, 406, 406, 700, 700, 406, 406, -46, -46, 98, 98, -46, -46, 266, 266, 266, 266, 52, 52, 70, 70, 94, 94, 52, 52, 266, 266, 266, 266, 238, 238, 406, 406, 238, 238, -87, -87, -55, -151, -55, 105, 105, -39, 105, -183, -87, 105, -39, 105, -87, -87, -55, -151, -55, 329, 329, 329, 329, -39, 105, -39, 273, 273, -183, -87, 105, -39, 105, -183, -87, 441, 441, -39, 105, -39, 273, 273, 46, 46, 50, 38, 50, 70, 70, 52, 70, 34, 46, 70, 52, 70, 88, 88, 92, 80, 92, 46, 46, 50, 38, 50, 329, 329, 329, 329, 294, 294, 504, 504, 294, 294, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 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330, 330, 1080, 1080, 330, 330, 600, 600, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481, -169, -73, 119, -25, 119, -169, -73, 455, 455, -25, 119, -25, 287, 287, 34, 46, 70, 52, 70, 76, 88, 34, 46, 455, 455, 406, 700, 406, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -376, -172, 236, -70, 236, -376, -172, 950, 950, -70, 236, -70, 593, 593, 34, 46, 70, 52, 70, 88, 100, 124, 106, 124, 76, 88, 34, 46, 184, 196, 34, 46, 88, 100, 509, 509, 460, 754, 460, 950, 950, 460, 838, 754, 460, 1510, 460, 838, -46, 98, -46, 266, 266, 52, 70, 94, 52, 266, 266, 238, 406, 238, -118, 188, -118, 545, 545, 52, 70, 106, 124, 94, 52, 202, 52, 106, 293, 293, 265, 433, 265, 545, 545, 265, 481, 433, 265, 865, 265, 481]\n assert candidate(expression = \"15-14*13+12*11-10*9+8*7\") == [107185, 197905, 22513, 197905, 113233, -11087, -20159, 3697, -11087, 186817, 102145, -20159, 83329, -20159, 7085, 14645, 29, 14645, 7589, -11087, -20159, -111187, -203419, 12321, -2463, -1539, -2463, -16323, 186817, 102145, -20159, 83329, -20159, 3557, -3499, -20159, -203419, 91953, -11535, -5067, -11535, -108555, 223665, 412665, 47265, 412665, 236265, -22735, -41635, 8065, -22735, 389565, 213165, -41635, 173965, -41635, 7085, 14645, 29, 14645, 7589, 5265, 12825, -1791, 12825, 5769, -22735, -41635, -122835, -224895, -22735, -41635, -122835, -224895, -241135, -441475, 12321, -2463, -1539, -2463, -16323, 26881, -3919, -1539, -3359, -3919, -17779, -3919, -17779, -34159, 185725, 101053, -21251, 82237, -21251, 2465, -4591, -21251, -204511, 90861, -12627, -6159, -12627, -109647, 389565, 213165, -41635, 173965, -41635, 2465, -4591, -10275, -17331, -41635, -224895, -41635, -224895, -441475, 90861, -12627, -6159, -12627, -109647, 192781, -22819, -6159, -18899, -22819, -119839, -22819, -119839, -234499, 7501, 13981, 1453, 13981, 7933, -947, -1595, 109, -947, 13189, 7141, -1595, 5797, -1595, 351, 891, -153, 891, 387, -947, -1595, -8097, -14685, 725, -331, -265, -331, -1321, 13189, 7141, -1595, 5797, -1595, 99, -405, -1595, -14685, 6413, -979, -517, -979, -7909, 223665, 412665, 47265, 412665, 236265, -22735, -41635, 8065, -22735, 389565, 213165, -41635, 173965, -41635, 123981, 228741, 26205, 228741, 130965, -12595, -23071, 4477, -12595, 215937, 118161, -23071, 96433, -23071, -1365, -825, -1869, -825, -1329, -3185, -2645, -3689, -2645, -3149, 351, 891, -153, 891, 387, -3185, -2645, -3689, -2645, -3149, -1469, -929, -1973, -929, -1433, -22735, -41635, -122835, -224895, -22735, -41635, -122835, -224895, -241135, -441475, -12595, -23071, -19745, -36161, -22735, -41635, -12595, -23071, -131285, -240365, -249585, -456945, -19745, -36161, -249585, -456945, -138045, -252741, 13049, -1735, -811, -1735, -15595, 27609, -3191, -811, -2631, -3191, -17051, -3191, -17051, -33431, 725, -331, -265, -331, -1321, 27609, -3191, 15285, -1787, -1981, -3801, -265, -3801, -2085, -3191, -17051, -3191, -17051, -33431, -1787, -2777, -3191, -1787, -18221, -34601, -2777, -34601, -19157, 185725, 101053, -21251, 82237, -21251, 2465, -4591, -21251, -204511, 90861, -12627, -6159, -12627, -109647, 389565, 213165, -41635, 173965, -41635, 2465, -4591, -10275, -17331, -41635, -224895, -41635, -224895, -441475, 90861, -12627, -6159, -12627, -109647, 192781, -22819, -6159, -18899, -22819, -119839, -22819, -119839, -234499, 12097, 6049, -2687, 4705, -2687, -993, -1497, -2687, -15777, 5321, -2071, -1609, -2071, -9001, 389565, 213165, -41635, 173965, -41635, 215937, 118161, -23071, 96433, -23071, -13005, -13509, -25745, -26249, -993, -1497, -25745, -26249, -13733, -14237, -41635, -224895, -41635, -224895, -441475, -23071, -36161, -41635, -23071, -240365, -456945, -36161, -456945, -252741, 91589, -11899, -5431, -11899, -108919, 193509, -22091, -5431, -18171, -22091, -119111, -22091, -119111, -233771, 5321, -2071, -1609, -2071, -9001, 193509, -22091, 107241, -12263, -13621, -26361, -1609, -26361, -14349, -22091, -119111, -22091, -119111, -233771, -12263, -19193, -22091, -12263, -127301, -241961, -19193, -241961, -133853, -7655, -14135, -1607, -14135, -8087, 793, 1441, -263, 793, -13343, -7295, 1441, -5951, 1441, -505, -1045, -1, -1045, -541, 793, 1441, 7943, 14531, -879, 177, 111, 177, 1167, -13343, -7295, 1441, -5951, 1441, -253, 251, 1441, 14531, -6567, 825, 363, 825, 7755, -15975, -29475, -3375, -29475, -16875, 1625, 2975, -575, 1625, -27825, -15225, 2975, -12425, 2975, -505, -1045, -1, -1045, -541, -375, -915, 129, -915, -411, 1625, 2975, 8775, 16065, 1625, 2975, 8775, 16065, 17225, 31535, -879, 177, 111, 177, 1167, -1919, 281, 111, 241, 281, 1271, 281, 1271, 2441, -13265, -7217, 1519, -5873, 1519, -175, 329, 1519, 14609, -6489, 903, 441, 903, 7833, -27825, -15225, 2975, -12425, 2975, -175, 329, 735, 1239, 2975, 16065, 2975, 16065, 31535, -6489, 903, 441, 903, 7833, -13769, 1631, 441, 1351, 1631, 8561, 1631, 8561, 16751, -7835, -14315, -1787, -14315, -8267, 613, 1261, -443, 613, -13523, -7475, 1261, -6131, 1261, -685, -1225, -181, -1225, -721, 613, 1261, 7763, 14351, -1059, -3, -69, -3, 987, -13523, -7475, 1261, -6131, 1261, -433, 71, 1261, 14351, -6747, 645, 183, 645, 7575, -7655, -14135, -1607, -14135, -8087, 793, 1441, -263, 793, -13343, -7295, 1441, -5951, 1441, -505, -1045, -1, -1045, -541, 793, 1441, 7943, 14531, -879, 177, 111, 177, 1167, -13343, -7295, 1441, -5951, 1441, -253, 251, 1441, 14531, -6567, 825, 363, 825, 7755, 214065, 394965, 45225, 394965, 226125, -21775, -39865, 7705, -21775, 372855, 204015, -39865, 166495, -39865, 114381, 211041, 24165, 211041, 120825, -11635, -21301, 4117, -11635, 199227, 109011, -21301, 88963, -21301, -15975, -29475, -3375, -29475, -16875, 1625, 2975, -575, 1625, -27825, -15225, 2975, -12425, 2975, 99045, 182745, 20925, 182745, 104625, -10075, -18445, 3565, -10075, 172515, 94395, -18445, 77035, -18445, -15975, -29475, -3375, -29475, -16875, 1625, 2975, -575, 1625, -27825, -15225, 2975, -12425, 2975, -2665, -3205, -2161, -3205, -2701, -4485, -5025, -3981, -5025, -4521, -949, -1489, -445, -1489, -985, -4485, -5025, -3981, -5025, -4521, -2769, -3309, -2265, -3309, -2805, -505, -1045, -1, -1045, -541, -375, -915, 129, -915, -411, -685, -1225, -181, -1225, -721, -505, -1045, -1, -1045, -541, -4335, -4875, -3831, -4875, -4371, -2619, -3159, -2115, -3159, -2655, -375, -915, 129, -915, -411, -2355, -2895, -1851, -2895, -2391, -375, -915, 129, -915, -411, -21775, -39865, -121875, -223125, -21775, -39865, -121875, -223125, -240175, -439705, -11635, -21301, -18785, -34391, -21775, -39865, -11635, -21301, -130325, -238595, -248625, -455175, -18785, -34391, -248625, -455175, -137085, -250971, 1625, 2975, 8775, 16065, 1625, 2975, 8775, 16065, 17225, 31535, -10075, -18445, -2925, -5355, 1625, 2975, 8775, 16065, -21775, -39865, -11635, -21301, 1625, 2975, -10075, -18445, 1625, 2975, -131625, -240975, -249925, -457555, -20085, -36771, -249925, -457555, -138385, -253351, 8775, 16065, 17225, 31535, -2925, -5355, 8775, 16065, -240175, -439705, -128635, -235501, 17225, 31535, -111475, -204085, 17225, 31535, 13161, -1623, -699, -1623, -15483, 27721, -3079, -699, -2519, -3079, -16939, -3079, -16939, -33319, 837, -219, -153, -219, -1209, 27721, -3079, 15397, -1675, -1869, -3689, -153, -3689, -1973, -3079, -16939, -3079, -16939, -33319, -1675, -2665, -3079, -1675, -18109, -34489, -2665, -34489, -19045, -879, 177, 111, 177, 1167, -1919, 281, 111, 241, 281, 1271, 281, 1271, 2441, -1059, -3, -69, -3, 987, -879, 177, 111, 177, 1167, 26521, -2959, 14197, -1555, -1919, 281, 12301, -1339, -1919, 281, -2049, -3869, -333, -3869, -2153, 111, 241, -69, 111, -3719, -2003, 241, -1739, 241, -2959, -16819, -2959, -16819, -33199, -1555, -2545, -2959, -1555, -17989, -34369, -2545, -34369, -18925, 281, 1271, 281, 1271, 2441, -1339, -349, 281, 1271, -2959, -1555, 281, -1339, 281, -18169, -34549, -2725, -34549, -19105, 1271, 2441, -349, 1271, -33199, -17755, 2441, -15379, 2441, 185815, 101143, -21161, 82327, -21161, 2555, -4501, -21161, -204421, 90951, -12537, -6069, -12537, -109557, 389655, 213255, -41545, 174055, -41545, 2555, -4501, -10185, -17241, -41545, -224805, -41545, -224805, -441385, 90951, -12537, -6069, -12537, -109557, 192871, -22729, -6069, -18809, -22729, -119749, -22729, -119749, -234409, 12187, 6139, -2597, 4795, -2597, -903, -1407, -2597, -15687, 5411, -1981, -1519, -1981, -8911, 389655, 213255, -41545, 174055, -41545, 216027, 118251, -22981, 96523, -22981, -12915, -13419, -25655, -26159, -903, -1407, -25655, -26159, -13643, -14147, -41545, -224805, -41545, -224805, -441385, -22981, -36071, -41545, -22981, -240275, -456855, -36071, -456855, -252651, 91679, -11809, -5341, -11809, -108829, 193599, -22001, -5341, -18081, -22001, -119021, -22001, -119021, -233681, 5411, -1981, -1519, -1981, -8911, 193599, -22001, 107331, -12173, -13531, -26271, -1519, -26271, -14259, -22001, -119021, -22001, -119021, -233681, -12173, -19103, -22001, -12173, -127211, -241871, -19103, -241871, -133763, -13265, -7217, 1519, -5873, 1519, -175, 329, 1519, 14609, -6489, 903, 441, 903, 7833, -27825, -15225, 2975, -12425, 2975, -175, 329, 735, 1239, 2975, 16065, 2975, 16065, 31535, -6489, 903, 441, 903, 7833, -13769, 1631, 441, 1351, 1631, 8561, 1631, 8561, 16751, -14525, -8477, 259, -7133, 259, -1435, -931, 259, 13349, -7749, -357, -819, -357, 6573, -13265, -7217, 1519, -5873, 1519, -175, 329, 1519, 14609, -6489, 903, 441, 903, 7833, 372855, 204015, -39865, 166495, -39865, 199227, 109011, -21301, 88963, -21301, -27825, -15225, 2975, -12425, 2975, 172515, 94395, -18445, 77035, -18445, -27825, -15225, 2975, -12425, 2975, -15295, -14791, -28035, -27531, -3283, -2779, -28035, -27531, -16023, -15519, -175, 329, 735, 1239, -1435, -931, -175, 329, -26985, -26481, -14973, -14469, 735, 1239, -13125, -12621, 735, 1239, -39865, -223125, -39865, -223125, -439705, -21301, -34391, -39865, -21301, -238595, -455175, -34391, -455175, -250971, 2975, 16065, 2975, 16065, 31535, -18445, -5355, 2975, 16065, -39865, -21301, 2975, -18445, 2975, -240975, -457555, -36771, -457555, -253351, 16065, 31535, -5355, 16065, -439705, -235501, 31535, -204085, 31535, 91791, -11697, -5229, -11697, -108717, 193711, -21889, -5229, -17969, -21889, -118909, -21889, -118909, -233569, 5523, -1869, -1407, -1869, -8799, 193711, -21889, 107443, -12061, -13419, -26159, -1407, -26159, -14147, -21889, -118909, -21889, -118909, -233569, -12061, -18991, -21889, -12061, -127099, -241759, -18991, -241759, -133651, -6489, 903, 441, 903, 7833, -13769, 1631, 441, 1351, 1631, 8561, 1631, 8561, 16751, -7749, -357, -819, -357, 6573, -6489, 903, 441, 903, 7833, 185311, -21049, 99043, -11221, -13769, 1631, 85771, -9709, -13769, 1631, -14679, -27419, -2667, -27419, -15407, 441, 1351, -819, 441, -26369, -14357, 1351, -12509, 1351, -21049, -118069, -21049, -118069, -232729, -11221, -18151, -21049, -11221, -126259, -240919, -18151, -240919, -132811, 1631, 8561, 1631, 8561, 16751, -9709, -2779, 1631, 8561, -21049, -11221, 1631, -9709, 1631, -127519, -242179, -19411, -242179, -134071, 8561, 16751, -2779, 8561, -232729, -124621, 16751, -107989, 16751]\n assert candidate(expression = \"100-50*2+25\") == [-1250, -25, 1350, 25, 125]\n assert candidate(expression = \"8*7+6-5*4+3\") == [-176, -80, 112, -32, 112, -176, -80, 448, 448, -32, 112, -32, 280, 280, 27, 39, 63, 45, 63, 69, 81, 27, 39, 448, 448, 399, 693, 399, -53, 91, -53, 259, 259, 45, 63, 87, 45, 259, 259, 231, 399, 231]\n assert candidate(expression = \"99*99-99+99\") == [-9801, 9801, 9603, 99, 9801]\n assert candidate(expression = \"4*3-2+1-5*6+7\") == [260, 148, 212, 92, 72, 260, 148, 116, 116, 92, 72, 92, 32, 32, -252, -140, -204, -84, -64, -260, -148, -252, -140, 260, 260, -156, -260, -156, 148, 128, 148, 88, 88, -84, -64, -92, -84, 148, 148, -44, -92, -44, 74, 46, 62, 32, 27, 74, 46, 38, 38, 32, 27, 32, 17, 17, -60, -32, -48, -18, -13, -54, -26, -42, -12, -7, -65, -37, -57, -29, -56, -28, -60, -32, -54, -26, 260, 260, -156, -260, -156, 182, 182, 0, 78, -65, 39, 52, 0, 78, 127, 107, 127, 67, 67, -105, -85, -113, -105, 127, 127, -65, -113, -65, 46, 41, 46, 31, 31, -18, -13, -12, -7, -23, -15, -14, -18, -12, 127, 127, -65, -113, -65, 91, 91, 7, 43, -23, 25, 31, 7, 43]\n assert candidate(expression = \"9*8*7-6*5*4+3*2*1\") == [-21096, -21096, -29736, -21096, -29736, -10728, -10728, -29736, -19368, -21096, -29736, -10728, -29736, -19368, -21096, -21096, -29736, -21096, -29736, -8568, -8568, -8568, -8568, -29736, -19368, -29736, -17208, -17208, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, -7704, -7704, -7704, -7704, 1872, 1872, -6192, -6192, 1872, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2196, -2196, -3276, -2196, -3276, -900, -900, -3276, -1980, -2196, -3276, -900, -3276, -1980, -2196, -2196, -3276, -2196, -3276, -630, -630, -630, -630, -3276, -1980, -3276, -1710, -1710, -2196, -3276, -900, -3276, -1980, -2196, -3276, -630, -630, -3276, -1980, -3276, -1710, -1710, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, 22500, 22500, 31500, 22500, 31500, 11700, 11700, 31500, 20700, 22500, 31500, 11700, 31500, 20700, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, 2340, 2340, 3276, 2340, 3276, 3600, 3600, 5040, 3600, 5040, 22500, 22500, 31500, 22500, 31500, -8082, -8082, -8082, -8082, 1494, 1494, -6570, -6570, 1494, 1494, -522, -522, -522, -522, 1494, 1494, 9054, 9054, -6570, -6570, 1494, 1494, 990, 990, 1494, 1494, 9054, 9054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2196, -3276, -900, -3276, -1980, -2196, -3276, -630, -630, -3276, -1980, -3276, -1710, -1710, 3600, 5040, 1872, 5040, 3312, 22500, 31500, 11700, 31500, 20700, -16560, -23184, 3600, 5040, 2340, 3276, 3600, 5040, 22500, 31500, -8082, -8082, 1494, -6570, 1494, -522, -522, 1494, 9054, -6570, 1494, 990, 1494, 9054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -21096, -21096, -29736, -21096, -29736, -10728, -10728, -29736, -19368, -21096, -29736, -10728, -29736, -19368, -21096, -21096, -29736, -21096, -29736, -8568, -8568, -8568, -8568, -29736, -19368, -29736, -17208, -17208, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, -7704, -7704, -7704, -7704, 1872, 1872, -6192, -6192, 1872, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 204, 204, 84, 204, 84, 348, 348, 84, 228, 204, 84, 348, 84, 228, 204, 204, 84, 204, 84, 378, 378, 378, 378, 84, 228, 84, 258, 258, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 204, 204, 84, 204, 84, 348, 348, 84, 228, 204, 84, 348, 84, 228, 204, 204, 84, 204, 84, 378, 378, 378, 378, 84, 228, 84, 258, 258, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, 22500, 22500, 31500, 22500, 31500, 11700, 11700, 31500, 20700, 22500, 31500, 11700, 31500, 20700, 3600, 3600, 5040, 3600, 5040, 1872, 1872, 5040, 3312, 3600, 5040, 1872, 5040, 3312, 24900, 24900, 34860, 24900, 34860, 12948, 12948, 34860, 22908, 24900, 34860, 12948, 34860, 22908, 24900, 24900, 34860, 24900, 34860, 12948, 12948, 34860, 22908, 24900, 34860, 12948, 34860, 22908, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, 2340, 2340, 3276, 2340, 3276, 3600, 3600, 5040, 3600, 5040, 22500, 22500, 31500, 22500, 31500, -16560, -16560, -23184, -16560, -23184, 3600, 3600, 5040, 3600, 5040, 4740, 4740, 6636, 4740, 6636, 4740, 4740, 6636, 4740, 6636, 3600, 3600, 5040, 3600, 5040, 22500, 22500, 31500, 22500, 31500, 3600, 3600, 5040, 3600, 5040, 24900, 24900, 34860, 24900, 34860, 24900, 24900, 34860, 24900, 34860, -8130, -8130, -8130, -8130, 1446, 1446, -6618, -6618, 1446, 1446, -570, -570, -570, -570, 1446, 1446, 9006, 9006, -6618, -6618, 1446, 1446, 942, 942, 1446, 1446, 9006, 9006, -8130, -8130, -8130, -8130, 1446, 1446, -6618, -6618, 1446, 1446, 390, 390, 390, 390, 390, 390, 390, 390, 1446, 1446, 9006, 9006, 1446, 1446, 9966, 9966, 9966, 9966, -6618, -6618, 1446, 1446, 942, 942, 1446, 1446, 9006, 9006, -6618, -6618, 1446, 1446, 1902, 1902, 1902, 1902, 1446, 1446, 9006, 9006, 1446, 1446, 9966, 9966, 9966, 9966, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 588, 732, 588, 762, 762, 588, 732, 588, 762, 762, 5040, 3312, 31500, 20700, 5040, 3312, 34860, 22908, 34860, 22908, -23184, 5040, 3276, 5040, 31500, -23184, 5040, 6636, 6636, 5040, 31500, 5040, 34860, 34860, -16266, -16266, 2886, -13242, 2886, -1146, -1146, 2886, 18006, -13242, 2886, 1878, 2886, 18006, -16266, -16266, 2886, -13242, 2886, 774, 774, 774, 774, 2886, 18006, 2886, 19926, 19926, -13242, 2886, 1878, 2886, 18006, -13242, 2886, 3798, 3798, 2886, 18006, 2886, 19926, 19926, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2196, -3276, -900, -3276, -1980, -2196, -3276, -630, -630, -3276, -1980, -3276, -1710, -1710, 3600, 5040, 1872, 5040, 3312, 22500, 31500, 11700, 31500, 20700, -16560, -23184, 3600, 5040, 2340, 3276, 3600, 5040, 22500, 31500, -8082, -8082, 1494, -6570, 1494, -522, -522, 1494, 9054, -6570, 1494, 990, 1494, 9054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -21096, -29736, -10728, -29736, -19368, -21096, -29736, -8568, -8568, -29736, -19368, -29736, -17208, -17208, 3600, 5040, 1872, 5040, 3312, -16560, -23184, 3600, 5040, -7704, -7704, 1872, -6192, 1872, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 204, 84, 348, 84, 228, 204, 84, 378, 378, 84, 228, 84, 258, 258, 3600, 5040, 1872, 5040, 3312, 22500, 31500, 11700, 31500, 20700, 3600, 5040, 1872, 5040, 3312, 24900, 34860, 12948, 34860, 22908, 24900, 34860, 12948, 34860, 22908, -16560, -23184, 3600, 5040, 2340, 3276, 3600, 5040, 22500, 31500, -16560, -23184, 3600, 5040, 4740, 6636, 4740, 6636, 3600, 5040, 22500, 31500, 3600, 5040, 24900, 34860, 24900, 34860, -8130, -8130, 1446, -6618, 1446, -570, -570, 1446, 9006, -6618, 1446, 942, 1446, 9006, -8130, -8130, 1446, -6618, 1446, 390, 390, 390, 390, 1446, 9006, 1446, 9966, 9966, -6618, 1446, 942, 1446, 9006, -6618, 1446, 1902, 1902, 1446, 9006, 1446, 9966, 9966, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, -2772, -1476, -2772, -1206, -1206, 5040, 3312, 31500, 20700, -23184, 5040, 3276, 5040, 31500, -16218, -16218, 2934, -13194, 2934, -1098, -1098, 2934, 18054, -13194, 2934, 1926, 2934, 18054, -29232, -18864, -29232, -16704, -16704, 5040, 3312, -23184, 5040, -15840, -15840, 3312, -12816, 3312, 588, 732, 588, 762, 762, 588, 732, 588, 762, 762, 5040, 3312, 31500, 20700, 5040, 3312, 34860, 22908, 34860, 22908, -23184, 5040, 3276, 5040, 31500, -23184, 5040, 6636, 6636, 5040, 31500, 5040, 34860, 34860, -16266, -16266, 2886, -13242, 2886, -1146, -1146, 2886, 18006, -13242, 2886, 1878, 2886, 18006, -16266, -16266, 2886, -13242, 2886, 774, 774, 774, 774, 2886, 18006, 2886, 19926, 19926, -13242, 2886, 1878, 2886, 18006, -13242, 2886, 3798, 3798, 2886, 18006, 2886, 19926, 19926]\n assert candidate(expression = \"7+8*3-2*5+6\") == [-145, -97, 95, -1, 95, 9, 15, 95, 249, -43, 53, 27, 53, 123, -285, -195, 165, -15, 165, 9, 15, 23, 29, 165, 319, 165, 319, 473, -43, 53, 27, 53, 123, -99, 81, 27, 41, 81, 151, 81, 151, 221]\n assert candidate(expression = \"88+12*4-6/2+5*9-7\") == []\n assert candidate(expression = \"6/2-3*1+8/4\") == []\n assert candidate(expression = \"2*3+4-5*6/3\") == []\n assert candidate(expression = \"1+2-3*4+5-6*7+8\") == [246, 126, 36, 78, -12, 246, 126, -132, -132, 78, -12, 78, -84, -84, 76, 36, 6, 20, -10, 66, 26, 76, 36, -132, -132, -162, -312, -162, 94, 4, 94, -68, -68, 20, -10, 10, 20, -68, -68, -82, -152, -82, 82, 42, 12, 26, -4, 82, 42, -44, -44, 26, -4, 26, -28, -28, -94, -54, -24, -38, -8, -88, -48, -18, -32, -2, -114, -74, -104, -64, -98, -58, -94, -54, -88, -48, -104, -104, -134, -284, -134, -44, -44, -164, -74, -464, -314, -224, -164, -74, 110, 20, 110, -52, -52, 36, 6, 26, 36, -52, -52, -66, -136, -66, 42, 12, 42, -12, -12, -38, -8, -32, -2, -58, -48, -42, -38, -32, -40, -40, -54, -124, -54, -12, -12, -68, -26, -208, -138, -96, -68, -26, 246, 126, 36, 78, -12, 246, 126, -132, -132, 78, -12, 78, -84, -84, 76, 36, 6, 20, -10, 66, 26, 76, 36, -132, -132, -162, -312, -162, 94, 4, 94, -68, -68, 20, -10, 10, 20, -68, -68, -82, -152, -82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, -54, -24, -38, -8, -88, -48, -18, -32, -2, -94, -54, -24, -38, -8, -85, -45, -15, -29, 1, -85, -45, -15, -29, 1, -114, -74, -104, -64, -98, -58, -94, -54, -88, -48, -114, -74, -104, -64, -90, -50, -90, -50, -94, -54, -88, -48, -94, -54, -85, -45, -85, -45, -90, -90, -120, -270, -120, -30, -30, -150, -60, -450, -300, -210, -150, -60, -90, -90, -120, -270, -120, 0, 0, 0, 0, -150, -60, -150, -15, -15, -450, -300, -210, -150, -60, -450, -300, -90, -90, -150, -60, -150, -15, -15, 110, 20, 110, -52, -52, 36, 6, 26, 36, -52, -52, -66, -136, -66, 42, 12, 42, -12, -12, -38, -8, -32, -2, -58, -48, -42, -38, -32, -40, -40, -54, -124, -54, -12, -12, -68, -26, -208, -138, -96, -68, -26, 110, 20, 110, -52, -52, 36, 6, 26, 36, -52, -52, -66, -136, -66, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -38, -8, -32, -2, -38, -8, -29, 1, -29, 1, -58, -48, -42, -38, -32, -58, -48, -34, -34, -38, -32, -38, -29, -29, -34, -34, -48, -118, -48, -6, -6, -62, -20, -202, -132, -90, -62, -20, -34, -34, -48, -118, -48, 8, 8, 8, 8, -62, -20, -62, 1, 1, -202, -132, -90, -62, -20, -202, -132, -34, -34, -62, -20, -62, 1, 1]\n assert candidate(expression = \"10+20+30+40+50+60+70+80+90\") == [450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450, 450]\n assert candidate(expression = \"1+2+3+4+5+6+7+8+9\") == [45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45]\n assert candidate(expression = \"2*3+4*5-6*7+8\") == [-674, -354, -114, -226, 14, -134, -54, -114, 426, -274, -34, -22, -34, 218, -1190, -630, -210, -406, 14, -134, -54, -110, -30, -30, 510, -210, 510, 870, -274, -34, -22, -34, 218, -502, -82, -22, 2, 2, 254, -82, 254, 422, -334, -174, -54, -110, 10, -64, -24, -54, 216, -134, -14, -8, -14, 112, -1190, -630, -210, -406, 14, -850, -450, -150, -290, 10, -44, -4, -20, 20, -64, -24, -20, 20, -40, 0, -30, 510, -210, 510, 870, 30, 300, -210, -150, 600, 960, 300, 960, 660, -282, -42, -30, -42, 210, -510, -90, -30, -6, -6, 246, -90, 246, 414, -134, -14, -8, -14, 112, -510, -90, -362, -62, 12, 36, -8, 36, 16, -6, 246, -90, 246, 414, 22, 148, -90, -62, 288, 456, 148, 456, 316]\n assert candidate(expression = \"5+6*7-8*9/2\") == []\n assert candidate(expression = \"9-8+7*6-5+4*3-2+1\") == [-6, 50, 57, 29, 71, -41, 85, 57, 127, 29, 71, 29, 71, 141, -6, -62, -69, -41, -83, 1, 43, 1, -69, 99, 169, -69, 85, -83, 15, 57, 15, 57, 127, -41, -83, 15, -41, 85, 155, -83, 71, -97, -36, -28, -27, -31, -25, -41, -23, -27, -17, -31, -25, -31, -25, -15, -6, -14, -15, -11, -17, -36, -44, -45, -41, -47, 1, 43, 1, -69, 1, -65, 1, -21, 1, -81, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 21, 63, 21, 63, 133, -35, -77, 21, -35, 91, 161, -77, 77, -91, -33, -27, -33, -27, -17, -11, -17, -41, -47, 21, -35, -33, -11, -41, 79, 149, -89, 65, -103, -23, -13, -17, -47, 65, -103, -97, -31, -121, -6, 114, 129, 69, 159, -81, 189, 129, 279, 69, 159, 69, 159, 309, -6, -126, -141, -81, -171, 9, 99, 9, -141, 219, 369, -141, 189, -171, 39, 129, 39, 129, 279, -81, -171, 39, -81, 189, 339, -171, 159, -201, -36, -28, -27, -31, -25, -41, -23, -27, -17, -31, -25, -31, -25, -15, -76, -68, -67, -71, -65, -81, -63, -67, -57, -71, -65, -71, -65, -55, -6, -14, -15, -11, -17, -36, -44, -45, -41, -47, -6, -14, -15, -11, -17, -36, -44, -45, -41, -47, -76, -84, -85, -81, -87, 9, 35, 9, -77, 9, -73, 9, -29, 9, -89, 9, 99, 9, -141, 9, -73, 9, -153, 9, -29, 9, -89, 9, -29, 9, -89, 9, -169, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 177, 327, -183, 147, -213, -21, -11, -61, -51, -15, -45, -15, -45, -85, 51, -117, -111, -45, -135, 147, -213, -111, -231, -45, -135, -45, -135, -255, 21, 63, 21, 63, 133, -35, -77, 21, -35, 91, 161, -77, 77, -91, -33, -27, -33, -27, -17, -11, -17, -41, -47, 21, -35, -33, -11, -41, 79, 149, -89, 65, -103, -23, -13, -17, -47, 65, -103, -97, -31, -121, 53, 143, 53, 143, 293, -67, -157, 53, -67, 203, 353, -157, 173, -187, -33, -27, -33, -27, -17, -73, -67, -73, -67, -57, -11, -17, -41, -47, -11, -17, -41, -47, -81, -87, 21, -35, -33, -11, -41, 53, -67, -33, -73, -11, -41, -11, -41, -81, 79, 149, -89, 65, -103, -23, -13, -17, -47, 65, -103, -97, -31, -121, 175, 325, -185, 145, -215, -23, -13, -63, -53, -17, -47, -17, -47, -87, 49, -119, -113, -47, -137, 145, -215, -113, -233, -47, -137, -47, -137, -257, 8, -48, -55, -27, -69, 43, -83, -55, -125, -27, -69, -27, -69, -139, 8, 64, 71, 43, 85, 1, -41, 1, 71, -97, -167, 71, -83, 85, -13, -55, -13, -55, -125, 43, 85, -13, 43, -83, -153, 85, -69, 99, 38, 30, 29, 33, 27, 43, 25, 29, 19, 33, 27, 33, 27, 17, 8, 16, 17, 13, 19, 38, 46, 47, 43, 49, 1, -41, 1, 71, 1, 67, 1, 23, 1, 83, -79, -149, 89, -65, 103, 23, 13, 17, 47, -65, 103, 97, 31, 121, -19, -61, -19, -61, -131, 37, 79, -19, 37, -89, -159, 79, -75, 93, 35, 29, 35, 29, 19, 13, 19, 43, 49, -19, 37, 35, 13, 43, -77, -147, 91, -63, 105, 25, 15, 19, 49, -63, 105, 99, 33, 123, -6, 42, 48, 24, 60, -36, 72, 48, 108, 24, 60, 24, 60, 120, -6, -54, -60, -36, -72, 0, 36, 0, -60, 84, 144, -60, 72, -72, 12, 48, 12, 48, 108, -36, -72, 12, -36, 72, 132, -72, 60, -84, 8, -56, -64, -32, -80, 48, -96, -64, -144, -32, -80, -32, -80, -160, 8, 72, 80, 48, 96, 0, -48, 0, 80, -112, -192, 80, -96, 96, -16, -64, -16, -64, -144, 48, 96, -16, 48, -96, -176, 96, -80, 112, -46, -54, -55, -51, -57, -41, -59, -55, -65, -51, -57, -51, -57, -67, -86, -94, -95, -91, -97, -81, -99, -95, -105, -91, -97, -91, -97, -107, 38, 30, 29, 33, 27, 43, 25, 29, 19, 33, 27, 33, 27, 17, -41, -49, -50, -46, -52, -36, -54, -50, -60, -46, -52, -46, -52, -62, 43, 35, 34, 38, 32, 48, 30, 34, 24, 38, 32, 38, 32, 22, -6, 2, 3, -1, 5, -36, -28, -27, -31, -25, -6, 2, 3, -1, 5, -36, -28, -27, -31, -25, -76, -68, -67, -71, -65, 8, 16, 17, 13, 19, 38, 46, 47, 43, 49, -6, 2, 3, -1, 5, 8, 16, 17, 13, 19, -46, -38, -37, -41, -35, -86, -78, -77, -81, -75, 38, 46, 47, 43, 49, -41, -33, -32, -36, -30, 43, 51, 52, 48, 54, 0, 44, 0, -68, 0, -64, 0, -20, 0, -80, 0, 108, 0, -132, 0, -64, 0, -144, 0, -20, 0, -80, 0, -20, 0, -80, 0, -160, 0, -40, 0, 72, 0, 68, 0, 24, 0, 84, 0, 36, 0, -60, 0, -48, 0, 80, 0, -100, 0, -180, 0, 68, 0, -90, 0, 78, 0, -4, 0, -64, 0, -4, 0, -64, 0, -144, 0, 24, 0, 84, 0, -4, 0, 24, 0, -84, 0, -164, 0, 84, 0, -74, 0, 94, 75, 145, -93, 61, -107, -27, -17, -21, -51, 61, -107, -101, -35, -125, 171, 321, -189, 141, -219, -27, -17, -67, -57, -21, -51, -21, -51, -91, 45, -123, -117, -51, -141, 141, -219, -117, -237, -51, -141, -51, -141, -261, -79, -149, 89, -65, 103, 23, 13, 17, 47, -65, 103, 97, 31, 121, 63, 123, -81, 51, -93, -91, -171, 101, -75, 117, -61, -71, -101, -111, 23, 13, -56, -66, 28, 18, 3, -27, 3, -27, -67, 17, 47, 3, 17, -37, -77, 47, -32, 52, 63, -105, -99, -33, -123, 159, -201, -99, -219, -33, -123, -33, -123, -243, -63, 105, 99, 33, 123, 51, -93, -75, 117, -153, -273, 99, -138, 114, -9, -99, -9, -99, -219, 33, 123, -9, 33, -129, -249, 123, -114, 138, 23, 65, 23, 65, 135, -33, -75, 23, -33, 93, 163, -75, 79, -89, -31, -25, -31, -25, -15, -9, -15, -39, -45, 23, -33, -31, -9, -39, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 55, 145, 55, 145, 295, -65, -155, 55, -65, 205, 355, -155, 175, -185, -31, -25, -31, -25, -15, -71, -65, -71, -65, -55, -9, -15, -39, -45, -9, -15, -39, -45, -79, -85, 23, -33, -31, -9, -39, 55, -65, -31, -71, -9, -39, -9, -39, -79, 81, 151, -87, 67, -101, -21, -11, -15, -45, 67, -101, -95, -29, -119, 177, 327, -183, 147, -213, -21, -11, -61, -51, -15, -45, -15, -45, -85, 51, -117, -111, -45, -135, 147, -213, -111, -231, -45, -135, -45, -135, -255, -19, -61, -19, -61, -131, 37, 79, -19, 37, -89, -159, 79, -75, 93, 35, 29, 35, 29, 19, 13, 19, 43, 49, -19, 37, 35, 13, 43, -77, -147, 91, -63, 105, 25, 15, 19, 49, -63, 105, 99, 33, 123, 19, 55, 19, 55, 115, -29, -65, 19, -29, 79, 139, -65, 67, -77, -23, -71, -23, -71, -151, 41, 89, -23, 41, -103, -183, 89, -87, 105, -49, -55, -49, -55, -65, -89, -95, -89, -95, -105, 35, 29, 35, 29, 19, -44, -50, -44, -50, -60, 40, 34, 40, 34, 24, -1, 5, -31, -25, -1, 5, -31, -25, -71, -65, 13, 19, 43, 49, -1, 5, 13, 19, -41, -35, -81, -75, 43, 49, -36, -30, 48, 54, 23, -33, -31, -9, -39, 55, -65, -31, -71, -9, -39, -9, -39, -79, -19, 37, 35, 13, 43, 19, -29, -23, 41, -49, -89, 35, -44, 40, -1, -31, -1, -31, -71, 13, 43, -1, 13, -41, -81, 43, -36, 48, 77, 147, -91, 63, -105, -25, -15, -19, -49, 63, -105, -99, -33, -123, 173, 323, -187, 143, -217, -25, -15, -65, -55, -19, -49, -19, -49, -89, 47, -121, -115, -49, -139, 143, -217, -115, -235, -49, -139, -49, -139, -259, -77, -147, 91, -63, 105, 25, 15, 19, 49, -63, 105, 99, 33, 123, 65, 125, -79, 53, -91, -89, -169, 103, -73, 119, -59, -69, -99, -109, 25, 15, -54, -64, 30, 20, 5, -25, 5, -25, -65, 19, 49, 5, 19, -35, -75, 49, -30, 54, 65, -103, -97, -31, -121, 161, -199, -97, -217, -31, -121, -31, -121, -241, -61, 107, 101, 35, 125, 53, -91, -73, 119, -151, -271, 101, -136, 116, -7, -97, -7, -97, -217, 35, 125, -7, 35, -127, -247, 125, -112, 140]\n assert candidate(expression = \"1*2-3+4*5-6/3\") == []\n assert candidate(expression = \"6*5-4*3+2*1\") == [-90, -90, -54, -90, -54, 30, 30, -30, 30, -90, -54, 30, -30, 30, 10, 10, 16, 10, 16, 30, 30, 130, 130, -40, 20, 20, 20, 80, -90, -54, 30, -30, 30, 10, 16, 30, 130, -40, 20, 20, 20, 80]\n assert candidate(expression = \"3-5+8*2-1+4*6\") == [182, 222, -202, 142, -242, 7, 12, -34, -41, 142, -242, -68, -74, -116, 302, 367, -322, 237, -387, 7, 12, 2, 7, -34, -41, -34, -41, -46, 117, -267, -93, -99, -141, 237, -387, -93, -123, -99, -141, -99, -141, -171, -186, -226, 198, -146, 238, -11, -16, 30, 37, -146, 238, 64, 70, 112, 230, 280, -250, 180, -300, -138, -168, 150, -108, 180, -43, -48, -48, -53, -11, -16, -45, -50, -13, -18, 14, 7, 14, 7, 2, 30, 37, 14, 30, 5, 0, 37, 3, 35, 132, -252, -78, -84, -126, 252, -372, -78, -108, -84, -126, -84, -126, -156, -156, 228, 54, 60, 102, 180, -300, -108, 180, -138, -168, 54, -150, 42, -36, -78, -36, -78, -108, 60, 102, -36, 60, -90, -120, 102, -102, 90]\n assert candidate(expression = \"100-50/2+20*3-10\") == []\n assert candidate(expression = \"5*3+2*8-9/3\") == []\n assert candidate(expression = \"12/4+3*2-1+8/2\") == []\n assert candidate(expression = \"100-99+98-97+96\") == [96, -96, 96, -96, -96, -94, 98, -290, -94, 96, 96, 98, -98, 98]\n assert candidate(expression = \"9-3+4-2*3\") == [8, 0, 8, -6, -6, 4, 12, -4, 4, 12, 12, 24, 0, 24]\n assert candidate(expression = \"1+1*1+1*1*1+1-1*1\") == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 7, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 7, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 3, 3]\n assert candidate(expression = \"4*9-3+2*5-1/1+7\") == []\n assert candidate(expression = \"1*2+3*4-5*6+7\") == [-181, -97, -37, -55, 5, -51, -23, -37, 93, -69, -9, -9, -9, 51, -305, -165, -65, -95, 5, -51, -23, -45, -17, -13, 117, -65, 117, 195, -69, -9, -9, -9, 51, -123, -23, -9, -3, 1, 61, -23, 61, 97, -181, -97, -37, -55, 5, -51, -23, -37, 93, -69, -9, -9, -9, 51, -305, -165, -65, -95, 5, -305, -165, -65, -95, 5, -51, -23, -45, -17, -51, -23, -45, -17, -45, -17, -13, 117, -65, 117, 195, -13, 117, -65, -65, 117, 195, 117, 195, 195, -69, -9, -9, -9, 51, -123, -23, -9, -3, 1, 61, -23, 61, 97, -69, -9, -9, -9, 51, -123, -23, -123, -23, -9, -3, -9, -3, -3, 1, 61, -23, 61, 97, 1, 61, -23, -23, 61, 97, 61, 97, 97]\n"}, "metadata": {"canonical_parameter_names": ["expression"], "leetcode_dataset_entry_point": "Solution().diffWaysToCompute", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var diffWaysToCompute = function(expression) {", "container": null, "callable": "diffWaysToCompute", "parameters": [{"name": "expression", "type": "string"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 242, "task_id": "valid-anagram", "difficulty": "Easy", "problem_description": "Given two strings s and t, return true if t is an anagram of s, and false otherwise.\n \nExample 1:\n\nInput: s = \"anagram\", t = \"nagaram\"\nOutput: true\n\nExample 2:\n\nInput: s = \"rat\", t = \"car\"\nOutput: false\n\n \nConstraints:\n\n1 <= s.length, t.length <= 5 * 104\ns and t consist of lowercase English letters.\n\n \nFollow up: What if the inputs contain Unicode characters? How would you adapt your solution to such a case?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(s = \"abcde\",t = \"edcba\") == True\n assert candidate(s = \"abc\",t = \"abcd\") == False\n assert candidate(s = \"apple\",t = \"pale\") == False\n assert candidate(s = \"hello\",t = \"bello\") == False\n assert candidate(s = \"aacc\",t = \"ccac\") == False\n assert candidate(s = \"abc\",t = \"def\") == False\n assert candidate(s = \"abc\",t = \"cba\") == True\n assert candidate(s = \"abcd\",t = \"abce\") == False\n assert candidate(s = \"anagram\",t = \"nagaram\") == True\n assert candidate(s = \"rat\",t = \"car\") == False\n assert candidate(s = \"a\",t = \"a\") == True\n assert candidate(s = \"ab\",t = \"ba\") == True\n assert candidate(s = \"listen\",t = \"silent\") == True\n assert candidate(s = \"abcd\",t = \"dcba\") == True\n assert candidate(s = \"triangle\",t = \"integral\") == True\n assert candidate(s = \"aabbcc\",t = \"abcabc\") == True\n assert candidate(s = \"\",t = \"\") == True\n assert candidate(s = \"ababababababababab\",t = \"bababababababababa\") == True\n assert candidate(s = \"hello world\",t = \"worldhello\") == False\n assert candidate(s = \"theeyes\",t = \"theysee\") == True\n assert candidate(s = \"repeatedcharactershere\",t = \"repeatedcharactershere\") == True\n assert candidate(s = \"ababababab\",t = \"bababababa\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzxxyywwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == True\n assert candidate(s = \"the quick brown fox\",t = \"xof nworb kciuq eht\") == True\n assert candidate(s = \"astronomer\",t = \"moonstarer\") == True\n assert candidate(s = \"thisisananagram\",t = \"isanagramthis\") == False\n assert candidate(s = \"spaces should be ignored\",t = \"should be ignored spaces\") == True\n assert candidate(s = \"aabbcc\",t = \"ccbbaa\") == True\n assert candidate(s = \"special!@#$%^&*()characters\",t = \"characters)!@#$%^&*()special\") == False\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxxyyyyzzzz\",t = \"zzzzyyyxxxwwwwvvvvuuuuttttssssrrrrqqqqppppooooonnnnmmmmllllkkkkjjjjiiiigggghhhhffffffeeeeeeeeddccccbbbbaaaa\") == False\n assert candidate(s = \"anagram\",t = \"nagarams\") == False\n assert candidate(s = \"dormitory\",t = \"dirtyroom\") == True\n assert candidate(s = \"1234567890\",t = \"0987654321\") == True\n assert candidate(s = \"anananana\",t = \"naanaanna\") == True\n assert candidate(s = \"\",t = \"a\") == False\n assert candidate(s = \"thisisanagramtest\",t = \"agamnartisiesttst\") == False\n assert candidate(s = \"hello world\",t = \"world hello\") == True\n assert candidate(s = \"a gentleman\",t = \"elegant man\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeddccbbaa\") == True\n assert candidate(s = \"aabbcc\",t = \"aabbc\") == False\n assert candidate(s = \"school master\",t = \"the classroom\") == True\n assert candidate(s = \"thisisaverylongstringthatwearetesting\",t = \"averylongstringthatwearetestingthisis\") == True\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",t = \"godzylathedelvropmusfixnworbquickthe\") == False\n assert candidate(s = \"thisisananagram\",t = \"isananagramthis\") == True\n assert candidate(s = \"funeral\",t = \"real fun\") == False\n assert candidate(s = \"unitedstates\",t = \"adtenisestatesu\") == False\n assert candidate(s = \"mississippi\",t = \"mississipi\") == False\n assert candidate(s = \"elevenplus\",t = \"twelvestop\") == False\n assert candidate(s = \"a\",t = \"b\") == False\n assert candidate(s = \"anagramanagramanagram\",t = \"nagaramnagaramnagaram\") == True\n assert candidate(s = \"aabbccdd\",t = \"ddbbaacc\") == True\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydoga\") == True\n assert candidate(s = \"abcdeabced\",t = \"abcedabcde\") == True\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",t = \"thelazydogjumpsoveraquickbrownfox\") == True\n assert candidate(s = \"pythonprogramming\",t = \"nohtypgnimmargorp\") == True\n assert candidate(s = \"forty five\",t = \"over fifty\") == True\n assert candidate(s = \"a!@#b$%^c&*()\",t = \"c&*()b$%^a!@#\") == True\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazygod\") == False\n assert candidate(s = \"noon\",t = \"noon\") == True\n assert candidate(s = \"anagrammatic\",t = \"icnagarammat\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zyxwvutsrqponmlkjihgfedcba\") == False\n assert candidate(s = \"abacabadabacaba\",t = \"bacabacabacaba\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggeeffddeebbaa\") == False\n assert candidate(s = \"the quick brown fox jumps over the lazy dog\",t = \"dog lazy the over jumps fox brown quick the\") == True\n assert candidate(s = \"conversation\",t = \"voices rant on\") == False\n assert candidate(s = \"eleven plus two\",t = \"twelve plus one\") == True\n assert candidate(s = \"the eyes\",t = \"they see\") == True\n assert candidate(s = \"conversation\",t = \"voicesranton\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggeeffddccbbbaa\") == False\n assert candidate(s = \"anagramanagram\",t = \"nagaramnagaram\") == True\n assert candidate(s = \"this is a test\",t = \"test a is this\") == True\n assert candidate(s = \"night\",t = \"thing\") == True\n assert candidate(s = \"aaabbbccc\",t = \"bbbaaacc\") == False\n assert candidate(s = \"samecharacters\",t = \"charactersames\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyxwvuttsrqponmlkjihgfeddcbaabbccddeeffgghhiijjkkllmmnnooppqqrrss\") == False\n assert candidate(s = \"mississippi\",t = \"ssmissippii\") == True\n assert candidate(s = \"abcabcabcabcabcabc\",t = \"abcabcabcabcabcabc\") == True\n assert candidate(s = \"xxyyzz\",t = \"zzxxyy\") == True\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",t = \"thequickbrownfoxjumpsoverthelazygod\") == True\n assert candidate(s = \"elevenpluszwo\",t = \"twelvezillion\") == False\n assert candidate(s = \"notanagramhere\",t = \"anagramherenot\") == True\n assert candidate(s = \"uniqueanagram\",t = \"nagramuniqueanagram\") == False\n assert candidate(s = \"fluster\",t = \"restful\") == True\n assert candidate(s = \"dormitory\",t = \"dirty room\") == False\n assert candidate(s = \"aaaaaa\",t = \"aaaaa\") == False\n assert candidate(s = \"punishments\",t = \"ninepunishment\") == False\n assert candidate(s = \"thirty\",t = \"typhrirt\") == False\n assert candidate(s = \"racecar\",t = \"carrace\") == True\n assert candidate(s = \"ab\",t = \"aabb\") == False\n assert candidate(s = \"a\",t = \"\") == False\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\",t = \"mnbvcxzlkjhgfdsapoiuytrewq\") == True\n assert candidate(s = \"abacax\",t = \"aacxab\") == True\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(s = \"questionnaire\",t = \"reinquirequest\") == False\n assert candidate(s = \"anagramatically\",t = \"gramaticallyanagram\") == False\n assert candidate(s = \"uniquecharacters\",t = \"uniquecharactersx\") == False\n assert candidate(s = \"abcdabcdabcd\",t = \"dcbaabcdabcd\") == True\n assert candidate(s = \"adobe\",t = \"abode\") == True\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzzyyxwwvvuuttssrrqqppoonnmlkkjjiihhggffeeeeddccbaab\") == False\n assert candidate(s = \"clint eastwood\",t = \"old west action\") == False\n assert candidate(s = \"abcabcabcabc\",t = \"cbacbacbacba\") == True\n assert candidate(s = \"schoolmaster\",t = \"theclassroom\") == True\n assert candidate(s = \"embarrassing\",t = \"backgroundsere\") == False\n assert candidate(s = \"racecar\",t = \"racecar\") == True\n assert candidate(s = \"nematocysts\",t = \"cytoplasmnets\") == False\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"zzyyxxwwvvuuttsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcbaa\") == False\n"}, "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().isAnagram", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isAnagram = function(s, t) {", "container": null, "callable": "isAnagram", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 257, "task_id": "binary-tree-paths", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, return all root-to-leaf paths in any order.\nA leaf is a node with no children.\n \nExample 1:\n\n\nInput: root = [1,2,3,null,5]\nOutput: [\"1->2->5\",\"1->3\"]\n\nExample 2:\n\nInput: root = [1]\nOutput: [\"1\"]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 100].\n-100 <= Node.val <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == ['1->2->4', '1->2->5', '1->3->6', '1->3->7']\n assert candidate(root = tree_node([1, 2, 3, None, 5])) == ['1->2->5', '1->3']\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7])) == ['-10->9', '-10->20->15', '-10->20->7']\n assert candidate(root = tree_node([-10, -20, -30, -40, None, -50, -60])) == ['-10->-20->-40', '-10->-30->-50', '-10->-30->-60']\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4])) == ['1->2->3->4']\n assert candidate(root = tree_node([-10, -5, 0, 5, 9])) == ['-10->-5->5', '-10->-5->9', '-10->0']\n assert candidate(root = tree_node([1])) == ['1']\n assert candidate(root = tree_node([1, None, 2, None, 3])) == ['1->2->3']\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == ['0->2->1->5', '0->2->1->1', '0->4->3->6', '0->4->-1->8']\n assert candidate(root = tree_node([3, 1, None, None, 2])) == ['3->1->2']\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, 21, 18, 22])) == ['3->9', '3->20->15->21', '3->20->7->18', '3->20->7->22']\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == ['1->2->3->4->5->6->7->8->9->10']\n assert candidate(root = tree_node([2, -3, 5, 1, None, -4, 6, -7, None, None, None, None, -8, -9, 7])) == ['2->-3->1->-7->-9', '2->-3->1->-7->7', '2->5->-4', '2->5->6->-8']\n assert candidate(root = tree_node([100, -50, 50, None, -100, None, 100, -50, None, 50, None, -100, None, 100])) == ['100->-50->-100->-50->-100', '100->50->100->50->100']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14', '1->3->7->15']\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, None, 9])) == ['5->4->11->7', '5->4->11->2->9', '5->8->13', '5->8->4->5', '5->8->4->1']\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, 8, None, 10, 11, None, 13, None, None, 16])) == ['1->2->4->8', '1->3->6->10->16', '1->3->6->11', '1->3->7->13']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None])) == ['1->2->4->8->16', '1->2->4->8->17', '1->2->4->9->18', '1->2->4->9->19', '1->2->5->10->20', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14', '1->3->7->15']\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])) == ['0->1->3->7', '0->1->3->8', '0->1->4->9', '0->1->4->10', '0->2->5->11', '0->2->5->12', '0->2->6->13', '0->2->6->14']\n assert candidate(root = tree_node([10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80, 90, -90, 100, -100])) == ['10->-10->-20->-40->-80', '10->-10->-20->-40->90', '10->-10->-20->50->-90', '10->-10->-20->50->100', '10->-10->30->-50->-100', '10->-10->30->60', '10->20->-30->-60', '10->20->-30->70', '10->20->40->-70', '10->20->40->80']\n assert candidate(root = tree_node([10, None, 20, None, 30, None, 40, None, 50, None, 60, None, 70, None, 80])) == ['10->20->30->40->50->60->70->80']\n assert candidate(root = tree_node([0, -2, 1, None, None, -3, None, -4, None, None, 5])) == ['0->-2', '0->1->-3->-4->5']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, 9, None, None, 10, None, None, 11, None, None, 12])) == ['1->2->4->8->11', '1->2->5->9', '1->3->6', '1->3->7->10->12']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, 16, 17, 18, 19, 20])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10->16', '1->2->5->11->17', '1->2->5->11->18', '1->3->6->12->19', '1->3->6->12->20', '1->3->6->13', '1->3->7->14', '1->3->7->15']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == ['1->2->4->8', '1->2->4->9->16->30', '1->2->4->9->17', '1->2->5->10->18', '1->2->5->10->19', '1->2->5->11->20', '1->2->5->11->21', '1->3->6->12->22', '1->3->6->12->23', '1->3->6->13->24', '1->3->6->13->25', '1->3->7->14->26', '1->3->7->14->27', '1->3->7->15->28', '1->3->7->15->29']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 8, 9, 10, 11, None, None, 16, 17, 18, 19])) == ['1->2->4->8', '1->2->4->9->16', '1->2->4->9->17', '1->2->5->10->18', '1->2->5->10->19', '1->2->5->11', '1->3']\n assert candidate(root = tree_node([8, 5, 1, 7, 6, 9, 12, None, None, 2, None, None, None, None, None, None, 3])) == ['8->5->7', '8->5->6->2->3', '8->1->9', '8->1->12']\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 6, None, None, None, 7, None, 8])) == ['1->2->5', '1->3->6->7->8']\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 4, 4])) == ['1->2->3->4', '1->2->3->4', '1->2->3->4', '1->2->3->4', '1->2']\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, None, -8, -9, -10, -11, -12, None, -13, None, None, -14])) == ['0->-1->-3->-7->-13', '0->-1->-4->-8->-14', '0->-1->-4->-9', '0->-2->-5->-10', '0->-2->-5->-11', '0->-2->-6->-12']\n assert candidate(root = tree_node([0, -3, 9, -10, None, 5])) == ['0->-3->-10', '0->9->5']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == ['1->2->4->8->12', '1->2->5->9->13', '1->3->6->10->14', '1->3->7->11->15']\n assert candidate(root = tree_node([0, -1, 1, -2, -3, 2, 3, -4, -5, -6, -7, 4, 5, 6, 7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31])) == ['0->-1->-2->-4->-8->-24', '0->-1->-2->-4->-8->-25', '0->-1->-2->-4->-9->-26', '0->-1->-2->-4->-9->-27', '0->-1->-2->-5->-10->-28', '0->-1->-2->-5->-10->-29', '0->-1->-2->-5->-11->-30', '0->-1->-2->-5->-11->-31', '0->-1->-3->-6->-12', '0->-1->-3->-6->-13', '0->-1->-3->-7->-14', '0->-1->-3->-7->-15', '0->1->2->4->-16', '0->1->2->4->-17', '0->1->2->5->-18', '0->1->2->5->-19', '0->1->3->6->-20', '0->1->3->6->-21', '0->1->3->7->-22', '0->1->3->7->-23']\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, None, None, None, 8])) == ['1->2->4->7', '1->3->5', '1->3->6->8']\n assert candidate(root = tree_node([3, 9, 20, 15, 7, 6, 8, 1, 2, None, None, None, None, None, 4])) == ['3->9->15->1', '3->9->15->2', '3->9->7', '3->20->6', '3->20->8->4']\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == ['1->2->3->4->5->6->7->8->9']\n assert candidate(root = tree_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == ['0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0', '0->0->0->0->0']\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, None, None, 18])) == ['3->9', '3->20->15->12', '3->20->7->18']\n assert candidate(root = tree_node([100, -50, 50, -25, 25, -75, 75, None, None, -100, 100, -125, 125])) == ['100->-50->-25', '100->-50->25->-100', '100->-50->25->100', '100->50->-75->-125', '100->50->-75->125', '100->50->75']\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, None, None, None, None, 16, 20])) == ['10->5->3', '10->5->7', '10->15->18->16', '10->15->18->20']\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == ['1->2->3->4->5->6->7->8->9->10->11->12->13->14->15']\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == ['5->4->11->7', '5->4->11->2', '5->8->13', '5->8->4->1']\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10])) == ['-1->-2->-4->-8', '-1->-2->-4->-9', '-1->-2->-5->-10', '-1->-3->-6', '-1->-3->-7']\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == ['1->2->3->4->5->6->7->8->9']\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == ['1->2->3->4->5->6->7->8->9->10']\n assert candidate(root = tree_node([5, -4, 8, -11, None, 17, 4, 7, 2, None, None, None, 1])) == ['5->-4->-11->7', '5->-4->-11->2', '5->8->17', '5->8->4->1']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 16])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14', '1->3->7->15']\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == ['1->2->3->4->5->6->7->8']\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1])) == ['10->5->3->3', '10->5->3->-2', '10->5->2->1', '10->-3->11']\n assert candidate(root = tree_node([100, -100, 50, -50, 25, 0, 75, None, -75, -25, None, 20, None, None, None, 60])) == ['100->-100->-50->-75->60', '100->-100->25->-25', '100->50->0->20', '100->50->75']\n assert candidate(root = tree_node([3, 9, 20, 8, None, 15, 7, 4, 6, None, None, 13, 18])) == ['3->9->8->4', '3->9->8->6', '3->20->15', '3->20->7->13', '3->20->7->18']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, 15])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->15']\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == ['1->2->3->4->5->6->7->8']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == ['1->2->4->8->16', '1->2->4->8->17', '1->2->4->9->18', '1->2->4->9->19', '1->2->5->10->20', '1->2->5->10->21', '1->2->5->11->22', '1->2->5->11->23', '1->3->6->12->24', '1->3->6->12->25', '1->3->6->13->26', '1->3->6->13->27', '1->3->7->14->28', '1->3->7->14->29', '1->3->7->15->30']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, 8, None, None, None, 9])) == ['1->2->4->7->9', '1->2->5->8', '1->3->6']\n assert candidate(root = tree_node([2, -3, 3, -4, -5, -6, -7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == ['2->-3->-4->8->16', '2->-3->-4->8->17', '2->-3->-4->9->18', '2->-3->-4->9->19', '2->-3->-5->10->20', '2->-3->-5->11', '2->3->-6->12', '2->3->-6->13', '2->3->-7->14', '2->3->-7->15']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, None, 9, None, None, 10, 11, None, None, 12, None])) == ['1->2->4->7->10', '1->2->4->7->11', '1->2->4->8', '1->2->5->9->12', '1->3->6']\n assert candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4])) == ['3->5->6', '3->5->2->7', '3->5->2->4', '3->1->0', '3->1->8']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, -1])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14', '1->3->7->15->-1']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None, None, 15, 16, 17, 18, 19, 20])) == ['1->2->4->8->15', '1->2->4->9->16', '1->2->4->9->17', '1->2->5->10->18', '1->2->5->10->19', '1->2->5->11->20', '1->3->6->12', '1->3->6->13', '1->3->7->14']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == ['1->2->4->8->16', '1->2->4->8->17', '1->2->4->9->18', '1->2->4->9->19', '1->2->5->10->20', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14', '1->3->7->15']\n assert candidate(root = tree_node([1, 2, 2, 3, None, 3, None, 4, None, 4])) == ['1->2->3->4', '1->2->3->4']\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == ['1->2->4->7->13', '1->2->4->7->14', '1->2->4->8->15', '1->3->5->9', '1->3->5->10', '1->3->6->11', '1->3->6->12']\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, None, 11, 12, None, 14, 15, None, None, 16, 17])) == ['1->2->4->8->14', '1->2->4->8->15', '1->2->4->9', '1->3->6->11->16', '1->3->6->11->17', '1->3->7->12']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14', '1->3->7->15']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None])) == ['1->2->4->8', '1->2->4->9', '1->2->5->10', '1->2->5->11', '1->3->6->12', '1->3->6->13', '1->3->7->14']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, 8, None, 9, None, 10])) == ['1->2->4->6->9', '1->2->4->7->10', '1->2->5->8', '1->3']\n assert candidate(root = tree_node([1, None, None])) == ['1']\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == ['1->2->3', '1->2->4', '1->2->4', '1->2->3']\n assert candidate(root = tree_node([0, -3, 9, -10, None, 5, -1, -6, None, -8, None, None, None, -11, None, -12, None, 13, -13, -14])) == ['0->-3->-10->-6->-11->13', '0->-3->-10->-6->-11->-13', '0->9->5->-8->-12->-14', '0->9->-1']\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == ['1->2->3->4->5->6->7->8->9->10->11->12->13->14->15->16->17->18->19->20']\n assert candidate(root = tree_node([2, -3, -3, -4, None, -5, -4, None, -6, None, -7])) == ['2->-3->-4->-6', '2->-3->-5->-7', '2->-3->-4']\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 13, 14, 18, 19])) == ['3->9', '3->20->15->13', '3->20->15->14', '3->20->7->18', '3->20->7->19']\n assert candidate(root = tree_node([3, 9, 20, 8, 10, 15, 7, None, None, None, None, 14, 16, 12, 17])) == ['3->9->8', '3->9->10', '3->20->15->14', '3->20->15->16', '3->20->7->12', '3->20->7->17']\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, 9, None, None, 10, 11])) == ['1->2->4->7->10', '1->2->4->7->11', '1->2->5->8', '1->2->5->9', '1->3->6']\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == ['0->-1->-3->-7->-15', '0->-1->-3->-8', '0->-1->-4->-9', '0->-1->-4->-10', '0->-2->-5->-11', '0->-2->-5->-12', '0->-2->-6->-13', '0->-2->-6->-14']\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == ['10->5->3->1', '10->5->7->6', '10->15->18']\n assert candidate(root = tree_node([3, 9, 20, 8, None, 15, 7, 6, 10, None, None, 13, 17, 16])) == ['3->9->8->6->16', '3->9->8->10', '3->20->15', '3->20->7->13', '3->20->7->17']\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == ['5->4->11->7', '5->4->11->2', '5->8->13', '5->8->4->5', '5->8->4->1']\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().binaryTreePaths", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var binaryTreePaths = function(root) {", "container": null, "callable": "binaryTreePaths", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 258, "task_id": "add-digits", "difficulty": "Easy", "problem_description": "Given an integer num, repeatedly add all its digits until the result has only one digit, and return it.\n \nExample 1:\n\nInput: num = 38\nOutput: 2\nExplanation: The process is\n38 --> 3 + 8 --> 11\n11 --> 1 + 1 --> 2 \nSince 2 has only one digit, return it.\n\nExample 2:\n\nInput: num = 0\nOutput: 0\n\n \nConstraints:\n\n0 <= num <= 231 - 1\n\n \nFollow up: Could you do it without any loop/recursion in O(1) runtime?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 10) == 1\n assert candidate(num = 9) == 9\n assert candidate(num = 111111111) == 9\n assert candidate(num = 47) == 2\n assert candidate(num = 456789) == 3\n assert candidate(num = 38) == 2\n assert candidate(num = 45) == 9\n assert candidate(num = 234567890) == 8\n assert candidate(num = 1000000000) == 1\n assert candidate(num = 942) == 6\n assert candidate(num = 123) == 6\n assert candidate(num = 987654321) == 9\n assert candidate(num = 0) == 0\n assert candidate(num = 4567) == 4\n assert candidate(num = 1) == 1\n assert candidate(num = 111) == 3\n assert candidate(num = 999999999) == 9\n assert candidate(num = 19) == 1\n assert candidate(num = 9999) == 9\n assert candidate(num = 10000) == 1\n assert candidate(num = 1010101010101010101) == 1\n assert candidate(num = 222222222) == 9\n assert candidate(num = 555555555) == 9\n assert candidate(num = 1234567890123456789) == 9\n assert candidate(num = 66666666666666666666) == 3\n assert candidate(num = 9999999999999999999) == 9\n assert candidate(num = 888888888) == 9\n assert candidate(num = 1111111111) == 1\n assert candidate(num = 123456789012345678901234567890) == 9\n assert candidate(num = 27) == 9\n assert candidate(num = 98765432109876543210) == 9\n assert candidate(num = 444444444) == 9\n assert candidate(num = 2222222222) == 2\n assert candidate(num = 88888888888888888888) == 7\n assert candidate(num = 33333333333333333333) == 6\n assert candidate(num = 5555555555555555555) == 5\n assert candidate(num = 999999999999999999) == 9\n assert candidate(num = 777777777) == 9\n assert candidate(num = 888888888888888888) == 9\n assert candidate(num = 1999999999999999999) == 1\n assert candidate(num = 666666666) == 9\n assert candidate(num = 123456789) == 9\n assert candidate(num = 9876543210) == 9\n assert candidate(num = 5) == 5\n assert candidate(num = 555555555555555555555555555555) == 6\n assert candidate(num = 333333333) == 9\n assert candidate(num = 11) == 2\n assert candidate(num = 1111111111111111111) == 1\n assert candidate(num = 4321098765432109876543210987654321) == 1\n assert candidate(num = 1234567890) == 9\n assert candidate(num = 101010101010101010101010101010) == 6\n assert candidate(num = 543210987654321) == 6\n assert candidate(num = 44444444444444444444) == 8\n assert candidate(num = 94528) == 1\n assert candidate(num = 12345678901234567890) == 9\n assert candidate(num = 8888888888888888888) == 8\n assert candidate(num = 18) == 9\n assert candidate(num = 77777777777777777777) == 5\n assert candidate(num = 987654321987654321) == 9\n assert candidate(num = 876543210987654321098765432109876543210) == 9\n assert candidate(num = 4321) == 1\n assert candidate(num = 22222222222222222222) == 4\n assert candidate(num = 9876543210987654321) == 9\n assert candidate(num = 369369369) == 9\n assert candidate(num = 898989898989898989898989898989) == 3\n assert candidate(num = 2222222222222222222) == 2\n assert candidate(num = 123456789123456789) == 9\n assert candidate(num = 9999999999) == 9\n assert candidate(num = 11111111111111111111) == 2\n assert candidate(num = 55555555555555555555) == 1\n assert candidate(num = 99999999999999999999) == 9\n assert candidate(num = 5689423749832749823749237492374923749237492374923749237492374923749237492374) == 2\n assert candidate(num = 191919191919191919191919191919) == 6\n assert candidate(num = 987654321098765432109876543210) == 9\n assert candidate(num = 12345678987654321) == 9\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().addDigits", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var addDigits = function(num) {", "container": null, "callable": "addDigits", "parameters": [{"name": "num", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 260, "task_id": "single-number-iii", "difficulty": "Medium", "problem_description": "Given an integer array nums, in which exactly two elements appear only once and all the other elements appear exactly twice. Find the two elements that appear only once. You can return the answer in any order.\nYou must write an algorithm that runs in linear runtime complexity and uses only constant extra space.\n \nExample 1:\n\nInput: nums = [1,2,1,3,2,5]\nOutput: [3,5]\nExplanation: [5, 3] is also a valid answer.\n\nExample 2:\n\nInput: nums = [-1,0]\nOutput: [-1,0]\n\nExample 3:\n\nInput: nums = [0,1]\nOutput: [1,0]\n\n \nConstraints:\n\n2 <= nums.length <= 3 * 104\n-231 <= nums[i] <= 231 - 1\nEach integer in nums will appear twice, only two integers will appear once.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648, 1, 2, 1, 3, 2, 5]) == [3, 5]\n assert candidate(nums = [3, 4, 5, 4, 3, 6]) == [5, 6]\n assert candidate(nums = [4, 1, 4, 13, 6, 7, 6, 7]) == [13, 1]\n assert candidate(nums = [4, 1, 4, 13, 6, 13, 2, 6]) == [1, 2]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8]) == [9, 1]\n assert candidate(nums = [2, 2, 3, 4, 3, 4, 5, 5, 6, 7]) == [7, 6]\n assert candidate(nums = [-1, 0]) == [-1, 0]\n assert candidate(nums = [0, 0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11]) == [0, 0]\n assert candidate(nums = [10, 1, 10, 3, 7, 3, 5, 5]) == [7, 1]\n assert candidate(nums = [10, 20, 10, 30, 40, 50, 40, 50]) == [30, 20]\n assert candidate(nums = [3, 1, 2, 3, 2, 5, 6, 6]) == [5, 1]\n assert candidate(nums = [0, 0, 1, 2, 3, 3, 4, 4, 5, 5]) == [1, 2]\n assert candidate(nums = [10, 20, 10, 30, 30, 40]) == [20, 40]\n assert candidate(nums = [1000000000, 2000000000, 1000000000, 3000000000]) == [3000000000, 2000000000]\n assert candidate(nums = [0, 1]) == [1, 0]\n assert candidate(nums = [1, -2, -2, 3, 3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 1, 12]) == [11, -15]\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2]) == [-2, -2147483648]\n assert candidate(nums = [0, 0, 1, 1, 2, 3]) == [3, 2]\n assert candidate(nums = [1000000000, 2000000000, 1000000000, 3000000000, 4000000000, 4000000000]) == [3000000000, 2000000000]\n assert candidate(nums = [4, 1, 4, 6, 7, 7]) == [1, 6]\n assert candidate(nums = [1000000000, 1000000000, 500000000, 2000000000]) == [500000000, 2000000000]\n assert candidate(nums = [-1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, 11]) == [11, 2]\n assert candidate(nums = [-2147483648, 2147483647, -2147483648, 2]) == [2147483647, 2]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 5, 6, 6]) == [5, 4]\n assert candidate(nums = [1, 1, 2, 3, 2, 4, 5, 5, 6, 6]) == [3, 4]\n assert candidate(nums = [1, 2, 1, 3, 2, 5]) == [3, 5]\n assert candidate(nums = [10, 1, 10, 3, 3, 5, 5, 2]) == [1, 2]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, 5]) == [5, -1000000000]\n assert candidate(nums = [1, 1, 2, 2, 3, 4]) == [3, 4]\n assert candidate(nums = [1000000000, 2000000000, 1000000000, 3000000000, 4000000000, 2000000000, 5000000000, 6000000000, 4000000000, 5000000000]) == [3000000000, 6000000000]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 1000, 2000]) == [1000, 2000]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]) == [60, 20]\n assert candidate(nums = [100, 200, 100, 300, 400, 500, 300, 400, 600, 500, 700, 800, 900, 800, 900, 1100, 1200, 1100, 1300, 1400, 1300, 1400, 1600, 1700]) == [44, 1108]\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21]) == [21, 20]\n assert candidate(nums = [987654321, 123456789, 987654321, 234567890, 345678901, 234567890, 456789012, 567890123, 345678901, 456789012, 678901234, 567890123, 789012345, 678901234, 890123456]) == [123456789, 436825017]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11]) == [8, 0]\n assert candidate(nums = [-2147483648, 2147483647, -2147483648, 1, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12]) == [2147483647, 0]\n assert candidate(nums = [5, 7, 5, 7, 9, 11, 9, 11, 13, 15, 13, 15, 17, 19, 17, 19, 21, 23, 21, 23, 25, 27, 25, 27, 29, 31, 29, 31, 33, 35, 33, 35, 37, 39]) == [39, 37]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 25]) == [0, 0]\n assert candidate(nums = [0, 1, 0, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20, 21, 22, 21, 22, 23, 24, 25, 26]) == [15, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 1, 2]) == [1, 34]\n assert candidate(nums = [999999999, 999999999, 1000000000, 1000000000, 1000000001, 1000000001, 1000000002, 1000000002, 1000000003, 1000000004, 1000000005, 1000000005]) == [1000000003, 1000000004]\n assert candidate(nums = [10000, 10000, 20000, 20000, 30000, 30000, 40000, 40000, 50000, 50000, 60000, 60000, 70000, 70000, 80000, 80000, 90000, 90000, 11111, 22222]) == [11111, 22222]\n assert candidate(nums = [1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 33]) == [31, 33]\n assert candidate(nums = [100000, 200000, 100000, 300000, 400000, 500000, 300000, 400000, 600000, 500000, 700000, 800000, 900000, 800000, 900000, 1100000, 1200000, 1100000, 1300000, 1400000, 1300000, 1400000, 1600000, 1700000]) == [34016, 1299744]\n assert candidate(nums = [-10, -10, -20, -20, -30, -30, -40, -40, -50, -50, -60, -60, -70, -70, -80, -80, -90, -90, 0, 99]) == [99, 0]\n assert candidate(nums = [100000, 100000, 200000, 300000, 400000, 500000, 200000, 300000, 400000, 500000, 600000, 700000, 800000, 900000, 600000, 700000, 800000, 900000, 1000000, 1000001]) == [1000001, 1000000]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 21]) == [19, 21]\n assert candidate(nums = [5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 22]) == [21, 22]\n assert candidate(nums = [0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 5, 7, 9, 11, 12, 11, 13, 13, 14, 12, 15, 16, 15, 17, 17, 18, 18, 19, 19, 20, 20]) == [12, 16]\n assert candidate(nums = [-2147483648, 2147483647, -2147483648, 100000, 200000, 100000, 300000, 300000, 400000, 2147483647, 400000, 500000, 600000, 500000, 600000]) == [200000, 0]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 31]) == [1, 0]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 19]) == [11, 10]\n assert candidate(nums = [1000000000, 1000000000, 2000000000, 2000000000, 3000000000, 4000000000]) == [3000000000, 4000000000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230]) == [231, 0]\n assert candidate(nums = [1000, 1001, 1000, 1002, 1002, 1003, 1003, 1004, 1004, 1005, 1005, 1006, 1006, 1007, 1007, 1008, 1008, 1009, 1009, 1010, 1011]) == [1001, 1]\n assert candidate(nums = [123, 123, 456, 456, 789, 789, 101112, 101112, 131415, 131415, 161718, 161718, 192021, 192021, 222324, 222324, 252627, 252627, 282930, 282930, 313233, 343536]) == [313233, 343536]\n assert candidate(nums = [1000, 2000, 1000, 3000, 4000, 5000, 3000, 4000, 6000, 5000, 7000, 8000, 9000, 8000, 9000, 11000, 12000, 11000, 13000, 14000, 13000, 14000, 16000, 17000, 18000, 19000, 18000, 19000, 21000, 22000, 21000, 22000, 23000, 24000, 23000, 24000, 25000, 26000]) == [14488, 25936]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]) == [9, 34]\n assert candidate(nums = [1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011]) == [1011, 1010]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 32]) == [31, 32]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31]) == [31, 30]\n assert candidate(nums = [-2147483648, 2147483647, -2147483648, 1, 2, 1, 3, 2]) == [2147483647, 3]\n assert candidate(nums = [-1000000000, -1000000000, 1000000000, 1000000000, 2147483647, -2147483648]) == [2147483647, -2147483648]\n assert candidate(nums = [-1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -10, -10, -11, -11, -12, -12, -13, -13, -14, -14, -15, -15, -16, -16, -17, -17, -18, -18, -19, -19, -20, -20, -21, -21, -22, -22, -23, -23, -24, -24, -25, -25, -26, -26, -27, -27, -28, -28, -29, -29, -30, -31]) == [-31, -30]\n assert candidate(nums = [1000000000, 1000000000, 2147483647, 2147483647, 123456789, -123456789]) == [-123456789, 123456789]\n assert candidate(nums = [100, 200, 100, 300, 200, 400, 400, 500, 500, 600, 600, 700, 700, 800, 800, 900, 900, 1000, 1000, 1100, 1100, 1200, 1300]) == [300, 420]\n assert candidate(nums = [0, 0, -1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -10, -11]) == [-11, -10]\n assert candidate(nums = [999999999, 999999999, 888888888, 888888888, 777777777, 777777777, 666666666, 666666666, 555555555, 555555555, 123456789, 987654321]) == [123456789, 987654321]\n assert candidate(nums = [100000000, 100000001, 100000000, 200000000, 200000000, 300000000, 300000000, 400000000, 400000000, 500000000, 500000000, 600000000, 600000000, 700000000, 700000000, 800000000, 800000000, 900000000, 900000000, 1000000002, 1000000003]) == [100000001, 1]\n assert candidate(nums = [1000, 1000, 2000, 3000, 3000, 4000, 4000, 5000, 5000, 6000, 6000, 7000, 7000, 8000, 8000, 9000, 9000, 10000, 10000, 11000, 12000]) == [11000, 10544]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 999999999, 999999999, 888888888, 888888888, 777777777, 777777777, 666666666, 666666666, 555555555, 123456789]) == [555555555, 123456789]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200]) == [1100, 1200]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -1, -2, -3, -4, -5, -6, -7, -8, -9, 100, 101]) == [101, 100]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2]) == [31, 3]\n assert candidate(nums = [1000000000, 999999999, 1000000000, 888888888, 777777777, 888888888, 666666666, 555555555, 666666666, 444444444, 333333333, 222222222, 222222222, 111111111, 111111111, 333333333, 444444444, 555555555, 777777777, 999999999]) == [0, 0]\n assert candidate(nums = [-1000000000, -999999999, -1000000000, -888888888, -777777777, -888888888, -666666666, -555555555, -666666666, -444444444, -333333333, -222222222, -222222222, -111111111, -111111111, -333333333, -444444444, -555555555, -777777777, -999999999]) == [0, 0]\n assert candidate(nums = [999999999, 999999999, 888888888, 888888888, 777777777, 777777777, 666666666, 666666666, 555555555, 555555555, 444444444, 333333333, 222222222, 111111111, 111111111, 222222222]) == [333333333, 444444444]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 5, 7, 9, 11, 12, 11, 13, 13, 14, 12, 15, 16, 15, 17, 17, 18, 18, 19, 19, 20, 20]) == [12, 16]\n assert candidate(nums = [-10, -20, -10, -30, -40, -50, -30, -40, -50, -60, -70, -80, -90, -100, -60, -70, -80, -90, -100, -110, -120]) == [-110, 100]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51]) == [51, 50]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100]) == [1100, 1000]\n assert candidate(nums = [1000000000, 1, 1000000000, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 11, 11, 13, 14]) == [14, 12]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]) == [30, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [11, 20]\n assert candidate(nums = [1, 1, 1000000000, 1000000000, -1, -1, 2000000000, 2000000000, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21]) == [11, 1]\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 31, 32, 33]) == [0, 0]\n assert candidate(nums = [100, 100, 200, 200, 300, 300, 400, 400, 500, 500, 600, 600, 700, 700, 800, 800, 900, 900, 1000, 1001, 1002, 1002]) == [1001, 1000]\n assert candidate(nums = [5, 7, 5, 7, 9, 11, 9, 11, 13, 15, 13, 15, 17, 19, 17, 19, 21, 23, 21, 23, 25, 27, 25, 27, 29, 31, 29, 31, 33, 35, 33, 35, 37, 39, 37, 39, 41, 43]) == [43, 41]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 22]) == [23, 21]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -2000000000, 3000000000, 3000000000, -4000000000, -4000000000, 5000000000, 6000000000]) == [4983875072, 5000000000]\n assert candidate(nums = [5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 21, 21, 23, 23, 25, 25, 27, 27, 29, 29, 31, 31, 33, 33, 35, 37]) == [35, 37]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21]) == [0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 5, 7, 9, 11, 12, 11, 13, 13, 14, 12]) == [12, 0]\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9]) == [9, 8]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 35]) == [35, 34]\n assert candidate(nums = [1000000000, 999999999, 1000000000, 888888888, 777777777, 888888888, 666666666, 666666666]) == [999999999, 777777777]\n assert candidate(nums = [1, 2, 1, 3, 2, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15]) == [2, 0]\n assert candidate(nums = [100000, 100000, 200000, 200000, 300000, 300000, 400000, 400000, 500000, 500000, 600000, 600000, 700000, 700000, 800000, 800000, 900000, 900000, 1, 2]) == [1, 2]\n assert candidate(nums = [-1000000000, -1000000000, 2000000000, 2000000000, 1000000, 1000000, -100000, -100000, 50000, 50000, 999999999, 1000000001]) == [999999999, 1000000001]\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12]) == [11, 12]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]) == [21, 28]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().singleNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var singleNumber = function(nums) {", "container": null, "callable": "singleNumber", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 263, "task_id": "ugly-number", "difficulty": "Easy", "problem_description": "An ugly number is a positive integer which does not have a prime factor other than 2, 3, and 5.\nGiven an integer n, return true if n is an ugly number.\n \nExample 1:\n\nInput: n = 6\nOutput: true\nExplanation: 6 = 2 × 3\n\nExample 2:\n\nInput: n = 1\nOutput: true\nExplanation: 1 has no prime factors.\n\nExample 3:\n\nInput: n = 14\nOutput: false\nExplanation: 14 is not ugly since it includes the prime factor 7.\n\n \nConstraints:\n\n-231 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == False\n assert candidate(n = 8) == True\n assert candidate(n = -2147483648) == False\n assert candidate(n = 100000) == True\n assert candidate(n = 100) == True\n assert candidate(n = 30) == True\n assert candidate(n = -1) == False\n assert candidate(n = 2147483648) == True\n assert candidate(n = 125) == True\n assert candidate(n = 14) == False\n assert candidate(n = 2147483647) == False\n assert candidate(n = 6) == True\n assert candidate(n = 1) == True\n assert candidate(n = 1000000000) == True\n assert candidate(n = 7) == False\n assert candidate(n = 1024) == True\n assert candidate(n = 59049) == True\n assert candidate(n = 72057594037927935) == False\n assert candidate(n = 45) == True\n assert candidate(n = 180000000) == True\n assert candidate(n = 135) == True\n assert candidate(n = 729) == True\n assert candidate(n = 2250000000) == True\n assert candidate(n = 8589934591) == False\n assert candidate(n = 216) == True\n assert candidate(n = 2000000000) == True\n assert candidate(n = 50000) == True\n assert candidate(n = 1000000002) == False\n assert candidate(n = 1968300000) == True\n assert candidate(n = 86400) == True\n assert candidate(n = 1000000000000) == True\n assert candidate(n = 60) == True\n assert candidate(n = 1500000000) == True\n assert candidate(n = 30000) == True\n assert candidate(n = 34359738368) == True\n assert candidate(n = 2500000000) == True\n assert candidate(n = 225) == True\n assert candidate(n = 15625) == True\n assert candidate(n = 3126) == False\n assert candidate(n = 720) == True\n assert candidate(n = 46656) == True\n assert candidate(n = 16000000) == True\n assert candidate(n = 250) == True\n assert candidate(n = 1048576) == True\n assert candidate(n = -10) == False\n assert candidate(n = 3600) == True\n assert candidate(n = 256) == True\n assert candidate(n = 1600000000) == True\n assert candidate(n = 2430000000) == True\n assert candidate(n = 2187000) == True\n assert candidate(n = 307200000) == True\n assert candidate(n = 1000000001) == False\n assert candidate(n = 112500000000) == True\n assert candidate(n = 24) == True\n assert candidate(n = 9765625) == True\n assert candidate(n = 531441) == True\n assert candidate(n = 987654321) == False\n assert candidate(n = 15) == True\n assert candidate(n = 180) == True\n assert candidate(n = 3125000000) == True\n assert candidate(n = 500000) == True\n assert candidate(n = 150000000) == True\n assert candidate(n = 8589934592) == True\n assert candidate(n = 1800000000) == True\n assert candidate(n = 3125) == True\n assert candidate(n = 6103515625) == True\n assert candidate(n = 2352) == False\n assert candidate(n = 120) == True\n assert candidate(n = 72057594037927936) == True\n assert candidate(n = 40500000) == True\n assert candidate(n = 105) == False\n assert candidate(n = 8388608) == True\n assert candidate(n = 243) == True\n assert candidate(n = 84) == False\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().isUgly", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isUgly = function(n) {", "container": null, "callable": "isUgly", "parameters": [{"name": "n", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 264, "task_id": "ugly-number-ii", "difficulty": "Medium", "problem_description": "An ugly number is a positive integer whose prime factors are limited to 2, 3, and 5.\nGiven an integer n, return the nth ugly number.\n \nExample 1:\n\nInput: n = 10\nOutput: 12\nExplanation: [1, 2, 3, 4, 5, 6, 8, 9, 10, 12] is the sequence of the first 10 ugly numbers.\n\nExample 2:\n\nInput: n = 1\nOutput: 1\nExplanation: 1 has no prime factors, therefore all of its prime factors are limited to 2, 3, and 5.\n\n \nConstraints:\n\n1 <= n <= 1690\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 15) == 24\n assert candidate(n = 200) == 16200\n assert candidate(n = 1690) == 2123366400\n assert candidate(n = 1) == 1\n assert candidate(n = 50) == 243\n assert candidate(n = 10) == 12\n assert candidate(n = 5) == 5\n assert candidate(n = 1400) == 516560652\n assert candidate(n = 3) == 3\n assert candidate(n = 1575) == 1230187500\n assert candidate(n = 1600) == 1399680000\n assert candidate(n = 1685) == 2066242608\n assert candidate(n = 900) == 26244000\n assert candidate(n = 1688) == 2099520000\n assert candidate(n = 100) == 1536\n assert candidate(n = 1000) == 51200000\n assert candidate(n = 300) == 82944\n assert candidate(n = 550) == 1555200\n assert candidate(n = 1200) == 174960000\n assert candidate(n = 600) == 2460375\n assert candidate(n = 4) == 4\n assert candidate(n = 1675) == 1990656000\n assert candidate(n = 1650) == 1769472000\n assert candidate(n = 1550) == 1093500000\n assert candidate(n = 1300) == 306110016\n assert candidate(n = 2) == 2\n assert candidate(n = 1024) == 60466176\n assert candidate(n = 8) == 9\n assert candidate(n = 1689) == 2109375000\n assert candidate(n = 800) == 12754584\n assert candidate(n = 400) == 311040\n assert candidate(n = 9) == 10\n assert candidate(n = 750) == 8748000\n assert candidate(n = 6) == 6\n assert candidate(n = 500) == 937500\n assert candidate(n = 7) == 8\n assert candidate(n = 1680) == 2025000000\n assert candidate(n = 1500) == 859963392\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().nthUglyNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var nthUglyNumber = function(n) {", "container": null, "callable": "nthUglyNumber", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 268, "task_id": "missing-number", "difficulty": "Easy", "problem_description": "Given an array nums containing n distinct numbers in the range [0, n], return the only number in the range that is missing from the array.\n \nExample 1:\n\nInput: nums = [3,0,1]\nOutput: 2\nExplanation:\nn = 3 since there are 3 numbers, so all numbers are in the range [0,3]. 2 is the missing number in the range since it does not appear in nums.\n\nExample 2:\n\nInput: nums = [0,1]\nOutput: 2\nExplanation:\nn = 2 since there are 2 numbers, so all numbers are in the range [0,2]. 2 is the missing number in the range since it does not appear in nums.\n\nExample 3:\n\nInput: nums = [9,6,4,2,3,5,7,0,1]\nOutput: 8\nExplanation:\nn = 9 since there are 9 numbers, so all numbers are in the range [0,9]. 8 is the missing number in the range since it does not appear in nums.\n\n\n\n \n\n\n \n\n \n \n\n\n\n\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 104\n0 <= nums[i] <= n\nAll the numbers of nums are unique.\n\n \nFollow up: Could you implement a solution using only O(1) extra space complexity and O(n) runtime complexity?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [3, 0, 1]) == 2\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(nums = [0]) == 1\n assert candidate(nums = [5, 2, 4, 6, 3, 0, 1]) == 7\n assert candidate(nums = [0, 2, 3, 4]) == 1\n assert candidate(nums = [8, 6, 4, 2, 0, 1, 3, 5, 7]) == 9\n assert candidate(nums = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 0\n assert candidate(nums = [5, 2, 4, 0, 1]) == 3\n assert candidate(nums = [0, 1]) == 2\n assert candidate(nums = [9, 6, 4, 2, 3, 5, 7, 0, 1]) == 8\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 10]) == 9\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 0\n assert candidate(nums = [0, 1, 2, 3, 5]) == 4\n assert candidate(nums = [1, 0, 2, 4]) == 3\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981, 9980, 9979, 9978, 9977, 9976, 9975, 9974, 9973, 9972, 9971, 9970, 9969, 9968, 9967, 9966, 9965, 9964, 9963, 9962, 9961, 9960, 9959, 9958, 9957, 9956, 9955, 9954, 9953, 9952, 9951, 9950, 9949, 9948, 9947, 9946, 9945, 9944, 9943, 9942, 9941, 9940, 9939, 9938, 9937, 9936, 9935, 9934, 9933, 9932, 9931, 9930, 9929, 9928, 9927, 9926, 9925, 9924, 9923, 9922, 9921, 9920, 9919, 9918, 9917, 9916, 9915, 9914, 9913, 9912, 9911, 9910, 9909, 9908, 9907, 9906, 9905, 9904, 9903, 9902, 9901, 9900]) == 10001\n assert candidate(nums = [14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 15\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15]) == 11\n assert candidate(nums = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16]) == 31\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981, 9980, 9979, 9978, 9977, 9976, 9975, 9974, 9973, 9972, 9971, 9970, 9969, 9968, 9967, 9966, 9965, 9964, 9963, 9962, 9961, 9960, 9959, 9958, 9957, 9956, 9955, 9954, 9953, 9952, 9951, 9950, 9949, 9948, 9947, 9946, 9945, 9944, 9943, 9942, 9941, 9940, 9939, 9938, 9937, 9936, 9935, 9934, 9933, 9932, 9931, 9930, 9929, 9928, 9927, 9926, 9925, 9924, 9923, 9922, 9921, 9920, 9919, 9918, 9917, 9916, 9915, 9914, 9913, 9912, 9911, 9910, 9909, 9908, 9907, 9906, 9905, 9904, 9903, 9902, 9901, 9900, 9899, 9898, 9897, 9896, 9895, 9894, 9893, 9892, 9891, 9890, 9889, 9888, 9887, 9886, 9885, 9884, 9883, 9882, 9881, 9880, 9879, 9878, 9877, 9876, 9875, 9874, 9873, 9872, 9871, 9870, 9869, 9868, 9867, 9866, 9865, 9864, 9863, 9862, 9861, 9860, 9859, 9858, 9857, 9856, 9855, 9854, 9853, 9852, 9851, 9850, 9849, 9848, 9847, 9846, 9845, 9844, 9843, 9842, 9841, 9840, 9839, 9838, 9837, 9836, 9835, 9834, 9833, 9832, 9831, 9830, 9829, 9828, 9827, 9826, 9825, 9824, 9823, 9822, 9821, 9820, 9819, 9818, 9817, 9816, 9815, 9814, 9813, 9812, 9811, 9810, 9809, 9808, 9807, 9806, 9805, 9804, 9803, 9802, 9801, 9800]) == 10001\n assert candidate(nums = [1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 15\n assert candidate(nums = [2, 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15]) == 14\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 12, 13, 14, 15]) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 12, 14, 15, 0]) == 16\n assert candidate(nums = [1, 0, 13, 14, 15, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0]) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 11, 13, 14, 15, 0]) == 16\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14]) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16]) == 15\n assert candidate(nums = [1, 3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 107\n assert candidate(nums = [5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981, 4980, 4979, 4978, 4977, 4976, 4975, 4974, 4973, 4972, 4971, 4970, 4969, 4968, 4967, 4966, 4965, 4964, 4963, 4962, 4961, 4960, 4959, 4958, 4957, 4956, 4955, 4954, 4953, 4952, 4951, 4950, 4949, 4948, 4947, 4946, 4945, 4944, 4943, 4942, 4941, 4940, 4939, 4938, 4937, 4936, 4935, 4934, 4933, 4932, 4931, 4930, 4929, 4928, 4927, 4926, 4925, 4924, 4923, 4922, 4921, 4920, 4919, 4918, 4917, 4916, 4915, 4914, 4913, 4912, 4911, 4910, 4909, 4908, 4907, 4906, 4905, 4904, 4903, 4902, 4901, 4900]) == 5001\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15]) == 13\n assert candidate(nums = [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0]) == 2\n assert candidate(nums = [15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == 14\n assert candidate(nums = [5000, 4999, 4998, 4997, 4996, 4995, 4994, 4993, 4992, 4991, 4990, 4989, 4988, 4987, 4986, 4985, 4984, 4983, 4982, 4981, 4980, 4979, 4978, 4977, 4976, 4975, 4974, 4973, 4972, 4971, 4970, 4969, 4968, 4967, 4966, 4965, 4964, 4963, 4962, 4961, 4960, 4959, 4958, 4957, 4956, 4955, 4954, 4953, 4952, 4951, 4950, 4949, 4948, 4947, 4946, 4945, 4944, 4943, 4942, 4941, 4940, 4939, 4938, 4937, 4936, 4935, 4934, 4933, 4932, 4931, 4930, 4929, 4928, 4927, 4926, 4925, 4924, 4923, 4922, 4921, 4920, 4919, 4918, 4917, 4916, 4915, 4914, 4913, 4912, 4911, 4910, 4909, 4908, 4907, 4906, 4905, 4904, 4903, 4902, 4901, 4900, 4899, 4898, 4897, 4896, 4895, 4894, 4893, 4892, 4891, 4890, 4889, 4888, 4887, 4886, 4885, 4884, 4883, 4882, 4881, 4880, 4879, 4878, 4877, 4876, 4875, 4874, 4873, 4872, 4871, 4870, 4869, 4868, 4867, 4866, 4865, 4864, 4863, 4862, 4861, 4860, 4859, 4858, 4857, 4856, 4855, 4854, 4853, 4852, 4851, 4850, 4849, 4848, 4847, 4846, 4845, 4844, 4843, 4842, 4841, 4840, 4839, 4838, 4837, 4836, 4835, 4834, 4833, 4832, 4831, 4830, 4829, 4828, 4827, 4826, 4825, 4824, 4823, 4822, 4821, 4820, 4819, 4818, 4817, 4816, 4815, 4814, 4813, 4812, 4811, 4810, 4809, 4808, 4807, 4806, 4805, 4804, 4803, 4802, 4801, 4800]) == 5001\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15]) == 9\n assert candidate(nums = [2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70, 69, 72, 71, 74, 73, 76, 75, 78, 77, 80, 79, 82, 81, 84, 83, 86, 85, 88, 87, 90, 89, 92, 91, 94, 93, 96, 95, 98, 97, 100, 99]) == 0\n assert candidate(nums = [42, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150]) == 213\n assert candidate(nums = [42, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 41\n assert candidate(nums = [33, 31, 35, 32, 30, 29, 34, 28, 36, 27, 37, 26, 38, 25, 39, 24, 40, 23, 41, 22, 42, 21, 43, 20, 44, 19, 45, 18, 46, 17, 47, 16, 48, 15, 49, 14, 50, 13, 51, 12, 52, 11, 53, 10, 54, 9, 55, 8, 56, 7, 57, 6, 58, 5, 59, 4, 60, 3, 61, 2, 62, 1]) == 0\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 13, 14, 15]) == 11\n assert candidate(nums = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 1\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().missingNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var missingNumber = function(nums) {", "container": null, "callable": "missingNumber", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 273, "task_id": "integer-to-english-words", "difficulty": "Hard", "problem_description": "Convert a non-negative integer num to its English words representation.\n \nExample 1:\n\nInput: num = 123\nOutput: \"One Hundred Twenty Three\"\n\nExample 2:\n\nInput: num = 12345\nOutput: \"Twelve Thousand Three Hundred Forty Five\"\n\nExample 3:\n\nInput: num = 1234567\nOutput: \"One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven\"\n\n \nConstraints:\n\n0 <= num <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 9) == \"Nine\"\n assert candidate(num = 10) == \"Ten\"\n assert candidate(num = 100000000) == \"One Hundred Million\"\n assert candidate(num = 1234567) == \"One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven\"\n assert candidate(num = 999) == \"Nine Hundred Ninety Nine\"\n assert candidate(num = 10000000) == \"Ten Million\"\n assert candidate(num = 29) == \"Twenty Nine\"\n assert candidate(num = 31) == \"Thirty One\"\n assert candidate(num = 30) == \"Thirty\"\n assert candidate(num = 1000000000) == \"One Billion\"\n assert candidate(num = 110) == \"One Hundred Ten\"\n assert candidate(num = 5) == \"Five\"\n assert candidate(num = 11) == \"Eleven\"\n assert candidate(num = 1000) == \"One Thousand\"\n assert candidate(num = 123) == \"One Hundred Twenty Three\"\n assert candidate(num = 12345) == \"Twelve Thousand Three Hundred Forty Five\"\n assert candidate(num = 1001) == \"One Thousand One\"\n assert candidate(num = 21) == \"Twenty One\"\n assert candidate(num = 0) == \"Zero\"\n assert candidate(num = 39) == \"Thirty Nine\"\n assert candidate(num = 100) == \"One Hundred\"\n assert candidate(num = 111) == \"One Hundred Eleven\"\n assert candidate(num = 2147483647) == \"Two Billion One Hundred Forty Seven Million Four Hundred Eighty Three Thousand Six Hundred Forty Seven\"\n assert candidate(num = 100000) == \"One Hundred Thousand\"\n assert candidate(num = 999999999) == \"Nine Hundred Ninety Nine Million Nine Hundred Ninety Nine Thousand Nine Hundred Ninety Nine\"\n assert candidate(num = 1000000) == \"One Million\"\n assert candidate(num = 999999) == \"Nine Hundred Ninety Nine Thousand Nine Hundred Ninety Nine\"\n assert candidate(num = 19) == \"Nineteen\"\n assert candidate(num = 10000) == \"Ten Thousand\"\n assert candidate(num = 101) == \"One Hundred One\"\n assert candidate(num = 500000050) == \"Five Hundred Million Fifty\"\n assert candidate(num = 111111111) == \"One Hundred Eleven Million One Hundred Eleven Thousand One Hundred Eleven\"\n assert candidate(num = 555555555) == \"Five Hundred Fifty Five Million Five Hundred Fifty Five Thousand Five Hundred Fifty Five\"\n assert candidate(num = 1111111111) == \"One Billion One Hundred Eleven Million One Hundred Eleven Thousand One Hundred Eleven\"\n assert candidate(num = 10000000000) == \"Ten Billion\"\n assert candidate(num = 890123456) == \"Eight Hundred Ninety Million One Hundred Twenty Three Thousand Four Hundred Fifty Six\"\n assert candidate(num = 508) == \"Five Hundred Eight\"\n assert candidate(num = 999999999999) == \"Nine Hundred Ninety Nine Billion Nine Hundred Ninety Nine Million Nine Hundred Ninety Nine Thousand Nine Hundred Ninety Nine\"\n assert candidate(num = 1010101010) == \"One Billion Ten Million One Hundred One Thousand Ten\"\n assert candidate(num = 50000050) == \"Fifty Million Fifty\"\n assert candidate(num = 99) == \"Ninety Nine\"\n assert candidate(num = 1000010001) == \"One Billion Ten Thousand One\"\n assert candidate(num = 807000000) == \"Eight Hundred Seven Million\"\n assert candidate(num = 900000009) == \"Nine Hundred Million Nine\"\n assert candidate(num = 123456789) == \"One Hundred Twenty Three Million Four Hundred Fifty Six Thousand Seven Hundred Eighty Nine\"\n assert candidate(num = 11000011) == \"Eleven Million Eleven\"\n assert candidate(num = 900000090) == \"Nine Hundred Million Ninety\"\n assert candidate(num = 1010001000) == \"One Billion Ten Million One Thousand\"\n assert candidate(num = 1000000001) == \"One Billion One\"\n assert candidate(num = 1001001001) == \"One Billion One Million One Thousand One\"\n assert candidate(num = 999000999) == \"Nine Hundred Ninety Nine Million Nine Hundred Ninety Nine\"\n assert candidate(num = 1234567890) == \"One Billion Two Hundred Thirty Four Million Five Hundred Sixty Seven Thousand Eight Hundred Ninety\"\n assert candidate(num = 2000000000) == \"Two Billion\"\n assert candidate(num = 9876) == \"Nine Thousand Eight Hundred Seventy Six\"\n assert candidate(num = 1000010) == \"One Million Ten\"\n assert candidate(num = 1000000000001) == \"Ten Hundred Billion One\"\n assert candidate(num = 987654321) == \"Nine Hundred Eighty Seven Million Six Hundred Fifty Four Thousand Three Hundred Twenty One\"\n assert candidate(num = 990000000) == \"Nine Hundred Ninety Million\"\n assert candidate(num = 123000456) == \"One Hundred Twenty Three Million Four Hundred Fifty Six\"\n assert candidate(num = 203040506) == \"Two Hundred Three Million Forty Thousand Five Hundred Six\"\n assert candidate(num = 101010101) == \"One Hundred One Million Ten Thousand One Hundred One\"\n assert candidate(num = 500000500) == \"Five Hundred Million Five Hundred\"\n assert candidate(num = 2100000100) == \"Two Billion One Hundred Million One Hundred\"\n assert candidate(num = 450000000) == \"Four Hundred Fifty Million\"\n assert candidate(num = 4321098765) == \"Four Billion Three Hundred Twenty One Million Ninety Eight Thousand Seven Hundred Sixty Five\"\n assert candidate(num = 123000000) == \"One Hundred Twenty Three Million\"\n assert candidate(num = 4321) == \"Four Thousand Three Hundred Twenty One\"\n assert candidate(num = 900009000) == \"Nine Hundred Million Nine Thousand\"\n assert candidate(num = 1100000000) == \"One Billion One Hundred Million\"\n assert candidate(num = 123400000) == \"One Hundred Twenty Three Million Four Hundred Thousand\"\n assert candidate(num = 1000001) == \"One Million One\"\n assert candidate(num = 9999) == \"Nine Thousand Nine Hundred Ninety Nine\"\n assert candidate(num = 900900000) == \"Nine Hundred Million Nine Hundred Thousand\"\n assert candidate(num = 60012003) == \"Sixty Million Twelve Thousand Three\"\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().numberToWords", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numberToWords = function(num) {", "container": null, "callable": "numberToWords", "parameters": [{"name": "num", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 274, "task_id": "h-index", "difficulty": "Medium", "problem_description": "Given an array of integers citations where citations[i] is the number of citations a researcher received for their ith paper, return the researcher's h-index.\nAccording to the definition of h-index on Wikipedia: The h-index is defined as the maximum value of h such that the given researcher has published at least h papers that have each been cited at least h times.\n \nExample 1:\n\nInput: citations = [3,0,6,1,5]\nOutput: 3\nExplanation: [3,0,6,1,5] means the researcher has 5 papers in total and each of them had received 3, 0, 6, 1, 5 citations respectively.\nSince the researcher has 3 papers with at least 3 citations each and the remaining two with no more than 3 citations each, their h-index is 3.\n\nExample 2:\n\nInput: citations = [1,3,1]\nOutput: 1\n\n \nConstraints:\n\nn == citations.length\n1 <= n <= 5000\n0 <= citations[i] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(citations = [10, 8, 5, 4, 3]) == 4\n assert candidate(citations = [1]) == 1\n assert candidate(citations = [3, 0, 6, 1, 5]) == 3\n assert candidate(citations = [0, 1, 2, 3, 4]) == 2\n assert candidate(citations = [1000, 999, 998, 997, 996]) == 5\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(citations = [0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [8, 8, 8, 8, 8, 8, 8]) == 7\n assert candidate(citations = [10, 10, 10, 10]) == 4\n assert candidate(citations = [1, 3, 1]) == 1\n assert candidate(citations = [100, 0, 1, 2]) == 2\n assert candidate(citations = [11, 15, 0, 6, 9, 12]) == 5\n assert candidate(citations = [0, 1, 2, 3, 4, 5]) == 3\n assert candidate(citations = [11, 15]) == 2\n assert candidate(citations = [1, 2, 3, 4, 5, 6]) == 3\n assert candidate(citations = [6, 5, 4, 3, 2, 1]) == 3\n assert candidate(citations = [4, 4, 4, 4, 3]) == 4\n assert candidate(citations = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 5\n assert candidate(citations = [0]) == 0\n assert candidate(citations = [1, 2, 3, 4, 5]) == 3\n assert candidate(citations = [0, 0, 0, 0]) == 0\n assert candidate(citations = [1000, 1000, 1000]) == 3\n assert candidate(citations = [5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [34, 23, 12, 45, 67, 89, 100, 99, 88, 77, 66, 55, 44, 33, 22, 11, 0]) == 14\n assert candidate(citations = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 7\n assert candidate(citations = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 10\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 1\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [10, 8, 5, 4, 3, 1, 0]) == 4\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 6\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1000]) == 1\n assert candidate(citations = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990, 989, 988, 987, 986, 985, 984, 983, 982, 981, 980]) == 20\n assert candidate(citations = [100, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 11\n assert candidate(citations = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 14\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 19\n assert candidate(citations = [0, 1000, 2000, 3000, 4000, 5000]) == 5\n assert candidate(citations = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15]) == 15\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1\n assert candidate(citations = [1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0]) == 10\n assert candidate(citations = [10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == 9\n assert candidate(citations = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == 9\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1000]) == 1\n assert candidate(citations = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 19\n assert candidate(citations = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 5\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10\n assert candidate(citations = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4]) == 3\n assert candidate(citations = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 3\n assert candidate(citations = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == 2\n assert candidate(citations = [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12]) == 6\n assert candidate(citations = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 5\n assert candidate(citations = [250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250, 250]) == 31\n assert candidate(citations = [0, 1000, 2, 500, 3, 750, 4, 250, 5, 125]) == 5\n assert candidate(citations = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [25, 20, 15, 10, 5, 0, 0, 0, 0, 0]) == 5\n assert candidate(citations = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 10\n assert candidate(citations = [10, 8, 5, 4, 3, 2, 1, 0]) == 4\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [0, 1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000]) == 5\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [500, 250, 125, 62, 31, 15, 7, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 7\n assert candidate(citations = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 3\n assert candidate(citations = [1, 100, 2, 99, 3, 98, 4, 97, 5, 96, 6, 95, 7, 94, 8, 93, 9, 92, 10, 91]) == 10\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [100, 50, 25, 10, 5, 2]) == 5\n assert candidate(citations = [50, 40, 30, 20, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 5\n assert candidate(citations = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7]) == 5\n assert candidate(citations = [1, 0, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15\n assert candidate(citations = [150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 14\n assert candidate(citations = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991]) == 10\n assert candidate(citations = [100, 50, 25, 12, 6, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 5\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 8\n assert candidate(citations = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == 9\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15\n"}, "metadata": {"canonical_parameter_names": ["citations"], "leetcode_dataset_entry_point": "Solution().hIndex", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var hIndex = function(citations) {", "container": null, "callable": "hIndex", "parameters": [{"name": "citations", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 275, "task_id": "h-index-ii", "difficulty": "Medium", "problem_description": "Given an array of integers citations where citations[i] is the number of citations a researcher received for their ith paper and citations is sorted in ascending order, return the researcher's h-index.\nAccording to the definition of h-index on Wikipedia: The h-index is defined as the maximum value of h such that the given researcher has published at least h papers that have each been cited at least h times.\nYou must write an algorithm that runs in logarithmic time.\n \nExample 1:\n\nInput: citations = [0,1,3,5,6]\nOutput: 3\nExplanation: [0,1,3,5,6] means the researcher has 5 papers in total and each of them had received 0, 1, 3, 5, 6 citations respectively.\nSince the researcher has 3 papers with at least 3 citations each and the remaining two with no more than 3 citations each, their h-index is 3.\n\nExample 2:\n\nInput: citations = [1,2,100]\nOutput: 2\n\n \nConstraints:\n\nn == citations.length\n1 <= n <= 105\n0 <= citations[i] <= 1000\ncitations is sorted in ascending order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(citations = [1]) == 1\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(citations = [100]) == 1\n assert candidate(citations = [0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [100, 100, 100, 100, 100]) == 5\n assert candidate(citations = [0, 0, 4, 4, 5, 6]) == 4\n assert candidate(citations = [0, 1, 2, 3, 4, 5]) == 3\n assert candidate(citations = [11, 15]) == 2\n assert candidate(citations = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 4\n assert candidate(citations = [1, 2, 2, 3, 3, 4, 4, 5, 5, 5]) == 4\n assert candidate(citations = [1, 2, 100]) == 2\n assert candidate(citations = [1, 3, 3, 3, 3, 3, 3]) == 3\n assert candidate(citations = [0]) == 0\n assert candidate(citations = [0, 1, 3, 5, 6]) == 3\n assert candidate(citations = [0, 0, 0, 0]) == 0\n assert candidate(citations = [1, 3, 8, 100]) == 3\n assert candidate(citations = [1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(citations = [5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [0, 0, 4, 4, 4, 5, 6]) == 4\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 4\n assert candidate(citations = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 10\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 25\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 50\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 10\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 20\n assert candidate(citations = [0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10]) == 9\n assert candidate(citations = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == 14\n assert candidate(citations = [1, 2, 3, 4, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 10\n assert candidate(citations = [10, 20, 30, 40, 50, 60, 70, 80, 90, 1000]) == 10\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 10, 10, 10, 10]) == 7\n assert candidate(citations = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 20\n assert candidate(citations = [0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10, 10]) == 7\n assert candidate(citations = [1, 1, 1, 1, 1, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [1, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 8\n assert candidate(citations = [1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 13\n assert candidate(citations = [1, 2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == 7\n assert candidate(citations = [0, 0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 4\n assert candidate(citations = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 2\n assert candidate(citations = [0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14]) == 12\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1\n assert candidate(citations = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 13\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 13\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]) == 11\n assert candidate(citations = [25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(citations = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 9\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30]) == 20\n assert candidate(citations = [0, 0, 0, 0, 0, 1, 1, 1, 1, 100]) == 1\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 2\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(citations = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 10\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15\n assert candidate(citations = [0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == 8\n assert candidate(citations = [0, 1, 1, 2, 2, 3, 3, 4, 4, 5]) == 3\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000]) == 1\n assert candidate(citations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 13\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(citations = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(citations = [1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(citations = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 20\n assert candidate(citations = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1000]) == 1\n assert candidate(citations = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 15\n assert candidate(citations = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == 10\n assert candidate(citations = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n"}, "metadata": {"canonical_parameter_names": ["citations"], "leetcode_dataset_entry_point": "Solution().hIndex", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var hIndex = function(citations) {", "container": null, "callable": "hIndex", "parameters": [{"name": "citations", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 279, "task_id": "perfect-squares", "difficulty": "Medium", "problem_description": "Given an integer n, return the least number of perfect square numbers that sum to n.\nA perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.\n \nExample 1:\n\nInput: n = 12\nOutput: 3\nExplanation: 12 = 4 + 4 + 4.\n\nExample 2:\n\nInput: n = 13\nOutput: 2\nExplanation: 13 = 4 + 9.\n\n \nConstraints:\n\n1 <= n <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 625) == 1\n assert candidate(n = 8) == 2\n assert candidate(n = 100) == 1\n assert candidate(n = 4) == 1\n assert candidate(n = 12) == 3\n assert candidate(n = 16) == 1\n assert candidate(n = 17) == 2\n assert candidate(n = 10000) == 1\n assert candidate(n = 9) == 1\n assert candidate(n = 9876) == 3\n assert candidate(n = 6) == 3\n assert candidate(n = 9999) == 4\n assert candidate(n = 23) == 4\n assert candidate(n = 1) == 1\n assert candidate(n = 10) == 2\n assert candidate(n = 13) == 2\n assert candidate(n = 25) == 1\n assert candidate(n = 3) == 3\n assert candidate(n = 9801) == 1\n assert candidate(n = 156) == 4\n assert candidate(n = 2356) == 3\n assert candidate(n = 63) == 4\n assert candidate(n = 4001) == 2\n assert candidate(n = 144) == 1\n assert candidate(n = 12345) == 3\n assert candidate(n = 8200) == 2\n assert candidate(n = 5678) == 3\n assert candidate(n = 2345) == 3\n assert candidate(n = 1111) == 4\n assert candidate(n = 1600) == 1\n assert candidate(n = 7500) == 3\n assert candidate(n = 50) == 2\n assert candidate(n = 3333) == 3\n assert candidate(n = 300) == 3\n assert candidate(n = 28) == 4\n assert candidate(n = 6250) == 2\n assert candidate(n = 8402) == 2\n assert candidate(n = 3000) == 3\n assert candidate(n = 64) == 1\n assert candidate(n = 98) == 2\n assert candidate(n = 2) == 2\n assert candidate(n = 8401) == 3\n assert candidate(n = 1024) == 1\n assert candidate(n = 38) == 3\n assert candidate(n = 7776) == 3\n assert candidate(n = 8000) == 2\n assert candidate(n = 169) == 1\n assert candidate(n = 75) == 3\n assert candidate(n = 5000) == 2\n assert candidate(n = 9500) == 4\n assert candidate(n = 19) == 3\n assert candidate(n = 7199) == 4\n assert candidate(n = 77) == 3\n assert candidate(n = 1999) == 4\n assert candidate(n = 5625) == 1\n assert candidate(n = 81) == 1\n assert candidate(n = 7654) == 3\n assert candidate(n = 48) == 3\n assert candidate(n = 4321) == 2\n assert candidate(n = 7777) == 3\n assert candidate(n = 6400) == 1\n assert candidate(n = 325) == 2\n assert candidate(n = 9000) == 2\n assert candidate(n = 4999) == 4\n assert candidate(n = 4369) == 2\n assert candidate(n = 400) == 1\n assert candidate(n = 78) == 3\n assert candidate(n = 31) == 4\n assert candidate(n = 1234) == 2\n assert candidate(n = 3125) == 2\n assert candidate(n = 2017) == 2\n assert candidate(n = 85) == 2\n assert candidate(n = 196) == 1\n assert candidate(n = 8999) == 4\n assert candidate(n = 84) == 3\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().numSquares", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numSquares = function(n) {", "container": null, "callable": "numSquares", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 282, "task_id": "expression-add-operators", "difficulty": "Hard", "problem_description": "Given a string num that contains only digits and an integer target, return all possibilities to insert the binary operators '+', '-', and/or '*' between the digits of num so that the resultant expression evaluates to the target value.\nNote that operands in the returned expressions should not contain leading zeros.\n \nExample 1:\n\nInput: num = \"123\", target = 6\nOutput: [\"1*2*3\",\"1+2+3\"]\nExplanation: Both \"1*2*3\" and \"1+2+3\" evaluate to 6.\n\nExample 2:\n\nInput: num = \"232\", target = 8\nOutput: [\"2*3+2\",\"2+3*2\"]\nExplanation: Both \"2*3+2\" and \"2+3*2\" evaluate to 8.\n\nExample 3:\n\nInput: num = \"3456237490\", target = 9191\nOutput: []\nExplanation: There are no expressions that can be created from \"3456237490\" to evaluate to 9191.\n\n \nConstraints:\n\n1 <= num.length <= 10\nnum consists of only digits.\n-231 <= target <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = \"232\",target = 8) == ['2+3*2', '2*3+2']\n assert candidate(num = \"123\",target = 6) == ['1+2+3', '1*2*3']\n assert candidate(num = \"00\",target = 0) == ['0+0', '0-0', '0*0']\n assert candidate(num = \"105\",target = 5) == ['1*0+5', '10-5']\n assert candidate(num = \"3\",target = 3) == ['3']\n assert candidate(num = \"34\",target = 14) == []\n assert candidate(num = \"3456237490\",target = 9191) == []\n assert candidate(num = \"12\",target = 3) == ['1+2']\n assert candidate(num = \"0105\",target = 5) == ['0+1*0+5', '0-1*0+5', '0*1+0+5', '0*1-0+5', '0*1*0+5', '0+10-5', '0*10+5']\n assert candidate(num = \"123456789\",target = 100) == ['1+2+3+4+5+6+7+8*9', '1+2+3-4+5+6+78+9', '1+2+3-4*5+6*7+8*9', '1+2+3*4-5-6+7+89', '1+2+3-45+67+8*9', '1+2-3*4+5*6+7+8*9', '1+2-3*4-5+6*7+8*9', '1+2*3+4+5+67+8+9', '1+2*3+4*5-6+7+8*9', '1+2*3-4-5+6+7+89', '1+2+34-5+67-8+9', '1+2+34*5+6-7-8*9', '1+2*34-56+78+9', '1-2+3*4+5+67+8+9', '1-2+3*4*5+6*7+8-9', '1-2+3*4*5-6+7*8-9', '1-2+3+45+6+7*8-9', '1-2-3+4*5+67+8+9', '1-2-3+45+6*7+8+9', '1-2-3+45-6+7*8+9', '1-2-3+45-6-7+8*9', '1-2*3+4*5+6+7+8*9', '1-2*3-4+5*6+7+8*9', '1-2*3-4-5+6*7+8*9', '1-2-34+56+7+8*9', '1*2+3+4*5+6+78-9', '1*2+3-4+5*6+78-9', '1*2+3*4+5-6+78+9', '1*2+3+45+67-8-9', '1*2-3+4-5+6+7+89', '1*2-3+4*5-6+78+9', '1*2*3+4+5+6+7+8*9', '1*2*3-4+5+6+78+9', '1*2*3-4*5+6*7+8*9', '1*2*3*4+5+6+7*8+9', '1*2*3*4+5+6-7+8*9', '1*2*3*4-5-6+78+9', '1*2*3-45+67+8*9', '1*2+34+5+6*7+8+9', '1*2+34+5-6+7*8+9', '1*2+34+5-6-7+8*9', '1*2+34+56+7-8+9', '1*2*34+56-7-8-9', '1+23-4+5+6+78-9', '1+23-4-5+6+7+8*9', '1+23-4+56+7+8+9', '1+23*4+5-6+7-8+9', '1+23*4-5+6+7+8-9', '1-23+4*5+6+7+89', '1-23-4+5*6+7+89', '1-23-4-5+6*7+89', '1*23+4+5+67-8+9', '1*23-4+5-6-7+89', '1+234-56-7-8*9', '1*234+5-67-8*9', '12+3+4+5-6-7+89', '12+3-4+5+67+8+9', '12+3*4+5+6+7*8+9', '12+3*4+5+6-7+8*9', '12+3*4-5-6+78+9', '12+3*45+6*7-89', '12-3+4*5+6+7*8+9', '12-3+4*5+6-7+8*9', '12-3-4+5-6+7+89', '12-3-4+5*6+7*8+9', '12-3-4+5*6-7+8*9', '12*3-4+5-6+78-9', '12*3-4-5-6+7+8*9', '12*3-4*5+67+8+9', '12+34+5*6+7+8+9', '12+34-5+6*7+8+9', '12+34-5-6+7*8+9', '12+34-5-6-7+8*9', '123+4-5+67-89', '123+4*5-6*7+8-9', '123-4-5-6-7+8-9', '123+45-67+8-9', '123-45-67+89']\n assert candidate(num = \"10000\",target = 1) == ['1+0+0+0+0', '1+0+0+0-0', '1+0+0+0*0', '1+0+0-0+0', '1+0+0-0-0', '1+0+0-0*0', '1+0+0*0+0', '1+0+0*0-0', '1+0+0*0*0', '1+0-0+0+0', '1+0-0+0-0', '1+0-0+0*0', '1+0-0-0+0', '1+0-0-0-0', '1+0-0-0*0', '1+0-0*0+0', '1+0-0*0-0', '1+0-0*0*0', '1+0*0+0+0', '1+0*0+0-0', '1+0*0+0*0', '1+0*0-0+0', '1+0*0-0-0', '1+0*0-0*0', '1+0*0*0+0', '1+0*0*0-0', '1+0*0*0*0', '1-0+0+0+0', '1-0+0+0-0', '1-0+0+0*0', '1-0+0-0+0', '1-0+0-0-0', '1-0+0-0*0', '1-0+0*0+0', '1-0+0*0-0', '1-0+0*0*0', '1-0-0+0+0', '1-0-0+0-0', '1-0-0+0*0', '1-0-0-0+0', '1-0-0-0-0', '1-0-0-0*0', '1-0-0*0+0', '1-0-0*0-0', '1-0-0*0*0', '1-0*0+0+0', '1-0*0+0-0', '1-0*0+0*0', '1-0*0-0+0', '1-0*0-0-0', '1-0*0-0*0', '1-0*0*0+0', '1-0*0*0-0', '1-0*0*0*0']\n assert candidate(num = \"9999999999\",target = 1000000000) == []\n assert candidate(num = \"123456789\",target = 4321) == []\n assert candidate(num = \"456\",target = 456) == ['456']\n assert candidate(num = \"12345\",target = 30) == ['1+2*3*4+5']\n assert candidate(num = \"1000000\",target = 1) == ['1+0+0+0+0+0+0', '1+0+0+0+0+0-0', '1+0+0+0+0+0*0', '1+0+0+0+0-0+0', '1+0+0+0+0-0-0', '1+0+0+0+0-0*0', '1+0+0+0+0*0+0', '1+0+0+0+0*0-0', '1+0+0+0+0*0*0', '1+0+0+0-0+0+0', '1+0+0+0-0+0-0', '1+0+0+0-0+0*0', '1+0+0+0-0-0+0', '1+0+0+0-0-0-0', '1+0+0+0-0-0*0', '1+0+0+0-0*0+0', '1+0+0+0-0*0-0', '1+0+0+0-0*0*0', '1+0+0+0*0+0+0', '1+0+0+0*0+0-0', '1+0+0+0*0+0*0', '1+0+0+0*0-0+0', '1+0+0+0*0-0-0', '1+0+0+0*0-0*0', '1+0+0+0*0*0+0', '1+0+0+0*0*0-0', '1+0+0+0*0*0*0', '1+0+0-0+0+0+0', '1+0+0-0+0+0-0', '1+0+0-0+0+0*0', '1+0+0-0+0-0+0', '1+0+0-0+0-0-0', '1+0+0-0+0-0*0', '1+0+0-0+0*0+0', '1+0+0-0+0*0-0', '1+0+0-0+0*0*0', '1+0+0-0-0+0+0', '1+0+0-0-0+0-0', '1+0+0-0-0+0*0', '1+0+0-0-0-0+0', '1+0+0-0-0-0-0', '1+0+0-0-0-0*0', '1+0+0-0-0*0+0', '1+0+0-0-0*0-0', '1+0+0-0-0*0*0', '1+0+0-0*0+0+0', '1+0+0-0*0+0-0', '1+0+0-0*0+0*0', '1+0+0-0*0-0+0', '1+0+0-0*0-0-0', '1+0+0-0*0-0*0', '1+0+0-0*0*0+0', '1+0+0-0*0*0-0', '1+0+0-0*0*0*0', '1+0+0*0+0+0+0', '1+0+0*0+0+0-0', '1+0+0*0+0+0*0', '1+0+0*0+0-0+0', '1+0+0*0+0-0-0', '1+0+0*0+0-0*0', '1+0+0*0+0*0+0', '1+0+0*0+0*0-0', '1+0+0*0+0*0*0', '1+0+0*0-0+0+0', '1+0+0*0-0+0-0', '1+0+0*0-0+0*0', '1+0+0*0-0-0+0', '1+0+0*0-0-0-0', '1+0+0*0-0-0*0', '1+0+0*0-0*0+0', '1+0+0*0-0*0-0', '1+0+0*0-0*0*0', '1+0+0*0*0+0+0', '1+0+0*0*0+0-0', '1+0+0*0*0+0*0', '1+0+0*0*0-0+0', '1+0+0*0*0-0-0', '1+0+0*0*0-0*0', '1+0+0*0*0*0+0', '1+0+0*0*0*0-0', '1+0+0*0*0*0*0', '1+0-0+0+0+0+0', '1+0-0+0+0+0-0', '1+0-0+0+0+0*0', '1+0-0+0+0-0+0', '1+0-0+0+0-0-0', '1+0-0+0+0-0*0', '1+0-0+0+0*0+0', '1+0-0+0+0*0-0', '1+0-0+0+0*0*0', '1+0-0+0-0+0+0', '1+0-0+0-0+0-0', '1+0-0+0-0+0*0', '1+0-0+0-0-0+0', '1+0-0+0-0-0-0', '1+0-0+0-0-0*0', '1+0-0+0-0*0+0', '1+0-0+0-0*0-0', '1+0-0+0-0*0*0', '1+0-0+0*0+0+0', '1+0-0+0*0+0-0', '1+0-0+0*0+0*0', '1+0-0+0*0-0+0', '1+0-0+0*0-0-0', '1+0-0+0*0-0*0', '1+0-0+0*0*0+0', '1+0-0+0*0*0-0', '1+0-0+0*0*0*0', '1+0-0-0+0+0+0', '1+0-0-0+0+0-0', '1+0-0-0+0+0*0', '1+0-0-0+0-0+0', '1+0-0-0+0-0-0', '1+0-0-0+0-0*0', '1+0-0-0+0*0+0', '1+0-0-0+0*0-0', '1+0-0-0+0*0*0', '1+0-0-0-0+0+0', '1+0-0-0-0+0-0', '1+0-0-0-0+0*0', '1+0-0-0-0-0+0', '1+0-0-0-0-0-0', '1+0-0-0-0-0*0', '1+0-0-0-0*0+0', '1+0-0-0-0*0-0', '1+0-0-0-0*0*0', '1+0-0-0*0+0+0', '1+0-0-0*0+0-0', '1+0-0-0*0+0*0', '1+0-0-0*0-0+0', '1+0-0-0*0-0-0', '1+0-0-0*0-0*0', '1+0-0-0*0*0+0', '1+0-0-0*0*0-0', '1+0-0-0*0*0*0', '1+0-0*0+0+0+0', '1+0-0*0+0+0-0', '1+0-0*0+0+0*0', '1+0-0*0+0-0+0', '1+0-0*0+0-0-0', '1+0-0*0+0-0*0', '1+0-0*0+0*0+0', '1+0-0*0+0*0-0', '1+0-0*0+0*0*0', '1+0-0*0-0+0+0', '1+0-0*0-0+0-0', '1+0-0*0-0+0*0', '1+0-0*0-0-0+0', '1+0-0*0-0-0-0', '1+0-0*0-0-0*0', '1+0-0*0-0*0+0', '1+0-0*0-0*0-0', '1+0-0*0-0*0*0', '1+0-0*0*0+0+0', '1+0-0*0*0+0-0', '1+0-0*0*0+0*0', '1+0-0*0*0-0+0', '1+0-0*0*0-0-0', '1+0-0*0*0-0*0', '1+0-0*0*0*0+0', '1+0-0*0*0*0-0', '1+0-0*0*0*0*0', '1+0*0+0+0+0+0', '1+0*0+0+0+0-0', '1+0*0+0+0+0*0', '1+0*0+0+0-0+0', '1+0*0+0+0-0-0', '1+0*0+0+0-0*0', '1+0*0+0+0*0+0', '1+0*0+0+0*0-0', '1+0*0+0+0*0*0', '1+0*0+0-0+0+0', '1+0*0+0-0+0-0', '1+0*0+0-0+0*0', '1+0*0+0-0-0+0', '1+0*0+0-0-0-0', '1+0*0+0-0-0*0', '1+0*0+0-0*0+0', '1+0*0+0-0*0-0', '1+0*0+0-0*0*0', '1+0*0+0*0+0+0', '1+0*0+0*0+0-0', '1+0*0+0*0+0*0', '1+0*0+0*0-0+0', '1+0*0+0*0-0-0', '1+0*0+0*0-0*0', '1+0*0+0*0*0+0', '1+0*0+0*0*0-0', '1+0*0+0*0*0*0', '1+0*0-0+0+0+0', '1+0*0-0+0+0-0', '1+0*0-0+0+0*0', '1+0*0-0+0-0+0', '1+0*0-0+0-0-0', '1+0*0-0+0-0*0', '1+0*0-0+0*0+0', '1+0*0-0+0*0-0', '1+0*0-0+0*0*0', '1+0*0-0-0+0+0', '1+0*0-0-0+0-0', '1+0*0-0-0+0*0', '1+0*0-0-0-0+0', '1+0*0-0-0-0-0', '1+0*0-0-0-0*0', '1+0*0-0-0*0+0', '1+0*0-0-0*0-0', '1+0*0-0-0*0*0', '1+0*0-0*0+0+0', '1+0*0-0*0+0-0', '1+0*0-0*0+0*0', '1+0*0-0*0-0+0', '1+0*0-0*0-0-0', '1+0*0-0*0-0*0', '1+0*0-0*0*0+0', '1+0*0-0*0*0-0', '1+0*0-0*0*0*0', '1+0*0*0+0+0+0', '1+0*0*0+0+0-0', '1+0*0*0+0+0*0', '1+0*0*0+0-0+0', '1+0*0*0+0-0-0', '1+0*0*0+0-0*0', '1+0*0*0+0*0+0', '1+0*0*0+0*0-0', '1+0*0*0+0*0*0', '1+0*0*0-0+0+0', '1+0*0*0-0+0-0', '1+0*0*0-0+0*0', '1+0*0*0-0-0+0', '1+0*0*0-0-0-0', '1+0*0*0-0-0*0', '1+0*0*0-0*0+0', '1+0*0*0-0*0-0', '1+0*0*0-0*0*0', '1+0*0*0*0+0+0', '1+0*0*0*0+0-0', '1+0*0*0*0+0*0', '1+0*0*0*0-0+0', '1+0*0*0*0-0-0', '1+0*0*0*0-0*0', '1+0*0*0*0*0+0', '1+0*0*0*0*0-0', '1+0*0*0*0*0*0', '1-0+0+0+0+0+0', '1-0+0+0+0+0-0', '1-0+0+0+0+0*0', '1-0+0+0+0-0+0', '1-0+0+0+0-0-0', '1-0+0+0+0-0*0', '1-0+0+0+0*0+0', '1-0+0+0+0*0-0', '1-0+0+0+0*0*0', '1-0+0+0-0+0+0', '1-0+0+0-0+0-0', '1-0+0+0-0+0*0', '1-0+0+0-0-0+0', '1-0+0+0-0-0-0', '1-0+0+0-0-0*0', '1-0+0+0-0*0+0', '1-0+0+0-0*0-0', '1-0+0+0-0*0*0', '1-0+0+0*0+0+0', '1-0+0+0*0+0-0', '1-0+0+0*0+0*0', '1-0+0+0*0-0+0', '1-0+0+0*0-0-0', '1-0+0+0*0-0*0', '1-0+0+0*0*0+0', '1-0+0+0*0*0-0', '1-0+0+0*0*0*0', '1-0+0-0+0+0+0', '1-0+0-0+0+0-0', '1-0+0-0+0+0*0', '1-0+0-0+0-0+0', '1-0+0-0+0-0-0', '1-0+0-0+0-0*0', '1-0+0-0+0*0+0', '1-0+0-0+0*0-0', '1-0+0-0+0*0*0', '1-0+0-0-0+0+0', '1-0+0-0-0+0-0', '1-0+0-0-0+0*0', '1-0+0-0-0-0+0', '1-0+0-0-0-0-0', '1-0+0-0-0-0*0', '1-0+0-0-0*0+0', '1-0+0-0-0*0-0', '1-0+0-0-0*0*0', '1-0+0-0*0+0+0', '1-0+0-0*0+0-0', '1-0+0-0*0+0*0', '1-0+0-0*0-0+0', '1-0+0-0*0-0-0', '1-0+0-0*0-0*0', '1-0+0-0*0*0+0', '1-0+0-0*0*0-0', '1-0+0-0*0*0*0', '1-0+0*0+0+0+0', '1-0+0*0+0+0-0', '1-0+0*0+0+0*0', '1-0+0*0+0-0+0', '1-0+0*0+0-0-0', '1-0+0*0+0-0*0', '1-0+0*0+0*0+0', '1-0+0*0+0*0-0', '1-0+0*0+0*0*0', '1-0+0*0-0+0+0', '1-0+0*0-0+0-0', '1-0+0*0-0+0*0', '1-0+0*0-0-0+0', '1-0+0*0-0-0-0', '1-0+0*0-0-0*0', '1-0+0*0-0*0+0', '1-0+0*0-0*0-0', '1-0+0*0-0*0*0', '1-0+0*0*0+0+0', '1-0+0*0*0+0-0', '1-0+0*0*0+0*0', '1-0+0*0*0-0+0', '1-0+0*0*0-0-0', '1-0+0*0*0-0*0', '1-0+0*0*0*0+0', '1-0+0*0*0*0-0', '1-0+0*0*0*0*0', '1-0-0+0+0+0+0', '1-0-0+0+0+0-0', '1-0-0+0+0+0*0', '1-0-0+0+0-0+0', '1-0-0+0+0-0-0', '1-0-0+0+0-0*0', '1-0-0+0+0*0+0', '1-0-0+0+0*0-0', '1-0-0+0+0*0*0', '1-0-0+0-0+0+0', '1-0-0+0-0+0-0', '1-0-0+0-0+0*0', '1-0-0+0-0-0+0', '1-0-0+0-0-0-0', '1-0-0+0-0-0*0', '1-0-0+0-0*0+0', '1-0-0+0-0*0-0', '1-0-0+0-0*0*0', '1-0-0+0*0+0+0', '1-0-0+0*0+0-0', '1-0-0+0*0+0*0', '1-0-0+0*0-0+0', '1-0-0+0*0-0-0', '1-0-0+0*0-0*0', '1-0-0+0*0*0+0', '1-0-0+0*0*0-0', '1-0-0+0*0*0*0', '1-0-0-0+0+0+0', '1-0-0-0+0+0-0', '1-0-0-0+0+0*0', '1-0-0-0+0-0+0', '1-0-0-0+0-0-0', '1-0-0-0+0-0*0', '1-0-0-0+0*0+0', '1-0-0-0+0*0-0', '1-0-0-0+0*0*0', '1-0-0-0-0+0+0', '1-0-0-0-0+0-0', '1-0-0-0-0+0*0', '1-0-0-0-0-0+0', '1-0-0-0-0-0-0', '1-0-0-0-0-0*0', '1-0-0-0-0*0+0', '1-0-0-0-0*0-0', '1-0-0-0-0*0*0', '1-0-0-0*0+0+0', '1-0-0-0*0+0-0', '1-0-0-0*0+0*0', '1-0-0-0*0-0+0', '1-0-0-0*0-0-0', '1-0-0-0*0-0*0', '1-0-0-0*0*0+0', '1-0-0-0*0*0-0', '1-0-0-0*0*0*0', '1-0-0*0+0+0+0', '1-0-0*0+0+0-0', '1-0-0*0+0+0*0', '1-0-0*0+0-0+0', '1-0-0*0+0-0-0', '1-0-0*0+0-0*0', '1-0-0*0+0*0+0', '1-0-0*0+0*0-0', '1-0-0*0+0*0*0', '1-0-0*0-0+0+0', '1-0-0*0-0+0-0', '1-0-0*0-0+0*0', '1-0-0*0-0-0+0', '1-0-0*0-0-0-0', '1-0-0*0-0-0*0', '1-0-0*0-0*0+0', '1-0-0*0-0*0-0', '1-0-0*0-0*0*0', '1-0-0*0*0+0+0', '1-0-0*0*0+0-0', '1-0-0*0*0+0*0', '1-0-0*0*0-0+0', '1-0-0*0*0-0-0', '1-0-0*0*0-0*0', '1-0-0*0*0*0+0', '1-0-0*0*0*0-0', '1-0-0*0*0*0*0', '1-0*0+0+0+0+0', '1-0*0+0+0+0-0', '1-0*0+0+0+0*0', '1-0*0+0+0-0+0', '1-0*0+0+0-0-0', '1-0*0+0+0-0*0', '1-0*0+0+0*0+0', '1-0*0+0+0*0-0', '1-0*0+0+0*0*0', '1-0*0+0-0+0+0', '1-0*0+0-0+0-0', '1-0*0+0-0+0*0', '1-0*0+0-0-0+0', '1-0*0+0-0-0-0', '1-0*0+0-0-0*0', '1-0*0+0-0*0+0', '1-0*0+0-0*0-0', '1-0*0+0-0*0*0', '1-0*0+0*0+0+0', '1-0*0+0*0+0-0', '1-0*0+0*0+0*0', '1-0*0+0*0-0+0', '1-0*0+0*0-0-0', '1-0*0+0*0-0*0', '1-0*0+0*0*0+0', '1-0*0+0*0*0-0', '1-0*0+0*0*0*0', '1-0*0-0+0+0+0', '1-0*0-0+0+0-0', '1-0*0-0+0+0*0', '1-0*0-0+0-0+0', '1-0*0-0+0-0-0', '1-0*0-0+0-0*0', '1-0*0-0+0*0+0', '1-0*0-0+0*0-0', '1-0*0-0+0*0*0', '1-0*0-0-0+0+0', '1-0*0-0-0+0-0', '1-0*0-0-0+0*0', '1-0*0-0-0-0+0', '1-0*0-0-0-0-0', '1-0*0-0-0-0*0', '1-0*0-0-0*0+0', '1-0*0-0-0*0-0', '1-0*0-0-0*0*0', '1-0*0-0*0+0+0', '1-0*0-0*0+0-0', '1-0*0-0*0+0*0', '1-0*0-0*0-0+0', '1-0*0-0*0-0-0', '1-0*0-0*0-0*0', '1-0*0-0*0*0+0', '1-0*0-0*0*0-0', '1-0*0-0*0*0*0', '1-0*0*0+0+0+0', '1-0*0*0+0+0-0', '1-0*0*0+0+0*0', '1-0*0*0+0-0+0', '1-0*0*0+0-0-0', '1-0*0*0+0-0*0', '1-0*0*0+0*0+0', '1-0*0*0+0*0-0', '1-0*0*0+0*0*0', '1-0*0*0-0+0+0', '1-0*0*0-0+0-0', '1-0*0*0-0+0*0', '1-0*0*0-0-0+0', '1-0*0*0-0-0-0', '1-0*0*0-0-0*0', '1-0*0*0-0*0+0', '1-0*0*0-0*0-0', '1-0*0*0-0*0*0', '1-0*0*0*0+0+0', '1-0*0*0*0+0-0', '1-0*0*0*0+0*0', '1-0*0*0*0-0+0', '1-0*0*0*0-0-0', '1-0*0*0*0-0*0', '1-0*0*0*0*0+0', '1-0*0*0*0*0-0', '1-0*0*0*0*0*0']\n assert candidate(num = \"999\",target = 27) == ['9+9+9']\n assert candidate(num = \"1000\",target = 0) == ['1*0+0+0', '1*0+0-0', '1*0+0*0', '1*0-0+0', '1*0-0-0', '1*0-0*0', '1*0*0+0', '1*0*0-0', '1*0*0*0', '10*0+0', '10*0-0', '10*0*0', '100*0']\n assert candidate(num = \"12345\",target = 15) == ['1+2+3+4+5', '1-2*3+4*5', '1*2*3+4+5', '1+23-4-5']\n assert candidate(num = \"55555\",target = 100) == ['5*5*5-5*5']\n assert candidate(num = \"123456789\",target = 0) == ['1+2+3+4-5+67-8*9', '1+2+3-4*5+6+7-8+9', '1+2+3*4*5+6-78+9', '1+2-3*4+5-6-7+8+9', '1+2-3*4-5+6+7-8+9', '1+2-3*4+56-7*8+9', '1+2-3*4-56+7*8+9', '1+2-3*4-56-7+8*9', '1+2*3+4+5-6+7-8-9', '1+2*3-4-5-6+7-8+9', '1+2*3*4+5+6*7-8*9', '1+2*3*4+5-6-7-8-9', '1+2-34-56+78+9', '1-2+3+4-5*6+7+8+9', '1-2+3+4*5+67-89', '1-2+3-4*5-6+7+8+9', '1-2+3*4+5-6+7-8-9', '1-2+3*4*5+6+7-8*9', '1-2+3*4*5+6-7*8-9', '1-2+3*4*5-6*7-8-9', '1-2+3+45+6*7-89', '1-2+3-45+6*7-8+9', '1-2-3+4+5+67-8*9', '1-2-3+4-5-67+8*9', '1-2-3+4*5-6+7-8-9', '1-2-3*4-5-6+7+8+9', '1-2-3*4-56+78-9', '1-2-3+45+6-7*8+9', '1-2-3+45-6*7-8+9', '1-2*3+4+5+6+7-8-9', '1-2*3-4+5-6-7+8+9', '1-2*3-4-5+6+7-8+9', '1-2*3-4*5+6*7-8-9', '1-2*3-4+56-7*8+9', '1-2*3-4-56+7*8+9', '1-2*3-4-56-7+8*9', '1-2*3*4+5-6+7+8+9', '1-2*3*4-56+7+8*9', '1-2*3-45+67-8-9', '1-2-34+5+6+7+8+9', '1-2-34+5-6*7+8*9', '1-2-34-5*6+7*8+9', '1-2-34-5*6-7+8*9', '1*2+3+4+5-6-7+8-9', '1*2+3+4-5+6+7-8-9', '1*2+3+4*5-6*7+8+9', '1*2+3+4+56+7-8*9', '1*2+3+4+56-7*8-9', '1*2+3+4-56+7*8-9', '1*2+3-4-5-6-7+8+9', '1*2+3+45-67+8+9', '1*2-3+4-5-6+7-8+9', '1*2-3-4+5+6-7-8+9', '1*2-3-4+5-6+7+8-9', '1*2-3*4+5-67+8*9', '1*2*3+4-5+67-8*9', '1*2*3-4*5+6+7-8+9', '1*2*3*4-5*6+7+8-9', '1*2+34+5+6-7*8+9', '1*2+34+5-6*7-8+9', '1*2+34-5*6-7-8+9', '1*2-34+56-7-8-9', '1*2*34+5+6-7-8*9', '1*2*34-5+6-78+9', '1+23-4+5-6*7+8+9', '1+23-4-5*6-7+8+9', '1+23-4*5+6+7-8-9', '1+23-4*5*6+7+89', '1+23*4-5-6+7-89', '1-23+4*5-6+7-8+9', '1-23-4-56-7+89', '1-23*4*5+6*78-9', '1*23+4-5+67-89', '1*23+4*5-6*7+8-9', '1*23-4-5-6-7+8-9', '1*23+45-67+8-9', '1*23-45-67+89', '12+3+4-5-6-7+8-9', '12+3-4+5-6+7-8-9', '12+3-4*5-67+8*9', '12+3*4-5*6+7+8-9', '12+3-45+6+7+8+9', '12+3-45-6*7+8*9', '12-3+4+5+6-7-8-9', '12-3+4+56-78+9', '12-3-4-5+6-7-8+9', '12-3-4-5-6+7+8-9', '12-3*4+5+67-8*9', '12-3*4-5-67+8*9', '12*3+4-5*6+7-8-9', '12*3+4+56-7-89', '12*3-4*5-6+7-8-9', '12*3-4-56+7+8+9', '12*3*4-5-67-8*9', '12*3+45+6-78-9', '12+34-5+6-7*8+9', '12+34-5-6*7-8+9', '12+34-56-7+8+9', '12-34+5*6-7+8-9', '123-4-5-6*7-8*9']\n assert candidate(num = \"2324\",target = 20) == []\n assert candidate(num = \"9999999999\",target = 9999999999) == ['9999999999']\n assert candidate(num = \"2020\",target = 4) == ['2+0+2+0', '2+0+2-0', '2-0+2+0', '2-0+2-0']\n assert candidate(num = \"2147483647\",target = 2147483647) == ['2147483647']\n assert candidate(num = \"5050\",target = 5000) == []\n assert candidate(num = \"999999999\",target = 81) == ['9+9+9+9+9+9+9+9+9', '999-9-9-9-9*99', '999-9-9-9-99*9', '999-9-9-9*99-9', '999-9-9-99*9-9', '999-9-9*99-9-9', '999-9-99*9-9-9', '999-9*99-9-9-9', '999-99*9-9-9-9']\n assert candidate(num = \"1230\",target = 3) == ['1+2+3*0', '1+2-3*0']\n assert candidate(num = \"0123\",target = 6) == ['0+1+2+3', '0+1*2*3', '0*1+2*3']\n assert candidate(num = \"2323\",target = 8) == []\n assert candidate(num = \"54321\",target = 13) == ['5+4+3+2-1', '5*4-3*2-1']\n assert candidate(num = \"1111111111\",target = 100) == ['1+1+1*111-1-1-11', '1+1+1*111-1-11-1', '1+1+1*111-11-1-1', '1+1-1+1*111-1-11', '1+1-1+1*111-11-1', '1+1-1-1+1*111-11', '1+1-1-1-1*11+111', '1+1-1-1*1-11+111', '1+1-1-1*1+111-11', '1+1-1-1-11+1*111', '1+1-1-1-11*1+111', '1+1-1-1-11+111*1', '1+1-1-1*11-1+111', '1+1-1-1*11+111-1', '1+1-1-1+111-1*11', '1+1-1-1+111*1-11', '1+1-1-1+111-11*1', '1+1-1*1-1-11+111', '1+1-1*1-1+111-11', '1+1-1*1-11-1+111', '1+1-1*1-11+111-1', '1+1-1*1+111-1-11', '1+1-1*1+111-11-1', '1+1-1-11+1*111-1', '1+1-1-11-1+1*111', '1+1-1-11-1*1+111', '1+1-1-11-1+111*1', '1+1-1-11*1-1+111', '1+1-1-11*1+111-1', '1+1-1-11+111-1*1', '1+1-1-11+111*1-1', '1+1-1*11-1-1+111', '1+1-1*11-1+111-1', '1+1-1*11+111-1-1', '1+1-1+111-1-1*11', '1+1-1+111-1*1-11', '1+1-1+111-1-11*1', '1+1-1+111-1*11-1', '1+1-1+111*1-1-11', '1+1-1+111*1-11-1', '1+1-1+111-11-1*1', '1+1-1+111-11*1-1', '1+1*1-1-1-11+111', '1+1*1-1-1+111-11', '1+1*1-1-11-1+111', '1+1*1-1-11+111-1', '1+1*1-1+111-1-11', '1+1*1-1+111-11-1', '1+1*1*1*111-1-11', '1+1*1*1*111-11-1', '1+1*1-11-1-1+111', '1+1*1-11-1+111-1', '1+1*1-11+111-1-1', '1+1*1+111-1-1-11', '1+1*1+111-1-11-1', '1+1*1+111-11-1-1', '1+1*1*111-1-1*11', '1+1*1*111-1*1-11', '1+1*1*111-1-11*1', '1+1*1*111-1*11-1', '1+1*1*111*1-1-11', '1+1*1*111*1-11-1', '1+1*1*111-11-1*1', '1+1*1*111-11*1-1', '1+1-11+1*111-1-1', '1+1-11-1+1*111-1', '1+1-11-1-1+1*111', '1+1-11-1-1*1+111', '1+1-11-1-1+111*1', '1+1-11-1*1-1+111', '1+1-11-1*1+111-1', '1+1-11-1+111-1*1', '1+1-11-1+111*1-1', '1+1-11*1-1-1+111', '1+1-11*1-1+111-1', '1+1-11*1+111-1-1', '1+1-11+111-1-1*1', '1+1-11+111-1*1-1', '1+1-11+111*1-1-1', '1+1*11*11-11-11', '1+1+111-1-1-1*11', '1+1+111-1-1*1-11', '1+1+111-1-1-11*1', '1+1+111-1-1*11-1', '1+1+111-1*1-1-11', '1+1+111-1*1-11-1', '1+1+111-1-11-1*1', '1+1+111-1-11*1-1', '1+1+111-1*11-1-1', '1+1+111*1-1-1-11', '1+1+111*1-1-11-1', '1+1+111*1-11-1-1', '1+1+111-11-1-1*1', '1+1+111-11-1*1-1', '1+1+111-11*1-1-1', '1+1*111+1-1-1-11', '1+1*111+1-1-11-1', '1+1*111+1-11-1-1', '1+1*111-1+1-1-11', '1+1*111-1+1-11-1', '1+1*111-1-1+1-11', '1+1*111-1-1*1*11', '1+1*111-1-1-11+1', '1+1*111-1-1*11*1', '1+1*111-1*1-1*11', '1+1*111-1*1*1-11', '1+1*111-1*1-11*1', '1+1*111-1*1*11-1', '1+1*111-1-11+1-1', '1+1*111-1-11-1+1', '1+1*111-1-11*1*1', '1+1*111-1*11-1*1', '1+1*111-1*11*1-1', '1+1*111*1-1-1*11', '1+1*111*1-1*1-11', '1+1*111*1-1-11*1', '1+1*111*1-1*11-1', '1+1*111*1*1-1-11', '1+1*111*1*1-11-1', '1+1*111*1-11-1*1', '1+1*111*1-11*1-1', '1+1*111-11+1-1-1', '1+1*111-11-1+1-1', '1+1*111-11-1-1+1', '1+1*111-11-1*1*1', '1+1*111-11*1-1*1', '1+1*111-11*1*1-1', '1-1+1+1*111-1-11', '1-1+1+1*111-11-1', '1-1+1-1+1*111-11', '1-1+1-1-1*11+111', '1-1+1-1*1-11+111', '1-1+1-1*1+111-11', '1-1+1-1-11+1*111', '1-1+1-1-11*1+111', '1-1+1-1-11+111*1', '1-1+1-1*11-1+111', '1-1+1-1*11+111-1', '1-1+1-1+111-1*11', '1-1+1-1+111*1-11', '1-1+1-1+111-11*1', '1-1+1*1-1-11+111', '1-1+1*1-1+111-11', '1-1+1*1*1*111-11', '1-1+1*1-11-1+111', '1-1+1*1-11+111-1', '1-1+1*1+111-1-11', '1-1+1*1+111-11-1', '1-1+1*1*111-1*11', '1-1+1*1*111*1-11', '1-1+1*1*111-11*1', '1-1+1-11+1*111-1', '1-1+1-11-1+1*111', '1-1+1-11-1*1+111', '1-1+1-11-1+111*1', '1-1+1-11*1-1+111', '1-1+1-11*1+111-1', '1-1+1-11+111-1*1', '1-1+1-11+111*1-1', '1-1+1+111-1-1*11', '1-1+1+111-1*1-11', '1-1+1+111-1-11*1', '1-1+1+111-1*11-1', '1-1+1+111*1-1-11', '1-1+1+111*1-11-1', '1-1+1+111-11-1*1', '1-1+1+111-11*1-1', '1-1+1*111+1-1-11', '1-1+1*111+1-11-1', '1-1+1*111-1+1-11', '1-1+1*111-1*1*11', '1-1+1*111-1-11+1', '1-1+1*111-1*11*1', '1-1+1*111*1-1*11', '1-1+1*111*1*1-11', '1-1+1*111*1-11*1', '1-1+1*111-11+1-1', '1-1+1*111-11-1+1', '1-1+1*111-11*1*1', '1-1-1+1+1*111-11', '1-1-1+1-1*11+111', '1-1-1+1*1-11+111', '1-1-1+1*1+111-11', '1-1-1+1-11+1*111', '1-1-1+1-11*1+111', '1-1-1+1-11+111*1', '1-1-1+1+111-1*11', '1-1-1+1+111*1-11', '1-1-1+1+111-11*1', '1-1-1+1*111+1-11', '1-1-1+1*111-11+1', '1-1-1-1*11+1+111', '1-1-1-1*11+111+1', '1-1-1*1+1-11+111', '1-1-1*1+1+111-11', '1-1-1*1*1*11+111', '1-1-1*1-11+1+111', '1-1-1*1-11+111+1', '1-1-1*1*11+1*111', '1-1-1*1*11*1+111', '1-1-1*1*11+111*1', '1-1-1*1+111+1-11', '1-1-1*1+111-11+1', '1-1-1-11+1+1*111', '1-1-1-11+1*1+111', '1-1-1-11+1+111*1', '1-1-1-11+1*111+1', '1-1-1-11*1+1+111', '1-1-1-11*1+111+1', '1-1-1-11+111+1*1', '1-1-1-11+111*1+1', '1-1-1*11+1-1+111', '1-1-1*11+1*1*111', '1-1-1*11+1+111-1', '1-1-1*11+1*111*1', '1-1-1*11-1+1+111', '1-1-1*11-1+111+1', '1-1-1*11*1+1*111', '1-1-1*11*1*1+111', '1-1-1*11*1+111*1', '1-1-1*11+111+1-1', '1-1-1*11+111-1+1', '1-1-1*11+111*1*1', '1-1-1+111+1-1*11', '1-1-1+111+1*1-11', '1-1-1+111+1-11*1', '1-1-1+111-1*11+1', '1-1-1+111*1+1-11', '1-1-1+111*1-11+1', '1-1-1+111-11+1*1', '1-1-1+111-11*1+1', '1-1*1+1-1-11+111', '1-1*1+1-1+111-11', '1-1*1+1*1*111-11', '1-1*1+1-11-1+111', '1-1*1+1-11+111-1', '1-1*1+1+111-1-11', '1-1*1+1+111-11-1', '1-1*1+1*111-1*11', '1-1*1+1*111*1-11', '1-1*1+1*111-11*1', '1-1*1-1+1-11+111', '1-1*1-1+1+111-11', '1-1*1-1*1*11+111', '1-1*1-1-11+1+111', '1-1*1-1-11+111+1', '1-1*1-1*11+1*111', '1-1*1-1*11*1+111', '1-1*1-1*11+111*1', '1-1*1-1+111+1-11', '1-1*1-1+111-11+1', '1-1*1*1+1*111-11', '1-1*1*1-1*11+111', '1-1*1*1*1-11+111', '1-1*1*1*1+111-11', '1-1*1*1-11+1*111', '1-1*1*1-11*1+111', '1-1*1*1-11+111*1', '1-1*1*1*11-1+111', '1-1*1*1*11+111-1', '1-1*1*1+111-1*11', '1-1*1*1+111*1-11', '1-1*1*1+111-11*1', '1-1*1-11+1-1+111', '1-1*1-11+1*1*111', '1-1*1-11+1+111-1', '1-1*1-11+1*111*1', '1-1*1-11-1+1+111', '1-1*1-11-1+111+1', '1-1*1-11*1+1*111', '1-1*1-11*1*1+111', '1-1*1-11*1+111*1', '1-1*1-11+111+1-1', '1-1*1-11+111-1+1', '1-1*1-11+111*1*1', '1-1*1*11+1*111-1', '1-1*1*11-1+1*111', '1-1*1*11-1*1+111', '1-1*1*11-1+111*1', '1-1*1*11*1-1+111', '1-1*1*11*1+111-1', '1-1*1*11+111-1*1', '1-1*1*11+111*1-1', '1-1*1+111+1-1-11', '1-1*1+111+1-11-1', '1-1*1+111-1+1-11', '1-1*1+111-1*1*11', '1-1*1+111-1-11+1', '1-1*1+111-1*11*1', '1-1*1+111*1-1*11', '1-1*1+111*1*1-11', '1-1*1+111*1-11*1', '1-1*1+111-11+1-1', '1-1*1+111-11-1+1', '1-1*1+111-11*1*1', '1-1-11+1+1*111-1', '1-1-11+1-1+1*111', '1-1-11+1-1*1+111', '1-1-11+1-1+111*1', '1-1-11+1*1-1+111', '1-1-11+1*1*1*111', '1-1-11+1*1+111-1', '1-1-11+1*1*111*1', '1-1-11+1+111-1*1', '1-1-11+1+111*1-1', '1-1-11+1*111+1-1', '1-1-11+1*111-1+1', '1-1-11+1*111*1*1', '1-1-11-1+1+1*111', '1-1-11-1+1*1+111', '1-1-11-1+1+111*1', '1-1-11-1+1*111+1', '1-1-11-1*1+1+111', '1-1-11-1*1+111+1', '1-1-11-1+111+1*1', '1-1-11-1+111*1+1', '1-1-11*1+1-1+111', '1-1-11*1+1*1*111', '1-1-11*1+1+111-1', '1-1-11*1+1*111*1', '1-1-11*1-1+1+111', '1-1-11*1-1+111+1', '1-1-11*1*1+1*111', '1-1-11*1*1*1+111', '1-1-11*1*1+111*1', '1-1-11*1+111+1-1', '1-1-11*1+111-1+1', '1-1-11*1+111*1*1', '1-1-11+111+1-1*1', '1-1-11+111+1*1-1', '1-1-11+111-1+1*1', '1-1-11+111-1*1+1', '1-1-11+111*1+1-1', '1-1-11+111*1-1+1', '1-1-11+111*1*1*1', '1-1*11+1-1-1+111', '1-1*11+1-1+111-1', '1-1*11+1*1*111-1', '1-1*11+1+111-1-1', '1-1*11+1*111-1*1', '1-1*11+1*111*1-1', '1-1*11-1+1-1+111', '1-1*11-1+1*1*111', '1-1*11-1+1+111-1', '1-1*11-1+1*111*1', '1-1*11-1-1+1+111', '1-1*11-1-1+111+1', '1-1*11-1*1+1*111', '1-1*11-1*1*1+111', '1-1*11-1*1+111*1', '1-1*11-1+111+1-1', '1-1*11-1+111-1+1', '1-1*11-1+111*1*1', '1-1*11*1+1*111-1', '1-1*11*1-1+1*111', '1-1*11*1-1*1+111', '1-1*11*1-1+111*1', '1-1*11*1*1-1+111', '1-1*11*1*1+111-1', '1-1*11*1+111-1*1', '1-1*11*1+111*1-1', '1-1*11+11*11-11', '1-1*11-11+11*11', '1-1*11+111+1-1-1', '1-1*11+111-1+1-1', '1-1*11+111-1-1+1', '1-1*11+111-1*1*1', '1-1*11+111*1-1*1', '1-1*11+111*1*1-1', '1-1+111+1-1-1*11', '1-1+111+1-1*1-11', '1-1+111+1-1-11*1', '1-1+111+1-1*11-1', '1-1+111+1*1-1-11', '1-1+111+1*1-11-1', '1-1+111+1-11-1*1', '1-1+111+1-11*1-1', 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'111+1-1*1-11*1*1', '111+1-1*1*11-1*1', '111+1-1*1*11*1-1', '111+1-1-11+1-1*1', '111+1-1-11+1*1-1', '111+1-1-11-1+1*1', '111+1-1-11-1*1+1', '111+1-1-11*1+1-1', '111+1-1-11*1-1+1', '111+1-1-11*1*1*1', '111+1-1*11+1-1-1', '111+1-1*11-1+1-1', '111+1-1*11-1-1+1', '111+1-1*11-1*1*1', '111+1-1*11*1-1*1', '111+1-1*11*1*1-1', '111+1*1+1-1-1-11', '111+1*1+1-1-11-1', '111+1*1+1-11-1-1', '111+1*1-1+1-1-11', '111+1*1-1+1-11-1', '111+1*1-1-1+1-11', '111+1*1-1-1*1*11', '111+1*1-1-1-11+1', '111+1*1-1-1*11*1', '111+1*1-1*1-1*11', '111+1*1-1*1*1-11', '111+1*1-1*1-11*1', '111+1*1-1*1*11-1', '111+1*1-1-11+1-1', '111+1*1-1-11-1+1', '111+1*1-1-11*1*1', '111+1*1-1*11-1*1', '111+1*1-1*11*1-1', '111+1*1*1-1-1*11', '111+1*1*1-1*1-11', '111+1*1*1-1-11*1', '111+1*1*1-1*11-1', '111+1*1*1*1-1-11', '111+1*1*1*1-11-1', '111+1*1*1-11-1*1', '111+1*1*1-11*1-1', '111+1*1-11+1-1-1', '111+1*1-11-1+1-1', '111+1*1-11-1-1+1', '111+1*1-11-1*1*1', '111+1*1-11*1-1*1', '111+1*1-11*1*1-1', '111+1-11+1-1-1*1', '111+1-11+1-1*1-1', '111+1-11+1*1-1-1', '111+1-11-1+1-1*1', '111+1-11-1+1*1-1', '111+1-11-1-1+1*1', '111+1-11-1-1*1+1', '111+1-11-1*1+1-1', '111+1-11-1*1-1+1', '111+1-11-1*1*1*1', '111+1-11*1+1-1-1', '111+1-11*1-1+1-1', '111+1-11*1-1-1+1', '111+1-11*1-1*1*1', '111+1-11*1*1-1*1', '111+1-11*1*1*1-1', '111+1*11-11-11', '111-1+1+1-1-1*11', '111-1+1+1-1*1-11', '111-1+1+1-1-11*1', '111-1+1+1-1*11-1', '111-1+1+1*1-1-11', '111-1+1+1*1-11-1', '111-1+1+1-11-1*1', '111-1+1+1-11*1-1', '111-1+1-1+1-1*11', '111-1+1-1+1*1-11', '111-1+1-1+1-11*1', '111-1+1-1-1*11+1', '111-1+1-1*1+1-11', '111-1+1-1*1*1*11', '111-1+1-1*1-11+1', '111-1+1-1*1*11*1', '111-1+1-1-11+1*1', '111-1+1-1-11*1+1', '111-1+1-1*11+1-1', '111-1+1-1*11-1+1', '111-1+1-1*11*1*1', '111-1+1*1+1-1-11', '111-1+1*1+1-11-1', '111-1+1*1-1+1-11', '111-1+1*1-1*1*11', '111-1+1*1-1-11+1', '111-1+1*1-1*11*1', '111-1+1*1*1-1*11', '111-1+1*1*1*1-11', '111-1+1*1*1-11*1', '111-1+1*1-11+1-1', '111-1+1*1-11-1+1', '111-1+1*1-11*1*1', '111-1+1-11+1-1*1', '111-1+1-11+1*1-1', '111-1+1-11-1+1*1', '111-1+1-11-1*1+1', '111-1+1-11*1+1-1', '111-1+1-11*1-1+1', '111-1+1-11*1*1*1', '111-1-1+1+1-1*11', '111-1-1+1+1*1-11', '111-1-1+1+1-11*1', '111-1-1+1-1*11+1', '111-1-1+1*1+1-11', '111-1-1+1*1-11+1', '111-1-1+1-11+1*1', '111-1-1+1-11*1+1', '111-1-1-1*11+1+1', '111-1-1*1+1+1-11', '111-1-1*1+1-11+1', '111-1-1*1*1*11+1', '111-1-1*1-11+1+1', '111-1-1*1*11+1*1', '111-1-1*1*11*1+1', '111-1-1-11+1+1*1', '111-1-1-11+1*1+1', '111-1-1-11*1+1+1', '111-1-1*11+1+1-1', '111-1-1*11+1-1+1', '111-1-1*11+1*1*1', '111-1-1*11-1+1+1', '111-1-1*11*1+1*1', '111-1-1*11*1*1+1', '111-1*1+1+1-1-11', '111-1*1+1+1-11-1', '111-1*1+1-1+1-11', '111-1*1+1-1*1*11', '111-1*1+1-1-11+1', '111-1*1+1-1*11*1', '111-1*1+1*1-1*11', '111-1*1+1*1*1-11', '111-1*1+1*1-11*1', '111-1*1+1-11+1-1', '111-1*1+1-11-1+1', '111-1*1+1-11*1*1', '111-1*1-1+1+1-11', '111-1*1-1+1-11+1', '111-1*1-1*1*11+1', '111-1*1-1-11+1+1', '111-1*1-1*11+1*1', '111-1*1-1*11*1+1', '111-1*1*1+1-1*11', '111-1*1*1+1*1-11', '111-1*1*1+1-11*1', '111-1*1*1-1*11+1', '111-1*1*1*1+1-11', '111-1*1*1*1*1*11', '111-1*1*1*1-11+1', '111-1*1*1*1*11*1', '111-1*1*1-11+1*1', '111-1*1*1-11*1+1', '111-1*1*1*11+1-1', '111-1*1*1*11-1+1', '111-1*1*1*11*1*1', '111-1*1-11+1+1-1', '111-1*1-11+1-1+1', '111-1*1-11+1*1*1', '111-1*1-11-1+1+1', '111-1*1-11*1+1*1', '111-1*1-11*1*1+1', '111-1*1*11+1-1*1', '111-1*1*11+1*1-1', '111-1*1*11-1+1*1', '111-1*1*11-1*1+1', '111-1*1*11*1+1-1', '111-1*1*11*1-1+1', '111-1*1*11*1*1*1', '111-1-11+1+1-1*1', '111-1-11+1+1*1-1', '111-1-11+1-1+1*1', '111-1-11+1-1*1+1', '111-1-11+1*1+1-1', '111-1-11+1*1-1+1', '111-1-11+1*1*1*1', '111-1-11-1+1+1*1', '111-1-11-1+1*1+1', '111-1-11-1*1+1+1', '111-1-11*1+1+1-1', '111-1-11*1+1-1+1', '111-1-11*1+1*1*1', '111-1-11*1-1+1+1', '111-1-11*1*1+1*1', '111-1-11*1*1*1+1', '111-1*11+1+1-1-1', '111-1*11+1-1+1-1', '111-1*11+1-1-1+1', '111-1*11+1-1*1*1', '111-1*11+1*1-1*1', '111-1*11+1*1*1-1', '111-1*11-1+1+1-1', '111-1*11-1+1-1+1', '111-1*11-1+1*1*1', '111-1*11-1-1+1+1', '111-1*11-1*1+1*1', '111-1*11-1*1*1+1', '111-1*11*1+1-1*1', '111-1*11*1+1*1-1', '111-1*11*1-1+1*1', '111-1*11*1-1*1+1', '111-1*11*1*1+1-1', '111-1*11*1*1-1+1', '111-1*11*1*1*1*1', '111-1*11+11-11', '111-1*11-11+11', '111*1+1+1-1-1-11', '111*1+1+1-1-11-1', '111*1+1+1-11-1-1', '111*1+1-1+1-1-11', '111*1+1-1+1-11-1', '111*1+1-1-1+1-11', '111*1+1-1-1*1*11', '111*1+1-1-1-11+1', '111*1+1-1-1*11*1', '111*1+1-1*1-1*11', '111*1+1-1*1*1-11', '111*1+1-1*1-11*1', '111*1+1-1*1*11-1', '111*1+1-1-11+1-1', '111*1+1-1-11-1+1', '111*1+1-1-11*1*1', '111*1+1-1*11-1*1', '111*1+1-1*11*1-1', '111*1+1*1-1-1*11', '111*1+1*1-1*1-11', '111*1+1*1-1-11*1', '111*1+1*1-1*11-1', '111*1+1*1*1-1-11', '111*1+1*1*1-11-1', '111*1+1*1-11-1*1', '111*1+1*1-11*1-1', '111*1+1-11+1-1-1', '111*1+1-11-1+1-1', '111*1+1-11-1-1+1', '111*1+1-11-1*1*1', '111*1+1-11*1-1*1', '111*1+1-11*1*1-1', '111*1-1+1+1-1-11', '111*1-1+1+1-11-1', '111*1-1+1-1+1-11', '111*1-1+1-1*1*11', '111*1-1+1-1-11+1', '111*1-1+1-1*11*1', '111*1-1+1*1-1*11', '111*1-1+1*1*1-11', '111*1-1+1*1-11*1', '111*1-1+1-11+1-1', '111*1-1+1-11-1+1', '111*1-1+1-11*1*1', '111*1-1-1+1+1-11', '111*1-1-1+1-11+1', '111*1-1-1*1*11+1', '111*1-1-1-11+1+1', '111*1-1-1*11+1*1', '111*1-1-1*11*1+1', '111*1-1*1+1-1*11', '111*1-1*1+1*1-11', '111*1-1*1+1-11*1', '111*1-1*1-1*11+1', '111*1-1*1*1+1-11', '111*1-1*1*1*1*11', '111*1-1*1*1-11+1', '111*1-1*1*1*11*1', '111*1-1*1-11+1*1', '111*1-1*1-11*1+1', '111*1-1*1*11+1-1', '111*1-1*1*11-1+1', '111*1-1*1*11*1*1', '111*1-1-11+1+1-1', '111*1-1-11+1-1+1', '111*1-1-11+1*1*1', '111*1-1-11-1+1+1', '111*1-1-11*1+1*1', '111*1-1-11*1*1+1', '111*1-1*11+1-1*1', '111*1-1*11+1*1-1', '111*1-1*11-1+1*1', '111*1-1*11-1*1+1', '111*1-1*11*1+1-1', '111*1-1*11*1-1+1', '111*1-1*11*1*1*1', '111*1*1+1-1-1*11', '111*1*1+1-1*1-11', '111*1*1+1-1-11*1', '111*1*1+1-1*11-1', '111*1*1+1*1-1-11', '111*1*1+1*1-11-1', '111*1*1+1-11-1*1', '111*1*1+1-11*1-1', '111*1*1-1+1-1*11', '111*1*1-1+1*1-11', '111*1*1-1+1-11*1', '111*1*1-1-1*11+1', '111*1*1-1*1+1-11', '111*1*1-1*1*1*11', '111*1*1-1*1-11+1', '111*1*1-1*1*11*1', '111*1*1-1-11+1*1', '111*1*1-1-11*1+1', '111*1*1-1*11+1-1', '111*1*1-1*11-1+1', '111*1*1-1*11*1*1', '111*1*1*1+1-1-11', '111*1*1*1+1-11-1', '111*1*1*1-1+1-11', '111*1*1*1-1*1*11', '111*1*1*1-1-11+1', '111*1*1*1-1*11*1', '111*1*1*1*1-1*11', '111*1*1*1*1*1-11', '111*1*1*1*1-11*1', '111*1*1*1-11+1-1', '111*1*1*1-11-1+1', '111*1*1*1-11*1*1', '111*1*1-11+1-1*1', '111*1*1-11+1*1-1', '111*1*1-11-1+1*1', '111*1*1-11-1*1+1', '111*1*1-11*1+1-1', '111*1*1-11*1-1+1', '111*1*1-11*1*1*1', '111*1+11-11-11', '111*1-11+1+1-1-1', '111*1-11+1-1+1-1', '111*1-11+1-1-1+1', '111*1-11+1-1*1*1', '111*1-11+1*1-1*1', '111*1-11+1*1*1-1', '111*1-11-1+1+1-1', '111*1-11-1+1-1+1', '111*1-11-1+1*1*1', '111*1-11-1-1+1+1', '111*1-11-1*1+1*1', '111*1-11-1*1*1+1', '111*1-11*1+1-1*1', '111*1-11*1+1*1-1', '111*1-11*1-1+1*1', '111*1-11*1-1*1+1', '111*1-11*1*1+1-1', '111*1-11*1*1-1+1', '111*1-11*1*1*1*1', '111*1-11+11-11', '111*1-11-11+11', '111+11-1*11-11', '111+11*1-11-11', '111+11-11-1*11', '111+11-11*1-11', '111+11-11-11*1', '111-11+1+1-1-1*1', '111-11+1+1-1*1-1', '111-11+1+1*1-1-1', '111-11+1-1+1-1*1', '111-11+1-1+1*1-1', '111-11+1-1-1+1*1', '111-11+1-1-1*1+1', '111-11+1-1*1+1-1', '111-11+1-1*1-1+1', '111-11+1-1*1*1*1', '111-11+1*1+1-1-1', '111-11+1*1-1+1-1', '111-11+1*1-1-1+1', '111-11+1*1-1*1*1', '111-11+1*1*1-1*1', '111-11+1*1*1*1-1', '111-11+1*11-11', '111-11-1+1+1-1*1', '111-11-1+1+1*1-1', '111-11-1+1-1+1*1', '111-11-1+1-1*1+1', '111-11-1+1*1+1-1', '111-11-1+1*1-1+1', '111-11-1+1*1*1*1', '111-11-1-1+1+1*1', '111-11-1-1+1*1+1', '111-11-1-1*1+1+1', '111-11-1*1+1+1-1', '111-11-1*1+1-1+1', '111-11-1*1+1*1*1', '111-11-1*1-1+1+1', '111-11-1*1*1+1*1', '111-11-1*1*1*1+1', '111-11-1*11+11', '111-11*1+1+1-1-1', '111-11*1+1-1+1-1', '111-11*1+1-1-1+1', '111-11*1+1-1*1*1', '111-11*1+1*1-1*1', '111-11*1+1*1*1-1', '111-11*1-1+1+1-1', '111-11*1-1+1-1+1', '111-11*1-1+1*1*1', '111-11*1-1-1+1+1', '111-11*1-1*1+1*1', '111-11*1-1*1*1+1', '111-11*1*1+1-1*1', '111-11*1*1+1*1-1', '111-11*1*1-1+1*1', '111-11*1*1-1*1+1', '111-11*1*1*1+1-1', '111-11*1*1*1-1+1', '111-11*1*1*1*1*1', '111-11*1+11-11', '111-11*1-11+11', '111-11+11-1*11', '111-11+11*1-11', '111-11+11-11*1', '111-11-11+1*11', '111-11-11*1+11', '111-11-11+11*1']\n assert candidate(num = \"2233\",target = 25) == []\n assert candidate(num = \"10000\",target = 10) == ['10+0+0+0', '10+0+0-0', '10+0+0*0', '10+0-0+0', '10+0-0-0', '10+0-0*0', '10+0*0+0', '10+0*0-0', '10+0*0*0', '10-0+0+0', '10-0+0-0', '10-0+0*0', '10-0-0+0', '10-0-0-0', '10-0-0*0', '10-0*0+0', '10-0*0-0', '10-0*0*0']\n assert candidate(num = \"1234567890\",target = 100) == ['1+2+3+4+5+6+7+8*9+0', '1+2+3+4+5+6+7+8*9-0', '1+2+3+4+5-6-7+8+90', '1+2+3+4-5+6+7-8+90', '1+2+3+4+56-7*8+90', '1+2+3+4-56+7*8+90', '1+2+3-4+5+6+78+9+0', '1+2+3-4+5+6+78+9-0', '1+2+3-4*5+6*7+8*9+0', '1+2+3-4*5+6*7+8*9-0', '1+2+3*4-5-6+7+89+0', '1+2+3*4-5-6+7+89-0', '1+2+3-45+67+8*9+0', '1+2+3-45+67+8*9-0', '1+2+3*45*6+7-8*90', '1+2-3-4+5-6+7+8+90', '1+2-3*4+5*6+7+8*9+0', '1+2-3*4+5*6+7+8*9-0', '1+2-3*4-5+6*7+8*9+0', '1+2-3*4-5+6*7+8*9-0', '1+2*3+4+5+6+78+9*0', '1+2*3+4+5+6+78-9*0', '1+2*3+4+5+67+8+9+0', '1+2*3+4+5+67+8+9-0', '1+2*3+4*5-6+7+8*9+0', '1+2*3+4*5-6+7+8*9-0', '1+2*3-4-5+6+7+89+0', '1+2*3-4-5+6+7+89-0', '1+2*3*4-5*6+7+8+90', '1+2*3*4*5-6-7-8+9*0', '1+2*3*4*5-6-7-8-9*0', '1+2+34-5+67-8+9+0', '1+2+34-5+67-8+9-0', '1+2+34*5+6-7-8*9+0', '1+2+34*5+6-7-8*9-0', '1+2+34+56+7+8*9*0', '1+2+34+56+7-8*9*0', '1+2+34+56+7+89*0', '1+2+34+56+7-89*0', '1+2-34+56-7-8+90', '1+2*34+5*6-7+8+9*0', '1+2*34+5*6-7+8-9*0', '1+2*34-56+78+9+0', '1+2*34-56+78+9-0', '1-2+3+4-5-6+7+8+90', '1-2+3-4+5+6-7+8+90', '1-2+3*4+5+6+78+9*0', '1-2+3*4+5+6+78-9*0', '1-2+3*4+5+67+8+9+0', '1-2+3*4+5+67+8+9-0', '1-2+3*4*5+6*7+8-9+0', '1-2+3*4*5+6*7+8-9-0', '1-2+3*4*5-6+7*8-9+0', '1-2+3*4*5-6+7*8-9-0', '1-2+3+45+6+7*8-9+0', '1-2+3+45+6+7*8-9-0', '1-2+3*45-6*7+8+9*0', '1-2+3*45-6*7+8-9*0', '1-2-3+4+5+6+7-8+90', '1-2-3+4*5+6+78+9*0', '1-2-3+4*5+6+78-9*0', '1-2-3+4*5+67+8+9+0', '1-2-3+4*5+67+8+9-0', '1-2-3-4+5*6+78+9*0', '1-2-3-4+5*6+78-9*0', '1-2-3-4*5+6*7-8+90', '1-2-3+45+6*7+8+9+0', '1-2-3+45+6*7+8+9-0', '1-2-3+45-6+7*8+9+0', '1-2-3+45-6+7*8+9-0', '1-2-3+45-6-7+8*9+0', '1-2-3+45-6-7+8*9-0', '1-2-3+45+67-8+9*0', '1-2-3+45+67-8-9*0', '1-2-3-45+67-8+90', '1-2*3+4*5+6+7+8*9+0', '1-2*3+4*5+6+7+8*9-0', '1-2*3+4*5-6-7+8+90', '1-2*3+4*5*6-7-8+9*0', '1-2*3+4*5*6-7-8-9*0', '1-2*3-4+5*6+7+8*9+0', '1-2*3-4+5*6+7+8*9-0', '1-2*3-4-5+6*7+8*9+0', '1-2*3-4-5+6*7+8*9-0', '1-2+34+5+6+7*8+9*0', '1-2+34+5+6+7*8-9*0', '1-2+34-5-6+78+9*0', '1-2+34-5-6+78-9*0', '1-2+34*5+6+7+8-90', '1-2-34+5*6+7+8+90', '1-2-34-5+6*7+8+90', '1-2-34-5-6+7*8+90', '1-2-34+56+7+8*9+0', '1-2-34+56+7+8*9-0', '1-2*34+5-6+78+90', '1-2-345+67*8-90', '1*2+3+4*5+6+78-9+0', '1*2+3+4*5+6+78-9-0', '1*2+3+4*5+67+8+9*0', '1*2+3+4*5+67+8-9*0', '1*2+3-4+5*6+78-9+0', '1*2+3-4+5*6+78-9-0', '1*2+3*4+5+6-7-8+90', '1*2+3*4+5-6+78+9+0', '1*2+3*4+5-6+78+9-0', '1*2+3*4+5*6+7*8+9*0', '1*2+3*4+5*6+7*8-9*0', '1*2+3+45+6*7+8+9*0', '1*2+3+45+6*7+8-9*0', '1*2+3+45-6+7*8+9*0', '1*2+3+45-6+7*8-9*0', '1*2+3+45+67-8-9+0', '1*2+3+45+67-8-9-0', '1*2+3-45+6*7+8+90', '1*2+3-45-6+7*8+90', '1*2-3+4-5+6+7+89+0', '1*2-3+4-5+6+7+89-0', '1*2-3+4*5+6-7-8+90', '1*2-3+4*5-6+78+9+0', '1*2-3+4*5-6+78+9-0', '1*2-3-4+5*6-7-8+90', '1*2-3+45-6*7+8+90', '1*2*3+4+5+6+7+8*9+0', '1*2*3+4+5+6+7+8*9-0', '1*2*3+4+5-6-7+8+90', '1*2*3+4-5+6+7-8+90', '1*2*3+4+56-7*8+90', '1*2*3+4-56+7*8+90', '1*2*3-4+5+6+78+9+0', '1*2*3-4+5+6+78+9-0', '1*2*3-4*5+6*7+8*9+0', '1*2*3-4*5+6*7+8*9-0', '1*2*3*4+5+6+7*8+9+0', '1*2*3*4+5+6+7*8+9-0', '1*2*3*4+5+6-7+8*9+0', '1*2*3*4+5+6-7+8*9-0', '1*2*3*4-5+6-7-8+90', '1*2*3*4-5-6+78+9+0', '1*2*3*4-5-6+78+9-0', '1*2*3-45+67+8*9+0', '1*2*3-45+67+8*9-0', '1*2+34+5+6*7+8+9+0', '1*2+34+5+6*7+8+9-0', '1*2+34+5-6+7*8+9+0', '1*2+34+5-6+7*8+9-0', '1*2+34+5-6-7+8*9+0', '1*2+34+5-6-7+8*9-0', '1*2+34+5*6-7*8+90', '1*2+34+5+67-8+9*0', '1*2+34+5+67-8-9*0', '1*2+34-5-6-7-8+90', '1*2+34*5+6-78+9*0', '1*2+34*5+6-78-9*0', '1*2+34+56+7-8+9+0', '1*2+34+56+7-8+9-0', '1*2*34+56-7-8-9+0', '1*2*34+56-7-8-9-0', '1+23+4+5+67+8*9*0', '1+23+4+5+67-8*9*0', '1+23+4+5+67+89*0', '1+23+4+5+67-89*0', '1+23+4*5-6*7+8+90', '1+23-4+5+6+78-9+0', '1+23-4+5+6+78-9-0', '1+23-4+5+67+8+9*0', '1+23-4+5+67+8-9*0', '1+23-4-5+6+7+8*9+0', '1+23-4-5+6+7+8*9-0', '1+23-4-5-6-7+8+90', '1+23-4+56+7+8+9+0', '1+23-4+56+7+8+9-0', '1+23*4+5-6+7-8+9+0', '1+23*4+5-6+7-8+9-0', '1+23*4-5+6+7+8-9+0', '1+23*4-5+6+7+8-9-0', '1+23+45-67+8+90', '1-23+4*5+6+7+89+0', '1-23+4*5+6+7+89-0', '1-23-4+5*6+7+89+0', '1-23-4+5*6+7+89-0', '1-23-4-5+6*7+89+0', '1-23-4-5+6*7+89-0', '1*23+4+5+67-8+9+0', '1*23+4+5+67-8+9-0', '1*23-4+5-6-7+89+0', '1*23-4+5-6-7+89-0', '1*23-4*5+6-7+8+90', '1*23*4-5+6+7+8*9*0', '1*23*4-5+6+7-8*9*0', '1*23*4-5+6+7+89*0', '1*23*4-5+6+7-89*0', '1+234+5+6-7*8-90', '1+234+5-6*7-8-90', '1+234-5*6-7-8-90', '1+234-56-7-8*9+0', '1+234-56-7-8*9-0', '1*234+5-67-8*9+0', '1*234+5-67-8*9-0', '1*234-56-78+9*0', '1*234-56-78-9*0', '12+3+4+5-6-7+89+0', '12+3+4+5-6-7+89-0', '12+3-4+5+6+78+9*0', '12+3-4+5+6+78-9*0', '12+3-4+5+67+8+9+0', '12+3-4+5+67+8+9-0', '12+3*4+5+6+7*8+9+0', '12+3*4+5+6+7*8+9-0', '12+3*4+5+6-7+8*9+0', '12+3*4+5+6-7+8*9-0', '12+3*4-5+6-7-8+90', '12+3*4-5-6+78+9+0', '12+3*4-5-6+78+9-0', '12+3*4*5-6-7*8+90', '12+3+45+6-7*8+90', '12+3+45-6*7-8+90', '12+3*45+6*7-89+0', '12+3*45+6*7-89-0', '12-3+4*5+6+7*8+9+0', '12-3+4*5+6+7*8+9-0', '12-3+4*5+6-7+8*9+0', '12-3+4*5+6-7+8*9-0', '12-3-4+5-6+7+89+0', '12-3-4+5-6+7+89-0', '12-3-4+5*6+7*8+9+0', '12-3-4+5*6+7*8+9-0', '12-3-4+5*6-7+8*9+0', '12-3-4+5*6-7+8*9-0', '12-3-4*5+6+7+8+90', '12-3*4+5+6+7-8+90', '12*3+4*5*6-7*8+9*0', '12*3+4*5*6-7*8-9*0', '12*3-4+5-6+78-9+0', '12*3-4+5-6+78-9-0', '12*3-4-5-6+7+8*9+0', '12*3-4-5-6+7+8*9-0', '12*3-4*5+6+78+9*0', '12*3-4*5+6+78-9*0', '12*3-4*5+67+8+9+0', '12*3-4*5+67+8+9-0', '12*3-4+56-78+90', '12*3*4-56-78+90', '12+34+5*6+7+8+9+0', '12+34+5*6+7+8+9-0', '12+34-5+6*7+8+9+0', '12+34-5+6*7+8+9-0', '12+34-5-6+7*8+9+0', '12+34-5-6+7*8+9-0', '12+34-5-6-7+8*9+0', '12+34-5-6-7+8*9-0', '12+34-5+67-8+9*0', '12+34-5+67-8-9*0', '12*34-5*6*7-8-90', '123+4-5+67-89+0', '123+4-5+67-89-0', '123+4*5-6*7+8-9+0', '123+4*5-6*7+8-9-0', '123-4-5-6-7+8-9+0', '123-4-5-6-7+8-9-0', '123-4+56+7+8-90', '123*4-56*7+8*9*0', '123*4-56*7-8*9*0', '123*4-56*7+89*0', '123*4-56*7-89*0', '123+45-67+8-9+0', '123+45-67+8-9-0', '123-45-67+89+0', '123-45-67+89-0']\n assert candidate(num = \"99999\",target = 99999) == ['99999']\n assert candidate(num = \"10000\",target = 0) == ['1*0+0+0+0', '1*0+0+0-0', '1*0+0+0*0', '1*0+0-0+0', '1*0+0-0-0', '1*0+0-0*0', '1*0+0*0+0', '1*0+0*0-0', '1*0+0*0*0', '1*0-0+0+0', '1*0-0+0-0', '1*0-0+0*0', '1*0-0-0+0', '1*0-0-0-0', '1*0-0-0*0', '1*0-0*0+0', '1*0-0*0-0', '1*0-0*0*0', '1*0*0+0+0', '1*0*0+0-0', '1*0*0+0*0', '1*0*0-0+0', '1*0*0-0-0', '1*0*0-0*0', '1*0*0*0+0', '1*0*0*0-0', '1*0*0*0*0', '10*0+0+0', '10*0+0-0', '10*0+0*0', '10*0-0+0', '10*0-0-0', '10*0-0*0', '10*0*0+0', '10*0*0-0', '10*0*0*0', '100*0+0', '100*0-0', '100*0*0', '1000*0']\n assert candidate(num = \"523\",target = 30) == ['5*2*3']\n assert candidate(num = \"24681012\",target = 24) == ['2+4+6+8+1+0+1+2', '2+4+6+8+1-0+1+2', '2+4+6+8*1*0+12', '2+4+6-8*1*0+12', '2+4+6-8+10*1*2', '2+4+6+81*0+12', '2+4+6-81*0+12', '2+4*6+8*1*0-1*2', '2+4*6+8*1*0*1-2', '2+4*6-8*1*0-1*2', '2+4*6-8*1*0*1-2', '2+4*6+81*0-1*2', '2+4*6+81*0*1-2', '2+4*6-81*0-1*2', '2+4*6-81*0*1-2', '2-4+6+8+1*0+12', '2-4+6+8-1*0+12', '2-4+6+8*1+0+12', '2-4+6+8*1-0+12', '2-4+6+8+10+1*2', '2-4+6+8+10*1+2', '2-4+6*8-10-12', '2*4+6+8+1+0-1+2', '2*4+6+8+1-0-1+2', '2*4+6+8+1*0+1*2', '2*4+6+8+1*0*1+2', '2*4+6+8-1+0+1+2', '2*4+6+8-1-0+1+2', '2*4+6+8-1*0+1*2', '2*4+6+8-1*0*1+2', '2*4+6+8*1+0+1*2', '2*4+6+8*1+0*1+2', '2*4+6+8*1-0+1*2', '2*4+6+8*1-0*1+2', '2*4+6+8-10+12', '2-46+8*10-12', '2*46-8*10+12', '24+6-8+1+0-1+2', '24+6-8+1-0-1+2', '24+6-8+1*0+1*2', '24+6-8+1*0*1+2', '24+6-8-1+0+1+2', '24+6-8-1-0+1+2', '24+6-8-1*0+1*2', '24+6-8-1*0*1+2', '24+6-8*1+0+1*2', '24+6-8*1+0*1+2', '24+6-8*1-0+1*2', '24+6-8*1-0*1+2', '24+6-8-10+12', '24+6*8*1*0*1*2', '24+6*8*1*0*12', '24+6*81*0*1*2', '24+6*81*0*12', '24-6+8+1+0-1-2', '24-6+8+1-0-1-2', '24-6+8+1*0-1*2', '24-6+8+1*0*1-2', '24-6+8-1+0+1-2', '24-6+8-1-0+1-2', '24-6+8-1*0-1*2', '24-6+8-1*0*1-2', '24-6+8*1+0-1*2', '24-6+8*1+0*1-2', '24-6+8*1-0-1*2', '24-6+8*1-0*1-2', '24-6+8+10-12', '24-6*8*1*0*1*2', '24-6*8*1*0*12', '24-6*81*0*1*2', '24-6*81*0*12', '24+68*1*0*1*2', '24+68*1*0*12', '24-68*1*0*1*2', '24-68*1*0*12', '24+681*0*1*2', '24+681*0*12', '24-681*0*1*2', '24-681*0*12']\n assert candidate(num = \"55555\",target = 3125) == ['5*5*5*5*5']\n assert candidate(num = \"12345\",target = 46) == []\n assert candidate(num = \"523\",target = 1) == []\n assert candidate(num = \"87654321\",target = 87654321) == ['87654321']\n assert candidate(num = \"1234\",target = 1) == ['1*2+3-4']\n assert candidate(num = \"101010\",target = 0) == ['1+0+1*0-1+0', '1+0+1*0-1-0', '1+0-1+0+1*0', '1+0-1+0-1*0', '1+0-1+0*1+0', '1+0-1+0*1-0', '1+0-1+0*1*0', '1+0-1+0*10', '1+0-1-0+1*0', '1+0-1-0-1*0', '1+0-1-0*1+0', '1+0-1-0*1-0', '1+0-1-0*1*0', '1+0-1-0*10', '1+0-1*0-1+0', '1+0-1*0-1-0', '1+0*1+0-1+0', '1+0*1+0-1-0', '1+0*1-0-1+0', '1+0*1-0-1-0', '1+0*1*0-1+0', '1+0*1*0-1-0', '1+0*10-1+0', '1+0*10-1-0', '1-0+1*0-1+0', '1-0+1*0-1-0', '1-0-1+0+1*0', '1-0-1+0-1*0', '1-0-1+0*1+0', '1-0-1+0*1-0', '1-0-1+0*1*0', '1-0-1+0*10', '1-0-1-0+1*0', '1-0-1-0-1*0', '1-0-1-0*1+0', '1-0-1-0*1-0', '1-0-1-0*1*0', '1-0-1-0*10', '1-0-1*0-1+0', '1-0-1*0-1-0', '1-0*1+0-1+0', '1-0*1+0-1-0', '1-0*1-0-1+0', '1-0*1-0-1-0', '1-0*1*0-1+0', '1-0*1*0-1-0', '1-0*10-1+0', '1-0*10-1-0', '1*0+1+0-1+0', '1*0+1+0-1-0', '1*0+1-0-1+0', '1*0+1-0-1-0', '1*0+1*0+1*0', '1*0+1*0-1*0', '1*0+1*0*1+0', '1*0+1*0*1-0', '1*0+1*0*1*0', '1*0+1*0*10', '1*0-1+0+1+0', '1*0-1+0+1-0', '1*0-1-0+1+0', '1*0-1-0+1-0', '1*0-1*0+1*0', '1*0-1*0-1*0', '1*0-1*0*1+0', '1*0-1*0*1-0', '1*0-1*0*1*0', '1*0-1*0*10', '1*0*1+0+1*0', '1*0*1+0-1*0', '1*0*1+0*1+0', '1*0*1+0*1-0', '1*0*1+0*1*0', '1*0*1+0*10', '1*0*1-0+1*0', '1*0*1-0-1*0', '1*0*1-0*1+0', '1*0*1-0*1-0', '1*0*1-0*1*0', '1*0*1-0*10', '1*0*1*0+1*0', '1*0*1*0-1*0', '1*0*1*0*1+0', '1*0*1*0*1-0', '1*0*1*0*1*0', '1*0*1*0*10', '1*0+10*1*0', '1*0+10-10', '1*0-10*1*0', '1*0-10+10', '1*0*10+1*0', '1*0*10-1*0', '1*0*10*1+0', '1*0*10*1-0', '1*0*10*1*0', '1*0*10*10', '1*0+101*0', '1*0-101*0', '1*0*101+0', '1*0*101-0', '1*0*101*0', '1*0*1010', '10+1*0-10', '10-1*0-10', '10*1+0-10', '10*1-0-10', '10*1*0+1*0', '10*1*0-1*0', '10*1*0*1+0', '10*1*0*1-0', '10*1*0*1*0', '10*1*0*10', '10-10+1*0', '10-10-1*0', '10-10*1+0', '10-10*1-0', '10*10*1*0', '10*101*0', '101*0+1*0', '101*0-1*0', '101*0*1+0', '101*0*1-0', '101*0*1*0', '101*0*10', '1010*1*0', '10101*0']\n assert candidate(num = \"123456\",target = 711) == []\n assert candidate(num = \"987654321\",target = 45) == ['9+8+7+6+5+4+3+2+1', '9+8+7+6+5+4+3*2*1', '9+8+7+6+5+4*3-2*1', '9+8+7+6+5*4-3-2*1', '9+8+7+6+5*4-3*2+1', '9+8+7+6-5-4+3+21', '9+8+7+6*5+4*3-21', '9+8+7+6*5-4-3-2*1', '9+8+7+6*5-4-3*2+1', '9+8+7+6*5-4*3+2+1', '9+8+7-6+5+4-3+21', '9+8+7-6+5*4+3*2+1', '9+8+7-6+5+43-21', '9+8+7*6-5+4*3-21', '9+8+7*6-5-4-3-2*1', '9+8+7*6-5-4-3*2+1', '9+8+7*6-5-4*3+2+1', '9+8+7*6-5*4+3+2+1', '9+8+7*6-5*4+3*2*1', '9+8+7+65-43-2+1', '9+8+7-65+43*2*1', '9+8-7+6+5+4*3*2*1', '9+8-7+6*5+4+3-2*1', '9+8-7-6+5+4+32*1', '9+8-7-6-5+43+2+1', '9+8*7+6-5*4-3-2-1', '9+8*7+6-5*4-3*2*1', '9+8*7-6-5+4*3-21', '9+8*7-6-5-4-3-2*1', '9+8*7-6-5-4-3*2+1', '9+8*7-6-5-4*3+2+1', '9+8*7-6-5*4+3+2+1', '9+8*7-6-5*4+3*2*1', '9+8*7-6*5+4+3+2+1', '9+8*7-6*5+4+3*2*1', '9+8*7-6*5+4*3-2*1', '9+8*7+65-43*2+1', '9+8*7-65+43+2*1', '9+8+76-54+3+2+1', '9+8+76-54+3*2*1', '9-8+7+6-5+4+32*1', '9-8+7-6-5*4+3*21', '9-8+7-6*5+4+3*21', '9-8+7*6+5+4-3*2-1', '9-8+7*6+5-4+3-2*1', '9-8+7*6+5*4+3-21', '9-8+7+65+4-32*1', '9-8+7+65-4-3-21', '9-8-7+6+5+43-2-1', '9-8-7-6+5*4*3-2-1', '9-8-7*6+54+32*1', '9-8-7+65+4+3-21', '9-8-7+65-4*3-2*1', '9-8*7+6+54+32*1', '9-8*7+65-4+32-1', '9-8+76+5-4-32-1', '9-8+76-5+4-32+1', '9-8-76+5*4*3*2*1', '9*8+7+6+5-43-2*1', '9*8+7+6-5-4-32+1', '9*8+7+6*5-43-21', '9*8+7-6+5-4*3-21', '9*8+7-6-5-4*3*2+1', '9*8+7-6*5-4+3-2-1', '9*8+7-6*5-4-3+2+1', '9*8+7*6-5-43-21', '9*8-7+6-5*4-3-2-1', '9*8-7+6-5*4-3*2*1', '9*8-7-6-5+4*3-21', '9*8-7-6-5-4-3-2*1', '9*8-7-6-5-4-3*2+1', '9*8-7-6-5-4*3+2+1', '9*8-7-6-5*4+3+2+1', '9*8-7-6-5*4+3*2*1', '9*8-7-6*5+4+3+2+1', '9*8-7-6*5+4+3*2*1', '9*8-7-6*5+4*3-2*1', '9*8-7*6+5+4+3+2+1', '9*8-7*6+5+4+3*2*1', '9*8-7*6+5+4*3-2*1', '9*8-7*6+5*4-3-2*1', '9*8-7*6+5*4-3*2+1', '9*8-7*6-5-4+3+21', '9*8-7+65-43*2+1', '9*8-7-65+43+2*1', '9*8-76+5+43+2-1', '9*8-76+54-3-2*1', '9*8-76+54-3*2+1', '9+87+6-5*4*3+2+1', '9+87-6-5-43+2+1', '9+87-65+4*3+2*1', '9+87-65-4-3+21', '9-87+6+54+3*21', '98+7-6+5+4-3*21', '98+7-6-54+3-2-1', '98+7-6-54-3+2+1', '98+7-65+4+3-2*1', '98-7+6-5*4-32*1', '98-7+6-54+3-2+1', '98-7-6+5-43-2*1', '98-7-6-5-4-32+1', '98-7*6+5*4-32+1', '98-7*6-5-4-3+2-1', '98+76*5-432-1', '98-76-5+4+3+21', '98-76-5-4+32*1', '98-76+54-32+1']\n assert candidate(num = \"000\",target = 0) == ['0+0+0', '0+0-0', '0+0*0', '0-0+0', '0-0-0', '0-0*0', '0*0+0', '0*0-0', '0*0*0']\n assert candidate(num = \"123456789\",target = 45) == ['1+2+3+4+5+6+7+8+9', '1+2+3+4+5-6*7+8*9', '1+2+3+4-5*6+7*8+9', '1+2+3+4-5*6-7+8*9', '1+2+3-4*5+6*7+8+9', '1+2+3-4*5-6+7*8+9', '1+2+3-4*5-6-7+8*9', '1+2+3*4+5+6*7-8-9', '1+2+3*4*5+6-7-8-9', '1+2+3-45+67+8+9', '1+2+3*45-6-78-9', '1+2-3+4*5+6*7-8-9', '1+2-3-4-5*6+7+8*9', '1+2-3*4+5*6+7+8+9', '1+2-3*4-5+6*7+8+9', '1+2-3*4-5-6+7*8+9', '1+2-3*4-5-6-7+8*9', '1+2-3*4*5+6+7+89', '1+2-3+45+6-7-8+9', '1+2-3+45-6+7+8-9', '1+2-3-45-6+7+89', '1+2*3+4*5-6+7+8+9', '1+2*3+4*5*6+7-89', '1+2*3-4-5-6*7+89', '1+2*3*4+5*6+7-8-9', '1+2*3*4-5+6*7-8-9', '1+2*3*4*5+6+7-89', '1+2-34+5+6+7*8+9', '1+2-34+5+6-7+8*9', '1+2-34-5-6+78+9', '1+2*34-5*6+7+8-9', '1-2+3+4-5*6+78-9', '1-2+3-4*5-6+78-9', '1-2+3*4*5-6-7+8-9', '1-2+3+45+6-7+8-9', '1-2+3-45+6-7+89', '1-2-3+4-5+67-8-9', '1-2-3*4+5+6+7*8-9', '1-2-3*4-5-6+78-9', '1-2-3+45-6-7+8+9', '1-2*3+4+5+6*7+8-9', '1-2*3+4+5-6+7*8-9', '1-2*3+4*5+6+7+8+9', '1-2*3+4*5-6*7+8*9', '1-2*3+4+56+7-8-9', '1-2*3-4+5*6+7+8+9', '1-2*3-4-5+6*7+8+9', '1-2*3-4-5-6+7*8+9', '1-2*3-4-5-6-7+8*9', '1-2*3*4+5-6+78-9', '1-2*3*4-5-6+7+8*9', '1-2*3+45-67+8*9', '1-2-34+5+6+78-9', '1-2-34-5+6+7+8*9', '1-2-34+56+7+8+9', '1-2*34+5*6-7+89', '1*2+3+4+5*6+7+8-9', '1*2+3+4-5+6*7+8-9', '1*2+3+4-5-6+7*8-9', '1*2+3*4-56+78+9', '1*2+3+45+67-8*9', '1*2+3-45+6+7+8*9', '1*2-3+4-5-6*7+89', '1*2-3-4*5+67+8-9', '1*2-3-4+56-7-8+9', '1*2-3*4+5+67-8-9', '1*2*3+4+5+6+7+8+9', '1*2*3+4+5-6*7+8*9', '1*2*3+4-5*6+7*8+9', '1*2*3+4-5*6-7+8*9', '1*2*3-4*5+6*7+8+9', '1*2*3-4*5-6+7*8+9', '1*2*3-4*5-6-7+8*9', '1*2*3*4+5+6-7+8+9', '1*2*3*4*5-6-78+9', '1*2*3-45+67+8+9', '1*2+34+5-6-7+8+9', '1*2+34-5+6+7-8+9', '1*2+34+56-7*8+9', '1*2+34-56+7*8+9', '1*2+34-56-7+8*9', '1*2-34+5*6+7*8-9', '1*2*34-5+6-7-8-9', '1*2*34+56-7-8*9', '1+23+4+5+6+7+8-9', '1+23+4-5*6+7*8-9', '1+23+4-5-67+89', '1+23-4-5+6+7+8+9', '1+23-4-5-6*7+8*9', '1+23-4*5+6*7+8-9', '1+23-4*5-6+7*8-9', '1+23*4+5-6-7*8+9', '1+23*4-5-6*7+8-9', '1+23*4-56+7-8+9', '1+23-45+67+8-9', '1-23+4-5+67-8+9', '1-23+4*5-6*7+89', '1-23-4+5+67+8-9', '1-23-4-5-6-7+89', '1-23*4+5+6*7+89', '1-23+45-67+89', '1*23+4*5-6+7-8+9', '1*23-4-56-7+89', '12+3+4-56-7+89', '12+3-4*5+67-8-9', '12+3*4+5+6-7+8+9', '12+3-45+6+78-9', '12+3*45-6-7-89', '12-3+4*5+6-7+8+9', '12-3+4+56-7-8-9', '12-3-4+5*6-7+8+9', '12-3-4-56+7+89', '12-3*4-5+67-8-9', '12-3*4*5+6+78+9', '12-3-45-6+78+9', '12*3+4+5+6-7-8+9', '12*3+4+5-6+7+8-9', '12*3-4-5-6+7+8+9', '12*3-4-56+78-9', '12*3*4-5*6-78+9', '12+34-5-6-7+8+9']\n assert candidate(num = \"999999999\",target = 999999999) == ['999999999']\n assert candidate(num = \"555555555\",target = 39916800) == []\n assert candidate(num = \"12323\",target = 25) == ['1-2+3+23', '1+23-2+3']\n assert candidate(num = \"101010101\",target = 50) == []\n assert candidate(num = \"1111\",target = 1) == ['1+1-1*1', '1+1*1-1', '1-1+1*1', '1-1*1+1', '1*1+1-1', '1*1-1+1', '1*1*1*1']\n assert candidate(num = \"999999999\",target = 899999999) == []\n assert candidate(num = \"1000000000\",target = 1000000000) == ['1000000000']\n assert candidate(num = \"2323\",target = 10) == ['2+3+2+3']\n assert candidate(num = \"100\",target = 0) == ['1*0+0', '1*0-0', '1*0*0', '10*0']\n assert candidate(num = \"222\",target = 24) == ['2+22', '22+2']\n assert candidate(num = \"1000\",target = 1) == ['1+0+0+0', '1+0+0-0', '1+0+0*0', '1+0-0+0', '1+0-0-0', '1+0-0*0', '1+0*0+0', '1+0*0-0', '1+0*0*0', '1-0+0+0', '1-0+0-0', '1-0+0*0', '1-0-0+0', '1-0-0-0', '1-0-0*0', '1-0*0+0', '1-0*0-0', '1-0*0*0']\n assert candidate(num = \"1234\",target = 10) == ['1+2+3+4', '1*2*3+4']\n assert candidate(num = \"223123\",target = 1) == ['2+2+3-1-2-3', '2+2+3-1*2*3', '2+2+3*1-2*3', '2+2-3+1+2-3', '2+2-3-1-2+3', '2+2-3*1*2+3', '2+2*3-1-2*3', '2-2+3-1+2-3', '2-2-3-1+2+3', '2-2*3+1*2+3', '2-2*3-1+2*3', '2-2*3*1+2+3', '2*2+3-1-2-3', '2*2+3-1*2*3', '2*2+3*1-2*3', '2*2-3+1+2-3', '2*2-3-1-2+3', '2*2-3*1*2+3', '2+23-1-23', '2-23-1+23', '22+3-1-23']\n assert candidate(num = \"1234123412\",target = 1234) == ['1+2+3+4-12+3*412', '1+2+3-4*1*2+3*412', '1+2+3-4+1234-1*2', '1+2+3-4+1234*1-2', '1+2+3+412*3+4-12', '1+2+3+412*3-4*1*2', '1+2+3*412+3+4-12', '1+2+3*412+3-4*1*2', '1+2+3*412-3-4+1*2', '1+2+3*412-3-4*1+2', '1+2-3-4+1*2+3*412', '1+2-3-4*1+2+3*412', '1+2-3+412*3-4+1*2', '1+2-3+412*3-4*1+2', '1+2*3-4+1234-1-2', '1+2+34*12*3+4+1+2', '1-2+3-4+1234+1*2', '1-2+3-4+1234*1+2', '1-2+3*412-3+4-1*2', '1-2+3*412-3+4*1-2', '1-2-3+4-1*2+3*412', '1-2-3+4*1-2+3*412', '1-2-3+412*3+4-1*2', '1-2-3+412*3+4*1-2', '1-2*3+4+1-2+3*412', '1-2*3+4+1234-1+2', '1-2*3+412*3+4+1-2', '1*2+3-4-1-2+3*412', '1*2+3-4+1234+1-2', '1*2+3+412*3-4-1-2', '1*2+3*412+3-4-1-2', '1*2+3*412-3-4+1+2', '1*2-3+4+1234-1-2', '1*2-3-4+1+2+3*412', '1*2-3+412*3-4+1+2', '1*2*3+4-12+3*412', '1*2*3-4*1*2+3*412', '1*2*3-4+1234-1*2', '1*2*3-4+1234*1-2', '1*2*3+412*3+4-12', '1*2*3+412*3-4*1*2', '1*2+34*12*3+4*1*2', '1*2+34*12*3-4+12', '12+3*412-3*4-1*2', '12+3*412-3*4*1-2', '12-3*4-1*2+3*412', '12-3*4*1-2+3*412', '12+34*12*3-4+1*2', '12+34*12*3-4*1+2', '1234+1+2+3-4-1*2', '1234+1+2+3-4*1-2', '1234+1+2*3-4-1-2', '1234+1-2+3-4+1*2', '1234+1-2+3-4*1+2', '1234+1-2*3+4-1+2', '1234+1*2+3-4+1-2', '1234+1*2-3+4-1-2', '1234+1*2*3-4-1*2', '1234+1*2*3-4*1-2', '1234-1+2-3+4-1*2', '1234-1+2-3+4*1-2', '1234-1+2*3-4+1-2', '1234-1-2-3+4+1*2', '1234-1-2-3+4*1+2', '1234-1-2*3+4+1+2', '1234-1*2+3-4+1+2', '1234-1*2-3+4-1+2', '1234-1*2*3+4+1*2', '1234-1*2*3+4*1+2', '1234*1+2+3-4+1-2', '1234*1+2-3+4-1-2', '1234*1+2*3-4-1*2', '1234*1+2*3-4*1-2', '1234*1-2+3-4+1+2', '1234*1-2-3+4-1+2', '1234*1-2*3+4+1*2', '1234*1-2*3+4*1+2']\n assert candidate(num = \"12345\",target = 27) == ['1+2*3+4*5', '12*3-4-5']\n assert candidate(num = \"100000000\",target = 100000000) == ['100000000']\n assert candidate(num = \"1234\",target = 24) == ['1*2*3*4', '12+3*4']\n assert candidate(num = \"987654321\",target = 100) == ['9+8+7+6*5+43+2+1', '9+8+7-6-5+43*2+1', '9+8+7*6+5+4+32*1', '9+8+7*6-5+43+2+1', '9+8+7*6*5-4*32+1', '9+8+7+65+4+3*2+1', '9+8+7+65+4*3-2+1', '9+8-7+65+4*3*2+1', '9+8*7+6+5+4*3*2*1', '9+8*7+6*5+4+3-2*1', '9+8*7-6+5+4+32*1', '9+8*7-6-5+43+2+1', '9+8+76+5+4-3+2-1', '9+8+76+5-4+3+2+1', '9+8+76+5-4+3*2*1', '9+8-76+54*3-2-1', '9-8+7+6+54+32*1', '9-8+7*6+5*4*3-2-1', '9-8+7+65-4+32-1', '9-8-7*6+54*3-21', '9-8-7+65+43-2*1', '9-8*7+6+54*3-21', '9-8*7*6-5+432*1', '9-8+76-5+4+3+21', '9-8+76-5-4+32*1', '9-8+76+54-32+1', '9*8+7+6+5+4+3+2+1', '9*8+7+6+5+4+3*2*1', '9*8+7+6+5+4*3-2*1', '9*8+7+6+5*4-3-2*1', '9*8+7+6+5*4-3*2+1', '9*8+7+6-5-4+3+21', '9*8+7+6*5+4*3-21', '9*8+7+6*5-4-3-2*1', '9*8+7+6*5-4-3*2+1', '9*8+7+6*5-4*3+2+1', '9*8+7-6+5+4-3+21', '9*8+7-6+5*4+3*2+1', '9*8+7-6+5+43-21', '9*8+7*6-5+4*3-21', '9*8+7*6-5-4-3-2*1', '9*8+7*6-5-4-3*2+1', '9*8+7*6-5-4*3+2+1', '9*8+7*6-5*4+3+2+1', '9*8+7*6-5*4+3*2*1', '9*8+7+65-43-2+1', '9*8+7-65+43*2*1', '9*8-7+6+5+4*3*2*1', '9*8-7+6*5+4+3-2*1', '9*8-7-6+5+4+32*1', '9*8-7-6-5+43+2+1', '9*8+76-54+3+2+1', '9*8+76-54+3*2*1', '9+87+6-5+4-3+2*1', '9+87+6-5-4+3*2+1', '9+87+6-5*4-3+21', '9+87-6+5+4+3-2*1', '9+87-6-5+4*3+2+1', '9+87*6-5*43*2-1', '98+7+6+5*4-32+1', '98+7+6-5-4-3+2-1', '98+7+6*5-4-32+1', '98+7-6+5-4+3-2-1', '98+7-6+5-4-3+2+1', '98+7-6-5+4+3-2+1', '98+7-6*5+4*3*2+1', '98+7*6+5-43-2*1', '98+7*6-5-4-32+1', '98-7+6+5+4-3-2-1', '98-7+6+5+4-3*2*1', '98-7+6+5-4+3-2+1', '98-7+6-5+4+3+2-1', '98-7-6+5+4+3+2+1', '98-7-6+5+4+3*2*1', '98-7-6+5+4*3-2*1', '98-7-6+5*4-3-2*1', '98-7-6+5*4-3*2+1', '98-7-6-5-4+3+21', '98-7*6+5*4+3+21', '98-76+54+3+21']\n"}, "metadata": {"canonical_parameter_names": ["num", "target"], "leetcode_dataset_entry_point": "Solution().addOperators", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var addOperators = function(num, target) {", "container": null, "callable": "addOperators", "parameters": [{"name": "num", "type": "string"}, {"name": "target", "type": "number"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 287, "task_id": "find-the-duplicate-number", "difficulty": "Medium", "problem_description": "Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.\nThere is only one repeated number in nums, return this repeated number.\nYou must solve the problem without modifying the array nums and using only constant extra space.\n \nExample 1:\n\nInput: nums = [1,3,4,2,2]\nOutput: 2\n\nExample 2:\n\nInput: nums = [3,1,3,4,2]\nOutput: 3\n\nExample 3:\n\nInput: nums = [3,3,3,3,3]\nOutput: 3\n \nConstraints:\n\n1 <= n <= 105\nnums.length == n + 1\n1 <= nums[i] <= n\nAll the integers in nums appear only once except for precisely one integer which appears two or more times.\n\n \nFollow up:\n\nHow can we prove that at least one duplicate number must exist in nums?\nCan you solve the problem in linear runtime complexity?\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 3, 3, 3, 3]) == 3\n assert candidate(nums = [1, 2, 2, 3, 4]) == 2\n assert candidate(nums = [7, 9, 7, 4, 6, 2, 3, 8, 5, 1]) == 7\n assert candidate(nums = [3, 1, 3, 4, 2]) == 3\n assert candidate(nums = [1, 2, 3, 4, 4, 4, 5]) == 4\n assert candidate(nums = [3, 3, 3, 3, 3]) == 3\n assert candidate(nums = [1, 3, 4, 2, 2]) == 2\n assert candidate(nums = [5, 1, 2, 3, 4, 5]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 6]) == 6\n assert candidate(nums = [1, 2, 3, 4, 4]) == 4\n assert candidate(nums = [1, 1, 2, 3, 4, 5]) == 1\n assert candidate(nums = [1, 1, 2, 3, 4]) == 1\n assert candidate(nums = [2, 2, 2, 2, 1]) == 2\n assert candidate(nums = [2, 2, 2, 2, 2]) == 2\n assert candidate(nums = [2, 1, 2, 3, 4, 5]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 5]) == 5\n assert candidate(nums = [1, 4, 4, 2, 3]) == 4\n assert candidate(nums = [2, 5, 9, 6, 9, 3, 8, 9, 7, 1]) == 9\n assert candidate(nums = [5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(nums = [1, 3, 2, 4, 5, 5, 6, 7, 8, 9]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 7]) == 7\n assert candidate(nums = [1, 3, 2, 5, 4, 6, 7, 8, 9, 10, 3]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10]) == 10\n assert candidate(nums = [2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 2]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5]) == 5\n assert candidate(nums = [5, 1, 4, 2, 5, 3, 5, 5, 5, 5]) == 5\n assert candidate(nums = [5, 4, 3, 2, 1, 6, 7, 8, 9, 2, 2]) == 2\n assert candidate(nums = [2, 1, 4, 3, 5, 6, 7, 8, 9, 10, 2]) == 2\n assert candidate(nums = [8, 7, 3, 6, 4, 2, 5, 7, 1, 9]) == 7\n assert candidate(nums = [1, 5, 2, 3, 5, 4, 5, 5, 5, 5, 5]) == 5\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == 1\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1]) == 1\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 2\n assert candidate(nums = [8, 9, 7, 6, 5, 4, 3, 2, 1, 8, 8]) == 8\n assert candidate(nums = [3, 2, 1, 4, 5, 6, 7, 8, 9, 10, 3]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4]) == 4\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == 2\n assert candidate(nums = [50000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 50000]) == 12\n assert candidate(nums = [1, 5, 3, 4, 2, 5]) == 5\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 8]) == 8\n assert candidate(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99991]) == 11\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9]) == 9\n assert candidate(nums = [10, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1]) == 1\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 6, 7, 8, 9, 10]) == 2\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 1]) == 1\n assert candidate(nums = [1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [8, 7, 6, 5, 4, 3, 2, 1, 1, 9, 10]) == 1\n assert candidate(nums = [100000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100000]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 6]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100]) == 11\n assert candidate(nums = [10, 8, 7, 4, 6, 2, 9, 5, 3, 10, 1]) == 10\n assert candidate(nums = [1, 3, 2, 5, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 5]) == 5\n assert candidate(nums = [5, 2, 4, 3, 1, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1]) == 1\n assert candidate(nums = [50000, 49999, 1, 2, 3, 4, 5, 6, 7, 8, 50000]) == 11\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 10]) == 1\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 5, 5]) == 5\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2]) == 2\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 7]) == 11\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 6, 7, 8, 9, 10]) == 1\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 9]) == 9\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 8, 8, 8, 8, 8]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3]) == 3\n assert candidate(nums = [1, 100000, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100000]) == 21\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 10]) == 1\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 5\n assert candidate(nums = [99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 99991]) == 11\n assert candidate(nums = [2, 3, 1, 4, 5, 6, 7, 8, 9, 10, 2]) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 1]) == 11\n assert candidate(nums = [5, 4, 3, 2, 1, 6, 5, 7, 8, 9, 10]) == 5\n assert candidate(nums = [1, 3, 5, 4, 2, 5, 6]) == 5\n assert candidate(nums = [8, 9, 7, 6, 5, 4, 3, 2, 1, 8]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 3\n assert candidate(nums = [10, 8, 9, 6, 3, 1, 2, 7, 4, 10, 5]) == 10\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 2]) == 11\n assert candidate(nums = [1, 5, 4, 2, 3, 6, 7, 8, 9, 9, 10]) == 9\n assert candidate(nums = [10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5]) == 5\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findDuplicate", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findDuplicate = function(nums) {", "container": null, "callable": "findDuplicate", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 290, "task_id": "word-pattern", "difficulty": "Easy", "problem_description": "Given a pattern and a string s, find if s follows the same pattern.\nHere follow means a full match, such that there is a bijection between a letter in pattern and a non-empty word in s. Specifically:\n\nEach letter in pattern maps to exactly one unique word in s.\nEach unique word in s maps to exactly one letter in pattern.\nNo two letters map to the same word, and no two words map to the same letter.\n\n \nExample 1:\n\nInput: pattern = \"abba\", s = \"dog cat cat dog\"\nOutput: true\nExplanation:\nThe bijection can be established as:\n\n'a' maps to \"dog\".\n'b' maps to \"cat\".\n\n\nExample 2:\n\nInput: pattern = \"abba\", s = \"dog cat cat fish\"\nOutput: false\n\nExample 3:\n\nInput: pattern = \"aaaa\", s = \"dog cat cat dog\"\nOutput: false\n\n \nConstraints:\n\n1 <= pattern.length <= 300\npattern contains only lower-case English letters.\n1 <= s.length <= 3000\ns contains only lowercase English letters and spaces ' '.\ns does not contain any leading or trailing spaces.\nAll the words in s are separated by a single space.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(pattern = \"aaaa\",s = \"dog cat cat dog\") == False\n assert candidate(pattern = \"abc\",s = \"dog dog dog\") == False\n assert candidate(pattern = \"abcd\",s = \"dog cat elephant fish\") == True\n assert candidate(pattern = \"aaaa\",s = \"dog dog dog dog\") == True\n assert candidate(pattern = \"he\",s = \"unit\") == False\n assert candidate(pattern = \"abb\",s = \"dog cat cat\") == True\n assert candidate(pattern = \"abab\",s = \"dog cat dog cat\") == True\n assert candidate(pattern = \"title\",s = \"title\") == False\n assert candidate(pattern = \"abc\",s = \"b c a\") == True\n assert candidate(pattern = \"abba\",s = \"dog dog dog dog\") == False\n assert candidate(pattern = \"aaa\",s = \"aa aa aa\") == True\n assert candidate(pattern = \"abc\",s = \"dog cat fish\") == True\n assert candidate(pattern = \"abba\",s = \"dog cat cat fish\") == False\n assert candidate(pattern = \"hello\",s = \"hello world\") == False\n assert candidate(pattern = \"abba\",s = \"dog cat cat dog\") == True\n assert candidate(pattern = \"jquery\",s = \"jquery\") == False\n assert candidate(pattern = \"a\",s = \"dog\") == True\n assert candidate(pattern = \"xyzyx\",s = \"apple banana cherry banana apple\") == True\n assert candidate(pattern = \"aabbccddeeff\",s = \"repeat a b c d e f\") == False\n assert candidate(pattern = \"aabbaa\",s = \"sun moon sun moon sun moon\") == False\n assert candidate(pattern = \"aabb\",s = \"apple banana apple banana\") == False\n assert candidate(pattern = \"abacaba\",s = \"car boat airplane car boat car airplane\") == False\n assert candidate(pattern = \"aabbccddeeff\",s = \"apple banana apple banana cherry cherry date date egg egg fig fig\") == False\n assert candidate(pattern = \"abcdefabc\",s = \"alpha beta gamma delta epsilon feta alpha beta gamma\") == True\n assert candidate(pattern = \"mnop\",s = \"red red blue blue\") == False\n assert candidate(pattern = \"qrstuv\",s = \"quick red slow tall ugly very\") == True\n assert candidate(pattern = \"aabbaa\",s = \"cat dog dog cat cat dog\") == False\n assert candidate(pattern = \"abcdab\",s = \"alpha beta gamma delta alpha beta\") == True\n assert candidate(pattern = \"pqrstuvw\",s = \"penny quill red slow tall usual very wavy\") == True\n assert candidate(pattern = \"aabbcc\",s = \"apple banana apple banana cherry cherry\") == False\n assert candidate(pattern = \"abcdef\",s = \"zebra lion tiger elephant fox dog\") == True\n assert candidate(pattern = \"abcabcabc\",s = \"cat dog bird cat dog bird cat dog bird\") == True\n assert candidate(pattern = \"aaaa\",s = \"cat cat cat cat\") == True\n assert candidate(pattern = \"abcdefgh\",s = \"alphabet in sequence\") == False\n assert candidate(pattern = \"abcdabcd\",s = \"sky cloud sun moon sky cloud sun moon\") == True\n assert candidate(pattern = \"abcabcabc\",s = \"car car car bike bike bike truck truck truck\") == False\n assert candidate(pattern = \"mnopq\",s = \"moon night ocean planet quest\") == True\n assert candidate(pattern = \"zzzz\",s = \"zebra zebra zebra zebra\") == True\n assert candidate(pattern = \"abcdabcd\",s = \"cat dog elephant fox cat dog elephant fox\") == True\n assert candidate(pattern = \"qrstuv\",s = \"zebra lion tiger bear eagle fox\") == True\n assert candidate(pattern = \"aaaaabbbbb\",s = \"cat cat cat cat cat dog dog dog dog dog\") == True\n assert candidate(pattern = \"xyxzy\",s = \"sky yacht sky yacht sky\") == False\n assert candidate(pattern = \"abcba\",s = \"tree bush grass bush tree\") == True\n assert candidate(pattern = \"qrstuvwx\",s = \"continuing the test\") == False\n assert candidate(pattern = \"abcabcabc\",s = \"hi ho ha hi ho ha hi ho ha\") == True\n assert candidate(pattern = \"abba\",s = \"ant bear bear ant\") == True\n assert candidate(pattern = \"pqrstuvw\",s = \"eight distinct words\") == False\n assert candidate(pattern = \"abab\",s = \"red blue red blue\") == True\n assert candidate(pattern = \"aabbcc\",s = \"moon moon star star sun sun\") == True\n assert candidate(pattern = \"aabbccdd\",s = \"red blue red blue red blue red blue\") == False\n assert candidate(pattern = \"abcdefg\",s = \"zebra ostrich lion tiger elephant seal fox\") == True\n assert candidate(pattern = \"abab\",s = \"apple banana apple banana\") == True\n assert candidate(pattern = \"ijklmnop\",s = \"another set of words\") == False\n assert candidate(pattern = \"aabbcc\",s = \"up down up down up down\") == False\n assert candidate(pattern = \"aabbcc\",s = \"red blue green red blue green\") == False\n assert candidate(pattern = \"mnopqrstuv\",s = \"elephant monkey lion tiger unicorn vampire werewolf goblin\") == False\n assert candidate(pattern = \"abcdefghij\",s = \"alpha beta gamma delta epsilon zeta eta theta iota kappa\") == True\n assert candidate(pattern = \"mnop\",s = \"moon night opus pug\") == True\n assert candidate(pattern = \"abcabc\",s = \"elephant elephant elephant dog dog dog\") == False\n assert candidate(pattern = \"abcb\",s = \"sun moon sun moon\") == False\n assert candidate(pattern = \"mnop\",s = \"moon night opal night\") == False\n assert candidate(pattern = \"mnopq\",s = \"five different words needed\") == False\n assert candidate(pattern = \"mnopqr\",s = \"man on top quick red\") == False\n assert candidate(pattern = \"abacaba\",s = \"car bike bus car bike car bike\") == False\n assert candidate(pattern = \"stuv\",s = \"shoe train umbrella vacuum\") == True\n assert candidate(pattern = \"qrst\",s = \"quick red small tall\") == True\n assert candidate(pattern = \"zzzz\",s = \"unique unique unique unique\") == True\n assert candidate(pattern = \"xyyx\",s = \"apple banana banana apple\") == True\n assert candidate(pattern = \"mnop\",s = \"moon night ocean planet\") == True\n assert candidate(pattern = \"aabbcc\",s = \"ant bee cat ant bee cat\") == False\n assert candidate(pattern = \"abcabcabc\",s = \"car boat plane car boat plane car boat plane\") == True\n assert candidate(pattern = \"vwxyzabc\",s = \"final set of words\") == False\n assert candidate(pattern = \"mnopqr\",s = \"moon night ocean pond quiet rain\") == True\n assert candidate(pattern = \"abab\",s = \"sun moon sun moon\") == True\n assert candidate(pattern = \"aabbaa\",s = \"hello world hello world hello world\") == False\n assert candidate(pattern = \"aaaa\",s = \"wolf wolf wolf wolf\") == True\n assert candidate(pattern = \"aabb\",s = \"red blue red blue\") == False\n assert candidate(pattern = \"abba\",s = \"hello world world hello\") == True\n assert candidate(pattern = \"abcdefg\",s = \"red blue green yellow purple orange pink\") == True\n assert candidate(pattern = \"mnopqr\",s = \"one two three four five six seven\") == False\n assert candidate(pattern = \"mnop\",s = \"mountain ocean night planet\") == True\n assert candidate(pattern = \"zzzzzzzzzz\",s = \"zero zero zero zero zero zero zero zero zero zero\") == True\n assert candidate(pattern = \"abcabc\",s = \"x y z x y z\") == True\n assert candidate(pattern = \"zzzz\",s = \"kite kite kite kite\") == True\n assert candidate(pattern = \"abac\",s = \"tree bush apple tree\") == False\n assert candidate(pattern = \"abcdabcd\",s = \"first second third fourth first second third fourth\") == True\n assert candidate(pattern = \"abcabc\",s = \"one two three one two three\") == True\n assert candidate(pattern = \"abac\",s = \"car truck airplane car\") == False\n assert candidate(pattern = \"zxyzzx\",s = \"zebra ostrich xerus zebra zebra xerus\") == False\n assert candidate(pattern = \"xyzx\",s = \"flower garden weed flower\") == True\n assert candidate(pattern = \"wwww\",s = \"word word word word\") == True\n assert candidate(pattern = \"abcd\",s = \"one two three four\") == True\n assert candidate(pattern = \"abac\",s = \"mango orange mango cherry\") == True\n assert candidate(pattern = \"xyzyxzyz\",s = \"red blue red blue red blue red blue\") == False\n assert candidate(pattern = \"xyyx\",s = \"xerox yellow yellow xerox\") == True\n assert candidate(pattern = \"abcabcabc\",s = \"sun moon earth sun moon earth sun moon earth\") == True\n assert candidate(pattern = \"xyzxyz\",s = \"moon sun moon sun moon sun\") == False\n assert candidate(pattern = \"xyzzyx\",s = \"tree bush apple apple bush tree\") == True\n assert candidate(pattern = \"zzzz\",s = \"star star star star\") == True\n assert candidate(pattern = \"abcdabcd\",s = \"one two three four one two three four\") == True\n assert candidate(pattern = \"abcdefghij\",s = \"one two three four five six seven eight nine ten\") == True\n assert candidate(pattern = \"abacaba\",s = \"sun moon sun moon earth sun moon\") == False\n assert candidate(pattern = \"abababa\",s = \"moon sun moon sun moon sun moon\") == True\n assert candidate(pattern = \"qrqrqr\",s = \"queen rabbit queen rabbit queen rabbit\") == True\n assert candidate(pattern = \"abcba\",s = \"start middle end middle start\") == True\n assert candidate(pattern = \"aabbaabb\",s = \"apple banana apple banana apple banana\") == False\n assert candidate(pattern = \"xyzx\",s = \"apple banana cherry apple\") == True\n assert candidate(pattern = \"abac\",s = \"one two three one\") == False\n assert candidate(pattern = \"abab\",s = \"up down up down down up\") == False\n assert candidate(pattern = \"ababab\",s = \"house car house car house car\") == True\n assert candidate(pattern = \"mnop\",s = \"red blue red green\") == False\n assert candidate(pattern = \"xyzz\",s = \"apple banana cherry cherry\") == True\n assert candidate(pattern = \"abca\",s = \"red blue green red\") == True\n assert candidate(pattern = \"ghijklmn\",s = \"next set of words\") == False\n assert candidate(pattern = \"aabbcc\",s = \"cat dog bird cat dog bird\") == False\n assert candidate(pattern = \"efgh\",s = \"elephant fox giraffe hippo\") == True\n assert candidate(pattern = \"aba\",s = \"car bike car\") == True\n assert candidate(pattern = \"abcdeabcde\",s = \"apple banana cat dog elephant apple banana cat dog elephant\") == True\n assert candidate(pattern = \"qrstuv\",s = \"table chair desk bed lamp shelf\") == True\n assert candidate(pattern = \"aabb\",s = \"car bike car bike\") == False\n assert candidate(pattern = \"mnop\",s = \"this is just a test\") == False\n assert candidate(pattern = \"mnopqrst\",s = \"more words for testing\") == False\n assert candidate(pattern = \"qrst\",s = \"unique words map correctly\") == True\n assert candidate(pattern = \"abcdefg\",s = \"one two three four five six seven\") == True\n assert candidate(pattern = \"aabbcc\",s = \"lion tiger lion tiger lion tiger\") == False\n assert candidate(pattern = \"abcabcabc\",s = \"hello world hello world hello world\") == False\n assert candidate(pattern = \"zzzzzz\",s = \"same same same same same same\") == True\n assert candidate(pattern = \"mnopqr\",s = \"zebra lion monkey narwhal otter penguin\") == True\n assert candidate(pattern = \"mnopq\",s = \"monster ocean night planet quest\") == True\n assert candidate(pattern = \"qrst\",s = \"quick red slow tall\") == True\n assert candidate(pattern = \"xyzxyz\",s = \"one two three one two three\") == True\n assert candidate(pattern = \"abacda\",s = \"car bike car dog car bike\") == False\n assert candidate(pattern = \"xyxzy\",s = \"red blue red blue green\") == False\n assert candidate(pattern = \"abcdefghij\",s = \"elephant monkey gorilla bear lion eagle wolf chicken dog ant\") == True\n assert candidate(pattern = \"aabbcc\",s = \"hello world hello world hello world\") == False\n assert candidate(pattern = \"aabbcc\",s = \"sun moon sun moon sun moon\") == False\n assert candidate(pattern = \"ababab\",s = \"red blue red blue red blue\") == True\n assert candidate(pattern = \"zzzz\",s = \"same same same same\") == True\n assert candidate(pattern = \"abcde\",s = \"alpha beta gamma delta epsilon\") == True\n assert candidate(pattern = \"abac\",s = \"hello world hello hello\") == False\n assert candidate(pattern = \"abcd\",s = \"alpha bravo charlie delta\") == True\n assert candidate(pattern = \"zzzz\",s = \"zoo zoo zoo zoo\") == True\n assert candidate(pattern = \"abcdefg\",s = \"pencil pen eraser notebook ruler glue scissor\") == True\n assert candidate(pattern = \"xyyx\",s = \"car truck truck car\") == True\n assert candidate(pattern = \"xyz\",s = \"sun moon stars\") == True\n assert candidate(pattern = \"abcdefg\",s = \"alpha bravo charlie delta echo foxtrot golf\") == True\n assert candidate(pattern = \"abcabcabc\",s = \"dog cat dog cat dog cat dog\") == False\n"}, "metadata": {"canonical_parameter_names": ["pattern", "s"], "leetcode_dataset_entry_point": "Solution().wordPattern", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var wordPattern = function(pattern, s) {", "container": null, "callable": "wordPattern", "parameters": [{"name": "pattern", "type": "string"}, {"name": "s", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 292, "task_id": "nim-game", "difficulty": "Easy", "problem_description": "You are playing the following Nim Game with your friend:\n\nInitially, there is a heap of stones on the table.\nYou and your friend will alternate taking turns, and you go first.\nOn each turn, the person whose turn it is will remove 1 to 3 stones from the heap.\nThe one who removes the last stone is the winner.\n\nGiven n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play optimally, otherwise return false.\n \nExample 1:\n\nInput: n = 4\nOutput: false\nExplanation: These are the possible outcomes:\n1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.\n2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.\n3. You remove 3 stones. Your friend removes the last stone. Your friend wins.\nIn all outcomes, your friend wins.\n\nExample 2:\n\nInput: n = 1\nOutput: true\n\nExample 3:\n\nInput: n = 2\nOutput: true\n\n \nConstraints:\n\n1 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == True\n assert candidate(n = 21) == True\n assert candidate(n = 2147483647) == True\n assert candidate(n = 104) == False\n assert candidate(n = 100) == False\n assert candidate(n = 10) == True\n assert candidate(n = 5) == True\n assert candidate(n = 28) == False\n assert candidate(n = 40) == False\n assert candidate(n = 4) == False\n assert candidate(n = 16) == False\n assert candidate(n = 33) == True\n assert candidate(n = 17) == True\n assert candidate(n = 37) == True\n assert candidate(n = 2) == True\n assert candidate(n = 23) == True\n assert candidate(n = 1024) == False\n assert candidate(n = 8) == False\n assert candidate(n = 27) == True\n assert candidate(n = 35) == True\n assert candidate(n = 32) == False\n assert candidate(n = 20) == False\n assert candidate(n = 19) == True\n assert candidate(n = 24) == False\n assert candidate(n = 15) == True\n assert candidate(n = 31) == True\n assert candidate(n = 1) == True\n assert candidate(n = 7) == True\n assert candidate(n = 13) == True\n assert candidate(n = 25) == True\n assert candidate(n = 2147483646) == True\n assert candidate(n = 536870912) == False\n assert candidate(n = 1000) == False\n assert candidate(n = 262143) == True\n assert candidate(n = 268435456) == False\n assert candidate(n = 300) == False\n assert candidate(n = 2147483643) == True\n assert candidate(n = 33554432) == False\n assert candidate(n = 333333333) == True\n assert candidate(n = 2048) == False\n assert candidate(n = 1048576) == False\n assert candidate(n = 999) == True\n assert candidate(n = 8191) == True\n assert candidate(n = 36) == False\n assert candidate(n = 1000000000) == False\n assert candidate(n = 11) == True\n assert candidate(n = 32768) == False\n assert candidate(n = 200) == False\n assert candidate(n = 1048575) == True\n assert candidate(n = 500) == False\n assert candidate(n = 29) == True\n assert candidate(n = 131071) == True\n assert candidate(n = 67108864) == False\n assert candidate(n = 524288) == False\n assert candidate(n = 524287) == True\n assert candidate(n = 268435455) == True\n assert candidate(n = 134217728) == False\n assert candidate(n = 1073741823) == True\n assert candidate(n = 80) == False\n assert candidate(n = 16777215) == True\n assert candidate(n = 256) == False\n assert candidate(n = 131072) == False\n assert candidate(n = 81) == True\n assert candidate(n = 9) == True\n assert candidate(n = 6) == True\n assert candidate(n = 123456789) == True\n assert candidate(n = 8388608) == False\n assert candidate(n = 63) == True\n assert candidate(n = 999999999) == True\n assert candidate(n = 130) == True\n assert candidate(n = 47) == True\n assert candidate(n = 4096) == False\n assert candidate(n = 67108863) == True\n assert candidate(n = 32767) == True\n assert candidate(n = 34) == True\n assert candidate(n = 16384) == False\n assert candidate(n = 123) == True\n assert candidate(n = 16777216) == False\n assert candidate(n = 4194303) == True\n assert candidate(n = 30) == True\n assert candidate(n = 345) == True\n assert candidate(n = 2147483644) == False\n assert candidate(n = 8192) == False\n assert candidate(n = 65536) == False\n assert candidate(n = 18) == True\n assert candidate(n = 1023) == True\n assert candidate(n = 127) == True\n assert candidate(n = 2147483641) == True\n assert candidate(n = 14) == True\n assert candidate(n = 26) == True\n assert candidate(n = 536870911) == True\n assert candidate(n = 1000000) == False\n assert candidate(n = 33554431) == True\n assert candidate(n = 1337) == True\n assert candidate(n = 2097152) == False\n assert candidate(n = 12) == False\n assert candidate(n = 50) == True\n assert candidate(n = 134217727) == True\n assert candidate(n = 99) == True\n assert candidate(n = 8388607) == True\n assert candidate(n = 2097151) == True\n assert candidate(n = 4194304) == False\n assert candidate(n = 64) == False\n assert candidate(n = 2147483645) == True\n assert candidate(n = 128) == False\n assert candidate(n = 1073741824) == False\n assert candidate(n = 22) == True\n assert candidate(n = 262144) == False\n assert candidate(n = 39) == True\n assert candidate(n = 2147483640) == False\n assert candidate(n = 2147483642) == True\n assert candidate(n = 65535) == True\n assert candidate(n = 512) == False\n assert candidate(n = 38) == True\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().canWinNim", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canWinNim = function(n) {", "container": null, "callable": "canWinNim", "parameters": [{"name": "n", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 299, "task_id": "bulls-and-cows", "difficulty": "Medium", "problem_description": "You are playing the Bulls and Cows game with your friend.\nYou write down a secret number and ask your friend to guess what the number is. When your friend makes a guess, you provide a hint with the following info:\n\nThe number of \"bulls\", which are digits in the guess that are in the correct position.\nThe number of \"cows\", which are digits in the guess that are in your secret number but are located in the wrong position. Specifically, the non-bull digits in the guess that could be rearranged such that they become bulls.\n\nGiven the secret number secret and your friend's guess guess, return the hint for your friend's guess.\nThe hint should be formatted as \"xAyB\", where x is the number of bulls and y is the number of cows. Note that both secret and guess may contain duplicate digits.\n \nExample 1:\n\nInput: secret = \"1807\", guess = \"7810\"\nOutput: \"1A3B\"\nExplanation: Bulls are connected with a '|' and cows are underlined:\n\"1807\"\n |\n\"7810\"\nExample 2:\n\nInput: secret = \"1123\", guess = \"0111\"\nOutput: \"1A1B\"\nExplanation: Bulls are connected with a '|' and cows are underlined:\n\"1123\" \"1123\"\n | or |\n\"0111\" \"0111\"\nNote that only one of the two unmatched 1s is counted as a cow since the non-bull digits can only be rearranged to allow one 1 to be a bull.\n\n \nConstraints:\n\n1 <= secret.length, guess.length <= 1000\nsecret.length == guess.length\nsecret and guess consist of digits only.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(secret = \"1010101010\",guess = \"0101010101\") == \"0A10B\"\n assert candidate(secret = \"1234567890\",guess = \"1111111111\") == \"1A0B\"\n assert candidate(secret = \"0000\",guess = \"1111\") == \"0A0B\"\n assert candidate(secret = \"111222333\",guess = \"333222111\") == \"3A6B\"\n assert candidate(secret = \"9999999999\",guess = \"1111111111\") == \"0A0B\"\n assert candidate(secret = \"1112\",guess = \"1122\") == \"3A0B\"\n assert candidate(secret = \"9305\",guess = \"7315\") == \"2A0B\"\n assert candidate(secret = \"1122\",guess = \"2211\") == \"0A4B\"\n assert candidate(secret = \"1234567890\",guess = \"0987654321\") == \"0A10B\"\n assert candidate(secret = \"1111\",guess = \"1111\") == \"4A0B\"\n assert candidate(secret = \"0000\",guess = \"0000\") == \"4A0B\"\n assert candidate(secret = \"5678901234\",guess = \"1234567890\") == \"0A10B\"\n assert candidate(secret = \"1234\",guess = \"4321\") == \"0A4B\"\n assert candidate(secret = \"111222333\",guess = \"123123123\") == \"3A6B\"\n assert candidate(secret = \"1234567890\",guess = \"9876543210\") == \"2A8B\"\n assert candidate(secret = \"1123\",guess = \"0111\") == \"1A1B\"\n assert candidate(secret = \"1807\",guess = \"7810\") == \"1A3B\"\n assert candidate(secret = \"2222\",guess = \"1111\") == \"0A0B\"\n assert candidate(secret = \"0000000000\",guess = \"0000000000\") == \"10A0B\"\n assert candidate(secret = \"1234567890\",guess = \"1234567890\") == \"10A0B\"\n assert candidate(secret = \"0000000000\",guess = \"1111111111\") == \"0A0B\"\n assert candidate(secret = \"12345678901234567890\",guess = \"09876543210987654321\") == \"0A20B\"\n assert candidate(secret = \"1112223334\",guess = \"4332221110\") == \"3A6B\"\n assert candidate(secret = \"9876543210\",guess = \"0123456789\") == \"0A10B\"\n assert candidate(secret = \"5555555555\",guess = \"5555555555\") == \"10A0B\"\n assert candidate(secret = \"1111111111\",guess = \"1212121212\") == \"5A0B\"\n assert candidate(secret = \"123123\",guess = \"321321\") == \"2A4B\"\n assert candidate(secret = \"111222\",guess = \"222111\") == \"0A6B\"\n assert candidate(secret = \"001122\",guess = \"221100\") == \"2A4B\"\n assert candidate(secret = \"111122223333444455556666777788889999\",guess = \"999988887777666655554444333322221111\") == \"4A32B\"\n assert candidate(secret = \"1234123412\",guess = \"1234123412\") == \"10A0B\"\n assert candidate(secret = \"1111111111111111\",guess = \"1111111111111111\") == \"16A0B\"\n assert candidate(secret = \"5656565656\",guess = \"6565656565\") == \"0A10B\"\n assert candidate(secret = \"11223344\",guess = \"44332211\") == \"0A8B\"\n assert candidate(secret = \"888888\",guess = \"888888\") == \"6A0B\"\n assert candidate(secret = \"0123456789\",guess = \"9876543210\") == \"0A10B\"\n assert candidate(secret = \"1111222233334444\",guess = \"4444333322221111\") == \"0A16B\"\n assert candidate(secret = \"12345678901234567890\",guess = \"12345678900000000000\") == \"11A0B\"\n assert candidate(secret = \"00000000\",guess = \"88888888\") == \"0A0B\"\n assert candidate(secret = \"12345678900000000000\",guess = \"00000000001234567890\") == \"2A18B\"\n assert candidate(secret = \"1010101010\",guess = \"1010101010\") == \"10A0B\"\n assert candidate(secret = \"11223344556677889900\",guess = \"00998877665544332211\") == \"0A20B\"\n assert candidate(secret = \"12345678901234567890\",guess = \"12345678901234567890\") == \"20A0B\"\n assert candidate(secret = \"2234567890\",guess = \"0987654322\") == \"0A10B\"\n assert candidate(secret = \"1000000001\",guess = \"0111111110\") == \"0A4B\"\n assert candidate(secret = \"9111111119\",guess = \"9111111119\") == \"10A0B\"\n assert candidate(secret = \"99887766554433221100\",guess = \"00112233445566778899\") == \"0A20B\"\n assert candidate(secret = \"1111111111\",guess = \"0000000001\") == \"1A0B\"\n assert candidate(secret = \"1000100010\",guess = \"0111011101\") == \"0A6B\"\n assert candidate(secret = \"11112222333344445555\",guess = \"55554444333322221111\") == \"4A16B\"\n assert candidate(secret = \"1223344556\",guess = \"1122334455\") == \"5A4B\"\n assert candidate(secret = \"1112223334\",guess = \"4332221119\") == \"3A6B\"\n assert candidate(secret = \"0011001100\",guess = \"1100110011\") == \"0A8B\"\n assert candidate(secret = \"9876543210\",guess = \"9876543210\") == \"10A0B\"\n assert candidate(secret = \"2222222222\",guess = \"2222222222\") == \"10A0B\"\n assert candidate(secret = \"999988887777\",guess = \"888877776666\") == \"0A8B\"\n assert candidate(secret = \"98765432109876543210\",guess = \"01234567890123456789\") == \"0A20B\"\n assert candidate(secret = \"1122334455\",guess = \"1122334455\") == \"10A0B\"\n assert candidate(secret = \"1234123412\",guess = \"2143214321\") == \"0A10B\"\n assert candidate(secret = \"12341234\",guess = \"43214321\") == \"0A8B\"\n assert candidate(secret = \"555555\",guess = \"555555\") == \"6A0B\"\n assert candidate(secret = \"1111111111\",guess = \"1111111111\") == \"10A0B\"\n assert candidate(secret = \"1111111111\",guess = \"2222222222\") == \"0A0B\"\n assert candidate(secret = \"1000000000\",guess = \"0111111111\") == \"0A2B\"\n assert candidate(secret = \"1112223334\",guess = \"1111111111\") == \"3A0B\"\n assert candidate(secret = \"0123012301\",guess = \"1032103210\") == \"0A10B\"\n assert candidate(secret = \"9999999999\",guess = \"9999999999\") == \"10A0B\"\n assert candidate(secret = \"9876543210\",guess = \"1234567890\") == \"2A8B\"\n assert candidate(secret = \"1231231231\",guess = \"3123123123\") == \"0A9B\"\n assert candidate(secret = \"5638472910\",guess = \"1092748356\") == \"0A10B\"\n assert candidate(secret = \"1112223334\",guess = \"4333222111\") == \"2A8B\"\n assert candidate(secret = \"12345678901234567890\",guess = \"98765432109876543210\") == \"4A16B\"\n assert candidate(secret = \"1020304050\",guess = \"0102030405\") == \"0A10B\"\n assert candidate(secret = \"5678901234\",guess = \"5566778899\") == \"1A4B\"\n assert candidate(secret = \"101010\",guess = \"010101\") == \"0A6B\"\n assert candidate(secret = \"1122334455\",guess = \"5544332211\") == \"2A8B\"\n assert candidate(secret = \"1234123412\",guess = \"2341234123\") == \"0A9B\"\n assert candidate(secret = \"33331111\",guess = \"11113333\") == \"0A8B\"\n assert candidate(secret = \"2222222222\",guess = \"1111111111\") == \"0A0B\"\n assert candidate(secret = \"1111111111\",guess = \"1010101010\") == \"5A0B\"\n assert candidate(secret = \"111222333444555666777888999000\",guess = \"000999888777666555444333222111\") == \"0A30B\"\n assert candidate(secret = \"99998888777766665555\",guess = \"55554444333322221111\") == \"0A4B\"\n assert candidate(secret = \"0000000000\",guess = \"9999999999\") == \"0A0B\"\n assert candidate(secret = \"1221122112\",guess = \"2112211221\") == \"0A10B\"\n assert candidate(secret = \"5678901234\",guess = \"0123456789\") == \"0A10B\"\n assert candidate(secret = \"04730865\",guess = \"58600074\") == \"1A6B\"\n assert candidate(secret = \"1223344556\",guess = \"1223344556\") == \"10A0B\"\n assert candidate(secret = \"1234567890\",guess = \"5432109876\") == \"2A8B\"\n assert candidate(secret = \"12345678901234567890\",guess = \"01234567890123456789\") == \"0A20B\"\n assert candidate(secret = \"0000111122223333\",guess = \"3333222211110000\") == \"0A16B\"\n assert candidate(secret = \"1234567890\",guess = \"0123456789\") == \"0A10B\"\n assert candidate(secret = \"000000\",guess = \"000000\") == \"6A0B\"\n assert candidate(secret = \"111122223333\",guess = \"111122223333\") == \"12A0B\"\n assert candidate(secret = \"111122223333\",guess = \"333344445555\") == \"0A4B\"\n assert candidate(secret = \"25432109876543210987654321\",guess = \"10987654321098765432125432\") == \"0A26B\"\n assert candidate(secret = \"9999999999\",guess = \"8888888888\") == \"0A0B\"\n assert candidate(secret = \"8888888888\",guess = \"8888888888\") == \"10A0B\"\n assert candidate(secret = \"2457\",guess = \"5247\") == \"1A3B\"\n assert candidate(secret = \"5608055740\",guess = \"5708055640\") == \"8A2B\"\n assert candidate(secret = \"1234555555\",guess = \"5555555551\") == \"5A2B\"\n assert candidate(secret = \"1223344556\",guess = \"6554433221\") == \"0A10B\"\n assert candidate(secret = \"00112233445566778899\",guess = \"99887766554433221100\") == \"0A20B\"\n assert candidate(secret = \"1234123412\",guess = \"2345234523\") == \"0A7B\"\n assert candidate(secret = \"122112\",guess = \"211221\") == \"0A6B\"\n assert candidate(secret = \"112233\",guess = \"332211\") == \"2A4B\"\n assert candidate(secret = \"1231231231\",guess = \"3213213213\") == \"3A6B\"\n assert candidate(secret = \"1212121212\",guess = \"2121212121\") == \"0A10B\"\n assert candidate(secret = \"1221\",guess = \"1122\") == \"2A2B\"\n assert candidate(secret = \"123456\",guess = \"654321\") == \"0A6B\"\n assert candidate(secret = \"000111222\",guess = \"222111000\") == \"3A6B\"\n assert candidate(secret = \"12213312\",guess = \"21123312\") == \"4A4B\"\n assert candidate(secret = \"8888\",guess = \"8888\") == \"4A0B\"\n assert candidate(secret = \"999999\",guess = \"123456\") == \"0A0B\"\n assert candidate(secret = \"9876543210\",guess = \"1098765432\") == \"0A10B\"\n assert candidate(secret = \"9000000000\",guess = \"9000000000\") == \"10A0B\"\n"}, "metadata": {"canonical_parameter_names": ["secret", "guess"], "leetcode_dataset_entry_point": "Solution().getHint", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getHint = function(secret, guess) {", "container": null, "callable": "getHint", "parameters": [{"name": "secret", "type": "string"}, {"name": "guess", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 300, "task_id": "longest-increasing-subsequence", "difficulty": "Medium", "problem_description": "Given an integer array nums, return the length of the longest strictly increasing subsequence.\n \nExample 1:\n\nInput: nums = [10,9,2,5,3,7,101,18]\nOutput: 4\nExplanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.\n\nExample 2:\n\nInput: nums = [0,1,0,3,2,3]\nOutput: 4\n\nExample 3:\n\nInput: nums = [7,7,7,7,7,7,7]\nOutput: 1\n\n \nConstraints:\n\n1 <= nums.length <= 2500\n-104 <= nums[i] <= 104\n\n \nFollow up: Can you come up with an algorithm that runs in O(n log(n)) time complexity?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7]) == 1\n assert candidate(nums = [1, 2, 2, 4, 5, 3]) == 4\n assert candidate(nums = [0, -1, 1]) == 2\n assert candidate(nums = [0, 1, 0, 3, 2, 3]) == 4\n assert candidate(nums = [1, 3, 5, 4, 7]) == 4\n assert candidate(nums = [1, 3, 6, 7, 9, 4, 10, 5, 6]) == 6\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18]) == 4\n assert candidate(nums = [1, 2, 2, 2, 2, 3, 4, 5]) == 5\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 2, 3]) == 3\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80]) == 6\n assert candidate(nums = [3, 4, -1, 0, 6, 2, 3]) == 4\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5]) == 5\n assert candidate(nums = [1, 3, 5, 7, 9]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [4, 10, 4, 3, 8, 9]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 50\n assert candidate(nums = [3, 1, 2, 4, 5, 7, 6, 8, 9, 10, 12, 11]) == 9\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110]) == 11\n assert candidate(nums = [-10, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 11\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80, 1, 3, 4, 7, 8, 10]) == 6\n assert candidate(nums = [2, 1, 5, 3, 6, 4, 8, 9, 7, 10, 12, 11, 13, 14]) == 9\n assert candidate(nums = [4, 10, 4, 3, 8, 9, 5, 6, 7, 8, 9, 10]) == 7\n assert candidate(nums = [100, 4, 200, 1, 3, 2, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115]) == 17\n assert candidate(nums = [2, 1, 5, 3, 7, 11, 8, 10, 13, 6, 9, 12, 15, 4, 14, 18, 16, 17, 19, 20]) == 11\n assert candidate(nums = [1, 2, 5, 3, 7, 10, 1, 12, 6, 8, 9, 11, 13]) == 8\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 102, 19, 103, 20, 104, 21, 105, 22, 106, 23, 107, 24, 108, 25, 109, 26, 110, 27]) == 13\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 100\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 19, 1, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 1, 27, 1, 28, 1, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 34, 1, 35, 1, 36, 1, 37, 1, 38, 1, 39, 1, 40, 1, 41, 1, 42, 1, 43, 1, 44, 1, 45, 1, 46, 1, 47, 1, 48, 1, 49, 1, 50]) == 50\n assert candidate(nums = [10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10001]) == 2\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == 15\n assert candidate(nums = [1, 3, 5, 4, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 15\n assert candidate(nums = [1, 3, 5, 4, 7, 9, 8, 11, 13, 15, 17, 16, 19, 21, 23, 22, 25, 27, 29, 28, 31, 33, 35, 34, 37, 39, 38, 41, 43, 45, 44, 47, 49, 48, 51, 53, 55, 54, 57, 59, 58, 61, 63, 65, 64, 67, 69, 68, 71, 73, 75, 74, 77, 79, 78]) == 40\n assert candidate(nums = [99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [1, 3, 5, 2, 4, 6, 3, 5, 7, 4, 6, 8, 5, 7, 9, 6, 8, 10, 7, 9, 11, 8, 10, 12, 9, 11, 13, 10, 12, 14]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 100\n assert candidate(nums = [1, 10, 9, 11, 5, 7, 3, 6, 4, 8, 2]) == 4\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991]) == 1\n assert candidate(nums = [1, 9, 3, 4, 5, 6, 7, 8, 2, 10]) == 8\n assert candidate(nums = [25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 50\n assert candidate(nums = [2, 2, 2, 1, 1, 1, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 4\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14]) == 14\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 5, 4, 6, 7, 8, 9, 10]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 30\n assert candidate(nums = [3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 11\n assert candidate(nums = [2, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 14\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4]) == 6\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120]) == 60\n assert candidate(nums = [100, 1, 101, 2, 102, 3, 103, 4, 104, 5, 105, 6, 106, 7, 107, 8, 108, 9, 109, 10]) == 10\n assert candidate(nums = [1, 3, 6, 7, 9, 4, 10, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 10\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 15\n assert candidate(nums = [-10000, 10000, -9999, 9999, -9998, 9998, -9997, 9997, -9996, 9996, -9995, 9995]) == 7\n assert candidate(nums = [1, 10, 11, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 2, 5, 3, 7, 101, 18]) == 53\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 11\n assert candidate(nums = [2, 2, 2, 2, 2, 3, 4, 5, 5, 6]) == 5\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200]) == 101\n assert candidate(nums = [300, 200, 100, 50, 25, 12, 6, 3, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 36\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 150, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 76\n assert candidate(nums = [23, 10, 12, 24, 25, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]) == 17\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1\n assert candidate(nums = [20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0]) == 1\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]) == 50\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [200, 199, 198, 197, 196, 195, 194, 193, 192, 191, 190, 189, 188, 187, 186, 185, 184, 183, 182, 181, 180, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1\n assert candidate(nums = [5, 8, 7, 1, 9, 12, 10, 14, 13, 17, 16, 20, 19, 23, 22, 26, 25, 29, 28, 32, 31]) == 11\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45]) == 23\n assert candidate(nums = [3, 1, 2, 5, 2, 4, 3, 6, 10, 9, 15, 8, 7]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 4, 6, 8, 100, 3, 2, 1]) == 6\n assert candidate(nums = [5, 14, 23, 37, 2, 55, 27, 44, 31, 8, 48, 15, 47, 49, 34, 10, 29, 6, 12, 3, 26, 13, 16, 46, 1, 4, 17, 24, 39, 32, 21, 43, 42, 35, 50, 7, 9, 40, 19, 28, 36, 18, 22, 30, 38, 25, 41]) == 13\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 20\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 1\n assert candidate(nums = [1, 2, 8, 6, 4, 5, 3, 7]) == 5\n assert candidate(nums = [1, 3, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12]) == 7\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990]) == 1\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 1\n assert candidate(nums = [1, 5, 3, 4, 6, 7, 8, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 18\n assert candidate(nums = [3, 1, 2, 4, 10, 6, 9, 2, 5, 3, 7, 101, 18, 8, 12, 15, 19, 20, 23, 25, 27, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100]) == 50\n assert candidate(nums = [5, 7, 7, 7, 7, 7, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 15\n assert candidate(nums = [2, 2, 2, 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981, 9980, 9979, 9978, 9977, 9976, 9975, 9974, 9973, 9972, 9971, 9970, 9969, 9968, 9967, 9966, 9965, 9964, 9963, 9962, 9961, 9960, 9959, 9958, 9957, 9956, 9955, 9954, 9953, 9952, 9951, 9950]) == 1\n assert candidate(nums = [1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1, 2500, 2, 2499, 3, 2498, 4, 2497, 5, 2496, 6, 2495, 7, 2494, 8, 2493, 9, 2492, 10, 2491]) == 11\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 15\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [23, 1, 24, 11, 13, 12, 31, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 17\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 50\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 5\n assert candidate(nums = [3, 5, 6, 2, 5, 4, 19, 5, 6, 7, 12]) == 6\n assert candidate(nums = [3, 1, 2, 5, 4, 8, 7, 10, 9, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22]) == 11\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 11\n assert candidate(nums = [1, 2, 5, 3, 6, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 18\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [3, 5, 6, 2, 5, 4, 19, 5, 6, 7, 12]) == 6\n assert candidate(nums = [1, 3, 5, 4, 7, 9, 8, 11, 10, 13, 15, 14, 17]) == 9\n assert candidate(nums = [1, 3, 5, 4, 7, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 22\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 1\n assert candidate(nums = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 0, -100, -200, -300, -400, -500, -600, -700, -800, -900, -1000, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 50\n assert candidate(nums = [1, 5, 3, 4, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == 18\n assert candidate(nums = [1, 3, 5, 4, 7, 9, 8, 11, 13, 12, 15, 17, 16, 19, 21, 20, 23, 25, 24, 27, 29, 28, 31, 33, 32, 35, 37, 36, 39, 41, 40, 43, 45, 44, 47, 49, 48, 51, 53, 52, 55, 57, 56, 59, 61, 60]) == 31\n assert candidate(nums = [1, 3, 5, 2, 8, 6, 10, 4, 12, 7, 14, 9, 16, 11, 18, 13, 20, 15, 22, 17, 24, 19, 26, 21, 28, 23, 30]) == 15\n assert candidate(nums = [1, 9, 2, 8, 3, 7, 4, 6, 5, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 16\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 22, 19, 23, 24]) == 7\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]) == 1\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 4, 6, 8, 10, 12, 14, 16, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 10\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 2\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 1\n assert candidate(nums = [5, 7, 4, 6, 2, 8, 3, 9, 1, 10]) == 5\n assert candidate(nums = [1, 3, 5, 4, 7]) == 4\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 1, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(nums = [1, 5, 3, 4, 7, 2, 6, 8, 9, 10, 11, 12, 13]) == 10\n assert candidate(nums = [1, 100, 2, 99, 3, 98, 4, 97, 5, 96, 6, 95, 7, 94, 8, 93, 9, 92, 10, 91]) == 11\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 50\n assert candidate(nums = [10, 22, 9, 33, 21, 50, 41, 60, 80, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 9\n assert candidate(nums = [5, 2, 8, 6, 3, 6, 9, 7]) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51]) == 26\n assert candidate(nums = [1, 5, 3, 4, 6, 7, 2, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 18\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 10\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == 1\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().lengthOfLIS", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var lengthOfLIS = function(nums) {", "container": null, "callable": "lengthOfLIS", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 306, "task_id": "additive-number", "difficulty": "Medium", "problem_description": "An additive number is a string whose digits can form an additive sequence.\nA valid additive sequence should contain at least three numbers. Except for the first two numbers, each subsequent number in the sequence must be the sum of the preceding two.\nGiven a string containing only digits, return true if it is an additive number or false otherwise.\nNote: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.\n \nExample 1:\n\nInput: \"112358\"\nOutput: true\nExplanation: \nThe digits can form an additive sequence: 1, 1, 2, 3, 5, 8. \n1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8\n\nExample 2:\n\nInput: \"199100199\"\nOutput: true\nExplanation: \nThe additive sequence is: 1, 99, 100, 199. \n1 + 99 = 100, 99 + 100 = 199\n\n \nConstraints:\n\n1 <= num.length <= 35\nnum consists only of digits.\n\n \nFollow up: How would you handle overflow for very large input integers?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = \"100000000000000000000000000000000000\") == False\n assert candidate(num = \"1203\") == False\n assert candidate(num = \"12358132134558914423337761098715972584467376111128914423337761098715972584467376\") == False\n assert candidate(num = \"000\") == True\n assert candidate(num = \"112358\") == True\n assert candidate(num = \"101\") == True\n assert candidate(num = \"1023\") == False\n assert candidate(num = \"111\") == False\n assert candidate(num = \"123456789101112131415\") == False\n assert candidate(num = \"199100199\") == True\n assert candidate(num = \"11112233558814332333776109871597258446737611112891442333776109871597258446737600\") == False\n assert candidate(num = \"1212243660100961962968965936565601271879009877665776613593530136146765122399774777472502727500\") == False\n assert candidate(num = \"199100199100199\") == False\n assert candidate(num = \"10110210305080130210406107080910111213141516171819202122232425262728293031323334353637383940\") == False\n assert candidate(num = \"2112358132134558914423337761098715972584467376111128914423337761098715972584467376220492347771287\") == False\n assert candidate(num = \"1112233558814327211122335588143272\") == False\n assert candidate(num = \"352118533731775752284871638259384606056366656831559420082325201446228041128569094840455200277408\") == False\n assert candidate(num = \"10102030508132134558914423337761098715972584467376\") == False\n assert candidate(num = \"300330033006601299619912909229\") == False\n assert candidate(num = \"550000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000550000000000000000000000000000000000000000000000000000000000000000000000\") == False\n assert candidate(num = \"55511223355881432909822637021898214553360131525527302283789507043051101080889100000\") == False\n assert candidate(num = \"555555555555555555555555555555555\") == False\n assert candidate(num = \"19900199\") == False\n assert candidate(num = \"30003\") == False\n assert candidate(num = \"3051853171590129631715903912962502507512501001250100200200300500801302103405508914423337761098715972584467376\") == False\n assert candidate(num = \"19910019900\") == False\n assert candidate(num = \"5745531324141546367890125508174615794760060485883631387953457734726182221445769627934652072761665542399776038945322296701\") == False\n assert candidate(num = \"899221133233445566778899876555\") == False\n assert candidate(num = \"111213142741681091772866447311811526410877018957986665552221177988707665563244118981001090199209210010912022032254497422444229947474727222024224646709115801009900991981983975965935905845745351276283462110581190099109921982983975965935905845745351276283462110581203202402604609051405190302203224464670911580100990099109921982983975965935905845745351276283462110581\") == False\n assert candidate(num = \"129911121325478121325478121325478\") == False\n assert candidate(num = \"0000000\") == True\n assert candidate(num = \"5368793321443682275858790555153493087535923479825334678016159736904802346340845063\") == False\n assert candidate(num = \"123456789101525406510517027544721991113132643570011287135791412876295855157142910811321344578\") == False\n assert candidate(num = \"199100199100199100199100199100199100199100199100199100199100199100199100199100199100199100199100199\") == False\n assert candidate(num = \"10101\") == False\n assert candidate(num = \"1991001991983973967957941893777514118293847772514624891438782221426638710909674597\") == False\n assert candidate(num = \"12122448917736695401454519004049053859146500549859595405049859595405049859595405049859595405\") == False\n assert candidate(num = \"305185365910589560661212\") == False\n assert candidate(num = \"12345678910111213141516171819202122232425\") == False\n assert candidate(num = \"123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130\") == False\n assert candidate(num = \"3005300800130021003400550089014402330377\") == False\n assert candidate(num = \"1299110111221332553886455100015001500300045007501200195031505050820132521303455558591405514559048549455448994344387823621848116309415534969431111042255597445104990005999100001099911000220003300055000880014300233003770061000983\") == False\n assert candidate(num = \"11112233558814323355881432335588\") == False\n assert candidate(num = \"5959119811172113294059805914902979115991111109805914902979115991\") == False\n assert candidate(num = \"98765432111122335588143323337761098715972584467376111128914423337761098715972584467376\") == False\n assert candidate(num = \"123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890\") == False\n assert candidate(num = \"1112233558814321345588\") == False\n assert candidate(num = \"92347625436528391098765432187654321\") == False\n assert candidate(num = \"0123581321345589144233377610987159725844673761111289144233377610987159725844673761111289144233377\") == False\n assert candidate(num = \"199100199199398597969492898581777066636056352287605388942716093879017705683542125777904752467997447441986163412654769912111098765432213455881433\") == False\n assert candidate(num = \"211758524167291746877551401998346226438183838811803565385890299919329691455\") == False\n assert candidate(num = \"11235813213455891442333776109871597258446737611112891442333776109871597258446737600123\") == False\n assert candidate(num = \"1234768011122335588143323337761098715972584467376111128914423337761098715972584467376\") == False\n assert candidate(num = \"1001002003005008001300\") == True\n assert candidate(num = \"1234567891011121314151617181920\") == False\n assert candidate(num = \"352139810401113513581639833758412122651368518021112902195751760821594112109021957517608215941121090219575176082159411210902195751760821594\") == False\n assert candidate(num = \"11122335588143\") == False\n assert candidate(num = \"211758234058327419099998\") == False\n assert candidate(num = \"10100101102103205308513\") == False\n assert candidate(num = \"5752689987964510450572356014182641347233140125408327326957105375467524896598145343\") == False\n assert candidate(num = \"1101122335588143213455881432134558828675514321345588143213455882867551432134558814321345588\") == False\n assert candidate(num = \"101102030508132134558914423337761098715972584467376\") == False\n assert candidate(num = \"1112233558814321345588143213455882867551432134558814321345588286755143213455881432134558828675514321345588143213455882867551432134558814321345588\") == False\n assert candidate(num = \"1299111112132538639841488932233898720971532865197530864209973547913264331210134756789079852484266\") == False\n assert candidate(num = \"12951122334558814323337761098715972584467376\") == False\n assert candidate(num = \"1212243660100961962968965936565601271879009877665776613593530136146765122399774777472502727500222\") == False\n assert candidate(num = \"212243651091524439844383271296199112214135589284144173337761098715972584467376\") == False\n assert candidate(num = \"111223355881433\") == False\n assert candidate(num = \"3175572624803186172814695510757016747589710586934673882534968156908264298619675998931\") == False\n assert candidate(num = \"123456789101112131415161718192021222324252627282930\") == False\n assert candidate(num = \"111223355881433233355881433233355881433233355881433\") == False\n assert candidate(num = \"10101010101010101010101010101010\") == False\n assert candidate(num = \"31940557016293489164500676297242200430930046356082642245568636631\") == False\n assert candidate(num = \"8981019082988190810089881819190810108988190829881908100898818191908101089881908298819081008988\") == False\n assert candidate(num = \"12358132134558914423337761098715972584467376111128914423337761098715972584467376111128914423337761098715972584467376111128914423337761098715972584467376111128914423337761098715972584467376111128914423337761098715972584467376111128914423337761098715972584467376111128914423337761098715972584467376\") == False\n assert candidate(num = \"10010020030050080013002100340055089\") == False\n assert candidate(num = \"1122345678910111213141516171819202122232425262728293031323334353637383940\") == False\n assert candidate(num = \"112233445566778899\") == False\n assert candidate(num = \"111122335588143\") == True\n assert candidate(num = \"19111912203153659816422578234520799598262971192393524758786050352083218672182710805015497586846097981324363146733192212428056781120567168772205832843917570355828832737185509783248648047935104544356078208075678306526165963732066388575682449695836013890215825360502011010311122335588143\") == False\n assert candidate(num = \"202040601002004081632641282565121024204840968192163843276865536131072262144524288\") == False\n assert candidate(num = \"1010203050813213455881433\") == False\n assert candidate(num = \"10000000000000000000000000000000000000000000000000000000000000000000000000000000001\") == False\n assert candidate(num = \"1010101010\") == False\n assert candidate(num = \"5555500000000000000000000000000000000000000000000000000000\") == False\n assert candidate(num = \"21175821271252318169634918448837766214888726074252\") == False\n assert candidate(num = \"3175823340583274190999988\") == False\n assert candidate(num = \"305081321345881431611015264177108919611571328211413552693182114391344738656105716826154\") == False\n assert candidate(num = \"3071185960741317127783240917118596074131712778324091711859607413171277832409171185960741317127783240917\") == False\n assert candidate(num = \"10001000200030005000800130021003400550089014402330377061098615972584467376111128914423337761098715972584467376\") == False\n assert candidate(num = \"234710172744711188299487767465434185296792587860343608720077093447431405448595334665\") == False\n assert candidate(num = \"31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679\") == False\n assert candidate(num = \"0000\") == True\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().isAdditiveNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isAdditiveNumber = function(num) {", "container": null, "callable": "isAdditiveNumber", "parameters": [{"name": "num", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 309, "task_id": "best-time-to-buy-and-sell-stock-with-cooldown", "difficulty": "Medium", "problem_description": "You are given an array prices where prices[i] is the price of a given stock on the ith day.\nFind the maximum profit you can achieve. You may complete as many transactions as you like (i.e., buy one and sell one share of the stock multiple times) with the following restrictions:\n\nAfter you sell your stock, you cannot buy stock on the next day (i.e., cooldown one day).\n\nNote: You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).\n \nExample 1:\n\nInput: prices = [1,2,3,0,2]\nOutput: 3\nExplanation: transactions = [buy, sell, cooldown, buy, sell]\n\nExample 2:\n\nInput: prices = [1]\nOutput: 0\n\n \nConstraints:\n\n1 <= prices.length <= 5000\n0 <= prices[i] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(prices = [1, 2, 4]) == 3\n assert candidate(prices = [1, 2, 3, 0, 2, 3, 1, 4, 2, 5]) == 7\n assert candidate(prices = [2, 1, 4, 5, 2, 9, 7]) == 10\n assert candidate(prices = [1]) == 0\n assert candidate(prices = [3, 2, 6, 5, 0, 3]) == 7\n assert candidate(prices = [3, 2, 1]) == 0\n assert candidate(prices = [8, 9, 7, 9, 10, 1, 2, 3, 4, 1, 5]) == 8\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 8, 3, 8, 2, 6]) == 10\n assert candidate(prices = [1, 3, 2, 8, 4, 9]) == 8\n assert candidate(prices = [6, 1, 3, 2, 4, 7]) == 6\n assert candidate(prices = [7, 1, 5, 3, 6, 4]) == 5\n assert candidate(prices = [5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [1, 2, 3, 4, 5]) == 4\n assert candidate(prices = [1, 2, 3, 0, 2]) == 3\n assert candidate(prices = [1, 3, 7, 5, 10, 3]) == 9\n assert candidate(prices = [8, 9, 2, 8, 4, 9]) == 7\n assert candidate(prices = [5, 2, 3, 4, 1, 6, 7, 8, 9, 1]) == 9\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 1, 4, 5, 4, 7, 8, 9, 3, 2, 1, 0, 12, 14, 16, 18, 20, 19, 18, 17, 16, 15, 14]) == 33\n assert candidate(prices = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 12\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 0, 0, 3, 1, 4, 0, 2, 1, 2, 0, 1, 3]) == 11\n assert candidate(prices = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 12\n assert candidate(prices = [1, 2, 3, 0, 2, 3, 4, 5, 0, 6, 7, 8, 0, 9]) == 21\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 9, 2, 5, 8]) == 12\n assert candidate(prices = [100, 50, 200, 10, 150, 80, 120, 20, 180, 100, 140, 50, 250, 200, 300, 150, 350, 300, 400, 250, 450, 400, 500, 350, 550, 500, 600, 450, 650]) == 1310\n assert candidate(prices = [1, 5, 3, 8, 12, 6, 2, 9, 15, 10, 13, 7, 16, 11]) == 33\n assert candidate(prices = [5, 1, 1, 2, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(prices = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == 8\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 19\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 19\n assert candidate(prices = [10, 1, 1, 6, 9, 10, 7, 12, 6, 7, 5, 18, 9]) == 26\n assert candidate(prices = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 27\n assert candidate(prices = [10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1]) == 45\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(prices = [1, 2, 3, 8, 7, 6, 5, 4, 3, 2, 1, 9]) == 15\n assert candidate(prices = [1, 2, 3, 0, 2, 5, 0, 6, 1, 8]) == 13\n assert candidate(prices = [10, 20, 10, 10, 10, 20, 30, 10, 40, 50, 10, 60, 70, 10, 80, 90, 10]) == 180\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 7, 8, 9, 10, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 9\n assert candidate(prices = [1, 4, 2, 7, 4, 8, 1, 10, 12, 20, 2]) == 25\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11]) == 10\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 6\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 3\n assert candidate(prices = [1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 5\n assert candidate(prices = [1, 5, 1, 3, 1, 7, 1, 9, 1, 11, 1, 13, 1, 15, 1, 17, 1, 19, 1, 21]) == 60\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 2, 8]) == 11\n assert candidate(prices = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 2\n assert candidate(prices = [10, 5, 20, 1, 15, 8, 12, 2, 18, 10, 14, 5, 25, 20, 30, 15, 35, 30, 40, 25, 45, 40, 50, 35, 55, 50, 60, 45, 65]) == 131\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2]) == 6\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == 14\n assert candidate(prices = [1, 2, 3, 0, 2, 3, 4, 5, 0, 6]) == 11\n assert candidate(prices = [6, 1, 3, 2, 4, 7]) == 6\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 8, 2, 10, 3, 5]) == 13\n assert candidate(prices = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == 15\n assert candidate(prices = [1, 2, 3, 0, 3, 2, 3, 0, 4, 2, 0, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0]) == 13\n assert candidate(prices = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == 16\n assert candidate(prices = [1, 2, 5, 0, 1, 8, 0, 3, 4, 0, 5, 2, 3, 8, 9, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 36\n assert candidate(prices = [1, 4, 2, 7, 2, 8, 3, 9, 1, 10, 1, 11, 1, 12, 1, 13]) == 34\n assert candidate(prices = [1, 5, 2, 3, 7, 1, 4, 2, 8, 3, 5]) == 14\n assert candidate(prices = [1, 2, 5, 0, 2, 1, 2, 0, 2, 1, 0, 2, 3, 4, 5, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 21\n assert candidate(prices = [100, 180, 260, 310, 40, 535, 695, 200, 400, 310, 350, 410, 300, 500, 600, 500, 400, 600, 700, 800, 900, 1000, 500, 1100, 1200, 1300]) == 2455\n assert candidate(prices = [5, 2, 5, 4, 6, 9, 1, 3, 2, 8, 1, 7, 6, 3, 8, 9, 10, 5]) == 20\n assert candidate(prices = [1, 2, 3, 4, 5, 0, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 0, 6, 7, 8, 9]) == 24\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 5, 2]) == 5\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]) == 9\n assert candidate(prices = [3, 1, 4, 8, 7, 2, 5, 10, 9, 6, 11]) == 20\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 1, 5, 3, 6, 4, 1, 5, 3, 6, 4, 1, 5, 3, 6, 4]) == 20\n assert candidate(prices = [1, 4, 2, 10, 7, 5, 15, 13, 9, 11]) == 21\n assert candidate(prices = [10, 20, 10, 5, 2, 3, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 58\n assert candidate(prices = [10, 14, 14, 14, 13, 10, 9, 8, 7, 6, 5, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 19\n assert candidate(prices = [100, 90, 80, 50, 25, 20, 10, 5, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [1, 2, 3, 0, 2, 1, 3, 4, 1, 5, 0, 6, 3]) == 11\n assert candidate(prices = [8, 6, 4, 6, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 4\n assert candidate(prices = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 4\n assert candidate(prices = [2, 3, 5, 0, 1, 8, 0, 3, 4, 0, 5, 2, 3, 8, 9, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7]) == 30\n assert candidate(prices = [1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 11\n assert candidate(prices = [1, 2, 3, 0, 2, 5, 0, 4, 6, 0, 3, 8, 0, 10]) == 20\n assert candidate(prices = [1, 4, 2, 7, 2, 4, 1, 6, 1, 5, 2, 7, 2, 4, 1, 6, 1, 5, 2, 7, 2, 4, 1, 6, 1, 5, 2, 7, 2, 4, 1]) == 36\n assert candidate(prices = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 0\n assert candidate(prices = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 12\n assert candidate(prices = [5, 2, 5, 0, 1, 8, 0, 3, 4, 0, 5, 2, 3, 8, 9, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 32\n assert candidate(prices = [7, 6, 4, 3, 1]) == 0\n assert candidate(prices = [8, 6, 4, 6, 8, 7, 3, 5, 1, 9]) == 12\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 9\n assert candidate(prices = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4]) == 11\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == 12\n assert candidate(prices = [1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5]) == 14\n assert candidate(prices = [6, 1, 3, 2, 8, 0, 4, 2, 5, 10, 1, 3]) == 15\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(prices = [3, 3, 5, 0, 0, 3, 1, 4]) == 6\n assert candidate(prices = [2, 1, 4, 5, 2, 9, 7, 10, 3, 12, 8, 15]) == 22\n assert candidate(prices = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 5\n assert candidate(prices = [7, 1, 5, 3, 6, 4, 3, 7, 8, 2, 5, 10, 4]) == 17\n assert candidate(prices = [1, 2, 3, 8, 4, 9, 0, 5, 6, 7, 8, 9, 10, 11, 12]) == 19\n assert candidate(prices = [10, 1, 2, 8, 4, 9, 5, 6, 3, 10]) == 15\n assert candidate(prices = [10, 5, 0, 2, 1, 7, 5, 3, 2, 8]) == 13\n assert candidate(prices = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 5\n assert candidate(prices = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 0\n assert candidate(prices = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 18\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 8, 1, 2, 4, 5]) == 15\n assert candidate(prices = [3, 2, 6, 5, 0, 3, 4, 7, 8, 0, 5, 2, 3, 8, 9, 1, 2, 3, 4, 5]) == 25\n assert candidate(prices = [1, 2, 3, 0, 2, 5, 6, 1, 2, 3, 4, 5, 6]) == 11\n assert candidate(prices = [10, 1, 1, 6, 9, 1, 6, 1, 4, 7]) == 14\n assert candidate(prices = [10, 1, 1, 6, 9, 10, 3, 1, 3, 9, 5, 5, 5, 4, 5, 5, 6, 6, 6, 8]) == 21\n assert candidate(prices = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(prices = [1, 2, 3, 0, 2, 1, 2, 0, 2, 1, 0, 2, 3, 4, 5, 0, 0, 1, 2, 3, 4]) == 14\n assert candidate(prices = [8, 6, 4, 3, 3, 2, 3, 5, 7, 8, 5, 3, 5, 7, 8]) == 11\n"}, "metadata": {"canonical_parameter_names": ["prices"], "leetcode_dataset_entry_point": "Solution().maxProfit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProfit = function(prices) {", "container": null, "callable": "maxProfit", "parameters": [{"name": "prices", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 310, "task_id": "minimum-height-trees", "difficulty": "Medium", "problem_description": "A tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.\nGiven a tree of n nodes labelled from 0 to n - 1, and an array of n - 1 edges where edges[i] = [ai, bi] indicates that there is an undirected edge between the two nodes ai and bi in the tree, you can choose any node of the tree as the root. When you select a node x as the root, the result tree has height h. Among all possible rooted trees, those with minimum height (i.e. min(h))  are called minimum height trees (MHTs).\nReturn a list of all MHTs' root labels. You can return the answer in any order.\nThe height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.\n \nExample 1:\n\n\nInput: n = 4, edges = [[1,0],[1,2],[1,3]]\nOutput: [1]\nExplanation: As shown, the height of the tree is 1 when the root is the node with label 1 which is the only MHT.\n\nExample 2:\n\n\nInput: n = 6, edges = [[3,0],[3,1],[3,2],[3,4],[5,4]]\nOutput: [3,4]\n\n \nConstraints:\n\n1 <= n <= 2 * 104\nedges.length == n - 1\n0 <= ai, bi < n\nai != bi\nAll the pairs (ai, bi) are distinct.\nThe given input is guaranteed to be a tree and there will be no repeated edges.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 2,edges = [[0, 1]]) == [0, 1]\n assert candidate(n = 10,edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4], [5, 6], [5, 7], [8, 5], [8, 9]]) == [4, 5]\n assert candidate(n = 6,edges = [[3, 0], [3, 1], [3, 2], [3, 4], [5, 4]]) == [3, 4]\n assert candidate(n = 5,edges = [[0, 1], [1, 2], [0, 3], [3, 4]]) == [0]\n assert candidate(n = 10,edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4], [5, 6], [5, 7], [8, 5], [9, 5]]) == [4]\n assert candidate(n = 1,edges = []) == [0]\n assert candidate(n = 7,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [3, 5], [4, 6]]) == [1, 2]\n assert candidate(n = 4,edges = [[1, 0], [1, 2], [1, 3]]) == [1]\n assert candidate(n = 9,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [3, 7], [3, 8]]) == [0]\n assert candidate(n = 12,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [4, 9], [5, 10], [5, 11]]) == [1, 2]\n assert candidate(n = 10,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [3, 7], [4, 8], [5, 9]]) == [0, 1]\n assert candidate(n = 10,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8], [8, 9]]) == [1]\n assert candidate(n = 12,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == [5, 6]\n assert candidate(n = 10,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [3, 7], [3, 8], [3, 9]]) == [0]\n assert candidate(n = 9,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8]]) == [0, 1]\n assert candidate(n = 9,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [5, 7], [5, 8]]) == [0, 2]\n assert candidate(n = 13,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9], [4, 10], [5, 11], [6, 12]]) == [0]\n assert candidate(n = 12,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11]]) == [1]\n assert candidate(n = 18,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 0]]) == []\n assert candidate(n = 15,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9], [4, 10], [5, 11], [6, 12], [7, 13], [8, 14]]) == [0]\n assert candidate(n = 18,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [4, 9], [5, 10], [5, 11], [6, 12], [6, 13], [7, 14], [7, 15], [10, 16], [10, 17]]) == [1, 2]\n assert candidate(n = 8,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [5, 7]]) == [0, 2]\n assert candidate(n = 12,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [6, 8], [6, 9], [7, 10], [7, 11]]) == [1, 3]\n assert candidate(n = 20,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [1, 6], [2, 7], [2, 8], [2, 9], [3, 10], [3, 11], [3, 12], [4, 13], [4, 14], [5, 15], [5, 16], [6, 17], [6, 18], [7, 19]]) == [0]\n assert candidate(n = 14,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 11]]) == [4, 5]\n assert candidate(n = 15,edges = [[0, 1], [1, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]) == [1, 2]\n assert candidate(n = 12,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11]]) == [1]\n assert candidate(n = 18,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [4, 9], [5, 10], [5, 11], [6, 12], [6, 13], [7, 14], [7, 15], [9, 16], [10, 17]]) == [1, 2]\n assert candidate(n = 11,edges = [[0, 1], [0, 2], [0, 3], [0, 4], [1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10]]) == [0]\n assert candidate(n = 10,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == [4, 5]\n assert candidate(n = 12,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9], [3, 10], [4, 11]]) == [0, 1]\n assert candidate(n = 14,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13]]) == [0]\n assert candidate(n = 11,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [6, 8], [6, 9], [9, 10]]) == [3]\n assert candidate(n = 8,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [3, 7]]) == [0]\n assert candidate(n = 13,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12]]) == [0]\n assert candidate(n = 15,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == [1]\n assert candidate(n = 11,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9], [4, 10]]) == [0, 1]\n assert candidate(n = 12,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11]]) == [0]\n assert candidate(n = 18,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17]]) == [8, 9]\n assert candidate(n = 8,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7]]) == [0, 1]\n assert candidate(n = 11,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10]]) == [0, 1]\n assert candidate(n = 18,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14], [7, 15], [8, 16], [9, 17]]) == [0, 1]\n assert candidate(n = 9,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == [4]\n assert candidate(n = 13,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9], [3, 10], [4, 11], [5, 12]]) == [0, 1]\n assert candidate(n = 15,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]) == [0]\n assert candidate(n = 11,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10]]) == [1, 2]\n assert candidate(n = 25,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [1, 6], [2, 7], [2, 8], [2, 9], [3, 10], [3, 11], [3, 12], [4, 13], [4, 14], [5, 15], [5, 16], [6, 17], [6, 18], [6, 19], [7, 20], [7, 21], [8, 22], [9, 23], [9, 24]]) == [0]\n assert candidate(n = 13,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 10], [11, 12]]) == []\n assert candidate(n = 16,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14], [7, 15]]) == [0, 1]\n assert candidate(n = 20,edges = [[0, 1], [0, 2], [0, 3], [0, 4], [1, 5], [1, 6], [1, 7], [1, 8], [2, 9], [2, 10], [2, 11], [2, 12], [3, 13], [3, 14], [3, 15], [3, 16], [4, 17], [4, 18], [4, 19]]) == [0]\n assert candidate(n = 15,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == [0]\n assert candidate(n = 10,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8], [5, 9]]) == [0]\n assert candidate(n = 20,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [1, 6], [2, 7], [2, 8], [3, 9], [3, 10], [3, 11], [4, 12], [4, 13], [5, 14], [5, 15], [6, 16], [6, 17], [7, 18], [8, 19]]) == [0]\n assert candidate(n = 10,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [4, 8], [4, 9]]) == [0, 1]\n assert candidate(n = 20,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19]]) == [9, 10]\n assert candidate(n = 20,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14], [7, 15], [7, 16], [8, 17], [8, 18], [9, 19]]) == [0, 1]\n assert candidate(n = 9,edges = [[0, 1], [1, 2], [2, 3], [2, 4], [4, 5], [4, 6], [6, 7], [6, 8]]) == [2, 4]\n assert candidate(n = 9,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8]]) == [0]\n assert candidate(n = 25,edges = [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14], [7, 15], [7, 16], [8, 17], [8, 18], [9, 19], [9, 20], [10, 21], [10, 22], [11, 23], [11, 24]]) == [0]\n assert candidate(n = 15,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9], [3, 10], [4, 11], [5, 12], [7, 13], [7, 14]]) == [0]\n assert candidate(n = 10,edges = [[0, 1], [0, 2], [0, 3], [1, 4], [1, 5], [2, 6], [2, 7], [3, 8], [3, 9]]) == [0]\n assert candidate(n = 11,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [5, 9], [6, 10]]) == [1]\n assert candidate(n = 15,edges = [[0, 1], [1, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12], [11, 13], [12, 14]]) == [1, 2]\n assert candidate(n = 12,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [0, 11]]) == []\n assert candidate(n = 14,edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13]]) == [6, 7]\n"}, "metadata": {"canonical_parameter_names": ["n", "edges"], "leetcode_dataset_entry_point": "Solution().findMinHeightTrees", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMinHeightTrees = function(n, edges) {", "container": null, "callable": "findMinHeightTrees", "parameters": [{"name": "n", "type": "number"}, {"name": "edges", "type": "number[][]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 312, "task_id": "burst-balloons", "difficulty": "Hard", "problem_description": "You are given n balloons, indexed from 0 to n - 1. Each balloon is painted with a number on it represented by an array nums. You are asked to burst all the balloons.\nIf you burst the ith balloon, you will get nums[i - 1] * nums[i] * nums[i + 1] coins. If i - 1 or i + 1 goes out of bounds of the array, then treat it as if there is a balloon with a 1 painted on it.\nReturn the maximum coins you can collect by bursting the balloons wisely.\n \nExample 1:\n\nInput: nums = [3,1,5,8]\nOutput: 167\nExplanation:\nnums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> []\ncoins = 3*1*5 + 3*5*8 + 1*3*8 + 1*8*1 = 167\nExample 2:\n\nInput: nums = [1,5]\nOutput: 10\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 300\n0 <= nums[i] <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 4, 3, 2, 1]) == 110\n assert candidate(nums = [1, 5]) == 10\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [7, 9, 8, 0, 7, 1, 3, 5, 5, 2, 3]) == 1654\n assert candidate(nums = [7, 9, 8, 0, 7, 1, 3, 5, 5, 7, 4, 5, 5, 5, 4]) == 2886\n assert candidate(nums = [3, 1, 5, 8]) == 167\n assert candidate(nums = [0, 0, 0]) == 0\n assert candidate(nums = [9, 76, 66, 18, 49, 79, 11, 31, 2, 83, 45, 12, 50, 88, 67, 34, 73, 39, 100, 87, 30, 6, 41, 72, 84, 17, 29, 63, 52, 75, 58, 92, 37, 35, 61, 43, 89, 64, 55, 19, 32, 62, 57, 90, 91, 33, 44, 27, 3, 76, 65, 68, 42, 8, 54, 60, 10, 80, 70, 12, 3, 5, 82, 46, 30, 81, 13, 26, 93, 14, 20, 78, 86, 25, 56, 1, 36, 59, 74, 15, 95, 16, 4, 7, 22, 69, 51, 38, 85, 23, 40, 94, 48, 6, 97, 24, 53, 9, 96, 21, 47, 77, 99, 31, 28, 45, 32]) == 35112384\n assert candidate(nums = [10, 10, 10, 10]) == 2110\n assert candidate(nums = [100]) == 100\n assert candidate(nums = [9, 76, 64, 21, 97, 60]) == 1086136\n assert candidate(nums = [8, 3, 8, 3, 8]) == 968\n assert candidate(nums = [0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 110\n assert candidate(nums = [7, 9, 8, 0, 7, 1, 3, 5, 5, 7, 3]) == 2107\n assert candidate(nums = [35, 16, 83, 87, 52, 15, 24, 91, 36, 80, 59, 27, 9, 81, 33, 17, 5, 74, 40, 85, 23, 47, 89, 69]) == 6802248\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == 5700600\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 10120\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 2420\n assert candidate(nums = [5, 8, 6, 2, 3, 7, 4, 1, 9]) == 1704\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == 32339900\n assert candidate(nums = [100, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 99]) == 474000\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 3, 7, 5, 1, 0, 5, 8, 2, 0, 9, 7, 4, 9, 4, 4, 5, 9, 2, 3, 0, 7, 8, 1, 6, 4, 0, 6, 2, 8, 6, 2, 0, 4, 9, 0, 3, 0, 1]) == 23783\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 2427280\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000]) == 1010101200000\n assert candidate(nums = [8, 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15]) == 15717\n assert candidate(nums = [1, 3, 1, 5, 1, 7, 1, 9, 1, 11]) == 1510\n assert candidate(nums = [50, 40, 30, 20, 10, 5, 2, 1, 2, 5, 10, 20, 30, 40, 50]) == 309374\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 14636200\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 243660\n assert candidate(nums = [3, 2, 1, 4, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19]) == 43888\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 4830\n assert candidate(nums = [1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100, 1, 100]) == 13150200\n assert candidate(nums = [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1]) == 2010\n assert candidate(nums = [9, 75, 1, 99, 2, 98, 3, 97, 4, 96, 5]) == 2737551\n assert candidate(nums = [100, 1, 100, 1, 100, 1, 100, 1, 100]) == 3050100\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 13680\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80]) == 15284100\n assert candidate(nums = [99, 1, 98, 2, 97, 3, 96, 4, 95, 5]) == 2906611\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 741\n assert candidate(nums = [50, 20, 30, 10, 40, 60, 70, 80, 90, 10]) == 1428550\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 30\n assert candidate(nums = [50, 25, 75, 40, 60, 10, 80, 30, 90]) == 1779840\n assert candidate(nums = [20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]) == 72420\n assert candidate(nums = [9, 7, 5, 3, 1, 2, 4, 6, 8, 10]) == 2100\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200]) == 98801200\n assert candidate(nums = [50, 25, 75, 20, 80, 15, 85, 10, 90, 5, 95, 40, 60, 35, 65, 30, 70, 45, 55, 2]) == 4854150\n assert candidate(nums = [82, 9, 60, 27, 69, 64, 53, 80, 74, 97, 22, 5, 35, 46, 91, 16, 51, 86, 58, 3, 53, 29, 37, 24, 36, 72, 39, 68, 55, 76, 59, 79, 85, 43, 87, 66, 89, 25, 47, 20, 90, 83, 33, 38, 92, 48, 57, 93, 95, 70, 56, 88, 45, 26, 75, 98, 65, 4, 42, 77, 18, 23, 31, 19, 94, 49, 32, 21, 100, 30, 17, 28, 40, 11, 63, 67, 7, 62, 13, 73, 12, 14, 78, 2, 54, 71, 15, 6, 41, 81, 52, 96, 34, 44, 99, 84, 50, 8, 39]) == 35359128\n assert candidate(nums = [2, 3, 2, 4, 2, 3, 2]) == 120\n assert candidate(nums = [1, 3, 1, 5, 1, 3]) == 90\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300]) == 243603300\n assert candidate(nums = [25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300]) == 82507800\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 2401100\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 2420\n assert candidate(nums = [9, 7, 6, 5, 4, 3, 2, 1]) == 1026\n assert candidate(nums = [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 940\n assert candidate(nums = [9, 7, 5, 3, 1]) == 495\n assert candidate(nums = [10, 100, 1000, 10000]) == 1010110000\n assert candidate(nums = [30, 20, 10, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 88180\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 243660\n assert candidate(nums = [99, 1, 100, 1, 99, 1, 100]) == 2019700\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 2401100\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5820\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 13680\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 2420\n assert candidate(nums = [100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50]) == 13005100\n assert candidate(nums = [23, 11, 77, 32, 45, 62, 88, 12, 56, 78, 91, 29, 48, 50, 65, 73, 82, 90, 18, 27]) == 5732245\n assert candidate(nums = [50, 24, 31, 29, 96, 9, 18, 45, 32, 27, 95, 38, 57, 47, 52, 56, 83, 40, 87, 91, 30, 72, 4, 36, 66, 6, 1, 49, 59, 27, 9, 81, 33, 17, 5, 74, 40, 85, 23, 47, 89, 69, 35, 16, 83, 87, 52, 15, 24, 91, 36, 80, 59, 27, 9, 81, 33, 17, 5, 74]) == 17249443\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 45602200\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 15220\n assert candidate(nums = [2, 3, 7, 5, 4, 1, 9, 6, 8, 2]) == 1723\n assert candidate(nums = [1, 3, 1, 5, 1, 7, 1, 9, 1]) == 617\n assert candidate(nums = [30, 20, 10, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == 49060\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 45640\n assert candidate(nums = [20, 30, 40, 50, 60, 70, 80, 90, 100]) == 2382100\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 2670380\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5820\n assert candidate(nums = [1, 10, 1, 10, 1, 10, 1, 10, 1, 10]) == 3520\n assert candidate(nums = [50, 20, 50, 20, 50, 20, 50, 20, 50, 20, 50, 20, 50, 20, 50, 20, 50, 20, 50, 20, 50, 20]) == 1676050\n assert candidate(nums = [2, 5, 1, 3, 4, 6, 8, 7, 10, 9, 12, 11, 14, 13, 15]) == 13653\n assert candidate(nums = [50, 24, 30, 98, 99, 5, 91, 41, 72, 7, 42, 62, 95, 69, 32, 24, 38, 80, 44, 79, 9, 26, 6, 47, 93, 64, 39, 87, 63, 77, 85, 48, 52, 82, 35, 73, 12, 23, 59, 3, 78, 54, 75, 94, 19, 13, 71, 68, 28, 31, 5, 46, 89, 37, 90, 8, 60, 25, 97, 10, 30, 67, 49, 81, 20, 76, 61, 34, 14, 88, 17, 22, 4, 51, 15, 70, 18, 43, 40, 96, 36, 65, 83, 29, 57, 56, 21, 53, 92, 27, 33, 84, 45, 86, 16, 58, 74]) == 33856230\n assert candidate(nums = [9, 7, 5, 8, 6, 4, 2, 1, 3, 10]) == 2474\n assert candidate(nums = [100, 0, 100, 0, 100, 0, 100, 0, 100, 0, 100, 0, 100, 0, 100, 0, 100, 0, 100, 0]) == 8010100\n assert candidate(nums = [5, 3, 8, 6, 2, 9, 1, 4, 7, 10, 11, 13, 12, 15, 14]) == 13102\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 9530\n assert candidate(nums = [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1]) == 1260\n assert candidate(nums = [23, 45, 67, 89, 12, 34, 56, 78, 90, 11, 33, 55, 77, 22, 44, 66, 88, 10, 30, 50]) == 5055964\n assert candidate(nums = [30, 20, 40, 50, 10]) == 99330\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 2401100\n assert candidate(nums = [10, 1, 100, 5, 10]) == 16110\n assert candidate(nums = [30, 20, 10, 5, 1, 2, 3, 4, 5, 10, 20, 30]) == 37940\n assert candidate(nums = [9, 7, 3, 4, 6, 1, 2, 8, 5]) == 1614\n assert candidate(nums = [10, 1, 9, 2, 8, 3, 7, 4, 6, 5]) == 2630\n assert candidate(nums = [9, 7, 3, 1, 8, 6, 5, 4, 2]) == 1677\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().maxCoins", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxCoins = function(nums) {", "container": null, "callable": "maxCoins", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 313, "task_id": "super-ugly-number", "difficulty": "Medium", "problem_description": "A super ugly number is a positive integer whose prime factors are in the array primes.\nGiven an integer n and an array of integers primes, return the nth super ugly number.\nThe nth super ugly number is guaranteed to fit in a 32-bit signed integer.\n \nExample 1:\n\nInput: n = 12, primes = [2,7,13,19]\nOutput: 32\nExplanation: [1,2,4,7,8,13,14,16,19,26,28,32] is the sequence of the first 12 super ugly numbers given primes = [2,7,13,19].\n\nExample 2:\n\nInput: n = 1, primes = [2,3,5]\nOutput: 1\nExplanation: 1 has no prime factors, therefore all of its prime factors are in the array primes = [2,3,5].\n\n \nConstraints:\n\n1 <= n <= 105\n1 <= primes.length <= 100\n2 <= primes[i] <= 1000\nprimes[i] is guaranteed to be a prime number.\nAll the values of primes are unique and sorted in ascending order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 5,primes = [2, 7, 11]) == 8\n assert candidate(n = 5,primes = [2, 11, 13, 17, 19]) == 11\n assert candidate(n = 3,primes = [2, 3, 5, 7]) == 3\n assert candidate(n = 15,primes = [3, 5, 7]) == 81\n assert candidate(n = 10,primes = [2, 3, 5]) == 12\n assert candidate(n = 20,primes = [2, 11, 13, 17, 19]) == 88\n assert candidate(n = 2,primes = [2, 7]) == 2\n assert candidate(n = 12,primes = [2, 7, 13, 19]) == 32\n assert candidate(n = 1,primes = [2, 3, 5]) == 1\n assert candidate(n = 100,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 136\n assert candidate(n = 20,primes = [3, 5, 7, 11, 13]) == 75\n assert candidate(n = 25,primes = [2, 7, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109]) == 56\n assert candidate(n = 200,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23]) == 384\n assert candidate(n = 150,primes = [2, 11, 13, 17, 19]) == 8704\n assert candidate(n = 750,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67]) == 1365\n assert candidate(n = 500,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397]) == 519\n assert candidate(n = 30,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 30\n assert candidate(n = 50,primes = [2, 5, 11, 13, 17]) == 272\n assert candidate(n = 10,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 10\n assert candidate(n = 500,primes = [2, 5, 7, 11, 13, 17, 19, 23, 29, 31]) == 3773\n assert candidate(n = 100,primes = [2, 3, 5, 7, 11]) == 280\n assert candidate(n = 200,primes = [2, 5, 7, 11, 13, 17, 19]) == 1444\n assert candidate(n = 2,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409]) == 2\n assert candidate(n = 50,primes = [2, 5, 7, 11, 13, 17, 19, 23, 29, 31]) == 104\n assert candidate(n = 250,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]) == 399\n assert candidate(n = 500,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 700\n assert candidate(n = 5000,primes = [2, 3, 5, 7, 11]) == 14975037\n assert candidate(n = 5000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]) == 12780\n assert candidate(n = 300,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 637\n assert candidate(n = 100000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 141797760\n assert candidate(n = 100,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]) == 100\n assert candidate(n = 300,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61]) == 424\n assert candidate(n = 30,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 30\n assert candidate(n = 75,primes = [2, 11, 13, 17, 19, 23, 29, 31, 37, 41]) == 418\n assert candidate(n = 5000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313]) == 8170\n assert candidate(n = 300,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]) == 578\n assert candidate(n = 50,primes = [29, 31, 37, 41, 43, 47]) == 48749\n assert candidate(n = 120,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 144\n assert candidate(n = 100,primes = [11, 13, 17, 19, 23]) == 83521\n assert candidate(n = 300,primes = [3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 3483\n assert candidate(n = 500,primes = [2, 3, 5, 7, 11]) == 8960\n assert candidate(n = 30000,primes = [2, 5, 11, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 3950350\n assert candidate(n = 250,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]) == 285\n assert candidate(n = 1000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23]) == 5474\n assert candidate(n = 300,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]) == 540\n assert candidate(n = 100000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]) == 294980\n assert candidate(n = 100,primes = [2, 3, 5, 7]) == 450\n assert candidate(n = 1000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]) == 3751\n assert candidate(n = 60,primes = [2, 7, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]) == 224\n assert candidate(n = 150,primes = [3, 5, 7, 11, 13, 17, 19]) == 1683\n assert candidate(n = 50,primes = [3, 5, 7, 13, 19, 23]) == 351\n assert candidate(n = 200,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 230\n assert candidate(n = 50,primes = [11, 13, 17, 19, 23]) == 6859\n assert candidate(n = 20000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]) == 94794\n assert candidate(n = 15000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]) == 40560\n assert candidate(n = 50000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]) == 383826\n assert candidate(n = 100,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 100\n assert candidate(n = 250,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313]) == 250\n assert candidate(n = 500,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]) == 850\n assert candidate(n = 1000,primes = [2, 5, 7, 11, 13, 17, 19]) == 48400\n assert candidate(n = 200,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 351\n assert candidate(n = 10000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 42718\n assert candidate(n = 125,primes = [2, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]) == 442\n assert candidate(n = 150,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]) == 182\n assert candidate(n = 40,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79]) == 40\n assert candidate(n = 1000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 4437\n assert candidate(n = 80,primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 253\n assert candidate(n = 75,primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 231\n assert candidate(n = 10000,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 42718\n assert candidate(n = 100,primes = [2, 3, 5, 7, 11, 13, 17, 19]) == 156\n assert candidate(n = 80,primes = [2, 5, 7, 11, 13, 17, 19, 23, 29, 31]) == 200\n assert candidate(n = 500,primes = [2, 5, 11, 13, 17, 19, 23, 29, 31, 37]) == 6256\n assert candidate(n = 100,primes = [2, 3, 5, 7]) == 450\n assert candidate(n = 40,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211]) == 40\n assert candidate(n = 150,primes = [2, 3, 5, 7]) == 1152\n assert candidate(n = 75,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 95\n assert candidate(n = 250,primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103]) == 817\n assert candidate(n = 75,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]) == 76\n assert candidate(n = 150,primes = [2, 5, 7, 11, 13, 17, 19]) == 845\n assert candidate(n = 1000,primes = [2, 3, 5]) == 51200000\n assert candidate(n = 500,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 928\n assert candidate(n = 75,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == 75\n assert candidate(n = 50000,primes = [3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79]) == 17610759\n assert candidate(n = 7500,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499]) == 11616\n assert candidate(n = 25,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23]) == 25\n assert candidate(n = 300,primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]) == 2457\n assert candidate(n = 75,primes = [5, 11, 13, 17, 19, 23, 29, 31, 37]) == 1375\n assert candidate(n = 75,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 82\n assert candidate(n = 20000,primes = [7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139]) == 2610239\n assert candidate(n = 750,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]) == 1323\n assert candidate(n = 15,primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 15\n assert candidate(n = 50,primes = [3, 7, 11, 13, 17, 19]) == 507\n assert candidate(n = 200,primes = [2, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79]) == 697\n assert candidate(n = 50,primes = [2, 5, 7, 11, 13, 17, 19, 23, 29]) == 112\n assert candidate(n = 50,primes = [3, 7, 11, 13, 17]) == 833\n"}, "metadata": {"canonical_parameter_names": ["n", "primes"], "leetcode_dataset_entry_point": "Solution().nthSuperUglyNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var nthSuperUglyNumber = function(n, primes) {", "container": null, "callable": "nthSuperUglyNumber", "parameters": [{"name": "n", "type": "number"}, {"name": "primes", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 315, "task_id": "count-of-smaller-numbers-after-self", "difficulty": "Hard", "problem_description": "Given an integer array nums, return an integer array counts where counts[i] is the number of smaller elements to the right of nums[i].\n \nExample 1:\n\nInput: nums = [5,2,6,1]\nOutput: [2,1,1,0]\nExplanation:\nTo the right of 5 there are 2 smaller elements (2 and 1).\nTo the right of 2 there is only 1 smaller element (1).\nTo the right of 6 there is 1 smaller element (1).\nTo the right of 1 there is 0 smaller element.\n\nExample 2:\n\nInput: nums = [-1]\nOutput: [0]\n\nExample 3:\n\nInput: nums = [-1,-1]\nOutput: [0,0]\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-104 <= nums[i] <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-1, -1]) == [0, 0]\n assert candidate(nums = [10000, -10000, 5000, 0, 5000]) == [4, 0, 1, 0, 0]\n assert candidate(nums = [4, 5, 6, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 1, 0, 1, 0, 1]) == [0, 2, 0, 1, 0, 0]\n assert candidate(nums = [0, -1, 1, -2, 2]) == [2, 1, 1, 0, 0]\n assert candidate(nums = [100, 200, 150, 100]) == [0, 2, 1, 0]\n assert candidate(nums = [100, 99, 98, 97, 96]) == [4, 3, 2, 1, 0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4]) == [6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [10000, -10000, 5000, 0, -5000]) == [4, 0, 2, 1, 0]\n assert candidate(nums = [-1]) == [0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1]) == [0]\n assert candidate(nums = [100, 99, 98, 97, 96, 95]) == [5, 4, 3, 2, 1, 0]\n assert candidate(nums = [5, 2, 6, 1, 8, 7, 4, 9]) == [3, 1, 2, 0, 2, 1, 0, 0]\n assert candidate(nums = [-5, -4, -3, -2, -1]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [0, 1, 2, 3, 4]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [5, 2, 6, 1]) == [2, 1, 1, 0]\n assert candidate(nums = [1, 1, 1, 1, 1]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [3, 2, 1, 0]) == [3, 2, 1, 0]\n assert candidate(nums = [5, 2, 5, 2, 3]) == [3, 0, 2, 0, 0]\n assert candidate(nums = [0, 2, 1, 5, 3, 4]) == [0, 1, 0, 2, 0, 0]\n assert candidate(nums = [3, 2, 1]) == [2, 1, 0]\n assert candidate(nums = [2, 2, 2, 2]) == [0, 0, 0, 0]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10]) == [0, 1, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 4, 3, 2, 1]) == [4, 3, 2, 1, 0]\n assert candidate(nums = [0, 1, 2, 3]) == [0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3]) == [0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 0, 2, 4, 6, 8]) == [1, 2, 3, 4, 5, 0, 0, 0, 0, 0]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]) == [1, 2, 3, 4, 5, 1, 1, 1, 1, 0]\n assert candidate(nums = [3, 2, 1, 0, -1, -2, -3]) == [6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 0]) == [7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [3, 2, 2, 6, 1]) == [3, 1, 1, 1, 0]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [10000, -10000, 5000, -5000, 0]) == [4, 0, 2, 0, 0]\n assert candidate(nums = [7, 8, 9, 1, 2, 3, 4, 5, 6]) == [6, 6, 6, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 3, 8, 6, 2, 7, 4, 1]) == [4, 2, 5, 3, 1, 2, 1, 0]\n assert candidate(nums = [-5, -4, -3, -2, -1, 0]) == [0, 0, 0, 0, 0, 0]\n assert candidate(nums = [3, 2, 2, 1, 1, 0, 0, -1, -1, -2, -2]) == [10, 8, 8, 6, 6, 4, 4, 2, 2, 0, 0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 2, 6, 1, 4, 3, 8, 7]) == [4, 1, 3, 0, 1, 0, 1, 0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [40, 38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [3, 2, 1, 4, 5, 0]) == [3, 2, 1, 1, 1, 0]\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1]) == [6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [8, 3, 6, 2, 5, 1, 7, 4]) == [7, 2, 4, 1, 2, 0, 1, 0]\n assert candidate(nums = [1, 3, 2, 3, 3, 2, 1]) == [0, 3, 1, 2, 2, 1, 0]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == [0, 4, 8, 0, 3, 6, 0, 2, 4, 0, 1, 2, 0, 0, 0]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [2, 0, 1]) == [2, 0, 0]\n assert candidate(nums = [3, 6, 4, 1, 8, 0, 5, 2, 9, 7]) == [3, 5, 3, 1, 4, 0, 1, 0, 1, 0]\n assert candidate(nums = [10000, -10000, 5000, 0, -5000, 10000, -10000]) == [5, 0, 3, 2, 1, 1, 0]\n assert candidate(nums = [0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5]) == [5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0]\n assert candidate(nums = [5, 2, 5, 1, 3, 3, 3, 2, 2, 1, 1]) == [9, 3, 8, 0, 4, 4, 4, 2, 2, 0, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [3, 4, 2, 1, 5]) == [2, 2, 1, 0, 0]\n assert candidate(nums = [0, 2, 1, 2, 1, 0, 1, 0, 2, 1, 0]) == [0, 7, 3, 6, 3, 0, 2, 0, 2, 1, 0]\n assert candidate(nums = [3, 2, 3, 1, 2, 4, 5]) == [3, 1, 2, 0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]) == [0, 1, 2, 3, 4, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3]) == [0, 2, 4, 0, 1, 2, 0, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 2, 6, 1, 9, 3, 8, 4]) == [4, 1, 3, 0, 3, 0, 1, 0]\n assert candidate(nums = [5, 2, 6, 1, 3, 7, 4, 8, 0, 9]) == [5, 2, 4, 1, 1, 2, 1, 1, 0, 0]\n assert candidate(nums = [-10000, -9999, -9998, -9997, -9996, -9995, -9994, -9993, -9992, -9991]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [7, 3, 5, 4, 6, 9, 2, 10, 1]) == [6, 2, 3, 2, 2, 2, 1, 1, 0]\n assert candidate(nums = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 0, -1, -2, -3, 10, 20, 30]) == [4, 4, 4, 3, 2, 1, 0, 0, 0, 0]\n assert candidate(nums = [2000, 1900, 1800, 1700, 1600, 1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]) == [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3]) == [0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [10000, -10000, 5000, 0, -5000, 2000, -2000, 7500, -7500, 10000]) == [8, 0, 5, 3, 1, 2, 1, 1, 0, 0]\n assert candidate(nums = [5, 2, 6, 1, 9, 3, 7, 0, 8, 4]) == [5, 2, 4, 1, 5, 1, 2, 0, 1, 0]\n assert candidate(nums = [10, 20, 10, 20, 10, 20, 10]) == [0, 3, 0, 2, 0, 1, 0]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [7, 9, 1, 4, 3, 8, 2, 5, 6]) == [6, 7, 0, 2, 1, 3, 0, 0, 0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [18, 16, 14, 12, 10, 8, 6, 4, 2, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 3, 2, 3, 3, 2, 2]) == [0, 3, 0, 2, 2, 0, 0]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981]) == [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [5, 2, 6, 1, 4, 3]) == [4, 1, 3, 0, 1, 0]\n assert candidate(nums = [2, 0, 1, 3, 0, 2, 0, 1]) == [5, 0, 2, 4, 0, 2, 0, 0]\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [10000, -10000, 5000, -5000, 0, 2000, -2000, 7000, -7000, 1000]) == [9, 0, 6, 1, 2, 3, 1, 2, 0, 0]\n assert candidate(nums = [1, 3, 2, 2, 3, 1, 0, 4, 5, 2, 2, 1, 3, 4]) == [1, 7, 3, 3, 5, 1, 0, 4, 5, 1, 1, 0, 0, 0]\n assert candidate(nums = [10, 20, 30, 40, 50, 15, 25, 35, 45, 55]) == [0, 1, 2, 3, 4, 0, 0, 0, 0, 0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [18, 16, 14, 12, 10, 8, 6, 4, 2, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [0, -1, -2, -3, -4, -5]) == [5, 4, 3, 2, 1, 0]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [15, 10, 5, 0, -5, -10, -15, 20, 25, 30, 35, 40, 45]) == [6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [10000, -10000, 5000, -5000, 0]) == [4, 0, 2, 0, 0]\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12]) == [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]\n assert candidate(nums = [10000, -10000, 5000, -5000, 0, 1, -1]) == [6, 0, 4, 0, 1, 1, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == [5, 0, 4, 0, 3, 0, 2, 0, 1, 0]\n assert candidate(nums = [10000, -10000, 5000, -5000, 7500, -7500, 2500, -2500, 0]) == [8, 0, 5, 1, 4, 0, 2, 0, 0]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [1, 3, 2, 5, 4, 8, 7, 10, 6, 9]) == [0, 1, 0, 1, 0, 2, 1, 2, 0, 0]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 2, 6, 1, 8, 9, 3, 4, 10, 7, 11, 12, 13, 14, 15]) == [4, 1, 3, 0, 3, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 10000, -10000, 5000, -5000, 2500, -2500, 1250, -1250, 625, -625]) == [5, 9, 0, 7, 0, 5, 0, 3, 0, 1, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 0, 0, 0]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == [8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [10, 20, 30, 40, 50, 0]) == [1, 1, 1, 1, 1, 0]\n assert candidate(nums = [3, 2, 1, 4, 5]) == [2, 1, 0, 0, 0]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5, 5]) == [0, 0, 0, 0, 0]\n assert candidate(nums = [5, 2, 6, 1, 8, 0, 7, 9]) == [3, 2, 2, 1, 2, 0, 0, 0]\n assert candidate(nums = [2, 0, 1, 3, 4, 0, 1, 2]) == [4, 0, 1, 3, 3, 0, 0, 0]\n assert candidate(nums = [-1, 2, 0, 1, -1, 2, 0, 1, -1, 2, 0, 1, -1, 2, 0, 1, -1, 2, 0, 1]) == [0, 14, 4, 8, 0, 11, 3, 6, 0, 8, 2, 4, 0, 5, 1, 2, 0, 2, 0, 0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 10000, -10000, 5000, -5000, 0, 0, 0, 0, 0]) == [2, 8, 0, 6, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == [0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1, 0, 0]\n assert candidate(nums = [10, 20, 30, 25, 15, 5, 40, 35, 20, 10, 50, 45, 30, 25, 15, 5]) == [2, 5, 8, 6, 3, 0, 7, 6, 3, 1, 5, 4, 3, 2, 1, 0]\n assert candidate(nums = [1, 3, 2, 3, 3, 2, 1]) == [0, 3, 1, 2, 2, 1, 0]\n assert candidate(nums = [5, 2, 6, 1, 8, 9, 3, 4]) == [4, 1, 3, 0, 2, 2, 0, 0]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().countSmaller", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countSmaller = function(nums) {", "container": null, "callable": "countSmaller", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 316, "task_id": "remove-duplicate-letters", "difficulty": "Medium", "problem_description": "Given a string s, remove duplicate letters so that every letter appears once and only once. You must make sure your result is the smallest in lexicographical order among all possible results.\n \nExample 1:\n\nInput: s = \"bcabc\"\nOutput: \"abc\"\n\nExample 2:\n\nInput: s = \"cbacdcbc\"\nOutput: \"acdb\"\n\n \nConstraints:\n\n1 <= s.length <= 104\ns consists of lowercase English letters.\n\n \nNote: This question is the same as 1081: https://leetcode.com/problems/smallest-subsequence-of-distinct-characters/\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"rumeblidofervobenly\") == \"rumbidfevonly\"\n assert candidate(s = \"thesqtitxyetpxooxlqskyae\") == \"heitpoxlqskya\"\n assert candidate(s = \"thesqquishs\") == \"tequihs\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"russell\") == \"rusel\"\n assert candidate(s = \"cbacdcbc\") == \"acdb\"\n assert candidate(s = \"zyxzyzzyxzy\") == \"xyz\"\n assert candidate(s = \"xyz\") == \"xyz\"\n assert candidate(s = \"leetcode\") == \"letcod\"\n assert candidate(s = \"abacbabcabacbacbacbabcaba\") == \"abc\"\n assert candidate(s = \"zyxzyxzyxzyxzyx\") == \"xyz\"\n assert candidate(s = \"banana\") == \"ban\"\n assert candidate(s = \"zyxzyxzyx\") == \"xyz\"\n assert candidate(s = \"abcd\") == \"abcd\"\n assert candidate(s = \"bcabc\") == \"abc\"\n assert candidate(s = \"bbaaccaabb\") == \"acb\"\n assert candidate(s = \"ecbacba\") == \"eacb\"\n assert candidate(s = \"aabbcc\") == \"abc\"\n assert candidate(s = \"abacb\") == \"abc\"\n assert candidate(s = \"sphnsdczdcphqvh\") == \"hnsczdpqv\"\n assert candidate(s = \"xyzzyx\") == \"xyz\"\n assert candidate(s = \"eliminate\") == \"elimnat\"\n assert candidate(s = \"bcaacbcbabcbabcbbbcabcabcb\") == \"abc\"\n assert candidate(s = \"cccbba\") == \"cba\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == \"zyxwvutsrqponmlkjihgfedcba\"\n assert candidate(s = \"ababcabcabc\") == \"abc\"\n assert candidate(s = \"vvvvvvvvvvvvvvvvvvvvvvvvvv\") == \"v\"\n assert candidate(s = \"xyzzyxwvutsrqponmlkjihgfedcbazyxzyxwvutsrqponmlkjihgfedcba\") == \"axzywvutsrqponmlkjihgfedcb\"\n assert candidate(s = \"eleven\") == \"elvn\"\n assert candidate(s = \"abcabcabcabc\") == \"abc\"\n assert candidate(s = \"mississsipissippi\") == \"mips\"\n assert candidate(s = \"kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk\") == \"k\"\n assert candidate(s = \"thisisaverycomplicatedstringwithmultiplesamecharacters\") == \"averycodingwhmulpst\"\n assert candidate(s = \"abcdabcdabcd\") == \"abcd\"\n assert candidate(s = \"vkgdffubqyfvcl\") == \"kgdfubqyvcl\"\n assert candidate(s = \"zyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxyzyxy\") == \"xyz\"\n assert candidate(s = \"thisisareallylongstringwithsomerepeatedcharacters\") == \"aelyginwhompdcrts\"\n assert candidate(s = \"aaaaabbbbccccdddd\") == \"abcd\"\n assert candidate(s = \"abcdabc\") == \"abcd\"\n assert candidate(s = \"abcdefghxyzzyxwvutsrqponmlkjihgfedcba\") == \"abcdefghxyzwvutsrqponmlkji\"\n assert candidate(s = \"abcdcbadef\") == \"abcdef\"\n assert candidate(s = \"elqodmxonqkdio\") == \"eldmxnqkio\"\n assert candidate(s = \"rclcar\") == \"clar\"\n assert candidate(s = \"aaabbbccc\") == \"abc\"\n assert candidate(s = \"abcdefghifghijklmnopqrstuvwxyz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"zabaxyzc\") == \"abxyzc\"\n assert candidate(s = \"zyxzyxzyxzyxcba\") == \"xyzcba\"\n assert candidate(s = \"abababababababab\") == \"ab\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"dedededededededed\") == \"de\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmzxcvbnmlkjhgfdsapoiuytrewq\") == \"abmzxcvnlkjhgfdspoiuytrewq\"\n assert candidate(s = \"abcdabcdabcdabcd\") == \"abcd\"\n assert candidate(s = \"limits\") == \"limts\"\n assert candidate(s = \"abcdzyxwvutsrqponmlkjihgfedcba\") == \"abcdzyxwvutsrqponmlkjihgfe\"\n assert candidate(s = \"zyzzyzxzyzy\") == \"xyz\"\n assert candidate(s = \"aabbbccddeeefffggghhhiiijjjkkkllmmmnnnooopppqqrrssttuuvvwwxxyyzz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"zzyyxxwwvvttsrqqponnmlkkjjiihggffeeddccbbaa\") == \"zyxwvtsrqponmlkjihgfedcba\"\n assert candidate(s = \"rsvwzxcvbnmasdfghjklpoiuytrewq\") == \"rsvwzxcbnmadfghjklpoiuyteq\"\n assert candidate(s = \"abacabadabacaba\") == \"abcd\"\n assert candidate(s = \"rquyaedetziwq\") == \"rquyadetziw\"\n assert candidate(s = \"dabdc\") == \"abdc\"\n assert candidate(s = \"pppippiiqipqqipiqipiiiiii\") == \"ipq\"\n assert candidate(s = \"abacbabc\") == \"abc\"\n assert candidate(s = \"abcdexyzabcdexyz\") == \"abcdexyz\"\n assert candidate(s = \"abcdexyzvwxycba\") == \"abcdexyzvw\"\n assert candidate(s = \"eccbbbbdec\") == \"bdec\"\n assert candidate(s = \"axbxa\") == \"abx\"\n assert candidate(s = \"rhythm\") == \"rhytm\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"cbacdcbcxd\") == \"abcxd\"\n assert candidate(s = \"pppqqqrrrssstttuuuvvvwwwxxxxyyyyzzzz\") == \"pqrstuvwxyz\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"elgoog\") == \"elgo\"\n assert candidate(s = \"abcdacdabcde\") == \"abcde\"\n assert candidate(s = \"cdadabcc\") == \"adbc\"\n assert candidate(s = \"abcdxyzzyxwvutsrqponmlkjihgfedcba\") == \"abcdxyzwvutsrqponmlkjihgfe\"\n assert candidate(s = \"nincompoop\") == \"incmop\"\n assert candidate(s = \"zzzzyyyxxxwwvvuuttssrrqqppoonnmmllkkiijjhhhgggffffeeeedddccccbbbaaa\") == \"zyxwvutsrqponmlkijhgfedcba\"\n assert candidate(s = \"leetcodeloveleetcode\") == \"cdelovt\"\n assert candidate(s = \"abcdefghijabcdejk\") == \"abcdefghijk\"\n assert candidate(s = \"abcdedcba\") == \"abcde\"\n assert candidate(s = \"aabbbccc\") == \"abc\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmzyxcvbnmlkjhgfdsapoiuytrewq\") == \"abmzxcvnlkjhgfdspoiuytrewq\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\") == \"abmqwertyuiopsdfghjklzxcvn\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzyxwvutsrqponmlkjihgfedcba\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"poiuytrewqlkjhgfdsazxcvbnmqwertyuioplkjhgfdsazxcvbnm\") == \"abmqwertyuioplkjhgfdszxcvn\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmnbvcxzlkjhgfdsapoiuytrewq\") == \"abmnvcxzlkjhgfdspoiuytrewq\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"abacabadabcabc\") == \"abcd\"\n assert candidate(s = \"abacbdcba\") == \"abcd\"\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == \"a\"\n assert candidate(s = \"mississippi\") == \"misp\"\n assert candidate(s = \"abcdexyzzyxwvtsrqponmlkjihgfe\") == \"abcdexyzwvtsrqponmlkjihgf\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba\") == \"azyxwvutsrqponmlkjihgfedcb\"\n assert candidate(s = \"aaaaaaaabbbbbbbbccccccccddddddddeeeeeeeefffffffff\") == \"abcdef\"\n assert candidate(s = \"ababababababababababababababababababab\") == \"ab\"\n assert candidate(s = \"zyxzyxzyxzyx\") == \"xyz\"\n assert candidate(s = \"razonator\") == \"azntor\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().removeDuplicateLetters", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeDuplicateLetters = function(s) {", "container": null, "callable": "removeDuplicateLetters", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 318, "task_id": "maximum-product-of-word-lengths", "difficulty": "Medium", "problem_description": "Given a string array words, return the maximum value of length(word[i]) * length(word[j]) where the two words do not share common letters. If no such two words exist, return 0.\n \nExample 1:\n\nInput: words = [\"abcw\",\"baz\",\"foo\",\"bar\",\"xtfn\",\"abcdef\"]\nOutput: 16\nExplanation: The two words can be \"abcw\", \"xtfn\".\n\nExample 2:\n\nInput: words = [\"a\",\"ab\",\"abc\",\"d\",\"cd\",\"bcd\",\"abcd\"]\nOutput: 4\nExplanation: The two words can be \"ab\", \"cd\".\n\nExample 3:\n\nInput: words = [\"a\",\"aa\",\"aaa\",\"aaaa\"]\nOutput: 0\nExplanation: No such pair of words.\n\n \nConstraints:\n\n2 <= words.length <= 1000\n1 <= words[i].length <= 1000\nwords[i] consists only of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(words = ['a', 'ab', 'abc', 'd', 'cd', 'bcd', 'abcd']) == 4\n assert candidate(words = ['eae', 'eaecbaaa', 'aadcba', 'bae', 'abc', 'abcbb', 'cba', 'abcd', 'ac', 'ba', 'aaaa', 'd', 'abac', 'ababc', 'abcabc', 'a', 'bc', 'b']) == 8\n assert candidate(words = ['abcw', 'baz', 'foo', 'bar', 'xtfn', 'abcdef']) == 16\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa']) == 0\n assert candidate(words = ['aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', 'aa']) == 0\n assert candidate(words = ['hello', 'world', 'python', 'programming']) == 0\n assert candidate(words = ['abc', 'def', 'ghi']) == 9\n assert candidate(words = ['arml', 'vb', 've', 'vef', 'k']) == 12\n assert candidate(words = ['eae', 'eaee', 'aaee', 'aee', 'eceeaeeea', 'cecceeaeea', 'eceeaeea']) == 0\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuvwxyzabcdefghijkl', 'abcdefghijklnmopqrstuvwxyz']) == 0\n assert candidate(words = ['unique', 'strings', 'without', 'common', 'characters', 'different', 'letters']) == 42\n assert candidate(words = ['unique', 'letters', 'pair', 'matches', 'product', 'maximum', 'distinct', 'words', 'solution', 'algorithm']) == 49\n assert candidate(words = ['xylophone', 'guitar', 'violin', 'flute', 'drum', 'piano', 'harp', 'cymbal', 'trumpet', 'trombone', 'saxophone', 'clarinet', 'oboe', 'bassoon', 'tuba']) == 54\n assert candidate(words = ['aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz', 'bbaacceegghhkkllmmnnooppqqrrssttuuvvwwxxyyzz', 'ccaabbeegghhkkllmmnnooppqqrrssttuuvvwwxxyyzz']) == 0\n assert candidate(words = ['abcdefghij', 'klmnopqrstu', 'vwxyzabcde', 'fghijklmno', 'pqrstuvwx', 'yzabcdefg', 'hijklmnop', 'qrstuvwxy', 'zabcdefghij', 'klmnopqrstu', 'vwxyzabcde', 'fghijklmno', 'pqrstuvwx', 'yzabcdefg', 'hijklmnop', 'qrstuvwxy']) == 121\n assert candidate(words = ['qwerty', 'asdfgh', 'zxcvbn', 'polkij', 'mnbvcx', 'lkjhgf', 'ertyui', 'opasdf', 'ghjklz', 'xcvbnm']) == 36\n assert candidate(words = ['abcdefghij', 'klmnopqrstu', 'vwxyzabcde', 'fghijklmno', 'pqrstuvwx', 'yzabcdefg', 'hijklmnop', 'qrstuvwxy', 'zabcdefghij', 'klmnopqrstu']) == 121\n assert candidate(words = ['aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz', 'mnopqrstuvwxyz', 'abcdef', 'ghijkl', 'qrstuv', 'wxyzab', 'cdefgh', 'ijklmn', 'opqrst', 'vwxyza', 'bcdefg', 'hijklm', 'nopqr', 'stuvw', 'xyza', 'bcdef', 'ghijk', 'lmnop', 'qrstu', 'vwxyz', 'abcdefg', 'hijklmn', 'opqrstu', 'vwxyzab', 'cdefghij', 'klmnopqr', 'stuvwxyz', 'abcdefghij', 'klmnopqrstu', 'vwxyzabcde', 'fghijklmnop', 'qrstuvwxy', 'zabcdefghi', 'jklmnopqrs', 'tuvwxyzabc', 'defghijklmno', 'pqrstuvwxyzabc', 'efghijklmnopqr', 'stuvwxyzabcd', 'tuvwxyzabcde', 'uvwxyzabcdefg', 'vwxyzabcdefgh', 'wxyzabcdefghi', 'xyzabcdefghij', 'yzabcdefghijk', 'zabcdefghijkl', 'abcdefghijkln']) == 168\n assert candidate(words = ['abcdefg', 'hijklmnop', 'qrstuv', 'wxyz', 'mnopqr', 'ghijkl', 'uvwxy', 'stuv', 'zabcde', 'fghij']) == 63\n assert candidate(words = ['qwertyuiop', 'asdfghjklzxcvbnm', 'qwerty', 'asdfgh', 'zxcvbn', 'mnbvcxz', 'lkjhgfdsa', 'poiuytrewq', 'bnmxcvz', 'poiuyt', 'lkjhgf', 'mnbvcx', 'lkjhgfdsazxcvbnm', 'qwertyuiopasdfghjklzxcvbnm']) == 160\n assert candidate(words = ['aabbccddeeff', 'ghhiiijjkkll', 'mmnnooppqqrr', 'ssttuuvvwwxx', 'yyzzzzz', 'abcdefg', 'hijklmnop', 'qrstuvwxyz', 'mnopqr', 'efghij', 'vwxyz', 'yzab', 'qrstuv', 'wxyzab', 'mnopqrstu', 'vwxyzabcd', 'efghijklm', 'nopqrstu', 'vwxyzab', 'cdefghij', 'klmnopqrstu', 'vwxyzabcd', 'efghijklmnopqr', 'stuvwxyzabcd']) == 168\n assert candidate(words = ['pqrs', 'tuvw', 'xyz', 'mnop', 'qrst', 'ijkl', 'efgh', 'abcd', 'nopqr', 'stuvw', 'xyzab', 'mnopqr', 'stuvwx', 'yzabcd', 'efghij', 'klmno', 'pqrstu', 'vwxyz', 'abcdefghij', 'klmnopqr', 'stuvwxyz', 'abcdefghijk', 'lmnopqrstu', 'vwxyzabcd', 'efghijklmnop', 'qrstu', 'vwxyzab', 'cdefghij', 'klmnopqrstu', 'vwxyzabcd', 'efghijklmnopqr', 'stuvwxyzabcd', 'mnopqrstu', 'vwxyzab', 'cdefghij', 'klmnopqrstu', 'vwxyzabcd', 'efghijklmnopqr', 'stuvwxyzabcd']) == 168\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'abcdefghij', 'klmnopqrst', 'tuvwxyz', 'abcdefghijklmno', 'pqrstuvwxyzabc']) == 105\n assert candidate(words = ['abcdefg', 'hijklmn', 'opqrstu', 'vwxyzab', 'cdefghi', 'jklmnop', 'qrstuvw', 'xyzabcd', 'efghijk', 'lmnopqr', 'stuvwxz', 'bcdefgh', 'ijklmno', 'pqrstuv', 'wxyzabc', 'defghij', 'klmnopq', 'rstuvwx', 'stuvwxy', 'tuwvxyz', 'uvwxyza', 'vwxyzb', 'wxyza', 'xyzab', 'yzabc', 'zabcd']) == 49\n assert candidate(words = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzabcdef', 'ghijklmo', 'nopqrstu', 'vwxyzabc', 'defghijk', 'lmnopqrs', 'tuvwxyz', 'abcdefghij', 'klmnopqr', 'stuvwxyzab', 'cdefghijkl', 'mnopqrstuv', 'wxyza', 'bcdefghijkl', 'mnopqrstuvw', 'xyzabcde', 'fghijklmno', 'pqrstuvwx', 'yzabcdefg', 'hijklmnopq', 'rstuvwxyz']) == 121\n assert candidate(words = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzabcd', 'efghij', 'klmnopqr', 'stuvwxyz', 'abcdijkl', 'mnopqrst', 'uvwxyzae', 'fghij', 'klmnop', 'qrstuv', 'yzab', 'efghi', 'klmno', 'pqrstuv', 'wxyz', 'abcd', 'efgh', 'ijkl', 'mnop', 'qrst', 'uvwx', 'yz', 'abc', 'def', 'ghi', 'jkl', 'mno', 'pqr', 'stu', 'vwx', 'yz']) == 64\n assert candidate(words = ['unique', 'letters', 'only', 'here', 'now', 'words', 'without', 'overlap', 'shared', 'characters', 'strings', 'distinct']) == 56\n assert candidate(words = ['aaaaabbbbbcccccdddddeeeeeffffffggggghhhhhhiiiiijjjjjjkkkkklllllmmmmmnnnnnooooo', 'pppppqqqqqrrrrrssssstttttuuuuuvvvvvwwwwwxxxxxyyyyyzzzzz', 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', 'bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb']) == 9898\n assert candidate(words = ['abcdefghijk', 'lmnopqrstuv', 'wxyzabcde', 'fghijklmn', 'opqrstuvw', 'xyzabcde', 'fghijklmn', 'opqrstuvw', 'xyzabcde', 'fghijklmn']) == 121\n assert candidate(words = ['unique', 'words', 'only', 'here', 'for', 'testing', 'purposes', 'please', 'do', 'not', 'reuse']) == 30\n assert candidate(words = ['abcdxyz', 'mnopqrs', 'tuvw', 'efghijkl', 'lmno', 'abxyz', 'mnop', 'tuwv', 'ijkl', 'efgh', 'lmn', 'abxyz', 'mnop', 'tuwv', 'ijkl', 'efgh', 'lmn', 'abxyz', 'mnop', 'tuwv']) == 56\n assert candidate(words = ['verylongwordindeed', 'anotherlongword', 'short', 'tiny', 'mediumsized', 'averylongword', 'tinywords', 'verysmall']) == 0\n assert candidate(words = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzab', 'cdefgh', 'ijklmn', 'opqrst', 'vwxyza', 'bcdefg', 'hijklmno', 'pqrstuvw', 'xyzabc', 'defghi', 'jklmnpqr', 'stuvwxyl', 'yzabcd', 'efghij', 'klmnopqr', 'stuvwxy', 'zabcde', 'fghijkln', 'opqrstuv', 'wxyza']) == 64\n assert candidate(words = ['unique', 'letters', 'only', 'here', 'these', 'words', 'have', 'no', 'commonality']) == 44\n assert candidate(words = ['abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy', 'z', 'abc', 'def', 'ghi', 'jkl', 'mno', 'pqr', 'stu', 'vwx', 'y']) == 25\n assert candidate(words = ['zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz', 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', 'bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb', 'cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc']) == 4356\n assert candidate(words = ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'qazwsxedcrfvtgbyhnujmiklop', 'mnbvcxzlkjhgfdsapoiuytrewq', 'asdfghjklzxcvbnm', 'qwertyuiopasdfghjklzxcvbnm', 'asdfghjklqwertyuiopzxcvbnm']) == 160\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'qwertyuiop', 'asdfghjkl', 'zxcvbnm']) == 90\n assert candidate(words = ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'qazwsxedc', 'rfvtgbyhn', 'ujmikolp', 'mnbvcxz', 'lkjhgfdsa', 'poiuytrewq', 'opmijnuhb', 'lyfgcrdxv', 'etahbdvsq']) == 90\n assert candidate(words = ['unique', 'words', 'only', 'here', 'not', 'sharing', 'any', 'letters', 'with', 'each', 'other', 'set', 'of', 'letters', 'are', 'different']) == 30\n assert candidate(words = ['abcdef', 'ghijkl', 'mnopqr', 'stuvwx', 'yzabcd', 'efghij', 'klmnop', 'qrstuv', 'wxyzab', 'cdefgh']) == 36\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'bcdefghijklmnopqrstuvwxyza', 'cdefghijklmnopqrstuvwxyzab']) == 0\n assert candidate(words = ['optimization', 'algorithms', 'coding', 'problems', 'data', 'structures', 'interview', 'preparation', 'practice']) == 32\n assert candidate(words = ['one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine', 'ten', 'eleven', 'twelve', 'thirteen', 'fourteen', 'fifteen', 'sixteen', 'seventeen', 'eighteen', 'nineteen', 'twenty']) == 36\n assert candidate(words = ['abcd', 'efgh', 'ijkl', 'mnop', 'qrst', 'uvwx', 'yzab', 'cdef', 'ghij', 'klmn', 'opqr', 'stuv', 'wxyz', 'mnopqr', 'stuvwx', 'yzabcd', 'efghij', 'klmno']) == 36\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'abcdefghij', 'klmnopqrstuvw', 'xyz', 'uvw', 'mnopqr', 'ghijkl']) == 130\n assert candidate(words = ['one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine', 'ten', 'eleven', 'twelve', 'thirteen', 'fourteen', 'fifteen', 'sixteen', 'seventeen', 'eighteen', 'nineteen', 'twenty', 'twentyone', 'twentytwo', 'twentythree', 'twentyfour', 'twentyfive', 'twentysix', 'twentyseven', 'twentyeight', 'twentynine', 'thirty']) == 44\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuv', 'abcdefghijk', 'qrstuvwxzy', 'abcdefgh', 'ijklmnop', 'qrstuvw', 'xyz', 'abcdefghij']) == 110\n assert candidate(words = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzabcdef', 'ghijklmo', 'nopqrstu', 'vwxyzabc', 'defghijk', 'lmnopqrs', 'tuvwxyz', 'abcdefghij', 'klmnopqr', 'stuvwxyzab', 'cdefghijkl', 'mnopqrstuv', 'wxyza', 'bcdefghijkl', 'mnopqrstuvw', 'xyzabcde', 'fghijklmno', 'pqrstuvwx', 'yzabcdefg', 'hijklmnopq', 'rstuvwxyz', 'abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy', 'zabcd', 'efghi', 'jklmn', 'opqrs', 'tuvwx', 'yzabc', 'defgh', 'ijklm', 'nopqr', 'stuvw', 'xyzab', 'cdefg', 'hijkl', 'mnopq', 'rstuv', 'wxyza', 'bcdef', 'ghijk', 'lmnop', 'qrstu', 'vwxyz', 'abcde', 'fghij', 'klmno', 'pqrst', 'uvwxy', 'zabcd']) == 121\n assert candidate(words = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzabcd', 'efghij', 'klmnopqr', 'stuvwxyz', 'abcdijkl', 'mnopqrst', 'uvwxyzae']) == 64\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'aa', 'bb', 'cc', 'dd', 'ee', 'ff', 'gg', 'hh', 'ii', 'jj', 'kk', 'll', 'mm', 'nn', 'oo', 'pp', 'qq', 'rr', 'ss', 'tt', 'uu', 'vv', 'ww', 'xx', 'yy', 'zz']) == 4\n assert candidate(words = ['aaaaaa', 'bbbbbb', 'cccccc', 'dddddd', 'eeeeee', 'ffffff', 'gggggg', 'hhhhhh', 'iiiiii', 'jjjjjj']) == 36\n assert candidate(words = ['this', 'is', 'a', 'test', 'of', 'the', 'maximum', 'product', 'function', 'with', 'various', 'lengths', 'and', 'characters']) == 49\n assert candidate(words = ['abcdefghij', 'klmnopqrstu', 'vwxyzabcde', 'fghijklmno', 'pqrstuvwxyzabc', 'defghijklmnopq', 'rstuvwxyzabcd', 'efghijklmnopqr', 'stuvwxyzabcde', 'tuvwxyzabcdef', 'uvwxyzabcdefg', 'vwxyzabcdefgh', 'wxyzabcdefghi', 'xyzabcdefghij', 'yzabcdefghijk', 'zabcdefghijkl', 'abcdefghijkln']) == 143\n assert candidate(words = ['abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzabcdef', 'ghijklmn', 'opqrstuv', 'wxyzabcd', 'efghijkl', 'mnopqrst', 'qrstuvwx']) == 64\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'abcdefghijklmnopqrstuvwxyz']) == 1\n assert candidate(words = ['aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz', 'zyxwvutsrqponmlkjihgfedcba', 'abcdefghijklmnopqrstuv', 'ghijklmnopqrstuvwxyz', 'mnopqrstuvwxyza', 'bcdefghijklmnopqrstuvwxyza']) == 0\n assert candidate(words = ['short', 'longerwords', 'tiny', 'largerwordsindeed', 'micro', 'nano', 'pico', 'femto', 'atto', 'zepto', 'yocto']) == 0\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == 1\n assert candidate(words = ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'mnbvcxz', 'lkjhgfdsa', 'poiuytrewq', 'asdfghjklpoiuytrewq', 'zxcvbnmlkjhgfdsapoiuytrewq']) == 133\n assert candidate(words = ['aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz', 'abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuvwxyzabcdefghijkl', 'abcdefghijqrstuvwxzy', 'uniquestringswithoutcommoncharacters', 'differentletters', 'optimizationalgorithms', 'codingproblems', 'datastructures', 'interviewpreparation', 'practice', 'abcdefgh', 'ijklmnop', 'qrstuvwx', 'yzabcd', 'efghij', 'klmnopqr', 'stuvwxyz', 'abcdijkl', 'mnopqrst', 'uvwxyzae']) == 112\n assert candidate(words = ['abcdexyz', 'mnopqrtuvw', 'ijklstuvwx', 'ghfxyz', 'abcdef', 'ghijklmn', 'opqrstuv', 'wxyz', 'abcd', 'efgh', 'ijkl', 'mnop', 'qrst', 'uvwx', 'yzab', 'mnop', 'qrst', 'uvwx', 'yzab']) == 80\n assert candidate(words = ['unique', 'letters', 'only', 'distinct', 'characters', 'different', 'setsof', 'words']) == 40\n assert candidate(words = ['abcdef', 'ghijkl', 'mnopqr', 'stuvwx', 'yzabcd', 'efghij', 'klmnop', 'qrstuv', 'wxyzaa', 'bcdefg']) == 36\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuvwxyzabcdefghijkl', 'abcdefghijqrstuvwxzy']) == 0\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqr', 'ghijkl', 'uvwxy', 'stuv', 'zabcde', 'fghij', 'qwerty', 'asdfghjklzxcvbnm', 'qwertyuiop', 'asdfgh', 'zxcvbn', 'mnbvcxz', 'lkjhgfdsa', 'poiuytrewq', 'bnmxcvz', 'poiuyt', 'lkjhgf', 'mnbvcx', 'lkjhgfdsazxcvbnm', 'qwertyuiopasdfghjklzxcvbnm']) == 160\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstuv', 'abcdefghij', 'klmnopqr', 'stuvwxyz']) == 100\n"}, "metadata": {"canonical_parameter_names": ["words"], "leetcode_dataset_entry_point": "Solution().maxProduct", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxProduct = function(words) {", "container": null, "callable": "maxProduct", "parameters": [{"name": "words", "type": "string[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 319, "task_id": "bulb-switcher", "difficulty": "Medium", "problem_description": "There are n bulbs that are initially off. You first turn on all the bulbs, then you turn off every second bulb.\nOn the third round, you toggle every third bulb (turning on if it's off or turning off if it's on). For the ith round, you toggle every i bulb. For the nth round, you only toggle the last bulb.\nReturn the number of bulbs that are on after n rounds.\n \nExample 1:\n\n\nInput: n = 3\nOutput: 1\nExplanation: At first, the three bulbs are [off, off, off].\nAfter the first round, the three bulbs are [on, on, on].\nAfter the second round, the three bulbs are [on, off, on].\nAfter the third round, the three bulbs are [on, off, off]. \nSo you should return 1 because there is only one bulb is on.\nExample 2:\n\nInput: n = 0\nOutput: 0\n\nExample 3:\n\nInput: n = 1\nOutput: 1\n\n \nConstraints:\n\n0 <= n <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 3) == 1\n assert candidate(n = 100) == 10\n assert candidate(n = 4) == 2\n assert candidate(n = 16) == 4\n assert candidate(n = 9) == 3\n assert candidate(n = 1000000) == 1000\n assert candidate(n = 1) == 1\n assert candidate(n = 1000000000) == 31622\n assert candidate(n = 1000) == 31\n assert candidate(n = 10) == 3\n assert candidate(n = 25) == 5\n assert candidate(n = 1089) == 33\n assert candidate(n = 729) == 27\n assert candidate(n = 324) == 18\n assert candidate(n = 2304) == 48\n assert candidate(n = 23) == 4\n assert candidate(n = 2048) == 45\n assert candidate(n = 5000) == 70\n assert candidate(n = 36) == 6\n assert candidate(n = 529) == 23\n assert candidate(n = 676) == 26\n assert candidate(n = 2500) == 50\n assert candidate(n = 32768) == 181\n assert candidate(n = 1156) == 34\n assert candidate(n = 100000000) == 10000\n assert candidate(n = 29) == 5\n assert candidate(n = 576) == 24\n assert candidate(n = 144) == 12\n assert candidate(n = 900) == 30\n assert candidate(n = 50000) == 223\n assert candidate(n = 1681) == 41\n assert candidate(n = 17) == 4\n assert candidate(n = 1225) == 35\n assert candidate(n = 784) == 28\n assert candidate(n = 2401) == 49\n assert candidate(n = 10000000) == 3162\n assert candidate(n = 100000) == 316\n assert candidate(n = 20000) == 141\n assert candidate(n = 256) == 16\n assert candidate(n = 2025) == 45\n assert candidate(n = 81) == 9\n assert candidate(n = 123456789) == 11111\n assert candidate(n = 121) == 11\n assert candidate(n = 999999) == 999\n assert candidate(n = 2209) == 47\n assert candidate(n = 999999999) == 31622\n assert candidate(n = 49) == 7\n assert candidate(n = 4096) == 64\n assert candidate(n = 2116) == 46\n assert candidate(n = 16384) == 128\n assert candidate(n = 289) == 17\n assert candidate(n = 23456789) == 4843\n assert candidate(n = 2) == 1\n assert candidate(n = 225) == 15\n assert candidate(n = 8192) == 90\n assert candidate(n = 1764) == 42\n assert candidate(n = 65536) == 256\n assert candidate(n = 1296) == 36\n assert candidate(n = 987654321) == 31426\n assert candidate(n = 15) == 3\n assert candidate(n = 500000) == 707\n assert candidate(n = 961) == 31\n assert candidate(n = 196) == 14\n assert candidate(n = 361) == 19\n assert candidate(n = 13) == 3\n assert candidate(n = 625) == 25\n assert candidate(n = 789456) == 888\n assert candidate(n = 1600) == 40\n assert candidate(n = 1849) == 43\n assert candidate(n = 841) == 29\n assert candidate(n = 64) == 8\n assert candidate(n = 484) == 22\n assert candidate(n = 10000) == 100\n assert candidate(n = 1024) == 32\n assert candidate(n = 1369) == 37\n assert candidate(n = 1936) == 44\n assert candidate(n = 1444) == 38\n assert candidate(n = 169) == 13\n assert candidate(n = 19) == 4\n assert candidate(n = 400) == 20\n assert candidate(n = 1049) == 32\n assert candidate(n = 123456) == 351\n assert candidate(n = 441) == 21\n assert candidate(n = 1521) == 39\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().bulbSwitch", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var bulbSwitch = function(n) {", "container": null, "callable": "bulbSwitch", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 321, "task_id": "create-maximum-number", "difficulty": "Hard", "problem_description": "You are given two integer arrays nums1 and nums2 of lengths m and n respectively. nums1 and nums2 represent the digits of two numbers. You are also given an integer k.\nCreate the maximum number of length k <= m + n from digits of the two numbers. The relative order of the digits from the same array must be preserved.\nReturn an array of the k digits representing the answer.\n \nExample 1:\n\nInput: nums1 = [3,4,6,5], nums2 = [9,1,2,5,8,3], k = 5\nOutput: [9,8,6,5,3]\n\nExample 2:\n\nInput: nums1 = [6,7], nums2 = [6,0,4], k = 5\nOutput: [6,7,6,0,4]\n\nExample 3:\n\nInput: nums1 = [3,9], nums2 = [8,9], k = 3\nOutput: [9,8,9]\n\n \nConstraints:\n\nm == nums1.length\nn == nums2.length\n1 <= m, n <= 500\n0 <= nums1[i], nums2[i] <= 9\n1 <= k <= m + n\nnums1 and nums2 do not have leading zeros.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [5, 5, 5, 5],nums2 = [5, 5, 5, 5],k = 7) == [5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0]\n assert candidate(nums1 = [3, 4, 6, 5],nums2 = [9, 1, 2, 5, 8, 3],k = 5) == [9, 8, 6, 5, 3]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 18) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1]\n assert candidate(nums1 = [6, 7],nums2 = [6, 0, 4],k = 5) == [6, 7, 6, 0, 4]\n assert candidate(nums1 = [1, 6, 5, 4, 3, 2, 1],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 7) == [9, 8, 7, 6, 6, 5, 5]\n assert candidate(nums1 = [3, 9],nums2 = [8, 9],k = 3) == [9, 8, 9]\n assert candidate(nums1 = [1],nums2 = [1],k = 2) == [1, 1]\n assert candidate(nums1 = [0],nums2 = [0],k = 1) == [0]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 0],k = 5) == [9, 4, 6, 8, 0]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],k = 5) == [5, 5, 4, 3, 2]\n assert candidate(nums1 = [7],nums2 = [9, 8, 2],k = 3) == [9, 8, 7]\n assert candidate(nums1 = [1, 6, 5, 4, 3, 2, 1],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 10) == [9, 8, 7, 6, 6, 5, 5, 4, 4, 3]\n assert candidate(nums1 = [1, 6, 5, 4, 3],nums2 = [9, 8, 7, 6, 5],k = 5) == [9, 8, 7, 6, 6]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5],k = 5) == [5, 5, 5, 5, 5]\n assert candidate(nums1 = [5, 6],nums2 = [4, 0, 9],k = 4) == [6, 4, 0, 9]\n assert candidate(nums1 = [8, 6, 9],nums2 = [5, 9, 7, 6, 3, 2, 1],k = 5) == [9, 9, 7, 6, 3]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 10) == [9, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 0],k = 9) == [4, 6, 8, 1, 3, 5, 7, 9, 0]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0],nums2 = [0, 2, 4, 6, 8, 1, 3, 5, 7, 9],k = 9) == [9, 8, 8, 1, 3, 5, 7, 9, 0]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 10) == [9, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums1 = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],nums2 = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 10) == [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums1 = [5, 6, 7, 8, 9],nums2 = [1, 2, 3, 4, 5],k = 10) == [5, 6, 7, 8, 9, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [1, 1, 1, 1, 1],k = 5) == [1, 1, 1, 1, 1]\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0]\n assert candidate(nums1 = [4, 3, 2, 1],nums2 = [8, 7, 6, 5],k = 7) == [8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [6, 7, 6, 5, 4, 3, 2, 1],nums2 = [8, 7, 6, 5, 4, 3, 2, 1, 0],k = 8) == [8, 7, 7, 6, 6, 5, 5, 4]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 10) == [9, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1],k = 5) == [1, 1, 1, 1, 1]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6, 7, 8, 9],k = 6) == [7, 8, 9, 1, 2, 3]\n assert candidate(nums1 = [3, 9, 5, 0, 8],nums2 = [4, 6, 1, 7, 2],k = 8) == [9, 6, 5, 1, 7, 2, 0, 8]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 0],k = 6) == [5, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [9, 9, 9, 9, 9],nums2 = [8, 8, 8, 8, 8],k = 8) == [9, 9, 9, 9, 9, 8, 8, 8]\n assert candidate(nums1 = [3, 5, 7, 9],nums2 = [1, 2, 8, 6],k = 5) == [9, 1, 2, 8, 6]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],k = 3) == [5, 5, 4]\n assert candidate(nums1 = [9, 9, 9, 9],nums2 = [9, 9, 9, 9],k = 7) == [9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 10) == [9, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 15) == [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [0, 2, 4, 6, 8],k = 6) == [9, 0, 2, 4, 6, 8]\n assert candidate(nums1 = [5, 5, 5, 5],nums2 = [6, 6, 6, 6],k = 7) == [6, 6, 6, 6, 5, 5, 5]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 9) == [9, 9, 8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 18) == [9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6, 7, 8, 9, 0],k = 9) == [5, 6, 7, 8, 9, 1, 2, 3, 0]\n assert candidate(nums1 = [0, 0, 0, 0],nums2 = [0, 0, 0, 0],k = 4) == [0, 0, 0, 0]\n assert candidate(nums1 = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],nums2 = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 10) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [1],k = 6) == [9, 8, 7, 6, 5, 4]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 9) == [9, 9, 8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [2, 2, 2, 2, 2],nums2 = [2, 2, 2, 2, 2],k = 8) == [2, 2, 2, 2, 2, 2, 2, 2]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 15) == [9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 0],k = 7) == [9, 1, 2, 3, 4, 5, 0]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 5) == [9, 9, 8, 7, 6]\n assert candidate(nums1 = [9, 3, 7, 8],nums2 = [5, 6, 2, 4, 3],k = 6) == [9, 8, 6, 2, 4, 3]\n assert candidate(nums1 = [9, 0, 9, 0, 9],nums2 = [9, 0, 9, 0, 9, 0, 9],k = 7) == [9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [9, 8, 7, 6, 5],k = 5) == [9, 8, 7, 6, 5]\n assert candidate(nums1 = [9, 9, 9, 9, 9, 9, 9, 9, 9],nums2 = [9, 9, 9, 9, 9, 9, 9, 9, 9],k = 15) == [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums1 = [9, 5, 3, 1, 7, 8],nums2 = [2, 6, 4, 0, 9, 5],k = 8) == [9, 9, 5, 5, 3, 1, 7, 8]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 10) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],nums2 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 15) == [9, 8, 7, 6, 5, 6, 7, 8, 9, 5, 4, 3, 2, 1, 0]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 0],k = 7) == [8, 1, 3, 5, 7, 9, 0]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6, 7, 8, 9, 10, 11, 12],k = 6) == [10, 11, 12, 1, 2, 3]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 8) == [9, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums1 = [5, 5, 5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5, 5, 5],k = 12) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [9, 8, 7, 6, 5],nums2 = [9, 8, 7, 6, 5],k = 10) == [9, 9, 8, 8, 7, 7, 6, 6, 5, 5]\n assert candidate(nums1 = [5, 4, 3, 2, 1],nums2 = [6, 7, 8, 9, 10],k = 5) == [10, 5, 4, 3, 2]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 0],k = 10) == [2, 4, 6, 8, 1, 3, 5, 7, 9, 0]\n assert candidate(nums1 = [8, 9, 0, 1, 2, 3, 4, 5, 6, 7],nums2 = [7, 6, 5, 4, 3, 2, 1, 0, 9, 8],k = 10) == [9, 9, 8, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(nums1 = [3, 5, 7, 9],nums2 = [1, 2, 4, 6, 8, 0],k = 6) == [9, 2, 4, 6, 8, 0]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 18) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [9, 9, 9, 9, 9],k = 7) == [9, 9, 9, 9, 9, 1, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 15) == [9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 4, 3, 2, 1]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [9, 9, 9, 9, 9],k = 7) == [9, 9, 9, 9, 9, 0, 0]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 9) == [9, 9, 8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9],nums2 = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8],k = 10) == [9, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10],k = 8) == [8, 9, 10, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [9, 5, 3, 1, 7],nums2 = [8, 6, 4, 2, 0],k = 10) == [9, 8, 6, 5, 4, 3, 2, 1, 7, 0]\n assert candidate(nums1 = [5, 3, 9, 7, 1],nums2 = [8, 6, 4, 2, 0],k = 7) == [9, 8, 7, 6, 4, 2, 1]\n assert candidate(nums1 = [8, 5, 2, 3, 9],nums2 = [6, 7, 4, 5, 1],k = 8) == [8, 7, 5, 5, 2, 3, 9, 1]\n assert candidate(nums1 = [9, 7, 5, 3, 1],nums2 = [8, 6, 4, 2, 0],k = 9) == [9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5],k = 9) == [5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],nums2 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 15) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 3]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == [1, 1, 1, 1, 1]\n assert candidate(nums1 = [9, 7, 5, 3, 1],nums2 = [1, 3, 5, 7, 9],k = 9) == [9, 7, 5, 3, 5, 7, 9, 3, 1]\n assert candidate(nums1 = [1, 2, 2, 1, 1],nums2 = [2, 2, 1, 1, 1],k = 5) == [2, 2, 2, 2, 1]\n assert candidate(nums1 = [9, 8, 7, 6, 5],nums2 = [5, 4, 3, 2, 1],k = 8) == [9, 8, 7, 6, 5, 5, 4, 3]\n assert candidate(nums1 = [3, 5, 7, 7, 8, 2, 1],nums2 = [6, 5, 3, 5, 6, 9, 8, 7],k = 10) == [9, 8, 7, 3, 5, 7, 7, 8, 2, 1]\n assert candidate(nums1 = [9, 9, 9, 9, 9],nums2 = [1, 1, 1, 1, 1],k = 5) == [9, 9, 9, 9, 9]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1],nums2 = [9, 9, 9, 9, 9, 9, 9],k = 10) == [9, 9, 9, 9, 9, 9, 9, 1, 1, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 17) == [9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 2, 1]\n assert candidate(nums1 = [9, 2, 5, 6, 3, 1],nums2 = [8, 6, 7, 4, 5, 9],k = 8) == [9, 8, 9, 2, 5, 6, 3, 1]\n assert candidate(nums1 = [5, 3, 9, 1, 2],nums2 = [8, 4, 7, 6, 0],k = 5) == [9, 8, 7, 6, 2]\n assert candidate(nums1 = [9, 9, 9, 9, 9],nums2 = [1, 2, 3, 4, 5],k = 9) == [9, 9, 9, 9, 9, 2, 3, 4, 5]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [9, 9, 8, 8, 7]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1],nums2 = [9, 9, 9, 9, 9, 9],k = 12) == [9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 8) == [9, 9, 8, 7, 6, 5, 4, 3]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11],nums2 = [2, 4, 6, 8, 10, 12],k = 11) == [4, 6, 8, 10, 12, 1, 3, 5, 7, 9, 11]\n assert candidate(nums1 = [9, 8, 7, 6, 5],nums2 = [4, 3, 2, 1, 0],k = 9) == [9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [9, 8, 7, 6, 5],nums2 = [5, 4, 3, 2, 1],k = 5) == [9, 8, 7, 6, 5]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [9, 8, 7],k = 8) == [9, 8, 7, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [3, 5, 7, 7, 6, 2, 1],nums2 = [8, 7, 6, 5, 3, 0, 9, 1],k = 9) == [9, 3, 5, 7, 7, 6, 2, 1, 1]\n assert candidate(nums1 = [5, 6, 7, 8, 9],nums2 = [1, 2, 3, 4, 5],k = 7) == [8, 9, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],k = 9) == [2, 2, 2, 2, 2, 2, 2, 2, 2]\n assert candidate(nums1 = [3, 4, 5, 1, 6],nums2 = [7, 8, 2, 9, 0],k = 8) == [8, 9, 3, 4, 5, 1, 6, 0]\n assert candidate(nums1 = [9, 5, 3, 1, 7, 8],nums2 = [6, 4, 2, 0, 9, 8],k = 7) == [9, 9, 8, 5, 3, 7, 8]\n assert candidate(nums1 = [9, 8, 7],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 10) == [9, 8, 7, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 0],nums2 = [0, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 15) == [9, 8, 7, 6, 5, 6, 7, 8, 9, 5, 4, 3, 2, 1, 0]\n assert candidate(nums1 = [0, 0, 0, 0],nums2 = [1, 1, 1, 1, 1, 1],k = 5) == [1, 1, 1, 1, 1]\n assert candidate(nums1 = [6, 7, 8, 9, 0],nums2 = [3, 4, 5, 6, 7, 8, 9],k = 10) == [8, 9, 3, 4, 5, 6, 7, 8, 9, 0]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],k = 8) == [5, 4, 3, 4, 5, 3, 2, 1]\n assert candidate(nums1 = [9, 8, 9, 8, 9],nums2 = [8, 9, 8, 9, 8],k = 9) == [9, 9, 8, 9, 8, 9, 8, 9, 8]\n assert candidate(nums1 = [5],nums2 = [5, 5, 5, 5, 5],k = 6) == [5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 10) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 0],k = 8) == [6, 8, 1, 3, 5, 7, 9, 0]\n assert candidate(nums1 = [1],nums2 = [2, 3, 4, 5, 6, 7, 8, 9],k = 6) == [5, 6, 7, 8, 9, 1]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [0, 2, 4, 6, 8],k = 10) == [1, 3, 5, 7, 9, 0, 2, 4, 6, 8]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [9, 9, 9, 9, 9],k = 5) == [9, 9, 9, 9, 9]\n assert candidate(nums1 = [9, 8, 7, 6, 5],nums2 = [9, 8, 7, 6, 5, 4],k = 7) == [9, 9, 8, 8, 7, 7, 6]\n assert candidate(nums1 = [6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6],k = 6) == [6, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [4, 4, 4, 4, 4],nums2 = [4, 4, 4, 4, 4],k = 9) == [4, 4, 4, 4, 4, 4, 4, 4, 4]\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2", "k"], "leetcode_dataset_entry_point": "Solution().maxNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxNumber = function(nums1, nums2, k) {", "container": null, "callable": "maxNumber", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 322, "task_id": "coin-change", "difficulty": "Medium", "problem_description": "You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.\nReturn the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.\nYou may assume that you have an infinite number of each kind of coin.\n \nExample 1:\n\nInput: coins = [1,2,5], amount = 11\nOutput: 3\nExplanation: 11 = 5 + 5 + 1\n\nExample 2:\n\nInput: coins = [2], amount = 3\nOutput: -1\n\nExample 3:\n\nInput: coins = [1], amount = 0\nOutput: 0\n\n \nConstraints:\n\n1 <= coins.length <= 12\n1 <= coins[i] <= 231 - 1\n0 <= amount <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(coins = [186, 419, 83, 408],amount = 6249) == 20\n assert candidate(coins = [3, 7, 405, 436],amount = 8839) == 25\n assert candidate(coins = [3, 7, 405],amount = 8839) == 71\n assert candidate(coins = [2, 5, 10, 1],amount = 27) == 4\n assert candidate(coins = [1, 2, 5],amount = 1) == 1\n assert candidate(coins = [1, 3, 4, 5],amount = 7) == 2\n assert candidate(coins = [1],amount = 0) == 0\n assert candidate(coins = [5, 7, 8],amount = 100) == 13\n assert candidate(coins = [1, 3, 4],amount = 6) == 2\n assert candidate(coins = [4, 2, 1],amount = 11) == 4\n assert candidate(coins = [1, 3, 4],amount = 6) == 2\n assert candidate(coins = [1, 2, 5],amount = 11) == 3\n assert candidate(coins = [1, 2, 5],amount = 0) == 0\n assert candidate(coins = [2],amount = 3) == -1\n assert candidate(coins = [70, 171, 358, 439, 286],amount = 9963) == 27\n assert candidate(coins = [3, 7, 405, 88, 43],amount = 6803) == 24\n assert candidate(coins = [5, 7],amount = 15) == 3\n assert candidate(coins = [18, 27, 41],amount = 987) == 26\n assert candidate(coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048],amount = 4095) == 12\n assert candidate(coins = [5, 15, 25, 50],amount = 3000) == 60\n assert candidate(coins = [1, 2, 4, 8, 16],amount = 2048) == 128\n assert candidate(coins = [10, 20, 30, 40, 50, 60],amount = 1234) == -1\n assert candidate(coins = [3, 5, 7, 9, 11],amount = 9876) == 898\n assert candidate(coins = [18, 24, 28],amount = 100) == 4\n assert candidate(coins = [17, 29, 31, 37, 41, 43],amount = 5000) == 118\n assert candidate(coins = [3, 5],amount = 11) == 3\n assert candidate(coins = [17, 29, 41, 53, 65],amount = 8300) == 136\n assert candidate(coins = [11, 22, 33, 44, 55],amount = 6600) == 120\n assert candidate(coins = [34, 7, 23, 32, 5, 62],amount = 9999) == 164\n assert candidate(coins = [1, 5, 25, 50],amount = 9999) == 208\n assert candidate(coins = [2, 3, 7, 10],amount = 500) == 50\n assert candidate(coins = [7, 14, 21, 28, 35, 42, 49, 56],amount = 1000) == -1\n assert candidate(coins = [3, 6, 9, 12, 15],amount = 1000) == -1\n assert candidate(coins = [1, 5, 10, 25, 50],amount = 78) == 5\n assert candidate(coins = [10, 20, 30, 40, 50],amount = 9999) == -1\n assert candidate(coins = [1, 7, 11],amount = 100) == 10\n assert candidate(coins = [2, 3, 6, 12, 24, 48],amount = 500) == 13\n assert candidate(coins = [1, 2, 4, 8, 16, 32, 64],amount = 1023) == 21\n assert candidate(coins = [1],amount = 10000) == 10000\n assert candidate(coins = [7, 14, 30, 50, 80],amount = 287) == 6\n assert candidate(coins = [2, 4, 8, 16, 32, 64, 128],amount = 1023) == -1\n assert candidate(coins = [1, 2, 5, 10, 20, 50, 100, 200],amount = 10002) == 51\n assert candidate(coins = [2, 3, 5, 7, 11, 13],amount = 5000) == 386\n assert candidate(coins = [3, 5, 7, 9, 11],amount = 10000) == 910\n assert candidate(coins = [7],amount = 100) == -1\n assert candidate(coins = [1, 5, 10, 25, 50, 100],amount = 99999) == 1007\n assert candidate(coins = [1, 2, 3, 5, 10],amount = 5000) == 500\n assert candidate(coins = [3, 6, 9, 12, 15],amount = 444) == 30\n assert candidate(coins = [3, 5, 7, 11, 13],amount = 997) == 77\n assert candidate(coins = [1, 3, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31],amount = 100) == 4\n assert candidate(coins = [7, 15, 23, 31],amount = 750) == 26\n assert candidate(coins = [23, 14, 5, 12],amount = 5000) == 220\n assert candidate(coins = [11, 23, 37, 41, 43, 47, 53],amount = 12345) == 235\n assert candidate(coins = [1, 5, 10, 25, 50, 100],amount = 357) == 7\n assert candidate(coins = [18, 24, 27, 36, 50],amount = 999) == 21\n assert candidate(coins = [1, 5, 10, 25, 50],amount = 9999) == 206\n assert candidate(coins = [1, 2, 5, 10, 20, 50, 100, 200],amount = 9999) == 56\n assert candidate(coins = [2, 5, 10, 25],amount = 100) == 4\n assert candidate(coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048],amount = 1048575) == 522\n assert candidate(coins = [7, 15, 23, 42],amount = 999) == 27\n assert candidate(coins = [7, 17, 23, 29, 31],amount = 1000) == 34\n assert candidate(coins = [1, 3, 4, 6, 8, 10],amount = 450) == 45\n assert candidate(coins = [1, 5, 10, 20, 50, 100],amount = 10001) == 101\n assert candidate(coins = [2, 3, 7],amount = 100) == 15\n assert candidate(coins = [5, 11, 23, 37, 41, 43, 61, 71, 73, 79, 83, 89],amount = 999) == 13\n assert candidate(coins = [1, 10, 100, 1000],amount = 9999) == 36\n assert candidate(coins = [1, 10, 25, 50, 100],amount = 12345) == 126\n assert candidate(coins = [186, 419, 83, 408],amount = 6249) == 20\n assert candidate(coins = [2, 3, 7],amount = 27) == 5\n assert candidate(coins = [3, 6, 9, 12, 15],amount = 9000) == 600\n assert candidate(coins = [1, 2, 5, 10, 20, 50, 100],amount = 9999) == 105\n assert candidate(coins = [5, 9, 12, 27, 31],amount = 1276) == 42\n assert candidate(coins = [2, 3, 7, 11, 19, 23],amount = 987) == 44\n assert candidate(coins = [10, 25, 50, 100],amount = 9876) == -1\n assert candidate(coins = [2, 6, 10, 14],amount = 9999) == -1\n assert candidate(coins = [10, 22, 35],amount = 1000) == 30\n assert candidate(coins = [2, 5, 11, 17, 23],amount = 1000) == 44\n assert candidate(coins = [23, 37, 41, 53, 67, 71],amount = 8675309) == 122189\n assert candidate(coins = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],amount = 12) == 12\n assert candidate(coins = [1, 6, 10],amount = 111) == 12\n assert candidate(coins = [7, 14, 33, 19, 100],amount = 12345) == 126\n assert candidate(coins = [13, 21, 34, 55, 89, 144],amount = 6765) == 51\n assert candidate(coins = [1, 2, 5, 10],amount = 27) == 4\n assert candidate(coins = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29],amount = 8000) == 277\n assert candidate(coins = [1, 5, 10, 25],amount = 99) == 9\n assert candidate(coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048],amount = 1023) == 10\n assert candidate(coins = [10, 15, 20],amount = 120) == 6\n assert candidate(coins = [1, 2, 3, 4, 5],amount = 10000) == 2000\n assert candidate(coins = [1, 11, 21, 31],amount = 10000) == 330\n assert candidate(coins = [1, 3, 5, 7, 9],amount = 10000) == 1112\n assert candidate(coins = [1, 2, 5, 10, 20, 50, 100, 200],amount = 399) == 8\n assert candidate(coins = [13, 19, 23, 29, 31, 37, 41],amount = 9998) == 246\n assert candidate(coins = [1, 6, 13, 37, 150],amount = 9999) == 71\n assert candidate(coins = [10, 20, 50, 100, 200],amount = 10000) == 50\n assert candidate(coins = [1, 5, 10, 25, 50],amount = 87) == 5\n assert candidate(coins = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],amount = 10000) == 1000\n assert candidate(coins = [100, 200, 300, 400, 500],amount = 9999) == -1\n assert candidate(coins = [1, 3, 4, 5],amount = 150) == 30\n assert candidate(coins = [2, 5, 10, 20],amount = 98) == 9\n assert candidate(coins = [1, 2, 5, 10, 25],amount = 9999) == 403\n assert candidate(coins = [10, 25, 50],amount = 9999) == -1\n assert candidate(coins = [11, 17, 29, 31],amount = 10000) == 324\n assert candidate(coins = [7, 14, 28, 29],amount = 10000) == 345\n assert candidate(coins = [10, 25, 50],amount = 99) == -1\n assert candidate(coins = [1, 3, 4, 5, 7],amount = 10000) == 1429\n assert candidate(coins = [100, 50, 20, 10, 5, 1],amount = 19876) == 202\n assert candidate(coins = [1, 3, 4, 5],amount = 15) == 3\n assert candidate(coins = [2, 5, 10, 20, 50, 100],amount = 9999) == 105\n assert candidate(coins = [13, 17, 19],amount = 1234) == 66\n assert candidate(coins = [1, 2, 5, 10, 20, 50, 100],amount = 3689) == 42\n assert candidate(coins = [335, 23, 102, 75, 402],amount = 9783) == 30\n assert candidate(coins = [2, 5, 10, 20, 50],amount = 399) == 12\n assert candidate(coins = [17, 29, 31, 37, 41, 43],amount = 8942) == 208\n assert candidate(coins = [2, 5, 10, 20, 50, 100],amount = 363) == 9\n assert candidate(coins = [12, 25, 50, 100, 200],amount = 3678) == 37\n assert candidate(coins = [13, 23, 33, 43, 53],amount = 888) == 26\n assert candidate(coins = [3, 6, 9, 12, 15, 18],amount = 100) == -1\n assert candidate(coins = [11, 17, 23],amount = 457) == 23\n assert candidate(coins = [2, 5, 10, 25],amount = 9999) == 403\n assert candidate(coins = [29, 81, 135, 50, 1],amount = 2101) == 19\n assert candidate(coins = [33, 37, 41, 43, 47, 53, 59],amount = 10000) == 170\n assert candidate(coins = [5, 11, 13],amount = 10000) == 770\n assert candidate(coins = [10, 20, 50, 100],amount = 345) == -1\n assert candidate(coins = [5, 10, 20, 50, 100],amount = 4321) == -1\n assert candidate(coins = [13, 112, 197, 84, 205],amount = 4873) == 26\n assert candidate(coins = [33, 77, 111, 155],amount = 8500) == 60\n assert candidate(coins = [7, 15, 23],amount = 1000) == 48\n"}, "metadata": {"canonical_parameter_names": ["coins", "amount"], "leetcode_dataset_entry_point": "Solution().coinChange", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var coinChange = function(coins, amount) {", "container": null, "callable": "coinChange", "parameters": [{"name": "coins", "type": "number[]"}, {"name": "amount", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 326, "task_id": "power-of-three", "difficulty": "Easy", "problem_description": "Given an integer n, return true if it is a power of three. Otherwise, return false.\nAn integer n is a power of three, if there exists an integer x such that n == 3x.\n \nExample 1:\n\nInput: n = 27\nOutput: true\nExplanation: 27 = 33\n\nExample 2:\n\nInput: n = 0\nOutput: false\nExplanation: There is no x where 3x = 0.\n\nExample 3:\n\nInput: n = -1\nOutput: false\nExplanation: There is no x where 3x = (-1).\n\n \nConstraints:\n\n-231 <= n <= 231 - 1\n\n \nFollow up: Could you solve it without loops/recursion?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == True\n assert candidate(n = 45) == False\n assert candidate(n = 729) == True\n assert candidate(n = 2147483647) == False\n assert candidate(n = 19683) == True\n assert candidate(n = 100) == False\n assert candidate(n = 244) == False\n assert candidate(n = 10) == False\n assert candidate(n = -1) == False\n assert candidate(n = -27) == False\n assert candidate(n = 0) == False\n assert candidate(n = -2147483648) == False\n assert candidate(n = 27) == True\n assert candidate(n = 6561) == True\n assert candidate(n = 2187) == True\n assert candidate(n = 1000000000) == False\n assert candidate(n = 81) == True\n assert candidate(n = -81) == False\n assert candidate(n = -243) == False\n assert candidate(n = 9) == True\n assert candidate(n = -3) == False\n assert candidate(n = 1) == True\n assert candidate(n = 243) == True\n assert candidate(n = 59049) == True\n assert candidate(n = 14124) == False\n assert candidate(n = 239148450531289) == False\n assert candidate(n = 32805) == False\n assert candidate(n = 2147483646) == False\n assert candidate(n = 797161567330890596) == False\n assert candidate(n = 12157665459056928802) == False\n assert candidate(n = 4096) == False\n assert candidate(n = -9) == False\n assert candidate(n = 82) == False\n assert candidate(n = 387420489) == True\n assert candidate(n = 1594323) == True\n assert candidate(n = 1000) == False\n assert candidate(n = 5) == False\n assert candidate(n = 28) == False\n assert candidate(n = 12157665459056928801) == True\n assert candidate(n = -19683) == False\n assert candidate(n = -162) == False\n assert candidate(n = 4) == False\n assert candidate(n = 59050) == False\n assert candidate(n = 2) == False\n assert candidate(n = 1162261469) == False\n assert candidate(n = -6561) == False\n assert candidate(n = 80) == False\n assert candidate(n = 14348907) == True\n assert candidate(n = 1073741824) == False\n assert candidate(n = 282429536481) == True\n assert candidate(n = 100000) == False\n assert candidate(n = 231) == False\n assert candidate(n = 4052555153018976267) == True\n assert candidate(n = 3645) == False\n assert candidate(n = -59049) == False\n assert candidate(n = 18) == False\n assert candidate(n = 500) == False\n assert candidate(n = 1594322) == False\n assert candidate(n = 20) == False\n assert candidate(n = 177147) == True\n assert candidate(n = -45) == False\n assert candidate(n = 19) == False\n assert candidate(n = 1162261467) == True\n assert candidate(n = 2188) == False\n assert candidate(n = 531441) == True\n assert candidate(n = 24) == False\n assert candidate(n = 129140163) == True\n assert candidate(n = 43046721) == True\n assert candidate(n = -1046527) == False\n assert candidate(n = 1162261468) == False\n assert candidate(n = 1162261466) == False\n assert candidate(n = 3486784401) == True\n assert candidate(n = 200) == False\n assert candidate(n = 6) == False\n assert candidate(n = 1111111111) == False\n assert candidate(n = 2125764400) == False\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().isPowerOfThree", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPowerOfThree = function(n) {", "container": null, "callable": "isPowerOfThree", "parameters": [{"name": "n", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 327, "task_id": "count-of-range-sum", "difficulty": "Hard", "problem_description": "Given an integer array nums and two integers lower and upper, return the number of range sums that lie in [lower, upper] inclusive.\nRange sum S(i, j) is defined as the sum of the elements in nums between indices i and j inclusive, where i <= j.\n \nExample 1:\n\nInput: nums = [-2,5,-1], lower = -2, upper = 2\nOutput: 3\nExplanation: The three ranges are: [0,0], [2,2], and [0,2] and their respective sums are: -2, -1, 2.\n\nExample 2:\n\nInput: nums = [0], lower = 0, upper = 0\nOutput: 1\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-231 <= nums[i] <= 231 - 1\n-105 <= lower <= upper <= 105\nThe answer is guaranteed to fit in a 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3],lower = -5,upper = 5) == 24\n assert candidate(nums = [100, 200, 300, 400, 500],lower = 150,upper = 1000) == 11\n assert candidate(nums = [-1, -2, -3, -4, -5],lower = -10,upper = -5) == 7\n assert candidate(nums = [1, 2, 3, 4, 5],lower = 1,upper = 5) == 7\n assert candidate(nums = [100, 100, 100, 100, 100],lower = 200,upper = 400) == 9\n assert candidate(nums = [0, 0, 0, 0, 0],lower = 0,upper = 0) == 15\n assert candidate(nums = [-2, 5, -1],lower = -2,upper = 2) == 3\n assert candidate(nums = [5, 5, 5, 5, 5],lower = 10,upper = 20) == 9\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000],lower = -2000000000,upper = 2000000000) == 10\n assert candidate(nums = [2147483647, -2147483648, -1, 0],lower = -1,upper = 1) == 4\n assert candidate(nums = [1, 2, 3],lower = 3,upper = 6) == 4\n assert candidate(nums = [0],lower = 0,upper = 0) == 1\n assert candidate(nums = [-1, -2, -3, -4, -5],lower = -10,upper = -1) == 12\n assert candidate(nums = [-1, -2, -3, -4, -5],lower = -10,upper = -3) == 10\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648],lower = -4294967295,upper = 4294967295) == 10\n assert candidate(nums = [3, -2, 1, 5, 4],lower = -3,upper = 7) == 11\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1],lower = -1,upper = 1) == 55\n assert candidate(nums = [1, 2, 3, 4, 5],lower = 1,upper = 10) == 12\n assert candidate(nums = [1, -1, 1, -1, 1, -1],lower = 0,upper = 1) == 15\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],lower = 0,upper = 0) == 210\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1],lower = -15,upper = -5) == 37\n assert candidate(nums = [100, -50, 200, -150, 300, -200, 400, -250, 500, -300],lower = 100,upper = 600) == 39\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],lower = -1,upper = 1) == 55\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],lower = 15,upper = 25) == 21\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],lower = 100,upper = 200) == 24\n assert candidate(nums = [1, -1, 1, -1, 1, -1],lower = 0,upper = 1) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],lower = 15,upper = 30) == 19\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125],lower = 500000000,upper = 2000000000) == 19\n assert candidate(nums = [5, 4, 3, 2, 1],lower = 2,upper = 7) == 8\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],lower = 1500,upper = 3500) == 23\n assert candidate(nums = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20],lower = -20,upper = 20) == 210\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],lower = -100,upper = -50) == 60\n assert candidate(nums = [-10, -20, -30, -40, -50],lower = -150,upper = -50) == 10\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],lower = -200,upper = -100) == 14\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = -2,upper = 2) == 55\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],lower = -1,upper = 1) == 55\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = 0,upper = 2) == 40\n assert candidate(nums = [100, -200, 300, -400, 500, -600, 700, -800, 900, -1000],lower = -500,upper = 500) == 40\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],lower = 100,upper = 500) == 37\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],lower = 15,upper = 30) == 19\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],lower = -500,upper = -100) == 37\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],lower = 50,upper = 100) == 40\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = -2,upper = 2) == 55\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000],lower = 5000000000,upper = 6000000000) == 1\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],lower = 1500,upper = 3000) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],lower = 10,upper = 20) == 14\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],lower = 5,upper = 20) == 24\n assert candidate(nums = [-1000000000, -1000000000, -1000000000, -1000000000, -1000000000],lower = -6000000000,upper = -5000000000) == 1\n assert candidate(nums = [100, -100, 200, -200, 300, -300, 400, -400, 500, -500, 600, -600, 700, -700, 800, -800, 900, -900, 1000, -1000],lower = -500,upper = 500) == 145\n assert candidate(nums = [100, 200, 300, 400, 500],lower = 150,upper = 1200) == 12\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000],lower = 500000000,upper = 1500000000) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],lower = 5,upper = 10) == 21\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = -5,upper = 5) == 465\n assert candidate(nums = [10, 20, 30, 40, 50],lower = 100,upper = 150) == 4\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50],lower = -50,upper = 50) == 55\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5],lower = -5,upper = 5) == 55\n assert candidate(nums = [5, -1, 5, -1, 5, -1, 5, -1, 5, -1, 5, -1, 5, -1, 5, -1, 5, -1, 5, -1],lower = 0,upper = 10) == 72\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],lower = -200,upper = 0) == 206\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],lower = -30,upper = -15) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1],lower = 5,upper = 15) == 37\n assert candidate(nums = [5, -1, 5, -1, 5, -1, 5, -1, 5, -1],lower = 1,upper = 9) == 32\n assert candidate(nums = [1000000000, 1000000000, -2000000000, 0, 1000000000, -1000000000],lower = -5000000000,upper = 5000000000) == 21\n assert candidate(nums = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10],lower = -10,upper = 10) == 55\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],lower = 25,upper = 45) == 13\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],lower = 150,upper = 450) == 30\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],lower = -30,upper = -15) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],lower = 55,upper = 100) == 73\n assert candidate(nums = [1, -100, 100, -10000, 10000, -1000000, 1000000, 1, -1, 10, -10],lower = -1000000,upper = 1000000) == 64\n assert candidate(nums = [1, 2, 3, -6, 2, 3, -6, 2, 3],lower = 1,upper = 5) == 23\n assert candidate(nums = [5, -5, 5, -5, 5, -5, 5, -5, 5, -5],lower = -10,upper = 10) == 55\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = -1,upper = 1) == 55\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],lower = -450,upper = -150) == 30\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1],lower = -5,upper = 5) == 90\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],lower = 0,upper = 0) == 55\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],lower = 0,upper = 200) == 206\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],lower = 0,upper = 5) == 40\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000],lower = -2000000000,upper = 2000000000) == 21\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = -1,upper = 1) == 210\n assert candidate(nums = [30, -10, 20, -20, 10, -10, 20, -20, 10, -10, 20, -20, 10, -10, 20, -20, 10, -10, 20, -20],lower = 0,upper = 20) == 135\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],lower = 15,upper = 30) == 31\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],lower = 5,upper = 15) == 19\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],lower = 3,upper = 7) == 30\n assert candidate(nums = [1000000000, 500000000, -1500000000, 2000000000, -2000000000, 1000000000],lower = -3000000000,upper = 3000000000) == 21\n assert candidate(nums = [100000000, 200000000, 300000000, -100000000, -200000000, -300000000],lower = 100000000,upper = 500000000) == 10\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],lower = -20,upper = -10) == 14\n assert candidate(nums = [100, 200, 300, 400, 500],lower = 500,upper = 1500) == 10\n assert candidate(nums = [-10, 10, -10, 10, -10, 10, -10, 10, -10, 10],lower = -20,upper = 20) == 55\n assert candidate(nums = [1, 2, 3, 4, 5, -5, -4, -3, -2, -1],lower = 0,upper = 10) == 27\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],lower = 5000000000,upper = 10000000000) == 21\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],lower = -20,upper = -5) == 24\n assert candidate(nums = [2147483647, -2147483647, 2147483647, -2147483647, 2147483647],lower = -4294967295,upper = 4294967295) == 15\n assert candidate(nums = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 10000000000],lower = -5000000000,upper = 15000000000) == 24\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1],lower = 0,upper = 0) == 25\n assert candidate(nums = [1, 2, 3, 4, 5, -5, -4, -3, -2, -1],lower = -10,upper = 0) == 27\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],lower = -15,upper = -5) == 19\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5],lower = -10,upper = 10) == 54\n assert candidate(nums = [1000000, -1000000, 1000000, -1000000, 1000000, -1000000, 1000000, -1000000],lower = 0,upper = 1) == 16\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],lower = 10000000000,upper = 15000000000) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],lower = 50,upper = 100) == 60\n assert candidate(nums = [-1, 0, 1, -1, 0, 1, -1, 0, 1, -1],lower = -1,upper = 1) == 55\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],lower = 0,upper = 0) == 55\n"}, "metadata": {"canonical_parameter_names": ["nums", "lower", "upper"], "leetcode_dataset_entry_point": "Solution().countRangeSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countRangeSum = function(nums, lower, upper) {", "container": null, "callable": "countRangeSum", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "lower", "type": "number"}, {"name": "upper", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 328, "task_id": "odd-even-linked-list", "difficulty": "Medium", "problem_description": "Given the head of a singly linked list, group all the nodes with odd indices together followed by the nodes with even indices, and return the reordered list.\nThe first node is considered odd, and the second node is even, and so on.\nNote that the relative order inside both the even and odd groups should remain as it was in the input.\nYou must solve the problem in O(1) extra space complexity and O(n) time complexity.\n \nExample 1:\n\n\nInput: head = [1,2,3,4,5]\nOutput: [1,3,5,2,4]\n\nExample 2:\n\n\nInput: head = [2,1,3,5,6,4,7]\nOutput: [2,3,6,7,1,5,4]\n\n \nConstraints:\n\nThe number of nodes in the linked list is in the range [0, 104].\n-106 <= Node.val <= 106\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(head = list_node([1, 2, 3])), list_node([1, 3, 2]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90])), list_node([10, 30, 50, 70, 90, 20, 40, 60, 80]))\n assert is_same_list(candidate(head = list_node([2, 1, 3, 5, 6, 4, 7])), list_node([2, 3, 6, 7, 1, 5, 4]))\n assert is_same_list(candidate(head = list_node([0])), list_node([0]))\n assert is_same_list(candidate(head = list_node([-1, 0, 1, -2, 2, -3, 3])), list_node([-1, 1, 2, 3, 0, -2, -3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5])), list_node([1, 3, 5, 2, 4]))\n assert candidate(head = list_node([])) == None\n assert is_same_list(candidate(head = list_node([1, 2])), list_node([1, 2]))\n assert is_same_list(candidate(head = list_node([1])), list_node([1]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4])), list_node([1, 3, 2, 4]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6])), list_node([1, 3, 5, 2, 4, 6]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 10])), list_node([1, 5, 9, 4, 8, 3, 7, 2, 6, 10]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1])), list_node([5, 3, 1, 4, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59])), list_node([1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59]))\n assert is_same_list(candidate(head = list_node([5, 3, 8, 6, 2, 4, 7, 1, 9])), list_node([5, 8, 2, 7, 9, 3, 6, 4, 1]))\n assert is_same_list(candidate(head = list_node([2, 3, 1, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14])), list_node([2, 1, 4, 6, 8, 10, 12, 14, 3, 5, 7, 9, 11, 13, 15]))\n assert is_same_list(candidate(head = list_node([-10, -20, -30, -40, -50, -60, -70, -80, -90, -100, -110, -120, -130, -140, -150])), list_node([-10, -30, -50, -70, -90, -110, -130, -150, -20, -40, -60, -80, -100, -120, -140]))\n assert is_same_list(candidate(head = list_node([10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11])), list_node([10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30])), list_node([-1, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, -23, -25, -27, -29, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20, -22, -24, -26, -28, -30]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])), list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5])), list_node([1, 2, 3, 4, 4, 5, 5, 5, 2, 3, 3, 4, 4, 5, 5]))\n assert is_same_list(candidate(head = list_node([5, 3, 8, 6, 2, 4, 7, 1, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([5, 8, 2, 7, 9, 11, 13, 15, 17, 19, 3, 6, 4, 1, 10, 12, 14, 16, 18, 20]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11])), list_node([5, 3, 1, 9, 7, 15, 13, 11, 4, 2, 10, 8, 6, 14, 12]))\n assert is_same_list(candidate(head = list_node([10, 21, 32, 43, 54, 65, 76, 87, 98, 109])), list_node([10, 32, 54, 76, 98, 21, 43, 65, 87, 109]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39])), list_node([1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([999999, -999999, 999998, -999998, 999997, -999997, 999996, -999996])), list_node([999999, 999998, 999997, 999996, -999999, -999998, -999997, -999996]))\n assert is_same_list(candidate(head = list_node([1000000, -1000000, 500000, -500000, 250000, -250000, 125000, -125000])), list_node([1000000, 500000, 250000, 125000, -1000000, -500000, -250000, -125000]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120])), list_node([10, 30, 50, 70, 90, 110, 20, 40, 60, 80, 100, 120]))\n assert is_same_list(candidate(head = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]))\n assert is_same_list(candidate(head = list_node([1, 10, 2, 9, 3, 8, 4, 7, 5, 6])), list_node([1, 2, 3, 4, 5, 10, 9, 8, 7, 6]))\n assert is_same_list(candidate(head = list_node([1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([999999, -999999, 999998, -999998, 999997, -999997, 999996, -999996, 999995, -999995, 999994, -999994, 999993, -999993, 999992, -999992, 999991, -999991, 999990, -999990])), list_node([999999, 999998, 999997, 999996, 999995, 999994, 999993, 999992, 999991, 999990, -999999, -999998, -999997, -999996, -999995, -999994, -999993, -999992, -999991, -999990]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([10, 8, 6, 4, 2, 9, 7, 5, 3, 1]))\n assert is_same_list(candidate(head = list_node([100000, -100000, 100000, -100000, 100000, -100000])), list_node([100000, 100000, 100000, -100000, -100000, -100000]))\n assert is_same_list(candidate(head = list_node([10000, -10000, 5000, -5000, 2500, -2500, 1250, -1250, 625, -625, 312, -312, 156, -156, 78, -78, 39, -39, 19, -19])), list_node([10000, 5000, 2500, 1250, 625, 312, 156, 78, 39, 19, -10000, -5000, -2500, -1250, -625, -312, -156, -78, -39, -19]))\n assert is_same_list(candidate(head = list_node([-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5])), list_node([-5, -3, -1, 1, 3, 5, -4, -2, 0, 2, 4]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49])), list_node([1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])), list_node([1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 11, 13, 15, 17, 19, 12, 14, 16, 18, 20])), list_node([1, 5, 9, 4, 8, 11, 15, 19, 14, 18, 3, 7, 2, 6, 10, 13, 17, 12, 16, 20]))\n assert is_same_list(candidate(head = list_node([10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 110])), list_node([10, 32, 54, 76, 98, 110, 21, 43, 65, 87, 109]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([-1, -3, -5, -7, -9, -2, -4, -6, -8, -10]))\n assert is_same_list(candidate(head = list_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])), list_node([0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4])), list_node([1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([1, 3, 2, 4, 5, 7, 6, 9, 8, 11, 10])), list_node([1, 2, 5, 6, 8, 10, 3, 4, 7, 9, 11]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([100, -200, 300, 0, 500, 600, -700, 800, 900, 1000])), list_node([100, 300, 500, -700, 900, -200, 0, 600, 800, 1000]))\n assert is_same_list(candidate(head = list_node([1000000, -1000000, 2000000, -2000000, 3000000, -3000000])), list_node([1000000, 2000000, 3000000, -1000000, -2000000, -3000000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9])), list_node([9, 7, 5, 3, 1, -1, -3, -5, -7, -9, 8, 6, 4, 2, 0, -2, -4, -6, -8]))\n assert is_same_list(candidate(head = list_node([100, -200, 300, -400, 500, -600, 700, -800, 900, -1000])), list_node([100, 300, 500, 700, 900, -200, -400, -600, -800, -1000]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_list(candidate(head = list_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])), list_node([-1, -3, -5, -7, -9, -11, -13, -15, -2, -4, -6, -8, -10, -12, -14]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 2, 4, 6, 8, 10, 12, 14]))\n assert is_same_list(candidate(head = list_node([5, 3, 1, 4, 2, 6, 8, 7, 9, 11, 13, 10, 12, 14, 15])), list_node([5, 1, 2, 8, 9, 13, 12, 15, 3, 4, 6, 7, 11, 10, 14]))\n assert is_same_list(candidate(head = list_node([100, 200, 300, 400, 500, 600, 700, 800, 900, 1000])), list_node([100, 300, 500, 700, 900, 200, 400, 600, 800, 1000]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50]))\n assert is_same_list(candidate(head = list_node([10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10])), list_node([10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, 9, 7, 5, 3, 1, -1, -3, -5, -7, -9]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210])), list_node([10, 30, 50, 70, 90, 110, 130, 150, 170, 190, 210, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150])), list_node([10, 30, 50, 70, 90, 110, 130, 150, 20, 40, 60, 80, 100, 120, 140]))\n assert is_same_list(candidate(head = list_node([1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]))\n assert is_same_list(candidate(head = list_node([999999, -999999, 999999, -999999, 999999, -999999, 999999, -999999, 999999, -999999, 999999, -999999])), list_node([999999, 999999, 999999, 999999, 999999, 999999, -999999, -999999, -999999, -999999, -999999, -999999]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 1, 3, 5, 7, 9])), list_node([2, 6, 10, 3, 7, 4, 8, 1, 5, 9]))\n assert is_same_list(candidate(head = list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20])), list_node([1, 5, 9, 13, 17, 2, 6, 10, 14, 18, 3, 7, 11, 15, 19, 4, 8, 12, 16, 20]))\n assert is_same_list(candidate(head = list_node([2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40])), list_node([2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40]))\n assert is_same_list(candidate(head = list_node([0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1])), list_node([0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]))\n assert is_same_list(candidate(head = list_node([5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5])), list_node([5, 3, 1, -1, -3, -5, 4, 2, 0, -2, -4]))\n assert is_same_list(candidate(head = list_node([100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991])), list_node([100000, 99998, 99996, 99994, 99992, 99999, 99997, 99995, 99993, 99991]))\n assert is_same_list(candidate(head = list_node([10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110])), list_node([10, 30, 50, 70, 90, 110, 20, 40, 60, 80, 100]))\n assert is_same_list(candidate(head = list_node([1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1])), list_node([1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]))\n assert is_same_list(candidate(head = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([9, 7, 5, 3, 1, 8, 6, 4, 2]))\n assert is_same_list(candidate(head = list_node([1000000, -1000000, 500000, -500000, 250000, -250000, 125000, -125000, 62500, -62500])), list_node([1000000, 500000, 250000, 125000, 62500, -1000000, -500000, -250000, -125000, -62500]))\n assert is_same_list(candidate(head = list_node([100000, -100000, 50000, -50000, 25000, -25000, 12500, -12500])), list_node([100000, 50000, 25000, 12500, -100000, -50000, -25000, -12500]))\n assert is_same_list(candidate(head = list_node([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3])), list_node([1, 1, 1, 2, 2, 3, 3, 3, 1, 1, 2, 2, 2, 3, 3]))\n assert is_same_list(candidate(head = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])), list_node([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24]))\n"}, "metadata": {"canonical_parameter_names": ["head"], "leetcode_dataset_entry_point": "Solution().oddEvenList", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var oddEvenList = function(head) {", "container": null, "callable": "oddEvenList", "parameters": [{"name": "head", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 329, "task_id": "longest-increasing-path-in-a-matrix", "difficulty": "Hard", "problem_description": "Given an m x n integers matrix, return the length of the longest increasing path in matrix.\nFrom each cell, you can either move in four directions: left, right, up, or down. You may not move diagonally or move outside the boundary (i.e., wrap-around is not allowed).\n \nExample 1:\n\n\nInput: matrix = [[9,9,4],[6,6,8],[2,1,1]]\nOutput: 4\nExplanation: The longest increasing path is [1, 2, 6, 9].\n\nExample 2:\n\n\nInput: matrix = [[3,4,5],[3,2,6],[2,2,1]]\nOutput: 4\nExplanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.\n\nExample 3:\n\nInput: matrix = [[1]]\nOutput: 1\n\n \nConstraints:\n\nm == matrix.length\nn == matrix[i].length\n1 <= m, n <= 200\n0 <= matrix[i][j] <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[1, 2, 3], [6, 5, 4], [7, 8, 9]]) == 9\n assert candidate(matrix = [[7, 8, 9], [9, 7, 8], [8, 9, 7]]) == 3\n assert candidate(matrix = [[1]]) == 1\n assert candidate(matrix = [[1, 2, 3, 4, 5], [16, 17, 24, 23, 6], [15, 26, 25, 22, 7], [14, 21, 18, 19, 8], [13, 12, 11, 10, 9]]) == 20\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == 5\n assert candidate(matrix = [[9, 9, 4], [6, 6, 8], [2, 1, 1]]) == 4\n assert candidate(matrix = [[3, 3, 3], [3, 3, 3], [3, 3, 3]]) == 1\n assert candidate(matrix = [[3, 4, 5], [3, 2, 6], [2, 2, 1]]) == 4\n assert candidate(matrix = [[1, 3, 5], [2, 6, 4], [7, 8, 9]]) == 5\n assert candidate(matrix = [[1, 2, 3, 4], [12, 13, 14, 5], [11, 16, 15, 6], [10, 9, 8, 7]]) == 16\n assert candidate(matrix = [[1, 20, 3, 10, 5], [6, 7, 8, 9, 11], [12, 13, 14, 15, 16], [17, 18, 19, 2, 1], [21, 22, 23, 24, 25]]) == 9\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [1, 3, 5, 7, 9]]) == 6\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20]]) == 8\n assert candidate(matrix = [[5, 8, 3, 2], [4, 10, 9, 7], [1, 6, 13, 12], [14, 11, 16, 15]]) == 5\n assert candidate(matrix = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9]]) == 9\n assert candidate(matrix = [[3, 3, 3, 3, 3], [3, 2, 2, 2, 3], [3, 2, 1, 2, 3], [3, 2, 2, 2, 3], [3, 3, 3, 3, 3]]) == 3\n assert candidate(matrix = [[10, 20, 30, 40], [41, 42, 43, 44], [45, 46, 47, 48], [49, 50, 51, 52]]) == 7\n assert candidate(matrix = [[1, 2, 3, 4], [12, 13, 14, 5], [11, 16, 15, 6], [10, 9, 8, 7]]) == 16\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [60, 59, 58, 57, 56, 55, 54, 53, 52, 51], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [80, 79, 78, 77, 76, 75, 74, 73, 72, 71], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [100, 99, 98, 97, 96, 95, 94, 93, 92, 91]]) == 100\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6]]) == 4\n assert candidate(matrix = [[9, 9, 9, 9], [9, 8, 7, 8], [9, 7, 6, 7], [9, 8, 7, 6]]) == 4\n assert candidate(matrix = [[7, 8, 9, 10], [6, 5, 4, 11], [15, 14, 13, 12], [16, 17, 18, 19]]) == 16\n assert candidate(matrix = [[1, 2, 3], [8, 9, 4], [7, 6, 5]]) == 9\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [14, 13, 12, 11, 10, 7], [15, 16, 17, 18, 19, 8], [20, 21, 22, 23, 24, 9], [25, 26, 27, 28, 29, 30]]) == 20\n assert candidate(matrix = [[10, 9, 8, 7, 6], [11, 10, 9, 8, 7], [12, 11, 10, 9, 8], [13, 12, 11, 10, 9], [14, 13, 12, 11, 10]]) == 9\n assert candidate(matrix = [[1, 2, 3, 4, 5], [16, 17, 24, 23, 6], [15, 26, 25, 22, 7], [14, 21, 18, 19, 8], [13, 12, 11, 10, 9], [32, 31, 30, 29, 28], [27, 26, 25, 24, 33], [34, 35, 36, 37, 38]]) == 20\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]]) == 10\n assert candidate(matrix = [[10, 16, 15, 21, 14], [9, 11, 17, 20, 13], [8, 12, 18, 19, 12], [7, 6, 5, 4, 3], [2, 1, 0, 9, 8]]) == 13\n assert candidate(matrix = [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]) == 10\n assert candidate(matrix = [[1, 0, 7], [2, 6, 8], [3, 5, 9]]) == 8\n assert candidate(matrix = [[5, 4, 3, 2, 1], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [20, 19, 18, 17, 16], [21, 22, 23, 24, 25]]) == 21\n assert candidate(matrix = [[1, 2, 3], [6, 5, 4], [7, 8, 9], [12, 11, 10]]) == 12\n assert candidate(matrix = [[1, 10, 9, 13, 14, 15], [2, 11, 12, 16, 17, 18], [3, 4, 5, 19, 20, 21], [6, 7, 8, 22, 23, 24], [10, 9, 8, 7, 6, 5]]) == 11\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [19, 18, 17, 16, 15, 14, 13, 12, 11, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [29, 28, 27, 26, 25, 24, 23, 22, 21, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [39, 38, 37, 36, 35, 34, 33, 32, 31, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [49, 48, 47, 46, 45, 44, 43, 42, 41, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [59, 58, 57, 56, 55, 54, 53, 52, 51, 50]]) == 50\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == 1\n assert candidate(matrix = [[1, 3, 1, 1], [1, 4, 1, 5], [1, 2, 1, 6], [1, 7, 1, 1]]) == 3\n assert candidate(matrix = [[5, 4, 3, 2, 1], [4, 3, 2, 1, 5], [3, 2, 1, 5, 4], [2, 1, 5, 4, 3], [1, 5, 4, 3, 2]]) == 5\n assert candidate(matrix = [[7, 8, 9, 10], [10, 6, 5, 4], [3, 2, 1, 12], [14, 13, 16, 15]]) == 6\n assert candidate(matrix = [[9, 8, 7, 6, 5], [8, 7, 6, 5, 4], [7, 6, 5, 4, 3], [6, 5, 4, 3, 2], [5, 4, 3, 2, 1]]) == 9\n assert candidate(matrix = [[1, 20, 3, 4, 5], [16, 17, 24, 23, 6], [15, 26, 25, 22, 7], [14, 21, 18, 19, 8], [13, 12, 11, 10, 9]]) == 18\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]]) == 11\n assert candidate(matrix = [[5, 8, 5, 8], [8, 8, 8, 8], [5, 8, 5, 8], [8, 8, 8, 8]]) == 2\n assert candidate(matrix = [[1, 3, 5, 7, 9], [10, 8, 6, 4, 2], [11, 13, 15, 17, 19], [20, 18, 16, 14, 12]]) == 12\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]]) == 21\n assert candidate(matrix = [[100, 99, 98, 97, 96], [95, 94, 93, 92, 91], [90, 89, 88, 87, 86], [85, 84, 83, 82, 81], [80, 79, 78, 77, 76]]) == 9\n assert candidate(matrix = [[10, 20, 30, 40, 50], [9, 8, 7, 6, 5], [4, 3, 2, 1, 0]]) == 11\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]]) == 9\n assert candidate(matrix = [[10, 9, 8, 7, 6], [19, 18, 17, 16, 15], [20, 21, 22, 23, 24], [29, 28, 27, 26, 25], [30, 31, 32, 33, 34]]) == 21\n assert candidate(matrix = [[3, 1, 6, 5, 9, 12], [10, 18, 4, 7, 11, 14], [17, 2, 19, 8, 13, 16], [15, 24, 21, 20, 23, 22]]) == 7\n assert candidate(matrix = [[5, 12, 15, 18, 19, 20, 21], [4, 9, 14, 17, 22, 23, 24], [3, 8, 13, 16, 25, 26, 27], [2, 7, 10, 11, 28, 29, 30], [1, 6, 5, 4, 31, 32, 33], [0, 1, 2, 3, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43]]) == 22\n assert candidate(matrix = [[1, 100, 1], [100, 1, 100], [1, 100, 1]]) == 2\n assert candidate(matrix = [[1, 2, 3], [6, 5, 4], [7, 8, 9], [10, 11, 12], [15, 14, 13], [16, 17, 18], [19, 20, 21], [24, 23, 22], [25, 26, 27], [30, 29, 28]]) == 26\n assert candidate(matrix = [[5, 3, 2, 4, 1], [4, 8, 7, 5, 6], [3, 9, 6, 2, 8], [1, 5, 4, 3, 2], [6, 7, 8, 9, 1]]) == 8\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [18, 17, 16, 15, 14, 13, 12, 11, 10], [19, 20, 21, 22, 23, 24, 25, 26, 27], [36, 35, 34, 33, 32, 31, 30, 29, 28], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54], [63, 62, 61, 60, 59, 58, 57, 56, 55], [64, 65, 66, 67, 68, 69, 70, 71, 72], [73, 74, 75, 76, 77, 78, 79, 80, 81]]) == 65\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]) == 10\n assert candidate(matrix = [[1, 2, 3], [6, 5, 4], [7, 8, 9]]) == 9\n assert candidate(matrix = [[10, 20, 10], [20, 30, 20], [10, 20, 30], [30, 40, 30], [20, 30, 40]]) == 3\n assert candidate(matrix = [[7, 7, 5, 2, 9], [6, 10, 11, 12, 8], [4, 5, 9, 8, 7], [3, 1, 6, 5, 4], [2, 3, 4, 5, 1]]) == 7\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20], [21, 23, 25, 27, 29]]) == 9\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [1, 2, 3], [4, 5, 6], [7, 8, 9], [1, 2, 3], [4, 5, 6], [7, 8, 9]]) == 5\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]]) == 13\n assert candidate(matrix = [[10, 11, 12, 13, 14, 15], [9, 8, 7, 6, 5, 16], [18, 17, 16, 15, 14, 13], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30]]) == 13\n assert candidate(matrix = [[9, 2, 3], [6, 5, 4], [3, 6, 9]]) == 6\n assert candidate(matrix = [[5, 6, 7, 8, 9], [4, 5, 6, 7, 8], [3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5]]) == 9\n assert candidate(matrix = [[1, 2, 3, 4, 5], [10, 9, 8, 7, 6], [11, 12, 13, 14, 15], [20, 19, 18, 17, 16], [21, 22, 23, 24, 25]]) == 25\n assert candidate(matrix = [[1, 2, 3, 4], [4, 3, 2, 1], [1, 2, 3, 4], [4, 3, 2, 1]]) == 4\n assert candidate(matrix = [[10, 9, 10, 11], [10, 8, 9, 10], [11, 9, 8, 9], [12, 10, 9, 8]]) == 4\n assert candidate(matrix = [[1, 3, 2], [6, 5, 4], [7, 8, 9], [12, 11, 10], [13, 15, 14], [18, 17, 16], [19, 21, 20], [24, 23, 22], [25, 27, 26], [30, 29, 28]]) == 22\n assert candidate(matrix = [[1, 15, 10], [20, 11, 16], [3, 21, 12], [4, 5, 6], [22, 23, 7], [8, 9, 13], [17, 18, 14], [24, 19, 25]]) == 10\n assert candidate(matrix = [[10, 6, 8], [9, 5, 7], [4, 1, 3], [12, 11, 13]]) == 4\n assert candidate(matrix = [[5, 8, 9, 10], [3, 4, 1, 2], [6, 7, 14, 13], [11, 12, 15, 16]]) == 6\n assert candidate(matrix = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [11, 13, 15, 17, 19], [12, 14, 16, 18, 20]]) == 8\n assert candidate(matrix = [[1, 5, 20, 11, 12, 13], [24, 23, 6, 15, 16, 17], [25, 22, 7, 14, 18, 19], [20, 9, 8, 7, 6, 5], [1, 2, 3, 4, 21, 26]]) == 11\n assert candidate(matrix = [[10, 16, 15, 14, 13], [9, 8, 7, 6, 5], [4, 3, 2, 1, 12], [17, 18, 19, 20, 11], [24, 23, 22, 21, 25]]) == 12\n assert candidate(matrix = [[10, 11, 12, 13], [9, 8, 7, 6], [14, 15, 16, 5], [17, 18, 19, 4], [20, 21, 22, 3], [23, 24, 25, 2]]) == 14\n assert candidate(matrix = [[9, 7, 5, 3, 1], [8, 6, 4, 2, 0], [11, 10, 9, 8, 7], [16, 15, 14, 13, 12], [17, 18, 19, 20, 21]]) == 12\n assert candidate(matrix = [[5, 5, 5, 5, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5, 5]]) == 1\n assert candidate(matrix = [[1, 2, 3], [6, 5, 4], [7, 8, 9], [12, 11, 10], [13, 14, 15]]) == 15\n assert candidate(matrix = [[1, 2, 3, 4, 5], [4, 3, 2, 1, 6], [7, 8, 9, 10, 11], [10, 9, 8, 7, 12], [13, 14, 15, 16, 17]]) == 13\n assert candidate(matrix = [[1, 10, 19, 28, 37], [2, 9, 18, 27, 36], [3, 8, 17, 26, 35], [4, 7, 16, 25, 34], [5, 6, 15, 24, 33]]) == 13\n assert candidate(matrix = [[9, 1, 2], [3, 8, 4], [5, 6, 7]]) == 4\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 2, 2, 2, 1], [1, 2, 3, 2, 1], [1, 2, 2, 2, 1], [1, 1, 1, 1, 1]]) == 3\n assert candidate(matrix = [[3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3, 3]]) == 1\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 1], [1, 2, 3, 3, 2, 1], [1, 2, 3, 4, 3, 1], [1, 2, 3, 3, 2, 1], [1, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1]]) == 4\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]]) == 14\n assert candidate(matrix = [[1, 2, 3], [6, 5, 4], [7, 8, 9], [12, 11, 10], [13, 14, 15]]) == 15\n assert candidate(matrix = [[3, 1, 6], [7, 5, 2], [4, 8, 9]]) == 4\n assert candidate(matrix = [[1, 10, 19, 28], [2, 9, 18, 27], [3, 8, 17, 26], [4, 7, 16, 25], [5, 6, 15, 24], [14, 13, 12, 11]]) == 12\n"}, "metadata": {"canonical_parameter_names": ["matrix"], "leetcode_dataset_entry_point": "Solution().longestIncreasingPath", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestIncreasingPath = function(matrix) {", "container": null, "callable": "longestIncreasingPath", "parameters": [{"name": "matrix", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 330, "task_id": "patching-array", "difficulty": "Hard", "problem_description": "Given a sorted integer array nums and an integer n, add/patch elements to the array such that any number in the range [1, n] inclusive can be formed by the sum of some elements in the array.\nReturn the minimum number of patches required.\n \nExample 1:\n\nInput: nums = [1,3], n = 6\nOutput: 1\nExplanation:\nCombinations of nums are [1], [3], [1,3], which form possible sums of: 1, 3, 4.\nNow if we add/patch 2 to nums, the combinations are: [1], [2], [3], [1,3], [2,3], [1,2,3].\nPossible sums are 1, 2, 3, 4, 5, 6, which now covers the range [1, 6].\nSo we only need 1 patch.\n\nExample 2:\n\nInput: nums = [1,5,10], n = 20\nOutput: 2\nExplanation: The two patches can be [2, 4].\n\nExample 3:\n\nInput: nums = [1,2,2], n = 5\nOutput: 0\n\n \nConstraints:\n\n1 <= nums.length <= 1000\n1 <= nums[i] <= 104\nnums is sorted in ascending order.\n1 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 8],n = 8) == 1\n assert candidate(nums = [1],n = 2) == 1\n assert candidate(nums = [],n = 8) == 4\n assert candidate(nums = [],n = 7) == 3\n assert candidate(nums = [1, 2, 4, 13],n = 30) == 2\n assert candidate(nums = [1, 2, 4, 13, 43],n = 100) == 2\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],n = 2047) == 0\n assert candidate(nums = [1, 3, 5, 7],n = 15) == 1\n assert candidate(nums = [1, 5, 10],n = 20) == 2\n assert candidate(nums = [1, 3],n = 6) == 1\n assert candidate(nums = [1, 4, 8],n = 10) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],n = 55) == 0\n assert candidate(nums = [1],n = 1) == 0\n assert candidate(nums = [1, 2, 3, 4, 5],n = 15) == 0\n assert candidate(nums = [1, 2, 2],n = 5) == 0\n assert candidate(nums = [1, 3, 9, 27, 81, 243, 729],n = 10000) == 9\n assert candidate(nums = [1, 4, 13, 40, 100],n = 1000) == 6\n assert candidate(nums = [1, 1, 1, 1, 1],n = 10) == 1\n assert candidate(nums = [1, 1000000000],n = 2000000000) == 29\n assert candidate(nums = [1, 2, 4, 13, 43],n = 100) == 2\n assert candidate(nums = [1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 768],n = 1024) == 0\n assert candidate(nums = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],n = 500) == 3\n assert candidate(nums = [1, 4, 9, 16, 25, 36],n = 500) == 5\n assert candidate(nums = [2, 6, 18, 54, 162],n = 500) == 6\n assert candidate(nums = [1, 4, 10, 20],n = 30) == 2\n assert candidate(nums = [1, 100, 10000, 1000000],n = 2000000) == 18\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29],n = 100) == 1\n assert candidate(nums = [1, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095],n = 8000) == 3\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536],n = 1000000) == 3\n assert candidate(nums = [1, 4, 10, 20, 50, 100],n = 500) == 5\n assert candidate(nums = [1, 2, 5, 7],n = 23) == 2\n assert candidate(nums = [1, 10, 100, 1000, 10000],n = 100000) == 13\n assert candidate(nums = [1, 2, 4, 8, 16, 32],n = 1000) == 4\n assert candidate(nums = [1, 2, 2, 5],n = 21) == 1\n assert candidate(nums = [1, 5, 10, 20, 50, 100, 200, 500],n = 1000) == 4\n assert candidate(nums = [1, 2, 3, 7, 11, 13],n = 100) == 2\n assert candidate(nums = [1, 2, 8, 32, 128],n = 1024) == 6\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000],n = 1000000) == 15\n assert candidate(nums = [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000],n = 10000) == 6\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],n = 2048) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],n = 1000) == 7\n assert candidate(nums = [1, 3, 9],n = 50) == 4\n assert candidate(nums = [5, 8, 15],n = 50) == 4\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],n = 100) == 0\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096],n = 8192) == 1\n assert candidate(nums = [1, 2, 5, 10, 20, 50, 100, 250, 500, 1000],n = 2000) == 3\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],n = 2048) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],n = 1024) == 1\n assert candidate(nums = [1, 2, 8, 16, 32, 64, 128],n = 256) == 2\n assert candidate(nums = [1, 2, 3, 5, 11, 21],n = 100) == 2\n assert candidate(nums = [1, 4, 10],n = 19) == 2\n assert candidate(nums = [1, 5, 10, 20, 50, 100],n = 10000) == 9\n assert candidate(nums = [1, 5, 10, 25, 50, 100],n = 1000) == 6\n assert candidate(nums = [1, 4, 10, 20, 25],n = 50) == 2\n assert candidate(nums = [2, 4, 6, 8],n = 20) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],n = 2047) == 0\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144],n = 200) == 0\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],n = 1024) == 1\n assert candidate(nums = [1, 3, 9, 27, 81],n = 243) == 5\n assert candidate(nums = [1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458, 2187, 4374, 6561, 13122, 19683, 39366],n = 50000) == 0\n assert candidate(nums = [1, 4, 13, 36, 104, 284, 780, 2184, 5964, 16216, 43792, 118764, 319524, 866208, 2359608, 6336584, 17335296, 46832600, 127132960, 341754864],n = 1000000000) == 15\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024],n = 1023) == 0\n assert candidate(nums = [2, 6, 18, 54, 162],n = 1000) == 7\n assert candidate(nums = [1, 5, 10, 25, 50, 100, 200, 500, 1000],n = 1500) == 4\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536],n = 100000000) == 10\n assert candidate(nums = [1, 2, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10922, 21845],n = 100000) == 2\n assert candidate(nums = [1, 3, 9, 27, 81],n = 200) == 4\n assert candidate(nums = [1, 4, 10, 20, 25, 50],n = 100) == 2\n assert candidate(nums = [1, 4, 10, 20, 25],n = 100) == 3\n assert candidate(nums = [1, 3, 9, 27, 81, 243, 729],n = 1000000) == 15\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128],n = 1000) == 3\n assert candidate(nums = [1, 2, 8, 16],n = 31) == 1\n assert candidate(nums = [1, 3, 7, 15, 31],n = 1000) == 6\n assert candidate(nums = [1, 1, 1, 1, 1, 1],n = 10) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],n = 10) == 0\n assert candidate(nums = [1, 2, 6],n = 14) == 2\n assert candidate(nums = [1, 2, 6, 18, 54, 162],n = 500) == 5\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512],n = 1023) == 1\n assert candidate(nums = [1, 5, 10, 20, 50],n = 1000) == 6\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],n = 20) == 1\n assert candidate(nums = [3, 7, 11, 15, 19],n = 50) == 2\n assert candidate(nums = [1, 5, 10, 20, 50, 100, 200, 500, 1000],n = 1500) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],n = 100) == 1\n assert candidate(nums = [1, 2, 6, 24, 120],n = 720) == 6\n assert candidate(nums = [1, 5, 10, 20, 50, 100],n = 200) == 3\n assert candidate(nums = [1, 2, 3, 6, 12, 24, 48, 96],n = 1024) == 3\n assert candidate(nums = [1, 3, 5, 7, 9],n = 20) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],n = 10) == 0\n assert candidate(nums = [1, 2, 2, 4, 8, 16],n = 31) == 0\n assert candidate(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23],n = 100) == 0\n assert candidate(nums = [10, 20, 30, 40, 50],n = 150) == 4\n assert candidate(nums = [2, 3, 6, 7, 8, 10],n = 50) == 2\n assert candidate(nums = [1, 3, 7, 15, 31, 63],n = 127) == 2\n assert candidate(nums = [1, 2, 2, 3, 3, 5, 8, 13, 21, 34],n = 100) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],n = 20) == 0\n assert candidate(nums = [2, 4, 8, 16, 32],n = 1024) == 6\n assert candidate(nums = [3, 7, 15, 31, 63, 127],n = 255) == 3\n assert candidate(nums = [1, 3, 5, 7, 9],n = 50) == 2\n assert candidate(nums = [1, 7, 15, 31, 63, 127],n = 200) == 3\n assert candidate(nums = [1, 4, 10, 20, 50, 100],n = 200) == 3\n assert candidate(nums = [1, 5, 10, 20, 50, 100],n = 1000) == 6\n assert candidate(nums = [1, 2, 4, 8, 16, 32],n = 1023) == 4\n assert candidate(nums = [1, 2, 5, 10, 20, 50, 100],n = 1000) == 5\n assert candidate(nums = [1, 2, 5, 10, 25, 50],n = 100) == 2\n assert candidate(nums = [1, 2, 4, 8, 16],n = 31) == 0\n"}, "metadata": {"canonical_parameter_names": ["nums", "n"], "leetcode_dataset_entry_point": "Solution().minPatches", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minPatches = function(nums, n) {", "container": null, "callable": "minPatches", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 331, "task_id": "verify-preorder-serialization-of-a-binary-tree", "difficulty": "Medium", "problem_description": "One way to serialize a binary tree is to use preorder traversal. When we encounter a non-null node, we record the node's value. If it is a null node, we record using a sentinel value such as '#'.\n\nFor example, the above binary tree can be serialized to the string \"9,3,4,#,#,1,#,#,2,#,6,#,#\", where '#' represents a null node.\nGiven a string of comma-separated values preorder, return true if it is a correct preorder traversal serialization of a binary tree.\nIt is guaranteed that each comma-separated value in the string must be either an integer or a character '#' representing null pointer.\nYou may assume that the input format is always valid.\n\nFor example, it could never contain two consecutive commas, such as \"1,,3\".\n\nNote: You are not allowed to reconstruct the tree.\n \nExample 1:\nInput: preorder = \"9,3,4,#,#,1,#,#,2,#,6,#,#\"\nOutput: true\nExample 2:\nInput: preorder = \"1,#\"\nOutput: false\nExample 3:\nInput: preorder = \"9,#,#,1\"\nOutput: false\n\n \nConstraints:\n\n1 <= preorder.length <= 104\npreorder consist of integers in the range [0, 100] and '#' separated by commas ','.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(preorder = \"1,2,#,#,3,4,#,#,5,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,#,#,5,6,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,#,#,4,5,#,#,#,#,6,7,#,#,#,#\") == False\n assert candidate(preorder = \"#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,#,#,5,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,#,#,5,#,#\") == True\n assert candidate(preorder = \"1,2,#,#,3,4,5,#,#,#,#,6,#,#,7,#,#\") == False\n assert candidate(preorder = \"1,2,3,#,#,4,5,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,#,4,#,#\") == True\n assert candidate(preorder = \"1,2,#,3,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,#,#,5,6,#,#,7,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,#,4,5,#,#,#\") == True\n assert candidate(preorder = \"1,#\") == False\n assert candidate(preorder = \"0,1,2,3,#,#,#,#,4,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,#,#,5,#,6,#,#\") == True\n assert candidate(preorder = \"0,0,0,0,#,#,#,0,#,#,#,0,#,#,#\") == False\n assert candidate(preorder = \"1,2,#,4,#,#,3,#,#\") == True\n assert candidate(preorder = \"9,3,4,#,#,1,#,#,2,#,6,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,#,#\") == True\n assert candidate(preorder = \"9,3,4,#,#,#,2,#,6,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,4,#,#,#,5,#,#\") == True\n assert candidate(preorder = \"1,2,#,3,#,#,4,#,#\") == True\n assert candidate(preorder = \"#,1\") == False\n assert candidate(preorder = \"1,2,#,3,4,#,#,5,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,#,5,#,#\") == False\n assert candidate(preorder = \"1,2,#,3,#,4,#,#,5,#,#,6,#,#\") == False\n assert candidate(preorder = \"9,#,#,1\") == False\n assert candidate(preorder = \"20,15,10,#,#,12,#,#,18,16,#,#,19,#,#,25,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,#,#,5,6,#,#,7,#,#,8,9,#,#,10,#,#,11,12,#,#,13,#,#,14,#,#,15,#,#\") == False\n assert candidate(preorder = \"10,5,3,#,#,8,7,#,#,#,9,#,11,#,12,#,#\") == True\n assert candidate(preorder = \"5,2,3,#,#,6,7,#,#,#,8,9,#,#,10,#,#\") == True\n assert candidate(preorder = \"5,4,2,1,#,#,#,3,#,#,7,6,#,#,8,#,#\") == True\n assert candidate(preorder = \"30,20,10,#,#,15,#,#,25,22,#,#,27,#,#,35,32,#,#,37,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,#,#,#,#,#,#,#,9,#,10,#,#,11,#,#,12,#,#,13,#,#,14,#,#,15,#,#\") == False\n assert candidate(preorder = \"9,4,#,6,7,#,#,8,#,#,5,3,#,#,#,#,1,#,#\") == False\n assert candidate(preorder = \"20,10,5,#,#,8,6,#,#,9,#,#,15,12,#,#,13,#,#,14,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,#,#,5,6,7,#,#,#,#,8,9,#,#,10,11,#,#,#,12,13,#,#,#,14,15,#,#,#,16,#,#\") == False\n assert candidate(preorder = \"7,3,2,#,#,6,#,#,4,#,5,#,#,1,#,9,#,#\") == False\n assert candidate(preorder = \"6,2,0,#,#,4,3,#,#,5,#,#\") == False\n assert candidate(preorder = \"10,4,3,2,#,#,#,5,#,6,#,#,8,7,#,#,#,9,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,#,#,#,8,9,10,11,12,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,6,7,#,#,8,9,#,#,#,10,11,#,#,#,12,13,#,#,#,14,#,#\") == False\n assert candidate(preorder = \"1,2,#,3,#,#,4,5,#,#,6,7,#,#,8,#,#,9,#,#,10,#,#\") == False\n assert candidate(preorder = \"1,2,#,#,3,4,5,#,#,#,6,7,8,9,#,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,#,8,9,#,#,10,#,#,11,12,#,#,13,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,9,#,#,#,#,#,10,11,12,#,#,#,13,14,15,#,#,#,16,17,18,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,8,#,#,#,9,#,10,#,#,11,12,#,#,13,#,#,14,#,#,15,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,#,5,#,#,#,6,7,8,#,#,9,#,#,10,11,12,#,#,#,13,14,15,#,#,#,16,17,18,#,#,#,19,20,#,#,#,21,22,23,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,#,7,#,8,9,#,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,6,7,#,#,#,8,9,#,#,#,10,11,#,#,#\") == False\n assert candidate(preorder = \"10,5,3,2,#,#,#,7,6,#,#,8,#,#,9,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,#,7,8,#,#,9,#,#,10,#,#\") == False\n assert candidate(preorder = \"5,2,1,#,#,#,6,3,#,#,7,8,#,#,9,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,#,#,#,#,9,10,11,#,#,#,12,13,14,#,#,#,15,16,17,#,#,#\") == False\n assert candidate(preorder = \"5,#,#,6,7,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,#,#,#,5,#,#,6,7,#,#,8,9,#,#,10,#,11,#,#\") == True\n assert candidate(preorder = \"3,1,0,#,#,#,2,#,4,5,#,#,#,6,#,#\") == False\n assert candidate(preorder = \"1,2,3,#,#,#,4,5,6,7,8,9,#,#,#,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,5,#,#,6,7,#,#,8,#,#,9,#,#\") == True\n assert candidate(preorder = \"5,1,0,#,#,2,#,#,6,3,#,#,#,7,#,8,#,#\") == False\n assert candidate(preorder = \"15,10,7,#,#,8,#,#,12,11,#,#,13,#,#,14,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,6,#,7,#,#,8,#,9,#,#\") == False\n assert candidate(preorder = \"9,4,1,#,#,2,#,#,5,3,#,#,6,#,#,7,#,#\") == False\n assert candidate(preorder = \"10,5,3,#,#,4,8,#,#,#,6,#,9,7,#,#,#,11,#,#\") == False\n assert candidate(preorder = \"100,50,25,#,#,30,#,#,75,60,#,#,80,#,#,125,110,#,#,130,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,#,8,9,#,#,10,11,#,#,12,13,#,#,14,15,#,#,16,17,#,#,18,19,#,#,20,21,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,#,#,3,4,5,#,#,#,6,7,8,9,#,#,#,10,11,#,#,#,12,13,#,#,#,14,15,#,#,#,16,17,#,#,#,18,19,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,#,6,7,8,9,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"100,50,25,#,#,75,#,#,150,125,#,#,175,#,#\") == True\n assert candidate(preorder = \"8,5,9,#,#,7,#,11,#,#,3,#,#,2,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,#,#,5,#,6,#,#,7,#,#,8,#,#,9,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,#,#,#,7,8,9,#,#,10,11,#,#,#,12,13,14,#,#,#,15,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,#,#,7,#,#,8,9,10,#,#,#,11,12,#,#,13,14,#,#,#,15,16,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,8,9,#,#,#,#,#,10,11,12,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,#,#,5,6,7,#,#,8,9,10,#,#,#,#,11,12,#,#,13,14,#,#,15,#,#,16,#,#,17,#,#,#,#,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"8,3,2,1,#,#,#,4,#,#,5,6,#,#,#,7,#,9,#,#\") == False\n assert candidate(preorder = \"6,2,0,8,#,#,#,5,#,#,7,#,3,#,#,1,0,#,9,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"5,3,6,8,#,#,#,4,#,#,2,9,#,#,10,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,#,5,6,#,#,#,7,8,#,#,9,10,#,#,#,11,12,#,#,#,13,#,#\") == False\n assert candidate(preorder = \"11,8,6,4,#,#,7,#,#,9,#,10,#,#,14,12,#,#,13,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,5,#,6,#,#,7,8,#,#,9,#,#,10,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,5,#,#,6,7,#,#,8,9,#,#,10,#,#,#\") == True\n assert candidate(preorder = \"15,10,5,#,#,7,#,#,20,17,#,#,25,#,#\") == True\n assert candidate(preorder = \"10,5,3,#,#,8,6,#,#,#,9,4,#,#,7,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,6,#,#,#,#,#,7,8,#,#,9,10,#,#,#,#\") == True\n assert candidate(preorder = \"3,1,2,#,#,4,5,#,#,#,6,7,8,#,#,#,#,9,#,#\") == False\n assert candidate(preorder = \"8,5,4,2,1,#,#,#,3,#,#,7,6,#,#,13,10,#,#,15,#,18,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,#,8,#,#,9,10,#,#,11,#,#\") == False\n assert candidate(preorder = \"9,8,7,6,#,#,5,4,3,#,#,2,#,#,1,#,#\") == False\n assert candidate(preorder = \"5,3,2,1,#,#,#,4,#,#,6,#,7,#,#\") == True\n assert candidate(preorder = \"5,3,2,#,#,4,#,#,6,#,7,8,#,#,9,#,10,#,#\") == True\n assert candidate(preorder = \"1,2,#,#,3,#,4,5,#,#,6,7,#,#,#,8,9,#,10,#,11,#,#\") == False\n assert candidate(preorder = \"9,3,4,#,#,1,#,#,2,#,6,7,#,#,8,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,#,8,9,#,#,10,11,#,#,12,#,13,#,14,#,#,15,#,#,16,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"2,1,#,#,3,#,#,4,#,#,5,#,#,6,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,#,7,8,9,#,#,10,#,#,11,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,#,6,7,8,#,#,#,9,#,#\") == False\n assert candidate(preorder = \"5,2,1,#,#,#,3,#,6,#,4,#,7,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,5,#,#,6,7,8,9,10,#,#,#,#,#,11,12,13,#,#,#,14,15,16,#,#,#,17,18,19,#,#,#,20,21,22,#,#,#,23,24,25,#,#,#\") == False\n assert candidate(preorder = \"3,9,#,#,20,15,#,#,7,#,#,6,#,#,18,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,7,#,8,#,9,#,10,#,11,#,12,#,13,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,6,7,8,9,#,#,#,#,#,10,11,12,13,#,#,#,#,#,14,15,16,17,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,#,#,4,5,6,7,#,#,#,#,8,9,#,#,10,#,#,#\") == True\n assert candidate(preorder = \"7,3,1,#,#,#,4,2,#,#,#,5,#,6,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,#,7,#,8,#,#,9,#,10,#,#,11,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,#,6,7,#,#,8,9,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,6,#,#,#,7,8,9,#,#,#,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,5,6,#,#,7,8,#,#,9,#,#,10,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,#,#,5,#,6,#,7,#,8,#,9,#,10,#,11,#,12,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,6,7,#,#,#,#,#,#,8,9,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,#,#,8,#,#,9,#,#,10,11,12,#,#,13,#,#,#,14,15,16,#,#,#,17,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,9,#,#,#,#,#,#,#,#,10,11,12,#,#,#,#,#,13,14,15,#,#,#,#,#,16,17,18,#,#,#,#,#,19,#,#\") == False\n assert candidate(preorder = \"5,1,#,#,4,3,6,#,#,#,2,#,7,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,#,#,#,5,#,6,#,7,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,#,4,#,5,#,6,#,7,#,8,#,9,#,10,#,11,#,12,#,#\") == False\n assert candidate(preorder = \"8,3,2,#,#,4,#,#,5,#,6,#,#,7,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,#,6,#,7,#,#,8,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,#,7,8,#,#,9,#,#,10,11,#,#,12,#,#,13,#,#\") == True\n assert candidate(preorder = \"9,3,4,5,#,#,#,1,#,#,2,7,#,#,8,#,#\") == True\n assert candidate(preorder = \"10,5,3,#,#,8,7,#,#,15,12,#,#,20,#,#\") == False\n assert candidate(preorder = \"9,6,5,#,#,#,13,10,#,#,15,#,18,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,7,#,8,#,#,9,#,10,#,11,#,#,#,#\") == True\n assert candidate(preorder = \"5,4,3,2,1,#,#,#,#,6,7,#,#,8,9,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,#,#,#,#,#,#,#,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"9,3,4,#,#,1,#,#,2,#,6,#,#,5,#,#,7,#,#,8,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,7,8,#,#,9,#,10,#,11,12,#,#,13,#,#,14,#,#,#,#,#,#,#,#\") == False\n assert candidate(preorder = \"10,5,3,2,#,#,4,#,#,7,#,6,#,#,8,9,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,7,#,#,8,9,#,#,10,11,#,#,12,13,#,#,14,15,#,#,16,17,#,#\") == False\n assert candidate(preorder = \"6,3,1,#,#,#,8,#,9,10,#,#,12,#,#\") == True\n assert candidate(preorder = \"8,5,3,#,2,#,#,4,#,#,6,1,#,#,7,#,#\") == True\n assert candidate(preorder = \"5,3,2,#,#,4,#,#,6,1,#,#,8,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,#,#,6,#,#,7,#,8,9,#,#,#,10,11,#,#,#,12,13,#,#,#,14,15,#,#,#\") == False\n assert candidate(preorder = \"1,2,#,3,#,4,5,#,#,6,#,7,#,8,#,#,9,#,10,#,11,#,#,#,#\") == False\n assert candidate(preorder = \"9,4,3,#,#,5,#,8,#,#,7,6,#,#,#,#\") == False\n assert candidate(preorder = \"5,1,4,#,#,3,#,#,6,2,#,#,8,#,#\") == True\n assert candidate(preorder = \"1,2,3,#,#,4,#,5,6,#,#,#,#\") == True\n assert candidate(preorder = \"1,2,3,4,5,6,#,#,7,8,#,#,9,10,#,#,#,11,12,#,#,#\") == False\n assert candidate(preorder = \"5,2,1,#,#,4,3,#,#,#,#,6,#,7,#,#\") == False\n assert candidate(preorder = \"1,2,3,#,#,4,#,5,#,6,7,#,#,#,#,#\") == False\n assert candidate(preorder = \"1,2,#,#,3,4,#,#,5,6,7,#,#,#,8,#,9,#,#\") == True\n assert candidate(preorder = \"2,1,0,#,#,#,3,#,4,#,5,#,#\") == True\n assert candidate(preorder = \"6,2,1,#,#,4,#,#,3,#,#,5,#,7,#,#\") == False\n"}, "metadata": {"canonical_parameter_names": ["preorder"], "leetcode_dataset_entry_point": "Solution().isValidSerialization", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isValidSerialization = function(preorder) {", "container": null, "callable": "isValidSerialization", "parameters": [{"name": "preorder", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 332, "task_id": "reconstruct-itinerary", "difficulty": "Hard", "problem_description": "You are given a list of airline tickets where tickets[i] = [fromi, toi] represent the departure and the arrival airports of one flight. Reconstruct the itinerary in order and return it.\nAll of the tickets belong to a man who departs from \"JFK\", thus, the itinerary must begin with \"JFK\". If there are multiple valid itineraries, you should return the itinerary that has the smallest lexical order when read as a single string.\n\nFor example, the itinerary [\"JFK\", \"LGA\"] has a smaller lexical order than [\"JFK\", \"LGB\"].\n\nYou may assume all tickets form at least one valid itinerary. You must use all the tickets once and only once.\n \nExample 1:\n\n\nInput: tickets = [[\"MUC\",\"LHR\"],[\"JFK\",\"MUC\"],[\"SFO\",\"SJC\"],[\"LHR\",\"SFO\"]]\nOutput: [\"JFK\",\"MUC\",\"LHR\",\"SFO\",\"SJC\"]\n\nExample 2:\n\n\nInput: tickets = [[\"JFK\",\"SFO\"],[\"JFK\",\"ATL\"],[\"SFO\",\"ATL\"],[\"ATL\",\"JFK\"],[\"ATL\",\"SFO\"]]\nOutput: [\"JFK\",\"ATL\",\"JFK\",\"SFO\",\"ATL\",\"SFO\"]\nExplanation: Another possible reconstruction is [\"JFK\",\"SFO\",\"ATL\",\"JFK\",\"ATL\",\"SFO\"] but it is larger in lexical order.\n\n \nConstraints:\n\n1 <= tickets.length <= 300\ntickets[i].length == 2\nfromi.length == 3\ntoi.length == 3\nfromi and toi consist of uppercase English letters.\nfromi != toi\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(tickets = [['JFK', 'NRT'], ['NRT', 'JFK']]) == ['JFK', 'NRT', 'JFK']\n assert candidate(tickets = [['JFK', 'MUC'], ['MUC', 'LHR'], ['LHR', 'SFO'], ['SFO', 'SJC']]) == ['JFK', 'MUC', 'LHR', 'SFO', 'SJC']\n assert candidate(tickets = [['JFK', 'AXA'], ['AXA', 'TIA'], ['TIA', 'JFK'], ['JFK', 'AXA']]) == ['JFK', 'AXA', 'TIA', 'JFK', 'AXA']\n assert candidate(tickets = [['EZE', 'TIA'], ['EZE', 'HOU'], ['AXA', 'TIA'], ['JFK', 'AXA'], ['ANU', 'JFK'], ['TIA', 'ANU'], ['JFK', 'TIA']]) == ['JFK', 'AXA', 'TIA', 'ANU', 'JFK', 'TIA']\n assert candidate(tickets = [['JFK', 'PEK'], ['PEK', 'LAX'], ['LAX', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SFO']]) == ['JFK', 'PEK', 'LAX', 'JFK', 'ORD', 'SFO']\n assert candidate(tickets = [['JFK', 'AXA'], ['AXA', 'TIA'], ['TIA', 'JFK'], ['JFK', 'TIA'], ['TIA', 'JFK']]) == ['JFK', 'AXA', 'TIA', 'JFK', 'TIA', 'JFK']\n assert candidate(tickets = [['MUC', 'LHR'], ['JFK', 'MUC'], ['SFO', 'SJC'], ['LHR', 'SFO']]) == ['JFK', 'MUC', 'LHR', 'SFO', 'SJC']\n assert candidate(tickets = [['JFK', 'KUL'], ['JFK', 'NRT'], ['NRT', 'JFK']]) == ['JFK', 'NRT', 'JFK', 'KUL']\n assert candidate(tickets = [['JFK', 'AAA'], ['JFK', 'BBB'], ['BBB', 'JFK']]) == ['JFK', 'BBB', 'JFK', 'AAA']\n assert candidate(tickets = [['JFK', 'SFO'], ['JFK', 'ATL'], ['SFO', 'ATL'], ['ATL', 'JFK'], ['ATL', 'SFO']]) == ['JFK', 'ATL', 'JFK', 'SFO', 'ATL', 'SFO']\n assert candidate(tickets = [['EZE', 'AXA'], ['TIA', 'ANU'], ['ANU', 'JFK'], ['JFK', 'ANU'], ['ANU', 'EZE'], ['TIA', 'ANU'], ['AXA', 'TIA'], ['TIA', 'JFK'], ['ANU', 'TIA'], ['JFK', 'TIA']]) == ['JFK', 'ANU', 'EZE', 'AXA', 'TIA', 'ANU', 'JFK', 'TIA', 'ANU', 'TIA', 'JFK']\n assert candidate(tickets = [['EZE', 'AXA'], ['TIA', 'ANU'], ['ANU', 'JFK'], ['JFK', 'TIA'], ['ANU', 'EZE'], ['TIA', 'ANU'], ['AXA', 'TIA'], ['TIA', 'JFK'], ['ANU', 'TIA'], ['JFK', 'TIA']]) == ['JFK', 'TIA', 'ANU', 'EZE', 'AXA', 'TIA', 'ANU', 'TIA', 'JFK', 'TIA', 'JFK']\n assert candidate(tickets = [['MUC', 'LHR'], ['JFK', 'MUC'], ['SFO', 'SJC'], ['LHR', 'SFO']]) == ['JFK', 'MUC', 'LHR', 'SFO', 'SJC']\n assert candidate(tickets = [['JFK', 'SFO'], ['JFK', 'ATL'], ['SFO', 'ATL'], ['ATL', 'JFK'], ['ATL', 'SFO']]) == ['JFK', 'ATL', 'JFK', 'SFO', 'ATL', 'SFO']\n assert candidate(tickets = [['EZE', 'AXA'], ['TIA', 'ANU'], ['ANU', 'JFK'], ['JFK', 'TIA'], ['AXA', 'TIA'], ['TIA', 'ANU'], ['AXA', 'EZE'], ['EZE', 'ANU'], ['AXA', 'TIA'], ['ANU', 'JFK'], ['JFK', 'TIA'], ['JFK', 'ANU'], ['ANU', 'EZE'], ['TIA', 'JFK'], ['EZE', 'TIA'], ['EZE', 'AXA'], ['AXA', 'TIA'], ['AXA', 'EZE'], ['TIA', 'AXA'], ['JFK', 'AXA'], ['AXA', 'TIA'], ['TIA', 'JFK'], ['AXA', 'EZE'], ['EZE', 'ANU'], ['JFK', 'TIA'], ['JFK', 'ANU'], ['ANU', 'JFK'], ['TIA', 'JFK'], ['JFK', 'TIA'], ['JFK', 'AXA'], ['AXA', 'TIA'], ['TIA', 'JFK'], ['AXA', 'EZE']]) == ['JFK', 'ANU', 'EZE', 'ANU', 'JFK', 'ANU', 'JFK', 'AXA', 'EZE', 'ANU', 'JFK', 'AXA', 'EZE', 'AXA', 'EZE', 'AXA', 'EZE', 'TIA', 'AXA', 'TIA', 'TIA', 'TIA', 'TIA', 'TIA', 'JFK', 'TIA', 'JFK', 'TIA', 'JFK', 'TIA', 'JFK', 'TIA', 'ANU', 'ANU']\n assert candidate(tickets = [['JFK', 'PDX'], ['PDX', 'JFK'], ['JFK', 'PDX'], ['PDX', 'LAX'], ['LAX', 'PDX'], ['PDX', 'JFK'], ['JFK', 'PDX'], ['PDX', 'LAX']]) == ['JFK', 'PDX', 'JFK', 'PDX', 'JFK', 'PDX', 'LAX', 'PDX', 'LAX']\n assert candidate(tickets = [['JFK', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK'], ['BKK', 'JFK'], ['JFK', 'LAX'], ['LAX', 'JFK'], ['JFK', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK'], ['BKK', 'LAX'], ['LAX', 'BKK'], ['BKK', 'SFO'], ['SFO', 'BKK']]) == ['JFK', 'BKK', 'JFK', 'BKK', 'LAX', 'BKK', 'LAX', 'BKK', 'LAX', 'BKK', 'LAX', 'BKK', 'LAX', 'BKK', 'LAX', 'BKK', 'LAX', 'JFK', 'LAX', 'BKK', 'SFO', 'BKK', 'SFO', 'BKK', 'SFO', 'BKK', 'SFO', 'BKK', 'SFO', 'BKK', 'SFO', 'BKK', 'SFO', 'BKK']\n assert candidate(tickets = [['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'DXB'], ['DXB', 'JFK']]) == ['JFK', 'LHR', 'DEL', 'DXB', 'JFK', 'LHR', 'DEL', 'DXB', 'JFK', 'LHR', 'DEL', 'DXB', 'JFK', 'LHR', 'DEL', 'DXB', 'JFK', 'LHR', 'DEL', 'DXB', 'JFK', 'LHR', 'DEL', 'DXB', 'JFK', 'LHR', 'DEL', 'DXB', 'JFK']\n assert candidate(tickets = [['JFK', 'BKK'], ['BKK', 'LHR'], ['LHR', 'AMS'], ['AMS', 'JFK'], ['JFK', 'DXB'], ['DXB', 'LAX'], ['LAX', 'BKK'], ['BKK', 'JFK']]) == ['JFK', 'BKK', 'JFK', 'DXB', 'LAX', 'BKK', 'LHR', 'AMS', 'JFK']\n assert candidate(tickets = [['JFK', 'IST'], ['IST', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK'], ['JFK', 'IST'], ['IST', 'SAW'], ['SAW', 'IST'], ['IST', 'JFK'], ['JFK', 'SAW'], ['SAW', 'JFK']]) == ['JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'IST', 'JFK', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'IST', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK', 'SAW', 'JFK']\n assert candidate(tickets = [['JFK', 'HOU'], ['HOU', 'SLC'], ['SLC', 'JFK'], ['JFK', 'HOU'], ['HOU', 'ORD'], ['ORD', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SLC'], ['SLC', 'HOU']]) == ['JFK', 'HOU', 'ORD', 'JFK', 'HOU', 'SLC', 'JFK', 'ORD', 'SLC', 'HOU']\n assert candidate(tickets = [['JFK', 'DEL'], ['DEL', 'BOM'], ['BOM', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LAX'], ['LAX', 'HOU'], ['HOU', 'SFO'], ['SFO', 'ORD'], ['ORD', 'JFK'], ['JFK', 'LAX'], ['LAX', 'JFK']]) == ['JFK', 'DEL', 'BOM', 'DXB', 'JFK', 'LAX', 'HOU', 'SFO', 'ORD', 'JFK', 'LAX', 'JFK']\n assert candidate(tickets = [['JFK', 'A'], ['A', 'B'], ['B', 'C'], ['C', 'D'], ['D', 'A'], ['A', 'JFK'], ['JFK', 'C']]) == ['JFK', 'A', 'B', 'C', 'D', 'A', 'JFK', 'C']\n assert candidate(tickets = [['JFK', 'A'], ['A', 'B'], ['B', 'C'], ['C', 'A'], ['A', 'D'], ['D', 'E'], ['E', 'F'], ['F', 'G'], ['G', 'F'], ['F', 'E'], ['E', 'D'], ['D', 'C'], ['C', 'B'], ['B', 'A'], ['A', 'JFK'], ['JFK', 'H'], ['H', 'I'], ['I', 'J'], ['J', 'H'], ['H', 'JFK'], ['JFK', 'K'], ['K', 'L'], ['L', 'M'], ['M', 'N'], ['N', 'O'], ['O', 'P'], ['P', 'Q'], ['Q', 'R'], ['R', 'S'], ['S', 'T'], ['T', 'U'], ['U', 'V'], ['V', 'W'], ['W', 'X'], ['X', 'Y'], ['Y', 'Z'], ['Z', 'W'], ['W', 'V'], ['V', 'U'], ['U', 'T'], ['T', 'S'], ['S', 'R'], ['R', 'Q'], ['Q', 'P'], ['P', 'O'], ['O', 'N'], ['N', 'M'], ['M', 'L'], ['L', 'K'], ['K', 'JFK'], ['JFK', 'G'], ['G', 'F'], ['F', 'E'], ['E', 'D'], ['D', 'C'], ['C', 'B'], ['B', 'A'], ['A', 'JFK']]) == ['JFK', 'A', 'B', 'A', 'D', 'C', 'A', 'JFK', 'G', 'F', 'E', 'D', 'E', 'F', 'G', 'F', 'E', 'D', 'C', 'B', 'C', 'B', 'A', 'JFK', 'H', 'I', 'J', 'H', 'JFK', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'W', 'V', 'U', 'T', 'S', 'R', 'Q', 'P', 'O', 'N', 'M', 'L', 'K', 'JFK']\n assert candidate(tickets = [['JFK', 'CDG'], ['CDG', 'MIA'], ['MIA', 'LAX'], ['LAX', 'HOU'], ['HOU', 'SFO'], ['SFO', 'HOU'], ['HOU', 'LAX'], ['LAX', 'MIA'], ['MIA', 'CDG'], ['CDG', 'JFK']]) == ['JFK', 'CDG', 'MIA', 'LAX', 'HOU', 'SFO', 'HOU', 'LAX', 'MIA', 'CDG', 'JFK']\n assert candidate(tickets = [['JFK', 'NRT'], ['NRT', 'JFK'], ['JFK', 'KUL'], ['KUL', 'NRT'], ['NRT', 'KUL'], ['KUL', 'JFK']]) == ['JFK', 'KUL', 'JFK', 'NRT', 'KUL', 'NRT', 'JFK']\n assert candidate(tickets = [['JFK', 'KUL'], ['KUL', 'LAX'], ['LAX', 'KUL'], ['KUL', 'SFO'], ['SFO', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SFO'], ['SFO', 'ORD'], ['ORD', 'JFK'], ['JFK', 'SFO']]) == ['JFK', 'KUL', 'LAX', 'KUL', 'SFO', 'JFK', 'ORD', 'JFK', 'SFO', 'ORD', 'SFO']\n assert candidate(tickets = [['JFK', 'AUA'], ['AUA', 'SYD'], ['SYD', 'LAX'], ['LAX', 'JFK'], ['JFK', 'PEK'], ['PEK', 'AUA'], ['AUA', 'SYD'], ['SYD', 'PEK'], ['PEK', 'JFK'], ['JFK', 'LAX'], ['LAX', 'SYD'], ['SYD', 'JFK'], ['JFK', 'AUA']]) == ['JFK', 'AUA', 'SYD', 'JFK', 'AUA', 'SYD', 'LAX', 'JFK', 'LAX', 'SYD', 'PEK', 'JFK', 'PEK', 'AUA']\n assert candidate(tickets = [['JFK', 'KUL'], ['KUL', 'LAX'], ['LAX', 'JFK'], ['JFK', 'HOU'], ['HOU', 'SFO'], ['SFO', 'JFK'], ['JFK', 'SLC'], ['SLC', 'HOU'], ['HOU', 'JFK']]) == ['JFK', 'HOU', 'JFK', 'KUL', 'LAX', 'JFK', 'SLC', 'HOU', 'SFO', 'JFK']\n assert candidate(tickets = [['JFK', 'IAH'], ['IAH', 'ORD'], ['ORD', 'DEN'], ['DEN', 'LAX'], ['LAX', 'SFO'], ['SFO', 'IAH'], ['IAH', 'ORD'], ['ORD', 'DEN'], ['DEN', 'LAX']]) == ['JFK', 'IAH', 'ORD', 'DEN', 'LAX', 'SFO', 'IAH', 'ORD', 'DEN', 'LAX']\n assert candidate(tickets = [['JFK', 'LGA'], ['LGA', 'JFK'], ['JFK', 'LGA'], ['LGA', 'JFK'], ['JFK', 'LGA'], ['LGA', 'JFK'], ['JFK', 'LGA'], ['LGA', 'JFK'], ['JFK', 'LGA'], ['LGA', 'JFK']]) == ['JFK', 'LGA', 'JFK', 'LGA', 'JFK', 'LGA', 'JFK', 'LGA', 'JFK', 'LGA', 'JFK']\n assert candidate(tickets = [['JFK', 'SFO'], ['SFO', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SFO'], ['SFO', 'LAX'], ['LAX', 'ORD'], ['ORD', 'JFK'], ['JFK', 'HOU'], ['HOU', 'SFO'], ['SFO', 'HOU']]) == ['JFK', 'HOU', 'SFO', 'JFK', 'ORD', 'JFK', 'SFO', 'LAX', 'JFK', 'SFO', 'LAX', 'ORD', 'SFO', 'HOU']\n assert candidate(tickets = [['JFK', 'AAA'], ['AAA', 'BBB'], ['BBB', 'CCC'], ['CCC', 'DDD'], ['DDD', 'JFK'], ['JFK', 'EZE'], ['EZE', 'JFK']]) == ['JFK', 'AAA', 'BBB', 'CCC', 'DDD', 'JFK', 'EZE', 'JFK']\n assert candidate(tickets = [['JFK', 'LAX'], ['LAX', 'SFO'], ['SFO', 'JFK'], ['JFK', 'LAX'], ['LAX', 'SFO'], ['SFO', 'LAX'], ['LAX', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'SFO'], ['SFO', 'JFK'], ['JFK', 'LAX'], ['LAX', 'SFO'], ['SFO', 'LAX'], ['LAX', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'SFO'], ['SFO', 'JFK'], ['JFK', 'LAX'], ['LAX', 'SFO'], ['SFO', 'LAX'], ['LAX', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'SFO'], ['SFO', 'JFK'], ['JFK', 'LAX'], ['LAX', 'SFO'], ['SFO', 'LAX'], ['LAX', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX']]) == ['JFK', 'LAX', 'JFK', 'LAX', 'JFK', 'LAX', 'JFK', 'LAX', 'JFK', 'LAX', 'SFO', 'JFK', 'SFO', 'JFK', 'SFO', 'JFK', 'SFO', 'JFK', 'SFO', 'LAX', 'SFO', 'LAX', 'SFO', 'LAX', 'SFO', 'LAX', 'SFO', 'LAX', 'SFO', 'LAX', 'SFO', 'LAX', 'SFO', 'LAX']\n assert candidate(tickets = [['JFK', 'KUL'], ['KUL', 'LAX'], ['LAX', 'JFK'], ['JFK', 'DUB'], ['DUB', 'ORD'], ['ORD', 'LAX'], ['LAX', 'HOU'], ['HOU', 'SFO'], ['SFO', 'JFK']]) == ['JFK', 'DUB', 'ORD', 'LAX', 'HOU', 'SFO', 'JFK', 'KUL', 'LAX', 'JFK']\n assert candidate(tickets = [['JFK', 'XYZ'], ['XYZ', 'ABC'], ['ABC', 'JKL'], ['JKL', 'MNO'], ['MNO', 'PQR'], ['PQR', 'JKL'], ['JKL', 'ABC'], ['ABC', 'XYZ'], ['XYZ', 'JFK'], ['JFK', 'MNO']]) == ['JFK', 'MNO', 'PQR', 'JKL', 'ABC', 'XYZ', 'JFK', 'XYZ', 'ABC', 'JKL', 'MNO']\n assert candidate(tickets = [['JFK', 'XYZ'], ['XYZ', 'ABC'], ['ABC', 'JFK'], ['JFK', 'XYZ'], ['XYZ', 'DEF'], ['DEF', 'ABC'], ['ABC', 'XYZ'], ['XYZ', 'DEF'], ['DEF', 'JFK']]) == ['JFK', 'XYZ', 'ABC', 'JFK', 'XYZ', 'DEF', 'ABC', 'XYZ', 'DEF', 'JFK']\n assert candidate(tickets = [['JFK', 'DEL'], ['DEL', 'JFK'], ['JFK', 'BOM'], ['BOM', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BOM'], ['BOM', 'JFK'], ['JFK', 'BOM'], ['BOM', 'DEL']]) == ['JFK', 'BOM', 'DEL', 'BOM', 'DEL', 'JFK', 'BOM', 'JFK', 'DEL', 'JFK', 'DEL']\n assert candidate(tickets = [['JFK', 'DEL'], ['DEL', 'BOM'], ['BOM', 'DEL'], ['DEL', 'LHR'], ['LHR', 'BOM'], ['BOM', 'SFO'], ['SFO', 'LHR'], ['LHR', 'SFO'], ['SFO', 'DEL'], ['DEL', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DEL'], ['DEL', 'BOM'], ['BOM', 'SFO'], ['SFO', 'JFK'], ['JFK', 'BOM'], ['BOM', 'LHR'], ['LHR', 'JFK'], ['JFK', 'SFO'], ['SFO', 'BOM']]) == ['JFK', 'BOM', 'DEL', 'BOM', 'LHR', 'BOM', 'SFO', 'BOM', 'SFO', 'DEL', 'JFK', 'DEL', 'LHR', 'JFK', 'LHR', 'SFO', 'JFK', 'SFO', 'LHR', 'DEL', 'BOM']\n assert candidate(tickets = [['JFK', 'BCN'], ['BCN', 'JFK'], ['JFK', 'MIA'], ['MIA', 'JFK'], ['JFK', 'DXB'], ['DXB', 'JFK'], ['JFK', 'SFO'], ['SFO', 'JFK']]) == ['JFK', 'BCN', 'JFK', 'DXB', 'JFK', 'MIA', 'JFK', 'SFO', 'JFK']\n assert candidate(tickets = [['JFK', 'DXB'], ['DXB', 'JFK'], ['JFK', 'DXB'], ['DXB', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'LHR'], ['LHR', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB'], ['DXB', 'JFK'], ['JFK', 'LHR'], ['LHR', 'DXB']]) == ['JFK', 'DXB', 'JFK', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'JFK', 'LHR', 'DXB', 'LHR', 'DXB', 'LHR', 'JFK', 'LHR', 'DXB']\n assert candidate(tickets = [['JFK', 'NRT'], ['NRT', 'JFK'], ['JFK', 'NRT'], ['NRT', 'PEK'], ['PEK', 'LAX'], ['LAX', 'PEK'], ['PEK', 'JFK'], ['JFK', 'LAX'], ['LAX', 'JFK'], ['JFK', 'PEK'], ['PEK', 'NRT'], ['NRT', 'LAX'], ['LAX', 'NRT'], ['NRT', 'JFK'], ['JFK', 'PEK'], ['PEK', 'LAX'], ['LAX', 'JFK']]) == ['JFK', 'LAX', 'JFK', 'NRT', 'JFK', 'NRT', 'JFK', 'PEK', 'JFK', 'PEK', 'LAX', 'NRT', 'LAX', 'PEK', 'NRT', 'PEK', 'LAX', 'JFK']\n assert candidate(tickets = [['JFK', 'FRA'], ['JFK', 'TIA'], ['FRA', 'JFK'], ['TIA', 'FRA'], ['FRA', 'TIA'], ['TIA', 'JFK']]) == ['JFK', 'FRA', 'JFK', 'TIA', 'FRA', 'TIA', 'JFK']\n assert candidate(tickets = [['JFK', 'YYZ'], ['YYZ', 'BOS'], ['BOS', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'YYZ'], ['YYZ', 'BOS'], ['BOS', 'JFK'], ['JFK', 'BOS'], ['BOS', 'YYZ'], ['YYZ', 'JFK']]) == ['JFK', 'BOS', 'JFK', 'YYZ', 'BOS', 'YYZ', 'BOS', 'YYZ', 'JFK', 'YYZ', 'JFK']\n assert candidate(tickets = [['JFK', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'YYZ'], ['YYZ', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'LHR'], ['LHR', 'JFK'], ['JFK', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR'], ['LHR', 'YYZ'], ['YYZ', 'JFK'], ['JFK', 'LHR']]) == ['JFK', 'LHR', 'JFK', 'LHR', 'YYZ', 'JFK', 'LHR', 'YYZ', 'JFK', 'LHR', 'YYZ', 'JFK', 'LHR', 'YYZ', 'JFK', 'LHR', 'YYZ', 'JFK', 'LHR', 'YYZ', 'JFK', 'YYZ', 'JFK', 'YYZ', 'JFK', 'YYZ', 'LHR', 'YYZ', 'LHR']\n assert candidate(tickets = [['JFK', 'NRT'], ['NRT', 'JFK'], ['JFK', 'KUL'], ['KUL', 'LAX'], ['LAX', 'NRT'], ['NRT', 'KUL'], ['KUL', 'JFK']]) == ['JFK', 'KUL', 'JFK', 'NRT', 'KUL', 'LAX', 'NRT', 'JFK']\n assert candidate(tickets = [['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'DEN'], ['DEN', 'LAX'], ['LAX', 'SFO'], ['SFO', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'DEN']]) == ['JFK', 'SFO', 'JFK', 'SFO', 'LAX', 'DEN', 'LAX', 'SFO', 'LAX', 'DEN']\n assert candidate(tickets = [['JFK', 'SFO'], ['SFO', 'ATL'], ['ATL', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SFO'], ['SFO', 'ORD'], ['ORD', 'ATL'], ['ATL', 'SFO'], ['SFO', 'JFK'], ['JFK', 'ORD'], ['ORD', 'ATL'], ['ATL', 'ORD'], ['ORD', 'SFO'], ['SFO', 'ATL'], ['ATL', 'JFK'], ['JFK', 'SFO'], ['SFO', 'ORD'], ['ORD', 'SFO'], ['SFO', 'ATL'], ['ATL', 'ORD'], ['ORD', 'JFK'], ['JFK', 'ATL'], ['ATL', 'ORD'], ['ORD', 'SFO'], ['SFO', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SFO'], ['SFO', 'ATL'], ['ATL', 'ORD'], ['ORD', 'JFK'], ['JFK', 'SFO']]) == ['JFK', 'ATL', 'JFK', 'ORD', 'ATL', 'JFK', 'ORD', 'ATL', 'ORD', 'JFK', 'ORD', 'JFK', 'SFO', 'ATL', 'ORD', 'SFO', 'ATL', 'ORD', 'SFO', 'ATL', 'ORD', 'SFO', 'ATL', 'SFO', 'JFK', 'SFO', 'JFK', 'SFO', 'ORD', 'SFO', 'ORD', 'SFO']\n assert candidate(tickets = [['JFK', 'ZRH'], ['ZRH', 'HOU'], ['HOU', 'JFK'], ['JFK', 'LHR'], ['LHR', 'HOU'], ['HOU', 'LHR'], ['LHR', 'ZRH'], ['ZRH', 'JFK']]) == ['JFK', 'LHR', 'HOU', 'JFK', 'ZRH', 'HOU', 'LHR', 'ZRH', 'JFK']\n assert candidate(tickets = [['JFK', 'IST'], ['IST', 'DXB'], ['DXB', 'ORD'], ['ORD', 'JFK'], ['JFK', 'IST'], ['IST', 'DXB'], ['DXB', 'ORD'], ['ORD', 'LAX'], ['LAX', 'JFK']]) == ['JFK', 'IST', 'DXB', 'ORD', 'JFK', 'IST', 'DXB', 'ORD', 'LAX', 'JFK']\n assert candidate(tickets = [['JFK', 'SFO'], ['SFO', 'ATL'], ['ATL', 'JFK'], ['JFK', 'SFO'], ['SFO', 'ORD'], ['ORD', 'SFO'], ['SFO', 'ATL'], ['ATL', 'SFO'], ['SFO', 'ORD'], ['ORD', 'JFK']]) == ['JFK', 'SFO', 'ATL', 'JFK', 'SFO', 'ATL', 'SFO', 'ORD', 'SFO', 'ORD', 'JFK']\n assert candidate(tickets = [['JFK', 'DXB'], ['DXB', 'SYD'], ['SYD', 'JFK'], ['JFK', 'DEL'], ['DEL', 'DXB'], ['DXB', 'SYD'], ['SYD', 'DEL'], ['DEL', 'JFK']]) == ['JFK', 'DEL', 'DXB', 'SYD', 'DEL', 'JFK', 'DXB', 'SYD', 'JFK']\n assert candidate(tickets = [['JFK', 'DXB'], ['DXB', 'BKK'], ['BKK', 'DXB'], ['DXB', 'JFK'], ['JFK', 'DEL'], ['DEL', 'DXB'], ['DXB', 'DEL'], ['DEL', 'BKK'], ['BKK', 'DEL'], ['DEL', 'JFK'], ['JFK', 'BKK'], ['BKK', 'JFK'], ['JFK', 'DXB']]) == ['JFK', 'BKK', 'DEL', 'BKK', 'DXB', 'BKK', 'JFK', 'DEL', 'DXB', 'DEL', 'JFK', 'DXB', 'JFK', 'DXB']\n assert candidate(tickets = [['JFK', 'CPT'], ['CPT', 'DEL'], ['DEL', 'DXB'], ['DXB', 'SFO'], ['SFO', 'HOU'], ['HOU', 'JFK'], ['JFK', 'BOM'], ['BOM', 'CPT'], ['CPT', 'HOU'], ['HOU', 'DXB'], ['DXB', 'JFK'], ['JFK', 'SFO'], ['SFO', 'DEL'], ['DEL', 'BOM'], ['BOM', 'HOU'], ['HOU', 'SFO'], ['SFO', 'DXB'], ['DXB', 'CPT'], ['CPT', 'BOM'], ['BOM', 'SFO']]) == ['JFK', 'BOM', 'CPT', 'BOM', 'HOU', 'DXB', 'CPT', 'DEL', 'BOM', 'SFO', 'DEL', 'DXB', 'JFK', 'CPT', 'HOU', 'JFK', 'SFO', 'DXB', 'SFO', 'HOU', 'SFO']\n assert candidate(tickets = [['JFK', 'LAX'], ['LAX', 'SFO'], ['SFO', 'HOU'], ['HOU', 'LAX'], ['LAX', 'JFK'], ['JFK', 'ORD'], ['ORD', 'SFO'], ['SFO', 'HOU'], ['HOU', 'ORD'], ['ORD', 'JFK']]) == ['JFK', 'LAX', 'JFK', 'ORD', 'SFO', 'HOU', 'LAX', 'SFO', 'HOU', 'ORD', 'JFK']\n assert candidate(tickets = [['JFK', 'NRT'], ['JFK', 'KUL'], ['NRT', 'JFK'], ['KUL', 'JFK'], ['JFK', 'NRT'], ['NRT', 'KUL'], ['KUL', 'NRT'], ['NRT', 'LAX'], ['LAX', 'HOU'], ['HOU', 'SYD'], ['SYD', 'JFK'], ['JFK', 'SYD'], ['SYD', 'HOU'], ['HOU', 'LAX'], ['LAX', 'NRT'], ['NRT', 'JFK'], ['JFK', 'LAX'], ['LAX', 'SYD'], ['SYD', 'JFK'], ['JFK', 'AUA'], ['AUA', 'SYD'], ['SYD', 'LAX'], ['LAX', 'JFK'], ['JFK', 'PEK'], ['PEK', 'AUA'], ['AUA', 'SYD'], ['SYD', 'PEK'], ['PEK', 'JFK']]) == ['JFK', 'AUA', 'SYD', 'HOU', 'LAX', 'HOU', 'SYD', 'JFK', 'KUL', 'JFK', 'LAX', 'JFK', 'NRT', 'JFK', 'NRT', 'JFK', 'PEK', 'AUA', 'SYD', 'JFK', 'SYD', 'LAX', 'NRT', 'KUL', 'NRT', 'LAX', 'SYD', 'PEK', 'JFK']\n assert candidate(tickets = [['JFK', 'A'], ['A', 'B'], ['B', 'C'], ['C', 'D'], ['D', 'E'], ['E', 'F'], ['F', 'G'], ['G', 'H'], ['H', 'I'], ['I', 'J'], ['J', 'K'], ['K', 'L'], ['L', 'M'], ['M', 'N'], ['N', 'O'], ['O', 'P'], ['P', 'Q'], ['Q', 'R'], ['R', 'S'], ['S', 'T'], ['T', 'U'], ['U', 'V'], ['V', 'W'], ['W', 'X'], ['X', 'Y'], ['Y', 'Z'], ['Z', 'A'], ['A', 'JFK'], ['JFK', 'Z'], ['Z', 'Y'], ['Y', 'X'], ['X', 'W'], ['W', 'V'], ['V', 'U'], ['U', 'T'], ['T', 'S'], ['S', 'R'], ['R', 'Q'], ['Q', 'P'], ['P', 'O'], ['O', 'N'], ['N', 'M'], ['M', 'L'], ['L', 'K'], ['K', 'J'], ['J', 'I'], ['I', 'H'], ['H', 'G'], ['G', 'F'], ['F', 'E'], ['E', 'D'], ['D', 'C'], ['C', 'B'], ['B', 'A'], ['A', 'JFK']]) == ['JFK', 'A', 'B', 'A', 'JFK', 'Z', 'Y', 'X', 'W', 'V', 'U', 'T', 'S', 'R', 'Q', 'P', 'O', 'N', 'M', 'L', 'K', 'J', 'I', 'H', 'G', 'F', 'E', 'D', 'C', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'A', 'JFK']\n assert candidate(tickets = [['JFK', 'NRT'], ['NRT', 'JFK'], ['JFK', 'KUL'], ['KUL', 'NRT'], ['NRT', 'JFK'], ['JFK', 'NRT']]) == ['JFK', 'KUL', 'NRT', 'JFK', 'NRT', 'JFK', 'NRT']\n assert candidate(tickets = [['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL'], ['DEL', 'BLR'], ['BLR', 'DEL'], ['DEL', 'JFK'], ['JFK', 'DEL']]) == ['JFK', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'BLR', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL', 'JFK', 'DEL']\n assert candidate(tickets = [['JFK', 'B'], ['B', 'JFK'], ['JFK', 'C'], ['C', 'JFK'], ['JFK', 'D'], ['D', 'JFK'], ['JFK', 'E'], ['E', 'JFK']]) == ['JFK', 'B', 'JFK', 'C', 'JFK', 'D', 'JFK', 'E', 'JFK']\n assert candidate(tickets = [['JFK', 'CDG'], ['CDG', 'HOU'], ['HOU', 'DXB'], ['DXB', 'SFO'], ['SFO', 'JFK'], ['JFK', 'DXB'], ['DXB', 'HOU'], ['HOU', 'CDG'], ['CDG', 'JFK'], ['JFK', 'HOU'], ['HOU', 'SFO'], ['SFO', 'DXB'], ['DXB', 'JFK'], ['JFK', 'SFO'], ['SFO', 'HOU'], ['HOU', 'CDG'], ['CDG', 'DXB'], ['DXB', 'SFO'], ['SFO', 'CDG'], ['CDG', 'HOU'], ['HOU', 'JFK'], ['JFK', 'CDG']]) == ['JFK', 'CDG', 'DXB', 'HOU', 'CDG', 'HOU', 'CDG', 'HOU', 'DXB', 'JFK', 'CDG', 'JFK', 'DXB', 'SFO', 'DXB', 'SFO', 'HOU', 'JFK', 'HOU', 'SFO', 'JFK', 'SFO', 'CDG']\n assert candidate(tickets = [['JFK', 'SFO'], ['SFO', 'DSM'], ['DSM', 'JFK'], ['JFK', 'SFO'], ['SFO', 'LAX'], ['LAX', 'JFK'], ['JFK', 'SFO'], ['SFO', 'DSM']]) == ['JFK', 'SFO', 'DSM', 'JFK', 'SFO', 'LAX', 'JFK', 'SFO', 'DSM']\n assert candidate(tickets = [['JFK', 'HOU'], ['HOU', 'LAX'], ['LAX', 'NRT'], ['NRT', 'DXB'], ['DXB', 'SFO'], ['SFO', 'MIA'], ['MIA', 'JFK'], ['JFK', 'HOU'], ['HOU', 'LAX'], ['LAX', 'NRT'], ['NRT', 'DXB'], ['DXB', 'SFO'], ['SFO', 'MIA'], ['MIA', 'JFK'], ['JFK', 'HOU'], ['HOU', 'LAX'], ['LAX', 'NRT'], ['NRT', 'DXB'], ['DXB', 'SFO'], ['SFO', 'MIA'], ['MIA', 'JFK'], ['JFK', 'HOU'], ['HOU', 'LAX'], ['LAX', 'NRT'], ['NRT', 'DXB'], ['DXB', 'SFO'], ['SFO', 'MIA'], ['MIA', 'JFK']]) == ['JFK', 'HOU', 'LAX', 'NRT', 'DXB', 'SFO', 'MIA', 'JFK', 'HOU', 'LAX', 'NRT', 'DXB', 'SFO', 'MIA', 'JFK', 'HOU', 'LAX', 'NRT', 'DXB', 'SFO', 'MIA', 'JFK', 'HOU', 'LAX', 'NRT', 'DXB', 'SFO', 'MIA', 'JFK']\n assert candidate(tickets = [['JFK', 'A'], ['A', 'B'], ['B', 'C'], ['C', 'A'], ['A', 'D'], ['D', 'E'], ['E', 'F'], ['F', 'G'], ['G', 'F'], ['F', 'E'], ['E', 'D'], ['D', 'C'], ['C', 'B'], ['B', 'A'], ['A', 'JFK'], ['JFK', 'H'], ['H', 'I'], ['I', 'J'], ['J', 'H'], ['H', 'JFK'], ['JFK', 'K'], ['K', 'L'], ['L', 'M'], ['M', 'N'], ['N', 'O'], ['O', 'P'], ['P', 'Q'], ['Q', 'R'], ['R', 'S'], ['S', 'T'], ['T', 'U'], ['U', 'V'], ['V', 'W'], ['W', 'X'], ['X', 'Y'], ['Y', 'Z'], ['Z', 'W'], ['W', 'V'], ['V', 'U'], ['U', 'T'], ['T', 'S'], ['S', 'R'], ['R', 'Q'], ['Q', 'P'], ['P', 'O'], ['O', 'N'], ['N', 'M'], ['M', 'L'], ['L', 'K'], ['K', 'JFK']]) == ['JFK', 'A', 'B', 'A', 'D', 'E', 'F', 'G', 'F', 'E', 'D', 'C', 'B', 'C', 'A', 'JFK', 'H', 'I', 'J', 'H', 'JFK', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z', 'W', 'V', 'U', 'T', 'S', 'R', 'Q', 'P', 'O', 'N', 'M', 'L', 'K', 'JFK']\n assert candidate(tickets = [['JFK', 'BOS'], ['BOS', 'SFO'], ['SFO', 'BOS'], ['BOS', 'JFK'], ['JFK', 'BOS'], ['BOS', 'JFK'], ['JFK', 'BOS'], ['BOS', 'SFO']]) == ['JFK', 'BOS', 'JFK', 'BOS', 'JFK', 'BOS', 'SFO', 'BOS', 'SFO']\n assert candidate(tickets = [['JFK', 'MEX'], ['MEX', 'LAX'], ['LAX', 'JFK'], ['JFK', 'MEX'], ['MEX', 'LAX'], ['LAX', 'MEX'], ['MEX', 'JFK'], ['JFK', 'LAX'], ['LAX', 'MEX'], ['MEX', 'LAX']]) == ['JFK', 'LAX', 'JFK', 'MEX', 'JFK', 'MEX', 'LAX', 'MEX', 'LAX', 'MEX', 'LAX']\n assert candidate(tickets = [['JFK', 'A'], ['A', 'B'], ['B', 'C'], ['C', 'A'], ['A', 'D'], ['D', 'E'], ['E', 'F'], ['F', 'G'], ['G', 'E'], ['E', 'D'], ['D', 'A'], ['A', 'C'], ['C', 'B'], ['B', 'A'], ['A', 'F'], ['F', 'E'], ['E', 'D'], ['D', 'C'], ['C', 'A'], ['A', 'B'], ['B', 'C'], ['C', 'D'], ['D', 'E'], ['E', 'F'], ['F', 'G'], ['G', 'F'], ['F', 'E'], ['E', 'D'], ['D', 'C'], ['C', 'B'], ['B', 'A'], ['A', 'JFK']]) == ['JFK', 'A', 'B', 'A', 'B', 'A', 'C', 'A', 'D', 'A', 'F', 'E', 'D', 'C', 'B', 'C', 'B', 'C', 'D', 'E', 'D', 'E', 'F', 'E', 'F', 'G', 'F', 'G', 'E', 'D', 'C', 'A', 'JFK']\n assert candidate(tickets = [['JFK', 'AAA'], ['AAA', 'BBB'], ['BBB', 'CCC'], ['CCC', 'DDD'], ['DDD', 'EEE'], ['EEE', 'DDD'], ['DDD', 'CCC'], ['CCC', 'BBB'], ['BBB', 'AAA'], ['AAA', 'JFK'], ['JFK', 'DDD'], ['DDD', 'EEE'], ['EEE', 'DDD'], ['DDD', 'CCC'], ['CCC', 'BBB'], ['BBB', 'AAA'], ['AAA', 'JFK']]) == ['JFK', 'AAA', 'BBB', 'AAA', 'JFK', 'DDD', 'CCC', 'BBB', 'CCC', 'DDD', 'EEE', 'DDD', 'EEE', 'DDD', 'CCC', 'BBB', 'AAA', 'JFK']\n assert candidate(tickets = [['JFK', 'AUA'], ['AUA', 'SFO'], ['SFO', 'HOU'], ['HOU', 'JFK'], ['JFK', 'AUA'], ['AUA', 'HOU'], ['HOU', 'SFO'], ['SFO', 'JFK'], ['JFK', 'AUA'], ['AUA', 'SFO'], ['SFO', 'HOU'], ['HOU', 'JFK']]) == ['JFK', 'AUA', 'HOU', 'JFK', 'AUA', 'SFO', 'HOU', 'JFK', 'AUA', 'SFO', 'HOU', 'SFO', 'JFK']\n"}, "metadata": {"canonical_parameter_names": ["tickets"], "leetcode_dataset_entry_point": "Solution().findItinerary", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findItinerary = function(tickets) {", "container": null, "callable": "findItinerary", "parameters": [{"name": "tickets", "type": "string[][]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 334, "task_id": "increasing-triplet-subsequence", "difficulty": "Medium", "problem_description": "Given an integer array nums, return true if there exists a triple of indices (i, j, k) such that i < j < k and nums[i] < nums[j] < nums[k]. If no such indices exists, return false.\n \nExample 1:\n\nInput: nums = [1,2,3,4,5]\nOutput: true\nExplanation: Any triplet where i < j < k is valid.\n\nExample 2:\n\nInput: nums = [5,4,3,2,1]\nOutput: false\nExplanation: No triplet exists.\n\nExample 3:\n\nInput: nums = [2,1,5,0,4,6]\nOutput: true\nExplanation: The triplet (3, 4, 5) is valid because nums[3] == 0 < nums[4] == 4 < nums[5] == 6.\n\n \nConstraints:\n\n1 <= nums.length <= 5 * 105\n-231 <= nums[i] <= 231 - 1\n\n \nFollow up: Could you implement a solution that runs in O(n) time complexity and O(1) space complexity?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 4, 3, 2, 1]) == False\n assert candidate(nums = [0, -1, 2, -3, 4, -5, 6, -7]) == True\n assert candidate(nums = [-1, 0, 1, 2, -1, -4]) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1]) == False\n assert candidate(nums = [20, 100, 10, 12, 5, 13]) == True\n assert candidate(nums = [1, 1, 1, 1, 1]) == False\n assert candidate(nums = [1, 2]) == False\n assert candidate(nums = [0, -1, 1]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2]) == False\n assert candidate(nums = [0, 4, 2, 1, 0, -1, -3]) == False\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18]) == True\n assert candidate(nums = [2, 1, 5, 0, 4, 6]) == True\n assert candidate(nums = [1, 2, 0, 4, 5]) == True\n assert candidate(nums = [1, 2, 3, 4, 5]) == True\n assert candidate(nums = [20, 100, 10, 12, 5, 13]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6]) == True\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18]) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 4, 5, 6, 5, 7, 5]) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 5]) == True\n assert candidate(nums = [2147483647, -2147483648, 0, 1, -1, 2, -2, 3, -3]) == True\n assert candidate(nums = [1000000000, 999999999, 1, 1000000001]) == False\n assert candidate(nums = [10, 20, 30, 15, 25, 35]) == True\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 1, 9, 2, 5, 1]) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 3]) == True\n assert candidate(nums = [1, 2, 0, 4, 5, 3, 6]) == True\n assert candidate(nums = [1, 5, 2, 4, 3, 6, 7, 8, 9, 10, 0]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 1, 3, 7]) == True\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]) == False\n assert candidate(nums = [9, 11, 13, 12, 14, 15, 16]) == True\n assert candidate(nums = [3, 1, 4, 2, 5, 7, 8]) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100, 1]) == False\n assert candidate(nums = [1, 3, 2, 4, 6, 5, 7, 8, 10, 9]) == True\n assert candidate(nums = [5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7]) == True\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8]) == True\n assert candidate(nums = [1, 2, 3, 2, 1, 4, 5]) == True\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 22, 23]) == True\n assert candidate(nums = [7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9]) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 4, 7]) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 5, 6, 7]) == True\n assert candidate(nums = [2, 1, 5, 0, 4, 6, 3, 8, 7, 9]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 4]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == True\n assert candidate(nums = [1, 20, 3, 10, 5, 15, 8, 25, 12]) == True\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == False\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1, -2, -3, -4, -5]) == False\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 5]) == True\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18, 102, 103]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == True\n assert candidate(nums = [-1000000000, -999999999, -1000000001, -1000000002, -1000000003]) == False\n assert candidate(nums = [10, 1, 11, 1, 12, 1, 13, 1]) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == False\n assert candidate(nums = [10, 1, 20, 2, 30, 3, 40, 4, 50, 5]) == True\n assert candidate(nums = [8, 10, 4, 6, 9, 1, 5, 3, 7, 2]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10]) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4]) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3]) == True\n assert candidate(nums = [3, 1, 4, 2, 5]) == True\n assert candidate(nums = [3, 5, 0, 2, 1, 4, 6, 7, 8, 9]) == True\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91]) == False\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == True\n assert candidate(nums = [1000000000, 999999999, 1000000001, 1000000002, 999999998]) == True\n assert candidate(nums = [7, 7, 7, 8, 7, 7, 7, 7, 9, 7]) == True\n assert candidate(nums = [8, 1, 2, 3, 7, 4, 5]) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 1, 2, 3, 4, 5]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 1, 3, 5]) == True\n assert candidate(nums = [8, 1, 3, 7, 4, 6, 2, 9, 5, 10]) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == False\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4, 10, 11, 12, 13, 14]) == True\n assert candidate(nums = [6, 5, 4, 8, 7, 9, 2, 1, 3, 4]) == True\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000]) == False\n assert candidate(nums = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6]) == True\n assert candidate(nums = [3, 2, 1, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5]) == False\n assert candidate(nums = [1000000000, 999999999, 1000000001, 999999998, 1000000002, 999999997, 1000000003]) == True\n assert candidate(nums = [1, 2, 0, 4, 5, 3, 7, 8, 6, 9]) == True\n assert candidate(nums = [-10, -20, -15, -25, -30, -5, -35]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1]) == True\n assert candidate(nums = [1000000000, 999999999, 1000000001, 1000000002, 1000000003]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == True\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8]) == False\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]) == True\n assert candidate(nums = [8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8]) == False\n assert candidate(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, -1, -2, -3]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [1000000000, 500000000, 750000000, 1000000001, 1000000002]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 0, 6, 7, 8]) == True\n assert candidate(nums = [3, 2, 1, 2, 1, 0, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [3, 1, 2, 4, 6, 5, 7, 9, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 4, 5, 6]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1]) == False\n assert candidate(nums = [1000000000, -1000000000, 500000000, -500000000, 100000000, -100000000, 50000000, -50000000]) == True\n assert candidate(nums = [1, 5, 0, 4, 2, 3, 6]) == True\n assert candidate(nums = [1, 2, 3, 4, 3, 5, 4, 6, 5, 7, 6, 8]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 4]) == True\n assert candidate(nums = [3, 1, 2, 4, 3, 5, 6, 1, 2, 7]) == True\n assert candidate(nums = [-1, 2, -3, 4, -5, 6, -7, 8, -9, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [10, 20, 15, 25, 30, 5, 35]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8]) == True\n assert candidate(nums = [1, 3, 2, 4, 3, 5]) == True\n assert candidate(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0]) == True\n assert candidate(nums = [8, 9, 7, 6, 5, 4, 3, 2, 1, 0]) == False\n assert candidate(nums = [1000000000, 999999999, 1000000001, 1000000002, 999999998, 1000000003]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 3, 5]) == True\n assert candidate(nums = [7, 7, 7, 1, 2, 8, 10, 9, 11]) == True\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 10]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9]) == False\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 1, 9, 5, 5, 5]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 4, 7, 6, 8, 9]) == True\n assert candidate(nums = [8, 7, 6, 5, 4, 3, 2, 1, 0]) == False\n assert candidate(nums = [5, 1, 4, 2, 3, 6]) == True\n assert candidate(nums = [2, 1, 3, 0, 4, -1, 5, 6, 7, 8]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 4, 5]) == True\n assert candidate(nums = [1, 2, 2, 1, 2, 3]) == True\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().increasingTriplet", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var increasingTriplet = function(nums) {", "container": null, "callable": "increasingTriplet", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 335, "task_id": "self-crossing", "difficulty": "Hard", "problem_description": "You are given an array of integers distance.\nYou start at the point (0, 0) on an X-Y plane, and you move distance[0] meters to the north, then distance[1] meters to the west, distance[2] meters to the south, distance[3] meters to the east, and so on. In other words, after each move, your direction changes counter-clockwise.\nReturn true if your path crosses itself or false if it does not.\n \nExample 1:\n\n\nInput: distance = [2,1,1,2]\nOutput: true\nExplanation: The path crosses itself at the point (0, 1).\n\nExample 2:\n\n\nInput: distance = [1,2,3,4]\nOutput: false\nExplanation: The path does not cross itself at any point.\n\nExample 3:\n\n\nInput: distance = [1,1,1,2,1]\nOutput: true\nExplanation: The path crosses itself at the point (0, 0).\n\n \nConstraints:\n\n1 <= distance.length <= 105\n1 <= distance[i] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(distance = [3, 5, 3, 4, 3, 4]) == True\n assert candidate(distance = [3, 3, 3, 2, 1]) == False\n assert candidate(distance = [1, 2, 3, 4, 1, 2, 3, 4]) == True\n assert candidate(distance = [1, 1, 1, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(distance = [1, 2, 3, 4, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == False\n assert candidate(distance = [3, 3, 3, 2, 1, 1]) == False\n assert candidate(distance = [1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 2, 2, 3, 4, 4, 5, 5]) == False\n assert candidate(distance = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5]) == True\n assert candidate(distance = [6, 6, 6, 6, 6, 1]) == True\n assert candidate(distance = [3, 3, 3, 2, 2, 3, 4]) == True\n assert candidate(distance = [1, 2, 3, 4]) == False\n assert candidate(distance = [1, 2, 3, 4, 5, 6]) == False\n assert candidate(distance = [2, 1, 1, 2]) == True\n assert candidate(distance = [1, 1, 2, 2, 3, 4, 5, 6, 7, 8]) == False\n assert candidate(distance = [5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(distance = [1, 2, 3, 4, 5]) == False\n assert candidate(distance = [1, 1, 2, 2, 3, 3]) == False\n assert candidate(distance = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == False\n assert candidate(distance = [10, 2, 10, 1, 10, 2, 10]) == True\n assert candidate(distance = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 3, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 2, 3, 4, 5, 4, 3, 2, 1, 1]) == True\n assert candidate(distance = [10, 10, 1, 1, 10, 10, 1, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [3, 1, 3, 1, 3, 1, 3]) == True\n assert candidate(distance = [1, 2, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == True\n assert candidate(distance = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2]) == True\n assert candidate(distance = [1, 3, 2, 2, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [10, 1, 1, 10, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 1]) == False\n assert candidate(distance = [3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3]) == True\n assert candidate(distance = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 1, 1]) == True\n assert candidate(distance = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == True\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == True\n assert candidate(distance = [1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 1]) == False\n assert candidate(distance = [5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [5, 10, 10, 5, 5, 10, 10, 5, 5, 10, 10]) == True\n assert candidate(distance = [1, 2, 3, 4, 3, 3, 2, 2, 1, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == True\n assert candidate(distance = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2]) == True\n assert candidate(distance = [1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1]) == True\n assert candidate(distance = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == False\n assert candidate(distance = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1]) == False\n assert candidate(distance = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19]) == False\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11]) == True\n assert candidate(distance = [5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1, 5, 5, 1, 1]) == True\n assert candidate(distance = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == True\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7]) == True\n assert candidate(distance = [1, 1, 2, 2, 3, 3, 2, 2, 1, 1]) == True\n assert candidate(distance = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 4, 5, 4, 5, 4]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5]) == True\n assert candidate(distance = [3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 1, 1]) == False\n assert candidate(distance = [5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1]) == True\n assert candidate(distance = [2, 3, 1, 4, 3, 2, 1]) == True\n assert candidate(distance = [8, 2, 8, 2, 8, 2, 8, 2, 8, 2]) == True\n assert candidate(distance = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 5, 5, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [5, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1]) == True\n assert candidate(distance = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 1]) == False\n assert candidate(distance = [2, 3, 1, 1, 2, 1, 1, 2, 3, 2]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [10, 10, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 3, 3, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == False\n assert candidate(distance = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == True\n assert candidate(distance = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == True\n assert candidate(distance = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == False\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == True\n assert candidate(distance = [5, 6, 7, 8, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 1]) == False\n assert candidate(distance = [1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1]) == True\n assert candidate(distance = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7]) == True\n assert candidate(distance = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == False\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == True\n assert candidate(distance = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == True\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 5, 5, 5]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 4, 3, 3, 2, 2, 1, 1]) == True\n assert candidate(distance = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 100]) == False\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(distance = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 3, 3, 2, 1, 2, 1]) == True\n assert candidate(distance = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8]) == True\n assert candidate(distance = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(distance = [5, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(distance = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n"}, "metadata": {"canonical_parameter_names": ["distance"], "leetcode_dataset_entry_point": "Solution().isSelfCrossing", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isSelfCrossing = function(distance) {", "container": null, "callable": "isSelfCrossing", "parameters": [{"name": "distance", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 336, "task_id": "palindrome-pairs", "difficulty": "Hard", "problem_description": "You are given a 0-indexed array of unique strings words.\nA palindrome pair is a pair of integers (i, j) such that:\n\n0 <= i, j < words.length,\ni != j, and\nwords[i] + words[j] (the concatenation of the two strings) is a palindrome.\n\nReturn an array of all the palindrome pairs of words.\nYou must write an algorithm with O(sum of words[i].length) runtime complexity.\n \nExample 1:\n\nInput: words = [\"abcd\",\"dcba\",\"lls\",\"s\",\"sssll\"]\nOutput: [[0,1],[1,0],[3,2],[2,4]]\nExplanation: The palindromes are [\"abcddcba\",\"dcbaabcd\",\"slls\",\"llssssll\"]\n\nExample 2:\n\nInput: words = [\"bat\",\"tab\",\"cat\"]\nOutput: [[0,1],[1,0]]\nExplanation: The palindromes are [\"battab\",\"tabbat\"]\n\nExample 3:\n\nInput: words = [\"a\",\"\"]\nOutput: [[0,1],[1,0]]\nExplanation: The palindromes are [\"a\",\"a\"]\n\n \nConstraints:\n\n1 <= words.length <= 5000\n0 <= words[i].length <= 300\nwords[i] consists of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(words = ['aabb', 'bbaa', 'abc', 'cba']) == [[0, 1], [1, 0], [2, 3], [3, 2]]\n assert candidate(words = ['bat', 'tab', 'cat']) == [[0, 1], [1, 0]]\n assert candidate(words = ['abc', 'cba', 'bca', 'xyz', 'zyx']) == [[0, 1], [1, 0], [3, 4], [4, 3]]\n assert candidate(words = ['abba', 'a', 'abc', 'cba']) == [[2, 3], [3, 2]]\n assert candidate(words = ['abcd', 'dcba', '', 'cba', 'abc']) == [[0, 3], [0, 1], [4, 1], [1, 0], [3, 4], [4, 3]]\n assert candidate(words = ['abba', 'a', 'abc', 'cba', 'bbaa', 'aba']) == [[2, 3], [3, 2]]\n assert candidate(words = ['ab', 'ba', 'abc', 'cba', 'abcd', 'dcba']) == [[0, 1], [1, 0], [2, 1], [2, 3], [0, 3], [3, 2], [4, 3], [4, 5], [2, 5], [5, 4]]\n assert candidate(words = ['aa', 'bb', 'aaa', 'bbb', 'aaaa', 'bbbb']) == [[0, 2], [2, 0], [1, 3], [3, 1], [2, 4], [4, 0], [0, 4], [4, 2], [3, 5], [5, 1], [1, 5], [5, 3]]\n assert candidate(words = ['aa', 'b', 'aaa', 'bb']) == [[0, 2], [2, 0], [3, 1], [1, 3]]\n assert candidate(words = ['a', '']) == [[0, 1], [1, 0]]\n assert candidate(words = ['abcd', 'dcba', 'lls', 's', 'sssll']) == [[0, 1], [1, 0], [3, 2], [2, 4]]\n assert candidate(words = ['abc', 'cba', 'bba', 'aab', 'aaa']) == [[0, 1], [1, 0]]\n assert candidate(words = ['a', 'b', 'c', 'd']) == []\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']) == []\n assert candidate(words = ['a', '']) == [[0, 1], [1, 0]]\n assert candidate(words = ['tacocat', 'racecar', 'banana', 'ananab', 'civic']) == [[2, 3], [3, 2]]\n assert candidate(words = ['aabb', 'bbaa', 'abab', 'baba', 'aaaa', 'bbbb']) == [[0, 1], [1, 0], [2, 3], [3, 2]]\n assert candidate(words = ['abcd', 'dcba']) == [[0, 1], [1, 0]]\n assert candidate(words = ['dcb', 'abcd', 'cba', 'abc', 'bca', 'bac', 'cab', 'a']) == [[0, 1], [1, 2], [2, 3], [3, 2], [5, 6], [6, 5]]\n assert candidate(words = ['abab', 'baba', 'abba', 'baab', 'aaaa', 'bbbb']) == [[0, 1], [1, 0]]\n assert candidate(words = ['abba', 'a', 'baa', 'b']) == [[2, 3]]\n assert candidate(words = ['abcd', 'dcba', 'lls', 's', 'sssll', 'ddsssll']) == [[0, 1], [1, 0], [3, 2], [2, 4]]\n assert candidate(words = ['a', 'abc', 'aba', 'xyz', 'zyx']) == [[3, 4], [4, 3]]\n assert candidate(words = ['', 'a', 'b', 'c', 'd']) == [[1, 0], [0, 1], [2, 0], [0, 2], [3, 0], [0, 3], [4, 0], [0, 4]]\n assert candidate(words = ['aabb', 'bbaa', 'aaaa', 'abba', 'baab']) == [[0, 1], [1, 0]]\n assert candidate(words = ['dcb', 'abcd', 'cba', 'cbcd']) == [[0, 1], [1, 2], [0, 3]]\n assert candidate(words = ['zxcvbnm', 'mnbvcxz', 'asdfghjkl', 'lkjhgfdsa', 'qwertyuiop', 'poiuytrewq', '1234567890', '0987654321', 'abcdefghij', 'jihgfedcba', 'klmnopqrst', 'tsrqponmlk', 'uvwxyz', 'zyxwvut', 'nopqrstu', 'utsrqpon', 'abcdefgh', 'hgfedcba', 'ijklmnop', 'ponmlkji', 'qrstuvwx', 'xwvutsrq', 'yz', 'zy', 'abcd', 'dcba', 'ab', 'ba', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 5], [5, 4], [6, 7], [7, 6], [8, 9], [9, 8], [10, 11], [11, 10], [13, 12], [14, 15], [15, 14], [16, 17], [17, 16], [18, 19], [19, 18], [20, 21], [21, 20], [22, 52], [53, 22], [22, 23], [23, 53], [52, 23], [23, 22], [24, 25], [25, 24], [26, 28], [29, 26], [26, 27], [27, 29], [28, 27], [27, 26]]\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa', 'aaaaaaaaaaa', 'aaaaaaaaaaaa', 'aaaaaaaaaaaaa', 'aaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaaaaaa', 'aaaaaaaaaaaaaaaaaaaa']) == [[1, 0], [0, 1], [2, 0], [1, 2], [2, 1], [0, 2], [3, 0], [2, 3], [3, 1], [1, 3], [3, 2], [0, 3], [4, 0], [3, 4], [4, 1], [2, 4], [4, 2], [1, 4], [4, 3], [0, 4], [5, 0], [4, 5], [5, 1], [3, 5], [5, 2], [2, 5], [5, 3], [1, 5], [5, 4], [0, 5], [6, 0], [5, 6], [6, 1], [4, 6], [6, 2], [3, 6], [6, 3], [2, 6], [6, 4], [1, 6], [6, 5], [0, 6], [7, 0], [6, 7], [7, 1], [5, 7], [7, 2], [4, 7], [7, 3], [3, 7], [7, 4], [2, 7], [7, 5], [1, 7], [7, 6], [0, 7], [8, 0], [7, 8], [8, 1], [6, 8], [8, 2], [5, 8], [8, 3], [4, 8], [8, 4], [3, 8], [8, 5], [2, 8], [8, 6], [1, 8], [8, 7], [0, 8], [9, 0], [8, 9], [9, 1], [7, 9], [9, 2], [6, 9], [9, 3], [5, 9], [9, 4], [4, 9], [9, 5], [3, 9], [9, 6], [2, 9], [9, 7], [1, 9], [9, 8], [0, 9], [10, 0], [9, 10], [10, 1], [8, 10], [10, 2], [7, 10], [10, 3], [6, 10], [10, 4], [5, 10], [10, 5], [4, 10], [10, 6], [3, 10], [10, 7], [2, 10], [10, 8], [1, 10], [10, 9], [0, 10], [11, 0], [10, 11], [11, 1], [9, 11], [11, 2], [8, 11], [11, 3], [7, 11], [11, 4], [6, 11], [11, 5], [5, 11], [11, 6], [4, 11], [11, 7], [3, 11], [11, 8], [2, 11], [11, 9], [1, 11], [11, 10], [0, 11], [12, 0], [11, 12], [12, 1], [10, 12], [12, 2], [9, 12], [12, 3], [8, 12], [12, 4], [7, 12], [12, 5], [6, 12], [12, 6], [5, 12], [12, 7], [4, 12], [12, 8], [3, 12], [12, 9], [2, 12], [12, 10], [1, 12], [12, 11], [0, 12], [13, 0], [12, 13], [13, 1], [11, 13], [13, 2], [10, 13], [13, 3], [9, 13], [13, 4], [8, 13], [13, 5], [7, 13], [13, 6], [6, 13], [13, 7], [5, 13], [13, 8], [4, 13], [13, 9], [3, 13], [13, 10], [2, 13], [13, 11], [1, 13], [13, 12], [0, 13], [14, 0], [13, 14], [14, 1], [12, 14], [14, 2], [11, 14], [14, 3], [10, 14], [14, 4], [9, 14], [14, 5], [8, 14], [14, 6], [7, 14], [14, 7], [6, 14], [14, 8], [5, 14], [14, 9], [4, 14], [14, 10], [3, 14], [14, 11], [2, 14], [14, 12], [1, 14], [14, 13], [0, 14], [15, 0], [14, 15], [15, 1], [13, 15], [15, 2], [12, 15], [15, 3], [11, 15], [15, 4], [10, 15], [15, 5], [9, 15], [15, 6], [8, 15], [15, 7], [7, 15], [15, 8], [6, 15], [15, 9], [5, 15], [15, 10], [4, 15], [15, 11], [3, 15], [15, 12], [2, 15], [15, 13], [1, 15], [15, 14], [0, 15], [16, 0], [15, 16], [16, 1], [14, 16], [16, 2], [13, 16], [16, 3], [12, 16], [16, 4], [11, 16], [16, 5], [10, 16], [16, 6], [9, 16], [16, 7], [8, 16], [16, 8], [7, 16], [16, 9], [6, 16], [16, 10], [5, 16], [16, 11], [4, 16], [16, 12], [3, 16], [16, 13], [2, 16], [16, 14], [1, 16], [16, 15], [0, 16], [17, 0], [16, 17], [17, 1], [15, 17], [17, 2], [14, 17], [17, 3], [13, 17], [17, 4], [12, 17], [17, 5], [11, 17], [17, 6], [10, 17], [17, 7], [9, 17], [17, 8], [8, 17], [17, 9], [7, 17], [17, 10], [6, 17], [17, 11], [5, 17], [17, 12], [4, 17], [17, 13], [3, 17], [17, 14], [2, 17], [17, 15], [1, 17], [17, 16], [0, 17], [18, 0], [17, 18], [18, 1], [16, 18], [18, 2], [15, 18], [18, 3], [14, 18], [18, 4], [13, 18], [18, 5], [12, 18], [18, 6], [11, 18], [18, 7], [10, 18], [18, 8], [9, 18], [18, 9], [8, 18], [18, 10], [7, 18], [18, 11], [6, 18], [18, 12], [5, 18], [18, 13], [4, 18], [18, 14], [3, 18], [18, 15], [2, 18], [18, 16], [1, 18], [18, 17], [0, 18], [19, 0], [18, 19], [19, 1], [17, 19], [19, 2], [16, 19], [19, 3], [15, 19], [19, 4], [14, 19], [19, 5], [13, 19], [19, 6], [12, 19], [19, 7], [11, 19], [19, 8], [10, 19], [19, 9], [9, 19], [19, 10], [8, 19], [19, 11], [7, 19], [19, 12], [6, 19], [19, 13], [5, 19], [19, 14], [4, 19], [19, 15], [3, 19], [19, 16], [2, 19], [19, 17], [1, 19], [19, 18], [0, 19]]\n assert candidate(words = ['a', 'b', 'c', '', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == [[0, 3], [3, 0], [1, 3], [3, 1], [2, 3], [3, 2], [4, 3], [3, 4], [5, 3], [3, 5], [6, 3], [3, 6], [7, 3], [3, 7], [8, 3], [3, 8], [9, 3], [3, 9], [10, 3], [3, 10], [11, 3], [3, 11], [12, 3], [3, 12], [13, 3], [3, 13], [14, 3], [3, 14], [15, 3], [3, 15], [16, 3], [3, 16], [17, 3], [3, 17], [18, 3], [3, 18], [19, 3], [3, 19], [20, 3], [3, 20], [21, 3], [3, 21], [22, 3], [3, 22], [23, 3], [3, 23], [24, 3], [3, 24], [25, 3], [3, 25], [26, 3], [3, 26]]\n assert candidate(words = ['noon', 'civic', 'level', 'rotor', 'deified', 'redder', 'repaper', 'refer', 'reviver', 'reviled']) == []\n assert candidate(words = ['abba', 'baab', 'aabb', 'bbaa', 'aaaa', 'aaab', 'abaa', 'baaa', 'bbba', 'baba']) == [[2, 3], [3, 2], [5, 7], [7, 5]]\n assert candidate(words = ['a', 'ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij']) == [[1, 0]]\n assert candidate(words = ['noon', 'civic', 'rotor', 'refer', 'deed', 'level', 'kayak', 'reviled', 'repaid']) == []\n assert candidate(words = ['race', 'car', '', '', 'racecar', 'ecar', 'cec', 'ceccec']) == [[0, 1], [0, 5], [2, 3], [4, 3], [3, 4], [5, 0], [6, 3], [3, 6], [7, 3], [7, 6], [6, 7], [3, 7]]\n assert candidate(words = ['abcdabcd', 'dcbaabcd', 'cdabcd', 'dcbabcd', 'abcbabc', 'cbababc', 'abcabcba', 'bcbabcba', 'cdcdcdcd', 'dcddcddc', 'abcd', 'dcba', 'cd', 'dc', 'abcdabc', 'dcbaabc', 'abc', 'cba']) == [[15, 1], [6, 17], [4, 7], [12, 9], [10, 17], [10, 11], [16, 11], [11, 10], [12, 13], [13, 12], [16, 17], [17, 16]]\n assert candidate(words = ['race', 'car', 'cec', 'dec', 'ded', 'level', 'deified', 'civic']) == [[0, 1]]\n assert candidate(words = ['abcde', 'edcba', 'fgh', 'hgf', 'xyz', 'zyx', 'ijk', 'kji', 'mnop', 'ponm', 'qrst', 'tsrq', 'uvw', 'wvu']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 5], [5, 4], [6, 7], [7, 6], [8, 9], [9, 8], [10, 11], [11, 10], [12, 13], [13, 12]]\n assert candidate(words = ['race', 'ecar', 'car', 'racecar', 'carrace', 'arcec', 'cecarr', 'racecarcar']) == [[0, 2], [0, 1], [1, 0]]\n assert candidate(words = ['aabbcc', 'ccbbaa', 'abcde', 'edcba', 'abcd', 'dcba']) == [[0, 1], [1, 0], [2, 5], [2, 3], [4, 3], [3, 2], [4, 5], [5, 4]]\n assert candidate(words = ['aabbcc', 'ccbbaa', 'abc', 'cba', 'abcd', 'dcba', 'abcde', 'edcba', 'abcdef', 'fedcba', 'abcdefg', 'gfedcba', 'abcdefgh', 'hgfedcba', 'abcdefghi', 'ihgfedcba']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 3], [4, 5], [2, 5], [5, 4], [6, 5], [6, 7], [4, 7], [7, 6], [8, 7], [8, 9], [6, 9], [9, 8], [10, 9], [10, 11], [8, 11], [11, 10], [12, 11], [12, 13], [10, 13], [13, 12], [14, 13], [14, 15], [12, 15], [15, 14]]\n assert candidate(words = ['abcde', 'edcba', 'fghij', 'jihgf', 'klmno', 'onmlk', 'pqrst', 'tsrqp', 'uvwxy', 'yxwuv']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 5], [5, 4], [6, 7], [7, 6]]\n assert candidate(words = ['abab', 'baba', 'ab', 'ba', 'a', 'b', '', 'aba', 'bab', 'bba', 'aab', 'baa']) == [[0, 4], [8, 0], [0, 7], [5, 0], [0, 1], [1, 5], [7, 1], [1, 8], [4, 1], [1, 0], [2, 4], [5, 2], [2, 3], [3, 5], [4, 3], [3, 2], [4, 6], [6, 4], [5, 6], [6, 5], [7, 6], [2, 7], [7, 3], [6, 7], [8, 6], [3, 8], [8, 2], [6, 8], [2, 9], [4, 9], [3, 10], [5, 10], [10, 11], [11, 5], [11, 2], [11, 10]]\n assert candidate(words = ['aabbcc', 'ccbbaa', 'abcabc', 'cbabca', 'bacbac', 'abacab', 'bacbac', 'cababc', 'bcaacb', 'aabb', 'bbaa', 'aabbaa', 'abbbaa', 'aaabbb', 'baaabb', 'aababb', 'abbaab', 'bababa']) == [[0, 10], [0, 1], [9, 1], [1, 0], [9, 10], [10, 9], [9, 11], [11, 10]]\n assert candidate(words = ['xyxy', 'yxyx', 'yxx', 'xx', 'xyyx', 'yyxy', 'xyx', 'yyy', 'xyyxxyy', 'yyxxyyx', 'xyyyxyx', 'yyxyxxy', 'xyyxyyx', 'yyxxyxy', 'xyyyxxy', 'yyxyxyx', 'xyyxyxy', 'yyxxyyy', 'xyyyxyy', 'yyxxyxy', 'xyyxyyx', 'yyxxyxy', 'xyyyxxy', 'yyxyxyx', 'xyyxyxy', 'yyxxyyy', 'xyyyxyy', 'yyxxyxy', 'xyyxyyx', 'yyxxyxy', 'xyyyxxy', 'yyxyxyx', 'xyyxyxy', 'yyxxyyy']) == [[0, 6], [0, 1], [6, 1], [1, 0], [3, 2], [8, 9], [9, 8], [12, 28], [16, 4], [20, 28], [24, 4], [32, 4]]\n assert candidate(words = ['abcde', 'edcba', 'fghij', 'jihgf', 'klmno', 'onmlk']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 5], [5, 4]]\n assert candidate(words = ['ab', 'ba', 'abc', 'cba', 'abcd', 'dcba', 'abcde', 'edcba', 'abcdef', 'fedcba', 'abcdefg', 'gfedcba']) == [[0, 1], [1, 0], [2, 1], [2, 3], [0, 3], [3, 2], [4, 3], [4, 5], [2, 5], [5, 4], [6, 5], [6, 7], [4, 7], [7, 6], [8, 7], [8, 9], [6, 9], [9, 8], [10, 9], [10, 11], [8, 11], [11, 10]]\n assert candidate(words = ['ab', 'ba', 'abc', 'cba', 'abcd', 'dcba', 'abcde', 'edcba', 'abcdef', 'fedcba', 'abcdefg', 'gfedcba', 'abcdefgh', 'hgfedcba', 'abcdefghi', 'ihgfedcba', 'abcdefghij', 'jihgfedcba', 'abcdefghijk', 'kjihgfedcba', 'abcdefghijkl', 'lkjihgfedcba', 'abcdefghijklm', 'mlkjihgfedcba', 'abcdefghijklmn', 'nmlkjihgfedcba', 'abcdefghijklmno', 'onmlkjihgfedcba', 'abcdefghijklmnop', 'ponmlkjihgfedcba', 'abcdefghijklmnopq', 'qponmlkjihgfedcba', 'abcdefghijklmnopqr', 'rponmlkjihgfedcba', 'abcdefghijklmnopqrs', 'spnmlkjihgfedcba', 'abcdefghijklmnopqrst', 'tspnmlkjihgfedcba', 'abcdefghijklmnopqrstu', 'ustpnmlkjihgfedcba', 'abcdefghijklmnopqrstuv', 'vustpnmlkjihgfedcba', 'abcdefghijklmnopqrstuvw', 'wvustpnmlkjihgfedcba', 'abcdefghijklmnopqrstuvwx', 'xwvustpnmlkjihgfedcba', 'abcdefghijklmnopqrstuvwxy', 'yxwvustpnmlkjihgfedcba', 'abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba']) == [[0, 1], [1, 0], [2, 1], [2, 3], [0, 3], [3, 2], [4, 3], [4, 5], [2, 5], [5, 4], [6, 5], [6, 7], [4, 7], [7, 6], [8, 7], [8, 9], [6, 9], [9, 8], [10, 9], [10, 11], [8, 11], [11, 10], [12, 11], [12, 13], [10, 13], [13, 12], [14, 13], [14, 15], [12, 15], [15, 14], [16, 15], [16, 17], [14, 17], [17, 16], [18, 17], [18, 19], [16, 19], [19, 18], [20, 19], [20, 21], [18, 21], [21, 20], [22, 21], [22, 23], [20, 23], [23, 22], [24, 23], [24, 25], [22, 25], [25, 24], [26, 25], [26, 27], [24, 27], [27, 26], [28, 27], [28, 29], [26, 29], [29, 28], [30, 29], [30, 31], [28, 31], [31, 30], [32, 31], [28, 33], [48, 49], [46, 49], [49, 48]]\n assert candidate(words = ['abcba', 'bcbaa', 'cbaab', 'baabc', 'aabcd', 'bcdcb', 'cdcbc', 'dcbcd', 'cbcdc', 'bcdbc', 'abcdc']) == [[2, 3], [3, 2], [6, 8], [8, 6]]\n assert candidate(words = ['abcde', 'edcba', '', '', 'abcdeedcba', 'aabcdeedcbaa', 'aaabcdeedcbaaa', 'aaaabcdeedcbaaaa', 'aaaaabcdeedcbaaaaa', 'abcdeedcbaaaaa', 'aabcdeedcbaaaaaa', 'aaabcdeedcbaaaaaaa', 'aaaabcdeedcbaaaaaaaa', 'aaaaabcdeedcbaaaaaaaaa', 'abcdeedcbaaaaaaaaaa']) == [[0, 1], [1, 0], [2, 3], [4, 3], [3, 4], [5, 3], [3, 5], [6, 3], [3, 6], [7, 3], [3, 7], [8, 3], [8, 9], [3, 8], [9, 4], [10, 5], [11, 6], [12, 7], [13, 9], [13, 8], [14, 4]]\n assert candidate(words = ['abacaba', 'abcbaca', 'abcdcba', 'abeceda', 'aabcdcbba', 'abcddcba', 'deified', 'civic', 'level', 'rotor', 'madam', 'refer', 'repaper', 'reviver', 'reviled', 'redder']) == []\n assert candidate(words = ['abacaba', 'acababa', 'bacabab', 'cabaaba', '', 'abacaba', 'acababa', 'bacabab', 'cabaaba']) == [[0, 4], [0, 5], [4, 0], [5, 4], [4, 5]]\n assert candidate(words = ['a', 'ab', 'abc', 'abcd', 'abcba', 'abccba', 'abcdcba', 'abccbaa']) == [[1, 0], [7, 5], [0, 7]]\n assert candidate(words = ['palindrome', 'emordnilap', 'word', 'drow', 'madam', 'ada', 'radar', 'kayak', 'reviled', 'devil']) == [[0, 1], [1, 0], [2, 3], [3, 2]]\n assert candidate(words = ['noon', 'moon', 'noontime', 'timenoon', 'time', 'emit']) == [[5, 2], [3, 5], [4, 5], [5, 4]]\n assert candidate(words = ['xyx', 'yxy', 'xxyy', 'yyxx', 'xyyx', 'yxxy', 'xyxx', 'yxx', 'xxy', 'yy', 'xy', 'yx', 'x', 'y', '', 'aaa', 'bbb', 'ccc', 'aaab', 'bbba', 'aaa', 'bbbb', 'cccc', 'dddd', 'dddb', 'bbbd', 'aaa', 'bbbb', 'cccc', 'dddd', 'dddb', 'bbbd']) == [[0, 14], [10, 0], [0, 11], [14, 0], [1, 14], [11, 1], [1, 10], [14, 1], [9, 2], [2, 7], [2, 3], [8, 3], [3, 9], [3, 2], [4, 14], [14, 4], [5, 14], [7, 5], [5, 8], [14, 5], [8, 6], [6, 11], [6, 0], [12, 6], [7, 13], [7, 10], [7, 8], [11, 8], [13, 8], [8, 7], [9, 14], [9, 13], [13, 9], [14, 9], [10, 12], [13, 10], [10, 11], [11, 13], [12, 11], [11, 10], [12, 14], [14, 12], [13, 14], [14, 13], [15, 14], [15, 26], [14, 15], [16, 14], [14, 16], [17, 14], [14, 17], [18, 26], [19, 16], [20, 14], [20, 26], [14, 20], [21, 14], [16, 21], [21, 16], [21, 27], [14, 21], [22, 14], [17, 22], [22, 17], [22, 28], [14, 22], [23, 14], [23, 29], [14, 23], [25, 16], [26, 14], [14, 26], [27, 14], [16, 27], [27, 16], [14, 27], [28, 14], [17, 28], [28, 17], [14, 28], [29, 14], [14, 29], [31, 16]]\n assert candidate(words = ['ab', 'ba', 'abc', 'cba', 'abcd', 'dcba', 'abcde', 'edcba', 'abcdef', 'fedcba', 'abcdefg', 'gfedcba', 'abcdefgh', 'hgfedcba', 'abcdefghi', 'ihgfedcba', 'abcdefghij', 'jihgfedcba']) == [[0, 1], [1, 0], [2, 1], [2, 3], [0, 3], [3, 2], [4, 3], [4, 5], [2, 5], [5, 4], [6, 5], [6, 7], [4, 7], [7, 6], [8, 7], [8, 9], [6, 9], [9, 8], [10, 9], [10, 11], [8, 11], [11, 10], [12, 11], [12, 13], [10, 13], [13, 12], [14, 13], [14, 15], [12, 15], [15, 14], [16, 15], [16, 17], [14, 17], [17, 16]]\n assert candidate(words = ['amanaplanacanalpanama', 'noon', 'civic', 'rotor', 'refer', 'deed', 'level', 'kayak', 'reviled', 'repaid']) == []\n assert candidate(words = ['aaaa', 'aaab', 'baaa', 'baba', 'abab', 'abba']) == [[1, 2], [2, 1], [3, 4], [4, 3]]\n assert candidate(words = ['abcdexyz', 'zyxcdeba', 'mnop', 'ponm', '', 'pponm', 'mnopq', 'zyxwvutsrqp', 'rqsponmlkjihgfedcba']) == [[2, 3], [3, 2], [2, 5], [6, 3]]\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == [[1, 0], [0, 1], [2, 0], [1, 2], [2, 1], [0, 2], [3, 0], [2, 3], [3, 1], [1, 3], [3, 2], [0, 3], [4, 0], [3, 4], [4, 1], [2, 4], [4, 2], [1, 4], [4, 3], [0, 4], [5, 0], [4, 5], [5, 1], [3, 5], [5, 2], [2, 5], [5, 3], [1, 5], [5, 4], [0, 5], [6, 0], [5, 6], [6, 1], [4, 6], [6, 2], [3, 6], [6, 3], [2, 6], [6, 4], [1, 6], [6, 5], [0, 6], [7, 0], [6, 7], [7, 1], [5, 7], [7, 2], [4, 7], [7, 3], [3, 7], [7, 4], [2, 7], [7, 5], [1, 7], [7, 6], [0, 7], [8, 0], [7, 8], [8, 1], [6, 8], [8, 2], [5, 8], [8, 3], [4, 8], [8, 4], [3, 8], [8, 5], [2, 8], [8, 6], [1, 8], [8, 7], [0, 8], [9, 0], [8, 9], [9, 1], [7, 9], [9, 2], [6, 9], [9, 3], [5, 9], [9, 4], [4, 9], [9, 5], [3, 9], [9, 6], [2, 9], [9, 7], [1, 9], [9, 8], [0, 9]]\n assert candidate(words = ['xyx', 'yxy', 'xyyx', 'yyxy', 'xyxyy', 'yxyxy', 'xyxyxy', 'yxyxyx', 'xyxyxyx', 'yxyxyxy', 'xyxyxyxy']) == [[1, 3], [3, 4], [4, 0], [5, 6], [6, 0], [1, 6], [6, 7], [7, 1], [0, 7], [7, 5], [7, 6], [6, 8], [8, 7], [7, 9], [9, 6], [9, 10], [10, 0], [5, 10], [1, 10], [10, 8]]\n assert candidate(words = ['race', 'ecar', 'car', 'arc', 'racer', 'carrace', '', 'a', 'aa', 'aaa']) == [[0, 2], [0, 1], [1, 0], [4, 1], [7, 6], [6, 7], [8, 6], [8, 7], [7, 8], [6, 8], [9, 6], [9, 7], [8, 9], [9, 8], [7, 9], [6, 9]]\n assert candidate(words = ['racecar', 'carerac', 'level', 'deified', 'civic']) == []\n assert candidate(words = ['noon', 'moon', 'noonmoon', 'moonoon', 'moonnoon', 'noonnoo']) == [[5, 4]]\n assert candidate(words = ['madam', 'racecar', 'level', 'noon', 'civic', 'rotor', 'refer', 'deified', 'reviled', 'deed', 'peep', 'radar', 'repaper', 'kayak', 'reviver', 'redder', 'repel']) == []\n assert candidate(words = ['aabbcc', 'ccbbaa', 'abcabc', 'cbacba', 'xyzzyx', 'yxzzxy', 'mnopqr', 'rqponm', '', 'pqr', 'qpon']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 8], [8, 4], [5, 8], [8, 5], [6, 7], [7, 6]]\n assert candidate(words = ['aabbcc', 'ccbbaa', 'bbccaa', 'aabb', 'bbaa', 'ccaa', 'aabbccaa', 'aabbccbb', 'aabbaa', 'bbcc', 'ccbb', 'aabbccc', 'ccbaab', 'bbccaabb', 'ccaabbbc', 'aabbbcc', 'ccbbbaa', 'bbcaabbcc', 'aabcc', 'bbaac', 'ccaab', 'bbaabbcc', 'aabbbccaa', 'aabbbccbb', 'aaabbccaa', 'aaabbccbb', 'aabbbbcc', 'bbccbbbb', 'aabbbbaa', 'bbaaaa', 'ccaabbbaa', 'aabbbcccc', 'cccaabbb', 'bbcccaabb', 'aabbbcccbb', 'bbbaaabbbc', 'ccbbbaabbb', 'bbbaabbbcc', 'aabbbbaabbcc', 'aabbbbaabbbc', 'bbbaabbccbb', 'bbbaabbbccc', 'bbbaaabbbcc', 'aabbbbaaabbb', 'bbbaaabbbb', 'aabbbaaaaabb', 'aabbbbaaaaab', 'aabbbaaaaaaa', 'bbaaaaaaabbb', 'bbaaaaaaaabb', 'bbaaaaaaabba', 'bbaaaaaaaaab', 'bbaaaaaaaaaa']) == [[10, 0], [0, 4], [0, 1], [3, 1], [1, 9], [1, 0], [2, 10], [3, 4], [4, 3], [6, 1], [7, 1], [3, 8], [8, 4], [9, 10], [10, 9], [11, 4], [11, 1], [12, 18], [15, 16], [16, 15], [19, 3], [1, 21], [22, 16], [23, 16], [27, 10], [29, 3], [31, 16], [36, 15], [36, 37], [16, 37], [37, 36], [10, 38], [41, 36], [44, 43], [52, 3]]\n assert candidate(words = ['xyx', 'yxy', 'yxx', 'xxz', 'zxx', 'zzz', 'zzxz', 'xzzx', 'zxzx', 'xzzxz', 'zxzzx', 'zxxxxz', 'xzxxxxz', 'zxzxzxz', 'xzzzzzzx', 'zzzzzzzz', 'zxxzzzxxz', 'zxzzzzzxz', 'xzxxxxzzx', 'zzxxxxzzz', 'zxzzzzzzx']) == [[3, 4], [4, 3], [9, 7], [9, 10], [7, 10], [10, 6], [10, 9], [11, 12], [8, 13], [15, 5], [5, 15], [14, 20]]\n assert candidate(words = ['abacaba', 'bacabab', 'cababac', 'abacabc', 'bacabc', 'cababc', 'abcabc', 'bcabc', 'cabc', 'abc', 'bc', 'c', '', 'a', 'b', 'ba', 'ab', 'ac', 'ca', 'bca', 'cab', 'abcba', 'bcbca', 'cabcb', 'abcabcba', 'bcabcbca', 'cabcbcab']) == [[0, 12], [12, 0], [15, 1], [2, 12], [12, 2], [11, 4], [9, 15], [10, 14], [11, 10], [11, 12], [12, 11], [13, 12], [12, 13], [14, 12], [12, 14], [15, 14], [13, 15], [15, 16], [16, 13], [14, 16], [16, 15], [17, 13], [11, 17], [17, 18], [18, 11], [13, 18], [18, 17], [17, 19], [15, 20], [20, 17], [21, 12], [12, 21], [17, 22], [23, 17]]\n assert candidate(words = ['noon', 'moon', 'noom', 'noon', 'moom', 'omo', 'moo', 'omo', 'm', 'oo', 'om', 'mo', '', 'n', 'nn', 'nno', 'onn', 'no', 'on', 'o', 'oo', 'ooo', 'oooo', 'ooooo', 'oooooo', 'ooooooo', 'oooooooo', 'ooooooooo']) == [[0, 12], [0, 3], [12, 0], [1, 2], [6, 2], [2, 1], [3, 12], [12, 3], [4, 12], [6, 4], [12, 4], [5, 12], [10, 5], [5, 11], [5, 7], [12, 5], [6, 8], [20, 6], [6, 10], [7, 12], [10, 7], [7, 11], [12, 7], [8, 12], [12, 8], [9, 12], [9, 19], [19, 9], [9, 20], [12, 9], [10, 19], [8, 10], [10, 11], [11, 8], [19, 11], [11, 10], [13, 12], [12, 13], [14, 12], [14, 13], [13, 14], [12, 14], [18, 15], [15, 14], [19, 15], [15, 16], [16, 19], [14, 16], [16, 17], [16, 15], [17, 13], [19, 17], [17, 18], [18, 19], [13, 18], [18, 17], [19, 12], [12, 19], [20, 12], [20, 19], [19, 20], [12, 20], [21, 12], [21, 19], [20, 21], [21, 20], [19, 21], [12, 21], [22, 12], [22, 19], [21, 22], [22, 20], [20, 22], [22, 21], [19, 22], [12, 22], [23, 12], [23, 19], [22, 23], [23, 20], [21, 23], [23, 21], [20, 23], [23, 22], [19, 23], [12, 23], [24, 12], [24, 19], [23, 24], [24, 20], [22, 24], [24, 21], [21, 24], [24, 22], [20, 24], [24, 23], [19, 24], [12, 24], [25, 12], [25, 19], [24, 25], [25, 20], [23, 25], [25, 21], [22, 25], [25, 22], [21, 25], [25, 23], [20, 25], [25, 24], [19, 25], [12, 25], [26, 12], [26, 19], [25, 26], [26, 20], [24, 26], [26, 21], [23, 26], [26, 22], [22, 26], [26, 23], [21, 26], [26, 24], [20, 26], [26, 25], [19, 26], [12, 26], [27, 12], [27, 19], [26, 27], [27, 20], [25, 27], [27, 21], [24, 27], [27, 22], [23, 27], [27, 23], [22, 27], [27, 24], [21, 27], [27, 25], [20, 27], [27, 26], [19, 27], [12, 27]]\n assert candidate(words = ['racecar', 'carerac', 'madam', 'level', 'noon', 'civic', 'rotor', 'refer', 'deified', 'redder', 'repaper', 'rotator', 'detartrated', 'reviled', 'repel', 'redivider', 'repaper', 'reviver', 'rotor', 'rotator', 'redder', 'refer', 'civic', 'level', 'rotor', 'repaper', 'rotator', 'deified', 'detartrated', 'refer', 'rotor', 'reviver', 'redder', 'repaper', 'repaper', 'rotor', 'repaper']) == [[3, 23], [5, 22], [6, 35], [7, 29], [8, 27], [9, 32], [10, 36], [11, 26], [12, 28], [16, 36], [17, 31], [18, 35], [19, 26], [20, 32], [21, 29], [24, 35], [25, 36], [30, 35], [33, 36], [34, 36]]\n assert candidate(words = ['aaaa', 'aaab', 'baaa', 'bbbb', 'aaaaa']) == [[1, 2], [2, 1], [0, 4], [4, 0]]\n assert candidate(words = ['a1b', 'b1a', 'abc2', '2cba', 'abcd3', '3dcba', 'abcde4', '4edcba', 'abcdef5', '5fedcba', 'abcdefg6', '6gfedcba', 'abcdefgh7', '7hgfedcba', 'abcdefghi8', '8ihgfedcba']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 5], [5, 4], [6, 7], [7, 6], [8, 9], [9, 8], [10, 11], [11, 10], [12, 13], [13, 12], [14, 15], [15, 14]]\n assert candidate(words = ['racecar', 'madam', 'rotor', 'refer', 'deed', 'level', 'kayak', 'reviled', 'repaid', 'noon', 'civic', 'rotor', 'refer', 'deed', 'level', 'kayak', 'reviled', 'repaid']) == [[2, 11], [3, 12], [4, 13], [5, 14], [6, 15]]\n assert candidate(words = ['aaaaa', 'bbbbb', 'ccccc', 'ddddd', 'eeeee', 'aaaa', 'bbbb', 'cccc', 'dddd', 'eeee', 'aaa', 'bbb', 'ccc', 'ddd', 'eee', 'aa', 'bb', 'cc', 'dd', 'ee', 'a', 'b', 'c', 'd', 'e', '', 'ab', 'ba', 'ac', 'ca', 'ad', 'da', 'ae', 'ea', 'bc', 'cb', 'bd', 'db', 'be', 'eb', 'cd', 'dc', 'ce', 'ec', 'de', 'ed', 'abc', 'cba', 'abd', 'dba', 'abe', 'eba', 'acd', 'dca', 'ace', 'eca', 'ade', 'eda', 'bcd', 'dcb', 'bce', 'ecb', 'bde', 'edb', 'cde', 'edc', 'cef', 'fec', 'def', 'fed', 'cef', 'fec', 'gfe', 'efg', 'geh', 'ehg', 'heg', 'geh', 'hic', 'cih', 'ich', 'hic', 'jid', 'dij', 'idj', 'jid', 'kil', 'lik', 'ilk', 'kil', 'lmn', 'nml', 'mln', 'lmn', 'nop', 'pon', 'opn', 'nop', 'qrs', 'srq', 'rsq', 'qrs', 'tuv', 'vtu', 'utv', 'tuv', 'wxy', 'yxw', 'xyw', 'wxy', 'zzz', 'zz', 'z']) == [[0, 25], [0, 20], [5, 0], [0, 15], [10, 0], [0, 10], [15, 0], [0, 5], [20, 0], [25, 0], [1, 25], [1, 21], [6, 1], [1, 16], [11, 1], [1, 11], [16, 1], [1, 6], [21, 1], [25, 1], [2, 25], [2, 22], [7, 2], [2, 17], [12, 2], [2, 12], [17, 2], [2, 7], [22, 2], [25, 2], [3, 25], [3, 23], [8, 3], [3, 18], [13, 3], [3, 13], [18, 3], [3, 8], [23, 3], [25, 3], [4, 25], [4, 24], [9, 4], [4, 19], [14, 4], [4, 14], [19, 4], [4, 9], [24, 4], [25, 4], [5, 25], [5, 20], [10, 5], [5, 15], [15, 5], [5, 10], [20, 5], [25, 5], [6, 25], [6, 21], [11, 6], [6, 16], [16, 6], [6, 11], [21, 6], [25, 6], [7, 25], [7, 22], [12, 7], [7, 17], [17, 7], [7, 12], [22, 7], [25, 7], [8, 25], [8, 23], [13, 8], [8, 18], [18, 8], [8, 13], [23, 8], [25, 8], [9, 25], [9, 24], [14, 9], [9, 19], [19, 9], [9, 14], [24, 9], [25, 9], [10, 25], [10, 20], [15, 10], [10, 15], [20, 10], [25, 10], [11, 25], [11, 21], [16, 11], [11, 16], [21, 11], [25, 11], [12, 25], [12, 22], [17, 12], [12, 17], [22, 12], [25, 12], [13, 25], [13, 23], [18, 13], [13, 18], [23, 13], [25, 13], [14, 25], [14, 24], [19, 14], [14, 19], [24, 14], [25, 14], [15, 25], [15, 20], [20, 15], [25, 15], [16, 25], [16, 21], [21, 16], [25, 16], [17, 25], [17, 22], [22, 17], [25, 17], [18, 25], [18, 23], [23, 18], [25, 18], [19, 25], [19, 24], [24, 19], [25, 19], [20, 25], [25, 20], [21, 25], [25, 21], [22, 25], [25, 22], [23, 25], [25, 23], [24, 25], [25, 24], [26, 20], [21, 26], [26, 27], [27, 21], [20, 27], [27, 26], [28, 20], [22, 28], [28, 29], [29, 22], [20, 29], [29, 28], [30, 20], [23, 30], [30, 31], [31, 23], [20, 31], [31, 30], [32, 20], [24, 32], [32, 33], [33, 24], [20, 33], [33, 32], [34, 21], [22, 34], [34, 35], [35, 22], [21, 35], [35, 34], [36, 21], [23, 36], [36, 37], [37, 23], [21, 37], [37, 36], [38, 21], [24, 38], [38, 39], [39, 24], [21, 39], [39, 38], [40, 22], [23, 40], [40, 41], [41, 23], [22, 41], [41, 40], [42, 22], [24, 42], [42, 43], [43, 24], [22, 43], [43, 42], [44, 23], [24, 44], [44, 45], [45, 24], [23, 45], [45, 44], [35, 46], [46, 27], [46, 47], [26, 47], [47, 34], [47, 46], [37, 48], [48, 27], [48, 49], [26, 49], [49, 36], [49, 48], [39, 50], [50, 27], [50, 51], [26, 51], [51, 38], [51, 50], [41, 52], [52, 29], [52, 53], [28, 53], [53, 40], [53, 52], [43, 54], [54, 29], [54, 55], [28, 55], [55, 42], [55, 54], [45, 56], [56, 31], [56, 57], [30, 57], [57, 44], [57, 56], [41, 58], [58, 35], [58, 59], [34, 59], [59, 40], [59, 58], [43, 60], [60, 35], [60, 61], [34, 61], [61, 42], [61, 60], [45, 62], [62, 37], [62, 63], [36, 63], [63, 44], [63, 62], [45, 64], [64, 41], [64, 65], [40, 65], [65, 44], [65, 64], [66, 43], [66, 71], [42, 67], [67, 70], [68, 45], [68, 69], [44, 69], [69, 68], [70, 43], [70, 71], [42, 71], [71, 70], [72, 73], [73, 72], [74, 76], [76, 77], [77, 76], [78, 79], [79, 81], [81, 79], [82, 83], [83, 85], [85, 83], [86, 87], [87, 89], [89, 87], [90, 91], [91, 93], [93, 91], [94, 95], [95, 97], [97, 95], [98, 99], [99, 101], [101, 99], [103, 104], [104, 103], [106, 107], [107, 109], [109, 107], [110, 25], [110, 112], [111, 110], [110, 111], [112, 110], [25, 110], [111, 25], [111, 112], [112, 111], [25, 111], [112, 25], [25, 112]]\n assert candidate(words = ['', 'a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == [[1, 0], [0, 1], [2, 0], [2, 1], [1, 2], [0, 2], [3, 0], [3, 1], [2, 3], [3, 2], [1, 3], [0, 3], [4, 0], [4, 1], [3, 4], [4, 2], [2, 4], [4, 3], [1, 4], [0, 4], [5, 0], [5, 1], [4, 5], [5, 2], [3, 5], [5, 3], [2, 5], [5, 4], [1, 5], [0, 5], [6, 0], [6, 1], [5, 6], [6, 2], [4, 6], [6, 3], [3, 6], [6, 4], [2, 6], [6, 5], [1, 6], [0, 6], [7, 0], [7, 1], [7, 2], [7, 3], [6, 7], [7, 4], [5, 7], [7, 5], [4, 7], [7, 6], [3, 7], [2, 7], [1, 7], [0, 7], [8, 0], [8, 1], [7, 8], [8, 2], [8, 3], [8, 4], [6, 8], [8, 5], [5, 8], [8, 6], [4, 8], [3, 8], [2, 8], [8, 7], [1, 8], [0, 8]]\n assert candidate(words = ['race', 'car', 'level', '', 'deified', 'civic', 'rotor', '', 'madam', 'refer', 'redder', 'repaper', 'reviled', 'deed', 'noon', 'detartrated', 'redivider', 'rotor']) == [[0, 1], [2, 7], [7, 2], [3, 7], [4, 7], [7, 4], [5, 7], [7, 5], [6, 7], [6, 17], [7, 6], [8, 7], [7, 8], [9, 7], [7, 9], [10, 7], [7, 10], [11, 7], [7, 11], [13, 7], [7, 13], [14, 7], [7, 14], [15, 7], [7, 15], [16, 7], [7, 16], [17, 7], [7, 17]]\n assert candidate(words = ['xabc', 'cba', 'abcx', 'abxcba', 'cabxa', 'bxcba', 'abcabc', 'bcabc', 'cbabc', 'xcba', 'bac', 'cabx', 'bacxab', 'xcbax', 'baxcb', 'cbaabc']) == [[1, 0], [2, 1], [2, 9], [2, 5], [9, 2], [11, 10], [0, 13], [13, 2]]\n assert candidate(words = ['ab', 'ba', 'abc', 'cba', 'abcd', 'dcba', 'abcde', 'edcba', 'abcdef', 'fedcba']) == [[0, 1], [1, 0], [2, 1], [2, 3], [0, 3], [3, 2], [4, 3], [4, 5], [2, 5], [5, 4], [6, 5], [6, 7], [4, 7], [7, 6], [8, 7], [8, 9], [6, 9], [9, 8]]\n assert candidate(words = ['noon', 'level', 'deified', 'civic', 'rotor', 'madam', 'refer', 'deed', 'peep', 'radar', 'reviled', 'repaid', 'detartrated', 'reviver', 'redder', 'repaper', 'pepper', 'repel', 'deterred', 'reworded', 'repeal', 'perpet', 'repressed', 'repellet', 'perpetual', 'repellect']) == []\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == []\n assert candidate(words = ['palindrome', 'emordnilap', 'detartrated', 'deified', 'repaid', 'stressed', 'desserts', 'deed', 'civic', 'rotor', 'refer', 'level', 'kayak', 'reviled']) == [[0, 1], [1, 0], [5, 6], [6, 5]]\n assert candidate(words = ['abcde', 'edcba', 'fghij', 'jihgf', 'klmno', 'onmlk', 'pqrstu', 'utsrqp', 'vwxyz', 'zyxwv']) == [[0, 1], [1, 0], [2, 3], [3, 2], [4, 5], [5, 4], [6, 7], [7, 6], [8, 9], [9, 8]]\n assert candidate(words = ['xabcx', 'xbax', 'xcabx', 'xcax', 'xbxc', 'xcabxx', 'xxcabx', 'abcxx', 'xxcba', 'abcdxx', 'xxdcba', 'xxabcd', 'dxxcba', 'xabxx', 'xxbax']) == [[7, 8], [8, 7], [9, 10], [10, 9], [7, 12], [13, 1], [13, 14], [14, 13]]\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa']) == [[1, 0], [0, 1], [2, 0], [1, 2], [2, 1], [0, 2], [3, 0], [2, 3], [3, 1], [1, 3], [3, 2], [0, 3], [4, 0], [3, 4], [4, 1], [2, 4], [4, 2], [1, 4], [4, 3], [0, 4], [5, 0], [4, 5], [5, 1], [3, 5], [5, 2], [2, 5], [5, 3], [1, 5], [5, 4], [0, 5], [6, 0], [5, 6], [6, 1], [4, 6], [6, 2], [3, 6], [6, 3], [2, 6], [6, 4], [1, 6], [6, 5], [0, 6]]\n assert candidate(words = ['', 'a', 'b', 'c', 'aa', 'bb', 'cc', 'aaa', 'bbb', 'ccc', 'aaaa', 'bbbb', 'cccc', 'aaaaa', 'bbbbb', 'ccccc']) == [[1, 0], [0, 1], [2, 0], [0, 2], [3, 0], [0, 3], [4, 0], [4, 1], [1, 4], [0, 4], [5, 0], [5, 2], [2, 5], [0, 5], [6, 0], [6, 3], [3, 6], [0, 6], [7, 0], [7, 1], [4, 7], [7, 4], [1, 7], [0, 7], [8, 0], [8, 2], [5, 8], [8, 5], [2, 8], [0, 8], [9, 0], [9, 3], [6, 9], [9, 6], [3, 9], [0, 9], [10, 0], [10, 1], [7, 10], [10, 4], [4, 10], [10, 7], [1, 10], [0, 10], [11, 0], [11, 2], [8, 11], [11, 5], [5, 11], [11, 8], [2, 11], [0, 11], [12, 0], [12, 3], [9, 12], [12, 6], [6, 12], [12, 9], [3, 12], [0, 12], [13, 0], [13, 1], [10, 13], [13, 4], [7, 13], [13, 7], [4, 13], [13, 10], [1, 13], [0, 13], [14, 0], [14, 2], [11, 14], [14, 5], [8, 14], [14, 8], [5, 14], [14, 11], [2, 14], [0, 14], [15, 0], [15, 3], [12, 15], [15, 6], [9, 15], [15, 9], [6, 15], [15, 12], [3, 15], [0, 15]]\n assert candidate(words = ['ab', 'ba', 'a', 'b', 'aba', 'bab', 'aa', 'bb', 'aaa', 'bbb']) == [[0, 2], [3, 0], [0, 1], [1, 3], [2, 1], [1, 0], [0, 4], [4, 1], [1, 5], [5, 0], [6, 2], [2, 6], [7, 3], [3, 7], [8, 2], [6, 8], [8, 6], [2, 8], [9, 3], [7, 9], [9, 7], [3, 9]]\n assert candidate(words = ['race', 'ecar', 'car', 'arc', 'civic', 'level', 'deified', 'rotor', 'redder', 'repaper']) == [[0, 2], [0, 1], [1, 0]]\n assert candidate(words = ['noon', 'moon', 'noonmoon', 'moonnoon', 'noonno', 'onnoon', 'noonmo', 'onnoom']) == [[4, 5], [5, 4]]\n assert candidate(words = ['aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa', 'aaaaaaaaaaa', 'aaaaaaaaaaaa', 'aaaaaaaaaaaaa', 'aaaaaaaaaaaaaa']) == [[0, 1], [1, 0], [1, 2], [0, 2], [2, 0], [2, 1], [2, 3], [1, 3], [0, 3], [3, 0], [3, 1], [3, 2], [3, 4], [2, 4], [1, 4], [0, 4], [4, 0], [4, 1], [4, 2], [4, 3], [4, 5], [3, 5], [2, 5], [1, 5], [0, 5], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 6], [4, 6], [3, 6], [2, 6], [1, 6], [0, 6], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [6, 5]]\n assert candidate(words = ['12321', '21312', '32123', '43234', '54345', '65456', '76567', '87678', '98789', '10901', '11011']) == []\n"}, "metadata": {"canonical_parameter_names": ["words"], "leetcode_dataset_entry_point": "Solution().palindromePairs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var palindromePairs = function(words) {", "container": null, "callable": "palindromePairs", "parameters": [{"name": "words", "type": "string[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 337, "task_id": "house-robber-iii", "difficulty": "Medium", "problem_description": "The thief has found himself a new place for his thievery again. There is only one entrance to this area, called root.\nBesides the root, each house has one and only one parent house. After a tour, the smart thief realized that all houses in this place form a binary tree. It will automatically contact the police if two directly-linked houses were broken into on the same night.\nGiven the root of the binary tree, return the maximum amount of money the thief can rob without alerting the police.\n \nExample 1:\n\n\nInput: root = [3,2,3,null,3,null,1]\nOutput: 7\nExplanation: Maximum amount of money the thief can rob = 3 + 3 + 1 = 7.\n\nExample 2:\n\n\nInput: root = [3,4,5,1,3,null,1]\nOutput: 9\nExplanation: Maximum amount of money the thief can rob = 4 + 5 = 9.\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 104].\n0 <= Node.val <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == 23\n assert candidate(root = tree_node([3, 2, None, 1, 3, None, 1])) == 7\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 9\n assert candidate(root = tree_node([3, 0, 0])) == 3\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == 38\n assert candidate(root = tree_node([3, 4, 5, 1, 3, None, 1])) == 9\n assert candidate(root = tree_node([2, 1, 3, None, 4, None, 7])) == 13\n assert candidate(root = tree_node([2, 1, 3, None, 4])) == 7\n assert candidate(root = tree_node([1, None, 3, 2, 4, None, 5, 6])) == 14\n assert candidate(root = tree_node([3, 2, 3, None, 3, None, 1])) == 7\n assert candidate(root = tree_node([0])) == 0\n assert candidate(root = tree_node([3, None, 4, None, 5])) == 8\n assert candidate(root = tree_node([10, 9, 20, None, None, 15, 7, None, 3, 18, None, 6, 2, 0, 1, 5, None, None, None, None, 4])) == 59\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 30\n assert candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, 1, None, 6, 8, None, None, None, 9])) == 55\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6, 8, 12, 14, 17, 19])) == 97\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 13, 17, 23, 27, 33, 37, 1, 3, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38])) == 418\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7])) == 17\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 5, 5, None, None, 6, 6, 7, 7, 8, 8, 9, 9])) == 63\n assert candidate(root = tree_node([2, 1, 3, None, 4, None, 5, None, 6])) == 13\n assert candidate(root = tree_node([5, 2, 13, None, 5, None, 14, 20, None, None, 9, 10, 3])) == 44\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 190])) == 980\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, None, 6, None, 11, 13, None, None, 18, 22])) == 104\n assert candidate(root = tree_node([3, 2, 3, 3, 3, None, 2, None, 1])) == 11\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15])) == 80\n assert candidate(root = tree_node([3000, 1000, 2000, 500, 700, None, 3000, None, 600, None, 800, None, 900])) == 7400\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, 9, None, None, 11, 13, None, None, 15, 17])) == 82\n assert candidate(root = tree_node([3, 2, 3, 2, None, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1])) == 16\n assert candidate(root = tree_node([100, 90, 80, 70, 60, 50, 40, 30, 20, 10])) == 320\n assert candidate(root = tree_node([3, 1, 4, 3, None, 1, 5])) == 12\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9])) == 18\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8, 13, None, None, None, None, 19])) == 61\n assert candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, 1, None, 6, 8, None, None, None, None, 18])) == 58\n assert candidate(root = tree_node([5, 1, 5, None, 7, 6, None, 4, None, 3, None, 2, 8, None, None, None, 9])) == 35\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, 18, 13, 17, 16, 19, 14, 21, 10, 11, None, 15])) == 137\n assert candidate(root = tree_node([6, 7, 8, 2, 7, 1, 3, 9, None, 1, 4, None, None, None, 5])) == 34\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8, None, 20, 17, 21])) == 92\n assert candidate(root = tree_node([6, 3, 7, 2, 5, None, 8, 1, 4, None, None, None, None, None, 9])) == 32\n assert candidate(root = tree_node([8, 4, 13, 2, 6, 10, 14, 1, None, 5, 7, None, None, 9, 12])) == 53\n assert candidate(root = tree_node([3, 2, 3, None, 3, None, 1, 5, 6, 7, 8, 9, 10, 11, 12])) == 63\n assert candidate(root = tree_node([15, 10, 20, 8, None, None, 25, None, None, None, 30])) == 60\n assert candidate(root = tree_node([50, 20, 50, 10, 30, 40, 60, 5, 15, None, None, None, None, None, 70])) == 210\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == 368\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 162\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 97\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, 6, 8, 9, 12, 14, 17, 19])) == 106\n assert candidate(root = tree_node([10, 5, None, 1, 7, None, 12, 0, 2, 6, 8, None, None, 11, 13, None, None, 3, 4, None, None, None, None, 9, 10])) == 76\n assert candidate(root = tree_node([5, 4, 7, 3, None, 2, 9, None, None, None, 10])) == 27\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == 259\n assert candidate(root = tree_node([3, 2, 3, None, 3, None, 1, None, None, 5, 6])) == 17\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180, 5, 15, 20, 35, 65, 70, 85, 105, 135, 145, 155, 175, 185, 190])) == 1890\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, 6, 8, 12, 14, 17, 9, 11, 2, 4, 16, 19, 20])) == 144\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 8, 12, None, None, 11, None, 10])) == 59\n assert candidate(root = tree_node([3, 2, 3, None, 3, None, 1, 5, 6, 7, 8, 9, 10])) == 45\n assert candidate(root = tree_node([9, 4, 17, 3, 6, 11, 20, 1, 5, 8, 13, None, 22, None, 2, None, None, 0, 2, None, 9, None, None, 7, 12, None, None, None, 2])) == 89\n assert candidate(root = tree_node([2, 1, 3, None, 4, None, 5, 6, None, 7, None, 8, None, 9, None, 10])) == 32\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, 8, 9, None, None, None, None, 10, 11, None, None, None, None, None, 12])) == 49\n assert candidate(root = tree_node([50, 20, 60, 10, 30, 55, 70, 5, 15, 25, 35, 51, 59, 65, 75, 1, 4, 9, 16, 24, 26, 34, 36, 50, 58, 61, 64, 66, 73, 76, 78])) == 891\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == 16\n assert candidate(root = tree_node([5, 4, 5, None, 1, 4, None, None, 2, 3])) == 14\n assert candidate(root = tree_node([10, 5, 15, 2, 7, 13, 18, 1, None, 6, 8, 9, 14, None, None, None, 19, None, 20])) == 100\n assert candidate(root = tree_node([5, 3, 7, 2, 5, None, 8, 1, None, 4, None, 6, None, 3, 5])) == 28\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, None, 6, None, 11, 13, None, None, 18, 22, 19, 23, 24, 25, 26, 27, 28, 29, 30])) == 283\n assert candidate(root = tree_node([50, 20, 60, 10, 30, 55, 70, 5, 15, 25, 35, 52, 58, 65, 75, 2, 7, 12, 17, 23, 27, 32, 37, 51, 56, 59, 64, 67, 72, 76, 78])) == 895\n assert candidate(root = tree_node([100, 50, 50, 25, 25, 25, 25, 10, 10, 10, 10, 10, 10, 10, 10])) == 200\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, None, 5, None, None, 6, None, None, None, 7])) == 13\n assert candidate(root = tree_node([2, 1, 3, None, 4, None, 5, None, 6, None, 7])) == 17\n assert candidate(root = tree_node([9, 4, 7, 3, 6, 5, 11, 2, 5, None, None, 8, None, 10, 12, None, None, None, None, None, 14])) == 63\n assert candidate(root = tree_node([3, 4, 5, 1, 3, None, 1, 5, 6, None, 2, 8, None, None, None, 9, None, None, 10])) == 41\n assert candidate(root = tree_node([8, 4, 13, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 12, 15])) == 80\n assert candidate(root = tree_node([7, 3, 8, 1, 4, 3, 9, 0, 2, 5, 6, None, None, None, None, None, 11])) == 43\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8])) == 45\n assert candidate(root = tree_node([10, 5, 15, 2, 7, 13, 18, 1, None, 6, 8, 9, 14, 19, 20])) == 97\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8, 14, 19, None, None, 13, None, None, None, None, None, None, 12])) == 75\n assert candidate(root = tree_node([5, 2, 8, 1, 3, None, 9, 0, None, None, 4, None, None, 6, None, 10])) == 34\n assert candidate(root = tree_node([10, 5, 15, 2, 7, 13, 18, 1, None, 6, 8, None, 14, None, None, 19])) == 77\n assert candidate(root = tree_node([50, 20, 30, 10, 40, None, None, 5, None, None, 55])) == 115\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, 2, None, None, None, 20])) == 45\n assert candidate(root = tree_node([5, 2, 6, 1, 3, None, 8, None, None, 4, 7, None, None, None, 9])) == 30\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 32\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9, 10, 11, 12])) == 56\n assert candidate(root = tree_node([7, 3, 8, 1, 4, 5, 9, 0, 2, 6, None, None, None, None, None, None, 10])) == 39\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13])) == 49\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 25\n assert candidate(root = tree_node([20, 10, 10, 5, 15, None, None, 3, 7, 12, 18])) == 60\n assert candidate(root = tree_node([8, 4, 13, 2, 6, 10, 17, 1, None, 5, 7, None, 12, None, None, None, 14])) == 65\n assert candidate(root = tree_node([7, 3, 8, 1, 4, 6, 9, 0, 2, 5, None, None, None, None, None, None, None, 10, 11, None, 12, None, 13, 14, 15, None, None, None, None, 16, 17])) == 101\n assert candidate(root = tree_node([3, 2, 3, None, 3, None, 1, 2, None, 4])) == 11\n assert candidate(root = tree_node([50, 20, 50, None, 30, None, 60, 10, 40, None, 70])) == 190\n assert candidate(root = tree_node([3, 1, 5, 0, 2, 4, 6])) == 15\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == 35\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().rob", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var rob = function(root) {", "container": null, "callable": "rob", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 338, "task_id": "counting-bits", "difficulty": "Easy", "problem_description": "Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.\n \nExample 1:\n\nInput: n = 2\nOutput: [0,1,1]\nExplanation:\n0 --> 0\n1 --> 1\n2 --> 10\n\nExample 2:\n\nInput: n = 5\nOutput: [0,1,1,2,1,2]\nExplanation:\n0 --> 0\n1 --> 1\n2 --> 10\n3 --> 11\n4 --> 100\n5 --> 101\n\n \nConstraints:\n\n0 <= n <= 105\n\n \nFollow up:\n\nIt is very easy to come up with a solution with a runtime of O(n log n). Can you do it in linear time O(n) and possibly in a single pass?\nCan you do it without using any built-in function (i.e., like __builtin_popcount in C++)?\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == [0]\n assert candidate(n = 10000) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 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7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5]\n assert candidate(n = 31) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5]\n assert candidate(n = 2) == [0, 1, 1]\n assert candidate(n = 100) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3]\n assert candidate(n = 1000) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6]\n assert candidate(n = 1) == [0, 1]\n assert candidate(n = 10) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2]\n assert candidate(n = 5) == [0, 1, 1, 2, 1, 2]\n assert candidate(n = 63) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6]\n assert candidate(n = 4096) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 1]\n assert candidate(n = 511) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9]\n assert candidate(n = 2047) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11]\n assert candidate(n = 300) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4]\n assert candidate(n = 64) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1]\n assert candidate(n = 254) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7]\n assert candidate(n = 1024) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1]\n assert candidate(n = 128) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1]\n assert candidate(n = 4095) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12]\n assert candidate(n = 8192) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 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6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 9, 10, 10, 11, 10, 11, 11, 12, 10, 11, 11, 12, 11, 12, 12, 13, 1]\n assert candidate(n = 2048) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 1]\n assert candidate(n = 8191) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 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9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 9, 10, 10, 11, 10, 11, 11, 12, 10, 11, 11, 12, 11, 12, 12, 13]\n assert candidate(n = 255) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8]\n assert candidate(n = 5000) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 7, 8, 8, 9, 8, 9, 9, 10, 8, 9, 9, 10, 9, 10, 10, 11, 8, 9, 9, 10, 9, 10, 10, 11, 9, 10, 10, 11, 10, 11, 11, 12, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 4, 5, 5, 6, 5, 6, 6, 7, 5]\n assert candidate(n = 768) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2]\n assert candidate(n = 256) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1]\n assert candidate(n = 1023) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10]\n assert candidate(n = 127) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7]\n assert candidate(n = 15) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]\n assert candidate(n = 200) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3]\n assert candidate(n = 512) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6, 7, 7, 8, 6, 7, 7, 8, 7, 8, 8, 9, 1]\n assert candidate(n = 500) == [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8, 5, 6, 6, 7, 6]\n assert candidate(n = 7) == [0, 1, 1, 2, 1, 2, 2, 3]\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countBits", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countBits = function(n) {", "container": null, "callable": "countBits", "parameters": [{"name": "n", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 342, "task_id": "power-of-four", "difficulty": "Easy", "problem_description": "Given an integer n, return true if it is a power of four. Otherwise, return false.\nAn integer n is a power of four, if there exists an integer x such that n == 4x.\n \nExample 1:\nInput: n = 16\nOutput: true\nExample 2:\nInput: n = 5\nOutput: false\nExample 3:\nInput: n = 1\nOutput: true\n\n \nConstraints:\n\n-231 <= n <= 231 - 1\n\n \nFollow up: Could you solve it without loops/recursion?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == False\n assert candidate(n = -16) == False\n assert candidate(n = 2147483647) == False\n assert candidate(n = 536870912) == False\n assert candidate(n = 4294967295) == False\n assert candidate(n = 268435456) == True\n assert candidate(n = 5) == False\n assert candidate(n = 16777216) == True\n assert candidate(n = 4) == True\n assert candidate(n = 64) == True\n assert candidate(n = 16) == True\n assert candidate(n = 2) == False\n assert candidate(n = 1024) == True\n assert candidate(n = 0) == False\n assert candidate(n = 8) == False\n assert candidate(n = -2147483648) == False\n assert candidate(n = 1048576) == True\n assert candidate(n = 2048) == False\n assert candidate(n = 65536) == True\n assert candidate(n = 18) == False\n assert candidate(n = 256) == True\n assert candidate(n = -4) == False\n assert candidate(n = 4294967296) == True\n assert candidate(n = 1) == True\n assert candidate(n = 1000000003) == False\n assert candidate(n = 1099511627776) == True\n assert candidate(n = -4294967296) == False\n assert candidate(n = 4096) == True\n assert candidate(n = 18446744073709551615) == False\n assert candidate(n = 1431655765) == False\n assert candidate(n = 1000000002) == False\n assert candidate(n = 16384) == True\n assert candidate(n = 2147483649) == False\n assert candidate(n = -1) == False\n assert candidate(n = 2199023255552) == True\n assert candidate(n = 4194304) == True\n assert candidate(n = 1073741823) == False\n assert candidate(n = 1152921504606846976) == True\n assert candidate(n = -65536) == False\n assert candidate(n = 34359738368) == True\n assert candidate(n = 9223372036854775807) == False\n assert candidate(n = 1073741824) == True\n assert candidate(n = 18014398509481984) == True\n assert candidate(n = 255) == False\n assert candidate(n = 2147483648) == False\n assert candidate(n = 17179869184) == True\n assert candidate(n = 4611686018427387904) == True\n assert candidate(n = 1000000000) == False\n assert candidate(n = 65535) == False\n assert candidate(n = 1000000001) == False\n assert candidate(n = 1000000004) == False\n assert candidate(n = 15) == False\n assert candidate(n = 35184372088832) == True\n assert candidate(n = 72057594037927936) == True\n assert candidate(n = 1073741825) == False\n assert candidate(n = 7) == False\n assert candidate(n = 10) == False\n assert candidate(n = 18446744073709551616) == True\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().isPowerOfFour", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPowerOfFour = function(n) {", "container": null, "callable": "isPowerOfFour", "parameters": [{"name": "n", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 343, "task_id": "integer-break", "difficulty": "Medium", "problem_description": "Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers.\nReturn the maximum product you can get.\n \nExample 1:\n\nInput: n = 2\nOutput: 1\nExplanation: 2 = 1 + 1, 1 × 1 = 1.\n\nExample 2:\n\nInput: n = 10\nOutput: 36\nExplanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.\n\n \nConstraints:\n\n2 <= n <= 58\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 11) == 54\n assert candidate(n = 30) == 59049\n assert candidate(n = 20) == 1458\n assert candidate(n = 2) == 1\n assert candidate(n = 10) == 36\n assert candidate(n = 58) == 1549681956\n assert candidate(n = 29) == 39366\n assert candidate(n = 45) == 14348907\n assert candidate(n = 49) == 57395628\n assert candidate(n = 12) == 81\n assert candidate(n = 47) == 28697814\n assert candidate(n = 53) == 258280326\n assert candidate(n = 57) == 1162261467\n assert candidate(n = 50) == 86093442\n assert candidate(n = 28) == 26244\n assert candidate(n = 56) == 774840978\n assert candidate(n = 40) == 2125764\n assert candidate(n = 37) == 708588\n assert candidate(n = 42) == 4782969\n assert candidate(n = 35) == 354294\n assert candidate(n = 18) == 729\n assert candidate(n = 32) == 118098\n assert candidate(n = 36) == 531441\n assert candidate(n = 19) == 972\n assert candidate(n = 48) == 43046721\n assert candidate(n = 15) == 243\n assert candidate(n = 6) == 9\n assert candidate(n = 55) == 516560652\n assert candidate(n = 13) == 108\n assert candidate(n = 25) == 8748\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().integerBreak", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var integerBreak = function(n) {", "container": null, "callable": "integerBreak", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 345, "task_id": "reverse-vowels-of-a-string", "difficulty": "Easy", "problem_description": "Given a string s, reverse only all the vowels in the string and return it.\nThe vowels are 'a', 'e', 'i', 'o', and 'u', and they can appear in both lower and upper cases, more than once.\n \nExample 1:\n\nInput: s = \"IceCreAm\"\nOutput: \"AceCreIm\"\nExplanation:\nThe vowels in s are ['I', 'e', 'e', 'A']. On reversing the vowels, s becomes \"AceCreIm\".\n\nExample 2:\n\nInput: s = \"leetcode\"\nOutput: \"leotcede\"\n\n \nConstraints:\n\n1 <= s.length <= 3 * 105\ns consist of printable ASCII characters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"hello\") == \"holle\"\n assert candidate(s = \"leetcode\") == \"leotcede\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().reverseVowels", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reverseVowels = function(s) {", "container": null, "callable": "reverseVowels", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 347, "task_id": "top-k-frequent-elements", "difficulty": "Medium", "problem_description": "Given an integer array nums and an integer k, return the k most frequent elements. You may return the answer in any order.\n \nExample 1:\nInput: nums = [1,1,1,2,2,3], k = 2\nOutput: [1,2]\nExample 2:\nInput: nums = [1], k = 1\nOutput: [1]\n\n \nConstraints:\n\n1 <= nums.length <= 105\n-104 <= nums[i] <= 104\nk is in the range [1, the number of unique elements in the array].\nIt is guaranteed that the answer is unique.\n\n \nFollow up: Your algorithm's time complexity must be better than O(n log n), where n is the array's size.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 3, 1, 1, 1, 3, 5, 2, 2, 2, 4, 4, 4, 4],k = 3) == [4, 1, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 10) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [5, 3, 1, 1, 1, 3, 73, 1],k = 1) == [1]\n assert candidate(nums = [1],k = 1) == [1]\n assert candidate(nums = [1, 1, 1, 2, 2, 3],k = 2) == [1, 2]\n assert candidate(nums = [-1, -1, -1, 2, 2, 3, 4, 4, 4, 4],k = 2) == [4, -1]\n assert candidate(nums = [1, 2],k = 2) == [1, 2]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 1, 1],k = 3) == [5, 4, 3]\n assert candidate(nums = [5, 3, 1, 1, 1, 3, 5, 7, 7, 7, 7],k = 3) == [7, 1, 5]\n assert candidate(nums = [4, 1, -1, 2, -1, 2, 3],k = 2) == [-1, 2]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 4) == [9, 8, 7, 6]\n assert candidate(nums = [-1000, -1000, -999, -999, -999, -998, -998, -998, -997, -997, -997, -997, -996, -996, -995, -994, -993, -992, -991, -990],k = 4) == [-997, -999, -998, -1000]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8],k = 3) == [8, 7, 6]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 3) == [9, 8, 7]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 6) == [9, 10, 8, 7, 6, 5]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 4) == [0, 1, 2, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],k = 20) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109],k = 3) == [100, 101, 102]\n assert candidate(nums = [7, 10, 11, 5, 2, 5, 5, 7, 11, 11, 5, 2, 10, 10, 10, 10, 10, 10, 10, 10],k = 2) == [10, 5]\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 5) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 4) == [9, 8, 7, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100],k = 10) == [100, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 5) == [0, 1, 2, 3, 4]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 550, 560, 570, 580, 590, 600, 610, 620, 630, 640, 650, 660, 670, 680, 690, 700, 710, 720, 730, 740, 750, 760, 770, 780, 790, 800, 810, 820, 830, 840, 850, 860, 870, 880, 890, 900, 910, 920, 930, 940, 950, 960, 970, 980, 990, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000],k = 5) == [1000, 10, 20, 30, 40]\n assert candidate(nums = [-5, -5, -5, -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 2) == [5, -5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5],k = 5) == [1, 2, 3, 4, 5]\n assert candidate(nums = [99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90],k = 5) == [99, 98, 97, 96, 95]\n assert candidate(nums = [-100, -200, -300, -400, -500, -600, -700, -800, -900, -1000, -100, -200, -300, -400, -500, -600, -700, -800, -900, -1000, -100, -200, -300, -400, -500, -600, -700, -800, -900, -1000, -100, -200, -300, -400, -500, -600, -700, -800, -900, -1000, -100, -200, -300, -400, -500, -600, -700, -800, -900, -1000],k = 4) == [-100, -200, -300, -400]\n assert candidate(nums = [100, 100, 100, 101, 101, 102, 103, 103, 103, 103, 104, 104, 104, 105, 105, 106, 106, 107, 108, 109, 110],k = 5) == [103, 100, 104, 101, 105]\n assert candidate(nums = [10000, 10000, 9999, 9999, 9999, 9998, 9998, 9997, 9996, 9995],k = 3) == [9999, 10000, 9998]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8],k = 5) == [8, 7, 6, 5, 4]\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 5) == [9, 8, 7, 6, 5]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 10) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().topKFrequent", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var topKFrequent = function(nums, k) {", "container": null, "callable": "topKFrequent", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 349, "task_id": "intersection-of-two-arrays", "difficulty": "Easy", "problem_description": "Given two integer arrays nums1 and nums2, return an array of their intersection. Each element in the result must be unique and you may return the result in any order.\n \nExample 1:\n\nInput: nums1 = [1,2,2,1], nums2 = [2,2]\nOutput: [2]\n\nExample 2:\n\nInput: nums1 = [4,9,5], nums2 = [9,4,9,8,4]\nOutput: [9,4]\nExplanation: [4,9] is also accepted.\n\n \nConstraints:\n\n1 <= nums1.length, nums2.length <= 1000\n0 <= nums1[i], nums2[i] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [4, 3, 2, 1]) == [1, 2, 3, 4]\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [1, 1, 1, 1]) == [1]\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [2, 4, 6, 8]) == []\n assert candidate(nums1 = [0, 0, 0, 0],nums2 = [0, 0, 0, 0]) == [0]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 0]) == [0, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [30, 40, 50, 60]) == [40, 30]\n assert candidate(nums1 = [1000],nums2 = [1000]) == [1000]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 2, 2, 1],nums2 = [2, 2]) == [2]\n assert candidate(nums1 = [1000, 1000, 1000],nums2 = [1000, 1000]) == [1000]\n assert candidate(nums1 = [10, 20, 30],nums2 = [30, 40, 50]) == [30]\n assert candidate(nums1 = [5, 5, 5, 5],nums2 = [5, 5, 5, 5]) == [5]\n assert candidate(nums1 = [4, 9, 5],nums2 = [9, 4, 9, 8, 4]) == [9, 4]\n assert candidate(nums1 = [0, 1000],nums2 = [500, 1000]) == [1000]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6]) == []\n assert candidate(nums1 = [1000, 1000],nums2 = [1000, 1000]) == [1000]\n assert candidate(nums1 = [500, 500, 500],nums2 = [500]) == [500]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [3, 4, 5, 6, 7]) == [3, 4, 5]\n assert candidate(nums1 = [0],nums2 = [0]) == [0]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [0, 2, 4, 6, 8]) == []\n assert candidate(nums1 = [0, 0, 0],nums2 = [0, 0, 0]) == [0]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 10, 20, 30, 40]) == [40, 10, 50, 20, 30]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0]) == [0]\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [500, 600, 700, 800, 900]) == [800, 900, 500, 600, 700]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [50, 51, 52, 53, 54, 55, 56, 57, 58, 59]) == [50]\n assert candidate(nums1 = [999, 998, 997, 996, 995],nums2 = [994, 993, 992, 991, 990]) == []\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1]\n assert candidate(nums1 = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],nums2 = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]) == [9, 18, 27]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 3, 5, 7, 9]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4],nums2 = [2, 2, 4, 4, 6, 6, 8, 8]) == [2, 4]\n assert candidate(nums1 = [1000, 0, 500, 250, 750],nums2 = [750, 500, 250, 0, 1000]) == [0, 1000, 750, 500, 250]\n assert candidate(nums1 = [250, 251, 252, 253, 254, 255, 256, 257, 258, 259],nums2 = [255, 256, 257, 258, 259, 260, 261, 262, 263, 264]) == [256, 257, 258, 259, 255]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1]) == [1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == [5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 10, 100, 1000],nums2 = [1000, 100, 10, 1]) == [1000, 1, 10, 100]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [300, 301, 302, 303, 304, 305, 306, 307, 308, 309],nums2 = [309, 310, 311, 312, 313, 314, 315, 316, 317, 318]) == [309]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990],nums2 = [990, 991, 992, 993, 994, 995, 996, 997, 998, 999]) == [992, 993, 994, 995, 996, 997, 998, 999, 990, 991]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [90, 100, 110, 120, 130, 140]) == [90, 100]\n assert candidate(nums1 = [1000],nums2 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == []\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [900, 1000, 1100, 1200, 1300]) == [1000, 900]\n assert candidate(nums1 = [1, 10, 100, 1000],nums2 = [1, 10, 100, 1000]) == [1000, 1, 10, 100]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5]) == [5]\n assert candidate(nums1 = [345, 678, 910, 1112, 1314],nums2 = [1314, 345, 567, 789, 910]) == [345, 1314, 910]\n assert candidate(nums1 = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [2, 4, 6, 8, 10]) == [2, 4, 6, 8, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 0, -1, -2]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [100, 200, 300, 400, 500]) == [100, 200, 300, 400, 500]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [200, 400, 600, 800, 1000]) == [200, 400]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 3, 5, 7, 9]) == [1, 3, 5, 7, 9]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 5, 5, 5, 5]) == [5]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == [10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == []\n assert candidate(nums1 = [1, 2, 3],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 60, 70, 80, 90]) == [50]\n assert candidate(nums1 = [999, 998, 997, 996, 995],nums2 = [995, 996, 997, 998, 999]) == [995, 996, 997, 998, 999]\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [4, 5, 6, 7, 8]) == [4, 5]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == []\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 60, 70, 80, 90, 100]) == [50]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == []\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [40, 50, 60, 70, 80]) == [40, 50]\n assert candidate(nums1 = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991],nums2 = [996, 997, 998, 999, 1000]) == [996, 997, 998, 999, 1000]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 400, 300, 200, 100, 500, 400, 300, 200, 100]) == [100, 200, 300, 400, 500]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 0]) == [0, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == []\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [3, 3, 4, 4, 5, 5]) == [3]\n assert candidate(nums1 = [500, 501, 502, 503, 504, 505],nums2 = [500, 501, 502, 503, 504, 505, 506, 507, 508, 509]) == [500, 501, 502, 503, 504, 505]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == []\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]) == []\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 60, 70, 80, 90]) == [50]\n assert candidate(nums1 = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],nums2 = [5, 15, 25, 35, 45]) == [35, 5, 45, 15, 25]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [3, 3, 3, 2, 2, 1, 1]) == [1, 2, 3]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 500, 500, 500, 500]) == [500]\n assert candidate(nums1 = [1, 1, 2, 3, 3],nums2 = [2, 2, 3, 3, 4, 4]) == [2, 3]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == [100, 70, 40, 10, 80, 50, 20, 90, 60, 30]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [5, 10, 15, 20, 25, 30]) == [10, 5, 15]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == [100, 200, 300, 400, 500]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == []\n assert candidate(nums1 = [7, 14, 21, 28, 35],nums2 = [35, 42, 49, 56, 63]) == [35]\n assert candidate(nums1 = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],nums2 = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == [30, 15]\n assert candidate(nums1 = [500, 501, 502, 503, 504, 505, 506, 507, 508, 509],nums2 = [505, 506, 507, 508, 509, 510, 511, 512, 513, 514]) == [505, 506, 507, 508, 509]\n assert candidate(nums1 = [5, 10, 15, 20, 25],nums2 = [5, 25, 10, 15, 20, 5, 25, 10, 15, 20]) == [5, 10, 15, 20, 25]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 100],nums2 = [100, 200, 300, 400, 500]) == [100]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == [2, 4, 6, 8, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == [10, 20, 5, 15]\n assert candidate(nums1 = [500, 501, 502, 503, 504, 505, 506, 507, 508, 509],nums2 = [500, 501, 502, 503, 504, 505, 506, 507, 508, 509]) == [500, 501, 502, 503, 504, 505, 506, 507, 508, 509]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [10, 11, 12, 13, 14, 15]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [2, 2, 3, 3, 4, 4]) == [2, 3]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 400, 300, 200, 100]) == [100, 200, 300, 400, 500]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6]) == []\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [5, 4, 3, 2, 1, 1, 2, 2, 3, 3]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [500, 500, 500, 500, 500],nums2 = [500, 500, 500, 500, 500]) == [500]\n assert candidate(nums1 = [5, 10, 15, 20, 25, 30],nums2 = [30, 25, 20, 15, 10, 5]) == [5, 10, 15, 20, 25, 30]\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900]) == [800, 900, 100, 200, 300, 400, 500, 600, 700]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [150, 250, 350, 450, 550]) == []\n assert candidate(nums1 = [100, 100, 100, 100],nums2 = [100, 100, 100]) == [100]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 600, 700, 800, 900]) == [500]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == [5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [100, 200, 300],nums2 = [300, 400, 500, 600, 700]) == [300]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [2, 4, 6, 8, 10]) == [2, 4]\n assert candidate(nums1 = [100, 200, 300],nums2 = [100, 200, 300, 400, 500]) == [200, 100, 300]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1000],nums2 = [1000, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [1, 2, 3, 4, 5, 6, 7, 1000, 8, 9]\n assert candidate(nums1 = [0, 100, 200, 300, 400],nums2 = [400, 300, 200, 100, 0]) == [0, 100, 200, 300, 400]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [15, 25, 35, 45, 55]) == []\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [100, 300, 500, 700, 900]) == [100, 500, 300]\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [15, 20, 25, 30, 35]) == [20, 30]\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2"], "leetcode_dataset_entry_point": "Solution().intersection", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var intersection = function(nums1, nums2) {", "container": null, "callable": "intersection", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 350, "task_id": "intersection-of-two-arrays-ii", "difficulty": "Easy", "problem_description": "Given two integer arrays nums1 and nums2, return an array of their intersection. Each element in the result must appear as many times as it shows in both arrays and you may return the result in any order.\n \nExample 1:\n\nInput: nums1 = [1,2,2,1], nums2 = [2,2]\nOutput: [2,2]\n\nExample 2:\n\nInput: nums1 = [4,9,5], nums2 = [9,4,9,8,4]\nOutput: [4,9]\nExplanation: [9,4] is also accepted.\n\n \nConstraints:\n\n1 <= nums1.length, nums2.length <= 1000\n0 <= nums1[i], nums2[i] <= 1000\n\n \nFollow up:\n\nWhat if the given array is already sorted? How would you optimize your algorithm?\nWhat if nums1's size is small compared to nums2's size? Which algorithm is better?\nWhat if elements of nums2 are stored on disk, and the memory is limited such that you cannot load all elements into the memory at once?\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 40, 30, 20, 10]) == [50, 40, 30, 20, 10]\n assert candidate(nums1 = [100, 200, 300],nums2 = [300, 200, 100]) == [300, 200, 100]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [3, 3, 3, 3, 1, 1]) == [3, 3, 1, 1]\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [2, 4, 6, 8]) == []\n assert candidate(nums1 = [0, 0, 0, 0],nums2 = [0, 0, 0, 0]) == [0, 0, 0, 0]\n assert candidate(nums1 = [0, 0, 0],nums2 = [0, 0, 0, 0]) == [0, 0, 0]\n assert candidate(nums1 = [1000, 1000, 1000],nums2 = [1000, 1000, 1000]) == [1000, 1000, 1000]\n assert candidate(nums1 = [1, 1, 2, 2],nums2 = [2, 2, 2, 2]) == [2, 2]\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [30, 40, 50, 60]) == [30, 40]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10]) == []\n assert candidate(nums1 = [1000],nums2 = [1000]) == [1000]\n assert candidate(nums1 = [1, 3, 2, 4],nums2 = [3, 2, 2, 1]) == [3, 2, 1]\n assert candidate(nums1 = [1000, 1000],nums2 = [1000, 1000, 1000]) == [1000, 1000]\n assert candidate(nums1 = [],nums2 = []) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1]) == [5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 2, 2, 1],nums2 = [2, 2]) == [2, 2]\n assert candidate(nums1 = [1000, 1000, 1000],nums2 = [1000, 1000]) == [1000, 1000]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5]) == [5, 5, 5, 5, 5]\n assert candidate(nums1 = [7, 8, 9],nums2 = [10, 11, 12]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10]) == []\n assert candidate(nums1 = [1],nums2 = [2]) == []\n assert candidate(nums1 = [4, 9, 5],nums2 = [9, 4, 9, 8, 4]) == [9, 4]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [1, 1, 1]) == [1, 1, 1]\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [1, 1]) == [1, 1]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5]) == [5, 5, 5, 5]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6]) == []\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [1, 1, 1]) == [1, 1, 1]\n assert candidate(nums1 = [1],nums2 = [1]) == [1]\n assert candidate(nums1 = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 999, 998, 997]) == [999, 998, 997]\n assert candidate(nums1 = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990],nums2 = [990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 999, 998, 997, 996, 995, 994, 993, 992, 991, 990]) == [990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [5, 5, 6, 6, 7, 7, 8, 8]) == [5, 6, 7, 8]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == [2, 4, 6, 8, 10]\n assert candidate(nums1 = [500, 500, 500, 500],nums2 = [500, 500, 500, 500, 500, 500, 500]) == [500, 500, 500, 500]\n assert candidate(nums1 = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4],nums2 = [1, 2, 2, 3, 3, 3, 4, 4]) == [1, 2, 2, 3, 3, 3, 4, 4]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == [3, 5, 7, 11, 13, 17, 19]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 40, 30, 20, 10, 10]) == [50, 40, 30, 20, 10]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [10, 11, 12, 13, 14, 15]\n assert candidate(nums1 = [1, 1, 2, 2, 2, 3, 3, 4, 4, 5],nums2 = [2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == [2, 2, 2, 3, 3, 4, 4, 5]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1]) == [1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == [5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [15, 20, 25, 30, 35, 40, 45, 50]) == [20, 30, 40, 50]\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [150, 250, 350, 450, 550, 650, 750, 850, 950]) == []\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],nums2 = [2, 4, 6, 8, 10, 12, 14]) == [2, 4, 6, 8, 10, 12, 14]\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [3, 4, 5, 6, 7]) == [3, 4, 5]\n assert candidate(nums1 = [999, 998, 997, 996, 995, 994, 993, 992, 991, 990],nums2 = [990, 991, 992, 993, 994, 995, 996, 997, 998, 999]) == [990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(nums1 = [3, 4, 4, 5, 6, 7, 8, 8, 9],nums2 = [4, 4, 8, 9, 10]) == [4, 4, 8, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]\n assert candidate(nums1 = [7, 7, 8, 8, 9, 9],nums2 = [7, 7, 7, 8, 8, 8, 9, 9, 9]) == [7, 7, 8, 8, 9, 9]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [100, 200, 300, 400, 500]) == [100, 200, 300, 400, 500]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 3, 5, 7, 9]) == [1, 3, 5, 7, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [1, 3, 5, 7, 9]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums1 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5]) == [5, 5, 5, 5, 5]\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [0, 0, 0]) == [0, 0, 0]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4],nums2 = [1, 1, 2, 2, 3, 3, 4, 4]) == [1, 1, 2, 2, 3, 3, 4, 4]\n assert candidate(nums1 = [33, 44, 55, 66, 77, 88, 99, 100],nums2 = [33, 66, 99, 100, 132, 165, 198, 231]) == [33, 66, 99, 100]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == []\n assert candidate(nums1 = [7, 7, 7, 7, 7],nums2 = [7, 7, 7, 7, 7, 7, 7]) == [7, 7, 7, 7, 7]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15],nums2 = [2, 4, 6, 8, 10, 12, 14, 16]) == []\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [100, 200, 300, 400, 500]) == [100, 200, 300, 400, 500]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 400, 300, 200, 100, 500, 400, 300, 200, 100]) == [500, 400, 300, 200, 100]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [1, 2, 3, 4, 5]) == [1]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1]) == [5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [2, 4, 6, 8, 10]) == [2, 4]\n assert candidate(nums1 = [7, 8, 9],nums2 = [1, 2, 3]) == []\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [1, 2, 2, 3, 4, 5, 5],nums2 = [5, 5, 4, 3, 2, 2, 1]) == [5, 5, 4, 3, 2, 2, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [5, 6, 7, 8, 9, 10, 11, 12, 13]) == [5, 6, 7, 8, 9]\n assert candidate(nums1 = [1],nums2 = [2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],nums2 = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == [5, 4, 3, 2, 1]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 400, 300, 200, 100, 100]) == [500, 400, 300, 200, 100]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1]) == [3, 3, 2, 2, 1, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [1, 1, 1, 1, 1]) == [1]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == [9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4],nums2 = [2, 2, 2, 2, 3, 3, 3, 3]) == [2, 2, 3, 3]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [2, 2, 4, 4, 6, 6, 8, 8, 10, 10]) == [2, 2, 4, 4]\n assert candidate(nums1 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],nums2 = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1]) == [1, 1, 1]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1]) == [1, 1, 1, 1]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == [5, 5, 4, 4, 3, 3, 2, 2, 1, 1]\n assert candidate(nums1 = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],nums2 = [3, 3, 3, 3, 3]) == [3, 3, 3, 3, 3]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [1, 1, 1, 2, 2, 3]) == [1, 1, 2, 2, 3]\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10]) == []\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]\n assert candidate(nums1 = [500, 500, 500, 500, 500],nums2 = [500, 500]) == [500, 500]\n assert candidate(nums1 = [1, 2, 2, 3, 4],nums2 = [2, 2, 4, 4, 6]) == [2, 2, 4]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],nums2 = [100, 200, 300, 400, 500]) == []\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 400, 300, 200, 100]) == [500, 400, 300, 200, 100]\n assert candidate(nums1 = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 7, 8, 9, 10],nums2 = [2, 2, 4, 4, 5, 5, 5, 10, 11, 12]) == [2, 2, 4, 4, 5, 5, 5, 10]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 2, 2, 3, 3, 4],nums2 = [2, 2, 3, 5]) == [2, 2, 3]\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums1 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == []\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],nums2 = [1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60],nums2 = [15, 25, 35, 45, 55, 65]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10]) == []\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == [5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [7, 7, 7, 8, 8, 9],nums2 = [8, 7, 9, 7, 7, 10]) == [8, 7, 9, 7, 7]\n assert candidate(nums1 = [5, 5, 5, 5, 5],nums2 = [5, 5, 5]) == [5, 5, 5]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [5, 15, 25, 35, 45, 55]) == []\n assert candidate(nums1 = [234, 456, 789, 123, 567, 890, 111, 222, 333, 444],nums2 = [111, 222, 333, 444, 555, 666, 777, 888, 999, 123]) == [111, 222, 333, 444, 123]\n assert candidate(nums1 = [3, 3, 3, 3, 3],nums2 = [3, 3, 3]) == [3, 3, 3]\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [50, 60, 70, 80, 90, 100, 110, 120, 130, 140]) == [50, 60, 70, 80, 90, 100]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [2, 2, 2, 2]) == []\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [500, 400, 300, 200, 100]) == [500, 400, 300, 200, 100]\n assert candidate(nums1 = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],nums2 = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]\n assert candidate(nums1 = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109],nums2 = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109]) == [100, 101, 102, 103, 104, 105, 106, 107, 108, 109]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 40, 30, 20, 10]) == [50, 40, 30, 20, 10]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],nums2 = [5, 10, 15, 20, 25, 30]) == [5, 10, 15, 20, 25, 30]\n assert candidate(nums1 = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],nums2 = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]) == [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100]\n assert candidate(nums1 = [1, 1, 2, 2, 3, 3],nums2 = [1, 2, 3, 4, 5, 6]) == [1, 2, 3]\n assert candidate(nums1 = [5, 1, 3, 3, 2, 4],nums2 = [3, 2, 2, 5, 1]) == [3, 2, 5, 1]\n assert candidate(nums1 = [500, 500, 500, 500, 500],nums2 = [500, 500, 500, 500, 500, 500, 500, 500, 500, 500]) == [500, 500, 500, 500, 500]\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2"], "leetcode_dataset_entry_point": "Solution().intersect", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var intersect = function(nums1, nums2) {", "container": null, "callable": "intersect", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 354, "task_id": "russian-doll-envelopes", "difficulty": "Hard", "problem_description": "You are given a 2D array of integers envelopes where envelopes[i] = [wi, hi] represents the width and the height of an envelope.\nOne envelope can fit into another if and only if both the width and height of one envelope are greater than the other envelope's width and height.\nReturn the maximum number of envelopes you can Russian doll (i.e., put one inside the other).\nNote: You cannot rotate an envelope.\n \nExample 1:\n\nInput: envelopes = [[5,4],[6,4],[6,7],[2,3]]\nOutput: 3\nExplanation: The maximum number of envelopes you can Russian doll is 3 ([2,3] => [5,4] => [6,7]).\n\nExample 2:\n\nInput: envelopes = [[1,1],[1,1],[1,1]]\nOutput: 1\n\n \nConstraints:\n\n1 <= envelopes.length <= 105\nenvelopes[i].length == 2\n1 <= wi, hi <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(envelopes = [[10, 16], [2, 3], [6, 8], [7, 19]]) == 3\n assert candidate(envelopes = [[1, 3], [3, 5], [6, 7], [8, 4], [9, 5]]) == 3\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3]]) == 3\n assert candidate(envelopes = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1]]) == 1\n assert candidate(envelopes = [[1, 3], [2, 5], [3, 7], [4, 9], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21]]) == 10\n assert candidate(envelopes = [[2, 100], [3, 200], [4, 300], [5, 500], [5, 400], [5, 250], [6, 370], [6, 360], [7, 380]]) == 5\n assert candidate(envelopes = [[10, 16], [2, 3], [6, 8], [7, 12]]) == 4\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 5\n assert candidate(envelopes = [[30, 50], [12, 2], [3, 4], [12, 15]]) == 3\n assert candidate(envelopes = [[2, 100], [3, 200], [4, 300], [5, 400], [5, 500], [5, 600], [6, 300], [6, 400], [6, 500]]) == 5\n assert candidate(envelopes = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 10\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5]]) == 4\n assert candidate(envelopes = [[4, 5], [4, 6], [6, 7], [2, 3]]) == 3\n assert candidate(envelopes = [[1, 1], [1, 1], [1, 1]]) == 1\n assert candidate(envelopes = [[10, 16], [2, 3], [6, 14], [1, 2], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16]]) == 7\n assert candidate(envelopes = [[3, 2], [4, 3], [5, 4], [1, 5], [6, 6], [7, 7], [2, 8], [8, 2], [9, 9], [10, 1], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15], [16, 16], [17, 17], [18, 18], [19, 19], [20, 20]]) == 16\n assert candidate(envelopes = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [10, 10], [20, 20], [30, 30], [40, 40], [50, 50], [60, 60], [70, 70], [80, 80], [90, 90]]) == 9\n assert candidate(envelopes = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15]]) == 6\n assert candidate(envelopes = [[2, 1], [1, 2], [3, 3], [2, 2], [3, 2], [4, 3], [4, 4], [5, 4], [5, 5], [6, 6]]) == 5\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [1, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 9\n assert candidate(envelopes = [[10, 10], [9, 9], [8, 8], [7, 7], [6, 6], [5, 5], [4, 4], [3, 3], [2, 2], [1, 1], [11, 11], [12, 12], [13, 13]]) == 13\n assert candidate(envelopes = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21], [21, 23], [23, 25], [25, 27], [27, 29]]) == 14\n assert candidate(envelopes = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [3, 1], [3, 2], [3, 3], [3, 4], [3, 5], [4, 1], [4, 2], [4, 3], [4, 4], [4, 5], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5]]) == 5\n assert candidate(envelopes = [[2, 100], [3, 200], [4, 300], [5, 400], [5, 500], [5, 600], [6, 300], [6, 400], [6, 500], [7, 350], [7, 450], [7, 550], [8, 300], [8, 400], [8, 500]]) == 6\n assert candidate(envelopes = [[10, 18], [9, 16], [8, 14], [7, 12], [6, 10], [5, 8], [4, 6], [3, 4], [2, 2], [1, 1], [11, 20], [12, 22], [13, 24], [14, 26], [15, 28], [16, 30], [17, 32], [18, 34], [19, 36], [20, 38], [21, 40], [22, 42], [23, 44], [24, 46], [25, 48], [26, 50], [27, 52], [28, 54], [29, 56], [30, 58]]) == 30\n assert candidate(envelopes = [[30, 50], [12, 2], [3, 4], [12, 15], [50, 50], [40, 40], [10, 14], [6, 7], [5, 6], [7, 8], [8, 9], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [3, 4], [3, 5], [3, 6], [3, 7], [3, 8], [4, 5], [4, 6], [4, 7], [4, 8], [5, 6], [5, 7], [5, 8], [6, 7], [6, 8], [7, 8]]) == 12\n assert candidate(envelopes = [[1, 3], [3, 5], [6, 7], [8, 4], [9, 5], [10, 6], [11, 8], [12, 9], [13, 10]]) == 7\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [5, 5], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13]]) == 9\n assert candidate(envelopes = [[1, 3], [3, 5], [6, 7], [8, 4], [9, 5], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12], [11, 13], [12, 14], [13, 15], [14, 16], [15, 17], [16, 18], [17, 19], [18, 20], [19, 21], [20, 22], [21, 23], [22, 24], [23, 25], [24, 26], [25, 27], [26, 28], [27, 29], [28, 30], [29, 31], [30, 32]]) == 30\n assert candidate(envelopes = [[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10], [6, 11], [7, 12], [8, 13]]) == 4\n assert candidate(envelopes = [[100000, 1], [99999, 2], [99998, 3], [99997, 4], [99996, 5], [99995, 6], [99994, 7], [99993, 8], [99992, 9], [99991, 10]]) == 1\n assert candidate(envelopes = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == 10\n assert candidate(envelopes = [[2, 3], [3, 5], [4, 7], [5, 11], [6, 13], [8, 17], [10, 19], [11, 23], [13, 29], [14, 31], [17, 37], [19, 41], [23, 43], [29, 47], [31, 53], [37, 59], [41, 61], [43, 67], [47, 71], [53, 73], [59, 79], [61, 83], [67, 89], [71, 97], [73, 101], [79, 103], [83, 107], [89, 109], [97, 113]]) == 29\n assert candidate(envelopes = [[2, 3], [5, 4], [6, 4], [6, 7], [8, 4], [9, 5], [10, 6], [11, 7], [12, 8], [13, 9]]) == 7\n assert candidate(envelopes = [[10, 1], [9, 2], [8, 3], [7, 4], [6, 5], [5, 6], [4, 7], [3, 8], [2, 9], [1, 10]]) == 1\n assert candidate(envelopes = [[4, 5], [4, 6], [6, 7], [2, 3], [1, 1], [5, 5], [7, 8], [8, 9], [9, 10], [1, 2]]) == 7\n assert candidate(envelopes = [[15, 20], [18, 23], [19, 24], [21, 26], [25, 30], [27, 32], [28, 33], [30, 35], [32, 37], [34, 39]]) == 10\n assert candidate(envelopes = [[10, 15], [12, 20], [8, 14], [13, 25], [15, 30], [11, 22], [9, 18], [14, 28]]) == 6\n assert candidate(envelopes = [[10, 15], [8, 12], [5, 7], [2, 4], [11, 16], [13, 18], [6, 9], [4, 6], [7, 10], [9, 11], [14, 17], [3, 5], [1, 3], [12, 14], [15, 19]]) == 12\n assert candidate(envelopes = [[15, 15], [10, 20], [20, 10], [30, 25], [25, 30], [5, 5], [20, 20], [10, 30]]) == 4\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [1, 10], [2, 9], [3, 8], [4, 7], [5, 8], [6, 9], [7, 10]]) == 9\n assert candidate(envelopes = [[2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 9\n assert candidate(envelopes = [[10, 20], [15, 25], [20, 30], [25, 35], [30, 40], [5, 15], [10, 25], [15, 30], [20, 35], [25, 40], [30, 45], [5, 25], [10, 30], [15, 35], [20, 40], [25, 45], [30, 50]]) == 6\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16]]) == 15\n assert candidate(envelopes = [[3, 5], [6, 7], [9, 11], [12, 14], [15, 17], [18, 20], [21, 23], [24, 26], [27, 29], [30, 32]]) == 10\n assert candidate(envelopes = [[5, 10], [4, 9], [3, 8], [2, 7], [1, 6], [10, 5], [9, 4], [8, 3], [7, 2], [6, 1]]) == 5\n assert candidate(envelopes = [[100, 1], [200, 2], [300, 3], [400, 4], [500, 5], [600, 6], [700, 7], [800, 8], [900, 9], [1000, 10], [1100, 11], [1200, 12], [1300, 13], [1400, 14], [1500, 15], [1600, 16], [1700, 17], [1800, 18], [1900, 19], [2000, 20]]) == 20\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 10\n assert candidate(envelopes = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [2, 2], [2, 3], [2, 4], [2, 5], [3, 3], [3, 4], [3, 5], [4, 4], [4, 5], [5, 5]]) == 5\n assert candidate(envelopes = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [100, 110], [110, 120], [120, 130], [130, 140], [140, 150]]) == 14\n assert candidate(envelopes = [[10, 1], [9, 2], [8, 3], [7, 4], [6, 5], [5, 6], [4, 7], [3, 8], [2, 9], [1, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15]]) == 6\n assert candidate(envelopes = [[10, 15], [12, 20], [5, 8], [7, 12], [6, 9], [11, 18], [9, 11]]) == 6\n assert candidate(envelopes = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11]]) == 11\n assert candidate(envelopes = [[30, 50], [25, 45], [20, 40], [15, 35], [10, 30], [5, 25], [45, 60], [40, 55], [35, 50], [30, 45], [25, 40], [20, 35], [15, 30], [10, 25], [5, 20], [55, 70], [50, 65], [45, 60], [40, 55], [35, 50], [30, 45], [25, 40], [20, 35], [15, 30], [10, 25], [5, 20], [60, 75], [55, 70], [50, 65], [45, 60], [40, 55], [35, 50], [30, 45], [25, 40]]) == 12\n assert candidate(envelopes = [[2, 5], [2, 6], [3, 5], [3, 6], [4, 5], [4, 6], [5, 5], [5, 6], [6, 5], [6, 6]]) == 2\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [10, 5], [8, 4], [11, 6], [7, 3], [9, 2], [12, 8], [13, 7], [4, 6], [15, 5], [14, 4], [16, 3], [17, 2], [18, 1], [19, 10], [20, 9]]) == 6\n assert candidate(envelopes = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96], [6, 95], [7, 94], [8, 93], [9, 92], [10, 91], [11, 90], [12, 89], [13, 88], [14, 87], [15, 86], [16, 85], [17, 84], [18, 83], [19, 82], [20, 81]]) == 1\n assert candidate(envelopes = [[100, 100], [101, 101], [102, 102], [103, 103], [104, 104], [105, 105], [106, 106], [107, 107], [108, 108], [109, 109]]) == 10\n assert candidate(envelopes = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [100, 110]]) == 10\n assert candidate(envelopes = [[1, 1], [2, 2], [2, 3], [3, 3], [4, 4], [5, 5], [5, 6], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 10\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [8, 6], [9, 7], [10, 8]]) == 5\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [8, 5], [9, 6], [10, 7], [11, 8]]) == 6\n assert candidate(envelopes = [[30, 50], [12, 2], [3, 4], [12, 15], [50, 50], [45, 20], [37, 6], [23, 47], [5, 8], [10, 12], [34, 25], [12, 35]]) == 6\n assert candidate(envelopes = [[1, 3], [3, 5], [6, 7], [8, 4], [9, 5], [11, 6], [12, 8], [13, 7], [14, 9]]) == 6\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [8, 5], [9, 6], [10, 7], [11, 8], [12, 9]]) == 7\n assert candidate(envelopes = [[1, 3], [2, 6], [3, 9], [4, 12], [5, 15], [6, 18], [7, 21], [8, 24], [9, 27], [10, 30]]) == 10\n assert candidate(envelopes = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13]]) == 13\n assert candidate(envelopes = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1], [1, 11], [2, 12], [3, 13], [4, 14], [5, 15], [6, 16], [7, 17], [8, 18], [9, 19], [10, 20]]) == 10\n assert candidate(envelopes = [[2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14]]) == 12\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [3, 6], [4, 8], [5, 10], [7, 12], [8, 14], [9, 16], [10, 18], [11, 20], [12, 22], [13, 24], [14, 26], [15, 28], [16, 30], [17, 32], [18, 34], [19, 36], [20, 38], [21, 40], [22, 42], [23, 44], [24, 46], [25, 48], [26, 50], [27, 52], [28, 54], [29, 56], [30, 58]]) == 28\n assert candidate(envelopes = [[46, 89], [50, 53], [52, 68], [72, 45], [77, 81], [40, 40], [66, 68], [10, 10], [20, 22], [30, 25], [40, 30], [50, 40], [60, 50], [70, 60], [80, 70], [90, 80], [100, 90]]) == 10\n assert candidate(envelopes = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1]]) == 10\n assert candidate(envelopes = [[1, 3], [1, 2], [2, 3], [2, 2], [3, 4], [3, 3], [4, 5], [4, 4], [5, 6], [5, 5], [6, 7], [6, 6], [7, 8], [7, 7], [8, 9], [8, 8], [9, 10], [9, 9], [10, 11], [10, 10]]) == 10\n assert candidate(envelopes = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]) == 5\n assert candidate(envelopes = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12]]) == 10\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21]]) == 20\n assert candidate(envelopes = [[2, 100], [3, 200], [4, 300], [5, 400], [5, 500], [5, 600], [6, 300], [6, 400], [6, 500], [7, 400], [8, 500], [9, 600]]) == 6\n assert candidate(envelopes = [[5, 10], [10, 5], [15, 10], [20, 5], [25, 10], [30, 5], [35, 10], [40, 5], [45, 10], [50, 5], [55, 10], [60, 5], [65, 10], [70, 5], [75, 10], [80, 5], [85, 10], [90, 5], [95, 10], [100, 5]]) == 2\n assert candidate(envelopes = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1], [11, 10], [12, 9], [13, 8], [14, 7], [15, 6], [16, 5], [17, 4], [18, 3], [19, 2], [20, 1]]) == 2\n assert candidate(envelopes = [[10, 18], [2, 15], [12, 16], [7, 13], [3, 11], [5, 14], [9, 12], [8, 10], [6, 17], [1, 9], [11, 8], [13, 7], [4, 6], [15, 5], [14, 4], [16, 3], [17, 2], [18, 1]]) == 5\n assert candidate(envelopes = [[5, 7], [8, 6], [6, 4], [9, 5], [2, 3], [3, 4], [4, 5], [7, 8], [1, 2], [10, 9]]) == 7\n assert candidate(envelopes = [[50, 50], [51, 51], [52, 52], [53, 53], [54, 54], [55, 55], [56, 56], [57, 57], [58, 58], [59, 59]]) == 10\n assert candidate(envelopes = [[10, 18], [2, 9], [4, 12], [5, 15], [1, 6], [7, 21], [8, 24], [9, 27], [11, 30], [3, 10]]) == 9\n assert candidate(envelopes = [[5, 1], [6, 2], [6, 3], [2, 4], [8, 5], [9, 6], [10, 7], [11, 8], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15]]) == 12\n assert candidate(envelopes = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12], [11, 13], [12, 14], [13, 15]]) == 13\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15]]) == 14\n assert candidate(envelopes = [[1, 3], [1, 4], [1, 5], [1, 6], [2, 4], [2, 5], [2, 6], [3, 5], [3, 6], [4, 6]]) == 4\n assert candidate(envelopes = [[20, 50], [10, 25], [30, 75], [5, 10], [25, 50], [15, 35], [35, 65], [40, 60], [50, 80], [55, 85], [60, 90], [65, 95], [70, 100], [75, 105], [80, 110], [85, 115], [90, 120], [95, 125], [100, 130], [105, 135]]) == 17\n assert candidate(envelopes = [[3, 4], [3, 5], [4, 5], [1, 3], [2, 4], [2, 5], [3, 6], [4, 6], [5, 7], [6, 8]]) == 6\n assert candidate(envelopes = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96], [6, 95], [7, 94], [8, 93], [9, 92], [10, 91], [11, 90], [12, 89], [13, 88], [14, 87], [15, 86]]) == 1\n assert candidate(envelopes = [[4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12], [10, 13], [11, 14], [12, 15], [13, 16], [14, 17], [15, 18]]) == 12\n assert candidate(envelopes = [[30, 50], [12, 2], [3, 4], [12, 15], [12, 13], [20, 20], [25, 30], [10, 5]]) == 6\n assert candidate(envelopes = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [24, 25], [25, 26], [26, 27], [27, 28], [28, 29], [29, 30], [30, 31], [31, 32], [32, 33], [33, 34], [34, 35], [35, 36], [36, 37], [37, 38], [38, 39], [39, 40]]) == 39\n assert candidate(envelopes = [[1, 100000], [2, 99999], [3, 99998], [4, 99997], [5, 99996], [6, 99995], [7, 99994], [8, 99993], [9, 99992], [10, 99991]]) == 1\n assert candidate(envelopes = [[5, 5], [4, 4], [3, 3], [2, 2], [1, 1], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13]]) == 13\n assert candidate(envelopes = [[5, 4], [6, 4], [6, 7], [2, 3], [5, 4], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21], [22, 23], [24, 25]]) == 12\n"}, "metadata": {"canonical_parameter_names": ["envelopes"], "leetcode_dataset_entry_point": "Solution().maxEnvelopes", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxEnvelopes = function(envelopes) {", "container": null, "callable": "maxEnvelopes", "parameters": [{"name": "envelopes", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 357, "task_id": "count-numbers-with-unique-digits", "difficulty": "Medium", "problem_description": "Given an integer n, return the count of all numbers with unique digits, x, where 0 <= x < 10n.\n \nExample 1:\n\nInput: n = 2\nOutput: 91\nExplanation: The answer should be the total numbers in the range of 0 ≤ x < 100, excluding 11,22,33,44,55,66,77,88,99\n\nExample 2:\n\nInput: n = 0\nOutput: 1\n\n \nConstraints:\n\n0 <= n <= 8\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 1\n assert candidate(n = 8) == 2345851\n assert candidate(n = 3) == 739\n assert candidate(n = 4) == 5275\n assert candidate(n = 6) == 168571\n assert candidate(n = 2) == 91\n assert candidate(n = 1) == 10\n assert candidate(n = 7) == 712891\n assert candidate(n = 5) == 32491\n assert candidate(n = 9) == 5611771\n assert candidate(n = 10) == 8877691\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countNumbersWithUniqueDigits", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countNumbersWithUniqueDigits = function(n) {", "container": null, "callable": "countNumbersWithUniqueDigits", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 363, "task_id": "max-sum-of-rectangle-no-larger-than-k", "difficulty": "Hard", "problem_description": "Given an m x n matrix matrix and an integer k, return the max sum of a rectangle in the matrix such that its sum is no larger than k.\nIt is guaranteed that there will be a rectangle with a sum no larger than k.\n \nExample 1:\n\n\nInput: matrix = [[1,0,1],[0,-2,3]], k = 2\nOutput: 2\nExplanation: Because the sum of the blue rectangle [[0, 1], [-2, 3]] is 2, and 2 is the max number no larger than k (k = 2).\n\nExample 2:\n\nInput: matrix = [[2,2,-1]], k = 3\nOutput: 3\n\n \nConstraints:\n\nm == matrix.length\nn == matrix[i].length\n1 <= m, n <= 100\n-100 <= matrix[i][j] <= 100\n-105 <= k <= 105\n\n \nFollow up: What if the number of rows is much larger than the number of columns?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[1, 0, 1], [0, 1, 0], [1, 0, 1]],k = 2) == 2\n assert candidate(matrix = [[5, 12, 4], [3, 9, 1], [11, 1, 3]],k = 17) == 17\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3]],k = 2) == 2\n assert candidate(matrix = [[1, 1, 1], [1, 1, 1], [1, 1, 1]],k = 2) == 2\n assert candidate(matrix = [[-1, -1, -1], [-1, -1, -1], [-1, -1, -1]],k = -3) == -3\n assert candidate(matrix = [[5, 6, 7], [8, 9, 10]],k = 24) == 19\n assert candidate(matrix = [[5, -4, -3, 4], [-3, -4, 4, 5], [5, 1, 5, -4]],k = 10) == 10\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],k = 20) == 18\n assert candidate(matrix = [[-10, -20, -30], [-40, -50, -60], [-70, -80, -90]],k = -200) == -210\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [1, 2, 1]],k = 4) == 4\n assert candidate(matrix = [[2, 2, -1]],k = 3) == 3\n assert candidate(matrix = [[-1, 0, 1, 0, -1], [0, 1, 0, -1, 0], [1, 0, -1, 0, 1]],k = 0) == 0\n assert candidate(matrix = [[10, 20, 30], [40, 50, 60], [70, 80, 90]],k = 200) == 180\n assert candidate(matrix = [[-1, -1, -1], [-1, -2, -3], [-3, -3, -4]],k = -5) == -5\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]],k = 15) == 15\n assert candidate(matrix = [[10, 20, 30], [-10, -20, -30], [15, 25, 35]],k = 25) == 25\n assert candidate(matrix = [[5, 5, -5, 0, -5], [5, 5, 0, 0, -5], [5, 5, -5, -5, 0], [0, -5, 0, 0, 5], [0, -5, 5, 5, 5]],k = 15) == 15\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]],k = 10) == 10\n assert candidate(matrix = [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1]],k = 0) == 0\n assert candidate(matrix = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [6, 7, 8, 9, 10], [10, 9, 8, 7, 6], [11, 12, 13, 14, 15]],k = 30) == 30\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],k = -100) == -102\n assert candidate(matrix = [[-5, 2, 3, -1, 4], [1, -6, 7, 8, -2], [0, 9, -3, 4, 5], [-1, -2, 3, 4, -6]],k = 5) == 5\n assert candidate(matrix = [[-10, -20, -30, -40, -50], [-40, -50, -60, -70, -80], [-30, -40, -50, -60, -70], [-20, -30, -40, -50, -60], [-10, -20, -30, -40, -50]],k = -100) == -100\n assert candidate(matrix = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[100, -200, 300, -400, 500], [-500, 400, -300, 200, -100], [100, 200, 300, 400, 500], [0, -1, -2, -3, -4]],k = 100) == 100\n assert candidate(matrix = [[-100, 100, -100, 100], [-100, 100, -100, 100], [-100, 100, -100, 100], [-100, 100, -100, 100]],k = -100) == -100\n assert candidate(matrix = [[100, -100, 100, -100], [100, -100, 100, -100], [100, -100, 100, -100], [100, -100, 100, -100]],k = 99) == 0\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 1], [3, 4, 5, 6, 1, 2], [4, 5, 6, 1, 2, 3], [5, 6, 1, 2, 3, 4], [6, 1, 2, 3, 4, 5]],k = 20) == 20\n assert candidate(matrix = [[-10, -10, -10], [-10, -10, -10], [-10, -10, -10]],k = -29) == -30\n assert candidate(matrix = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[100, -100, 100, -100], [100, -100, 100, -100], [-100, 100, -100, 100], [-100, 100, -100, 100]],k = 0) == 0\n assert candidate(matrix = [[-10, 10, 20, 30], [-20, 5, -15, 10], [15, -25, 20, 5], [0, -5, 10, 15]],k = 25) == 25\n assert candidate(matrix = [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]],k = 10) == 9\n assert candidate(matrix = [[3, 2, 1, 4], [1, -1, 2, 3], [2, 1, 1, 2], [4, 2, -1, 3]],k = 5) == 5\n assert candidate(matrix = [[-2, -3, -4, 0], [-5, -3, -2, -1], [0, -1, 2, 3], [4, 2, -1, 3]],k = -1) == -1\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]],k = 40) == 40\n assert candidate(matrix = [[0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],k = 50) == 50\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],k = -10) == -10\n assert candidate(matrix = [[5, -4, -3, 4, -2], [2, -3, 4, 5, -1], [-3, 5, 1, 5, -4], [0, 0, 0, 0, 0]],k = 10) == 10\n assert candidate(matrix = [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],k = 5) == 5\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],k = 200) == 198\n assert candidate(matrix = [[-10, -20, -30, -40, -50], [-50, -40, -30, -20, -10], [0, 10, 20, 30, 40], [50, 40, 30, 20, 10], [60, 50, 40, 30, 20]],k = -25) == -30\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]],k = 30) == 30\n assert candidate(matrix = [[-1, -2, -3], [-3, -4, -5], [-5, -6, -7], [-7, -8, -9], [-9, -10, -11]],k = -20) == -20\n assert candidate(matrix = [[5, 10, 15, -5, 20], [10, -20, 25, 30, -15], [5, 15, -25, 10, 0], [0, 5, 10, -15, 20]],k = 40) == 40\n assert candidate(matrix = [[1, -2, 3, -4, 5], [2, -3, 4, -5, 6], [3, -4, 5, -6, 7], [4, -5, 6, -7, 8]],k = 5) == 5\n assert candidate(matrix = [[-5, 4, -10, 5], [-2, -3, 8, -4], [3, 5, -9, 1], [7, -6, 4, 2]],k = -1) == -1\n assert candidate(matrix = [[-5, 3, 4, 1, -2], [-1, 2, -3, 4, 5], [2, -1, -1, 1, -1], [3, -3, 2, -2, 1]],k = 5) == 5\n assert candidate(matrix = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, -2, 3, -4, 5], [1, 2, -1, 3, -2]],k = 3) == 3\n assert candidate(matrix = [[-1, 3, 2, 4, -5, -3], [2, 1, 2, 3, -1, 2], [4, 0, -1, 2, -1, 3], [-2, -2, 3, -3, -2, 2], [3, 3, 0, -2, -3, 1], [3, 0, -2, 3, 1, 3]],k = 5) == 5\n assert candidate(matrix = [[9, 7, -6, -4, 8], [-2, -5, 7, 2, -3], [3, 10, -4, 1, -2], [7, -6, 5, 4, 3]],k = 15) == 15\n assert candidate(matrix = [[-5, 3, 6, 2, -2], [-1, 2, -4, -4, 1], [2, -3, -3, -1, 5], [3, 1, 1, 2, -1], [3, 2, -1, 0, -4]],k = 3) == 3\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-5, -4, -3, -2, -1], [1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [-2, -3, -4, -5, -6]],k = -10) == -10\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20], [-21, -22, -23, -24, -25]],k = -50) == -50\n assert candidate(matrix = [[100, -100, 100], [-100, 100, -100], [100, -100, 100]],k = 150) == 100\n assert candidate(matrix = [[100, -100, 100, -100, 100], [-100, 100, -100, 100, -100], [100, -100, 100, -100, 100], [-100, 100, -100, 100, -100], [100, -100, 100, -100, 100]],k = 0) == 0\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]],k = 5) == 5\n assert candidate(matrix = [[1, -1, 1, -1, 1, -1], [-1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1], [-1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1], [-1, 1, -1, 1, -1, 1]],k = 1) == 1\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [-4, -3, -2, -1, 0], [-3, -2, -1, 0, 1], [-2, -1, 0, 1, 2], [-1, 0, 1, 2, 3]],k = -1) == -1\n assert candidate(matrix = [[-1, 2, -3, 4, -5], [5, -4, 3, -2, 1], [-1, 2, -3, 4, -5], [5, -4, 3, -2, 1], [-1, 2, -3, 4, -5]],k = 0) == 0\n assert candidate(matrix = [[1, -1, 2, -2, 3, -3], [4, -4, 5, -5, 6, -6], [7, -7, 8, -8, 9, -9]],k = 15) == 15\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [20, 19, 18, 17, 16, 15, 14, 13, 12, 11]],k = 50) == 50\n assert candidate(matrix = [[-1, 2, -3, 4, 5, -6], [7, 8, -9, 10, 11, -12], [13, 14, -15, 16, 17, -18]],k = 15) == 15\n assert candidate(matrix = [[1, -1, 1, -1, 1], [-1, 1, -1, 1, -1], [1, -1, 1, -1, 1], [-1, 1, -1, 1, -1], [1, -1, 1, -1, 1]],k = 2) == 1\n assert candidate(matrix = [[100, -100, 100], [-100, 100, -100], [100, -100, 100]],k = 0) == 0\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36]],k = 150) == 150\n assert candidate(matrix = [[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[100, -100, 100], [-100, 100, -100], [100, -100, 100], [100, -100, 100]],k = 50) == 0\n assert candidate(matrix = [[1, -1, 1, -1, 1, -1], [1, -1, 1, -1, 1, -1], [1, -1, 1, -1, 1, -1], [1, -1, 1, -1, 1, -1], [1, -1, 1, -1, 1, -1]],k = 0) == 0\n assert candidate(matrix = [[100, -100, 100], [-100, 100, -100], [100, -100, 100]],k = 200) == 100\n assert candidate(matrix = [[-1, -2, -3, -4, -5], [-2, -3, -4, -5, -6], [-3, -4, -5, -6, -7], [-4, -5, -6, -7, -8], [-5, -6, -7, -8, -9]],k = -15) == -15\n assert candidate(matrix = [[-10, 0, 10, -20, 0, 20], [-100, 0, 100, -200, 0, 200], [-1000, 0, 1000, -2000, 0, 2000], [-10000, 0, 10000, -20000, 0, 20000]],k = 5000) == 2220\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]],k = 15) == 15\n assert candidate(matrix = [[50, -50, 50, -50, 50], [-50, 50, -50, 50, -50], [50, -50, 50, -50, 50], [-50, 50, -50, 50, -50], [50, -50, 50, -50, 50]],k = 50) == 50\n assert candidate(matrix = [[-1, 0, 0, 0, -1], [-1, 1, 1, 1, -1], [-1, 1, 0, 1, -1], [-1, 0, 1, 0, -1]],k = 2) == 2\n assert candidate(matrix = [[-2, 3, 5, -1], [1, -3, 2, 4], [3, 2, -4, 1], [-1, 5, 2, -6]],k = 5) == 5\n assert candidate(matrix = [[-1, -1, 2, -2, 3, -3], [1, -2, -1, -3, 4, -4], [2, 3, 1, -1, 2, -2], [-1, 2, 0, -3, 3, 2], [3, 3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0]],k = 10) == 10\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 8]],k = 30) == 30\n assert candidate(matrix = [[-1, -2, -3, -4], [-2, -3, -4, -5], [-3, -4, -5, -6]],k = -5) == -5\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],k = 20) == 20\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]],k = 150) == 150\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]],k = 18) == 18\n assert candidate(matrix = [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]],k = 1) == 1\n assert candidate(matrix = [[-5, 10, -20, 15, 25], [-1, 2, 3, -4, 5], [20, -25, 30, -35, 40], [-10, 15, 20, -25, 30]],k = 10) == 10\n assert candidate(matrix = [[-1, 0, 1, -1, 0, 1], [-1, 0, 1, -1, 0, 1], [-1, 0, 1, -1, 0, 1]],k = 0) == 0\n assert candidate(matrix = [[100, -100, 200, -200, 300], [10, -10, 20, -20, 30], [1, -1, 2, -2, 3], [100, -100, 200, -200, 300], [10, -10, 20, -20, 30]],k = 250) == 242\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],k = 100) == 99\n assert candidate(matrix = [[-5, 0, 4, -1, 1], [-3, -3, 3, 0, -2], [1, -2, 4, 1, -1], [-1, 0, -1, 0, 0], [1, 1, 1, -1, 1]],k = 3) == 3\n assert candidate(matrix = [[-10, -20, -30], [-40, -50, -60], [-70, -80, -90]],k = -150) == -150\n assert candidate(matrix = [[1, 2, 3, 4], [2, 3, 4, 5], [3, 4, 5, 6], [4, 5, 6, 7]],k = 15) == 15\n assert candidate(matrix = [[1, -1, 2, -2], [-1, 1, -2, 2], [2, -2, 1, -1], [-2, 2, -1, 1]],k = 3) == 2\n assert candidate(matrix = [[1, 0, -1, 0, 1], [0, 1, 0, -1, 0], [-1, 0, 1, 0, -1], [0, -1, 0, 1, 0], [1, 0, -1, 0, 1]],k = 2) == 2\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, -2, 3, -2, 3], [1, 0, 1, 0, 1]],k = 2) == 2\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9]],k = 15) == 15\n assert candidate(matrix = [[5, 6, 7, 8], [4, 3, 2, 1], [9, 10, 11, 12]],k = 30) == 30\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [1, -1, 2]],k = 2) == 2\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [3, 2, -1]],k = 4) == 4\n assert candidate(matrix = [[5, 9, 7, 4, 6], [9, 7, 4, 6, 5], [4, 6, 5, 9, 7], [6, 5, 9, 7, 4]],k = 20) == 20\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]],k = 15) == 15\n assert candidate(matrix = [[1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[-100, -100, -100], [-100, -100, -100], [-100, -100, -100]],k = -300) == -300\n assert candidate(matrix = [[-5, 6, -7, 8], [4, -3, 2, -1], [9, -10, 11, -12]],k = 5) == 5\n assert candidate(matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]],k = -5) == -5\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [3, 2, 1], [-1, -1, -1]],k = 2) == 2\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [3, 2, 1]],k = 5) == 5\n assert candidate(matrix = [[1, 1, 1], [1, 1, 1], [1, 1, 1]],k = 5) == 4\n assert candidate(matrix = [[10, 10, 10], [10, 10, 10], [10, 10, 10]],k = 30) == 30\n assert candidate(matrix = [[2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2, 2], [2, 2, 2, 2, 2]],k = 10) == 10\n assert candidate(matrix = [[100, 100, 100], [100, 100, 100], [100, 100, 100]],k = 299) == 200\n assert candidate(matrix = [[-2, -3, -4, -5], [-6, -7, -8, -9], [-10, -11, -12, -13]],k = -15) == -15\n assert candidate(matrix = [[1]],k = 0) == -inf\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],k = 15) == 15\n assert candidate(matrix = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9]],k = 25) == 25\n assert candidate(matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]],k = -1) == -1\n assert candidate(matrix = [[-1, 3, 2, -4, 1, 2], [3, 2, -1, 4, -3, -2], [2, 1, -3, 4, 1, -3]],k = 10) == 10\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, 1, 0, 1, 0], [1, 0, 1, 0, 1], [0, 1, 0, 1, 0]],k = 3) == 3\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]],k = 20) == 20\n assert candidate(matrix = [[0, 0, 0], [0, 0, 0], [0, 0, 0]],k = 0) == 0\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [1, -1, 1]],k = 1) == 1\n assert candidate(matrix = [[-5, -4, -3], [-4, -3, -2], [-3, -2, -1]],k = -8) == -8\n assert candidate(matrix = [[100, -100], [100, -100]],k = 0) == 0\n assert candidate(matrix = [[10, 20, 30], [40, 50, 60], [70, 80, 90]],k = 150) == 150\n assert candidate(matrix = [[-1, -1, -1], [-1, -1, -1], [-1, -1, -1]],k = -2) == -2\n assert candidate(matrix = [[10, 11, 12], [9, 10, 11], [8, 9, 10]],k = 29) == 27\n assert candidate(matrix = [[-1, 0, 1], [-2, -1, 2], [-3, -2, 3]],k = -1) == -1\n assert candidate(matrix = [[-5, -4, -3], [-2, -1, 0], [1, 2, 3]],k = -5) == -5\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [4, 5, 6]],k = 10) == 10\n assert candidate(matrix = [[-5, -4, -3, -4], [-3, -4, 4, 5], [5, 1, 5, -4]],k = -10) == -10\n assert candidate(matrix = [[10, 10, 10], [10, -10, 10], [10, 10, -10]],k = 30) == 30\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]],k = 30) == 30\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [0, 3, -1]],k = 4) == 4\n assert candidate(matrix = [[-1, 1], [-2, 2], [-3, 3]],k = 1) == 1\n assert candidate(matrix = [[3, 3, 3], [3, 3, 3], [3, 3, 3]],k = 27) == 27\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, -2, 3, -2, 3], [3, 2, 1, 2, 1]],k = 4) == 4\n assert candidate(matrix = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 3, 5, 7, 9], [9, 7, 5, 3, 1]],k = 15) == 15\n assert candidate(matrix = [[-1, -1, -1], [-1, -1, -1], [-1, -1, -1]],k = -1) == -1\n assert candidate(matrix = [[1]],k = 1) == 1\n assert candidate(matrix = [[5, 12, 11, 18, 22], [2, 4, 3, 10, 19], [1, 3, 8, 12, 22], [9, 18, 10, 24, 25], [10, 14, 10, 12, 25]],k = 50) == 50\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6]],k = 15) == 12\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],k = 10) == 9\n assert candidate(matrix = [[3, 2, 1, 4, 7], [2, 1, 3, 2, 5], [1, 4, 2, 2, 3]],k = 13) == 13\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [4, 5, 6], [-3, -4, 4, 5]],k = 3) == 3\n assert candidate(matrix = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]],k = 25) == 24\n assert candidate(matrix = [[5, 6, 3, 4, 8], [4, 3, 1, 4, 6], [5, 8, 7, 3, 4], [3, 8, 8, 8, 5], [5, 7, 2, 4, 7]],k = 20) == 20\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [-9, -8, -7, -6, -5], [-4, -3, -2, -1, 0]],k = 10) == 10\n assert candidate(matrix = [[1, 0], [0, 1]],k = 2) == 2\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [4, 1, 0]],k = 5) == 5\n assert candidate(matrix = [[1, 0, 1, 0], [0, -2, 3, 1], [3, 2, -1, 0]],k = 3) == 3\n assert candidate(matrix = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9]],k = -10) == -11\n assert candidate(matrix = [[5, 10, 15], [20, 25, 30]],k = 45) == 45\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [3, 2, 1]],k = 4) == 4\n assert candidate(matrix = [[-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, -1], [-1, -1, -1, -1]],k = -4) == -4\n assert candidate(matrix = [[5, 10, 15], [20, 25, 30], [35, 40, 45]],k = 100) == 90\n assert candidate(matrix = [[5, 12, -100, 4, -5], [-3, 1, 4, -3, -4], [2, 3, 4, -3, 4], [1, -2, 3, -2, 1]],k = 7) == 7\n assert candidate(matrix = [[5, 2, 3], [1, 6, 7], [4, 8, 9]],k = 20) == 19\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8]],k = 16) == 16\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [3, 2, -1]],k = 5) == 5\n assert candidate(matrix = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8]],k = 20) == 20\n assert candidate(matrix = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],k = 1) == 1\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [5, 4, 3, 2, 1], [0, 0, 0, 0, 0], [1, 2, 3, 4, 5], [-1, -2, -3, -4, -5]],k = 2) == 2\n assert candidate(matrix = [[-1, -1], [-1, -1]],k = -2) == -2\n assert candidate(matrix = [[2, 2], [2, 2], [2, 2]],k = 6) == 6\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, -2, 3, -2, 3], [-3, -4, 4, 5, -4], [5, 1, 5, -4, 1]],k = 5) == 5\n assert candidate(matrix = [[100, 100, 100], [100, 100, 100], [100, 100, 100]],k = 100) == 100\n assert candidate(matrix = [[3, 3, 3, 10000], [-10000, -10000, -10000, -3], [3, 3, 3, 10000]],k = 9) == 9\n assert candidate(matrix = [[1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 1]],k = 1) == 1\n assert candidate(matrix = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1]],k = 1) == 1\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, 1, 0, 1, 0], [1, 0, 1, 0, 1], [0, 1, 0, 1, 0], [1, 0, 1, 0, 1]],k = 2) == 2\n assert candidate(matrix = [[5, 5, 5], [5, 5, 5], [5, 5, 5]],k = 15) == 15\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, 0, 0, 0]],k = 3) == 3\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [1, 0, 1]],k = 4) == 4\n assert candidate(matrix = [[0, 0], [0, 0]],k = 0) == 0\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15]],k = 15) == 15\n assert candidate(matrix = [[2, 2, 2, 2], [2, 2, 2, 2], [2, 2, 2, 2]],k = 7) == 6\n assert candidate(matrix = [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]],k = 8) == 8\n assert candidate(matrix = [[100, 100], [100, 100]],k = 200) == 200\n assert candidate(matrix = [[-1, -1], [-2, -2]],k = -2) == -2\n assert candidate(matrix = [[-1, -1], [-1, -1]],k = -3) == -4\n assert candidate(matrix = [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]],k = 25) == 24\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]],k = 3) == 3\n assert candidate(matrix = [[1, 2], [3, 4], [5, 6], [7, 8]],k = 10) == 10\n assert candidate(matrix = [[1, 0, 1, 0], [0, 1, 0, 1], [1, 0, 1, 0], [0, 1, 0, 1]],k = 2) == 2\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [1, 2, -1]],k = 4) == 4\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6]],k = 15) == 15\n assert candidate(matrix = [[1, 1], [1, 1]],k = 3) == 2\n assert candidate(matrix = [[1, 10, 100, 1000]],k = 1500) == 1111\n assert candidate(matrix = [[5, 6, 7], [8, 9, 10], [11, 12, 13]],k = 30) == 30\n assert candidate(matrix = [[-1, -1], [-1, -1], [-1, -1], [-1, -1], [-1, -1]],k = -2) == -2\n assert candidate(matrix = [[5, 10, 15], [20, 25, 30]],k = 50) == 45\n assert candidate(matrix = [[-2, -1, -3], [-3, -1, -2], [-1, -3, -2]],k = -4) == -4\n assert candidate(matrix = [[-1, 7, 8], [-9, 4, 5]],k = 14) == 14\n assert candidate(matrix = [[1, 0, 1, 0, 1], [0, -2, 3, -2, 1], [1, 1, 1, 1, 1]],k = 3) == 3\n assert candidate(matrix = [[-1, -1, -1], [-1, -1, -1], [-1, -1, -1]],k = -5) == -6\n assert candidate(matrix = [[1, 0, 1], [0, -2, 3], [-1, -1, -1]],k = -1) == -1\n assert candidate(matrix = [[5, 6, 7, 8], [1, 2, 3, 4], [9, 10, 11, 12], [13, 14, 15, 16]],k = 20) == 19\n assert candidate(matrix = [[1, 2], [3, 4]],k = 10) == 10\n assert candidate(matrix = [[-1, 2], [-3, 4]],k = 1) == 1\n assert candidate(matrix = [[5, 3, 1, 4, 2], [8, 6, 9, 7, 5], [3, 2, 8, 6, 4], [1, 4, 5, 2, 3], [7, 5, 4, 8, 6]],k = 25) == 25\n assert candidate(matrix = [[1, 2], [3, 4]],k = 6) == 6\n assert candidate(matrix = [[10, 10, 10], [10, 10, 10], [10, 10, 10]],k = 50) == 40\n assert candidate(matrix = [[-1, 0, -1], [0, 2, -3], [3, -2, 1], [1, -1, 1]],k = 1) == 1\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],k = 30) == 28\n assert candidate(matrix = [[-100, -100, -100], [-100, -100, -100], [-100, -100, -100]],k = -100) == -100\n"}, "metadata": {"canonical_parameter_names": ["matrix", "k"], "leetcode_dataset_entry_point": "Solution().maxSumSubmatrix", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxSumSubmatrix = function(matrix, k) {", "container": null, "callable": "maxSumSubmatrix", "parameters": [{"name": "matrix", "type": "number[][]"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 365, "task_id": "water-and-jug-problem", "difficulty": "Medium", "problem_description": "You are given two jugs with capacities x liters and y liters. You have an infinite water supply. Return whether the total amount of water in both jugs may reach target using the following operations:\n\nFill either jug completely with water.\nCompletely empty either jug.\nPour water from one jug into another until the receiving jug is full, or the transferring jug is empty.\n\n \nExample 1: \n\nInput: x = 3, y = 5, target = 4 \nOutput: true \nExplanation:\nFollow these steps to reach a total of 4 liters:\n\nFill the 5-liter jug (0, 5).\nPour from the 5-liter jug into the 3-liter jug, leaving 2 liters (3, 2).\nEmpty the 3-liter jug (0, 2).\nTransfer the 2 liters from the 5-liter jug to the 3-liter jug (2, 0).\nFill the 5-liter jug again (2, 5).\nPour from the 5-liter jug into the 3-liter jug until the 3-liter jug is full. This leaves 4 liters in the 5-liter jug (3, 4).\nEmpty the 3-liter jug. Now, you have exactly 4 liters in the 5-liter jug (0, 4).\n\nReference: The Die Hard example.\n\nExample 2: \n\nInput: x = 2, y = 6, target = 5 \nOutput: false \n\nExample 3: \n\nInput: x = 1, y = 2, target = 3 \nOutput: true \nExplanation: Fill both jugs. The total amount of water in both jugs is equal to 3 now.\n\n \nConstraints:\n\n1 <= x, y, target <= 103\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(x = 3,y = 7,target = 1) == True\n assert candidate(x = 7,y = 3,target = 1) == True\n assert candidate(x = 8,y = 5,target = 9) == True\n assert candidate(x = 2,y = 6,target = 5) == False\n assert candidate(x = 10,y = 10,target = 15) == False\n assert candidate(x = 5,y = 5,target = 10) == True\n assert candidate(x = 5,y = 3,target = 8) == True\n assert candidate(x = 7,y = 11,target = 6) == True\n assert candidate(x = 7,y = 3,target = 2) == True\n assert candidate(x = 4,y = 9,target = 6) == True\n assert candidate(x = 1,y = 2,target = 3) == True\n assert candidate(x = 1,y = 1,target = 2) == True\n assert candidate(x = 10,y = 10,target = 20) == True\n assert candidate(x = 8,y = 11,target = 15) == True\n assert candidate(x = 34,y = 5,target = 6) == True\n assert candidate(x = 100,y = 333,target = 500) == False\n assert candidate(x = 5,y = 2,target = 3) == True\n assert candidate(x = 4,y = 4,target = 7) == False\n assert candidate(x = 3,y = 5,target = 4) == True\n assert candidate(x = 29,y = 31,target = 30) == True\n assert candidate(x = 23,y = 39,target = 11) == True\n assert candidate(x = 67,y = 79,target = 178) == False\n assert candidate(x = 666,y = 777,target = 1434) == False\n assert candidate(x = 23,y = 54,target = 77) == True\n assert candidate(x = 17,y = 13,target = 20) == True\n assert candidate(x = 200,y = 300,target = 500) == True\n assert candidate(x = 311,y = 271,target = 582) == True\n assert candidate(x = 53,y = 67,target = 134) == False\n assert candidate(x = 400,y = 500,target = 800) == True\n assert candidate(x = 31,y = 47,target = 78) == True\n assert candidate(x = 47,y = 61,target = 110) == False\n assert candidate(x = 61,y = 41,target = 29) == True\n assert candidate(x = 23,y = 29,target = 42) == True\n assert candidate(x = 103,y = 113,target = 326) == False\n assert candidate(x = 500,y = 300,target = 400) == True\n assert candidate(x = 73,y = 21,target = 50) == True\n assert candidate(x = 100,y = 33,target = 67) == True\n assert candidate(x = 79,y = 97,target = 236) == False\n assert candidate(x = 97,y = 107,target = 294) == False\n assert candidate(x = 33,y = 44,target = 77) == True\n assert candidate(x = 97,y = 101,target = 73) == True\n assert candidate(x = 31,y = 47,target = 20) == True\n assert candidate(x = 13,y = 17,target = 30) == True\n assert candidate(x = 200,y = 125,target = 325) == True\n assert candidate(x = 123,y = 456,target = 579) == True\n assert candidate(x = 41,y = 97,target = 86) == True\n assert candidate(x = 61,y = 79,target = 89) == True\n assert candidate(x = 23,y = 37,target = 60) == True\n assert candidate(x = 727,y = 1019,target = 1746) == True\n assert candidate(x = 29,y = 41,target = 59) == True\n assert candidate(x = 127,y = 139,target = 414) == False\n assert candidate(x = 101,y = 109,target = 310) == False\n assert candidate(x = 29,y = 31,target = 60) == True\n assert candidate(x = 61,y = 122,target = 183) == True\n assert candidate(x = 97,y = 54,target = 43) == True\n assert candidate(x = 149,y = 163,target = 510) == False\n assert candidate(x = 89,y = 103,target = 270) == False\n assert candidate(x = 97,y = 61,target = 73) == True\n assert candidate(x = 100,y = 75,target = 250) == False\n assert candidate(x = 53,y = 19,target = 67) == True\n assert candidate(x = 113,y = 137,target = 390) == False\n assert candidate(x = 81,y = 147,target = 108) == True\n assert candidate(x = 500,y = 600,target = 1000) == True\n assert candidate(x = 157,y = 173,target = 550) == False\n assert candidate(x = 253,y = 103,target = 356) == True\n assert candidate(x = 500,y = 750,target = 1000) == True\n assert candidate(x = 113,y = 131,target = 119) == True\n assert candidate(x = 250,y = 350,target = 600) == True\n assert candidate(x = 71,y = 23,target = 37) == True\n assert candidate(x = 59,y = 17,target = 50) == True\n assert candidate(x = 23,y = 37,target = 29) == True\n assert candidate(x = 221,y = 359,target = 285) == True\n assert candidate(x = 151,y = 167,target = 526) == False\n assert candidate(x = 41,y = 37,target = 78) == True\n assert candidate(x = 13,y = 17,target = 29) == True\n assert candidate(x = 53,y = 47,target = 100) == True\n assert candidate(x = 61,y = 73,target = 164) == False\n assert candidate(x = 17,y = 23,target = 30) == True\n assert candidate(x = 101,y = 37,target = 88) == True\n assert candidate(x = 400,y = 1000,target = 500) == False\n assert candidate(x = 59,y = 61,target = 120) == True\n assert candidate(x = 333,y = 444,target = 777) == True\n assert candidate(x = 61,y = 41,target = 183) == False\n assert candidate(x = 97,y = 59,target = 156) == True\n assert candidate(x = 83,y = 53,target = 109) == True\n assert candidate(x = 101,y = 103,target = 206) == False\n assert candidate(x = 8,y = 13,target = 19) == True\n assert candidate(x = 73,y = 89,target = 210) == False\n assert candidate(x = 17,y = 13,target = 26) == True\n assert candidate(x = 401,y = 199,target = 202) == True\n assert candidate(x = 139,y = 157,target = 482) == False\n assert candidate(x = 601,y = 409,target = 500) == True\n assert candidate(x = 71,y = 83,target = 101) == True\n assert candidate(x = 101,y = 139,target = 240) == True\n assert candidate(x = 100,y = 37,target = 101) == True\n assert candidate(x = 97,y = 101,target = 199) == False\n assert candidate(x = 41,y = 43,target = 84) == True\n assert candidate(x = 101,y = 103,target = 204) == True\n assert candidate(x = 53,y = 89,target = 31) == True\n assert candidate(x = 109,y = 131,target = 366) == False\n assert candidate(x = 71,y = 83,target = 194) == False\n assert candidate(x = 750,y = 900,target = 1500) == True\n assert candidate(x = 43,y = 59,target = 102) == True\n assert candidate(x = 400,y = 150,target = 250) == True\n assert candidate(x = 19,y = 23,target = 42) == True\n assert candidate(x = 13,y = 29,target = 17) == True\n assert candidate(x = 301,y = 197,target = 498) == True\n assert candidate(x = 111,y = 333,target = 444) == True\n assert candidate(x = 787,y = 359,target = 428) == True\n assert candidate(x = 29,y = 41,target = 58) == True\n assert candidate(x = 137,y = 151,target = 458) == False\n assert candidate(x = 59,y = 71,target = 150) == False\n assert candidate(x = 89,y = 67,target = 52) == True\n assert candidate(x = 333,y = 222,target = 111) == True\n assert candidate(x = 71,y = 73,target = 144) == True\n assert candidate(x = 13,y = 17,target = 24) == True\n assert candidate(x = 45,y = 10,target = 75) == False\n assert candidate(x = 800,y = 900,target = 1600) == True\n assert candidate(x = 13,y = 17,target = 20) == True\n assert candidate(x = 100,y = 300,target = 200) == True\n assert candidate(x = 37,y = 53,target = 90) == True\n assert candidate(x = 1000,y = 1001,target = 2001) == True\n assert candidate(x = 1000,y = 333,target = 667) == True\n assert candidate(x = 13,y = 17,target = 39) == False\n assert candidate(x = 313,y = 509,target = 822) == True\n assert candidate(x = 43,y = 59,target = 37) == True\n assert candidate(x = 131,y = 149,target = 442) == False\n assert candidate(x = 107,y = 127,target = 350) == False\n assert candidate(x = 47,y = 19,target = 28) == True\n assert candidate(x = 97,y = 101,target = 198) == True\n assert candidate(x = 200,y = 123,target = 323) == True\n assert candidate(x = 101,y = 202,target = 303) == True\n assert candidate(x = 55,y = 77,target = 110) == True\n assert candidate(x = 89,y = 71,target = 160) == True\n assert candidate(x = 101,y = 89,target = 190) == True\n assert candidate(x = 53,y = 109,target = 162) == True\n assert candidate(x = 23,y = 17,target = 30) == True\n assert candidate(x = 100,y = 33,target = 66) == True\n assert candidate(x = 23,y = 31,target = 54) == True\n assert candidate(x = 17,y = 37,target = 41) == True\n assert candidate(x = 83,y = 101,target = 254) == False\n assert candidate(x = 5,y = 7,target = 11) == True\n assert candidate(x = 22,y = 33,target = 55) == True\n assert candidate(x = 10,y = 15,target = 25) == True\n assert candidate(x = 5,y = 2,target = 7) == True\n assert candidate(x = 7,y = 13,target = 20) == True\n assert candidate(x = 3,y = 3,target = 1) == False\n assert candidate(x = 7,y = 13,target = 1) == True\n assert candidate(x = 3,y = 9,target = 6) == True\n assert candidate(x = 4,y = 9,target = 8) == True\n assert candidate(x = 10,y = 15,target = 7) == False\n assert candidate(x = 33,y = 55,target = 11) == True\n assert candidate(x = 10,y = 15,target = 5) == True\n assert candidate(x = 333,y = 444,target = 111) == True\n assert candidate(x = 1000,y = 1000,target = 1500) == False\n assert candidate(x = 5,y = 11,target = 2) == True\n assert candidate(x = 8,y = 12,target = 16) == True\n assert candidate(x = 10,y = 15,target = 20) == True\n assert candidate(x = 7,y = 11,target = 8) == True\n assert candidate(x = 1,y = 1,target = 0) == True\n assert candidate(x = 6,y = 6,target = 6) == True\n assert candidate(x = 3,y = 7,target = 2) == True\n assert candidate(x = 8,y = 17,target = 15) == True\n assert candidate(x = 7,y = 11,target = 1) == True\n assert candidate(x = 500,y = 1000,target = 750) == False\n assert candidate(x = 7,y = 11,target = 2) == True\n assert candidate(x = 13,y = 19,target = 32) == True\n assert candidate(x = 4,y = 9,target = 7) == True\n assert candidate(x = 220,y = 340,target = 560) == True\n assert candidate(x = 4,y = 9,target = 13) == True\n assert candidate(x = 3,y = 1,target = 2) == True\n assert candidate(x = 500,y = 200,target = 400) == True\n assert candidate(x = 6,y = 19,target = 5) == True\n assert candidate(x = 500,y = 500,target = 1000) == True\n assert candidate(x = 8,y = 3,target = 5) == True\n assert candidate(x = 8,y = 11,target = 13) == True\n assert candidate(x = 4,y = 17,target = 20) == True\n assert candidate(x = 5,y = 7,target = 12) == True\n assert candidate(x = 2,y = 3,target = 1) == True\n assert candidate(x = 3,y = 3,target = 6) == True\n assert candidate(x = 5,y = 3,target = 2) == True\n assert candidate(x = 333,y = 666,target = 999) == True\n assert candidate(x = 4,y = 10,target = 8) == True\n assert candidate(x = 5,y = 10,target = 15) == True\n assert candidate(x = 8,y = 3,target = 11) == True\n assert candidate(x = 100,y = 300,target = 500) == False\n assert candidate(x = 8,y = 11,target = 1) == True\n assert candidate(x = 7,y = 13,target = 10) == True\n assert candidate(x = 22,y = 26,target = 16) == True\n assert candidate(x = 7,y = 11,target = 18) == True\n assert candidate(x = 34,y = 51,target = 68) == True\n assert candidate(x = 4,y = 6,target = 8) == True\n"}, "metadata": {"canonical_parameter_names": ["x", "y", "target"], "leetcode_dataset_entry_point": "Solution().canMeasureWater", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canMeasureWater = function(x, y, target) {", "container": null, "callable": "canMeasureWater", "parameters": [{"name": "x", "type": "number"}, {"name": "y", "type": "number"}, {"name": "target", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 367, "task_id": "valid-perfect-square", "difficulty": "Easy", "problem_description": "Given a positive integer num, return true if num is a perfect square or false otherwise.\nA perfect square is an integer that is the square of an integer. In other words, it is the product of some integer with itself.\nYou must not use any built-in library function, such as sqrt.\n \nExample 1:\n\nInput: num = 16\nOutput: true\nExplanation: We return true because 4 * 4 = 16 and 4 is an integer.\n\nExample 2:\n\nInput: num = 14\nOutput: false\nExplanation: We return false because 3.742 * 3.742 = 14 and 3.742 is not an integer.\n\n \nConstraints:\n\n1 <= num <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 14) == False\n assert candidate(num = 9) == True\n assert candidate(num = 1000000000) == False\n assert candidate(num = 49) == True\n assert candidate(num = 50) == False\n assert candidate(num = 25) == True\n assert candidate(num = 0) == False\n assert candidate(num = 4) == True\n assert candidate(num = 1524157875) == False\n assert candidate(num = 1) == True\n assert candidate(num = 100) == True\n assert candidate(num = 152415787501905210) == False\n assert candidate(num = 99) == False\n assert candidate(num = 2147483647) == False\n assert candidate(num = 101) == False\n assert candidate(num = 16) == True\n assert candidate(num = 26) == False\n assert candidate(num = 15) == False\n assert candidate(num = 12345678987654321) == True\n assert candidate(num = 10) == False\n assert candidate(num = 361294659455137) == False\n assert candidate(num = 9801) == True\n assert candidate(num = 100000000) == True\n assert candidate(num = 4503599627370496) == True\n assert candidate(num = 401) == False\n assert candidate(num = 12345678987654322) == False\n assert candidate(num = 104976) == True\n assert candidate(num = 1025) == False\n assert candidate(num = 123456789) == False\n assert candidate(num = 18014398509481984) == True\n assert candidate(num = 18014398509481985) == False\n assert candidate(num = 9223372036854775807) == False\n assert candidate(num = 1000000001) == False\n assert candidate(num = 2500) == True\n assert candidate(num = 100000001) == False\n assert candidate(num = 2304) == True\n assert candidate(num = 207936) == True\n assert candidate(num = 400) == True\n assert candidate(num = 4294967296) == True\n assert candidate(num = 2) == False\n assert candidate(num = 46656000000) == True\n assert candidate(num = 3) == False\n assert candidate(num = 141376) == True\n assert candidate(num = 1024) == True\n assert candidate(num = 1000000000000) == True\n assert candidate(num = 16777216) == True\n assert candidate(num = 999999999) == False\n assert candidate(num = 1000000) == True\n assert candidate(num = 1000001) == False\n assert candidate(num = 1073741824) == True\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().isPerfectSquare", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isPerfectSquare = function(num) {", "container": null, "callable": "isPerfectSquare", "parameters": [{"name": "num", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 368, "task_id": "largest-divisible-subset", "difficulty": "Medium", "problem_description": "Given a set of distinct positive integers nums, return the largest subset answer such that every pair (answer[i], answer[j]) of elements in this subset satisfies:\n\nanswer[i] % answer[j] == 0, or\nanswer[j] % answer[i] == 0\n\nIf there are multiple solutions, return any of them.\n \nExample 1:\n\nInput: nums = [1,2,3]\nOutput: [1,2]\nExplanation: [1,3] is also accepted.\n\nExample 2:\n\nInput: nums = [1,2,4,8]\nOutput: [1,2,4,8]\n\n \nConstraints:\n\n1 <= nums.length <= 1000\n1 <= nums[i] <= 2 * 109\nAll the integers in nums are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15]) == [9, 3, 1]\n assert candidate(nums = [100, 200, 400, 800, 1600, 3200]) == [3200, 1600, 800, 400, 200, 100]\n assert candidate(nums = [1, 5, 10, 20, 25, 50]) == [20, 10, 5, 1]\n assert candidate(nums = [2, 3, 5, 7, 11, 13]) == [2]\n assert candidate(nums = [2, 3, 5, 7, 11]) == [2]\n assert candidate(nums = [3, 9, 20, 18, 15]) == [18, 9, 3]\n assert candidate(nums = [3, 6, 9, 12, 18]) == [12, 6, 3]\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128]) == [128, 64, 32, 16, 8, 4, 2]\n assert candidate(nums = [18, 3, 6, 2, 9]) == [18, 9, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [8, 4, 2, 1]\n assert candidate(nums = [1, 3, 5, 7, 9]) == [9, 3, 1]\n assert candidate(nums = [7, 14, 28, 56, 112]) == [112, 56, 28, 14, 7]\n assert candidate(nums = [1]) == [1]\n assert candidate(nums = [1, 2, 4, 8]) == [8, 4, 2, 1]\n assert candidate(nums = [5, 10, 15, 20, 25, 30]) == [20, 10, 5]\n assert candidate(nums = [10, 5, 2, 6]) == [6, 2]\n assert candidate(nums = [10, 5, 3, 15, 20]) == [20, 10, 5]\n assert candidate(nums = [100, 200, 400, 800, 1600]) == [1600, 800, 400, 200, 100]\n assert candidate(nums = [3, 6, 9, 12, 18, 24]) == [24, 12, 6, 3]\n assert candidate(nums = [7, 14, 28, 56, 112, 224]) == [224, 112, 56, 28, 14, 7]\n assert candidate(nums = [2, 4, 8, 16, 32, 64]) == [64, 32, 16, 8, 4, 2]\n assert candidate(nums = [7, 14, 28, 35, 56, 112]) == [112, 56, 28, 14, 7]\n assert candidate(nums = [1, 3, 6, 24]) == [24, 6, 3, 1]\n assert candidate(nums = [18, 36, 54, 9, 18, 27, 54]) == [54, 54, 18, 18, 9]\n assert candidate(nums = [21, 28, 35, 42, 56, 70, 84, 98, 140, 168, 196, 245, 280, 392, 420, 588, 784, 980, 1372, 1764, 2744, 3528, 5588, 7056, 11176, 14112, 22352, 28224, 44704, 56448, 89408, 178816]) == [56448, 28224, 14112, 7056, 3528, 1764, 588, 84, 42, 21]\n assert candidate(nums = [5, 10, 15, 20, 25]) == [20, 10, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 18, 24, 30, 36, 40, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720]) == [720, 360, 180, 90, 30, 10, 5, 1]\n assert candidate(nums = [4, 8, 10, 240]) == [240, 8, 4]\n assert candidate(nums = [18, 9, 3, 6, 2, 12]) == [12, 6, 3]\n assert candidate(nums = [1, 2, 3]) == [2, 1]\n assert candidate(nums = [1, 3, 6, 18, 54]) == [54, 18, 6, 3, 1]\n assert candidate(nums = [3, 9, 27, 81, 243, 729]) == [729, 243, 81, 27, 9, 3]\n assert candidate(nums = [1, 3, 6, 24, 48]) == [48, 24, 6, 3, 1]\n assert candidate(nums = [3, 9, 27, 81]) == [81, 27, 9, 3]\n assert candidate(nums = [18, 54, 9, 27, 3, 81]) == [54, 27, 9, 3]\n assert candidate(nums = [9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969]) == [4782969, 1594323, 531441, 177147, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9]\n assert candidate(nums = [6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120]) == [96, 48, 24, 12, 6]\n assert candidate(nums = [1, 3, 5, 15, 25, 75, 125, 375, 625, 1875, 3125, 9375, 15625, 46875, 78125, 234375, 390625, 1171875]) == [1171875, 390625, 78125, 15625, 3125, 625, 125, 25, 5, 1]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == [80, 40, 20, 10, 5]\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 1073741825]) == [1073741824, 536870912, 268435456, 134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]\n assert candidate(nums = [21, 42, 84, 168, 336, 672, 1344, 2688, 5376, 10752, 21504, 43008, 86016, 172032, 344064]) == [344064, 172032, 86016, 43008, 21504, 10752, 5376, 2688, 1344, 672, 336, 168, 84, 42, 21]\n assert candidate(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510, 527, 544, 561, 578, 595, 612, 629, 646, 663, 680, 697, 714, 731, 748, 765, 782, 805, 822, 839, 856, 873, 890, 907, 924, 941, 958, 975, 992]) == [544, 272, 136, 68, 34, 17]\n assert candidate(nums = [7, 14, 28, 49, 98, 196, 392, 784, 1568, 3136, 6272, 12544, 25088, 50176, 100352, 200704, 401408, 802816, 1605632, 3211264]) == [3211264, 1605632, 802816, 401408, 200704, 100352, 50176, 25088, 12544, 6272, 3136, 1568, 784, 392, 196, 98, 49, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [16, 8, 4, 2, 1]\n assert candidate(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220]) == [176, 88, 44, 22, 11]\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 175, 185, 195, 205, 215, 225, 235, 245, 255, 265, 275, 285, 295, 305]) == [135, 45, 15, 5]\n assert candidate(nums = [1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]) == [1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]\n assert candidate(nums = [5, 10, 20, 25, 50, 100, 125, 200, 250, 500, 1000]) == [1000, 500, 250, 125, 25, 5]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375, 380, 385, 390, 395, 400]) == [320, 160, 80, 40, 20, 10, 5]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 3100, 3200, 3300, 3400, 3500, 3600, 3700, 3800, 3900, 4000, 4100, 4200, 4300, 4400, 4500, 4600, 4700, 4800, 4900, 5000, 5100, 5200, 5300, 5400, 5500, 5600, 5700, 5800, 5900, 6000, 6100, 6200, 6300, 6400, 6500, 6600, 6700, 6800, 6900, 7000, 7100, 7200, 7300, 7400, 7500, 7600, 7700, 7800, 7900, 8000, 8100, 8200, 8300, 8400, 8500, 8600, 8700, 8800, 8900, 9000, 9100, 9200, 9300, 9400, 9500, 9600, 9700, 9800, 9900, 10000]) == [6400, 3200, 1600, 800, 400, 200, 100]\n assert candidate(nums = [5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125, 244140625, 1220703125, 6103515625]) == [6103515625, 1220703125, 244140625, 48828125, 9765625, 1953125, 390625, 78125, 15625, 3125, 625, 125, 25, 5]\n assert candidate(nums = [13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390]) == [208, 104, 52, 26, 13]\n assert candidate(nums = [1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467]) == [1162261467, 387420489, 129140163, 43046721, 14348907, 4782969, 1594323, 531441, 177147, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3, 1]\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]) == [524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]\n assert candidate(nums = [256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304]) == [4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256]\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824]) == [1073741824, 536870912, 268435456, 134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]\n assert candidate(nums = [19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399, 418, 437, 456, 475, 494, 513, 532, 551, 570]) == [304, 152, 76, 38, 19]\n assert candidate(nums = [3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467]) == [1162261467, 387420489, 129140163, 43046721, 14348907, 4782969, 1594323, 531441, 177147, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3]\n assert candidate(nums = [100, 200, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, 819200, 1638400]) == [1638400, 819200, 409600, 204800, 102400, 51200, 25600, 12800, 6400, 3200, 1600, 800, 400, 200, 100]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313]) == [2]\n assert candidate(nums = [7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016]) == [3670016, 1835008, 917504, 458752, 229376, 114688, 57344, 28672, 14336, 7168, 3584, 1792, 896, 448, 224, 112, 56, 28, 14, 7]\n assert candidate(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510]) == [272, 136, 68, 34, 17]\n assert candidate(nums = [360, 720, 1080, 1440, 1800, 2160, 2520, 2880, 3240, 3600, 3960, 4320, 4680, 5040, 5400, 5760, 6120, 6480, 6840, 7200]) == [5760, 2880, 1440, 720, 360]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == [64, 32, 16, 8, 4, 2, 1]\n assert candidate(nums = [15, 30, 60, 120, 240, 480, 960, 1920, 3840, 7680, 15360, 30720, 61440, 122880, 245760]) == [245760, 122880, 61440, 30720, 15360, 7680, 3840, 1920, 960, 480, 240, 120, 60, 30, 15]\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824]) == [1073741824, 536870912, 268435456, 134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2]\n assert candidate(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583, 594, 605, 616, 627, 638, 649, 660, 671, 682, 693, 704, 715, 726, 737, 748, 759, 770]) == [704, 352, 176, 88, 44, 22, 11]\n assert candidate(nums = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364, 371, 378, 385, 392, 399, 406, 413, 420, 427, 434, 441, 448, 455, 462, 469, 476, 483, 490, 497, 504, 511, 518, 525, 532, 539]) == [448, 224, 112, 56, 28, 14, 7]\n assert candidate(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]) == [2, 1]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300]) == [160, 80, 40, 20, 10, 5]\n assert candidate(nums = [1, 3, 6, 18, 27, 54, 81, 162, 486, 972, 1458, 2916, 3888, 59049, 118098, 177147, 354294, 531441, 1062882, 1594323, 3188646]) == [3188646, 1062882, 354294, 118098, 1458, 486, 162, 54, 18, 6, 3, 1]\n assert candidate(nums = [3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429506481, 847288519443, 2541865558329]) == [94143178827, 31381059609, 10460353203, 3486784401, 1162261467, 387420489, 129140163, 43046721, 14348907, 4782969, 1594323, 531441, 177147, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3]\n assert candidate(nums = [2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098, 354294, 1062882, 3188646, 9565938, 28697814, 86093442, 258280326, 774840978, 2324522934]) == [2324522934, 774840978, 258280326, 86093442, 28697814, 9565938, 3188646, 1062882, 354294, 118098, 39366, 13122, 4374, 1458, 486, 162, 54, 18, 6, 2]\n assert candidate(nums = [5, 10, 15, 20, 25, 50, 75, 100, 150, 250, 500, 750, 1000, 1500, 2500, 5000, 7500, 10000]) == [10000, 5000, 2500, 500, 250, 50, 25, 5]\n assert candidate(nums = [3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467]) == [1162261467, 387420489, 129140163, 43046721, 14348907, 4782969, 1594323, 531441, 177147, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3]\n assert candidate(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330]) == [176, 88, 44, 22, 11]\n assert candidate(nums = [7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604, 16807, 33614, 67228, 117649, 235298, 470596]) == [470596, 235298, 117649, 16807, 2401, 343, 49, 7]\n assert candidate(nums = [15, 30, 45, 60, 90, 120, 180, 240, 360, 480, 720, 1440, 2160, 2880, 4320, 8640, 12960, 17280, 25920, 34560, 51840, 103680, 155520, 207360, 311040, 622080, 933120, 1244160, 1866240, 3732480, 5598720, 7465920, 11197440, 22394880]) == [22394880, 11197440, 5598720, 1866240, 933120, 311040, 155520, 51840, 25920, 12960, 4320, 2160, 720, 360, 180, 90, 45, 15]\n assert candidate(nums = [49, 98, 147, 196, 245, 294, 343, 392, 441, 490, 539, 588, 637, 686, 735, 784, 833, 882, 931, 980]) == [784, 392, 196, 98, 49]\n assert candidate(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583, 594, 605, 616, 627, 638, 649, 660, 671, 682, 693, 704, 715, 726, 737, 748, 759, 770, 781, 792, 803, 814, 825, 836, 847, 858, 869, 880, 891, 902, 913, 924, 935, 946, 957, 968, 979, 990]) == [704, 352, 176, 88, 44, 22, 11]\n assert candidate(nums = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364, 371, 378, 385, 392, 399, 406, 413, 420, 427, 434, 441, 448, 455, 462, 469, 476, 483, 490, 497, 504]) == [448, 224, 112, 56, 28, 14, 7]\n assert candidate(nums = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210]) == [112, 56, 28, 14, 7]\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576]) == [1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2]\n assert candidate(nums = [3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329, 7625597484987, 22876792454961, 68630377364883, 205891132094649, 617673396283947, 1853020188851841, 5559060566555523, 16677181699666569]) == [16677181699666569, 5559060566555523, 1853020188851841, 617673396283947, 205891132094649, 68630377364883, 22876792454961, 7625597484987, 2541865828329, 847288609443, 282429536481, 94143178827, 31381059609, 10460353203, 3486784401, 1162261467, 387420489, 129140163, 43046721, 14348907, 4782969, 1594323, 531441, 177147, 59049, 19683, 6561, 2187, 729, 243, 81, 27, 9, 3]\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125, 976562, 488281, 244140, 122070, 61035]) == [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300]) == [160, 80, 40, 20, 10, 5]\n assert candidate(nums = [23, 46, 69, 92, 115, 138, 161, 184, 207, 230, 253, 276, 299, 322, 345, 368, 391, 414, 437, 460, 483, 506, 529, 552, 575, 598, 621, 644, 667, 690]) == [368, 184, 92, 46, 23]\n assert candidate(nums = [33, 66, 99, 132, 165, 198, 231, 264, 297, 330, 363, 396, 429, 462, 495, 528, 561, 594, 627, 660]) == [528, 264, 132, 66, 33]\n assert candidate(nums = [999983, 1999966, 2999949, 3999932, 4999915, 5999898, 6999881, 7999864, 8999847, 9999830, 10999813, 11999796, 12999779, 13999762, 14999745, 15999728, 16999711, 17999694, 18999677, 19999660]) == [15999728, 7999864, 3999932, 1999966, 999983]\n assert candidate(nums = [10, 20, 40, 5, 80, 160, 320, 400, 800, 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, 819200, 1638400]) == [1638400, 819200, 409600, 204800, 102400, 51200, 25600, 12800, 6400, 3200, 1600, 800, 400, 80, 40, 20, 10, 5]\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150]) == [80, 40, 20, 10, 5]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113]) == [2]\n assert candidate(nums = [1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125, 244140625]) == [244140625, 48828125, 9765625, 1953125, 390625, 78125, 15625, 3125, 625, 125, 25, 5, 1]\n assert candidate(nums = [8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072]) == [131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8]\n assert candidate(nums = [10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840]) == [163840, 81920, 40960, 20480, 10240, 5120, 2560, 1280, 640, 320, 160, 80, 40, 20, 10]\n assert candidate(nums = [121, 242, 363, 484, 605, 726, 847, 968, 1089, 1210, 1321, 1432, 1543, 1654, 1765, 1876, 1987, 2098, 2209, 2320]) == [968, 484, 242, 121]\n assert candidate(nums = [17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425]) == [272, 136, 68, 34, 17]\n assert candidate(nums = [13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390]) == [208, 104, 52, 26, 13]\n assert candidate(nums = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824]) == [1073741824, 536870912, 268435456, 134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2]\n assert candidate(nums = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, 357, 364, 371, 378, 385, 392, 399, 406, 413, 420, 427, 434, 441, 448, 455, 462, 469, 476, 483, 490, 497, 504, 511, 518, 525, 532, 539, 546, 553, 560, 567, 574, 581, 588, 595, 602, 609, 616, 623, 630]) == [448, 224, 112, 56, 28, 14, 7]\n assert candidate(nums = [1023, 2046, 3069, 4092, 5115, 6138, 7161, 8184, 9207, 10230, 11253, 12276, 13299, 14322, 15345, 16368, 17391, 18414, 19437, 20460, 21483, 22506, 23529, 24552, 25575, 26598, 27621, 28644, 29667, 30690, 31713, 32736, 33759, 34782, 35805, 36828, 37851, 38874, 39897, 40920, 41943, 42966, 43989, 45012, 46035, 47058, 48081, 49104, 50127, 51150, 52173, 53196, 54219, 55242, 56265, 57288, 58311, 59334, 60357, 61380, 62403, 63426, 64449, 65472, 66495, 67518, 68541, 69564, 70587, 71610, 72633, 73656, 74679, 75702, 76725, 77748, 78771, 79794, 80817, 81840, 82863, 83886, 84909, 85932, 86955, 87978, 88901, 89924, 90947, 91970, 92993, 94016, 95039, 96062, 97085, 98108, 99131]) == [65472, 32736, 16368, 8184, 4092, 2046, 1023]\n assert candidate(nums = [11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330]) == [176, 88, 44, 22, 11]\n assert candidate(nums = [5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120]) == [5368709120, 2684354560, 1342177280, 671088640, 335544320, 167772160, 83886080, 41943040, 20971520, 10485760, 5242880, 2621440, 1310720, 655360, 327680, 163840, 81920, 40960, 20480, 10240, 5120, 2560, 1280, 640, 320, 160, 80, 40, 20, 10, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [16, 8, 4, 2, 1]\n assert candidate(nums = [13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, 663, 676, 689, 702, 715, 728, 741, 754, 767, 780, 793, 806, 819, 832, 845, 858, 871, 884, 897, 910, 923, 936, 949, 962, 975, 988, 1001]) == [832, 416, 208, 104, 52, 26, 13]\n assert candidate(nums = [6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588, 594, 600]) == [384, 192, 96, 48, 24, 12, 6]\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == [2]\n assert candidate(nums = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175]) == [112, 56, 28, 14, 7]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201]) == [81, 27, 9, 3, 1]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().largestDivisibleSubset", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var largestDivisibleSubset = function(nums) {", "container": null, "callable": "largestDivisibleSubset", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 371, "task_id": "sum-of-two-integers", "difficulty": "Medium", "problem_description": "Given two integers a and b, return the sum of the two integers without using the operators + and -.\n \nExample 1:\nInput: a = 1, b = 2\nOutput: 3\nExample 2:\nInput: a = 2, b = 3\nOutput: 5\n\n \nConstraints:\n\n-1000 <= a, b <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(a = 1000,b = -1000) == 0\n assert candidate(a = -2,b = -3) == -5\n assert candidate(a = 0,b = 5) == 5\n assert candidate(a = 500,b = 500) == 1000\n assert candidate(a = -5,b = -5) == -10\n assert candidate(a = 1,b = 2) == 3\n assert candidate(a = 999,b = 1) == 1000\n assert candidate(a = -5,b = 5) == 0\n assert candidate(a = -1000,b = 1000) == 0\n assert candidate(a = -500,b = 500) == 0\n assert candidate(a = -500,b = -500) == -1000\n assert candidate(a = 0,b = 0) == 0\n assert candidate(a = -1,b = 1) == 0\n assert candidate(a = 2,b = 3) == 5\n assert candidate(a = -999,b = -1) == -1000\n assert candidate(a = -7,b = -13) == -20\n assert candidate(a = -999,b = 1) == -998\n assert candidate(a = -128,b = 256) == 128\n assert candidate(a = -999,b = 999) == 0\n assert candidate(a = 1234,b = -5678) == -4444\n assert candidate(a = 7,b = 13) == 20\n assert candidate(a = 7,b = -7) == 0\n assert candidate(a = 256,b = 255) == 511\n assert candidate(a = 0,b = -1) == -1\n assert candidate(a = -223,b = -777) == -1000\n assert candidate(a = -1000,b = -999) == -1999\n assert candidate(a = -1234,b = 5678) == 4444\n assert candidate(a = -123,b = 456) == 333\n assert candidate(a = 1,b = 0) == 1\n assert candidate(a = 7,b = -3) == 4\n assert candidate(a = 678,b = 322) == 1000\n assert candidate(a = 500,b = 501) == 1001\n assert candidate(a = -789,b = 321) == -468\n assert candidate(a = 1,b = 999) == 1000\n assert candidate(a = 456,b = 123) == 579\n assert candidate(a = 1,b = -1) == 0\n assert candidate(a = 7,b = -13) == -6\n assert candidate(a = 512,b = -512) == 0\n assert candidate(a = -314,b = 157) == -157\n assert candidate(a = 499,b = 500) == 999\n assert candidate(a = 256,b = 256) == 512\n assert candidate(a = 314,b = -157) == 157\n assert candidate(a = 223,b = -777) == -554\n assert candidate(a = 1234,b = -1234) == 0\n assert candidate(a = -1,b = -999) == -1000\n assert candidate(a = 456,b = -789) == -333\n assert candidate(a = 456,b = -234) == 222\n assert candidate(a = -777,b = -223) == -1000\n assert candidate(a = -678,b = -322) == -1000\n assert candidate(a = 789,b = -321) == 468\n assert candidate(a = -333,b = -667) == -1000\n assert candidate(a = 0,b = -1000) == -1000\n assert candidate(a = -7,b = 3) == -4\n assert candidate(a = -456,b = -123) == -579\n assert candidate(a = -500,b = 250) == -250\n assert candidate(a = 345,b = 678) == 1023\n assert candidate(a = 1000,b = 0) == 1000\n assert candidate(a = -321,b = 654) == 333\n assert candidate(a = 333,b = 667) == 1000\n assert candidate(a = 0,b = 1000) == 1000\n assert candidate(a = -256,b = -256) == -512\n assert candidate(a = -777,b = 223) == -554\n assert candidate(a = -1000,b = 0) == -1000\n assert candidate(a = -123,b = -456) == -579\n assert candidate(a = -456,b = 123) == -333\n assert candidate(a = 777,b = 223) == 1000\n assert candidate(a = -789,b = 456) == -333\n assert candidate(a = 63,b = 127) == 190\n assert candidate(a = -500,b = -499) == -999\n assert candidate(a = 100,b = -100) == 0\n assert candidate(a = -1,b = 0) == -1\n assert candidate(a = 999,b = -999) == 0\n assert candidate(a = 1000,b = -999) == 1\n assert candidate(a = 123,b = 456) == 579\n assert candidate(a = 1000,b = 999) == 1999\n assert candidate(a = 123,b = -456) == -333\n assert candidate(a = -256,b = -255) == -511\n assert candidate(a = 500,b = -250) == 250\n assert candidate(a = 1024,b = -1024) == 0\n assert candidate(a = -7,b = 13) == 6\n"}, "metadata": {"canonical_parameter_names": ["a", "b"], "leetcode_dataset_entry_point": "Solution().getSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getSum = function(a, b) {", "container": null, "callable": "getSum", "parameters": [{"name": "a", "type": "number"}, {"name": "b", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 373, "task_id": "find-k-pairs-with-smallest-sums", "difficulty": "Medium", "problem_description": "You are given two integer arrays nums1 and nums2 sorted in non-decreasing order and an integer k.\nDefine a pair (u, v) which consists of one element from the first array and one element from the second array.\nReturn the k pairs (u1, v1), (u2, v2), ..., (uk, vk) with the smallest sums.\n \nExample 1:\n\nInput: nums1 = [1,7,11], nums2 = [2,4,6], k = 3\nOutput: [[1,2],[1,4],[1,6]]\nExplanation: The first 3 pairs are returned from the sequence: [1,2],[1,4],[1,6],[7,2],[7,4],[11,2],[7,6],[11,4],[11,6]\n\nExample 2:\n\nInput: nums1 = [1,1,2], nums2 = [1,2,3], k = 2\nOutput: [[1,1],[1,1]]\nExplanation: The first 2 pairs are returned from the sequence: [1,1],[1,1],[1,2],[2,1],[1,2],[2,2],[1,3],[1,3],[2,3]\n\n \nConstraints:\n\n1 <= nums1.length, nums2.length <= 105\n-109 <= nums1[i], nums2[i] <= 109\nnums1 and nums2 both are sorted in non-decreasing order.\n1 <= k <= 104\nk <= nums1.length * nums2.length\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [1, 2],nums2 = [3],k = 3) == [[1, 3], [2, 3]]\n assert candidate(nums1 = [5, 8, 8, 10],nums2 = [1, 7, 11, 11],k = 10) == [[5, 1], [8, 1], [8, 1], [10, 1], [5, 7], [8, 7], [8, 7], [5, 11], [5, 11], [10, 7]]\n assert candidate(nums1 = [1, 1, 2],nums2 = [1, 2, 3],k = 4) == [[1, 1], [1, 1], [1, 2], [1, 2]]\n assert candidate(nums1 = [1, 7, 11],nums2 = [2, 4, 6],k = 3) == [[1, 2], [1, 4], [1, 6]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [1, 2, 3, 4, 5],k = 10) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [4, 1]]\n assert candidate(nums1 = [5, 8, 12],nums2 = [9, 10, 11],k = 4) == [[5, 9], [5, 10], [5, 11], [8, 9]]\n assert candidate(nums1 = [1, 1, 2],nums2 = [1, 2, 3],k = 2) == [[1, 1], [1, 1]]\n assert candidate(nums1 = [5, 8, 8, 9],nums2 = [1, 1, 1, 1],k = 4) == [[5, 1], [5, 1], [5, 1], [5, 1]]\n assert candidate(nums1 = [1, 1, 2],nums2 = [1, 2, 3],k = 10) == [[1, 1], [1, 1], [1, 2], [1, 2], [2, 1], [1, 3], [1, 3], [2, 2], [2, 3]]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6],k = 5) == [[1, 4], [1, 5], [2, 4], [1, 6], [2, 5]]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6],k = 6) == [[1, 4], [1, 5], [2, 4], [1, 6], [2, 5], [3, 4]]\n assert candidate(nums1 = [-10, -8, 0, 5, 6],nums2 = [1, 3, 4, 7, 8],k = 4) == [[-10, 1], [-10, 3], [-8, 1], [-10, 4]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10],k = 1) == [[1, 6]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],k = 7) == [[1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 5], [2, 4]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1],k = 5) == [[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10],k = 8) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 20) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 100) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [1, 12], [3, 10], [5, 8], [7, 6], [9, 4], [11, 2], [1, 14], [3, 12], [5, 10], [7, 8], [9, 6], [11, 4], [13, 2], [1, 16], [3, 14], [5, 12], [7, 10], [9, 8], [11, 6], [13, 4], [15, 2], [1, 18], [3, 16], [5, 14], [7, 12], [9, 10], [11, 8], [13, 6], [15, 4], [17, 2], [1, 20], [3, 18], [5, 16], [7, 14], [9, 12], [11, 10], [13, 8], [15, 6], [17, 4], [19, 2], [3, 20], [5, 18], [7, 16], [9, 14], [11, 12], [13, 10], [15, 8], [17, 6], [19, 4], [5, 20], [7, 18], [9, 16], [11, 14], [13, 12], [15, 10], [17, 8], [19, 6], [7, 20], [9, 18], [11, 16], [13, 14], [15, 12], [17, 10], [19, 8], [9, 20], [11, 18], [13, 16], [15, 14], [17, 12], [19, 10], [11, 20], [13, 18], [15, 16], [17, 14], [19, 12], [13, 20], [15, 18], [17, 16], [19, 14], [15, 20], [17, 18], [19, 16], [17, 20], [19, 18], [19, 20]]\n assert candidate(nums1 = [-1000000000, -500000000, 0, 500000000, 1000000000],nums2 = [-1000000000, -500000000, 0, 500000000, 1000000000],k = 10) == [[-1000000000, -1000000000], [-1000000000, -500000000], [-500000000, -1000000000], [-1000000000, 0], [-500000000, -500000000], [0, -1000000000], [-1000000000, 500000000], [-500000000, 0], [0, -500000000], [500000000, -1000000000]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10],k = 15) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-5, 0, 5],k = 5) == [[-10, -5], [-10, 0], [-5, -5], [-10, 5], [-5, 0]]\n assert candidate(nums1 = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004],nums2 = [-1000000004, -1000000003, -1000000002, -1000000001, -1000000000],k = 10) == [[1000000000, -1000000004], [1000000000, -1000000003], [1000000001, -1000000004], [1000000000, -1000000002], [1000000001, -1000000003], [1000000002, -1000000004], [1000000000, -1000000001], [1000000001, -1000000002], [1000000002, -1000000003], [1000000003, -1000000004]]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [2, 2, 2, 2, 2],k = 25) == [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]\n assert candidate(nums1 = [1000000000, 2000000000, 3000000000],nums2 = [1000000000, 2000000000, 3000000000],k = 3) == [[1000000000, 1000000000], [1000000000, 2000000000], [2000000000, 1000000000]]\n assert candidate(nums1 = [1, 5, 8, 12, 15],nums2 = [2, 4, 6, 8, 10],k = 5) == [[1, 2], [1, 4], [1, 6], [5, 2], [1, 8]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13],nums2 = [2, 4, 6, 8, 10, 12, 14],k = 20) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [1, 12], [3, 10], [5, 8], [7, 6], [9, 4]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],k = 15) == [[1, -10], [1, -9], [2, -10], [1, -8], [2, -9], [3, -10], [1, -7], [2, -8], [3, -9], [4, -10], [1, -6], [2, -7], [3, -8], [4, -9], [5, -10]]\n assert candidate(nums1 = [1, 5, 9, 13, 17],nums2 = [2, 6, 10, 14, 18],k = 10) == [[1, 2], [1, 6], [5, 2], [1, 10], [5, 6], [9, 2], [1, 14], [5, 10], [9, 6], [13, 2]]\n assert candidate(nums1 = [1000000000, 1000000001, 1000000002],nums2 = [999999999, 1000000000, 1000000001],k = 5) == [[1000000000, 999999999], [1000000000, 1000000000], [1000000001, 999999999], [1000000000, 1000000001], [1000000001, 1000000000]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 15) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10],k = 10) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2]]\n assert candidate(nums1 = [-10, -5, 0, 10],nums2 = [-15, -10, 5, 15],k = 6) == [[-10, -15], [-10, -10], [-5, -15], [-5, -10], [0, -15], [0, -10]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-20, -10, 0, 10, 20],k = 15) == [[-10, -20], [-5, -20], [-10, -10], [0, -20], [-5, -10], [5, -20], [-10, 0], [0, -10], [10, -20], [-5, 0], [5, -10], [-10, 10], [0, 0], [10, -10], [-5, 10]]\n assert candidate(nums1 = [-10, 0, 10],nums2 = [-10, 0, 10],k = 5) == [[-10, -10], [-10, 0], [0, -10], [-10, 10], [0, 0]]\n assert candidate(nums1 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [-9, -8, -7, -6, -5, -4, -3, -2, -1, 0],k = 5) == [[0, -9], [0, -8], [1, -9], [0, -7], [1, -8]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [1, 3, 5, 7, 9],k = 15) == [[1, 1], [1, 3], [3, 1], [1, 5], [3, 3], [5, 1], [1, 7], [3, 5], [5, 3], [7, 1], [1, 9], [3, 7], [5, 5], [7, 3], [9, 1]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-20, -15, -10, -5, 0],k = 15) == [[-10, -20], [-10, -15], [-5, -20], [-10, -10], [-5, -15], [0, -20], [-10, -5], [-5, -10], [0, -15], [5, -20], [-10, 0], [-5, -5], [0, -10], [5, -15], [10, -20]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 15) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [4, 1], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 25) == [[1, 10], [1, 9], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 10], [2, 9], [2, 8], [2, 7], [2, 6], [2, 5], [2, 4], [2, 3], [2, 2], [2, 1], [3, 10], [3, 9], [3, 8], [3, 7], [3, 6]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10],k = 25) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [3, 10], [5, 8], [7, 6], [9, 4], [5, 10], [7, 8], [9, 6], [7, 10], [9, 8], [9, 10]]\n assert candidate(nums1 = [1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5]]\n assert candidate(nums1 = [-1000000000, -999999999],nums2 = [-1000000000, -999999999],k = 2) == [[-1000000000, -1000000000], [-1000000000, -999999999]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],k = 5) == [[1, 5], [1, 4], [1, 3], [1, 2], [1, 1]]\n assert candidate(nums1 = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 8, 9, 10, 10],nums2 = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 8, 9, 10, 10],k = 100) == [[1, 1], [1, 2], [1, 2], [2, 1], [2, 1], [1, 3], [1, 3], [1, 3], [2, 2], [2, 2], [2, 2], [2, 2], [3, 1], [3, 1], [3, 1], [1, 4], [1, 4], [2, 3], [2, 3], [2, 3], [2, 3], [2, 3], [2, 3], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [4, 1], [4, 1], [1, 5], [1, 5], [1, 5], [1, 5], [2, 4], [2, 4], [2, 4], [2, 4], [3, 3], [3, 3], [3, 3], [3, 3], [3, 3], [3, 3], [3, 3], [3, 3], [3, 3], [4, 2], [4, 2], [4, 2], [4, 2], [5, 1], [5, 1], [5, 1], [5, 1], [1, 6], [1, 6], [1, 6], [2, 5], [2, 5], [2, 5], [2, 5], [2, 5], [2, 5], [2, 5], [2, 5], [3, 4], [3, 4], [3, 4], [3, 4], [3, 4], [3, 4], [4, 3], [4, 3], [4, 3], [4, 3], [4, 3], [4, 3], [5, 2], [5, 2], [5, 2], [5, 2], [5, 2], [5, 2], [5, 2], [5, 2], [6, 1], [6, 1], [6, 1], [1, 7], [2, 6], [2, 6], [2, 6], [2, 6], [2, 6], [2, 6], [3, 5], [3, 5], [3, 5]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10],k = 5) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4]]\n assert candidate(nums1 = [1000000000],nums2 = [1000000000],k = 1) == [[1000000000, 1000000000]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3],k = 5) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-20, -15, -10, -5, 0],k = 12) == [[-10, -20], [-10, -15], [-5, -20], [-10, -10], [-5, -15], [0, -20], [-10, -5], [-5, -10], [0, -15], [5, -20], [-10, 0], [-5, -5]]\n assert candidate(nums1 = [1, 10, 100, 1000],nums2 = [2, 20, 200, 2000],k = 20) == [[1, 2], [10, 2], [1, 20], [10, 20], [100, 2], [100, 20], [1, 200], [10, 200], [100, 200], [1000, 2], [1000, 20], [1000, 200], [1, 2000], [10, 2000], [100, 2000], [1000, 2000]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 20) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [1, 12], [3, 10], [5, 8], [7, 6], [9, 4]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10],k = 12) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 30) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [1, 12], [3, 10], [5, 8], [7, 6], [9, 4], [11, 2], [1, 14], [3, 12], [5, 10], [7, 8], [9, 6], [11, 4], [13, 2], [1, 16], [3, 14]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [10, 20, 30, 40, 50],k = 1) == [[1, 10]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 10) == [[1, 6], [1, 7], [2, 6], [1, 8], [2, 7], [3, 6], [1, 9], [2, 8], [3, 7], [4, 6]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3],k = 100) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [2, 3], [3, 2], [4, 1], [3, 3], [4, 2], [5, 1], [4, 3], [5, 2], [6, 1], [5, 3], [6, 2], [7, 1], [6, 3], [7, 2], [8, 1], [7, 3], [8, 2], [9, 1], [8, 3], [9, 2], [10, 1], [9, 3], [10, 2], [10, 3]]\n assert candidate(nums1 = [-100, -99, -98, -97, -96],nums2 = [-95, -94, -93, -92, -91],k = 10) == [[-100, -95], [-100, -94], [-99, -95], [-100, -93], [-99, -94], [-98, -95], [-100, -92], [-99, -93], [-98, -94], [-97, -95]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 25) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 50) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [1, 12], [3, 10], [5, 8], [7, 6], [9, 4], [11, 2], [1, 14], [3, 12], [5, 10], [7, 8], [9, 6], [11, 4], [13, 2], [1, 16], [3, 14], [5, 12], [7, 10], [9, 8], [11, 6], [13, 4], [15, 2], [1, 18], [3, 16], [5, 14], [7, 12], [9, 10], [11, 8], [13, 6], [15, 4], [17, 2], [1, 20], [3, 18], [5, 16], [7, 14], [9, 12]]\n assert candidate(nums1 = [-1, -2, -3],nums2 = [-10, -20, -30],k = 5) == [[-3, -10], [-3, -20], [-3, -30], [-2, -10], [-2, -20]]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [1, 2, 3, 4, 5],k = 12) == [[10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [20, 1], [20, 2], [20, 3], [20, 4], [20, 5], [30, 1], [30, 2]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-20, -10, 0, 10, 20],k = 3) == [[-10, -20], [-5, -20], [-10, -10]]\n assert candidate(nums1 = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],nums2 = [1, 2, 3, 4, 5],k = 10) == [[5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [10, 1], [10, 2], [10, 3], [10, 4], [10, 5]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 15) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [4, 1], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],k = 5) == [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]\n assert candidate(nums1 = [-10, -8, -6, -4, -2],nums2 = [-9, -7, -5, -3, -1],k = 5) == [[-10, -9], [-10, -7], [-8, -9], [-10, -5], [-8, -7]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 1) == [[1, 10]]\n assert candidate(nums1 = [-1, -2, -3, -4, -5],nums2 = [-10, -9, -8, -7, -6],k = 8) == [[-5, -10], [-4, -10], [-5, -9], [-3, -10], [-4, -9], [-5, -8], [-2, -10], [-3, -9]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 1) == [[1, 1]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 0) == []\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [2, 2, 2, 2, 2],k = 5) == [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [1, 2, 3, 4, 5],k = 1) == [[1, 1]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 10) == [[1, 10], [1, 10], [1, 10], [1, 10], [1, 10], [1, 10], [1, 10], [1, 10], [1, 10], [1, 10]]\n assert candidate(nums1 = [100, 200, 300],nums2 = [100, 200, 300],k = 9) == [[100, 100], [100, 200], [200, 100], [100, 300], [200, 200], [300, 100], [200, 300], [300, 200], [300, 300]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 20) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [4, 1], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [1, 6], [2, 5], [3, 4], [4, 3], [5, 2]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 15) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1],k = 10) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [50, 150, 250, 350, 450],k = 20) == [[100, 50], [100, 150], [200, 50], [100, 250], [200, 150], [300, 50], [100, 350], [200, 250], [300, 150], [400, 50], [100, 450], [200, 350], [300, 250], [400, 150], [500, 50], [200, 450], [300, 350], [400, 250], [500, 150], [300, 450]]\n assert candidate(nums1 = [-1, -1, -1],nums2 = [-1, -1, -1],k = 3) == [[-1, -1], [-1, -1], [-1, -1]]\n assert candidate(nums1 = [1],nums2 = [1],k = 1) == [[1, 1]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 100) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [4, 1], [1, 5], [2, 4], [3, 3], [4, 2], [5, 1], [1, 6], [2, 5], [3, 4], [4, 3], [5, 2], [6, 1], [1, 7], [2, 6], [3, 5], [4, 4], [5, 3], [6, 2], [7, 1], [1, 8], [2, 7], [3, 6], [4, 5], [5, 4], [6, 3], [7, 2], [8, 1], [1, 9], [2, 8], [3, 7], [4, 6], [5, 5], [6, 4], [7, 3], [8, 2], [9, 1], [1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1], [2, 10], [3, 9], [4, 8], [5, 7], [6, 6], [7, 5], [8, 4], [9, 3], [10, 2], [3, 10], [4, 9], [5, 8], [6, 7], [7, 6], [8, 5], [9, 4], [10, 3], [4, 10], [5, 9], [6, 8], [7, 7], [8, 6], [9, 5], [10, 4], [5, 10], [6, 9], [7, 8], [8, 7], [9, 6], [10, 5], [6, 10], [7, 9], [8, 8], [9, 7], [10, 6], [7, 10], [8, 9], [9, 8], [10, 7], [8, 10], [9, 9], [10, 8], [9, 10], [10, 9], [10, 10]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1],k = 25) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-5, 0, 5, 10, 15],k = 8) == [[-10, -5], [-10, 0], [-5, -5], [-10, 5], [-5, 0], [0, -5], [-10, 10], [-5, 5]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [1, 2, 3, 4, 5],k = 1) == [[1, 1]]\n assert candidate(nums1 = [1, 2, 3],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 100) == [[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [1, 5], [2, 4], [3, 3], [1, 6], [2, 5], [3, 4], [1, 7], [2, 6], [3, 5], [1, 8], [2, 7], [3, 6], [1, 9], [2, 8], [3, 7], [1, 10], [2, 9], [3, 8], [2, 10], [3, 9], [3, 10]]\n assert candidate(nums1 = [-1, -1, -1, -1, -1],nums2 = [1, 1, 1, 1, 1],k = 10) == [[-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1], [-1, 1]]\n assert candidate(nums1 = [1000000000, 2000000000, 3000000000],nums2 = [1000000000, 2000000000, 3000000000],k = 9) == [[1000000000, 1000000000], [1000000000, 2000000000], [2000000000, 1000000000], [1000000000, 3000000000], [2000000000, 2000000000], [3000000000, 1000000000], [2000000000, 3000000000], [3000000000, 2000000000], [3000000000, 3000000000]]\n assert candidate(nums1 = [-1, -2, -3, -4, -5],nums2 = [-10, -9, -8, -7, -6],k = 7) == [[-5, -10], [-4, -10], [-5, -9], [-3, -10], [-4, -9], [-5, -8], [-2, -10]]\n assert candidate(nums1 = [1, 10, 100, 1000, 10000],nums2 = [5, 50, 500, 5000, 50000],k = 9) == [[1, 5], [10, 5], [1, 50], [10, 50], [100, 5], [100, 50], [1, 500], [10, 500], [100, 500]]\n assert candidate(nums1 = [-10, -5, 0, 5, 10],nums2 = [-20, -15, -10, 0, 15, 20],k = 15) == [[-10, -20], [-10, -15], [-5, -20], [-10, -10], [-5, -15], [0, -20], [-5, -10], [0, -15], [5, -20], [-10, 0], [0, -10], [5, -15], [10, -20], [-5, 0], [5, -10]]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15],nums2 = [2, 4, 6, 8, 10, 12, 14, 16],k = 20) == [[1, 2], [1, 4], [3, 2], [1, 6], [3, 4], [5, 2], [1, 8], [3, 6], [5, 4], [7, 2], [1, 10], [3, 8], [5, 6], [7, 4], [9, 2], [1, 12], [3, 10], [5, 8], [7, 6], [9, 4]]\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 30) == [[1, 11], [1, 12], [2, 11], [1, 13], [2, 12], [3, 11], [1, 14], [2, 13], [3, 12], [4, 11], [1, 15], [2, 14], [3, 13], [4, 12], [5, 11], [1, 16], [2, 15], [3, 14], [4, 13], [5, 12], [6, 11], [1, 17], [2, 16], [3, 15], [4, 14], [5, 13], [6, 12], [7, 11], [1, 18], [2, 17]]\n assert candidate(nums1 = [1000000000],nums2 = [-1000000000],k = 1) == [[1000000000, -1000000000]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 15) == [[1, 10], [1, 9], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 10], [2, 9], [2, 8], [2, 7], [2, 6]]\n assert candidate(nums1 = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1],nums2 = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 25) == [[-10, -1], [-10, -2], [-10, -3], [-10, -4], [-10, -5], [-10, -6], [-10, -7], [-10, -8], [-10, -9], [-10, -10], [-9, -1], [-9, -2], [-9, -3], [-9, -4], [-9, -5], [-9, -6], [-9, -7], [-9, -8], [-9, -9], [-9, -10], [-8, -1], [-8, -2], [-8, -3], [-8, -4], [-8, -5]]\n assert candidate(nums1 = [1, 2, 3],nums2 = [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 12) == [[1, 4], [1, 5], [2, 4], [1, 6], [2, 5], [3, 4], [1, 7], [2, 6], [3, 5], [1, 8], [2, 7], [3, 6]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],k = 8) == [[1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 5], [2, 4], [2, 3]]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 20) == [[1, 6], [1, 7], [2, 6], [1, 8], [2, 7], [3, 6], [1, 9], [2, 8], [3, 7], [4, 6], [1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [1, 11], [2, 10], [3, 9], [4, 8], [5, 7]]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 25) == [[1, 10], [1, 9], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 10], [2, 9], [2, 8], [2, 7], [2, 6], [2, 5], [2, 4], [2, 3], [2, 2], [2, 1], [3, 10], [3, 9], [3, 8], [3, 7], [3, 6]]\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2", "k"], "leetcode_dataset_entry_point": "Solution().kSmallestPairs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var kSmallestPairs = function(nums1, nums2, k) {", "container": null, "callable": "kSmallestPairs", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 375, "task_id": "guess-number-higher-or-lower-ii", "difficulty": "Medium", "problem_description": "We are playing the Guessing Game. The game will work as follows:\n\nI pick a number between 1 and n.\nYou guess a number.\nIf you guess the right number, you win the game.\nIf you guess the wrong number, then I will tell you whether the number I picked is higher or lower, and you will continue guessing.\nEvery time you guess a wrong number x, you will pay x dollars. If you run out of money, you lose the game.\n\nGiven a particular n, return the minimum amount of money you need to guarantee a win regardless of what number I pick.\n \nExample 1:\n\n\nInput: n = 10\nOutput: 16\nExplanation: The winning strategy is as follows:\n- The range is [1,10]. Guess 7.\n  - If this is my number, your total is $0. Otherwise, you pay $7.\n  - If my number is higher, the range is [8,10]. Guess 9.\n  - If this is my number, your total is $7. Otherwise, you pay $9.\n  - If my number is higher, it must be 10. Guess 10. Your total is $7 + $9 = $16.\n  - If my number is lower, it must be 8. Guess 8. Your total is $7 + $9 = $16.\n  - If my number is lower, the range is [1,6]. Guess 3.\n  - If this is my number, your total is $7. Otherwise, you pay $3.\n  - If my number is higher, the range is [4,6]. Guess 5.\n  - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $5.\n  - If my number is higher, it must be 6. Guess 6. Your total is $7 + $3 + $5 = $15.\n  - If my number is lower, it must be 4. Guess 4. Your total is $7 + $3 + $5 = $15.\n  - If my number is lower, the range is [1,2]. Guess 1.\n  - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $1.\n  - If my number is higher, it must be 2. Guess 2. Your total is $7 + $3 + $1 = $11.\nThe worst case in all these scenarios is that you pay $16. Hence, you only need $16 to guarantee a win.\n\nExample 2:\n\nInput: n = 1\nOutput: 0\nExplanation: There is only one possible number, so you can guess 1 and not have to pay anything.\n\nExample 3:\n\nInput: n = 2\nOutput: 1\nExplanation: There are two possible numbers, 1 and 2.\n- Guess 1.\n  - If this is my number, your total is $0. Otherwise, you pay $1.\n  - If my number is higher, it must be 2. Guess 2. Your total is $1.\nThe worst case is that you pay $1.\n\n \nConstraints:\n\n1 <= n <= 200\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 100) == 400\n assert candidate(n = 15) == 30\n assert candidate(n = 200) == 952\n assert candidate(n = 2) == 1\n assert candidate(n = 1) == 0\n assert candidate(n = 10) == 16\n assert candidate(n = 5) == 6\n assert candidate(n = 150) == 692\n assert candidate(n = 3) == 2\n assert candidate(n = 130) == 585\n assert candidate(n = 125) == 560\n assert candidate(n = 12) == 21\n assert candidate(n = 110) == 460\n assert candidate(n = 50) == 172\n assert candidate(n = 60) == 214\n assert candidate(n = 155) == 718\n assert candidate(n = 30) == 79\n assert candidate(n = 40) == 119\n assert candidate(n = 4) == 4\n assert candidate(n = 80) == 295\n assert candidate(n = 75) == 274\n assert candidate(n = 140) == 635\n assert candidate(n = 18) == 42\n assert candidate(n = 120) == 529\n assert candidate(n = 160) == 743\n assert candidate(n = 199) == 946\n assert candidate(n = 180) == 843\n assert candidate(n = 90) == 345\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().getMoneyAmount", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getMoneyAmount = function(n) {", "container": null, "callable": "getMoneyAmount", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 376, "task_id": "wiggle-subsequence", "difficulty": "Medium", "problem_description": "A wiggle sequence is a sequence where the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with one element and a sequence with two non-equal elements are trivially wiggle sequences.\n\nFor example, [1, 7, 4, 9, 2, 5] is a wiggle sequence because the differences (6, -3, 5, -7, 3) alternate between positive and negative.\nIn contrast, [1, 4, 7, 2, 5] and [1, 7, 4, 5, 5] are not wiggle sequences. The first is not because its first two differences are positive, and the second is not because its last difference is zero.\n\nA subsequence is obtained by deleting some elements (possibly zero) from the original sequence, leaving the remaining elements in their original order.\nGiven an integer array nums, return the length of the longest wiggle subsequence of nums.\n \nExample 1:\n\nInput: nums = [1,7,4,9,2,5]\nOutput: 6\nExplanation: The entire sequence is a wiggle sequence with differences (6, -3, 5, -7, 3).\n\nExample 2:\n\nInput: nums = [1,17,5,10,13,15,10,5,16,8]\nOutput: 7\nExplanation: There are several subsequences that achieve this length.\nOne is [1, 17, 10, 13, 10, 16, 8] with differences (16, -7, 3, -3, 6, -8).\n\nExample 3:\n\nInput: nums = [1,2,3,4,5,6,7,8,9]\nOutput: 2\n\n \nConstraints:\n\n1 <= nums.length <= 1000\n0 <= nums[i] <= 1000\n\n \nFollow up: Could you solve this in O(n) time?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 2, 3]) == 2\n assert candidate(nums = [80, 80, 80, 80, 80, 80]) == 1\n assert candidate(nums = [3, 3, 3, 2, 5, 25, 50, 41, 60, 70, 55, 65, 80, 90, 99]) == 7\n assert candidate(nums = [1, 1, 1, 1]) == 1\n assert candidate(nums = [2, 1]) == 2\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [0, 0]) == 1\n assert candidate(nums = [1, 3, 7, 4, 9, 2, 5]) == 6\n assert candidate(nums = [0, 0, 1, 0, 0, 2, 0, 0, 3]) == 6\n assert candidate(nums = [1, 3, 2, 2, 3, 1, 4]) == 6\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 2\n assert candidate(nums = [3, 3, 3, 2, 5]) == 3\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5]) == 2\n assert candidate(nums = [1, 7, 4, 9, 2, 5]) == 6\n assert candidate(nums = [5, 5, 5, 5, 5, 5]) == 1\n assert candidate(nums = [3, 3, 3, 2, 5, 25, 35, 45]) == 3\n assert candidate(nums = [1, 2]) == 2\n assert candidate(nums = [1, 17, 5, 10, 13, 15, 10, 5, 16, 8]) == 7\n assert candidate(nums = [1, 1]) == 1\n assert candidate(nums = [100, 100]) == 1\n assert candidate(nums = [1, 3, 2, 1]) == 3\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5]) == 2\n assert candidate(nums = [3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [1, 3, 2, 2, 3, 1, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 8\n assert candidate(nums = [10, 20, 10, 20, 30, 20, 30, 40, 30, 40, 50, 40, 50, 60]) == 10\n assert candidate(nums = [5, 3, 1, 2, 3, 4, 5, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]) == 6\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5]) == 3\n assert candidate(nums = [3, 3, 3, 2, 1, 4, 5, 6, 7, 8, 9, 10]) == 3\n assert candidate(nums = [1, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 4]) == 14\n assert candidate(nums = [3, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3]) == 3\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 20\n assert candidate(nums = [1, 18, 3, 7, 10, 14, 6, 15, 4, 9, 12]) == 8\n assert candidate(nums = [50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100, 50, 100]) == 16\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 2\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2]) == 8\n assert candidate(nums = [5, 3, 3, 3, 5, 5, 2, 3, 4, 3, 2, 1]) == 6\n assert candidate(nums = [1, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14]) == 26\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4]) == 6\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7]) == 2\n assert candidate(nums = [1, 3, 2, 4, 5, 3, 6, 7, 8, 6, 9, 10, 11, 10]) == 9\n assert candidate(nums = [1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 16\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 1, 2, 3, 4]) == 8\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 2\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 3\n assert candidate(nums = [1, 18, 5, 10, 13, 15, 10, 5, 16, 8, 17, 7, 18]) == 10\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81]) == 2\n assert candidate(nums = [100, 4, 200, 1, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 7\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1]) == 2\n assert candidate(nums = [1, 18, 3, 7, 10, 13, 10, 5, 16, 8, 20, 15]) == 9\n assert candidate(nums = [8, 4, 6, 2, 3, 5, 7, 1, 9, 11, 10, 12, 14, 13, 15]) == 11\n assert candidate(nums = [5, 3, 3, 5, 2, 1, 6, 1, 2, 3, 4]) == 7\n assert candidate(nums = [1000, 0, 1000, 0, 1000, 0, 1000, 0, 1000, 0]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 3\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5, 4, 3, 4, 5]) == 14\n assert candidate(nums = [3, 3, 3, 2, 5, 25, 2, 5, 25, 2, 5, 25]) == 7\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 39\n assert candidate(nums = [10, 15, 10, 5, 15, 5, 20, 10, 25, 15, 30, 20]) == 11\n assert candidate(nums = [1, 3, 2, 5, 3, 7, 5, 9, 7, 11, 9, 13, 11, 15, 13, 17, 15, 19, 17, 21]) == 20\n assert candidate(nums = [1, 10, 3, 100, 4, 101, 5, 102, 6, 103, 7, 104, 8, 105, 9, 106]) == 16\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9]) == 2\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 2, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15]) == 26\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4]) == 4\n assert candidate(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == 12\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [10, 11, 12, 13, 14, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 3\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 2\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10]) == 19\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14]) == 24\n assert candidate(nums = [3, 3, 3, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2]) == 18\n assert candidate(nums = [10, 20, 30, 25, 20, 15, 25, 30, 20, 10]) == 5\n assert candidate(nums = [8, 3, 5, 1, 4, 2, 10, 9, 12, 6, 14, 7]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 2\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2]) == 7\n assert candidate(nums = [89, 45, 68, 90, 29, 34, 67, 30, 89, 21, 55, 62, 87, 90, 21, 56, 89, 34, 67, 23]) == 14\n assert candidate(nums = [8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6]) == 20\n assert candidate(nums = [1000, 999, 998, 999, 998, 997, 998, 997, 996, 997, 996, 995]) == 8\n assert candidate(nums = [1, 3, 7, 10, 9, 8, 2, 1, 5, 7, 10, 12, 8, 6, 4, 2, 3, 5, 7]) == 6\n assert candidate(nums = [999, 1000, 999, 1000, 999, 1000, 999, 1000, 999, 1000]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 2\n assert candidate(nums = [10, 20, 30, 25, 20, 15, 10, 15, 20, 25, 30]) == 4\n assert candidate(nums = [1, 18, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]) == 4\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5]) == 4\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 3\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5]) == 1\n assert candidate(nums = [1, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14]) == 15\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1]) == 11\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 2\n assert candidate(nums = [10, 90, 49, 2, 1, 100, 67, 89, 34, 67, 33, 21, 50, 41, 66, 70]) == 12\n assert candidate(nums = [500, 400, 500, 400, 500, 400, 500, 400, 500, 400, 500, 400, 500, 400]) == 14\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 4, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5]) == 8\n assert candidate(nums = [1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == 7\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8]) == 15\n assert candidate(nums = [1, 2, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 10, 9, 10, 11]) == 16\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2]) == 14\n assert candidate(nums = [3, 3, 3, 2, 5, 5, 4, 8, 8, 9, 10, 10]) == 5\n assert candidate(nums = [1, 18, 9, 14, 7, 11, 3, 8, 16, 5]) == 9\n assert candidate(nums = [5, 10, 5, 10, 5, 10, 5, 10, 5]) == 9\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1]) == 3\n assert candidate(nums = [1, 18, 17, 19, 20, 21, 15, 10, 22, 23, 24, 14, 13, 12, 25, 26, 27, 9, 8, 7]) == 9\n assert candidate(nums = [2, 3, 1, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12]) == 20\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4]) == 4\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == 2\n assert candidate(nums = [1, 100, 1, 99, 2, 98, 3, 97, 4, 96, 5, 95, 6, 94, 7, 93, 8, 92]) == 18\n assert candidate(nums = [100, 44, 61, 78, 54, 48, 101, 56, 30, 93, 47, 72, 38]) == 10\n assert candidate(nums = [8, 4, 5, 7, 7, 5, 4, 9, 2, 9, 10, 13, 7, 4, 8, 20]) == 9\n assert candidate(nums = [100, 40, 20, 60, 30, 50, 40, 80, 70, 90]) == 9\n assert candidate(nums = [100, 90, 95, 110, 105, 115, 100, 120, 80]) == 8\n assert candidate(nums = [100, 4, 200, 1, 3, 2, 3, 5, 4]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 2\n assert candidate(nums = [100, 90, 80, 90, 100, 95, 105, 92, 107, 85, 110, 75, 115, 65, 120, 55, 125, 45, 130, 35]) == 18\n assert candidate(nums = [5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5]) == 29\n assert candidate(nums = [1, 3, 2, 3, 1, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6]) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1]) == 5\n assert candidate(nums = [10, 20, 15, 25, 20, 30, 25, 35, 30, 40, 35, 45, 40, 50]) == 14\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4, 3, 2, 3, 4]) == 10\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8]) == 2\n assert candidate(nums = [3, 1, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11]) == 17\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 20\n assert candidate(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == 20\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [3, 1, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9]) == 16\n assert candidate(nums = [8, 4, 10, 3, 5, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 7\n assert candidate(nums = [3, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3]) == 3\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4]) == 6\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1]) == 5\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 102\n assert candidate(nums = [9, 8, 8, 5, 3, 5, 3, 4, 5, 0, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0]) == 8\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().wiggleMaxLength", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var wiggleMaxLength = function(nums) {", "container": null, "callable": "wiggleMaxLength", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 377, "task_id": "combination-sum-iv", "difficulty": "Medium", "problem_description": "Given an array of distinct integers nums and a target integer target, return the number of possible combinations that add up to target.\nThe test cases are generated so that the answer can fit in a 32-bit integer.\n \nExample 1:\n\nInput: nums = [1,2,3], target = 4\nOutput: 7\nExplanation:\nThe possible combination ways are:\n(1, 1, 1, 1)\n(1, 1, 2)\n(1, 2, 1)\n(1, 3)\n(2, 1, 1)\n(2, 2)\n(3, 1)\nNote that different sequences are counted as different combinations.\n\nExample 2:\n\nInput: nums = [9], target = 3\nOutput: 0\n\n \nConstraints:\n\n1 <= nums.length <= 200\n1 <= nums[i] <= 1000\nAll the elements of nums are unique.\n1 <= target <= 1000\n\n \nFollow up: What if negative numbers are allowed in the given array? How does it change the problem? What limitation we need to add to the question to allow negative numbers?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 5, 10],target = 100) == 8437020668201\n assert candidate(nums = [10, 20, 30],target = 100) == 274\n assert candidate(nums = [1, 2, 3],target = 4) == 7\n assert candidate(nums = [5, 50, 75],target = 95) == 16\n assert candidate(nums = [5, 1, 3],target = 8) == 19\n assert candidate(nums = [5, 10, 20],target = 100) == 46754\n assert candidate(nums = [2, 1, 5],target = 10) == 128\n assert candidate(nums = [4, 2, 1],target = 32) == 39882198\n assert candidate(nums = [9],target = 3) == 0\n assert candidate(nums = [1],target = 100) == 1\n assert candidate(nums = [2, 5, 10, 20],target = 25) == 119\n assert candidate(nums = [1, 2, 3, 4, 5],target = 50) == 256641310658978\n assert candidate(nums = [3, 33, 333],target = 33333) == 536100562017203100794406478687994186977009406170595938319227925094657614236234534558497196506399133621225707174188255190262018651187114351423083457111666117940448620061113293355456633188716465870563000681683793687796224312428969140578915943823395340466419187662119723474059441129216706040810975420885186072698747890615839765847357654198486205747679514159771503546254190608498526147691685468717339503106831214240554923976550226131423821899358941678177012767249757000151516175351605183646515289758127657594483351312820284135270121698193471863249963552248305706529133764410797262033127315996385879310273241411999616601791470886920119787124471456014799082324567146236951447774466096290384104870153132091954155668459053293520897201265795242933843325164440604889046037137996023050079472589183707593322481815544873436357989\n assert candidate(nums = [2, 1, 5],target = 8) == 44\n assert candidate(nums = [15, 25, 5, 50, 100],target = 100) == 4600\n assert candidate(nums = [7, 14],target = 300) == 0\n assert candidate(nums = [1, 2, 5],target = 50) == 237139442616\n assert candidate(nums = [1, 2, 3, 4, 5],target = 10) == 464\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 20) == 10000000000\n assert candidate(nums = [4, 11, 3, 4, 1],target = 21) == 46333\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 20) == 104857600000000000000000000\n assert candidate(nums = [10, 20, 30],target = 50) == 13\n assert candidate(nums = [1, 2, 5],target = 25) == 382396\n assert candidate(nums = [18, 23, 50, 51],target = 200) == 493\n assert candidate(nums = [33, 29, 40, 12, 54, 23, 67, 34, 74],target = 1000) == 1004803376074700418269474690624\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 50) == 551742150354112\n assert candidate(nums = [1, 2, 3, 4, 5],target = 50) == 256641310658978\n assert candidate(nums = [7, 14, 21, 28],target = 100) == 0\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64],target = 256) == 1054787931172699885204409659786242855354657339703519197691828406\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50],target = 500) == 154640480926757717819\n assert candidate(nums = [999, 1000],target = 1999) == 2\n assert candidate(nums = [3, 6, 9, 12],target = 100) == 0\n assert candidate(nums = [2, 5, 10, 20],target = 30) == 417\n assert candidate(nums = [5, 10, 25, 50],target = 100) == 27517\n assert candidate(nums = [1, 2, 4, 8, 16],target = 32) == 47350055\n assert candidate(nums = [10, 20, 30, 40],target = 100) == 401\n assert candidate(nums = [1, 10, 25, 50],target = 100) == 37971048\n assert candidate(nums = [4, 8, 15, 16, 23, 42],target = 100) == 878907\n assert candidate(nums = [1, 2, 3, 4, 5],target = 200) == 27870089767928389254900226744638057842249669417272614584184\n assert candidate(nums = [2, 3, 5],target = 30) == 15778\n assert candidate(nums = [2, 6, 10, 14, 18, 22, 26, 30],target = 300) == 9697818790261047025454697667566\n assert candidate(nums = [1, 2],target = 100) == 573147844013817084101\n assert candidate(nums = [1, 3, 6, 9, 12, 15, 18],target = 100) == 9103419367826082596\n assert candidate(nums = [1, 2, 4, 5],target = 15) == 4185\n assert candidate(nums = [1, 2, 5, 10, 20, 50],target = 1000) == 55418612077363252135298307641829396865446477611253299547057401338234391162164785712545427782637930869475332856306540999148459057137429772224203347607997227631647056712144679002353744573917660746726513112253869324256573236618890333589\n assert candidate(nums = [3, 7, 15],target = 120) == 92796380\n assert candidate(nums = [2, 3, 6, 7],target = 100) == 2724220005886008\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 120) == 541461698816\n assert candidate(nums = [7, 14, 21, 28, 35],target = 100) == 0\n assert candidate(nums = [4, 10, 40, 100],target = 150) == 3504031\n assert candidate(nums = [3, 7, 8],target = 11) == 2\n assert candidate(nums = [2, 3, 6, 7, 9],target = 20) == 576\n assert candidate(nums = [2, 3, 7, 8, 10],target = 200) == 3100714643409982098043972616729\n assert candidate(nums = [50, 25, 75, 20, 10],target = 200) == 197308\n assert candidate(nums = [1, 5, 10, 25],target = 100) == 8577828731901\n assert candidate(nums = [3, 33, 333],target = 1000) == 0\n assert candidate(nums = [1, 10, 100, 1000],target = 1111) == 367666448776500415514786890083984627942520976458183669725570752318436882775368470747436\n assert candidate(nums = [2, 3, 6, 7],target = 12) == 26\n assert candidate(nums = [3, 6, 9, 12],target = 30) == 401\n assert candidate(nums = [1, 5, 10],target = 25) == 915\n assert candidate(nums = [2, 3, 6, 7, 10],target = 300) == 1885220157798436983841368320280668830805551392497\n assert candidate(nums = [100, 200, 300, 400, 500],target = 1000) == 464\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 500) == 1286219641702273366742255356065111897930066144490719649670364060629213518690220561526989033769595304532418065557510304805412593714309986391307281509696\n assert candidate(nums = [3, 7, 11, 15, 19, 23, 27, 31],target = 300) == 14374578728716948696671279\n assert candidate(nums = [5, 8, 12, 16, 20, 24, 28, 32, 36, 40],target = 500) == 42034412043805359239945977920635459\n assert candidate(nums = [2, 5, 10, 20],target = 100) == 11826629775\n assert candidate(nums = [10, 20, 30, 40, 50],target = 150) == 13624\n assert candidate(nums = [1, 2, 5, 10],target = 100) == 119179977936469835383520\n assert candidate(nums = [3, 8, 10],target = 120) == 317567468\n assert candidate(nums = [1, 2, 3, 4, 5],target = 15) == 13624\n assert candidate(nums = [1, 3, 5, 7, 9],target = 25) == 70464\n assert candidate(nums = [33, 39, 45, 51, 60],target = 150) == 29\n assert candidate(nums = [3, 5, 7, 8, 9],target = 50) == 252672\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30],target = 100) == 0\n assert candidate(nums = [5, 50, 500],target = 1000) == 1816691941426948\n assert candidate(nums = [1, 2, 3, 4, 5],target = 10) == 464\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],target = 250) == 551742150354112\n assert candidate(nums = [15, 25, 35, 45],target = 200) == 6259\n assert candidate(nums = [1, 5, 10],target = 50) == 1919938\n assert candidate(nums = [10, 20, 30],target = 100) == 274\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],target = 300) == 222217726411850455445265344483183426006475036048672509776477817\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 100) == 606147434557459526483161067501\n assert candidate(nums = [50, 150, 250, 350, 450],target = 1000) == 6475\n assert candidate(nums = [50, 25, 75, 125],target = 250) == 331\n assert candidate(nums = [5, 10, 15, 20, 25, 30],target = 100) == 463968\n assert candidate(nums = [1, 5, 10, 25, 50, 100],target = 1000) == 3861392372529553044883315945420265874789274045115117175074863427403559146375333246873046775291634059748511012129487397547119298455362\n assert candidate(nums = [15, 25, 35],target = 100) == 25\n assert candidate(nums = [1, 2, 4, 8, 16],target = 100) == 3001542533296576909276367\n assert candidate(nums = [2, 4, 6, 8, 10],target = 20) == 464\n assert candidate(nums = [1, 3, 4, 5, 6],target = 20) == 22750\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],target = 500) == 353368918335207375428\n assert candidate(nums = [1, 3, 4],target = 10) == 64\n assert candidate(nums = [1, 10, 100, 1000],target = 1000) == 753729672939848505929078336767198285353713318174400841581842662144837938547270\n assert candidate(nums = [1, 5, 10, 25],target = 50) == 1931845\n assert candidate(nums = [2, 3, 6, 7],target = 15) == 78\n assert candidate(nums = [1, 3, 4, 5],target = 13) == 424\n assert candidate(nums = [13, 17, 19, 23, 29],target = 100) == 256\n assert candidate(nums = [3, 5, 7, 10],target = 20) == 35\n assert candidate(nums = [2, 3, 6, 7],target = 30) == 19096\n assert candidate(nums = [7, 14, 28],target = 1000) == 0\n assert candidate(nums = [2, 3, 6, 7, 9],target = 120) == 14544576409221128865\n assert candidate(nums = [7, 14, 21, 28, 35],target = 105) == 13624\n assert candidate(nums = [7, 14, 28, 35, 56],target = 100) == 0\n assert candidate(nums = [4, 7, 9],target = 20) == 7\n assert candidate(nums = [3, 5, 10, 15],target = 50) == 12043\n assert candidate(nums = [15, 25, 35],target = 1000) == 48781528629177572921\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 50) == 12574441114\n assert candidate(nums = [3, 5, 7],target = 15) == 8\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128],target = 256) == 1054787931172699885204409659788147413348784265452313995416385159\n assert candidate(nums = [3, 5, 10, 20],target = 1000) == 214391693407662746979155838789092372951985494367397337570037572730823254282910703400057102167\n assert candidate(nums = [1, 5, 10, 25, 50, 100],target = 200) == 169121161302579810731290745\n assert candidate(nums = [3, 5, 7, 9],target = 150) == 12883204547325702\n assert candidate(nums = [4, 10, 40, 25],target = 100) == 18984\n assert candidate(nums = [1, 2, 4, 8, 16],target = 31) == 26805983\n assert candidate(nums = [10, 20, 30, 40, 50],target = 200) == 400096\n assert candidate(nums = [1, 100, 101, 102],target = 300) == 45158\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().combinationSum4", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var combinationSum4 = function(nums, target) {", "container": null, "callable": "combinationSum4", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 378, "task_id": "kth-smallest-element-in-a-sorted-matrix", "difficulty": "Medium", "problem_description": "Given an n x n matrix where each of the rows and columns is sorted in ascending order, return the kth smallest element in the matrix.\nNote that it is the kth smallest element in the sorted order, not the kth distinct element.\nYou must find a solution with a memory complexity better than O(n2).\n \nExample 1:\n\nInput: matrix = [[1,5,9],[10,11,13],[12,13,15]], k = 8\nOutput: 13\nExplanation: The elements in the matrix are [1,5,9,10,11,12,13,13,15], and the 8th smallest number is 13\n\nExample 2:\n\nInput: matrix = [[-5]], k = 1\nOutput: -5\n\n \nConstraints:\n\nn == matrix.length == matrix[i].length\n1 <= n <= 300\n-109 <= matrix[i][j] <= 109\nAll the rows and columns of matrix are guaranteed to be sorted in non-decreasing order.\n1 <= k <= n2\n\n \nFollow up:\n\nCould you solve the problem with a constant memory (i.e., O(1) memory complexity)?\nCould you solve the problem in O(n) time complexity? The solution may be too advanced for an interview but you may find reading this paper fun.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matrix = [[1, 2], [1, 3]],k = 1) == 1\n assert candidate(matrix = [[5, 9, 11], [9, 11, 13], [12, 13, 15]],k = 5) == 11\n assert candidate(matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]],k = 4) == 4\n assert candidate(matrix = [[1, 3, 5], [6, 7, 12], [11, 14, 14]],k = 4) == 6\n assert candidate(matrix = [[1, 2], [1, 3]],k = 3) == 2\n assert candidate(matrix = [[1, 5, 9], [10, 11, 13], [12, 13, 15]],k = 8) == 13\n assert candidate(matrix = [[-5]],k = 1) == -5\n assert candidate(matrix = [[5, 19, 21, 30, 32], [22, 27, 31, 36, 38], [23, 29, 34, 37, 41], [42, 46, 49, 50, 51], [48, 52, 53, 55, 57]],k = 15) == 41\n assert candidate(matrix = [[5, 9, 11], [9, 11, 13], [10, 12, 15]],k = 5) == 11\n assert candidate(matrix = [[1, 3, 5], [6, 7, 12], [11, 14, 14]],k = 3) == 5\n assert candidate(matrix = [[1, 2], [1, 3]],k = 2) == 1\n assert candidate(matrix = [[1, 3, 5], [6, 7, 12], [11, 14, 14]],k = 6) == 11\n assert candidate(matrix = [[1, 2], [3, 4]],k = 2) == 2\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],k = 15) == 15\n assert candidate(matrix = [[1, 3, 5], [6, 7, 12], [11, 14, 14]],k = 5) == 7\n assert candidate(matrix = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9]],k = 24) == 8\n assert candidate(matrix = [[1, 4, 7, 10, 13], [2, 5, 8, 11, 14], [3, 6, 9, 12, 15], [4, 7, 10, 13, 16], [5, 8, 11, 14, 17]],k = 13) == 9\n assert candidate(matrix = [[-1000, -900, -800, -700, -600], [-500, -400, -300, -200, -100], [0, 100, 200, 300, 400], [500, 600, 700, 800, 900], [1000, 1100, 1200, 1300, 1400]],k = 9) == -200\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-9, -4, 1, 6, 11], [-8, -3, 2, 7, 12], [-7, -2, 3, 8, 13], [-6, -1, 4, 9, 14]],k = 12) == 1\n assert candidate(matrix = [[-50, -45, -40, -35, -30], [-25, -20, -15, -10, -5], [0, 5, 10, 15, 20], [25, 30, 35, 40, 45], [50, 55, 60, 65, 70]],k = 12) == 5\n assert candidate(matrix = [[10, 20, 30, 40, 50], [15, 25, 35, 45, 55], [27, 37, 47, 57, 67], [38, 48, 58, 68, 78], [49, 59, 69, 79, 89]],k = 25) == 89\n assert candidate(matrix = [[-100, -90, -80], [-70, -60, -50], [-40, -30, -20]],k = 7) == -40\n assert candidate(matrix = [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]],k = 1) == 1\n assert candidate(matrix = [[-1, 3, 4], [2, 6, 9], [3, 6, 9]],k = 6) == 6\n assert candidate(matrix = [[1, 4, 7, 10, 13, 16, 19], [3, 6, 9, 12, 15, 18, 21], [5, 8, 11, 14, 17, 20, 23], [7, 10, 13, 16, 19, 22, 25], [9, 12, 15, 18, 21, 24, 27], [11, 14, 17, 20, 23, 26, 29], [13, 16, 19, 22, 25, 28, 31]],k = 20) == 14\n assert candidate(matrix = [[-100, -90, -80, -70, -60], [-50, -40, -30, -20, -10], [0, 10, 20, 30, 40], [50, 60, 70, 80, 90], [100, 110, 120, 130, 140]],k = 11) == 0\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],k = 16) == 16\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-8, -3, 2, 7, 12], [-6, -1, 4, 9, 14], [-4, 1, 6, 11, 16], [-2, 3, 8, 13, 18]],k = 13) == 4\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],k = 37) == 37\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]],k = 11) == 1\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],k = 50) == 50\n assert candidate(matrix = [[-100, -50, 0, 50, 100], [-90, -40, 10, 60, 110], [-80, -30, 20, 70, 120], [-70, -20, 30, 80, 130], [-60, -10, 40, 90, 140]],k = 9) == -20\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11], [13, 15, 17, 19, 21, 23], [25, 27, 29, 31, 33, 35], [37, 39, 41, 43, 45, 47], [49, 51, 53, 55, 57, 59], [61, 63, 65, 67, 69, 71]],k = 18) == 35\n assert candidate(matrix = [[-10, -8, -6, -4, -2], [-9, -7, -5, -3, -1], [0, 2, 4, 6, 8], [9, 11, 13, 15, 17], [18, 20, 22, 24, 26]],k = 13) == 4\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54], [55, 56, 57, 58, 59, 60, 61, 62, 63], [64, 65, 66, 67, 68, 69, 70, 71, 72], [73, 74, 75, 76, 77, 78, 79, 80, 81]],k = 40) == 40\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36]],k = 23) == 23\n assert candidate(matrix = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]],k = 12) == 1\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],k = 12) == 12\n assert candidate(matrix = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25]],k = 25) == 25\n assert candidate(matrix = [[5, 10, 15, 20], [25, 30, 35, 40], [45, 50, 55, 60], [65, 70, 75, 80]],k = 10) == 50\n assert candidate(matrix = [[5, 11, 13, 20, 24], [9, 17, 22, 25, 30], [10, 18, 23, 26, 31], [12, 19, 24, 27, 32], [15, 20, 25, 29, 33]],k = 13) == 22\n assert candidate(matrix = [[-1000000000, -999999999, -999999998], [-999999997, -999999996, -999999995], [-999999994, -999999993, -999999992]],k = 5) == -999999996\n assert candidate(matrix = [[-10, -5, 0, 5, 10], [-8, -3, 2, 7, 12], [-6, -1, 4, 8, 14], [-4, 1, 6, 9, 16], [-2, 3, 7, 10, 18]],k = 13) == 4\n assert candidate(matrix = [[-10, -5, -3], [-2, 0, 1], [5, 8, 10]],k = 5) == 0\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11], [13, 15, 17, 19, 21, 23], [25, 27, 29, 31, 33, 35], [37, 39, 41, 43, 45, 47], [49, 51, 53, 55, 57, 59], [61, 63, 65, 67, 69, 71]],k = 21) == 41\n assert candidate(matrix = [[-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1], [-1, -1, -1, -1, -1]],k = 10) == -1\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],k = 21) == 15\n assert candidate(matrix = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 2], [1, 1, 1, 2, 2], [1, 1, 2, 2, 3], [1, 2, 2, 3, 4]],k = 12) == 1\n assert candidate(matrix = [[-10, -7, -3, 0, 2], [0, 1, 2, 3, 4], [3, 4, 5, 6, 7], [5, 6, 7, 8, 9], [8, 9, 10, 11, 12]],k = 13) == 5\n assert candidate(matrix = [[-10, -7, -4, -1, 2], [-9, -6, -3, 0, 3], [-8, -5, -2, 1, 4], [-7, -4, -1, 2, 5], [-6, -3, 0, 3, 6]],k = 20) == 2\n assert candidate(matrix = [[1, 5, 9, 13, 17, 21], [2, 6, 10, 14, 18, 22], [3, 7, 11, 15, 19, 23], [4, 8, 12, 16, 20, 24], [5, 9, 13, 17, 21, 25], [6, 10, 14, 18, 22, 26]],k = 20) == 14\n assert candidate(matrix = [[5, 7, 7, 8, 8, 9, 9, 10, 10], [6, 7, 8, 8, 8, 9, 10, 10, 11], [7, 8, 8, 8, 9, 9, 10, 10, 11], [8, 9, 9, 9, 10, 10, 11, 11, 11], [8, 9, 10, 10, 10, 11, 11, 11, 12], [9, 10, 10, 11, 11, 11, 12, 12, 12], [9, 10, 10, 11, 11, 12, 12, 12, 13], [10, 10, 11, 11, 12, 12, 12, 13, 13], [10, 11, 11, 12, 12, 12, 13, 13, 14]],k = 25) == 9\n assert candidate(matrix = [[5, 9, 14, 20], [7, 11, 16, 22], [9, 13, 18, 24], [10, 15, 20, 25]],k = 7) == 13\n assert candidate(matrix = [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [40, 41, 42, 43, 44, 45, 46, 47, 48, 49], [50, 51, 52, 53, 54, 55, 56, 57, 58, 59], [60, 61, 62, 63, 64, 65, 66, 67, 68, 69], [70, 71, 72, 73, 74, 75, 76, 77, 78, 79], [80, 81, 82, 83, 84, 85, 86, 87, 88, 89]],k = 51) == 40\n assert candidate(matrix = [[100, 101, 102, 103, 104], [105, 106, 107, 108, 109], [110, 111, 112, 113, 114], [115, 116, 117, 118, 119], [120, 121, 122, 123, 124]],k = 13) == 112\n assert candidate(matrix = [[-10, -8, -6, -4], [-3, -2, 0, 2], [3, 5, 7, 9], [11, 13, 15, 17]],k = 10) == 5\n assert candidate(matrix = [[-10, -5, -3], [0, 2, 5], [8, 10, 20]],k = 5) == 2\n assert candidate(matrix = [[-1000000000, -999999999, -999999998], [-999999997, -999999996, -999999995], [-999999994, -999999993, -999999992]],k = 5) == -999999996\n assert candidate(matrix = [[100, 200, 300], [400, 500, 600], [700, 800, 900]],k = 8) == 800\n assert candidate(matrix = [[-10, -9, -8, -7], [-6, -5, -4, -3], [-2, -1, 0, 1], [2, 3, 4, 5]],k = 8) == -3\n assert candidate(matrix = [[-1000000000, -999999999, -999999998], [-999999997, -999999996, -999999995], [-999999994, -999999993, -999999992]],k = 2) == -999999999\n assert candidate(matrix = [[1, 2, 2, 2, 3], [2, 2, 2, 2, 3], [2, 2, 2, 3, 3], [2, 2, 3, 3, 3], [2, 3, 3, 3, 3]],k = 10) == 2\n assert candidate(matrix = [[-5, -4, -3, -2, -1, 0], [1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30]],k = 35) == 29\n assert candidate(matrix = [[1, 5, 9, 13, 17], [2, 6, 10, 14, 18], [3, 7, 11, 15, 19], [4, 8, 12, 16, 20], [5, 9, 13, 17, 21]],k = 1) == 1\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],k = 55) == 55\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],k = 17) == 17\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]],k = 65) == 65\n assert candidate(matrix = [[-100, -90, -80, -70, -60], [10, 20, 30, 40, 50], [60, 70, 80, 90, 100], [110, 120, 130, 140, 150], [160, 170, 180, 190, 200]],k = 25) == 200\n assert candidate(matrix = [[1000, 1001, 1002, 1003], [1004, 1005, 1006, 1007], [1008, 1009, 1010, 1011], [1012, 1013, 1014, 1015]],k = 9) == 1008\n assert candidate(matrix = [[-3, -2, -1, 1, 2, 3], [1, 1, 2, 3, 4, 5], [2, 2, 3, 4, 5, 6], [3, 3, 4, 5, 6, 7], [4, 4, 5, 6, 7, 8], [5, 5, 6, 7, 8, 9]],k = 18) == 4\n assert candidate(matrix = [[-1000, -500, -100, -50, -1], [0, 100, 200, 300, 400], [500, 600, 700, 800, 900], [1000, 1100, 1200, 1300, 1400], [1500, 1600, 1700, 1800, 1900]],k = 25) == 1900\n assert candidate(matrix = [[1, 3, 5, 7], [8, 11, 13, 16], [20, 23, 25, 28], [31, 33, 35, 38]],k = 12) == 28\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]],k = 13) == 1\n assert candidate(matrix = [[1, 3, 6, 9], [2, 4, 8, 12], [3, 5, 11, 15], [4, 7, 13, 17]],k = 7) == 5\n assert candidate(matrix = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 2, 2, 2, 2], [1, 2, 3, 3, 3, 3, 3, 3, 3, 3], [1, 2, 3, 4, 4, 4, 4, 4, 4, 4], [1, 2, 3, 4, 5, 5, 5, 5, 5, 5], [1, 2, 3, 4, 5, 6, 6, 6, 6, 6], [1, 2, 3, 4, 5, 6, 7, 7, 7, 7], [1, 2, 3, 4, 5, 6, 7, 8, 8, 8], [1, 2, 3, 4, 5, 6, 7, 8, 9, 9], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]],k = 100) == 10\n assert candidate(matrix = [[-1000000000, -1000000000, -1000000000], [0, 0, 0], [1000000000, 1000000000, 1000000000]],k = 5) == 0\n assert candidate(matrix = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28], [29, 30, 31, 32, 33, 34, 35], [36, 37, 38, 39, 40, 41, 42], [43, 44, 45, 46, 47, 48, 49]],k = 30) == 30\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],k = 1) == -5\n assert candidate(matrix = [[-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]],k = 13) == 7\n assert candidate(matrix = [[-10, -5, -1, 0, 1, 5, 10], [0, 0, 1, 1, 2, 6, 12], [1, 2, 2, 3, 4, 7, 14], [2, 3, 3, 4, 5, 8, 16], [3, 4, 4, 5, 6, 9, 18], [5, 6, 6, 7, 8, 11, 20], [10, 12, 14, 16, 18, 20, 25]],k = 25) == 5\n assert candidate(matrix = [[2, 6, 10, 14, 18], [3, 7, 11, 15, 19], [4, 8, 12, 16, 20], [5, 9, 13, 17, 21], [6, 10, 14, 18, 22]],k = 25) == 22\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],k = 15) == 15\n assert candidate(matrix = [[0, 1, 2, 3, 4, 5], [6, 7, 8, 9, 10, 11], [12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23], [24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35]],k = 20) == 19\n assert candidate(matrix = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30]],k = 17) == 17\n assert candidate(matrix = [[-5, -4, -3], [-2, -1, 0], [1, 2, 3]],k = 5) == -1\n assert candidate(matrix = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [41, 43, 45, 47, 49, 51, 53, 55, 57, 59], [61, 63, 65, 67, 69, 71, 73, 75, 77, 79], [81, 83, 85, 87, 89, 91, 93, 95, 97, 99], [101, 103, 105, 107, 109, 111, 113, 115, 117, 119], [121, 123, 125, 127, 129, 131, 133, 135, 137, 139], [141, 143, 145, 147, 149, 151, 153, 155, 157, 159], [161, 163, 165, 167, 169, 171, 173, 175, 177, 179], [181, 183, 185, 187, 189, 191, 193, 195, 197, 199]],k = 50) == 99\n assert candidate(matrix = [[-50, -45, -40, -35, -30], [-35, -30, -25, -20, -15], [-30, -25, -20, -15, -10], [-25, -20, -15, -10, -5], [-20, -15, -10, -5, 0]],k = 1) == -50\n assert candidate(matrix = [[1, 3, 5, 7, 9], [11, 13, 15, 17, 19], [21, 23, 25, 27, 29], [31, 33, 35, 37, 39], [41, 43, 45, 47, 49]],k = 27) == 49\n"}, "metadata": {"canonical_parameter_names": ["matrix", "k"], "leetcode_dataset_entry_point": "Solution().kthSmallest", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var kthSmallest = function(matrix, k) {", "container": null, "callable": "kthSmallest", "parameters": [{"name": "matrix", "type": "number[][]"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 383, "task_id": "ransom-note", "difficulty": "Easy", "problem_description": "Given two strings ransomNote and magazine, return true if ransomNote can be constructed by using the letters from magazine and false otherwise.\nEach letter in magazine can only be used once in ransomNote.\n \nExample 1:\nInput: ransomNote = \"a\", magazine = \"b\"\nOutput: false\nExample 2:\nInput: ransomNote = \"aa\", magazine = \"ab\"\nOutput: false\nExample 3:\nInput: ransomNote = \"aa\", magazine = \"aab\"\nOutput: true\n\n \nConstraints:\n\n1 <= ransomNote.length, magazine.length <= 105\nransomNote and magazine consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(ransomNote = \"abc\",magazine = \"def\") == False\n assert candidate(ransomNote = \"hello\",magazine = \"hll\") == False\n assert candidate(ransomNote = \"mississippi\",magazine = \"mspsisgp\") == False\n assert candidate(ransomNote = \"aa\",magazine = \"ab\") == False\n assert candidate(ransomNote = \"aabbcc\",magazine = \"abc\") == False\n assert candidate(ransomNote = \"construct\",magazine = \"nstructco\") == True\n assert candidate(ransomNote = \"abc\",magazine = \"cba\") == True\n assert candidate(ransomNote = \"\",magazine = \"abc\") == True\n assert candidate(ransomNote = \"hello\",magazine = \"ohell\") == True\n assert candidate(ransomNote = \"abc\",magazine = \"aabbcc\") == True\n assert candidate(ransomNote = \"world\",magazine = \"dlrow\") == True\n assert candidate(ransomNote = \"hello\",magazine = \"ehlol\") == True\n assert candidate(ransomNote = \"zzz\",magazine = \"zzzz\") == True\n assert candidate(ransomNote = \"abc\",magazine = \"\") == False\n assert candidate(ransomNote = \"testcase\",magazine = \"case测试\") == False\n assert candidate(ransomNote = \"aa\",magazine = \"aab\") == True\n assert candidate(ransomNote = \"a\",magazine = \"a\") == True\n assert candidate(ransomNote = \"abcdef\",magazine = \"fedcba\") == True\n assert candidate(ransomNote = \"python\",magazine = \"ypthon\") == True\n assert candidate(ransomNote = \"world\",magazine = \"word\") == False\n assert candidate(ransomNote = \"hello\",magazine = \"hello\") == True\n assert candidate(ransomNote = \"a\",magazine = \"b\") == False\n assert candidate(ransomNote = \"abc\",magazine = \"aabbc\") == True\n assert candidate(ransomNote = \"algorithm\",magazine = \"logarithm\") == True\n assert candidate(ransomNote = \"test\",magazine = \"ttewst\") == True\n assert candidate(ransomNote = \"xyz\",magazine = \"abcxyz\") == True\n assert candidate(ransomNote = \"\",magazine = \"\") == True\n assert candidate(ransomNote = \"datastructures\",magazine = \"structuredatas\") == True\n assert candidate(ransomNote = \"aaabb\",magazine = \"aab\") == False\n assert candidate(ransomNote = \"zzzz\",magazine = \"zzzzzzzz\") == True\n assert candidate(ransomNote = \"elephant\",magazine = \"telephantl\") == True\n assert candidate(ransomNote = \"example\",magazine = \"ampleex\") == True\n assert candidate(ransomNote = \"uniquecharacters\",magazine = \"charactersunique\") == True\n assert candidate(ransomNote = \"abcdefghijklmnopqrstuvwxyz\",magazine = \"zyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(ransomNote = \"xylophone\",magazine = \"phonepolyx\") == True\n assert candidate(ransomNote = \"zzzzz\",magazine = \"zzzzzzzzzz\") == True\n assert candidate(ransomNote = \"aquickbrownfoxjumpsoverthelazydog\",magazine = \"thequickbrownfoxjumpsoverthelazydog\") == False\n assert candidate(ransomNote = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",magazine = \"zzzzzyyyyxxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeeeddccbbaa\") == True\n assert candidate(ransomNote = \"programming\",magazine = \"gimmnoprramg\") == True\n assert candidate(ransomNote = \"abcdabcdabcd\",magazine = \"abcabcabc\") == False\n assert candidate(ransomNote = \"casecasecase\",magazine = \"casecase\") == False\n assert candidate(ransomNote = \"abacabadabacaba\",magazine = \"aaaaaaaaaabbbbbbbbbbcccccccccc\") == False\n assert candidate(ransomNote = \"almost\",magazine = \"almostly\") == True\n assert candidate(ransomNote = \"abracadabra\",magazine = \"acabradabra\") == True\n assert candidate(ransomNote = \"supercalifragilisticexpialidocious\",magazine = \"supercalifragilisticexpialidocious\") == True\n assert candidate(ransomNote = \"characters\",magazine = \"characterscharacters\") == True\n assert candidate(ransomNote = \"unavailable\",magazine = \"availableun\") == True\n assert candidate(ransomNote = \"repeatedletters\",magazine = \"rreeppddeeaatteedllettterss\") == True\n assert candidate(ransomNote = \"thedefaultvalue\",magazine = \"thedefultvalue\") == False\n assert candidate(ransomNote = \"abcdabcd\",magazine = \"dcba\") == False\n assert candidate(ransomNote = \"aabbaabb\",magazine = \"abababab\") == True\n assert candidate(ransomNote = \"xyz\",magazine = \"zyxzyxzyx\") == True\n assert candidate(ransomNote = \"thisisanadditionaltest\",magazine = \"thisisanadditionalteest\") == True\n assert candidate(ransomNote = \"aaaaabbbbcccc\",magazine = \"abcabcabcabcabc\") == True\n assert candidate(ransomNote = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",magazine = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == True\n assert candidate(ransomNote = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",magazine = \"zzzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == True\n assert candidate(ransomNote = \"pythonprogramming\",magazine = \"programmingpython\") == True\n assert candidate(ransomNote = \"algorithm\",magazine = \"logarithmz\") == True\n assert candidate(ransomNote = \"aaaaaaabbbbbbb\",magazine = \"bbbbbbbbaaaaaa\") == False\n assert candidate(ransomNote = \"longerstringwithmorecharacters\",magazine = \"longerstringwithmorecharactersandextraletters\") == True\n assert candidate(ransomNote = \"datastructure\",magazine = \"structureadta\") == True\n assert candidate(ransomNote = \"uniqueletters\",magazine = \"eulinettsqu\") == False\n assert candidate(ransomNote = \"alabama\",magazine = \"aalabmmab\") == True\n assert candidate(ransomNote = \"abcde\",magazine = \"fghij\") == False\n assert candidate(ransomNote = \"programming\",magazine = \"progarmmnig\") == True\n assert candidate(ransomNote = \"racecar\",magazine = \"carrace\") == True\n assert candidate(ransomNote = \"abcdabcd\",magazine = \"dcbaabcd\") == True\n assert candidate(ransomNote = \"x\",magazine = \"y\") == False\n assert candidate(ransomNote = \"noleftovers\",magazine = \"noleftovers\") == True\n assert candidate(ransomNote = \"abracadabra\",magazine = \"acarambadbr\") == False\n assert candidate(ransomNote = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",magazine = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == True\n assert candidate(ransomNote = \"abcabcabcabc\",magazine = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == False\n assert candidate(ransomNote = \"congratulations\",magazine = \"congratulationsareinorder\") == True\n assert candidate(ransomNote = \"longerransomnote\",magazine = \"longerransomnoteandmore\") == True\n assert candidate(ransomNote = \"lowercaseonly\",magazine = \"lowercaseonlylowercaseonly\") == True\n assert candidate(ransomNote = \"thisisaverylongstringthatweneedtocheck\",magazine = \"thisisaverylongstringthatwehave\") == False\n assert candidate(ransomNote = \"abcdefghijk\",magazine = \"kjihgfedcba\") == True\n assert candidate(ransomNote = \"thequickbrownfoxjumpsoverthelazydog\",magazine = \"quickbrownfoxjumpsoverthelazydogthe\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"mmississippi\") == True\n assert candidate(ransomNote = \"longstringwithmanysamecharacterssssssss\",magazine = \"sssssssssssssssssssssssssssssssssss\") == False\n assert candidate(ransomNote = \"unique\",magazine = \"ueinque\") == True\n assert candidate(ransomNote = \"qwertyuiopasdfghjklzxcvbnm\",magazine = \"qwertyuiopasdfghjklzxcvbnm\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"ppissimiss\") == False\n assert candidate(ransomNote = \"sampleinput\",magazine = \"sampleinputandsomeextraletters\") == True\n assert candidate(ransomNote = \"aabbcc\",magazine = \"abcabc\") == True\n assert candidate(ransomNote = \"same\",magazine = \"same\") == True\n assert candidate(ransomNote = \"repeatedcharacters\",magazine = \"repeatedcharacterse\") == True\n assert candidate(ransomNote = \"abacax\",magazine = \"abcax\") == False\n assert candidate(ransomNote = \"unique\",magazine = \"unqeiu\") == True\n assert candidate(ransomNote = \"abracadabra\",magazine = \"aacdrabbra\") == False\n assert candidate(ransomNote = \"aabbccddeeff\",magazine = \"fedcba\") == False\n assert candidate(ransomNote = \"zzzz\",magazine = \"zzzzzzzzzz\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"sssinppimm\") == False\n assert candidate(ransomNote = \"xxyyzz\",magazine = \"xzyyzzxx\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"ssssmissipppii\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"misisapip\") == False\n assert candidate(ransomNote = \"complexity\",magazine = \"txicopmlxity\") == False\n assert candidate(ransomNote = \"onemore\",magazine = \"onemoreexample\") == True\n assert candidate(ransomNote = \"thisisaverylongstringthatshouldpass\",magazine = \"thisisaverylongstringthatshouldpassandmore\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"ppisissimm\") == False\n assert candidate(ransomNote = \"banana\",magazine = \"anbananab\") == True\n assert candidate(ransomNote = \"programming\",magazine = \"rgmepnmoainrg\") == True\n assert candidate(ransomNote = \"construction\",magazine = \"ncostruticion\") == True\n assert candidate(ransomNote = \"banana\",magazine = \"nabnanaa\") == True\n assert candidate(ransomNote = \"short\",magazine = \"shortandlong\") == True\n assert candidate(ransomNote = \"overlap\",magazine = \"overlaplap\") == True\n assert candidate(ransomNote = \"aabbcc\",magazine = \"abcabcabc\") == True\n assert candidate(ransomNote = \"zxy\",magazine = \"zyxzyx\") == True\n assert candidate(ransomNote = \"xylophone\",magazine = \"enphonxylox\") == True\n assert candidate(ransomNote = \"hellohellohello\",magazine = \"hellohellohellobbb\") == True\n assert candidate(ransomNote = \"single\",magazine = \"singles\") == True\n assert candidate(ransomNote = \"thisisaverylongstringthatshouldpass\",magazine = \"thisisaverylongstringthatshouldpass\") == True\n assert candidate(ransomNote = \"zzzzzz\",magazine = \"zzzzzzzzzz\") == True\n assert candidate(ransomNote = \"abcd\",magazine = \"dcba\") == True\n assert candidate(ransomNote = \"mississippi\",magazine = \"ppisimiss\") == False\n assert candidate(ransomNote = \"almostthere\",magazine = \"almostherethere\") == True\n assert candidate(ransomNote = \"thisisatest\",magazine = \"thisisnotatest\") == True\n assert candidate(ransomNote = \"complexity\",magazine = \"xxxxcomplexityyyyy\") == True\n assert candidate(ransomNote = \"python\",magazine = \"nohtyp\") == True\n assert candidate(ransomNote = \"toolong\",magazine = \"too\") == False\n assert candidate(ransomNote = \"a\",magazine = \"abcdefghijklmnopqrstuvwxyz\") == True\n assert candidate(ransomNote = \"abracadabra\",magazine = \"acazabra\") == False\n assert candidate(ransomNote = \"programming\",magazine = \"grammproing\") == True\n assert candidate(ransomNote = \"zapples\",magazine = \"paplezzzas\") == True\n assert candidate(ransomNote = \"caseinsensitive\",magazine = \"CaseInsensitive\") == False\n assert candidate(ransomNote = \"python\",magazine = \"typythonn\") == True\n assert candidate(ransomNote = \"programming\",magazine = \"progmminglanguage\") == False\n assert candidate(ransomNote = \"abcdefg\",magazine = \"gfedcba\") == True\n assert candidate(ransomNote = \"thisisaverylongstringthatshouldfail\",magazine = \"thisisaverylongstringthatshoul\") == False\n assert candidate(ransomNote = \"challenge\",magazine = \"lengchalleng\") == True\n assert candidate(ransomNote = \"hellohellohello\",magazine = \"hellohello\") == False\n assert candidate(ransomNote = \"thisisaverylongransomnotethatwillsurelymakethetestcaseinteresting\",magazine = \"thisisaverylongmagazinesamplethatshouldcontainmanyoftheransomletters\") == False\n assert candidate(ransomNote = \"missingchar\",magazine = \"missingcha\") == False\n assert candidate(ransomNote = \"interview\",magazine = \"vwnteriview\") == True\n assert candidate(ransomNote = \"repeatedletters\",magazine = \"repetettadledtresletters\") == True\n assert candidate(ransomNote = \"aabbccddeeffgg\",magazine = \"aabbccddeeffgghh\") == True\n assert candidate(ransomNote = \"repeatedletters\",magazine = \"lettersrepated\") == False\n assert candidate(ransomNote = \"abcdabcdabcd\",magazine = \"abcdabcd\") == False\n assert candidate(ransomNote = \"racecar\",magazine = \"racecar\") == True\n assert candidate(ransomNote = \"programming\",magazine = \"gnimmargorp\") == True\n assert candidate(ransomNote = \"aabbc\",magazine = \"aabbc\") == True\n"}, "metadata": {"canonical_parameter_names": ["ransomNote", "magazine"], "leetcode_dataset_entry_point": "Solution().canConstruct", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canConstruct = function(ransomNote, magazine) {", "container": null, "callable": "canConstruct", "parameters": [{"name": "ransomNote", "type": "string"}, {"name": "magazine", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 386, "task_id": "lexicographical-numbers", "difficulty": "Medium", "problem_description": "Given an integer n, return all the numbers in the range [1, n] sorted in lexicographical order.\nYou must write an algorithm that runs in O(n) time and uses O(1) extra space. \n \nExample 1:\nInput: n = 13\nOutput: [1,10,11,12,13,2,3,4,5,6,7,8,9]\nExample 2:\nInput: n = 2\nOutput: [1,2]\n\n \nConstraints:\n\n1 <= n <= 5 * 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 4321) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 253, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 254, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 255, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 256, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 257, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 258, 2580, 2581, 2582, 2583, 2584, 2585, 2586, 2587, 2588, 2589, 259, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 26, 260, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2607, 2608, 2609, 261, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 262, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 263, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 264, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 265, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 266, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 267, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 268, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 269, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 27, 270, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 271, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 272, 2720, 2721, 2722, 2723, 2724, 2725, 2726, 2727, 2728, 2729, 273, 2730, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 274, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747, 2748, 2749, 275, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759, 276, 2760, 2761, 2762, 2763, 2764, 2765, 2766, 2767, 2768, 2769, 277, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 278, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 279, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 28, 280, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 281, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 282, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 283, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 284, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 285, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 286, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 287, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 288, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 289, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898, 2899, 29, 290, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909, 291, 2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 292, 2920, 2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 293, 2930, 2931, 2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 294, 2940, 2941, 2942, 2943, 2944, 2945, 2946, 2947, 2948, 2949, 295, 2950, 2951, 2952, 2953, 2954, 2955, 2956, 2957, 2958, 2959, 296, 2960, 2961, 2962, 2963, 2964, 2965, 2966, 2967, 2968, 2969, 297, 2970, 2971, 2972, 2973, 2974, 2975, 2976, 2977, 2978, 2979, 298, 2980, 2981, 2982, 2983, 2984, 2985, 2986, 2987, 2988, 2989, 299, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999, 3, 30, 300, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 301, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 302, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 303, 3030, 3031, 3032, 3033, 3034, 3035, 3036, 3037, 3038, 3039, 304, 3040, 3041, 3042, 3043, 3044, 3045, 3046, 3047, 3048, 3049, 305, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 306, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 307, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 308, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 309, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 31, 310, 3100, 3101, 3102, 3103, 3104, 3105, 3106, 3107, 3108, 3109, 311, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 312, 3120, 3121, 3122, 3123, 3124, 3125, 3126, 3127, 3128, 3129, 313, 3130, 3131, 3132, 3133, 3134, 3135, 3136, 3137, 3138, 3139, 314, 3140, 3141, 3142, 3143, 3144, 3145, 3146, 3147, 3148, 3149, 315, 3150, 3151, 3152, 3153, 3154, 3155, 3156, 3157, 3158, 3159, 316, 3160, 3161, 3162, 3163, 3164, 3165, 3166, 3167, 3168, 3169, 317, 3170, 3171, 3172, 3173, 3174, 3175, 3176, 3177, 3178, 3179, 318, 3180, 3181, 3182, 3183, 3184, 3185, 3186, 3187, 3188, 3189, 319, 3190, 3191, 3192, 3193, 3194, 3195, 3196, 3197, 3198, 3199, 32, 320, 3200, 3201, 3202, 3203, 3204, 3205, 3206, 3207, 3208, 3209, 321, 3210, 3211, 3212, 3213, 3214, 3215, 3216, 3217, 3218, 3219, 322, 3220, 3221, 3222, 3223, 3224, 3225, 3226, 3227, 3228, 3229, 323, 3230, 3231, 3232, 3233, 3234, 3235, 3236, 3237, 3238, 3239, 324, 3240, 3241, 3242, 3243, 3244, 3245, 3246, 3247, 3248, 3249, 325, 3250, 3251, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 326, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 327, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 328, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 329, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 33, 330, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 331, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 332, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 333, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 334, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 335, 3350, 3351, 3352, 3353, 3354, 3355, 3356, 3357, 3358, 3359, 336, 3360, 3361, 3362, 3363, 3364, 3365, 3366, 3367, 3368, 3369, 337, 3370, 3371, 3372, 3373, 3374, 3375, 3376, 3377, 3378, 3379, 338, 3380, 3381, 3382, 3383, 3384, 3385, 3386, 3387, 3388, 3389, 339, 3390, 3391, 3392, 3393, 3394, 3395, 3396, 3397, 3398, 3399, 34, 340, 3400, 3401, 3402, 3403, 3404, 3405, 3406, 3407, 3408, 3409, 341, 3410, 3411, 3412, 3413, 3414, 3415, 3416, 3417, 3418, 3419, 342, 3420, 3421, 3422, 3423, 3424, 3425, 3426, 3427, 3428, 3429, 343, 3430, 3431, 3432, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 344, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 3449, 345, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 3458, 3459, 346, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 347, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 348, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 349, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 35, 350, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3507, 3508, 3509, 351, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 352, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 353, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 354, 3540, 3541, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3549, 355, 3550, 3551, 3552, 3553, 3554, 3555, 3556, 3557, 3558, 3559, 356, 3560, 3561, 3562, 3563, 3564, 3565, 3566, 3567, 3568, 3569, 357, 3570, 3571, 3572, 3573, 3574, 3575, 3576, 3577, 3578, 3579, 358, 3580, 3581, 3582, 3583, 3584, 3585, 3586, 3587, 3588, 3589, 359, 3590, 3591, 3592, 3593, 3594, 3595, 3596, 3597, 3598, 3599, 36, 360, 3600, 3601, 3602, 3603, 3604, 3605, 3606, 3607, 3608, 3609, 361, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 362, 3620, 3621, 3622, 3623, 3624, 3625, 3626, 3627, 3628, 3629, 363, 3630, 3631, 3632, 3633, 3634, 3635, 3636, 3637, 3638, 3639, 364, 3640, 3641, 3642, 3643, 3644, 3645, 3646, 3647, 3648, 3649, 365, 3650, 3651, 3652, 3653, 3654, 3655, 3656, 3657, 3658, 3659, 366, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 367, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 368, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 369, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 37, 370, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 371, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 372, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 373, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 374, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 375, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 376, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 377, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 378, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 379, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 38, 380, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 381, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 382, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 383, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 384, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 385, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 386, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 387, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 388, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 389, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 39, 390, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 391, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 392, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 393, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 394, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 395, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 396, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 397, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 398, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 399, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4, 40, 400, 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 401, 4010, 4011, 4012, 4013, 4014, 4015, 4016, 4017, 4018, 4019, 402, 4020, 4021, 4022, 4023, 4024, 4025, 4026, 4027, 4028, 4029, 403, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 404, 4040, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048, 4049, 405, 4050, 4051, 4052, 4053, 4054, 4055, 4056, 4057, 4058, 4059, 406, 4060, 4061, 4062, 4063, 4064, 4065, 4066, 4067, 4068, 4069, 407, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 408, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 409, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 41, 410, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 411, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 412, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 413, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 414, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 415, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 4158, 4159, 416, 4160, 4161, 4162, 4163, 4164, 4165, 4166, 4167, 4168, 4169, 417, 4170, 4171, 4172, 4173, 4174, 4175, 4176, 4177, 4178, 4179, 418, 4180, 4181, 4182, 4183, 4184, 4185, 4186, 4187, 4188, 4189, 419, 4190, 4191, 4192, 4193, 4194, 4195, 4196, 4197, 4198, 4199, 42, 420, 4200, 4201, 4202, 4203, 4204, 4205, 4206, 4207, 4208, 4209, 421, 4210, 4211, 4212, 4213, 4214, 4215, 4216, 4217, 4218, 4219, 422, 4220, 4221, 4222, 4223, 4224, 4225, 4226, 4227, 4228, 4229, 423, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 424, 4240, 4241, 4242, 4243, 4244, 4245, 4246, 4247, 4248, 4249, 425, 4250, 4251, 4252, 4253, 4254, 4255, 4256, 4257, 4258, 4259, 426, 4260, 4261, 4262, 4263, 4264, 4265, 4266, 4267, 4268, 4269, 427, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 428, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 429, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 43, 430, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 431, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 432, 4320, 4321, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 10) == [1, 10, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(n = 999) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 99) == [1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 2) == [1, 2]\n assert candidate(n = 100) == [1, 10, 100, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 1) == [1]\n assert candidate(n = 13) == [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(n = 5) == [1, 2, 3, 4, 5]\n assert candidate(n = 1010) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 105) == [1, 10, 100, 101, 102, 103, 104, 105, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 1111) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 4000) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 253, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 254, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 255, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 256, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 257, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 258, 2580, 2581, 2582, 2583, 2584, 2585, 2586, 2587, 2588, 2589, 259, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 26, 260, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2607, 2608, 2609, 261, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 262, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 263, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 264, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 265, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 266, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 267, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 268, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 269, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 27, 270, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 271, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 272, 2720, 2721, 2722, 2723, 2724, 2725, 2726, 2727, 2728, 2729, 273, 2730, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 274, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747, 2748, 2749, 275, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759, 276, 2760, 2761, 2762, 2763, 2764, 2765, 2766, 2767, 2768, 2769, 277, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 278, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 279, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 28, 280, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 281, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 282, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 283, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 284, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 285, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 286, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 287, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 288, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 289, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898, 2899, 29, 290, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909, 291, 2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 292, 2920, 2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 293, 2930, 2931, 2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 294, 2940, 2941, 2942, 2943, 2944, 2945, 2946, 2947, 2948, 2949, 295, 2950, 2951, 2952, 2953, 2954, 2955, 2956, 2957, 2958, 2959, 296, 2960, 2961, 2962, 2963, 2964, 2965, 2966, 2967, 2968, 2969, 297, 2970, 2971, 2972, 2973, 2974, 2975, 2976, 2977, 2978, 2979, 298, 2980, 2981, 2982, 2983, 2984, 2985, 2986, 2987, 2988, 2989, 299, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999, 3, 30, 300, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 301, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 302, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 303, 3030, 3031, 3032, 3033, 3034, 3035, 3036, 3037, 3038, 3039, 304, 3040, 3041, 3042, 3043, 3044, 3045, 3046, 3047, 3048, 3049, 305, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 306, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 307, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 308, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 309, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 31, 310, 3100, 3101, 3102, 3103, 3104, 3105, 3106, 3107, 3108, 3109, 311, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 312, 3120, 3121, 3122, 3123, 3124, 3125, 3126, 3127, 3128, 3129, 313, 3130, 3131, 3132, 3133, 3134, 3135, 3136, 3137, 3138, 3139, 314, 3140, 3141, 3142, 3143, 3144, 3145, 3146, 3147, 3148, 3149, 315, 3150, 3151, 3152, 3153, 3154, 3155, 3156, 3157, 3158, 3159, 316, 3160, 3161, 3162, 3163, 3164, 3165, 3166, 3167, 3168, 3169, 317, 3170, 3171, 3172, 3173, 3174, 3175, 3176, 3177, 3178, 3179, 318, 3180, 3181, 3182, 3183, 3184, 3185, 3186, 3187, 3188, 3189, 319, 3190, 3191, 3192, 3193, 3194, 3195, 3196, 3197, 3198, 3199, 32, 320, 3200, 3201, 3202, 3203, 3204, 3205, 3206, 3207, 3208, 3209, 321, 3210, 3211, 3212, 3213, 3214, 3215, 3216, 3217, 3218, 3219, 322, 3220, 3221, 3222, 3223, 3224, 3225, 3226, 3227, 3228, 3229, 323, 3230, 3231, 3232, 3233, 3234, 3235, 3236, 3237, 3238, 3239, 324, 3240, 3241, 3242, 3243, 3244, 3245, 3246, 3247, 3248, 3249, 325, 3250, 3251, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 326, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 327, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 328, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 329, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 33, 330, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 331, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 332, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 333, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 334, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 335, 3350, 3351, 3352, 3353, 3354, 3355, 3356, 3357, 3358, 3359, 336, 3360, 3361, 3362, 3363, 3364, 3365, 3366, 3367, 3368, 3369, 337, 3370, 3371, 3372, 3373, 3374, 3375, 3376, 3377, 3378, 3379, 338, 3380, 3381, 3382, 3383, 3384, 3385, 3386, 3387, 3388, 3389, 339, 3390, 3391, 3392, 3393, 3394, 3395, 3396, 3397, 3398, 3399, 34, 340, 3400, 3401, 3402, 3403, 3404, 3405, 3406, 3407, 3408, 3409, 341, 3410, 3411, 3412, 3413, 3414, 3415, 3416, 3417, 3418, 3419, 342, 3420, 3421, 3422, 3423, 3424, 3425, 3426, 3427, 3428, 3429, 343, 3430, 3431, 3432, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 344, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 3449, 345, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 3458, 3459, 346, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 347, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 348, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 349, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 35, 350, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3507, 3508, 3509, 351, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 352, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 353, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 354, 3540, 3541, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3549, 355, 3550, 3551, 3552, 3553, 3554, 3555, 3556, 3557, 3558, 3559, 356, 3560, 3561, 3562, 3563, 3564, 3565, 3566, 3567, 3568, 3569, 357, 3570, 3571, 3572, 3573, 3574, 3575, 3576, 3577, 3578, 3579, 358, 3580, 3581, 3582, 3583, 3584, 3585, 3586, 3587, 3588, 3589, 359, 3590, 3591, 3592, 3593, 3594, 3595, 3596, 3597, 3598, 3599, 36, 360, 3600, 3601, 3602, 3603, 3604, 3605, 3606, 3607, 3608, 3609, 361, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 362, 3620, 3621, 3622, 3623, 3624, 3625, 3626, 3627, 3628, 3629, 363, 3630, 3631, 3632, 3633, 3634, 3635, 3636, 3637, 3638, 3639, 364, 3640, 3641, 3642, 3643, 3644, 3645, 3646, 3647, 3648, 3649, 365, 3650, 3651, 3652, 3653, 3654, 3655, 3656, 3657, 3658, 3659, 366, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 367, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 368, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 369, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 37, 370, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 371, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 372, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 373, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 374, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 375, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 376, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 377, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 378, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 379, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 38, 380, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 381, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 382, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 383, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 384, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 385, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 386, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 387, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 388, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 389, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 39, 390, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 391, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 392, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 393, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 394, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 395, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 396, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 397, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 398, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 399, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4, 40, 400, 4000, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 2345) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 324) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 111) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 1000) == [1, 10, 100, 1000, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 3333) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 253, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 254, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 255, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 256, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 257, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 258, 2580, 2581, 2582, 2583, 2584, 2585, 2586, 2587, 2588, 2589, 259, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 26, 260, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2607, 2608, 2609, 261, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 262, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 263, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 264, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 265, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 266, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 267, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 268, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 269, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 27, 270, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 271, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 272, 2720, 2721, 2722, 2723, 2724, 2725, 2726, 2727, 2728, 2729, 273, 2730, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 274, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747, 2748, 2749, 275, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759, 276, 2760, 2761, 2762, 2763, 2764, 2765, 2766, 2767, 2768, 2769, 277, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 278, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 279, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 28, 280, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 281, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 282, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 283, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 284, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 285, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 286, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 287, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 288, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 289, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898, 2899, 29, 290, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909, 291, 2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 292, 2920, 2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 293, 2930, 2931, 2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 294, 2940, 2941, 2942, 2943, 2944, 2945, 2946, 2947, 2948, 2949, 295, 2950, 2951, 2952, 2953, 2954, 2955, 2956, 2957, 2958, 2959, 296, 2960, 2961, 2962, 2963, 2964, 2965, 2966, 2967, 2968, 2969, 297, 2970, 2971, 2972, 2973, 2974, 2975, 2976, 2977, 2978, 2979, 298, 2980, 2981, 2982, 2983, 2984, 2985, 2986, 2987, 2988, 2989, 299, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999, 3, 30, 300, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 301, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 302, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 303, 3030, 3031, 3032, 3033, 3034, 3035, 3036, 3037, 3038, 3039, 304, 3040, 3041, 3042, 3043, 3044, 3045, 3046, 3047, 3048, 3049, 305, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 306, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 307, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 308, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 309, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 31, 310, 3100, 3101, 3102, 3103, 3104, 3105, 3106, 3107, 3108, 3109, 311, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 312, 3120, 3121, 3122, 3123, 3124, 3125, 3126, 3127, 3128, 3129, 313, 3130, 3131, 3132, 3133, 3134, 3135, 3136, 3137, 3138, 3139, 314, 3140, 3141, 3142, 3143, 3144, 3145, 3146, 3147, 3148, 3149, 315, 3150, 3151, 3152, 3153, 3154, 3155, 3156, 3157, 3158, 3159, 316, 3160, 3161, 3162, 3163, 3164, 3165, 3166, 3167, 3168, 3169, 317, 3170, 3171, 3172, 3173, 3174, 3175, 3176, 3177, 3178, 3179, 318, 3180, 3181, 3182, 3183, 3184, 3185, 3186, 3187, 3188, 3189, 319, 3190, 3191, 3192, 3193, 3194, 3195, 3196, 3197, 3198, 3199, 32, 320, 3200, 3201, 3202, 3203, 3204, 3205, 3206, 3207, 3208, 3209, 321, 3210, 3211, 3212, 3213, 3214, 3215, 3216, 3217, 3218, 3219, 322, 3220, 3221, 3222, 3223, 3224, 3225, 3226, 3227, 3228, 3229, 323, 3230, 3231, 3232, 3233, 3234, 3235, 3236, 3237, 3238, 3239, 324, 3240, 3241, 3242, 3243, 3244, 3245, 3246, 3247, 3248, 3249, 325, 3250, 3251, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 326, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 327, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 328, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 329, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 33, 330, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 331, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 332, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 333, 3330, 3331, 3332, 3333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 300) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 3000) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 253, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 254, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 255, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 256, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 257, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 258, 2580, 2581, 2582, 2583, 2584, 2585, 2586, 2587, 2588, 2589, 259, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 26, 260, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2607, 2608, 2609, 261, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 262, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 263, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 264, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 265, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 266, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 267, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 268, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 269, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 27, 270, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 271, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 272, 2720, 2721, 2722, 2723, 2724, 2725, 2726, 2727, 2728, 2729, 273, 2730, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 274, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747, 2748, 2749, 275, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759, 276, 2760, 2761, 2762, 2763, 2764, 2765, 2766, 2767, 2768, 2769, 277, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 278, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 279, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 28, 280, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 281, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 282, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 283, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 284, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 285, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 286, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 287, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 288, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 289, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898, 2899, 29, 290, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909, 291, 2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 292, 2920, 2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 293, 2930, 2931, 2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 294, 2940, 2941, 2942, 2943, 2944, 2945, 2946, 2947, 2948, 2949, 295, 2950, 2951, 2952, 2953, 2954, 2955, 2956, 2957, 2958, 2959, 296, 2960, 2961, 2962, 2963, 2964, 2965, 2966, 2967, 2968, 2969, 297, 2970, 2971, 2972, 2973, 2974, 2975, 2976, 2977, 2978, 2979, 298, 2980, 2981, 2982, 2983, 2984, 2985, 2986, 2987, 2988, 2989, 299, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999, 3, 30, 300, 3000, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 3456) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 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2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 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3443, 3444, 3445, 3446, 3447, 3448, 3449, 345, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 345) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 1001) == [1, 10, 100, 1000, 1001, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 1024) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 101) == [1, 10, 100, 101, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 2020) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 5555) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 253, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 254, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 255, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 256, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 257, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 258, 2580, 2581, 2582, 2583, 2584, 2585, 2586, 2587, 2588, 2589, 259, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 26, 260, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2607, 2608, 2609, 261, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 262, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 263, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 264, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 265, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 266, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 267, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 268, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 269, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 27, 270, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 271, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 272, 2720, 2721, 2722, 2723, 2724, 2725, 2726, 2727, 2728, 2729, 273, 2730, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 274, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747, 2748, 2749, 275, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759, 276, 2760, 2761, 2762, 2763, 2764, 2765, 2766, 2767, 2768, 2769, 277, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 278, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 279, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 28, 280, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 281, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 282, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 283, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 284, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 285, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 286, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 287, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 288, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 289, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898, 2899, 29, 290, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909, 291, 2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 292, 2920, 2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 293, 2930, 2931, 2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 294, 2940, 2941, 2942, 2943, 2944, 2945, 2946, 2947, 2948, 2949, 295, 2950, 2951, 2952, 2953, 2954, 2955, 2956, 2957, 2958, 2959, 296, 2960, 2961, 2962, 2963, 2964, 2965, 2966, 2967, 2968, 2969, 297, 2970, 2971, 2972, 2973, 2974, 2975, 2976, 2977, 2978, 2979, 298, 2980, 2981, 2982, 2983, 2984, 2985, 2986, 2987, 2988, 2989, 299, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999, 3, 30, 300, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 301, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 302, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 303, 3030, 3031, 3032, 3033, 3034, 3035, 3036, 3037, 3038, 3039, 304, 3040, 3041, 3042, 3043, 3044, 3045, 3046, 3047, 3048, 3049, 305, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 306, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 307, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 308, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 309, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 31, 310, 3100, 3101, 3102, 3103, 3104, 3105, 3106, 3107, 3108, 3109, 311, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 312, 3120, 3121, 3122, 3123, 3124, 3125, 3126, 3127, 3128, 3129, 313, 3130, 3131, 3132, 3133, 3134, 3135, 3136, 3137, 3138, 3139, 314, 3140, 3141, 3142, 3143, 3144, 3145, 3146, 3147, 3148, 3149, 315, 3150, 3151, 3152, 3153, 3154, 3155, 3156, 3157, 3158, 3159, 316, 3160, 3161, 3162, 3163, 3164, 3165, 3166, 3167, 3168, 3169, 317, 3170, 3171, 3172, 3173, 3174, 3175, 3176, 3177, 3178, 3179, 318, 3180, 3181, 3182, 3183, 3184, 3185, 3186, 3187, 3188, 3189, 319, 3190, 3191, 3192, 3193, 3194, 3195, 3196, 3197, 3198, 3199, 32, 320, 3200, 3201, 3202, 3203, 3204, 3205, 3206, 3207, 3208, 3209, 321, 3210, 3211, 3212, 3213, 3214, 3215, 3216, 3217, 3218, 3219, 322, 3220, 3221, 3222, 3223, 3224, 3225, 3226, 3227, 3228, 3229, 323, 3230, 3231, 3232, 3233, 3234, 3235, 3236, 3237, 3238, 3239, 324, 3240, 3241, 3242, 3243, 3244, 3245, 3246, 3247, 3248, 3249, 325, 3250, 3251, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 326, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 327, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 328, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 329, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 33, 330, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 331, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 332, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 333, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 334, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 335, 3350, 3351, 3352, 3353, 3354, 3355, 3356, 3357, 3358, 3359, 336, 3360, 3361, 3362, 3363, 3364, 3365, 3366, 3367, 3368, 3369, 337, 3370, 3371, 3372, 3373, 3374, 3375, 3376, 3377, 3378, 3379, 338, 3380, 3381, 3382, 3383, 3384, 3385, 3386, 3387, 3388, 3389, 339, 3390, 3391, 3392, 3393, 3394, 3395, 3396, 3397, 3398, 3399, 34, 340, 3400, 3401, 3402, 3403, 3404, 3405, 3406, 3407, 3408, 3409, 341, 3410, 3411, 3412, 3413, 3414, 3415, 3416, 3417, 3418, 3419, 342, 3420, 3421, 3422, 3423, 3424, 3425, 3426, 3427, 3428, 3429, 343, 3430, 3431, 3432, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 344, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 3449, 345, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 3458, 3459, 346, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 347, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 348, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 349, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 35, 350, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3507, 3508, 3509, 351, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 352, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 353, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 354, 3540, 3541, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3549, 355, 3550, 3551, 3552, 3553, 3554, 3555, 3556, 3557, 3558, 3559, 356, 3560, 3561, 3562, 3563, 3564, 3565, 3566, 3567, 3568, 3569, 357, 3570, 3571, 3572, 3573, 3574, 3575, 3576, 3577, 3578, 3579, 358, 3580, 3581, 3582, 3583, 3584, 3585, 3586, 3587, 3588, 3589, 359, 3590, 3591, 3592, 3593, 3594, 3595, 3596, 3597, 3598, 3599, 36, 360, 3600, 3601, 3602, 3603, 3604, 3605, 3606, 3607, 3608, 3609, 361, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 362, 3620, 3621, 3622, 3623, 3624, 3625, 3626, 3627, 3628, 3629, 363, 3630, 3631, 3632, 3633, 3634, 3635, 3636, 3637, 3638, 3639, 364, 3640, 3641, 3642, 3643, 3644, 3645, 3646, 3647, 3648, 3649, 365, 3650, 3651, 3652, 3653, 3654, 3655, 3656, 3657, 3658, 3659, 366, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 367, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 368, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 369, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 37, 370, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 371, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 372, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 373, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 374, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 375, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 376, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 377, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 378, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 379, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 38, 380, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 381, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 382, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 383, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 384, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 385, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 386, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 387, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 388, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 389, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 39, 390, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 391, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 392, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 393, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 394, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 395, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 396, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 397, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 398, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 399, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4, 40, 400, 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 401, 4010, 4011, 4012, 4013, 4014, 4015, 4016, 4017, 4018, 4019, 402, 4020, 4021, 4022, 4023, 4024, 4025, 4026, 4027, 4028, 4029, 403, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 404, 4040, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048, 4049, 405, 4050, 4051, 4052, 4053, 4054, 4055, 4056, 4057, 4058, 4059, 406, 4060, 4061, 4062, 4063, 4064, 4065, 4066, 4067, 4068, 4069, 407, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 408, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 409, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 41, 410, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 411, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 412, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 413, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 414, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 415, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 4158, 4159, 416, 4160, 4161, 4162, 4163, 4164, 4165, 4166, 4167, 4168, 4169, 417, 4170, 4171, 4172, 4173, 4174, 4175, 4176, 4177, 4178, 4179, 418, 4180, 4181, 4182, 4183, 4184, 4185, 4186, 4187, 4188, 4189, 419, 4190, 4191, 4192, 4193, 4194, 4195, 4196, 4197, 4198, 4199, 42, 420, 4200, 4201, 4202, 4203, 4204, 4205, 4206, 4207, 4208, 4209, 421, 4210, 4211, 4212, 4213, 4214, 4215, 4216, 4217, 4218, 4219, 422, 4220, 4221, 4222, 4223, 4224, 4225, 4226, 4227, 4228, 4229, 423, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 424, 4240, 4241, 4242, 4243, 4244, 4245, 4246, 4247, 4248, 4249, 425, 4250, 4251, 4252, 4253, 4254, 4255, 4256, 4257, 4258, 4259, 426, 4260, 4261, 4262, 4263, 4264, 4265, 4266, 4267, 4268, 4269, 427, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 428, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 429, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 43, 430, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 431, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 432, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 433, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 434, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 435, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 436, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 437, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 438, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 439, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 44, 440, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 441, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 442, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 443, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 444, 4440, 4441, 4442, 4443, 4444, 4445, 4446, 4447, 4448, 4449, 445, 4450, 4451, 4452, 4453, 4454, 4455, 4456, 4457, 4458, 4459, 446, 4460, 4461, 4462, 4463, 4464, 4465, 4466, 4467, 4468, 4469, 447, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4478, 4479, 448, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489, 449, 4490, 4491, 4492, 4493, 4494, 4495, 4496, 4497, 4498, 4499, 45, 450, 4500, 4501, 4502, 4503, 4504, 4505, 4506, 4507, 4508, 4509, 451, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 452, 4520, 4521, 4522, 4523, 4524, 4525, 4526, 4527, 4528, 4529, 453, 4530, 4531, 4532, 4533, 4534, 4535, 4536, 4537, 4538, 4539, 454, 4540, 4541, 4542, 4543, 4544, 4545, 4546, 4547, 4548, 4549, 455, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4557, 4558, 4559, 456, 4560, 4561, 4562, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 457, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 458, 4580, 4581, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 459, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 46, 460, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 461, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 462, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 463, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 464, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 465, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 466, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 467, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 468, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 469, 4690, 4691, 4692, 4693, 4694, 4695, 4696, 4697, 4698, 4699, 47, 470, 4700, 4701, 4702, 4703, 4704, 4705, 4706, 4707, 4708, 4709, 471, 4710, 4711, 4712, 4713, 4714, 4715, 4716, 4717, 4718, 4719, 472, 4720, 4721, 4722, 4723, 4724, 4725, 4726, 4727, 4728, 4729, 473, 4730, 4731, 4732, 4733, 4734, 4735, 4736, 4737, 4738, 4739, 474, 4740, 4741, 4742, 4743, 4744, 4745, 4746, 4747, 4748, 4749, 475, 4750, 4751, 4752, 4753, 4754, 4755, 4756, 4757, 4758, 4759, 476, 4760, 4761, 4762, 4763, 4764, 4765, 4766, 4767, 4768, 4769, 477, 4770, 4771, 4772, 4773, 4774, 4775, 4776, 4777, 4778, 4779, 478, 4780, 4781, 4782, 4783, 4784, 4785, 4786, 4787, 4788, 4789, 479, 4790, 4791, 4792, 4793, 4794, 4795, 4796, 4797, 4798, 4799, 48, 480, 4800, 4801, 4802, 4803, 4804, 4805, 4806, 4807, 4808, 4809, 481, 4810, 4811, 4812, 4813, 4814, 4815, 4816, 4817, 4818, 4819, 482, 4820, 4821, 4822, 4823, 4824, 4825, 4826, 4827, 4828, 4829, 483, 4830, 4831, 4832, 4833, 4834, 4835, 4836, 4837, 4838, 4839, 484, 4840, 4841, 4842, 4843, 4844, 4845, 4846, 4847, 4848, 4849, 485, 4850, 4851, 4852, 4853, 4854, 4855, 4856, 4857, 4858, 4859, 486, 4860, 4861, 4862, 4863, 4864, 4865, 4866, 4867, 4868, 4869, 487, 4870, 4871, 4872, 4873, 4874, 4875, 4876, 4877, 4878, 4879, 488, 4880, 4881, 4882, 4883, 4884, 4885, 4886, 4887, 4888, 4889, 489, 4890, 4891, 4892, 4893, 4894, 4895, 4896, 4897, 4898, 4899, 49, 490, 4900, 4901, 4902, 4903, 4904, 4905, 4906, 4907, 4908, 4909, 491, 4910, 4911, 4912, 4913, 4914, 4915, 4916, 4917, 4918, 4919, 492, 4920, 4921, 4922, 4923, 4924, 4925, 4926, 4927, 4928, 4929, 493, 4930, 4931, 4932, 4933, 4934, 4935, 4936, 4937, 4938, 4939, 494, 4940, 4941, 4942, 4943, 4944, 4945, 4946, 4947, 4948, 4949, 495, 4950, 4951, 4952, 4953, 4954, 4955, 4956, 4957, 4958, 4959, 496, 4960, 4961, 4962, 4963, 4964, 4965, 4966, 4967, 4968, 4969, 497, 4970, 4971, 4972, 4973, 4974, 4975, 4976, 4977, 4978, 4979, 498, 4980, 4981, 4982, 4983, 4984, 4985, 4986, 4987, 4988, 4989, 499, 4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5, 50, 500, 5000, 5001, 5002, 5003, 5004, 5005, 5006, 5007, 5008, 5009, 501, 5010, 5011, 5012, 5013, 5014, 5015, 5016, 5017, 5018, 5019, 502, 5020, 5021, 5022, 5023, 5024, 5025, 5026, 5027, 5028, 5029, 503, 5030, 5031, 5032, 5033, 5034, 5035, 5036, 5037, 5038, 5039, 504, 5040, 5041, 5042, 5043, 5044, 5045, 5046, 5047, 5048, 5049, 505, 5050, 5051, 5052, 5053, 5054, 5055, 5056, 5057, 5058, 5059, 506, 5060, 5061, 5062, 5063, 5064, 5065, 5066, 5067, 5068, 5069, 507, 5070, 5071, 5072, 5073, 5074, 5075, 5076, 5077, 5078, 5079, 508, 5080, 5081, 5082, 5083, 5084, 5085, 5086, 5087, 5088, 5089, 509, 5090, 5091, 5092, 5093, 5094, 5095, 5096, 5097, 5098, 5099, 51, 510, 5100, 5101, 5102, 5103, 5104, 5105, 5106, 5107, 5108, 5109, 511, 5110, 5111, 5112, 5113, 5114, 5115, 5116, 5117, 5118, 5119, 512, 5120, 5121, 5122, 5123, 5124, 5125, 5126, 5127, 5128, 5129, 513, 5130, 5131, 5132, 5133, 5134, 5135, 5136, 5137, 5138, 5139, 514, 5140, 5141, 5142, 5143, 5144, 5145, 5146, 5147, 5148, 5149, 515, 5150, 5151, 5152, 5153, 5154, 5155, 5156, 5157, 5158, 5159, 516, 5160, 5161, 5162, 5163, 5164, 5165, 5166, 5167, 5168, 5169, 517, 5170, 5171, 5172, 5173, 5174, 5175, 5176, 5177, 5178, 5179, 518, 5180, 5181, 5182, 5183, 5184, 5185, 5186, 5187, 5188, 5189, 519, 5190, 5191, 5192, 5193, 5194, 5195, 5196, 5197, 5198, 5199, 52, 520, 5200, 5201, 5202, 5203, 5204, 5205, 5206, 5207, 5208, 5209, 521, 5210, 5211, 5212, 5213, 5214, 5215, 5216, 5217, 5218, 5219, 522, 5220, 5221, 5222, 5223, 5224, 5225, 5226, 5227, 5228, 5229, 523, 5230, 5231, 5232, 5233, 5234, 5235, 5236, 5237, 5238, 5239, 524, 5240, 5241, 5242, 5243, 5244, 5245, 5246, 5247, 5248, 5249, 525, 5250, 5251, 5252, 5253, 5254, 5255, 5256, 5257, 5258, 5259, 526, 5260, 5261, 5262, 5263, 5264, 5265, 5266, 5267, 5268, 5269, 527, 5270, 5271, 5272, 5273, 5274, 5275, 5276, 5277, 5278, 5279, 528, 5280, 5281, 5282, 5283, 5284, 5285, 5286, 5287, 5288, 5289, 529, 5290, 5291, 5292, 5293, 5294, 5295, 5296, 5297, 5298, 5299, 53, 530, 5300, 5301, 5302, 5303, 5304, 5305, 5306, 5307, 5308, 5309, 531, 5310, 5311, 5312, 5313, 5314, 5315, 5316, 5317, 5318, 5319, 532, 5320, 5321, 5322, 5323, 5324, 5325, 5326, 5327, 5328, 5329, 533, 5330, 5331, 5332, 5333, 5334, 5335, 5336, 5337, 5338, 5339, 534, 5340, 5341, 5342, 5343, 5344, 5345, 5346, 5347, 5348, 5349, 535, 5350, 5351, 5352, 5353, 5354, 5355, 5356, 5357, 5358, 5359, 536, 5360, 5361, 5362, 5363, 5364, 5365, 5366, 5367, 5368, 5369, 537, 5370, 5371, 5372, 5373, 5374, 5375, 5376, 5377, 5378, 5379, 538, 5380, 5381, 5382, 5383, 5384, 5385, 5386, 5387, 5388, 5389, 539, 5390, 5391, 5392, 5393, 5394, 5395, 5396, 5397, 5398, 5399, 54, 540, 5400, 5401, 5402, 5403, 5404, 5405, 5406, 5407, 5408, 5409, 541, 5410, 5411, 5412, 5413, 5414, 5415, 5416, 5417, 5418, 5419, 542, 5420, 5421, 5422, 5423, 5424, 5425, 5426, 5427, 5428, 5429, 543, 5430, 5431, 5432, 5433, 5434, 5435, 5436, 5437, 5438, 5439, 544, 5440, 5441, 5442, 5443, 5444, 5445, 5446, 5447, 5448, 5449, 545, 5450, 5451, 5452, 5453, 5454, 5455, 5456, 5457, 5458, 5459, 546, 5460, 5461, 5462, 5463, 5464, 5465, 5466, 5467, 5468, 5469, 547, 5470, 5471, 5472, 5473, 5474, 5475, 5476, 5477, 5478, 5479, 548, 5480, 5481, 5482, 5483, 5484, 5485, 5486, 5487, 5488, 5489, 549, 5490, 5491, 5492, 5493, 5494, 5495, 5496, 5497, 5498, 5499, 55, 550, 5500, 5501, 5502, 5503, 5504, 5505, 5506, 5507, 5508, 5509, 551, 5510, 5511, 5512, 5513, 5514, 5515, 5516, 5517, 5518, 5519, 552, 5520, 5521, 5522, 5523, 5524, 5525, 5526, 5527, 5528, 5529, 553, 5530, 5531, 5532, 5533, 5534, 5535, 5536, 5537, 5538, 5539, 554, 5540, 5541, 5542, 5543, 5544, 5545, 5546, 5547, 5548, 5549, 555, 5550, 5551, 5552, 5553, 5554, 5555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 5000) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 251, 2510, 2511, 2512, 2513, 2514, 2515, 2516, 2517, 2518, 2519, 252, 2520, 2521, 2522, 2523, 2524, 2525, 2526, 2527, 2528, 2529, 253, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 254, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 255, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 2557, 2558, 2559, 256, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2567, 2568, 2569, 257, 2570, 2571, 2572, 2573, 2574, 2575, 2576, 2577, 2578, 2579, 258, 2580, 2581, 2582, 2583, 2584, 2585, 2586, 2587, 2588, 2589, 259, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2597, 2598, 2599, 26, 260, 2600, 2601, 2602, 2603, 2604, 2605, 2606, 2607, 2608, 2609, 261, 2610, 2611, 2612, 2613, 2614, 2615, 2616, 2617, 2618, 2619, 262, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627, 2628, 2629, 263, 2630, 2631, 2632, 2633, 2634, 2635, 2636, 2637, 2638, 2639, 264, 2640, 2641, 2642, 2643, 2644, 2645, 2646, 2647, 2648, 2649, 265, 2650, 2651, 2652, 2653, 2654, 2655, 2656, 2657, 2658, 2659, 266, 2660, 2661, 2662, 2663, 2664, 2665, 2666, 2667, 2668, 2669, 267, 2670, 2671, 2672, 2673, 2674, 2675, 2676, 2677, 2678, 2679, 268, 2680, 2681, 2682, 2683, 2684, 2685, 2686, 2687, 2688, 2689, 269, 2690, 2691, 2692, 2693, 2694, 2695, 2696, 2697, 2698, 2699, 27, 270, 2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 271, 2710, 2711, 2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 272, 2720, 2721, 2722, 2723, 2724, 2725, 2726, 2727, 2728, 2729, 273, 2730, 2731, 2732, 2733, 2734, 2735, 2736, 2737, 2738, 2739, 274, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747, 2748, 2749, 275, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759, 276, 2760, 2761, 2762, 2763, 2764, 2765, 2766, 2767, 2768, 2769, 277, 2770, 2771, 2772, 2773, 2774, 2775, 2776, 2777, 2778, 2779, 278, 2780, 2781, 2782, 2783, 2784, 2785, 2786, 2787, 2788, 2789, 279, 2790, 2791, 2792, 2793, 2794, 2795, 2796, 2797, 2798, 2799, 28, 280, 2800, 2801, 2802, 2803, 2804, 2805, 2806, 2807, 2808, 2809, 281, 2810, 2811, 2812, 2813, 2814, 2815, 2816, 2817, 2818, 2819, 282, 2820, 2821, 2822, 2823, 2824, 2825, 2826, 2827, 2828, 2829, 283, 2830, 2831, 2832, 2833, 2834, 2835, 2836, 2837, 2838, 2839, 284, 2840, 2841, 2842, 2843, 2844, 2845, 2846, 2847, 2848, 2849, 285, 2850, 2851, 2852, 2853, 2854, 2855, 2856, 2857, 2858, 2859, 286, 2860, 2861, 2862, 2863, 2864, 2865, 2866, 2867, 2868, 2869, 287, 2870, 2871, 2872, 2873, 2874, 2875, 2876, 2877, 2878, 2879, 288, 2880, 2881, 2882, 2883, 2884, 2885, 2886, 2887, 2888, 2889, 289, 2890, 2891, 2892, 2893, 2894, 2895, 2896, 2897, 2898, 2899, 29, 290, 2900, 2901, 2902, 2903, 2904, 2905, 2906, 2907, 2908, 2909, 291, 2910, 2911, 2912, 2913, 2914, 2915, 2916, 2917, 2918, 2919, 292, 2920, 2921, 2922, 2923, 2924, 2925, 2926, 2927, 2928, 2929, 293, 2930, 2931, 2932, 2933, 2934, 2935, 2936, 2937, 2938, 2939, 294, 2940, 2941, 2942, 2943, 2944, 2945, 2946, 2947, 2948, 2949, 295, 2950, 2951, 2952, 2953, 2954, 2955, 2956, 2957, 2958, 2959, 296, 2960, 2961, 2962, 2963, 2964, 2965, 2966, 2967, 2968, 2969, 297, 2970, 2971, 2972, 2973, 2974, 2975, 2976, 2977, 2978, 2979, 298, 2980, 2981, 2982, 2983, 2984, 2985, 2986, 2987, 2988, 2989, 299, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999, 3, 30, 300, 3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, 301, 3010, 3011, 3012, 3013, 3014, 3015, 3016, 3017, 3018, 3019, 302, 3020, 3021, 3022, 3023, 3024, 3025, 3026, 3027, 3028, 3029, 303, 3030, 3031, 3032, 3033, 3034, 3035, 3036, 3037, 3038, 3039, 304, 3040, 3041, 3042, 3043, 3044, 3045, 3046, 3047, 3048, 3049, 305, 3050, 3051, 3052, 3053, 3054, 3055, 3056, 3057, 3058, 3059, 306, 3060, 3061, 3062, 3063, 3064, 3065, 3066, 3067, 3068, 3069, 307, 3070, 3071, 3072, 3073, 3074, 3075, 3076, 3077, 3078, 3079, 308, 3080, 3081, 3082, 3083, 3084, 3085, 3086, 3087, 3088, 3089, 309, 3090, 3091, 3092, 3093, 3094, 3095, 3096, 3097, 3098, 3099, 31, 310, 3100, 3101, 3102, 3103, 3104, 3105, 3106, 3107, 3108, 3109, 311, 3110, 3111, 3112, 3113, 3114, 3115, 3116, 3117, 3118, 3119, 312, 3120, 3121, 3122, 3123, 3124, 3125, 3126, 3127, 3128, 3129, 313, 3130, 3131, 3132, 3133, 3134, 3135, 3136, 3137, 3138, 3139, 314, 3140, 3141, 3142, 3143, 3144, 3145, 3146, 3147, 3148, 3149, 315, 3150, 3151, 3152, 3153, 3154, 3155, 3156, 3157, 3158, 3159, 316, 3160, 3161, 3162, 3163, 3164, 3165, 3166, 3167, 3168, 3169, 317, 3170, 3171, 3172, 3173, 3174, 3175, 3176, 3177, 3178, 3179, 318, 3180, 3181, 3182, 3183, 3184, 3185, 3186, 3187, 3188, 3189, 319, 3190, 3191, 3192, 3193, 3194, 3195, 3196, 3197, 3198, 3199, 32, 320, 3200, 3201, 3202, 3203, 3204, 3205, 3206, 3207, 3208, 3209, 321, 3210, 3211, 3212, 3213, 3214, 3215, 3216, 3217, 3218, 3219, 322, 3220, 3221, 3222, 3223, 3224, 3225, 3226, 3227, 3228, 3229, 323, 3230, 3231, 3232, 3233, 3234, 3235, 3236, 3237, 3238, 3239, 324, 3240, 3241, 3242, 3243, 3244, 3245, 3246, 3247, 3248, 3249, 325, 3250, 3251, 3252, 3253, 3254, 3255, 3256, 3257, 3258, 3259, 326, 3260, 3261, 3262, 3263, 3264, 3265, 3266, 3267, 3268, 3269, 327, 3270, 3271, 3272, 3273, 3274, 3275, 3276, 3277, 3278, 3279, 328, 3280, 3281, 3282, 3283, 3284, 3285, 3286, 3287, 3288, 3289, 329, 3290, 3291, 3292, 3293, 3294, 3295, 3296, 3297, 3298, 3299, 33, 330, 3300, 3301, 3302, 3303, 3304, 3305, 3306, 3307, 3308, 3309, 331, 3310, 3311, 3312, 3313, 3314, 3315, 3316, 3317, 3318, 3319, 332, 3320, 3321, 3322, 3323, 3324, 3325, 3326, 3327, 3328, 3329, 333, 3330, 3331, 3332, 3333, 3334, 3335, 3336, 3337, 3338, 3339, 334, 3340, 3341, 3342, 3343, 3344, 3345, 3346, 3347, 3348, 3349, 335, 3350, 3351, 3352, 3353, 3354, 3355, 3356, 3357, 3358, 3359, 336, 3360, 3361, 3362, 3363, 3364, 3365, 3366, 3367, 3368, 3369, 337, 3370, 3371, 3372, 3373, 3374, 3375, 3376, 3377, 3378, 3379, 338, 3380, 3381, 3382, 3383, 3384, 3385, 3386, 3387, 3388, 3389, 339, 3390, 3391, 3392, 3393, 3394, 3395, 3396, 3397, 3398, 3399, 34, 340, 3400, 3401, 3402, 3403, 3404, 3405, 3406, 3407, 3408, 3409, 341, 3410, 3411, 3412, 3413, 3414, 3415, 3416, 3417, 3418, 3419, 342, 3420, 3421, 3422, 3423, 3424, 3425, 3426, 3427, 3428, 3429, 343, 3430, 3431, 3432, 3433, 3434, 3435, 3436, 3437, 3438, 3439, 344, 3440, 3441, 3442, 3443, 3444, 3445, 3446, 3447, 3448, 3449, 345, 3450, 3451, 3452, 3453, 3454, 3455, 3456, 3457, 3458, 3459, 346, 3460, 3461, 3462, 3463, 3464, 3465, 3466, 3467, 3468, 3469, 347, 3470, 3471, 3472, 3473, 3474, 3475, 3476, 3477, 3478, 3479, 348, 3480, 3481, 3482, 3483, 3484, 3485, 3486, 3487, 3488, 3489, 349, 3490, 3491, 3492, 3493, 3494, 3495, 3496, 3497, 3498, 3499, 35, 350, 3500, 3501, 3502, 3503, 3504, 3505, 3506, 3507, 3508, 3509, 351, 3510, 3511, 3512, 3513, 3514, 3515, 3516, 3517, 3518, 3519, 352, 3520, 3521, 3522, 3523, 3524, 3525, 3526, 3527, 3528, 3529, 353, 3530, 3531, 3532, 3533, 3534, 3535, 3536, 3537, 3538, 3539, 354, 3540, 3541, 3542, 3543, 3544, 3545, 3546, 3547, 3548, 3549, 355, 3550, 3551, 3552, 3553, 3554, 3555, 3556, 3557, 3558, 3559, 356, 3560, 3561, 3562, 3563, 3564, 3565, 3566, 3567, 3568, 3569, 357, 3570, 3571, 3572, 3573, 3574, 3575, 3576, 3577, 3578, 3579, 358, 3580, 3581, 3582, 3583, 3584, 3585, 3586, 3587, 3588, 3589, 359, 3590, 3591, 3592, 3593, 3594, 3595, 3596, 3597, 3598, 3599, 36, 360, 3600, 3601, 3602, 3603, 3604, 3605, 3606, 3607, 3608, 3609, 361, 3610, 3611, 3612, 3613, 3614, 3615, 3616, 3617, 3618, 3619, 362, 3620, 3621, 3622, 3623, 3624, 3625, 3626, 3627, 3628, 3629, 363, 3630, 3631, 3632, 3633, 3634, 3635, 3636, 3637, 3638, 3639, 364, 3640, 3641, 3642, 3643, 3644, 3645, 3646, 3647, 3648, 3649, 365, 3650, 3651, 3652, 3653, 3654, 3655, 3656, 3657, 3658, 3659, 366, 3660, 3661, 3662, 3663, 3664, 3665, 3666, 3667, 3668, 3669, 367, 3670, 3671, 3672, 3673, 3674, 3675, 3676, 3677, 3678, 3679, 368, 3680, 3681, 3682, 3683, 3684, 3685, 3686, 3687, 3688, 3689, 369, 3690, 3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 37, 370, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 371, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 372, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 373, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 374, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 375, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 376, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 377, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 378, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 379, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 38, 380, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 381, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 382, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 383, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 384, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 385, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 386, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 387, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 388, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 389, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 39, 390, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 391, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 392, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 393, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 394, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 395, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 396, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 397, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 398, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 399, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4, 40, 400, 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 401, 4010, 4011, 4012, 4013, 4014, 4015, 4016, 4017, 4018, 4019, 402, 4020, 4021, 4022, 4023, 4024, 4025, 4026, 4027, 4028, 4029, 403, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 404, 4040, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048, 4049, 405, 4050, 4051, 4052, 4053, 4054, 4055, 4056, 4057, 4058, 4059, 406, 4060, 4061, 4062, 4063, 4064, 4065, 4066, 4067, 4068, 4069, 407, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 408, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 409, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 41, 410, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 411, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 412, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 413, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 414, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 415, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 4158, 4159, 416, 4160, 4161, 4162, 4163, 4164, 4165, 4166, 4167, 4168, 4169, 417, 4170, 4171, 4172, 4173, 4174, 4175, 4176, 4177, 4178, 4179, 418, 4180, 4181, 4182, 4183, 4184, 4185, 4186, 4187, 4188, 4189, 419, 4190, 4191, 4192, 4193, 4194, 4195, 4196, 4197, 4198, 4199, 42, 420, 4200, 4201, 4202, 4203, 4204, 4205, 4206, 4207, 4208, 4209, 421, 4210, 4211, 4212, 4213, 4214, 4215, 4216, 4217, 4218, 4219, 422, 4220, 4221, 4222, 4223, 4224, 4225, 4226, 4227, 4228, 4229, 423, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 424, 4240, 4241, 4242, 4243, 4244, 4245, 4246, 4247, 4248, 4249, 425, 4250, 4251, 4252, 4253, 4254, 4255, 4256, 4257, 4258, 4259, 426, 4260, 4261, 4262, 4263, 4264, 4265, 4266, 4267, 4268, 4269, 427, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 428, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 429, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 43, 430, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 431, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 432, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 433, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 434, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 435, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 436, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 437, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 438, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 439, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 44, 440, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 441, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 442, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 443, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 444, 4440, 4441, 4442, 4443, 4444, 4445, 4446, 4447, 4448, 4449, 445, 4450, 4451, 4452, 4453, 4454, 4455, 4456, 4457, 4458, 4459, 446, 4460, 4461, 4462, 4463, 4464, 4465, 4466, 4467, 4468, 4469, 447, 4470, 4471, 4472, 4473, 4474, 4475, 4476, 4477, 4478, 4479, 448, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489, 449, 4490, 4491, 4492, 4493, 4494, 4495, 4496, 4497, 4498, 4499, 45, 450, 4500, 4501, 4502, 4503, 4504, 4505, 4506, 4507, 4508, 4509, 451, 4510, 4511, 4512, 4513, 4514, 4515, 4516, 4517, 4518, 4519, 452, 4520, 4521, 4522, 4523, 4524, 4525, 4526, 4527, 4528, 4529, 453, 4530, 4531, 4532, 4533, 4534, 4535, 4536, 4537, 4538, 4539, 454, 4540, 4541, 4542, 4543, 4544, 4545, 4546, 4547, 4548, 4549, 455, 4550, 4551, 4552, 4553, 4554, 4555, 4556, 4557, 4558, 4559, 456, 4560, 4561, 4562, 4563, 4564, 4565, 4566, 4567, 4568, 4569, 457, 4570, 4571, 4572, 4573, 4574, 4575, 4576, 4577, 4578, 4579, 458, 4580, 4581, 4582, 4583, 4584, 4585, 4586, 4587, 4588, 4589, 459, 4590, 4591, 4592, 4593, 4594, 4595, 4596, 4597, 4598, 4599, 46, 460, 4600, 4601, 4602, 4603, 4604, 4605, 4606, 4607, 4608, 4609, 461, 4610, 4611, 4612, 4613, 4614, 4615, 4616, 4617, 4618, 4619, 462, 4620, 4621, 4622, 4623, 4624, 4625, 4626, 4627, 4628, 4629, 463, 4630, 4631, 4632, 4633, 4634, 4635, 4636, 4637, 4638, 4639, 464, 4640, 4641, 4642, 4643, 4644, 4645, 4646, 4647, 4648, 4649, 465, 4650, 4651, 4652, 4653, 4654, 4655, 4656, 4657, 4658, 4659, 466, 4660, 4661, 4662, 4663, 4664, 4665, 4666, 4667, 4668, 4669, 467, 4670, 4671, 4672, 4673, 4674, 4675, 4676, 4677, 4678, 4679, 468, 4680, 4681, 4682, 4683, 4684, 4685, 4686, 4687, 4688, 4689, 469, 4690, 4691, 4692, 4693, 4694, 4695, 4696, 4697, 4698, 4699, 47, 470, 4700, 4701, 4702, 4703, 4704, 4705, 4706, 4707, 4708, 4709, 471, 4710, 4711, 4712, 4713, 4714, 4715, 4716, 4717, 4718, 4719, 472, 4720, 4721, 4722, 4723, 4724, 4725, 4726, 4727, 4728, 4729, 473, 4730, 4731, 4732, 4733, 4734, 4735, 4736, 4737, 4738, 4739, 474, 4740, 4741, 4742, 4743, 4744, 4745, 4746, 4747, 4748, 4749, 475, 4750, 4751, 4752, 4753, 4754, 4755, 4756, 4757, 4758, 4759, 476, 4760, 4761, 4762, 4763, 4764, 4765, 4766, 4767, 4768, 4769, 477, 4770, 4771, 4772, 4773, 4774, 4775, 4776, 4777, 4778, 4779, 478, 4780, 4781, 4782, 4783, 4784, 4785, 4786, 4787, 4788, 4789, 479, 4790, 4791, 4792, 4793, 4794, 4795, 4796, 4797, 4798, 4799, 48, 480, 4800, 4801, 4802, 4803, 4804, 4805, 4806, 4807, 4808, 4809, 481, 4810, 4811, 4812, 4813, 4814, 4815, 4816, 4817, 4818, 4819, 482, 4820, 4821, 4822, 4823, 4824, 4825, 4826, 4827, 4828, 4829, 483, 4830, 4831, 4832, 4833, 4834, 4835, 4836, 4837, 4838, 4839, 484, 4840, 4841, 4842, 4843, 4844, 4845, 4846, 4847, 4848, 4849, 485, 4850, 4851, 4852, 4853, 4854, 4855, 4856, 4857, 4858, 4859, 486, 4860, 4861, 4862, 4863, 4864, 4865, 4866, 4867, 4868, 4869, 487, 4870, 4871, 4872, 4873, 4874, 4875, 4876, 4877, 4878, 4879, 488, 4880, 4881, 4882, 4883, 4884, 4885, 4886, 4887, 4888, 4889, 489, 4890, 4891, 4892, 4893, 4894, 4895, 4896, 4897, 4898, 4899, 49, 490, 4900, 4901, 4902, 4903, 4904, 4905, 4906, 4907, 4908, 4909, 491, 4910, 4911, 4912, 4913, 4914, 4915, 4916, 4917, 4918, 4919, 492, 4920, 4921, 4922, 4923, 4924, 4925, 4926, 4927, 4928, 4929, 493, 4930, 4931, 4932, 4933, 4934, 4935, 4936, 4937, 4938, 4939, 494, 4940, 4941, 4942, 4943, 4944, 4945, 4946, 4947, 4948, 4949, 495, 4950, 4951, 4952, 4953, 4954, 4955, 4956, 4957, 4958, 4959, 496, 4960, 4961, 4962, 4963, 4964, 4965, 4966, 4967, 4968, 4969, 497, 4970, 4971, 4972, 4973, 4974, 4975, 4976, 4977, 4978, 4979, 498, 4980, 4981, 4982, 4983, 4984, 4985, 4986, 4987, 4988, 4989, 499, 4990, 4991, 4992, 4993, 4994, 4995, 4996, 4997, 4998, 4999, 5, 50, 500, 5000, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 256) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 1023) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 4444) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 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2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 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3691, 3692, 3693, 3694, 3695, 3696, 3697, 3698, 3699, 37, 370, 3700, 3701, 3702, 3703, 3704, 3705, 3706, 3707, 3708, 3709, 371, 3710, 3711, 3712, 3713, 3714, 3715, 3716, 3717, 3718, 3719, 372, 3720, 3721, 3722, 3723, 3724, 3725, 3726, 3727, 3728, 3729, 373, 3730, 3731, 3732, 3733, 3734, 3735, 3736, 3737, 3738, 3739, 374, 3740, 3741, 3742, 3743, 3744, 3745, 3746, 3747, 3748, 3749, 375, 3750, 3751, 3752, 3753, 3754, 3755, 3756, 3757, 3758, 3759, 376, 3760, 3761, 3762, 3763, 3764, 3765, 3766, 3767, 3768, 3769, 377, 3770, 3771, 3772, 3773, 3774, 3775, 3776, 3777, 3778, 3779, 378, 3780, 3781, 3782, 3783, 3784, 3785, 3786, 3787, 3788, 3789, 379, 3790, 3791, 3792, 3793, 3794, 3795, 3796, 3797, 3798, 3799, 38, 380, 3800, 3801, 3802, 3803, 3804, 3805, 3806, 3807, 3808, 3809, 381, 3810, 3811, 3812, 3813, 3814, 3815, 3816, 3817, 3818, 3819, 382, 3820, 3821, 3822, 3823, 3824, 3825, 3826, 3827, 3828, 3829, 383, 3830, 3831, 3832, 3833, 3834, 3835, 3836, 3837, 3838, 3839, 384, 3840, 3841, 3842, 3843, 3844, 3845, 3846, 3847, 3848, 3849, 385, 3850, 3851, 3852, 3853, 3854, 3855, 3856, 3857, 3858, 3859, 386, 3860, 3861, 3862, 3863, 3864, 3865, 3866, 3867, 3868, 3869, 387, 3870, 3871, 3872, 3873, 3874, 3875, 3876, 3877, 3878, 3879, 388, 3880, 3881, 3882, 3883, 3884, 3885, 3886, 3887, 3888, 3889, 389, 3890, 3891, 3892, 3893, 3894, 3895, 3896, 3897, 3898, 3899, 39, 390, 3900, 3901, 3902, 3903, 3904, 3905, 3906, 3907, 3908, 3909, 391, 3910, 3911, 3912, 3913, 3914, 3915, 3916, 3917, 3918, 3919, 392, 3920, 3921, 3922, 3923, 3924, 3925, 3926, 3927, 3928, 3929, 393, 3930, 3931, 3932, 3933, 3934, 3935, 3936, 3937, 3938, 3939, 394, 3940, 3941, 3942, 3943, 3944, 3945, 3946, 3947, 3948, 3949, 395, 3950, 3951, 3952, 3953, 3954, 3955, 3956, 3957, 3958, 3959, 396, 3960, 3961, 3962, 3963, 3964, 3965, 3966, 3967, 3968, 3969, 397, 3970, 3971, 3972, 3973, 3974, 3975, 3976, 3977, 3978, 3979, 398, 3980, 3981, 3982, 3983, 3984, 3985, 3986, 3987, 3988, 3989, 399, 3990, 3991, 3992, 3993, 3994, 3995, 3996, 3997, 3998, 3999, 4, 40, 400, 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 401, 4010, 4011, 4012, 4013, 4014, 4015, 4016, 4017, 4018, 4019, 402, 4020, 4021, 4022, 4023, 4024, 4025, 4026, 4027, 4028, 4029, 403, 4030, 4031, 4032, 4033, 4034, 4035, 4036, 4037, 4038, 4039, 404, 4040, 4041, 4042, 4043, 4044, 4045, 4046, 4047, 4048, 4049, 405, 4050, 4051, 4052, 4053, 4054, 4055, 4056, 4057, 4058, 4059, 406, 4060, 4061, 4062, 4063, 4064, 4065, 4066, 4067, 4068, 4069, 407, 4070, 4071, 4072, 4073, 4074, 4075, 4076, 4077, 4078, 4079, 408, 4080, 4081, 4082, 4083, 4084, 4085, 4086, 4087, 4088, 4089, 409, 4090, 4091, 4092, 4093, 4094, 4095, 4096, 4097, 4098, 4099, 41, 410, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 411, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 412, 4120, 4121, 4122, 4123, 4124, 4125, 4126, 4127, 4128, 4129, 413, 4130, 4131, 4132, 4133, 4134, 4135, 4136, 4137, 4138, 4139, 414, 4140, 4141, 4142, 4143, 4144, 4145, 4146, 4147, 4148, 4149, 415, 4150, 4151, 4152, 4153, 4154, 4155, 4156, 4157, 4158, 4159, 416, 4160, 4161, 4162, 4163, 4164, 4165, 4166, 4167, 4168, 4169, 417, 4170, 4171, 4172, 4173, 4174, 4175, 4176, 4177, 4178, 4179, 418, 4180, 4181, 4182, 4183, 4184, 4185, 4186, 4187, 4188, 4189, 419, 4190, 4191, 4192, 4193, 4194, 4195, 4196, 4197, 4198, 4199, 42, 420, 4200, 4201, 4202, 4203, 4204, 4205, 4206, 4207, 4208, 4209, 421, 4210, 4211, 4212, 4213, 4214, 4215, 4216, 4217, 4218, 4219, 422, 4220, 4221, 4222, 4223, 4224, 4225, 4226, 4227, 4228, 4229, 423, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 424, 4240, 4241, 4242, 4243, 4244, 4245, 4246, 4247, 4248, 4249, 425, 4250, 4251, 4252, 4253, 4254, 4255, 4256, 4257, 4258, 4259, 426, 4260, 4261, 4262, 4263, 4264, 4265, 4266, 4267, 4268, 4269, 427, 4270, 4271, 4272, 4273, 4274, 4275, 4276, 4277, 4278, 4279, 428, 4280, 4281, 4282, 4283, 4284, 4285, 4286, 4287, 4288, 4289, 429, 4290, 4291, 4292, 4293, 4294, 4295, 4296, 4297, 4298, 4299, 43, 430, 4300, 4301, 4302, 4303, 4304, 4305, 4306, 4307, 4308, 4309, 431, 4310, 4311, 4312, 4313, 4314, 4315, 4316, 4317, 4318, 4319, 432, 4320, 4321, 4322, 4323, 4324, 4325, 4326, 4327, 4328, 4329, 433, 4330, 4331, 4332, 4333, 4334, 4335, 4336, 4337, 4338, 4339, 434, 4340, 4341, 4342, 4343, 4344, 4345, 4346, 4347, 4348, 4349, 435, 4350, 4351, 4352, 4353, 4354, 4355, 4356, 4357, 4358, 4359, 436, 4360, 4361, 4362, 4363, 4364, 4365, 4366, 4367, 4368, 4369, 437, 4370, 4371, 4372, 4373, 4374, 4375, 4376, 4377, 4378, 4379, 438, 4380, 4381, 4382, 4383, 4384, 4385, 4386, 4387, 4388, 4389, 439, 4390, 4391, 4392, 4393, 4394, 4395, 4396, 4397, 4398, 4399, 44, 440, 4400, 4401, 4402, 4403, 4404, 4405, 4406, 4407, 4408, 4409, 441, 4410, 4411, 4412, 4413, 4414, 4415, 4416, 4417, 4418, 4419, 442, 4420, 4421, 4422, 4423, 4424, 4425, 4426, 4427, 4428, 4429, 443, 4430, 4431, 4432, 4433, 4434, 4435, 4436, 4437, 4438, 4439, 444, 4440, 4441, 4442, 4443, 4444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 2222) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 2500) == [1, 10, 100, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 101, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 102, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 103, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 104, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 105, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 106, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 107, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 108, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 109, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 11, 110, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 111, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 112, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 113, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 114, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 115, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 116, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 117, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 118, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 119, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 12, 120, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 121, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 122, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 123, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 1238, 1239, 124, 1240, 1241, 1242, 1243, 1244, 1245, 1246, 1247, 1248, 1249, 125, 1250, 1251, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 126, 1260, 1261, 1262, 1263, 1264, 1265, 1266, 1267, 1268, 1269, 127, 1270, 1271, 1272, 1273, 1274, 1275, 1276, 1277, 1278, 1279, 128, 1280, 1281, 1282, 1283, 1284, 1285, 1286, 1287, 1288, 1289, 129, 1290, 1291, 1292, 1293, 1294, 1295, 1296, 1297, 1298, 1299, 13, 130, 1300, 1301, 1302, 1303, 1304, 1305, 1306, 1307, 1308, 1309, 131, 1310, 1311, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 132, 1320, 1321, 1322, 1323, 1324, 1325, 1326, 1327, 1328, 1329, 133, 1330, 1331, 1332, 1333, 1334, 1335, 1336, 1337, 1338, 1339, 134, 1340, 1341, 1342, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 135, 1350, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1359, 136, 1360, 1361, 1362, 1363, 1364, 1365, 1366, 1367, 1368, 1369, 137, 1370, 1371, 1372, 1373, 1374, 1375, 1376, 1377, 1378, 1379, 138, 1380, 1381, 1382, 1383, 1384, 1385, 1386, 1387, 1388, 1389, 139, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 14, 140, 1400, 1401, 1402, 1403, 1404, 1405, 1406, 1407, 1408, 1409, 141, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 142, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 143, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 144, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 145, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 146, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 147, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 148, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 149, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 15, 150, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 151, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 152, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 153, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 154, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 155, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 156, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 157, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 158, 1580, 1581, 1582, 1583, 1584, 1585, 1586, 1587, 1588, 1589, 159, 1590, 1591, 1592, 1593, 1594, 1595, 1596, 1597, 1598, 1599, 16, 160, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 161, 1610, 1611, 1612, 1613, 1614, 1615, 1616, 1617, 1618, 1619, 162, 1620, 1621, 1622, 1623, 1624, 1625, 1626, 1627, 1628, 1629, 163, 1630, 1631, 1632, 1633, 1634, 1635, 1636, 1637, 1638, 1639, 164, 1640, 1641, 1642, 1643, 1644, 1645, 1646, 1647, 1648, 1649, 165, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1658, 1659, 166, 1660, 1661, 1662, 1663, 1664, 1665, 1666, 1667, 1668, 1669, 167, 1670, 1671, 1672, 1673, 1674, 1675, 1676, 1677, 1678, 1679, 168, 1680, 1681, 1682, 1683, 1684, 1685, 1686, 1687, 1688, 1689, 169, 1690, 1691, 1692, 1693, 1694, 1695, 1696, 1697, 1698, 1699, 17, 170, 1700, 1701, 1702, 1703, 1704, 1705, 1706, 1707, 1708, 1709, 171, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 1717, 1718, 1719, 172, 1720, 1721, 1722, 1723, 1724, 1725, 1726, 1727, 1728, 1729, 173, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 174, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 175, 1750, 1751, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 176, 1760, 1761, 1762, 1763, 1764, 1765, 1766, 1767, 1768, 1769, 177, 1770, 1771, 1772, 1773, 1774, 1775, 1776, 1777, 1778, 1779, 178, 1780, 1781, 1782, 1783, 1784, 1785, 1786, 1787, 1788, 1789, 179, 1790, 1791, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 18, 180, 1800, 1801, 1802, 1803, 1804, 1805, 1806, 1807, 1808, 1809, 181, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 1819, 182, 1820, 1821, 1822, 1823, 1824, 1825, 1826, 1827, 1828, 1829, 183, 1830, 1831, 1832, 1833, 1834, 1835, 1836, 1837, 1838, 1839, 184, 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 185, 1850, 1851, 1852, 1853, 1854, 1855, 1856, 1857, 1858, 1859, 186, 1860, 1861, 1862, 1863, 1864, 1865, 1866, 1867, 1868, 1869, 187, 1870, 1871, 1872, 1873, 1874, 1875, 1876, 1877, 1878, 1879, 188, 1880, 1881, 1882, 1883, 1884, 1885, 1886, 1887, 1888, 1889, 189, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 19, 190, 1900, 1901, 1902, 1903, 1904, 1905, 1906, 1907, 1908, 1909, 191, 1910, 1911, 1912, 1913, 1914, 1915, 1916, 1917, 1918, 1919, 192, 1920, 1921, 1922, 1923, 1924, 1925, 1926, 1927, 1928, 1929, 193, 1930, 1931, 1932, 1933, 1934, 1935, 1936, 1937, 1938, 1939, 194, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1947, 1948, 1949, 195, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 196, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 197, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 198, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 199, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2, 20, 200, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 201, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 202, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 203, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 204, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 205, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 206, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 207, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 208, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 209, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 21, 210, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 211, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 212, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 213, 2130, 2131, 2132, 2133, 2134, 2135, 2136, 2137, 2138, 2139, 214, 2140, 2141, 2142, 2143, 2144, 2145, 2146, 2147, 2148, 2149, 215, 2150, 2151, 2152, 2153, 2154, 2155, 2156, 2157, 2158, 2159, 216, 2160, 2161, 2162, 2163, 2164, 2165, 2166, 2167, 2168, 2169, 217, 2170, 2171, 2172, 2173, 2174, 2175, 2176, 2177, 2178, 2179, 218, 2180, 2181, 2182, 2183, 2184, 2185, 2186, 2187, 2188, 2189, 219, 2190, 2191, 2192, 2193, 2194, 2195, 2196, 2197, 2198, 2199, 22, 220, 2200, 2201, 2202, 2203, 2204, 2205, 2206, 2207, 2208, 2209, 221, 2210, 2211, 2212, 2213, 2214, 2215, 2216, 2217, 2218, 2219, 222, 2220, 2221, 2222, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 223, 2230, 2231, 2232, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 224, 2240, 2241, 2242, 2243, 2244, 2245, 2246, 2247, 2248, 2249, 225, 2250, 2251, 2252, 2253, 2254, 2255, 2256, 2257, 2258, 2259, 226, 2260, 2261, 2262, 2263, 2264, 2265, 2266, 2267, 2268, 2269, 227, 2270, 2271, 2272, 2273, 2274, 2275, 2276, 2277, 2278, 2279, 228, 2280, 2281, 2282, 2283, 2284, 2285, 2286, 2287, 2288, 2289, 229, 2290, 2291, 2292, 2293, 2294, 2295, 2296, 2297, 2298, 2299, 23, 230, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2309, 231, 2310, 2311, 2312, 2313, 2314, 2315, 2316, 2317, 2318, 2319, 232, 2320, 2321, 2322, 2323, 2324, 2325, 2326, 2327, 2328, 2329, 233, 2330, 2331, 2332, 2333, 2334, 2335, 2336, 2337, 2338, 2339, 234, 2340, 2341, 2342, 2343, 2344, 2345, 2346, 2347, 2348, 2349, 235, 2350, 2351, 2352, 2353, 2354, 2355, 2356, 2357, 2358, 2359, 236, 2360, 2361, 2362, 2363, 2364, 2365, 2366, 2367, 2368, 2369, 237, 2370, 2371, 2372, 2373, 2374, 2375, 2376, 2377, 2378, 2379, 238, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387, 2388, 2389, 239, 2390, 2391, 2392, 2393, 2394, 2395, 2396, 2397, 2398, 2399, 24, 240, 2400, 2401, 2402, 2403, 2404, 2405, 2406, 2407, 2408, 2409, 241, 2410, 2411, 2412, 2413, 2414, 2415, 2416, 2417, 2418, 2419, 242, 2420, 2421, 2422, 2423, 2424, 2425, 2426, 2427, 2428, 2429, 243, 2430, 2431, 2432, 2433, 2434, 2435, 2436, 2437, 2438, 2439, 244, 2440, 2441, 2442, 2443, 2444, 2445, 2446, 2447, 2448, 2449, 245, 2450, 2451, 2452, 2453, 2454, 2455, 2456, 2457, 2458, 2459, 246, 2460, 2461, 2462, 2463, 2464, 2465, 2466, 2467, 2468, 2469, 247, 2470, 2471, 2472, 2473, 2474, 2475, 2476, 2477, 2478, 2479, 248, 2480, 2481, 2482, 2483, 2484, 2485, 2486, 2487, 2488, 2489, 249, 2490, 2491, 2492, 2493, 2494, 2495, 2496, 2497, 2498, 2499, 25, 250, 2500, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 51, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 52, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 53, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 54, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 55, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 56, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 57, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 58, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 59, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 6, 60, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 61, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 62, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 63, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 64, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 65, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 66, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 67, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 68, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 69, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 7, 70, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 71, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 72, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 73, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 74, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 75, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 76, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 77, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 78, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 79, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 8, 80, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 81, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 82, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 83, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 84, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 85, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 86, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 87, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 88, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 89, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 9, 90, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 91, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 92, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 93, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 94, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 95, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 96, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 97, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 98, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 99, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n assert candidate(n = 200) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 109) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 199) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n assert candidate(n = 500) == [1, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 13, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 14, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 15, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 16, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 17, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 18, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 19, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 2, 20, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 21, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 23, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 24, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 25, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 26, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 27, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 28, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 29, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 3, 30, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 31, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 32, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 33, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 34, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 35, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 36, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 37, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 38, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 39, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 4, 40, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 41, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 42, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 43, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 44, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 45, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 46, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 47, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 48, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 49, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 5, 50, 500, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().lexicalOrder", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var lexicalOrder = function(n) {", "container": null, "callable": "lexicalOrder", "parameters": [{"name": "n", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 387, "task_id": "first-unique-character-in-a-string", "difficulty": "Easy", "problem_description": "Given a string s, find the first non-repeating character in it and return its index. If it does not exist, return -1.\n \nExample 1:\n\nInput: s = \"leetcode\"\nOutput: 0\nExplanation:\nThe character 'l' at index 0 is the first character that does not occur at any other index.\n\nExample 2:\n\nInput: s = \"loveleetcode\"\nOutput: 2\n\nExample 3:\n\nInput: s = \"aabb\"\nOutput: -1\n\n \nConstraints:\n\n1 <= s.length <= 105\ns consists of only lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aabbbccccddeeeeeffffffgggggghhhhhhiiiiiiiijjjjjjjjjkkkkkkkkkkklllllllllllllmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnooooooooollllllllllllllllmmmmmmmmmmmmmmmmmnnnnnnnnnnnnnnnnnp\") == 165\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 0\n assert candidate(s = \"abcdef\") == 0\n assert candidate(s = \"aabbccddee\") == -1\n assert candidate(s = \"a\") == 0\n assert candidate(s = \"abacabadabacaba\") == 7\n assert candidate(s = \"abcdabcde\") == 8\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == -1\n assert candidate(s = \"swiss\") == 1\n assert candidate(s = \"abacabadabc\") == 7\n assert candidate(s = \"\") == -1\n assert candidate(s = \"repetition\") == 0\n assert candidate(s = \"zzz\") == -1\n assert candidate(s = \"aabbccddeeffg\") == 12\n assert candidate(s = \"leetcode\") == 0\n assert candidate(s = \"aabb\") == -1\n assert candidate(s = \"loveleetcode\") == 2\n assert candidate(s = \"abcdabcdf\") == 8\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\") == -1\n assert candidate(s = \"development\") == 0\n assert candidate(s = \"aabbcceeff\") == -1\n assert candidate(s = \"zzyyxxwwvvuuttrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == -1\n assert candidate(s = \"algorithm\") == 0\n assert candidate(s = \"unique\") == 1\n assert candidate(s = \"z\") == 0\n assert candidate(s = \"abbacd\") == 4\n assert candidate(s = \"aabbcceeffgghhiijjklmnopqrstuvwxyz\") == 18\n assert candidate(s = \"character\") == 1\n assert candidate(s = \"bba\") == 2\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 0\n assert candidate(s = \"abcdefg\") == 0\n assert candidate(s = \"thisisjustafancysentence\") == 1\n assert candidate(s = \"almostunique\") == 0\n assert candidate(s = \"repetitionsofletters\") == 2\n assert candidate(s = \"abacabadabacabadabacabad\") == -1\n assert candidate(s = \"xyzzyzxyz\") == -1\n assert candidate(s = \"almosteverycharacterisunique\") == 1\n assert candidate(s = \"uniquecharactersarecool\") == 1\n assert candidate(s = \"abcdedcba\") == 4\n assert candidate(s = \"verylongstringwithmanyanonymouscharacterssssssssssssssssssssssss\") == 0\n assert candidate(s = \"uniqueidentifier\") == 3\n assert candidate(s = \"abracadabra\") == 4\n assert candidate(s = \"allcharactersrepeatmorethanonce\") == 12\n assert candidate(s = \"abacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabadabacabad\") == -1\n assert candidate(s = \"xylophone\") == 0\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == -1\n assert candidate(s = \"unrepeatedcharacterstring\") == 0\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzyxwvutsrqponmlkjihgfedcba\") == -1\n assert candidate(s = \"bbaaccddeeffgghhiijjkkllmmnnoopqrrssttuuvvwwxxyyzz\") == 30\n assert candidate(s = \"zzzzzyyyyxxxxwwvvvttrrssqqppoonnmmlkkjjiihhggffeedcba\") == 34\n assert candidate(s = \"thisisaverylongstringwithnomanynonrepeatingcharacters\") == 7\n assert candidate(s = \"xyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 0\n assert candidate(s = \"firstuniquicharacter\") == 0\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyz\") == 50\n assert candidate(s = \"nocharactersrepeat\") == 0\n assert candidate(s = \"wovwovwov\") == -1\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == -1\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == -1\n assert candidate(s = \"abcdefghijabcdefghijabcdefghij\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzz\") == -1\n assert candidate(s = \"aabbaaccddeeffaabbccddeeffaabbccddeeff\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwooxxyyzz\") == -1\n assert candidate(s = \"banana\") == 0\n assert candidate(s = \"thisisaverylongstringwithseveralcharacters\") == 10\n assert candidate(s = \"aaaaabbbbbcccccdddddeeeeefffffggggghhhhiiiiijjjjkkkkklllllmmmmmnnnnnooooo\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwxyzz\") == 44\n assert candidate(s = \"s\") == 0\n assert candidate(s = \"swissknife\") == 1\n assert candidate(s = \"abacaxabacayabacaza\") == 5\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwxyz\") == 44\n assert candidate(s = \"thisproblemhasaveryunusalcharacterdistribution\") == 4\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzz\") == -1\n assert candidate(s = \"aabbcdeef\") == 4\n assert candidate(s = \"aabbcdeeffgg\") == 4\n assert candidate(s = \"abcdefghijhgfedcba\") == 8\n assert candidate(s = \"single\") == 0\n assert candidate(s = \"uniquecharacter\") == 1\n assert candidate(s = \"mississippi\") == 0\n assert candidate(s = \"hashmapimplementation\") == 2\n assert candidate(s = \"abcdabcdbacd\") == -1\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == -1\n assert candidate(s = \"supercalifragilisticexpialidocious\") == 9\n assert candidate(s = \"firstnonrepeatingcharacter\") == 0\n assert candidate(s = \"zzzzyyyyyxxxxxwwwwvvvvuuuuttttssssrrrrqqqqpppooooonnnnmmmmllllkkkkjjjjiiiihhhhggggffffeeeeddddccccbbbbaaaa\") == -1\n assert candidate(s = \"onlyonecharacterrepeats\") == 2\n assert candidate(s = \"ababababababababababababababababababab\") == -1\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwooxxyyzzzz\") == -1\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\") == 3\n assert candidate(s = \"bbaaccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzza\") == -1\n assert candidate(s = \"almostuniquecharacter\") == 1\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().firstUniqChar", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var firstUniqChar = function(s) {", "container": null, "callable": "firstUniqChar", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 388, "task_id": "longest-absolute-file-path", "difficulty": "Medium", "problem_description": "Suppose we have a file system that stores both files and directories. An example of one system is represented in the following picture:\n\nHere, we have dir as the only directory in the root. dir contains two subdirectories, subdir1 and subdir2. subdir1 contains a file file1.ext and subdirectory subsubdir1. subdir2 contains a subdirectory subsubdir2, which contains a file file2.ext.\nIn text form, it looks like this (with ⟶ representing the tab character):\n\ndir\n⟶ subdir1\n⟶ ⟶ file1.ext\n⟶ ⟶ subsubdir1\n⟶ subdir2\n⟶ ⟶ subsubdir2\n⟶ ⟶ ⟶ file2.ext\n\nIf we were to write this representation in code, it will look like this: \"dir\\n\\tsubdir1\\n\\t\\tfile1.ext\\n\\t\\tsubsubdir1\\n\\tsubdir2\\n\\t\\tsubsubdir2\\n\\t\\t\\tfile2.ext\". Note that the '\\n' and '\\t' are the new-line and tab characters.\nEvery file and directory has a unique absolute path in the file system, which is the order of directories that must be opened to reach the file/directory itself, all concatenated by '/'s. Using the above example, the absolute path to file2.ext is \"dir/subdir2/subsubdir2/file2.ext\". Each directory name consists of letters, digits, and/or spaces. Each file name is of the form name.extension, where name and extension consist of letters, digits, and/or spaces.\nGiven a string input representing the file system in the explained format, return the length of the longest absolute path to a file in the abstracted file system. If there is no file in the system, return 0.\nNote that the testcases are generated such that the file system is valid and no file or directory name has length 0.\n \nExample 1:\n\n\nInput: input = \"dir\\n\\tsubdir1\\n\\tsubdir2\\n\\t\\tfile.ext\"\nOutput: 20\nExplanation: We have only one file, and the absolute path is \"dir/subdir2/file.ext\" of length 20.\n\nExample 2:\n\n\nInput: input = \"dir\\n\\tsubdir1\\n\\t\\tfile1.ext\\n\\t\\tsubsubdir1\\n\\tsubdir2\\n\\t\\tsubsubdir2\\n\\t\\t\\tfile2.ext\"\nOutput: 32\nExplanation: We have two files:\n\"dir/subdir1/file1.ext\" of length 21\n\"dir/subdir2/subsubdir2/file2.ext\" of length 32.\nWe return 32 since it is the longest absolute path to a file.\n\nExample 3:\n\nInput: input = \"a\"\nOutput: 0\nExplanation: We do not have any files, just a single directory named \"a\".\n\n \nConstraints:\n\n1 <= input.length <= 104\ninput may contain lowercase or uppercase English letters, a new line character '\\n', a tab character '\\t', a dot '.', a space ' ', and digits.\nAll file and directory names have positive length.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(input = \"dir\\n\\tsubdir1\\n\\tsubdir2\\n\\t\\tfile.ext\") == 20\n assert candidate(input = \"dir\\n\\tsubdir1\\n\\t\\tfile1.ext\\n\\t\\tsubsubdir1\\n\\tsubdir2\\n\\t\\tsubsubdir2\\n\\t\\t\\tfile2.ext\") == 32\n assert candidate(input = \"a\") == 0\n assert candidate(input = \"file1.txt\\nfile2.txt\\nlongfile.txt\") == 12\n"}, "metadata": {"canonical_parameter_names": ["input"], "leetcode_dataset_entry_point": "Solution().lengthLongestPath", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var lengthLongestPath = function(input) {", "container": null, "callable": "lengthLongestPath", "parameters": [{"name": "input", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 389, "task_id": "find-the-difference", "difficulty": "Easy", "problem_description": "You are given two strings s and t.\nString t is generated by random shuffling string s and then add one more letter at a random position.\nReturn the letter that was added to t.\n \nExample 1:\n\nInput: s = \"abcd\", t = \"abcde\"\nOutput: \"e\"\nExplanation: 'e' is the letter that was added.\n\nExample 2:\n\nInput: s = \"\", t = \"y\"\nOutput: \"y\"\n\n \nConstraints:\n\n0 <= s.length <= 1000\nt.length == s.length + 1\ns and t consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcd\",t = \"abcde\") == \"e\"\n assert candidate(s = \"aeiou\",t = \"aeiouf\") == \"f\"\n assert candidate(s = \"python\",t = \"ypthon\") == None\n assert candidate(s = \"abcdxyz\",t = \"abcdzyxw\") == \"w\"\n assert candidate(s = \"a\",t = \"ab\") == \"b\"\n assert candidate(s = \"xyz\",t = \"zyxw\") == \"w\"\n assert candidate(s = \"\",t = \"y\") == \"y\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyza\") == \"a\"\n assert candidate(s = \"hello\",t = \"helloa\") == \"a\"\n assert candidate(s = \"hello\",t = \"hleloa\") == \"a\"\n assert candidate(s = \"aeiou\",t = \"aeiozu\") == \"z\"\n assert candidate(s = \"hello\",t = \"ohell\") == None\n assert candidate(s = \"ae\",t = \"aea\") == \"a\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzp\") == \"p\"\n assert candidate(s = \"thisisaverylongstringfortesting\",t = \"thisisaverylongstringfortestingz\") == \"z\"\n assert candidate(s = \"thisisaverylongstringwithalotofcharacters\",t = \"thisisaverylongstringwithalotofcharactersz\") == \"z\"\n assert candidate(s = \"almostsame\",t = \"almostsamee\") == \"e\"\n assert candidate(s = \"abcdabcdabcdabcdabcdabcd\",t = \"abcdabcdabcdabcdabcdabcde\") == \"e\"\n assert candidate(s = \"thisisaverylongstringwithsomerepeatingcharacters\",t = \"thisisaverylongstringwithsomerepeatingcharactersist\") == \"i\"\n assert candidate(s = \"sameletters\",t = \"samesletters\") == \"s\"\n assert candidate(s = \"mississippi\",t = \"mississippix\") == \"x\"\n assert candidate(s = \"thisisaverylongstringthatcontainsavarietyofcharacters\",t = \"thisisaverylongstringthatcontainsavarietyofcharactorst\") == \"o\"\n assert candidate(s = \"mississippi\",t = \"mississippiw\") == \"w\"\n assert candidate(s = \"samechar\",t = \"samechars\") == \"s\"\n assert candidate(s = \"quickbrownfoxjumps\",t = \"quickbrownfoxjumpsl\") == \"l\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammingz\") == \"z\"\n assert candidate(s = \"singlecharacter\",t = \"singlecharacterr\") == \"r\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzj\") == \"j\"\n assert candidate(s = \"abcdabcdabcd\",t = \"abcdabcdabcdd\") == \"d\"\n assert candidate(s = \"uniqueletters\",t = \"uniquelettersx\") == \"x\"\n assert candidate(s = \"xyzzzxyzzz\",t = \"xyzzzxyzzzx\") == \"x\"\n assert candidate(s = \"alibabacloud\",t = \"alibabacloudu\") == \"u\"\n assert candidate(s = \"xyxzyzy\",t = \"xyxzyzyz\") == \"z\"\n assert candidate(s = \"abcdabcdabcd\",t = \"abcdabcdabcdx\") == \"x\"\n assert candidate(s = \"different\",t = \"differenti\") == \"i\"\n assert candidate(s = \"finding\",t = \"findinwg\") == \"w\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzx\") == \"x\"\n assert candidate(s = \"onemore\",t = \"onemroem\") == \"m\"\n assert candidate(s = \"hellothereeveryone\",t = \"hellothereeveryonex\") == \"x\"\n assert candidate(s = \"mississippi\",t = \"mississippip\") == \"p\"\n assert candidate(s = \"pneumonoultramicroscopicsilicovolcanoconiosis\",t = \"pneumonoultramicroscopicsilicovolcanoconiosisp\") == \"p\"\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydogg\") == \"g\"\n assert candidate(s = \"hellothisisanexample\",t = \"thisisanexamplehelloo\") == \"o\"\n assert candidate(s = \"short\",t = \"horst\") == None\n assert candidate(s = \"abracadabra\",t = \"abracadabrak\") == \"k\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammings\") == \"s\"\n assert candidate(s = \"mamamamamamama\",t = \"mmamamamamamama\") == \"m\"\n assert candidate(s = \"qwert\",t = \"wqret\") == None\n assert candidate(s = \"repeatedcharactershhhhh\",t = \"repeatedcharactershhhhha\") == \"a\"\n assert candidate(s = \"abcdabcdabcd\",t = \"abcdabcdabcde\") == \"e\"\n assert candidate(s = \"abcdabcd\",t = \"abcdabcde\") == \"e\"\n assert candidate(s = \"uniqueletters\",t = \"enuiqtelrstsu\") == \"s\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzaaa\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzaaab\") == \"b\"\n assert candidate(s = \"uniquecharacters\",t = \"uniquecharactersn\") == \"n\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",t = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"qwertypoiuytrewq\",t = \"qwertypoiuytrewqa\") == \"a\"\n assert candidate(s = \"abcdefghijklnmopqrstuvwxyz\",t = \"zyxwvutsrqponmlkjihgfedcbaq\") == \"q\"\n assert candidate(s = \"samecharacters\",t = \"samecharactersc\") == \"c\"\n assert candidate(s = \"specialcharacters!@#$%^&*()\",t = \"specialcharacters!@#$%^&*()s\") == \"s\"\n assert candidate(s = \"repeatedletters\",t = \"repeadetletters\") == None\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzz\") == \"z\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzq\") == \"q\"\n assert candidate(s = \"onetwothree\",t = \"onetwothreefour\") == \"f\"\n assert candidate(s = \"short\",t = \"shorrt\") == \"r\"\n assert candidate(s = \"uniqueletters\",t = \"eniqulettersu\") == None\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydogq\") == \"q\"\n assert candidate(s = \"onetwothree\",t = \"onetwothreef\") == \"f\"\n assert candidate(s = \"hellothere\",t = \"hellotherex\") == \"x\"\n assert candidate(s = \"uniqueletter\",t = \"uniqueletteru\") == \"u\"\n assert candidate(s = \"uniqueletters\",t = \"enuiqueletters\") == \"e\"\n assert candidate(s = \"thisisalongstring\",t = \"thisisalongstringx\") == \"x\"\n assert candidate(s = \"nogapsbetweenletters\",t = \"nogapsbetweenlettersn\") == \"n\"\n assert candidate(s = \"abcdefg\",t = \"gfedcbaa\") == \"a\"\n assert candidate(s = \"repeated\",t = \"repeatedr\") == \"r\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammingg\") == \"g\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzb\") == \"b\"\n assert candidate(s = \"balloon\",t = \"ooblaanl\") == \"a\"\n assert candidate(s = \"sameletters\",t = \"smaleetters\") == None\n assert candidate(s = \"randomstring\",t = \"randomstrings\") == \"s\"\n assert candidate(s = \"uniqueletters\",t = \"uniqueletterst\") == \"t\"\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",t = \"thequickbrownfoxjumpsoverthelazydoga\") == \"a\"\n assert candidate(s = \"xyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxz\",t = \"xyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzj\") == \"j\"\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",t = \"quickbrownfoxjumpsoverthelazydogm\") == \"m\"\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",t = \"thequickbrownfoxjumpsoverthelazydogp\") == \"p\"\n assert candidate(s = \"xyzz\",t = \"xyzzz\") == \"z\"\n assert candidate(s = \"repeatedlettersinthisstring\",t = \"repeatedlettersinthisstringi\") == \"i\"\n assert candidate(s = \"aaaabbbbccccddddeee\",t = \"aaaabbbbccccddddeeef\") == \"f\"\n assert candidate(s = \"zzzzzzzzzz\",t = \"zzzzzzzzzzz\") == \"z\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzz\") == \"z\"\n assert candidate(s = \"thesameletterrepeatedseveraltime\",t = \"thesameletterrepeatedseveraltimee\") == \"e\"\n assert candidate(s = \"duplicatecharacters\",t = \"duplicatecharacterst\") == \"t\"\n assert candidate(s = \"complexinputwithdifferentcharacters\",t = \"complexinputwithdifferentcharactersg\") == \"g\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",t = \"abcdefghijklmnopqrstuvwxyzx\") == \"x\"\n assert candidate(s = \"pythonprogramming\",t = \"pythonprogrammingo\") == \"o\"\n assert candidate(s = \"xyzz\",t = \"xyzzy\") == \"y\"\n"}, "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().findTheDifference", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findTheDifference = function(s, t) {", "container": null, "callable": "findTheDifference", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "character", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 390, "task_id": "elimination-game", "difficulty": "Medium", "problem_description": "You have a list arr of all integers in the range [1, n] sorted in a strictly increasing order. Apply the following algorithm on arr:\n\nStarting from left to right, remove the first number and every other number afterward until you reach the end of the list.\nRepeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.\nKeep repeating the steps again, alternating left to right and right to left, until a single number remains.\n\nGiven the integer n, return the last number that remains in arr.\n \nExample 1:\n\nInput: n = 9\nOutput: 6\nExplanation:\narr = [1, 2, 3, 4, 5, 6, 7, 8, 9]\narr = [2, 4, 6, 8]\narr = [2, 6]\narr = [6]\n\nExample 2:\n\nInput: n = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= n <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 11) == 8\n assert candidate(n = 100) == 54\n assert candidate(n = 9) == 6\n assert candidate(n = 1000000) == 481110\n assert candidate(n = 2) == 2\n assert candidate(n = 20) == 6\n assert candidate(n = 1) == 1\n assert candidate(n = 1000000000) == 534765398\n assert candidate(n = 1000) == 510\n assert candidate(n = 10) == 8\n assert candidate(n = 25) == 14\n assert candidate(n = 244140) == 130558\n assert candidate(n = 15258) == 8160\n assert candidate(n = 3) == 2\n assert candidate(n = 3814) == 2040\n assert candidate(n = 119) == 56\n assert candidate(n = 29) == 14\n assert candidate(n = 999999999) == 534765056\n assert candidate(n = 12345) == 5502\n assert candidate(n = 4096) == 1366\n assert candidate(n = 976562) == 522232\n assert candidate(n = 1953125) == 908662\n assert candidate(n = 50) == 24\n assert candidate(n = 2047) == 1024\n assert candidate(n = 16383) == 8192\n assert candidate(n = 5) == 2\n assert candidate(n = 10001) == 5974\n assert candidate(n = 16384) == 5462\n assert candidate(n = 59) == 32\n assert candidate(n = 250000000) == 133691350\n assert candidate(n = 238) == 128\n assert candidate(n = 4) == 2\n assert candidate(n = 125000000) == 58154326\n assert candidate(n = 10000) == 5974\n assert candidate(n = 1001) == 510\n assert candidate(n = 15625000) == 8355710\n assert candidate(n = 7812500) == 3634646\n assert candidate(n = 62500000) == 33422838\n assert candidate(n = 122070) == 56792\n assert candidate(n = 50000000) == 33551830\n assert candidate(n = 128) == 86\n assert candidate(n = 1024) == 342\n assert candidate(n = 101) == 54\n assert candidate(n = 10000000) == 6150102\n assert candidate(n = 61035) == 32640\n assert candidate(n = 100000) == 55286\n assert candidate(n = 2048) == 1366\n assert candidate(n = 1048576) == 349526\n assert candidate(n = 999) == 504\n assert candidate(n = 953) == 510\n assert candidate(n = 3906250) == 2088928\n assert candidate(n = 8192) == 5462\n assert candidate(n = 30517) == 14198\n assert candidate(n = 65536) == 21846\n assert candidate(n = 5000) == 2014\n assert candidate(n = 7629) == 3550\n assert candidate(n = 256) == 86\n assert candidate(n = 1023) == 512\n assert candidate(n = 9999) == 5984\n assert candidate(n = 31250000) == 14538582\n assert candidate(n = 476) == 222\n assert candidate(n = 1000000001) == 534765398\n assert candidate(n = 127) == 64\n assert candidate(n = 987654321) == 534740470\n assert candidate(n = 5000000) == 1924950\n assert candidate(n = 500000) == 259446\n assert candidate(n = 488281) == 227166\n assert candidate(n = 98765) == 54750\n assert candidate(n = 500000000) == 232617302\n assert candidate(n = 31) == 16\n assert candidate(n = 1000001) == 481110\n assert candidate(n = 14) == 8\n assert candidate(n = 512) == 342\n assert candidate(n = 999999) == 481152\n assert candidate(n = 123456) == 63318\n assert candidate(n = 500) == 246\n assert candidate(n = 1907) == 888\n assert candidate(n = 7) == 4\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().lastRemaining", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var lastRemaining = function(n) {", "container": null, "callable": "lastRemaining", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 391, "task_id": "perfect-rectangle", "difficulty": "Hard", "problem_description": "Given an array rectangles where rectangles[i] = [xi, yi, ai, bi] represents an axis-aligned rectangle. The bottom-left point of the rectangle is (xi, yi) and the top-right point of it is (ai, bi).\nReturn true if all the rectangles together form an exact cover of a rectangular region.\n \nExample 1:\n\n\nInput: rectangles = [[1,1,3,3],[3,1,4,2],[3,2,4,4],[1,3,2,4],[2,3,3,4]]\nOutput: true\nExplanation: All 5 rectangles together form an exact cover of a rectangular region.\n\nExample 2:\n\n\nInput: rectangles = [[1,1,2,3],[1,3,2,4],[3,1,4,2],[3,2,4,4]]\nOutput: false\nExplanation: Because there is a gap between the two rectangular regions.\n\nExample 3:\n\n\nInput: rectangles = [[1,1,3,3],[3,1,4,2],[1,3,2,4],[2,2,4,4]]\nOutput: false\nExplanation: Because two of the rectangles overlap with each other.\n\n \nConstraints:\n\n1 <= rectangles.length <= 2 * 104\nrectangles[i].length == 4\n-105 <= xi < ai <= 105\n-105 <= yi < bi <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 3, 2], [1, 0, 2, 2]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 4, 2], [3, 2, 4, 4], [1, 3, 2, 4], [2, 3, 3, 4]]) == True\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 2, 4, 4], [2, 0, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 0, 4, 2], [0, 2, 2, 4], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 4], [3, 1, 4, 2], [3, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2]]) == True\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 4, 2], [1, 3, 2, 4], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [2, 2, 4, 4], [3, 3, 5, 5], [4, 4, 6, 6], [5, 5, 7, 7], [6, 6, 8, 8], [7, 7, 9, 9], [8, 8, 10, 10]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [5, 0, 10, 5], [0, 5, 5, 10], [5, 5, 10, 10], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [2, 2, 3, 3], [3, 2, 4, 3], [2, 3, 3, 4], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 3], [0, 3, 1, 4], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [0, 4, 3, 5]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 4, 4], [2, 2, 5, 5], [3, 3, 6, 6], [4, 4, 7, 7], [5, 5, 8, 8], [6, 6, 9, 9], [7, 7, 10, 10]]) == False\n assert candidate(rectangles = [[1, 1, 11, 11], [2, 2, 10, 10], [3, 3, 9, 9], [4, 4, 8, 8], [5, 5, 7, 7], [6, 6, 7, 7], [6, 6, 7, 7], [7, 7, 8, 8]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [0, -1, 1, 0]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 9, 9], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [5, 5, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [2, 1, 3, 2]]) == False\n assert candidate(rectangles = [[-10, -10, 10, 10], [0, 0, 5, 5], [5, 5, 10, 10], [-10, 0, -5, 5], [-5, 0, 0, 5]]) == False\n assert candidate(rectangles = [[1, 1, 10, 10], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [1, 5, 5, 10], [5, 1, 10, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [2, 0, 3, 2], [3, 0, 4, 2], [0, 2, 4, 3]]) == True\n assert candidate(rectangles = [[1, 1, 4, 4], [2, 2, 3, 3], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [2, 1, 3, 2], [0, 2, 1, 3], [1, 2, 2, 3], [2, 2, 3, 3]]) == True\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 3, 3], [3, 1, 5, 3], [5, 1, 7, 3], [7, 1, 9, 3], [1, 3, 3, 5], [3, 3, 5, 5], [5, 3, 7, 5], [7, 3, 9, 5], [1, 5, 3, 7], [3, 5, 5, 7], [5, 5, 7, 7], [7, 5, 9, 7], [1, 7, 3, 9], [3, 7, 5, 9], [5, 7, 7, 9], [7, 7, 9, 9]]) == False\n assert candidate(rectangles = [[-10, -10, -5, -5], [-5, -5, 0, 0], [0, 0, 5, 5], [5, 5, 10, 10], [-10, 0, -5, 5], [-5, 0, 0, 5], [0, 0, 5, 10], [5, 0, 10, 10], [-10, 5, -5, 10], [-5, 5, 0, 10], [0, 5, 5, 15], [5, 5, 10, 15]]) == False\n assert candidate(rectangles = [[0, 0, 6, 6], [1, 1, 5, 5], [2, 2, 4, 4], [3, 3, 5, 5], [1, 2, 5, 3], [2, 1, 4, 5], [2, 3, 5, 4]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 5, 3], [1, 3, 5, 5], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [0, 4, 2, 6], [2, 0, 4, 2], [2, 2, 4, 4], [2, 4, 4, 6]]) == True\n assert candidate(rectangles = [[-2, -2, 0, 0], [0, 0, 2, 2], [2, 2, 4, 4], [-2, 2, 0, 4], [0, -2, 2, 0], [2, -2, 4, 0]]) == False\n assert candidate(rectangles = [[-100000, -100000, 100000, 100000]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 2, 2], [0, 0, 4, 4], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [1, 3, 3, 5], [3, 1, 5, 3], [3, 3, 5, 5], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[-2, -2, 3, 3], [1, 1, 4, 4], [0, 0, 1, 1], [3, 3, 4, 4], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 9, 9], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [5, 5, 5, 5], [0, 10, 10, 11], [0, 11, 10, 12], [0, 12, 10, 13]]) == False\n assert candidate(rectangles = [[1, 1, 3, 3], [3, 1, 5, 3], [1, 3, 3, 5], [3, 3, 5, 5], [1, 1, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 4, 4], [2, 2, 3, 3], [5, 5, 8, 8], [6, 6, 7, 7], [1, 5, 4, 8], [5, 1, 8, 4], [2, 6, 3, 7], [6, 2, 7, 3]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 2, 2], [0, 0, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4], [0, 4, 2, 6], [2, 4, 4, 6], [0, 6, 4, 8]]) == True\n assert candidate(rectangles = [[-100000, -100000, 100000, 100000], [0, 0, 1, 1]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [0, 5, 2, 7], [2, 5, 5, 7], [2, 2, 3, 3], [3, 2, 5, 2]]) == False\n assert candidate(rectangles = [[-1, -1, 1, 1], [-1, 1, 1, 3], [1, -1, 3, 1], [1, 1, 3, 3]]) == True\n assert candidate(rectangles = [[0, 0, 5, 5], [1, 1, 2, 2], [3, 3, 4, 4], [2, 2, 3, 3], [0, 4, 5, 5], [4, 0, 5, 4]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [2, 1, 3, 2], [0, 2, 1, 3], [1, 2, 2, 3], [2, 2, 3, 3], [0, 0, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 5, 5], [1, 1, 4, 4], [2, 2, 3, 3], [0, 5, 5, 6], [5, 0, 6, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4]]) == True\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [-1, -1, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [1, 1, 3, 3], [2, 2, 4, 4], [3, 3, 5, 5], [4, 4, 6, 6], [5, 5, 7, 7], [6, 6, 8, 8], [7, 7, 9, 9]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 2], [0, 2, 2, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 1], [2, 0, 4, 1], [0, 1, 1, 2], [1, 1, 3, 2], [3, 1, 4, 2], [0, 2, 1, 3], [1, 2, 3, 3], [3, 2, 4, 3]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 0, 2, 2]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [2, 0, 4, 2], [0, 2, 2, 4], [2, 2, 4, 4], [1, 1, 3, 3], [1, 3, 3, 4], [3, 1, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 1000, 1000], [250, 250, 750, 750], [500, 500, 501, 501], [501, 501, 502, 502], [502, 502, 503, 503]]) == False\n assert candidate(rectangles = [[1, 1, 2, 2], [2, 2, 3, 3], [1, 2, 2, 3], [2, 1, 3, 2], [1, 3, 2, 4], [3, 1, 4, 2]]) == False\n assert candidate(rectangles = [[0, 0, 6, 6], [1, 1, 5, 5], [2, 2, 4, 4], [1, 2, 2, 3], [2, 1, 3, 2], [3, 3, 4, 4], [4, 4, 5, 5]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [2, 2, 4, 4], [3, 3, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [0, 0, 5, 5]]) == False\n assert candidate(rectangles = [[-2, -2, 2, 2], [-2, 2, 2, 4], [2, -2, 4, 2], [2, 2, 4, 4]]) == True\n assert candidate(rectangles = [[0, 0, 3, 3], [1, 1, 2, 2], [2, 2, 3, 3], [1, 2, 2, 3], [2, 1, 3, 2]]) == False\n assert candidate(rectangles = [[0, 0, 1, 3], [1, 0, 2, 3], [2, 0, 3, 3], [0, 3, 1, 6], [1, 3, 2, 6], [2, 3, 3, 6], [0, 6, 1, 9], [1, 6, 2, 9], [2, 6, 3, 9]]) == True\n assert candidate(rectangles = [[1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [1, 5, 2, 6], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [2, 4, 3, 5], [2, 5, 3, 6]]) == True\n assert candidate(rectangles = [[-1, -1, 1, 1], [-1, 1, 1, 3], [-1, -1, -1, 3], [-1, 1, -1, 3], [1, -1, 3, 1], [1, 1, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 0, 2, 3]]) == False\n assert candidate(rectangles = [[0, 0, 3, 3], [3, 0, 6, 3], [6, 0, 9, 3], [0, 3, 3, 6], [3, 3, 6, 6], [6, 3, 9, 6]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [0, 5, 5, 6]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3]]) == True\n assert candidate(rectangles = [[1, 1, 5, 5], [5, 5, 9, 9], [1, 5, 5, 9], [5, 1, 9, 5], [3, 3, 4, 4]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [1, 5, 3, 7], [3, 5, 5, 7], [1, 7, 3, 9], [3, 7, 5, 9]]) == True\n assert candidate(rectangles = [[0, 0, 10, 5], [0, 5, 10, 10], [0, 0, 5, 10], [5, 0, 10, 5], [5, 5, 10, 10]]) == False\n assert candidate(rectangles = [[-2, -2, 0, 0], [0, 0, 2, 2], [2, 2, 4, 4], [-2, 2, 0, 4], [-2, 4, 0, 6]]) == False\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 5], [2, 1, 3, 3], [2, 3, 3, 5], [3, 1, 4, 3], [3, 3, 4, 5], [4, 1, 5, 3], [4, 3, 5, 5]]) == True\n assert candidate(rectangles = [[0, 0, 4, 4], [1, 1, 3, 3], [2, 2, 4, 4], [0, 1, 1, 2], [1, 0, 2, 1]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 9, 9], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [5, 5, 5, 5], [6, 6, 4, 4], [7, 7, 3, 3], [8, 8, 2, 2], [9, 9, 1, 1]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 3, 2], [0, 2, 3, 3], [0, 3, 3, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [1, 0, 2, 1], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3], [0, 3, 1, 4], [1, 3, 2, 4]]) == True\n assert candidate(rectangles = [[0, 0, 1, 1], [0, 1, 1, 2], [0, 2, 1, 3], [0, 3, 1, 4], [0, 4, 1, 5], [1, 0, 2, 1], [1, 1, 2, 2], [1, 2, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [2, 0, 3, 1], [2, 1, 3, 2], [2, 2, 3, 3], [2, 3, 3, 4], [2, 4, 3, 5]]) == True\n assert candidate(rectangles = [[1, 1, 2, 2], [1, 2, 2, 3], [2, 1, 3, 2], [2, 2, 3, 3], [1.5, 1.5, 2.5, 2.5]]) == False\n assert candidate(rectangles = [[1, 1, 10, 10], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [5, 5, 5, 5]]) == False\n assert candidate(rectangles = [[0, 0, 1, 2], [1, 0, 2, 1], [2, 0, 3, 2], [0, 2, 3, 3], [0, 1, 3, 2]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [0, 0, 5, 5], [5, 0, 10, 5], [0, 5, 5, 10], [5, 5, 10, 10], [1, 1, 4, 4]]) == False\n assert candidate(rectangles = [[-100, -100, 100, 100], [0, 0, 200, 200], [50, 50, 150, 150], [100, 100, 200, 200]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 5, 5], [5, 5, 9, 9], [0, 5, 5, 10], [5, 0, 10, 5]]) == False\n assert candidate(rectangles = [[-2, -2, 2, 2], [-1, -1, 1, 1], [0, 0, 2, 2], [1, 1, 3, 3], [2, 2, 4, 4]]) == False\n assert candidate(rectangles = [[-5, -5, 5, 5], [0, 0, 3, 3], [3, 3, 6, 6], [-6, -6, -3, -3], [-3, -3, 0, 0]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [5, 5, 6, 6]]) == False\n assert candidate(rectangles = [[0, 0, 2, 1], [0, 1, 2, 2], [0, 2, 2, 3], [0, 3, 2, 4], [1, 0, 3, 1], [1, 1, 3, 2], [1, 2, 3, 3], [1, 3, 3, 4]]) == False\n assert candidate(rectangles = [[-5, -5, -3, -3], [-3, -3, 0, 0], [0, 0, 3, 3], [3, 3, 5, 5], [1, 1, 2, 2], [2, 2, 3, 3]]) == False\n assert candidate(rectangles = [[0, 0, 10, 10], [1, 1, 9, 9], [2, 2, 8, 8], [3, 3, 7, 7], [4, 4, 6, 6], [5, 5, 5, 5], [1, 4, 2, 5], [4, 1, 5, 2], [3, 6, 4, 7], [6, 3, 7, 4]]) == False\n assert candidate(rectangles = [[0, 0, 2, 2], [0, 2, 2, 4], [2, 0, 4, 2], [2, 2, 4, 4], [1, 1, 3, 3], [3, 1, 5, 3], [3, 3, 5, 5]]) == False\n assert candidate(rectangles = [[-10000, -10000, 10000, 10000], [-10000, -10000, 0, 0], [0, 0, 10000, 10000]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5], [5, 5, 6, 6], [6, 6, 7, 7], [7, 7, 8, 8], [8, 8, 9, 9], [9, 9, 10, 10]]) == False\n assert candidate(rectangles = [[1, 1, 2, 3], [1, 3, 2, 4], [1, 4, 2, 5], [1, 5, 2, 6], [1, 6, 2, 7], [1, 7, 2, 8], [1, 8, 2, 9]]) == True\n assert candidate(rectangles = [[0, 0, 100000, 1], [0, 1, 100000, 2], [0, 2, 100000, 3], [0, 3, 100000, 4], [0, 4, 100000, 5]]) == True\n assert candidate(rectangles = [[0, 0, 5, 5], [0, 5, 5, 10], [5, 0, 10, 5], [5, 5, 10, 10], [2, 2, 3, 3], [7, 7, 8, 8]]) == False\n assert candidate(rectangles = [[0, 0, 1, 1], [1, 0, 2, 1], [2, 0, 3, 1], [0, 1, 1, 2], [1, 1, 2, 2], [0, 2, 1, 3], [1, 2, 2, 3]]) == False\n assert candidate(rectangles = [[0, 0, 4, 4], [1, 1, 3, 3], [2, 2, 4, 4], [0, 1, 2, 3], [1, 0, 3, 2], [1, 2, 3, 4], [2, 1, 4, 3]]) == False\n assert candidate(rectangles = [[1, 1, 5, 5], [2, 2, 4, 4], [3, 3, 3, 4], [1, 1, 2, 2], [2, 2, 3, 3], [3, 3, 4, 4], [4, 4, 5, 5]]) == False\n assert candidate(rectangles = [[-1, -1, 0, 0], [0, 0, 1, 1], [1, 1, 2, 2], [2, 2, 3, 3]]) == False\n"}, "metadata": {"canonical_parameter_names": ["rectangles"], "leetcode_dataset_entry_point": "Solution().isRectangleCover", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isRectangleCover = function(rectangles) {", "container": null, "callable": "isRectangleCover", "parameters": [{"name": "rectangles", "type": "number[][]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 392, "task_id": "is-subsequence", "difficulty": "Easy", "problem_description": "Given two strings s and t, return true if s is a subsequence of t, or false otherwise.\nA subsequence of a string is a new string that is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (i.e., \"ace\" is a subsequence of \"abcde\" while \"aec\" is not).\n \nExample 1:\nInput: s = \"abc\", t = \"ahbgdc\"\nOutput: true\nExample 2:\nInput: s = \"axc\", t = \"ahbgdc\"\nOutput: false\n\n \nConstraints:\n\n0 <= s.length <= 100\n0 <= t.length <= 104\ns and t consist only of lowercase English letters.\n\n \nFollow up: Suppose there are lots of incoming s, say s1, s2, ..., sk where k >= 109, and you want to check one by one to see if t has its subsequence. In this scenario, how would you change your code?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abc\",t = \"abdc\") == True\n assert candidate(s = \"ab\",t = ('baab',)) == False\n assert candidate(s = \"xyz\",t = \"abcdefghijklmnopqrstuvwxyz\") == True\n assert candidate(s = \"aec\",t = \"abcde\") == False\n assert candidate(s = \"\",t = \"ahbgdc\") == True\n assert candidate(s = \"\",t = \"\") == True\n assert candidate(s = \"zyx\",t = \"abcdefghijklmnopqrstuvwxyz\") == False\n assert candidate(s = \"abcd\",t = \"abcde\") == True\n assert candidate(s = \"abc\",t = \"abcbc\") == True\n assert candidate(s = \"bb\",t = \"aabbb\") == True\n assert candidate(s = \"aaaaaa\",t = \"bbaaaa\") == False\n assert candidate(s = \"abc\",t = \"bahbgdca\") == True\n assert candidate(s = \"ab\",t = \"baab\") == True\n assert candidate(s = \"bd\",t = \"abcde\") == True\n assert candidate(s = \"bd\",t = \"abcd\") == True\n assert candidate(s = \"axc\",t = \"ahbgdc\") == False\n assert candidate(s = \"a\",t = \"ahbgdc\") == True\n assert candidate(s = \"a\",t = \"a\") == True\n assert candidate(s = \"abc\",t = \"ahbgdc\") == True\n assert candidate(s = \"acb\",t = \"ahbgdc\") == False\n assert candidate(s = \"bcd\",t = \"ahbgdc\") == False\n assert candidate(s = \"abc\",t = \"\") == False\n assert candidate(s = \"ahbgdc\",t = \"ahbgdc\") == True\n assert candidate(s = \"abcd\",t = \"abbbcd\") == True\n assert candidate(s = \"b\",t = \"abcde\") == True\n assert candidate(s = \"abc\",t = \"abc\") == True\n assert candidate(s = \"abc\",t = \"abcde\") == True\n assert candidate(s = \"test\",t = \"ttttteeeesstttt\") == True\n assert candidate(s = \"challenge\",t = \"chllenge\") == False\n assert candidate(s = \"leetcode\",t = \"lleettccooddee\") == True\n assert candidate(s = \"consecutive\",t = \"consecutivve\") == True\n assert candidate(s = \"example\",t = \"exxample\") == True\n assert candidate(s = \"interview\",t = \"intrvw\") == False\n assert candidate(s = \"substring\",t = \"subtrring\") == False\n assert candidate(s = \"hello\",t = \"ohellomyworld\") == True\n assert candidate(s = \"characters\",t = \"characttrrs\") == False\n assert candidate(s = \"python\",t = \"pyyyynntthhoonn\") == True\n assert candidate(s = \"challenge\",t = \"cchhaalllleennnggggeee\") == True\n assert candidate(s = \"algorithm\",t = \"aggglllllllllooooooorrrrrriiiiiiiiiimmmmmm\") == False\n assert candidate(s = \"a\",t = \"\") == False\n assert candidate(s = \"complexity\",t = \"ccllllcooooooommmppppppllllleeeeeexxxxxxyyyyyyytttttttt\") == False\n assert candidate(s = \"\",t = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == True\n assert candidate(s = \"word\",t = \"wwwooorrrrdddd\") == True\n assert candidate(s = \"algorithm\",t = \"algotihm\") == False\n assert candidate(s = \"repeated\",t = \"reppeted\") == False\n assert candidate(s = \"dynamic\",t = \"dyyyyynnaaaaaammmmcccciiiiiiiiinnnnnnnnggggggg\") == False\n assert candidate(s = \"abcd\",t = \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\") == True\n assert candidate(s = \"abcdabcd\",t = \"abxycdxeyzabcd\") == True\n assert candidate(s = \"complex\",t = \"complxc\") == False\n assert candidate(s = \"interview\",t = \"iiiiinnnnnttttttterrrrrrrrreevvvvvvvvvw\") == False\n assert candidate(s = \"mississippi\",t = \"mmissiissippiissippississippi\") == True\n assert candidate(s = \"substrings\",t = \"sssssuuuuubbstrrrrrriiiiinnnggggggsss\") == True\n assert candidate(s = \"substring\",t = \"ssssuusssubbssssttrrrriiiinnngggggg\") == True\n assert candidate(s = \"sequence\",t = \"seqqqqquuuuueeeennnnccceeeeee\") == True\n assert candidate(s = \"programming\",t = \"ppppprrogggggggrrrrrroooooogggggggaaaaammmmiiiiinnnnnggggggg\") == True\n assert candidate(s = \"repeated\",t = \"reeeepppeeeaaaatteeedd\") == True\n assert candidate(s = \"abcabcabc\",t = \"aabbccabcabcabc\") == True\n assert candidate(s = \"z\",t = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == True\n assert candidate(s = \"consecutive\",t = \"ccoonnnsseecccccoooooonnnsssccceeeeeevvvvvvvveeeennnnnnncccccccceeeeeee\") == False\n assert candidate(s = \"\",t = \"a\") == True\n assert candidate(s = \"hello\",t = \"hhelllllooooworld\") == True\n assert candidate(s = \"example\",t = \"eeeexxaample\") == True\n assert candidate(s = \"subsequence\",t = \"ssubsuuubbbbsssseeeeeqqqqqqqqqqccceeeennnnneeeeee\") == False\n assert candidate(s = \"characters\",t = \"ccccchhhhaaaaaarrrrrrrtttteeeeeeccchhhhaaaaaarrrrrrrtttteeeeee\") == False\n assert candidate(s = \"abcdef\",t = \"fedcbazyxwvutsrqponmlkjihgfedcba\") == False\n assert candidate(s = \"subsequence\",t = \"substringsequence\") == True\n assert candidate(s = \"abcdefg\",t = \"axbxcxdxexfxgx\") == True\n assert candidate(s = \"abcdefg\",t = \"azbycxdwevfug\") == True\n assert candidate(s = \"sequence\",t = \"sqeuences\") == False\n"}, "metadata": {"canonical_parameter_names": ["s", "t"], "leetcode_dataset_entry_point": "Solution().isSubsequence", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var isSubsequence = function(s, t) {", "container": null, "callable": "isSubsequence", "parameters": [{"name": "s", "type": "string"}, {"name": "t", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 393, "task_id": "utf-8-validation", "difficulty": "Medium", "problem_description": "Given an integer array data representing the data, return whether it is a valid UTF-8 encoding (i.e. it translates to a sequence of valid UTF-8 encoded characters).\nA character in UTF8 can be from 1 to 4 bytes long, subjected to the following rules:\n\nFor a 1-byte character, the first bit is a 0, followed by its Unicode code.\nFor an n-bytes character, the first n bits are all one's, the n + 1 bit is 0, followed by n - 1 bytes with the most significant 2 bits being 10.\n\nThis is how the UTF-8 encoding would work:\n\n Number of Bytes | UTF-8 Octet Sequence\n | (binary)\n --------------------+-----------------------------------------\n 1 | 0xxxxxxx\n 2 | 110xxxxx 10xxxxxx\n 3 | 1110xxxx 10xxxxxx 10xxxxxx\n 4 | 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx\n\nx denotes a bit in the binary form of a byte that may be either 0 or 1.\nNote: The input is an array of integers. Only the least significant 8 bits of each integer is used to store the data. This means each integer represents only 1 byte of data.\n \nExample 1:\n\nInput: data = [197,130,1]\nOutput: true\nExplanation: data represents the octet sequence: 11000101 10000010 00000001.\nIt is a valid utf-8 encoding for a 2-bytes character followed by a 1-byte character.\n\nExample 2:\n\nInput: data = [235,140,4]\nOutput: false\nExplanation: data represented the octet sequence: 11101011 10001100 00000100.\nThe first 3 bits are all one's and the 4th bit is 0 means it is a 3-bytes character.\nThe next byte is a continuation byte which starts with 10 and that's correct.\nBut the second continuation byte does not start with 10, so it is invalid.\n\n \nConstraints:\n\n1 <= data.length <= 2 * 104\n0 <= data[i] <= 255\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(data = [237, 130, 130, 130]) == False\n assert candidate(data = [237, 128, 128, 130, 128, 128]) == False\n assert candidate(data = [238, 130, 130]) == True\n assert candidate(data = [31, 130, 130, 130]) == False\n assert candidate(data = [237, 130, 130, 130, 130]) == False\n assert candidate(data = [228, 189, 160]) == True\n assert candidate(data = [235, 140, 4]) == False\n assert candidate(data = [240, 162, 134, 142]) == True\n assert candidate(data = [237, 130, 130, 130, 130, 130, 130]) == False\n assert candidate(data = [251, 117, 104, 101, 108, 108, 111]) == False\n assert candidate(data = [240, 162, 134, 161]) == True\n assert candidate(data = [145]) == False\n assert candidate(data = [238, 130, 69]) == False\n assert candidate(data = [228, 189, 160, 229, 165, 189]) == True\n assert candidate(data = [197, 130, 1]) == True\n assert candidate(data = [235, 140, 4]) == False\n assert candidate(data = [197, 130, 1]) == True\n assert candidate(data = [192, 128, 191, 127]) == False\n assert candidate(data = [250, 145, 145, 145]) == False\n assert candidate(data = [0]) == True\n assert candidate(data = [240, 162, 134, 140]) == True\n assert candidate(data = [255]) == False\n assert candidate(data = [65, 66, 67, 68]) == True\n assert candidate(data = [224, 184, 148, 163]) == False\n assert candidate(data = [248, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [192, 128]) == True\n assert candidate(data = [240, 162, 138, 147, 145]) == False\n assert candidate(data = [237, 130, 130, 130]) == False\n assert candidate(data = [240, 162, 134, 142, 240, 162, 134, 142, 240, 162, 134, 142]) == True\n assert candidate(data = [252, 128, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139]) == False\n assert candidate(data = [110, 188, 142, 224, 160, 128]) == False\n assert candidate(data = [192, 128, 192, 128, 192, 128, 192, 192]) == False\n assert candidate(data = [225, 184, 165, 225, 184, 170, 225, 184, 185, 225, 184, 190]) == True\n assert candidate(data = [224, 160, 128, 224, 160, 128, 224, 160, 128]) == True\n assert candidate(data = [240, 159, 146, 150, 240, 159, 146, 150, 240, 159, 146, 150]) == True\n assert candidate(data = [240, 184, 152, 168, 224, 164, 174, 240, 157, 151, 166]) == True\n assert candidate(data = [248, 130, 130, 130, 130]) == False\n assert candidate(data = [248, 144, 144, 144, 144, 144]) == False\n assert candidate(data = [192, 128, 192, 128, 192, 128]) == True\n assert candidate(data = [240, 144, 144, 144, 144, 144, 144, 144]) == False\n assert candidate(data = [192, 128, 224, 162, 128, 240, 144, 128]) == False\n assert candidate(data = [248, 130, 129, 128, 128, 128, 128]) == False\n assert candidate(data = [235, 140, 141, 236, 140, 141, 237, 140, 141]) == True\n assert candidate(data = [224, 168, 128, 225, 184, 141, 225, 184, 172, 225, 184, 170, 225, 185, 172, 225, 184, 162]) == True\n assert candidate(data = [192, 128, 224, 160, 128, 225, 184, 160]) == True\n assert candidate(data = [244, 160, 128, 128, 244, 160, 128, 128]) == True\n assert candidate(data = [255, 255, 255, 255]) == False\n assert candidate(data = [225, 184, 160, 225, 184, 161, 225, 184, 162]) == True\n assert candidate(data = [192, 128, 192, 128, 192, 128, 192, 128]) == True\n assert candidate(data = [248, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [250, 145, 145, 145, 145]) == False\n assert candidate(data = [225, 184, 168, 225, 184, 169, 225, 184, 170]) == True\n assert candidate(data = [240, 159, 191, 191, 240, 159, 191, 191]) == True\n assert candidate(data = [224, 162, 130, 192, 128]) == True\n assert candidate(data = [192, 128, 192, 129, 192, 130, 192, 131, 192, 132, 192, 133, 192, 134, 192, 135, 192, 136, 192, 137, 192, 138, 192, 139, 192, 140, 192, 141, 192, 142, 192, 143]) == True\n assert candidate(data = [225, 184, 150, 225, 184, 185, 225, 184, 186, 225, 184, 187, 225, 184, 188]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [230, 138, 142, 230, 138, 143, 230, 138, 144]) == True\n assert candidate(data = [65, 66, 67, 68, 69, 70, 71, 72]) == True\n assert candidate(data = [240, 144, 144, 144, 240, 144, 144, 144, 240, 144, 144, 144, 240, 144, 144, 144]) == True\n assert candidate(data = [239, 188, 140, 239, 188, 141, 239, 188, 142, 239, 188, 143]) == True\n assert candidate(data = [225, 186, 130, 225, 186, 130, 225, 186, 130, 225, 186, 130, 225, 186, 130, 225, 186, 130]) == True\n assert candidate(data = [224, 160, 128, 224, 160, 129, 224, 160, 130]) == True\n assert candidate(data = [240, 159, 146, 140, 224, 164, 162, 194, 161]) == True\n assert candidate(data = [240, 128, 128, 128, 224, 160, 128, 192, 128]) == True\n assert candidate(data = [253, 160, 160, 160, 160, 160, 160, 160]) == False\n assert candidate(data = [244, 141, 132, 132, 244, 141, 132, 132]) == True\n assert candidate(data = [250, 145, 130, 147, 128, 130, 147, 128]) == False\n assert candidate(data = [240, 184, 144, 144, 240, 184, 144, 144]) == True\n assert candidate(data = [239, 187, 191, 239, 187, 191, 239, 187, 191]) == True\n assert candidate(data = [128, 129, 130, 131, 132, 133, 134, 135]) == False\n assert candidate(data = [192, 128, 224, 162, 130, 240, 159, 146, 150]) == True\n assert candidate(data = [255, 192, 128, 145]) == False\n assert candidate(data = [250, 154, 141, 154, 141, 154, 141, 154]) == False\n assert candidate(data = [252, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(data = [6, 239, 191, 191, 224, 160, 128, 239, 191, 191]) == True\n assert candidate(data = [224, 160, 128, 225, 184, 160, 239, 189, 191]) == True\n assert candidate(data = [225, 186, 185, 225, 186, 185, 225, 186, 185]) == True\n assert candidate(data = [224, 160, 128, 225, 184, 128, 237, 128, 128, 240, 144, 128, 128]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [250, 145, 130, 128, 10]) == False\n assert candidate(data = [239, 187, 191, 239, 187, 191, 239, 187, 191, 239, 187, 191]) == True\n assert candidate(data = [240, 128, 128, 128, 240, 129, 129, 129]) == True\n assert candidate(data = [191, 128, 191, 128, 191, 128]) == False\n assert candidate(data = [255, 140, 140, 140]) == False\n assert candidate(data = [192, 128, 224, 162, 138, 240, 159, 146, 150]) == True\n assert candidate(data = [128, 191, 223, 239, 255, 0, 127, 192]) == False\n assert candidate(data = [240, 144, 144, 128, 240, 144, 144, 144]) == True\n assert candidate(data = [240, 159, 146, 150, 240, 159, 146, 150]) == True\n assert candidate(data = [240, 145, 129, 128, 128]) == False\n assert candidate(data = [240, 145, 145, 145, 240, 145, 145, 145]) == True\n assert candidate(data = [234, 162, 134, 235, 140, 4, 236, 128, 132]) == False\n assert candidate(data = [240, 184, 152, 149, 240, 184, 152, 150]) == True\n assert candidate(data = [192, 128, 224, 160, 128, 240, 144, 128, 128]) == True\n assert candidate(data = [192, 128, 192, 128, 192, 128, 192, 128]) == True\n assert candidate(data = [240, 145, 128, 147, 128, 130, 147, 128, 237, 128, 128, 237, 128, 128]) == False\n assert candidate(data = [240, 145, 128, 128, 240, 145, 128, 128, 240, 145, 128, 128]) == True\n assert candidate(data = [224, 160, 128, 128, 224, 160, 128, 128, 224, 160, 128, 128]) == False\n assert candidate(data = [225, 184, 165, 225, 184, 170, 225, 184, 185]) == True\n assert candidate(data = [192, 128, 192, 128, 192, 128, 128, 192]) == False\n assert candidate(data = [224, 160, 128, 224, 160, 128, 192, 128, 128]) == False\n assert candidate(data = [239, 189, 191, 239, 189, 191]) == True\n assert candidate(data = [194, 128, 224, 160, 128, 240, 176, 128, 248, 192, 128, 128]) == False\n assert candidate(data = [192, 128, 224, 162, 138, 147, 240, 144, 144, 144, 0]) == False\n assert candidate(data = [239, 188, 140, 239, 188, 141, 239, 188, 142]) == True\n assert candidate(data = [10, 192, 128, 11, 194, 191, 14, 224, 160, 128, 15, 225, 184, 160]) == True\n assert candidate(data = [194, 128, 224, 160, 128, 240, 144, 128, 128, 250, 144, 128, 128]) == False\n assert candidate(data = [0, 0, 0, 0, 0, 0, 0, 0]) == True\n assert candidate(data = [11111000, 10000000, 10000000, 10000000, 10000000]) == False\n assert candidate(data = [224, 160, 128, 237, 130, 176, 240, 144, 144, 128]) == True\n assert candidate(data = [255, 160, 130, 145]) == False\n assert candidate(data = [225, 186, 130, 225, 186, 130, 225, 186, 130]) == True\n assert candidate(data = [128, 129, 130, 131, 132, 133, 134, 135, 136, 137]) == False\n assert candidate(data = [240, 145, 129, 128, 240, 145, 129, 128, 240, 145, 129, 128]) == True\n assert candidate(data = [228, 189, 160, 229, 165, 189, 228, 184, 173]) == True\n assert candidate(data = [224, 162, 138, 224, 162, 138]) == True\n assert candidate(data = [194, 128, 226, 128, 128, 239, 184, 141]) == True\n assert candidate(data = [248, 130, 130, 130, 130, 130, 130, 130]) == False\n assert candidate(data = [240, 159, 146, 150, 192, 128, 224, 162, 130]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [240, 144, 144, 144, 144]) == False\n assert candidate(data = [10, 192, 130, 224, 162, 138, 240, 144, 144, 144, 192, 130]) == True\n assert candidate(data = [248, 130, 130, 130, 130, 130, 130]) == False\n assert candidate(data = [240, 145, 130, 128, 225, 186, 130, 192, 128]) == True\n assert candidate(data = [255, 255, 255, 255]) == False\n assert candidate(data = [192, 129, 192, 130, 192, 131, 192, 132]) == True\n assert candidate(data = [240, 144, 144, 144, 240, 144, 144, 144]) == True\n assert candidate(data = [255, 128, 128, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [240, 162, 138, 147, 240, 162, 138, 147]) == True\n assert candidate(data = [250, 145, 145, 145, 145, 145, 145, 145, 145]) == False\n assert candidate(data = [248, 128, 128, 128, 128, 128]) == False\n assert candidate(data = [192, 128, 224, 162, 138, 240, 144, 144, 144]) == True\n assert candidate(data = [237, 140, 141, 142, 143, 144, 145]) == False\n"}, "metadata": {"canonical_parameter_names": ["data"], "leetcode_dataset_entry_point": "Solution().validUtf8", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var validUtf8 = function(data) {", "container": null, "callable": "validUtf8", "parameters": [{"name": "data", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 394, "task_id": "decode-string", "difficulty": "Medium", "problem_description": "Given an encoded string, return its decoded string.\nThe encoding rule is: k[encoded_string], where the encoded_string inside the square brackets is being repeated exactly k times. Note that k is guaranteed to be a positive integer.\nYou may assume that the input string is always valid; there are no extra white spaces, square brackets are well-formed, etc. Furthermore, you may assume that the original data does not contain any digits and that digits are only for those repeat numbers, k. For example, there will not be input like 3a or 2[4].\nThe test cases are generated so that the length of the output will never exceed 105.\n \nExample 1:\n\nInput: s = \"3[a]2[bc]\"\nOutput: \"aaabcbc\"\n\nExample 2:\n\nInput: s = \"3[a2[c]]\"\nOutput: \"accaccacc\"\n\nExample 3:\n\nInput: s = \"2[abc]3[cd]ef\"\nOutput: \"abcabccdcdcdef\"\n\n \nConstraints:\n\n1 <= s.length <= 30\ns consists of lowercase English letters, digits, and square brackets '[]'.\ns is guaranteed to be a valid input.\nAll the integers in s are in the range [1, 300].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"2[ab3[cd]]\") == \"abcdcdcdabcdcdcd\"\n assert candidate(s = \"2[ab3[c]]\") == \"abcccabccc\"\n assert candidate(s = \"1[a1[b1[c]]]\") == \"abc\"\n assert candidate(s = \"2[3[a]]\") == \"aaaaaa\"\n assert candidate(s = \"a1[b]\") == \"ab\"\n assert candidate(s = \"3[a3[b]1[c]]\") == \"abbbcabbbcabbbc\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"10[abc]\") == \"abcabcabcabcabcabcabcabcabcabc\"\n assert candidate(s = \"1[2[3[4[a]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"2[3[a]b]\") == \"aaabaaab\"\n assert candidate(s = \"4[ab]\") == \"abababab\"\n assert candidate(s = \"1[a2[b3[c]]]\") == \"abcccbccc\"\n assert candidate(s = \"10[a]\") == \"aaaaaaaaaa\"\n assert candidate(s = \"a2[b]c\") == \"abbc\"\n assert candidate(s = \"2[abc]3[cd]ef\") == \"abcabccdcdcdef\"\n assert candidate(s = \"1[a]\") == \"a\"\n assert candidate(s = \"3[a2[c]]\") == \"accaccacc\"\n assert candidate(s = \"3[a]2[bc]\") == \"aaabcbc\"\n assert candidate(s = \"abc\") == \"abc\"\n assert candidate(s = \"3[a3[b2[c]]]\") == \"abccbccbccabccbccbccabccbccbcc\"\n assert candidate(s = \"100[ab]\") == \"abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababab\"\n assert candidate(s = \"a[b]\") == \"a\"\n assert candidate(s = \"2[b3[c]]\") == \"bcccbccc\"\n assert candidate(s = \"1[xyz]2[uvw]\") == \"xyzuvwuvw\"\n assert candidate(s = \"a2[b3[c]]\") == \"abcccbccc\"\n assert candidate(s = \"1[a1[b]]\") == \"ab\"\n assert candidate(s = \"4[3[z]2[y]]\") == \"zzzyyzzzyyzzzyyzzzyy\"\n assert candidate(s = \"5[ab3[c2[d]]]\") == \"abcddcddcddabcddcddcddabcddcddcddabcddcddcddabcddcddcdd\"\n assert candidate(s = \"5[a1[b2[c3[d4[e]]]]]\") == \"abcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeeeabcdeeeedeeeedeeeecdeeeedeeeedeeee\"\n assert candidate(s = \"a2[b3[c4[d5[e6[f7[g]]]]]]\") == \"abcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggbcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggcdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggdefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfgggggggefgggggggfgggggggfgggggggfgggggggfgggggggfggggggg\"\n assert candidate(s = \"abc3[d2[e1[f]]]\") == \"abcdefefdefefdefef\"\n assert candidate(s = \"5[a2[b3[c4[d]]]]\") == \"abcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcdddd\"\n assert candidate(s = \"3[2[mn]1[op]2[qr]]\") == \"mnmnopqrqrmnmnopqrqrmnmnopqrqr\"\n assert candidate(s = \"5[c2[d]]\") == \"cddcddcddcddcdd\"\n assert candidate(s = \"a1[b2[c3[d]]]\") == \"abcdddcddd\"\n assert candidate(s = \"7[2[x]3[y]]\") == \"xxyyyxxyyyxxyyyxxyyyxxyyyxxyyyxxyyy\"\n assert candidate(s = \"2[ab3[cd]]4[ef5[gh]]\") == \"abcdcdcdabcdcdcdefghghghghghefghghghghghefghghghghghefghghghghgh\"\n assert candidate(s = \"3[ab2[c]]4[de]\") == \"abccabccabccdededede\"\n assert candidate(s = \"4[ab3[c2[d]]]\") == \"abcddcddcddabcddcddcddabcddcddcddabcddcddcdd\"\n assert candidate(s = \"3[a2[b1[c0[d]]]]\") == \"abcbcabcbcabcbc\"\n assert candidate(s = \"3[a4[b5[c6[d7[e8[f]]]]]]\") == \"abcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffbcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffcdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffeffffffffdeffffffffeffffffffeffffffffeffffffffeffffffffeffffff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assert candidate(s = \"3[2[a]1[b]]2[3[c]4[d]]\") == \"aabaabaabcccddddcccdddd\"\n assert candidate(s = \"abc2[def3[ghi]]jkl4[mno5[pqr]]stu\") == \"abcdefghighighidefghighighijklmnopqrpqrpqrpqrpqrmnopqrpqrpqrpqrpqrmnopqrpqrpqrpqrpqrmnopqrpqrpqrpqrpqrstu\"\n assert candidate(s = \"2[3[a]2[b3[c]2[d]]]\") == \"aaabcccddbcccddaaabcccddbcccdd\"\n assert candidate(s = \"6[ab2[cd3[ef]]]\") == \"abcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefefabcdefefefcdefefef\"\n assert candidate(s = \"7[fg]2[h3[i]]\") == \"fgfgfgfgfgfgfghiiihiii\"\n assert candidate(s = \"7[x2[y3[z4[w]]]]\") == \"xyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwwwxyzwwwwzwwwwzwwwwyzwwwwzwwwwzwwww\"\n assert candidate(s = \"5[2[x3[y]]4[z]]\") == \"xyyyxyyyzzzzxyyyxyyyzzzzxyyyxyyyzzzzxyyyxyyyzzzzxyyyxyyyzzzz\"\n assert candidate(s = \"6[ab2[cd3[ef4[gh]]]]\") == \"abcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghghabcdefghghghghefghghghghefghghghghcdefghghghghefghghghghefghghghgh\"\n assert candidate(s = \"2[x2[y3[z]]]1[a]\") == \"xyzzzyzzzxyzzzyzzza\"\n assert candidate(s = \"7[z]6[y5[x4[w3[v2[u1[t]]]]]]\") == \"zzzzzzzyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututyxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvututxwvututvututvututwvututvututvututwvututvututvututwvututvututvutut\"\n assert candidate(s = \"2[a3[b4[c]]]\") == \"abccccbccccbccccabccccbccccbcccc\"\n assert candidate(s = \"10[a9[bc3[de]]]\") == \"abcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededeabcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdededebcdedede\"\n assert candidate(s = \"3[ab]4[cd]5[ef]\") == \"abababcdcdcdcdefefefefef\"\n assert candidate(s = \"10[ab]\") == \"abababababababababab\"\n assert candidate(s = \"5[4[3[2[1[x]]]]]\") == \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n assert candidate(s = \"2[ab3[cd4[ef]]]\") == \"abcdefefefefcdefefefefcdefefefefabcdefefefefcdefefefefcdefefefef\"\n assert candidate(s = \"5[ab]3[cd]2[ef1[gh]]\") == \"abababababcdcdcdefghefgh\"\n assert candidate(s = \"7[2[pq]3[rs]]\") == \"pqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrspqpqrsrsrs\"\n assert candidate(s = \"2[3[a]b]4[c5[d]]\") == \"aaabaaabcdddddcdddddcdddddcddddd\"\n assert candidate(s = \"3[2[3[4[a]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"6[2[a]3[b]]\") == \"aabbbaabbbaabbbaabbbaabbbaabbb\"\n assert candidate(s = \"2[abc3[def4[ghi5[jkl]]]]\") == \"abcdefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklabcdefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkldefghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljklghijkljkljkljkljkl\"\n assert candidate(s = \"2[a3[b4[c5[d6[e]]]]]\") == \"abcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeeabcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeebcdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeeecdeeeeeedeeeeeedeeeeeedeeeeeedeeeeee\"\n assert candidate(s = \"3[2[1[0[]]]]\") == \"\"\n assert candidate(s = \"10[f9[g]]\") == \"fgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfgggggggggfggggggggg\"\n assert candidate(s = \"15[abc10[de]]\") == \"abcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdedededededededededeabcdededededededededede\"\n assert candidate(s = \"5[k9[l10[m]]]\") == \"klmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmklmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmmlmmmmmmmmmm\"\n assert candidate(s = \"5[xy2[z3[w4[v]]]]\") == \"xyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvvxyzwvvvvwvvvvwvvvvzwvvvvwvvvvwvvvv\"\n assert candidate(s = \"1[1[1[1[ab]]]]\") == \"ab\"\n assert candidate(s = \"5[1[2[3[4[5[a]]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"4[ab2[c]]\") == \"abccabccabccabcc\"\n assert candidate(s = \"4[a2[b3[c]]]\") == \"abcccbcccabcccbcccabcccbcccabcccbccc\"\n assert candidate(s = \"2[x3[y4[z]]]\") == \"xyzzzzyzzzzyzzzzxyzzzzyzzzzyzzzz\"\n assert candidate(s = \"3[2[3[4[a]]]5[b]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaabbbbbaaaaaaaaaaaaaaaaaaaaaaaabbbbbaaaaaaaaaaaaaaaaaaaaaaaabbbbb\"\n assert candidate(s = \"10[ab2[cd]ef3[gh]]\") == \"abcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghghabcdcdefghghgh\"\n assert candidate(s = \"5[abc2[def]]\") == \"abcdefdefabcdefdefabcdefdefabcdefdefabcdefdef\"\n assert candidate(s = \"3[2[3[a2[b]]]]\") == \"abbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabbabb\"\n assert candidate(s = \"2[3[ab]]\") == \"abababababab\"\n assert candidate(s = \"3[xy2[z]]2[ab]\") == \"xyzzxyzzxyzzabab\"\n assert candidate(s = \"10[1[a]2[b]3[c]4[d]5[e]]\") == \"abbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeeeabbcccddddeeeee\"\n assert candidate(s = \"3[2[3[4[x]]]]\") == \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n assert candidate(s = \"2[3[a]b4[c]]\") == \"aaabccccaaabcccc\"\n assert candidate(s = \"10[x]\") == \"xxxxxxxxxx\"\n assert candidate(s = \"4[2[xy]z]\") == \"xyxyzxyxyzxyxyzxyxyz\"\n assert candidate(s = \"6[a5[b4[c3[d2[e1[f]]]]]]\") == \"abcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefabcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefbcdefefdefefdefefcdefefdefefdefefcdefefdefefdefefcdefefdefefdefef\"\n assert candidate(s = \"4[x5[yz]w]\") == \"xyzyzyzyzyzwxyzyzyzyzyzwxyzyzyzyzyzwxyzyzyzyzyzw\"\n assert candidate(s = \"4[3[2[b1[c]]]]\") == \"bcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbc\"\n assert candidate(s = \"2[x3[xy4[z]]]\") == \"xxyzzzzxyzzzzxyzzzzxxyzzzzxyzzzzxyzzzz\"\n assert candidate(s = \"2[3[a2[b]]c]\") == \"abbabbabbcabbabbabbc\"\n assert candidate(s = \"9[abc]8[def]7[ghi]\") == \"abcabcabcabcabcabcabcabcabcdefdefdefdefdefdefdefdefghighighighighighighi\"\n assert candidate(s = \"4[ab]5[cd]\") == \"ababababcdcdcdcdcd\"\n assert candidate(s = \"2[3[xy]z]\") == \"xyxyxyzxyxyxyz\"\n assert candidate(s = \"4[x3[y2[z]]]\") == \"xyzzyzzyzzxyzzyzzyzzxyzzyzzyzzxyzzyzzyzz\"\n assert candidate(s = \"3[2[a]b]\") == \"aabaabaab\"\n assert candidate(s = \"abc2[3[de]fg]\") == \"abcdededefgdededefg\"\n assert candidate(s = \"1[abc2[def3[ghi]]]\") == \"abcdefghighighidefghighighi\"\n assert candidate(s = \"2[abc2[def3[ghi]]]\") == \"abcdefghighighidefghighighiabcdefghighighidefghighighi\"\n assert candidate(s = \"1[2[3[4[5[a]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"5[ab3[cd]]\") == \"abcdcdcdabcdcdcdabcdcdcdabcdcdcdabcdcdcd\"\n assert candidate(s = \"2[x3[y4[z]]]1[w]\") == \"xyzzzzyzzzzyzzzzxyzzzzyzzzzyzzzzw\"\n assert candidate(s = \"7[2[a]3[b]]\") == \"aabbbaabbbaabbbaabbbaabbbaabbbaabbb\"\n assert candidate(s = \"9[8[7[6[5[4[3[2[1[0[a]]]]]]]]]]\") == \"\"\n assert candidate(s = \"4[x5[y]]\") == \"xyyyyyxyyyyyxyyyyyxyyyyy\"\n assert candidate(s = \"2[abc3[def4[ghi]]]\") == \"abcdefghighighighidefghighighighidefghighighighiabcdefghighighighidefghighighighidefghighighighi\"\n assert candidate(s = \"5[ab2[c]]3[xy]2[de]\") == \"abccabccabccabccabccxyxyxydede\"\n assert candidate(s = \"5[abc2[de]]\") == \"abcdedeabcdedeabcdedeabcdedeabcdede\"\n assert candidate(s = \"7[k2[3[xyz]]]\") == \"kxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyzkxyzxyzxyzxyzxyzxyz\"\n assert candidate(s = \"1[abc2[def]]\") == \"abcdefdef\"\n assert candidate(s = \"2[3[4[5[6[7[8[9[0[1[a]]]]]]]]]]\") == \"\"\n assert candidate(s = \"3[2[1[x]]]\") == \"xxxxxx\"\n assert candidate(s = \"5[ab2[cd]]\") == \"abcdcdabcdcdabcdcdabcdcdabcdcd\"\n assert candidate(s = \"6[5[4[3[2[1[a]]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"7[xyz]3[abc2[def1[ghi]]]\") == \"xyzxyzxyzxyzxyzxyzxyzabcdefghidefghiabcdefghidefghiabcdefghidefghi\"\n assert candidate(s = \"x1[y2[z3[a4[b5[c]]]]]\") == \"xyzabcccccbcccccbcccccbcccccabcccccbcccccbcccccbcccccabcccccbcccccbcccccbccccczabcccccbcccccbcccccbcccccabcccccbcccccbcccccbcccccabcccccbcccccbcccccbccccc\"\n assert candidate(s = \"3[ab2[c3[d]]]\") == \"abcdddcdddabcdddcdddabcdddcddd\"\n assert candidate(s = \"6[a2[b3[c4[d]]]]\") == \"abcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcddddabcddddcddddcddddbcddddcddddcdddd\"\n assert candidate(s = \"15[a]\") == \"aaaaaaaaaaaaaaa\"\n assert candidate(s = \"5[2[3[a]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"2[xy3[z]]4[ab]\") == \"xyzzzxyzzzabababab\"\n assert candidate(s = \"1[a2[b3[c4[d5[e]]]]]\") == \"abcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeebcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeee\"\n assert candidate(s = \"4[a3[b]]\") == \"abbbabbbabbbabbb\"\n assert candidate(s = \"2[ab]3[cd]4[ef]\") == \"ababcdcdcdefefefef\"\n assert candidate(s = \"1[2[3[4[5[6[7[8[9[0[x]]]]]]]]]]\") == \"\"\n assert candidate(s = \"1[2[3[4[5[6[x]]]]]]\") == \"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n assert candidate(s = \"2[a3[b4[c5[d6[e7[f]]]]]]\") == \"abcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffabcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffbcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffcdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffffdefffffffefffffffefffffffefffffffefffffffefffffff\"\n assert candidate(s = \"4[a3[b2[c1[d]]]]\") == \"abcdcdbcdcdbcdcdabcdcdbcdcdbcdcdabcdcdbcdcdbcdcdabcdcdbcdcdbcdcd\"\n assert candidate(s = \"3[2[3[4[5[a]]]]]\") == \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\"\n assert candidate(s = \"1[xyz]2[uvw]3[2[abc]3[def]]4[ghi]\") == \"xyzuvwuvwabcabcdefdefdefabcabcdefdefdefabcabcdefdefdefghighighighi\"\n assert candidate(s = \"3[xyz2[abc]4[def]]5[ghi]\") == \"xyzabcabcdefdefdefdefxyzabcabcdefdefdefdefxyzabcabcdefdefdefdefghighighighighi\"\n assert candidate(s = \"2[2[2[2[2[abc]]]]]\") == \"abcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc\"\n assert candidate(s = \"3[b2[c]1[d]]4[e]\") == \"bccdbccdbccdeeee\"\n assert candidate(s = \"a2[b3[c4[d5[e]]]]\") == \"abcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeebcdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeeecdeeeeedeeeeedeeeeedeeeee\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().decodeString", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var decodeString = function(s) {", "container": null, "callable": "decodeString", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 395, "task_id": "longest-substring-with-at-least-k-repeating-characters", "difficulty": "Medium", "problem_description": "Given a string s and an integer k, return the length of the longest substring of s such that the frequency of each character in this substring is greater than or equal to k.\nif no such substring exists, return 0.\n \nExample 1:\n\nInput: s = \"aaabb\", k = 3\nOutput: 3\nExplanation: The longest substring is \"aaa\", as 'a' is repeated 3 times.\n\nExample 2:\n\nInput: s = \"ababbc\", k = 2\nOutput: 5\nExplanation: The longest substring is \"ababb\", as 'a' is repeated 2 times and 'b' is repeated 3 times.\n\n \nConstraints:\n\n1 <= s.length <= 104\ns consists of only lowercase English letters.\n1 <= k <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcabcabc\",k = 3) == 9\n assert candidate(s = \"abcdefg\",k = 1) == 7\n assert candidate(s = \"bbaaacccddddeee\",k = 4) == 4\n assert candidate(s = \"\",k = 1) == 0\n assert candidate(s = \"aabcabb\",k = 2) == 2\n assert candidate(s = \"aaa\",k = 4) == 0\n assert candidate(s = \"a\",k = 1) == 1\n assert candidate(s = \"aaaabbbbcccc\",k = 5) == 0\n assert candidate(s = \"a\",k = 2) == 0\n assert candidate(s = \"aabbcc\",k = 1) == 6\n assert candidate(s = \"abcde\",k = 2) == 0\n assert candidate(s = \"aabbbccc\",k = 3) == 6\n assert candidate(s = \"aabbbcccc\",k = 3) == 7\n assert candidate(s = \"aaabb\",k = 3) == 3\n assert candidate(s = \"zzzzzzzz\",k = 5) == 8\n assert candidate(s = \"abcd\",k = 1) == 4\n assert candidate(s = \"ababbc\",k = 2) == 5\n assert candidate(s = \"aabcccddddeee\",k = 2) == 10\n assert candidate(s = \"aaabbbcccddd\",k = 4) == 0\n assert candidate(s = \"abcabcabcabc\",k = 3) == 12\n assert candidate(s = \"zzzzzzzzzz\",k = 1) == 10\n assert candidate(s = \"aabbccddeeff\",k = 1) == 12\n assert candidate(s = \"abcdefabcdefabcdef\",k = 3) == 18\n assert candidate(s = \"xyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxyxy\",k = 2) == 36\n assert candidate(s = \"aabbccddeeffgghhii\",k = 2) == 18\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\",k = 1) == 26\n assert candidate(s = \"aabbccddeeffgghhiijjkk\",k = 2) == 22\n assert candidate(s = \"aabccceeddd\",k = 3) == 3\n assert candidate(s = \"abacabadabacabadabacabad\",k = 2) == 24\n assert candidate(s = \"qqwweerrttyyuuiiooppaassddffgg\",k = 3) == 0\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzz\",k = 5) == 20\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",k = 1) == 52\n assert candidate(s = \"aabbccddeeeefff\",k = 3) == 7\n assert candidate(s = \"aabaaaabbbaaaabb\",k = 3) == 16\n assert candidate(s = \"aabbccddeeff\",k = 2) == 12\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 1) == 56\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 1) == 34\n assert candidate(s = \"xyzzzzzzzzzzxy\",k = 10) == 10\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\",k = 3) == 60\n assert candidate(s = \"abcdabcabcabcd\",k = 2) == 14\n assert candidate(s = \"abcdabcdbcdabcd\",k = 2) == 15\n assert candidate(s = \"aabaaaabbbaabbccbbbaaacccaa\",k = 3) == 27\n assert candidate(s = \"abccbaabccba\",k = 2) == 12\n assert candidate(s = \"mississippi\",k = 2) == 10\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",k = 5) == 0\n assert candidate(s = \"abcabcabcabcabc\",k = 2) == 15\n assert candidate(s = \"bbaaacccddddeee\",k = 3) == 13\n assert candidate(s = \"abcdabcdabcdabcdabcd\",k = 5) == 20\n assert candidate(s = \"aaaaaaaaaabbbbbbbbbbcccccccccc\",k = 10) == 30\n assert candidate(s = \"abababababab\",k = 3) == 12\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",k = 26) == 0\n assert candidate(s = \"ababababababababababababababababababababababababababababababab\",k = 2) == 62\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 50) == 60\n assert candidate(s = \"aabbaaaccbbccaaaaccccbbbbaaaaa\",k = 6) == 30\n assert candidate(s = \"abacabadabacaba\",k = 2) == 0\n assert candidate(s = \"abcbacbabcbabc\",k = 3) == 14\n assert candidate(s = \"bbaaacccddddeeeeffffgggghhhh\",k = 4) == 20\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",k = 1) == 30\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 25) == 60\n assert candidate(s = \"aaabbbcccddd\",k = 3) == 12\n assert candidate(s = \"abcdabcdabcdabcdabcdabcd\",k = 2) == 24\n assert candidate(s = \"abcabcabcabc\",k = 2) == 12\n assert candidate(s = \"bbaaacccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxxyyyyzzzz\",k = 4) == 92\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",k = 10) == 30\n assert candidate(s = \"xyzzzzzyx\",k = 3) == 5\n assert candidate(s = \"zzzzzyyyyxxxxwwwwvvvv\",k = 5) == 5\n assert candidate(s = \"aabbccddeeffgg\",k = 2) == 14\n assert candidate(s = \"aabbccddeeffgg\",k = 3) == 0\n assert candidate(s = \"aabbaaabbbaaaabb\",k = 3) == 16\n assert candidate(s = \"ababababababababababababababab\",k = 3) == 30\n assert candidate(s = \"mnopqrstuv\",k = 1) == 10\n assert candidate(s = \"abcabcabcabc\",k = 1) == 12\n assert candidate(s = \"xyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 30) == 58\n assert candidate(s = \"abcdefghigklmnopqrstuvwxyz\",k = 1) == 26\n assert candidate(s = \"aabbccddeeffgghhiijjkk\",k = 3) == 0\n assert candidate(s = \"zzzzzzzzzzzzzz\",k = 12) == 14\n assert candidate(s = \"xyzzazaxxzyzyzyzyzxzyzyzyzxzyzyzyz\",k = 2) == 34\n assert candidate(s = \"aabbaaaccbbccaaaaccccbbbbaaaaa\",k = 3) == 30\n assert candidate(s = \"aabaaaadaaabaaaadaaabaaaa\",k = 3) == 4\n assert candidate(s = \"aabbccddeeffgg\",k = 4) == 0\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzz\",k = 10) == 20\n assert candidate(s = \"abccbaabccccddddeeeee\",k = 2) == 21\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",k = 2) == 30\n assert candidate(s = \"thisisjustaverylongteststring\",k = 3) == 0\n assert candidate(s = \"abababababababababababababababab\",k = 5) == 32\n assert candidate(s = \"zzzzzyyyyyxxxx\",k = 4) == 14\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 15) == 60\n assert candidate(s = \"abcbcbcbcbcbcbcbcbcbcbcbcbcb\",k = 2) == 27\n assert candidate(s = \"xyzzxyzzxyzz\",k = 3) == 12\n assert candidate(s = \"aabbbccccdddd\",k = 4) == 8\n assert candidate(s = \"mississippi\",k = 3) == 7\n assert candidate(s = \"aabacbebebe\",k = 3) == 6\n assert candidate(s = \"zzzzzyyyyyxxxxwwwwvvvvuuuuttttssssrrrrqqqqpppplllloooonnnnmmmkkkjjjiiihhhhggggffffeeeeddddccccbbbbaaaaa\",k = 5) == 10\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",k = 1) == 26\n assert candidate(s = \"abacabadabacaba\",k = 3) == 0\n assert candidate(s = \"xyzzzzzzzzzyx\",k = 2) == 13\n assert candidate(s = \"aabbcdefgghijklmno\",k = 2) == 4\n assert candidate(s = \"ppppppqqqqrrrssstttuuuvvvvwwwwwxxxxxyyyyyzzzz\",k = 5) == 15\n assert candidate(s = \"abcabcabcabcabcabc\",k = 2) == 18\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",k = 1) == 60\n assert candidate(s = \"zzzzzaaazzzzzzzzzz\",k = 5) == 10\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",k = 3) == 0\n assert candidate(s = \"zzzzzzzzzzzzzzzzzz\",k = 5) == 18\n assert candidate(s = \"abababababababababababababababababababab\",k = 5) == 40\n assert candidate(s = \"xyzzzxyzzzxyzzz\",k = 3) == 15\n assert candidate(s = \"aabababababababababababababababa\",k = 5) == 32\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",k = 2) == 52\n assert candidate(s = \"aabbccddeeffgghhiijjkk\",k = 4) == 0\n assert candidate(s = \"abcdefgh\",k = 2) == 0\n"}, "metadata": {"canonical_parameter_names": ["s", "k"], "leetcode_dataset_entry_point": "Solution().longestSubstring", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestSubstring = function(s, k) {", "container": null, "callable": "longestSubstring", "parameters": [{"name": "s", "type": "string"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 396, "task_id": "rotate-function", "difficulty": "Medium", "problem_description": "You are given an integer array nums of length n.\nAssume arrk to be an array obtained by rotating nums by k positions clock-wise. We define the rotation function F on nums as follow:\n\nF(k) = 0 * arrk[0] + 1 * arrk[1] + ... + (n - 1) * arrk[n - 1].\n\nReturn the maximum value of F(0), F(1), ..., F(n-1).\nThe test cases are generated so that the answer fits in a 32-bit integer.\n \nExample 1:\n\nInput: nums = [4,3,2,6]\nOutput: 26\nExplanation:\nF(0) = (0 * 4) + (1 * 3) + (2 * 2) + (3 * 6) = 0 + 3 + 4 + 18 = 25\nF(1) = (0 * 6) + (1 * 4) + (2 * 3) + (3 * 2) = 0 + 4 + 6 + 6 = 16\nF(2) = (0 * 2) + (1 * 6) + (2 * 4) + (3 * 3) = 0 + 6 + 8 + 9 = 23\nF(3) = (0 * 3) + (1 * 2) + (2 * 6) + (3 * 4) = 0 + 2 + 12 + 12 = 26\nSo the maximum value of F(0), F(1), F(2), F(3) is F(3) = 26.\n\nExample 2:\n\nInput: nums = [100]\nOutput: 0\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 105\n-100 <= nums[i] <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, -1, 1, -1, 1]) == 6\n assert candidate(nums = [1, 0, 0, 0, 1]) == 7\n assert candidate(nums = [10, -10, 20, -20]) == 50\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 330\n assert candidate(nums = [1, 0, 0, 0]) == 3\n assert candidate(nums = [100]) == 0\n assert candidate(nums = [1, -1, 1, -1]) == 2\n assert candidate(nums = [10, 20, 30, 40, 50]) == 400\n assert candidate(nums = [4, 3, 2, 6]) == 26\n assert candidate(nums = [-1, -2, -3, -4, -5]) == -25\n assert candidate(nums = [5, 5, 5, 5, 5]) == 50\n assert candidate(nums = [0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [5, 5, 5, 5]) == 30\n assert candidate(nums = [1, 2, 3, 4, 5]) == 40\n assert candidate(nums = [100, -100, 100, -100, 100]) == 600\n assert candidate(nums = [0, 0, 0, 0]) == 0\n assert candidate(nums = [-1, -2, -3, -4]) == -12\n assert candidate(nums = [1, 0, 0, 0, 0]) == 4\n assert candidate(nums = [1, 2]) == 2\n assert candidate(nums = [5, 3, 1, 2, 4]) == 37\n assert candidate(nums = [-1, 0, 1]) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 41650\n assert candidate(nums = [-10, -20, -30, -40, -50, -60]) == -430\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 266000\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 56\n assert candidate(nums = [-100, -99, -98, -97, -96, -95, -94, -93, -92, -91, -90]) == -5115\n assert candidate(nums = [99, 98, 97, 96, 95, 94, 93, 92, 91, 90]) == 4295\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]) == 9\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 21750\n assert candidate(nums = [-99, -98, -97, -96, -95, -94, -93, -92, -91, -90]) == -4170\n assert candidate(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == 4500\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 33000\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70]) == 1120\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 29\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == 285\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == 7\n assert candidate(nums = [10, 20, 30, 40, 50, 60]) == 700\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90]) == 5280\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15]) == -700\n assert candidate(nums = [-10, 20, -30, 40, -50, 60]) == 180\n assert candidate(nums = [-10, 1, -20, 2, -30, 3, -40, 4]) == -206\n assert candidate(nums = [0, 1, -1, 2, -2, 3, -3]) == 15\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40]) == 210\n assert candidate(nums = [1000, -1000, 2000, -2000, 3000, -3000, 4000, -4000, 5000, -5000]) == 35000\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]) == 9\n assert candidate(nums = [-10, 0, 10, -20, 20, -30, 30, -40, 40, -50]) == 110\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 435\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50]) == 350\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 2]) == 17\n assert candidate(nums = [-50, -50, -50, -50, -50]) == -500\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1050\n assert candidate(nums = [5, 1, 4, 2, 8, 3, 7, 6, 9, 0]) == 263\n assert candidate(nums = [100, 0, -100, 200, 0, -200, 300, 0, -300, 400]) == 3000\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == 210\n assert candidate(nums = [-50, -50, -50, -50, -50, -50, -50, -50, -50, -50]) == -2250\n assert candidate(nums = [-1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10, -11, 11, -12, 12, -13, 13, -14, 14, -15, 15]) == 120\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == 21\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 1120\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 330\n assert candidate(nums = [50, 50, 50, 50, 50]) == 500\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == 35\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 715\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 3300\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [50, -50, 40, -40, 30, -30, 20, -20, 10, -10]) == 350\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 26600\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 190\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == 5\n assert candidate(nums = [-10, 0, 10, -20, 0, 20, -30, 0, 30, -40]) == 120\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 5200\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 110\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 1900\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [100, 0, -100, 50, 0, -50, 25, 0, -25, 12]) == 746\n assert candidate(nums = [1000, -1000, 1000, -1000, 1000, -1000]) == 3000\n assert candidate(nums = [0, 1, -1, 2, -2, 3, -3, 4, -4, 5]) == 35\n assert candidate(nums = [100, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 1140\n assert candidate(nums = [99, -99, 98, -98, 97, -97, 96, -96, 95, -95]) == 505\n assert candidate(nums = [50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]) == 550\n assert candidate(nums = [100, 0, -100, 200, 0, -200, 300, 0, -300, 400, 0, -400]) == 2800\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 2660\n assert candidate(nums = [90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]) == 3500\n assert candidate(nums = [7, 1, 3, 4, 6, 5]) == 84\n assert candidate(nums = [100, -100, 200, -200, 300, -300, 400, -400, 500, -500, 600, -600, 700, -700, 800, -800, 900, -900, 1000, -1000]) == 14500\n assert candidate(nums = [100, -50, 200, -25, 300, -75]) == 2000\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 2250\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20]) == 190\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().maxRotateFunction", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var maxRotateFunction = function(nums) {", "container": null, "callable": "maxRotateFunction", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 397, "task_id": "integer-replacement", "difficulty": "Medium", "problem_description": "Given a positive integer n, you can apply one of the following operations:\n\nIf n is even, replace n with n / 2.\nIf n is odd, replace n with either n + 1 or n - 1.\n\nReturn the minimum number of operations needed for n to become 1.\n \nExample 1:\n\nInput: n = 8\nOutput: 3\nExplanation: 8 -> 4 -> 2 -> 1\n\nExample 2:\n\nInput: n = 7\nOutput: 4\nExplanation: 7 -> 8 -> 4 -> 2 -> 1\nor 7 -> 6 -> 3 -> 2 -> 1\n\nExample 3:\n\nInput: n = 4\nOutput: 2\n\n \nConstraints:\n\n1 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == 3\n assert candidate(n = 15) == 5\n assert candidate(n = 4) == 2\n assert candidate(n = 2147483647) == 32\n assert candidate(n = 1) == 0\n assert candidate(n = 1000000000) == 38\n assert candidate(n = 7) == 4\n assert candidate(n = 317) == 11\n assert candidate(n = 63) == 7\n assert candidate(n = 21) == 6\n assert candidate(n = 32767) == 16\n assert candidate(n = 50000) == 20\n assert candidate(n = 2047) == 12\n assert candidate(n = 16383) == 15\n assert candidate(n = 5) == 3\n assert candidate(n = 123) == 9\n assert candidate(n = 134217727) == 28\n assert candidate(n = 64) == 6\n assert candidate(n = 99) == 9\n assert candidate(n = 1073741823) == 31\n assert candidate(n = 23) == 6\n assert candidate(n = 51) == 8\n assert candidate(n = 16777215) == 25\n assert candidate(n = 101) == 9\n assert candidate(n = 99999999) == 32\n assert candidate(n = 2048) == 11\n assert candidate(n = 999) == 13\n assert candidate(n = 27) == 7\n assert candidate(n = 8191) == 14\n assert candidate(n = 1023) == 11\n assert candidate(n = 19) == 6\n assert candidate(n = 65535) == 17\n assert candidate(n = 513) == 10\n assert candidate(n = 127) == 8\n assert candidate(n = 1048575) == 21\n assert candidate(n = 31) == 6\n assert candidate(n = 1000000) == 24\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().integerReplacement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var integerReplacement = function(n) {", "container": null, "callable": "integerReplacement", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 399, "task_id": "evaluate-division", "difficulty": "Medium", "problem_description": "You are given an array of variable pairs equations and an array of real numbers values, where equations[i] = [Ai, Bi] and values[i] represent the equation Ai / Bi = values[i]. Each Ai or Bi is a string that represents a single variable.\nYou are also given some queries, where queries[j] = [Cj, Dj] represents the jth query where you must find the answer for Cj / Dj = ?.\nReturn the answers to all queries. If a single answer cannot be determined, return -1.0.\nNote: The input is always valid. You may assume that evaluating the queries will not result in division by zero and that there is no contradiction.\nNote: The variables that do not occur in the list of equations are undefined, so the answer cannot be determined for them.\n \nExample 1:\n\nInput: equations = [[\"a\",\"b\"],[\"b\",\"c\"]], values = [2.0,3.0], queries = [[\"a\",\"c\"],[\"b\",\"a\"],[\"a\",\"e\"],[\"a\",\"a\"],[\"x\",\"x\"]]\nOutput: [6.00000,0.50000,-1.00000,1.00000,-1.00000]\nExplanation: \nGiven: a / b = 2.0, b / c = 3.0\nqueries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? \nreturn: [6.0, 0.5, -1.0, 1.0, -1.0 ]\nnote: x is undefined => -1.0\nExample 2:\n\nInput: equations = [[\"a\",\"b\"],[\"b\",\"c\"],[\"bc\",\"cd\"]], values = [1.5,2.5,5.0], queries = [[\"a\",\"c\"],[\"c\",\"b\"],[\"bc\",\"cd\"],[\"cd\",\"bc\"]]\nOutput: [3.75000,0.40000,5.00000,0.20000]\n\nExample 3:\n\nInput: equations = [[\"a\",\"b\"]], values = [0.5], queries = [[\"a\",\"b\"],[\"b\",\"a\"],[\"a\",\"c\"],[\"x\",\"y\"]]\nOutput: [0.50000,2.00000,-1.00000,-1.00000]\n\n \nConstraints:\n\n1 <= equations.length <= 20\nequations[i].length == 2\n1 <= Ai.length, Bi.length <= 5\nvalues.length == equations.length\n0.0 < values[i] <= 20.0\n1 <= queries.length <= 20\nqueries[i].length == 2\n1 <= Cj.length, Dj.length <= 5\nAi, Bi, Cj, Dj consist of lower case English letters and digits.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(equations = [['a1', 'b1'], ['a2', 'b2'], ['a3', 'b3']],values = [1.1, 2.2, 3.3],queries = [['a1', 'b1'], ['a2', 'b2'], ['a3', 'b3'], ['b1', 'a1']]) == [1.1, 2.2, 3.3, 0.9090909090909091]\n assert candidate(equations = [['a', 'b'], ['b', 'c']],values = [2.0, 3.0],queries = [['a', 'c'], ['b', 'a'], ['a', 'e'], ['a', 'a'], ['x', 'x']]) == [6.0, 0.5, -1, 1.0, -1]\n assert candidate(equations = [['a', 'b']],values = [0.5],queries = [['a', 'b'], ['b', 'a'], ['a', 'c'], ['x', 'y']]) == [0.5, 2.0, -1, -1]\n assert candidate(equations = [['x1', 'x2'], ['x3', 'x4']],values = [2.0, 3.0],queries = [['x1', 'x2'], ['x3', 'x4'], ['x1', 'x3']]) == [2.0, 3.0, -1]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['bc', 'cd']],values = [1.5, 2.5, 5.0],queries = [['a', 'c'], ['c', 'b'], ['bc', 'cd'], ['cd', 'bc']]) == [3.75, 0.4, 5.0, 0.2]\n assert candidate(equations = [['x1', 'x2'], ['x2', 'x3'], ['x3', 'x4']],values = [2.0, 3.0, 4.0],queries = [['x1', 'x4'], ['x4', 'x1'], ['x1', 'x5']]) == [24.0, 0.041666666666666664, -1]\n assert candidate(equations = [['m1', 'm2'], ['m2', 'm3'], ['m3', 'm4'], ['m4', 'm1'], ['m1', 'm5']],values = [1.2, 2.3, 3.4, 4.5, 5.6],queries = [['m1', 'm3'], ['m3', 'm1'], ['m2', 'm4'], ['m4', 'm2'], ['m1', 'm6']]) == [2.76, 0.3623188405797102, 7.8199999999999985, 0.1278772378516624, -1]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'd'], ['d', 'a']],values = [2.0, 3.0, 0.5, 0.333],queries = [['a', 'c'], ['c', 'a'], ['b', 'd'], ['d', 'b'], ['a', 'a'], ['e', 'e']]) == [6.0, 0.16666666666666666, 1.5, 0.6666666666666666, 1.0, -1]\n assert candidate(equations = [['alpha', 'beta'], ['beta', 'gamma'], ['gamma', 'delta'], ['delta', 'epsilon'], ['epsilon', 'zeta'], ['zeta', 'eta'], ['eta', 'theta'], ['theta', 'iota'], ['iota', 'kappa'], ['kappa', 'lambda']],values = [2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0],queries = [['alpha', 'lambda'], ['lambda', 'alpha'], ['beta', 'kappa'], ['kappa', 'beta'], ['gamma', 'iota'], ['iota', 'gamma'], ['delta', 'theta'], ['theta', 'delta'], ['epsilon', 'eta'], ['eta', 'epsilon'], ['alpha', 'mu']]) == [39916800.0, 2.505210838544172e-08, 1814400.0, 5.511463844797178e-07, 60480.0, 1.6534391534391536e-05, 1680.0, 0.0005952380952380953, 42.0, 0.023809523809523808, -1]\n assert candidate(equations = [['nodeA', 'nodeB'], ['nodeB', 'nodeC'], ['nodeC', 'nodeD'], ['nodeD', 'nodeE'], ['nodeE', 'nodeF'], ['nodeF', 'nodeG'], ['nodeG', 'nodeH'], ['nodeH', 'nodeI'], ['nodeI', 'nodeJ'], ['nodeJ', 'nodeA']],values = [1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1],queries = [['nodeA', 'nodeJ'], ['nodeJ', 'nodeA'], ['nodeB', 'nodeD'], ['nodeD', 'nodeB'], ['nodeE', 'nodeH'], ['nodeH', 'nodeE'], ['nodeF', 'nodeG'], ['nodeG', 'nodeF'], ['nodeA', 'nodeK']]) == [60.9493248, 0.016407072650622703, 1.8199999999999998, 0.5494505494505495, 4.896000000000001, 0.20424836601307186, 1.7, 0.5882352941176471, -1]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'd'], ['d', 'e'], ['e', 'f'], ['f', 'g']],values = [2.0, 3.0, 4.0, 5.0, 6.0, 7.0],queries = [['a', 'g'], ['g', 'a'], ['b', 'f'], ['f', 'b'], ['c', 'e'], ['e', 'c'], ['a', 'h'], ['h', 'a']]) == [5040.0, 0.0001984126984126984, 360.0, 0.002777777777777778, 20.0, 0.05, -1, -1]\n assert candidate(equations = [['alpha', 'beta'], ['beta', 'gamma'], ['gamma', 'delta'], ['delta', 'epsilon']],values = [1.2, 1.3, 1.4, 1.5],queries = [['alpha', 'epsilon'], ['epsilon', 'alpha'], ['beta', 'delta'], ['gamma', 'beta'], ['alpha', 'zeta']]) == [3.2759999999999994, 0.30525030525030533, 1.8199999999999996, 0.7692307692307693, -1]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['a', 'd'], ['d', 'e'], ['e', 'f']],values = [2.0, 3.0, 4.0, 5.0, 6.0],queries = [['a', 'f'], ['f', 'a'], ['b', 'e'], ['c', 'd'], ['x', 'y']]) == [120.0, 0.008333333333333333, 10.0, 0.6666666666666666, -1]\n assert candidate(equations = [['var1', 'var2'], ['var2', 'var3'], ['var3', 'var4'], ['var4', 'var5'], ['var5', 'var6'], ['var6', 'var7']],values = [2.0, 2.0, 2.0, 2.0, 2.0, 2.0],queries = [['var1', 'var7'], ['var7', 'var1'], ['var2', 'var6'], ['var3', 'var5'], ['x', 'y']]) == [64.0, 0.015625, 16.0, 4.0, -1]\n assert candidate(equations = [['alpha', 'beta'], ['beta', 'gamma'], ['gamma', 'delta'], ['delta', 'epsilon'], ['epsilon', 'zeta']],values = [1.2, 1.3, 1.4, 1.5, 1.6],queries = [['alpha', 'zeta'], ['zeta', 'alpha'], ['alpha', 'epsilon'], ['epsilon', 'alpha'], ['alpha', 'delta'], ['delta', 'alpha'], ['alpha', 'gamma'], ['gamma', 'alpha'], ['alpha', 'beta'], ['beta', 'alpha'], ['zeta', 'beta'], ['beta', 'zeta'], ['zeta', 'gamma'], ['gamma', 'zeta'], ['zeta', 'delta'], ['delta', 'zeta'], ['zeta', 'epsilon'], ['epsilon', 'zeta'], ['a', 'a'], ['b', 'b']]) == [5.2416, 0.19078144078144077, 3.276, 0.3052503052503053, 2.1839999999999997, 0.4578754578754579, 1.5599999999999998, 0.6410256410256411, 1.2, 0.8333333333333334, 0.22893772893772893, 4.368, 0.2976190476190476, 3.3600000000000003, 0.41666666666666663, 2.4000000000000004, 0.625, 1.6, -1, -1]\n assert candidate(equations = [['node1', 'node2'], ['node2', 'node3'], ['node3', 'node4'], ['node4', 'node1'], ['node1', 'node5']],values = [3.0, 4.0, 5.0, 6.0, 7.0],queries = [['node1', 'node5'], ['node5', 'node1'], ['node2', 'node4'], ['node3', 'node2'], ['node4', 'node3'], ['node1', 'node6']]) == [7.0, 0.14285714285714285, 20.0, 0.25, 0.19999999999999998, -1]\n assert candidate(equations = [['v1', 'v2'], ['v2', 'v3'], ['v3', 'v4'], ['v4', 'v1']],values = [3.0, 4.0, 5.0, 6.0],queries = [['v1', 'v4'], ['v4', 'v1'], ['v2', 'v3'], ['v3', 'v2'], ['v5', 'v5']]) == [60.0, 0.016666666666666666, 4.0, 0.25, -1]\n assert candidate(equations = [['var1', 'var2'], ['var2', 'var3'], ['var3', 'var4'], ['var4', 'var5'], ['var5', 'var6'], ['var6', 'var7'], ['var7', 'var8'], ['var8', 'var9'], ['var9', 'var10']],values = [2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0],queries = [['var1', 'var10'], ['var10', 'var1'], ['var2', 'var9'], ['var9', 'var2'], ['var3', 'var8'], ['var8', 'var3'], ['var4', 'var7'], ['var7', 'var4'], ['var5', 'var6'], ['var6', 'var5']]) == [3628800.0, 2.755731922398589e-07, 181440.0, 5.5114638447971785e-06, 6720.0, 0.00014880952380952382, 210.0, 0.004761904761904762, 6.0, 0.16666666666666666]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'd'], ['d', 'e'], ['e', 'f']],values = [1.0, 2.0, 3.0, 4.0, 5.0],queries = [['a', 'f'], ['f', 'a'], ['b', 'd'], ['d', 'b'], ['c', 'e'], ['e', 'c']]) == [120.0, 0.008333333333333333, 6.0, 0.16666666666666666, 12.0, 0.08333333333333333]\n assert candidate(equations = [['u1', 'u2'], ['u2', 'u3'], ['u3', 'u4'], ['u4', 'u5'], ['u5', 'u6'], ['u6', 'u1'], ['u1', 'u7'], ['u7', 'u8']],values = [1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8],queries = [['u1', 'u8'], ['u8', 'u1'], ['u2', 'u7'], ['u7', 'u2'], ['u3', 'u6'], ['u6', 'u3']]) == [67.76, 0.014757969303423848, 7.0, 0.14285714285714288, 79.86, 0.01252191334835963]\n assert candidate(equations = [['var1', 'var2'], ['var2', 'var3'], ['var3', 'var4'], ['var4', 'var5']],values = [2.0, 3.0, 4.0, 5.0],queries = [['var1', 'var5'], ['var5', 'var1'], ['var2', 'var4'], ['var3', 'var2'], ['var1', 'var6']]) == [120.0, 0.008333333333333333, 12.0, 0.3333333333333333, -1]\n assert candidate(equations = [['q1', 'q2'], ['q2', 'q3'], ['q3', 'q4'], ['q4', 'q5'], ['q5', 'q6'], ['q6', 'q1'], ['q1', 'q7'], ['q7', 'q8'], ['q8', 'q9']],values = [0.5, 1.2, 1.8, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0],queries = [['q1', 'q9'], ['q9', 'q1'], ['q2', 'q8'], ['q8', 'q2'], ['q3', 'q7'], ['q7', 'q3']]) == [90.00000000000001, 0.01111111111111111, 36.00000000000001, 0.027777777777777773, 6.666666666666668, 0.14999999999999997]\n assert candidate(equations = [['alpha', 'beta'], ['beta', 'gamma'], ['gamma', 'delta'], ['delta', 'epsilon'], ['epsilon', 'zeta'], ['zeta', 'eta']],values = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6],queries = [['alpha', 'zeta'], ['zeta', 'alpha'], ['beta', 'epsilon'], ['epsilon', 'beta'], ['gamma', 'eta'], ['eta', 'gamma']]) == [0.0012000000000000001, 833.3333333333333, 0.024, 41.666666666666664, 0.036, 27.77777777777778]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'd'], ['d', 'e']],values = [2.0, 0.5, 3.0, 0.25],queries = [['a', 'e'], ['e', 'a'], ['a', 'd'], ['d', 'a'], ['b', 'c'], ['c', 'b'], ['a', 'x']]) == [0.75, 1.3333333333333333, 3.0, 0.3333333333333333, 0.5, 2.0, -1]\n assert candidate(equations = [['alpha', 'beta'], ['beta', 'gamma'], ['gamma', 'delta'], ['delta', 'epsilon'], ['epsilon', 'zeta'], ['zeta', 'eta'], ['eta', 'theta'], ['theta', 'iota']],values = [1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9],queries = [['alpha', 'iota'], ['iota', 'alpha'], ['beta', 'theta'], ['gamma', 'delta'], ['z', 'z']]) == [30.4746624, 0.032814145301245407, 13.366080000000002, 1.4, -1]\n assert candidate(equations = [['v1', 'v2'], ['v2', 'v3'], ['v3', 'v4'], ['v4', 'v5'], ['v5', 'v6'], ['v6', 'v7'], ['v7', 'v8'], ['v8', 'v9'], ['v9', 'v10'], ['v10', 'v11'], ['v11', 'v12'], ['v12', 'v13'], ['v13', 'v14'], ['v14', 'v15']],values = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0],queries = [['v1', 'v15'], ['v15', 'v14'], ['v14', 'v13'], ['v13', 'v12'], ['v12', 'v11'], ['v11', 'v10'], ['v10', 'v9'], ['v9', 'v8'], ['v8', 'v7'], ['v7', 'v6'], ['v6', 'v5'], ['v5', 'v4'], ['v4', 'v3'], ['v3', 'v2'], ['v2', 'v1'], ['v1', 'v16']]) == [87178291200.0, 0.07142857142857142, 0.07692307692307693, 0.08333333333333333, 0.09090909090909091, 0.1, 0.1111111111111111, 0.125, 0.14285714285714285, 0.16666666666666666, 0.2, 0.25, 0.3333333333333333, 0.5, 1.0, -1]\n assert candidate(equations = [['m1', 'm2'], ['m2', 'm3'], ['m3', 'm4'], ['m4', 'm5'], ['m5', 'm6']],values = [1.1, 1.2, 1.3, 1.4, 1.5],queries = [['m1', 'm6'], ['m6', 'm1'], ['m2', 'm4'], ['m3', 'm5'], ['m1', 'm7']]) == [3.6035999999999997, 0.2775002775002775, 1.56, 1.8199999999999996, -1]\n assert candidate(equations = [['x1', 'y1'], ['y1', 'z1'], ['x2', 'y2'], ['y2', 'z2'], ['x3', 'y3'], ['y3', 'z3'], ['x4', 'y4'], ['y4', 'z4']],values = [0.5, 2.0, 1.5, 3.0, 2.5, 4.0, 3.5, 5.0],queries = [['x1', 'z4'], ['z4', 'x1'], ['y2', 'z2'], ['x3', 'y3'], ['a', 'b']]) == [-1, -1, 3.0, 2.5, -1]\n assert candidate(equations = [['a1', 'b1'], ['b1', 'c1'], ['c1', 'd1'], ['d1', 'e1'], ['e1', 'f1'], ['f1', 'g1'], ['g1', 'h1']],values = [1.2, 2.3, 3.4, 4.5, 5.6, 6.7, 7.8],queries = [['a1', 'h1'], ['h1', 'a1'], ['b1', 'g1'], ['g1', 'b1'], ['c1', 'f1'], ['f1', 'c1']]) == [12358.277567999996, 8.09174251425909e-05, 1320.3287999999995, 0.0007573870993346508, 85.67999999999999, 0.011671335200746967]\n assert candidate(equations = [['m1', 'n1'], ['n1', 'o1'], ['o1', 'p1'], ['p1', 'q1']],values = [2.5, 3.5, 4.5, 5.5],queries = [['m1', 'q1'], ['q1', 'm1'], ['n1', 'p1'], ['p1', 'n1'], ['m1', 'x1'], ['x1', 'm1']]) == [216.5625, 0.004617604617604618, 15.75, 0.06349206349206349, -1, -1]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['a', 'd'], ['d', 'e']],values = [2.0, 3.0, 4.0, 5.0],queries = [['a', 'c'], ['c', 'a'], ['a', 'e'], ['e', 'a'], ['x', 'x']]) == [6.000000000000001, 0.16666666666666666, 20.0, 0.05, -1]\n assert candidate(equations = [['x1', 'x2'], ['x2', 'x3'], ['x3', 'x4'], ['x4', 'x5'], ['x5', 'x6']],values = [1.1, 1.2, 1.3, 1.4, 1.5],queries = [['x1', 'x6'], ['x6', 'x1'], ['x1', 'x5'], ['x5', 'x1'], ['x1', 'x4'], ['x4', 'x1'], ['x1', 'x3'], ['x3', 'x1'], ['x1', 'x2'], ['x2', 'x1'], ['x6', 'x2'], ['x2', 'x6'], ['x6', 'x3'], ['x3', 'x6'], ['x6', 'x4'], ['x4', 'x6'], ['x6', 'x5'], ['x5', 'x6']]) == [3.6035999999999997, 0.2775002775002775, 2.4023999999999996, 0.4162504162504163, 1.7160000000000002, 0.5827505827505827, 1.32, 0.7575757575757575, 1.1, 0.909090909090909, 0.30525030525030533, 3.2759999999999994, 0.3663003663003664, 2.7299999999999995, 0.4761904761904763, 2.0999999999999996, 0.6666666666666666, 1.5]\n assert candidate(equations = [['p1', 'q1'], ['p2', 'q2'], ['q1', 'q2'], ['q2', 'p1'], ['p1', 'p2']],values = [1.1, 2.2, 3.3, 4.4, 5.5],queries = [['p1', 'p2'], ['p2', 'p1'], ['q1', 'q2'], ['q2', 'q1'], ['p1', 'q3']]) == [1.65, 0.6060606060606061, 3.3, 0.30303030303030304, -1]\n assert candidate(equations = [['p1', 'p2'], ['p2', 'p3'], ['p3', 'p4'], ['p4', 'p5']],values = [0.5, 1.5, 2.5, 3.5],queries = [['p1', 'p5'], ['p5', 'p1'], ['p2', 'p4'], ['p4', 'p2'], ['p1', 'p6']]) == [6.5625, 0.1523809523809524, 3.75, 0.26666666666666666, -1]\n assert candidate(equations = [['n1', 'n2'], ['n2', 'n3'], ['n3', 'n4'], ['n4', 'n1'], ['n1', 'n5'], ['n5', 'n6']],values = [0.7, 1.1, 1.3, 1.7, 2.1, 2.3],queries = [['n1', 'n4'], ['n4', 'n1'], ['n2', 'n5'], ['n5', 'n2'], ['n3', 'n6'], ['n6', 'n3']]) == [1.0010000000000001, 0.9990009990009989, 3.0000000000000004, 0.3333333333333333, 6.2727272727272725, 0.15942028985507248]\n assert candidate(equations = [['p', 'q'], ['q', 'r'], ['r', 's'], ['s', 't'], ['t', 'u']],values = [1.1, 1.2, 1.3, 1.4, 1.5],queries = [['p', 'u'], ['u', 'p'], ['q', 't'], ['r', 's'], ['z', 'z']]) == [3.6035999999999997, 0.2775002775002775, 2.1839999999999997, 1.3, -1]\n assert candidate(equations = [['m1', 'n1'], ['n1', 'o1'], ['o1', 'p1'], ['p1', 'q1']],values = [1.5, 2.5, 3.5, 4.5],queries = [['m1', 'o1'], ['o1', 'm1'], ['n1', 'q1'], ['q1', 'n1'], ['p1', 'p1']]) == [3.75, 0.26666666666666666, 39.375, 0.025396825396825397, 1.0]\n assert candidate(equations = [['p', 'q'], ['q', 'r'], ['r', 's'], ['s', 't']],values = [0.5, 2.0, 3.0, 4.0],queries = [['p', 't'], ['t', 'p'], ['q', 's'], ['s', 'q'], ['r', 'p'], ['x', 'y']]) == [12.0, 0.08333333333333333, 6.0, 0.16666666666666666, 1.0, -1]\n assert candidate(equations = [['u1', 'v1'], ['v1', 'w1'], ['u2', 'v2'], ['v2', 'w2'], ['u3', 'v3'], ['v3', 'w3'], ['u4', 'v4'], ['v4', 'w4']],values = [2.1, 2.2, 3.1, 3.2, 4.1, 4.2, 5.1, 5.2],queries = [['u1', 'w4'], ['w4', 'u1'], ['v2', 'w2'], ['u3', 'v3'], ['a', 'b']]) == [-1, -1, 3.2, 4.1, -1]\n assert candidate(equations = [['x0', 'y0'], ['y0', 'z0'], ['z0', 'x1'], ['x1', 'y1'], ['y1', 'z1'], ['z1', 'w1'], ['w1', 'x2']],values = [1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7],queries = [['x0', 'x2'], ['x2', 'x0'], ['y0', 'w1'], ['w1', 'y0'], ['z0', 'z1'], ['z1', 'z0'], ['x1', 'y1']]) == [9821.534184000002, 0.00010181708695053704, 1159.5672000000002, 0.0008623907264710488, 79.86, 0.012521913348359628, 4.4]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'd'], ['d', 'e'], ['e', 'f'], ['f', 'g'], ['g', 'h'], ['h', 'i'], ['i', 'j']],values = [2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0],queries = [['a', 'j'], ['j', 'a'], ['b', 'd'], ['d', 'b'], ['e', 'h'], ['h', 'e'], ['f', 'g'], ['g', 'f'], ['a', 'k']]) == [3628800.0, 2.755731922398589e-07, 12.0, 0.08333333333333333, 336.0, 0.002976190476190476, 7.0, 0.14285714285714285, -1]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'a'], ['d', 'e'], ['e', 'f'], ['f', 'd']],values = [2.0, 3.0, 0.5, 4.0, 5.0, 0.25],queries = [['a', 'f'], ['f', 'a'], ['b', 'e'], ['c', 'd'], ['x', 'y']]) == [-1, -1, -1, -1, -1]\n assert candidate(equations = [['m1', 'n1'], ['n1', 'o1'], ['m2', 'n2'], ['n2', 'o2'], ['m3', 'n3'], ['n3', 'o3']],values = [1.5, 2.5, 3.5, 4.5, 5.5, 6.5],queries = [['m1', 'o3'], ['o3', 'm1'], ['n2', 'o2'], ['m3', 'n3'], ['a', 'b']]) == [-1, -1, 4.5, 5.5, -1]\n assert candidate(equations = [['x1', 'y1'], ['y1', 'z1'], ['z1', 'w1'], ['x1', 'w1'], ['w1', 'x1'], ['y1', 'w1']],values = [2.0, 3.0, 4.0, 24.0, 0.0416667, 12.0],queries = [['x1', 'z1'], ['z1', 'x1'], ['y1', 'w1'], ['w1', 'y1'], ['x1', 'y1'], ['y1', 'x1']]) == [6.0, 0.16666666666666666, 12.0, 0.08333333333333333, 2.0, 0.5]\n assert candidate(equations = [['x1', 'x2'], ['x2', 'x3'], ['x3', 'x4'], ['x4', 'x5']],values = [2.0, 3.0, 4.0, 5.0],queries = [['x1', 'x5'], ['x5', 'x1'], ['x2', 'x4'], ['x3', 'x2'], ['x1', 'x6']]) == [120.0, 0.008333333333333333, 12.0, 0.3333333333333333, -1]\n assert candidate(equations = [['x1', 'y1'], ['x2', 'y2'], ['x3', 'y3'], ['y1', 'y2'], ['y2', 'y3'], ['y3', 'x1']],values = [1.1, 2.2, 3.3, 4.4, 5.5, 6.6],queries = [['x1', 'y3'], ['y3', 'x1'], ['x2', 'y1'], ['y1', 'x2'], ['x3', 'y2'], ['y2', 'x3'], ['x1', 'x4']]) == [26.620000000000005, 0.03756574004507888, 0.5, 2.0, 0.6, 1.6666666666666667, -1]\n assert candidate(equations = [['var1', 'var2'], ['var2', 'var3'], ['var3', 'var4'], ['var4', 'var5'], ['var5', 'var6'], ['var6', 'var7'], ['var7', 'var8'], ['var8', 'var9']],values = [1.11, 2.22, 3.33, 4.44, 5.55, 6.66, 7.77, 8.88],queries = [['var1', 'var9'], ['var9', 'var1'], ['var2', 'var8'], ['var8', 'var2'], ['var3', 'var7'], ['var7', 'var3']]) == [92918.9628750124, 1.0762065880407262e-05, 9426.889342891443, 0.00010607953096999833, 546.5053476000002, 0.0018298082615138891]\n assert candidate(equations = [['var1', 'var2'], ['var2', 'var3'], ['var3', 'var4'], ['var4', 'var5'], ['var5', 'var1']],values = [1.1, 2.2, 3.3, 4.4, 5.5],queries = [['var1', 'var3'], ['var3', 'var1'], ['var2', 'var4'], ['var4', 'var2'], ['var1', 'var5'], ['var5', 'var1'], ['var1', 'var6']]) == [2.4200000000000004, 0.4132231404958677, 7.26, 0.13774104683195593, 35.138400000000004, 0.02845889397354461, -1]\n assert candidate(equations = [['v1', 'v2'], ['v2', 'v3'], ['v3', 'v4'], ['v4', 'v5'], ['v5', 'v6']],values = [1.2, 1.5, 1.7, 1.9, 2.1],queries = [['v1', 'v6'], ['v6', 'v1'], ['v2', 'v5'], ['v5', 'v2'], ['v3', 'v4']]) == [12.209399999999997, 0.08190410667190855, 4.844999999999999, 0.20639834881320954, 1.7]\n assert candidate(equations = [['p1', 'p2'], ['p2', 'p3'], ['p3', 'p4'], ['p4', 'p5'], ['p5', 'p1']],values = [2.0, 3.0, 0.5, 0.25, 4.0],queries = [['p1', 'p3'], ['p3', 'p1'], ['p2', 'p5'], ['p4', 'p2'], ['p1', 'p6']]) == [6.0, 0.16666666666666666, 0.375, 0.6666666666666666, -1]\n assert candidate(equations = [['m', 'n'], ['n', 'o'], ['o', 'p'], ['p', 'q'], ['q', 'r']],values = [2.0, 3.0, 4.0, 5.0, 6.0],queries = [['m', 'r'], ['r', 'q'], ['q', 'p'], ['p', 'o'], ['o', 'n'], ['n', 'm']]) == [720.0, 0.16666666666666666, 0.2, 0.25, 0.3333333333333333, 0.5]\n assert candidate(equations = [['x', 'y'], ['y', 'z'], ['z', 'w'], ['w', 'v'], ['v', 'u'], ['u', 't']],values = [2.0, 3.0, 4.0, 5.0, 6.0, 7.0],queries = [['x', 't'], ['t', 'x'], ['y', 'u'], ['u', 'y'], ['z', 'v'], ['v', 'z']]) == [5040.0, 0.0001984126984126984, 360.0, 0.002777777777777778, 20.0, 0.05]\n assert candidate(equations = [['m', 'n'], ['n', 'o'], ['o', 'p'], ['p', 'q'], ['q', 'r'], ['r', 's']],values = [1.5, 2.5, 3.5, 4.5, 5.5, 6.5],queries = [['m', 's'], ['s', 'm'], ['m', 'r'], ['r', 'm'], ['m', 'q'], ['q', 'm'], ['m', 'p'], ['p', 'm'], ['m', 'o'], ['o', 'm'], ['m', 'n'], ['n', 'm'], ['t', 't']]) == [2111.484375, 0.0004736004736004736, 324.84375, 0.0030784030784030783, 59.0625, 0.016931216931216932, 13.125, 0.0761904761904762, 3.75, 0.26666666666666666, 1.5, 0.6666666666666666, -1]\n assert candidate(equations = [['s1', 's2'], ['s2', 's3'], ['s3', 's4'], ['s4', 's5'], ['s5', 's1'], ['s1', 's6'], ['s6', 's2']],values = [1.1, 1.2, 1.3, 1.4, 1.5, 2.0, 0.5],queries = [['s1', 's5'], ['s5', 's1'], ['s2', 's4'], ['s3', 's2'], ['s1', 's7']]) == [2.4024, 0.41625041625041626, 1.56, 0.8333333333333335, -1]\n assert candidate(equations = [['x1', 'x2'], ['x2', 'x3'], ['x3', 'x4'], ['x4', 'x5'], ['x5', 'x6'], ['x6', 'x7'], ['x7', 'x1']],values = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0],queries = [['x1', 'x7'], ['x7', 'x1'], ['x2', 'x5'], ['x5', 'x2'], ['x3', 'x6'], ['x6', 'x3']]) == [720.0, 0.001388888888888889, 24.0, 0.041666666666666664, 60.0, 0.016666666666666666]\n assert candidate(equations = [['a', 'b'], ['b', 'c'], ['c', 'd'], ['d', 'e']],values = [2.0, 3.0, 4.0, 5.0],queries = [['a', 'e'], ['e', 'a'], ['a', 'd'], ['d', 'a'], ['x', 'y']]) == [120.0, 0.008333333333333333, 24.0, 0.041666666666666664, -1]\n assert candidate(equations = [['node1', 'node2'], ['node2', 'node3'], ['node3', 'node4'], ['node4', 'node5'], ['node5', 'node6'], ['node6', 'node7'], ['node7', 'node8'], ['node8', 'node9']],values = [1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8],queries = [['node1', 'node9'], ['node9', 'node1'], ['node2', 'node8'], ['node8', 'node2'], ['node3', 'node7'], ['node7', 'node3'], ['node4', 'node6'], ['node6', 'node4'], ['node1', 'node10']]) == [17.6432256, 0.0566789782476057, 8.91072, 0.11222437693025929, 4.368, 0.2289377289377289, 2.0999999999999996, 0.4761904761904762, -1]\n"}, "metadata": {"canonical_parameter_names": ["equations", "values", "queries"], "leetcode_dataset_entry_point": "Solution().calcEquation", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var calcEquation = function(equations, values, queries) {", "container": null, "callable": "calcEquation", "parameters": [{"name": "equations", "type": "string[][]"}, {"name": "values", "type": "number[]"}, {"name": "queries", "type": "string[][]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 400, "task_id": "nth-digit", "difficulty": "Medium", "problem_description": "Given an integer n, return the nth digit of the infinite integer sequence [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...].\n \nExample 1:\n\nInput: n = 3\nOutput: 3\n\nExample 2:\n\nInput: n = 11\nOutput: 0\nExplanation: The 11th digit of the sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... is a 0, which is part of the number 10.\n\n \nConstraints:\n\n1 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == 3\n assert candidate(n = 11) == 0\n assert candidate(n = 231) == 3\n assert candidate(n = 15) == 2\n assert candidate(n = 2147483647) == 2\n assert candidate(n = 1000000) == 1\n assert candidate(n = 123456789) == 2\n assert candidate(n = 100) == 5\n assert candidate(n = 1000) == 3\n assert candidate(n = 99999) == 1\n assert candidate(n = 999999999) == 9\n assert candidate(n = 2147483646) == 2\n assert candidate(n = 12345) == 3\n assert candidate(n = 2000000000) == 3\n assert candidate(n = 50000) == 1\n assert candidate(n = 50) == 3\n assert candidate(n = 190) == 1\n assert candidate(n = 987654) == 3\n assert candidate(n = 123) == 6\n assert candidate(n = 300) == 6\n assert candidate(n = 99) == 4\n assert candidate(n = 10000) == 7\n assert candidate(n = 1001) == 7\n assert candidate(n = 8976543) == 4\n assert candidate(n = 2100000000) == 5\n assert candidate(n = 360) == 6\n assert candidate(n = 2147483645) == 7\n assert candidate(n = 777777777) == 0\n assert candidate(n = 100000) == 2\n assert candidate(n = 20000) == 7\n assert candidate(n = 999) == 9\n assert candidate(n = 1000000010) == 2\n assert candidate(n = 5000) == 2\n assert candidate(n = 256) == 1\n assert candidate(n = 1000000000) == 1\n assert candidate(n = 1000000001) == 2\n assert candidate(n = 111111111) == 7\n assert candidate(n = 987654321) == 7\n assert candidate(n = 888888888) == 0\n assert candidate(n = 2500) == 8\n assert candidate(n = 500000) == 5\n assert candidate(n = 189) == 9\n assert candidate(n = 150000000) == 8\n assert candidate(n = 500000000) == 8\n assert candidate(n = 9) == 9\n assert candidate(n = 1234567) == 2\n assert candidate(n = 19999) == 2\n assert candidate(n = 999999) == 4\n assert candidate(n = 123456) == 6\n assert candidate(n = 10) == 1\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().findNthDigit", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findNthDigit = function(n) {", "container": null, "callable": "findNthDigit", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 401, "task_id": "binary-watch", "difficulty": "Easy", "problem_description": "A binary watch has 4 LEDs on the top to represent the hours (0-11), and 6 LEDs on the bottom to represent the minutes (0-59). Each LED represents a zero or one, with the least significant bit on the right.\n\nFor example, the below binary watch reads \"4:51\".\n\n\nGiven an integer turnedOn which represents the number of LEDs that are currently on (ignoring the PM), return all possible times the watch could represent. You may return the answer in any order.\nThe hour must not contain a leading zero.\n\nFor example, \"01:00\" is not valid. It should be \"1:00\".\n\nThe minute must consist of two digits and may contain a leading zero.\n\nFor example, \"10:2\" is not valid. It should be \"10:02\".\n\n \nExample 1:\nInput: turnedOn = 1\nOutput: [\"0:01\",\"0:02\",\"0:04\",\"0:08\",\"0:16\",\"0:32\",\"1:00\",\"2:00\",\"4:00\",\"8:00\"]\nExample 2:\nInput: turnedOn = 9\nOutput: []\n\n \nConstraints:\n\n0 <= turnedOn <= 10\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(turnedOn = 5) == ['0:31', '0:47', '0:55', '0:59', '1:15', '1:23', '1:27', '1:29', '1:30', '1:39', '1:43', '1:45', '1:46', '1:51', '1:53', '1:54', '1:57', '1:58', '2:15', '2:23', '2:27', '2:29', '2:30', '2:39', '2:43', '2:45', '2:46', '2:51', '2:53', '2:54', '2:57', '2:58', '3:07', '3:11', '3:13', '3:14', '3:19', '3:21', '3:22', '3:25', '3:26', '3:28', '3:35', '3:37', '3:38', '3:41', '3:42', '3:44', '3:49', '3:50', '3:52', '3:56', '4:15', '4:23', '4:27', '4:29', '4:30', '4:39', '4:43', '4:45', '4:46', '4:51', '4:53', '4:54', '4:57', '4:58', '5:07', '5:11', '5:13', '5:14', '5:19', '5:21', '5:22', '5:25', '5:26', '5:28', '5:35', '5:37', '5:38', '5:41', '5:42', '5:44', '5:49', '5:50', '5:52', '5:56', '6:07', '6:11', '6:13', '6:14', '6:19', '6:21', '6:22', '6:25', '6:26', '6:28', '6:35', '6:37', '6:38', '6:41', '6:42', '6:44', '6:49', '6:50', '6:52', '6:56', '7:03', '7:05', '7:06', '7:09', '7:10', '7:12', '7:17', '7:18', '7:20', '7:24', '7:33', '7:34', '7:36', '7:40', '7:48', '8:15', '8:23', '8:27', '8:29', '8:30', '8:39', '8:43', '8:45', '8:46', '8:51', '8:53', '8:54', '8:57', '8:58', '9:07', '9:11', '9:13', '9:14', '9:19', '9:21', '9:22', '9:25', '9:26', '9:28', '9:35', '9:37', '9:38', '9:41', '9:42', '9:44', '9:49', '9:50', '9:52', '9:56', '10:07', '10:11', '10:13', '10:14', '10:19', '10:21', '10:22', '10:25', '10:26', '10:28', '10:35', '10:37', '10:38', '10:41', '10:42', '10:44', '10:49', '10:50', '10:52', '10:56', '11:03', '11:05', '11:06', '11:09', '11:10', '11:12', '11:17', '11:18', '11:20', '11:24', '11:33', '11:34', '11:36', '11:40', '11:48']\n assert candidate(turnedOn = 8) == ['7:31', '7:47', '7:55', '7:59', '11:31', '11:47', '11:55', '11:59']\n assert candidate(turnedOn = 0) == ['0:00']\n assert candidate(turnedOn = 9) == []\n assert candidate(turnedOn = 3) == ['0:07', '0:11', '0:13', '0:14', '0:19', '0:21', '0:22', '0:25', '0:26', '0:28', '0:35', '0:37', '0:38', '0:41', '0:42', '0:44', '0:49', '0:50', '0:52', '0:56', '1:03', '1:05', '1:06', '1:09', '1:10', '1:12', '1:17', '1:18', '1:20', '1:24', '1:33', '1:34', '1:36', '1:40', '1:48', '2:03', '2:05', '2:06', '2:09', '2:10', '2:12', '2:17', '2:18', '2:20', '2:24', '2:33', '2:34', '2:36', '2:40', '2:48', '3:01', '3:02', '3:04', '3:08', '3:16', '3:32', '4:03', '4:05', '4:06', '4:09', '4:10', '4:12', '4:17', '4:18', '4:20', '4:24', '4:33', '4:34', '4:36', '4:40', '4:48', '5:01', '5:02', '5:04', '5:08', '5:16', '5:32', '6:01', '6:02', '6:04', '6:08', '6:16', '6:32', '7:00', '8:03', '8:05', '8:06', '8:09', '8:10', '8:12', '8:17', '8:18', '8:20', '8:24', '8:33', '8:34', '8:36', '8:40', '8:48', '9:01', '9:02', '9:04', '9:08', '9:16', '9:32', '10:01', '10:02', '10:04', '10:08', '10:16', '10:32', '11:00']\n assert candidate(turnedOn = 10) == []\n assert candidate(turnedOn = 4) == ['0:15', '0:23', '0:27', '0:29', '0:30', '0:39', '0:43', '0:45', '0:46', '0:51', '0:53', '0:54', '0:57', '0:58', '1:07', '1:11', '1:13', '1:14', '1:19', '1:21', '1:22', '1:25', '1:26', '1:28', '1:35', '1:37', '1:38', '1:41', '1:42', '1:44', '1:49', '1:50', '1:52', '1:56', '2:07', '2:11', '2:13', '2:14', '2:19', '2:21', '2:22', '2:25', '2:26', '2:28', '2:35', '2:37', '2:38', '2:41', '2:42', '2:44', '2:49', '2:50', '2:52', '2:56', '3:03', '3:05', '3:06', '3:09', '3:10', '3:12', '3:17', '3:18', '3:20', '3:24', '3:33', '3:34', '3:36', '3:40', '3:48', '4:07', '4:11', '4:13', '4:14', '4:19', '4:21', '4:22', '4:25', '4:26', '4:28', '4:35', '4:37', '4:38', '4:41', '4:42', '4:44', '4:49', '4:50', '4:52', '4:56', '5:03', '5:05', '5:06', '5:09', '5:10', '5:12', '5:17', '5:18', '5:20', '5:24', '5:33', '5:34', '5:36', '5:40', '5:48', '6:03', '6:05', '6:06', '6:09', '6:10', '6:12', '6:17', '6:18', '6:20', '6:24', '6:33', '6:34', '6:36', '6:40', '6:48', '7:01', '7:02', '7:04', '7:08', '7:16', '7:32', '8:07', '8:11', '8:13', '8:14', '8:19', '8:21', '8:22', '8:25', '8:26', '8:28', '8:35', '8:37', '8:38', '8:41', '8:42', '8:44', '8:49', '8:50', '8:52', '8:56', '9:03', '9:05', '9:06', '9:09', '9:10', '9:12', '9:17', '9:18', '9:20', '9:24', '9:33', '9:34', '9:36', '9:40', '9:48', '10:03', '10:05', '10:06', '10:09', '10:10', '10:12', '10:17', '10:18', '10:20', '10:24', '10:33', '10:34', '10:36', '10:40', '10:48', '11:01', '11:02', '11:04', '11:08', '11:16', '11:32']\n assert candidate(turnedOn = 2) == ['0:03', '0:05', '0:06', '0:09', '0:10', '0:12', '0:17', '0:18', '0:20', '0:24', '0:33', '0:34', '0:36', '0:40', '0:48', '1:01', '1:02', '1:04', '1:08', '1:16', '1:32', '2:01', '2:02', '2:04', '2:08', '2:16', '2:32', '3:00', '4:01', '4:02', '4:04', '4:08', '4:16', '4:32', '5:00', '6:00', '8:01', '8:02', '8:04', '8:08', '8:16', '8:32', '9:00', '10:00']\n assert candidate(turnedOn = 6) == ['1:31', '1:47', '1:55', '1:59', '2:31', '2:47', '2:55', '2:59', '3:15', '3:23', '3:27', '3:29', '3:30', '3:39', '3:43', '3:45', '3:46', '3:51', '3:53', '3:54', '3:57', '3:58', '4:31', '4:47', '4:55', '4:59', '5:15', '5:23', '5:27', '5:29', '5:30', '5:39', '5:43', '5:45', '5:46', '5:51', '5:53', '5:54', '5:57', '5:58', '6:15', '6:23', '6:27', '6:29', '6:30', '6:39', '6:43', '6:45', '6:46', '6:51', '6:53', '6:54', '6:57', '6:58', '7:07', '7:11', '7:13', '7:14', '7:19', '7:21', '7:22', '7:25', '7:26', '7:28', '7:35', '7:37', '7:38', '7:41', '7:42', '7:44', '7:49', '7:50', '7:52', '7:56', '8:31', '8:47', '8:55', '8:59', '9:15', '9:23', '9:27', '9:29', '9:30', '9:39', '9:43', '9:45', '9:46', '9:51', '9:53', '9:54', '9:57', '9:58', '10:15', '10:23', '10:27', '10:29', '10:30', '10:39', '10:43', '10:45', '10:46', '10:51', '10:53', '10:54', '10:57', '10:58', '11:07', '11:11', '11:13', '11:14', '11:19', '11:21', '11:22', '11:25', '11:26', '11:28', '11:35', '11:37', '11:38', '11:41', '11:42', '11:44', '11:49', '11:50', '11:52', '11:56']\n assert candidate(turnedOn = 1) == ['0:01', '0:02', '0:04', '0:08', '0:16', '0:32', '1:00', '2:00', '4:00', '8:00']\n assert candidate(turnedOn = 7) == ['3:31', '3:47', '3:55', '3:59', '5:31', '5:47', '5:55', '5:59', '6:31', '6:47', '6:55', '6:59', '7:15', '7:23', '7:27', '7:29', '7:30', '7:39', '7:43', '7:45', '7:46', '7:51', '7:53', '7:54', '7:57', '7:58', '9:31', '9:47', '9:55', '9:59', '10:31', '10:47', '10:55', '10:59', '11:15', '11:23', '11:27', '11:29', '11:30', '11:39', '11:43', '11:45', '11:46', '11:51', '11:53', '11:54', '11:57', '11:58']\n assert candidate(turnedOn = 11) == []\n"}, "metadata": {"canonical_parameter_names": ["turnedOn"], "leetcode_dataset_entry_point": "Solution().readBinaryWatch", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var readBinaryWatch = function(turnedOn) {", "container": null, "callable": "readBinaryWatch", "parameters": [{"name": "turnedOn", "type": "number"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 402, "task_id": "remove-k-digits", "difficulty": "Medium", "problem_description": "Given string num representing a non-negative integer num, and an integer k, return the smallest possible integer after removing k digits from num.\n \nExample 1:\n\nInput: num = \"1432219\", k = 3\nOutput: \"1219\"\nExplanation: Remove the three digits 4, 3, and 2 to form the new number 1219 which is the smallest.\n\nExample 2:\n\nInput: num = \"10200\", k = 1\nOutput: \"200\"\nExplanation: Remove the leading 1 and the number is 200. Note that the output must not contain leading zeroes.\n\nExample 3:\n\nInput: num = \"10\", k = 2\nOutput: \"0\"\nExplanation: Remove all the digits from the number and it is left with nothing which is 0.\n\n \nConstraints:\n\n1 <= k <= num.length <= 105\nnum consists of only digits.\nnum does not have any leading zeros except for the zero itself.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = \"100\",k = 1) == \"0\"\n assert candidate(num = \"999\",k = 2) == \"9\"\n assert candidate(num = \"1234567890\",k = 9) == \"0\"\n assert candidate(num = \"111111\",k = 2) == \"1111\"\n assert candidate(num = \"987654321\",k = 5) == \"4321\"\n assert candidate(num = \"11111\",k = 2) == \"111\"\n assert candidate(num = \"12345\",k = 2) == \"123\"\n assert candidate(num = \"1111\",k = 2) == \"11\"\n assert candidate(num = \"10001\",k = 1) == \"1\"\n assert candidate(num = \"123456789\",k = 5) == \"1234\"\n assert candidate(num = \"112\",k = 1) == \"11\"\n assert candidate(num = \"99991\",k = 1) == \"9991\"\n assert candidate(num = \"123123\",k = 3) == \"112\"\n assert candidate(num = \"10200\",k = 1) == \"200\"\n assert candidate(num = \"1234567890\",k = 5) == \"12340\"\n assert candidate(num = \"1432219\",k = 3) == \"1219\"\n assert candidate(num = \"9999\",k = 2) == \"99\"\n assert candidate(num = \"10\",k = 1) == \"0\"\n assert candidate(num = \"10\",k = 2) == \"0\"\n assert candidate(num = \"100100\",k = 3) == \"0\"\n assert candidate(num = \"333222111\",k = 5) == \"2111\"\n assert candidate(num = \"9999999999\",k = 5) == \"99999\"\n assert candidate(num = \"12345678900000000000\",k = 10) == \"0\"\n assert candidate(num = \"110011001100\",k = 6) == \"0\"\n assert candidate(num = \"123123123123\",k = 6) == \"111123\"\n assert candidate(num = \"123454321\",k = 4) == \"12321\"\n assert candidate(num = \"111999111999\",k = 6) == \"111111\"\n assert candidate(num = \"2020202020\",k = 5) == \"0\"\n assert candidate(num = \"100100100100100\",k = 5) == \"0\"\n assert candidate(num = \"532354235\",k = 4) == \"23235\"\n assert candidate(num = \"1000000000\",k = 9) == \"0\"\n assert candidate(num = \"3847283948574859234895742389475\",k = 20) == \"22342389475\"\n assert candidate(num = \"999888777666\",k = 6) == \"777666\"\n assert candidate(num = \"100010001\",k = 3) == \"0\"\n assert candidate(num = \"111000111000\",k = 6) == \"0\"\n assert candidate(num = \"5432100000\",k = 2) == \"32100000\"\n assert candidate(num = \"123456789987654321\",k = 10) == \"12344321\"\n assert candidate(num = \"1221221221\",k = 5) == \"11121\"\n assert candidate(num = \"00000000000000000000\",k = 10) == \"0\"\n assert candidate(num = \"111222333444\",k = 6) == \"111222\"\n assert candidate(num = \"12345678901234567890\",k = 10) == \"123456780\"\n assert candidate(num = \"1000000000\",k = 8) == \"0\"\n assert candidate(num = \"100010001000\",k = 6) == \"0\"\n assert candidate(num = \"10000000000000000000\",k = 15) == \"0\"\n assert candidate(num = \"59112346758\",k = 4) == \"1123458\"\n assert candidate(num = \"1122334455\",k = 5) == \"11223\"\n assert candidate(num = \"100100100100\",k = 5) == \"0\"\n assert candidate(num = \"100100100100\",k = 6) == \"0\"\n assert candidate(num = \"5959595959\",k = 5) == \"55555\"\n assert candidate(num = \"111222333\",k = 5) == \"1112\"\n assert candidate(num = \"12345678900000000000\",k = 15) == \"0\"\n assert candidate(num = \"1000100010001000\",k = 8) == \"0\"\n assert candidate(num = \"11111111111111111111\",k = 15) == \"11111\"\n assert candidate(num = \"1098765432\",k = 5) == \"5432\"\n assert candidate(num = \"12341234\",k = 4) == \"1123\"\n assert candidate(num = \"987654321098765432109876543210\",k = 20) == \"76543210\"\n assert candidate(num = \"100010001000\",k = 5) == \"0\"\n assert candidate(num = \"999111999111\",k = 4) == \"11199111\"\n assert candidate(num = \"98765432101234567890\",k = 10) == \"123456780\"\n assert candidate(num = \"1234512345\",k = 5) == \"11234\"\n assert candidate(num = \"100010001\",k = 4) == \"0\"\n assert candidate(num = \"12345678909876543210\",k = 15) == \"3210\"\n assert candidate(num = \"98765432100000\",k = 10) == \"0\"\n assert candidate(num = \"99887766554433221100\",k = 10) == \"4433221100\"\n assert candidate(num = \"100020003000\",k = 3) == \"0\"\n assert candidate(num = \"123412341234\",k = 6) == \"111234\"\n assert candidate(num = \"98765432100000000000\",k = 10) == \"0\"\n assert candidate(num = \"100000000000000000000000000000000000000000000000\",k = 50) == \"0\"\n assert candidate(num = \"98765432100123456789\",k = 10) == \"12345678\"\n assert candidate(num = \"9876543210\",k = 5) == \"43210\"\n assert candidate(num = \"98765432109876543210\",k = 10) == \"876543210\"\n assert candidate(num = \"101010101010\",k = 5) == \"10\"\n assert candidate(num = \"123456789\",k = 4) == \"12345\"\n assert candidate(num = \"5432154321\",k = 5) == \"14321\"\n assert candidate(num = \"533729941590110\",k = 5) == \"2941590110\"\n assert candidate(num = \"100100100100100100100100100100100100100\",k = 20) == \"0\"\n assert candidate(num = \"123321123321\",k = 5) == \"1112321\"\n assert candidate(num = \"1000100010\",k = 5) == \"0\"\n assert candidate(num = \"55555555555555555555\",k = 15) == \"55555\"\n assert candidate(num = \"111222333\",k = 4) == \"11122\"\n assert candidate(num = \"1234567890\",k = 1) == \"123456780\"\n assert candidate(num = \"59595959\",k = 4) == \"5555\"\n assert candidate(num = \"999887766554433221100\",k = 10) == \"54433221100\"\n assert candidate(num = \"10000000000000000000\",k = 10) == \"0\"\n assert candidate(num = \"533721121233121212\",k = 7) == \"11123121212\"\n assert candidate(num = \"11111111111111111111\",k = 10) == \"1111111111\"\n assert candidate(num = \"5432109876543210\",k = 10) == \"43210\"\n assert candidate(num = \"543210123456789\",k = 5) == \"123456789\"\n assert candidate(num = \"9999999999\",k = 9) == \"9\"\n assert candidate(num = \"1010101010\",k = 5) == \"0\"\n assert candidate(num = \"123456789012345678901234567890\",k = 20) == \"12345670\"\n assert candidate(num = \"111222333444555666777888999000111222\",k = 20) == \"1112223000111222\"\n assert candidate(num = \"100100100\",k = 3) == \"0\"\n assert candidate(num = \"999888777666555444333222111000\",k = 15) == \"444333222111000\"\n assert candidate(num = \"12003004005\",k = 3) == \"4005\"\n assert candidate(num = \"5959595959\",k = 4) == \"555559\"\n assert candidate(num = \"129384756\",k = 3) == \"123456\"\n assert candidate(num = \"0000000000\",k = 5) == \"0\"\n assert candidate(num = \"3332211\",k = 3) == \"2211\"\n assert candidate(num = \"1223344556677889900\",k = 10) == \"122334400\"\n assert candidate(num = \"111222333444555\",k = 10) == \"11122\"\n assert candidate(num = \"54321\",k = 2) == \"321\"\n assert candidate(num = \"999999999999\",k = 11) == \"9\"\n assert candidate(num = \"999999999\",k = 5) == \"9999\"\n assert candidate(num = \"120012001200\",k = 6) == \"0\"\n assert candidate(num = \"11223344556677889900\",k = 15) == \"11200\"\n assert candidate(num = \"999999999999\",k = 6) == \"999999\"\n assert candidate(num = \"100000000000000000000\",k = 19) == \"0\"\n assert candidate(num = \"100010001\",k = 6) == \"0\"\n assert candidate(num = \"123045607890\",k = 5) == \"407890\"\n assert candidate(num = \"123456789000000000000000000000000000000000000000\",k = 50) == \"0\"\n"}, "metadata": {"canonical_parameter_names": ["num", "k"], "leetcode_dataset_entry_point": "Solution().removeKdigits", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var removeKdigits = function(num, k) {", "container": null, "callable": "removeKdigits", "parameters": [{"name": "num", "type": "string"}, {"name": "k", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 403, "task_id": "frog-jump", "difficulty": "Hard", "problem_description": "A frog is crossing a river. The river is divided into some number of units, and at each unit, there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.\nGiven a list of stones positions (in units) in sorted ascending order, determine if the frog can cross the river by landing on the last stone. Initially, the frog is on the first stone and assumes the first jump must be 1 unit.\nIf the frog's last jump was k units, its next jump must be either k - 1, k, or k + 1 units. The frog can only jump in the forward direction.\n \nExample 1:\n\nInput: stones = [0,1,3,5,6,8,12,17]\nOutput: true\nExplanation: The frog can jump to the last stone by jumping 1 unit to the 2nd stone, then 2 units to the 3rd stone, then 2 units to the 4th stone, then 3 units to the 6th stone, 4 units to the 7th stone, and 5 units to the 8th stone.\n\nExample 2:\n\nInput: stones = [0,1,2,3,4,8,9,11]\nOutput: false\nExplanation: There is no way to jump to the last stone as the gap between the 5th and 6th stone is too large.\n\n \nConstraints:\n\n2 <= stones.length <= 2000\n0 <= stones[i] <= 231 - 1\nstones[0] == 0\nstones is sorted in a strictly increasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(stones = [0, 1, 3, 8, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == False\n assert candidate(stones = [0, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21]) == True\n assert candidate(stones = [0, 1, 4, 8, 16]) == False\n assert candidate(stones = [0, 2, 5, 6, 8, 10, 11, 13, 15, 17, 18, 19, 20]) == False\n assert candidate(stones = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(stones = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == True\n assert candidate(stones = [0, 1, 4, 8, 10, 12, 15, 17, 20]) == False\n assert candidate(stones = [0, 1, 2]) == True\n assert candidate(stones = [0, 1, 4, 8, 9, 11]) == False\n assert candidate(stones = [0, 2]) == False\n assert candidate(stones = [0, 1, 2, 3, 4, 8, 9, 11]) == False\n assert candidate(stones = [0, 1, 4, 5, 6, 8, 9, 11, 17, 20, 21]) == False\n assert candidate(stones = [0, 1, 2, 5, 7, 9, 11, 12, 14, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 30]) == False\n assert candidate(stones = [0, 1, 4, 5, 6, 8, 9, 12]) == False\n assert candidate(stones = [0, 1, 3, 5, 6, 8, 12, 17]) == True\n assert candidate(stones = [0, 1, 4, 5, 6, 8, 12, 13, 14, 17, 19]) == False\n assert candidate(stones = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == True\n assert candidate(stones = [0, 1, 3, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214]) == True\n assert candidate(stones = [0, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172]) == True\n assert candidate(stones = [0, 1, 5, 8, 13, 21, 26, 35, 45, 56, 68, 81, 95, 110, 126]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153]) == True\n assert candidate(stones = [0, 1, 3, 7, 14, 23, 34, 47, 62, 79, 98, 119, 142, 167, 194, 223, 254, 287, 322, 359, 398, 439, 482, 527, 574, 623, 674, 727, 782, 839, 898, 959, 1022, 1087, 1154, 1223, 1294, 1367, 1442, 1519, 1598, 1679, 1762, 1847, 1934, 2023, 2114, 2207, 2302, 2400]) == False\n assert candidate(stones = [0, 1, 6, 15, 26, 39, 54, 71, 90, 111]) == False\n assert candidate(stones = [0, 1, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85]) == False\n assert candidate(stones = [0, 1, 5, 9, 14, 20, 27, 35, 44]) == False\n assert candidate(stones = [0, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497]) == True\n assert candidate(stones = [0, 1, 12, 26, 42, 60, 80, 102, 126, 152, 180, 210, 242, 276, 312]) == False\n assert candidate(stones = [0, 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, 157]) == False\n assert candidate(stones = [0, 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 899, 972, 1048, 1127, 1209, 1294, 1382, 1473, 1567, 1664, 1764, 1867, 1973, 2082, 2194, 2309, 2427, 2548, 2672, 2800, 2931, 3065, 3202, 3342, 3485, 3631, 3779, 3929, 4082, 4238, 4397, 4559, 4724, 4892, 5063, 5237, 5414, 5594, 5777, 5963, 6152, 6344, 6539, 6737, 6938, 7142, 7349, 7559, 7772, 7988, 8207, 8429, 8654, 8882, 9113, 9347, 9584, 9824]) == False\n assert candidate(stones = [0, 1, 3, 7, 15, 31, 63, 127]) == False\n assert candidate(stones = [0, 1, 4, 8, 13, 21, 31, 44, 60, 79, 101, 126, 154]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253]) == True\n assert candidate(stones = [0, 1, 4, 8, 14, 22, 32, 44, 58, 74, 92, 112, 134, 158, 184, 212, 242, 274, 308, 344, 382, 422, 464, 508, 554, 602, 652, 704, 758, 814, 872, 932, 994, 1058, 1124, 1192, 1262, 1334, 1408, 1484, 1562, 1642, 1724, 1808, 1894, 1982, 2072, 2164, 2258, 2354, 2452, 2552, 2654, 2758, 2864, 2972, 3082, 3194, 3308, 3424, 3542, 3662, 3784, 3908, 4034, 4162, 4292, 4424, 4558, 4694, 4832, 4972, 5114, 5258, 5404, 5552, 5702, 5854, 6008, 6164, 6322, 6482, 6644, 6808, 6974, 7142, 7312, 7484, 7658, 7834, 8012, 8192, 8374, 8558, 8744, 8932, 9122, 9314, 9508, 9704, 9902, 10102]) == False\n assert candidate(stones = [0, 1, 3, 5, 9, 15, 23, 33, 45, 59, 75, 93, 113, 135, 159, 185, 213, 243, 275, 309, 345, 383, 423]) == False\n assert candidate(stones = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]) == True\n assert candidate(stones = [0, 1, 2, 5, 7, 10, 14, 19]) == False\n assert candidate(stones = [0, 1, 3, 7, 11, 17, 23, 31, 41, 53]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 299, 323, 348, 374, 401, 429]) == True\n assert candidate(stones = [0, 1, 5, 11, 18, 27, 37, 48, 60, 74, 89, 105, 122, 140, 159]) == False\n assert candidate(stones = [0, 1, 3, 7, 9, 11, 14, 17, 19, 21, 24, 28, 31, 35, 39]) == False\n assert candidate(stones = [0, 1, 5, 14, 26, 40, 55, 71, 88, 106, 125, 145, 166, 188, 211, 235, 260, 286, 313]) == False\n assert candidate(stones = [0, 1, 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 400]) == False\n assert candidate(stones = [0, 1, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 220]) == False\n assert candidate(stones = [0, 1, 4, 9, 15, 22, 30, 40, 51, 63, 76, 90, 105]) == False\n assert candidate(stones = [0, 1, 2, 5, 7, 9, 10, 11, 12, 13, 14, 17, 19, 20, 23, 26, 29, 31]) == False\n assert candidate(stones = [0, 1, 5, 9, 15, 22, 30, 39, 50, 62]) == False\n assert candidate(stones = [0, 1, 11, 24, 39, 56, 75, 96, 119, 144, 171, 199, 229, 261]) == False\n assert candidate(stones = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121]) == False\n assert candidate(stones = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801, 10000]) == False\n assert candidate(stones = [0, 1, 7, 16, 28, 42, 58, 77, 98, 121]) == False\n assert candidate(stones = [0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 26]) == False\n assert candidate(stones = [0, 1, 5, 11, 21, 34, 50, 69, 91, 116, 145, 178, 215, 256, 301, 350, 403, 460, 521, 586, 655, 728, 805, 886, 972]) == False\n assert candidate(stones = [0, 1, 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88]) == False\n assert candidate(stones = [0, 1, 9, 20, 33, 48, 65, 84, 105, 128, 153, 180]) == False\n assert candidate(stones = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]) == False\n assert candidate(stones = [0, 1, 2, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30]) == True\n assert candidate(stones = [0, 1, 4, 10, 19, 30, 43, 58, 75, 94, 115, 138, 163, 190, 219]) == False\n assert candidate(stones = [0, 1, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301]) == False\n assert candidate(stones = [0, 1, 2, 4, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256]) == False\n assert candidate(stones = [0, 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 15, 17, 19, 21, 23]) == True\n assert candidate(stones = [0, 1, 3, 5, 9, 13, 15, 19, 22, 26, 30, 34, 38, 42, 46]) == False\n assert candidate(stones = [0, 1, 2, 3, 7, 12, 16, 24, 28, 35]) == False\n assert candidate(stones = [0, 1, 3, 7, 11, 13, 15, 17, 19, 23, 27]) == False\n assert candidate(stones = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(stones = [0, 1, 2, 6, 10, 18, 22, 26, 32, 38, 44, 48, 52, 58, 64, 70]) == False\n assert candidate(stones = [0, 1, 3, 5, 11, 21, 33, 47, 63, 81, 101, 123, 147, 173, 201, 231, 263, 297, 333, 371, 411, 453, 497, 543, 591, 641, 693, 747, 803, 861, 921, 983]) == False\n assert candidate(stones = [0, 1, 3, 7, 14, 23, 34, 46, 60, 75, 91, 108, 127, 147, 169]) == False\n assert candidate(stones = [0, 1, 2, 5, 8, 10, 14, 17, 21, 25, 30]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55]) == True\n assert candidate(stones = [0, 1, 2, 4, 8, 16, 25, 35, 46, 58, 71, 85, 100, 116, 133, 151, 170, 190, 211, 233, 256, 280, 305, 331, 358, 386, 415, 445, 476, 508, 541, 575, 610, 646, 683, 721, 760, 800, 841, 883, 926, 970, 1015, 1061, 1108, 1156, 1205, 1255, 1306, 1358, 1411, 1465, 1520, 1576, 1633, 1691, 1750, 1810, 1871, 1933, 1996, 2060, 2125, 2191, 2258, 2326, 2395, 2465, 2536, 2608, 2681, 2755, 2830, 2906, 2983, 3061, 3140, 3220, 3301, 3383, 3466, 3550, 3635, 3721, 3808, 3896, 3985, 4075, 4166, 4258, 4351, 4445, 4540, 4636, 4733, 4831, 4930, 5030]) == False\n assert candidate(stones = [0, 1, 2, 3, 7, 11, 13, 15, 18, 20]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91]) == True\n assert candidate(stones = [0, 1, 8, 19, 32, 47, 64, 83, 104, 127, 152]) == False\n assert candidate(stones = [0, 1, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144]) == False\n assert candidate(stones = [0, 1, 5, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990]) == False\n assert candidate(stones = [0, 1, 6, 10, 14, 19, 24, 30, 37, 45, 54, 64, 75, 87, 100]) == False\n assert candidate(stones = [0, 1, 3, 5, 7, 9, 11, 13, 15, 18, 20, 23]) == True\n assert candidate(stones = [0, 1, 2, 4, 5, 6, 8, 9, 11, 13, 16, 18, 21, 24, 27, 31, 35, 39, 44, 49, 54, 59, 65, 71, 78, 85, 92, 100, 108, 116, 125, 134, 144, 154, 165, 176, 188, 201, 214, 228, 243, 259, 275, 292, 310, 329, 348, 368, 388, 409, 430, 452, 475, 498, 522, 547, 573, 600, 628, 657, 687, 718, 750, 783, 817, 852, 888, 925, 963, 1002, 1042, 1083, 1125, 1168, 1212, 1257, 1303, 1350, 1400, 1451]) == False\n assert candidate(stones = [0, 1, 4, 7, 11, 16, 22, 29, 37, 46]) == False\n assert candidate(stones = [0, 1, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65]) == False\n assert candidate(stones = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540, 1596, 1653, 1711, 1770, 1830, 1891, 1953]) == True\n"}, "metadata": {"canonical_parameter_names": ["stones"], "leetcode_dataset_entry_point": "Solution().canCross", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canCross = function(stones) {", "container": null, "callable": "canCross", "parameters": [{"name": "stones", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 404, "task_id": "sum-of-left-leaves", "difficulty": "Easy", "problem_description": "Given the root of a binary tree, return the sum of all left leaves.\nA leaf is a node with no children. A left leaf is a leaf that is the left child of another node.\n \nExample 1:\n\n\nInput: root = [3,9,20,null,null,15,7]\nOutput: 24\nExplanation: There are two left leaves in the binary tree, with values 9 and 15 respectively.\n\nExample 2:\n\nInput: root = [1]\nOutput: 0\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 1000].\n-1000 <= Node.val <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([0, 2, 4, 1, None, 3, -1, 5, 1, None, 6, None, 8])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5])) == 4\n assert candidate(root = tree_node([3, 9, 20, 15, 7])) == 15\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 0\n assert candidate(root = tree_node([-9, -3, 2, None, 4, 4, 0, -6, None, -5])) == -11\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, None, None, None, 8])) == 7\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, None, 1])) == 1\n assert candidate(root = tree_node([3, 9, 20, 8, None, 15, 7, None, 4])) == 15\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])) == 40\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])) == 21\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, None, None, 7])) == 6\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == 24\n assert candidate(root = tree_node([1])) == 0\n assert candidate(root = tree_node([1, None, 2, None, None, None, 3, None, None, None, None, None, 4])) == 0\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 9])) == 7\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 190])) == 340\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, 6, 8, 13, 17, 22])) == 26\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6])) == 6\n assert candidate(root = tree_node([5, 2, -3, None, -4, None, 1, None, None, -5, None, -6, None, -7, None, -8])) == -8\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])) == 288\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190, 5, None, 35, None, 45, 65, 85, 95, 105, 135, 145, 155, 165, 185, 195])) == 780\n assert candidate(root = tree_node([33, 18, 50, 8, None, 32, 60, 2, 11, None, 46, None, None, 29, None, None, 59, None, None])) == 29\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, 7, None, None, 8, 9])) == 18\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == 8\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, None, 17])) == 12\n assert candidate(root = tree_node([3, 5, 1, 6, 2, 0, 8, None, None, 7, 4, None, None, None, None, 9, 10])) == 15\n assert candidate(root = tree_node([5, 15, 1, None, 6, None, 7, 8, 9, None, None, None, None, 10, 11])) == 18\n assert candidate(root = tree_node([5, 15, 7, None, 9, None, 11, None, None, 13, 14])) == 13\n assert candidate(root = tree_node([2, 1, 3, 4, None, 5, 6, None, 7, 8, None, 9, 10, 11, None, 12, 13, 14, None, 15])) == 52\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, None, None, 4, 8, 11, 13, 18, 25])) == 36\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, None, 8])) == 10\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 12, 18, 16, 19, 14, 17])) == 39\n assert candidate(root = tree_node([10, 9, 20, 8, None, 15, 25, 7, None, None, 18, 23, 30, 17, None, None, None, 24])) == 41\n assert candidate(root = tree_node([10, 5, 20, None, None, 15, 25, None, None, None, 30])) == 20\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, 6, None, None, None, None, 7, 8, 9])) == 10\n assert candidate(root = tree_node([5, 3, 8, 2, 4, 7, 9, 1, None, None, None, None, None, None, 10])) == 8\n assert candidate(root = tree_node([3, 9, 20, 4, 5, 6, 7, None, None, None, 8, None, None, 9, None, None, 10, None, None, 11, None, None, 12, None, None, 13, None, None, 14, None, None, 15])) == 19\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 1, None, None, None, 2])) == 11\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == 20\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30])) == 0\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180, 5, None, None, 20, None, 40, 70, None, None, 90, 100, 120, 130, 150, None, None, 170, 190, 200])) == 670\n assert candidate(root = tree_node([1, 2, 3, None, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 36\n assert candidate(root = tree_node([5, 3, 8, 2, 4, None, 9, 1, None, 6, 7, None, 10])) == 7\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == 80\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, None, None, 6, None, None, 7, None, None, 8, None, 9])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 44\n assert candidate(root = tree_node([50, 25, 75, 12, 37, 63, 87, 6, 18, 31, 43, 56, 70, 81, 93])) == 174\n assert candidate(root = tree_node([50, 25, 75, 10, 30, 60, 90, 5, None, 28, 40, 55, 65, 85, 100, None, None, None, 26, 32])) == 177\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == 7\n assert candidate(root = tree_node([1, 2, 2, 3, None, 3, None, 4, 4, None, None, 5, 5])) == 8\n assert candidate(root = tree_node([10, 5, 15, None, 7, 12, 20, None, None, 6, 8, 13, 18])) == 19\n assert candidate(root = tree_node([1, None, 2, 3, None, 4, None, 5, 6, 7, None, 8, None, 9, 10, None, 11, 12])) == 12\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])) == 494\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, None, 2, 6, None, None, 10])) == 6\n assert candidate(root = tree_node([10, None, 20, 30, 40, 50, 60, None, None, 70, 80])) == 70\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 25, 26])) == 49\n assert candidate(root = tree_node([20, 15, 25, 10, 18, None, 30, 5, 12, None, 17, 22, 35, None, None, None, None, None, 16])) == 27\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == 0\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, 16, 17, 18, 19, None, None, None, None, 20])) == 45\n assert candidate(root = tree_node([2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 44\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, 0, 2, 6, None, None, 15, None, None, None, None, 16])) == 22\n assert candidate(root = tree_node([20, 10, 30, None, 15, 25, 35, None, 17, 23, None, None, None, 27, 32, 37])) == 64\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, None, 5, 6, None, None, None, None, 7, 8, None, 9])) == 5\n assert candidate(root = tree_node([20, 15, 25, 10, 18, None, 30, 5, 12, 16, 19, 27, 35, 3, None, 14, 21, 26, 28, 32, 34, 36, None, None, None, None, None, None, None, None, None, None, None, None, None])) == 111\n assert candidate(root = tree_node([5, None, 10, None, 15, None, 20, None, 25, None, 30, None, 35])) == 0\n assert candidate(root = tree_node([100, 50, 200, 25, 75, None, 300, None, 35, None, 85, 150, None, None, 400])) == 150\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 65, 85, 115, 135, 165, 185])) == 355\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, None, 6, 7, None, None, 8, 9])) == 8\n assert candidate(root = tree_node([8, 4, 12, None, 6, 10, 14, 5, None, 7, None, 9, None, 11, None, 13, None, 15])) == 39\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8])) == 7\n assert candidate(root = tree_node([3, 1, 4, None, 2])) == 0\n assert candidate(root = tree_node([12, 6, 18, 3, 9, 15, 21, 1, 5, None, None, 11, None, None, 19, 22])) == 33\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32])) == 200\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6])) == 0\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, 1, None, None, None, None, 8])) == 1\n assert candidate(root = tree_node([8, 6, 10, 5, 7, 9, 11, 4, None, None, None, None, None, 3])) == 16\n assert candidate(root = tree_node([10, None, 20, None, 30, None, 40, None, 50, None, 60, None, 70, None, 80, None, 90, None, 100])) == 0\n assert candidate(root = tree_node([7, 3, 15, None, 8, 10, None, 5, 9, 11, 13, None, None, None, 12])) == 16\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, 6, 7, None, None, None, None, None, 8])) == 6\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 9\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 0\n assert candidate(root = tree_node([10, 5, 15, None, None, None, 25])) == 5\n assert candidate(root = tree_node([0, -1, 2, -2, None, -3, None, -4])) == -7\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, None, 8, 12, 22, 28, None, 32, None, None, 4, 7, None, 9, 11, 13, 14, 16, 17, 18, 19, 21, 23, 24, 26, 27, 29, 31, 33, 34])) == 162\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180])) == 340\n assert candidate(root = tree_node([5, 15, 20, 30, 5, None, 25, 45, None, None, 35, 40, 50])) == 85\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, None, 8, 12, None, None, None, None, None, None, 9, None, 11])) == 46\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, None, None, None, None, None, None, 28, None, 32, None, None, 35, 36])) == 114\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, None, None, 11, 12, None, 13, None, None, 14])) == 35\n assert candidate(root = tree_node([10, 8, 15, 3, 5, None, 20, 1, 4, 6, None, None, None, 17])) == 23\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30])) == 30\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, 9, None, None, 10, 11])) == 18\n assert candidate(root = tree_node([23, 18, 15, 20, 25, 16, 10, None, 22, None, None, 19, None, None, 8])) == 19\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == 25\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().sumOfLeftLeaves", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var sumOfLeftLeaves = function(root) {", "container": null, "callable": "sumOfLeftLeaves", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 405, "task_id": "convert-a-number-to-hexadecimal", "difficulty": "Easy", "problem_description": "Given a 32-bit integer num, return a string representing its hexadecimal representation. For negative integers, two’s complement method is used.\nAll the letters in the answer string should be lowercase characters, and there should not be any leading zeros in the answer except for the zero itself.\nNote: You are not allowed to use any built-in library method to directly solve this problem.\n \nExample 1:\nInput: num = 26\nOutput: \"1a\"\nExample 2:\nInput: num = -1\nOutput: \"ffffffff\"\n\n \nConstraints:\n\n-231 <= num <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 31) == \"1f\"\n assert candidate(num = 10) == \"a\"\n assert candidate(num = -4294967296) == \"\"\n assert candidate(num = 16777215) == \"ffffff\"\n assert candidate(num = -16777215) == \"ff000001\"\n assert candidate(num = -1) == \"ffffffff\"\n assert candidate(num = 4294967295) == \"ffffffff\"\n assert candidate(num = 0) == \"0\"\n assert candidate(num = -2147483648) == \"80000000\"\n assert candidate(num = -255) == \"ffffff01\"\n assert candidate(num = 255) == \"ff\"\n assert candidate(num = 1) == \"1\"\n assert candidate(num = -10) == \"fffffff6\"\n assert candidate(num = -4095) == \"fffff001\"\n assert candidate(num = 4095) == \"fff\"\n assert candidate(num = 2147483647) == \"7fffffff\"\n assert candidate(num = 16) == \"10\"\n assert candidate(num = 26) == \"1a\"\n assert candidate(num = 2097152) == \"200000\"\n assert candidate(num = -4096) == \"fffff000\"\n assert candidate(num = -1048575) == \"fff00001\"\n assert candidate(num = -16777216) == \"ff000000\"\n assert candidate(num = 1099511627776) == \"\"\n assert candidate(num = -2147483647) == \"80000001\"\n assert candidate(num = 67553994410557436) == \"fffffffc\"\n assert candidate(num = 1048575) == \"fffff\"\n assert candidate(num = -1024) == \"fffffc00\"\n assert candidate(num = -134217728) == \"f8000000\"\n assert candidate(num = -8589934591) == \"1\"\n assert candidate(num = -31) == \"ffffffe1\"\n assert candidate(num = 123456789) == \"75bcd15\"\n assert candidate(num = 65535) == \"ffff\"\n assert candidate(num = -15) == \"fffffff1\"\n assert candidate(num = 32768) == \"8000\"\n assert candidate(num = -131072) == \"fffe0000\"\n assert candidate(num = -89478485) == \"faaaaaab\"\n assert candidate(num = -65535) == \"ffff0001\"\n assert candidate(num = 2147483646) == \"7ffffffe\"\n assert candidate(num = 134217728) == \"8000000\"\n assert candidate(num = -987654321) == \"c521974f\"\n assert candidate(num = 268435456) == \"10000000\"\n assert candidate(num = 8589934591) == \"ffffffff\"\n assert candidate(num = 4096) == \"1000\"\n assert candidate(num = -268435456) == \"f0000000\"\n assert candidate(num = 1048576) == \"100000\"\n assert candidate(num = -1073741825) == \"bfffffff\"\n assert candidate(num = -123456789) == \"f8a432eb\"\n assert candidate(num = 1024) == \"400\"\n assert candidate(num = -4294967294) == \"2\"\n assert candidate(num = -256) == \"ffffff00\"\n assert candidate(num = 16777216) == \"1000000\"\n assert candidate(num = -1000000) == \"fff0bdc0\"\n assert candidate(num = -1048576) == \"fff00000\"\n assert candidate(num = -16) == \"fffffff0\"\n assert candidate(num = 1000000) == \"f4240\"\n assert candidate(num = 89478485) == \"5555555\"\n assert candidate(num = 65536) == \"10000\"\n assert candidate(num = 4294967294) == \"fffffffe\"\n assert candidate(num = -2) == \"fffffffe\"\n assert candidate(num = 15) == \"f\"\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().toHex", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var toHex = function(num) {", "container": null, "callable": "toHex", "parameters": [{"name": "num", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 406, "task_id": "queue-reconstruction-by-height", "difficulty": "Medium", "problem_description": "You are given an array of people, people, which are the attributes of some people in a queue (not necessarily in order). Each people[i] = [hi, ki] represents the ith person of height hi with exactly ki other people in front who have a height greater than or equal to hi.\nReconstruct and return the queue that is represented by the input array people. The returned queue should be formatted as an array queue, where queue[j] = [hj, kj] is the attributes of the jth person in the queue (queue[0] is the person at the front of the queue).\n \nExample 1:\n\nInput: people = [[7,0],[4,4],[7,1],[5,0],[6,1],[5,2]]\nOutput: [[5,0],[7,0],[5,2],[6,1],[4,4],[7,1]]\nExplanation:\nPerson 0 has height 5 with no other people taller or the same height in front.\nPerson 1 has height 7 with no other people taller or the same height in front.\nPerson 2 has height 5 with two persons taller or the same height in front, which is person 0 and 1.\nPerson 3 has height 6 with one person taller or the same height in front, which is person 1.\nPerson 4 has height 4 with four people taller or the same height in front, which are people 0, 1, 2, and 3.\nPerson 5 has height 7 with one person taller or the same height in front, which is person 1.\nHence [[5,0],[7,0],[5,2],[6,1],[4,4],[7,1]] is the reconstructed queue.\n\nExample 2:\n\nInput: people = [[6,0],[5,0],[4,0],[3,2],[2,2],[1,4]]\nOutput: [[4,0],[5,0],[2,2],[3,2],[1,4],[6,0]]\n\n \nConstraints:\n\n1 <= people.length <= 2000\n0 <= hi <= 106\n0 <= ki < people.length\nIt is guaranteed that the queue can be reconstructed.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(people = [[9, 0], [7, 0], [5, 0], [6, 1], [3, 2], [2, 2], [1, 4], [8, 1]]) == [[5, 0], [7, 0], [2, 2], [3, 2], [1, 4], [6, 1], [9, 0], [8, 1]]\n assert candidate(people = [[5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]) == [[5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5]]\n assert candidate(people = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]\n assert candidate(people = [[5, 2], [7, 0], [5, 0], [6, 1], [3, 2], [2, 2], [1, 4], [8, 1]]) == [[5, 0], [7, 0], [2, 2], [3, 2], [1, 4], [5, 2], [6, 1], [8, 1]]\n assert candidate(people = [[6, 0], [5, 0], [4, 0], [3, 2], [2, 2], [1, 4]]) == [[4, 0], [5, 0], [2, 2], [3, 2], [1, 4], [6, 0]]\n assert candidate(people = [[2, 4], [3, 4], [9, 0], [0, 6], [7, 1], [3, 1], [8, 5], [1, 5], [4, 2], [5, 0]]) == [[5, 0], [3, 1], [9, 0], [4, 2], [2, 4], [1, 5], [0, 6], [3, 4], [7, 1], [8, 5]]\n assert candidate(people = [[9, 0], [7, 0], [5, 2], [6, 1], [3, 3], [8, 2], [4, 4]]) == [[7, 0], [6, 1], [5, 2], [3, 3], [9, 0], [4, 4], [8, 2]]\n assert candidate(people = [[7, 0], [4, 4], [7, 1], [5, 0], [6, 1], [5, 2]]) == [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1]]\n assert candidate(people = [[9, 0], [7, 0], [5, 2], [6, 1], [3, 3], [8, 2], [5, 1], [6, 0]]) == [[6, 0], [5, 1], [5, 2], [3, 3], [6, 1], [7, 0], [9, 0], [8, 2]]\n assert candidate(people = [[9, 0], [7, 0], [5, 2], [6, 1], [3, 4], [8, 2], [4, 3]]) == [[7, 0], [6, 1], [5, 2], [4, 3], [3, 4], [9, 0], [8, 2]]\n assert candidate(people = [[10, 0], [8, 0], [6, 0], [7, 0], [5, 0], [9, 0]]) == [[5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0]]\n assert candidate(people = [[1, 9], [3, 4], [7, 0], [2, 5], [1, 0], [2, 3], [6, 0], [8, 6], [9, 7], [3, 8]]) == [[1, 0], [6, 0], [7, 0], [9, 7], [2, 3], [8, 6], [2, 5], [3, 4], [3, 8], [1, 9]]\n assert candidate(people = [[9, 0], [7, 0], [5, 2], [6, 1], [3, 3], [8, 2], [4, 4], [2, 6]]) == [[7, 0], [6, 1], [5, 2], [3, 3], [9, 0], [4, 4], [2, 6], [8, 2]]\n assert candidate(people = [[7, 0], [4, 4], [7, 1], [5, 0], [6, 1], [5, 2], [8, 2], [8, 1]]) == [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1], [8, 1], [8, 2]]\n assert candidate(people = [[70, 4], [55, 3], [65, 2], [75, 1], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0]]) == [[85, 0], [75, 1], [65, 2], [55, 3], [95, 0], [105, 0], [70, 4], [115, 0], [125, 0], [135, 0]]\n assert candidate(people = [[70, 5], [55, 0], [65, 3], [75, 1], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [145, 1], [155, 2], [165, 3]]) == [[55, 0], [85, 0], [75, 1], [95, 0], [65, 3], [105, 0], [115, 0], [70, 5], [125, 0], [135, 0], [165, 3], [145, 1], [155, 2]]\n assert candidate(people = [[9, 0], [7, 0], [5, 2], [6, 1], [3, 3], [8, 2], [4, 4], [7, 1], [5, 0], [6, 0], [5, 1], [4, 0], [4, 1], [3, 0], [3, 1]]) == [[3, 0], [3, 1], [4, 0], [3, 3], [4, 1], [5, 0], [5, 1], [4, 4], [5, 2], [6, 0], [6, 1], [7, 0], [7, 1], [9, 0], [8, 2]]\n assert candidate(people = [[1, 4], [2, 3], [3, 2], [4, 1], [5, 0], [6, 1], [7, 2], [8, 3], [9, 4], [10, 5]]) == [[5, 0], [4, 1], [3, 2], [2, 3], [1, 4], [10, 5], [6, 1], [9, 4], [7, 2], [8, 3]]\n assert candidate(people = [[5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5]]) == [[5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 5], [5, 4], [5, 3], [5, 2], [5, 1], [5, 0]]\n assert candidate(people = [[150, 0], [140, 1], [130, 2], [120, 3], [110, 4], [100, 5], [90, 6], [80, 7], [70, 8], [60, 9]]) == [[150, 0], [140, 1], [130, 2], [120, 3], [110, 4], [100, 5], [90, 6], [80, 7], [70, 8], [60, 9]]\n assert candidate(people = [[10, 0], [8, 1], [9, 0], [8, 2], [9, 1], [7, 3], [6, 2], [5, 4], [4, 5]]) == [[9, 0], [8, 1], [6, 2], [8, 2], [5, 4], [4, 5], [7, 3], [9, 1], [10, 0]]\n assert candidate(people = [[100, 10], [99, 9], [98, 8], [97, 7], [96, 6], [95, 5], [94, 4], [93, 3], [92, 2], [91, 1], [90, 0]]) == [[90, 0], [100, 10], [91, 1], [99, 9], [92, 2], [98, 8], [93, 3], [97, 7], [94, 4], [96, 6], [95, 5]]\n assert candidate(people = [[5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [5, 1], [6, 1], [7, 1], [8, 1]]) == [[5, 0], [5, 1], [6, 0], [6, 1], [7, 0], [7, 1], [8, 0], [8, 1], [9, 0], [10, 0]]\n assert candidate(people = [[7, 0], [4, 4], [7, 1], [5, 0], [6, 1], [5, 2], [5, 3], [6, 2], [5, 1], [7, 2]]) == [[5, 0], [5, 1], [5, 2], [5, 3], [4, 4], [7, 0], [6, 1], [6, 2], [7, 1], [7, 2]]\n assert candidate(people = [[15, 0], [15, 1], [15, 2], [15, 3], [15, 4], [15, 5], [15, 6], [15, 7], [15, 8], [15, 9], [15, 10]]) == [[15, 0], [15, 1], [15, 2], [15, 3], [15, 4], [15, 5], [15, 6], [15, 7], [15, 8], [15, 9], [15, 10]]\n assert candidate(people = [[7, 0], [7, 1], [7, 2], [7, 3], [7, 4], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4]]) == [[5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4]]\n assert candidate(people = [[12, 0], [10, 0], [10, 1], [10, 2], [11, 0], [11, 1], [11, 2], [9, 0], [9, 1], [9, 2], [9, 3]]) == [[9, 0], [9, 1], [9, 2], [9, 3], [10, 0], [10, 1], [10, 2], [11, 0], [11, 1], [11, 2], [12, 0]]\n assert candidate(people = [[7, 0], [4, 4], [7, 1], [5, 0], [6, 1], [5, 2], [8, 2], [8, 1], [9, 3], [10, 4]]) == [[5, 0], [7, 0], [5, 2], [6, 1], [4, 4], [7, 1], [10, 4], [8, 1], [8, 2], [9, 3]]\n assert candidate(people = [[20, 0], [19, 1], [18, 2], [17, 3], [16, 4], [15, 5], [14, 6], [13, 7], [12, 8], [11, 9], [10, 10], [9, 11], [8, 12]]) == [[20, 0], [19, 1], [18, 2], [17, 3], [16, 4], [15, 5], [14, 6], [13, 7], [12, 8], [11, 9], [10, 10], [9, 11], [8, 12]]\n assert candidate(people = [[200, 0], [190, 1], [180, 2], [170, 3], [160, 4], [150, 5], [140, 6], [130, 7], [120, 8], [110, 9], [100, 10]]) == [[200, 0], [190, 1], [180, 2], [170, 3], [160, 4], [150, 5], [140, 6], [130, 7], [120, 8], [110, 9], [100, 10]]\n assert candidate(people = [[5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5]]) == [[5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5], [5, 5]]\n assert candidate(people = [[12, 2], [11, 3], [10, 4], [9, 5], [8, 6], [7, 7], [6, 8], [5, 9], [4, 10], [3, 11], [2, 12], [1, 13], [0, 14]]) == [[12, 2], [11, 3], [10, 4], [9, 5], [8, 6], [7, 7], [6, 8], [5, 9], [4, 10], [3, 11], [2, 12], [1, 13], [0, 14]]\n assert candidate(people = [[70, 0], [100, 0], [90, 0], [80, 0], [75, 0], [72, 0], [69, 0], [66, 0], [63, 0], [60, 0], [57, 0], [54, 0], [51, 0], [48, 0], [45, 0], [42, 0], [39, 0], [36, 0], [33, 0], [30, 0]]) == [[30, 0], [33, 0], [36, 0], [39, 0], [42, 0], [45, 0], [48, 0], [51, 0], [54, 0], [57, 0], [60, 0], [63, 0], [66, 0], [69, 0], [70, 0], [72, 0], [75, 0], [80, 0], [90, 0], [100, 0]]\n assert candidate(people = [[10, 0], [8, 1], [9, 0], [10, 1], [11, 0], [8, 2], [9, 2], [10, 2], [11, 1], [12, 0]]) == [[9, 0], [8, 1], [8, 2], [10, 0], [9, 2], [10, 1], [10, 2], [11, 0], [11, 1], [12, 0]]\n assert candidate(people = [[70, 2], [55, 3], [65, 0], [75, 1], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [145, 1], [155, 2], [165, 3], [175, 4], [185, 5]]) == [[65, 0], [85, 0], [75, 1], [55, 3], [70, 2], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [185, 5], [145, 1], [175, 4], [155, 2], [165, 3]]\n assert candidate(people = [[10, 0], [8, 0], [9, 0], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0]]) == [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0]]\n assert candidate(people = [[1, 0], [2, 1], [2, 0], [3, 0], [3, 1], [3, 2], [4, 0], [4, 1], [4, 2], [4, 3]]) == [[1, 0], [2, 0], [2, 1], [3, 0], [3, 1], [3, 2], [4, 0], [4, 1], [4, 2], [4, 3]]\n assert candidate(people = [[70, 2], [55, 3], [65, 0], [75, 1], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [145, 1], [155, 2]]) == [[65, 0], [85, 0], [75, 1], [55, 3], [70, 2], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [155, 2], [145, 1]]\n assert candidate(people = [[5, 0], [4, 1], [3, 2], [2, 3], [1, 4], [6, 0], [7, 1], [8, 2], [9, 3], [10, 4]]) == [[5, 0], [4, 1], [3, 2], [2, 3], [1, 4], [6, 0], [10, 4], [7, 1], [9, 3], [8, 2]]\n assert candidate(people = [[5, 5], [6, 3], [7, 1], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0]]) == [[8, 0], [7, 1], [9, 0], [6, 3], [10, 0], [5, 5], [11, 0], [12, 0], [13, 0], [14, 0]]\n assert candidate(people = [[8, 0], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14]]) == [[8, 0], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9], [8, 10], [8, 11], [8, 12], [8, 13], [8, 14]]\n assert candidate(people = [[20, 0], [15, 0], [10, 0], [5, 0], [4, 1], [3, 2], [2, 3], [1, 4], [0, 5], [25, 0]]) == [[5, 0], [4, 1], [3, 2], [2, 3], [1, 4], [0, 5], [10, 0], [15, 0], [20, 0], [25, 0]]\n assert candidate(people = [[100, 0], [90, 1], [80, 2], [70, 3], [60, 4], [50, 5], [40, 4], [30, 3], [20, 2], [10, 1]]) == [[100, 0], [10, 1], [90, 1], [20, 2], [80, 2], [30, 3], [70, 3], [40, 4], [60, 4], [50, 5]]\n assert candidate(people = [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]) == [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]\n assert candidate(people = [[210, 4], [200, 2], [190, 2], [180, 3], [170, 4], [160, 1], [150, 1], [140, 2], [130, 3], [120, 0]]) == [[120, 0], [210, 4], [150, 1], [140, 2], [130, 3], [160, 1], [200, 2], [190, 2], [180, 3], [170, 4]]\n assert candidate(people = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10], [12, 11], [13, 12], [14, 13], [15, 14], [16, 15], [17, 16], [18, 17], [19, 18], [20, 19], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == [[1, 0], [1, 1], [20, 19], [2, 1], [2, 2], [19, 18], [3, 2], [3, 3], [18, 17], [4, 3], [4, 4], [17, 16], [5, 4], [5, 5], [16, 15], [6, 5], [6, 6], [15, 14], [7, 6], [7, 7], [14, 13], [8, 7], [8, 8], [13, 12], [9, 8], [9, 9], [12, 11], [10, 9], [10, 10], [11, 10]]\n assert candidate(people = [[1, 9], [2, 8], [3, 7], [4, 6], [5, 5], [6, 4], [7, 3], [8, 2], [9, 1], [10, 0]]) == [[10, 0], [9, 1], [8, 2], [7, 3], [6, 4], [5, 5], [4, 6], [3, 7], [2, 8], [1, 9]]\n assert candidate(people = [[10, 2], [9, 1], [8, 0], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0]]) == [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [10, 2], [9, 1]]\n assert candidate(people = [[10, 10], [9, 9], [8, 8], [7, 7], [6, 6], [5, 5], [4, 4], [3, 3], [2, 2], [1, 1], [0, 0]]) == [[0, 0], [10, 10], [1, 1], [9, 9], [2, 2], [8, 8], [3, 3], [7, 7], [4, 4], [6, 6], [5, 5]]\n assert candidate(people = [[70, 0], [55, 0], [65, 1], [75, 0], [85, 1], [95, 1], [105, 2], [115, 3], [125, 4], [135, 5]]) == [[55, 0], [70, 0], [65, 1], [75, 0], [135, 5], [85, 1], [95, 1], [125, 4], [105, 2], [115, 3]]\n assert candidate(people = [[80, 0], [90, 0], [100, 0], [110, 0], [120, 0], [130, 0], [140, 0], [150, 0], [160, 0], [170, 0], [180, 0], [190, 0], [200, 0]]) == [[80, 0], [90, 0], [100, 0], [110, 0], [120, 0], [130, 0], [140, 0], [150, 0], [160, 0], [170, 0], [180, 0], [190, 0], [200, 0]]\n assert candidate(people = [[70, 5], [55, 0], [65, 2], [75, 0], [85, 1], [95, 3], [105, 1], [115, 2], [125, 0], [135, 4]]) == [[55, 0], [75, 0], [125, 0], [65, 2], [85, 1], [105, 1], [135, 4], [70, 5], [95, 3], [115, 2]]\n assert candidate(people = [[10, 0], [10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [10, 9], [10, 10], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 22], [10, 23], [10, 24], [10, 25], [10, 26], [10, 27], [10, 28], [10, 29], [10, 30], [10, 31], [10, 32], [10, 33], [10, 34], [10, 35], [10, 36], [10, 37], [10, 38], [10, 39], [10, 40], [10, 41], [10, 42], [10, 43], [10, 44], [10, 45], [10, 46], [10, 47], [10, 48], [10, 49]]) == [[10, 0], [10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [10, 9], [10, 10], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15], [10, 16], [10, 17], [10, 18], [10, 19], [10, 20], [10, 21], [10, 22], [10, 23], [10, 24], [10, 25], [10, 26], [10, 27], [10, 28], [10, 29], [10, 30], [10, 31], [10, 32], [10, 33], [10, 34], [10, 35], [10, 36], [10, 37], [10, 38], [10, 39], [10, 40], [10, 41], [10, 42], [10, 43], [10, 44], [10, 45], [10, 46], [10, 47], [10, 48], [10, 49]]\n assert candidate(people = [[1000, 0], [900, 1], [800, 2], [700, 3], [600, 4], [500, 5], [400, 6], [300, 7], [200, 8], [100, 9], [50, 10], [49, 10], [48, 10], [47, 10], [46, 10], [45, 10], [44, 10], [43, 10], [42, 10], [41, 10], [40, 10], [39, 10], [38, 10], [37, 10], [36, 10], [35, 10], [34, 10], [33, 10], [32, 10], [31, 10], [30, 10], [29, 10], [28, 10], [27, 10], [26, 10], [25, 10], [24, 10], [23, 10], [22, 10], [21, 10], [20, 10], [19, 10], [18, 10], [17, 10], [16, 10], [15, 10], [14, 10], [13, 10], [12, 10], [11, 10], [10, 10], [9, 10], [8, 10], [7, 10], [6, 10], [5, 10], [4, 10], [3, 10], [2, 10], [1, 10]]) == [[1000, 0], [900, 1], [800, 2], [700, 3], [600, 4], [500, 5], [400, 6], [300, 7], [200, 8], [100, 9], [1, 10], [2, 10], [3, 10], [4, 10], [5, 10], [6, 10], [7, 10], [8, 10], [9, 10], [10, 10], [11, 10], [12, 10], [13, 10], [14, 10], [15, 10], [16, 10], [17, 10], [18, 10], [19, 10], [20, 10], [21, 10], [22, 10], [23, 10], [24, 10], [25, 10], [26, 10], [27, 10], [28, 10], [29, 10], [30, 10], [31, 10], [32, 10], [33, 10], [34, 10], [35, 10], [36, 10], [37, 10], [38, 10], [39, 10], [40, 10], [41, 10], [42, 10], [43, 10], [44, 10], [45, 10], [46, 10], [47, 10], [48, 10], [49, 10], [50, 10]]\n assert candidate(people = [[5, 0], [3, 4], [5, 2], [5, 1], [4, 1], [4, 0], [3, 1], [2, 2], [1, 3], [0, 4]]) == [[4, 0], [3, 1], [2, 2], [1, 3], [0, 4], [4, 1], [5, 0], [3, 4], [5, 1], [5, 2]]\n assert candidate(people = [[20, 0], [19, 1], [18, 2], [17, 3], [16, 4], [15, 5], [14, 6], [13, 7], [12, 8], [11, 9], [10, 10], [9, 11], [8, 12], [7, 13], [6, 14], [5, 15], [4, 16], [3, 17], [2, 18], [1, 19]]) == [[20, 0], [19, 1], [18, 2], [17, 3], [16, 4], [15, 5], [14, 6], [13, 7], [12, 8], [11, 9], [10, 10], [9, 11], [8, 12], [7, 13], [6, 14], [5, 15], [4, 16], [3, 17], [2, 18], [1, 19]]\n assert candidate(people = [[7, 0], [7, 1], [7, 2], [7, 3], [7, 4], [7, 5], [6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6], [6, 7]]) == [[6, 0], [6, 1], [6, 2], [6, 3], [6, 4], [6, 5], [6, 6], [6, 7], [7, 0], [7, 1], [7, 2], [7, 3], [7, 4], [7, 5]]\n assert candidate(people = [[100, 0], [99, 1], [98, 2], [97, 3], [96, 4], [95, 5], [94, 6], [93, 7], [92, 8], [91, 9], [90, 10]]) == [[100, 0], [99, 1], [98, 2], [97, 3], [96, 4], [95, 5], [94, 6], [93, 7], [92, 8], [91, 9], [90, 10]]\n assert candidate(people = [[10, 0], [9, 1], [8, 2], [7, 3], [6, 4], [5, 5], [4, 6], [3, 7], [2, 8], [1, 9], [0, 10], [11, 0], [12, 1]]) == [[10, 0], [9, 1], [8, 2], [7, 3], [6, 4], [5, 5], [4, 6], [3, 7], [2, 8], [1, 9], [0, 10], [11, 0], [12, 1]]\n assert candidate(people = [[70, 5], [55, 0], [65, 3], [75, 1], [85, 4], [95, 2], [105, 0], [115, 2], [125, 1], [135, 0]]) == [[55, 0], [105, 0], [75, 1], [135, 0], [65, 3], [95, 2], [125, 1], [70, 5], [85, 4], [115, 2]]\n assert candidate(people = [[100, 0], [99, 1], [98, 2], [97, 3], [96, 4], [95, 5], [94, 6], [93, 7], [92, 8], [91, 9], [90, 10], [89, 11]]) == [[100, 0], [99, 1], [98, 2], [97, 3], [96, 4], [95, 5], [94, 6], [93, 7], [92, 8], [91, 9], [90, 10], [89, 11]]\n assert candidate(people = [[3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2]]) == [[3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2], [3, 2]]\n assert candidate(people = [[20, 0], [18, 1], [16, 2], [14, 3], [12, 4], [10, 5], [8, 6], [6, 7], [4, 8], [2, 9]]) == [[20, 0], [18, 1], [16, 2], [14, 3], [12, 4], [10, 5], [8, 6], [6, 7], [4, 8], [2, 9]]\n assert candidate(people = [[100, 0], [95, 0], [90, 0], [85, 0], [80, 0], [75, 0], [70, 0], [65, 0], [60, 0], [55, 0], [50, 0], [45, 0], [40, 0], [35, 0], [30, 0], [25, 0], [20, 0], [15, 0], [10, 0], [5, 0], [98, 1], [93, 1], [88, 1], [83, 1], [78, 1], [73, 1], [68, 1], [63, 1], [58, 1], [53, 1], [48, 1], [43, 1], [38, 1], [33, 1], [28, 1], [23, 1], [18, 1], [13, 1], [8, 1], [3, 1], [96, 2], [91, 2], [86, 2], [81, 2], [76, 2], [71, 2], [66, 2], [61, 2], [56, 2], [51, 2], [46, 2], [41, 2], [36, 2], [31, 2], [26, 2], [21, 2], [16, 2], [11, 2], [6, 2], [1, 2], [94, 3], [89, 3], [84, 3], [79, 3], [74, 3], [69, 3], [64, 3], [59, 3], [54, 3], [49, 3], [44, 3], [39, 3], [34, 3], [29, 3], [24, 3], [19, 3], [14, 3], [9, 3], [4, 3], [92, 4], [87, 4], [82, 4], [77, 4], [72, 4], [67, 4], [62, 4], [57, 4], [52, 4], [47, 4], [42, 4], [37, 4], [32, 4], [27, 4], [22, 4], [17, 4], [12, 4], [7, 4], [2, 4], [85, 5], [80, 5], [75, 5], [70, 5], [65, 5], [60, 5], [55, 5], [50, 5], [45, 5], [40, 5], [35, 5], [30, 5], [25, 5], [20, 5], [15, 5], [10, 5], [5, 5], [0, 5]]) == [[5, 0], [3, 1], [1, 2], [10, 0], [8, 1], [0, 5], [2, 4], [4, 3], [6, 2], [15, 0], [5, 5], [13, 1], [7, 4], [9, 3], [11, 2], [20, 0], [10, 5], [18, 1], [12, 4], [14, 3], [16, 2], [25, 0], [15, 5], [23, 1], [17, 4], [19, 3], [21, 2], [30, 0], [20, 5], [28, 1], [22, 4], [24, 3], [26, 2], [35, 0], [25, 5], [33, 1], [27, 4], [29, 3], [31, 2], [40, 0], [30, 5], [38, 1], [32, 4], [34, 3], [36, 2], [45, 0], [35, 5], [43, 1], [37, 4], [39, 3], [41, 2], [50, 0], [40, 5], [48, 1], [42, 4], [44, 3], [46, 2], [55, 0], [45, 5], [53, 1], [47, 4], [49, 3], [51, 2], [60, 0], [50, 5], [58, 1], [52, 4], [54, 3], [56, 2], [65, 0], [55, 5], [63, 1], [57, 4], [59, 3], [61, 2], [70, 0], [60, 5], [68, 1], [62, 4], [64, 3], [66, 2], [75, 0], [65, 5], [73, 1], [67, 4], [69, 3], [71, 2], [80, 0], [70, 5], [78, 1], [72, 4], [74, 3], [76, 2], [85, 0], [75, 5], [83, 1], [77, 4], [79, 3], [81, 2], [90, 0], [80, 5], [88, 1], [82, 4], [84, 3], [86, 2], [95, 0], [85, 5], [93, 1], [87, 4], [89, 3], [91, 2], [100, 0], [98, 1], [92, 4], [94, 3], [96, 2]]\n assert candidate(people = [[200, 0], [190, 0], [190, 1], [180, 0], [180, 1], [180, 2], [170, 0], [170, 1], [170, 2], [170, 3], [160, 0], [160, 1], [160, 2], [160, 3], [150, 0], [150, 1], [150, 2], [150, 3], [140, 0], [140, 1], [140, 2], [140, 3]]) == [[140, 0], [140, 1], [140, 2], [140, 3], [150, 0], [150, 1], [150, 2], [150, 3], [160, 0], [160, 1], [160, 2], [160, 3], [170, 0], [170, 1], [170, 2], [170, 3], [180, 0], [180, 1], [180, 2], [190, 0], [190, 1], [200, 0]]\n assert candidate(people = [[150, 0], [150, 1], [150, 2], [150, 3], [150, 4], [150, 5], [150, 6], [150, 7], [150, 8], [150, 9], [150, 10], [150, 11], [150, 12], [150, 13], [150, 14], [150, 15], [150, 16], [150, 17], [150, 18], [150, 19], [150, 20], [150, 21], [150, 22], [150, 23], [150, 24], [150, 25], [150, 26], [150, 27], [150, 28], [150, 29]]) == [[150, 0], [150, 1], [150, 2], [150, 3], [150, 4], [150, 5], [150, 6], [150, 7], [150, 8], [150, 9], [150, 10], [150, 11], [150, 12], [150, 13], [150, 14], [150, 15], [150, 16], [150, 17], [150, 18], [150, 19], [150, 20], [150, 21], [150, 22], [150, 23], [150, 24], [150, 25], [150, 26], [150, 27], [150, 28], [150, 29]]\n assert candidate(people = [[7, 0], [4, 4], [7, 1], [5, 0], [6, 1], [5, 2], [3, 2], [2, 3], [1, 4], [0, 5]]) == [[5, 0], [7, 0], [3, 2], [2, 3], [1, 4], [0, 5], [5, 2], [6, 1], [4, 4], [7, 1]]\n assert candidate(people = [[5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0]]) == [[5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0]]\n assert candidate(people = [[15, 0], [14, 0], [14, 1], [13, 0], [12, 0], [12, 1], [11, 0], [11, 2], [10, 0], [10, 3], [9, 0], [9, 4]]) == [[9, 0], [10, 0], [11, 0], [12, 0], [9, 4], [10, 3], [11, 2], [12, 1], [13, 0], [14, 0], [14, 1], [15, 0]]\n assert candidate(people = [[70, 2], [55, 3], [65, 0], [75, 1], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [145, 1], [155, 2], [165, 3], [175, 4]]) == [[65, 0], [85, 0], [75, 1], [55, 3], [70, 2], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0], [175, 4], [145, 1], [165, 3], [155, 2]]\n assert candidate(people = [[150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0]]) == [[150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0], [150, 0]]\n assert candidate(people = [[120, 2], [110, 2], [100, 1], [90, 1], [80, 1], [70, 0], [60, 0], [50, 0]]) == [[50, 0], [60, 0], [70, 0], [120, 2], [80, 1], [90, 1], [100, 1], [110, 2]]\n assert candidate(people = [[8, 0], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9]]) == [[8, 0], [8, 1], [8, 2], [8, 3], [8, 4], [8, 5], [8, 6], [8, 7], [8, 8], [8, 9]]\n assert candidate(people = [[15, 0], [15, 1], [15, 2], [15, 3], [14, 0], [14, 1], [14, 2], [13, 0], [13, 1], [13, 2], [13, 3], [12, 0], [12, 1], [12, 2], [12, 3], [11, 0], [11, 1], [11, 2], [11, 3]]) == [[11, 0], [11, 1], [11, 2], [11, 3], [12, 0], [12, 1], [12, 2], [12, 3], [13, 0], [13, 1], [13, 2], [13, 3], [14, 0], [14, 1], [14, 2], [15, 0], [15, 1], [15, 2], [15, 3]]\n assert candidate(people = [[100, 0], [90, 0], [90, 1], [80, 0], [80, 1], [80, 2], [70, 0], [70, 1], [70, 2], [70, 3]]) == [[70, 0], [70, 1], [70, 2], [70, 3], [80, 0], [80, 1], [80, 2], [90, 0], [90, 1], [100, 0]]\n assert candidate(people = [[10, 0], [8, 0], [9, 0], [7, 1], [7, 0], [6, 2], [5, 3], [4, 4]]) == [[7, 0], [7, 1], [6, 2], [5, 3], [4, 4], [8, 0], [9, 0], [10, 0]]\n assert candidate(people = [[100, 0], [90, 0], [80, 0], [70, 0], [60, 0], [50, 0], [40, 0], [30, 0], [20, 0], [10, 0]]) == [[10, 0], [20, 0], [30, 0], [40, 0], [50, 0], [60, 0], [70, 0], [80, 0], [90, 0], [100, 0]]\n assert candidate(people = [[150, 3], [150, 2], [150, 1], [150, 0], [149, 0], [149, 1], [148, 0], [148, 1], [147, 0], [147, 1]]) == [[147, 0], [147, 1], [148, 0], [148, 1], [149, 0], [149, 1], [150, 0], [150, 1], [150, 2], [150, 3]]\n assert candidate(people = [[5, 2], [5, 1], [5, 0], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10]]) == [[5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [5, 6], [5, 7], [5, 8], [5, 9], [5, 10]]\n assert candidate(people = [[15, 0], [14, 1], [13, 2], [12, 3], [11, 4], [10, 5], [9, 6], [8, 7]]) == [[15, 0], [14, 1], [13, 2], [12, 3], [11, 4], [10, 5], [9, 6], [8, 7]]\n assert candidate(people = [[120, 5], [110, 3], [100, 0], [90, 2], [80, 4], [70, 1], [60, 6], [50, 7], [40, 5], [30, 3], [20, 2], [10, 1]]) == [[100, 0], [10, 1], [70, 1], [20, 2], [120, 5], [30, 3], [90, 2], [110, 3], [40, 5], [80, 4], [60, 6], [50, 7]]\n assert candidate(people = [[10, 3], [9, 0], [8, 1], [7, 2], [6, 3], [5, 4], [4, 5], [3, 6], [2, 7], [1, 8]]) == [[9, 0], [8, 1], [7, 2], [6, 3], [5, 4], [4, 5], [3, 6], [2, 7], [1, 8], [10, 3]]\n assert candidate(people = [[1, 0], [2, 1], [3, 2], [4, 3], [5, 4], [6, 5], [7, 6], [8, 7], [9, 8], [10, 9], [11, 10]]) == [[1, 0], [11, 10], [2, 1], [10, 9], [3, 2], [9, 8], [4, 3], [8, 7], [5, 4], [7, 6], [6, 5]]\n assert candidate(people = [[500, 0], [400, 1], [300, 2], [200, 3], [100, 4], [50, 5], [49, 5], [48, 5], [47, 5], [46, 5], [45, 5], [44, 5], [43, 5], [42, 5], [41, 5], [40, 5], [39, 5], [38, 5], [37, 5], [36, 5], [35, 5], [34, 5], [33, 5], [32, 5], [31, 5], [30, 5], [29, 5], [28, 5], [27, 5], [26, 5], [25, 5], [24, 5], [23, 5], [22, 5], [21, 5], [20, 5], [19, 5], [18, 5], [17, 5], [16, 5], [15, 5], [14, 5], [13, 5], [12, 5], [11, 5], [10, 5], [9, 5], [8, 5], [7, 5], [6, 5], [5, 5], [4, 5], [3, 5], [2, 5], [1, 5]]) == [[500, 0], [400, 1], [300, 2], [200, 3], [100, 4], [1, 5], [2, 5], [3, 5], [4, 5], [5, 5], [6, 5], [7, 5], [8, 5], [9, 5], [10, 5], [11, 5], [12, 5], [13, 5], [14, 5], [15, 5], [16, 5], [17, 5], [18, 5], [19, 5], [20, 5], [21, 5], [22, 5], [23, 5], [24, 5], [25, 5], [26, 5], [27, 5], [28, 5], [29, 5], [30, 5], [31, 5], [32, 5], [33, 5], [34, 5], [35, 5], [36, 5], [37, 5], [38, 5], [39, 5], [40, 5], [41, 5], [42, 5], [43, 5], [44, 5], [45, 5], [46, 5], [47, 5], [48, 5], [49, 5], [50, 5]]\n assert candidate(people = [[2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19]]) == [[2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [2, 5], [2, 6], [2, 7], [2, 8], [2, 9], [2, 10], [2, 11], [2, 12], [2, 13], [2, 14], [2, 15], [2, 16], [2, 17], [2, 18], [2, 19]]\n assert candidate(people = [[10, 0], [9, 1], [10, 1], [8, 2], [9, 2], [10, 2], [7, 3], [8, 3], [9, 3], [10, 3], [6, 4], [7, 4], [8, 4], [9, 4], [10, 4]]) == [[10, 0], [9, 1], [8, 2], [7, 3], [6, 4], [7, 4], [8, 3], [8, 4], [9, 2], [9, 3], [9, 4], [10, 1], [10, 2], [10, 3], [10, 4]]\n assert candidate(people = [[70, 0], [55, 0], [65, 0], [75, 0], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0]]) == [[55, 0], [65, 0], [70, 0], [75, 0], [85, 0], [95, 0], [105, 0], [115, 0], [125, 0], [135, 0]]\n assert candidate(people = [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]) == [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]\n assert candidate(people = [[10, 0], [9, 0], [8, 0], [7, 0], [6, 0], [5, 0], [4, 0], [3, 0], [2, 0], [1, 0]]) == [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0]]\n assert candidate(people = [[100, 0], [90, 1], [80, 2], [70, 3], [60, 4], [50, 5], [40, 6], [30, 7], [20, 8], [10, 9], [0, 10], [110, 0], [120, 1]]) == [[100, 0], [90, 1], [80, 2], [70, 3], [60, 4], [50, 5], [40, 6], [30, 7], [20, 8], [10, 9], [0, 10], [110, 0], [120, 1]]\n assert candidate(people = [[100, 0], [90, 1], [80, 2], [70, 3], [60, 4], [50, 5], [40, 6], [30, 7], [20, 8], [10, 9]]) == [[100, 0], [90, 1], [80, 2], [70, 3], [60, 4], [50, 5], [40, 6], [30, 7], [20, 8], [10, 9]]\n assert candidate(people = [[5, 0], [7, 0], [5, 2], [6, 1], [5, 4], [5, 1], [5, 3], [6, 0], [7, 1], [5, 5]]) == [[5, 0], [5, 1], [5, 2], [5, 3], [5, 4], [5, 5], [6, 0], [6, 1], [7, 0], [7, 1]]\n assert candidate(people = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0], [20, 0]]) == [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0], [10, 0], [11, 0], [12, 0], [13, 0], [14, 0], [15, 0], [16, 0], [17, 0], [18, 0], [19, 0], [20, 0]]\n assert candidate(people = [[10, 0], [9, 1], [8, 2], [7, 3], [6, 4], [5, 5], [4, 6], [3, 7], [2, 8], [1, 9], [0, 10]]) == [[10, 0], [9, 1], [8, 2], [7, 3], [6, 4], [5, 5], [4, 6], [3, 7], [2, 8], [1, 9], [0, 10]]\n assert candidate(people = [[20, 0], [18, 2], [17, 4], [19, 1], [18, 1], [17, 3], [20, 1], [19, 0], [18, 0], [17, 2], [16, 5], [15, 6]]) == [[18, 0], [18, 1], [17, 2], [17, 3], [17, 4], [16, 5], [15, 6], [18, 2], [19, 0], [19, 1], [20, 0], [20, 1]]\n assert candidate(people = [[10, 0], [10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [10, 9], [10, 10], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15]]) == [[10, 0], [10, 1], [10, 2], [10, 3], [10, 4], [10, 5], [10, 6], [10, 7], [10, 8], [10, 9], [10, 10], [10, 11], [10, 12], [10, 13], [10, 14], [10, 15]]\n assert candidate(people = [[70, 0], [55, 1], [65, 0], [75, 0], [85, 2], [95, 1], [105, 0], [115, 2], [125, 3], [135, 2]]) == [[65, 0], [55, 1], [70, 0], [75, 0], [105, 0], [95, 1], [85, 2], [135, 2], [125, 3], [115, 2]]\n assert candidate(people = [[10, 0], [8, 0], [9, 0], [9, 1], [8, 1], [7, 0], [6, 0], [6, 1], [5, 2], [4, 3]]) == [[6, 0], [6, 1], [5, 2], [4, 3], [7, 0], [8, 0], [8, 1], [9, 0], [9, 1], [10, 0]]\n assert candidate(people = [[5, 0], [4, 0], [3, 0], [2, 0], [1, 0], [5, 1], [4, 1], [3, 1], [2, 1], [1, 1], [5, 2], [4, 2], [3, 2], [2, 2], [1, 2], [5, 3], [4, 3], [3, 3], [2, 3], [1, 3], [5, 4], [4, 4], [3, 4], [2, 4], [1, 4]]) == [[1, 0], [1, 1], [1, 2], [1, 3], [1, 4], [2, 0], [2, 1], [2, 2], [2, 3], [2, 4], [3, 0], [3, 1], [3, 2], [3, 3], [3, 4], [4, 0], [4, 1], [4, 2], [4, 3], [4, 4], [5, 0], [5, 1], [5, 2], [5, 3], [5, 4]]\n assert candidate(people = [[60, 0], [60, 1], [60, 2], [60, 3], [60, 4], [60, 5], [60, 6], [60, 7], [60, 8], [60, 9], [60, 10]]) == [[60, 0], [60, 1], [60, 2], [60, 3], [60, 4], [60, 5], [60, 6], [60, 7], [60, 8], [60, 9], [60, 10]]\n assert candidate(people = [[120, 0], [120, 1], [120, 2], [120, 3], [120, 4], [120, 5], [120, 6], [120, 7], [120, 8], [120, 9], [120, 10], [120, 11], [120, 12], [120, 13], [120, 14], [120, 15], [120, 16], [120, 17], [120, 18], [120, 19]]) == [[120, 0], [120, 1], [120, 2], [120, 3], [120, 4], [120, 5], [120, 6], [120, 7], [120, 8], [120, 9], [120, 10], [120, 11], [120, 12], [120, 13], [120, 14], [120, 15], [120, 16], [120, 17], [120, 18], [120, 19]]\n"}, "metadata": {"canonical_parameter_names": ["people"], "leetcode_dataset_entry_point": "Solution().reconstructQueue", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reconstructQueue = function(people) {", "container": null, "callable": "reconstructQueue", "parameters": [{"name": "people", "type": "number[][]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 407, "task_id": "trapping-rain-water-ii", "difficulty": "Hard", "problem_description": "Given an m x n integer matrix heightMap representing the height of each unit cell in a 2D elevation map, return the volume of water it can trap after raining.\n \nExample 1:\n\n\nInput: heightMap = [[1,4,3,1,3,2],[3,2,1,3,2,4],[2,3,3,2,3,1]]\nOutput: 4\nExplanation: After the rain, water is trapped between the blocks.\nWe have two small ponds 1 and 3 units trapped.\nThe total volume of water trapped is 4.\n\nExample 2:\n\n\nInput: heightMap = [[3,3,3,3,3],[3,2,2,2,3],[3,2,1,2,3],[3,2,2,2,3],[3,3,3,3,3]]\nOutput: 10\n\n \nConstraints:\n\nm == heightMap.length\nn == heightMap[i].length\n1 <= m, n <= 200\n0 <= heightMap[i][j] <= 2 * 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(heightMap = [[5, 5, 5, 5, 5], [5, 1, 2, 1, 5], [5, 2, 3, 2, 5], [5, 1, 2, 1, 5], [5, 5, 5, 5, 5]]) == 30\n assert candidate(heightMap = [[1, 2], [2, 1]]) == 0\n assert candidate(heightMap = [[1, 2, 3], [0, 1, 0], [1, 2, 1]]) == 0\n assert candidate(heightMap = [[1]]) == 0\n assert candidate(heightMap = [[12, 13, 1, 12], [13, 4, 13, 12], [13, 8, 10, 12], [12, 13, 12, 12], [13, 13, 13, 13]]) == 14\n assert candidate(heightMap = [[7, 8, 9, 10, 9], [8, 9, 10, 11, 10], [9, 10, 11, 12, 11], [10, 11, 12, 13, 12], [11, 12, 13, 14, 13]]) == 0\n assert candidate(heightMap = [[1, 1, 1, 1, 1], [1, 0, 0, 0, 1], [1, 0, 4, 0, 1], [1, 0, 0, 0, 1], [1, 1, 1, 1, 1]]) == 8\n assert candidate(heightMap = [[10, 20, 10], [20, 5, 20], [10, 20, 10]]) == 15\n assert candidate(heightMap = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 2, 3, 4, 5], [5, 4, 3, 2, 1]]) == 0\n assert candidate(heightMap = [[3, 3, 3, 3, 3], [3, 2, 2, 2, 3], [3, 2, 1, 2, 3], [3, 2, 2, 2, 3], [3, 3, 3, 3, 3]]) == 10\n assert candidate(heightMap = [[2, 2, 2], [2, 1, 2], [2, 2, 2]]) == 1\n assert candidate(heightMap = [[10, 9, 8, 7, 6], [9, 8, 7, 6, 5], [8, 7, 6, 5, 4], [7, 6, 5, 4, 3], [6, 5, 4, 3, 2]]) == 0\n assert candidate(heightMap = [[3, 3, 3], [3, 1, 3], [3, 3, 3]]) == 2\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2], [3, 2, 1, 3, 2, 4], [2, 3, 3, 2, 3, 1]]) == 4\n assert candidate(heightMap = [[5, 8, 7, 7, 5], [5, 2, 1, 2, 5], [5, 3, 0, 3, 5], [5, 4, 4, 4, 5], [5, 5, 5, 5, 5]]) == 22\n assert candidate(heightMap = [[5, 15, 25, 35, 45], [5, 10, 10, 10, 10], [15, 10, 10, 10, 15], [25, 10, 10, 10, 25], [35, 10, 10, 10, 35], [45, 40, 30, 20, 15]]) == 0\n assert candidate(heightMap = [[1, 5, 3, 2, 4, 1, 2], [2, 3, 4, 2, 1, 4, 2], [3, 4, 2, 1, 5, 3, 4], [1, 3, 2, 4, 3, 2, 1], [2, 4, 5, 3, 2, 1, 2], [1, 3, 4, 2, 1, 3, 4]]) == 3\n assert candidate(heightMap = [[1, 3, 5, 7, 5, 3, 1], [3, 5, 7, 9, 7, 5, 3], [5, 7, 9, 11, 9, 7, 5], [7, 9, 11, 13, 11, 9, 7], [5, 7, 9, 11, 9, 7, 5], [3, 5, 7, 9, 7, 5, 3], [1, 3, 5, 7, 5, 3, 1]]) == 0\n assert candidate(heightMap = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9]]) == 0\n assert candidate(heightMap = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1]]) == 0\n assert candidate(heightMap = [[10, 14, 13, 15, 14, 13, 12], [15, 9, 8, 13, 12, 11, 10], [14, 10, 9, 12, 11, 10, 9], [13, 11, 10, 11, 10, 9, 8], [12, 12, 11, 10, 9, 8, 7], [11, 13, 12, 11, 10, 9, 8], [10, 14, 13, 12, 11, 10, 9]]) == 9\n assert candidate(heightMap = [[9, 1, 9, 1, 9, 1, 9, 1, 9], [1, 9, 1, 9, 1, 9, 1, 9, 1], [9, 1, 9, 1, 9, 1, 9, 1, 9], [1, 9, 1, 9, 1, 9, 1, 9, 1], [9, 1, 9, 1, 1, 1, 9, 1, 9], [1, 9, 1, 9, 1, 9, 1, 9, 1], [9, 1, 9, 1, 9, 1, 9, 1, 9]]) == 144\n assert candidate(heightMap = [[8, 8, 8, 8, 8, 8, 8, 8, 8], [8, 2, 2, 2, 2, 2, 2, 2, 8], [8, 2, 6, 6, 6, 6, 6, 2, 8], [8, 2, 6, 3, 3, 3, 6, 2, 8], [8, 2, 6, 3, 1, 3, 6, 2, 8], [8, 2, 6, 3, 3, 3, 6, 2, 8], [8, 2, 6, 6, 6, 6, 6, 2, 8], [8, 2, 2, 2, 2, 2, 2, 2, 8], [8, 8, 8, 8, 8, 8, 8, 8, 8]]) == 223\n assert candidate(heightMap = [[10, 20, 30, 40, 50], [40, 30, 20, 10, 40], [50, 40, 30, 20, 50], [40, 10, 20, 30, 40], [50, 50, 50, 50, 50]]) == 70\n assert candidate(heightMap = [[5, 8, 7, 7], [5, 2, 1, 5], [6, 1, 1, 4], [6, 3, 3, 8]]) == 7\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2, 4, 5, 1], [3, 2, 1, 3, 2, 4, 2, 3, 4], [2, 3, 3, 2, 3, 1, 4, 2, 1]]) == 5\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2, 5, 6, 3, 1], [3, 2, 1, 3, 2, 4, 1, 5, 3, 2], [2, 3, 3, 2, 3, 1, 3, 4, 1, 1], [3, 2, 1, 3, 2, 4, 1, 5, 3, 2], [2, 3, 3, 2, 3, 1, 3, 4, 1, 1], [3, 2, 1, 3, 2, 4, 1, 5, 3, 2], [2, 3, 3, 2, 3, 1, 3, 4, 1, 1]]) == 24\n assert candidate(heightMap = [[1, 2, 3, 4, 5], [2, 1, 2, 1, 2], [3, 2, 1, 2, 3], [4, 3, 2, 3, 4], [5, 4, 3, 4, 5]]) == 3\n assert candidate(heightMap = [[5, 8, 7, 7], [5, 2, 1, 5], [6, 1, 5, 4], [2, 1, 4, 3], [6, 3, 1, 2]]) == 3\n assert candidate(heightMap = [[8, 12, 9, 10, 11, 10], [13, 7, 6, 9, 8, 12], [14, 8, 7, 8, 7, 11], [15, 9, 8, 9, 8, 10], [16, 10, 9, 10, 9, 11], [17, 11, 10, 11, 10, 12]]) == 14\n assert candidate(heightMap = [[5, 5, 5, 1], [5, 1, 1, 5], [5, 1, 1, 5], [5, 5, 5, 1]]) == 16\n assert candidate(heightMap = [[3, 3, 3, 3, 3, 3], [3, 1, 1, 1, 1, 3], [3, 1, 2, 2, 1, 3], [3, 1, 2, 2, 1, 3], [3, 1, 1, 1, 1, 3], [3, 3, 3, 3, 3, 3]]) == 28\n assert candidate(heightMap = [[1, 1, 1, 1, 1, 1], [1, 100, 100, 100, 100, 1], [1, 100, 1, 1, 100, 1], [1, 100, 1, 1, 100, 1], [1, 100, 100, 100, 100, 1], [1, 1, 1, 1, 1, 1]]) == 396\n assert candidate(heightMap = [[1, 2, 3, 4, 5], [16, 17, 18, 19, 6], [15, 24, 25, 20, 7], [14, 23, 22, 21, 8], [13, 12, 11, 10, 9]]) == 0\n assert candidate(heightMap = [[12, 13, 12, 15, 14, 13], [16, 10, 9, 14, 13, 17], [15, 11, 10, 13, 12, 16], [14, 12, 11, 12, 11, 15], [13, 14, 13, 14, 13, 14]]) == 10\n assert candidate(heightMap = [[10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 1, 1, 1, 1, 1, 1, 1, 1, 10], [10, 1, 8, 8, 8, 8, 8, 8, 1, 10], [10, 1, 8, 5, 5, 5, 5, 5, 1, 10], [10, 1, 8, 5, 3, 3, 3, 5, 1, 10], [10, 1, 8, 5, 3, 1, 3, 5, 1, 10], [10, 1, 8, 5, 3, 3, 3, 5, 1, 10], [10, 1, 8, 5, 5, 5, 5, 5, 1, 10], [10, 1, 1, 1, 1, 1, 1, 1, 1, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]]) == 419\n assert candidate(heightMap = [[12, 13, 12, 11, 12, 13, 12], [13, 12, 11, 10, 11, 12, 13], [12, 11, 10, 9, 10, 11, 12], [11, 10, 9, 8, 9, 10, 11], [12, 11, 10, 9, 10, 11, 12], [13, 12, 11, 10, 11, 12, 13], [12, 13, 12, 11, 12, 13, 12]]) == 19\n assert candidate(heightMap = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]]) == 0\n assert candidate(heightMap = [[10, 20, 30, 40, 30, 20, 10], [20, 10, 10, 10, 10, 10, 20], [30, 10, 20, 30, 20, 10, 30], [40, 10, 30, 40, 30, 10, 40], [30, 10, 20, 30, 20, 10, 30], [20, 10, 10, 10, 10, 10, 20], [10, 20, 30, 40, 30, 20, 10]]) == 160\n assert candidate(heightMap = [[12, 13, 14, 15, 16, 17, 18, 19, 20], [11, 10, 9, 8, 7, 6, 5, 4, 3], [12, 13, 14, 15, 16, 17, 18, 19, 20], [11, 10, 9, 8, 7, 6, 5, 4, 3], [12, 13, 14, 15, 16, 17, 18, 19, 20], [11, 10, 9, 8, 7, 6, 5, 4, 3], [12, 13, 14, 15, 16, 17, 18, 19, 20], [11, 10, 9, 8, 7, 6, 5, 4, 3], [12, 13, 14, 15, 16, 17, 18, 19, 20]]) == 0\n assert candidate(heightMap = [[10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 1, 2, 3, 4, 5, 4, 3, 10], [10, 2, 1, 2, 3, 4, 3, 2, 10], [10, 3, 2, 1, 2, 3, 2, 1, 10], [10, 4, 3, 2, 1, 2, 1, 2, 10], [10, 5, 4, 3, 2, 1, 2, 3, 10], [10, 4, 5, 4, 3, 2, 3, 4, 10], [10, 3, 4, 5, 4, 3, 2, 1, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10]]) == 355\n assert candidate(heightMap = [[3, 3, 3, 3, 3, 3, 3], [3, 2, 2, 2, 1, 2, 3], [3, 2, 1, 1, 0, 1, 3], [3, 2, 2, 2, 1, 2, 3], [3, 3, 3, 3, 3, 3, 3]]) == 22\n assert candidate(heightMap = [[1, 1, 1, 1, 1, 1], [1, 2, 3, 3, 2, 1], [1, 2, 4, 4, 2, 1], [1, 2, 3, 3, 2, 1], [1, 1, 1, 1, 1, 1]]) == 0\n assert candidate(heightMap = [[6, 8, 6, 8, 6, 8, 6, 8, 6], [8, 6, 8, 6, 8, 6, 8, 6, 8], [6, 8, 6, 8, 6, 8, 6, 8, 6], [8, 6, 8, 6, 8, 6, 8, 6, 8], [6, 8, 6, 8, 6, 8, 6, 8, 6]]) == 22\n assert candidate(heightMap = [[3, 3, 3, 3, 3, 3, 3], [3, 2, 2, 2, 2, 2, 3], [3, 2, 1, 1, 1, 2, 3], [3, 2, 1, 0, 1, 2, 3], [3, 2, 1, 1, 1, 2, 3], [3, 2, 2, 2, 2, 2, 3], [3, 3, 3, 3, 3, 3, 3]]) == 35\n assert candidate(heightMap = [[9, 9, 9, 9, 9, 9, 9], [9, 0, 0, 0, 0, 0, 9], [9, 0, 9, 9, 9, 0, 9], [9, 0, 9, 0, 9, 0, 9], [9, 0, 9, 9, 9, 0, 9], [9, 0, 0, 0, 0, 0, 9], [9, 9, 9, 9, 9, 9, 9]]) == 153\n assert candidate(heightMap = [[3, 2, 1, 2, 3, 4, 3, 2, 1], [3, 2, 1, 2, 3, 4, 3, 2, 1], [3, 2, 1, 2, 3, 4, 3, 2, 1], [3, 2, 1, 2, 3, 4, 3, 2, 1]]) == 0\n assert candidate(heightMap = [[5, 1, 5, 1, 5, 1, 5], [1, 5, 1, 5, 1, 5, 1], [5, 1, 5, 1, 5, 1, 5], [1, 5, 1, 5, 1, 5, 1], [5, 1, 5, 1, 5, 1, 5]]) == 28\n assert candidate(heightMap = [[3, 3, 3, 3, 3, 3], [3, 1, 2, 1, 2, 3], [3, 2, 1, 2, 1, 3], [3, 1, 2, 1, 2, 3], [3, 3, 3, 3, 3, 3]]) == 18\n assert candidate(heightMap = [[7, 5, 7, 9, 9, 4, 7, 8], [7, 5, 7, 6, 6, 4, 7, 8], [7, 5, 7, 5, 5, 4, 7, 8], [9, 9, 9, 9, 5, 9, 9, 9], [9, 5, 9, 9, 5, 9, 9, 9], [9, 5, 5, 5, 5, 9, 9, 9], [9, 5, 9, 9, 5, 9, 9, 9], [9, 5, 9, 9, 9, 9, 9, 9]]) == 0\n assert candidate(heightMap = [[20, 15, 10, 15, 20], [15, 10, 5, 10, 15], [10, 5, 0, 5, 10], [15, 10, 5, 10, 15], [20, 15, 10, 15, 20]]) == 30\n assert candidate(heightMap = [[8, 7, 9, 6, 8, 7, 9], [7, 6, 8, 5, 7, 6, 8], [9, 8, 7, 6, 9, 8, 7], [6, 5, 6, 5, 6, 5, 6], [8, 7, 8, 7, 8, 7, 8], [7, 6, 7, 6, 7, 6, 7], [9, 8, 9, 8, 9, 8, 9]]) == 9\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2, 5, 1, 3, 2], [3, 2, 1, 3, 2, 4, 1, 5, 1, 4], [2, 3, 3, 2, 3, 1, 3, 1, 3, 3], [1, 2, 1, 2, 1, 3, 2, 1, 2, 1], [3, 4, 3, 4, 3, 2, 1, 2, 1, 2]]) == 14\n assert candidate(heightMap = [[9, 1, 9, 1, 9, 1], [1, 2, 1, 2, 1, 2], [9, 1, 9, 1, 9, 1], [1, 2, 1, 2, 1, 2], [9, 1, 9, 1, 9, 1], [1, 2, 1, 2, 1, 2]]) == 8\n assert candidate(heightMap = [[2, 1, 2, 1, 2], [1, 2, 1, 2, 1], [2, 1, 2, 1, 2], [1, 2, 1, 2, 1], [2, 1, 2, 1, 2]]) == 4\n assert candidate(heightMap = [[10, 20, 30, 20, 10], [20, 15, 10, 15, 20], [30, 10, 5, 10, 30], [20, 15, 10, 15, 20], [10, 20, 30, 20, 10]]) == 75\n assert candidate(heightMap = [[6, 8, 6, 8, 6, 8, 6], [8, 6, 8, 6, 8, 6, 8], [6, 8, 6, 8, 6, 8, 6], [8, 6, 8, 6, 8, 6, 8], [6, 8, 6, 8, 6, 8, 6], [8, 6, 8, 6, 8, 6, 8], [6, 8, 6, 8, 6, 8, 6]]) == 26\n assert candidate(heightMap = [[0, 0, 0, 0, 0], [0, 1, 2, 1, 0], [0, 2, 3, 2, 0], [0, 1, 2, 1, 0], [0, 0, 0, 0, 0]]) == 0\n assert candidate(heightMap = [[12, 13, 12, 13, 12], [13, 11, 10, 11, 13], [12, 10, 9, 10, 12], [13, 11, 10, 11, 13], [12, 13, 12, 13, 12]]) == 15\n assert candidate(heightMap = [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [3, 1, 5, 5, 5, 5, 5, 5, 5, 1, 3], [3, 1, 5, 3, 3, 3, 3, 3, 5, 1, 3], [3, 1, 5, 3, 1, 1, 1, 3, 5, 1, 3], [3, 1, 5, 3, 1, 0, 1, 3, 5, 1, 3], [3, 1, 5, 3, 1, 1, 1, 3, 5, 1, 3], [3, 1, 5, 3, 3, 3, 3, 3, 5, 1, 3], [3, 1, 5, 5, 5, 5, 5, 5, 5, 1, 3], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]]) == 133\n assert candidate(heightMap = [[7, 7, 7, 7, 7, 7, 7], [7, 2, 2, 2, 2, 2, 7], [7, 2, 5, 5, 5, 2, 7], [7, 2, 5, 1, 5, 2, 7], [7, 2, 5, 5, 5, 2, 7], [7, 2, 2, 2, 2, 2, 7], [7, 7, 7, 7, 7, 7, 7]]) == 102\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2, 5, 6, 7, 8, 9, 10], [3, 2, 1, 3, 2, 4, 9, 8, 7, 6, 5, 4], [2, 3, 3, 2, 3, 1, 4, 5, 6, 7, 8, 9], [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1], [1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8], [8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3], [7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4], [6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5]]) == 12\n assert candidate(heightMap = [[1, 2, 3, 4, 5, 4, 3, 2, 1], [2, 3, 4, 5, 6, 5, 4, 3, 2], [3, 4, 5, 6, 7, 6, 5, 4, 3], [4, 5, 6, 7, 8, 7, 6, 5, 4], [5, 6, 7, 8, 9, 8, 7, 6, 5], [4, 5, 6, 7, 8, 7, 6, 5, 4], [3, 4, 5, 6, 7, 6, 5, 4, 3], [2, 3, 4, 5, 6, 5, 4, 3, 2], [1, 2, 3, 4, 5, 4, 3, 2, 1]]) == 0\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2, 5], [3, 2, 1, 3, 2, 4, 5], [2, 3, 3, 2, 3, 1, 5], [6, 6, 6, 6, 6, 6, 6]]) == 7\n assert candidate(heightMap = [[12, 13, 14, 15, 16], [11, 10, 9, 8, 17], [18, 19, 20, 7, 6], [5, 4, 3, 2, 1], [21, 22, 23, 24, 25]]) == 0\n assert candidate(heightMap = [[5, 5, 5, 5, 5, 5], [5, 1, 2, 3, 4, 5], [5, 2, 3, 4, 5, 5], [5, 3, 4, 5, 5, 5], [5, 4, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5]]) == 20\n assert candidate(heightMap = [[10, 10, 10, 10, 10], [10, 9, 9, 9, 10], [10, 9, 8, 9, 10], [10, 9, 9, 9, 10], [10, 10, 10, 10, 10]]) == 10\n assert candidate(heightMap = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == 183\n assert candidate(heightMap = [[12, 13, 14, 15, 16], [11, 10, 9, 8, 7], [6, 5, 4, 3, 2], [1, 2, 3, 4, 5], [6, 7, 8, 9, 10]]) == 0\n assert candidate(heightMap = [[5, 5, 5, 5, 5, 5], [5, 4, 4, 4, 4, 5], [5, 4, 3, 3, 4, 5], [5, 4, 3, 3, 4, 5], [5, 4, 4, 4, 4, 5], [5, 5, 5, 5, 5, 5]]) == 20\n assert candidate(heightMap = [[5, 5, 5, 5, 5], [5, 1, 1, 1, 5], [5, 1, 4, 1, 5], [5, 1, 1, 1, 5], [5, 5, 5, 5, 5]]) == 33\n assert candidate(heightMap = [[7, 8, 9, 10, 9, 8, 7], [6, 5, 4, 3, 4, 5, 6], [7, 8, 9, 10, 9, 8, 7], [6, 5, 4, 3, 4, 5, 6]]) == 9\n assert candidate(heightMap = [[5, 5, 5, 5, 5], [5, 4, 4, 4, 5], [5, 4, 3, 4, 5], [5, 4, 4, 4, 5], [5, 5, 5, 5, 5]]) == 10\n assert candidate(heightMap = [[5, 8, 7, 7, 5], [5, 2, 1, 2, 5], [5, 1, 3, 1, 5], [5, 2, 1, 2, 5], [5, 5, 5, 5, 5]]) == 30\n assert candidate(heightMap = [[12, 13, 14, 15, 16], [11, 10, 9, 8, 7], [10, 9, 8, 7, 6], [9, 8, 7, 6, 5], [8, 7, 6, 5, 4]]) == 0\n assert candidate(heightMap = [[10, 20, 10, 20, 10, 20, 10], [20, 10, 20, 10, 20, 10, 20], [10, 20, 10, 20, 10, 20, 10], [20, 10, 20, 10, 20, 10, 20], [10, 20, 10, 20, 10, 20, 10]]) == 80\n assert candidate(heightMap = [[1, 4, 3, 1, 3, 2], [3, 2, 1, 3, 2, 4], [2, 3, 3, 2, 3, 1], [4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 4]]) == 4\n assert candidate(heightMap = [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 1, 1, 1, 1, 1, 1, 1, 1, 7], [7, 1, 6, 6, 6, 6, 6, 6, 1, 7], [7, 1, 6, 5, 5, 5, 5, 6, 1, 7], [7, 1, 6, 5, 4, 4, 5, 6, 1, 7], [7, 1, 6, 5, 4, 4, 5, 6, 1, 7], [7, 1, 6, 5, 5, 5, 5, 6, 1, 7], [7, 1, 6, 6, 6, 6, 6, 6, 1, 7], [7, 1, 1, 1, 1, 1, 1, 1, 1, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]]) == 224\n"}, "metadata": {"canonical_parameter_names": ["heightMap"], "leetcode_dataset_entry_point": "Solution().trapRainWater", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var trapRainWater = function(heightMap) {", "container": null, "callable": "trapRainWater", "parameters": [{"name": "heightMap", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 409, "task_id": "longest-palindrome", "difficulty": "Easy", "problem_description": "Given a string s which consists of lowercase or uppercase letters, return the length of the longest palindrome that can be built with those letters.\nLetters are case sensitive, for example, \"Aa\" is not considered a palindrome.\n \nExample 1:\n\nInput: s = \"abccccdd\"\nOutput: 7\nExplanation: One longest palindrome that can be built is \"dccaccd\", whose length is 7.\n\nExample 2:\n\nInput: s = \"a\"\nOutput: 1\nExplanation: The longest palindrome that can be built is \"a\", whose length is 1.\n\n \nConstraints:\n\n1 <= s.length <= 2000\ns consists of lowercase and/or uppercase English letters only.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aabbccc\") == 7\n assert candidate(s = \"abccccdd\") == 7\n assert candidate(s = \"zyyzzzzz\") == 8\n assert candidate(s = \"abcdedcba\") == 9\n assert candidate(s = \"aabbbb\") == 6\n assert candidate(s = \"aaaaa\") == 5\n assert candidate(s = \"aabbccddee\") == 10\n assert candidate(s = \"a\") == 1\n assert candidate(s = \"aaabbbaa\") == 7\n assert candidate(s = \"aabbbccc\") == 7\n assert candidate(s = \"aabbbbccc\") == 9\n assert candidate(s = \"zzzz\") == 4\n assert candidate(s = \"aabbc\") == 5\n assert candidate(s = \"\") == 0\n assert candidate(s = \"aabbb\") == 5\n assert candidate(s = \"abcde\") == 1\n assert candidate(s = \"Aa\") == 1\n assert candidate(s = \"racecar\") == 7\n assert candidate(s = \"aabb\") == 4\n assert candidate(s = \"abbccc\") == 5\n assert candidate(s = \"abcadcb\") == 7\n assert candidate(s = \"abcABC\") == 1\n assert candidate(s = \"abba\") == 4\n assert candidate(s = \"abc\") == 1\n assert candidate(s = \"aabbccddeeffgghhii\") == 18\n assert candidate(s = \"aabbccddeeff\") == 12\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\") == 52\n assert candidate(s = \"aabbbbcccc\") == 10\n assert candidate(s = \"zzzzzzzz\") == 8\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 1\n assert candidate(s = \"abcdefg\") == 1\n assert candidate(s = \"aAbBcCdDeEfFgGhHiIjJkKlLmMnNoOpPqQrRsStTuUvVwWxXyYzZ\") == 1\n assert candidate(s = \"abAB\") == 1\n assert candidate(s = \"aaAAbbBBccCCddDDeeEEffFFggGGhhHHiiJJkkLLmmNNooPPqqRRssSStttUuuVvvWwwXxxYyyZzz\") == 71\n assert candidate(s = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == 49\n assert candidate(s = \"deified\") == 7\n assert candidate(s = \"AaBbCcDdEeFfGg\") == 1\n assert candidate(s = \"abcABCabcABCabcABC\") == 13\n assert candidate(s = \"abcdeABCDEabcdeABCDEabcdeABCDEabcdeABCDE\") == 40\n assert candidate(s = \"abcdabcabcdabcabcdabcabcdabcabcdabcabcdabcabcdabcabcdabcdabcabcdabcabcdabc\") == 71\n assert candidate(s = \"Aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 51\n assert candidate(s = \"AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\") == 1\n assert candidate(s = \"abacabadabacaba\") == 15\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzAAAaaaBBBbbbCCCcccDDDdddEEEeeeFFFfffGGGgggHHHhhhIIIiiiJJJjjjKKKkkkLLLlllMMMmmmNNNnnnOOOoooPPPpppQQQqqqRRRrrrSSSsssTTTtttUUUuuuVVVvvvWWWwwwXXXxxxYYYyyyZZZzzz\") == 157\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\") == 1\n assert candidate(s = \"abacabadabacabadabacabadabacabad\") == 32\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaABCDEFGHIJKLMNOPQRSTUVWXYZ\") == 1\n assert candidate(s = \"bAabA\") == 5\n assert candidate(s = \"rotor\") == 5\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyz\") == 51\n assert candidate(s = \"noon\") == 4\n assert candidate(s = \"banana\") == 5\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg\") == 56\n assert candidate(s = \"abbcccdddd\") == 9\n assert candidate(s = \"aabbccddeeeffffffgggg\") == 21\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 52\n assert candidate(s = \"bbaaaacccddeeefffggghhhiiijjjkkklllmmmnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz\") == 55\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == 71\n assert candidate(s = \"abbacdfee\") == 7\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzzzzzzz\") == 58\n assert candidate(s = \"AxA\") == 3\n assert candidate(s = \"aaabbbbcccc\") == 11\n assert candidate(s = \"thisisatest\") == 7\n assert candidate(s = \"mississippi\") == 11\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 52\n assert candidate(s = \"zyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyxzyx\") == 49\n assert candidate(s = \"level\") == 5\n assert candidate(s = \"Aaaaaaaa\") == 7\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().longestPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestPalindrome = function(s) {", "container": null, "callable": "longestPalindrome", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 410, "task_id": "split-array-largest-sum", "difficulty": "Hard", "problem_description": "Given an integer array nums and an integer k, split nums into k non-empty subarrays such that the largest sum of any subarray is minimized.\nReturn the minimized largest sum of the split.\nA subarray is a contiguous part of the array.\n \nExample 1:\n\nInput: nums = [7,2,5,10,8], k = 2\nOutput: 18\nExplanation: There are four ways to split nums into two subarrays.\nThe best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.\n\nExample 2:\n\nInput: nums = [1,2,3,4,5], k = 2\nOutput: 9\nExplanation: There are four ways to split nums into two subarrays.\nThe best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.\n\n \nConstraints:\n\n1 <= nums.length <= 1000\n0 <= nums[i] <= 106\n1 <= k <= min(50, nums.length)\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [7, 2, 5, 10, 8],k = 2) == 18\n assert candidate(nums = [5, 5, 5, 5, 5],k = 5) == 5\n assert candidate(nums = [10, 10, 10, 10],k = 2) == 20\n assert candidate(nums = [10, 5, 13, 4, 8, 4, 5, 11, 14, 9, 15],k = 6) == 23\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == 15\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 10) == 5\n assert candidate(nums = [10, 10, 10, 10, 10],k = 5) == 10\n assert candidate(nums = [1, 2, 3, 4, 5],k = 2) == 9\n assert candidate(nums = [1, 1000000, 1],k = 2) == 1000001\n assert candidate(nums = [1, 4, 4],k = 3) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 3) == 17\n assert candidate(nums = [10, 5, 13, 4, 8, 4, 5, 11, 14, 9, 15],k = 8) == 15\n assert candidate(nums = [4, 2, 5, 1, 7],k = 3) == 7\n assert candidate(nums = [10, 5, 13, 4, 8, 4, 5, 11, 14, 9, 15],k = 3) == 38\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == 1\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == 0\n assert candidate(nums = [1000000],k = 1) == 1000000\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == 4\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 5) == 150\n assert candidate(nums = [3, 2, 5, 7, 1, 10, 4, 2, 8, 6, 3],k = 4) == 17\n assert candidate(nums = [100, 400, 500, 300, 200],k = 3) == 500\n assert candidate(nums = [1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000, 1],k = 5) == 1001\n assert candidate(nums = [4, 2, 5, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 7) == 37\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096],k = 7) == 4096\n assert candidate(nums = [20, 30, 10, 40, 50, 60, 70, 80],k = 3) == 150\n assert candidate(nums = [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000],k = 5) == 200000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 6) == 87\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5],k = 3) == 17\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == 21\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],k = 5) == 15000\n assert candidate(nums = [1000, 900, 800, 700, 600, 500, 400, 300, 200, 100],k = 2) == 2800\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == 4\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000],k = 3) == 1000000\n assert candidate(nums = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000],k = 10) == 1000\n assert candidate(nums = [5, 1, 4, 2, 3, 6, 7, 8, 9, 10],k = 4) == 17\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == 21\n assert candidate(nums = [50, 30, 20, 10, 40, 60, 70, 80, 90, 100],k = 4) == 170\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == 28\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],k = 5) == 8\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 7) == 30\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],k = 6) == 250\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 4) == 17\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],k = 5) == 1500\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 10) == 63\n assert candidate(nums = [1000000, 1, 1000000, 1, 1000000],k = 2) == 2000001\n assert candidate(nums = [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000],k = 2) == 5000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 3) == 74\n assert candidate(nums = [9, 18, 27, 36, 45, 54, 63, 72, 81, 90],k = 9) == 90\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == 28\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],k = 3) == 2100\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],k = 7) == 230\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],k = 7) == 230\n assert candidate(nums = [7, 3, 8, 7, 10, 1, 12, 6, 7, 6, 8, 9],k = 5) == 18\n assert candidate(nums = [3, 5, 8, 10, 15, 18, 20],k = 3) == 33\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],k = 5) == 2800\n assert candidate(nums = [100, 200, 300, 400, 500],k = 2) == 900\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 3) == 7\n assert candidate(nums = [100, 50, 20, 30, 10, 80, 90, 40, 60, 70],k = 3) == 200\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],k = 4) == 1700\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],k = 10) == 280\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 15) == 28\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120],k = 5) == 210\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 3) == 17\n assert candidate(nums = [100, 400, 300, 100, 500, 300, 200],k = 4) == 500\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == 46\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 15) == 42\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15],k = 20) == 15\n assert candidate(nums = [1, 1000, 1, 1000, 1, 1000, 1, 1000, 1, 1000],k = 2) == 3002\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 5) == 150\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],k = 8) == 210\n assert candidate(nums = [3, 2, 4, 1, 5, 9, 7, 6, 8, 10],k = 4) == 16\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 15) == 11\n assert candidate(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1],k = 5) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == 46\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == 15\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 4) == 170\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 50) == 10\n assert candidate(nums = [1000000, 999999, 888888, 777777, 666666, 555555, 444444, 333333, 222222, 111111],k = 5) == 1666665\n assert candidate(nums = [9, 7, 6, 5, 4, 3, 2, 1],k = 4) == 11\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 6) == 17\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 15) == 28\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 1) == 210\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().splitArray", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var splitArray = function(nums, k) {", "container": null, "callable": "splitArray", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 412, "task_id": "fizz-buzz", "difficulty": "Easy", "problem_description": "Given an integer n, return a string array answer (1-indexed) where:\n\nanswer[i] == \"FizzBuzz\" if i is divisible by 3 and 5.\nanswer[i] == \"Fizz\" if i is divisible by 3.\nanswer[i] == \"Buzz\" if i is divisible by 5.\nanswer[i] == i (as a string) if none of the above conditions are true.\n\n \nExample 1:\nInput: n = 3\nOutput: [\"1\",\"2\",\"Fizz\"]\nExample 2:\nInput: n = 5\nOutput: [\"1\",\"2\",\"Fizz\",\"4\",\"Buzz\"]\nExample 3:\nInput: n = 15\nOutput: [\"1\",\"2\",\"Fizz\",\"4\",\"Buzz\",\"Fizz\",\"7\",\"8\",\"Fizz\",\"Buzz\",\"11\",\"Fizz\",\"13\",\"14\",\"FizzBuzz\"]\n\n \nConstraints:\n\n1 <= n <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 3) == ['1', '2', 'Fizz']\n assert candidate(n = 100) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz']\n assert candidate(n = 15) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz']\n assert candidate(n = 1) == ['1']\n assert candidate(n = 50) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz']\n assert candidate(n = 5) == ['1', '2', 'Fizz', '4', 'Buzz']\n assert candidate(n = 4000) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz', '1001', 'Fizz', '1003', '1004', 'FizzBuzz', '1006', '1007', 'Fizz', '1009', 'Buzz', 'Fizz', '1012', '1013', 'Fizz', 'Buzz', '1016', 'Fizz', '1018', '1019', 'FizzBuzz', '1021', '1022', 'Fizz', '1024', 'Buzz', 'Fizz', '1027', '1028', 'Fizz', 'Buzz', '1031', 'Fizz', '1033', '1034', 'FizzBuzz', '1036', '1037', 'Fizz', '1039', 'Buzz', 'Fizz', '1042', '1043', 'Fizz', 'Buzz', '1046', 'Fizz', '1048', '1049', 'FizzBuzz', '1051', '1052', 'Fizz', '1054', 'Buzz', 'Fizz', '1057', '1058', 'Fizz', 'Buzz', '1061', 'Fizz', '1063', '1064', 'FizzBuzz', '1066', '1067', 'Fizz', '1069', 'Buzz', 'Fizz', '1072', '1073', 'Fizz', 'Buzz', '1076', 'Fizz', '1078', '1079', 'FizzBuzz', '1081', '1082', 'Fizz', '1084', 'Buzz', 'Fizz', '1087', '1088', 'Fizz', 'Buzz', '1091', 'Fizz', '1093', '1094', 'FizzBuzz', '1096', '1097', 'Fizz', '1099', 'Buzz', 'Fizz', '1102', '1103', 'Fizz', 'Buzz', '1106', 'Fizz', '1108', '1109', 'FizzBuzz', '1111', '1112', 'Fizz', '1114', 'Buzz', 'Fizz', '1117', '1118', 'Fizz', 'Buzz', '1121', 'Fizz', '1123', '1124', 'FizzBuzz', '1126', '1127', 'Fizz', '1129', 'Buzz', 'Fizz', '1132', '1133', 'Fizz', 'Buzz', '1136', 'Fizz', '1138', '1139', 'FizzBuzz', '1141', '1142', 'Fizz', '1144', 'Buzz', 'Fizz', '1147', '1148', 'Fizz', 'Buzz', '1151', 'Fizz', '1153', '1154', 'FizzBuzz', '1156', '1157', 'Fizz', '1159', 'Buzz', 'Fizz', '1162', '1163', 'Fizz', 'Buzz', '1166', 'Fizz', '1168', '1169', 'FizzBuzz', '1171', '1172', 'Fizz', '1174', 'Buzz', 'Fizz', '1177', '1178', 'Fizz', 'Buzz', '1181', 'Fizz', '1183', '1184', 'FizzBuzz', '1186', '1187', 'Fizz', '1189', 'Buzz', 'Fizz', '1192', '1193', 'Fizz', 'Buzz', '1196', 'Fizz', '1198', '1199', 'FizzBuzz', '1201', '1202', 'Fizz', '1204', 'Buzz', 'Fizz', '1207', '1208', 'Fizz', 'Buzz', '1211', 'Fizz', '1213', '1214', 'FizzBuzz', '1216', '1217', 'Fizz', '1219', 'Buzz', 'Fizz', '1222', '1223', 'Fizz', 'Buzz', '1226', 'Fizz', '1228', '1229', 'FizzBuzz', '1231', '1232', 'Fizz', '1234', 'Buzz', 'Fizz', '1237', '1238', 'Fizz', 'Buzz', '1241', 'Fizz', '1243', '1244', 'FizzBuzz', '1246', '1247', 'Fizz', '1249', 'Buzz', 'Fizz', '1252', '1253', 'Fizz', 'Buzz', '1256', 'Fizz', '1258', '1259', 'FizzBuzz', '1261', '1262', 'Fizz', '1264', 'Buzz', 'Fizz', '1267', '1268', 'Fizz', 'Buzz', '1271', 'Fizz', '1273', '1274', 'FizzBuzz', '1276', '1277', 'Fizz', '1279', 'Buzz', 'Fizz', '1282', '1283', 'Fizz', 'Buzz', '1286', 'Fizz', '1288', '1289', 'FizzBuzz', '1291', '1292', 'Fizz', '1294', 'Buzz', 'Fizz', '1297', '1298', 'Fizz', 'Buzz', '1301', 'Fizz', '1303', '1304', 'FizzBuzz', '1306', '1307', 'Fizz', '1309', 'Buzz', 'Fizz', '1312', '1313', 'Fizz', 'Buzz', '1316', 'Fizz', '1318', '1319', 'FizzBuzz', '1321', '1322', 'Fizz', '1324', 'Buzz', 'Fizz', '1327', '1328', 'Fizz', 'Buzz', '1331', 'Fizz', '1333', '1334', 'FizzBuzz', '1336', '1337', 'Fizz', '1339', 'Buzz', 'Fizz', '1342', '1343', 'Fizz', 'Buzz', '1346', 'Fizz', '1348', '1349', 'FizzBuzz', '1351', '1352', 'Fizz', '1354', 'Buzz', 'Fizz', '1357', '1358', 'Fizz', 'Buzz', '1361', 'Fizz', '1363', '1364', 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'FizzBuzz', '3286', '3287', 'Fizz', '3289', 'Buzz', 'Fizz', '3292', '3293', 'Fizz', 'Buzz', '3296', 'Fizz', '3298', '3299', 'FizzBuzz', '3301', '3302', 'Fizz', '3304', 'Buzz', 'Fizz', '3307', '3308', 'Fizz', 'Buzz', '3311', 'Fizz', '3313', '3314', 'FizzBuzz', '3316', '3317', 'Fizz', '3319', 'Buzz', 'Fizz', '3322', '3323', 'Fizz', 'Buzz', '3326', 'Fizz', '3328', '3329', 'FizzBuzz', '3331', '3332', 'Fizz', '3334', 'Buzz', 'Fizz', '3337', '3338', 'Fizz', 'Buzz', '3341', 'Fizz', '3343', '3344', 'FizzBuzz', '3346', '3347', 'Fizz', '3349', 'Buzz', 'Fizz', '3352', '3353', 'Fizz', 'Buzz', '3356', 'Fizz', '3358', '3359', 'FizzBuzz', '3361', '3362', 'Fizz', '3364', 'Buzz', 'Fizz', '3367', '3368', 'Fizz', 'Buzz', '3371', 'Fizz', '3373', '3374', 'FizzBuzz', '3376', '3377', 'Fizz', '3379', 'Buzz', 'Fizz', '3382', '3383', 'Fizz', 'Buzz', '3386', 'Fizz', '3388', '3389', 'FizzBuzz', '3391', '3392', 'Fizz', '3394', 'Buzz', 'Fizz', '3397', '3398', 'Fizz', 'Buzz', '3401', 'Fizz', '3403', '3404', 'FizzBuzz', '3406', '3407', 'Fizz', '3409', 'Buzz', 'Fizz', '3412', '3413', 'Fizz', 'Buzz', '3416', 'Fizz', '3418', '3419', 'FizzBuzz', '3421', '3422', 'Fizz', '3424', 'Buzz', 'Fizz', '3427', '3428', 'Fizz', 'Buzz', '3431', 'Fizz', '3433', '3434', 'FizzBuzz', '3436', '3437', 'Fizz', '3439', 'Buzz', 'Fizz', '3442', '3443', 'Fizz', 'Buzz', '3446', 'Fizz', '3448', '3449', 'FizzBuzz', '3451', '3452', 'Fizz', '3454', 'Buzz', 'Fizz', '3457', '3458', 'Fizz', 'Buzz', '3461', 'Fizz', '3463', '3464', 'FizzBuzz', '3466', '3467', 'Fizz', '3469', 'Buzz', 'Fizz', '3472', '3473', 'Fizz', 'Buzz', '3476', 'Fizz', '3478', '3479', 'FizzBuzz', '3481', '3482', 'Fizz', '3484', 'Buzz', 'Fizz', '3487', '3488', 'Fizz', 'Buzz', '3491', 'Fizz', '3493', '3494', 'FizzBuzz', '3496', '3497', 'Fizz', '3499', 'Buzz', 'Fizz', '3502', '3503', 'Fizz', 'Buzz', '3506', 'Fizz', '3508', '3509', 'FizzBuzz', '3511', '3512', 'Fizz', '3514', 'Buzz', 'Fizz', '3517', '3518', 'Fizz', 'Buzz', '3521', 'Fizz', '3523', '3524', 'FizzBuzz', '3526', '3527', 'Fizz', '3529', 'Buzz', 'Fizz', '3532', '3533', 'Fizz', 'Buzz', '3536', 'Fizz', '3538', '3539', 'FizzBuzz', '3541', '3542', 'Fizz', '3544', 'Buzz', 'Fizz', '3547', '3548', 'Fizz', 'Buzz', '3551', 'Fizz', '3553', '3554', 'FizzBuzz', '3556', '3557', 'Fizz', '3559', 'Buzz', 'Fizz', '3562', '3563', 'Fizz', 'Buzz', '3566', 'Fizz', '3568', '3569', 'FizzBuzz', '3571', '3572', 'Fizz', '3574', 'Buzz', 'Fizz', '3577', '3578', 'Fizz', 'Buzz', '3581', 'Fizz', '3583', '3584', 'FizzBuzz', '3586', '3587', 'Fizz', '3589', 'Buzz', 'Fizz', '3592', '3593', 'Fizz', 'Buzz', '3596', 'Fizz', '3598', '3599', 'FizzBuzz', '3601', '3602', 'Fizz', '3604', 'Buzz', 'Fizz', '3607', '3608', 'Fizz', 'Buzz', '3611', 'Fizz', '3613', '3614', 'FizzBuzz', '3616', '3617', 'Fizz', '3619', 'Buzz', 'Fizz', '3622', '3623', 'Fizz', 'Buzz', '3626', 'Fizz', '3628', '3629', 'FizzBuzz', '3631', '3632', 'Fizz', '3634', 'Buzz', 'Fizz', '3637', '3638', 'Fizz', 'Buzz', '3641', 'Fizz', '3643', '3644', 'FizzBuzz', '3646', '3647', 'Fizz', '3649', 'Buzz', 'Fizz', '3652', '3653', 'Fizz', 'Buzz', '3656', 'Fizz', '3658', '3659', 'FizzBuzz', '3661', '3662', 'Fizz', '3664', 'Buzz', 'Fizz', '3667', '3668', 'Fizz', 'Buzz', '3671', 'Fizz', '3673', '3674', 'FizzBuzz', '3676', '3677', 'Fizz', '3679', 'Buzz', 'Fizz', '3682', '3683', 'Fizz', 'Buzz', '3686', 'Fizz', '3688', '3689', 'FizzBuzz', '3691', '3692', 'Fizz', '3694', 'Buzz', 'Fizz', '3697', '3698', 'Fizz', 'Buzz', '3701', 'Fizz', '3703', '3704', 'FizzBuzz', '3706', '3707', 'Fizz', '3709', 'Buzz', 'Fizz', '3712', '3713', 'Fizz', 'Buzz', '3716', 'Fizz', '3718', '3719', 'FizzBuzz', '3721', '3722', 'Fizz', '3724', 'Buzz', 'Fizz', '3727', '3728', 'Fizz', 'Buzz', '3731', 'Fizz', '3733', '3734', 'FizzBuzz', '3736', '3737', 'Fizz', '3739', 'Buzz', 'Fizz', '3742', '3743', 'Fizz', 'Buzz', '3746', 'Fizz', '3748', '3749', 'FizzBuzz', '3751', '3752', 'Fizz', '3754', 'Buzz', 'Fizz', '3757', '3758', 'Fizz', 'Buzz', '3761', 'Fizz', '3763', '3764', 'FizzBuzz', '3766', '3767', 'Fizz', '3769', 'Buzz', 'Fizz', '3772', '3773', 'Fizz', 'Buzz', '3776', 'Fizz', '3778', '3779', 'FizzBuzz', '3781', '3782', 'Fizz', '3784', 'Buzz', 'Fizz', '3787', '3788', 'Fizz', 'Buzz', '3791', 'Fizz', '3793', '3794', 'FizzBuzz', '3796', '3797', 'Fizz', '3799', 'Buzz', 'Fizz', '3802', '3803', 'Fizz', 'Buzz', '3806', 'Fizz', '3808', '3809', 'FizzBuzz', '3811', '3812', 'Fizz', '3814', 'Buzz', 'Fizz', '3817', '3818', 'Fizz', 'Buzz', '3821', 'Fizz', '3823', '3824', 'FizzBuzz', '3826', '3827', 'Fizz', '3829', 'Buzz', 'Fizz', '3832', '3833', 'Fizz', 'Buzz', '3836', 'Fizz', '3838', '3839', 'FizzBuzz', '3841', '3842', 'Fizz', '3844', 'Buzz', 'Fizz', '3847', '3848', 'Fizz', 'Buzz', '3851', 'Fizz', '3853', '3854', 'FizzBuzz', '3856', '3857', 'Fizz', '3859', 'Buzz', 'Fizz', '3862', '3863', 'Fizz', 'Buzz', '3866', 'Fizz', '3868', '3869', 'FizzBuzz', '3871', '3872', 'Fizz', '3874', 'Buzz', 'Fizz', '3877', '3878', 'Fizz', 'Buzz', '3881', 'Fizz', '3883', '3884', 'FizzBuzz', '3886', '3887', 'Fizz', '3889', 'Buzz', 'Fizz', '3892', '3893', 'Fizz', 'Buzz', '3896', 'Fizz', '3898', '3899', 'FizzBuzz', '3901', '3902', 'Fizz', '3904', 'Buzz', 'Fizz', '3907', '3908', 'Fizz', 'Buzz', '3911', 'Fizz', '3913', '3914', 'FizzBuzz', '3916', '3917', 'Fizz', '3919', 'Buzz', 'Fizz', '3922', '3923', 'Fizz', 'Buzz', '3926', 'Fizz', '3928', '3929', 'FizzBuzz', '3931', '3932', 'Fizz', '3934', 'Buzz', 'Fizz', '3937', '3938', 'Fizz', 'Buzz', '3941', 'Fizz', '3943', '3944', 'FizzBuzz', '3946', '3947', 'Fizz', '3949', 'Buzz', 'Fizz', '3952', '3953', 'Fizz', 'Buzz', '3956', 'Fizz', '3958', '3959', 'FizzBuzz', '3961', '3962', 'Fizz', '3964', 'Buzz', 'Fizz', '3967', '3968', 'Fizz', 'Buzz', '3971', 'Fizz', '3973', '3974', 'FizzBuzz', '3976', '3977', 'Fizz', '3979', 'Buzz', 'Fizz', '3982', '3983', 'Fizz', 'Buzz', '3986', 'Fizz', '3988', '3989', 'FizzBuzz', '3991', '3992', 'Fizz', '3994', 'Buzz', 'Fizz', '3997', '3998', 'Fizz', 'Buzz']\n assert candidate(n = 210) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz']\n assert candidate(n = 45) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz']\n assert candidate(n = 1010) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz', '1001', 'Fizz', '1003', '1004', 'FizzBuzz', '1006', '1007', 'Fizz', '1009', 'Buzz']\n assert candidate(n = 53) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53']\n assert candidate(n = 2000) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz', '1001', 'Fizz', '1003', '1004', 'FizzBuzz', '1006', '1007', 'Fizz', '1009', 'Buzz', 'Fizz', '1012', '1013', 'Fizz', 'Buzz', '1016', 'Fizz', '1018', '1019', 'FizzBuzz', '1021', '1022', 'Fizz', '1024', 'Buzz', 'Fizz', '1027', '1028', 'Fizz', 'Buzz', '1031', 'Fizz', '1033', '1034', 'FizzBuzz', '1036', '1037', 'Fizz', '1039', 'Buzz', 'Fizz', '1042', '1043', 'Fizz', 'Buzz', '1046', 'Fizz', '1048', '1049', 'FizzBuzz', '1051', '1052', 'Fizz', '1054', 'Buzz', 'Fizz', '1057', '1058', 'Fizz', 'Buzz', '1061', 'Fizz', '1063', '1064', 'FizzBuzz', '1066', '1067', 'Fizz', '1069', 'Buzz', 'Fizz', '1072', '1073', 'Fizz', 'Buzz', '1076', 'Fizz', '1078', '1079', 'FizzBuzz', '1081', '1082', 'Fizz', '1084', 'Buzz', 'Fizz', '1087', '1088', 'Fizz', 'Buzz', '1091', 'Fizz', '1093', '1094', 'FizzBuzz', '1096', '1097', 'Fizz', '1099', 'Buzz', 'Fizz', '1102', '1103', 'Fizz', 'Buzz', '1106', 'Fizz', '1108', '1109', 'FizzBuzz', '1111', '1112', 'Fizz', '1114', 'Buzz', 'Fizz', '1117', '1118', 'Fizz', 'Buzz', '1121', 'Fizz', '1123', '1124', 'FizzBuzz', '1126', '1127', 'Fizz', '1129', 'Buzz', 'Fizz', '1132', '1133', 'Fizz', 'Buzz', '1136', 'Fizz', '1138', '1139', 'FizzBuzz', '1141', '1142', 'Fizz', '1144', 'Buzz', 'Fizz', '1147', '1148', 'Fizz', 'Buzz', '1151', 'Fizz', '1153', '1154', 'FizzBuzz', '1156', '1157', 'Fizz', '1159', 'Buzz', 'Fizz', '1162', '1163', 'Fizz', 'Buzz', '1166', 'Fizz', '1168', '1169', 'FizzBuzz', '1171', '1172', 'Fizz', '1174', 'Buzz', 'Fizz', '1177', '1178', 'Fizz', 'Buzz', '1181', 'Fizz', '1183', '1184', 'FizzBuzz', '1186', '1187', 'Fizz', '1189', 'Buzz', 'Fizz', '1192', '1193', 'Fizz', 'Buzz', '1196', 'Fizz', '1198', '1199', 'FizzBuzz', '1201', '1202', 'Fizz', '1204', 'Buzz', 'Fizz', '1207', '1208', 'Fizz', 'Buzz', '1211', 'Fizz', '1213', '1214', 'FizzBuzz', '1216', '1217', 'Fizz', '1219', 'Buzz', 'Fizz', '1222', '1223', 'Fizz', 'Buzz', '1226', 'Fizz', '1228', '1229', 'FizzBuzz', '1231', '1232', 'Fizz', '1234', 'Buzz', 'Fizz', '1237', '1238', 'Fizz', 'Buzz', '1241', 'Fizz', '1243', '1244', 'FizzBuzz', '1246', '1247', 'Fizz', '1249', 'Buzz', 'Fizz', '1252', '1253', 'Fizz', 'Buzz', '1256', 'Fizz', '1258', '1259', 'FizzBuzz', '1261', '1262', 'Fizz', '1264', 'Buzz', 'Fizz', '1267', '1268', 'Fizz', 'Buzz', '1271', 'Fizz', '1273', '1274', 'FizzBuzz', '1276', '1277', 'Fizz', '1279', 'Buzz', 'Fizz', '1282', '1283', 'Fizz', 'Buzz', '1286', 'Fizz', '1288', '1289', 'FizzBuzz', '1291', '1292', 'Fizz', '1294', 'Buzz', 'Fizz', '1297', '1298', 'Fizz', 'Buzz', '1301', 'Fizz', '1303', '1304', 'FizzBuzz', '1306', '1307', 'Fizz', '1309', 'Buzz', 'Fizz', '1312', '1313', 'Fizz', 'Buzz', '1316', 'Fizz', '1318', '1319', 'FizzBuzz', '1321', '1322', 'Fizz', '1324', 'Buzz', 'Fizz', '1327', '1328', 'Fizz', 'Buzz', '1331', 'Fizz', '1333', '1334', 'FizzBuzz', '1336', '1337', 'Fizz', '1339', 'Buzz', 'Fizz', '1342', '1343', 'Fizz', 'Buzz', '1346', 'Fizz', '1348', '1349', 'FizzBuzz', '1351', '1352', 'Fizz', '1354', 'Buzz', 'Fizz', '1357', '1358', 'Fizz', 'Buzz', '1361', 'Fizz', '1363', '1364', 'FizzBuzz', '1366', '1367', 'Fizz', '1369', 'Buzz', 'Fizz', '1372', '1373', 'Fizz', 'Buzz', '1376', 'Fizz', '1378', '1379', 'FizzBuzz', '1381', '1382', 'Fizz', '1384', 'Buzz', 'Fizz', '1387', '1388', 'Fizz', 'Buzz', '1391', 'Fizz', '1393', '1394', 'FizzBuzz', '1396', '1397', 'Fizz', '1399', 'Buzz', 'Fizz', '1402', '1403', 'Fizz', 'Buzz', '1406', 'Fizz', '1408', '1409', 'FizzBuzz', '1411', '1412', 'Fizz', '1414', 'Buzz', 'Fizz', '1417', '1418', 'Fizz', 'Buzz', '1421', 'Fizz', '1423', '1424', 'FizzBuzz', '1426', '1427', 'Fizz', '1429', 'Buzz', 'Fizz', '1432', '1433', 'Fizz', 'Buzz', '1436', 'Fizz', '1438', '1439', 'FizzBuzz', '1441', '1442', 'Fizz', '1444', 'Buzz', 'Fizz', '1447', '1448', 'Fizz', 'Buzz', '1451', 'Fizz', '1453', '1454', 'FizzBuzz', '1456', '1457', 'Fizz', '1459', 'Buzz', 'Fizz', '1462', '1463', 'Fizz', 'Buzz', '1466', 'Fizz', '1468', '1469', 'FizzBuzz', '1471', '1472', 'Fizz', '1474', 'Buzz', 'Fizz', '1477', '1478', 'Fizz', 'Buzz', '1481', 'Fizz', '1483', '1484', 'FizzBuzz', '1486', '1487', 'Fizz', '1489', 'Buzz', 'Fizz', '1492', '1493', 'Fizz', 'Buzz', '1496', 'Fizz', '1498', '1499', 'FizzBuzz', '1501', '1502', 'Fizz', '1504', 'Buzz', 'Fizz', '1507', '1508', 'Fizz', 'Buzz', '1511', 'Fizz', '1513', '1514', 'FizzBuzz', '1516', '1517', 'Fizz', '1519', 'Buzz', 'Fizz', '1522', '1523', 'Fizz', 'Buzz', '1526', 'Fizz', '1528', '1529', 'FizzBuzz', '1531', '1532', 'Fizz', '1534', 'Buzz', 'Fizz', '1537', '1538', 'Fizz', 'Buzz', '1541', 'Fizz', '1543', '1544', 'FizzBuzz', '1546', '1547', 'Fizz', '1549', 'Buzz', 'Fizz', '1552', '1553', 'Fizz', 'Buzz', '1556', 'Fizz', '1558', '1559', 'FizzBuzz', '1561', '1562', 'Fizz', '1564', 'Buzz', 'Fizz', '1567', '1568', 'Fizz', 'Buzz', '1571', 'Fizz', '1573', '1574', 'FizzBuzz', '1576', '1577', 'Fizz', '1579', 'Buzz', 'Fizz', '1582', '1583', 'Fizz', 'Buzz', '1586', 'Fizz', '1588', '1589', 'FizzBuzz', '1591', '1592', 'Fizz', '1594', 'Buzz', 'Fizz', '1597', '1598', 'Fizz', 'Buzz', '1601', 'Fizz', '1603', '1604', 'FizzBuzz', '1606', '1607', 'Fizz', '1609', 'Buzz', 'Fizz', '1612', '1613', 'Fizz', 'Buzz', '1616', 'Fizz', '1618', '1619', 'FizzBuzz', '1621', '1622', 'Fizz', '1624', 'Buzz', 'Fizz', '1627', '1628', 'Fizz', 'Buzz', '1631', 'Fizz', '1633', '1634', 'FizzBuzz', '1636', '1637', 'Fizz', '1639', 'Buzz', 'Fizz', '1642', '1643', 'Fizz', 'Buzz', '1646', 'Fizz', '1648', '1649', 'FizzBuzz', '1651', '1652', 'Fizz', '1654', 'Buzz', 'Fizz', '1657', '1658', 'Fizz', 'Buzz', '1661', 'Fizz', '1663', '1664', 'FizzBuzz', '1666', '1667', 'Fizz', '1669', 'Buzz', 'Fizz', '1672', '1673', 'Fizz', 'Buzz', '1676', 'Fizz', '1678', '1679', 'FizzBuzz', '1681', '1682', 'Fizz', '1684', 'Buzz', 'Fizz', '1687', '1688', 'Fizz', 'Buzz', '1691', 'Fizz', '1693', '1694', 'FizzBuzz', '1696', '1697', 'Fizz', '1699', 'Buzz', 'Fizz', '1702', '1703', 'Fizz', 'Buzz', '1706', 'Fizz', '1708', '1709', 'FizzBuzz', '1711', '1712', 'Fizz', '1714', 'Buzz', 'Fizz', '1717', '1718', 'Fizz', 'Buzz', '1721', 'Fizz', '1723', '1724', 'FizzBuzz', '1726', '1727', 'Fizz', '1729', 'Buzz', 'Fizz', '1732', '1733', 'Fizz', 'Buzz', '1736', 'Fizz', '1738', '1739', 'FizzBuzz', '1741', '1742', 'Fizz', '1744', 'Buzz', 'Fizz', '1747', '1748', 'Fizz', 'Buzz', '1751', 'Fizz', '1753', '1754', 'FizzBuzz', '1756', '1757', 'Fizz', '1759', 'Buzz', 'Fizz', '1762', '1763', 'Fizz', 'Buzz', '1766', 'Fizz', '1768', '1769', 'FizzBuzz', '1771', '1772', 'Fizz', '1774', 'Buzz', 'Fizz', '1777', '1778', 'Fizz', 'Buzz', '1781', 'Fizz', '1783', '1784', 'FizzBuzz', '1786', '1787', 'Fizz', '1789', 'Buzz', 'Fizz', '1792', '1793', 'Fizz', 'Buzz', '1796', 'Fizz', '1798', '1799', 'FizzBuzz', '1801', '1802', 'Fizz', '1804', 'Buzz', 'Fizz', '1807', '1808', 'Fizz', 'Buzz', '1811', 'Fizz', '1813', '1814', 'FizzBuzz', '1816', '1817', 'Fizz', '1819', 'Buzz', 'Fizz', '1822', '1823', 'Fizz', 'Buzz', '1826', 'Fizz', '1828', '1829', 'FizzBuzz', '1831', '1832', 'Fizz', '1834', 'Buzz', 'Fizz', '1837', '1838', 'Fizz', 'Buzz', '1841', 'Fizz', '1843', '1844', 'FizzBuzz', '1846', '1847', 'Fizz', '1849', 'Buzz', 'Fizz', '1852', '1853', 'Fizz', 'Buzz', '1856', 'Fizz', '1858', '1859', 'FizzBuzz', '1861', '1862', 'Fizz', '1864', 'Buzz', 'Fizz', '1867', '1868', 'Fizz', 'Buzz', '1871', 'Fizz', '1873', '1874', 'FizzBuzz', '1876', '1877', 'Fizz', '1879', 'Buzz', 'Fizz', '1882', '1883', 'Fizz', 'Buzz', '1886', 'Fizz', '1888', '1889', 'FizzBuzz', '1891', '1892', 'Fizz', '1894', 'Buzz', 'Fizz', '1897', '1898', 'Fizz', 'Buzz', '1901', 'Fizz', '1903', '1904', 'FizzBuzz', '1906', '1907', 'Fizz', '1909', 'Buzz', 'Fizz', '1912', '1913', 'Fizz', 'Buzz', '1916', 'Fizz', '1918', '1919', 'FizzBuzz', '1921', '1922', 'Fizz', '1924', 'Buzz', 'Fizz', '1927', '1928', 'Fizz', 'Buzz', '1931', 'Fizz', '1933', '1934', 'FizzBuzz', '1936', '1937', 'Fizz', '1939', 'Buzz', 'Fizz', '1942', '1943', 'Fizz', 'Buzz', '1946', 'Fizz', '1948', '1949', 'FizzBuzz', '1951', '1952', 'Fizz', '1954', 'Buzz', 'Fizz', '1957', '1958', 'Fizz', 'Buzz', '1961', 'Fizz', '1963', '1964', 'FizzBuzz', '1966', '1967', 'Fizz', '1969', 'Buzz', 'Fizz', '1972', '1973', 'Fizz', 'Buzz', '1976', 'Fizz', '1978', '1979', 'FizzBuzz', '1981', '1982', 'Fizz', '1984', 'Buzz', 'Fizz', '1987', '1988', 'Fizz', 'Buzz', '1991', 'Fizz', '1993', '1994', 'FizzBuzz', '1996', '1997', 'Fizz', '1999', 'Buzz']\n assert candidate(n = 1000) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz']\n assert candidate(n = 3333) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', 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'FizzBuzz', '2011', '2012', 'Fizz', '2014', 'Buzz', 'Fizz', '2017', '2018', 'Fizz', 'Buzz', '2021', 'Fizz', '2023', '2024', 'FizzBuzz', '2026', '2027', 'Fizz', '2029', 'Buzz', 'Fizz', '2032', '2033', 'Fizz', 'Buzz', '2036', 'Fizz', '2038', '2039', 'FizzBuzz', '2041', '2042', 'Fizz', '2044', 'Buzz', 'Fizz', '2047', '2048', 'Fizz', 'Buzz', '2051', 'Fizz', '2053', '2054', 'FizzBuzz', '2056', '2057', 'Fizz', '2059', 'Buzz', 'Fizz', '2062', '2063', 'Fizz', 'Buzz', '2066', 'Fizz', '2068', '2069', 'FizzBuzz', '2071', '2072', 'Fizz', '2074', 'Buzz', 'Fizz', '2077', '2078', 'Fizz', 'Buzz', '2081', 'Fizz', '2083', '2084', 'FizzBuzz', '2086', '2087', 'Fizz', '2089', 'Buzz', 'Fizz', '2092', '2093', 'Fizz', 'Buzz', '2096', 'Fizz', '2098', '2099', 'FizzBuzz', '2101', '2102', 'Fizz', '2104', 'Buzz', 'Fizz', '2107', '2108', 'Fizz', 'Buzz', '2111', 'Fizz', '2113', '2114', 'FizzBuzz', '2116', '2117', 'Fizz', '2119', 'Buzz', 'Fizz', '2122', '2123', 'Fizz', 'Buzz', '2126', 'Fizz', '2128', '2129', 'FizzBuzz', '2131', '2132', 'Fizz', '2134', 'Buzz', 'Fizz', '2137', '2138', 'Fizz', 'Buzz', '2141', 'Fizz', '2143', '2144', 'FizzBuzz', '2146', '2147', 'Fizz', '2149', 'Buzz', 'Fizz', '2152', '2153', 'Fizz', 'Buzz', '2156', 'Fizz', '2158', '2159', 'FizzBuzz', '2161', '2162', 'Fizz', '2164', 'Buzz', 'Fizz', '2167', '2168', 'Fizz', 'Buzz', '2171', 'Fizz', '2173', '2174', 'FizzBuzz', '2176', '2177', 'Fizz', '2179', 'Buzz', 'Fizz', '2182', '2183', 'Fizz', 'Buzz', '2186', 'Fizz', '2188', '2189', 'FizzBuzz', '2191', '2192', 'Fizz', '2194', 'Buzz', 'Fizz', '2197', '2198', 'Fizz', 'Buzz', '2201', 'Fizz', '2203', '2204', 'FizzBuzz', '2206', '2207', 'Fizz', '2209', 'Buzz', 'Fizz', '2212', '2213', 'Fizz', 'Buzz', '2216', 'Fizz', '2218', '2219', 'FizzBuzz', '2221', '2222', 'Fizz', '2224', 'Buzz', 'Fizz', '2227', '2228', 'Fizz', 'Buzz', '2231', 'Fizz', '2233', '2234', 'FizzBuzz', '2236', '2237', 'Fizz', '2239', 'Buzz', 'Fizz', '2242', '2243', 'Fizz', 'Buzz', '2246', 'Fizz', '2248', '2249', 'FizzBuzz', '2251', '2252', 'Fizz', '2254', 'Buzz', 'Fizz', '2257', '2258', 'Fizz', 'Buzz', '2261', 'Fizz', '2263', '2264', 'FizzBuzz', '2266', '2267', 'Fizz', '2269', 'Buzz', 'Fizz', '2272', '2273', 'Fizz', 'Buzz', '2276', 'Fizz', '2278', '2279', 'FizzBuzz', '2281', '2282', 'Fizz', '2284', 'Buzz', 'Fizz', '2287', '2288', 'Fizz', 'Buzz', '2291', 'Fizz', '2293', '2294', 'FizzBuzz', '2296', '2297', 'Fizz', '2299', 'Buzz', 'Fizz', '2302', '2303', 'Fizz', 'Buzz', '2306', 'Fizz', '2308', '2309', 'FizzBuzz', '2311', '2312', 'Fizz', '2314', 'Buzz', 'Fizz', '2317', '2318', 'Fizz', 'Buzz', '2321', 'Fizz', '2323', '2324', 'FizzBuzz', '2326', '2327', 'Fizz', '2329', 'Buzz', 'Fizz', '2332', '2333', 'Fizz', 'Buzz', '2336', 'Fizz', '2338', '2339', 'FizzBuzz', '2341', '2342', 'Fizz', '2344', 'Buzz', 'Fizz', '2347', '2348', 'Fizz', 'Buzz', '2351', 'Fizz', '2353', '2354', 'FizzBuzz', '2356', '2357', 'Fizz', '2359', 'Buzz', 'Fizz', '2362', '2363', 'Fizz', 'Buzz', '2366', 'Fizz', '2368', '2369', 'FizzBuzz', '2371', '2372', 'Fizz', '2374', 'Buzz', 'Fizz', '2377', '2378', 'Fizz', 'Buzz', '2381', 'Fizz', '2383', '2384', 'FizzBuzz', '2386', '2387', 'Fizz', '2389', 'Buzz', 'Fizz', '2392', '2393', 'Fizz', 'Buzz', '2396', 'Fizz', '2398', '2399', 'FizzBuzz', '2401', '2402', 'Fizz', '2404', 'Buzz', 'Fizz', '2407', '2408', 'Fizz', 'Buzz', '2411', 'Fizz', '2413', '2414', 'FizzBuzz', '2416', '2417', 'Fizz', '2419', 'Buzz', 'Fizz', '2422', '2423', 'Fizz', 'Buzz', '2426', 'Fizz', '2428', '2429', 'FizzBuzz', '2431', '2432', 'Fizz', '2434', 'Buzz', 'Fizz', '2437', '2438', 'Fizz', 'Buzz', '2441', 'Fizz', '2443', '2444', 'FizzBuzz', '2446', '2447', 'Fizz', '2449', 'Buzz', 'Fizz', '2452', '2453', 'Fizz', 'Buzz', '2456', 'Fizz', '2458', '2459', 'FizzBuzz', '2461', '2462', 'Fizz', '2464', 'Buzz', 'Fizz', '2467', '2468', 'Fizz', 'Buzz', '2471', 'Fizz', '2473', '2474', 'FizzBuzz', '2476', '2477', 'Fizz', '2479', 'Buzz', 'Fizz', '2482', '2483', 'Fizz', 'Buzz', '2486', 'Fizz', '2488', '2489', 'FizzBuzz', '2491', '2492', 'Fizz', '2494', 'Buzz', 'Fizz', '2497', '2498', 'Fizz', 'Buzz', '2501', 'Fizz', '2503', '2504', 'FizzBuzz', '2506', '2507', 'Fizz', '2509', 'Buzz', 'Fizz', '2512', '2513', 'Fizz', 'Buzz', '2516', 'Fizz', '2518', '2519', 'FizzBuzz', '2521', '2522', 'Fizz', '2524', 'Buzz', 'Fizz', '2527', '2528', 'Fizz', 'Buzz', '2531', 'Fizz', '2533', '2534', 'FizzBuzz', '2536', '2537', 'Fizz', '2539', 'Buzz', 'Fizz', '2542', '2543', 'Fizz', 'Buzz', '2546', 'Fizz', '2548', '2549', 'FizzBuzz', '2551', '2552', 'Fizz', '2554', 'Buzz', 'Fizz', '2557', '2558', 'Fizz', 'Buzz', '2561', 'Fizz', '2563', '2564', 'FizzBuzz', '2566', '2567', 'Fizz', '2569', 'Buzz', 'Fizz', '2572', '2573', 'Fizz', 'Buzz', '2576', 'Fizz', '2578', '2579', 'FizzBuzz', '2581', '2582', 'Fizz', '2584', 'Buzz', 'Fizz', '2587', '2588', 'Fizz', 'Buzz', '2591', 'Fizz', '2593', '2594', 'FizzBuzz', '2596', '2597', 'Fizz', '2599', 'Buzz', 'Fizz', '2602', '2603', 'Fizz', 'Buzz', '2606', 'Fizz', '2608', '2609', 'FizzBuzz', '2611', '2612', 'Fizz', '2614', 'Buzz', 'Fizz', '2617', '2618', 'Fizz', 'Buzz', '2621', 'Fizz', '2623', '2624', 'FizzBuzz', '2626', '2627', 'Fizz', '2629', 'Buzz', 'Fizz', '2632', '2633', 'Fizz', 'Buzz', '2636', 'Fizz', '2638', '2639', 'FizzBuzz', '2641', '2642', 'Fizz', '2644', 'Buzz', 'Fizz', '2647', '2648', 'Fizz', 'Buzz', '2651', 'Fizz', '2653', '2654', 'FizzBuzz', '2656', '2657', 'Fizz', '2659', 'Buzz', 'Fizz', '2662', '2663', 'Fizz', 'Buzz', '2666', 'Fizz', '2668', '2669', 'FizzBuzz', '2671', '2672', 'Fizz', '2674', 'Buzz', 'Fizz', '2677', '2678', 'Fizz', 'Buzz', '2681', 'Fizz', '2683', '2684', 'FizzBuzz', '2686', '2687', 'Fizz', '2689', 'Buzz', 'Fizz', '2692', '2693', 'Fizz', 'Buzz', '2696', 'Fizz', '2698', '2699', 'FizzBuzz', '2701', '2702', 'Fizz', '2704', 'Buzz', 'Fizz', '2707', '2708', 'Fizz', 'Buzz', '2711', 'Fizz', '2713', '2714', 'FizzBuzz', '2716', '2717', 'Fizz', '2719', 'Buzz', 'Fizz', '2722', '2723', 'Fizz', 'Buzz', '2726', 'Fizz', '2728', '2729', 'FizzBuzz', '2731', '2732', 'Fizz', '2734', 'Buzz', 'Fizz', '2737', '2738', 'Fizz', 'Buzz', '2741', 'Fizz', '2743', '2744', 'FizzBuzz', '2746', '2747', 'Fizz', '2749', 'Buzz', 'Fizz', '2752', '2753', 'Fizz', 'Buzz', '2756', 'Fizz', '2758', '2759', 'FizzBuzz', '2761', '2762', 'Fizz', '2764', 'Buzz', 'Fizz', '2767', '2768', 'Fizz', 'Buzz', '2771', 'Fizz', '2773', '2774', 'FizzBuzz', '2776', '2777', 'Fizz', '2779', 'Buzz', 'Fizz', '2782', '2783', 'Fizz', 'Buzz', '2786', 'Fizz', '2788', '2789', 'FizzBuzz', '2791', '2792', 'Fizz', '2794', 'Buzz', 'Fizz', '2797', '2798', 'Fizz', 'Buzz', '2801', 'Fizz', '2803', '2804', 'FizzBuzz', '2806', '2807', 'Fizz', '2809', 'Buzz', 'Fizz', '2812', '2813', 'Fizz', 'Buzz', '2816', 'Fizz', '2818', '2819', 'FizzBuzz', '2821', '2822', 'Fizz', '2824', 'Buzz', 'Fizz', '2827', '2828', 'Fizz', 'Buzz', '2831', 'Fizz', '2833', '2834', 'FizzBuzz', '2836', '2837', 'Fizz', '2839', 'Buzz', 'Fizz', '2842', '2843', 'Fizz', 'Buzz', '2846', 'Fizz', '2848', '2849', 'FizzBuzz', '2851', '2852', 'Fizz', '2854', 'Buzz', 'Fizz', '2857', '2858', 'Fizz', 'Buzz', '2861', 'Fizz', '2863', '2864', 'FizzBuzz', '2866', '2867', 'Fizz', '2869', 'Buzz', 'Fizz', '2872', '2873', 'Fizz', 'Buzz', '2876', 'Fizz', '2878', '2879', 'FizzBuzz', '2881', '2882', 'Fizz', '2884', 'Buzz', 'Fizz', '2887', '2888', 'Fizz', 'Buzz', '2891', 'Fizz', '2893', '2894', 'FizzBuzz', '2896', '2897', 'Fizz', '2899', 'Buzz', 'Fizz', '2902', '2903', 'Fizz', 'Buzz', '2906', 'Fizz', '2908', '2909', 'FizzBuzz', '2911', '2912', 'Fizz', '2914', 'Buzz', 'Fizz', '2917', '2918', 'Fizz', 'Buzz', '2921', 'Fizz', '2923', '2924', 'FizzBuzz', '2926', '2927', 'Fizz', '2929', 'Buzz', 'Fizz', '2932', '2933', 'Fizz', 'Buzz', '2936', 'Fizz', '2938', '2939', 'FizzBuzz', '2941', '2942', 'Fizz', '2944', 'Buzz', 'Fizz', '2947', '2948', 'Fizz', 'Buzz', '2951', 'Fizz', '2953', '2954', 'FizzBuzz', '2956', '2957', 'Fizz', '2959', 'Buzz', 'Fizz', '2962', '2963', 'Fizz', 'Buzz', '2966', 'Fizz', '2968', '2969', 'FizzBuzz', '2971', '2972', 'Fizz', '2974', 'Buzz', 'Fizz', '2977', '2978', 'Fizz', 'Buzz', '2981', 'Fizz', '2983', '2984', 'FizzBuzz', '2986', '2987', 'Fizz', '2989', 'Buzz', 'Fizz', '2992', '2993', 'Fizz', 'Buzz', '2996', 'Fizz', '2998', '2999', 'FizzBuzz', '3001', '3002', 'Fizz', '3004', 'Buzz', 'Fizz', '3007', '3008', 'Fizz', 'Buzz', '3011', 'Fizz', '3013', '3014', 'FizzBuzz', '3016', '3017', 'Fizz', '3019', 'Buzz', 'Fizz', '3022', '3023', 'Fizz', 'Buzz', '3026', 'Fizz', '3028', '3029', 'FizzBuzz', '3031', '3032', 'Fizz', '3034', 'Buzz', 'Fizz', '3037', '3038', 'Fizz', 'Buzz', '3041', 'Fizz', '3043', '3044', 'FizzBuzz', '3046', '3047', 'Fizz', '3049', 'Buzz', 'Fizz', '3052', '3053', 'Fizz', 'Buzz', '3056', 'Fizz', '3058', '3059', 'FizzBuzz', '3061', '3062', 'Fizz', '3064', 'Buzz', 'Fizz', '3067', '3068', 'Fizz', 'Buzz', '3071', 'Fizz', '3073', '3074', 'FizzBuzz', '3076', '3077', 'Fizz', '3079', 'Buzz', 'Fizz', '3082', '3083', 'Fizz', 'Buzz', '3086', 'Fizz', '3088', '3089', 'FizzBuzz', '3091', '3092', 'Fizz', '3094', 'Buzz', 'Fizz', '3097', '3098', 'Fizz', 'Buzz', '3101', 'Fizz', '3103', '3104', 'FizzBuzz', '3106', '3107', 'Fizz', '3109', 'Buzz', 'Fizz', '3112', '3113', 'Fizz', 'Buzz', '3116', 'Fizz', '3118', '3119', 'FizzBuzz', '3121', '3122', 'Fizz', '3124', 'Buzz', 'Fizz', '3127', '3128', 'Fizz', 'Buzz', '3131', 'Fizz', '3133', '3134', 'FizzBuzz', '3136', '3137', 'Fizz', '3139', 'Buzz', 'Fizz', '3142', '3143', 'Fizz', 'Buzz', '3146', 'Fizz', '3148', '3149', 'FizzBuzz', '3151', '3152', 'Fizz', '3154', 'Buzz', 'Fizz', '3157', '3158', 'Fizz', 'Buzz', '3161', 'Fizz', '3163', '3164', 'FizzBuzz', '3166', '3167', 'Fizz', '3169', 'Buzz', 'Fizz', '3172', '3173', 'Fizz', 'Buzz', '3176', 'Fizz', '3178', '3179', 'FizzBuzz', '3181', '3182', 'Fizz', '3184', 'Buzz', 'Fizz', '3187', '3188', 'Fizz', 'Buzz', '3191', 'Fizz', '3193', '3194', 'FizzBuzz', '3196', '3197', 'Fizz', '3199', 'Buzz', 'Fizz', '3202', '3203', 'Fizz', 'Buzz', '3206', 'Fizz', '3208', '3209', 'FizzBuzz', '3211', '3212', 'Fizz', '3214', 'Buzz', 'Fizz', '3217', '3218', 'Fizz', 'Buzz', '3221', 'Fizz', '3223', '3224', 'FizzBuzz', '3226', '3227', 'Fizz', '3229', 'Buzz', 'Fizz', '3232', '3233', 'Fizz', 'Buzz', '3236', 'Fizz', '3238', '3239', 'FizzBuzz', '3241', '3242', 'Fizz', '3244', 'Buzz', 'Fizz', '3247', '3248', 'Fizz', 'Buzz', '3251', 'Fizz', '3253', '3254', 'FizzBuzz', '3256', '3257', 'Fizz', '3259', 'Buzz', 'Fizz', '3262', '3263', 'Fizz', 'Buzz', '3266', 'Fizz', '3268', '3269', 'FizzBuzz', '3271', '3272', 'Fizz', '3274', 'Buzz', 'Fizz', '3277', '3278', 'Fizz', 'Buzz', '3281', 'Fizz', '3283', '3284', 'FizzBuzz', '3286', '3287', 'Fizz', '3289', 'Buzz', 'Fizz', '3292', '3293', 'Fizz', 'Buzz', '3296', 'Fizz', '3298', '3299', 'FizzBuzz', '3301', '3302', 'Fizz', '3304', 'Buzz', 'Fizz', '3307', '3308', 'Fizz', 'Buzz', '3311', 'Fizz', '3313', '3314', 'FizzBuzz', '3316', '3317', 'Fizz', '3319', 'Buzz', 'Fizz', '3322', '3323', 'Fizz', 'Buzz', '3326', 'Fizz', '3328', '3329', 'FizzBuzz', '3331', '3332', 'Fizz']\n assert candidate(n = 300) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz']\n assert candidate(n = 60) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz']\n assert candidate(n = 3000) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz', '1001', 'Fizz', '1003', '1004', 'FizzBuzz', '1006', '1007', 'Fizz', '1009', 'Buzz', 'Fizz', '1012', '1013', 'Fizz', 'Buzz', '1016', 'Fizz', '1018', '1019', 'FizzBuzz', '1021', '1022', 'Fizz', '1024', 'Buzz', 'Fizz', '1027', '1028', 'Fizz', 'Buzz', '1031', 'Fizz', '1033', '1034', 'FizzBuzz', '1036', '1037', 'Fizz', '1039', 'Buzz', 'Fizz', '1042', '1043', 'Fizz', 'Buzz', '1046', 'Fizz', '1048', '1049', 'FizzBuzz', '1051', '1052', 'Fizz', '1054', 'Buzz', 'Fizz', '1057', '1058', 'Fizz', 'Buzz', '1061', 'Fizz', '1063', '1064', 'FizzBuzz', '1066', '1067', 'Fizz', '1069', 'Buzz', 'Fizz', '1072', '1073', 'Fizz', 'Buzz', '1076', 'Fizz', '1078', '1079', 'FizzBuzz', '1081', '1082', 'Fizz', '1084', 'Buzz', 'Fizz', '1087', '1088', 'Fizz', 'Buzz', '1091', 'Fizz', '1093', '1094', 'FizzBuzz', '1096', '1097', 'Fizz', '1099', 'Buzz', 'Fizz', '1102', '1103', 'Fizz', 'Buzz', '1106', 'Fizz', '1108', '1109', 'FizzBuzz', '1111', '1112', 'Fizz', '1114', 'Buzz', 'Fizz', '1117', '1118', 'Fizz', 'Buzz', '1121', 'Fizz', '1123', '1124', 'FizzBuzz', '1126', '1127', 'Fizz', '1129', 'Buzz', 'Fizz', '1132', '1133', 'Fizz', 'Buzz', '1136', 'Fizz', '1138', '1139', 'FizzBuzz', '1141', '1142', 'Fizz', '1144', 'Buzz', 'Fizz', '1147', '1148', 'Fizz', 'Buzz', '1151', 'Fizz', '1153', '1154', 'FizzBuzz', '1156', '1157', 'Fizz', '1159', 'Buzz', 'Fizz', '1162', '1163', 'Fizz', 'Buzz', '1166', 'Fizz', '1168', '1169', 'FizzBuzz', '1171', '1172', 'Fizz', '1174', 'Buzz', 'Fizz', '1177', '1178', 'Fizz', 'Buzz', '1181', 'Fizz', '1183', '1184', 'FizzBuzz', '1186', '1187', 'Fizz', '1189', 'Buzz', 'Fizz', '1192', '1193', 'Fizz', 'Buzz', '1196', 'Fizz', '1198', '1199', 'FizzBuzz', '1201', '1202', 'Fizz', '1204', 'Buzz', 'Fizz', '1207', '1208', 'Fizz', 'Buzz', '1211', 'Fizz', '1213', '1214', 'FizzBuzz', '1216', '1217', 'Fizz', '1219', 'Buzz', 'Fizz', '1222', '1223', 'Fizz', 'Buzz', '1226', 'Fizz', '1228', '1229', 'FizzBuzz', '1231', '1232', 'Fizz', '1234', 'Buzz', 'Fizz', '1237', '1238', 'Fizz', 'Buzz', '1241', 'Fizz', '1243', '1244', 'FizzBuzz', '1246', '1247', 'Fizz', '1249', 'Buzz', 'Fizz', '1252', '1253', 'Fizz', 'Buzz', '1256', 'Fizz', '1258', '1259', 'FizzBuzz', '1261', '1262', 'Fizz', '1264', 'Buzz', 'Fizz', '1267', '1268', 'Fizz', 'Buzz', '1271', 'Fizz', '1273', '1274', 'FizzBuzz', '1276', '1277', 'Fizz', '1279', 'Buzz', 'Fizz', '1282', '1283', 'Fizz', 'Buzz', '1286', 'Fizz', '1288', '1289', 'FizzBuzz', '1291', '1292', 'Fizz', '1294', 'Buzz', 'Fizz', '1297', '1298', 'Fizz', 'Buzz', '1301', 'Fizz', '1303', '1304', 'FizzBuzz', '1306', '1307', 'Fizz', '1309', 'Buzz', 'Fizz', '1312', '1313', 'Fizz', 'Buzz', '1316', 'Fizz', '1318', '1319', 'FizzBuzz', '1321', '1322', 'Fizz', '1324', 'Buzz', 'Fizz', '1327', '1328', 'Fizz', 'Buzz', '1331', 'Fizz', '1333', '1334', 'FizzBuzz', '1336', '1337', 'Fizz', '1339', 'Buzz', 'Fizz', '1342', '1343', 'Fizz', 'Buzz', '1346', 'Fizz', '1348', '1349', 'FizzBuzz', '1351', '1352', 'Fizz', '1354', 'Buzz', 'Fizz', '1357', '1358', 'Fizz', 'Buzz', '1361', 'Fizz', '1363', '1364', 'FizzBuzz', '1366', '1367', 'Fizz', '1369', 'Buzz', 'Fizz', '1372', '1373', 'Fizz', 'Buzz', '1376', 'Fizz', '1378', '1379', 'FizzBuzz', '1381', '1382', 'Fizz', '1384', 'Buzz', 'Fizz', '1387', '1388', 'Fizz', 'Buzz', '1391', 'Fizz', '1393', '1394', 'FizzBuzz', '1396', '1397', 'Fizz', '1399', 'Buzz', 'Fizz', '1402', '1403', 'Fizz', 'Buzz', '1406', 'Fizz', '1408', '1409', 'FizzBuzz', '1411', '1412', 'Fizz', '1414', 'Buzz', 'Fizz', '1417', '1418', 'Fizz', 'Buzz', '1421', 'Fizz', '1423', '1424', 'FizzBuzz', '1426', '1427', 'Fizz', '1429', 'Buzz', 'Fizz', '1432', '1433', 'Fizz', 'Buzz', '1436', 'Fizz', '1438', '1439', 'FizzBuzz', '1441', '1442', 'Fizz', '1444', 'Buzz', 'Fizz', '1447', '1448', 'Fizz', 'Buzz', '1451', 'Fizz', '1453', '1454', 'FizzBuzz', '1456', '1457', 'Fizz', '1459', 'Buzz', 'Fizz', '1462', '1463', 'Fizz', 'Buzz', '1466', 'Fizz', '1468', '1469', 'FizzBuzz', '1471', '1472', 'Fizz', '1474', 'Buzz', 'Fizz', '1477', '1478', 'Fizz', 'Buzz', '1481', 'Fizz', '1483', '1484', 'FizzBuzz', '1486', '1487', 'Fizz', '1489', 'Buzz', 'Fizz', '1492', '1493', 'Fizz', 'Buzz', '1496', 'Fizz', '1498', '1499', 'FizzBuzz', '1501', '1502', 'Fizz', '1504', 'Buzz', 'Fizz', '1507', '1508', 'Fizz', 'Buzz', '1511', 'Fizz', '1513', '1514', 'FizzBuzz', '1516', '1517', 'Fizz', '1519', 'Buzz', 'Fizz', '1522', '1523', 'Fizz', 'Buzz', '1526', 'Fizz', '1528', '1529', 'FizzBuzz', '1531', '1532', 'Fizz', '1534', 'Buzz', 'Fizz', '1537', '1538', 'Fizz', 'Buzz', '1541', 'Fizz', '1543', '1544', 'FizzBuzz', '1546', '1547', 'Fizz', '1549', 'Buzz', 'Fizz', '1552', '1553', 'Fizz', 'Buzz', '1556', 'Fizz', '1558', '1559', 'FizzBuzz', '1561', '1562', 'Fizz', '1564', 'Buzz', 'Fizz', '1567', '1568', 'Fizz', 'Buzz', '1571', 'Fizz', '1573', '1574', 'FizzBuzz', '1576', '1577', 'Fizz', '1579', 'Buzz', 'Fizz', '1582', '1583', 'Fizz', 'Buzz', '1586', 'Fizz', '1588', '1589', 'FizzBuzz', '1591', '1592', 'Fizz', '1594', 'Buzz', 'Fizz', '1597', '1598', 'Fizz', 'Buzz', '1601', 'Fizz', '1603', '1604', 'FizzBuzz', '1606', '1607', 'Fizz', '1609', 'Buzz', 'Fizz', '1612', '1613', 'Fizz', 'Buzz', '1616', 'Fizz', '1618', '1619', 'FizzBuzz', '1621', '1622', 'Fizz', '1624', 'Buzz', 'Fizz', '1627', '1628', 'Fizz', 'Buzz', '1631', 'Fizz', '1633', '1634', 'FizzBuzz', '1636', '1637', 'Fizz', '1639', 'Buzz', 'Fizz', '1642', '1643', 'Fizz', 'Buzz', '1646', 'Fizz', '1648', '1649', 'FizzBuzz', '1651', '1652', 'Fizz', '1654', 'Buzz', 'Fizz', '1657', '1658', 'Fizz', 'Buzz', '1661', 'Fizz', '1663', '1664', 'FizzBuzz', '1666', '1667', 'Fizz', '1669', 'Buzz', 'Fizz', '1672', '1673', 'Fizz', 'Buzz', '1676', 'Fizz', '1678', '1679', 'FizzBuzz', '1681', '1682', 'Fizz', '1684', 'Buzz', 'Fizz', '1687', '1688', 'Fizz', 'Buzz', '1691', 'Fizz', '1693', '1694', 'FizzBuzz', '1696', '1697', 'Fizz', '1699', 'Buzz', 'Fizz', '1702', '1703', 'Fizz', 'Buzz', '1706', 'Fizz', '1708', '1709', 'FizzBuzz', '1711', '1712', 'Fizz', '1714', 'Buzz', 'Fizz', '1717', '1718', 'Fizz', 'Buzz', '1721', 'Fizz', '1723', '1724', 'FizzBuzz', '1726', '1727', 'Fizz', '1729', 'Buzz', 'Fizz', '1732', '1733', 'Fizz', 'Buzz', '1736', 'Fizz', '1738', '1739', 'FizzBuzz', '1741', '1742', 'Fizz', '1744', 'Buzz', 'Fizz', '1747', '1748', 'Fizz', 'Buzz', '1751', 'Fizz', '1753', '1754', 'FizzBuzz', '1756', '1757', 'Fizz', '1759', 'Buzz', 'Fizz', '1762', '1763', 'Fizz', 'Buzz', '1766', 'Fizz', '1768', '1769', 'FizzBuzz', '1771', '1772', 'Fizz', '1774', 'Buzz', 'Fizz', '1777', '1778', 'Fizz', 'Buzz', '1781', 'Fizz', '1783', '1784', 'FizzBuzz', '1786', '1787', 'Fizz', '1789', 'Buzz', 'Fizz', '1792', '1793', 'Fizz', 'Buzz', '1796', 'Fizz', '1798', '1799', 'FizzBuzz', '1801', '1802', 'Fizz', '1804', 'Buzz', 'Fizz', '1807', '1808', 'Fizz', 'Buzz', '1811', 'Fizz', '1813', '1814', 'FizzBuzz', '1816', '1817', 'Fizz', '1819', 'Buzz', 'Fizz', '1822', '1823', 'Fizz', 'Buzz', '1826', 'Fizz', '1828', '1829', 'FizzBuzz', '1831', '1832', 'Fizz', '1834', 'Buzz', 'Fizz', '1837', '1838', 'Fizz', 'Buzz', '1841', 'Fizz', '1843', '1844', 'FizzBuzz', '1846', '1847', 'Fizz', '1849', 'Buzz', 'Fizz', '1852', '1853', 'Fizz', 'Buzz', '1856', 'Fizz', '1858', '1859', 'FizzBuzz', '1861', '1862', 'Fizz', '1864', 'Buzz', 'Fizz', '1867', '1868', 'Fizz', 'Buzz', '1871', 'Fizz', '1873', '1874', 'FizzBuzz', '1876', '1877', 'Fizz', '1879', 'Buzz', 'Fizz', '1882', '1883', 'Fizz', 'Buzz', '1886', 'Fizz', '1888', '1889', 'FizzBuzz', '1891', '1892', 'Fizz', '1894', 'Buzz', 'Fizz', '1897', '1898', 'Fizz', 'Buzz', '1901', 'Fizz', '1903', '1904', 'FizzBuzz', '1906', '1907', 'Fizz', '1909', 'Buzz', 'Fizz', '1912', '1913', 'Fizz', 'Buzz', '1916', 'Fizz', '1918', '1919', 'FizzBuzz', '1921', '1922', 'Fizz', '1924', 'Buzz', 'Fizz', '1927', '1928', 'Fizz', 'Buzz', '1931', 'Fizz', '1933', '1934', 'FizzBuzz', '1936', '1937', 'Fizz', '1939', 'Buzz', 'Fizz', '1942', '1943', 'Fizz', 'Buzz', '1946', 'Fizz', '1948', '1949', 'FizzBuzz', '1951', '1952', 'Fizz', '1954', 'Buzz', 'Fizz', '1957', '1958', 'Fizz', 'Buzz', '1961', 'Fizz', '1963', '1964', 'FizzBuzz', '1966', '1967', 'Fizz', '1969', 'Buzz', 'Fizz', '1972', '1973', 'Fizz', 'Buzz', '1976', 'Fizz', '1978', '1979', 'FizzBuzz', '1981', '1982', 'Fizz', '1984', 'Buzz', 'Fizz', '1987', '1988', 'Fizz', 'Buzz', '1991', 'Fizz', '1993', '1994', 'FizzBuzz', '1996', '1997', 'Fizz', '1999', 'Buzz', 'Fizz', '2002', '2003', 'Fizz', 'Buzz', '2006', 'Fizz', '2008', '2009', 'FizzBuzz', '2011', '2012', 'Fizz', '2014', 'Buzz', 'Fizz', '2017', '2018', 'Fizz', 'Buzz', '2021', 'Fizz', '2023', '2024', 'FizzBuzz', '2026', '2027', 'Fizz', '2029', 'Buzz', 'Fizz', '2032', '2033', 'Fizz', 'Buzz', '2036', 'Fizz', '2038', '2039', 'FizzBuzz', '2041', '2042', 'Fizz', '2044', 'Buzz', 'Fizz', '2047', '2048', 'Fizz', 'Buzz', '2051', 'Fizz', '2053', '2054', 'FizzBuzz', '2056', '2057', 'Fizz', '2059', 'Buzz', 'Fizz', '2062', '2063', 'Fizz', 'Buzz', '2066', 'Fizz', '2068', '2069', 'FizzBuzz', '2071', '2072', 'Fizz', '2074', 'Buzz', 'Fizz', '2077', '2078', 'Fizz', 'Buzz', '2081', 'Fizz', '2083', '2084', 'FizzBuzz', '2086', '2087', 'Fizz', '2089', 'Buzz', 'Fizz', '2092', '2093', 'Fizz', 'Buzz', '2096', 'Fizz', '2098', '2099', 'FizzBuzz', '2101', '2102', 'Fizz', '2104', 'Buzz', 'Fizz', '2107', '2108', 'Fizz', 'Buzz', '2111', 'Fizz', '2113', '2114', 'FizzBuzz', '2116', '2117', 'Fizz', '2119', 'Buzz', 'Fizz', '2122', '2123', 'Fizz', 'Buzz', '2126', 'Fizz', '2128', '2129', 'FizzBuzz', '2131', '2132', 'Fizz', '2134', 'Buzz', 'Fizz', '2137', '2138', 'Fizz', 'Buzz', '2141', 'Fizz', '2143', '2144', 'FizzBuzz', '2146', '2147', 'Fizz', '2149', 'Buzz', 'Fizz', '2152', '2153', 'Fizz', 'Buzz', '2156', 'Fizz', '2158', '2159', 'FizzBuzz', '2161', '2162', 'Fizz', '2164', 'Buzz', 'Fizz', '2167', '2168', 'Fizz', 'Buzz', '2171', 'Fizz', '2173', '2174', 'FizzBuzz', '2176', '2177', 'Fizz', '2179', 'Buzz', 'Fizz', '2182', '2183', 'Fizz', 'Buzz', '2186', 'Fizz', '2188', '2189', 'FizzBuzz', '2191', '2192', 'Fizz', '2194', 'Buzz', 'Fizz', '2197', '2198', 'Fizz', 'Buzz', '2201', 'Fizz', '2203', '2204', 'FizzBuzz', '2206', '2207', 'Fizz', '2209', 'Buzz', 'Fizz', '2212', '2213', 'Fizz', 'Buzz', '2216', 'Fizz', '2218', '2219', 'FizzBuzz', '2221', '2222', 'Fizz', '2224', 'Buzz', 'Fizz', '2227', '2228', 'Fizz', 'Buzz', '2231', 'Fizz', '2233', '2234', 'FizzBuzz', '2236', '2237', 'Fizz', '2239', 'Buzz', 'Fizz', '2242', '2243', 'Fizz', 'Buzz', '2246', 'Fizz', '2248', '2249', 'FizzBuzz', '2251', '2252', 'Fizz', '2254', 'Buzz', 'Fizz', '2257', '2258', 'Fizz', 'Buzz', '2261', 'Fizz', '2263', '2264', 'FizzBuzz', '2266', '2267', 'Fizz', '2269', 'Buzz', 'Fizz', '2272', '2273', 'Fizz', 'Buzz', '2276', 'Fizz', '2278', '2279', 'FizzBuzz', '2281', '2282', 'Fizz', '2284', 'Buzz', 'Fizz', '2287', '2288', 'Fizz', 'Buzz', '2291', 'Fizz', '2293', '2294', 'FizzBuzz', '2296', '2297', 'Fizz', '2299', 'Buzz', 'Fizz', '2302', '2303', 'Fizz', 'Buzz', '2306', 'Fizz', '2308', '2309', 'FizzBuzz', '2311', '2312', 'Fizz', '2314', 'Buzz', 'Fizz', '2317', '2318', 'Fizz', 'Buzz', '2321', 'Fizz', '2323', '2324', 'FizzBuzz', '2326', '2327', 'Fizz', '2329', 'Buzz', 'Fizz', '2332', '2333', 'Fizz', 'Buzz', '2336', 'Fizz', '2338', '2339', 'FizzBuzz', '2341', '2342', 'Fizz', '2344', 'Buzz', 'Fizz', '2347', '2348', 'Fizz', 'Buzz', '2351', 'Fizz', '2353', '2354', 'FizzBuzz', '2356', '2357', 'Fizz', '2359', 'Buzz', 'Fizz', '2362', '2363', 'Fizz', 'Buzz', '2366', 'Fizz', '2368', '2369', 'FizzBuzz', '2371', '2372', 'Fizz', '2374', 'Buzz', 'Fizz', '2377', '2378', 'Fizz', 'Buzz', '2381', 'Fizz', '2383', '2384', 'FizzBuzz', '2386', '2387', 'Fizz', '2389', 'Buzz', 'Fizz', '2392', '2393', 'Fizz', 'Buzz', '2396', 'Fizz', '2398', '2399', 'FizzBuzz', '2401', '2402', 'Fizz', '2404', 'Buzz', 'Fizz', '2407', '2408', 'Fizz', 'Buzz', '2411', 'Fizz', '2413', '2414', 'FizzBuzz', '2416', '2417', 'Fizz', '2419', 'Buzz', 'Fizz', '2422', '2423', 'Fizz', 'Buzz', '2426', 'Fizz', '2428', '2429', 'FizzBuzz', '2431', '2432', 'Fizz', '2434', 'Buzz', 'Fizz', '2437', '2438', 'Fizz', 'Buzz', '2441', 'Fizz', '2443', '2444', 'FizzBuzz', '2446', '2447', 'Fizz', '2449', 'Buzz', 'Fizz', '2452', '2453', 'Fizz', 'Buzz', '2456', 'Fizz', '2458', '2459', 'FizzBuzz', '2461', '2462', 'Fizz', '2464', 'Buzz', 'Fizz', '2467', '2468', 'Fizz', 'Buzz', '2471', 'Fizz', '2473', '2474', 'FizzBuzz', '2476', '2477', 'Fizz', '2479', 'Buzz', 'Fizz', '2482', '2483', 'Fizz', 'Buzz', '2486', 'Fizz', '2488', '2489', 'FizzBuzz', '2491', '2492', 'Fizz', '2494', 'Buzz', 'Fizz', '2497', '2498', 'Fizz', 'Buzz', '2501', 'Fizz', '2503', '2504', 'FizzBuzz', '2506', '2507', 'Fizz', '2509', 'Buzz', 'Fizz', '2512', '2513', 'Fizz', 'Buzz', '2516', 'Fizz', '2518', '2519', 'FizzBuzz', '2521', '2522', 'Fizz', '2524', 'Buzz', 'Fizz', '2527', '2528', 'Fizz', 'Buzz', '2531', 'Fizz', '2533', '2534', 'FizzBuzz', '2536', '2537', 'Fizz', '2539', 'Buzz', 'Fizz', '2542', '2543', 'Fizz', 'Buzz', '2546', 'Fizz', '2548', '2549', 'FizzBuzz', '2551', '2552', 'Fizz', '2554', 'Buzz', 'Fizz', '2557', '2558', 'Fizz', 'Buzz', '2561', 'Fizz', '2563', '2564', 'FizzBuzz', '2566', '2567', 'Fizz', '2569', 'Buzz', 'Fizz', '2572', '2573', 'Fizz', 'Buzz', '2576', 'Fizz', '2578', '2579', 'FizzBuzz', '2581', '2582', 'Fizz', '2584', 'Buzz', 'Fizz', '2587', '2588', 'Fizz', 'Buzz', '2591', 'Fizz', '2593', '2594', 'FizzBuzz', '2596', '2597', 'Fizz', '2599', 'Buzz', 'Fizz', '2602', '2603', 'Fizz', 'Buzz', '2606', 'Fizz', '2608', '2609', 'FizzBuzz', '2611', '2612', 'Fizz', '2614', 'Buzz', 'Fizz', '2617', '2618', 'Fizz', 'Buzz', '2621', 'Fizz', '2623', '2624', 'FizzBuzz', '2626', '2627', 'Fizz', '2629', 'Buzz', 'Fizz', '2632', '2633', 'Fizz', 'Buzz', '2636', 'Fizz', '2638', '2639', 'FizzBuzz', '2641', '2642', 'Fizz', '2644', 'Buzz', 'Fizz', '2647', '2648', 'Fizz', 'Buzz', '2651', 'Fizz', '2653', '2654', 'FizzBuzz', '2656', '2657', 'Fizz', '2659', 'Buzz', 'Fizz', '2662', '2663', 'Fizz', 'Buzz', '2666', 'Fizz', '2668', '2669', 'FizzBuzz', '2671', '2672', 'Fizz', '2674', 'Buzz', 'Fizz', '2677', '2678', 'Fizz', 'Buzz', '2681', 'Fizz', '2683', '2684', 'FizzBuzz', '2686', '2687', 'Fizz', '2689', 'Buzz', 'Fizz', '2692', '2693', 'Fizz', 'Buzz', '2696', 'Fizz', '2698', '2699', 'FizzBuzz', '2701', '2702', 'Fizz', '2704', 'Buzz', 'Fizz', '2707', '2708', 'Fizz', 'Buzz', '2711', 'Fizz', '2713', '2714', 'FizzBuzz', '2716', '2717', 'Fizz', '2719', 'Buzz', 'Fizz', '2722', '2723', 'Fizz', 'Buzz', '2726', 'Fizz', '2728', '2729', 'FizzBuzz', '2731', '2732', 'Fizz', '2734', 'Buzz', 'Fizz', '2737', '2738', 'Fizz', 'Buzz', '2741', 'Fizz', '2743', '2744', 'FizzBuzz', '2746', '2747', 'Fizz', '2749', 'Buzz', 'Fizz', '2752', '2753', 'Fizz', 'Buzz', '2756', 'Fizz', '2758', '2759', 'FizzBuzz', '2761', '2762', 'Fizz', '2764', 'Buzz', 'Fizz', '2767', '2768', 'Fizz', 'Buzz', '2771', 'Fizz', '2773', '2774', 'FizzBuzz', '2776', '2777', 'Fizz', '2779', 'Buzz', 'Fizz', '2782', '2783', 'Fizz', 'Buzz', '2786', 'Fizz', '2788', '2789', 'FizzBuzz', '2791', '2792', 'Fizz', '2794', 'Buzz', 'Fizz', '2797', '2798', 'Fizz', 'Buzz', '2801', 'Fizz', '2803', '2804', 'FizzBuzz', '2806', '2807', 'Fizz', '2809', 'Buzz', 'Fizz', '2812', '2813', 'Fizz', 'Buzz', '2816', 'Fizz', '2818', '2819', 'FizzBuzz', '2821', '2822', 'Fizz', '2824', 'Buzz', 'Fizz', '2827', '2828', 'Fizz', 'Buzz', '2831', 'Fizz', '2833', '2834', 'FizzBuzz', '2836', '2837', 'Fizz', '2839', 'Buzz', 'Fizz', '2842', '2843', 'Fizz', 'Buzz', '2846', 'Fizz', '2848', '2849', 'FizzBuzz', '2851', '2852', 'Fizz', '2854', 'Buzz', 'Fizz', '2857', '2858', 'Fizz', 'Buzz', '2861', 'Fizz', '2863', '2864', 'FizzBuzz', '2866', '2867', 'Fizz', '2869', 'Buzz', 'Fizz', '2872', '2873', 'Fizz', 'Buzz', '2876', 'Fizz', '2878', '2879', 'FizzBuzz', '2881', '2882', 'Fizz', '2884', 'Buzz', 'Fizz', '2887', '2888', 'Fizz', 'Buzz', '2891', 'Fizz', '2893', '2894', 'FizzBuzz', '2896', '2897', 'Fizz', '2899', 'Buzz', 'Fizz', '2902', '2903', 'Fizz', 'Buzz', '2906', 'Fizz', '2908', '2909', 'FizzBuzz', '2911', '2912', 'Fizz', '2914', 'Buzz', 'Fizz', '2917', '2918', 'Fizz', 'Buzz', '2921', 'Fizz', '2923', '2924', 'FizzBuzz', '2926', '2927', 'Fizz', '2929', 'Buzz', 'Fizz', '2932', '2933', 'Fizz', 'Buzz', '2936', 'Fizz', '2938', '2939', 'FizzBuzz', '2941', '2942', 'Fizz', '2944', 'Buzz', 'Fizz', '2947', '2948', 'Fizz', 'Buzz', '2951', 'Fizz', '2953', '2954', 'FizzBuzz', '2956', '2957', 'Fizz', '2959', 'Buzz', 'Fizz', '2962', '2963', 'Fizz', 'Buzz', '2966', 'Fizz', '2968', '2969', 'FizzBuzz', '2971', '2972', 'Fizz', '2974', 'Buzz', 'Fizz', '2977', '2978', 'Fizz', 'Buzz', '2981', 'Fizz', '2983', '2984', 'FizzBuzz', '2986', '2987', 'Fizz', '2989', 'Buzz', 'Fizz', '2992', '2993', 'Fizz', 'Buzz', '2996', 'Fizz', '2998', '2999', 'FizzBuzz']\n assert candidate(n = 30) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz']\n assert candidate(n = 99) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz']\n assert candidate(n = 2) == ['1', '2']\n assert candidate(n = 23) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23']\n assert candidate(n = 42) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz']\n assert candidate(n = 1024) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz', '1001', 'Fizz', '1003', '1004', 'FizzBuzz', '1006', '1007', 'Fizz', '1009', 'Buzz', 'Fizz', '1012', '1013', 'Fizz', 'Buzz', '1016', 'Fizz', '1018', '1019', 'FizzBuzz', '1021', '1022', 'Fizz', '1024']\n assert candidate(n = 101) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101']\n assert candidate(n = 250) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz']\n assert candidate(n = 2048) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz', 'Buzz', '1001', 'Fizz', '1003', '1004', 'FizzBuzz', '1006', '1007', 'Fizz', '1009', 'Buzz', 'Fizz', '1012', '1013', 'Fizz', 'Buzz', '1016', 'Fizz', '1018', '1019', 'FizzBuzz', '1021', '1022', 'Fizz', '1024', 'Buzz', 'Fizz', '1027', '1028', 'Fizz', 'Buzz', '1031', 'Fizz', '1033', '1034', 'FizzBuzz', '1036', '1037', 'Fizz', '1039', 'Buzz', 'Fizz', '1042', '1043', 'Fizz', 'Buzz', '1046', 'Fizz', '1048', '1049', 'FizzBuzz', '1051', '1052', 'Fizz', '1054', 'Buzz', 'Fizz', '1057', '1058', 'Fizz', 'Buzz', '1061', 'Fizz', '1063', '1064', 'FizzBuzz', '1066', '1067', 'Fizz', '1069', 'Buzz', 'Fizz', '1072', '1073', 'Fizz', 'Buzz', '1076', 'Fizz', '1078', '1079', 'FizzBuzz', '1081', '1082', 'Fizz', '1084', 'Buzz', 'Fizz', '1087', '1088', 'Fizz', 'Buzz', '1091', 'Fizz', '1093', '1094', 'FizzBuzz', '1096', '1097', 'Fizz', '1099', 'Buzz', 'Fizz', '1102', '1103', 'Fizz', 'Buzz', '1106', 'Fizz', '1108', '1109', 'FizzBuzz', '1111', '1112', 'Fizz', '1114', 'Buzz', 'Fizz', '1117', '1118', 'Fizz', 'Buzz', '1121', 'Fizz', '1123', '1124', 'FizzBuzz', '1126', '1127', 'Fizz', '1129', 'Buzz', 'Fizz', '1132', '1133', 'Fizz', 'Buzz', '1136', 'Fizz', '1138', '1139', 'FizzBuzz', '1141', '1142', 'Fizz', '1144', 'Buzz', 'Fizz', '1147', '1148', 'Fizz', 'Buzz', '1151', 'Fizz', '1153', '1154', 'FizzBuzz', '1156', '1157', 'Fizz', '1159', 'Buzz', 'Fizz', '1162', '1163', 'Fizz', 'Buzz', '1166', 'Fizz', '1168', '1169', 'FizzBuzz', '1171', '1172', 'Fizz', '1174', 'Buzz', 'Fizz', '1177', '1178', 'Fizz', 'Buzz', '1181', 'Fizz', '1183', '1184', 'FizzBuzz', '1186', '1187', 'Fizz', '1189', 'Buzz', 'Fizz', '1192', '1193', 'Fizz', 'Buzz', '1196', 'Fizz', '1198', '1199', 'FizzBuzz', '1201', '1202', 'Fizz', '1204', 'Buzz', 'Fizz', '1207', '1208', 'Fizz', 'Buzz', '1211', 'Fizz', '1213', '1214', 'FizzBuzz', '1216', '1217', 'Fizz', '1219', 'Buzz', 'Fizz', '1222', '1223', 'Fizz', 'Buzz', '1226', 'Fizz', '1228', '1229', 'FizzBuzz', '1231', '1232', 'Fizz', '1234', 'Buzz', 'Fizz', '1237', '1238', 'Fizz', 'Buzz', '1241', 'Fizz', '1243', '1244', 'FizzBuzz', '1246', '1247', 'Fizz', '1249', 'Buzz', 'Fizz', '1252', '1253', 'Fizz', 'Buzz', '1256', 'Fizz', '1258', '1259', 'FizzBuzz', '1261', '1262', 'Fizz', '1264', 'Buzz', 'Fizz', '1267', '1268', 'Fizz', 'Buzz', '1271', 'Fizz', '1273', '1274', 'FizzBuzz', '1276', '1277', 'Fizz', '1279', 'Buzz', 'Fizz', '1282', '1283', 'Fizz', 'Buzz', '1286', 'Fizz', '1288', '1289', 'FizzBuzz', '1291', '1292', 'Fizz', '1294', 'Buzz', 'Fizz', '1297', '1298', 'Fizz', 'Buzz', '1301', 'Fizz', '1303', '1304', 'FizzBuzz', '1306', '1307', 'Fizz', '1309', 'Buzz', 'Fizz', '1312', '1313', 'Fizz', 'Buzz', '1316', 'Fizz', '1318', '1319', 'FizzBuzz', '1321', '1322', 'Fizz', '1324', 'Buzz', 'Fizz', '1327', '1328', 'Fizz', 'Buzz', '1331', 'Fizz', '1333', '1334', 'FizzBuzz', '1336', '1337', 'Fizz', '1339', 'Buzz', 'Fizz', '1342', '1343', 'Fizz', 'Buzz', '1346', 'Fizz', '1348', '1349', 'FizzBuzz', '1351', '1352', 'Fizz', '1354', 'Buzz', 'Fizz', '1357', '1358', 'Fizz', 'Buzz', '1361', 'Fizz', '1363', '1364', 'FizzBuzz', '1366', '1367', 'Fizz', '1369', 'Buzz', 'Fizz', '1372', '1373', 'Fizz', 'Buzz', '1376', 'Fizz', '1378', '1379', 'FizzBuzz', '1381', '1382', 'Fizz', '1384', 'Buzz', 'Fizz', '1387', '1388', 'Fizz', 'Buzz', '1391', 'Fizz', '1393', '1394', 'FizzBuzz', '1396', '1397', 'Fizz', '1399', 'Buzz', 'Fizz', '1402', '1403', 'Fizz', 'Buzz', '1406', 'Fizz', '1408', '1409', 'FizzBuzz', '1411', '1412', 'Fizz', '1414', 'Buzz', 'Fizz', '1417', '1418', 'Fizz', 'Buzz', '1421', 'Fizz', '1423', '1424', 'FizzBuzz', '1426', '1427', 'Fizz', '1429', 'Buzz', 'Fizz', '1432', '1433', 'Fizz', 'Buzz', '1436', 'Fizz', '1438', '1439', 'FizzBuzz', '1441', '1442', 'Fizz', '1444', 'Buzz', 'Fizz', '1447', '1448', 'Fizz', 'Buzz', '1451', 'Fizz', '1453', '1454', 'FizzBuzz', '1456', '1457', 'Fizz', '1459', 'Buzz', 'Fizz', '1462', '1463', 'Fizz', 'Buzz', '1466', 'Fizz', '1468', '1469', 'FizzBuzz', '1471', '1472', 'Fizz', '1474', 'Buzz', 'Fizz', '1477', '1478', 'Fizz', 'Buzz', '1481', 'Fizz', '1483', '1484', 'FizzBuzz', '1486', '1487', 'Fizz', '1489', 'Buzz', 'Fizz', '1492', '1493', 'Fizz', 'Buzz', '1496', 'Fizz', '1498', '1499', 'FizzBuzz', '1501', '1502', 'Fizz', '1504', 'Buzz', 'Fizz', '1507', '1508', 'Fizz', 'Buzz', '1511', 'Fizz', '1513', '1514', 'FizzBuzz', '1516', '1517', 'Fizz', '1519', 'Buzz', 'Fizz', '1522', '1523', 'Fizz', 'Buzz', '1526', 'Fizz', '1528', '1529', 'FizzBuzz', '1531', '1532', 'Fizz', '1534', 'Buzz', 'Fizz', '1537', '1538', 'Fizz', 'Buzz', '1541', 'Fizz', '1543', '1544', 'FizzBuzz', '1546', '1547', 'Fizz', '1549', 'Buzz', 'Fizz', '1552', '1553', 'Fizz', 'Buzz', '1556', 'Fizz', '1558', '1559', 'FizzBuzz', '1561', '1562', 'Fizz', '1564', 'Buzz', 'Fizz', '1567', '1568', 'Fizz', 'Buzz', '1571', 'Fizz', '1573', '1574', 'FizzBuzz', '1576', '1577', 'Fizz', '1579', 'Buzz', 'Fizz', '1582', '1583', 'Fizz', 'Buzz', '1586', 'Fizz', '1588', '1589', 'FizzBuzz', '1591', '1592', 'Fizz', '1594', 'Buzz', 'Fizz', '1597', '1598', 'Fizz', 'Buzz', '1601', 'Fizz', '1603', '1604', 'FizzBuzz', '1606', '1607', 'Fizz', '1609', 'Buzz', 'Fizz', '1612', '1613', 'Fizz', 'Buzz', '1616', 'Fizz', '1618', '1619', 'FizzBuzz', '1621', '1622', 'Fizz', '1624', 'Buzz', 'Fizz', '1627', '1628', 'Fizz', 'Buzz', '1631', 'Fizz', '1633', '1634', 'FizzBuzz', '1636', '1637', 'Fizz', '1639', 'Buzz', 'Fizz', '1642', '1643', 'Fizz', 'Buzz', '1646', 'Fizz', '1648', '1649', 'FizzBuzz', '1651', '1652', 'Fizz', '1654', 'Buzz', 'Fizz', '1657', '1658', 'Fizz', 'Buzz', '1661', 'Fizz', '1663', '1664', 'FizzBuzz', '1666', '1667', 'Fizz', '1669', 'Buzz', 'Fizz', '1672', '1673', 'Fizz', 'Buzz', '1676', 'Fizz', '1678', '1679', 'FizzBuzz', '1681', '1682', 'Fizz', '1684', 'Buzz', 'Fizz', '1687', '1688', 'Fizz', 'Buzz', '1691', 'Fizz', '1693', '1694', 'FizzBuzz', '1696', '1697', 'Fizz', '1699', 'Buzz', 'Fizz', '1702', '1703', 'Fizz', 'Buzz', '1706', 'Fizz', '1708', '1709', 'FizzBuzz', '1711', '1712', 'Fizz', '1714', 'Buzz', 'Fizz', '1717', '1718', 'Fizz', 'Buzz', '1721', 'Fizz', '1723', '1724', 'FizzBuzz', '1726', '1727', 'Fizz', '1729', 'Buzz', 'Fizz', '1732', '1733', 'Fizz', 'Buzz', '1736', 'Fizz', '1738', '1739', 'FizzBuzz', '1741', '1742', 'Fizz', '1744', 'Buzz', 'Fizz', '1747', '1748', 'Fizz', 'Buzz', '1751', 'Fizz', '1753', '1754', 'FizzBuzz', '1756', '1757', 'Fizz', '1759', 'Buzz', 'Fizz', '1762', '1763', 'Fizz', 'Buzz', '1766', 'Fizz', '1768', '1769', 'FizzBuzz', '1771', '1772', 'Fizz', '1774', 'Buzz', 'Fizz', '1777', '1778', 'Fizz', 'Buzz', '1781', 'Fizz', '1783', '1784', 'FizzBuzz', '1786', '1787', 'Fizz', '1789', 'Buzz', 'Fizz', '1792', '1793', 'Fizz', 'Buzz', '1796', 'Fizz', '1798', '1799', 'FizzBuzz', '1801', '1802', 'Fizz', '1804', 'Buzz', 'Fizz', '1807', '1808', 'Fizz', 'Buzz', '1811', 'Fizz', '1813', '1814', 'FizzBuzz', '1816', '1817', 'Fizz', '1819', 'Buzz', 'Fizz', '1822', '1823', 'Fizz', 'Buzz', '1826', 'Fizz', '1828', '1829', 'FizzBuzz', '1831', '1832', 'Fizz', '1834', 'Buzz', 'Fizz', '1837', '1838', 'Fizz', 'Buzz', '1841', 'Fizz', '1843', '1844', 'FizzBuzz', '1846', '1847', 'Fizz', '1849', 'Buzz', 'Fizz', '1852', '1853', 'Fizz', 'Buzz', '1856', 'Fizz', '1858', '1859', 'FizzBuzz', '1861', '1862', 'Fizz', '1864', 'Buzz', 'Fizz', '1867', '1868', 'Fizz', 'Buzz', '1871', 'Fizz', '1873', '1874', 'FizzBuzz', '1876', '1877', 'Fizz', '1879', 'Buzz', 'Fizz', '1882', '1883', 'Fizz', 'Buzz', '1886', 'Fizz', '1888', '1889', 'FizzBuzz', '1891', '1892', 'Fizz', '1894', 'Buzz', 'Fizz', '1897', '1898', 'Fizz', 'Buzz', '1901', 'Fizz', '1903', '1904', 'FizzBuzz', '1906', '1907', 'Fizz', '1909', 'Buzz', 'Fizz', '1912', '1913', 'Fizz', 'Buzz', '1916', 'Fizz', '1918', '1919', 'FizzBuzz', '1921', '1922', 'Fizz', '1924', 'Buzz', 'Fizz', '1927', '1928', 'Fizz', 'Buzz', '1931', 'Fizz', '1933', '1934', 'FizzBuzz', '1936', '1937', 'Fizz', '1939', 'Buzz', 'Fizz', '1942', '1943', 'Fizz', 'Buzz', '1946', 'Fizz', '1948', '1949', 'FizzBuzz', '1951', '1952', 'Fizz', '1954', 'Buzz', 'Fizz', '1957', '1958', 'Fizz', 'Buzz', '1961', 'Fizz', '1963', '1964', 'FizzBuzz', '1966', '1967', 'Fizz', '1969', 'Buzz', 'Fizz', '1972', '1973', 'Fizz', 'Buzz', '1976', 'Fizz', '1978', '1979', 'FizzBuzz', '1981', '1982', 'Fizz', '1984', 'Buzz', 'Fizz', '1987', '1988', 'Fizz', 'Buzz', '1991', 'Fizz', '1993', '1994', 'FizzBuzz', '1996', '1997', 'Fizz', '1999', 'Buzz', 'Fizz', '2002', '2003', 'Fizz', 'Buzz', '2006', 'Fizz', '2008', '2009', 'FizzBuzz', '2011', '2012', 'Fizz', '2014', 'Buzz', 'Fizz', '2017', '2018', 'Fizz', 'Buzz', '2021', 'Fizz', '2023', '2024', 'FizzBuzz', '2026', '2027', 'Fizz', '2029', 'Buzz', 'Fizz', '2032', '2033', 'Fizz', 'Buzz', '2036', 'Fizz', '2038', '2039', 'FizzBuzz', '2041', '2042', 'Fizz', '2044', 'Buzz', 'Fizz', '2047', '2048']\n assert candidate(n = 999) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz', '751', '752', 'Fizz', '754', 'Buzz', 'Fizz', '757', '758', 'Fizz', 'Buzz', '761', 'Fizz', '763', '764', 'FizzBuzz', '766', '767', 'Fizz', '769', 'Buzz', 'Fizz', '772', '773', 'Fizz', 'Buzz', '776', 'Fizz', '778', '779', 'FizzBuzz', '781', '782', 'Fizz', '784', 'Buzz', 'Fizz', '787', '788', 'Fizz', 'Buzz', '791', 'Fizz', '793', '794', 'FizzBuzz', '796', '797', 'Fizz', '799', 'Buzz', 'Fizz', '802', '803', 'Fizz', 'Buzz', '806', 'Fizz', '808', '809', 'FizzBuzz', '811', '812', 'Fizz', '814', 'Buzz', 'Fizz', '817', '818', 'Fizz', 'Buzz', '821', 'Fizz', '823', '824', 'FizzBuzz', '826', '827', 'Fizz', '829', 'Buzz', 'Fizz', '832', '833', 'Fizz', 'Buzz', '836', 'Fizz', '838', '839', 'FizzBuzz', '841', '842', 'Fizz', '844', 'Buzz', 'Fizz', '847', '848', 'Fizz', 'Buzz', '851', 'Fizz', '853', '854', 'FizzBuzz', '856', '857', 'Fizz', '859', 'Buzz', 'Fizz', '862', '863', 'Fizz', 'Buzz', '866', 'Fizz', '868', '869', 'FizzBuzz', '871', '872', 'Fizz', '874', 'Buzz', 'Fizz', '877', '878', 'Fizz', 'Buzz', '881', 'Fizz', '883', '884', 'FizzBuzz', '886', '887', 'Fizz', '889', 'Buzz', 'Fizz', '892', '893', 'Fizz', 'Buzz', '896', 'Fizz', '898', '899', 'FizzBuzz', '901', '902', 'Fizz', '904', 'Buzz', 'Fizz', '907', '908', 'Fizz', 'Buzz', '911', 'Fizz', '913', '914', 'FizzBuzz', '916', '917', 'Fizz', '919', 'Buzz', 'Fizz', '922', '923', 'Fizz', 'Buzz', '926', 'Fizz', '928', '929', 'FizzBuzz', '931', '932', 'Fizz', '934', 'Buzz', 'Fizz', '937', '938', 'Fizz', 'Buzz', '941', 'Fizz', '943', '944', 'FizzBuzz', '946', '947', 'Fizz', '949', 'Buzz', 'Fizz', '952', '953', 'Fizz', 'Buzz', '956', 'Fizz', '958', '959', 'FizzBuzz', '961', '962', 'Fizz', '964', 'Buzz', 'Fizz', '967', '968', 'Fizz', 'Buzz', '971', 'Fizz', '973', '974', 'FizzBuzz', '976', '977', 'Fizz', '979', 'Buzz', 'Fizz', '982', '983', 'Fizz', 'Buzz', '986', 'Fizz', '988', '989', 'FizzBuzz', '991', '992', 'Fizz', '994', 'Buzz', 'Fizz', '997', '998', 'Fizz']\n assert candidate(n = 35) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz']\n assert candidate(n = 347) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347']\n assert candidate(n = 75) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz']\n assert candidate(n = 256) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256']\n assert candidate(n = 20) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz']\n assert candidate(n = 81) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz']\n assert candidate(n = 150) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz']\n assert candidate(n = 2500) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', 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'FizzBuzz', '2026', '2027', 'Fizz', '2029', 'Buzz', 'Fizz', '2032', '2033', 'Fizz', 'Buzz', '2036', 'Fizz', '2038', '2039', 'FizzBuzz', '2041', '2042', 'Fizz', '2044', 'Buzz', 'Fizz', '2047', '2048', 'Fizz', 'Buzz', '2051', 'Fizz', '2053', '2054', 'FizzBuzz', '2056', '2057', 'Fizz', '2059', 'Buzz', 'Fizz', '2062', '2063', 'Fizz', 'Buzz', '2066', 'Fizz', '2068', '2069', 'FizzBuzz', '2071', '2072', 'Fizz', '2074', 'Buzz', 'Fizz', '2077', '2078', 'Fizz', 'Buzz', '2081', 'Fizz', '2083', '2084', 'FizzBuzz', '2086', '2087', 'Fizz', '2089', 'Buzz', 'Fizz', '2092', '2093', 'Fizz', 'Buzz', '2096', 'Fizz', '2098', '2099', 'FizzBuzz', '2101', '2102', 'Fizz', '2104', 'Buzz', 'Fizz', '2107', '2108', 'Fizz', 'Buzz', '2111', 'Fizz', '2113', '2114', 'FizzBuzz', '2116', '2117', 'Fizz', '2119', 'Buzz', 'Fizz', '2122', '2123', 'Fizz', 'Buzz', '2126', 'Fizz', '2128', '2129', 'FizzBuzz', '2131', '2132', 'Fizz', '2134', 'Buzz', 'Fizz', '2137', '2138', 'Fizz', 'Buzz', '2141', 'Fizz', '2143', '2144', 'FizzBuzz', '2146', '2147', 'Fizz', '2149', 'Buzz', 'Fizz', '2152', '2153', 'Fizz', 'Buzz', '2156', 'Fizz', '2158', '2159', 'FizzBuzz', '2161', '2162', 'Fizz', '2164', 'Buzz', 'Fizz', '2167', '2168', 'Fizz', 'Buzz', '2171', 'Fizz', '2173', '2174', 'FizzBuzz', '2176', '2177', 'Fizz', '2179', 'Buzz', 'Fizz', '2182', '2183', 'Fizz', 'Buzz', '2186', 'Fizz', '2188', '2189', 'FizzBuzz', '2191', '2192', 'Fizz', '2194', 'Buzz', 'Fizz', '2197', '2198', 'Fizz', 'Buzz', '2201', 'Fizz', '2203', '2204', 'FizzBuzz', '2206', '2207', 'Fizz', '2209', 'Buzz', 'Fizz', '2212', '2213', 'Fizz', 'Buzz', '2216', 'Fizz', '2218', '2219', 'FizzBuzz', '2221', '2222', 'Fizz', '2224', 'Buzz', 'Fizz', '2227', '2228', 'Fizz', 'Buzz', '2231', 'Fizz', '2233', '2234', 'FizzBuzz', '2236', '2237', 'Fizz', '2239', 'Buzz', 'Fizz', '2242', '2243', 'Fizz', 'Buzz', '2246', 'Fizz', '2248', '2249', 'FizzBuzz', '2251', '2252', 'Fizz', '2254', 'Buzz', 'Fizz', '2257', '2258', 'Fizz', 'Buzz', '2261', 'Fizz', '2263', '2264', 'FizzBuzz', '2266', '2267', 'Fizz', '2269', 'Buzz', 'Fizz', '2272', '2273', 'Fizz', 'Buzz', '2276', 'Fizz', '2278', '2279', 'FizzBuzz', '2281', '2282', 'Fizz', '2284', 'Buzz', 'Fizz', '2287', '2288', 'Fizz', 'Buzz', '2291', 'Fizz', '2293', '2294', 'FizzBuzz', '2296', '2297', 'Fizz', '2299', 'Buzz', 'Fizz', '2302', '2303', 'Fizz', 'Buzz', '2306', 'Fizz', '2308', '2309', 'FizzBuzz', '2311', '2312', 'Fizz', '2314', 'Buzz', 'Fizz', '2317', '2318', 'Fizz', 'Buzz', '2321', 'Fizz', '2323', '2324', 'FizzBuzz', '2326', '2327', 'Fizz', '2329', 'Buzz', 'Fizz', '2332', '2333', 'Fizz', 'Buzz', '2336', 'Fizz', '2338', '2339', 'FizzBuzz', '2341', '2342', 'Fizz', '2344', 'Buzz', 'Fizz', '2347', '2348', 'Fizz', 'Buzz', '2351', 'Fizz', '2353', '2354', 'FizzBuzz', '2356', '2357', 'Fizz', '2359', 'Buzz', 'Fizz', '2362', '2363', 'Fizz', 'Buzz', '2366', 'Fizz', '2368', '2369', 'FizzBuzz', '2371', '2372', 'Fizz', '2374', 'Buzz', 'Fizz', '2377', '2378', 'Fizz', 'Buzz', '2381', 'Fizz', '2383', '2384', 'FizzBuzz', '2386', '2387', 'Fizz', '2389', 'Buzz', 'Fizz', '2392', '2393', 'Fizz', 'Buzz', '2396', 'Fizz', '2398', '2399', 'FizzBuzz', '2401', '2402', 'Fizz', '2404', 'Buzz', 'Fizz', '2407', '2408', 'Fizz', 'Buzz', '2411', 'Fizz', '2413', '2414', 'FizzBuzz', '2416', '2417', 'Fizz', '2419', 'Buzz', 'Fizz', '2422', '2423', 'Fizz', 'Buzz', '2426', 'Fizz', '2428', '2429', 'FizzBuzz', '2431', '2432', 'Fizz', '2434', 'Buzz', 'Fizz', '2437', '2438', 'Fizz', 'Buzz', '2441', 'Fizz', '2443', '2444', 'FizzBuzz', '2446', '2447', 'Fizz', '2449', 'Buzz', 'Fizz', '2452', '2453', 'Fizz', 'Buzz', '2456', 'Fizz', '2458', '2459', 'FizzBuzz', '2461', '2462', 'Fizz', '2464', 'Buzz', 'Fizz', '2467', '2468', 'Fizz', 'Buzz', '2471', 'Fizz', '2473', '2474', 'FizzBuzz', '2476', '2477', 'Fizz', '2479', 'Buzz', 'Fizz', '2482', '2483', 'Fizz', 'Buzz', '2486', 'Fizz', '2488', '2489', 'FizzBuzz', '2491', '2492', 'Fizz', '2494', 'Buzz', 'Fizz', '2497', '2498', 'Fizz', 'Buzz']\n assert candidate(n = 200) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz']\n assert candidate(n = 83) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83']\n assert candidate(n = 6) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz']\n assert candidate(n = 120) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz']\n assert candidate(n = 750) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz', '106', '107', 'Fizz', '109', 'Buzz', 'Fizz', '112', '113', 'Fizz', 'Buzz', '116', 'Fizz', '118', '119', 'FizzBuzz', '121', '122', 'Fizz', '124', 'Buzz', 'Fizz', '127', '128', 'Fizz', 'Buzz', '131', 'Fizz', '133', '134', 'FizzBuzz', '136', '137', 'Fizz', '139', 'Buzz', 'Fizz', '142', '143', 'Fizz', 'Buzz', '146', 'Fizz', '148', '149', 'FizzBuzz', '151', '152', 'Fizz', '154', 'Buzz', 'Fizz', '157', '158', 'Fizz', 'Buzz', '161', 'Fizz', '163', '164', 'FizzBuzz', '166', '167', 'Fizz', '169', 'Buzz', 'Fizz', '172', '173', 'Fizz', 'Buzz', '176', 'Fizz', '178', '179', 'FizzBuzz', '181', '182', 'Fizz', '184', 'Buzz', 'Fizz', '187', '188', 'Fizz', 'Buzz', '191', 'Fizz', '193', '194', 'FizzBuzz', '196', '197', 'Fizz', '199', 'Buzz', 'Fizz', '202', '203', 'Fizz', 'Buzz', '206', 'Fizz', '208', '209', 'FizzBuzz', '211', '212', 'Fizz', '214', 'Buzz', 'Fizz', '217', '218', 'Fizz', 'Buzz', '221', 'Fizz', '223', '224', 'FizzBuzz', '226', '227', 'Fizz', '229', 'Buzz', 'Fizz', '232', '233', 'Fizz', 'Buzz', '236', 'Fizz', '238', '239', 'FizzBuzz', '241', '242', 'Fizz', '244', 'Buzz', 'Fizz', '247', '248', 'Fizz', 'Buzz', '251', 'Fizz', '253', '254', 'FizzBuzz', '256', '257', 'Fizz', '259', 'Buzz', 'Fizz', '262', '263', 'Fizz', 'Buzz', '266', 'Fizz', '268', '269', 'FizzBuzz', '271', '272', 'Fizz', '274', 'Buzz', 'Fizz', '277', '278', 'Fizz', 'Buzz', '281', 'Fizz', '283', '284', 'FizzBuzz', '286', '287', 'Fizz', '289', 'Buzz', 'Fizz', '292', '293', 'Fizz', 'Buzz', '296', 'Fizz', '298', '299', 'FizzBuzz', '301', '302', 'Fizz', '304', 'Buzz', 'Fizz', '307', '308', 'Fizz', 'Buzz', '311', 'Fizz', '313', '314', 'FizzBuzz', '316', '317', 'Fizz', '319', 'Buzz', 'Fizz', '322', '323', 'Fizz', 'Buzz', '326', 'Fizz', '328', '329', 'FizzBuzz', '331', '332', 'Fizz', '334', 'Buzz', 'Fizz', '337', '338', 'Fizz', 'Buzz', '341', 'Fizz', '343', '344', 'FizzBuzz', '346', '347', 'Fizz', '349', 'Buzz', 'Fizz', '352', '353', 'Fizz', 'Buzz', '356', 'Fizz', '358', '359', 'FizzBuzz', '361', '362', 'Fizz', '364', 'Buzz', 'Fizz', '367', '368', 'Fizz', 'Buzz', '371', 'Fizz', '373', '374', 'FizzBuzz', '376', '377', 'Fizz', '379', 'Buzz', 'Fizz', '382', '383', 'Fizz', 'Buzz', '386', 'Fizz', '388', '389', 'FizzBuzz', '391', '392', 'Fizz', '394', 'Buzz', 'Fizz', '397', '398', 'Fizz', 'Buzz', '401', 'Fizz', '403', '404', 'FizzBuzz', '406', '407', 'Fizz', '409', 'Buzz', 'Fizz', '412', '413', 'Fizz', 'Buzz', '416', 'Fizz', '418', '419', 'FizzBuzz', '421', '422', 'Fizz', '424', 'Buzz', 'Fizz', '427', '428', 'Fizz', 'Buzz', '431', 'Fizz', '433', '434', 'FizzBuzz', '436', '437', 'Fizz', '439', 'Buzz', 'Fizz', '442', '443', 'Fizz', 'Buzz', '446', 'Fizz', '448', '449', 'FizzBuzz', '451', '452', 'Fizz', '454', 'Buzz', 'Fizz', '457', '458', 'Fizz', 'Buzz', '461', 'Fizz', '463', '464', 'FizzBuzz', '466', '467', 'Fizz', '469', 'Buzz', 'Fizz', '472', '473', 'Fizz', 'Buzz', '476', 'Fizz', '478', '479', 'FizzBuzz', '481', '482', 'Fizz', '484', 'Buzz', 'Fizz', '487', '488', 'Fizz', 'Buzz', '491', 'Fizz', '493', '494', 'FizzBuzz', '496', '497', 'Fizz', '499', 'Buzz', 'Fizz', '502', '503', 'Fizz', 'Buzz', '506', 'Fizz', '508', '509', 'FizzBuzz', '511', '512', 'Fizz', '514', 'Buzz', 'Fizz', '517', '518', 'Fizz', 'Buzz', '521', 'Fizz', '523', '524', 'FizzBuzz', '526', '527', 'Fizz', '529', 'Buzz', 'Fizz', '532', '533', 'Fizz', 'Buzz', '536', 'Fizz', '538', '539', 'FizzBuzz', '541', '542', 'Fizz', '544', 'Buzz', 'Fizz', '547', '548', 'Fizz', 'Buzz', '551', 'Fizz', '553', '554', 'FizzBuzz', '556', '557', 'Fizz', '559', 'Buzz', 'Fizz', '562', '563', 'Fizz', 'Buzz', '566', 'Fizz', '568', '569', 'FizzBuzz', '571', '572', 'Fizz', '574', 'Buzz', 'Fizz', '577', '578', 'Fizz', 'Buzz', '581', 'Fizz', '583', '584', 'FizzBuzz', '586', '587', 'Fizz', '589', 'Buzz', 'Fizz', '592', '593', 'Fizz', 'Buzz', '596', 'Fizz', '598', '599', 'FizzBuzz', '601', '602', 'Fizz', '604', 'Buzz', 'Fizz', '607', '608', 'Fizz', 'Buzz', '611', 'Fizz', '613', '614', 'FizzBuzz', '616', '617', 'Fizz', '619', 'Buzz', 'Fizz', '622', '623', 'Fizz', 'Buzz', '626', 'Fizz', '628', '629', 'FizzBuzz', '631', '632', 'Fizz', '634', 'Buzz', 'Fizz', '637', '638', 'Fizz', 'Buzz', '641', 'Fizz', '643', '644', 'FizzBuzz', '646', '647', 'Fizz', '649', 'Buzz', 'Fizz', '652', '653', 'Fizz', 'Buzz', '656', 'Fizz', '658', '659', 'FizzBuzz', '661', '662', 'Fizz', '664', 'Buzz', 'Fizz', '667', '668', 'Fizz', 'Buzz', '671', 'Fizz', '673', '674', 'FizzBuzz', '676', '677', 'Fizz', '679', 'Buzz', 'Fizz', '682', '683', 'Fizz', 'Buzz', '686', 'Fizz', '688', '689', 'FizzBuzz', '691', '692', 'Fizz', '694', 'Buzz', 'Fizz', '697', '698', 'Fizz', 'Buzz', '701', 'Fizz', '703', '704', 'FizzBuzz', '706', '707', 'Fizz', '709', 'Buzz', 'Fizz', '712', '713', 'Fizz', 'Buzz', '716', 'Fizz', '718', '719', 'FizzBuzz', '721', '722', 'Fizz', '724', 'Buzz', 'Fizz', '727', '728', 'Fizz', 'Buzz', '731', 'Fizz', '733', '734', 'FizzBuzz', '736', '737', 'Fizz', '739', 'Buzz', 'Fizz', '742', '743', 'Fizz', 'Buzz', '746', 'Fizz', '748', '749', 'FizzBuzz']\n assert candidate(n = 105) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz', '56', 'Fizz', '58', '59', 'FizzBuzz', '61', '62', 'Fizz', '64', 'Buzz', 'Fizz', '67', '68', 'Fizz', 'Buzz', '71', 'Fizz', '73', '74', 'FizzBuzz', '76', '77', 'Fizz', '79', 'Buzz', 'Fizz', '82', '83', 'Fizz', 'Buzz', '86', 'Fizz', '88', '89', 'FizzBuzz', '91', '92', 'Fizz', '94', 'Buzz', 'Fizz', '97', '98', 'Fizz', 'Buzz', '101', 'Fizz', '103', '104', 'FizzBuzz']\n assert candidate(n = 55) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz', '26', 'Fizz', '28', '29', 'FizzBuzz', '31', '32', 'Fizz', '34', 'Buzz', 'Fizz', '37', '38', 'Fizz', 'Buzz', '41', 'Fizz', '43', '44', 'FizzBuzz', '46', '47', 'Fizz', '49', 'Buzz', 'Fizz', '52', '53', 'Fizz', 'Buzz']\n assert candidate(n = 10) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz']\n assert candidate(n = 25) == ['1', '2', 'Fizz', '4', 'Buzz', 'Fizz', '7', '8', 'Fizz', 'Buzz', '11', 'Fizz', '13', '14', 'FizzBuzz', '16', '17', 'Fizz', '19', 'Buzz', 'Fizz', '22', '23', 'Fizz', 'Buzz']\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().fizzBuzz", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var fizzBuzz = function(n) {", "container": null, "callable": "fizzBuzz", "parameters": [{"name": "n", "type": "number"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 413, "task_id": "arithmetic-slices", "difficulty": "Medium", "problem_description": "An integer array is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.\n\nFor example, [1,3,5,7,9], [7,7,7,7], and [3,-1,-5,-9] are arithmetic sequences.\n\nGiven an integer array nums, return the number of arithmetic subarrays of nums.\nA subarray is a contiguous subsequence of the array.\n \nExample 1:\n\nInput: nums = [1,2,3,4]\nOutput: 3\nExplanation: We have 3 arithmetic slices in nums: [1, 2, 3], [2, 3, 4] and [1,2,3,4] itself.\n\nExample 2:\n\nInput: nums = [1]\nOutput: 0\n\n \nConstraints:\n\n1 <= nums.length <= 5000\n-1000 <= nums[i] <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 36\n assert candidate(nums = [1, 2, 4, 5, 6, 7]) == 3\n assert candidate(nums = [3, -1, -5, -9]) == 3\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 36\n assert candidate(nums = [1, 3, 5, 7, 9]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 36\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [10, 7, 4, 3, 2, 1]) == 4\n assert candidate(nums = [1, 2, 3, 4]) == 3\n assert candidate(nums = [7, 7, 7, 7]) == 3\n assert candidate(nums = [10, 7, 7, 7, 7, 7, 10]) == 6\n assert candidate(nums = [3, -1, -5, -9]) == 3\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 36\n assert candidate(nums = [2]) == 0\n assert candidate(nums = [5, 5, 5, 5, 5]) == 6\n assert candidate(nums = [1, 3, 5, 7, 9]) == 6\n assert candidate(nums = [1, 2, 3, 4, 5]) == 6\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13]) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 28\n assert candidate(nums = [1, 2, 2, 3]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1]) == 6\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6]) == 6\n assert candidate(nums = [1, 2, 3, 5, 7, 9]) == 4\n assert candidate(nums = [1, 2]) == 0\n assert candidate(nums = [1, 2, 4, 5, 6, 7, 8]) == 6\n assert candidate(nums = [7, 7, 7, 7]) == 3\n assert candidate(nums = [1, 2, 3, 8, 9, 10]) == 2\n assert candidate(nums = [0, 1, 2, 3, 6, 9, 12, 15, 18, 21]) == 18\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 29\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15]) == 21\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]) == 1\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15]) == 16\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1, -1]) == 25\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35]) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 7, 9, 11, 13, 15]) == 16\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 36\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 36\n assert candidate(nums = [1, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 45\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 0\n assert candidate(nums = [10, 5, 0, -5, -10, -15, -20]) == 15\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70]) == 78\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 171\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 29\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 72\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21]) == 28\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33]) == 45\n assert candidate(nums = [10, 5, 0, -5, -10, -15, -20, -25]) == 21\n assert candidate(nums = [10, 11, 12, 10, 11, 12, 14, 16, 18, 20]) == 8\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3]) == 18\n assert candidate(nums = [1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15]) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 91\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 171\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5]) == 28\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 36\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 406\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50]) == 28\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]) == 406\n assert candidate(nums = [1, 2, 3, 4, 2, 4, 6, 8, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -8, -6, -4, -2]) == 60\n assert candidate(nums = [1, 3, 5, 7, 9, 12, 15, 18, 21, 24]) == 16\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23]) == 36\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 3, 2, 1, 2, 3, 4, 5, 6]) == 17\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 72\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10]) == 10\n assert candidate(nums = [10, 20, 30, 20, 10, 20, 30, 20, 10]) == 4\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5]) == 15\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 4, 5, 6, 7, 8]) == 16\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 276\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17]) == 22\n assert candidate(nums = [1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 5, 6]) == 9\n assert candidate(nums = [2, 4, 6, 8, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 42\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 91\n assert candidate(nums = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55]) == 1\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 36\n assert candidate(nums = [100, 200, 300, 200, 100, 200, 300, 400]) == 5\n assert candidate(nums = [10, 20, 30, 40, 50, 40, 30, 20, 10, 0, -10]) == 21\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200]) == 55\n assert candidate(nums = [1, 2, 3, 4, 2, 4, 6, 8, 10, 12]) == 13\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 0\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 92\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 36\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 91\n assert candidate(nums = [1, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20]) == 1\n assert candidate(nums = [10, 20, 30, 40, 50, 40, 30, 20, 10, 0, -10, -20, -30]) == 34\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45]) == 0\n assert candidate(nums = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991]) == 36\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900]) == 28\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 91\n assert candidate(nums = [7, 7, 7, 7, 7, 8, 9, 10, 11, 12]) == 16\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 141\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 36\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1, 0, -1, -2, -3]) == 21\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1, -1, -3, -5, -7]) == 46\n assert candidate(nums = [1, 2, 3, 4, 3, 3, 3, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 43\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 171\n assert candidate(nums = [1, 3, 5, 6, 8, 10, 12, 14, 16, 18]) == 16\n assert candidate(nums = [1000, 999, 998, 997, 996, 995, 994, 993, 992, 991]) == 36\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 812\n assert candidate(nums = [3, -1, -5, -9, -13, -17, -21, -25, -29, -33]) == 36\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 406\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 45\n assert candidate(nums = [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 78\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22]) == 45\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 36\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 91\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1, 2, 3, 4, 5]) == 13\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 36\n assert candidate(nums = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 45\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 276\n assert candidate(nums = [10, 5, 0, -5, -10, -15, -20, -25]) == 21\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 36\n assert candidate(nums = [5, 5, 5, 4, 4, 4, 5, 5, 5, 6, 6, 6]) == 4\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80]) == 105\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6]) == 120\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17]) == 22\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 91\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 36\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3]) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 28\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15]) == 21\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 171\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75]) == 91\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 91\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 36\n assert candidate(nums = [10, 20, 30, 40, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40]) == 42\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 91\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130]) == 66\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 171\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9]) == 18\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]) == 55\n assert candidate(nums = [1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10]) == 12\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28]) == 78\n assert candidate(nums = [1, 3, 5, 7, 9, 12, 15, 18, 21, 24]) == 16\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 78\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]) == 4\n assert candidate(nums = [1, 2, 3, 2, 1, 0, -1, -2, -3, -2, -1]) == 17\n assert candidate(nums = [-10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40]) == 45\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1, -1, -3, -5, -7, -9]) == 55\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == 171\n assert candidate(nums = [5, 7, 9, 11, 13, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10]) == 51\n assert candidate(nums = [1, 2, 4, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 45\n assert candidate(nums = [1, 1, 1, 1, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9]) == 18\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1770\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 171\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3]) == 30\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28]) == 36\n assert candidate(nums = [2, 5, 8, 11, 14, 17, 20, 23, 26, 29]) == 36\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 36\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18]) == 28\n assert candidate(nums = [3, 1, -1, -3, -5, -7, -9, -11]) == 21\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 36\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 36\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 36\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27]) == 55\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10, 11, 12]) == 17\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 45\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4]) == 75\n assert candidate(nums = [7, 7, 7, 8, 9, 10, 11, 12, 13, 14]) == 22\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 35\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4]) == 15\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == 0\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5]) == 12\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 153\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7]) == 7\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 903\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 36\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55]) == 1\n assert candidate(nums = [3, -3, -9, -15, -21, -27, -33, -39, -45, -51, -57, -63, -69, -75, -81]) == 91\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().numberOfArithmeticSlices", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numberOfArithmeticSlices = function(nums) {", "container": null, "callable": "numberOfArithmeticSlices", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 414, "task_id": "third-maximum-number", "difficulty": "Easy", "problem_description": "Given an integer array nums, return the third distinct maximum number in this array. If the third maximum does not exist, return the maximum number.\n \nExample 1:\n\nInput: nums = [3,2,1]\nOutput: 1\nExplanation:\nThe first distinct maximum is 3.\nThe second distinct maximum is 2.\nThe third distinct maximum is 1.\n\nExample 2:\n\nInput: nums = [1,2]\nOutput: 2\nExplanation:\nThe first distinct maximum is 2.\nThe second distinct maximum is 1.\nThe third distinct maximum does not exist, so the maximum (2) is returned instead.\n\nExample 3:\n\nInput: nums = [2,2,3,1]\nOutput: 1\nExplanation:\nThe first distinct maximum is 3.\nThe second distinct maximum is 2 (both 2's are counted together since they have the same value).\nThe third distinct maximum is 1.\n\n \nConstraints:\n\n1 <= nums.length <= 104\n-231 <= nums[i] <= 231 - 1\n\n \nFollow up: Can you find an O(n) solution?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [10, 10, 10, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 3\n assert candidate(nums = [1, 2, -2147483648]) == -2147483648\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 8\n assert candidate(nums = [1, 2, 2, 3, 3, 4]) == 2\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [2, 2, 3, 1]) == 1\n assert candidate(nums = [1000000000, 1000000000, 1000000000]) == 1000000000\n assert candidate(nums = [5, 5, 5, 5]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5]) == 3\n assert candidate(nums = [1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [-2147483648, 1, 2]) == -2147483648\n assert candidate(nums = [1, 2, 2, 5, 3, 5]) == 2\n assert candidate(nums = [5, 2, 4, 1, 3]) == 3\n assert candidate(nums = [2, 2, 3, 1, 4]) == 2\n assert candidate(nums = [3, 3, 3, 3, 2, 2, 1]) == 1\n assert candidate(nums = [3, 2, 1]) == 1\n assert candidate(nums = [2, 2, 3, 3, 3, 1, 1]) == 1\n assert candidate(nums = [5, 2, 2]) == 5\n assert candidate(nums = [1, 2, 2, 3, 4]) == 2\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1]) == 1000000000\n assert candidate(nums = [1, 2]) == 2\n assert candidate(nums = [2, 3, 1, 4, 5]) == 3\n assert candidate(nums = [5, 2, 4, 1, 3, 3, 2, 4, 5]) == 3\n assert candidate(nums = [1000000, 999999, 999998]) == 999998\n assert candidate(nums = [-1, -2, -3]) == -3\n assert candidate(nums = [2147483647, -2147483648, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 9\n assert candidate(nums = [3, 3, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, -1, -1, -1, -2, -2, -2]) == 1\n assert candidate(nums = [-2147483648, 2147483647, 0]) == -2147483648\n assert candidate(nums = [-2147483648, 2147483647, 0, -1, 1]) == 0\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10]) == 8\n assert candidate(nums = [-2147483648, 2147483647, 0, 1, -1]) == 0\n assert candidate(nums = [5, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1]) == 3\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3]) == 1\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 13\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 3\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995]) == 999999998\n assert candidate(nums = [-2147483648, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 7\n assert candidate(nums = [3, 3, 2, 2, 1, 1, 0, 0, -1, -1, -2, -2, -3, -3]) == 1\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 1000000000\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 8\n assert candidate(nums = [5, 1, 5, 2, 5, 3, 5, 4]) == 3\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 3\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [1000000000, 1000000001, 1000000002]) == 1000000000\n assert candidate(nums = [-1000000000, -999999999, -999999998, -999999997, -999999996, -999999995, -999999994, -999999993, -999999992, -999999991]) == -999999993\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 999999999, 999999999, 999999998]) == 999999998\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 13\n assert candidate(nums = [5, 1, 5, 2, 5, 3, 5, 4, 5, 5]) == 3\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [7, 7, 7, 8, 8, 9]) == 7\n assert candidate(nums = [-2147483648, 0, 2147483647]) == -2147483648\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 7\n assert candidate(nums = [-2147483648, 2147483647, -2147483648, 2147483647, 0]) == -2147483648\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2]) == 3\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 3\n assert candidate(nums = [1, 2, 2]) == 2\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 8\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9]) == 7\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 8\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 3\n assert candidate(nums = [5, 2, 2, 3, 1, 4, 4, 4, 4, 4]) == 3\n assert candidate(nums = [10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0, -1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -10, -10]) == 8\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11]) == 9\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 7\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6]) == 4\n assert candidate(nums = [1, 1000000000, -1000000000, 500000000, -500000000, 250000000, -250000000, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 250000000\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1, 2]) == 1\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991]) == 999999998\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 23\n assert candidate(nums = [10, 10, 10, 9, 9, 9, 8, 8, 8, 7, 7, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == 38\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 18\n assert candidate(nums = [10, 20, 30, 20, 10, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30]) == 80\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 28\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [100, 100, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50]) == 98\n assert candidate(nums = [10, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 8\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 8\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 2\n assert candidate(nums = [1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 3\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6]) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 13\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 7\n assert candidate(nums = [1, 2, 3, 1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005, 1000000006]) == 1000000004\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 2\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == 8\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8]) == 6\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 18\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]) == 2\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 500000000, -500000000, 250000000, -250000000, 0]) == 250000000\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == 48\n assert candidate(nums = [1, 1000000000, 2, 999999999, 3, 999999998, 4, 999999997, 5, 999999996]) == 999999998\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 8\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90]) == 80\n assert candidate(nums = [10, 10, 10, 9, 9, 9, 8, 8, 8, 7, 7, 7, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, -1, -1, -1]) == 8\n assert candidate(nums = [-1000000000, -1000000001, -1000000002, -1000000003]) == -1000000002\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003]) == 1000000001\n assert candidate(nums = [1000000000, 999999999, 999999998, 1, 2, 3]) == 999999998\n assert candidate(nums = [100, 90, 90, 80, 80, 70, 70, 60, 60, 50]) == 80\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 2\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50]) == 80\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 80\n assert candidate(nums = [5, 3, 5, 2, 5, 3, 3, 9, 0, 123, 123, 123, 456]) == 9\n assert candidate(nums = [1000000000, -1000000000, 0]) == -1000000000\n assert candidate(nums = [100, 90, 90, 80, 80, 80, 70, 60, 50, 40]) == 80\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7]) == 5\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == -30\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30]) == 30\n assert candidate(nums = [2, 3, 1, 4, 5, 6, 7, 8, 9, 10]) == 8\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996]) == 999999998\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().thirdMax", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var thirdMax = function(nums) {", "container": null, "callable": "thirdMax", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 415, "task_id": "add-strings", "difficulty": "Easy", "problem_description": "Given two non-negative integers, num1 and num2 represented as string, return the sum of num1 and num2 as a string.\nYou must solve the problem without using any built-in library for handling large integers (such as BigInteger). You must also not convert the inputs to integers directly.\n \nExample 1:\n\nInput: num1 = \"11\", num2 = \"123\"\nOutput: \"134\"\n\nExample 2:\n\nInput: num1 = \"456\", num2 = \"77\"\nOutput: \"533\"\n\nExample 3:\n\nInput: num1 = \"0\", num2 = \"0\"\nOutput: \"0\"\n\n \nConstraints:\n\n1 <= num1.length, num2.length <= 104\nnum1 and num2 consist of only digits.\nnum1 and num2 don't have any leading zeros except for the zero itself.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num1 = \"500\",num2 = \"500\") == \"1000\"\n assert candidate(num1 = \"11\",num2 = \"123\") == \"134\"\n assert candidate(num1 = \"1000\",num2 = \"2000\") == \"3000\"\n assert candidate(num1 = \"10000\",num2 = \"20000\") == \"30000\"\n assert candidate(num1 = \"123456789\",num2 = \"987654321\") == \"1111111110\"\n assert candidate(num1 = \"10\",num2 = \"10\") == \"20\"\n assert candidate(num1 = \"1\",num2 = \"1\") == \"2\"\n assert candidate(num1 = \"111111\",num2 = \"111111\") == \"222222\"\n assert candidate(num1 = \"9999\",num2 = \"1\") == \"10000\"\n assert candidate(num1 = \"456\",num2 = \"77\") == \"533\"\n assert candidate(num1 = \"0\",num2 = \"0\") == \"0\"\n assert candidate(num1 = \"999999999\",num2 = \"1\") == \"1000000000\"\n assert candidate(num1 = \"1111\",num2 = \"1111\") == \"2222\"\n assert candidate(num1 = \"1\",num2 = \"99999\") == \"100000\"\n assert candidate(num1 = \"9876543210\",num2 = \"9876543210\") == \"19753086420\"\n assert candidate(num1 = \"999\",num2 = \"1\") == \"1000\"\n assert candidate(num1 = \"123456789012345678901234567890\",num2 = \"987654321098765432109876543210\") == \"1111111110111111111011111111100\"\n assert candidate(num1 = \"100000000000000000000000000000000000000000000000000\",num2 = \"1\") == \"100000000000000000000000000000000000000000000000001\"\n assert candidate(num1 = \"999999999999999999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"1000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"500000000000000000000000000000\",num2 = \"500000000000000000000000000000\") == \"1000000000000000000000000000000\"\n assert candidate(num1 = \"55555555555555555555\",num2 = \"44444444444444444444\") == \"99999999999999999999\"\n assert candidate(num1 = \"1000000000000000000000000000000\",num2 = \"999999999999999999999999999999\") == \"1999999999999999999999999999999\"\n assert candidate(num1 = \"00000000000000000000000000000000000000000000000000\",num2 = \"00000000000000000000000000000000000000000000000000\") == \"00000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"1000000000\",num2 = \"999999999\") == \"1999999999\"\n assert candidate(num1 = \"0000000000000000000000000000000000000000000000000000000000000000\",num2 = \"0\") == \"0000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"9999999999999999999999999999999\",num2 = \"9999999999999999999999999999999\") == \"19999999999999999999999999999998\"\n assert candidate(num1 = \"100000000000000000000000000000\",num2 = \"200000000000000000000000000000\") == \"300000000000000000000000000000\"\n assert candidate(num1 = \"222222222222222222222222222222222222222222222222222\",num2 = \"777777777777777777777777777777777777777777777777777\") == \"999999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"12345678901234567890\",num2 = \"98765432109876543210\") == \"111111111011111111100\"\n assert candidate(num1 = \"9999999999999999999999999\",num2 = \"1\") == \"10000000000000000000000000\"\n assert candidate(num1 = \"1111111111111111111111111111111111111111111111111111111111111111\",num2 = \"2222222222222222222222222222222222222222222222222222222222222222\") == \"3333333333333333333333333333333333333333333333333333333333333333\"\n assert candidate(num1 = \"11111111111111111111111111111111111111111111111111111111111111111111111111111\",num2 = \"8888888888888888888888888888888888888888888888888888888888888888888888888888\") == \"19999999999999999999999999999999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"999999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"1000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"1\",num2 = \"99999999999999999999999999999999999999999999999999\") == \"100000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"987654321\",num2 = \"123456789\") == \"1111111110\"\n assert candidate(num1 = \"11111111111111111111\",num2 = \"22222222222222222222\") == \"33333333333333333333\"\n assert candidate(num1 = \"50000000000000000000000000000000000000000000000000\",num2 = \"50000000000000000000000000000000000000000000000000\") == \"100000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"10\",num2 = \"999999999999999999999999999999\") == \"1000000000000000000000000000009\"\n assert candidate(num1 = \"100000000000000000000000000000000000000000000000000000000000000000000000000000\",num2 = \"100000000000000000000000000000000000000000000000000000000000000000000000000000\") == \"200000000000000000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"50000000000000000000000000000000000000000000000000000000000000000000000000000\",num2 = \"50000000000000000000000000000000000000000000000000000000000000000000000000000\") == \"100000000000000000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"9999999999999999999999999999999\",num2 = \"1\") == \"10000000000000000000000000000000\"\n assert candidate(num1 = \"5678901234567890\",num2 = \"9876543210987654\") == \"15555444445555544\"\n assert candidate(num1 = \"999999999999999999999999999999999999\",num2 = \"1\") == \"1000000000000000000000000000000000000\"\n assert candidate(num1 = \"1000000000000000000000000000000000000000000000000000000000000000\",num2 = \"1000000000000000000000000000000000000000000000000000000000000000\") == \"2000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"111111111111111111111111111111111111\",num2 = \"222222222222222222222222222222222222\") == \"333333333333333333333333333333333333\"\n assert candidate(num1 = \"111111111111111111111111111111\",num2 = \"222222222222222222222222222222\") == \"333333333333333333333333333333\"\n assert candidate(num1 = \"1234567890\",num2 = \"9876543210\") == \"11111111100\"\n assert candidate(num1 = \"5555555555555555555555555555555555555555555555555555555555555555555555555555\",num2 = \"44444444444444444444444444444444444444444444444444444444444444444444444444444\") == \"49999999999999999999999999999999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"987654321098765432109876543210\",num2 = \"123456789012345678901234567890\") == \"1111111110111111111011111111100\"\n assert candidate(num1 = \"0\",num2 = \"9999999999999999999999999\") == \"9999999999999999999999999\"\n assert candidate(num1 = \"9999999999999999999999999999999999999999999999999\",num2 = \"9999999999999999999999999999999999999999999999999\") == \"19999999999999999999999999999999999999999999999998\"\n assert candidate(num1 = \"2222222222222222222222222222222\",num2 = \"7777777777777777777777777777777\") == \"9999999999999999999999999999999\"\n assert candidate(num1 = \"5\",num2 = \"5\") == \"10\"\n assert candidate(num1 = \"1111111111111111111111111111111\",num2 = \"8888888888888888888888888888888\") == \"9999999999999999999999999999999\"\n assert candidate(num1 = \"10000000000000000000000000000000\",num2 = \"1\") == \"10000000000000000000000000000001\"\n assert candidate(num1 = \"1\",num2 = \"999999999999999999999999999999\") == \"1000000000000000000000000000000\"\n assert candidate(num1 = \"555555555555555555\",num2 = \"444444444444444444\") == \"999999999999999999\"\n assert candidate(num1 = \"10000000000000000000\",num2 = \"1\") == \"10000000000000000001\"\n assert candidate(num1 = \"999999999999999999999999999999999999999999999999999999999999999999999999999\",num2 = \"999999999999999999999999999999999999999999999999999999999999999999999999999\") == \"1999999999999999999999999999999999999999999999999999999999999999999999999998\"\n assert candidate(num1 = \"56789123456789123456789\",num2 = \"432109876543210987654321\") == \"488899000000000111111110\"\n assert candidate(num1 = \"10000000000000000000\",num2 = \"10000000000000000000\") == \"20000000000000000000\"\n assert candidate(num1 = \"1\",num2 = \"0\") == \"1\"\n assert candidate(num1 = \"999999999999999999999999999998\",num2 = \"2\") == \"1000000000000000000000000000000\"\n assert candidate(num1 = \"99999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"100000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"99999999999999999999\",num2 = \"1\") == \"100000000000000000000\"\n assert candidate(num1 = \"0\",num2 = \"999999999999999999\") == \"999999999999999999\"\n assert candidate(num1 = \"111111111111111111111111111111\",num2 = \"111111111111111111111111111111\") == \"222222222222222222222222222222\"\n assert candidate(num1 = \"9999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"10000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"999999999999999999999999999999999999999999999999999999999999999999999999999\",num2 = \"1\") == \"1000000000000000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"4294967295\",num2 = \"1\") == \"4294967296\"\n assert candidate(num1 = \"10000000000000000000000000\",num2 = \"20000000000000000000000000\") == \"30000000000000000000000000\"\n assert candidate(num1 = \"1\",num2 = \"9999999999999999999999999\") == \"10000000000000000000000000\"\n assert candidate(num1 = \"9\",num2 = \"999999999999999999\") == \"1000000000000000008\"\n assert candidate(num1 = \"0\",num2 = \"99999999999999999999999999999999999999999999999999\") == \"99999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"111111111111111111111111111111111111111111111111111\",num2 = \"88888888888888888888888888888888888888888888888888\") == \"199999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"99999999999999999999999999999999999999999999999999\",num2 = \"99999999999999999999999999999999999999999999999999\") == \"199999999999999999999999999999999999999999999999998\"\n assert candidate(num1 = \"1010101010101010101010101010101010101010101010101010101010101010\",num2 = \"1\") == \"1010101010101010101010101010101010101010101010101010101010101011\"\n assert candidate(num1 = \"54321\",num2 = \"678901234567890\") == \"678901234622211\"\n assert candidate(num1 = \"999999999999999999999999999999\",num2 = \"1\") == \"1000000000000000000000000000000\"\n assert candidate(num1 = \"0\",num2 = \"10000000000000000000000000000000\") == \"10000000000000000000000000000000\"\n assert candidate(num1 = \"1\",num2 = \"999999999999999999999999999999999999999999999999999999999999999999999999999\") == \"1000000000000000000000000000000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"999999999999999999\",num2 = \"1\") == \"1000000000000000000\"\n assert candidate(num1 = \"111111111111111111111111111111111111111111111111111111111111111\",num2 = \"222222222222222222222222222222222222222222222222222222222222222\") == \"333333333333333333333333333333333333333333333333333333333333333\"\n assert candidate(num1 = \"1\",num2 = \"9999999999999999999999999999999999999999999999999\") == \"10000000000000000000000000000000000000000000000000\"\n assert candidate(num1 = \"999999999999999999999999999999\",num2 = \"999999999999999999999999999999\") == \"1999999999999999999999999999998\"\n assert candidate(num1 = \"1\",num2 = \"2\") == \"3\"\n assert candidate(num1 = \"11111111111111111111111111111111111111111111111111\",num2 = \"8888888888888888888888888888888888888888888888888\") == \"19999999999999999999999999999999999999999999999999\"\n assert candidate(num1 = \"12345678901234567890123456789012345678901234567890\",num2 = \"98765432109876543210987654321098765432109876543210\") == \"111111111011111111101111111110111111111011111111100\"\n assert candidate(num1 = \"555555555555555555555555555555\",num2 = \"444444444444444444444444444444\") == \"999999999999999999999999999999\"\n assert candidate(num1 = \"55555555555555555555555555555555555555555555555555\",num2 = \"55555555555555555555555555555555555555555555555555\") == \"111111111111111111111111111111111111111111111111110\"\n assert candidate(num1 = \"123456789123456789123456789123456789123456789123456789\",num2 = \"987654321987654321987654321987654321987654321987654321\") == \"1111111111111111111111111111111111111111111111111111110\"\n assert candidate(num1 = \"246802468024680246802468024680\",num2 = \"135791357913579135791357913579\") == \"382593825938259382593825938259\"\n"}, "metadata": {"canonical_parameter_names": ["num1", "num2"], "leetcode_dataset_entry_point": "Solution().addStrings", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var addStrings = function(num1, num2) {", "container": null, "callable": "addStrings", "parameters": [{"name": "num1", "type": "string"}, {"name": "num2", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 416, "task_id": "partition-equal-subset-sum", "difficulty": "Medium", "problem_description": "Given an integer array nums, return true if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or false otherwise.\n \nExample 1:\n\nInput: nums = [1,5,11,5]\nOutput: true\nExplanation: The array can be partitioned as [1, 5, 5] and [11].\n\nExample 2:\n\nInput: nums = [1,2,3,5]\nOutput: false\nExplanation: The array cannot be partitioned into equal sum subsets.\n\n \nConstraints:\n\n1 <= nums.length <= 200\n1 <= nums[i] <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5]) == False\n assert candidate(nums = [1, 5, 11, 5]) == True\n assert candidate(nums = [1, 2, 2, 3]) == True\n assert candidate(nums = [1, 2, 3, 4]) == True\n assert candidate(nums = [2, 2, 3, 3]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7]) == True\n assert candidate(nums = [2, 2, 3, 5]) == False\n assert candidate(nums = [2, 2, 3, 6]) == False\n assert candidate(nums = [1, 2, 3, 5]) == False\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == True\n assert candidate(nums = [99, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(nums = [1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608]) == True\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == True\n assert candidate(nums = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190]) == False\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == False\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == False\n assert candidate(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]) == False\n assert candidate(nums = [100, 200, 300, 400, 500, 500]) == True\n assert candidate(nums = [1, 2, 5, 6, 8, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54]) == False\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [7, 14, 3, 9, 1, 4, 13, 2, 3, 10, 5, 3, 5, 8, 6, 9, 6, 5, 14, 4, 5, 8, 6, 4, 10, 1, 4, 9, 1, 3, 1, 5, 4, 3, 9, 1, 5, 9, 1, 2, 9, 1, 8, 1, 14, 5, 8, 3, 13, 14, 1, 10, 1, 1, 1, 5, 14, 1, 14, 5, 14, 1, 8, 10, 9, 5, 14, 10, 13]) == False\n assert candidate(nums = [5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == False\n assert candidate(nums = [10, 20, 15, 5, 5]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == True\n assert candidate(nums = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == False\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40]) == False\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == False\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]) == True\n assert candidate(nums = [10, 20, 15, 5, 5]) == False\n assert candidate(nums = [15, 10, 20, 30, 50, 50]) == False\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == True\n assert candidate(nums = [8, 15, 3, 7, 15, 16, 9, 16, 8, 15, 7, 13, 16, 3, 14, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == True\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == True\n assert candidate(nums = [3, 3, 3, 3, 10, 5, 5, 5]) == False\n assert candidate(nums = [1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000, 20000, 50000, 100000, 200000, 500000, 1000000, 2000000]) == False\n assert candidate(nums = [23, 13, 2, 16, 21, 5, 14, 11, 7, 9, 4, 18, 3, 6, 8, 10, 12, 15, 17, 20]) == True\n assert candidate(nums = [15, 20, 25, 30, 35, 40, 45, 50, 55, 60]) == False\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]) == True\n assert candidate(nums = [33, 14, 60, 22, 5, 9, 38, 35, 7, 3, 19, 25, 36, 29, 28, 17, 41, 21, 18, 19]) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384]) == False\n assert candidate(nums = [99, 98, 97, 96, 95, 94, 93, 92, 91, 90]) == False\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 16]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == False\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [10, 2, 30, 12, 3, 1]) == False\n assert candidate(nums = [100, 200, 300, 400, 500, 100, 200, 300, 400, 500]) == True\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == True\n assert candidate(nums = [99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99]) == True\n assert candidate(nums = [7, 15, 6, 5, 9, 8, 3, 5, 4, 4, 5, 7, 9, 6, 5, 4, 5, 9, 10, 5]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 100]) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250]) == False\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]) == False\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [4, 4, 4, 4, 4, 4, 4, 4, 4, 4]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == True\n assert candidate(nums = [15, 20, 25, 30, 35, 40, 45, 50]) == True\n assert candidate(nums = [100, 100, 100, 100, 100, 100, 100, 100, 100, 100]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70]) == True\n assert candidate(nums = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == True\n assert candidate(nums = [99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == True\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 55]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == False\n assert candidate(nums = [50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350]) == True\n assert candidate(nums = [42, 39, 27, 27, 38, 29, 37, 29, 43, 42, 27, 26, 28, 38, 37, 29, 30, 29, 39, 26]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == True\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == True\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().canPartition", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canPartition = function(nums) {", "container": null, "callable": "canPartition", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 417, "task_id": "pacific-atlantic-water-flow", "difficulty": "Medium", "problem_description": "There is an m x n rectangular island that borders both the Pacific Ocean and Atlantic Ocean. The Pacific Ocean touches the island's left and top edges, and the Atlantic Ocean touches the island's right and bottom edges.\nThe island is partitioned into a grid of square cells. You are given an m x n integer matrix heights where heights[r][c] represents the height above sea level of the cell at coordinate (r, c).\nThe island receives a lot of rain, and the rain water can flow to neighboring cells directly north, south, east, and west if the neighboring cell's height is less than or equal to the current cell's height. Water can flow from any cell adjacent to an ocean into the ocean.\nReturn a 2D list of grid coordinates result where result[i] = [ri, ci] denotes that rain water can flow from cell (ri, ci) to both the Pacific and Atlantic oceans.\n \nExample 1:\n\n\nInput: heights = [[1,2,2,3,5],[3,2,3,4,4],[2,4,5,3,1],[6,7,1,4,5],[5,1,1,2,4]]\nOutput: [[0,4],[1,3],[1,4],[2,2],[3,0],[3,1],[4,0]]\nExplanation: The following cells can flow to the Pacific and Atlantic oceans, as shown below:\n[0,4]: [0,4] -> Pacific Ocean \n  [0,4] -> Atlantic Ocean\n[1,3]: [1,3] -> [0,3] -> Pacific Ocean \n  [1,3] -> [1,4] -> Atlantic Ocean\n[1,4]: [1,4] -> [1,3] -> [0,3] -> Pacific Ocean \n  [1,4] -> Atlantic Ocean\n[2,2]: [2,2] -> [1,2] -> [0,2] -> Pacific Ocean \n  [2,2] -> [2,3] -> [2,4] -> Atlantic Ocean\n[3,0]: [3,0] -> Pacific Ocean \n  [3,0] -> [4,0] -> Atlantic Ocean\n[3,1]: [3,1] -> [3,0] -> Pacific Ocean \n  [3,1] -> [4,1] -> Atlantic Ocean\n[4,0]: [4,0] -> Pacific Ocean \n [4,0] -> Atlantic Ocean\nNote that there are other possible paths for these cells to flow to the Pacific and Atlantic oceans.\n\nExample 2:\n\nInput: heights = [[1]]\nOutput: [[0,0]]\nExplanation: The water can flow from the only cell to the Pacific and Atlantic oceans.\n\n \nConstraints:\n\nm == heights.length\nn == heights[r].length\n1 <= m, n <= 200\n0 <= heights[r][c] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(heights = [[1, 2, 3, 4, 5], [2, 2, 2, 2, 2], [1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 2, 3, 4, 5]]) == [(0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2, 2, 3, 5], [3, 2, 3, 4, 4], [2, 4, 5, 3, 1], [6, 7, 1, 4, 5], [5, 1, 1, 2, 4]]) == [(0, 4), (1, 3), (1, 4), (2, 2), (3, 0), (3, 1), (4, 0)]\n assert candidate(heights = [[10, 10, 10], [10, 1, 10], [10, 10, 10]]) == [(0, 0), (0, 1), (0, 2), (1, 0), (1, 2), (2, 0), (2, 1), (2, 2)]\n assert candidate(heights = [[1]]) == [(0, 0)]\n assert candidate(heights = [[3, 3, 3, 3, 3], [3, 2, 2, 2, 3], [3, 2, 1, 2, 3], [3, 2, 2, 2, 3], [3, 3, 3, 3, 3]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 4), (2, 0), (2, 4), (3, 0), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2], [2, 3]]) == [(0, 1), (1, 0), (1, 1)]\n assert candidate(heights = [[1, 2, 3, 4, 5], [16, 17, 18, 19, 6], [15, 24, 25, 20, 7], [14, 23, 22, 21, 8], [13, 12, 11, 10, 9]]) == [(0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2, 3], [8, 9, 4], [7, 6, 5]]) == [(0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 1], [1, 2, 3, 3, 3, 2, 1], [1, 2, 3, 4, 3, 2, 1], [1, 2, 3, 3, 3, 2, 1], [1, 2, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9, 10, 11], [5, 6, 7, 8, 9, 10, 11, 12]]) == [(0, 7), (1, 7), (2, 7), (3, 7), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7)]\n assert candidate(heights = [[1, 2, 3], [6, 5, 4], [7, 8, 9]]) == [(0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]\n assert candidate(heights = [[10, 10, 10, 10, 10, 10], [10, 20, 20, 20, 20, 10], [10, 20, 30, 30, 20, 10], [10, 20, 30, 30, 20, 10], [10, 20, 20, 20, 20, 10], [10, 10, 10, 10, 10, 10]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[5, 4, 5, 4, 5], [4, 3, 4, 3, 4], [5, 4, 5, 4, 5], [4, 3, 4, 3, 4], [5, 4, 5, 4, 5]]) == [(0, 4), (4, 0)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [20, 19, 18, 17, 16, 15, 14, 13, 12, 11]]) == [(0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)]\n assert candidate(heights = [[1, 2, 3, 4, 5], [2, 3, 4, 5, 6], [3, 4, 5, 6, 7], [4, 5, 6, 7, 8], [5, 6, 7, 8, 9], [4, 5, 6, 7, 8], [3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5]]) == [(0, 4), (1, 4), (2, 4), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4)]\n assert candidate(heights = [[10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [11, 10, 9, 8, 7, 6, 5, 4, 3, 2], [12, 11, 10, 9, 8, 7, 6, 5, 4, 3], [13, 12, 11, 10, 9, 8, 7, 6, 5, 4], [14, 13, 12, 11, 10, 9, 8, 7, 6, 5], [15, 14, 13, 12, 11, 10, 9, 8, 7, 6], [16, 15, 14, 13, 12, 11, 10, 9, 8, 7], [17, 16, 15, 14, 13, 12, 11, 10, 9, 8], [18, 17, 16, 15, 14, 13, 12, 11, 10, 9], [19, 18, 17, 16, 15, 14, 13, 12, 11, 10]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (5, 9), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7), (6, 8), (6, 9), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (7, 8), (7, 9), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]]) == [(0, 10), (0, 11), (0, 12), (0, 13), (0, 14), (0, 15), (0, 16), (0, 17), (0, 18), (0, 19), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 10), (2, 11), (2, 12), (2, 13), (2, 14), (2, 15), (2, 16), (2, 17), (2, 18), (2, 19), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (4, 13), (4, 14), (4, 15), (4, 16), (4, 17), (4, 18), (4, 19)]\n assert candidate(heights = [[10, 10, 10, 10], [10, 9, 8, 7], [10, 8, 7, 6], [10, 7, 6, 5], [10, 6, 5, 4], [10, 5, 4, 3], [10, 4, 3, 2], [10, 3, 2, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0)]\n assert candidate(heights = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [4, 5, 6, 7, 8], [3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [1, 2, 3, 4, 5]]) == [(0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4)]\n assert candidate(heights = [[1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]) == [(0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9)]\n assert candidate(heights = [[1, 2, 2, 3, 5, 6], [3, 2, 3, 4, 4, 5], [2, 4, 5, 3, 1, 6], [6, 7, 1, 4, 5, 7], [5, 1, 1, 2, 4, 8], [9, 8, 7, 6, 5, 4]]) == [(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 0)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 1], [1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1], [1, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [6, 5, 4], [3, 2, 1]]) == [(0, 2), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (4, 0)]\n assert candidate(heights = [[5, 5, 5, 5, 5], [5, 1, 2, 3, 5], [5, 4, 3, 2, 5], [5, 3, 3, 3, 5], [5, 5, 5, 5, 5]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 4), (2, 0), (2, 4), (3, 0), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60], [61, 62, 63, 64, 65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76, 77, 78, 79, 80], [81, 82, 83, 84, 85, 86, 87, 88, 89, 90], [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]]) == [(0, 9), (1, 9), (2, 9), (3, 9), (4, 9), (5, 9), (6, 9), (7, 9), (8, 9), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9)]\n assert candidate(heights = [[5, 4, 5], [1, 2, 6], [7, 4, 6]]) == [(0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]\n assert candidate(heights = [[3, 3, 3, 3, 3, 3], [3, 0, 0, 0, 0, 3], [3, 0, 9, 8, 0, 3], [3, 0, 7, 6, 0, 3], [3, 0, 0, 0, 0, 3], [3, 3, 3, 3, 3, 3]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 5), (2, 0), (2, 5), (3, 0), (3, 5), (4, 0), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[1, 2, 2, 3, 5, 6, 7], [3, 2, 3, 4, 4, 5, 6], [2, 4, 5, 3, 1, 4, 5], [6, 7, 1, 4, 5, 6, 7], [5, 1, 1, 2, 4, 5, 6], [5, 1, 1, 2, 4, 5, 6]]) == [(0, 6), (1, 6), (2, 2), (3, 0), (3, 1), (4, 0), (5, 0)]\n assert candidate(heights = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [2, 3, 4, 5, 6], [6, 5, 4, 3, 2], [3, 4, 5, 6, 7]]) == [(0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[3, 3, 3, 3, 3, 3], [3, 2, 2, 2, 2, 3], [3, 2, 1, 1, 2, 3], [3, 2, 1, 1, 2, 3], [3, 2, 2, 2, 2, 3], [3, 3, 3, 3, 3, 3]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 5), (2, 0), (2, 5), (3, 0), (3, 5), (4, 0), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[10, 10, 10, 10, 10, 10], [10, 1, 1, 1, 1, 10], [10, 1, 2, 2, 1, 10], [10, 1, 2, 2, 1, 10], [10, 1, 1, 1, 1, 10], [10, 10, 10, 10, 10, 10]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 5), (2, 0), (2, 5), (3, 0), (3, 5), (4, 0), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [19, 17, 15, 13, 11, 9, 7, 5, 3, 1], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]]) == [(0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9)]\n assert candidate(heights = [[10, 20, 10, 20, 10], [20, 30, 20, 30, 20], [10, 20, 10, 20, 10], [20, 30, 20, 30, 20], [10, 20, 10, 20, 10]]) == [(0, 3), (0, 4), (1, 3), (1, 4), (3, 0), (3, 1), (4, 0), (4, 1)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]) == [(0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 1], [1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1], [1, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[1, 2, 2, 1, 2], [2, 2, 2, 2, 2], [2, 2, 1, 2, 2], [1, 2, 2, 1, 2], [2, 2, 2, 2, 2]]) == [(0, 1), (0, 2), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[5, 4, 5], [1, 2, 6], [7, 4, 8], [9, 1, 2], [3, 6, 7], [4, 6, 8]]) == [(0, 2), (1, 2), (2, 2), (4, 1), (4, 2), (5, 0), (5, 1), (5, 2)]\n assert candidate(heights = [[10, 11, 16, 21, 17], [14, 17, 24, 25, 22], [13, 18, 23, 24, 21], [12, 19, 22, 23, 20], [11, 16, 19, 20, 19]]) == [(0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3), (4, 0), (4, 1), (4, 2), (4, 3)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [1, 2, 3, 3, 3, 3, 3, 3, 2, 1], [1, 2, 3, 4, 4, 4, 4, 3, 2, 1], [1, 2, 3, 4, 5, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 6, 5, 4, 3, 1], [1, 2, 3, 4, 5, 5, 4, 3, 2, 1], [1, 2, 3, 4, 4, 4, 4, 3, 2, 1], [1, 2, 3, 3, 3, 3, 3, 3, 2, 1], [1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (5, 9), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7), (6, 8), (6, 9), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (7, 8), (7, 9), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9), (10, 0), (10, 1), (10, 2), (10, 3), (10, 4), (10, 5), (10, 6), (10, 7), (10, 8), (10, 9)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6], [6, 5, 4, 3, 2, 1], [2, 3, 4, 5, 6, 7], [7, 6, 5, 4, 3, 2], [3, 4, 5, 6, 7, 8], [8, 7, 6, 5, 4, 3]]) == [(0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (4, 2), (4, 3), (4, 4), (4, 5), (5, 0), (5, 1), (5, 2)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [1, 2, 3, 3, 3, 3, 3, 3, 2, 1], [1, 2, 3, 4, 4, 4, 4, 3, 2, 1], [1, 2, 3, 4, 5, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 5, 4, 3, 2, 1], [1, 2, 3, 4, 4, 4, 4, 3, 2, 1], [1, 2, 3, 3, 3, 3, 3, 3, 2, 1], [1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (5, 9), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7), (6, 8), (6, 9), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (7, 8), (7, 9), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9)]\n assert candidate(heights = [[1, 5, 5, 5, 5, 5, 5, 5, 5, 5], [2, 3, 4, 5, 5, 5, 5, 5, 5, 5], [2, 2, 3, 4, 5, 5, 5, 5, 5, 5], [2, 2, 2, 3, 4, 5, 5, 5, 5, 5], [2, 2, 2, 2, 3, 4, 5, 5, 5, 5], [2, 2, 2, 2, 2, 3, 4, 5, 5, 5], [2, 2, 2, 2, 2, 2, 3, 4, 5, 5], [2, 2, 2, 2, 2, 2, 2, 3, 4, 5], [2, 2, 2, 2, 2, 2, 2, 2, 3, 4], [2, 2, 2, 2, 2, 2, 2, 2, 2, 3]]) == [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (5, 9), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7), (6, 8), (6, 9), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (7, 8), (7, 9), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9)]\n assert candidate(heights = [[1, 2, 2, 3, 5, 6], [3, 2, 3, 4, 4, 5], [2, 4, 5, 3, 1, 4], [6, 7, 1, 4, 5, 6], [5, 1, 1, 2, 4, 5], [5, 1, 1, 2, 4, 1]]) == [(0, 5), (1, 5), (2, 2), (3, 0), (3, 1), (4, 0), (5, 0)]\n assert candidate(heights = [[1, 2, 2, 3, 4, 5], [2, 3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 8], [4, 5, 6, 7, 8, 9], [5, 6, 7, 8, 9, 10], [6, 7, 8, 9, 10, 11]]) == [(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[1, 2, 3, 4, 5], [10, 9, 8, 7, 6], [11, 12, 13, 14, 15], [20, 19, 18, 17, 16], [21, 22, 23, 24, 25]]) == [(0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]) == [(0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9)]\n assert candidate(heights = [[1, 2, 3, 2, 1], [4, 5, 6, 5, 4], [7, 8, 9, 8, 7], [4, 5, 6, 5, 4], [1, 2, 3, 2, 1]]) == [(0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2)]\n assert candidate(heights = [[5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 1, 1, 1, 5], [5, 1, 2, 2, 2, 1, 5], [5, 1, 2, 3, 2, 1, 5], [5, 1, 2, 2, 2, 1, 5], [5, 1, 1, 1, 1, 1, 5], [5, 5, 5, 5, 5, 5, 5]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (1, 0), (1, 6), (2, 0), (2, 6), (3, 0), (3, 6), (4, 0), (4, 6), (5, 0), (5, 6), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)]\n assert candidate(heights = [[1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [1, 3, 5, 7, 9], [2, 4, 6, 8, 10], [1, 3, 5, 7, 9]]) == [(0, 4), (1, 4), (2, 4), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 2, 2, 3, 5, 6], [3, 2, 3, 4, 4, 5], [2, 4, 5, 3, 1, 2], [6, 7, 1, 4, 5, 3], [5, 1, 1, 2, 4, 1], [4, 3, 2, 1, 1, 1]]) == [(0, 5), (1, 5), (3, 0), (3, 1), (4, 0), (5, 0)]\n assert candidate(heights = [[1, 1, 1, 1, 1], [1, 2, 2, 2, 1], [1, 2, 3, 2, 1], [1, 2, 2, 2, 1], [1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 1], [1, 2, 3, 3, 2, 1], [1, 2, 2, 2, 2, 1], [1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5)]\n assert candidate(heights = [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 1, 1, 1, 1, 1, 1, 1, 1, 5], [5, 1, 2, 2, 2, 2, 2, 2, 1, 5], [5, 1, 2, 3, 3, 3, 3, 2, 1, 5], [5, 1, 2, 3, 4, 4, 3, 2, 1, 5], [5, 1, 2, 3, 4, 5, 4, 3, 2, 5], [5, 1, 2, 3, 4, 4, 3, 2, 1, 5], [5, 1, 2, 3, 3, 3, 3, 2, 1, 5], [5, 1, 2, 2, 2, 2, 2, 2, 1, 5], [5, 1, 1, 1, 1, 1, 1, 1, 1, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 9), (2, 0), (2, 9), (3, 0), (3, 9), (4, 0), (4, 9), (5, 0), (5, 9), (6, 0), (6, 9), (7, 0), (7, 9), (8, 0), (8, 9), (9, 0), (9, 9), (10, 0), (10, 1), (10, 2), (10, 3), (10, 4), (10, 5), (10, 6), (10, 7), (10, 8), (10, 9)]\n assert candidate(heights = [[1, 2, 3], [6, 5, 4], [7, 8, 9], [12, 15, 14], [13, 16, 17]]) == [(0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2)]\n assert candidate(heights = [[1, 2, 2, 3, 5], [3, 2, 3, 4, 4], [2, 4, 8, 3, 1], [6, 7, 1, 4, 5], [5, 1, 1, 2, 4], [4, 3, 2, 1, 0]]) == [(0, 4), (1, 3), (1, 4), (2, 2), (3, 0), (3, 1), (4, 0), (5, 0)]\n assert candidate(heights = [[10, 10, 10, 10], [10, 20, 20, 10], [10, 20, 10, 10], [10, 10, 10, 10]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3)]\n assert candidate(heights = [[3, 3, 3, 3], [3, 0, 0, 3], [3, 0, 0, 3], [3, 3, 3, 3]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 3), (2, 0), (2, 3), (3, 0), (3, 1), (3, 2), (3, 3)]\n assert candidate(heights = [[5, 1, 3, 4, 5], [6, 2, 3, 4, 6], [1, 2, 3, 4, 7], [2, 3, 4, 5, 8], [3, 4, 5, 6, 9]]) == [(0, 4), (1, 4), (2, 4), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n assert candidate(heights = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [1, 2, 3, 3, 3, 3, 3, 3, 2, 1], [1, 2, 3, 4, 4, 4, 4, 3, 2, 1], [1, 2, 3, 4, 5, 5, 4, 3, 2, 1], [1, 2, 3, 4, 5, 4, 3, 2, 2, 1], [1, 2, 3, 4, 4, 3, 2, 2, 1, 1], [1, 2, 3, 3, 3, 2, 2, 1, 1, 1], [1, 2, 2, 2, 2, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (5, 9), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7), (6, 8), (6, 9), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (7, 8), (7, 9), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9)]\n assert candidate(heights = [[1, 4, 3, 4, 5, 6], [2, 4, 3, 4, 5, 6], [3, 4, 3, 4, 5, 6], [4, 4, 3, 4, 5, 6], [5, 4, 3, 4, 5, 6], [6, 4, 3, 4, 5, 6]]) == [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]\n assert candidate(heights = [[1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1, 2, 3, 4, 5]]) == [(0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4)]\n"}, "metadata": {"canonical_parameter_names": ["heights"], "leetcode_dataset_entry_point": "Solution().pacificAtlantic", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var pacificAtlantic = function(heights) {", "container": null, "callable": "pacificAtlantic", "parameters": [{"name": "heights", "type": "number[][]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 419, "task_id": "battleships-in-a-board", "difficulty": "Medium", "problem_description": "Given an m x n matrix board where each cell is a battleship 'X' or empty '.', return the number of the battleships on board.\nBattleships can only be placed horizontally or vertically on board. In other words, they can only be made of the shape 1 x k (1 row, k columns) or k x 1 (k rows, 1 column), where k can be of any size. At least one horizontal or vertical cell separates between two battleships (i.e., there are no adjacent battleships).\n \nExample 1:\n\n\nInput: board = [[\"X\",\".\",\".\",\"X\"],[\".\",\".\",\".\",\"X\"],[\".\",\".\",\".\",\"X\"]]\nOutput: 2\n\nExample 2:\n\nInput: board = [[\".\"]]\nOutput: 0\n\n \nConstraints:\n\nm == board.length\nn == board[i].length\n1 <= m, n <= 200\nboard[i][j] is either '.' or 'X'.\n\n \nFollow up: Could you do it in one-pass, using only O(1) extra memory and without modifying the values board?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = [['X', '.', '.', 'X'], ['.', '.', '.', 'X'], ['.', '.', '.', 'X']]) == 2\n assert candidate(board = [['X', 'X', 'X'], ['.', '.', '.'], ['X', 'X', 'X']]) == 2\n assert candidate(board = [['.']]) == 0\n assert candidate(board = [['X', '.', '.'], ['.', 'X', '.'], ['.', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', '.'], ['X', 'X', '.'], ['.', '.', 'X']]) == 2\n assert candidate(board = [['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X']]) == 3\n assert candidate(board = [['.', '.', '.', '.'], ['.', 'X', 'X', 'X'], ['.', 'X', '.', '.'], ['.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['.', '.', '.', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 5\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '.'], ['.', '.', 'X', 'X', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', 'X', 'X', '.']]) == 2\n assert candidate(board = [['X', 'X', 'X', 'X', '.'], ['X', '.', '.', '.', '.'], ['.', '.', '.', 'X', 'X'], ['.', '.', '.', 'X', 'X']]) == 2\n assert candidate(board = [['X', '.', '.', 'X', 'X'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', 'X', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', 'X', '.', 'X'], ['.', '.', '.', 'X', '.', '.'], ['X', 'X', '.', 'X', 'X', 'X'], ['.', 'X', '.', '.', '.', '.'], ['X', 'X', '.', 'X', '.', 'X']]) == 7\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['.', '.', '.', '.', '.']]) == 3\n assert candidate(board = [['X', '.', '.', '.', '.'], ['.', 'X', '.', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', '.', 'X', '.'], ['.', '.', '.', '.', 'X']]) == 5\n assert candidate(board = [['.', '.', '.', '.'], ['X', 'X', 'X', '.'], ['.', 'X', '.', '.'], ['.', 'X', '.', '.']]) == 1\n assert candidate(board = [['X', '.', '.', '.'], ['.', '.', '.', '.'], ['.', '.', 'X', '.'], ['.', '.', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', '.', 'X'], ['.', '.', 'X', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.'], ['X', '.', '.', '.', 'X']]) == 6\n assert candidate(board = [['X', 'X', 'X', '.', '.'], ['X', '.', '.', '.', '.'], ['X', 'X', '.', 'X', '.'], ['.', '.', '.', 'X', '.'], ['.', '.', '.', 'X', 'X']]) == 2\n assert candidate(board = [['X', 'X', 'X', '.', '.'], ['X', 'X', 'X', '.', '.'], ['X', 'X', 'X', '.', '.'], ['.', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', '.', '.', '.'], ['.', '.', 'X', '.'], ['.', '.', '.', '.'], ['X', '.', '.', '.']]) == 3\n assert candidate(board = [['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X']]) == 2\n assert candidate(board = [['X', '.', '.', 'X', '.'], ['X', '.', '.', 'X', '.'], ['X', '.', '.', 'X', '.'], ['X', '.', '.', 'X', '.'], ['X', '.', '.', 'X', '.']]) == 2\n assert candidate(board = [['X', 'X', 'X', 'X', 'X'], ['.', 'X', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.']]) == 2\n assert candidate(board = [['X', '.', '.', '.', 'X'], ['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', '.'], ['X', '.', '.', '.', 'X']]) == 5\n assert candidate(board = [['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.']]) == 2\n assert candidate(board = [['X', '.', '.', 'X'], ['X', '.', '.', 'X'], ['X', '.', '.', 'X']]) == 2\n assert candidate(board = [['X', 'X', 'X', '.'], ['.', '.', '.', 'X'], ['X', 'X', 'X', 'X'], ['.', 'X', '.', '.']]) == 3\n assert candidate(board = [['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', '.']]) == 1\n assert candidate(board = [['.', '.', '.', '.'], ['X', 'X', 'X', 'X'], ['.', '.', '.', '.'], ['X', '.', 'X', '.']]) == 3\n assert candidate(board = [['X', 'X', '.', '.', '.'], ['X', 'X', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['.', '.', '.', '.', 'X'], ['.', '.', 'X', '.', '.'], ['.', '.', 'X', '.', 'X']]) == 5\n assert candidate(board = [['X', '.', '.', 'X', '.', 'X', '.', 'X'], ['X', '.', '.', 'X', '.', 'X', '.', 'X'], ['.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X', '.', 'X', '.']]) == 8\n assert candidate(board = [['X', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', '.', 'X', '.'], ['.', '.', '.', '.', 'X']]) == 4\n assert candidate(board = [['X', '.', '.', 'X'], ['X', '.', '.', 'X'], ['X', '.', '.', 'X'], ['X', '.', '.', 'X']]) == 2\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['.', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['.', '.', '.', '.', '.']]) == 5\n assert candidate(board = [['X', '.', 'X', '.'], ['X', '.', '.', 'X'], ['X', '.', '.', 'X'], ['X', '.', '.', 'X']]) == 3\n assert candidate(board = [['.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.'], ['X', 'X', 'X', '.', '.', '.'], ['.', '.', '.', 'X', 'X', 'X'], ['.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.']]) == 2\n assert candidate(board = [['X', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 4\n assert candidate(board = [['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', 'X', '.', 'X'], ['.', '.', 'X', 'X'], ['X', '.', 'X', '.'], ['.', 'X', 'X', 'X']]) == 5\n assert candidate(board = [['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', '.', 'X', '.', '.', '.', 'X'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', 'X', 'X', '.', '.', 'X', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', 'X', '.', '.', '.', 'X']]) == 8\n assert candidate(board = [['X', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', '.', 'X', '.'], ['X', '.', 'X', '.'], ['X', '.', '.', '.']]) == 2\n assert candidate(board = [['X', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.'], ['X', 'X', 'X', '.', '.'], ['.', '.', '.', 'X', 'X'], ['.', '.', '.', 'X', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', 'X', '.'], ['.', '.', '.', 'X', '.'], ['X', '.', '.', 'X', '.'], ['.', '.', '.', 'X', '.'], ['X', '.', '.', 'X', '.']]) == 4\n assert candidate(board = [['X', '.', 'X', '.', 'X', '.', 'X', '.', 'X'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', 'X', '.', 'X', '.', 'X', '.', 'X'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X', '.', 'X', '.', 'X']]) == 14\n assert candidate(board = [['.', '.', '.', 'X', 'X'], ['.', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.'], ['X', 'X', 'X', '.', '.'], ['.', '.', 'X', '.', '.']]) == 3\n assert candidate(board = [['X', 'X', 'X', '.', '.', '.', '.', '.', '.'], ['.', 'X', '.', '.', '.', '.', '.', '.', '.'], ['X', 'X', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', 'X', 'X', 'X'], ['.', '.', '.', '.', '.', '.', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', 'X', 'X', 'X']]) == 4\n assert candidate(board = [['X', '.', 'X', '.'], ['.', '.', '.', '.'], ['X', '.', 'X', '.'], ['.', '.', '.', '.']]) == 4\n assert candidate(board = [['X', '.', '.', '.'], ['X', '.', 'X', 'X'], ['.', 'X', '.', '.'], ['X', '.', 'X', '.']]) == 5\n assert candidate(board = [['.', 'X', '.', 'X', '.'], ['X', '.', 'X', '.', 'X'], ['.', 'X', '.', 'X', '.'], ['X', '.', 'X', '.', 'X'], ['.', 'X', '.', 'X', '.']]) == 12\n assert candidate(board = [['X', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X', '.', 'X', '.']]) == 13\n assert candidate(board = [['.', 'X', '.', 'X', '.'], ['X', 'X', '.', 'X', 'X'], ['.', 'X', '.', 'X', '.'], ['X', 'X', '.', 'X', 'X'], ['.', 'X', '.', 'X', '.']]) == 4\n assert candidate(board = [['X', 'X', '.', '.'], ['X', '.', 'X', '.'], ['.', '.', '.', '.'], ['.', 'X', '.', 'X']]) == 4\n assert candidate(board = [['X', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['X', '.', '.', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['X', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', '.', 'X', '.'], ['X', '.', 'X', '.'], ['X', '.', 'X', '.']]) == 2\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 5\n assert candidate(board = [['X', 'X', '.', 'X'], ['X', '.', 'X', '.'], ['.', '.', 'X', 'X'], ['.', '.', 'X', '.']]) == 3\n assert candidate(board = [['.', 'X', '.', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', '.', 'X', '.'], ['.', '.', '.', '.', 'X'], ['.', '.', '.', '.', '.']]) == 4\n assert candidate(board = [['X', 'X', '.', '.', '.', '.', '.', 'X'], ['.', '.', 'X', 'X', '.', '.', '.', 'X'], ['X', '.', 'X', '.', 'X', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.'], ['X', 'X', '.', '.', '.', '.', '.', 'X']]) == 8\n assert candidate(board = [['X', 'X', '.', 'X', 'X'], ['.', '.', '.', '.', '.'], ['X', 'X', '.', 'X', 'X'], ['.', '.', '.', '.', '.'], ['X', 'X', '.', 'X', 'X']]) == 6\n assert candidate(board = [['X', 'X', 'X', '.', '.'], ['.', '.', '.', 'X', 'X'], ['.', '.', '.', '.', 'X'], ['X', 'X', 'X', '.', '.'], ['X', '.', '.', '.', '.']]) == 3\n assert candidate(board = [['X', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X']]) == 3\n assert candidate(board = [['X', 'X', 'X', '.', 'X'], ['X', '.', 'X', 'X', '.'], ['.', '.', '.', 'X', 'X'], ['X', 'X', '.', 'X', '.']]) == 3\n assert candidate(board = [['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.']]) == 0\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['.', '.', 'X', '.', '.'], ['X', '.', 'X', '.', 'X'], ['.', '.', 'X', '.', '.'], ['X', '.', 'X', '.', 'X']]) == 7\n assert candidate(board = [['X', 'X', 'X', '.', 'X'], ['X', 'X', 'X', '.', 'X'], ['X', 'X', 'X', '.', 'X'], ['X', 'X', 'X', '.', 'X']]) == 2\n assert candidate(board = [['.', '.', '.', '.', '.'], ['.', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.'], ['.', 'X', '.', '.', '.'], ['.', 'X', '.', '.', '.']]) == 2\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', '.'], ['.', '.', 'X', '.'], ['.', '.', 'X', 'X'], ['X', '.', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', '.'], ['.', 'X', '.', '.'], ['.', '.', 'X', '.'], ['.', '.', '.', 'X']]) == 4\n assert candidate(board = [['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', 'X', '.', 'X', '.', 'X', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X', '.', 'X', '.', 'X'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', 'X', '.', 'X', '.', 'X', '.', 'X', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == 13\n assert candidate(board = [['X', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.']]) == 1\n assert candidate(board = [['X', '.', '.', '.', '.'], ['X', '.', 'X', '.', '.'], ['X', '.', '.', 'X', '.'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X']]) == 4\n assert candidate(board = [['X', '.', '.', '.', '.'], ['X', '.', 'X', 'X', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', 'X', '.', '.'], ['X', '.', '.', '.', 'X']]) == 4\n assert candidate(board = [['.', '.', '.', '.', '.'], ['X', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.'], ['X', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.']]) == 2\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 3\n assert candidate(board = [['X', '.', 'X', 'X', 'X'], ['X', '.', '.', '.', '.'], ['X', '.', '.', '.', '.'], ['X', 'X', 'X', 'X', 'X']]) == 2\n assert candidate(board = [['.', 'X', '.', 'X', '.'], ['X', '.', 'X', '.', 'X'], ['.', 'X', '.', 'X', '.'], ['X', '.', 'X', '.', 'X']]) == 10\n assert candidate(board = [['X', 'X', '.', 'X'], ['.', 'X', '.', 'X'], ['.', 'X', '.', 'X']]) == 2\n assert candidate(board = [['X', 'X', 'X', 'X', 'X'], ['.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 4\n assert candidate(board = [['X', 'X', 'X', 'X', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', '.', '.', '.', 'X'], ['X', 'X', 'X', 'X', 'X']]) == 1\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['X', 'X', 'X', 'X', '.'], ['.', '.', 'X', 'X', 'X'], ['X', '.', 'X', '.', 'X'], ['X', '.', 'X', '.', 'X']]) == 4\n assert candidate(board = [['.', 'X', '.', 'X', '.'], ['.', 'X', '.', 'X', '.'], ['.', 'X', '.', 'X', '.'], ['.', 'X', '.', 'X', '.'], ['.', 'X', '.', 'X', '.']]) == 2\n assert candidate(board = [['X', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.'], ['.', '.', '.', 'X', '.'], ['.', '.', '.', '.', 'X'], ['.', '.', '.', '.', '.']]) == 4\n assert candidate(board = [['X', 'X', 'X', 'X', 'X'], ['X', 'X', 'X', 'X', 'X'], ['X', 'X', 'X', 'X', 'X'], ['X', 'X', 'X', 'X', 'X'], ['X', 'X', 'X', 'X', 'X']]) == 1\n assert candidate(board = [['.', '.', '.', '.', 'X', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.', '.', 'X', '.', '.'], ['.', '.', '.', '.', 'X', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.']]) == 4\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['.', 'X', '.', 'X', '.'], ['X', '.', 'X', '.', 'X'], ['.', 'X', '.', 'X', '.'], ['X', '.', 'X', '.', 'X']]) == 13\n assert candidate(board = [['X', 'X', '.', 'X'], ['X', 'X', '.', 'X'], ['.', '.', '.', 'X'], ['X', 'X', 'X', 'X']]) == 3\n assert candidate(board = [['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['X', 'X', 'X', 'X', 'X']]) == 1\n assert candidate(board = [['X', 'X', 'X', '.', '.'], ['X', '.', '.', '.', '.'], ['X', '.', 'X', 'X', 'X'], ['.', '.', '.', 'X', '.'], ['.', '.', '.', 'X', '.']]) == 2\n assert candidate(board = [['X', '.', 'X', '.', 'X'], ['.', '.', 'X', '.', 'X'], ['X', 'X', 'X', 'X', '.'], ['.', '.', '.', '.', '.'], ['X', '.', 'X', '.', 'X']]) == 7\n assert candidate(board = [['X', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', 'X', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', 'X', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', 'X', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', 'X', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', 'X', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', 'X', '.', '.']]) == 7\n assert candidate(board = [['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.']]) == 0\n assert candidate(board = [['X', 'X', '.', 'X', 'X', '.', 'X', 'X', '.', 'X'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['X', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['.', '.', '.', '.', '.', '.', '.', '.', '.', '.'], ['X', 'X', '.', 'X', 'X', '.', 'X', 'X', '.', 'X']]) == 9\n assert candidate(board = [['X', 'X', 'X', 'X'], ['.', '.', '.', '.'], ['X', 'X', 'X', 'X'], ['.', '.', '.', '.']]) == 2\n assert candidate(board = [['X', 'X', '.', '.'], ['.', '.', '.', 'X'], ['.', '.', '.', 'X'], ['.', '.', 'X', 'X']]) == 3\n assert candidate(board = [['X', '.', '.', '.'], ['X', 'X', '.', '.'], ['.', '.', '.', 'X'], ['.', '.', 'X', 'X']]) == 3\n"}, "metadata": {"canonical_parameter_names": ["board"], "leetcode_dataset_entry_point": "Solution().countBattleships", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countBattleships = function(board) {", "container": null, "callable": "countBattleships", "parameters": [{"name": "board", "type": "character[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 420, "task_id": "strong-password-checker", "difficulty": "Hard", "problem_description": "A password is considered strong if the below conditions are all met:\n\nIt has at least 6 characters and at most 20 characters.\nIt contains at least one lowercase letter, at least one uppercase letter, and at least one digit.\nIt does not contain three repeating characters in a row (i.e., \"Baaabb0\" is weak, but \"Baaba0\" is strong).\n\nGiven a string password, return the minimum number of steps required to make password strong. if password is already strong, return 0.\nIn one step, you can:\n\nInsert one character to password,\nDelete one character from password, or\nReplace one character of password with another character.\n\n \nExample 1:\nInput: password = \"a\"\nOutput: 5\nExample 2:\nInput: password = \"aA1\"\nOutput: 3\nExample 3:\nInput: password = \"1337C0d3\"\nOutput: 0\n\n \nConstraints:\n\n1 <= password.length <= 50\npassword consists of letters, digits, dot '.' or exclamation mark '!'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(password = \"AAAbbb\") == 2\n assert candidate(password = \"aA1\") == 3\n assert candidate(password = \"Aa1234567890\") == 0\n assert candidate(password = \"........##@\") == 3\n assert candidate(password = \"Aaaaaa1A\") == 1\n assert candidate(password = \"Passwo0rd!!\") == 0\n assert candidate(password = \"A1b2C3\") == 0\n assert candidate(password = \"...!!!\") == 3\n assert candidate(password = \"A1b2C3d4E5f6G7\") == 0\n assert candidate(password = \"111111111111111111\") == 6\n assert candidate(password = \"A1B2C3D4E5F6G7H8I9J0\") == 1\n assert candidate(password = \"Aa1234567890!@#$%^\") == 0\n assert candidate(password = \"Aa1!Aa1!Aa1!Aa1!\") == 0\n assert candidate(password = \"Aa1111111111111111\") == 5\n assert candidate(password = \"A1A1A1A1\") == 1\n assert candidate(password = \"password\") == 2\n assert candidate(password = \"Aaaaaa\") == 1\n assert candidate(password = \"AAAAAaaaaaaa\") == 3\n assert candidate(password = \"Aa1234567890Aa1\") == 0\n assert candidate(password = \"Aa111\") == 1\n assert candidate(password = \"AaAaAaAaAaAaAaAaAaAa\") == 1\n assert candidate(password = \"aaa111\") == 2\n assert candidate(password = \"A1B2C3D4E5F6G7H8I9J0K\") == 2\n assert candidate(password = \"Aa1234567890123456\") == 0\n assert candidate(password = \"A1b2C3d4\") == 0\n assert candidate(password = \"12345678901234567890\") == 2\n assert candidate(password = \"aaaaaaa\") == 2\n assert candidate(password = \"Aa1234567890123\") == 0\n assert candidate(password = \"!@#$%^&*()_+\") == 3\n assert candidate(password = \"Aaa111\") == 1\n assert candidate(password = \"a\") == 5\n assert candidate(password = \"Aa1234567890Aa1234567890\") == 4\n assert candidate(password = \"AaAaAaAaAaAaAaAaAaA1\") == 0\n assert candidate(password = \"Aaaaaa1\") == 1\n assert candidate(password = \"............aaa\") == 5\n assert candidate(password = \"Aa1234567890!@#$%^&*()\") == 2\n assert candidate(password = \"Aa1234567890Aa123456\") == 0\n assert candidate(password = \"11111111111111111111\") == 6\n assert candidate(password = \"1337C0d3\") == 0\n assert candidate(password = \"Password123\") == 0\n assert candidate(password = \"aaaaaaaaaaaaaaaaaaaaa\") == 7\n assert candidate(password = \"Aa123456\") == 0\n assert candidate(password = \"ABABABABABABABABAB\") == 2\n assert candidate(password = \"ABABABABABABABABABAB1\") == 2\n assert candidate(password = \"Aa1234567890Aa123\") == 0\n assert candidate(password = \"aaaaaaaaaaaaaa1A\") == 4\n assert candidate(password = \"abcABC123!@#\") == 0\n assert candidate(password = \"A1b2C3D4E5F6G7H8I9J0\") == 0\n assert candidate(password = \"AAAbbbccc111111111111111111\") == 11\n assert candidate(password = \"AAAbbbCCCddd1111111111111111111\") == 15\n assert candidate(password = \"aaaabbbbccccddddeee\") == 5\n assert candidate(password = \"111222333444555666777888999000\") == 12\n assert candidate(password = \"abcABC123!!!123!!!123!!!123!!!\") == 10\n assert candidate(password = \"P@ssw0rd!\") == 0\n assert candidate(password = \"!@#$%^&*()_+~`|}{[]:;?><,./-=!@#$%^&*()\") == 22\n assert candidate(password = \"AaBbCc1234567890123456789012345678901234567890\") == 26\n assert candidate(password = \"AAAbbbCCCddd11111111111111111111\") == 16\n assert candidate(password = \"Aa1Aa1Aa1Aa1Aa1Aa1Aa1\") == 1\n assert candidate(password = \"A1A1A1A1A1A1A1A1A1A1\") == 1\n assert candidate(password = \"A1A1A1A1A1A1A1A1A1A1A1A1A\") == 6\n assert candidate(password = \"Aaaaaaaaaa1111111111!!!!!!!!!\") == 14\n assert candidate(password = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == 15\n assert candidate(password = \"abcdefgH1!\") == 0\n assert candidate(password = \"123456789012345678901234567890\") == 12\n assert candidate(password = \"aaaaaaaAAAAAA1111111\") == 6\n assert candidate(password = \"Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!\") == 28\n assert candidate(password = \"Password123Password123\") == 2\n assert candidate(password = \"abcABC123!@#abcABC123!@#abcABC123!@#\") == 16\n assert candidate(password = \"Aa1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!\") == 56\n assert candidate(password = \"aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1\") == 28\n assert candidate(password = \"!@#$%^&*()_+~`|}{[]:;?><,./-=\") == 12\n assert candidate(password = \"AaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAa\") == 55\n assert candidate(password = \"AAAbbbCCCddd1111111111111111111111\") == 18\n assert candidate(password = \"abcdefghijklmnopqrstuvwxyz\") == 8\n assert candidate(password = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\") == 19\n assert candidate(password = \"xX1234567890Xx1234567890Xx1234567890\") == 16\n assert candidate(password = \"Aa1Bb2Cc3Dd4Ee5Ff6Gg7Hh8Ii9Jj0KkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\") == 42\n assert candidate(password = \"aA1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1\") == 23\n assert candidate(password = \"aabababababababababa\") == 2\n assert candidate(password = \"Aa123456789012345\") == 0\n assert candidate(password = \"Password!Password!Pass\") == 3\n assert candidate(password = \"A1!aA1!aA1!aA1!aA1!aA1!aA1!a\") == 8\n assert candidate(password = \"A1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!\") == 11\n assert candidate(password = \"aaaaaaaaaaaaaaaaaaaa\") == 6\n assert candidate(password = \"1234567890!@#$%^&*()_+~`|}{[]:;?><,./-=\") == 21\n assert candidate(password = \"A1A1A1A1A1A1A1A1A1A1A1A1A1\") == 7\n assert candidate(password = \"A1B1C1D1E1F1G1H1I1J1K1L1M1N1O1P1Q1R1S1T1U1V1W1X1Y1Z1\") == 33\n assert candidate(password = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 40\n assert candidate(password = \"bbbbbbbbbbbbbbbbb\") == 5\n assert candidate(password = \"Aa1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!\") == 20\n assert candidate(password = \"A1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!a\") == 12\n assert candidate(password = \"!aA1!aA1!aA1!aA1!aA1\") == 0\n assert candidate(password = \"AaaBBB111\") == 2\n assert candidate(password = \"Aa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!aAa!\") == 44\n assert candidate(password = \"A1A1A1A1A1A1A1A1A1A1A1\") == 3\n assert candidate(password = \"AAAbbbCCCddd11111111111111111111111\") == 19\n assert candidate(password = \"aAaAaAaAaAaAaAaAaAaAaAaAaA\") == 7\n assert candidate(password = \"aaAAaaAAaaAAaaAAaa\") == 1\n assert candidate(password = \"Aa!b@c#d$e%f^g&h*i(j)k\") == 3\n assert candidate(password = \"A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1A1\") == 23\n assert candidate(password = \"Aa1!Aa1!Aa1!\") == 0\n assert candidate(password = \"Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1A\") == 23\n assert candidate(password = \"aA1!aA1!aA1!aA1!aA1!\") == 0\n assert candidate(password = \"abAB1111111111111111\") == 5\n assert candidate(password = \"cccccccccccccccccccccccccccccccccccccccccccccccccccc\") == 38\n assert candidate(password = \"aaaaaaaAAAAAA666666\") == 6\n assert candidate(password = \"aaaAAA111!!!\") == 4\n assert candidate(password = \"aAaAaAaAaAaAaAaAaAaAaAaA\") == 5\n assert candidate(password = \"Aa111111111111111111\") == 6\n assert candidate(password = \"a!b@c#d$e%f^g&h*i(j)\") == 2\n assert candidate(password = \"aaAA111111111111111\") == 5\n assert candidate(password = \"A1!aA1!aA1!aA1!aA1!aA1!aA1!aA1\") == 10\n assert candidate(password = \"abcABC123abcABC123\") == 0\n assert candidate(password = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 28\n assert candidate(password = \"abcABC123!@#abcABC123!@#\") == 4\n assert candidate(password = \"Aa1Bb2Ccc3Ddd\") == 0\n assert candidate(password = \"AAAbbbCCCccc111111111\") == 7\n assert candidate(password = \"abcABC!@#abcABC!@#abcABC!@#\") == 8\n assert candidate(password = \"Abcde!23456789\") == 0\n assert candidate(password = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == 9\n assert candidate(password = \"AAAbbbCCCddd111111111111111111111111\") == 20\n assert candidate(password = \"aaabbbccc111222333\") == 6\n assert candidate(password = \"aA1bB2cC3dD4eE5fF6\") == 0\n assert candidate(password = \"aaaaaaaAAAAAA6666666\") == 6\n assert candidate(password = \"Aa1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!\") == 40\n assert candidate(password = \"Aa!b@c#d$e%f^g&h*i(j)\") == 2\n assert candidate(password = \"abcABC123abcABC123abcABC123\") == 7\n assert candidate(password = \"Aa1234567890123456789\") == 1\n assert candidate(password = \"!@#$%^&*()\") == 3\n assert candidate(password = \"!@#$%^&*()_+~`1234567890qwertyuiopasdfghjklzxcvbnmQWERTYUIOPASDFGHJKLZXCVBNM\") == 56\n assert candidate(password = \"aA1!aA1!aA1!aA1!\") == 0\n assert candidate(password = \"aA1aA1aA1aA1aA1aA1\") == 0\n assert candidate(password = \"111222333444555666777888999000111222333\") == 21\n assert candidate(password = \"123!@#abcDEF\") == 0\n assert candidate(password = \"aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1aA1\") == 22\n assert candidate(password = \"Aa1Aa1Aa1Aa1Aa1Aa1\") == 0\n assert candidate(password = \"Abc!1\") == 1\n assert candidate(password = \"aaaAAAbBBB11111111111111\") == 8\n assert candidate(password = \"AaaBBBcccDDD123\") == 3\n assert candidate(password = \"AAAbbccccdddEEF1234567890\") == 5\n assert candidate(password = \"aA111aA111aA111aA111\") == 4\n assert candidate(password = \"aaaaaaaAAAAAA66666666666666666666\") == 18\n assert candidate(password = \"0123456789012345678901234567890\") == 13\n assert candidate(password = \"aA1!aA1!aA1!aA1!aA1!aA1!\") == 4\n assert candidate(password = \"A1b2C3d4E5f6G7H8I9J0KLMN\") == 4\n assert candidate(password = \"aA1234567890Aa1234567890aA1234567890\") == 16\n assert candidate(password = \"1234567890AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\") == 42\n assert candidate(password = \"abcdefghijABCD1234567890\") == 4\n assert candidate(password = \"Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!\") == 32\n assert candidate(password = \"AaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAa\") == 15\n assert candidate(password = \"Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!Aa1!\") == 12\n assert candidate(password = \"1234567890!@#$%^&*()_+\") == 4\n assert candidate(password = \"AAAbbbCCCddd111111111111111111\") == 14\n assert candidate(password = \"Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1\") == 31\n assert candidate(password = \"123!@#abcDEF123!@#abcDEF\") == 4\n assert candidate(password = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == 13\n assert candidate(password = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\") == 8\n assert candidate(password = \"AAAbbbCCCddd111111111111111111111\") == 17\n assert candidate(password = \"abcdefgHIJKLmnopQR1234567890!@#$%^&*()\") == 18\n assert candidate(password = \"A1!aA1!aA1!aA1!aA1!aA1!aA1!aA\") == 9\n assert candidate(password = \"a!B@c#D$e%F^G&H*I(J)\") == 1\n assert candidate(password = \"!@#$%^&*()!@#$%^&*()!@#$%^&*()!@#$%^&*()!@#$%^&*()!@#$%^&*()!@#$%^&*()\") == 53\n assert candidate(password = \"xXyYzZ0987654321@#\") == 0\n assert candidate(password = \"Password1Password1\") == 0\n assert candidate(password = \"Aa1aA1aA1aA1aA1aA1aA1\") == 1\n assert candidate(password = \"Aa12345678901234567890\") == 2\n assert candidate(password = \"Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1Aa1\") == 46\n assert candidate(password = \"aaAaaaAaaaAaaaAaaaAaaaA\") == 5\n assert candidate(password = \"00000000000000000000000000000000\") == 18\n assert candidate(password = \"aaaaaaaaaAAA9\") == 4\n assert candidate(password = \"Aaaaabbbb1\") == 2\n assert candidate(password = \"111222333444555666777888999000111222333444555666777888999000\") == 42\n assert candidate(password = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == 11\n assert candidate(password = \"Aa1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!aA1!\") == 16\n"}, "metadata": {"canonical_parameter_names": ["password"], "leetcode_dataset_entry_point": "Solution().strongPasswordChecker", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var strongPasswordChecker = function(password) {", "container": null, "callable": "strongPasswordChecker", "parameters": [{"name": "password", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 421, "task_id": "maximum-xor-of-two-numbers-in-an-array", "difficulty": "Medium", "problem_description": "Given an integer array nums, return the maximum result of nums[i] XOR nums[j], where 0 <= i <= j < n.\n \nExample 1:\n\nInput: nums = [3,10,5,25,2,8]\nOutput: 28\nExplanation: The maximum result is 5 XOR 25 = 28.\n\nExample 2:\n\nInput: nums = [14,70,53,83,49,91,36,80,92,51,66,70]\nOutput: 127\n\n \nConstraints:\n\n1 <= nums.length <= 2 * 105\n0 <= nums[i] <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [3, 10, 5, 25, 2, 8]) == 28\n assert candidate(nums = [14, 70, 53, 83, 49, 91, 36, 80, 92, 51, 66, 70]) == 127\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == 15\n assert candidate(nums = [1000000000, 2147483647, 0, 1]) == 2147483647\n assert candidate(nums = [4, 6, 7, 2, 1]) == 7\n assert candidate(nums = [0, 1]) == 1\n assert candidate(nums = [0, 0, 0, 0]) == 0\n assert candidate(nums = [3000000000, 2147483647, 1, 0]) == 2147483647\n assert candidate(nums = [8, 10, 2]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5]) == 7\n assert candidate(nums = [999999999, 888888888, 777777777, 666666666, 555555555, 444444444, 333333333, 222222222, 111111111, 1]) == 1036069302\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]) == 31\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 30\n assert candidate(nums = [16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 255]) == 240\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == 125\n assert candidate(nums = [8, 17, 24, 32, 41, 50, 58, 67, 75, 82, 91, 99]) == 123\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576]) == 1572864\n assert candidate(nums = [1000000000, 2000000000, 3000000000, 1, 2, 3, 4, 5]) == 2000000005\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]) == 786432\n assert candidate(nums = [16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192]) == 12288\n assert candidate(nums = [123456789, 987654321, 1122334455, 5566778899, 9988776655]) == 2017140294\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643, 2147483642, 2147483641, 2147483640, 2147483639, 2147483638]) == 15\n assert candidate(nums = [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575]) == 1048574\n assert candidate(nums = [2147483647, 0, 1, 2147483646, 2]) == 2147483647\n assert candidate(nums = [8, 1, 2, 12, 7, 6]) == 15\n assert candidate(nums = [999999999, 888888888, 777777777, 666666666, 555555555, 444444444, 333333333, 222222222, 111111111]) == 1036069302\n assert candidate(nums = [8, 10, 1, 3, 127, 255, 2, 5, 7, 15, 31, 63]) == 254\n assert candidate(nums = [8388607, 16777214, 33554431, 67108862, 134217727, 268435454, 536870911, 1073741822]) == 1065353217\n assert candidate(nums = [123456789, 987654321, 1122334455, 5566778899, 9988776655, 5544332211, 1111111111, 2222222222, 3333333333, 4444444444]) == 2087766500\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000, 600000000, 700000000, 800000000, 900000000]) == 1047438080\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]) == 62\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005, 1000000006]) == 7\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576]) == 1572864\n assert candidate(nums = [8, 10, 2, 14, 7, 3, 9, 1, 13, 5, 11, 6, 4, 12, 0, 15]) == 15\n assert candidate(nums = [123456789, 987654321, 111111111, 222222222, 333333333, 444444444, 555555555]) == 1032168868\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207]) == 254\n assert candidate(nums = [2147483647, 0, 1073741823, 1, 536870911, 2, 268435455, 3, 134217727, 4, 67108863, 5, 33554431, 6, 16777215, 7, 8388607, 8, 4194303, 9, 2097151, 10, 1048575, 11, 524287, 12, 262143, 13, 131071, 14, 65535, 15, 32767, 16]) == 2147483647\n assert candidate(nums = [1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575]) == 1047552\n assert candidate(nums = [15, 30, 45, 60, 75, 90, 105, 120, 135, 150]) == 255\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004]) == 7\n assert candidate(nums = [123456789, 234567890, 345678901, 456789012, 567890123, 678901234, 789012345, 890123456, 901234567]) == 1022202311\n assert candidate(nums = [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023]) == 1022\n assert candidate(nums = [2147483647, 0]) == 2147483647\n assert candidate(nums = [65535, 65534, 65533, 65532, 65531, 65530, 65529, 65528, 65527, 65526, 65525, 65524, 65523, 65522, 65521, 65520]) == 15\n assert candidate(nums = [255, 254, 253, 252, 251, 250, 249, 248, 247, 246, 245, 244, 243, 242, 241, 240]) == 15\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072]) == 196608\n assert candidate(nums = [8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]) == 6144\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000]) == 100311872\n assert candidate(nums = [3, 10, 5, 25, 2, 8, 12, 17, 20, 23, 28, 31]) == 31\n assert candidate(nums = [1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575]) == 1048574\n assert candidate(nums = [123456789, 987654321, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666, 777777777]) == 1036069302\n assert candidate(nums = [999999999, 888888888, 777777777, 666666666, 555555555, 444444444, 333333333, 222222222, 111111111, 0]) == 1036069302\n assert candidate(nums = [134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144]) == 201326592\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == 15\n assert candidate(nums = [13, 1, 7, 3, 9, 2, 8, 4, 6, 10, 5, 11, 12, 14, 15]) == 15\n assert candidate(nums = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 10000000000]) == 2114852352\n assert candidate(nums = [13, 26, 52, 104, 208, 416, 832, 1664, 3328, 6656, 13312]) == 14592\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63]) == 62\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643, 2147483642, 2147483641, 2147483640]) == 7\n assert candidate(nums = [1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071]) == 130048\n assert candidate(nums = [2147483647, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 2147483647\n assert candidate(nums = [16777215, 8388607, 4194303, 2097151, 1048575, 524287, 262143, 131071, 65535, 32767, 16383, 8191, 4095, 2047, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1]) == 16777214\n assert candidate(nums = [1073741824, 536870912, 268435456, 134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152]) == 1610612736\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200]) == 1992\n assert candidate(nums = [2000000000, 1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250]) == 2043881088\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000]) == 1021940544\n assert candidate(nums = [6, 10, 1, 8, 3, 4, 9, 7, 2, 5]) == 15\n assert candidate(nums = [987654321, 123456789, 999999999, 111111111, 888888888, 222222222, 777777777, 333333333]) == 1032171812\n assert candidate(nums = [123456789, 987654321, 456789123, 321987654, 789123456, 654321987, 891234567, 219876543]) == 1032168868\n assert candidate(nums = [4, 6, 7, 2, 1]) == 7\n assert candidate(nums = [1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483647, 0]) == 2147483647\n assert candidate(nums = [16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320]) == 496\n assert candidate(nums = [1023, 511, 255, 127, 63, 31, 15, 7, 3, 1]) == 1022\n assert candidate(nums = [13, 29, 31, 45, 66, 78, 90, 103, 114, 129, 143, 155]) == 253\n assert candidate(nums = [8, 10, 15, 17, 3, 5, 18, 12]) == 30\n assert candidate(nums = [234, 567, 890, 1234, 5678, 9012, 3456, 7890, 12345, 67890]) == 80139\n assert candidate(nums = [2147483647, 0, 1, 2147483646, 1073741823, 1073741824, 536870911, 536870912]) == 2147483647\n assert candidate(nums = [100000000, 200000000, 300000000, 400000000, 500000000, 600000000, 700000000, 800000000, 900000000, 1000000000]) == 1047472896\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]) == 98304\n assert candidate(nums = [1073741823, 536870911, 268435455, 134217727, 67108863, 33554431, 16777215, 8388607, 4194303, 2097151]) == 1071644672\n assert candidate(nums = [5, 3, 9, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191]) == 8188\n assert candidate(nums = [123, 456, 789, 101112, 131415, 161718, 192021, 222324, 252627]) == 261454\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120]) == 31\n assert candidate(nums = [255, 127, 63, 31, 15, 7, 3, 1]) == 254\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 62\n assert candidate(nums = [16, 8, 4, 2, 1, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384]) == 24576\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643]) == 7\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003]) == 3\n assert candidate(nums = [9, 5, 2, 7, 6, 8, 4, 1, 3, 10, 15, 20]) == 30\n assert candidate(nums = [13, 29, 18, 23, 56, 78, 99, 101, 112, 134, 156, 178]) == 255\n assert candidate(nums = [123456789, 987654321, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666]) == 1036069302\n assert candidate(nums = [13, 1, 24, 31, 29, 2, 7, 0, 30, 19]) == 31\n assert candidate(nums = [111111111, 222222222, 333333333, 444444444, 555555555, 666666666, 777777777, 888888888, 999999999]) == 1036069302\n assert candidate(nums = [2147483647, 0, 1, 2147483646]) == 2147483647\n assert candidate(nums = [1073741823, 1073741822, 1073741821, 1073741820, 1073741819, 1073741818, 1073741817, 1073741816]) == 7\n assert candidate(nums = [123456789, 987654321, 111222333, 444555666, 777888999, 101010101, 202020202, 303030303, 404040404, 505050505]) == 1032168868\n assert candidate(nums = [1, 1073741823, 2147483647, 1073741824, 1073741825, 1073741826, 1073741827, 1073741828, 1073741829, 1073741830]) == 2147483647\n assert candidate(nums = [32, 16, 8, 4, 2, 1]) == 48\n assert candidate(nums = [134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]) == 201326592\n assert candidate(nums = [123456789, 987654321, 234567891, 198765432, 345678912, 298765431, 456789123, 398765432, 567891234, 498765431, 678912345, 598765432, 789123456, 698765431, 891234567, 798765432, 912345678, 898765431, 1234567890, 9876543210, 1122334455, 2233445566, 3344556677, 4455667788, 5566778899]) == 2146912412\n assert candidate(nums = [128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152]) == 3145728\n assert candidate(nums = [1073741823, 1073741824, 1073741822, 1073741825]) == 2147483647\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findMaximumXOR", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMaximumXOR = function(nums) {", "container": null, "callable": "findMaximumXOR", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 423, "task_id": "reconstruct-original-digits-from-english", "difficulty": "Medium", "problem_description": "Given a string s containing an out-of-order English representation of digits 0-9, return the digits in ascending order.\n \nExample 1:\nInput: s = \"owoztneoer\"\nOutput: \"012\"\nExample 2:\nInput: s = \"fviefuro\"\nOutput: \"45\"\n\n \nConstraints:\n\n1 <= s.length <= 105\ns[i] is one of the characters [\"e\",\"g\",\"f\",\"i\",\"h\",\"o\",\"n\",\"s\",\"r\",\"u\",\"t\",\"w\",\"v\",\"x\",\"z\"].\ns is guaranteed to be valid.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"sevensixfivefourthree\") == \"34567\"\n assert candidate(s = \"fivefivethree\") == \"355\"\n assert candidate(s = \"oneonetwothreefourfivesixseveneightnine\") == \"1123456789\"\n assert candidate(s = \"fivefivesixsix\") == \"5566\"\n assert candidate(s = \"sixseveneightnine\") == \"6789\"\n assert candidate(s = \"nieseve\") == \"79\"\n assert candidate(s = \"onetwothree\") == \"123\"\n assert candidate(s = \"neon\") == \"1\"\n assert candidate(s = \"zerozerozerozerozero\") == \"00000\"\n assert candidate(s = \"zerofourzerooneeight\") == \"00148\"\n assert candidate(s = \"zerozerozero\") == \"000\"\n assert candidate(s = \"oneonezero\") == \"011\"\n assert candidate(s = \"eightonefivefourtwozerosixseventhree\") == \"012345678\"\n assert candidate(s = \"owoztneoer\") == \"012\"\n assert candidate(s = \"giosx\") == \"168\"\n assert candidate(s = \"oneoneeightoneeightone\") == \"111188\"\n assert candidate(s = \"fviefuro\") == \"45\"\n assert candidate(s = \"fourfoursixsixzero\") == \"04466\"\n assert candidate(s = \"twotwothreeelevensixsixzerozerozerozerozerozeronine\") == \"000000223669\"\n assert candidate(s = \"ennnoowewe\") == \"22\"\n assert candidate(s = \"eighteighteighthree\") == \"3888\"\n assert candidate(s = \"zerotwofour\") == \"024\"\n assert candidate(s = \"sixsixsix\") == \"666\"\n assert candidate(s = \"ninezeroonetwothreefourfivesixseveneightnine\") == \"01234567899\"\n assert candidate(s = \"nine\") == \"9\"\n assert candidate(s = \"oneeighttwothree\") == \"1238\"\n assert candidate(s = \"fivefourthreeoneeighttwosixsevenzerozerozero\") == \"00012345678\"\n assert candidate(s = \"twothree\") == \"23\"\n assert candidate(s = \"ninennine\") == \"99\"\n assert candidate(s = \"seven\") == \"7\"\n assert candidate(s = \"eight\") == \"8\"\n assert candidate(s = \"fivefivesevensevenseven\") == \"55777\"\n assert candidate(s = \"six\") == \"6\"\n assert candidate(s = \"fourfoursixsix\") == \"4466\"\n assert candidate(s = \"zeroonetwothreefourfivesixseveneightnine\") == \"0123456789\"\n assert candidate(s = \"twozeroonetwothreefourfivesixseveneightnine\") == \"01223456789\"\n assert candidate(s = \"uqpie\") == \"499\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnine\") == \"123456789\"\n assert candidate(s = \"nineeightsevenfoursixthreeonetwozero\") == \"012346789\"\n assert candidate(s = \"threethreethreethreethreethreethreethreethreethree\") == \"3333333333\"\n assert candidate(s = \"fiveseveneightfourzerotwothree\") == \"0234578\"\n assert candidate(s = \"fourzeroeighteightsixtwotwo\") == \"0224688\"\n assert candidate(s = \"fivefivesixsixsevensevenzerozero\") == \"00556677\"\n assert candidate(s = \"fivefourseveneightonesixninezero\") == \"01456789\"\n assert candidate(s = \"nineeightsevenzerosixfivethreezeroonetwo\") == \"0012356789\"\n assert candidate(s = \"sixseveneightsixsixsixsixtwosix\") == \"266666678\"\n assert candidate(s = \"fourfourfourfourfourfourfourfourfourfour\") == \"4444444444\"\n assert candidate(s = \"fourfoursixsixzerozerotwoeighttwoeighttwoeight\") == \"002224466888\"\n assert candidate(s = \"twotwotwothreeeighthree\") == \"222338\"\n assert candidate(s = \"fivesixseveneightninezeroonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefour\") == \"0111111111122222222223333333333333333333444444444456789\"\n assert candidate(s = \"eightfiveeightfiveeight\") == \"55888\"\n assert candidate(s = \"threeseveneightzeronineseven\") == \"037789\"\n assert candidate(s = \"onetwoonetwoonetwoonetwoone\") == \"111112222\"\n assert candidate(s = \"fourtwoeightzerosixsixsixsixtwoeight\") == \"0224666688\"\n assert candidate(s = \"twotwothreefourfoursix\") == \"223446\"\n assert candidate(s = \"zerowzerowzerowzerowzero\") == \"000002222\"\n assert candidate(s = \"sixtwoneightwozerotwozero\") == \"0022268\"\n assert candidate(s = \"fivetwofivesixfivesevenfivethree\") == \"23555567\"\n assert candidate(s = \"onefourthreezeroonetwoeightthreezero\") == \"001123348\"\n assert candidate(s = \"zerozerotwoonetwoonetwothreefour\") == \"001122234\"\n assert candidate(s = \"nineeightsevensixfivetwothreeonezero\") == \"012356789\"\n assert candidate(s = \"sevensevensevensevenseven\") == \"77777\"\n assert candidate(s = \"onetwothreefourfivesixseveneightninezeroonetwothree\") == \"0112233456789\"\n assert candidate(s = \"twotwoeighteightzerosixsixthree\") == \"02236688\"\n assert candidate(s = \"twothreefourfivesixseveneightnineseveneightsixfivethreeonezeroonetwothree\") == \"011223334556677889\"\n assert candidate(s = \"twoeightfourzerosixonetwoeight\") == \"01224688\"\n assert candidate(s = \"fourfourfoursixsixsix\") == \"444666\"\n assert candidate(s = \"twoseveneightzerozeroeightone\") == \"0012788\"\n assert candidate(s = \"zeroonetwothreefourfivesixseveneightninenineeight\") == \"012345678899\"\n assert candidate(s = \"fourzerotwoonetwoonetwothreefour\") == \"011222344\"\n assert candidate(s = \"eighteightsevensevensevensixsixsixsixsixtwo\") == \"26666677788\"\n assert candidate(s = \"nineninethreeeight\") == \"3899\"\n assert candidate(s = \"fiveeighttwofourzero\") == \"02458\"\n assert candidate(s = \"sevenonethreesevenzero\") == \"01377\"\n assert candidate(s = \"sixsixsixsixsixsixsixsix\") == \"66666666\"\n assert candidate(s = \"oneoneoneoneoneone\") == \"111111\"\n assert candidate(s = \"fiveseveneightsevensevenfoursixsixsix\") == \"456667778\"\n assert candidate(s = \"nineeightsevensixfivenineeightseven\") == \"56778899\"\n assert candidate(s = \"threeeightfivesixtwonine\") == \"235689\"\n assert candidate(s = \"sixfivesixfivesixfive\") == \"555666\"\n assert candidate(s = \"onezerotwothreefourfivesixseveneightnine\") == \"0123456789\"\n assert candidate(s = \"fiveeighteighteighteighteightsixsixsixsixsixtwo\") == \"256666688888\"\n assert candidate(s = \"seveneightzeroonetwothreefourfivesixnine\") == \"0123456789\"\n assert candidate(s = \"oneeighttwosixthreesevenfourfiveoneeight\") == \"1123456788\"\n assert candidate(s = \"fivefivefivefive\") == \"5555\"\n assert candidate(s = \"eighteenteeneighteeneighteen\") == \"888\"\n assert candidate(s = \"nineeightsevensixfivofoureightseven\") == \"145677889\"\n assert candidate(s = \"sixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsixsix\") == \"66666666666666666666666666\"\n assert candidate(s = \"twoeightfiveonesixsixeightthreezeroonetwo\") == \"01122356688\"\n assert candidate(s = \"sixsixsixsixsixsixsixsixsixsixtwoeightzero\") == \"0266666666668\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnineeightsevenzerozero\") == \"0012345677889\"\n assert candidate(s = \"fivefivesixsixsevensevensevenseven\") == \"55667777\"\n assert candidate(s = \"seveneightnineeightseven\") == \"77889\"\n assert candidate(s = \"threeeighthreesixtwozeroonetwo\") == \"01223368\"\n assert candidate(s = \"twoseveneightzerozeroeightoneonetwothreefour\") == \"00112234788\"\n assert candidate(s = \"threeeighttwotwoeightzerozerozero\") == \"00022388\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnineseveneight\") == \"12345677889\"\n assert candidate(s = \"sevenfoursixsixthreeeight\") == \"346678\"\n assert candidate(s = \"zeroseveneightfivefourthreeonetwoeighttwozeroonetwothreefour\") == \"001122233445788\"\n assert candidate(s = \"threeonetwozeroeightfivesixsevennine\") == \"012356789\"\n assert candidate(s = \"zerotwofoursixeightzerofoursixeight\") == \"002446688\"\n assert candidate(s = \"sevensixsixsixseven\") == \"66677\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnineeightfoursixthreeonetwozero\") == \"0112233445667889\"\n assert candidate(s = \"sixsixfivefivethreeeightthreezerotwo\") == \"023355668\"\n assert candidate(s = \"twotwosixsixsixthreeeight\") == \"2236668\"\n assert candidate(s = \"threeeightzeroseveneighttwoeightthree\") == \"02337888\"\n assert candidate(s = \"sixsixsixsixsixsixsixsixsixsixsixsixsixsix\") == \"66666666666666\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnineseven\") == \"1234567789\"\n assert candidate(s = \"nineteennineteennineeighteighteight\") == \"888999\"\n assert candidate(s = \"threeseveneightzeroninesevenonefour\") == \"01347789\"\n assert candidate(s = \"zerotwozeroonetwozeroonetwozeroone\") == \"0000111222\"\n assert candidate(s = \"sixsixsixfivefivetwoonetwoonetwo\") == \"1122255666\"\n assert candidate(s = \"fiveeightfiveonezeroeighttwoseven\") == \"01255788\"\n assert candidate(s = \"oneeighteighteightsixsixtwoonetwo\") == \"112266888\"\n assert candidate(s = \"eightsixthreezerosixtwozero\") == \"0023668\"\n assert candidate(s = \"sixsixsixsixsixsixsix\") == \"6666666\"\n assert candidate(s = \"sixseveneightninezerotwoonetwoonetwothreefour\") == \"011222346789\"\n assert candidate(s = \"zerotwozeroonetwozeroonetwozerooneonetwothreefourfivesixseveneightnine\") == \"0000111122223456789\"\n assert candidate(s = \"zerofivefivesixsixsixsixzeroseveneight\") == \"0055666678\"\n assert candidate(s = \"sixsevensixsevensixsevensix\") == \"6666777\"\n assert candidate(s = \"nineeightsevenfoursixthreeonetwo\") == \"12346789\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnineninenine\") == \"12345678999\"\n assert candidate(s = \"fourninesixfourthreezeroonetwoeightfour\") == \"0123444689\"\n assert candidate(s = \"zerotwozerozerozerozero\") == \"000002\"\n assert candidate(s = \"twothreefourfivesixseveneightnineeightseven\") == \"2345677889\"\n assert candidate(s = \"eighteennineteensixthreezerozero\") == \"003689\"\n assert candidate(s = \"onetwothreefourfivesixseveneightoneninezero\") == \"01123456789\"\n assert candidate(s = \"oneonetwothreefourfivesixseveneightninezeroonetwothreefourfivesixseveneightninezero\") == \"001112233445566778899\"\n assert candidate(s = \"fivefivefivefivefivefivefivefivefivefiveonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefourthreeonetwothreefour\") == \"1111122222333333333444445555555555\"\n assert candidate(s = \"sixsixsixsixsixfivefivefive\") == \"55566666\"\n assert candidate(s = \"threeonetwoeightsevenzero\") == \"012378\"\n assert candidate(s = \"sixsixsixsixsixsixsixsixsixsix\") == \"6666666666\"\n assert candidate(s = \"zerotwoonetwoonetwothreefourfivesixseveneightnine\") == \"0112223456789\"\n assert candidate(s = \"fivefourthreeonetwozeroeighteighttwo\") == \"012234588\"\n assert candidate(s = \"twosevensixsixeighttwosix\") == \"2266678\"\n assert candidate(s = \"zerofourfourfourfourfourfourfour\") == \"04444444\"\n assert candidate(s = \"threethreeeighttwofivefour\") == \"233458\"\n assert candidate(s = \"sixeighteighteensixeighteighteen\") == \"668888\"\n assert candidate(s = \"zeronineeightsevensixfivetwoonezero\") == \"001256789\"\n assert candidate(s = \"nineeightsevenfoursixzeronineeightsevenfoursix\") == \"04466778899\"\n assert candidate(s = \"eighteighteightsevensevensevenfoursixsixsix\") == \"4666777888\"\n assert candidate(s = \"zerotwothreefourfivesixseveneightnineonezero\") == \"00123456789\"\n assert candidate(s = \"fivethreefournineeighttwoseven\") == \"2345789\"\n assert candidate(s = \"threeeightthreeeightthreeeight\") == \"333888\"\n assert candidate(s = \"twotwotwofourfourfourfoursixsixsixsix\") == \"22244446666\"\n assert candidate(s = \"zerotwoonetwoonetwo\") == \"011222\"\n assert candidate(s = \"twotwoonetwoonetwoonezerozero\") == \"001112222\"\n assert candidate(s = \"ninenineninenineninenineninenineninenine\") == \"9999999999\"\n assert candidate(s = \"sixsixsixsevensevensevenfivefifivefive\") == \"5555666777\"\n assert candidate(s = \"threeeightsevenfourfivesixtwothree\") == \"23345678\"\n assert candidate(s = \"sixsixsixsixsixtwoonetwoonetwo\") == \"1122266666\"\n assert candidate(s = \"eightonetwozerofourfivesixnine\") == \"01245689\"\n assert candidate(s = \"eightsevenfoursixthreeonetwoeightseventhree\") == \"1233467788\"\n assert candidate(s = \"eightsevenfoursixthreeonetwoeightseven\") == \"123467788\"\n assert candidate(s = \"zerofourzerofourzerofour\") == \"000444\"\n assert candidate(s = \"onetwothreefourfivesixseveneightninenineeightsevenfoursixthreeonetwoeightseventhree\") == \"11223334456677788899\"\n assert candidate(s = \"sixsixsixsixsixsixsixsixsixsixtwoeightzeroonetwothreefourthreeonetwothreefour\") == \"0112223334466666666668\"\n assert candidate(s = \"nineeightsevenzerosixfoursixtwoonezero\") == \"0012466789\"\n assert candidate(s = \"fivezeroonetwothreefourfivesixseveneightninezero\") == \"001234556789\"\n assert candidate(s = \"threeeighttwozerofoureightonezeronine\") == \"001234889\"\n assert candidate(s = \"sevenzerothreeeightonetwozerozero\") == \"00012378\"\n assert candidate(s = \"fourzerosixfourzerosixfourzerosix\") == \"000444666\"\n assert candidate(s = \"fivefivefivefivefivefivefivefivefivefive\") == \"5555555555\"\n assert candidate(s = \"eighteighttwotwozerofourfour\") == \"0224488\"\n assert candidate(s = \"zeroonetwothreefourfivesixseveneightnineseveneightsixfivethreeonezeroonetwothreeonetwothreefour\") == \"001111222333344556677889\"\n assert candidate(s = \"zeroninetwoeighttwofiveeight\") == \"0225889\"\n assert candidate(s = \"onetwothreefourfivesixseveneightninenineninenine\") == \"123456789999\"\n assert candidate(s = \"sevenonesevenoneseven\") == \"11777\"\n assert candidate(s = \"onezerozeroonetwothreefourfivesixseveneightnine\") == \"001123456789\"\n assert candidate(s = \"zerotwoonetwoonetwothreefourfivesixseven\") == \"01122234567\"\n assert candidate(s = \"onetwothreefourfivesixseveneightninezeroonetwothreefourfivesixseveneightnine\") == \"0112233445566778899\"\n assert candidate(s = \"zeroseveneightfourzeroseveneightfour\") == \"00447788\"\n assert candidate(s = \"twofourfivesixeighteight\") == \"245688\"\n assert candidate(s = \"onetwothreefourfivesixseveneightnineonetwothreefourfivesixseveneightnineonetwothreefourfivesixseveneightnine\") == \"111222333444555666777888999\"\n assert candidate(s = \"ninethreetwoeightsevenfivesixonefour\") == \"123456789\"\n assert candidate(s = \"twoseventhreesixthreeeight\") == \"233678\"\n assert candidate(s = \"zerofourzerofivefivefourfour\") == \"0044455\"\n assert candidate(s = \"onetwothreefourfivesixseveneightninezero\") == \"0123456789\"\n assert candidate(s = \"zerotwothreefourfivesixseveneightnineonezerotwothreefourfivesixseveneightninenine\") == \"00122334455667788999\"\n assert candidate(s = \"nineeightsevensixfivethreetwoonezero\") == \"012356789\"\n assert candidate(s = \"nineeightsixfoureeightfoureeighttwo\") == \"24468889\"\n assert candidate(s = \"nineeighteensixeightsixsixsix\") == \"6666889\"\n assert candidate(s = \"onetwothreefourfivesixseveneightninenine\") == \"1234567899\"\n assert candidate(s = \"threeeightonethreeeightthree\") == \"133388\"\n assert candidate(s = \"zerotwothreefourfivesixseveneightnine\") == \"023456789\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().originalDigits", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var originalDigits = function(s) {", "container": null, "callable": "originalDigits", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 424, "task_id": "longest-repeating-character-replacement", "difficulty": "Medium", "problem_description": "You are given a string s and an integer k. You can choose any character of the string and change it to any other uppercase English character. You can perform this operation at most k times.\nReturn the length of the longest substring containing the same letter you can get after performing the above operations.\n \nExample 1:\n\nInput: s = \"ABAB\", k = 2\nOutput: 4\nExplanation: Replace the two 'A's with two 'B's or vice versa.\n\nExample 2:\n\nInput: s = \"AABABBA\", k = 1\nOutput: 4\nExplanation: Replace the one 'A' in the middle with 'B' and form \"AABBBBA\".\nThe substring \"BBBB\" has the longest repeating letters, which is 4.\nThere may exists other ways to achieve this answer too.\n \nConstraints:\n\n1 <= s.length <= 105\ns consists of only uppercase English letters.\n0 <= k <= s.length\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"ABABABAB\",k = 3) == 7\n assert candidate(s = \"AAAAAAAAAAAAABBBAABBCCDDEE\",k = 5) == 20\n assert candidate(s = \"AABBCCDD\",k = 2) == 4\n assert candidate(s = \"\",k = 0) == 0\n assert candidate(s = \"A\",k = 1) == 1\n assert candidate(s = \"AABAABBBCCCC\",k = 3) == 7\n assert candidate(s = \"ABBBB\",k = 0) == 4\n assert candidate(s = \"ABCCDEEEEE\",k = 3) == 8\n assert candidate(s = \"ABAB\",k = 2) == 4\n assert candidate(s = \"AABBB\",k = 2) == 5\n assert candidate(s = \"ZYXWVUTSRQPONMLKJIHGFEDCBA\",k = 25) == 26\n assert candidate(s = \"ABACBCAB\",k = 2) == 4\n assert candidate(s = \"ABBB\",k = 0) == 3\n assert candidate(s = \"ABBB\",k = 1) == 4\n assert candidate(s = \"ABCDE\",k = 1) == 2\n assert candidate(s = \"AABABBA\",k = 1) == 4\n assert candidate(s = \"AAABBBCCC\",k = 3) == 6\n assert candidate(s = \"AAAA\",k = 2) == 4\n assert candidate(s = \"ABCDE\",k = 3) == 4\n assert candidate(s = \"ABCDE\",k = 2) == 3\n assert candidate(s = \"AABBBBCCDDDDD\",k = 2) == 7\n assert candidate(s = \"ACBACBACBACBACBACBACBACBACBACBAC\",k = 5) == 8\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",k = 0) == 40\n assert candidate(s = \"AAAAAAAAAABBBBBBBBBBCCCCCCCCCCDDDDDDDDDDD\",k = 15) == 26\n assert candidate(s = \"AAAAAAAAAA\",k = 5) == 10\n assert candidate(s = \"ABCABCABCABCABCABCABCABCABCABC\",k = 10) == 16\n assert candidate(s = \"AAAAAAAAAAAABBBBCCCC\",k = 10) == 20\n assert candidate(s = \"ABABABAB\",k = 1) == 3\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ\",k = 25) == 27\n assert candidate(s = \"AAABBBCCCDDDAAABBBCCCDDD\",k = 7) == 10\n assert candidate(s = \"QWERTYUIOPASDFGHJKLZXCVBNM\",k = 24) == 25\n assert candidate(s = \"AAAAAAAAAAAABBBCCCCCCAAAAAAAAAAA\",k = 6) == 18\n assert candidate(s = \"AAABBBAABBCCDDDDDDDEEFFGGHHIIJJJKKKLLLMMMNNN\",k = 25) == 32\n assert candidate(s = \"AAAAAAAAAABBBBBBBBBBBCCCCCCDDDDDDDDDDD\",k = 25) == 36\n assert candidate(s = \"MMMMNNNNOOOO\",k = 5) == 9\n assert candidate(s = \"AAAAAAAAABBB\",k = 2) == 11\n assert candidate(s = \"AABABABABAB\",k = 5) == 11\n assert candidate(s = \"ABABABABABABABABABABABABABABABABAB\",k = 15) == 31\n assert candidate(s = \"ABACABAACBACABCABACBACABCABACBACABCABACBACABCABACBACAB\",k = 20) == 36\n assert candidate(s = \"AAAAAAAAAABBBBBBBBCCCCCCCCCC\",k = 10) == 20\n assert candidate(s = \"ABCDEABCDEABCDEABCDEABCDE\",k = 10) == 13\n assert candidate(s = \"ABBCCCDDDDEEEEEFFFFFF\",k = 6) == 12\n assert candidate(s = \"ABABABABABABABABAB\",k = 10) == 18\n assert candidate(s = \"ABACABACABACABACABACABACABACABACABACABAC\",k = 15) == 31\n assert candidate(s = \"ABABABABABABABABABABABABABABABABABABABAB\",k = 15) == 31\n assert candidate(s = \"ABABABABABABABABABABABABABABABAB\",k = 0) == 1\n assert candidate(s = \"AABABABABABABABABABABABABABABABAB\",k = 5) == 12\n assert candidate(s = \"AABCABCABCABCABCABC\",k = 4) == 8\n assert candidate(s = \"BAAAAAAAAAABAAAAAAAAAAB\",k = 5) == 23\n assert candidate(s = \"AABBCCDDEEFFGG\",k = 3) == 5\n assert candidate(s = \"ACACACACACACAC\",k = 2) == 5\n assert candidate(s = \"AAABBBCCCDDDAAABBBCCCDDDAAABBBCCCDDD\",k = 20) == 29\n assert candidate(s = \"ABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABABAB\",k = 10) == 21\n assert candidate(s = \"ABACABACABACABACABACABACABACABAC\",k = 5) == 11\n assert candidate(s = \"AAABBBCCCDDD\",k = 4) == 7\n assert candidate(s = \"XYZXYZXYZXYZXYZXYZXYZXYZ\",k = 15) == 23\n assert candidate(s = \"ABCDEABCDEABCDEABCDEABCDEABCDE\",k = 6) == 8\n assert candidate(s = \"ABBBABAABBBBBBBBAAABBB\",k = 5) == 17\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",k = 100) == 60\n assert candidate(s = \"AAAAAAAAAAABBBBBBBBBBB\",k = 10) == 21\n assert candidate(s = \"ABABABABAB\",k = 5) == 10\n assert candidate(s = \"AAABBCCDDEEFFF\",k = 4) == 7\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAB\",k = 1) == 24\n assert candidate(s = \"XYZXYZXYZXYZ\",k = 3) == 5\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\",k = 26) == 26\n assert candidate(s = \"ABABABABABABABAB\",k = 8) == 16\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAA\",k = 0) == 20\n assert candidate(s = \"AABBBCCCDDDDDEEEEFFFFFFGGGGGGHHHHHIIIJJJKKKLLLLMMMMNNNNOOOOPPPP\",k = 30) == 36\n assert candidate(s = \"BBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAA\",k = 5) == 26\n assert candidate(s = \"AABABBAACCCDDDEEE\",k = 3) == 8\n assert candidate(s = \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\",k = 0) == 106\n assert candidate(s = \"AAAAAAAABBBBBBBB\",k = 0) == 8\n assert candidate(s = \"ABABABABABABAB\",k = 7) == 14\n assert candidate(s = \"AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXXYYYYZZZZ\",k = 50) == 54\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAB\",k = 50) == 41\n assert candidate(s = \"MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM\",k = 100) == 44\n assert candidate(s = \"ABCABCABCABCABCABCABCABC\",k = 15) == 23\n assert candidate(s = \"AABBBCCDDEE\",k = 2) == 5\n assert candidate(s = \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\",k = 1000) == 31\n assert candidate(s = \"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\",k = 100) == 108\n assert candidate(s = \"AABBCCDDEEFFGGHHIIJJKKLLMMNNOOPPQQRRSSTTUUVVWWXXYYZZ\",k = 20) == 22\n assert candidate(s = \"AAABBBCCCDDD\",k = 3) == 6\n assert candidate(s = \"AAAAA\",k = 0) == 5\n assert candidate(s = \"AABBBCCCDDDD\",k = 3) == 7\n assert candidate(s = \"AAABBBCCCDDDEEEFFF\",k = 6) == 9\n assert candidate(s = \"AAAAAAAAABBBBBBBBCCCCCCCCCC\",k = 10) == 20\n assert candidate(s = \"BBBAAAABBBAAAABBBAAAABBB\",k = 5) == 13\n assert candidate(s = \"ABABABABABABABABABAB\",k = 5) == 11\n assert candidate(s = \"ACACACACACACACACACACACAC\",k = 5) == 11\n assert candidate(s = \"ABACABACABAC\",k = 4) == 9\n assert candidate(s = \"ABABABABABABABABABAB\",k = 10) == 20\n assert candidate(s = \"AAAAAAABBBCCCDDDDDD\",k = 5) == 12\n assert candidate(s = \"BBBBAAAACCCD\",k = 4) == 8\n assert candidate(s = \"QWERTYUIOPASDFGHJKLZXCVBNM\",k = 26) == 26\n assert candidate(s = \"XYZXYZXYZXYZXYZXYZ\",k = 6) == 10\n assert candidate(s = \"AAAAAAAAAAABBBBCCCCCDDDD\",k = 10) == 21\n assert candidate(s = \"BBBBAAAACCCCDDDD\",k = 5) == 9\n assert candidate(s = \"XYZXYZXYZXYZXYZXYZXYZXYZ\",k = 20) == 24\n assert candidate(s = \"AAAAAAAABBBBBBBB\",k = 3) == 11\n assert candidate(s = \"AAAAAAAAAAAAAAAABBB\",k = 2) == 18\n assert candidate(s = \"XYZXYZXYZ\",k = 3) == 5\n assert candidate(s = \"AABBCDEEFGHIJKLLMNOPQRSTUVWXYZ\",k = 25) == 27\n assert candidate(s = \"AABABBAABBCCDDEEFFGG\",k = 4) == 9\n assert candidate(s = \"AABBCCDDEEFFGGHHIIJJKKLLMMNNOOPPQQRRSSTTUUVVWWXXYYZZ\",k = 25) == 27\n assert candidate(s = \"AAABBBCCCDDD\",k = 6) == 9\n"}, "metadata": {"canonical_parameter_names": ["s", "k"], "leetcode_dataset_entry_point": "Solution().characterReplacement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var characterReplacement = function(s, k) {", "container": null, "callable": "characterReplacement", "parameters": [{"name": "s", "type": "string"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 433, "task_id": "minimum-genetic-mutation", "difficulty": "Medium", "problem_description": "A gene string can be represented by an 8-character long string, with choices from 'A', 'C', 'G', and 'T'.\nSuppose we need to investigate a mutation from a gene string startGene to a gene string endGene where one mutation is defined as one single character changed in the gene string.\n\nFor example, \"AACCGGTT\" --> \"AACCGGTA\" is one mutation.\n\nThere is also a gene bank bank that records all the valid gene mutations. A gene must be in bank to make it a valid gene string.\nGiven the two gene strings startGene and endGene and the gene bank bank, return the minimum number of mutations needed to mutate from startGene to endGene. If there is no such a mutation, return -1.\nNote that the starting point is assumed to be valid, so it might not be included in the bank.\n \nExample 1:\n\nInput: startGene = \"AACCGGTT\", endGene = \"AACCGGTA\", bank = [\"AACCGGTA\"]\nOutput: 1\n\nExample 2:\n\nInput: startGene = \"AACCGGTT\", endGene = \"AAACGGTA\", bank = [\"AACCGGTA\",\"AACCGCTA\",\"AAACGGTA\"]\nOutput: 2\n\n \nConstraints:\n\n0 <= bank.length <= 10\nstartGene.length == endGene.length == bank[i].length == 8\nstartGene, endGene, and bank[i] consist of only the characters ['A', 'C', 'G', 'T'].\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAACGGTA\",bank = ['AACCGGTA', 'AACCGCTA', 'AAACGGTA']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = ['AACCGGTA']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = []) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = ['TACCGGTA']) == -1\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"CCCCCCCC\",bank = ['AAAAAAAA', 'AAAAAAAC', 'AAAAAACC', 'AAAAACCC', 'AAAACCCC', 'AAACCCCC', 'AACCCCCC', 'ACCCCCCC', 'CCCCCCCC']) == 8\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCAAAA\",bank = ['AACCAAAA', 'AACCAAAT', 'AACCAATA', 'AACCGAAA', 'AACCAATA', 'AACCAATT', 'AACAAATT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT']) == 4\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCTGCTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'AACCGGAC', 'ACCGGCTA', 'ACCTGCTA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTTTCCCC\",bank = ['AAACGGCT', 'AACCGGCA', 'AAACGGTA', 'AAACGGCC', 'TTTTCCCC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGCGCG\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'ACCGCGTA', 'ACCGCGCG', 'ACCGCGCT', 'ACCGCGTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTTTCCCC\",bank = ['AACCGGTA', 'AACCGGCA', 'AACCGGCT', 'AACCGGCG', 'TTACGGCG', 'TTACGGCC', 'TTACGGTC', 'TTACGGTT', 'TTAGGGTT', 'TTAGGGTC', 'TTAGGGCC', 'TTAGGGCG', 'TTTTGGCG', 'TTTTGGCC', 'TTTTGGTC', 'TTTTGGTT', 'TTTTGGGA', 'TTTTGGAA', 'TTTTGGAT', 'TTTTGCAA', 'TTTTGCCA', 'TTTTGCTA', 'TTTTGCAC', 'TTTTGCGA', 'TTTTGCAG', 'TTTTGCGT', 'TTTTGCTC', 'TTTTGCCG', 'TTTTGGCG', 'TTTTGCCC', 'TTTTCCCC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGCCGACT\",bank = ['AACCGGCA', 'AACCGGAA', 'AACCGGGA', 'GGCCGGTA', 'GGCCGGCA', 'GGCCGGAA', 'GGCCGGGA', 'GGCCGACT']) == -1\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"TTTTTTTT\",bank = ['AAAAAGGG', 'AAAGGGGG', 'AAGGGGGG', 'AGGGGGGG', 'GGGGGGGG', 'GGGGGGGT', 'GGGGGGTT', 'GGGGGTTT', 'GGGGTTTT', 'GGGTTTTT', 'GGTTTTTT', 'GTTTTTTT', 'TTTTTTTT']) == -1\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"TTTTTTTT\",bank = ['AAAAAACC', 'AAAAACCC', 'AAAAACGG', 'AAAACGGG', 'AAACGGGG', 'AACGGGGG', 'ACGGGGGG', 'CGGGGGGG', 'TTTTTTTA', 'TTTTTTAG', 'TTTTTTCG', 'TTTTTCGG', 'TTTTGCGG', 'TTTTGGGG', 'TTTGCGGG', 'TTTGGGGG', 'TTGCGGGG', 'TTGGGGGG', 'TGCGGGGG', 'TGGGGGGG', 'GCGGGGGG', 'GGGGGGGG']) == -1\n assert candidate(startGene = \"ACAGACGG\",endGene = \"AACCGGGA\",bank = ['AACGACGG', 'AACGACGT', 'AACGGCGT', 'AACGGCGA', 'AACGGGGA', 'AACCGGGA']) == -1\n assert candidate(startGene = \"ACGTACGT\",endGene = \"TTACGTAC\",bank = ['ACGTACGA', 'TTACGTAA', 'TTACGTAC', 'TTACGTCG', 'ACGTACGG']) == -1\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"CCCCCCCC\",bank = ['AAAAAACC', 'AAAAACCC', 'AAAACCCC', 'AAACCCCC', 'AACCACCC', 'AACCCCAC', 'AACCACCC', 'ACCAACCC', 'ACCCACCC', 'CCCCCCCC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GACCGGTA\",bank = ['AACCGGCA', 'GACCGGTA', 'AACCGGCT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT', 'GACCGGTT', 'GACCGGTC', 'GACCGGTA', 'GACCGGAC']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGTAA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGTC', 'AACCGTCA', 'AACCGTAA']) == 4\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGCT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTTTTTTT\",bank = ['AAACGGTA', 'AACCGCTA', 'AAACGGTT', 'TTTTGGTT', 'TTTTTGGT', 'TTTTTTGT', 'TTTTTTTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGGGGGGG\",bank = ['AACCGGTA', 'AACCGGTC', 'TACCGGTT', 'GGACGGTT', 'GGGGGGTA', 'GGGGGGTT', 'GGGGGGGT', 'GGGGGGGG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"CGCGCGCG\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'CGCGGGTA', 'CGCGCGCG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGAACTTT\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'GAACGGTA', 'GGAACTTA', 'GGAACTTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGCT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT', 'AACCGGTC', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGCT\",bank = ['AACCGGCA', 'AACCGGCG', 'AACCGGCT', 'AACCGGCT', 'AACCGGCT']) == 1\n assert candidate(startGene = \"AAAACCCC\",endGene = \"CCCCAAAA\",bank = ['AAAACCCA', 'AAAACCAA', 'AAAACCAA', 'AAAACAAA', 'AAACAAAA', 'AACAAAAA', 'ACAAAAAA', 'CAAAAAAA', 'CAAACCAA', 'CCAACCAA', 'CCCCAAAC', 'CCCCACAA', 'CCCCAACC', 'CCCCAAAC', 'CCCCAACA', 'CCCCAAAA']) == -1\n assert candidate(startGene = \"AAAAACCC\",endGene = \"CCCCCCCC\",bank = ['AAAACCCC', 'AAACCCCC', 'AACCCCCC', 'AACCACCC', 'AACCGCCC', 'AACCGCCC', 'AACCGGCC', 'AACCGGTC', 'AACCGGTA', 'AACCGGTT', 'AACCGGCT', 'AACCGGCG', 'AACCGGCA', 'AACCGGCC', 'AACCGGCG', 'AACCGGCA', 'GGCCCCCC', 'GGCCCACC', 'GGCCCCGC', 'GGCCCCGA', 'GGCCCCTC', 'GGCCCCTG', 'GGCCCCTA', 'GGCCGGCC', 'GGCCGGCG', 'GGCCGGCA', 'GGCCGGTC', 'GGCCGGTA', 'GGCCGGTT', 'GGCCGCCC', 'GGCCGGGG', 'CCCCGGGG', 'CCCCGGGC', 'CCCCGGCG', 'CCCCGGCA', 'CCCCGGTC', 'CCCCGGTA', 'CCCCGGTT', 'CCCCGCCC', 'CCCCGGGG', 'CCCCCCCC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTCGCGCG\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'TTCGCGTA', 'TTCGCGCG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAGGCGTT\",bank = ['AACCGGTA', 'AACCGGCT', 'AACCGGCA', 'AACCGGCG', 'AACCGGTC', 'AACCGCTA', 'AAACGGTA', 'AACAGGTA', 'AAACGGTC', 'AAACGGCT', 'AAACGGCG', 'AAACGGTT', 'AAGGCGTA', 'AAGGCGTC', 'AAGGCGCA', 'AAGGCGCG', 'AAGGCGCT', 'AAGGCGTT']) == -1\n assert candidate(startGene = \"AAAAACCC\",endGene = \"GGGGCCCC\",bank = ['AAAACCCC', 'AAAGCCCC', 'AAGGCCCC', 'GGGGCCCC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'AAACGGCA', 'AACCGGCA', 'AAACGGTA', 'AAACGGCA', 'AACCGGCA', 'AAACGGTA', 'AAACGGCA']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGGGGGGA\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'GGGGGGTT', 'GGGGGGTA', 'GGGGGGGA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTA\",bank = ['AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAAAAAAA\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'AAAAAGTA', 'AAAAAAAA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTTTTTTT\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'AACCGGAC', 'TTTTTTTA', 'TTTTTTTT']) == -1\n assert candidate(startGene = \"AAAAACCC\",endGene = \"CCCCGGGG\",bank = ['AACCCCCC', 'ACCCCCCG', 'ACCACCCC', 'ACCACCCC', 'ACCCCACG', 'CCCCGGGA', 'CCCCGGGG']) == -1\n assert candidate(startGene = \"GGGGCCCC\",endGene = \"AACCGGTT\",bank = ['GGGGCCCG', 'GGGGCCCT', 'GGGGCCTT', 'GGGGCCGG', 'GGGGACGG', 'GGGAGCGG', 'GGGAACGG', 'GGAACCGG', 'GAACCGGG', 'AACCGGGG', 'AACCGGTT']) == -1\n assert candidate(startGene = \"TTTTTTTT\",endGene = \"AAAAAAAA\",bank = ['ATTTTTTT', 'AATTTTTT', 'AAATTTTT', 'AAAATTTT', 'AAAAATTT', 'AAAAATTA', 'AAAAAATT', 'AAAAAAAT', 'AAAAAAAC', 'AAAACAAA', 'AAACAAAA', 'AACAAAAA', 'ACAAAAAA', 'CAAAAAAA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AGCTAGCA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AACCGGTA', 'AGCTAGCA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGTGTA\",bank = ['AACCGGTA', 'AACCGCTA', 'AAACGGTA', 'ACCGTGTA', 'ACCGTGGT', 'ACCGTGTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGCGCG\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'ACCGCGTA', 'ACCGCGCG', 'ACCGCGCT', 'ACCGCGTT', 'ACCGCGGA', 'ACCGCGGC', 'ACCGCGCC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AGCGGTTA\",bank = ['AACCGGTA', 'AACCGGCT', 'AACCGGCA', 'AACCGGCG', 'AACCGGTC', 'AACCGCTA', 'AAACGGTA', 'AACAGGTA', 'AAACGGTC', 'AAACGGCT', 'AAACGGCG', 'AAACGGTT', 'AAGGCGTA', 'AAGGCGTC', 'AAGGCGCA', 'AAGGCGCG', 'AAGGCGCT', 'AAGGCGTT', 'AGCGGTTA', 'AGCGGCTA', 'AGCGGCTC', 'AGCGGCGT', 'AGCGGCGC', 'AGCGGCCC', 'AGCGGGTA', 'AGCGGGCA', 'AGCGGGCG', 'AGCGGGCT', 'AGCGGGAA', 'AGCGGGAC', 'AGCGGGAG', 'AGCGGCGT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGGTTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGCT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT', 'ACCGGTTA', 'ACCGGGTA', 'ACCGGATA', 'ACCGGTTT']) == -1\n assert candidate(startGene = \"GACCGGTA\",endGene = \"AACCGGTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGCT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT', 'GACCGGTT', 'GACCGGTC', 'GACCGGTA', 'GACCGGAC']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGTGGT\",bank = ['AACCGGTA', 'AACCGGCA', 'AACCGGCG', 'AACCGGCT', 'AACCGGAT', 'AACCGGAA', 'AACCGCAT', 'AACCGCCT', 'AACCGCGT', 'AACCGCGC', 'AAACGGTA', 'AAACGGCA', 'AAACGGCG', 'AAACGGCT', 'AAACGGAT', 'AAACGGAA', 'AAACGGCA', 'AAACGGCC', 'AAACGCCG', 'AAACGCCT', 'ACCGGGTA', 'ACCGGGCA', 'ACCGGGCG', 'ACCGGGCT', 'ACCGGGAT', 'ACCGGGAA', 'ACCGGGCA', 'ACCGGGCC', 'ACCGGGCG', 'ACCGGGCT', 'ACCGGCTA', 'ACCGGCCA', 'ACCGGCGT', 'ACCGGCGC', 'ACCGGCCT', 'ACCGGCCC', 'ACCGGTAA', 'ACCGGTCG', 'ACCGGTTA', 'ACCGGTCA', 'ACCGGTCC', 'ACCGGTCG', 'ACCGGTCA', 'ACCGGTCC', 'ACCGGTCG', 'ACCGGTCA', 'ACCGGTCC', 'ACCGTGGC', 'ACCGTGGT']) == -1\n assert candidate(startGene = \"AAACGGTA\",endGene = \"AACCGGTA\",bank = ['AAACGGTT', 'AACCGGTT', 'AACCGGTA']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GACCGGTA\",bank = ['AACCGGTA', 'AACCGGCA', 'AACCGGAA', 'AACCGGTC', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'GACCGGTA']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGGA\",bank = ['AACCGGTA', 'AACCGGCA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGGGGGGG\",bank = ['AACCGGTA', 'AAACGGTA', 'GGAAAAAA', 'GGGGGGGA', 'GGGGGGGG']) == -1\n assert candidate(startGene = \"GAGGACAA\",endGene = \"AACCGGTA\",bank = ['AACCGGTA', 'GAGGAGAA', 'GAGGAGGA', 'GAGGACGA', 'GAGGACCA', 'GAGGACTA', 'GAGGACAA', 'GAGGACAT', 'GAAGACAA', 'AACGACAA', 'AACGGCAA', 'AACGGGAA', 'AACGGGTA', 'AACCGGTA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGGCTA\",bank = ['AACCGGTA', 'AACCGCTA', 'ACCGGCTA', 'ACCGGCTC', 'ACCGGCCC', 'ACCGGTTA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAACGGGA\",bank = ['AACCGGTA', 'AAACGGTA', 'AAACGGCA', 'AAACGGAA', 'AAACGGGA', 'AAACGGGA']) == 3\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACGGTACC\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'AACCGGAC', 'ACGGTACC']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTCCGGAA\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'AAACGGCA', 'TTACGGTA', 'TTACGGCA', 'TTCCGGTA', 'TTCCGGCA', 'TTCCGGAA', 'GGCCGGTA', 'GGCCGGCA', 'GGCCGGAA', 'TTCCGGTG', 'TTCCGGTC', 'TTCCGGAU', 'TTCCGGAC', 'TTCCGGAG', 'TTCCGGAT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTC\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'AACCGGAC', 'AACCGGTC']) == 1\n assert candidate(startGene = \"AAAAACCC\",endGene = \"GGGGGGGG\",bank = ['AAAACCCC', 'AAACCCCC', 'AACCCCCC', 'AACCACCC', 'AACCGCCC', 'AACCGGCC', 'AACCGGTC', 'AACCGGTA', 'AACCGGTT', 'AACCGGCT', 'AACCGGCG', 'AACCGGCA', 'GGCCCCCC', 'GGCCCACC', 'GGCCCCGC', 'GGCCCCGA', 'GGCCCCTC', 'GGCCCCTG', 'GGCCCCTA', 'GGCCGGCC', 'GGCCGGCG', 'GGCCGGCA', 'GGCCGGTC', 'GGCCGGTA', 'GGCCGGTT', 'GGCCGCCC', 'GGCCGGGG', 'GGGGGGGG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGGGGGGG\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'GGGGGGTA', 'GGGGGGGG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAAAAAGG\",bank = ['AACCGGTA', 'AACCGGCA', 'AACCGGCG', 'AACCGGCT', 'AACCGGAT', 'AACCGGAA', 'AACCGCAC', 'AACCGCCA', 'AACCGCCG', 'AACCGCCT', 'AAACGGTA', 'AAACGGCA', 'AAACGGCG', 'AAACGGCT', 'AAACGGAT', 'AAACGGAA', 'AAACGGCA', 'AAACGGCC', 'AAACGCCG', 'AAACGCCT', 'AAAAGGTA', 'AAAAGGCA', 'AAAAGGCG', 'AAAAGGCT', 'AAAAGGAA', 'AAAAGGAC', 'AAAAGGAG', 'AAAAAGTA', 'AAAAAGCA', 'AAAAAGCG', 'AAAAAGCT', 'AAAAAGAA', 'AAAAAGAC', 'AAAAAGAG', 'AAAAAAGT', 'AAAAAAGC', 'AAAAAAGA', 'AAAAAAGG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAACGGCC\",bank = ['AAACGGTA', 'AAACGGCA', 'AAACGGCC', 'AACCGGCA', 'AACCGGTA', 'AACCGGTC']) == 4\n assert candidate(startGene = \"AGCTATAG\",endGene = \"GACTGTAG\",bank = ['AGCTATAC', 'AGCTGTAG', 'AGCTTTAG', 'GACTATAG', 'GACTGTAG', 'GACTTTAG', 'GAATATAG', 'GGCTATAG', 'AGGTATAG']) == 3\n assert candidate(startGene = \"AAGAACGG\",endGene = \"GGAACGGT\",bank = ['AAGAACGA', 'AAGAACGG', 'AAGAACGT', 'AAGACGGT', 'AAGGACGT', 'AGGAACGT', 'GGAACGGT', 'GGAACGGC', 'GGAACGGA', 'GGGAACGA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"CGGTTTAA\",bank = ['AACCGGTA', 'AACCGGTC', 'AACCGGTA', 'CCCGGGTT', 'CGGTTTTT', 'CGGTTTAA', 'CGGTTTTG', 'CGGTGGAA', 'CGGACGAA', 'AACCGGAG', 'AACCGGCG', 'AACCGGGA', 'AACCGGTT', 'AACCGGAT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTT', 'AACCGGTA', 'AACCGGTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAACGGGA\",bank = ['AACCGGTA', 'AACCGCTA', 'AAACGGTA', 'AAACGGGA', 'AAACGGGC', 'AACCGGGT', 'AACCGGGG']) == 3\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"TTTTTTTT\",bank = ['AAAAAAGA', 'AAAACAAA', 'AAACAAAA', 'AAGAAAAA', 'AGAAAAAA', 'GAAAAAAA', 'TAAAAAAA', 'TTAAAAAA', 'TTTAAAAA', 'TTTTAAAA', 'TTTTTAAA', 'TTTTTTAA', 'TTTTTTTA', 'TTTTTTTT']) == 8\n assert candidate(startGene = \"ACGTACGT\",endGene = \"TGCATGCA\",bank = ['ACGTACGA', 'ACGTACGC', 'ACGTCAGT', 'TACGACGT', 'TGCATGCA', 'TGCATGCG', 'TGCATGTA', 'TGCAACGT', 'TGCGACGT', 'TGCAACGG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTCCGCCC\",bank = ['AACCGGTA', 'AACCGGTC', 'AACCGGCA', 'AACCGGCC', 'AACCGGCG', 'AACCGGCT', 'AACCGGAT', 'AACCGGAC', 'AACCGGAG', 'AACCGGAA', 'AACCGCAT', 'AACCGCCT', 'AACCGCGT', 'AACCGCGC', 'AACCGCCT', 'AACCGCCC', 'AACCAGCC', 'AACCAGCA', 'AACCAGCT', 'AACCAGCG', 'AACCGCCA', 'AACCGCCC', 'AACCGCCA', 'AACCGCCC', 'AACCGCCT', 'AACCGCCA', 'AACCGCCG', 'AACCGCCC', 'AACCGCCC', 'AACCGCCC', 'TTACGGCC', 'TTACGGCA', 'TTACGGCT', 'TTACGGCG', 'TTACGGTA', 'TTACGGTC', 'TTACGGAA', 'TTACGGAC', 'TTACGGAG', 'TTACGGCG', 'TTACGGCA', 'TTACGGCT', 'TTACGGCG', 'TTAGGGCC', 'TTAGGGCA', 'TTAGGGCT', 'TTAGGGCG', 'TTAGGGTA', 'TTAGGGTC', 'TTAGGGAA', 'TTAGGGAC', 'TTAGGGAG', 'TTAGGGCG', 'TTAGGGCA', 'TTAGGGCT', 'TTAGGGCG', 'TTTTGGCC', 'TTTTGGCA', 'TTTTGGCT', 'TTTTGGCG', 'TTTTGGTA', 'TTTTGGTC', 'TTTTGGAA', 'TTTTGGAC', 'TTTTGGAG', 'TTTTGGCA', 'TTTTGGCC', 'TTTTGGCT', 'TTTTGGCG', 'TTTTGGAA', 'TTTTGGAC', 'TTTTGGAG', 'TTTTGCAA', 'TTTTGCCA', 'TTTTGCTA', 'TTTTGCAC', 'TTTTGCGA', 'TTTTGCAG', 'TTTTGCGT', 'TTTTGCTC', 'TTTTGCCG', 'TTTTGGCG', 'TTTTGCCC', 'TTTTCCCC']) == -1\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"AAAAAAAA\",bank = ['AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA', 'AAAAAAAA']) == 0\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGCT\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'AACCGGAC', 'AACCGGCA', 'AACCGGCT']) == 1\n assert candidate(startGene = \"AAAAAAAA\",endGene = \"TTTTTTTT\",bank = ['AAAAAAAA', 'AAAACCCC', 'AAAAACCC', 'AAAAAACC', 'AAAAAAAC', 'AAAAAAAT', 'AAAAAATT', 'AAAAATTT', 'AAAATTTT', 'AAATTTTT', 'AATTTTTT', 'ATTTTTTT', 'TTTTTTTT']) == 8\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGGTTA\",bank = ['AACCGGTA', 'AACCGGCT', 'AACCGGCA', 'ACCGGTTA', 'ACCGGGTA', 'ACCGGTCG', 'ACCGGCTA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAGCGGTA\",bank = ['AACCGGTA', 'AAGCGGTA', 'AACCGCTA', 'AAACGGTA']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"CGTACGTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AAACGGTA', 'AACCGGAC', 'CGTACGTA', 'CGTACGTT', 'CGTACGCA']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTC\",bank = ['AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA', 'AACCGGGA']) == 1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TTTTTTTT\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'TTTTGGTA', 'TTTTTTTA', 'TTTTTTTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAGCGGTA\",bank = ['AACCGGCA', 'AACCGGTA', 'AACCGGTA', 'AAGCGGTA']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AAACGGTA\",bank = ['AACCGGTA', 'AACCGCTA', 'AAACGGTA', 'AACCGGCA', 'AACCGGAA', 'AAACGGCA', 'AAACGGAA', 'AACCGGTC', 'AAACGGTC', 'AAACGGCA', 'AAACGGAA', 'AACCGGTT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTA', 'AACCGGTC', 'AACCGGTT', 'AACCGGTA', 'AACCGGTT']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"TACCGGTA\",bank = ['AACCGGTC', 'TACCGGTA', 'AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'TACCGGTA', 'TACCGGTT', 'TACCGGTC']) == 2\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GGGGGGGG\",bank = ['AACCGGTA', 'AACCGGCA', 'AACCGGGA', 'AAGCGGGA', 'AAGCGGTA', 'AAGCGGGA', 'GGGGGGGA', 'GGGGGGGG']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"AACCGGTT\",bank = ['AACCGGTA', 'AACCGGCT', 'AACCGGCA', 'AACCGGCG', 'AACCGGTC', 'AACCGCTA', 'AAACGGTA', 'AACAGGTA', 'AAACGGTC', 'AAACGGCT', 'AAACGGCG', 'AAACGGTT', 'AAGGCGTA', 'AAGGCGTC', 'AAGGCGCA', 'AAGGCGCG', 'AAGGCGCT', 'AAGGCGTT']) == 0\n assert candidate(startGene = \"AACCGGTT\",endGene = \"GACCGGTA\",bank = ['AACCGGCA', 'GACCGGTA', 'AACCGGCT', 'AACCGGAA', 'AACCGGAT', 'AACCGGTT']) == -1\n assert candidate(startGene = \"AACCGGTT\",endGene = \"ACCGCGCG\",bank = ['AACCGGTA', 'AACCGGCA', 'AAACGGTA', 'ACCGCGTA', 'ACCGCGCG', 'ACCGCGCT', 'ACCGCGTT', 'ACCGCGGA']) == -1\n"}, "metadata": {"canonical_parameter_names": ["startGene", "endGene", "bank"], "leetcode_dataset_entry_point": "Solution().minMutation", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minMutation = function(startGene, endGene, bank) {", "container": null, "callable": "minMutation", "parameters": [{"name": "startGene", "type": "string"}, {"name": "endGene", "type": "string"}, {"name": "bank", "type": "string[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 434, "task_id": "number-of-segments-in-a-string", "difficulty": "Easy", "problem_description": "Given a string s, return the number of segments in the string.\nA segment is defined to be a contiguous sequence of non-space characters.\n \nExample 1:\n\nInput: s = \"Hello, my name is John\"\nOutput: 5\nExplanation: The five segments are [\"Hello,\", \"my\", \"name\", \"is\", \"John\"]\n\nExample 2:\n\nInput: s = \"Hello\"\nOutput: 1\n\n \nConstraints:\n\n0 <= s.length <= 300\ns consists of lowercase and uppercase English letters, digits, or one of the following characters \"!@#$%^&*()_+-=',.:\".\nThe only space character in s is ' '.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"Hello, my name is John\") == 5\n assert candidate(s = \"Hello\") == 1\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().countSegments", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countSegments = function(s) {", "container": null, "callable": "countSegments", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 435, "task_id": "non-overlapping-intervals", "difficulty": "Medium", "problem_description": "Given an array of intervals intervals where intervals[i] = [starti, endi], return the minimum number of intervals you need to remove to make the rest of the intervals non-overlapping.\nNote that intervals which only touch at a point are non-overlapping. For example, [1, 2] and [2, 3] are non-overlapping.\n \nExample 1:\n\nInput: intervals = [[1,2],[2,3],[3,4],[1,3]]\nOutput: 1\nExplanation: [1,3] can be removed and the rest of the intervals are non-overlapping.\n\nExample 2:\n\nInput: intervals = [[1,2],[1,2],[1,2]]\nOutput: 2\nExplanation: You need to remove two [1,2] to make the rest of the intervals non-overlapping.\n\nExample 3:\n\nInput: intervals = [[1,2],[2,3]]\nOutput: 0\nExplanation: You don't need to remove any of the intervals since they're already non-overlapping.\n\n \nConstraints:\n\n1 <= intervals.length <= 105\nintervals[i].length == 2\n-5 * 104 <= starti < endi <= 5 * 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [1, 3]]) == 1\n assert candidate(intervals = [[-2, -1], [1, 2], [-1, 1], [2, 3]]) == 0\n assert candidate(intervals = [[1, 5], [2, 3], [4, 6], [7, 8]]) == 1\n assert candidate(intervals = [[1, 2], [2, 3]]) == 0\n assert candidate(intervals = [[0, 2], [1, 3], [2, 4], [3, 5]]) == 2\n assert candidate(intervals = [[-5, -4], [-4, -3], [-3, -2], [-2, -1]]) == 0\n assert candidate(intervals = [[-2, -1], [0, 1], [1, 2], [2, 3]]) == 0\n assert candidate(intervals = [[1, 10], [2, 3], [4, 5], [6, 7], [8, 9]]) == 1\n assert candidate(intervals = [[1, 100], [11, 22], [1, 11], [2, 12]]) == 2\n assert candidate(intervals = [[1, 10], [2, 6], [3, 5], [7, 9]]) == 2\n assert candidate(intervals = [[-5, 5], [0, 1], [1, 2], [2, 3], [3, 4]]) == 1\n assert candidate(intervals = [[1, 3], [2, 4], [3, 5], [4, 6]]) == 2\n assert candidate(intervals = [[1, 2], [1, 2], [1, 2]]) == 2\n assert candidate(intervals = [[-1, 1], [1, 2], [2, 3], [3, 4]]) == 0\n assert candidate(intervals = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == 0\n assert candidate(intervals = [[-1, 1], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]]) == 4\n assert candidate(intervals = [[1, 4], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 1\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]]) == 0\n assert candidate(intervals = [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) == 6\n assert candidate(intervals = [[-10, 0], [-5, -2], [0, 5], [5, 10]]) == 1\n assert candidate(intervals = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96], [6, 95], [7, 94], [8, 93], [9, 92], [10, 91]]) == 9\n assert candidate(intervals = [[-5, 0], [0, 5], [5, 10], [10, 15], [-4, 1], [2, 8]]) == 2\n assert candidate(intervals = [[5, 10], [6, 8], [8, 10], [9, 12], [10, 14]]) == 2\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 0\n assert candidate(intervals = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]]) == 3\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 0\n assert candidate(intervals = [[-1, 1], [0, 2], [-2, 0], [1, 3]]) == 2\n assert candidate(intervals = [[1, 10], [5, 15], [10, 20], [15, 25]]) == 2\n assert candidate(intervals = [[1, 10000], [5000, 15000], [10000, 20000], [15000, 25000]]) == 2\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14]]) == 0\n assert candidate(intervals = [[-1, 1], [0, 2], [2, 3], [-3, -2]]) == 1\n assert candidate(intervals = [[-50000, 50000], [-49999, 49999], [0, 1], [1, 2], [2, 3]]) == 2\n assert candidate(intervals = [[-5, 5], [-4, 4], [-3, 3], [-2, 2], [-1, 1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5]]) == 5\n assert candidate(intervals = [[1, 10], [2, 3], [4, 5], [6, 7], [8, 9], [9, 10]]) == 1\n assert candidate(intervals = [[0, 10], [10, 20], [20, 30], [30, 40], [0, 40]]) == 1\n assert candidate(intervals = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6]]) == 4\n assert candidate(intervals = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == 0\n assert candidate(intervals = [[-1, 1], [-2, -1], [1, 2], [0, 1], [2, 3], [3, 4], [4, 5]]) == 1\n assert candidate(intervals = [[1, 5], [2, 3], [4, 6], [7, 8], [9, 10], [11, 12]]) == 1\n assert candidate(intervals = [[-50000, 50000], [0, 1], [1, 2], [2, 3], [3, 4]]) == 1\n assert candidate(intervals = [[1, 20], [3, 5], [2, 4], [6, 7], [8, 10], [11, 12]]) == 2\n assert candidate(intervals = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1]]) == 4\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20], [1, 11], [11, 21], [21, 31], [31, 41], [41, 51]]) == 2\n assert candidate(intervals = [[-1, 1], [0, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 1\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 0\n assert candidate(intervals = [[1, 10], [2, 3], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]]) == 3\n assert candidate(intervals = [[1, 3], [1, 2], [2, 3], [2, 4], [3, 5], [4, 6], [5, 7]]) == 3\n assert candidate(intervals = [[1, 5], [3, 7], [6, 10], [10, 15], [14, 20]]) == 2\n assert candidate(intervals = [[5, 10], [15, 20], [5, 15], [10, 25], [25, 30]]) == 2\n assert candidate(intervals = [[1, 20], [5, 10], [15, 25], [20, 30], [25, 35], [30, 40], [35, 45], [40, 50], [45, 55], [50, 60]]) == 5\n assert candidate(intervals = [[1, 4], [2, 5], [3, 6], [4, 7], [5, 8]]) == 3\n assert candidate(intervals = [[-5, 5], [0, 10], [5, 15], [10, 20]]) == 2\n assert candidate(intervals = [[1, 4], [2, 5], [3, 6], [4, 7]]) == 2\n assert candidate(intervals = [[1, 3], [1, 2], [1, 1], [1, 0], [0, 1], [0, 0], [-1, 0], [-2, -1]]) == 3\n assert candidate(intervals = [[-1, 1], [-2, -1], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]]) == 4\n assert candidate(intervals = [[-5, -3], [-4, -2], [-3, -1], [-2, 0], [-1, 1], [0, 2], [2, 4], [4, 6]]) == 3\n assert candidate(intervals = [[0, 5], [1, 6], [2, 7], [3, 8], [4, 9], [5, 10], [6, 11], [7, 12], [8, 13], [9, 14]]) == 8\n assert candidate(intervals = [[10, 20], [15, 25], [20, 30], [25, 35], [30, 40], [35, 45]]) == 3\n assert candidate(intervals = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96]]) == 4\n assert candidate(intervals = [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) == 9\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 0\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 0\n assert candidate(intervals = [[1, 3], [1, 4], [1, 5], [2, 4], [2, 5], [3, 5], [3, 6], [4, 6], [4, 7], [5, 7]]) == 7\n assert candidate(intervals = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96], [6, 95], [7, 94]]) == 6\n assert candidate(intervals = [[1, 10], [2, 5], [3, 7], [4, 8], [5, 9], [6, 11]]) == 4\n assert candidate(intervals = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11]]) == 9\n assert candidate(intervals = [[1, 10], [5, 15], [10, 20], [15, 25], [20, 30], [25, 35], [30, 40], [35, 45], [40, 50], [45, 55], [50, 60], [55, 65], [60, 70], [65, 75], [70, 80]]) == 7\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16]]) == 0\n assert candidate(intervals = [[-10000, -9000], [-8000, -7000], [-6000, -5000], [-4000, -3000], [-2000, -1000], [0, 1000], [1000, 2000], [2000, 3000], [3000, 4000]]) == 0\n assert candidate(intervals = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7]]) == 5\n assert candidate(intervals = [[-1, 1], [1, 3], [2, 4], [3, 5]]) == 1\n assert candidate(intervals = [[-50000, 50000], [49999, 50001], [-50001, -49999], [-10000, 10000]]) == 1\n assert candidate(intervals = [[1, 3], [2, 5], [3, 7], [4, 9], [5, 11], [6, 13], [7, 15], [8, 17], [9, 19], [10, 21]]) == 7\n assert candidate(intervals = [[1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14], [11, 15], [12, 16], [13, 17], [14, 18], [15, 19]]) == 11\n assert candidate(intervals = [[1, 2], [3, 4], [2, 3], [4, 5], [3, 4], [5, 6]]) == 1\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [1, 10], [11, 20]]) == 1\n assert candidate(intervals = [[1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9]]) == 4\n assert candidate(intervals = [[1, 10], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11]]) == 1\n assert candidate(intervals = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21], [1, 21]]) == 1\n assert candidate(intervals = [[1, 4], [2, 8], [3, 9], [4, 10], [5, 11], [6, 12]]) == 4\n assert candidate(intervals = [[10, 20], [20, 30], [30, 40], [15, 25], [25, 35], [35, 45]]) == 3\n assert candidate(intervals = [[1, 5], [2, 3], [3, 4], [4, 5], [5, 6]]) == 1\n assert candidate(intervals = [[-1, 0], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 0\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45], [45, 50]]) == 0\n assert candidate(intervals = [[-5, -3], [-4, -2], [-3, -1], [-2, 0], [-1, 1], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6]]) == 5\n assert candidate(intervals = [[1, 10], [2, 3], [4, 5], [6, 7], [8, 9], [1, 2], [3, 4], [5, 6], [7, 8], [9, 10]]) == 1\n assert candidate(intervals = [[1, 3], [1, 3], [1, 3], [1, 3]]) == 3\n assert candidate(intervals = [[-1, 1], [0, 2], [-2, -1], [1, 3], [2, 4], [-3, -2], [4, 5]]) == 2\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [1, 11]]) == 1\n assert candidate(intervals = [[-10, -5], [-5, 0], [0, 5], [5, 10], [10, 15], [15, 20], [20, 25], [25, 30]]) == 0\n assert candidate(intervals = [[1, 3], [2, 4], [2, 5], [3, 6], [3, 7], [4, 8], [5, 9]]) == 5\n assert candidate(intervals = [[1, 3], [2, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10]]) == 3\n assert candidate(intervals = [[1, 2], [1, 2], [1, 2], [2, 3], [2, 3], [2, 3], [3, 4], [3, 4], [3, 4]]) == 6\n assert candidate(intervals = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7]]) == 2\n assert candidate(intervals = [[10, 20], [15, 25], [20, 30], [25, 35], [30, 40], [5, 15], [25, 35]]) == 4\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10]]) == 5\n assert candidate(intervals = [[-10, 0], [0, 10], [10, 20], [-20, -10], [-10, -5], [-5, 0], [0, 5], [5, 10], [10, 15]]) == 3\n assert candidate(intervals = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 0\n assert candidate(intervals = [[1, 5], [2, 3], [4, 6], [7, 8], [8, 9], [9, 10]]) == 1\n assert candidate(intervals = [[1, 1000], [2, 999], [3, 998], [4, 997], [5, 996], [6, 995], [7, 994], [8, 993]]) == 7\n assert candidate(intervals = [[1, 4], [2, 6], [8, 10], [15, 18]]) == 1\n assert candidate(intervals = [[-1, 1], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6]]) == 3\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 0\n assert candidate(intervals = [[1, 5], [5, 10], [10, 15], [15, 20]]) == 0\n assert candidate(intervals = [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) == 5\n assert candidate(intervals = [[1, 5], [5, 10], [10, 15], [15, 20], [20, 25], [1, 25]]) == 1\n assert candidate(intervals = [[1, 5], [3, 7], [4, 10], [6, 12]]) == 2\n"}, "metadata": {"canonical_parameter_names": ["intervals"], "leetcode_dataset_entry_point": "Solution().eraseOverlapIntervals", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var eraseOverlapIntervals = function(intervals) {", "container": null, "callable": "eraseOverlapIntervals", "parameters": [{"name": "intervals", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 436, "task_id": "find-right-interval", "difficulty": "Medium", "problem_description": "You are given an array of intervals, where intervals[i] = [starti, endi] and each starti is unique.\nThe right interval for an interval i is an interval j such that startj >= endi and startj is minimized. Note that i may equal j.\nReturn an array of right interval indices for each interval i. If no right interval exists for interval i, then put -1 at index i.\n \nExample 1:\n\nInput: intervals = [[1,2]]\nOutput: [-1]\nExplanation: There is only one interval in the collection, so it outputs -1.\n\nExample 2:\n\nInput: intervals = [[3,4],[2,3],[1,2]]\nOutput: [-1,0,1]\nExplanation: There is no right interval for [3,4].\nThe right interval for [2,3] is [3,4] since start0 = 3 is the smallest start that is >= end1 = 3.\nThe right interval for [1,2] is [2,3] since start1 = 2 is the smallest start that is >= end2 = 2.\n\nExample 3:\n\nInput: intervals = [[1,4],[2,3],[3,4]]\nOutput: [-1,2,-1]\nExplanation: There is no right interval for [1,4] and [3,4].\nThe right interval for [2,3] is [3,4] since start2 = 3 is the smallest start that is >= end1 = 3.\n\n \nConstraints:\n\n1 <= intervals.length <= 2 * 104\nintervals[i].length == 2\n-106 <= starti <= endi <= 106\nThe start point of each interval is unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(intervals = [[-1, 1], [0, 2], [1, 3], [2, 4], [3, 5]]) == [2, 3, 4, -1, -1]\n assert candidate(intervals = [[5, 10], [2, 3], [1, 5], [8, 12]]) == [-1, 0, 0, -1]\n assert candidate(intervals = [[10, 20], [20, 30], [5, 15], [30, 40]]) == [1, 3, 1, -1]\n assert candidate(intervals = [[1, 3], [4, 7], [8, 10], [9, 12]]) == [1, 2, -1, -1]\n assert candidate(intervals = [[-10, -5], [-5, 0], [0, 5], [5, 10]]) == [1, 2, 3, -1]\n assert candidate(intervals = [[5, 5], [6, 6], [7, 7], [8, 8]]) == [0, 1, 2, 3]\n assert candidate(intervals = [[3, 4], [2, 3], [1, 2]]) == [-1, 0, 1]\n assert candidate(intervals = [[1, 5], [2, 6], [3, 7], [4, 8]]) == [-1, -1, -1, -1]\n assert candidate(intervals = [[1, 5], [6, 8], [9, 10]]) == [1, 2, -1]\n assert candidate(intervals = [[-1, 0], [0, 1], [1, 2], [2, 3]]) == [1, 2, 3, -1]\n assert candidate(intervals = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6]]) == [-1, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[-10, -5], [-5, 0], [0, 5], [5, 10], [10, 15]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400]]) == [2, 3, 4, -1, -1]\n assert candidate(intervals = [[1, 4], [2, 3], [3, 4]]) == [-1, 2, -1]\n assert candidate(intervals = [[1, 2]]) == [-1]\n assert candidate(intervals = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[1000000, 1000001], [999999, 1000000], [999998, 999999], [999997, 999998], [999996, 999997]]) == [-1, 0, 1, 2, 3]\n assert candidate(intervals = [[5, 10], [15, 20], [25, 30], [10, 15], [20, 25], [30, 35]]) == [3, 4, 5, 1, 2, -1]\n assert candidate(intervals = [[1, 10], [11, 20], [21, 30], [31, 40], [41, 50], [51, 60], [61, 70], [71, 80], [81, 90], [91, 100], [101, 110], [111, 120], [121, 130], [131, 140], [141, 150], [151, 160], [161, 170], [171, 180], [181, 190], [191, 200]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, -1]\n assert candidate(intervals = [[100000, 100001], [99999, 100000], [99998, 99999], [99997, 99998]]) == [-1, 0, 1, 2]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16]]) == [1, 2, 3, 4, 5, 6, 7, -1]\n assert candidate(intervals = [[-10, 0], [-5, -2], [0, 5], [5, 10]]) == [2, 2, 3, -1]\n assert candidate(intervals = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == [1, 2, 3, 4, 5, 6, 7, 8, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == [1, 2, 3, 4, 5, 6, 7, 8, -1]\n assert candidate(intervals = [[5, 6], [4, 7], [1, 10], [2, 8], [3, 9], [6, 11]]) == [5, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, -1]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20], [21, 22], [23, 24], [25, 26], [27, 28], [29, 30], [31, 32], [33, 34], [35, 36], [37, 38], [39, 40]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, -1]\n assert candidate(intervals = [[-1, 0], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, -1]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14], [16, 17], [19, 20], [22, 23], [25, 26], [28, 29]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[1, 100], [50, 150], [100, 200], [150, 250], [200, 300], [250, 350], [300, 400]]) == [2, 3, 4, 5, 6, -1, -1]\n assert candidate(intervals = [[-1, 0], [-3, -2], [-5, -4], [-7, -6], [-9, -8], [0, 1], [1, 2], [2, 3], [3, 4]]) == [5, 0, 1, 2, 3, 6, 7, 8, -1]\n assert candidate(intervals = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12], [7, 14], [8, 16], [9, 18], [10, 20]]) == [1, 3, 5, 7, 9, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 1000000], [1000001, 2000000], [2000001, 3000000], [3000001, 4000000]]) == [1, 2, 3, -1]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14], [16, 17], [19, 20], [22, 23], [25, 26], [28, 29], [31, 32], [34, 35], [37, 38], [40, 41], [43, 44], [46, 47], [49, 50]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, -1]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13], [14, 14], [15, 15]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(intervals = [[1, 2000], [2, 1999], [3, 1998], [4, 1997], [5, 1996], [6, 1995], [7, 1994], [8, 1993], [9, 1992]]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 100], [2, 98], [3, 96], [4, 94], [5, 92], [6, 90], [7, 88], [8, 86], [9, 84], [10, 82]]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 1000000], [100000, 2000000], [200000, 3000000], [300000, 4000000], [400000, 5000000]]) == [-1, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[-10, -5], [-9, -4], [-8, -3], [-7, -2], [-6, -1], [0, 5], [6, 10]]) == [5, 5, 5, 5, 5, 6, -1]\n assert candidate(intervals = [[-1000000, -999999], [-999998, -999997], [-999996, -999995], [-999994, -999993], [-999992, -999991]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[-1000000, -500000], [-500000, 0], [0, 500000], [500000, 1000000]]) == [1, 2, 3, -1]\n assert candidate(intervals = [[1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == [4, 5, 6, 7, 8, 9, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(intervals = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(intervals = [[-5, -1], [-4, 0], [-3, 1], [-2, 2], [-1, 3], [0, 4]]) == [4, 5, -1, -1, -1, -1]\n assert candidate(intervals = [[1, 1000000], [2, 999999], [3, 999998], [4, 999997], [5, 999996], [6, 999995], [7, 999994], [8, 999993], [9, 999992], [10, 999991]]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[-1000, -900], [-901, -800], [-801, -700], [-701, -600], [-601, -500], [-501, -400], [-401, -300]]) == [2, 3, 4, 5, 6, -1, -1]\n assert candidate(intervals = [[-1000, 1000], [-500, 500], [-100, 100], [-50, 50], [-10, 10], [-5, 5], [-2, 2], [-1, 1], [0, 0]]) == [-1, -1, -1, -1, -1, -1, -1, -1, 8]\n assert candidate(intervals = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10]]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[-5, 0], [-4, 1], [-3, 2], [-2, 3], [-1, 4], [0, 5], [1, 6], [2, 7], [3, 8], [4, 9], [5, 10], [6, 11], [7, 12], [8, 13], [9, 14]]) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[-5, 0], [0, 5], [-10, -5], [5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35]]) == [1, 3, 0, 4, 5, 6, 7, 8, -1]\n assert candidate(intervals = [[-10, -5], [-8, -2], [-6, 0], [-3, 3], [1, 7], [4, 10], [5, 9], [8, 12]]) == [3, 4, 4, 5, 7, -1, -1, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, -1]\n assert candidate(intervals = [[-1000000, -900000], [-900000, -800000], [-800000, -700000], [-700000, -600000], [-600000, -500000]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[100000, 100001], [99999, 100000], [99998, 99999], [99997, 99998], [99996, 99997]]) == [-1, 0, 1, 2, 3]\n assert candidate(intervals = [[-5, 0], [-4, -1], [-3, -2], [-2, -3], [-1, -4], [0, -5]]) == [5, 4, 3, 2, 1, 0]\n assert candidate(intervals = [[100, 200], [201, 300], [301, 400], [401, 500], [501, 600], [601, 700]]) == [1, 2, 3, 4, 5, -1]\n assert candidate(intervals = [[1000000, -1000000], [-1000000, 1000000], [500000, 600000], [600000, 700000]]) == [1, 0, 3, 0]\n assert candidate(intervals = [[-10, -5], [-8, -3], [-6, -1], [0, 5], [2, 7]]) == [3, 3, 3, -1, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == [1, 2, 3, 4, 5, 6, 7, 8, -1]\n assert candidate(intervals = [[-10, -5], [-7, -2], [-3, -1], [0, 4], [5, 10]]) == [2, 3, 3, 4, -1]\n assert candidate(intervals = [[-10, -5], [-5, -1], [-1, 0], [0, 5], [5, 10]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45], [45, 50], [50, 55], [55, 60]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1]\n assert candidate(intervals = [[-5, -4], [-4, -3], [-3, -2], [-2, -1], [-1, 0], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, -1]\n assert candidate(intervals = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400], [350, 450], [400, 500]]) == [2, 3, 4, 5, 6, -1, -1]\n assert candidate(intervals = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400], [350, 450], [400, 500]]) == [2, 3, 4, 5, 6, -1, -1]\n assert candidate(intervals = [[1, 3], [4, 6], [7, 9], [10, 12], [13, 15], [16, 18], [19, 21]]) == [1, 2, 3, 4, 5, 6, -1]\n assert candidate(intervals = [[1, 20], [21, 30], [31, 40], [41, 50], [51, 60]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[1, 20], [2, 19], [3, 18], [4, 17], [5, 16], [6, 15], [7, 14], [8, 13], [9, 12], [10, 11]]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[-10, -5], [-8, -4], [-7, -3], [-3, -1]]) == [3, 3, 3, -1]\n assert candidate(intervals = [[10, 15], [5, 10], [2, 5], [-3, 2], [-10, -3], [-20, -10], [-30, -20]]) == [-1, 0, 1, 2, 3, 4, 5]\n assert candidate(intervals = [[-1000000, -900000], [-800000, -700000], [-600000, -500000], [-400000, -300000], [-200000, -100000]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[-1000, -999], [-999, -998], [-998, -997], [-997, -996], [-996, -995], [-995, -994], [-994, -993], [-993, -992]]) == [1, 2, 3, 4, 5, 6, 7, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1]\n assert candidate(intervals = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [21, 25]]) == [1, 2, 3, 4, 5, -1]\n assert candidate(intervals = [[-5, -3], [-3, -1], [-1, 1], [1, 3], [3, 5]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[1, 3], [4, 7], [8, 11], [12, 15], [16, 19], [20, 23]]) == [1, 2, 3, 4, 5, -1]\n assert candidate(intervals = [[-50, -20], [-30, -10], [-25, -15], [-40, -35], [-1, 5], [6, 10]]) == [4, 4, 4, 1, 5, -1]\n assert candidate(intervals = [[1, 100], [2, 99], [3, 98], [4, 97], [5, 96], [6, 95], [7, 94], [8, 93], [9, 92]]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(intervals = [[-1, 0], [0, 1], [1, 2], [2, 3], [3, 4]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[1, 2], [10, 11], [20, 21], [30, 31], [40, 41], [50, 51], [60, 61], [70, 71], [80, 81], [90, 91]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[1, 2], [4, 5], [7, 8], [10, 11], [13, 14], [16, 17], [19, 20], [22, 23], [25, 26], [28, 29], [31, 32], [34, 35], [37, 38], [40, 41], [43, 44], [46, 47], [49, 50], [52, 53], [55, 56], [58, 59]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, -1]\n assert candidate(intervals = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1]]) == [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]\n assert candidate(intervals = [[1000, 1001], [1002, 1003], [1004, 1005], [1006, 1007], [1008, 1009], [1010, 1011], [1012, 1013], [1014, 1015], [1016, 1017], [1018, 1019]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[1, 4], [4, 5], [6, 7], [8, 10], [10, 15], [15, 20], [20, 30], [30, 40], [40, 50]]) == [1, 2, 3, 4, 5, 6, 7, 8, -1]\n assert candidate(intervals = [[100, 150], [200, 250], [50, 100], [0, 50], [250, 300], [150, 200], [300, 350]]) == [5, 4, 0, 2, 6, 1, -1]\n assert candidate(intervals = [[-5, 0], [-4, -2], [-3, -1], [-2, 0], [-1, 1], [0, 2], [1, 3], [2, 4], [3, 5], [4, 6]]) == [5, 3, 4, 5, 6, 7, 8, 9, -1, -1]\n assert candidate(intervals = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [100, 110]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[-10, 0], [-5, -1], [0, 5], [5, 10], [10, 15]]) == [2, 2, 3, 4, -1]\n assert candidate(intervals = [[1, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == [1, 2, 3, 4, 5, 6, -1]\n assert candidate(intervals = [[-1, 0], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1]\n assert candidate(intervals = [[5, 10], [20, 25], [10, 15], [15, 20], [0, 5], [25, 30], [30, 35], [35, 40], [40, 45], [45, 50]]) == [2, 5, 3, 1, 0, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[-5, -2], [-2, -1], [-1, 0], [0, 1], [1, 2], [2, 5], [5, 8], [8, 10]]) == [1, 2, 3, 4, 5, 6, 7, -1]\n assert candidate(intervals = [[10, 15], [20, 25], [12, 18], [16, 20], [21, 23], [19, 24], [25, 30], [28, 35]]) == [3, 6, 5, 1, 6, 6, -1, -1]\n assert candidate(intervals = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12], [11, 13], [12, 14]]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, -1, -1]\n assert candidate(intervals = [[5, 10], [10, 15], [15, 20], [20, 25], [25, 30]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[1, 1000000], [1000001, 2000000], [2000001, 3000000], [3000001, 4000000], [4000001, 5000000]]) == [1, 2, 3, 4, -1]\n assert candidate(intervals = [[-1000000, -999999], [-999998, -999997], [-999996, -999995], [-999994, -999993], [-999992, -999991], [-999990, -999989], [-999988, -999987], [-999986, -999985], [-999984, -999983]]) == [1, 2, 3, 4, 5, 6, 7, 8, -1]\n assert candidate(intervals = [[1000000, 1000001], [500000, 500001], [250000, 250001], [125000, 125001], [62500, 62501], [31250, 31251], [15625, 15626], [7812, 7813], [3906, 3907], [1953, 1954]]) == [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(intervals = [[1, 1000000], [-1000000, -1], [0, 0], [500000, 600000], [-600000, -500000]]) == [-1, 2, 2, -1, 2]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == [1, 2, 3, 4, 5, 6, 7, -1]\n assert candidate(intervals = [[1, 10], [2, 11], [3, 12], [4, 13], [5, 14]]) == [-1, -1, -1, -1, -1]\n assert candidate(intervals = [[-100, -50], [-51, -1], [-101, -60], [0, 10], [-1, 0], [50, 100], [101, 150], [151, 200]]) == [4, 4, 1, 5, 3, 6, 7, -1]\n assert candidate(intervals = [[-1000000, -500000], [-500000, 0], [0, 500000], [500000, 1000000], [-750000, -250000], [-250000, 250000], [250000, 750000]]) == [1, 2, 3, -1, 5, 6, -1]\n assert candidate(intervals = [[-10, 0], [0, 10], [10, 20], [20, 30]]) == [1, 2, 3, -1]\n assert candidate(intervals = [[-1, 2], [0, 3], [2, 4], [4, 6], [6, 8], [8, 10], [10, 12], [12, 14], [14, 16], [16, 18]]) == [2, 3, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(intervals = [[-1, 2], [0, 3], [1, 4], [2, 5], [3, 6], [4, 7], [5, 8], [6, 9], [7, 10], [8, 11], [9, 12]]) == [3, 4, 5, 6, 7, 8, 9, 10, -1, -1, -1]\n assert candidate(intervals = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, -1]\n assert candidate(intervals = [[5, 15], [10, 20], [15, 25], [20, 30], [25, 35]]) == [2, 3, 4, -1, -1]\n assert candidate(intervals = [[-100, 0], [-50, 50], [0, 100], [50, 150], [100, 200], [150, 250]]) == [2, 3, 4, 5, -1, -1]\n"}, "metadata": {"canonical_parameter_names": ["intervals"], "leetcode_dataset_entry_point": "Solution().findRightInterval", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findRightInterval = function(intervals) {", "container": null, "callable": "findRightInterval", "parameters": [{"name": "intervals", "type": "number[][]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 437, "task_id": "path-sum-iii", "difficulty": "Medium", "problem_description": "Given the root of a binary tree and an integer targetSum, return the number of paths where the sum of the values along the path equals targetSum.\nThe path does not need to start or end at the root or a leaf, but it must go downwards (i.e., traveling only from parent nodes to child nodes).\n \nExample 1:\n\n\nInput: root = [10,5,-3,3,2,null,11,3,-2,null,1], targetSum = 8\nOutput: 3\nExplanation: The paths that sum to 8 are shown.\n\nExample 2:\n\nInput: root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22\nOutput: 3\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 1000].\n-109 <= Node.val <= 109\n-1000 <= targetSum <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([]),targetSum = 0) == 0\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5]),targetSum = 3) == 2\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1]),targetSum = 8) == 3\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1]),targetSum = 22) == 3\n assert candidate(root = tree_node([1, -2, -3]),targetSum = -2) == 2\n assert candidate(root = tree_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),targetSum = 2) == 47\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, -1, -2]),targetSum = 22) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 33) == 0\n assert candidate(root = tree_node([1000, 500, -300, 300, 200, None, 1100, 300, -200, None, 1000, None, None, None, None]),targetSum = 800) == 2\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 1, None, -1, None, -1, 2]),targetSum = 8) == 4\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]),targetSum = 45) == 1\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]),targetSum = 10) == 2\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),targetSum = 22) == 3\n assert candidate(root = tree_node([100, -100, -100, -100, -100, -100, -100, -100, None, None, None, -100, None, None, None, -100]),targetSum = -100) == 13\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 1, None, 2, None, 3, None, 4, None, 5]),targetSum = 8) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, -25, -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]),targetSum = 0) == 1\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 38) == 0\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),targetSum = 8) == 1\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, 2, None, None, None, None, 3]),targetSum = 22) == 3\n assert candidate(root = tree_node([10, -2, 3, 4, -5, 6, -7, 8, 9, -10, 11, -12, 13, -14, 15]),targetSum = 7) == 1\n assert candidate(root = tree_node([10, 5, 5, 3, 3, 3, 3, None, None, 1, 1, 1, 1, None, None, None, None, 2, 2, 2, 2, 2, 2, 2, 2]),targetSum = 8) == 6\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),targetSum = 10) == 3\n assert candidate(root = tree_node([0, 0, 0, 0, 0, None, None, 0, 0, 0, None, 0, 0, None, 0, None, 0, None, 0, 0, 0, None, 0, 0, None, 0, 0, None, 0, None, 0, None, 0, 0, 0, None, 0, 0, None, 0, None, 0, None, 0, 0, 0, None, 0]),targetSum = 0) == 186\n assert candidate(root = tree_node([100, 50, -50, 25, 25, -25, -25, 12, None, None, 3, None, None, None, None, -3, None, None, -3]),targetSum = 25) == 5\n assert candidate(root = tree_node([100, -100, 0, 50, -50, 25, -25, None, None, None, None, 10, -10, 5, -5]),targetSum = 0) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15]),targetSum = 5) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 45) == 0\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 0, 1, None, -1]),targetSum = 8) == 4\n assert candidate(root = tree_node([0, 0, 0, 0, 0, 0, 0, 0, 0]),targetSum = 0) == 25\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 28) == 0\n assert candidate(root = tree_node([10, -1, 3, 5, -2, 2, -3, None, None, None, None, 1, -1, None, -1, None, None, None, None, None, None, -1, None, -1, None, None, None, None, None, -1]),targetSum = 5) == 2\n assert candidate(root = tree_node([-2, None, -3, None, -4, None, -5, None, -6]),targetSum = -6) == 1\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),targetSum = 15) == 4\n assert candidate(root = tree_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),targetSum = 0) == 124\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),targetSum = 35) == 2\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1, None, -3, None, None, None, None, None]),targetSum = -2) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),targetSum = 15) == 4\n assert candidate(root = tree_node([100, 50, -30, 30, 20, None, 110, 30, -20, None, 1, None, None, None, None]),targetSum = 80) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]),targetSum = 15) == 4\n assert candidate(root = tree_node([100, 200, 300, 400, 500, None, 600, None, None, None, None, None, 700]),targetSum = 1000) == 1\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, None, None, None, None, 2, None, None, 3]),targetSum = 22) == 3\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 1, 1, 1, 1, None, None, None, None, None, None, None, None, None]),targetSum = 8) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 15) == 4\n assert candidate(root = tree_node([-1, None, -2, None, -3, None, -4, -5, None]),targetSum = -6) == 1\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1]),targetSum = 3) == 1\n assert candidate(root = tree_node([10, 5, 10, 3, 3, 2, 1, None, None, 3, -2, None, 1, None, -1, 2, None, 1, None, None, None, None, 1]),targetSum = 8) == 3\n assert candidate(root = tree_node([100, 50, 200, 25, 75, 150, 300, 10, 40, 60, 90, 125, 175, 250, 350, 5, 15, 35, 45, 55, 85, 105, 115, 145, 165, 185, 225, 275, 295, 315, 335]),targetSum = 100) == 3\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1]),targetSum = -1) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]),targetSum = 46) == 2\n assert candidate(root = tree_node([5, -10, 15, 20, -20, 25, -25, None, 30, 35, None, 40, 45, None, None, None, None, None, 50, 55]),targetSum = 10) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51]),targetSum = 55) == 2\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 22) == 3\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, -1, -2, None, None, 2, 1]),targetSum = 22) == 3\n assert candidate(root = tree_node([0, 1, 1, 1, None, None, 1, 1, None, None, None, None, 1, None, 1, None, 1]),targetSum = 2) == 8\n assert candidate(root = tree_node([0, 1, 1, 1, None, None, 1, None, None, None, 1, None, None, None, 1]),targetSum = 2) == 5\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]),targetSum = 22) == 10\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),targetSum = 38) == 1\n assert candidate(root = tree_node([1, -2, -3, 1, 3, -2, None, -1, None, -1, 0, None, -3, None, None, None, -2, None, 1]),targetSum = 3) == 3\n assert candidate(root = tree_node([1, -2, 3, 4, -5, 6, -7, 8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25]),targetSum = 10) == 2\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 1, None, 2, None, 1, None, None, None, None, 1, 1, None, 2, None, 1, None, None, None, None, 1]),targetSum = 6) == 3\n assert candidate(root = tree_node([-10, -3, -5, -8, -9, -1, -2, -12, None, -4, None, None, None, -6, -7]),targetSum = -8) == 2\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 1, None, 2, None, 1, None, None, None, None, 1]),targetSum = 8) == 4\n assert candidate(root = tree_node([10, 5, 5, 3, 2, 2, 1, 3, -2, None, 1, None, -1, 0, None, None, None, None, None, None, 0, None, None, None, None, None, None, 0, None]),targetSum = 8) == 3\n assert candidate(root = tree_node([-10, -5, -3, -3, -2, -11, -3, -3, -2, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1, None, None, -1]),targetSum = -8) == 4\n assert candidate(root = tree_node([0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]),targetSum = 6) == 16\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),targetSum = 23) == 1\n assert candidate(root = tree_node([10, 15, 3, 7, 20, -15, None, -20, -10, None, 10, None, None, None, 5]),targetSum = 10) == 2\n assert candidate(root = tree_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),targetSum = 10) == 14\n"}, "metadata": {"canonical_parameter_names": ["root", "targetSum"], "leetcode_dataset_entry_point": "Solution().pathSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var pathSum = function(root, targetSum) {", "container": null, "callable": "pathSum", "parameters": [{"name": "root", "type": "TreeNode"}, {"name": "targetSum", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 438, "task_id": "find-all-anagrams-in-a-string", "difficulty": "Medium", "problem_description": "Given two strings s and p, return an array of all the start indices of p's anagrams in s. You may return the answer in any order.\n \nExample 1:\n\nInput: s = \"cbaebabacd\", p = \"abc\"\nOutput: [0,6]\nExplanation:\nThe substring with start index = 0 is \"cba\", which is an anagram of \"abc\".\nThe substring with start index = 6 is \"bac\", which is an anagram of \"abc\".\n\nExample 2:\n\nInput: s = \"abab\", p = \"ab\"\nOutput: [0,1,2]\nExplanation:\nThe substring with start index = 0 is \"ab\", which is an anagram of \"ab\".\nThe substring with start index = 1 is \"ba\", which is an anagram of \"ab\".\nThe substring with start index = 2 is \"ab\", which is an anagram of \"ab\".\n\n \nConstraints:\n\n1 <= s.length, p.length <= 3 * 104\ns and p consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"hello\",p = \"billion\") == []\n assert candidate(s = \"aaaaa\",p = \"a\") == [0, 1, 2, 3, 4]\n assert candidate(s = \"bbaa\",p = \"ab\") == [1]\n assert candidate(s = \"abab\",p = \"ab\") == [0, 1, 2]\n assert candidate(s = \"abacbabc\",p = \"abc\") == [1, 2, 3, 5]\n assert candidate(s = \"a\",p = \"a\") == [0]\n assert candidate(s = \"aaaaaa\",p = \"aa\") == [0, 1, 2, 3, 4]\n assert candidate(s = \"cbaebabacd\",p = \"abc\") == [0, 6]\n assert candidate(s = \"xyz\",p = \"zyx\") == [0]\n assert candidate(s = \"aaaaaaaaaa\",p = \"aaa\") == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(s = \"mississippi\",p = \"issi\") == [1, 4]\n assert candidate(s = \"abcabcabc\",p = \"abc\") == [0, 1, 2, 3, 4, 5, 6]\n assert candidate(s = \"aabbcc\",p = \"abc\") == []\n assert candidate(s = \"mississippi\",p = \"issip\") == [4]\n assert candidate(s = \"abcd\",p = \"efgh\") == []\n assert candidate(s = \"abcde\",p = \"fgh\") == []\n assert candidate(s = \"abcdefg\",p = \"gfedcba\") == [0]\n assert candidate(s = \"aabbccdd\",p = \"abcd\") == []\n assert candidate(s = \"hello\",p = \"oll\") == [2]\n assert candidate(s = \"p\",p = \"p\") == [0]\n assert candidate(s = \"zdhfkahfewrfsad\",p = \"fes\") == []\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",p = \"zzzz\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]\n assert candidate(s = \"ananananan\",p = \"nana\") == [0, 1, 2, 3, 4, 5, 6]\n assert candidate(s = \"ababababababababababababababababababababababababababababababababab\",p = \"baba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62]\n assert candidate(s = \"zzzzzzzzzzzzzzzz\",p = \"zzzz\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(s = \"anagramanagramanagram\",p = \"anagramanagram\") == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(s = \"xxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzzxxyyzz\",p = \"xxyyzz\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66]\n assert candidate(s = \"aquickbrownfoxjumpsoverthelazydog\",p = \"quick\") == [1]\n assert candidate(s = \"xyzzxyzz\",p = \"xyz\") == [0, 3, 4]\n assert candidate(s = \"almostanagram\",p = \"anagram\") == [6]\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",p = \"abcdefghijklmnop\") == [0, 26]\n assert candidate(s = \"abcdabcdeabcdabcdeabcdabcde\",p = \"abcde\") == [4, 5, 6, 7, 8, 13, 14, 15, 16, 17, 22]\n assert candidate(s = \"aabbccddeeffgghhii\",p = \"abcdefghi\") == []\n assert candidate(s = \"aquickbrownfoxjumpsoverlazydog\",p = \"lazy\") == [23]\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",p = \"zzzzzz\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110]\n assert candidate(s = \"thisisaverylongstringtocheckanagrams\",p = \"strings\") == []\n assert candidate(s = \"xyxzyzyx\",p = \"zyx\") == [1, 2, 5]\n assert candidate(s = \"bbaaaaab\",p = \"ab\") == [1, 6]\n assert candidate(s = \"bcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbc\",p = \"bbccbb\") == []\n assert candidate(s = \"abababababababababababababababababababababababababababababababababababababababababababab\",p = \"bab\") == [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85]\n assert candidate(s = \"abcabcabcabcabcabc\",p = \"abcabc\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(s = \"abcdabcdabcdabcd\",p = \"dcba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",p = \"mnopqrstuvwxyz\") == []\n assert candidate(s = \"thisisanotherexample\",p = \"ample\") == [15]\n assert candidate(s = \"acbabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabcabc\",p = \"bcab\") == [1, 2, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61]\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",p = \"zyxwvutsrqponmlkjihgfedcba\") == []\n assert candidate(s = \"xyzzzzzyxyzzzzzyxyzzzzzy\",p = \"zzzzzyxy\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(s = \"repeatedpatternrepeatedpatternrepeated\",p = \"repeatedpattern\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]\n assert candidate(s = \"eidbaooo\",p = \"ab\") == [3]\n assert candidate(s = \"acdfgdcagdfgdsf\",p = \"gcd\") == [4]\n assert candidate(s = \"abcdefgabcdefg\",p = \"gfedcba\") == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",p = \"mnopqrstuvwxzy\") == []\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\",p = \"xyz\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42]\n assert candidate(s = \"bcbcbcbcbcbc\",p = \"bccb\") == [0, 1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(s = \"abcdefghij\",p = \"ihgfedcba\") == [0]\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\",p = \"cba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",p = \"zzz\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103]\n assert candidate(s = \"aaaaaaaaaabbbbbbbbbbcccccccccc\",p = \"abc\") == []\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",p = \"zyxwvutsrqponmlkjihgfedcba\") == [0]\n assert candidate(s = \"pneumonoultramicroscopicsilicovolcanoconiosis\",p = \"pneumonia\") == []\n assert candidate(s = \"counterexampletofindallanagramsinaverylargeinputstring\",p = \"example\") == [7]\n assert candidate(s = \"zazazazazaz\",p = \"aaa\") == []\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",p = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == [0]\n assert candidate(s = \"thisisateststring\",p = \"test\") == [7]\n assert candidate(s = \"ababababababababababababababababa\",p = \"baba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\",p = \"xyzzyx\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]\n assert candidate(s = \"anagramananagramanagramanagramanagram\",p = \"nagaram\") == [0, 1, 2, 3, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(s = \"abcdabcde\",p = \"cde\") == [6]\n assert candidate(s = \"abacbabcabcab\",p = \"abc\") == [1, 2, 3, 5, 6, 7, 8, 9, 10]\n assert candidate(s = \"anananananananananananananananananananananana\",p = \"nana\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41]\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaab\",p = \"ba\") == [26]\n assert candidate(s = \"acbabcabcabcabcabcabcabcabcabcabc\",p = \"bac\") == [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(s = \"aaaaaaaaaaaab\",p = \"aaaab\") == [8]\n assert candidate(s = \"ldfldjflsdkflsdkjfldsjkfldsjfldsjflsdkjfldskjflds\",p = \"sdkjf\") == [13, 19, 35, 41]\n assert candidate(s = \"abababababababababab\",p = \"abab\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(s = \"aabbccddeeffaabbccddeeff\",p = \"abcdef\") == []\n assert candidate(s = \"zzzzzzzzzz\",p = \"zzz\") == [0, 1, 2, 3, 4, 5, 6, 7]\n assert candidate(s = \"zxyzzxyz\",p = \"xyz\") == [0, 1, 4, 5]\n assert candidate(s = \"thisisanexampleofaverylongstringwherefindinganagramsisnotthatstraightforward\",p = \"anagram\") == [44]\n assert candidate(s = \"anagramananagramananagram\",p = \"anagram\") == [0, 1, 2, 3, 9, 10, 11, 12, 18]\n assert candidate(s = \"anananananananananananananananananana\",p = \"anana\") == [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32]\n assert candidate(s = \"abcdefghij\",p = \"jihgfedcba\") == [0]\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\",p = \"aaaaaa\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46]\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",p = \"mnopqr\") == []\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\",p = \"mnbvcxzlkjhgfdsapoiuytrewq\") == [0]\n assert candidate(s = \"acbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacbacb\",p = \"acbac\") == [0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63]\n assert candidate(s = \"hellohellohellohellohellohellohellohellohellohello\",p = \"world\") == []\n assert candidate(s = \"anagramanagramanagram\",p = \"nagaram\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\",p = \"mnbvcxzlkjhgfdsapoiuytrewq\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]\n assert candidate(s = \"layer\",p = \"relay\") == [0]\n assert candidate(s = \"quickbrownfoxjumpsoverthelazydog\",p = \"thequickbrownfoxjumpsover\") == [0]\n assert candidate(s = \"llllllllllllllllllllllllllllllllllllll\",p = \"ll\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]\n assert candidate(s = \"abababababababababab\",p = \"baba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaab\",p = \"aab\") == [62]\n assert candidate(s = \"qazwsxedcrfvtgbyhnujmikolp\",p = \"lopihgfytvremkluzxwqjncbv\") == []\n assert candidate(s = \"abacabadabacaba\",p = \"abacab\") == [0, 1, 8, 9]\n assert candidate(s = \"thisisaverylongstringwithseveralrepeatingcharacters\",p = \"characters\") == [41]\n assert candidate(s = \"aabbccddeeffgghhii\",p = \"iihhggffeeddccbbaa\") == [0]\n assert candidate(s = \"thisisanagram\",p = \"nagaram\") == [6]\n assert candidate(s = \"ababababababababababababababababababababababababababab\",p = \"baba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",p = \"zyxwvutsrqponmlkjihgfedcba\") == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]\n assert candidate(s = \"aabbccddeeff\",p = \"abcdef\") == []\n"}, "metadata": {"canonical_parameter_names": ["s", "p"], "leetcode_dataset_entry_point": "Solution().findAnagrams", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findAnagrams = function(s, p) {", "container": null, "callable": "findAnagrams", "parameters": [{"name": "s", "type": "string"}, {"name": "p", "type": "string"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 440, "task_id": "k-th-smallest-in-lexicographical-order", "difficulty": "Hard", "problem_description": "Given two integers n and k, return the kth lexicographically smallest integer in the range [1, n].\n \nExample 1:\n\nInput: n = 13, k = 2\nOutput: 10\nExplanation: The lexicographical order is [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9], so the second smallest number is 10.\n\nExample 2:\n\nInput: n = 1, k = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= k <= n <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 13,k = 2) == 10\n assert candidate(n = 1,k = 1) == 1\n assert candidate(n = 100000,k = 50000) == 54998\n assert candidate(n = 10,k = 10) == 9\n assert candidate(n = 1000000,k = 100000) == 189998\n assert candidate(n = 200,k = 150) == 53\n assert candidate(n = 10,k = 1) == 1\n assert candidate(n = 1000,k = 100) == 188\n assert candidate(n = 999999999,k = 500000000) == 549999999\n assert candidate(n = 999,k = 999) == 999\n assert candidate(n = 99999,k = 50000) == 54999\n assert candidate(n = 2,k = 1) == 1\n assert candidate(n = 100,k = 10) == 17\n assert candidate(n = 1000000000,k = 100000000) == 189999998\n assert candidate(n = 20,k = 15) == 4\n assert candidate(n = 999999999,k = 123456789) == 211111103\n assert candidate(n = 999999999,k = 999999999) == 999999999\n assert candidate(n = 1000,k = 50) == 142\n assert candidate(n = 50,k = 25) == 31\n assert candidate(n = 10000,k = 9876) == 9887\n assert candidate(n = 98765,k = 87654) == 88888\n assert candidate(n = 111111111,k = 55555555) == 49999998\n assert candidate(n = 999999990,k = 500000000) == 549999999\n assert candidate(n = 987654321,k = 456789012) == 511110104\n assert candidate(n = 123456789,k = 123456789) == 99999999\n assert candidate(n = 1000000000,k = 500000000) == 549999998\n assert candidate(n = 1000000000,k = 1) == 1\n assert candidate(n = 333333333,k = 111111111) == 199999999\n assert candidate(n = 897654321,k = 123456789) == 211111103\n assert candidate(n = 456789123,k = 222222222) == 299999999\n assert candidate(n = 999999999,k = 1) == 1\n assert candidate(n = 987654321,k = 987654320) == 99999998\n assert candidate(n = 700000000,k = 700000000) == 99999999\n assert candidate(n = 777777777,k = 333333333) == 399999999\n assert candidate(n = 111111111,k = 33333333) == 29999998\n assert candidate(n = 200000000,k = 150000000) == 54999998\n assert candidate(n = 500,k = 250) == 323\n assert candidate(n = 500000000,k = 1) == 1\n assert candidate(n = 123456789,k = 1) == 1\n assert candidate(n = 10000,k = 5000) == 5498\n assert candidate(n = 777777777,k = 222222222) == 299999999\n assert candidate(n = 999999998,k = 999999998) == 999999998\n assert candidate(n = 500000000,k = 300000000) == 369999999\n assert candidate(n = 876543210,k = 123456789) == 211111103\n assert candidate(n = 987654321,k = 123456789) == 211111103\n assert candidate(n = 999999990,k = 999999990) == 999999990\n assert candidate(n = 2147483647,k = 1073741823) == 1966367637\n assert candidate(n = 500,k = 1) == 1\n assert candidate(n = 666666666,k = 333333333) == 399999999\n assert candidate(n = 123456789,k = 98765432) == 77777776\n assert candidate(n = 98765,k = 45678) == 51107\n assert candidate(n = 10000,k = 1000) == 1898\n assert candidate(n = 500000000,k = 250000000) == 324999998\n assert candidate(n = 10000,k = 9999) == 9998\n assert candidate(n = 500,k = 499) == 98\n assert candidate(n = 1000000000,k = 123456789) == 211111102\n assert candidate(n = 876543210,k = 543210987) == 588889887\n assert candidate(n = 400000000,k = 200000000) == 279999999\n assert candidate(n = 600000000,k = 500000000) == 549999999\n assert candidate(n = 876543210,k = 432109876) == 488898887\n assert candidate(n = 100000000,k = 99999999) == 99999998\n assert candidate(n = 800000000,k = 123456789) == 211111103\n assert candidate(n = 555555555,k = 277777777) == 349999998\n assert candidate(n = 987654321,k = 87654321) == 178888887\n assert candidate(n = 87654321,k = 5000000) == 14499998\n assert candidate(n = 1000000,k = 1000000) == 999999\n assert candidate(n = 888888888,k = 444444444) == 499999999\n assert candidate(n = 876543210,k = 345678901) == 411111004\n assert candidate(n = 987654321,k = 1) == 1\n assert candidate(n = 99999999,k = 50000000) == 54999999\n assert candidate(n = 999999999,k = 999999998) == 999999998\n assert candidate(n = 333333333,k = 166666666) == 249999998\n assert candidate(n = 1234567,k = 999999) == 788887\n assert candidate(n = 100000000,k = 10000000) == 18999998\n assert candidate(n = 100000000,k = 50000000) == 54999998\n assert candidate(n = 100000,k = 99999) == 99998\n assert candidate(n = 1000,k = 500) == 548\n assert candidate(n = 1234567,k = 345678) == 199998\n assert candidate(n = 123456789,k = 67890123) == 49989999\n assert candidate(n = 999999,k = 500000) == 549999\n assert candidate(n = 800000000,k = 400000000) == 459999999\n assert candidate(n = 1234567,k = 678901) == 499899\n assert candidate(n = 200000000,k = 100000000) == 189999999\n assert candidate(n = 100000,k = 75000) == 77498\n assert candidate(n = 2147483647,k = 1000000000) == 1899999999\n assert candidate(n = 300000000,k = 150000000) == 234999998\n assert candidate(n = 900000000,k = 800000000) == 819999999\n assert candidate(n = 300000000,k = 100000000) == 189999999\n assert candidate(n = 899999999,k = 500000000) == 549999999\n assert candidate(n = 1000000,k = 999999) == 999998\n assert candidate(n = 98765,k = 12345) == 21107\n assert candidate(n = 234567890,k = 123456789) == 211111103\n assert candidate(n = 2147483647,k = 1500000000) == 417264712\n assert candidate(n = 600000000,k = 300000000) == 369999999\n"}, "metadata": {"canonical_parameter_names": ["n", "k"], "leetcode_dataset_entry_point": "Solution().findKthNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findKthNumber = function(n, k) {", "container": null, "callable": "findKthNumber", "parameters": [{"name": "n", "type": "number"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 441, "task_id": "arranging-coins", "difficulty": "Easy", "problem_description": "You have n coins and you want to build a staircase with these coins. The staircase consists of k rows where the ith row has exactly i coins. The last row of the staircase may be incomplete.\nGiven the integer n, return the number of complete rows of the staircase you will build.\n \nExample 1:\n\n\nInput: n = 5\nOutput: 2\nExplanation: Because the 3rd row is incomplete, we return 2.\n\nExample 2:\n\n\nInput: n = 8\nOutput: 3\nExplanation: Because the 4th row is incomplete, we return 3.\n\n \nConstraints:\n\n1 <= n <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == 3\n assert candidate(n = 100) == 13\n assert candidate(n = 30) == 7\n assert candidate(n = 15) == 5\n assert candidate(n = 22) == 6\n assert candidate(n = 21) == 6\n assert candidate(n = 2147483647) == 65535\n assert candidate(n = 1804289383) == 60070\n assert candidate(n = 1) == 1\n assert candidate(n = 180) == 18\n assert candidate(n = 10) == 4\n assert candidate(n = 5) == 2\n assert candidate(n = 210) == 20\n assert candidate(n = 45) == 9\n assert candidate(n = 171) == 18\n assert candidate(n = 3) == 2\n assert candidate(n = 576) == 33\n assert candidate(n = 2147483646) == 65535\n assert candidate(n = 12) == 4\n assert candidate(n = 7) == 3\n assert candidate(n = 70) == 11\n assert candidate(n = 1000) == 44\n assert candidate(n = 28) == 7\n assert candidate(n = 64) == 10\n assert candidate(n = 16) == 5\n assert candidate(n = 10000) == 140\n assert candidate(n = 1001) == 44\n assert candidate(n = 2) == 1\n assert candidate(n = 80) == 12\n assert candidate(n = 165) == 17\n assert candidate(n = 6678) == 115\n assert candidate(n = 101) == 13\n assert candidate(n = 100000) == 446\n assert candidate(n = 18) == 5\n assert candidate(n = 256) == 22\n assert candidate(n = 36) == 8\n assert candidate(n = 500) == 31\n assert candidate(n = 1000000000) == 44720\n assert candidate(n = 1999) == 62\n assert candidate(n = 987654321) == 44443\n assert candidate(n = 5000000) == 3161\n assert candidate(n = 325) == 25\n assert candidate(n = 441) == 29\n assert candidate(n = 136) == 16\n assert candidate(n = 500000000) == 31622\n assert candidate(n = 1000000) == 1413\n assert candidate(n = 6) == 3\n assert candidate(n = 123456789) == 15712\n assert candidate(n = 120) == 15\n assert candidate(n = 1999999999) == 63245\n assert candidate(n = 123456) == 496\n assert candidate(n = 5050) == 100\n assert candidate(n = 55) == 10\n assert candidate(n = 84) == 12\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().arrangeCoins", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var arrangeCoins = function(n) {", "container": null, "callable": "arrangeCoins", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 442, "task_id": "find-all-duplicates-in-an-array", "difficulty": "Medium", "problem_description": "Given an integer array nums of length n where all the integers of nums are in the range [1, n] and each integer appears at most twice, return an array of all the integers that appears twice.\nYou must write an algorithm that runs in O(n) time and uses only constant auxiliary space, excluding the space needed to store the output\n \nExample 1:\nInput: nums = [4,3,2,7,8,2,3,1]\nOutput: [2,3]\nExample 2:\nInput: nums = [1,1,2]\nOutput: [1]\nExample 3:\nInput: nums = [1]\nOutput: []\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 105\n1 <= nums[i] <= n\nEach element in nums appears once or twice.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 2]) == [1]\n assert candidate(nums = [5, 3, 2, 3, 5, 1]) == [3, 5]\n assert candidate(nums = [1]) == []\n assert candidate(nums = [5, 3, 1, 2, 4, 3, 5]) == [3, 5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9]) == [10, 9]\n assert candidate(nums = [5, 4, 6, 7, 9, 3, 10, 9, 5, 6]) == [5, 6, 9]\n assert candidate(nums = [10, 2, 5, 10, 9, 1, 1, 4, 3, 7]) == [1, 10]\n assert candidate(nums = [4, 3, 2, 7, 8, 2, 3, 1]) == [3, 2]\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 2, 3]) == [1, 2, 3]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5]) == [2, 4, 3]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5]) == [2, 4, 3, 5]\n assert candidate(nums = [5, 3, 4, 5, 3, 2, 1, 2, 4]) == [3, 5, 2, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2]) == [1, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 15]) == [10, 13, 5, 8, 15]\n assert candidate(nums = [3, 3, 2, 2, 1, 1, 6, 6, 5, 5, 4, 4, 10, 10, 9, 9, 8, 8, 7, 7]) == [2, 4, 5, 10, 3, 9, 6, 8, 1, 7]\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]\n assert candidate(nums = [2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36]) == [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [3, 6, 2, 7, 4, 8, 1, 9, 5, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [50, 50, 49, 49, 48, 48, 47, 47, 46, 46, 45, 45, 44, 44, 43, 43, 42, 42, 41, 41, 40, 40, 39, 39, 38, 38, 37, 37, 36, 36, 35, 35, 34, 34, 33, 33, 32, 32, 31, 31, 30, 30, 29, 29, 28, 28, 27, 27, 26, 26, 25, 25, 24, 24, 23, 23, 22, 22, 21, 21, 20, 20, 19, 19, 18, 18, 17, 17, 16, 16, 15, 15, 14, 14, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == [38, 25, 39, 24, 31, 23, 40, 22, 35, 21, 41, 20, 30, 19, 42, 18, 36, 17, 43, 16, 29, 15, 44, 14, 33, 13, 45, 12, 28, 11, 46, 10, 37, 9, 47, 8, 27, 7, 48, 6, 32, 5, 49, 4, 26, 3, 50, 2, 34, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4]) == [3, 4]\n assert candidate(nums = [5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == [3, 6, 5, 7, 2, 8, 4, 9, 1, 10]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 10]) == [5, 2, 10]\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4]) == [5, 6, 7, 8, 9, 10, 1, 2, 3, 4]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 1, 1, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == [2, 1, 7, 12, 5, 13, 8, 14, 4, 15, 9, 16, 6, 17, 10, 18, 3, 19, 11, 20]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 25]) == [19, 2, 20, 16, 10, 22, 14, 18, 24, 12, 25]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 1]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == [3, 6, 2, 7, 4, 8, 1, 9, 5, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25]) == [13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25]\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]) == [2, 4, 5, 6, 7, 8, 9, 10, 1, 3]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10]) == [5, 1, 6, 3, 7, 1, 8, 4, 9, 2]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14]) == [4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20]) == [3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [8, 2, 3, 2, 1, 5, 6, 3, 7, 4, 8, 5]) == [3, 2, 8, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [1, 2, 3, 4, 5]\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2]\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14]) == [5, 10, 6, 7, 8, 9]\n assert candidate(nums = [5, 5, 5, 5, 5, 1, 2, 3, 4, 1]) == [5, 5, 5, 5, 1]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findDuplicates", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findDuplicates = function(nums) {", "container": null, "callable": "findDuplicates", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 443, "task_id": "string-compression", "difficulty": "Medium", "problem_description": "Given an array of characters chars, compress it using the following algorithm:\nBegin with an empty string s. For each group of consecutive repeating characters in chars:\n\nIf the group's length is 1, append the character to s.\nOtherwise, append the character followed by the group's length.\n\nThe compressed string s should not be returned separately, but instead, be stored in the input character array chars. Note that group lengths that are 10 or longer will be split into multiple characters in chars.\nAfter you are done modifying the input array, return the new length of the array.\nYou must write an algorithm that uses only constant extra space.\n \nExample 1:\n\nInput: chars = [\"a\",\"a\",\"b\",\"b\",\"c\",\"c\",\"c\"]\nOutput: Return 6, and the first 6 characters of the input array should be: [\"a\",\"2\",\"b\",\"2\",\"c\",\"3\"]\nExplanation: The groups are \"aa\", \"bb\", and \"ccc\". This compresses to \"a2b2c3\".\n\nExample 2:\n\nInput: chars = [\"a\"]\nOutput: Return 1, and the first character of the input array should be: [\"a\"]\nExplanation: The only group is \"a\", which remains uncompressed since it's a single character.\n\nExample 3:\n\nInput: chars = [\"a\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\",\"b\"]\nOutput: Return 4, and the first 4 characters of the input array should be: [\"a\",\"b\",\"1\",\"2\"].\nExplanation: The groups are \"a\" and \"bbbbbbbbbbbb\". This compresses to \"ab12\".\n \nConstraints:\n\n1 <= chars.length <= 2000\nchars[i] is a lowercase English letter, uppercase English letter, digit, or symbol.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(chars = ['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a']) == 3\n assert candidate(chars = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']) == 10\n assert candidate(chars = ['a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b']) == 4\n assert candidate(chars = ['a', 'a', 'b', 'b', 'c', 'c', 'c']) == 6\n assert candidate(chars = ['a', '2', 'b', '2', 'c', '3']) == 6\n assert candidate(chars = ['a', 'a', 'a', 'b', 'b', 'a', 'a']) == 6\n assert candidate(chars = ['a']) == 1\n assert candidate(chars = ['a', 'b', 'c']) == 3\n assert candidate(chars = ['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c', 'c']) == 9\n assert candidate(chars = ['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a']) == 3\n assert candidate(chars = ['a', 'a', 'a', 'b', 'b', 'c', 'c', 'c', 'c', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'e', 'e', 'f', 'f', 'g', 'g', 'g', 'g', 'g', 'g', 'g', 'g']) == 14\n assert candidate(chars = ['a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b']) == 20\n assert candidate(chars = ['a', '1', '1', '2', '2', '2', '3', '3', '3', '3', '4', '4', '4', '4', '4', '5', '5', '5', '5', '5', '5', '5', '5', '5', '5']) == 12\n assert candidate(chars = ['x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x']) == 3\n assert candidate(chars = ['a', 'b', 'b', 'a', 'a', 'a', 'c', 'c', 'c', 'c', 'd', 'd', 'd', 'd', 'd', 'e', 'e', 'e', 'e', 'e', 'e']) == 11\n assert candidate(chars = ['a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'a', 'a', 'a', 'a', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c']) == 12\n assert candidate(chars = ['a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b']) == 20\n assert candidate(chars = ['m', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm', 'm']) == 3\n assert candidate(chars = ['a', 'a', 'a', 'b', 'b', 'b', 'c', 'c', 'c', 'd', 'd', 'd', 'e', 'e', 'e', 'f', 'f', 'f', 'g', 'g', 'g', 'h', 'h', 'h', 'i', 'i', 'i', 'j', 'j', 'j', 'k', 'k', 'k', 'l', 'l', 'l', 'm', 'm', 'm', 'n', 'n', 'n', 'o', 'o', 'o', 'p', 'p', 'p', 'q', 'q', 'q', 'r', 'r', 'r', 's', 's', 's', 't', 't', 't', 'u', 'u', 'u', 'v', 'v', 'v', 'w', 'w', 'w', 'x', 'x', 'x', 'y', 'y', 'y', 'z', 'z', 'z']) == 52\n assert candidate(chars = ['a', 'a', 'b', 'b', 'b', 'b', 'c', 'c', 'c', 'c', 'c', 'c', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd']) == 9\n assert candidate(chars = ['a', 'a', 'b', 'b', 'b', 'b', 'b', 'c', 'c', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd', 'd']) == 9\n assert candidate(chars = ['x', 'y', 'y', 'z', 'z', 'z', 'x', 'y', 'y', 'z', 'z', 'z', 'x', 'y', 'y', 'z', 'z', 'z', 'x', 'y', 'y', 'z', 'z', 'z']) == 20\n assert candidate(chars = ['x', 'x', 'x', 'y', 'y', 'z', 'z', 'z', 'z', 'z', 'w', 'w', 'w', 'w', 'w', 'w', 'w', 'w', 'w', 'w', 'w', 'w']) == 9\n assert candidate(chars = ['a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c']) == 24\n assert candidate(chars = ['a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b', 'a', 'b']) == 82\n"}, "metadata": {"canonical_parameter_names": ["chars"], "leetcode_dataset_entry_point": "Solution().compress", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var compress = function(chars) {", "container": null, "callable": "compress", "parameters": [{"name": "chars", "type": "character[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 445, "task_id": "add-two-numbers-ii", "difficulty": "Medium", "problem_description": "You are given two non-empty linked lists representing two non-negative integers. The most significant digit comes first and each of their nodes contains a single digit. Add the two numbers and return the sum as a linked list.\nYou may assume the two numbers do not contain any leading zero, except the number 0 itself.\n \nExample 1:\n\n\nInput: l1 = [7,2,4,3], l2 = [5,6,4]\nOutput: [7,8,0,7]\n\nExample 2:\n\nInput: l1 = [2,4,3], l2 = [5,6,4]\nOutput: [8,0,7]\n\nExample 3:\n\nInput: l1 = [0], l2 = [0]\nOutput: [0]\n\n \nConstraints:\n\nThe number of nodes in each linked list is in the range [1, 100].\n0 <= Node.val <= 9\nIt is guaranteed that the list represents a number that does not have leading zeros.\n\n \nFollow up: Could you solve it without reversing the input lists?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9])), list_node([1, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([9, 8, 7])), list_node([1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([7, 2, 4, 3]),l2 = list_node([5, 6, 4])), list_node([7, 8, 0, 7]))\n assert is_same_list(candidate(l1 = list_node([2, 4, 3]),l2 = list_node([5, 6, 4])), list_node([8, 0, 7]))\n assert is_same_list(candidate(l1 = list_node([0]),l2 = list_node([0])), list_node([0]))\n assert is_same_list(candidate(l1 = list_node([5]),l2 = list_node([5])), list_node([1, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9]),l2 = list_node([1])), list_node([1, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5])), list_node([6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 6, 4])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 6, 5]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),l2 = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([5]),l2 = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([4, 5, 6, 7, 8, 9])), list_node([4, 5, 6, 9, 1, 2]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),l2 = list_node([1])), list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9])), list_node([1, 2, 3, 4, 5, 6, 7, 9, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9]),l2 = list_node([1, 1, 1, 1])), list_node([1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([3, 2, 1]),l2 = list_node([6, 5, 4, 3, 2, 1])), list_node([6, 5, 4, 6, 4, 2]))\n assert is_same_list(candidate(l1 = list_node([6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]),l2 = list_node([4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]),l2 = list_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 0, 9]),l2 = list_node([1, 0, 1])), list_node([1, 0, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6])), list_node([6, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 7]))\n assert is_same_list(candidate(l1 = list_node([5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),l2 = list_node([5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([2, 3, 5, 7, 11, 13, 17, 19]),l2 = list_node([23, 29, 31, 37, 41, 43, 47, 53])), list_node([2, 8, 6, 0, 9, 8, 3, 1, 2]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9]),l2 = list_node([1, 0, 0, 0])), list_node([1, 9, 9, 9]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([6, 7, 8, 9, 0])), list_node([8, 0, 2, 3, 5]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9]),l2 = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])), list_node([1, 1, 1, 1, 2, 1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]),l2 = list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2])), list_node([4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4]))\n assert is_same_list(candidate(l1 = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),l2 = list_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])), list_node([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1])), list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([6, 7, 8, 9, 0, 1])), list_node([6, 9, 1, 2, 4, 6]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([1])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9]),l2 = list_node([9, 9, 9, 9, 9, 9, 9])), list_node([1, 9, 9, 9, 9, 9, 9, 8]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([1])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),l2 = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3]),l2 = list_node([4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])), list_node([4, 5, 6, 7, 9, 0, 1, 2, 3, 4, 5, 6, 7, 9, 0, 1, 2, 3, 4, 5, 6, 7, 9, 0, 2, 4, 3]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9]),l2 = list_node([1])), list_node([1, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0]),l2 = list_node([9, 0, 9, 0, 9, 0, 9, 0, 9, 0])), list_node([1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([5, 4, 3, 2, 1]),l2 = list_node([1, 2, 3, 4, 5])), list_node([6, 6, 6, 6, 6]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([9, 8, 7, 6, 6, 6, 6, 6, 6]))\n assert is_same_list(candidate(l1 = list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]),l2 = list_node([8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8])), list_node([8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([1])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]),l2 = list_node([1])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0]),l2 = list_node([1])), list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1])), list_node([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]))\n assert is_same_list(candidate(l1 = list_node([9, 9]),l2 = list_node([1, 1, 1])), list_node([2, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]),l2 = list_node([9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9])), list_node([1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),l2 = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([9, 9, 9]),l2 = list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1])), list_node([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5]),l2 = list_node([5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 6, 6, 6, 6, 6]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9]),l2 = list_node([9, 8, 7, 6, 5, 4, 3, 2, 1])), list_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 0]))\n assert is_same_list(candidate(l1 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),l2 = list_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 0])), list_node([2, 4, 6, 9, 1, 3, 5, 7, 8, 0]))\n"}, "metadata": {"canonical_parameter_names": ["l1", "l2"], "leetcode_dataset_entry_point": "Solution().addTwoNumbers", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var addTwoNumbers = function(l1, l2) {", "container": null, "callable": "addTwoNumbers", "parameters": [{"name": "l1", "type": "ListNode"}, {"name": "l2", "type": "ListNode"}], "return_type": "ListNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 446, "task_id": "arithmetic-slices-ii-subsequence", "difficulty": "Hard", "problem_description": "Given an integer array nums, return the number of all the arithmetic subsequences of nums.\nA sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same.\n\nFor example, [1, 3, 5, 7, 9], [7, 7, 7, 7], and [3, -1, -5, -9] are arithmetic sequences.\nFor example, [1, 1, 2, 5, 7] is not an arithmetic sequence.\n\nA subsequence of an array is a sequence that can be formed by removing some elements (possibly none) of the array.\n\nFor example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].\n\nThe test cases are generated so that the answer fits in 32-bit integer.\n \nExample 1:\n\nInput: nums = [2,4,6,8,10]\nOutput: 7\nExplanation: All arithmetic subsequence slices are:\n[2,4,6]\n[4,6,8]\n[6,8,10]\n[2,4,6,8]\n[4,6,8,10]\n[2,4,6,8,10]\n[2,6,10]\n\nExample 2:\n\nInput: nums = [7,7,7,7,7]\nOutput: 16\nExplanation: Any subsequence of this array is arithmetic.\n\n \nConstraints:\n\n1  <= nums.length <= 1000\n-231 <= nums[i] <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15]) == 29\n assert candidate(nums = [1, 2, 3, 8, 9]) == 1\n assert candidate(nums = [2, 4, 6, 8, 10]) == 7\n assert candidate(nums = [1, 3, 5, 7, 9]) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [10, 20, 30, 40, 50]) == 7\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 55\n assert candidate(nums = [1, 1, 2, 5, 7]) == 0\n assert candidate(nums = [0, 2000000000, -294967296, -294967296]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 7\n assert candidate(nums = [10, 9, 4, 6, 8, 4, 3, 9, 1, 3, 5, 7]) == 10\n assert candidate(nums = [1, 2, 3, 8, 13, 18]) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 11]) == 12\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1]) == 99\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34]) == 6\n assert candidate(nums = [7, 7, 7, 7, 7]) == 16\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 968\n assert candidate(nums = [1, 2, 3, 4, 5, 6]) == 12\n assert candidate(nums = [1, 2]) == 0\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3]) == 99\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64]) == 0\n assert candidate(nums = [1, 2, 3]) == 1\n assert candidate(nums = [1, 2, 3, 8, 9, 10]) == 2\n assert candidate(nums = [3, 1, 2, 2, 4, 5]) == 1\n assert candidate(nums = [3, 1, 2, 5, 7]) == 1\n assert candidate(nums = [1, 7, 10, 15, 27, 29]) == 1\n assert candidate(nums = [1, 2, 1, 2, 1]) == 1\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]) == 9\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 968\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 194\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 55\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96]) == 198\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 55\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36]) == 90\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 0\n assert candidate(nums = [1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288]) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 602\n assert candidate(nums = [10, 7, 4, 3, 2, 1, -1, -2, -3, -4]) == 20\n assert candidate(nums = [1000, 990, 980, 970, 960, 950, 940, 930, 920, 910, 900, 890, 880, 870, 860, 850, 840, 830, 820, 810, 800]) == 390\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52]) == 263\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256]) == 0\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]) == 13\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 164\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33]) == 72\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45]) == 1\n assert candidate(nums = [-5, -1, 3, 7, 11, 15, 19, 23]) == 29\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49, 55]) == 55\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 72\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1048365\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]) == 55\n assert candidate(nums = [10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40, 40]) == 139\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 164\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 344\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 946\n assert candidate(nums = [5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35]) == 72\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 60\n assert candidate(nums = [1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91]) == 72\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == 1152921504606845145\n assert candidate(nums = [1, 3, 5, 7, 9, 12, 15, 18, 21, 24]) == 22\n assert candidate(nums = [5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47]) == 164\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 55\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 604\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 0\n assert candidate(nums = [10, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38]) == 55\n assert candidate(nums = [1, 7, 10, 15, 27, 29, 33, 51]) == 3\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 100\n assert candidate(nums = [1, 3, 5, 9, 15, 25, 39, 57, 79, 105, 135]) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 164\n assert candidate(nums = [10, 12, 14, 18, 22, 26, 30, 34, 38, 42, 46]) == 56\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 55\n assert candidate(nums = [5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 72\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 1981\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6]) == 4172\n assert candidate(nums = [1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28]) == 62\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == 65294\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 1048365\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 32647\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 4256\n assert candidate(nums = [1, 7, 10, 15, 27, 29, 33, 37, 41, 45, 49]) == 13\n assert candidate(nums = [5, 8, 11, 14, 17, 20, 23, 26, 29, 32]) == 55\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6]) == 160\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == 164\n assert candidate(nums = [10, 20, 10, 20, 10, 20, 10, 20, 10, 20]) == 32\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == 90\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57]) == 164\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]) == 1936\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40]) == 137\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]) == 8\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49]) == 604\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8]) == 772\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77]) == 344\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 1294\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35]) == 263\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 344\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58]) == 344\n assert candidate(nums = [1, 2, 4, 6, 8, 10, 14, 16, 18, 20, 24, 26, 28, 30, 34, 36, 38, 40]) == 72\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 344\n assert candidate(nums = [1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 114\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 56\n assert candidate(nums = [-2, -1, 1, 4, 8, 13, 19, 26, 34, 43, 53, 64]) == 4\n assert candidate(nums = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 946\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 391\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90]) == 41\n assert candidate(nums = [2, 4, 6, 8, 12, 14, 16, 20, 22, 24, 28]) == 32\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]) == 72\n assert candidate(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 28\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 164\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 72\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54]) == 264\n assert candidate(nums = [10, 7, 4, 1, -2, -5, -8, -11, -14]) == 41\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45]) == 41\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 55\n assert candidate(nums = [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == 364\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25]) == 113\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91]) == 3\n assert candidate(nums = [1, 3, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37]) == 355\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61, 67, 73]) == 113\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49, 55, 61]) == 72\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == 57\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1]) == 48\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768]) == 0\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40]) == 164\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 968\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120]) == 90\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13]) == 25208\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 344\n assert candidate(nums = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31]) == 72\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800]) == 29\n assert candidate(nums = [1, 7, 13, 19, 25, 31, 37, 43, 49]) == 41\n assert candidate(nums = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45]) == 90\n assert candidate(nums = [10, 7, 4, 3, 2, 1, -1, -4, -7, -10]) == 16\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 55\n assert candidate(nums = [1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100]) == 90\n assert candidate(nums = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 17\n assert candidate(nums = [1, 3, 5, 3, 1, -1, -3, -5, -3, -1, 1, 3, 5]) == 53\n assert candidate(nums = [10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 72\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39]) == 113\n assert candidate(nums = [1, 2, 3, 6, 9, 12, 15, 18, 21]) == 21\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9]) == 1584\n assert candidate(nums = [1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9]) == 323\n assert candidate(nums = [1, 2, 3, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3]) == 1370\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 55\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 55\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 0\n assert candidate(nums = [3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 160\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 72\n assert candidate(nums = [3, 6, 9, 15, 18, 21, 27, 30, 33, 39, 42, 45]) == 40\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 968\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7]) == 165\n assert candidate(nums = [5, 10, 15, 25, 35, 45, 55, 65, 75, 85]) == 42\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 32647\n assert candidate(nums = [1, 7, 10, 15, 27, 29, 33, 18]) == 1\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7]) == 5029\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23]) == 90\n assert candidate(nums = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45]) == 164\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 55\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 164\n assert candidate(nums = [1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79]) == 4\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 32647\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().numberOfArithmeticSlices", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numberOfArithmeticSlices = function(nums) {", "container": null, "callable": "numberOfArithmeticSlices", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 447, "task_id": "number-of-boomerangs", "difficulty": "Medium", "problem_description": "You are given n points in the plane that are all distinct, where points[i] = [xi, yi]. A boomerang is a tuple of points (i, j, k) such that the distance between i and j equals the distance between i and k (the order of the tuple matters).\nReturn the number of boomerangs.\n \nExample 1:\n\nInput: points = [[0,0],[1,0],[2,0]]\nOutput: 2\nExplanation: The two boomerangs are [[1,0],[0,0],[2,0]] and [[1,0],[2,0],[0,0]].\n\nExample 2:\n\nInput: points = [[1,1],[2,2],[3,3]]\nOutput: 2\n\nExample 3:\n\nInput: points = [[1,1]]\nOutput: 0\n\n \nConstraints:\n\nn == points.length\n1 <= n <= 500\npoints[i].length == 2\n-104 <= xi, yi <= 104\nAll the points are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0]]) == 8\n assert candidate(points = [[1, 0], [0, 0], [0, 1]]) == 2\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [0, 2]]) == 4\n assert candidate(points = [[0, 0], [1, 0], [2, 0]]) == 2\n assert candidate(points = [[0, 0], [1, 0], [-1, 0], [0, 1], [0, -1]]) == 20\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4]]) == 4\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 0]]) == 4\n assert candidate(points = [[10000, 10000], [-10000, -10000], [0, 0]]) == 2\n assert candidate(points = [[1, 1], [2, 2], [3, 3]]) == 2\n assert candidate(points = [[1, 1], [2, 2], [1, 1], [2, 2]]) == 16\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1]]) == 8\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3]]) == 4\n assert candidate(points = [[0, 0], [0, 1], [1, 0], [1, 1]]) == 8\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [2, 0]]) == 8\n assert candidate(points = [[-1, 0], [0, 0], [1, 0]]) == 2\n assert candidate(points = [[1, 1]]) == 0\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [2, 3], [3, 2], [1, 2], [2, 1]]) == 38\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 2], [2, 1], [1, 2]]) == 38\n assert candidate(points = [[-2, -2], [-1, -1], [1, 1], [2, 2], [-3, -3], [3, 3], [-4, -4], [4, 4]]) == 16\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10]]) == 8\n assert candidate(points = [[-1, 0], [0, -1], [1, 0], [0, 1], [0, 0]]) == 20\n assert candidate(points = [[-1, -1], [1, 1], [2, 2], [3, 3], [4, 4], [-1, 1], [1, -1], [-2, -2], [-3, -3], [-4, -4]]) == 48\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [2, 1]]) == 24\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [2, 0], [0, 1], [0, 2], [2, 1], [2, 2], [1, 2], [2, 1]]) == 136\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 8\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [1, 0], [1, 1], [1, 2], [1, 3], [1, 4]]) == 64\n assert candidate(points = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 3], [3, 4], [4, 5]]) == 16\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [4, 0], [4, 2], [0, 4], [2, 4], [4, 4]]) == 88\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 40\n assert candidate(points = [[1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2]]) == 40\n assert candidate(points = [[5, 5], [5, 10], [10, 5], [10, 10], [7, 7], [8, 8]]) == 16\n assert candidate(points = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 24\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [1, 1], [-1, -1], [-1, 1], [1, -1]]) == 48\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 1], [1, 3], [3, 1], [2, 3], [3, 2], [2, 0], [0, 2], [3, 0], [0, 3]]) == 192\n assert candidate(points = [[-10000, -10000], [10000, 10000], [0, 0], [5000, 5000], [-5000, -5000], [2000, 2000], [-2000, -2000]]) == 10\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [0, 2], [0, 3], [0, 4]]) == 18\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [2, 0], [2, 1], [0, 1], [0, 2], [1, 2], [2, 2], [3, 2]]) == 104\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 2], [3, 3], [4, 4]]) == 104\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 18\n assert candidate(points = [[10000, 10000], [10001, 10001], [10002, 10002], [10003, 10003], [10004, 10004]]) == 8\n assert candidate(points = [[100, 100], [101, 101], [102, 102], [100, 102], [102, 100], [101, 100], [100, 101], [102, 101], [101, 102]]) == 88\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4]]) == 12\n assert candidate(points = [[-1, -1], [0, 0], [1, 1], [2, 2], [3, 3], [-1, 1], [-2, 2], [-3, 3], [1, -1], [2, -2], [3, -3]]) == 78\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [1, -1], [-1, 1], [-1, -1]]) == 20\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1]]) == 20\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, -1], [0, 1]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12], [13, 13]]) == 72\n assert candidate(points = [[0, 0], [10000, 10000], [-10000, -10000], [10000, -10000], [-10000, 10000]]) == 20\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [1, 1]]) == 12\n assert candidate(points = [[0, 0], [0, 5], [5, 0], [5, 5], [2, 2], [3, 3], [4, 4]]) == 24\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [2, 1], [2, 2], [3, 2], [3, 3], [4, 3], [4, 4], [5, 4]]) == 40\n assert candidate(points = [[0, 0], [0, 1], [1, 0], [1, 1], [2, 2], [2, 1], [1, 2]]) == 38\n assert candidate(points = [[0, 1], [1, 0], [1, 2], [2, 1], [2, 3], [3, 2]]) == 24\n assert candidate(points = [[0, 0], [1, 2], [1, -2], [2, 4], [2, -4], [-1, 2], [-1, -2]]) == 18\n assert candidate(points = [[0, 0], [0, 1], [0, 2], [0, 3], [0, 4], [0, 5], [0, 6], [0, 7], [0, 8], [0, 9]]) == 40\n assert candidate(points = [[0, 0], [10, 0], [20, 0], [0, 10], [10, 10], [20, 10], [0, 20], [10, 20], [20, 20]]) == 88\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7]]) == 18\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1], [1, 1], [2, 1], [3, 1], [0, 2], [1, 2], [2, 2], [3, 2]]) == 164\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [1, 1], [1, -1]]) == 20\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [1, 1]]) == 20\n assert candidate(points = [[0, 0], [1, 1], [1, 0], [0, 1], [2, 2], [2, 0], [0, 2]]) == 42\n assert candidate(points = [[-1000, -1000], [-1000, -999], [-999, -1000], [-999, -999], [-1001, -1001], [-1001, -1000], [-1000, -1001]]) == 38\n assert candidate(points = [[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1], [10, 1]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [1, 1], [0, 1], [0.5, 0.5], [1.5, 0.5], [1.5, 1.5], [0.5, 1.5]]) == 60\n assert candidate(points = [[-5, 5], [-3, -3], [-1, 1], [-2, -2], [0, 0], [2, 2], [3, 3], [5, -5], [4, 4]]) == 32\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, 1], [0, -1]]) == 20\n assert candidate(points = [[10, 10], [10, 20], [20, 20], [20, 10], [10, 15]]) == 12\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [1, 0], [0, 1], [2, 0], [0, 2]]) == 42\n assert candidate(points = [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], [-1, 1], [0, 1], [1, 1], [-1, 2], [0, 2], [1, 2]]) == 164\n assert candidate(points = [[-1, 0], [0, 1], [1, -1], [-2, 0], [0, 2], [2, -2], [-3, 0], [0, 3], [3, -3], [-4, 0]]) == 32\n assert candidate(points = [[-10000, -10000], [-9999, -9999], [-9998, -9998], [-9997, -9997], [-9996, -9996]]) == 8\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [0, 1], [1, 1], [2, 1], [0, 2], [1, 2], [2, 2]]) == 88\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [0, 1]]) == 6\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2]]) == 24\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 1], [2, 2]]) == 12\n assert candidate(points = [[1, 2], [2, 4], [3, 6], [4, 8], [5, 10], [6, 12]]) == 12\n assert candidate(points = [[1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2], [2, 1], [1, 2], [2, 2], [3, 3]]) == 104\n assert candidate(points = [[100, 100], [101, 100], [100, 101], [101, 101], [102, 102], [102, 101], [101, 102]]) == 38\n assert candidate(points = [[0, 0], [0, 2], [2, 0], [2, 2], [1, 1], [1, 3], [3, 1], [3, 3], [2, 3], [3, 2]]) == 92\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], [7, 0], [8, 0], [9, 0]]) == 40\n assert candidate(points = [[0, 0], [1, 0], [2, 0], [3, 0], [4, 0], [5, 0]]) == 12\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 24\n assert candidate(points = [[-1, 0], [1, 0], [0, -1], [0, 1], [0, 0]]) == 20\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10], [11, 11], [12, 12]]) == 60\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5]]) == 8\n assert candidate(points = [[1, 1], [2, 2], [3, 3], [4, 4], [5, 5], [6, 6], [7, 7], [8, 8], [9, 9], [10, 10]]) == 40\n assert candidate(points = [[0, 0], [1, 1], [2, 2], [1, 2], [2, 1]]) == 12\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [2, 0], [0, 2], [1, 2]]) == 38\n assert candidate(points = [[100, 100], [101, 100], [100, 101], [101, 101], [100, 99], [101, 99], [99, 100], [99, 101], [99, 99]]) == 88\n assert candidate(points = [[-2, -2], [-1, -1], [0, 0], [1, 1], [2, 2], [1, 0], [0, 1]]) == 26\n assert candidate(points = [[0, 0], [1, 2], [2, 1], [2, 3], [3, 2], [1, 3]]) == 18\n assert candidate(points = [[0, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2], [3, 0], [3, 1], [3, 2], [4, 0]]) == 94\n assert candidate(points = [[-1, 0], [0, 0], [1, 0], [0, -1], [0, 1], [1, 1], [-1, -1], [1, -1], [-1, 1]]) == 88\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1], [1, 1], [-1, -1]]) == 38\n assert candidate(points = [[-5, -5], [-5, 0], [0, -5], [0, 0], [2, 2], [3, 3], [4, 4]]) == 18\n assert candidate(points = [[0, 0], [1, 0], [0, 1], [1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]) == 60\n"}, "metadata": {"canonical_parameter_names": ["points"], "leetcode_dataset_entry_point": "Solution().numberOfBoomerangs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var numberOfBoomerangs = function(points) {", "container": null, "callable": "numberOfBoomerangs", "parameters": [{"name": "points", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 448, "task_id": "find-all-numbers-disappeared-in-an-array", "difficulty": "Easy", "problem_description": "Given an array nums of n integers where nums[i] is in the range [1, n], return an array of all the integers in the range [1, n] that do not appear in nums.\n \nExample 1:\nInput: nums = [4,3,2,7,8,2,3,1]\nOutput: [5,6]\nExample 2:\nInput: nums = [1,1]\nOutput: [2]\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 105\n1 <= nums[i] <= n\n\n \nFollow up: Could you do it without extra space and in O(n) runtime? You may assume the returned list does not count as extra space.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 4, 3, 2, 1]) == []\n assert candidate(nums = [10, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == []\n assert candidate(nums = [1, 1]) == [2]\n assert candidate(nums = [4, 3, 2, 7, 8, 2, 3, 1]) == [5, 6]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5]) == [6, 7, 8, 9]\n assert candidate(nums = [3, 3, 3, 3, 3]) == [1, 2, 4, 5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [2, 2, 2, 2]) == [1, 3, 4]\n assert candidate(nums = [1, 2, 3, 4, 5]) == []\n assert candidate(nums = [1, 2, 2, 3, 3]) == [4, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == []\n assert candidate(nums = [5, 4, 3, 2, 1, 1, 1, 1, 1, 1]) == [6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15]) == [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5]) == [21, 22, 23, 24, 25]\n assert candidate(nums = [2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105]) == []\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4, 11, 12, 13, 14, 15, 16]) == [10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50]) == []\n assert candidate(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == [51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 10]) == [11, 12, 13]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [1, 2, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8]) == [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]\n assert candidate(nums = [100000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [21]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == []\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2]) == [21]\n assert candidate(nums = [50000, 49999, 49998, 49997, 49996, 49995, 49994, 49993, 49992, 49991, 49990, 49989, 49988, 49987, 49986, 49985, 49984, 49983, 49982, 49981, 49980, 49979, 49978, 49977, 49976, 49975, 49974, 49973, 49972, 49971, 49970, 49969, 49968, 49967, 49966, 49965, 49964, 49963, 49962, 49961, 49960, 49959, 49958, 49957, 49956, 49955, 49954, 49953, 49952, 49951, 49950, 49949, 49948, 49947, 49946, 49945, 49944, 49943, 49942, 49941, 49940, 49939, 49938, 49937, 49936, 49935, 49934, 49933, 49932, 49931, 49930, 49929, 49928, 49927, 49926, 49925, 49924, 49923, 49922, 49921, 49920, 49919, 49918, 49917, 49916, 49915, 49914, 49913, 49912, 49911, 49910, 49909, 49908, 49907, 49906, 49905, 49904, 49903, 49902, 49901, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == []\n assert candidate(nums = [5, 5, 5, 5, 5]) == [1, 2, 3, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 19, 18, 17, 16]) == [21, 22, 23, 24, 25]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [3, 1, 2, 5, 3, 3, 4, 6, 8, 7, 9, 10, 10]) == [11, 12, 13]\n assert candidate(nums = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16]) == [1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 99989, 99988, 99987, 99986, 99985, 99984, 99983, 99982, 99981, 99980, 99979, 99978, 99977, 99976, 99975, 99974, 99973, 99972, 99971, 99970, 99969, 99968, 99967, 99966, 99965, 99964, 99963, 99962, 99961, 99960, 99959, 99958, 99957, 99956, 99955, 99954, 99953, 99952, 99951, 99950, 99949, 99948, 99947, 99946, 99945, 99944, 99943, 99942, 99941, 99940, 99939, 99938, 99937, 99936, 99935, 99934, 99933, 99932, 99931, 99930, 99929, 99928, 99927, 99926, 99925, 99924, 99923, 99922, 99921, 99920, 99919, 99918, 99917, 99916, 99915, 99914, 99913, 99912, 99911, 99910, 99909, 99908, 99907, 99906, 99905, 99904, 99903, 99902, 99901, 1, 2, 3, 4, 5]) == [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105]\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]) == [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == []\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [1, 2, 3, 4, 6, 7, 8, 9, 10]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [100000, 99999, 99998, 99997, 99996, 99995, 99994, 99993, 99992, 99991, 99990, 1, 2, 3, 4, 5]) == [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == [2, 4, 6, 8, 10, 12, 14]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [5, 3, 1, 2, 3, 6, 7, 4, 9, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == [41]\n assert candidate(nums = [3, 3, 3, 1, 2, 2, 2, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10]) == [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 1, 1, 1]) == [2, 3, 4]\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 20]) == [11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1]) == [21, 22, 23, 24, 25]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21]) == [20]\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == [17, 18, 19, 20]\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 2, 4, 5]) == [6, 7, 8, 9]\n assert candidate(nums = [90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [11, 12, 13, 14, 15, 16, 17, 18, 19]\n assert candidate(nums = [1, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9]) == [2, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]\n assert candidate(nums = [100000, 100000, 100000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [11, 12, 13]\n assert candidate(nums = [50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000, 50000]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [10000, 9999, 9998, 9997, 9996, 9995, 9994, 9993, 9992, 9991, 9990, 9989, 9988, 9987, 9986, 9985, 9984, 9983, 9982, 9981, 9980, 9979, 9978, 9977, 9976, 9975, 9974, 9973, 9972, 9971, 9970, 9969, 9968, 9967, 9966, 9965, 9964, 9963, 9962, 9961, 9960, 9959, 9958, 9957, 9956, 9955, 9954, 9953, 9952, 9951, 9950, 9949, 9948, 9947, 9946, 9945, 9944, 9943, 9942, 9941, 9940, 9939, 9938, 9937, 9936, 9935, 9934, 9933, 9932, 9931, 9930, 9929, 9928, 9927, 9926, 9925, 9924, 9923, 9922, 9921, 9920, 9919, 9918, 9917, 9916, 9915, 9914, 9913, 9912, 9911, 9910, 9909, 9908, 9907, 9906, 9905, 9904, 9903, 9902, 9901, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40]) == []\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n assert candidate(nums = [2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 1]) == [101]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findDisappearedNumbers", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findDisappearedNumbers = function(nums) {", "container": null, "callable": "findDisappearedNumbers", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 450, "task_id": "delete-node-in-a-bst", "difficulty": "Medium", "problem_description": "Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.\nBasically, the deletion can be divided into two stages:\n\nSearch for a node to remove.\nIf the node is found, delete the node.\n\n \nExample 1:\n\n\nInput: root = [5,3,6,2,4,null,7], key = 3\nOutput: [5,4,6,2,null,null,7]\nExplanation: Given key to delete is 3. So we find the node with value 3 and delete it.\nOne valid answer is [5,4,6,2,null,null,7], shown in the above BST.\nPlease notice that another valid answer is [5,2,6,null,4,null,7] and it's also accepted.\n\n\nExample 2:\n\nInput: root = [5,3,6,2,4,null,7], key = 0\nOutput: [5,3,6,2,4,null,7]\nExplanation: The tree does not contain a node with value = 0.\n\nExample 3:\n\nInput: root = [], key = 0\nOutput: []\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 104].\n-105 <= Node.val <= 105\nEach node has a unique value.\nroot is a valid binary search tree.\n-105 <= key <= 105\n\n \nFollow up: Could you solve it with time complexity O(height of tree)?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(root = tree_node([1, None, 2]),key = 1), tree_node([2]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7]),key = 7), tree_node([5, 3, 6, 2, 4]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7]),key = 3), tree_node([5, 4, 6, 2, None, None, 7]))\n assert candidate(root = tree_node([]),key = 0) == None\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7]),key = 0), tree_node([5, 3, 6, 2, 4, None, 7]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7]),key = 2), tree_node([5, 3, 6, None, 4, None, 7]))\n assert is_same_tree(candidate(root = tree_node([2, 1, 3]),key = 2), tree_node([3, 1]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, None, 40, 60, 80]),key = 50), tree_node([70, 60, 80, 30, None, None, None, None, 40]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7]),key = 4), tree_node([5, 3, 6, 2, None, None, 7]))\n assert candidate(root = tree_node([1]),key = 1) == None\n assert is_same_tree(candidate(root = tree_node([1, 2, None]),key = 2), tree_node([1, 2]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 8, 12, 16, 19, 21, 24, 27, 32]),key = 20), tree_node([25, 22, 30, 21, 24, 27, 32, 15, None, None, None, None, None, None, None, 10, 18, 8, 12, 16, 19]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 9), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),key = 3), tree_node([10, 5, 15, None, 7, 12, 18]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 55), tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 3), tree_node([1, 2, 7, 4, 5, 14, 15, 8, 9, 10, 11, 6, None, None, None, None, None, None, None, None, None, None, None, 12, 13]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85, 5, 15, None, None, None, None, 32, 42, 47, None, 52, 62, 67, 72, 78, 82, 87, 90, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None]),key = 40), tree_node([50, 30, 70, 20, 45, 60, 80, 10, 25, 32, 42, 55, 65, 75, 85, 5, 15, None, None, 35, None, None, None, 47, None, 52, 62, 67, 72, 78, 82, 87, 90]))\n assert is_same_tree(candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75]),key = 50), tree_node([40, 20, 60, 10, 30, 55, 70, 5, 15, 25, 35, 45, None, 65, 75]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 11), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 4), tree_node([7, 5, 8, 2, None, None, None, 1, 3, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 2), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, None, 27, None, None, None, None, None, 8]),key = 15), tree_node([25, 20, 35, 10, None, 30, 40, 5, 12, 27, None, None, None, None, None, 8]))\n assert is_same_tree(candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19]),key = 12), tree_node([8, 4, 14, 2, 6, 13, 15, 1, 3, 5, 7, 10, None, None, None, 17, 19, None, None, None, None, None, None, 9, 11]))\n assert is_same_tree(candidate(root = tree_node([70, 30, 100, 20, 50, 80, 110, 10, 25, 40, 60, 75, 85, 105, 120, 5, 15, 22, 27, 35, 45, 55, 72, 78, 82, 87, 102, 108, 115, 125]),key = 70), tree_node([100, 80, 110, 75, 85, 105, 120, 78, 82, 87, 102, 108, 115, 125, None, 30, None, None, None, None, None, None, None, None, None, None, None, None, None, 20, 50, 10, 25, 40, 60, 5, 15, 22, 27, 35, 45, 55, 72]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, 16, 19]),key = 10), tree_node([15, 12, 18, 11, 13, 16, 19, 5, None, None, None, None, None, None, None, 3, 7, 1, None, 6, 8]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 7), tree_node([4, 2, 8, 1, 3, 5, None, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 1), tree_node([4, 2, 7, 10, 3, 5, 8, 9]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),key = 15), tree_node([10, 5, 18, 3, 7]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, None, None, 6, 8, None, None, None, None, 16, 25]),key = 7), tree_node([10, 5, 15, 2, 8, None, 20, None, None, 16, 25, None, None, 6]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]),key = 25), tree_node([20, 15, 30, 10, 17, 27, 35, 5, 12, 16, 18, 26, 32, 34, None, 3, 8, None, None, None, None, None, 19, 22, None, None, None, 28, 31, None, None, None, 9, 11, None, 21, 23, None, None, None, None, 33, 36, None, None, None, None, None, 24, None, None, None, None, None, 14]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8]),key = 5), tree_node([10, 7, 15, 6, 8, None, 18, 3, None, None, None, None, None, 1]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, None, None, 9, 20]),key = 15), tree_node([7, 3, 20, None, None, 9]))\n assert is_same_tree(candidate(root = tree_node([1, 0, 2, 0, 1]),key = 0), tree_node([1, 1, 2, 0]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 9), tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([8, 5, 12, 3, 7, 10, 15, 2, 4, 6, 9, 11, 13, 14, 17, 1, None, None, None, None, None, None, None, None, None, None, 16, 18]),key = 10), tree_node([8, 5, 12, 3, 7, 13, 15, 2, 4, 6, 9, 11, 16, 14, 17, 1, None, None, None, None, None, None, None, None, None, None, None, 18]))\n assert is_same_tree(candidate(root = tree_node([3, 2, 4, 1, None, None, 5]),key = 4), tree_node([3, 2, 5, 1]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 15), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 4), tree_node([5, 3, 7, 2, None, 6, 8]))\n assert is_same_tree(candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 48, None, None, None, None, None, None, None, None, None, None, None, 33, 42]),key = 15), tree_node([30, 20, 45, 18, 25, 40, 50, 10, None, None, None, 35, 48, None, None, 5, 12, None, 33, 42]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),key = 12), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 85), tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, None, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 3), tree_node([4, 2, 7, 1, None, 5, 8, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 8), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]),key = 5), tree_node([20, 15, 25, 10, 17, 22, 30, 8, 12, 16, 18, 21, 23, 27, 35, 3, 9, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, 33, 36, 11, None, None, 14, None, None, None, None, 28, 31]))\n assert is_same_tree(candidate(root = tree_node([30, 10, 40, 5, 15, 35, 50, 1, 7, None, 18, 32, 45, 55, 60, None, None, None, None, 8, None, None, 23, 27, None, None, None, 42, 48, None, None, None, 53, None, 57, None, 62]),key = 30), tree_node([40, 35, 50, 32, 45, 55, 60, 10, 23, 27, None, None, None, 42, 48, 5, 15, None, 53, None, 57, None, 62, None, None, 1, 7, None, 18, None, None, None, None, None, None, None, None, None, None, 8]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 12, 17, 22, 27, 32, 37, 1, 4, 6, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31, 33, 36, 38, 39]),key = 20), tree_node([30, 25, 35, 22, 27, 32, 37, 21, 23, 26, 28, 31, 33, 36, 38, 10, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 5, 15, 3, 7, 12, 17, 1, 4, 6, 8, 11, 13, 16, 18, 39]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5]),key = 3), tree_node([1, None, 2, None, 4, None, 5]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 65), tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 50), tree_node([70, 60, 80, 65, None, None, 85, 30, None, None, None, 20, 40, 10, None, None, 55, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 8), tree_node([4, 2, 7, 1, 3, 5, None, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 13), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, None, 5, 9, 12, None, 7, None, None, None, 11, 13]),key = 8), tree_node([10, 9, 12, 3, None, None, 11, None, 5, None, None, None, 7, 13]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18]),key = 5), tree_node([10, 7, 15, 3, None, None, 18]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 5), tree_node([7, 6, 8, 3, None, None, None, 2, 4]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 2), tree_node([4, 3, 7, 1, None, 5, 8, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 2), tree_node([5, 3, 7, None, 4, 6, 8]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6]),key = 5), tree_node([10, 7, 15, 6, None, 13, 18, 3, None, None, None, None, None, 1]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, None, 75, None, 200, None, 125, 175, 250]),key = 150), tree_node([100, 50, 200, None, 75, 175, 250, None, 125]))\n assert is_same_tree(candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, None, 18, 25, 35, 48, None, None, None, None, 19]),key = 20), tree_node([30, 15, 45, 10, 25, 40, 50, 5, None, 18, None, 35, 48, None, None, None, None, 19]))\n assert is_same_tree(candidate(root = tree_node([30, 20, 40, 15, 25, 35, 45, 10, None, None, 22, 32, 37, 42, 47, 5, None, None, None, None, 18, None, 24, 27, None, None, None, None, None, None, None, None, None, None, None]),key = 20), tree_node([30, 25, 40, 15, 22, 35, 45, 10, None, None, None, 32, 37, 42, 47, 5, None, None, 18, None, 24, 27]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85]),key = 30), tree_node([50, 40, 70, 35, 45, 60, 80, 20, None, None, None, 55, 65, 75, 85, 10, 25]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, None, 14, None, None, 2]),key = 100), tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, None, 14, None, None, 2]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, None, None, 3.5, 4.5]),key = 3), tree_node([5, 4, 6, 3.5, 4.5, None, 7, 2]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 4), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]),key = 5), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5]),key = 4), tree_node([1, 2, None, 3, None, 4, None, 5]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 5), tree_node([4, 2, 7, 1, 3, None, 8, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]),key = 20), tree_node([25, 22, 30, 21, 23, 27, 35, 15, None, None, 24, 26, 32, 34, None, 10, 17, None, 14, None, None, None, None, 28, 31, 5, 12, 16, 18, None, None, None, None, None, None, 3, 8, None, None, None, None, None, 19, None, None, None, 9, 11, None, 33, 36]))\n assert is_same_tree(candidate(root = tree_node([15, 10, 20, 8, 12, 17, 25, 5, 9, 11, 13, 16, 18, 22, 27, 3, 7, None, None, None, None, 14, None, 19, 21, 23, 26, 28, None, None, None, None, None, None, None, None]),key = 15), tree_node([20, 17, 25, 16, 18, 22, 27, 19, 21, 23, 26, 28, None, None, None, 10, None, None, None, None, None, None, None, None, None, 8, 12, 5, 9, 11, 13, 3, 7, None, None, None, None, 14]))\n assert is_same_tree(candidate(root = tree_node([15, 10, 20, 8, 12, 17, 25, 6, 9, 11, 13, 16, 18, 22, 28]),key = 15), tree_node([20, 17, 25, 16, 18, 22, 28, 10, None, None, None, None, None, None, None, 8, 12, 6, 9, 11, 13]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]),key = 10), tree_node([4, 2, 7, 1, 3, 5, 8, 9, 10]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 5, 12, None, 17, None, None, None, None, 1, None]),key = 15), tree_node([20, 18, 25, 10, 17, 22, 30, 5, 12, None, None, None, None, None, None, 1]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 8, 2, 4, 7, 9, None, 10, None, None, None, None, 6]),key = 3), tree_node([5, 4, 8, 2, None, 7, 9, None, 10, None, None, 6]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]),key = 30), tree_node([20, 15, 25, 10, 17, 22, 35, 5, 12, 16, 18, 21, 23, 34, None, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 28, 31, None, None, None, 9, 11, None, None, 14, 27, None, None, None, 33, 36, None, None, None, None, 26, 32]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),key = 7), tree_node([10, 5, 15, 3, None, 12, 18]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, 17, 19]),key = 10), tree_node([15, 12, 18, 11, 13, 17, 19, 5, None, None, None, None, None, None, None, 3, 7, 1, None, 6, 8]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 6), tree_node([5, 3, 7, 2, 4, None, 8]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),key = 12), tree_node([10, 5, 15, 3, 7, None, 18]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 130, 160, 180]),key = 100), tree_node([150, 125, 175, 110, 130, 160, 180, 50, None, None, None, None, None, None, None, 25, 75, 10, 30, 60, 80]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, 4, 6, 8, 11, 13, 16, 19]),key = 5), tree_node([10, 7, 15, 6, 8, 12, 18, 3, None, None, None, 11, 13, 16, 19, 1, 4]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, 17, 19]),key = 7), tree_node([10, 5, 15, 3, 8, 12, 18, 1, None, 6, None, 11, 13, 17, 19]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7]),key = 4), tree_node([6, 5, 7, 2, None, None, None, 1, 3]))\n assert is_same_tree(candidate(root = tree_node([5, 4, None, 3, None, 2, None, 1]),key = 5), tree_node([4, 3, None, 2, None, 1]))\n assert is_same_tree(candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9]),key = 1), tree_node([2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 1), tree_node([3, 6, 7, 12, 13, 14, 15, 2, None, None, None, None, None, None, None, 4, 5, 8, 9, 10, 11]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 2, 7, None, 18, None, None, 6, 8]),key = 5), tree_node([10, 7, 15, 6, 8, None, 18, 2]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 85, 115, 140, 160, 185, None, None, None, None, 28, None, 55, 90, None, 105, 110, 130, 135, None, None, None, None, None, None, None, None, 190, None, 195]),key = 100), tree_node([150, 125, 175, 115, 140, 160, 185, 50, 105, 110, 130, 135, None, None, None, 25, 75, None, 195, None, None, None, None, None, None, 10, 35, 60, 85, None, None, None, None, None, None, 28, None, 55, 90, None, None, None, None, None, 190]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, 17, 19]),key = 15), tree_node([10, 5, 18, 3, 7, 17, 19, 1, None, 6, 8, 12, None, None, None, None, None, None, None, None, None, 11, 13]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),key = 15), tree_node([10, 5, 18, 3, 7, 12]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 15, 25, 35, 45, 55, 65, 75, 85]),key = 60), tree_node([50, 30, 70, 20, 40, 65, 80, 15, 25, 35, 45, 55, None, 75, 85]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13, None, None]),key = 10), tree_node([8, 3, 14, 1, 6, 13, None, None, None, 4, 7]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]),key = 11), tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]))\n assert is_same_tree(candidate(root = tree_node([4, 2, 7, 1, 3, 6, 9, None, None, None, None, None, 8]),key = 6), tree_node([4, 2, 7, 1, 3, 8, 9]))\n assert is_same_tree(candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 48, 3, 7, None, 13, 17, None, 23, None, 33, 43, 47, None, 52]),key = 30), tree_node([45, 40, 50, 35, 48, 3, 7, 47, None, 52, None, None, None, None, None, 15, None, None, None, 10, 20, 5, 12, 18, 25, None, 13, 17, None, 23, None, 33, 43]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 5, 12, 17, 19, 21, 24, 28, 35]),key = 20), tree_node([25, 22, 30, 21, 24, 28, 35, 15, None, None, None, None, None, None, None, 10, 18, 5, 12, 17, 19]))\n assert is_same_tree(candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75]),key = 20), tree_node([40, 30, 60, 25, 35, 50, 70, 10, None, None, None, 45, 55, 65, 75, 5, 15]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 10), tree_node([50, 30, 70, 20, 40, 60, 80, None, None, None, 55, 65, None, None, 85, None, 90]))\n assert is_same_tree(candidate(root = tree_node([25, 10, 30, 5, 15, 28, 35, 3, 7, 12, 18, None, 29, 32, 34, 36]),key = 30), tree_node([25, 10, 35, 5, 15, 32, 34, 3, 7, 12, 18, 28, None, None, None, 36, None, None, None, None, None, None, None, None, 29]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 8, 13, 18, 23, 17, 22, 21, 24, None, None, None, 16, None, None, None, None, None, None, None, 19]),key = 15), tree_node([7, 3, 20, None, None, 8, 13, 18, 23, 17, 22, 21, 24, None, None, None, 16, None, None, 9, None, None, None, None, 19]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 80), tree_node([50, 30, 70, 20, 40, 60, 85, 10, None, None, 55, 65, None, None, None, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),key = 18), tree_node([10, 5, 15, 3, 7, 12]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 70), tree_node([50, 30, 80, 20, 40, 60, 85, 10, None, None, 55, 65, None, None, None, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18]),key = 10), tree_node([15, 12, 18, 5, None, None, None, 3, 7]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, None, 7, 12, 20, None, None, 6, 8]),key = 10), tree_node([15, 12, 20, 6, 8, None, None, 5, None, None, None, None, 7]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, None, 14, None, None, 2]),key = 10), tree_node([15, 12, 18, 11, 13, None, 14, 5, None, None, None, None, None, 3, 7, 1, None, 6, 8, None, None, 2]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 90), tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 6), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180]),key = 100), tree_node([150, 125, 175, 110, 140, 160, 180, 50, None, None, None, None, None, None, None, 25, 75, 10, 30, 60, 80]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, 1]),key = 3), tree_node([5, 4, 6, 2, None, None, 7, 1]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 12), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6]),key = 15), tree_node([10, 5, 18, 3, 7, 13, None, 1, None, 6]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 8, 10]),key = 15), tree_node([7, 3, 20, None, None, 8, 10, 9]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 8), tree_node([5, 3, 7, 2, 4, 6]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85]),key = 50), tree_node([70, 60, 80, 55, 65, 75, 85, 30, None, None, None, None, None, None, None, 20, 40, 10, 25, 35, 45]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 12, 18, 23, 28, 33, 37]),key = 10), tree_node([20, 15, 30, 12, 18, 25, 35, 5, None, None, None, 23, 28, 33, 37, 3, 7]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 7), tree_node([1, 2, 3, 4, 5, 6, 15, 8, 9, 10, 11, 12, 13, 14]))\n assert is_same_tree(candidate(root = tree_node([8, 5, 10, 2, 6, 9, 12, None, None, 3, 7, None, None, None, None, None, None]),key = 6), tree_node([8, 5, 10, 2, 7, 9, 12, None, None, 3]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 20), tree_node([50, 30, 70, 10, 40, 60, 80, None, None, None, 55, 65, None, None, 85, None, 90]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, None, None, 12, 17, None, None, None, None, None, None]),key = 10), tree_node([20, 15, 30, 12, 17, 25, 35, 5]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 10), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None]),key = 40), tree_node([50, 30, 70, 20, 45, 60, 80, 10, 25, 35, None, 55, 65, 75, 85]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, 17, 19]),key = 20), tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 8, 11, 13, 17, 19]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, 16, 18, 21, 23, 27, 35, 3, 8, None, None, None, None, None, 19, None, None, None, 24, 26, 32, 34, None, None, None, None, 9, 11, None, None, 14, None, None, None, None, 28, 31, 33, 36]),key = 15), tree_node([20, 17, 25, 16, 18, 22, 30, 10, None, None, 19, 21, 23, 27, 35, 5, 12, 11, None, None, None, None, 24, 26, 32, 34, None, 3, 8, None, None, None, None, None, 14, None, None, None, None, 28, 31, None, None, None, 9, None, None, None, None, None, None, 33, 36]))\n assert is_same_tree(candidate(root = tree_node([50, 20, 80, 15, 30, 70, 90, 10, 18, 25, 35, 60, 75, 85, 95]),key = 50), tree_node([80, 70, 90, 60, 75, 85, 95, 20, None, None, None, None, None, None, None, 15, 30, 10, 18, 25, 35]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 3), tree_node([5, 4, 7, 2, None, 6, 8]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 14), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]),key = 10), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 85, 110, 140, 160, 180]),key = 100), tree_node([150, 125, 175, 110, 140, 160, 180, 50, None, None, None, None, None, None, None, 25, 75, 10, 35, 60, 85]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 30), tree_node([50, 40, 70, 20, 55, 60, 80, 10, None, None, 90, 65, None, None, 85]))\n assert is_same_tree(candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75]),key = 30), tree_node([40, 20, 60, 10, 35, 50, 70, 5, 15, 25, None, 45, 55, 65, 75]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 40), tree_node([50, 30, 70, 20, 55, 60, 80, 10, None, None, 90, 65, None, None, 85]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 90]),key = 50), tree_node([70, 60, 80, 55, 65, 75, 90, 30, None, None, None, None, None, None, None, 20, 40, 10, 25, 35, 45]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, None, None, 3.5, None, None, 6.5]),key = 3), tree_node([5, 4, 6, 3.5, None, None, 7, 2, None, None, 6.5]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8]),key = 7), tree_node([5, 3, 8, 2, 4, 6]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, None, 55, 65, None, None, 85, None, None, None, 90]),key = 60), tree_node([50, 30, 70, 20, 40, 65, 80, 10, None, None, 55, None, None, None, 85, None, None, None, 90]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, None, None, 4, 5]),key = 2), tree_node([1, 2, 3, None, None, 4, 5]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]),key = 5), tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 18, 23, 28, 33, 38, 1, None, 6, None, 11, 13, None, 17, 19, None, 22, 24, 27, 29, None, 32, 34, None, 37, 39]),key = 20), tree_node([30, 25, 35, 23, 28, 33, 38, 19, None, 22, 24, 27, 29, None, 32, 10, None, None, None, None, None, None, None, None, None, None, None, 5, 15, 2, 7, 12, 18, 1, None, 6, None, 11, 13, None, 17, 34, None, 37, 39]))\n"}, "metadata": {"canonical_parameter_names": ["root", "key"], "leetcode_dataset_entry_point": "Solution().deleteNode", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var deleteNode = function(root, key) {", "container": null, "callable": "deleteNode", "parameters": [{"name": "root", "type": "TreeNode"}, {"name": "key", "type": "number"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 451, "task_id": "sort-characters-by-frequency", "difficulty": "Medium", "problem_description": "Given a string s, sort it in decreasing order based on the frequency of the characters. The frequency of a character is the number of times it appears in the string.\nReturn the sorted string. If there are multiple answers, return any of them.\n \nExample 1:\n\nInput: s = \"tree\"\nOutput: \"eert\"\nExplanation: 'e' appears twice while 'r' and 't' both appear once.\nSo 'e' must appear before both 'r' and 't'. Therefore \"eetr\" is also a valid answer.\n\nExample 2:\n\nInput: s = \"cccaaa\"\nOutput: \"aaaccc\"\nExplanation: Both 'c' and 'a' appear three times, so both \"cccaaa\" and \"aaaccc\" are valid answers.\nNote that \"cacaca\" is incorrect, as the same characters must be together.\n\nExample 3:\n\nInput: s = \"Aabb\"\nOutput: \"bbAa\"\nExplanation: \"bbaA\" is also a valid answer, but \"Aabb\" is incorrect.\nNote that 'A' and 'a' are treated as two different characters.\n\n \nConstraints:\n\n1 <= s.length <= 5 * 105\ns consists of uppercase and lowercase English letters and digits.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"aA\") == \"aA\"\n assert candidate(s = \"2a554442f544asf\") == \"4444455522aaffs\"\n assert candidate(s = \"2a554442f544asfasss\") == \"44444ssssaaa55522ff\"\n assert candidate(s = \"zzzzZZZZ\") == \"zzzzZZZZ\"\n assert candidate(s = \"bbaaccdd\") == \"bbaaccdd\"\n assert candidate(s = \"1223334444\") == \"4444333221\"\n assert candidate(s = \"cccaaa\") == \"cccaaa\"\n assert candidate(s = \"tree\") == \"eetr\"\n assert candidate(s = \"aAaaaAaA\") == \"aaaaaAAA\"\n assert candidate(s = \"a\") == \"a\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"\") == \"\"\n assert candidate(s = \"aAaaaAaaAAaAa\") == \"aaaaaaaaAAAAA\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"aAaaaAaaAA\") == \"aaaaaaAAAA\"\n assert candidate(s = \"Aabb\") == \"bbAa\"\n assert candidate(s = \"1234567890\") == \"1234567890\"\n assert candidate(s = \"bbaacc\") == \"bbaacc\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiiiiiijjjjjjjjjkkkkkkkkkkllllllllllllmmmmmmmmmmmmm\") == \"mmmmmmmmmmmmmllllllllllllkkkkkkkkkkjjjjjjjjjiiiiiiiaaaabbbbccccddddeeeeffffgggghhhh\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzAA\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzzAA\"\n assert candidate(s = \"AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\") == \"AaBbCcDdEeFfGgHhIiJjKkLlMmNnOoPpQqRrSsTtUuVvWwXxYyZz\"\n assert candidate(s = \"a1b2c3d4e5f6g7h8i9j0a1b2c3d4e5f6g7h8i9j0a1b2c3d4e5f6g7h8i9j0\") == \"aaa111bbb222ccc333ddd444eee555fff666ggg777hhh888iii999jjj000\"\n assert candidate(s = \"eLeetCoDe\") == \"eeeeLtCoD\"\n assert candidate(s = \"!!!!!!@@@@@@########$$$$$$$&&&&&&&&&&(((((()))))))\") == \"&&&&&&&&&&########$$$$$$$)))))))!!!!!!@@@@@@((((((\"\n assert candidate(s = \"112233445566778899001122334455\") == \"111122223333444455556677889900\"\n assert candidate(s = \"abcABC123abcABC123abcABC\") == \"aaabbbcccAAABBBCCC112233\"\n assert candidate(s = \"anagram\") == \"aaangrm\"\n assert candidate(s = \"a1b2c3d4e5f6g7h8i9j0A1B2C3D4E5F6G7H8I9J0\") == \"11223344556677889900abcdefghijABCDEFGHIJ\"\n assert candidate(s = \"frequencysorttestcase\") == \"eeeessstttrrccfqunyoa\"\n assert candidate(s = \"frequencySort\") == \"rreefquncySot\"\n assert candidate(s = \"aaaaaaaaaabbccccdddd\") == \"aaaaaaaaaaccccddddbb\"\n assert candidate(s = \"leetcode\") == \"eeeltcod\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzAABBCCDDEEFFGGHHIİJKKLLMMNNOOPPQQRRSSTTUUVVWWXXYYZZ\") == \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzAABBCCDDEEFFGGHHKKLLMMNNOOPPQQRRSSTTUUVVWWXXYYZZIİJ\"\n assert candidate(s = \"thisisaverylongtestcasewithmixedcharacters1234567890!@#$%^&*()\") == \"tttttssssseeeeeiiiiaaaahhhrrrcccvylongwmxd1234567890!@#$%^&*()\"\n assert candidate(s = \"ZzYyXxWwVvUuTtSsRrQqPpOoNnMmLlKkJjIiHhGgFfEeDdCcBbAa1234567890\") == \"ZzYyXxWwVvUuTtSsRrQqPpOoNnMmLlKkJjIiHhGgFfEeDdCcBbAa1234567890\"\n assert candidate(s = \"abcABC123xyzXYZ!@#\") == \"abcABC123xyzXYZ!@#\"\n assert candidate(s = \"01233210\") == \"00112233\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzzABCDEFGHIJKLMNOPQRSTUVWXYZ\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzzABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n assert candidate(s = \"111222333444555666777888999000\") == \"111222333444555666777888999000\"\n assert candidate(s = \"repeatedcharactersaretestedhere\") == \"eeeeeeeeerrrrraaaattttddcchhssp\"\n assert candidate(s = \"aaAAbbBBccCCddDDeeEEffFFggGGhhHHiiIIjjJJkkKKllLLmmMMnnNNooppQQrrSSttUUvvWWxxYYzzZZ\") == \"aaAAbbBBccCCddDDeeEEffFFggGGhhHHiiIIjjJJkkKKllLLmmMMnnNNooppQQrrSSttUUvvWWxxYYzzZZ\"\n assert candidate(s = \"1234567890abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\") == \"1234567890abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n assert candidate(s = \"mississippi\") == \"iiiissssppm\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\") == \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\"\n assert candidate(s = \"aabbccddeeffgghhiiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\") == \"iiiaabbccddeeffgghhjjkkllmmnnooppqqrrssttuuvvwwxxyyzz1234567890\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\"\n assert candidate(s = \"Mississippi\") == \"iiiissssppM\"\n assert candidate(s = \"aAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaAaA\") == \"aaaaaaaaaaaaaaaaaaaaAAAAAAAAAAAAAAAAAAAA\"\n assert candidate(s = \"123456789012345678901234567890\") == \"111222333444555666777888999000\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == \"zyxwvutsrqponmlkjihgfedcba\"\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().frequencySort", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var frequencySort = function(s) {", "container": null, "callable": "frequencySort", "parameters": [{"name": "s", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 452, "task_id": "minimum-number-of-arrows-to-burst-balloons", "difficulty": "Medium", "problem_description": "There are some spherical balloons taped onto a flat wall that represents the XY-plane. The balloons are represented as a 2D integer array points where points[i] = [xstart, xend] denotes a balloon whose horizontal diameter stretches between xstart and xend. You do not know the exact y-coordinates of the balloons.\nArrows can be shot up directly vertically (in the positive y-direction) from different points along the x-axis. A balloon with xstart and xend is burst by an arrow shot at x if xstart <= x <= xend. There is no limit to the number of arrows that can be shot. A shot arrow keeps traveling up infinitely, bursting any balloons in its path.\nGiven the array points, return the minimum number of arrows that must be shot to burst all balloons.\n \nExample 1:\n\nInput: points = [[10,16],[2,8],[1,6],[7,12]]\nOutput: 2\nExplanation: The balloons can be burst by 2 arrows:\n- Shoot an arrow at x = 6, bursting the balloons [2,8] and [1,6].\n- Shoot an arrow at x = 11, bursting the balloons [10,16] and [7,12].\n\nExample 2:\n\nInput: points = [[1,2],[3,4],[5,6],[7,8]]\nOutput: 4\nExplanation: One arrow needs to be shot for each balloon for a total of 4 arrows.\n\nExample 3:\n\nInput: points = [[1,2],[2,3],[3,4],[4,5]]\nOutput: 2\nExplanation: The balloons can be burst by 2 arrows:\n- Shoot an arrow at x = 2, bursting the balloons [1,2] and [2,3].\n- Shoot an arrow at x = 4, bursting the balloons [3,4] and [4,5].\n\n \nConstraints:\n\n1 <= points.length <= 105\npoints[i].length == 2\n-231 <= xstart < xend <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5]]) == 2\n assert candidate(points = [[10, 16], [2, 8], [1, 6], [7, 12]]) == 2\n assert candidate(points = [[1, 100], [2, 99], [3, 98]]) == 1\n assert candidate(points = [[3, 9], [7, 12], [3, 8], [6, 8], [9, 10], [2, 9], [0, 9], [3, 9], [0, 6], [2, 8]]) == 2\n assert candidate(points = [[1, 2], [3, 4], [5, 6], [7, 8]]) == 4\n assert candidate(points = [[0, 9], [0, 5], [4, 8], [7, 8], [9, 10], [9, 12], [4, 5], [4, 9], [5, 9], [8, 10]]) == 3\n assert candidate(points = [[1, 9], [2, 8], [3, 7], [4, 6], [5, 5]]) == 1\n assert candidate(points = [[-2147483646, -2147483645], [2147483646, 2147483647]]) == 2\n assert candidate(points = [[-5, 5], [-4, 4], [-3, 3], [-2, 2], [-1, 1], [0, 0]]) == 1\n assert candidate(points = [[-1000000000, 1000000000], [-999999999, 999999999], [-999999998, 999999998], [1, 2], [2, 3], [3, 4]]) == 2\n assert candidate(points = [[-1, -1], [-1, 0], [0, 0], [0, 1], [1, 1]]) == 3\n assert candidate(points = [[-100, 0], [-90, 10], [-80, 20], [-70, 30], [-60, 40], [-50, 50], [-40, 60], [-30, 70], [-20, 80], [-10, 90]]) == 1\n assert candidate(points = [[1, 1000], [100, 900], [200, 800], [300, 700], [400, 600], [500, 500]]) == 1\n assert candidate(points = [[-100, 100], [-90, 90], [-80, 80], [-70, 70], [-60, 60], [-50, 50], [-40, 40], [-30, 30], [-20, 20], [-10, 10], [0, 0]]) == 1\n assert candidate(points = [[-100000, 100000], [-50000, 50000], [-25000, 25000], [0, 0]]) == 1\n assert candidate(points = [[1, 2], [2, 5], [5, 7], [6, 10], [10, 15], [15, 20]]) == 3\n assert candidate(points = [[-10, 10], [-5, 5], [0, 0], [5, 15], [10, 20], [15, 25], [20, 30]]) == 3\n assert candidate(points = [[5, 10], [15, 20], [25, 30], [5, 15], [10, 20], [15, 25]]) == 3\n assert candidate(points = [[1, 2], [2, 5], [5, 8], [8, 10], [10, 12], [12, 15], [15, 18], [18, 20], [20, 22], [22, 25], [25, 30], [30, 35], [35, 40]]) == 7\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [1, 10]]) == 5\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [-4, 4], [-5, 5], [-6, 6], [-7, 7], [-8, 8], [-9, 9], [-10, 10]]) == 1\n assert candidate(points = [[-1000, -500], [-499, -300], [-299, -100], [-99, 0], [1, 100], [101, 200], [201, 300], [301, 400], [401, 500], [501, 600]]) == 10\n assert candidate(points = [[-10, 0], [0, 10], [5, 15], [10, 20]]) == 2\n assert candidate(points = [[1, 10], [11, 20], [21, 30], [31, 40], [41, 50], [51, 60], [61, 70], [71, 80], [81, 90], [91, 100]]) == 10\n assert candidate(points = [[-2147483648, 2147483647], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 4\n assert candidate(points = [[1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == 2\n assert candidate(points = [[-1, 1], [0, 0], [1, 2], [2, 3], [3, 4], [4, 5]]) == 3\n assert candidate(points = [[-1000000000, 1000000000], [-500000000, 500000000], [0, 0], [500000000, 1000000000], [-1000000000, 500000000], [0, 1000000000], [-500000000, 0]]) == 2\n assert candidate(points = [[1, 5], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 4\n assert candidate(points = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12]]) == 4\n assert candidate(points = [[1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [21, 25], [25, 29], [29, 33], [33, 37]]) == 5\n assert candidate(points = [[-10, 15], [-5, 20], [0, 25], [5, 30], [10, 35], [15, 40], [20, 45], [25, 50]]) == 2\n assert candidate(points = [[-100, -50], [-50, 0], [0, 50], [50, 100], [25, 75]]) == 2\n assert candidate(points = [[-100, -90], [-90, -80], [-80, -70], [-70, -60], [-60, -50], [-50, -40], [-40, -30], [-30, -20], [-20, -10]]) == 5\n assert candidate(points = [[-5, 5], [-4, 4], [-3, 3], [-2, 2], [-1, 1], [0, 0], [1, 1], [2, 2], [3, 3], [4, 4], [5, 5]]) == 6\n assert candidate(points = [[10, 20], [10, 15], [10, 10], [15, 20], [20, 30], [25, 35], [30, 40], [35, 45], [40, 50]]) == 4\n assert candidate(points = [[-100, -50], [-75, -25], [-50, 0], [-25, 25], [0, 50], [25, 75], [50, 100], [-100, 0], [0, 100]]) == 3\n assert candidate(points = [[-10, 10], [-5, 5], [0, 0], [1, 3], [-1, 1], [2, 4], [-3, -1]]) == 3\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [0, 0], [1, 1], [2, 2], [3, 3]]) == 4\n assert candidate(points = [[-100, -90], [-80, -70], [-60, -50], [-40, -30], [-20, -10], [0, 10], [20, 30], [40, 50], [60, 70], [80, 90], [100, 110]]) == 11\n assert candidate(points = [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]) == 1\n assert candidate(points = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [1, 100]]) == 5\n assert candidate(points = [[-10, -8], [-7, -5], [-3, -1], [0, 2], [3, 5], [6, 8], [9, 11], [12, 14]]) == 8\n assert candidate(points = [[-5, -3], [-4, -2], [-3, -1], [-2, 0], [-1, 1], [0, 2], [1, 3], [2, 4], [3, 5]]) == 3\n assert candidate(points = [[-1000, 1000], [500, 1500], [-1500, -500], [0, 500], [500, 1000]]) == 2\n assert candidate(points = [[1, 1000], [2, 999], [3, 998], [4, 997], [5, 996], [6, 995], [7, 994], [8, 993], [9, 992], [10, 991], [11, 990], [12, 989], [13, 988], [14, 987]]) == 1\n assert candidate(points = [[-5, -3], [-4, -2], [-1, 1], [0, 2], [1, 3], [2, 4]]) == 3\n assert candidate(points = [[1, 5], [2, 6], [3, 7], [4, 8], [5, 9], [6, 10], [7, 11], [8, 12], [9, 13], [10, 14]]) == 2\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15]]) == 7\n assert candidate(points = [[-1, 1], [-1, 2], [0, 2], [1, 3], [0, 3], [-1, 3]]) == 1\n assert candidate(points = [[1, 5], [2, 8], [3, 9], [4, 10], [5, 11], [6, 12], [7, 13], [8, 14], [9, 15]]) == 2\n assert candidate(points = [[-10, 5], [0, 10], [5, 15], [10, 20], [15, 25], [20, 30], [25, 35]]) == 3\n assert candidate(points = [[-5, 5], [0, 10], [-10, 0], [5, 15], [-15, -5], [10, 20], [-20, -10], [15, 25], [-25, -15], [20, 30]]) == 4\n assert candidate(points = [[-2147483648, 2147483647], [-2147483647, 2147483646], [-2147483646, 2147483645], [-2147483645, 2147483644], [-2147483644, 2147483643]]) == 1\n assert candidate(points = [[-10, -1], [0, 1], [2, 3], [5, 7], [10, 12], [15, 17], [20, 22], [25, 27], [30, 32]]) == 9\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 3\n assert candidate(points = [[1, 5], [2, 8], [3, 10], [4, 12], [5, 14], [6, 16]]) == 2\n assert candidate(points = [[-2147483646, -2147483645], [2147483645, 2147483646], [-2147483647, -2147483646], [2147483647, 2147483648]]) == 3\n assert candidate(points = [[-500, 500], [-400, 400], [-300, 300], [-200, 200], [-100, 100], [0, 0]]) == 1\n assert candidate(points = [[-10, 10], [-9, 9], [-8, 8], [-7, 7], [-6, 6], [-5, 5], [-4, 4], [-3, 3], [-2, 2], [-1, 1], [0, 0]]) == 1\n assert candidate(points = [[1, 100], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == 5\n assert candidate(points = [[1, 5], [2, 3], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10], [9, 11], [10, 12], [11, 13]]) == 4\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]]) == 5\n assert candidate(points = [[1, 20], [2, 19], [3, 18], [4, 17], [5, 16], [6, 15], [7, 14], [8, 13], [9, 12], [10, 11]]) == 1\n assert candidate(points = [[1, 1], [1, 2], [2, 2], [2, 3], [3, 3], [3, 4], [4, 4], [4, 5], [5, 5], [5, 6], [6, 6], [6, 7], [7, 7], [7, 8]]) == 7\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16]]) == 8\n assert candidate(points = [[10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == 5\n assert candidate(points = [[-1000000, 1000000], [0, 1000000], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 4\n assert candidate(points = [[1, 50], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [1, 3], [3, 5], [5, 7], [7, 9], [2, 4], [4, 6], [6, 8], [8, 10]]) == 5\n assert candidate(points = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == 10\n assert candidate(points = [[100, 150], [120, 200], [130, 180], [160, 210], [170, 220], [180, 230]]) == 2\n assert candidate(points = [[100, 200], [150, 250], [200, 300], [250, 350], [300, 400], [350, 450], [400, 500], [450, 550], [500, 600]]) == 3\n assert candidate(points = [[-2, -1], [-1, 0], [0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [1, 3], [3, 4], [4, 5], [1, 5], [5, 6], [6, 7], [1, 7], [7, 8]]) == 4\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [6, 5], [7, 4], [8, 3], [9, 2], [10, 1]]) == 5\n assert candidate(points = [[10, 16], [2, 8], [1, 6], [7, 12], [3, 11], [14, 17], [9, 13], [6, 10]]) == 3\n assert candidate(points = [[-1, 1], [-2, 2], [-3, 3], [-4, 4], [-5, 5], [-6, 6], [-7, 7], [-8, 8], [-9, 9], [-10, 10]]) == 1\n assert candidate(points = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10], [1, 11]]) == 1\n assert candidate(points = [[1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10]]) == 1\n assert candidate(points = [[1, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9], [8, 10]]) == 3\n assert candidate(points = [[1, 10], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [11, 12], [12, 13], [13, 14]]) == 6\n assert candidate(points = [[0, 9], [2, 8], [3, 7], [6, 10], [1, 5], [4, 6], [7, 11], [8, 12], [9, 13], [10, 14]]) == 2\n assert candidate(points = [[1, 2], [2, 5], [5, 10], [10, 15], [15, 20], [20, 25], [25, 30], [30, 35], [35, 40], [40, 45]]) == 5\n assert candidate(points = [[1, 5], [5, 10], [10, 15], [15, 20], [20, 25]]) == 3\n assert candidate(points = [[-5, -1], [0, 5], [10, 15], [1, 9]]) == 3\n assert candidate(points = [[-10, -5], [-5, 0], [0, 5], [5, 10], [10, 15], [15, 20], [20, 25]]) == 4\n assert candidate(points = [[1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5], [1, 5]]) == 1\n assert candidate(points = [[1, 2], [3, 5], [4, 8], [5, 10], [6, 12], [7, 15], [8, 20]]) == 3\n assert candidate(points = [[1, 1], [1, 2], [1, 3], [1, 4], [1, 5], [1, 6], [1, 7], [1, 8], [1, 9], [1, 10]]) == 1\n assert candidate(points = [[1, 1], [1, 2], [2, 3], [2, 4], [3, 5], [4, 6], [5, 7], [6, 8], [7, 9]]) == 4\n assert candidate(points = [[-10, -1], [1, 2], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17]]) == 9\n assert candidate(points = [[-2147483646, -2147483645], [-2147483645, -2147483644], [-2147483644, -2147483643]]) == 2\n assert candidate(points = [[1, 3], [3, 5], [5, 7], [7, 9], [9, 11], [11, 13], [13, 15], [15, 17], [17, 19], [19, 21]]) == 5\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9]]) == 4\n assert candidate(points = [[1000, 2000], [1500, 2500], [2000, 3000], [2500, 3500], [3000, 4000], [3500, 4500], [4000, 5000]]) == 3\n assert candidate(points = [[-10, -5], [0, 0], [5, 10], [15, 20], [25, 30], [35, 40]]) == 6\n assert candidate(points = [[-10, 0], [-5, 5], [0, 10], [5, 15], [10, 20]]) == 2\n assert candidate(points = [[1, 1000], [2, 999], [3, 998], [4, 997], [5, 996], [6, 995], [7, 994], [8, 993], [9, 992], [10, 991]]) == 1\n assert candidate(points = [[1, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80], [80, 90], [90, 100], [100, 110]]) == 5\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [11, 20], [12, 19], [13, 18], [14, 17], [15, 16]]) == 2\n assert candidate(points = [[5, 10], [15, 20], [10, 15], [25, 30], [18, 25]]) == 3\n assert candidate(points = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15]]) == 7\n assert candidate(points = [[10, 20], [15, 25], [20, 30], [25, 35], [30, 40], [35, 45], [40, 50], [45, 55], [50, 60]]) == 3\n assert candidate(points = [[1, 10], [5, 15], [10, 20], [15, 25], [20, 30]]) == 2\n assert candidate(points = [[1, 10], [2, 9], [3, 8], [4, 7], [5, 6], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60]]) == 4\n assert candidate(points = [[1, 10], [10, 20], [20, 30], [30, 40], [40, 50], [50, 60], [60, 70], [70, 80]]) == 4\n assert candidate(points = [[1, 2], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21]]) == 10\n assert candidate(points = [[1, 1000000], [2, 999999], [3, 999998], [4, 999997], [5, 999996], [6, 999995], [7, 999994], [8, 999993], [9, 999992], [10, 999991]]) == 1\n"}, "metadata": {"canonical_parameter_names": ["points"], "leetcode_dataset_entry_point": "Solution().findMinArrowShots", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMinArrowShots = function(points) {", "container": null, "callable": "findMinArrowShots", "parameters": [{"name": "points", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 453, "task_id": "minimum-moves-to-equal-array-elements", "difficulty": "Medium", "problem_description": "Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal.\nIn one move, you can increment n - 1 elements of the array by 1.\n \nExample 1:\n\nInput: nums = [1,2,3]\nOutput: 3\nExplanation: Only three moves are needed (remember each move increments two elements):\n[1,2,3] => [2,3,3] => [3,4,3] => [4,4,4]\n\nExample 2:\n\nInput: nums = [1,1,1]\nOutput: 0\n\n \nConstraints:\n\nn == nums.length\n1 <= nums.length <= 105\n-109 <= nums[i] <= 109\nThe answer is guaranteed to fit in a 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1000000000, -1000000000]) == 2000000000\n assert candidate(nums = [1, 2, 100]) == 100\n assert candidate(nums = [10, 15, 20]) == 15\n assert candidate(nums = [1, 1, 1]) == 0\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 45\n assert candidate(nums = [1, 3, 5, 7, 9]) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 45\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == 20\n assert candidate(nums = [5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [1, 2, 1, 4]) == 4\n assert candidate(nums = [-5, -4, -3, -2, -1]) == 10\n assert candidate(nums = [100, 99, 98, 97, 96]) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 45\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [-1000000000, -1000000000, -1000000000]) == 0\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 20\n assert candidate(nums = [4, 5, 6, 7]) == 6\n assert candidate(nums = [1000000000, -1000000000, 0]) == 3000000000\n assert candidate(nums = [1, 2, 3]) == 3\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [5, 6, 8, 13]) == 12\n assert candidate(nums = [-1, 1, 0, -3]) == 9\n assert candidate(nums = [1, 2, 1, 2, 1]) == 2\n assert candidate(nums = [-1, 0, 1]) == 3\n assert candidate(nums = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 5490\n assert candidate(nums = [29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == 210\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 19000\n assert candidate(nums = [-1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000, -1000000000]) == 0\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]) == 950\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 55\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 4500\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 225\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == 45\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90]) == 55\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15]) == 105\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 380\n assert candidate(nums = [-1000000000, -1000000000, -1000000000, -1000000000, -1000000000]) == 0\n assert candidate(nums = [1, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 1111111092\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 100, 200, 300, 400, 500]) == 2000\n assert candidate(nums = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55]) == 210\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 1111111101\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 90\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 90\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 45\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1000000000]) == 999999999\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [1, 1000000000, 2, 999999999, 3, 999999998]) == 2999999997\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 2036\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == 2100\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 105\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 20\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990]) == 45\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 55\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 450\n assert candidate(nums = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145, 155, 165, 175, 185, 195]) == 1900\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1000000000]) == 999999999\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 210\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 1900\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991]) == 45\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 190\n assert candidate(nums = [-100, 0, 100, -200, 0, 200, -300, 0, 300, -400, 0, 400, -500, 0, 500]) == 7500\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 300\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250]) == 3000\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 1]) == 81\n assert candidate(nums = [100, 100, 100, 100, 100, 99, 99, 99, 99, 99]) == 5\n assert candidate(nums = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 10000000000]) == 45000000000\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6]) == 70\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == 450\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 190\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1]) == 8999999991\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().minMoves", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minMoves = function(nums) {", "container": null, "callable": "minMoves", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 454, "task_id": "4sum-ii", "difficulty": "Medium", "problem_description": "Given four integer arrays nums1, nums2, nums3, and nums4 all of length n, return the number of tuples (i, j, k, l) such that:\n\n0 <= i, j, k, l < n\nnums1[i] + nums2[j] + nums3[k] + nums4[l] == 0\n\n \nExample 1:\n\nInput: nums1 = [1,2], nums2 = [-2,-1], nums3 = [-1,2], nums4 = [0,2]\nOutput: 2\nExplanation:\nThe two tuples are:\n1. (0, 0, 0, 1) -> nums1[0] + nums2[0] + nums3[0] + nums4[1] = 1 + (-2) + (-1) + 2 = 0\n2. (1, 1, 0, 0) -> nums1[1] + nums2[1] + nums3[0] + nums4[0] = 2 + (-1) + (-1) + 0 = 0\n\nExample 2:\n\nInput: nums1 = [0], nums2 = [0], nums3 = [0], nums4 = [0]\nOutput: 1\n\n \nConstraints:\n\nn == nums1.length\nn == nums2.length\nn == nums3.length\nn == nums4.length\n1 <= n <= 200\n-228 <= nums1[i], nums2[i], nums3[i], nums4[i] <= 228\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [100000000, 200000000],nums2 = [-300000000, -400000000],nums3 = [500000000, 600000000],nums4 = [-700000000, -800000000]) == 0\n assert candidate(nums1 = [1, 2, 3],nums2 = [-1, -2, -3],nums3 = [1, -1, 0],nums4 = [0, 2, -2]) == 13\n assert candidate(nums1 = [1, 2, 3],nums2 = [-1, -2, -3],nums3 = [1, 2, 3],nums4 = [-1, -2, -3]) == 19\n assert candidate(nums1 = [-1, -2, -3],nums2 = [3, 2, 1],nums3 = [1, -2, 3],nums4 = [-3, 2, 1]) == 10\n assert candidate(nums1 = [-1, 1, 0],nums2 = [-1, 1, 0],nums3 = [-1, 1, 0],nums4 = [-1, 1, 0]) == 19\n assert candidate(nums1 = [0],nums2 = [0],nums3 = [0],nums4 = [0]) == 1\n assert candidate(nums1 = [-1, -1, -1, -1],nums2 = [1, 1, 1, 1],nums3 = [-1, -1, -1, -1],nums4 = [1, 1, 1, 1]) == 256\n assert candidate(nums1 = [1, 2, 3],nums2 = [-1, -2, -3],nums3 = [0, 1, -1],nums4 = [0, -1, 1]) == 19\n assert candidate(nums1 = [1, 0, -1],nums2 = [1, 0, -1],nums3 = [1, 0, -1],nums4 = [1, 0, -1]) == 19\n assert candidate(nums1 = [1, -1],nums2 = [1, -1],nums3 = [1, -1],nums4 = [1, -1]) == 6\n assert candidate(nums1 = [100000000, -100000000],nums2 = [100000000, -100000000],nums3 = [100000000, -100000000],nums4 = [100000000, -100000000]) == 6\n assert candidate(nums1 = [1, 2, 3],nums2 = [-3, -2, -1],nums3 = [-1, 2, 1],nums4 = [0, 2, -2]) == 12\n assert candidate(nums1 = [100, 200],nums2 = [-100, -200],nums3 = [100, 200],nums4 = [-100, -200]) == 6\n assert candidate(nums1 = [1, 2],nums2 = [-2, -1],nums3 = [-1, 2],nums4 = [0, 2]) == 2\n assert candidate(nums1 = [-1, -1, -1],nums2 = [-1, -1, -1],nums3 = [-1, -1, -1],nums4 = [-1, -1, -1]) == 0\n assert candidate(nums1 = [0, 1, -1],nums2 = [-1, 1, 0],nums3 = [0, -1, 1],nums4 = [1, 0, -1]) == 19\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [-100, -200, -300, -400, -500],nums3 = [500, -500, 500, -500, 500],nums4 = [-500, 500, -500, 500, -500]) == 65\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [1, 2, 3, 4],nums3 = [-1, -2, -3, -4],nums4 = [-1, -2, -3, -4]) == 44\n assert candidate(nums1 = [1, -1, 1, -1],nums2 = [1, -1, 1, -1],nums3 = [1, -1, 1, -1],nums4 = [1, -1, 1, -1]) == 96\n assert candidate(nums1 = [1, 1, 1, 1, 1],nums2 = [-1, -1, -1, -1, -1],nums3 = [0, 0, 0, 0, 0],nums4 = [0, 0, 0, 0, 0]) == 625\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [-10, -20, -30, -40],nums3 = [5, 10, 15, 20],nums4 = [-5, -10, -15, -20]) == 28\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [-1, -2, -3, -4, -5],nums3 = [0, 0, 0, 0, 0],nums4 = [0, 0, 0, 0, 0]) == 125\n assert candidate(nums1 = [-10, 10, -10, 10],nums2 = [10, -10, 10, -10],nums3 = [5, -5, 5, -5],nums4 = [-5, 5, -5, 5]) == 64\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80],nums2 = [-10, -20, -30, -40, -50, -60, -70, -80],nums3 = [1, 2, 3, 4, 5, 6, 7, 8],nums4 = [-1, -2, -3, -4, -5, -6, -7, -8]) == 64\n assert candidate(nums1 = [-1, 0, 1, 2],nums2 = [1, -1, 2, -2],nums3 = [2, 1, -1, -2],nums4 = [-2, 2, -1, 1]) == 33\n assert candidate(nums1 = [0, 0, 0, 0],nums2 = [0, 0, 0, 0],nums3 = [0, 0, 0, 0],nums4 = [0, 0, 0, 0]) == 256\n assert candidate(nums1 = [100, 200, 300, 400],nums2 = [-100, -200, -300, -400],nums3 = [1, 2, 3, 4],nums4 = [-1, -2, -3, -4]) == 16\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [-1, -1, -1, -1],nums3 = [1, 1, 1, 1],nums4 = [-1, -1, -1, -1]) == 256\n assert candidate(nums1 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums2 = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1],nums3 = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2],nums4 = [-2, -2, -2, -2, -2, -2, -2, -2, -2, -2]) == 10000\n assert candidate(nums1 = [100, 200, 300, 400],nums2 = [-100, -200, -300, -400],nums3 = [50, 100, 150, 200],nums4 = [-50, -100, -150, -200]) == 28\n assert candidate(nums1 = [100, 200, 300, 400],nums2 = [-100, -200, -300, -400],nums3 = [50, 150, 250, 350],nums4 = [-50, -150, -250, -350]) == 44\n assert candidate(nums1 = [100, 200, 300, 400],nums2 = [-400, -300, -200, -100],nums3 = [50, 150, 250, 350],nums4 = [-350, -250, -150, -50]) == 44\n assert candidate(nums1 = [1, 0, -1, -2],nums2 = [2, -2, 1, 0],nums3 = [-1, 0, 1, 2],nums4 = [1, -1, -2, 2]) == 36\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [-10, -20, -30, -40],nums3 = [10, 20, 30, 40],nums4 = [5, 15, 25, 35]) == 0\n assert candidate(nums1 = [0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0],nums3 = [0, 0, 0, 0, 0],nums4 = [0, 0, 0, 0, 0]) == 625\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [-1, -2, -3, -4, -5],nums3 = [1, 2, 3, 4, 5],nums4 = [-1, -2, -3, -4, -5]) == 85\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1],nums3 = [-1, -2, -3, -4, -5],nums4 = [-5, -4, -3, -2, -1]) == 85\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [-1, -2, -3, -4],nums3 = [0, 0, 0, 0],nums4 = [0, 0, 0, 0]) == 64\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [-10, -20, -30, -40],nums3 = [10, -10, 20, -20],nums4 = [-10, 10, -20, 20]) == 36\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [-1, -2, -3, -4],nums3 = [1, -1, 1, -1],nums4 = [2, -2, 2, -2]) == 32\n assert candidate(nums1 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],nums2 = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],nums3 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums4 = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 100\n assert candidate(nums1 = [25, -25, 50, -50],nums2 = [30, -30, 60, -60],nums3 = [10, -10, 20, -20],nums4 = [15, -15, 30, -30]) == 10\n assert candidate(nums1 = [1, -2, 3, -4],nums2 = [4, -3, 2, -1],nums3 = [-1, 2, -3, 4],nums4 = [1, -2, 3, -4]) == 36\n assert candidate(nums1 = [100000000, -100000000, 200000000, -200000000],nums2 = [50000000, -50000000, 150000000, -150000000],nums3 = [25000000, -25000000, 75000000, -75000000],nums4 = [12500000, -12500000, 37500000, -37500000]) == 0\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [2, 2, 2, 2],nums3 = [-3, -3, -3, -3],nums4 = [4, 4, 4, 4]) == 0\n assert candidate(nums1 = [1, -1, 2, -2, 3, -3],nums2 = [-3, 3, -2, 2, -1, 1],nums3 = [2, -2, 1, -1, 3, -3],nums4 = [-3, 3, 2, -2, 1, -1]) == 122\n assert candidate(nums1 = [10, -10, 20, -20],nums2 = [1, -1, 2, -2],nums3 = [3, -3, 4, -4],nums4 = [-4, 4, -3, 3]) == 2\n assert candidate(nums1 = [123, -123, 246, -246],nums2 = [369, -369, 738, -738],nums3 = [456, -456, 912, -912],nums4 = [-912, -456, 456, 912]) == 0\n assert candidate(nums1 = [100, -100, 200, -200],nums2 = [150, -150, 250, -250],nums3 = [200, -200, 300, -300],nums4 = [250, -250, 350, -350]) == 22\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6],nums2 = [-1, -2, -3, -4, -5, -6],nums3 = [1, -1, 2, -2, 3, -3],nums4 = [-1, 1, -2, 2, -3, 3]) == 128\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [-5, -4, -3, -2, -1],nums3 = [1, 1, 1, 1, 1],nums4 = [-1, -1, -1, -1, -1]) == 125\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [-1, -2, -3, -4, -5],nums3 = [5, -5, 5, -5, 5],nums4 = [-5, 5, -5, 5, -5]) == 65\n assert candidate(nums1 = [1, -1, 2, -2],nums2 = [1, -1, 2, -2],nums3 = [1, -1, 2, -2],nums4 = [1, -1, 2, -2]) == 36\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [-10, -20, -30, -40],nums3 = [5, 15, 25, 35],nums4 = [-5, -15, -25, -35]) == 44\n assert candidate(nums1 = [100, 200, 300, 400, 500],nums2 = [-500, -400, -300, -200, -100],nums3 = [50, 150, 250, 350, 450],nums4 = [-450, -350, -250, -150, -50]) == 85\n assert candidate(nums1 = [7, -7, 14, -14],nums2 = [21, -21, 42, -42],nums3 = [6, -6, 12, -12],nums4 = [28, -28, 56, -56]) == 0\n assert candidate(nums1 = [10, -10, 20, -20],nums2 = [5, -5, 15, -15],nums3 = [3, -3, 12, -12],nums4 = [8, -8, 17, -17]) == 12\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],nums3 = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],nums4 = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == 1000\n assert candidate(nums1 = [1, -1, 1, -1],nums2 = [2, -2, 2, -2],nums3 = [3, -3, 3, -3],nums4 = [4, -4, 4, -4]) == 32\n assert candidate(nums1 = [1, -1, 1, -1, 1, -1, 1, -1],nums2 = [1, -1, 1, -1, 1, -1, 1, -1],nums3 = [1, -1, 1, -1, 1, -1, 1, -1],nums4 = [1, -1, 1, -1, 1, -1, 1, -1]) == 1536\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0, 0, 0],nums3 = [0, 0, 0, 0, 0, 0, 0, 0],nums4 = [0, 0, 0, 0, 0, 0, 0, 0]) == 4096\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [5, 6, 7, 8],nums3 = [-1, -2, -3, -4],nums4 = [-5, -6, -7, -8]) == 44\n assert candidate(nums1 = [-10, -9, -8, -7],nums2 = [7, 8, 9, 10],nums3 = [-5, 5, -5, 5],nums4 = [5, -5, 5, -5]) == 32\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [-4, -3, -2, -1],nums3 = [1, 2, 3, 4],nums4 = [-4, -3, -2, -1]) == 44\n assert candidate(nums1 = [-1, -2, -3, -4],nums2 = [1, 2, 3, 4],nums3 = [-1, -2, -3, -4],nums4 = [1, 2, 3, 4]) == 44\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [1, 1, 1, 1],nums3 = [-2, -2, -2, -2],nums4 = [-2, -2, -2, -2]) == 0\n assert candidate(nums1 = [100000000, 100000000, 100000000, 100000000],nums2 = [-250000000, 0, 250000000, 0],nums3 = [125000000, -125000000, 125000000, -125000000],nums4 = [-125000000, 125000000, -125000000, 125000000]) == 0\n assert candidate(nums1 = [1, -1, 2, -2],nums2 = [2, -2, 1, -1],nums3 = [3, -3, 4, -4],nums4 = [-4, 4, -3, 3]) == 24\n assert candidate(nums1 = [5, 10, 15, 20],nums2 = [-20, -15, -10, -5],nums3 = [25, 30, 35, 40],nums4 = [-40, -35, -30, -25]) == 44\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [-10, -20, -30, -40, -50],nums3 = [5, 10, 15, 20, 25],nums4 = [-5, -10, -15, -20, -25]) == 55\n assert candidate(nums1 = [0, 0, 0, 0, 0, 0],nums2 = [0, 0, 0, 0, 0, 0],nums3 = [0, 0, 0, 0, 0, 0],nums4 = [0, 0, 0, 0, 0, 0]) == 1296\n assert candidate(nums1 = [1, 2, 3, -6],nums2 = [-2, -3, 4, 1],nums3 = [0, 0, 0, 0],nums4 = [5, -5, 5, -5]) == 16\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [-1, -2, -3, -4],nums3 = [1, -1, 1, -1],nums4 = [-1, 1, -1, 1]) == 48\n assert candidate(nums1 = [-10, -20, -30, -40],nums2 = [10, 20, 30, 40],nums3 = [5, 15, 25, 35],nums4 = [-5, -15, -25, -35]) == 44\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [1, 1, 1, 1],nums3 = [-2, -2, -2, -2],nums4 = [2, 2, 2, 2]) == 0\n assert candidate(nums1 = [1, -2, 3, 4],nums2 = [-3, 2, 1, -1],nums3 = [2, -1, -3, 4],nums4 = [-4, 1, 2, 3]) == 21\n assert candidate(nums1 = [-1, 1, -2, 2],nums2 = [-1, 1, -2, 2],nums3 = [-1, 1, -2, 2],nums4 = [-1, 1, -2, 2]) == 36\n assert candidate(nums1 = [-100000000, 100000000, -200000000, 200000000],nums2 = [200000000, -200000000, 100000000, -100000000],nums3 = [-50000000, 50000000, -50000000, 50000000],nums4 = [50000000, -50000000, 50000000, -50000000]) == 48\n assert candidate(nums1 = [-23456789, 23456789, -98765432, 98765432],nums2 = [-45678912, 45678912, -87654321, 87654321],nums3 = [56789123, -56789123, 43210987, -43210987],nums4 = [-67891234, 67891234, -32109876, 32109876]) == 0\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7],nums2 = [-7, -6, -5, -4, -3, -2, -1],nums3 = [1, 2, 3, 4, 5, 6, 7],nums4 = [-7, -6, -5, -4, -3, -2, -1]) == 231\n assert candidate(nums1 = [100, -100, 200, -200],nums2 = [300, -300, 600, -600],nums3 = [100, -100, 200, -200],nums4 = [200, -200, 400, -400]) == 12\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [1, 2, 3, 4],nums3 = [1, 2, 3, 4],nums4 = [-8, 8, -8, 8]) == 24\n assert candidate(nums1 = [5, -4, 3, 2],nums2 = [-2, 6, -1, 0],nums3 = [1, -3, 4, -5],nums4 = [0, 1, -1, 2]) == 16\n assert candidate(nums1 = [150, 100, 50, 0],nums2 = [-50, -100, -150, -200],nums3 = [250, 200, 150, 100],nums4 = [-100, -150, -200, -250]) == 40\n assert candidate(nums1 = [100000000, -100000000, 50000000, -50000000],nums2 = [100000000, -100000000, 50000000, -50000000],nums3 = [100000000, -100000000, 50000000, -50000000],nums4 = [100000000, -100000000, 50000000, -50000000]) == 36\n assert candidate(nums1 = [1, 1, 1, 1],nums2 = [1, 1, 1, 1],nums3 = [-1, -1, -1, -1],nums4 = [-1, -1, -1, -1]) == 256\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [-10, -20, -30, -40],nums3 = [1, 2, 3, 4],nums4 = [-1, -2, -3, -4]) == 16\n assert candidate(nums1 = [5, 5, 5, 5],nums2 = [-5, -5, -5, -5],nums3 = [10, 10, 10, 10],nums4 = [-10, -10, -10, -10]) == 256\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8],nums2 = [-1, -2, -3, -4, -5, -6, -7, -8],nums3 = [1, 2, 3, 4, 5, 6, 7, 8],nums4 = [-1, -2, -3, -4, -5, -6, -7, -8]) == 344\n assert candidate(nums1 = [10, -10, 20, -20],nums2 = [-10, 10, -20, 20],nums3 = [30, -30, 40, -40],nums4 = [-40, 40, -30, 30]) == 24\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [-4, -3, -2, -1],nums3 = [0, 0, 0, 0],nums4 = [1, 1, 1, 1]) == 48\n assert candidate(nums1 = [5, -5, 5, -5],nums2 = [5, -5, 5, -5],nums3 = [5, -5, 5, -5],nums4 = [5, -5, 5, -5]) == 96\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6],nums2 = [-6, -5, -4, -3, -2, -1],nums3 = [0, 0, 0, 0, 0, 0],nums4 = [0, 0, 0, 0, 0, 0]) == 216\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [-40, -30, -20, -10],nums3 = [5, 15, 25, 35],nums4 = [-35, -25, -15, -5]) == 44\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8],nums2 = [-8, -7, -6, -5, -4, -3, -2, -1],nums3 = [8, 7, 6, 5, 4, 3, 2, 1],nums4 = [-1, -2, -3, -4, -5, -6, -7, -8]) == 344\n assert candidate(nums1 = [5, 3, -4, 1],nums2 = [-1, 4, -2, 6],nums3 = [-3, 5, 2, -7],nums4 = [1, 2, -4, -3]) == 12\n assert candidate(nums1 = [5, -5, 10, -10],nums2 = [5, -5, 10, -10],nums3 = [5, -5, 10, -10],nums4 = [5, -5, 10, -10]) == 36\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2", "nums3", "nums4"], "leetcode_dataset_entry_point": "Solution().fourSumCount", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var fourSumCount = function(nums1, nums2, nums3, nums4) {", "container": null, "callable": "fourSumCount", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}, {"name": "nums3", "type": "number[]"}, {"name": "nums4", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 455, "task_id": "assign-cookies", "difficulty": "Easy", "problem_description": "Assume you are an awesome parent and want to give your children some cookies. But, you should give each child at most one cookie.\nEach child i has a greed factor g[i], which is the minimum size of a cookie that the child will be content with; and each cookie j has a size s[j]. If s[j] >= g[i], we can assign the cookie j to the child i, and the child i will be content. Your goal is to maximize the number of your content children and output the maximum number.\n \nExample 1:\n\nInput: g = [1,2,3], s = [1,1]\nOutput: 1\nExplanation: You have 3 children and 2 cookies. The greed factors of 3 children are 1, 2, 3. \nAnd even though you have 2 cookies, since their size is both 1, you could only make the child whose greed factor is 1 content.\nYou need to output 1.\n\nExample 2:\n\nInput: g = [1,2], s = [1,2,3]\nOutput: 2\nExplanation: You have 2 children and 3 cookies. The greed factors of 2 children are 1, 2. \nYou have 3 cookies and their sizes are big enough to gratify all of the children, \nYou need to output 2.\n\n \nConstraints:\n\n1 <= g.length <= 3 * 104\n0 <= s.length <= 3 * 104\n1 <= g[i], s[j] <= 231 - 1\n\n \nNote: This question is the same as 2410: Maximum Matching of Players With Trainers.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(g = [1, 2, 3, 4, 5],s = [5, 4, 3, 2, 1]) == 5\n assert candidate(g = [1, 3, 5],s = [2, 4, 6]) == 3\n assert candidate(g = [3, 3, 3, 3],s = [1, 1, 1, 1]) == 0\n assert candidate(g = [1, 1, 1, 1],s = [1, 1, 1, 1]) == 4\n assert candidate(g = [1, 2, 3],s = [1, 2, 3, 4]) == 3\n assert candidate(g = [1, 2, 3, 4, 5],s = [1, 2, 3]) == 3\n assert candidate(g = [5, 5, 5, 5],s = [5, 5, 5, 5]) == 4\n assert candidate(g = [1, 2],s = [1, 2, 3]) == 2\n assert candidate(g = [1],s = [1]) == 1\n assert candidate(g = [10, 20, 30],s = [1, 2, 3]) == 0\n assert candidate(g = [],s = [1, 2, 3, 4, 5]) == 0\n assert candidate(g = [10, 9, 8, 7],s = [5, 6, 7, 8]) == 2\n assert candidate(g = [1, 2, 3],s = []) == 0\n assert candidate(g = [1, 2, 3],s = [1, 2, 3, 4, 5]) == 3\n assert candidate(g = [5, 5, 5, 5, 5],s = [5, 5, 5, 5]) == 4\n assert candidate(g = [1, 2, 3, 4, 5],s = []) == 0\n assert candidate(g = [1, 2, 3],s = [3, 2, 1]) == 3\n assert candidate(g = [1, 3, 5, 7],s = [2, 4, 6, 8]) == 4\n assert candidate(g = [],s = [1, 2, 3]) == 0\n assert candidate(g = [1, 2, 3, 4, 5],s = [1, 2]) == 2\n assert candidate(g = [1, 1, 1, 1],s = [10, 10, 10, 10]) == 4\n assert candidate(g = [1, 2, 3],s = [1, 1]) == 1\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [1, 10, 100, 1000, 10000],s = [1, 2, 3, 4, 5]) == 1\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 10\n assert candidate(g = [1, 3, 5, 7, 9],s = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 5\n assert candidate(g = [2147483647, 2147483647, 2147483647],s = [2147483647, 2147483647, 2147483647, 2147483647, 2147483647]) == 3\n assert candidate(g = [5, 4, 3, 2, 1],s = [1, 2, 3, 4, 5]) == 5\n assert candidate(g = [1, 3, 5, 7, 9],s = [2, 4, 6, 8, 10]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [10, 9, 8, 7, 6],s = [5, 6, 7, 8, 9]) == 4\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 10\n assert candidate(g = [1000000000, 1000000000, 1000000000],s = [1000000000, 1000000000, 1000000000]) == 3\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 10\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 2, 3, 4, 5]) == 5\n assert candidate(g = [10, 20, 30, 40, 50],s = [1, 10, 100, 1000, 10000]) == 4\n assert candidate(g = [3, 5, 7, 9, 11],s = [2, 4, 6, 8, 10]) == 4\n assert candidate(g = [3, 5, 7, 9, 11],s = [2, 4, 6, 8, 10]) == 4\n assert candidate(g = [100, 101, 102, 103, 104],s = [100, 101, 102, 103, 104, 105]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 15\n assert candidate(g = [1, 3, 5, 7, 9],s = [2, 4, 6, 8, 10]) == 5\n assert candidate(g = [1, 2, 3, 4, 5],s = [1, 2, 2, 2, 2]) == 2\n assert candidate(g = [1, 2, 3, 4, 5],s = [5, 4, 3, 2, 1]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],s = [1, 3, 5, 7, 9, 11, 13, 15]) == 8\n assert candidate(g = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],s = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 10\n assert candidate(g = [1, 3, 5, 7, 9],s = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 5\n assert candidate(g = [231, 230, 229, 228, 227, 226, 225, 224, 223, 222],s = [230, 229, 228, 227, 226, 225, 224, 223, 222, 221]) == 9\n assert candidate(g = [5, 5, 5, 5, 5],s = [1, 2, 3, 4, 5]) == 1\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000]) == 5\n assert candidate(g = [1, 2, 2, 3, 4],s = [1, 2, 2, 3]) == 4\n assert candidate(g = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 2\n assert candidate(g = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],s = [15, 25, 35, 45, 55, 65, 75, 85, 95]) == 9\n assert candidate(g = [100, 200, 300, 400, 500],s = [500, 400, 300, 200, 100]) == 5\n assert candidate(g = [100, 200, 300],s = [50, 150, 250, 350]) == 3\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 20\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [10, 9, 8, 7, 6],s = [1, 2, 3, 4, 5]) == 0\n assert candidate(g = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],s = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 10\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [5, 5, 5, 5, 5]) == 5\n assert candidate(g = [1, 2, 3, 4, 5],s = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 3, 5, 7, 9]) == 5\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 10\n assert candidate(g = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],s = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 10\n assert candidate(g = [1000000000, 1000000000, 1000000000],s = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 3\n assert candidate(g = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000],s = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000]) == 5\n assert candidate(g = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],s = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105]) == 10\n assert candidate(g = [1, 2, 3, 4, 5],s = [3, 3, 3, 3, 3]) == 3\n assert candidate(g = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],s = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == 15\n assert candidate(g = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 8\n assert candidate(g = [10, 20, 30, 40, 50],s = [15, 25, 35, 45, 55]) == 5\n assert candidate(g = [3, 1, 5, 2, 4],s = [2, 3, 5, 6, 7]) == 5\n assert candidate(g = [1, 1, 1, 1, 1],s = [5, 5, 5, 5, 5]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],s = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == 20\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],s = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 15\n assert candidate(g = [1, 2, 3, 4, 5],s = []) == 0\n assert candidate(g = [5, 8, 12, 16, 20],s = [1, 3, 4, 5, 9, 12, 15]) == 3\n assert candidate(g = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(g = [3, 4, 5, 6, 7, 8, 9, 10],s = [5, 6, 7, 8, 9]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 10\n assert candidate(g = [100, 200, 300, 400, 500],s = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500]) == 5\n assert candidate(g = [1, 1, 1, 1, 1],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 5\n assert candidate(g = [10, 20, 30, 40, 50],s = [5, 15, 25, 35, 45]) == 4\n assert candidate(g = [10, 20, 30, 40, 50],s = [1, 2, 3, 4, 5]) == 0\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],s = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 10\n assert candidate(g = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],s = [500, 500, 500, 500, 500, 500, 500, 500, 500, 500]) == 5\n assert candidate(g = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(g = [10, 9, 8, 7, 6],s = [5, 6, 7, 8, 9, 10]) == 5\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 10\n assert candidate(g = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],s = [1, 2, 3, 4, 5]) == 5\n assert candidate(g = [100, 200, 300],s = [50, 150, 250, 350]) == 3\n assert candidate(g = [1, 3, 5, 7],s = [2, 4, 6, 8]) == 4\n assert candidate(g = [10, 10, 10, 10, 10],s = [1, 2, 3, 4, 5]) == 0\n assert candidate(g = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],s = [1, 3, 5, 7, 9, 11, 13, 15]) == 8\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 10\n assert candidate(g = [1, 3, 5, 7, 9],s = [2, 4, 6, 8, 10, 12, 14, 16, 18]) == 5\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [5, 4, 3, 2, 1, 10, 9, 8, 7, 6]) == 10\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [1, 1, 1, 1, 1]) == 5\n assert candidate(g = [1, 3, 5, 7, 9],s = [2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(g = [3, 3, 3, 3, 3],s = [1, 2, 3, 4, 5]) == 3\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [1, 1, 1, 1, 1, 1]) == 6\n assert candidate(g = [5, 5, 5, 5, 5],s = [5, 5, 5, 5, 5]) == 5\n assert candidate(g = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],s = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105]) == 10\n assert candidate(g = [1, 2, 3, 4, 5],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 1\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == 10\n assert candidate(g = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 5\n assert candidate(g = [],s = [1, 2, 3, 4, 5]) == 0\n assert candidate(g = [5, 5, 5, 5, 5],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(g = [1, 2, 3, 4, 5],s = [6, 7, 8, 9, 10]) == 5\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 20\n assert candidate(g = [5, 10, 3, 8, 6],s = [1, 2, 3, 7, 9]) == 3\n assert candidate(g = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n assert candidate(g = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],s = [10, 10, 9, 9, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == 20\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 10\n assert candidate(g = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],s = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 6\n assert candidate(g = [1, 2, 3, 4, 5],s = [1, 1, 1, 1, 1]) == 1\n assert candidate(g = [1, 2, 3, 4, 5],s = [10000, 20000, 30000, 40000, 50000]) == 5\n assert candidate(g = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],s = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(g = [3, 2, 1],s = [1, 1, 1]) == 1\n assert candidate(g = [2, 2, 2, 2, 2],s = [1, 1, 1, 1, 1]) == 0\n assert candidate(g = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],s = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 10\n"}, "metadata": {"canonical_parameter_names": ["g", "s"], "leetcode_dataset_entry_point": "Solution().findContentChildren", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findContentChildren = function(g, s) {", "container": null, "callable": "findContentChildren", "parameters": [{"name": "g", "type": "number[]"}, {"name": "s", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 456, "task_id": "132-pattern", "difficulty": "Medium", "problem_description": "Given an array of n integers nums, a 132 pattern is a subsequence of three integers nums[i], nums[j] and nums[k] such that i < j < k and nums[i] < nums[k] < nums[j].\nReturn true if there is a 132 pattern in nums, otherwise, return false.\n \nExample 1:\n\nInput: nums = [1,2,3,4]\nOutput: false\nExplanation: There is no 132 pattern in the sequence.\n\nExample 2:\n\nInput: nums = [3,1,4,2]\nOutput: true\nExplanation: There is a 132 pattern in the sequence: [1, 4, 2].\n\nExample 3:\n\nInput: nums = [-1,3,2,0]\nOutput: true\nExplanation: There are three 132 patterns in the sequence: [-1, 3, 2], [-1, 3, 0] and [-1, 2, 0].\n\n \nConstraints:\n\nn == nums.length\n1 <= n <= 2 * 105\n-109 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-1, 3, 2, 0]) == True\n assert candidate(nums = [1, 3, 2, 4, 5]) == True\n assert candidate(nums = [3, 5, 0, 2, 3]) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [1]) == False\n assert candidate(nums = [1, 2, 3, 4]) == False\n assert candidate(nums = [1, 2, 3, 3, 3, 4]) == False\n assert candidate(nums = [1, 2, 3, 4, 5]) == False\n assert candidate(nums = [1, 2, 3, -4, -3, -1]) == False\n assert candidate(nums = [3, 5, 0, 2, 4]) == True\n assert candidate(nums = [8, 10, 4, 6]) == False\n assert candidate(nums = [3, 1, 4, 2]) == True\n assert candidate(nums = [5, 4, 3, 2, 1]) == False\n assert candidate(nums = [1, 2]) == False\n assert candidate(nums = [1, 2, 3, 2, 1]) == True\n assert candidate(nums = [3, 3, 3, 3, 3]) == False\n assert candidate(nums = [3, 5, 4, 2, 5]) == True\n assert candidate(nums = [1, 0, 1, -4, -3]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 0, -1, -2]) == False\n assert candidate(nums = [5, 6, 7, 8, 9, 1, 2, 3, 4, 10]) == False\n assert candidate(nums = [3, 5, 0, 3, 4]) == True\n assert candidate(nums = [3, 5, 0, 2, 4, 6, 1]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == False\n assert candidate(nums = [2, 1, 3, 5, 0, 4, 6, 7]) == True\n assert candidate(nums = [5, 1, 6, 3, 4, 2, 7]) == True\n assert candidate(nums = [3, 1, 4, 2, 5, 3, 6, 4, 7]) == True\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 8, 9]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 2, 4, 6, 8, 10, 3, 5, 7, 9]) == True\n assert candidate(nums = [19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == False\n assert candidate(nums = [-2, -3, 0, 1, -1, -4, 2, 3]) == True\n assert candidate(nums = [3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 0]) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == False\n assert candidate(nums = [12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 14]) == False\n assert candidate(nums = [8, 10, 4, 6, 2, 1, 9, 5]) == True\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 11]) == False\n assert candidate(nums = [1, 3, 2, 4, 6, 5, 7, 8, 10, 9, 11]) == True\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [3, 1, 4, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [1, 3, 2, 4, 6, 5, 7, 8, 10, 9, 11, 13, 12, 14, 15]) == True\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3]) == False\n assert candidate(nums = [3, 1, 4, 2, 5, 0]) == True\n assert candidate(nums = [10, 9, 8, 7, 11, 10, 12, 11, 13, 14]) == True\n assert candidate(nums = [8, 10, 4, 6, 2, 1, 9, 5, 7, 3]) == True\n assert candidate(nums = [7, 11, 5, 9, 6, 10, 3, 8, 2, 12]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, -1, 2, -2, 3, -3]) == True\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 8, 9, 11, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9]) == True\n assert candidate(nums = [5, 1, 5, 5, 2, 5, 4]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 5, 7, 9, 2, 4, 6, 8, 10]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == False\n assert candidate(nums = [1, 5, 3, 4, 2, 1, 6, 7, 8, 9, 10, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 3, 2, 4, 5, 6, 7, 8, 9, 0, 1, 3, 2, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 10, 15, 20]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 1, 3, 2, 4, 5, 6, 7, 8, 9, 0]) == True\n assert candidate(nums = [8, 10, 4, 6, 2, 1, 9]) == True\n assert candidate(nums = [7, 1, 3, 2, 6, 5, 8, 4, 9, 0]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 0]) == True\n assert candidate(nums = [1, 2, 4, 3, 5, 6, 0]) == True\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == True\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 0, 8, 9]) == False\n assert candidate(nums = [3, 1, 4, 2, 5, 6, 0, 7, 8, 9]) == True\n assert candidate(nums = [3, 5, 0, 2, 1, 4]) == True\n assert candidate(nums = [5, 1, 6, 4, 7, 3, 8, 2, 9]) == True\n assert candidate(nums = [3, 1, 4, 2, 5, 3, 6, 4, 7, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3]) == True\n assert candidate(nums = [3, 1, 4, 2, 5, 3]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1, 6]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 14, 12, 10, 8, 6, 4, 2, 0]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 1, 2]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, 12]) == False\n assert candidate(nums = [3, 5, 0, 3, 4]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == False\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == False\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]) == False\n assert candidate(nums = [3, 1, 4, 2, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == False\n assert candidate(nums = [3, 5, 0, 2, 8, 6, 7, 4, 1]) == True\n assert candidate(nums = [3, 1, 2, 4, 5, 0]) == False\n assert candidate(nums = [-1, -2, 2, 1, -3, -4, 3, 4]) == True\n assert candidate(nums = [1, 2, 0, 3, 4, -1, 5]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 1]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [1, 5, 4, 6, 7, 8, 9, 10, 2, 3]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 3, 2, 1, 4, 5, 6, 7, 8, 9, 10, 8, 9, 10, 11]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 50, 60, 70, 80, 90, 100, 55, 65, 75, 85]) == True\n assert candidate(nums = [1, 3, 2, 4, 6, 5, 7, 8, 9, 10]) == True\n assert candidate(nums = [3, 5, 0, 2, 3, 1, 4]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0]) == False\n assert candidate(nums = [1000000000, -1000000000, 500000000, 250000000, 750000000, 375000000, 625000000]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == False\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [3, 5, 0, 2, 4, 1]) == True\n assert candidate(nums = [25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == True\n assert candidate(nums = [1, 5, 3, 2, 4]) == True\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == True\n assert candidate(nums = [3, 1, 2, 4, 5, 6, 7, 8, 9, 0]) == False\n assert candidate(nums = [9, 11, 8, 9, 10, 7, 6, 5, 12]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 0]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 0, 7]) == True\n assert candidate(nums = [3, 1, 3, 2, 4, 3]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20]) == False\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 3, 9, 3, 2, 8, 8, 4, 6]) == True\n assert candidate(nums = [8, 10, 4, 6, 2, 1, 9, 5]) == True\n assert candidate(nums = [1, 5, 3, 4, 2]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 11, 12, 13, 14]) == False\n assert candidate(nums = [3, 5, 0, 2, 8, 7, 6, 4, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == True\n assert candidate(nums = [5, 3, 4, 2, 1, 6, 7, 8, 9, 10]) == False\n assert candidate(nums = [8, 10, 4, 6, 2, 1, 9, 5, 7]) == True\n assert candidate(nums = [3, 5, 0, 2, 1]) == True\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == True\n assert candidate(nums = [3, 5, 0, 2, 8, 6, 7, 4, 1, 12, 14, 13, 11, 9, 10, 15, 16, 17, 18, 19]) == True\n assert candidate(nums = [5, 3, 1, 2, 4, 6, 7, 8, 0]) == False\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 2, 9]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 55, 65, 75]) == True\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1]) == False\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == False\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100]) == False\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == False\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().find132pattern", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var find132pattern = function(nums) {", "container": null, "callable": "find132pattern", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 457, "task_id": "circular-array-loop", "difficulty": "Medium", "problem_description": "You are playing a game involving a circular array of non-zero integers nums. Each nums[i] denotes the number of indices forward/backward you must move if you are located at index i:\n\nIf nums[i] is positive, move nums[i] steps forward, and\nIf nums[i] is negative, move nums[i] steps backward.\n\nSince the array is circular, you may assume that moving forward from the last element puts you on the first element, and moving backwards from the first element puts you on the last element.\nA cycle in the array consists of a sequence of indices seq of length k where:\n\nFollowing the movement rules above results in the repeating index sequence seq[0] -> seq[1] -> ... -> seq[k - 1] -> seq[0] -> ...\nEvery nums[seq[j]] is either all positive or all negative.\nk > 1\n\nReturn true if there is a cycle in nums, or false otherwise.\n \nExample 1:\n\n\nInput: nums = [2,-1,1,2,2]\nOutput: true\nExplanation: The graph shows how the indices are connected. White nodes are jumping forward, while red is jumping backward.\nWe can see the cycle 0 --> 2 --> 3 --> 0 --> ..., and all of its nodes are white (jumping in the same direction).\n\nExample 2:\n\n\nInput: nums = [-1,-2,-3,-4,-5,6]\nOutput: false\nExplanation: The graph shows how the indices are connected. White nodes are jumping forward, while red is jumping backward.\nThe only cycle is of size 1, so we return false.\n\nExample 3:\n\n\nInput: nums = [1,-1,5,1,4]\nOutput: true\nExplanation: The graph shows how the indices are connected. White nodes are jumping forward, while red is jumping backward.\nWe can see the cycle 0 --> 1 --> 0 --> ..., and while it is of size > 1, it has a node jumping forward and a node jumping backward, so it is not a cycle.\nWe can see the cycle 3 --> 4 --> 3 --> ..., and all of its nodes are white (jumping in the same direction).\n\n \nConstraints:\n\n1 <= nums.length <= 5000\n-1000 <= nums[i] <= 1000\nnums[i] != 0\n\n \nFollow up: Could you solve it in O(n) time complexity and O(1) extra space complexity?\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [-5, 1, 1, 4, 2]) == True\n assert candidate(nums = [-1, 2, -1, 2, -1]) == False\n assert candidate(nums = [-1, -2, -3, -4, -5, 6]) == False\n assert candidate(nums = [-2, -3, -4, -5, -6]) == False\n assert candidate(nums = [1, 2, -1, -2, 3]) == False\n assert candidate(nums = [5, 1, 1, 2, 2]) == False\n assert candidate(nums = [1]) == False\n assert candidate(nums = [5, -1, 1, 4, 2]) == True\n assert candidate(nums = [-1, -1, -1, -1, -1]) == True\n assert candidate(nums = [-1, 2]) == False\n assert candidate(nums = [-1, 2, -1, -2, -1]) == False\n assert candidate(nums = [-1, -2, -3, -4, -5]) == False\n assert candidate(nums = [-5, -4, -3, -2, -1]) == True\n assert candidate(nums = [-1, 1, -1, 1, -1]) == False\n assert candidate(nums = [2, -1, 1, 2, 2]) == True\n assert candidate(nums = [1, 2, 3, 4, 5]) == True\n assert candidate(nums = [3, 1, 2, 4, 3]) == True\n assert candidate(nums = [1, -1, 5, 1, 4]) == True\n assert candidate(nums = [-2, 1, -1, -2, -2]) == False\n assert candidate(nums = [-2, -2, -2, -2, -2]) == True\n assert candidate(nums = [3, 1, 2]) == True\n assert candidate(nums = [5, 2, 3, 4, -1]) == False\n assert candidate(nums = [2, 2, 2, 2, 2]) == True\n assert candidate(nums = [1, 2, -3, -4, 5, 6, -7, -8, 9, 10, -11, -12, 13, 14, -15, -16, 17, 18, -19, -20]) == False\n assert candidate(nums = [-10, 9, 8, -7, 6, -5, 4, -3, 2, -1]) == False\n assert candidate(nums = [-2, -3, -1, 3, 2, 1, 5]) == True\n assert candidate(nums = [10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -11]) == False\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80, 90, -90, 100, -100]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [3, 2, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == True\n assert candidate(nums = [3, 1, 2, -2, -5, 6, -1]) == False\n assert candidate(nums = [5, 4, 3, 2, 1, -1, -2, -3, -4, -5]) == False\n assert candidate(nums = [5, 1, 4, 2, 0, 6, 3]) == True\n assert candidate(nums = [5, -1, 5, -1, 5, -1, 5, -1, 5, -1]) == False\n assert candidate(nums = [1, 2, 3, 4, -1, -2, -3, -4]) == False\n assert candidate(nums = [5, -5, 5, -5, 5, -5, 5, -5, 5, -5]) == False\n assert candidate(nums = [2, 3, 1, -4, -4, 2]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [4, 2, 3, 1, 1, -1, -1]) == False\n assert candidate(nums = [-3, -1, -2, -3, -1, -2, -3, -1, -2, -3]) == True\n assert candidate(nums = [2, 3, -1, 4, -1, -2]) == False\n assert candidate(nums = [-3, 3, 2, 1, -2, -1, 4, -4]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, -6, -5, -4, -3, -2, -1]) == False\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == True\n assert candidate(nums = [3, 1, 2, 3, 1, 2, 3]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == True\n assert candidate(nums = [1, 2, -1, -2, 1, 2, -1, -2, 1, 2, -1, -2]) == False\n assert candidate(nums = [0, 1, 1, 4, -1, 2, -1, -3, -2, 4, -5, 5, 6, 7, -7, 8, 9, 10, 11, -11, 12, -12, 13, -13, 14, -14, 15, -15, 16, -16, 17, -17, 18, -18, 19, -19, 20, -20, 21, -21, 22, -22, 23, -23, 24, -24, 25, -25, 26, -26, 27, -27, 28, -28, 29, -29, 30, -30, 31, -31, 32, -32, 33, -33, 34, -34, 35, -35, 36, -36, 37, -37, 38, -38, 39, -39, 40, -40, 41, -41, 42, -42, 43, -43, 44, -44, 45, -45, 46, -46, 47, -47, 48, -48, 49, -49, 50, -50]) == False\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == True\n assert candidate(nums = [5, 4, 3, 2, 1, -5, -4, -3, -2, -1]) == False\n assert candidate(nums = [5, -1, 3, 2, -3, 4, -4, 2, 1, -1]) == False\n assert candidate(nums = [-2, 1, -1, -2, -2, 2, -1, 2, 1, -1]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, -10]) == True\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == False\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]) == False\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, -10, -20, -30, -40, -50, -60, -70, -80, -90]) == False\n assert candidate(nums = [2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20]) == False\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20]) == False\n assert candidate(nums = [10, -10, 20, -20, 30, -30, 40, -40, 50, -50]) == False\n assert candidate(nums = [3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == True\n assert candidate(nums = [5, -2, 5, -2, 5, -2, 5, -2]) == True\n assert candidate(nums = [3, 1, 2, -3, 4, 2, 1, -4, 2, 3]) == False\n assert candidate(nums = [3, 1, 2, -1, -2, 4]) == False\n assert candidate(nums = [1, 2, -1, 2, -1, 2, -1, 2, -1, 2]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5]) == False\n assert candidate(nums = [-1, 2, 2, -1, -2, 1]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == False\n assert candidate(nums = [3, 1, 2, -2, -1]) == False\n assert candidate(nums = [2, 1, -1, -2, 2, 3, -3, -2, 1]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -2, -3, -4, -5, -6, -7, -8, -9]) == False\n assert candidate(nums = [2, 3, -2, 2, -3, 2, -2, 3, -3, 1]) == False\n assert candidate(nums = [5, 3, 2, 1, 4, -2, -1, -3, -1]) == False\n assert candidate(nums = [2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 1]) == True\n assert candidate(nums = [10, -10, 10, -10, 10, -10, 10, -10, 10, -10]) == False\n assert candidate(nums = [5, 5, 2, 1, -2, -1, -3, -5, 4, 4, 3, 2, -2, -3, -4, -5, 1, 1, 2, 3]) == False\n assert candidate(nums = [1, 2, -3, 4, -5, 6, -7, 8, -9, 10]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == False\n assert candidate(nums = [10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10]) == True\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == False\n assert candidate(nums = [3, 1, 2, 4, -1]) == False\n assert candidate(nums = [1, -2, 3, -4, 5, -6, 7, -8, 9, -10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50]) == False\n assert candidate(nums = [-2, -3, -4, -5, 6, 7]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [-2, -3, -4, -5, -6, -1]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, -1, -2, -3, -4, -5]) == False\n assert candidate(nums = [5, 1, 3, 2, 2, -1, 4]) == False\n assert candidate(nums = [10, 10, -10, -10, 10, -10, 10, -10]) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [-1, 1, -1, 1, -1, 1, -1, 1]) == False\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == True\n assert candidate(nums = [5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5]) == False\n assert candidate(nums = [3, 1, 2, -2, 4, 2]) == True\n assert candidate(nums = [3, 1, 2, 4, 0, 2, -1, -3, -1]) == False\n assert candidate(nums = [-1, 2, 1, -2, 2, -1, 2, -1]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [5, 4, 3, 2, 1, -1]) == False\n assert candidate(nums = [2, 2, -2, -2, 2, 2, -2, -2]) == False\n assert candidate(nums = [1, 2, -1, -2, 3, 2, -3, 3]) == False\n assert candidate(nums = [2, -1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == False\n assert candidate(nums = [-5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5, -5]) == True\n assert candidate(nums = [4, -1, 2, -1, -1, 2, -1, 4]) == False\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == False\n assert candidate(nums = [1, -1, 1, -1, 1, -1]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 2, 3, -4, -3, -2, -1, 4, 3, 2]) == False\n assert candidate(nums = [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]) == True\n assert candidate(nums = [10, -10, 10, -10, 10, -10]) == True\n assert candidate(nums = [-2, -3, -4, -5, -6, -7, -8, -9, -10, -1]) == False\n assert candidate(nums = [-2, -3, -4, 0, -1, -6]) == False\n assert candidate(nums = [1, 1, 1, 1, 1, -1, -1, -1, -1, -1]) == False\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().circularArrayLoop", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var circularArrayLoop = function(nums) {", "container": null, "callable": "circularArrayLoop", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 458, "task_id": "poor-pigs", "difficulty": "Hard", "problem_description": "There are buckets buckets of liquid, where exactly one of the buckets is poisonous. To figure out which one is poisonous, you feed some number of (poor) pigs the liquid to see whether they will die or not. Unfortunately, you only have minutesToTest minutes to determine which bucket is poisonous.\nYou can feed the pigs according to these steps:\n\nChoose some live pigs to feed.\nFor each pig, choose which buckets to feed it. The pig will consume all the chosen buckets simultaneously and will take no time. Each pig can feed from any number of buckets, and each bucket can be fed from by any number of pigs.\nWait for minutesToDie minutes. You may not feed any other pigs during this time.\nAfter minutesToDie minutes have passed, any pigs that have been fed the poisonous bucket will die, and all others will survive.\nRepeat this process until you run out of time.\n\nGiven buckets, minutesToDie, and minutesToTest, return the minimum number of pigs needed to figure out which bucket is poisonous within the allotted time.\n \nExample 1:\n\nInput: buckets = 4, minutesToDie = 15, minutesToTest = 15\nOutput: 2\nExplanation: We can determine the poisonous bucket as follows:\nAt time 0, feed the first pig buckets 1 and 2, and feed the second pig buckets 2 and 3.\nAt time 15, there are 4 possible outcomes:\n- If only the first pig dies, then bucket 1 must be poisonous.\n- If only the second pig dies, then bucket 3 must be poisonous.\n- If both pigs die, then bucket 2 must be poisonous.\n- If neither pig dies, then bucket 4 must be poisonous.\n\nExample 2:\n\nInput: buckets = 4, minutesToDie = 15, minutesToTest = 30\nOutput: 2\nExplanation: We can determine the poisonous bucket as follows:\nAt time 0, feed the first pig bucket 1, and feed the second pig bucket 2.\nAt time 15, there are 2 possible outcomes:\n- If either pig dies, then the poisonous bucket is the one it was fed.\n- If neither pig dies, then feed the first pig bucket 3, and feed the second pig bucket 4.\nAt time 30, one of the two pigs must die, and the poisonous bucket is the one it was fed.\n\n \nConstraints:\n\n1 <= buckets <= 1000\n1 <= minutesToDie <= minutesToTest <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(buckets = 4,minutesToDie = 15,minutesToTest = 15) == 2\n assert candidate(buckets = 1,minutesToDie = 1,minutesToTest = 1) == 0\n assert candidate(buckets = 1000,minutesToDie = 1,minutesToTest = 100) == 2\n assert candidate(buckets = 4,minutesToDie = 15,minutesToTest = 30) == 2\n assert candidate(buckets = 1,minutesToDie = 10,minutesToTest = 10) == 0\n assert candidate(buckets = 8,minutesToDie = 10,minutesToTest = 40) == 2\n assert candidate(buckets = 10,minutesToDie = 5,minutesToTest = 10) == 3\n assert candidate(buckets = 1,minutesToDie = 10,minutesToTest = 100) == 0\n assert candidate(buckets = 1000,minutesToDie = 1,minutesToTest = 1) == 10\n assert candidate(buckets = 10,minutesToDie = 5,minutesToTest = 20) == 2\n assert candidate(buckets = 100,minutesToDie = 10,minutesToTest = 60) == 3\n assert candidate(buckets = 10,minutesToDie = 5,minutesToTest = 25) == 2\n assert candidate(buckets = 8,minutesToDie = 10,minutesToTest = 30) == 2\n assert candidate(buckets = 1024,minutesToDie = 1,minutesToTest = 10) == 3\n assert candidate(buckets = 9,minutesToDie = 25,minutesToTest = 75) == 2\n assert candidate(buckets = 27,minutesToDie = 3,minutesToTest = 9) == 3\n assert candidate(buckets = 500,minutesToDie = 5,minutesToTest = 20) == 4\n assert candidate(buckets = 81,minutesToDie = 2,minutesToTest = 4) == 4\n assert candidate(buckets = 250,minutesToDie = 25,minutesToTest = 100) == 4\n assert candidate(buckets = 625,minutesToDie = 20,minutesToTest = 100) == 4\n assert candidate(buckets = 625,minutesToDie = 10,minutesToTest = 30) == 5\n assert candidate(buckets = 3125,minutesToDie = 5,minutesToTest = 20) == 5\n assert candidate(buckets = 999,minutesToDie = 1,minutesToTest = 99) == 2\n assert candidate(buckets = 243,minutesToDie = 1,minutesToTest = 5) == 4\n assert candidate(buckets = 1296,minutesToDie = 6,minutesToTest = 18) == 6\n assert candidate(buckets = 243,minutesToDie = 18,minutesToTest = 90) == 4\n assert candidate(buckets = 729,minutesToDie = 3,minutesToTest = 9) == 5\n assert candidate(buckets = 512,minutesToDie = 5,minutesToTest = 25) == 4\n assert candidate(buckets = 64,minutesToDie = 4,minutesToTest = 16) == 3\n assert candidate(buckets = 256,minutesToDie = 5,minutesToTest = 10) == 6\n assert candidate(buckets = 350,minutesToDie = 7,minutesToTest = 35) == 4\n assert candidate(buckets = 500,minutesToDie = 20,minutesToTest = 100) == 4\n assert candidate(buckets = 343,minutesToDie = 7,minutesToTest = 21) == 5\n assert candidate(buckets = 128,minutesToDie = 8,minutesToTest = 32) == 4\n assert candidate(buckets = 64,minutesToDie = 2,minutesToTest = 6) == 3\n assert candidate(buckets = 81,minutesToDie = 9,minutesToTest = 27) == 4\n assert candidate(buckets = 125,minutesToDie = 25,minutesToTest = 125) == 3\n assert candidate(buckets = 450,minutesToDie = 12,minutesToTest = 60) == 4\n assert candidate(buckets = 441,minutesToDie = 20,minutesToTest = 60) == 5\n assert candidate(buckets = 3125,minutesToDie = 15,minutesToTest = 60) == 5\n assert candidate(buckets = 512,minutesToDie = 15,minutesToTest = 30) == 6\n assert candidate(buckets = 729,minutesToDie = 9,minutesToTest = 27) == 5\n assert candidate(buckets = 216,minutesToDie = 10,minutesToTest = 50) == 3\n assert candidate(buckets = 27,minutesToDie = 1,minutesToTest = 3) == 3\n assert candidate(buckets = 243,minutesToDie = 9,minutesToTest = 27) == 4\n assert candidate(buckets = 1024,minutesToDie = 4,minutesToTest = 12) == 5\n assert candidate(buckets = 512,minutesToDie = 5,minutesToTest = 20) == 4\n assert candidate(buckets = 81,minutesToDie = 30,minutesToTest = 90) == 4\n assert candidate(buckets = 512,minutesToDie = 2,minutesToTest = 10) == 4\n assert candidate(buckets = 128,minutesToDie = 15,minutesToTest = 60) == 4\n assert candidate(buckets = 300,minutesToDie = 3,minutesToTest = 9) == 5\n assert candidate(buckets = 999,minutesToDie = 2,minutesToTest = 20) == 3\n assert candidate(buckets = 999,minutesToDie = 1,minutesToTest = 10) == 3\n assert candidate(buckets = 16,minutesToDie = 4,minutesToTest = 16) == 2\n assert candidate(buckets = 343,minutesToDie = 7,minutesToTest = 42) == 3\n assert candidate(buckets = 343,minutesToDie = 2,minutesToTest = 14) == 3\n assert candidate(buckets = 125,minutesToDie = 5,minutesToTest = 25) == 3\n assert candidate(buckets = 9,minutesToDie = 3,minutesToTest = 9) == 2\n assert candidate(buckets = 600,minutesToDie = 10,minutesToTest = 50) == 4\n assert candidate(buckets = 750,minutesToDie = 20,minutesToTest = 100) == 4\n assert candidate(buckets = 216,minutesToDie = 6,minutesToTest = 30) == 3\n assert candidate(buckets = 961,minutesToDie = 30,minutesToTest = 90) == 5\n assert candidate(buckets = 125,minutesToDie = 10,minutesToTest = 50) == 3\n assert candidate(buckets = 256,minutesToDie = 15,minutesToTest = 75) == 4\n assert candidate(buckets = 800,minutesToDie = 15,minutesToTest = 75) == 4\n assert candidate(buckets = 729,minutesToDie = 10,minutesToTest = 30) == 5\n assert candidate(buckets = 750,minutesToDie = 15,minutesToTest = 45) == 5\n assert candidate(buckets = 100,minutesToDie = 1,minutesToTest = 10) == 2\n assert candidate(buckets = 500,minutesToDie = 5,minutesToTest = 30) == 4\n assert candidate(buckets = 500,minutesToDie = 5,minutesToTest = 25) == 4\n assert candidate(buckets = 1024,minutesToDie = 10,minutesToTest = 40) == 5\n assert candidate(buckets = 9,minutesToDie = 3,minutesToTest = 6) == 2\n assert candidate(buckets = 27,minutesToDie = 6,minutesToTest = 18) == 3\n assert candidate(buckets = 27,minutesToDie = 5,minutesToTest = 15) == 3\n assert candidate(buckets = 256,minutesToDie = 10,minutesToTest = 40) == 4\n assert candidate(buckets = 81,minutesToDie = 4,minutesToTest = 16) == 3\n assert candidate(buckets = 441,minutesToDie = 7,minutesToTest = 49) == 3\n assert candidate(buckets = 441,minutesToDie = 14,minutesToTest = 70) == 4\n assert candidate(buckets = 64,minutesToDie = 20,minutesToTest = 100) == 3\n assert candidate(buckets = 256,minutesToDie = 1,minutesToTest = 7) == 3\n assert candidate(buckets = 999,minutesToDie = 2,minutesToTest = 4) == 7\n assert candidate(buckets = 81,minutesToDie = 10,minutesToTest = 50) == 3\n assert candidate(buckets = 64,minutesToDie = 1,minutesToTest = 6) == 3\n assert candidate(buckets = 128,minutesToDie = 2,minutesToTest = 16) == 3\n assert candidate(buckets = 999,minutesToDie = 2,minutesToTest = 100) == 2\n assert candidate(buckets = 1024,minutesToDie = 8,minutesToTest = 32) == 5\n assert candidate(buckets = 81,minutesToDie = 3,minutesToTest = 9) == 4\n assert candidate(buckets = 81,minutesToDie = 5,minutesToTest = 15) == 4\n assert candidate(buckets = 125,minutesToDie = 5,minutesToTest = 20) == 3\n assert candidate(buckets = 961,minutesToDie = 6,minutesToTest = 36) == 4\n assert candidate(buckets = 729,minutesToDie = 1,minutesToTest = 5) == 4\n assert candidate(buckets = 169,minutesToDie = 13,minutesToTest = 39) == 4\n assert candidate(buckets = 750,minutesToDie = 10,minutesToTest = 50) == 4\n assert candidate(buckets = 625,minutesToDie = 10,minutesToTest = 40) == 4\n assert candidate(buckets = 256,minutesToDie = 4,minutesToTest = 16) == 4\n assert candidate(buckets = 256,minutesToDie = 15,minutesToTest = 45) == 4\n assert candidate(buckets = 729,minutesToDie = 12,minutesToTest = 36) == 5\n assert candidate(buckets = 3125,minutesToDie = 4,minutesToTest = 20) == 5\n assert candidate(buckets = 200,minutesToDie = 4,minutesToTest = 20) == 3\n"}, "metadata": {"canonical_parameter_names": ["buckets", "minutesToDie", "minutesToTest"], "leetcode_dataset_entry_point": "Solution().poorPigs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var poorPigs = function(buckets, minutesToDie, minutesToTest) {", "container": null, "callable": "poorPigs", "parameters": [{"name": "buckets", "type": "number"}, {"name": "minutesToDie", "type": "number"}, {"name": "minutesToTest", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 459, "task_id": "repeated-substring-pattern", "difficulty": "Easy", "problem_description": "Given a string s, check if it can be constructed by taking a substring of it and appending multiple copies of the substring together.\n \nExample 1:\n\nInput: s = \"abab\"\nOutput: true\nExplanation: It is the substring \"ab\" twice.\n\nExample 2:\n\nInput: s = \"aba\"\nOutput: false\n\nExample 3:\n\nInput: s = \"abcabcabcabc\"\nOutput: true\nExplanation: It is the substring \"abc\" four times or the substring \"abcabc\" twice.\n\n \nConstraints:\n\n1 <= s.length <= 104\ns consists of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abac\") == False\n assert candidate(s = \"abcdef\") == False\n assert candidate(s = \"abababab\") == True\n assert candidate(s = \"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\") == True\n assert candidate(s = \"a\") == False\n assert candidate(s = \"abab\") == True\n assert candidate(s = \"abcabcabc\") == True\n assert candidate(s = \"abcabcabcabc\") == True\n assert candidate(s = \"bcbcbcbcbcbcbcbcbcbc\") == True\n assert candidate(s = \"babab\") == False\n assert candidate(s = \"abcabc\") == True\n assert candidate(s = \"abcdabcd\") == True\n assert candidate(s = \"abababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababababab\") == True\n assert candidate(s = \"xyzxyzxyz\") == True\n assert candidate(s = \"abcdabcdabcd\") == True\n assert candidate(s = \"abc\") == False\n assert candidate(s = \"aaaa\") == True\n assert candidate(s = \"aba\") == False\n assert candidate(s = \"abcabcab\") == False\n assert candidate(s = \"ababab\") == True\n assert candidate(s = \"xyzxyzxyzxyz\") == True\n assert candidate(s = \"abacababacab\") == True\n assert candidate(s = \"bb\") == True\n assert candidate(s = \"abcabcabcabcabcabcabc\") == True\n assert candidate(s = \"aabbccddeeaabbccddeeaabbccddeeaabbccdd\") == False\n assert candidate(s = \"abbaabbaabba\") == True\n assert candidate(s = \"xyxyxyxyxyxy\") == True\n assert candidate(s = \"aaaabaaaabaaaaaab\") == False\n assert candidate(s = \"bcbcbcbcbcbcbcbc\") == True\n assert candidate(s = \"aaaaaaaab\") == False\n assert candidate(s = \"abacabacabac\") == True\n assert candidate(s = \"alibabaalibabaalibaba\") == True\n assert candidate(s = \"mnopqrsmnopqrsmnopqrsmnopqrsmnopqrsmnopqrs\") == True\n assert candidate(s = \"aabbccddeeffaabbccddeeffaabbccddeeff\") == True\n assert candidate(s = \"abcdeabcdeabcdeabcdeabcde\") == True\n assert candidate(s = \"qwertyuiopqwertyuiop\") == True\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzz\") == True\n assert candidate(s = \"abcdefabcdefabcdef\") == True\n assert candidate(s = \"abacbabacbabacb\") == True\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabc\") == True\n assert candidate(s = \"abcababcababcab\") == True\n assert candidate(s = \"abababababababababababababababababababababababab\") == True\n assert candidate(s = \"xyzxyzxyzxyzxyzxyz\") == True\n assert candidate(s = \"ababababab\") == True\n assert candidate(s = \"abcdabcdabcdabcdabcdabcdabcdabcd\") == True\n assert candidate(s = \"ababababababababababababababab\") == True\n assert candidate(s = \"bababababa\") == True\n assert candidate(s = \"aabbccddeeaabbccddeeaabbccddeeaabbccddeedded\") == False\n assert candidate(s = \"racecaracecar\") == False\n assert candidate(s = \"ababababa\") == False\n assert candidate(s = \"abababababababab\") == True\n assert candidate(s = \"aaaaaa\") == True\n assert candidate(s = \"abcabcabcabcabcabcabcabc\") == True\n assert candidate(s = \"abcdefabcdefabcdefabcdef\") == True\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabcabcabcabcabc\") == True\n assert candidate(s = \"lmnolmnonlmnonlmnonlmnolmnonlmnonlmnonlmnolmno\") == False\n assert candidate(s = \"abbaabbaabbaabbaabbaabbaabbaabba\") == True\n assert candidate(s = \"hellohellohello\") == True\n assert candidate(s = \"abacabacabacabacabacabacabacabac\") == True\n assert candidate(s = \"abababababab\") == True\n assert candidate(s = \"banana\") == False\n assert candidate(s = \"zzzzzzzzzzzz\") == True\n assert candidate(s = \"abcdeabcdeabcdeabcde\") == True\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\") == True\n assert candidate(s = \"aabbccddeeffaabbccddeeffaabbccddeeffaabbccddeeffaabbccddeeff\") == True\n assert candidate(s = \"abcabcabcabcabcabc\") == True\n assert candidate(s = \"abababababababababababababababab\") == True\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabcabc\") == True\n assert candidate(s = \"abcabcabcabcabcab\") == False\n assert candidate(s = \"aabbaabbccddeeaabbccddeeaabbccddeeaabbccddeedded\") == False\n assert candidate(s = \"abcdabcdabcdabcdabcdabcd\") == True\n assert candidate(s = \"hello\") == False\n assert candidate(s = \"xyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxxyxyxxyxyxxyxxyx\") == False\n assert candidate(s = \"xyzxyzxyzxyzxyz\") == True\n assert candidate(s = \"mississippi\") == False\n assert candidate(s = \"abcabcabcabcabcabcabcabcabcabcabcabc\") == True\n assert candidate(s = \"xyxyxyxyxyxyxyxyxyxyxy\") == True\n assert candidate(s = \"abcdefghijkabcdefghijkabcdefghijkabcdefghijkabcdefghijkabcdefghijk\") == True\n assert candidate(s = \"abcabcabcabcabc\") == True\n assert candidate(s = \"abcdabcdabcdabcd\") == True\n assert candidate(s = \"abcdefghabcdefghabcdefgh\") == True\n assert candidate(s = \"zzzzzzzz\") == True\n assert candidate(s = \"aaaaaaa\") == True\n assert candidate(s = \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\") == True\n assert candidate(s = \"aabbccddeeffaabbccddeeff\") == True\n assert candidate(s = \"abcdabcda\") == False\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == True\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().repeatedSubstringPattern", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var repeatedSubstringPattern = function(s) {", "container": null, "callable": "repeatedSubstringPattern", "parameters": [{"name": "s", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 461, "task_id": "hamming-distance", "difficulty": "Easy", "problem_description": "The Hamming distance between two integers is the number of positions at which the corresponding bits are different.\nGiven two integers x and y, return the Hamming distance between them.\n \nExample 1:\n\nInput: x = 1, y = 4\nOutput: 2\nExplanation:\n1 (0 0 0 1)\n4 (0 1 0 0)\n ↑ ↑\nThe above arrows point to positions where the corresponding bits are different.\n\nExample 2:\n\nInput: x = 3, y = 1\nOutput: 1\n\n \nConstraints:\n\n0 <= x, y <= 231 - 1\n\n \nNote: This question is the same as 2220: Minimum Bit Flips to Convert Number.\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(x = 3,y = 1) == 1\n assert candidate(x = 7,y = 15) == 1\n assert candidate(x = 1073741823,y = 2147483647) == 1\n assert candidate(x = 1023,y = 512) == 9\n assert candidate(x = 2147483647,y = 0) == 31\n assert candidate(x = 2147483647,y = 1) == 30\n assert candidate(x = 1,y = 4) == 2\n assert candidate(x = 1023,y = 511) == 1\n assert candidate(x = 16,y = 32) == 2\n assert candidate(x = 1073741824,y = 1073741823) == 31\n assert candidate(x = 0,y = 0) == 0\n assert candidate(x = 255,y = 0) == 8\n assert candidate(x = 1,y = 1) == 0\n assert candidate(x = 15,y = 15) == 0\n assert candidate(x = 2147483647,y = 2147483647) == 0\n assert candidate(x = 15,y = 9) == 2\n assert candidate(x = 555,y = 666) == 4\n assert candidate(x = 18446744073709551615,y = 9223372036854775807) == 1\n assert candidate(x = 33554432,y = 67108863) == 25\n assert candidate(x = 1717986918,y = 858993459) == 16\n assert candidate(x = 4095,y = 1023) == 2\n assert candidate(x = 33554431,y = 16777215) == 1\n assert candidate(x = 268435455,y = 134217727) == 1\n assert candidate(x = 4294967295,y = 2147483647) == 1\n assert candidate(x = 1357924680,y = 2468135790) == 15\n assert candidate(x = 65535,y = 32768) == 15\n assert candidate(x = 16777215,y = 16777216) == 25\n assert candidate(x = 2147483647,y = 2147483646) == 1\n assert candidate(x = 262143,y = 131071) == 1\n assert candidate(x = 13579,y = 24680) == 8\n assert candidate(x = 4294967295,y = 1) == 31\n assert candidate(x = 100000000,y = 100000001) == 1\n assert candidate(x = 2047,y = 4094) == 2\n assert candidate(x = 255,y = 127) == 1\n assert candidate(x = 0,y = 2147483647) == 31\n assert candidate(x = 33554431,y = 33554432) == 26\n assert candidate(x = 1000000000,y = 1000000001) == 1\n assert candidate(x = 134217728,y = 8388607) == 24\n assert candidate(x = 536870911,y = 536870912) == 30\n assert candidate(x = 268435456,y = 536870912) == 2\n assert candidate(x = 8,y = 16) == 2\n assert candidate(x = 1048575,y = 2097150) == 2\n assert candidate(x = 128,y = 32) == 2\n assert candidate(x = 8191,y = 4095) == 1\n assert candidate(x = 1048575,y = 524288) == 19\n assert candidate(x = 511,y = 255) == 1\n assert candidate(x = 1048576,y = 2097152) == 2\n assert candidate(x = 123456789,y = 987654321) == 15\n assert candidate(x = 1000000007,y = 1000000008) == 4\n assert candidate(x = 1073741824,y = 536870912) == 2\n assert candidate(x = 123,y = 456) == 6\n assert candidate(x = 67108863,y = 67108864) == 27\n assert candidate(x = 134217727,y = 268435455) == 1\n assert candidate(x = 1024,y = 511) == 10\n assert candidate(x = 1073741824,y = 2147483647) == 30\n assert candidate(x = 8,y = 24) == 1\n assert candidate(x = 1048575,y = 1048574) == 1\n assert candidate(x = 131071,y = 32768) == 16\n assert candidate(x = 65535,y = 65534) == 1\n assert candidate(x = 16777215,y = 0) == 24\n assert candidate(x = 8675309,y = 196418) == 11\n assert candidate(x = 5,y = 10) == 4\n assert candidate(x = 13,y = 29) == 1\n assert candidate(x = 8,y = 32) == 2\n assert candidate(x = 5,y = 255) == 6\n assert candidate(x = 131071,y = 1048575) == 3\n assert candidate(x = 17,y = 34) == 4\n assert candidate(x = 4095,y = 1) == 11\n assert candidate(x = 1048576,y = 524288) == 2\n assert candidate(x = 65535,y = 255) == 8\n assert candidate(x = 16777215,y = 8388608) == 23\n assert candidate(x = 0,y = 1073741824) == 1\n assert candidate(x = 1,y = 2147483647) == 30\n assert candidate(x = 858993459,y = 2147483647) == 15\n assert candidate(x = 65535,y = 0) == 16\n assert candidate(x = 500,y = 1000) == 4\n assert candidate(x = 8388607,y = 16777216) == 24\n assert candidate(x = 268435455,y = 268435456) == 29\n assert candidate(x = 4294967295,y = 0) == 32\n assert candidate(x = 131071,y = 65535) == 1\n assert candidate(x = 16777215,y = 65536) == 23\n assert candidate(x = 131072,y = 262144) == 2\n assert candidate(x = 16777215,y = 1) == 23\n assert candidate(x = 1048575,y = 2097151) == 1\n assert candidate(x = 2147483647,y = 1073741823) == 1\n assert candidate(x = 8191,y = 0) == 13\n assert candidate(x = 32768,y = 65535) == 15\n assert candidate(x = 1048575,y = 1048576) == 21\n"}, "metadata": {"canonical_parameter_names": ["x", "y"], "leetcode_dataset_entry_point": "Solution().hammingDistance", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var hammingDistance = function(x, y) {", "container": null, "callable": "hammingDistance", "parameters": [{"name": "x", "type": "number"}, {"name": "y", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 462, "task_id": "minimum-moves-to-equal-array-elements-ii", "difficulty": "Medium", "problem_description": "Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal.\nIn one move, you can increment or decrement an element of the array by 1.\nTest cases are designed so that the answer will fit in a 32-bit integer.\n \nExample 1:\n\nInput: nums = [1,2,3]\nOutput: 2\nExplanation:\nOnly two moves are needed (remember each move increments or decrements one element):\n[1,2,3] => [2,2,3] => [2,2,2]\n\nExample 2:\n\nInput: nums = [1,10,2,9]\nOutput: 16\n\n \nConstraints:\n\nn == nums.length\n1 <= nums.length <= 105\n-109 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 1, 1]) == 0\n assert candidate(nums = [1, 1, 1, 1]) == 0\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == 20\n assert candidate(nums = [1, 3, 5, 7, 9]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 25\n assert candidate(nums = [1, 0, 0, 8, 6]) == 14\n assert candidate(nums = [1, 2, 3, 4, 5]) == 6\n assert candidate(nums = [-1, 1, 1, 0, -1, -1]) == 5\n assert candidate(nums = [1, 10, 2, 9]) == 16\n assert candidate(nums = [1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [100, 200, 300, 400, 500]) == 600\n assert candidate(nums = [-10, -20, -30, -40, -50]) == 60\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == 8\n assert candidate(nums = [10, 5, 15, 20, 0]) == 30\n assert candidate(nums = [1000000000, -1000000000, 0]) == 2000000000\n assert candidate(nums = [1000000000, -1000000000, 0]) == 2000000000\n assert candidate(nums = [1, 2, 3]) == 2\n assert candidate(nums = [1, 2, 9, 10]) == 16\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [-1, 1, 0]) == 2\n assert candidate(nums = [-1, 0, 1]) == 2\n assert candidate(nums = [100, 100, 100]) == 0\n assert candidate(nums = [-1, 1, -2, 2, -3, 3, -4, 4, -5, 5]) == 30\n assert candidate(nums = [10, 1, 2, 7, 5]) == 14\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 10000\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == 250\n assert candidate(nums = [100, 200, 300, 400, 500]) == 600\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 200]) == 190\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 12\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 225\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7]) == 19\n assert candidate(nums = [-10, -20, -30, -40, -50]) == 60\n assert candidate(nums = [1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6]) == 31\n assert candidate(nums = [1, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 1110988899\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4]) == 8\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10]) == 110\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 50\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == 50\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == 60\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1000000000]) == 999999999\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 25\n assert candidate(nums = [1000000000, -1000000000, 0, 500000000, -500000000]) == 3000000000\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3]) == 10\n assert candidate(nums = [-1000000000, -2000000000, -3000000000, -4000000000, -5000000000, -6000000000, -7000000000, -8000000000, -9000000000, -10000000000]) == 25000000000\n assert candidate(nums = [1, 1000000000, 2, 999999999, 3, 999999998, 4, 999999997, 5]) == 3999999984\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 56\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 25\n assert candidate(nums = [-100, 0, 100, 200, 300, 400, 500, 600, 700, 800, 900]) == 3000\n assert candidate(nums = [1000000000, -1000000000, 500000000, -500000000]) == 3000000000\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 250\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [-5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23]) == 112\n assert candidate(nums = [1, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120]) == 219\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59]) == 450\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 100\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 156\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2]) == 7\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 30\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 2, 9, 10, 11, 20]) == 29\n assert candidate(nums = [-5, -4, -3, -2, -1, 0]) == 9\n assert candidate(nums = [1000000000, -1000000000, 2000000000, -2000000000]) == 6000000000\n assert candidate(nums = [1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 10000000000]) == 25000000000\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7]) == 34\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 100\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110]) == 300\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == 560\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == 25\n assert candidate(nums = [10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12]) == 10\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11]) == 18\n assert candidate(nums = [100, 101, 102, 103, 104]) == 6\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().minMoves2", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var minMoves2 = function(nums) {", "container": null, "callable": "minMoves2", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 463, "task_id": "island-perimeter", "difficulty": "Easy", "problem_description": "You are given row x col grid representing a map where grid[i][j] = 1 represents land and grid[i][j] = 0 represents water.\nGrid cells are connected horizontally/vertically (not diagonally). The grid is completely surrounded by water, and there is exactly one island (i.e., one or more connected land cells).\nThe island doesn't have \"lakes\", meaning the water inside isn't connected to the water around the island. One cell is a square with side length 1. The grid is rectangular, width and height don't exceed 100. Determine the perimeter of the island.\n \nExample 1:\n\n\nInput: grid = [[0,1,0,0],[1,1,1,0],[0,1,0,0],[1,1,0,0]]\nOutput: 16\nExplanation: The perimeter is the 16 yellow stripes in the image above.\n\nExample 2:\n\nInput: grid = [[1]]\nOutput: 4\n\nExample 3:\n\nInput: grid = [[1,0]]\nOutput: 4\n\n \nConstraints:\n\nrow == grid.length\ncol == grid[i].length\n1 <= row, col <= 100\ngrid[i][j] is 0 or 1.\nThere is exactly one island in grid.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(grid = [[0, 1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]) == 12\n assert candidate(grid = [[1]]) == 4\n assert candidate(grid = [[1, 1, 1], [1, 0, 1], [1, 1, 1]]) == 16\n assert candidate(grid = [[0, 1, 0, 1, 0], [1, 1, 1, 1, 1], [0, 1, 0, 1, 0]]) == 20\n assert candidate(grid = [[1, 0]]) == 4\n assert candidate(grid = [[0, 1, 1, 0], [1, 1, 1, 1], [0, 1, 1, 0]]) == 14\n assert candidate(grid = [[0, 1, 0, 0], [1, 1, 1, 0], [0, 1, 0, 0], [1, 1, 0, 0]]) == 16\n assert candidate(grid = [[1, 1, 0, 0], [1, 1, 0, 0], [0, 0, 1, 1], [0, 0, 1, 1]]) == 16\n assert candidate(grid = [[0, 0, 0, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 0, 0, 0]]) == 8\n assert candidate(grid = [[0, 0, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 0, 1, 0]]) == 14\n assert candidate(grid = [[1, 1, 0, 0], [0, 1, 0, 0], [0, 1, 0, 1], [1, 1, 0, 0]]) == 18\n assert candidate(grid = [[1, 1], [1, 1]]) == 8\n assert candidate(grid = [[1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 1, 0, 1]]) == 48\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 38\n assert candidate(grid = [[0, 1, 1, 0, 0, 0], [1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 22\n assert candidate(grid = [[0, 1, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 1, 0]]) == 18\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1]]) == 64\n assert candidate(grid = [[1, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 1]]) == 24\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1]]) == 72\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 36\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 28\n assert candidate(grid = [[0, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 1, 0, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]) == 16\n assert candidate(grid = [[0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0]]) == 20\n assert candidate(grid = [[1, 1, 1, 1, 0, 0, 0, 0], [1, 0, 0, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0]]) == 38\n assert candidate(grid = [[0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 30\n assert candidate(grid = [[1, 1, 1, 0, 1, 1, 1], [1, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 0, 1], [1, 0, 1, 0, 1, 0, 1], [1, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 1], [1, 1, 1, 0, 1, 1, 1]]) == 64\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 0, 0, 0], [0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 1, 1, 1, 1, 1, 0, 0], [0, 0, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 32\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 0, 1, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 36\n assert candidate(grid = [[0, 1, 0, 0, 0, 0], [1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0]]) == 28\n assert candidate(grid = [[1, 1, 1, 1, 1], [1, 0, 0, 0, 1], [1, 0, 1, 0, 1], [1, 0, 0, 0, 1], [1, 1, 1, 1, 1]]) == 36\n assert candidate(grid = [[1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 1, 0], [1, 1, 0, 0, 1, 1], [0, 1, 1, 1, 1, 0], [1, 0, 1, 0, 1, 0]]) == 40\n assert candidate(grid = [[0, 1, 1, 1, 0], [1, 1, 1, 1, 1], [1, 0, 0, 0, 1], [1, 1, 1, 1, 1], [0, 1, 1, 1, 0]]) == 28\n assert candidate(grid = [[0, 1, 0, 1, 0], [1, 1, 1, 1, 1], [0, 1, 0, 1, 0], [1, 1, 1, 1, 1], [0, 1, 0, 1, 0]]) == 32\n assert candidate(grid = [[1, 1, 1, 1, 0], [1, 0, 0, 1, 0], [1, 1, 1, 1, 0], [0, 0, 0, 0, 0]]) == 20\n assert candidate(grid = [[0, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 0, 0, 1, 1, 0], [0, 0, 0, 1, 1, 0]]) == 20\n assert candidate(grid = [[1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 1], [1, 0, 1, 1, 0, 1], [1, 0, 1, 1, 0, 1], [1, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1]]) == 48\n assert candidate(grid = [[1, 0, 0, 1, 1], [1, 1, 0, 0, 1], [0, 1, 1, 0, 0], [0, 0, 1, 1, 0], [1, 1, 0, 0, 1]]) == 34\n assert candidate(grid = [[0, 1, 0, 0, 0, 1, 0], [1, 1, 1, 0, 1, 1, 1], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 1, 1, 0, 0]]) == 34\n assert candidate(grid = [[0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0]]) == 32\n assert candidate(grid = [[0, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 1, 0, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1]]) == 62\n assert candidate(grid = [[1, 1, 0, 0, 1, 1], [1, 0, 0, 0, 0, 1], [1, 1, 1, 0, 0, 1], [1, 0, 0, 0, 0, 1], [1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0]]) == 36\n assert candidate(grid = [[1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]]) == 156\n assert candidate(grid = [[1, 0, 0, 0, 1], [1, 1, 0, 1, 1], [0, 1, 1, 1, 0], [0, 0, 1, 0, 0], [1, 1, 0, 1, 1]]) == 34\n assert candidate(grid = [[0, 1, 1, 1, 0], [1, 1, 0, 1, 1], [1, 0, 1, 0, 1], [0, 1, 1, 1, 0]]) == 30\n assert candidate(grid = [[1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1, 0, 1]]) == 92\n assert candidate(grid = [[0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 0], [0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0]]) == 24\n assert candidate(grid = [[0, 0, 1, 0, 0], [0, 1, 1, 1, 0], [1, 1, 0, 1, 1], [0, 1, 1, 1, 0], [0, 0, 1, 0, 0]]) == 24\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0]]) == 64\n assert candidate(grid = [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1]]) == 32\n assert candidate(grid = [[1, 1, 1, 0, 0], [1, 0, 0, 0, 1], [1, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 0, 1, 1, 1]]) == 30\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 42\n assert candidate(grid = [[0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0, 1], [0, 1, 0, 1, 0, 1, 0]]) == 68\n assert candidate(grid = [[1, 1, 1, 0, 0], [1, 0, 1, 1, 0], [1, 1, 1, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]) == 18\n assert candidate(grid = [[0, 1, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0]]) == 18\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0, 0], [0, 1, 0, 1, 0, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 30\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 1, 1, 0, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 48\n assert candidate(grid = [[1, 0, 0, 1, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 1, 1, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 0]]) == 36\n assert candidate(grid = [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 1, 0, 1, 1, 0], [0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]) == 20\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 1, 0, 0, 0, 0, 1, 0, 1], [1, 0, 1, 1, 1, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]) == 88\n assert candidate(grid = [[0, 0, 0, 1, 1, 0, 0], [0, 1, 1, 1, 1, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0]]) == 28\n assert candidate(grid = [[1, 1, 1, 1, 1, 1, 0], [1, 0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 40\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 1, 0, 0, 0, 1, 0], [0, 0, 1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0]]) == 32\n assert candidate(grid = [[1, 1, 1, 1, 1, 0], [1, 0, 0, 0, 1, 0], [1, 0, 1, 0, 1, 0], [1, 0, 0, 0, 1, 0], [1, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0]]) == 36\n assert candidate(grid = [[1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 1], [0, 0, 1, 0, 1, 0], [0, 1, 0, 1, 0, 0]]) == 38\n assert candidate(grid = [[1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1], [1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 1, 1]]) == 40\n assert candidate(grid = [[1, 1, 0, 1, 1], [0, 1, 1, 1, 0], [0, 1, 0, 1, 0], [1, 1, 1, 1, 1], [0, 0, 1, 0, 0]]) == 30\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 0, 1, 1, 1, 0], [0, 1, 0, 0, 0, 0, 1, 0], [0, 1, 1, 1, 1, 0, 1, 0], [0, 0, 1, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 34\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 1, 1, 1, 1, 1, 0], [0, 0, 1, 0, 0, 1, 1, 0], [0, 0, 1, 1, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0]]) == 32\n assert candidate(grid = [[1, 0, 1, 0, 1], [0, 1, 1, 1, 0], [1, 1, 0, 1, 1], [0, 1, 1, 1, 0], [1, 0, 1, 0, 1]]) == 40\n assert candidate(grid = [[0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0], [0, 1, 0, 1, 1, 1, 0], [0, 1, 0, 1, 0, 1, 0], [0, 1, 1, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0]]) == 32\n assert candidate(grid = [[1, 0, 0, 1], [0, 1, 1, 0], [1, 1, 0, 1], [1, 0, 1, 0]]) == 28\n assert candidate(grid = [[1, 0, 0, 1, 1, 0, 0, 1], [1, 1, 0, 1, 1, 0, 1, 1], [0, 0, 1, 1, 1, 1, 0, 0], [1, 1, 1, 0, 0, 1, 1, 1], [0, 1, 1, 1, 1, 1, 1, 0], [0, 0, 0, 1, 1, 0, 0, 0]]) == 50\n"}, "metadata": {"canonical_parameter_names": ["grid"], "leetcode_dataset_entry_point": "Solution().islandPerimeter", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var islandPerimeter = function(grid) {", "container": null, "callable": "islandPerimeter", "parameters": [{"name": "grid", "type": "number[][]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 464, "task_id": "can-i-win", "difficulty": "Medium", "problem_description": "In the \"100 game\" two players take turns adding, to a running total, any integer from 1 to 10. The player who first causes the running total to reach or exceed 100 wins.\nWhat if we change the game so that players cannot re-use integers?\nFor example, two players might take turns drawing from a common pool of numbers from 1 to 15 without replacement until they reach a total >= 100.\nGiven two integers maxChoosableInteger and desiredTotal, return true if the first player to move can force a win, otherwise, return false. Assume both players play optimally.\n \nExample 1:\n\nInput: maxChoosableInteger = 10, desiredTotal = 11\nOutput: false\nExplanation:\nNo matter which integer the first player choose, the first player will lose.\nThe first player can choose an integer from 1 up to 10.\nIf the first player choose 1, the second player can only choose integers from 2 up to 10.\nThe second player will win by choosing 10 and get a total = 11, which is >= desiredTotal.\nSame with other integers chosen by the first player, the second player will always win.\n\nExample 2:\n\nInput: maxChoosableInteger = 10, desiredTotal = 0\nOutput: true\n\nExample 3:\n\nInput: maxChoosableInteger = 10, desiredTotal = 1\nOutput: true\n\n \nConstraints:\n\n1 <= maxChoosableInteger <= 20\n0 <= desiredTotal <= 300\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(maxChoosableInteger = 15,desiredTotal = 50) == True\n assert candidate(maxChoosableInteger = 10,desiredTotal = 0) == True\n assert candidate(maxChoosableInteger = 10,desiredTotal = 15) == True\n assert candidate(maxChoosableInteger = 8,desiredTotal = 25) == False\n assert candidate(maxChoosableInteger = 10,desiredTotal = 40) == False\n assert candidate(maxChoosableInteger = 10,desiredTotal = 25) == True\n assert candidate(maxChoosableInteger = 20,desiredTotal = 21) == False\n assert candidate(maxChoosableInteger = 5,desiredTotal = 50) == False\n assert candidate(maxChoosableInteger = 10,desiredTotal = 100) == False\n assert candidate(maxChoosableInteger = 20,desiredTotal = 28) == True\n assert candidate(maxChoosableInteger = 15,desiredTotal = 100) == True\n assert candidate(maxChoosableInteger = 12,desiredTotal = 30) == False\n assert candidate(maxChoosableInteger = 7,desiredTotal = 15) == False\n assert candidate(maxChoosableInteger = 6,desiredTotal = 16) == True\n assert candidate(maxChoosableInteger = 10,desiredTotal = 1) == True\n assert candidate(maxChoosableInteger = 3,desiredTotal = 8) == False\n assert candidate(maxChoosableInteger = 20,desiredTotal = 300) == False\n assert candidate(maxChoosableInteger = 10,desiredTotal = 11) == False\n assert candidate(maxChoosableInteger = 16,desiredTotal = 80) == True\n assert candidate(maxChoosableInteger = 18,desiredTotal = 150) == False\n assert candidate(maxChoosableInteger = 15,desiredTotal = 70) == False\n assert candidate(maxChoosableInteger = 8,desiredTotal = 30) == True\n assert candidate(maxChoosableInteger = 20,desiredTotal = 199) == False\n assert candidate(maxChoosableInteger = 9,desiredTotal = 36) == True\n assert candidate(maxChoosableInteger = 16,desiredTotal = 85) == False\n assert candidate(maxChoosableInteger = 20,desiredTotal = 200) == False\n assert candidate(maxChoosableInteger = 18,desiredTotal = 120) == False\n assert candidate(maxChoosableInteger = 11,desiredTotal = 33) == True\n assert candidate(maxChoosableInteger = 13,desiredTotal = 45) == True\n assert candidate(maxChoosableInteger = 10,desiredTotal = 99) == False\n assert candidate(maxChoosableInteger = 16,desiredTotal = 90) == False\n assert candidate(maxChoosableInteger = 14,desiredTotal = 49) == True\n assert candidate(maxChoosableInteger = 13,desiredTotal = 30) == True\n assert candidate(maxChoosableInteger = 20,desiredTotal = 180) == False\n assert candidate(maxChoosableInteger = 14,desiredTotal = 60) == False\n assert candidate(maxChoosableInteger = 13,desiredTotal = 80) == True\n assert candidate(maxChoosableInteger = 14,desiredTotal = 80) == True\n assert candidate(maxChoosableInteger = 16,desiredTotal = 60) == True\n assert candidate(maxChoosableInteger = 12,desiredTotal = 80) == False\n assert candidate(maxChoosableInteger = 10,desiredTotal = 55) == False\n assert candidate(maxChoosableInteger = 19,desiredTotal = 135) == True\n assert candidate(maxChoosableInteger = 14,desiredTotal = 99) == False\n assert candidate(maxChoosableInteger = 19,desiredTotal = 110) == True\n assert candidate(maxChoosableInteger = 12,desiredTotal = 75) == False\n assert candidate(maxChoosableInteger = 5,desiredTotal = 15) == True\n assert candidate(maxChoosableInteger = 14,desiredTotal = 95) == False\n assert candidate(maxChoosableInteger = 7,desiredTotal = 28) == True\n assert candidate(maxChoosableInteger = 14,desiredTotal = 50) == True\n assert candidate(maxChoosableInteger = 20,desiredTotal = 250) == False\n assert candidate(maxChoosableInteger = 17,desiredTotal = 140) == True\n assert candidate(maxChoosableInteger = 19,desiredTotal = 180) == True\n assert candidate(maxChoosableInteger = 16,desiredTotal = 110) == False\n assert candidate(maxChoosableInteger = 13,desiredTotal = 60) == True\n assert candidate(maxChoosableInteger = 9,desiredTotal = 45) == True\n assert candidate(maxChoosableInteger = 12,desiredTotal = 35) == True\n assert candidate(maxChoosableInteger = 17,desiredTotal = 85) == True\n assert candidate(maxChoosableInteger = 20,desiredTotal = 150) == False\n assert candidate(maxChoosableInteger = 15,desiredTotal = 80) == True\n assert candidate(maxChoosableInteger = 8,desiredTotal = 28) == True\n assert candidate(maxChoosableInteger = 7,desiredTotal = 25) == True\n assert candidate(maxChoosableInteger = 18,desiredTotal = 130) == True\n assert candidate(maxChoosableInteger = 11,desiredTotal = 55) == True\n assert candidate(maxChoosableInteger = 17,desiredTotal = 90) == True\n assert candidate(maxChoosableInteger = 17,desiredTotal = 100) == True\n assert candidate(maxChoosableInteger = 16,desiredTotal = 120) == True\n assert candidate(maxChoosableInteger = 20,desiredTotal = 130) == False\n assert candidate(maxChoosableInteger = 19,desiredTotal = 120) == True\n assert candidate(maxChoosableInteger = 16,desiredTotal = 130) == False\n assert candidate(maxChoosableInteger = 7,desiredTotal = 20) == True\n assert candidate(maxChoosableInteger = 18,desiredTotal = 180) == False\n assert candidate(maxChoosableInteger = 18,desiredTotal = 100) == True\n assert candidate(maxChoosableInteger = 12,desiredTotal = 60) == False\n assert candidate(maxChoosableInteger = 15,desiredTotal = 120) == True\n assert candidate(maxChoosableInteger = 14,desiredTotal = 70) == True\n assert candidate(maxChoosableInteger = 10,desiredTotal = 50) == False\n"}, "metadata": {"canonical_parameter_names": ["maxChoosableInteger", "desiredTotal"], "leetcode_dataset_entry_point": "Solution().canIWin", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var canIWin = function(maxChoosableInteger, desiredTotal) {", "container": null, "callable": "canIWin", "parameters": [{"name": "maxChoosableInteger", "type": "number"}, {"name": "desiredTotal", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 466, "task_id": "count-the-repetitions", "difficulty": "Hard", "problem_description": "We define str = [s, n] as the string str which consists of the string s concatenated n times.\n\nFor example, str == [\"abc\", 3] ==\"abcabcabc\".\n\nWe define that string s1 can be obtained from string s2 if we can remove some characters from s2 such that it becomes s1.\n\nFor example, s1 = \"abc\" can be obtained from s2 = \"abdbec\" based on our definition by removing the bolded underlined characters.\n\nYou are given two strings s1 and s2 and two integers n1 and n2. You have the two strings str1 = [s1, n1] and str2 = [s2, n2].\nReturn the maximum integer m such that str = [str2, m] can be obtained from str1.\n \nExample 1:\nInput: s1 = \"acb\", n1 = 4, s2 = \"ab\", n2 = 2\nOutput: 2\nExample 2:\nInput: s1 = \"acb\", n1 = 1, s2 = \"acb\", n2 = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= s1.length, s2.length <= 100\ns1 and s2 consist of lowercase English letters.\n1 <= n1, n2 <= 106\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s1 = \"acb\",n1 = 1,s2 = \"acb\",n2 = 1) == 1\n assert candidate(s1 = \"aaa\",n1 = 3,s2 = \"a\",n2 = 1) == 9\n assert candidate(s1 = \"aabaacaabaab\",n1 = 8,s2 = \"aab\",n2 = 1) == 24\n assert candidate(s1 = \"acb\",n1 = 4,s2 = \"ab\",n2 = 2) == 2\n assert candidate(s1 = \"abcde\",n1 = 2,s2 = \"ace\",n2 = 1) == 2\n assert candidate(s1 = \"banana\",n1 = 10,s2 = \"nan\",n2 = 1) == 10\n assert candidate(s1 = \"abcdabcd\",n1 = 5,s2 = \"abc\",n2 = 2) == 5\n assert candidate(s1 = \"aabbccddeeff\",n1 = 5,s2 = \"abcdef\",n2 = 1) == 5\n assert candidate(s1 = \"zzzzzzzz\",n1 = 1000,s2 = \"zz\",n2 = 100) == 40\n assert candidate(s1 = \"aabbcc\",n1 = 1000,s2 = \"abcabcabcabcabcabcabcabc\",n2 = 50) == 2\n assert candidate(s1 = \"abcdefg\",n1 = 500,s2 = \"aceg\",n2 = 100) == 5\n assert candidate(s1 = \"aabbccdd\",n1 = 25,s2 = \"abcdabcd\",n2 = 2) == 6\n assert candidate(s1 = \"hello\",n1 = 20,s2 = \"lohel\",n2 = 4) == 4\n assert candidate(s1 = \"pqrs\",n1 = 100,s2 = \"rqpqsr\",n2 = 5) == 5\n assert candidate(s1 = \"abcdefg\",n1 = 100,s2 = \"aceg\",n2 = 5) == 20\n assert candidate(s1 = \"zzzzz\",n1 = 1000000,s2 = \"z\",n2 = 1) == 5000000\n assert candidate(s1 = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",n1 = 100,s2 = \"zyxwvutsrqponmlkjihgfedcba\",n2 = 1) == 3\n assert candidate(s1 = \"zabzabczb\",n1 = 10,s2 = \"abc\",n2 = 2) == 5\n assert candidate(s1 = \"xyzxyzxyz\",n1 = 5,s2 = \"xyz\",n2 = 1) == 15\n assert candidate(s1 = \"abcdefghijklmnopqrstuvwxyz\",n1 = 100,s2 = \"zyxwvutsrqponmlkjihgfedcba\",n2 = 50) == 0\n assert candidate(s1 = \"abcd\",n1 = 100000,s2 = \"dabc\",n2 = 1000) == 99\n assert candidate(s1 = \"abcdef\",n1 = 20,s2 = \"fedcba\",n2 = 1) == 3\n assert candidate(s1 = \"xyzxyz\",n1 = 3,s2 = \"xyzxyzxyz\",n2 = 1) == 2\n assert candidate(s1 = \"hellohello\",n1 = 10,s2 = \"lohe\",n2 = 1) == 19\n assert candidate(s1 = \"abcdefgh\",n1 = 10,s2 = \"aceg\",n2 = 1) == 10\n assert candidate(s1 = \"xyzxyzxyz\",n1 = 100,s2 = \"xyzxyzxyz\",n2 = 20) == 5\n assert candidate(s1 = \"xyz\",n1 = 50000,s2 = \"xzy\",n2 = 10000) == 2\n assert candidate(s1 = \"abcdef\",n1 = 15,s2 = \"defabc\",n2 = 3) == 4\n assert candidate(s1 = \"abcabcabcabcabcabcabcabc\",n1 = 10,s2 = \"abcabcabcabcabcabcabcabc\",n2 = 1) == 10\n assert candidate(s1 = \"acb\",n1 = 10,s2 = \"acbacb\",n2 = 1) == 5\n assert candidate(s1 = \"abcdefg\",n1 = 10,s2 = \"xyz\",n2 = 1) == 0\n assert candidate(s1 = \"ababababab\",n1 = 20,s2 = \"abab\",n2 = 5) == 10\n assert candidate(s1 = \"abcabcabcabcabc\",n1 = 999,s2 = \"abab\",n2 = 125) == 19\n assert candidate(s1 = \"aaa\",n1 = 10,s2 = \"aa\",n2 = 2) == 7\n assert candidate(s1 = \"mississippi\",n1 = 100,s2 = \"issi\",n2 = 5) == 20\n assert candidate(s1 = \"aabbccddeeffgg\",n1 = 20,s2 = \"abcdefg\",n2 = 2) == 10\n assert candidate(s1 = \"zzzzzzzzzz\",n1 = 1000,s2 = \"zz\",n2 = 100) == 50\n assert candidate(s1 = \"qwertyuiop\",n1 = 50,s2 = \"qrp\",n2 = 10) == 5\n assert candidate(s1 = \"xyzxyzxyz\",n1 = 15,s2 = \"zyxzyx\",n2 = 1) == 11\n assert candidate(s1 = \"abcabcabc\",n1 = 500,s2 = \"cab\",n2 = 250) == 5\n assert candidate(s1 = \"xyz\",n1 = 5,s2 = \"xz\",n2 = 1) == 5\n assert candidate(s1 = \"abcabcabcabcabcabcabcabc\",n1 = 10,s2 = \"abc\",n2 = 1) == 80\n assert candidate(s1 = \"xyz\",n1 = 1000000,s2 = \"xyzz\",n2 = 1000) == 500\n assert candidate(s1 = \"hello\",n1 = 10,s2 = \"heo\",n2 = 1) == 10\n assert candidate(s1 = \"abcabcabcabc\",n1 = 12,s2 = \"abcabc\",n2 = 2) == 12\n assert candidate(s1 = \"abacabadabacaba\",n1 = 200,s2 = \"abad\",n2 = 10) == 20\n assert candidate(s1 = \"xyz\",n1 = 10,s2 = \"yxz\",n2 = 1) == 5\n assert candidate(s1 = \"abacabadaba\",n1 = 1000,s2 = \"abad\",n2 = 250) == 4\n assert candidate(s1 = \"abababa\",n1 = 10,s2 = \"aba\",n2 = 2) == 10\n assert candidate(s1 = \"abcd\",n1 = 50,s2 = \"bd\",n2 = 10) == 5\n assert candidate(s1 = \"abcde\",n1 = 1,s2 = \"edcba\",n2 = 1) == 0\n assert candidate(s1 = \"zabzabczabc\",n1 = 10,s2 = \"abc\",n2 = 3) == 6\n assert candidate(s1 = \"aaaaaaab\",n1 = 1000,s2 = \"aab\",n2 = 100) == 10\n assert candidate(s1 = \"abcdef\",n1 = 6,s2 = \"fed\",n2 = 1) == 2\n assert candidate(s1 = \"aabbcc\",n1 = 10,s2 = \"abc\",n2 = 2) == 5\n assert candidate(s1 = \"ababcabc\",n1 = 10,s2 = \"abc\",n2 = 2) == 10\n assert candidate(s1 = \"aaaa\",n1 = 1000000,s2 = \"aa\",n2 = 100000) == 20\n assert candidate(s1 = \"abcdef\",n1 = 999999,s2 = \"fabcde\",n2 = 100000) == 9\n assert candidate(s1 = \"aaaaa\",n1 = 100000,s2 = \"aa\",n2 = 10000) == 25\n assert candidate(s1 = \"abccbaabccba\",n1 = 20,s2 = \"abc\",n2 = 4) == 10\n assert candidate(s1 = \"ababababababababababab\",n1 = 100,s2 = \"baba\",n2 = 25) == 21\n assert candidate(s1 = \"aeiou\",n1 = 10000,s2 = \"aeiouaeiou\",n2 = 500) == 10\n assert candidate(s1 = \"mississippi\",n1 = 3,s2 = \"issi\",n2 = 1) == 3\n assert candidate(s1 = \"abcdabcdabcd\",n1 = 3,s2 = \"abcd\",n2 = 1) == 9\n assert candidate(s1 = \"qwertyuiop\",n1 = 50,s2 = \"qo\",n2 = 10) == 5\n assert candidate(s1 = \"abcdefghijklmnopqrstuvwxyz\",n1 = 1000,s2 = \"abcdefghijklmnopqrstuvwxyz\",n2 = 10) == 100\n assert candidate(s1 = \"abcdabcdabcdabcd\",n1 = 20,s2 = \"abc\",n2 = 5) == 16\n assert candidate(s1 = \"abcd\",n1 = 100,s2 = \"dabc\",n2 = 50) == 1\n assert candidate(s1 = \"abababa\",n1 = 1000,s2 = \"aba\",n2 = 10) == 200\n assert candidate(s1 = \"banana\",n1 = 20,s2 = \"ban\",n2 = 5) == 4\n assert candidate(s1 = \"xyzabc\",n1 = 5,s2 = \"cab\",n2 = 2) == 2\n assert candidate(s1 = \"aaa\",n1 = 500,s2 = \"a\",n2 = 100) == 15\n assert candidate(s1 = \"xyxzyxyxyxy\",n1 = 2,s2 = \"xyz\",n2 = 1) == 2\n assert candidate(s1 = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",n1 = 1000000,s2 = \"zzz\",n2 = 100000) == 113\n assert candidate(s1 = \"ababab\",n1 = 5,s2 = \"ab\",n2 = 2) == 7\n assert candidate(s1 = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",n1 = 10,s2 = \"abcdefghijklmnopqrstuvwxyz\",n2 = 1) == 10\n assert candidate(s1 = \"aabbcc\",n1 = 3,s2 = \"abc\",n2 = 1) == 3\n assert candidate(s1 = \"ababcabcabc\",n1 = 6,s2 = \"abcabc\",n2 = 1) == 9\n assert candidate(s1 = \"abcdabcdabcd\",n1 = 500,s2 = \"abcd\",n2 = 125) == 12\n assert candidate(s1 = \"aabbccddeeff\",n1 = 1000,s2 = \"abcdef\",n2 = 10) == 100\n assert candidate(s1 = \"abcabcabcabc\",n1 = 10,s2 = \"abcabc\",n2 = 1) == 20\n assert candidate(s1 = \"aaaabbbbcccc\",n1 = 10,s2 = \"abccba\",n2 = 2) == 2\n assert candidate(s1 = \"abababab\",n1 = 100,s2 = \"aba\",n2 = 15) == 13\n assert candidate(s1 = \"abcdefghij\",n1 = 50,s2 = \"adgj\",n2 = 5) == 10\n assert candidate(s1 = \"mississippi\",n1 = 10,s2 = \"issi\",n2 = 1) == 10\n assert candidate(s1 = \"aaaaaa\",n1 = 1000000,s2 = \"aa\",n2 = 100000) == 30\n assert candidate(s1 = \"abcd\",n1 = 10000,s2 = \"dcba\",n2 = 1000) == 3\n assert candidate(s1 = \"aaaaaaaa\",n1 = 100000,s2 = \"aa\",n2 = 10000) == 40\n assert candidate(s1 = \"ab\",n1 = 1000000,s2 = \"a\",n2 = 500000) == 2\n assert candidate(s1 = \"aaaabaabaabaaaaaa\",n1 = 5,s2 = \"aab\",n2 = 1) == 15\n assert candidate(s1 = \"xyzabc\",n1 = 5,s2 = \"xz\",n2 = 1) == 5\n assert candidate(s1 = \"abababa\",n1 = 7,s2 = \"baab\",n2 = 1) == 7\n assert candidate(s1 = \"banana\",n1 = 10,s2 = \"an\",n2 = 2) == 10\n assert candidate(s1 = \"abcabcabcabc\",n1 = 500,s2 = \"bcab\",n2 = 125) == 8\n assert candidate(s1 = \"abcdabcd\",n1 = 100,s2 = \"cdab\",n2 = 10) == 19\n assert candidate(s1 = \"abcabcabc\",n1 = 1000,s2 = \"abcabc\",n2 = 200) == 7\n assert candidate(s1 = \"abcabcabc\",n1 = 1000,s2 = \"abc\",n2 = 100) == 30\n assert candidate(s1 = \"aaa\",n1 = 1000000,s2 = \"a\",n2 = 1) == 3000000\n assert candidate(s1 = \"abcdefghijklmnopqrstuvwxyz\",n1 = 10000,s2 = \"zyxwvutsrqponmlkjihgfedcba\",n2 = 5000) == 0\n assert candidate(s1 = \"zzzzzzzzzz\",n1 = 1000,s2 = \"z\",n2 = 100) == 100\n assert candidate(s1 = \"abcdefghijklmnopqrstuvwxyz\",n1 = 1000,s2 = \"zyxwvutsrqponmlkjihgfedcba\",n2 = 10) == 3\n assert candidate(s1 = \"mnopqrstuvwxyz\",n1 = 10000,s2 = \"mnop\",n2 = 2000) == 5\n assert candidate(s1 = \"abcdabcdabcdabcd\",n1 = 500,s2 = \"dcbadcbadcbadcba\",n2 = 100) == 1\n assert candidate(s1 = \"abcabcabcabc\",n1 = 100,s2 = \"abcabc\",n2 = 5) == 40\n assert candidate(s1 = \"abab\",n1 = 3,s2 = \"ab\",n2 = 2) == 3\n assert candidate(s1 = \"abacabacabacabac\",n1 = 1000,s2 = \"acabacabacabacab\",n2 = 250) == 3\n assert candidate(s1 = \"baba\",n1 = 20,s2 = \"ab\",n2 = 5) == 7\n assert candidate(s1 = \"babccbababcabbbabcbbabbbbabcbbb\",n1 = 100,s2 = \"babccbabab\",n2 = 10) == 10\n"}, "metadata": {"canonical_parameter_names": ["s1", "n1", "s2", "n2"], "leetcode_dataset_entry_point": "Solution().getMaxRepetitions", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getMaxRepetitions = function(s1, n1, s2, n2) {", "container": null, "callable": "getMaxRepetitions", "parameters": [{"name": "s1", "type": "string"}, {"name": "n1", "type": "number"}, {"name": "s2", "type": "string"}, {"name": "n2", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 467, "task_id": "unique-substrings-in-wraparound-string", "difficulty": "Medium", "problem_description": "We define the string base to be the infinite wraparound string of \"abcdefghijklmnopqrstuvwxyz\", so base will look like this:\n\n\"...zabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcd....\".\n\nGiven a string s, return the number of unique non-empty substrings of s are present in base.\n \nExample 1:\n\nInput: s = \"a\"\nOutput: 1\nExplanation: Only the substring \"a\" of s is in base.\n\nExample 2:\n\nInput: s = \"cac\"\nOutput: 2\nExplanation: There are two substrings (\"a\", \"c\") of s in base.\n\nExample 3:\n\nInput: s = \"zab\"\nOutput: 6\nExplanation: There are six substrings (\"z\", \"a\", \"b\", \"za\", \"ab\", and \"zab\") of s in base.\n\n \nConstraints:\n\n1 <= s.length <= 105\ns consists of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"qpqprstuvwxyzqpqprstuvwxyzqpqprstuvwxyz\") == 48\n assert candidate(s = \"abczabczabcz\") == 10\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 351\n assert candidate(s = \"azza\") == 3\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"za\") == 3\n assert candidate(s = \"qpqprstuvwxyz\") == 48\n assert candidate(s = \"zaabcdefghijklmnopqrstuvwxyz\") == 352\n assert candidate(s = \"a\") == 1\n assert candidate(s = \"abcabcabc\") == 6\n assert candidate(s = \"zabcdefghijklmnopqrstuvwxyz\") == 377\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"xyzxyzxyz\") == 6\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == 1027\n assert candidate(s = \"abcd\") == 10\n assert candidate(s = \"abczab\") == 9\n assert candidate(s = \"cac\") == 2\n assert candidate(s = \"cab\") == 4\n assert candidate(s = \"zab\") == 6\n assert candidate(s = \"zabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == 1053\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"abcabcdabcdeabcdefabcdefg\") == 28\n assert candidate(s = \"mnopqrstuvwxyza\") == 120\n assert candidate(s = \"pqrstuvwxyzabcdefghijklmno\") == 351\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnooooqqqqrrrrssssttttuuuuvvvvwwwwxxxxyyyyzzzz\") == 48\n assert candidate(s = \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\") == 10\n assert candidate(s = \"mnopqrstuvwxyzabcdefghijkl\") == 351\n assert candidate(s = \"nopqrstuvwxyzabcdefghijklmno\") == 403\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"aaaaaaaaaabbbbbbbbcccccccc\") == 5\n assert candidate(s = \"qrstuvqrstuvqrstuvqrstuvqrstuvqrstuvqrstuvqrstuvqrstuv\") == 21\n assert candidate(s = \"vwxyzabcdefghijklmnopqrstu\") == 351\n assert candidate(s = \"abcdbca\") == 10\n assert candidate(s = \"zabzabzabzabzabzabzabzabzabzabzabzabzabzabzab\") == 6\n assert candidate(s = \"abacabadabacaba\") == 5\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n assert candidate(s = \"abcabcabcabc\") == 6\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == 1703\n assert candidate(s = \"cdefghijklmnopqrstuvwxyzab\") == 351\n assert candidate(s = \"abcdefghijabcdefghijabcdefghijabcdefghijabcdefghijabcdefghijabcdefghijabcdefghij\") == 55\n assert candidate(s = \"abababababababababababababababababababab\") == 3\n assert candidate(s = \"abcdefgabcdefgabcdefgabcdefg\") == 28\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == 3055\n assert candidate(s = \"abcdzabcde\") == 21\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzaabcdefghijklmnopqrstuvwxyzab\") == 403\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == 351\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyza\") == 377\n assert candidate(s = \"zzzzzzzzzz\") == 1\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\") == 2379\n assert candidate(s = \"qpqrstuvwxyzabcdefghijklmno\") == 351\n assert candidate(s = \"xyzabcdezyxabcdezyxabcdezyxabcdezyxabcdezyxabcdezyx\") == 36\n assert candidate(s = \"aaaabbbbccccddddeeeeffffgggghhhhiiiijjjjkkkkllllmmmmnnnnooooppppqqqqrrrrssssttttuuuuvvvvwwwwxxxxyyyyzzzz\") == 51\n assert candidate(s = \"xyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyz\") == 6\n assert candidate(s = \"qpqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba\") == 27\n assert candidate(s = \"abcdabcdeabcdefabcdefgabcdefg\") == 28\n assert candidate(s = \"abcdzabcdezabcdefzabcdefgzabcdefgz\") == 36\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\") == 351\n assert candidate(s = \"mnopqrstuvwxyzabcdefghijklmnop\") == 455\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbaabcdefghijklmnopqrstuvwxyz\") == 351\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 51\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba\") == 351\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(s = \"xyzabcdefghijklmnopqrstuvwxyz\") == 429\n assert candidate(s = \"xyzabc\") == 21\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 1\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().findSubstringInWraproundString", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findSubstringInWraproundString = function(s) {", "container": null, "callable": "findSubstringInWraproundString", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 468, "task_id": "validate-ip-address", "difficulty": "Medium", "problem_description": "Given a string queryIP, return \"IPv4\" if IP is a valid IPv4 address, \"IPv6\" if IP is a valid IPv6 address or \"Neither\" if IP is not a correct IP of any type.\nA valid IPv4 address is an IP in the form \"x1.x2.x3.x4\" where 0 <= xi <= 255 and xi cannot contain leading zeros. For example, \"192.168.1.1\" and \"192.168.1.0\" are valid IPv4 addresses while \"192.168.01.1\", \"192.168.1.00\", and \"192.168@1.1\" are invalid IPv4 addresses.\nA valid IPv6 address is an IP in the form \"x1:x2:x3:x4:x5:x6:x7:x8\" where:\n\n1 <= xi.length <= 4\nxi is a hexadecimal string which may contain digits, lowercase English letter ('a' to 'f') and upper-case English letters ('A' to 'F').\nLeading zeros are allowed in xi.\n\nFor example, \"2001:0db8:85a3:0000:0000:8a2e:0370:7334\" and \"2001:db8:85a3:0:0:8A2E:0370:7334\" are valid IPv6 addresses, while \"2001:0db8:85a3::8A2E:037j:7334\" and \"02001:0db8:85a3:0000:0000:8a2e:0370:7334\" are invalid IPv6 addresses.\n \nExample 1:\n\nInput: queryIP = \"172.16.254.1\"\nOutput: \"IPv4\"\nExplanation: This is a valid IPv4 address, return \"IPv4\".\n\nExample 2:\n\nInput: queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334\"\nOutput: \"IPv6\"\nExplanation: This is a valid IPv6 address, return \"IPv6\".\n\nExample 3:\n\nInput: queryIP = \"256.256.256.256\"\nOutput: \"Neither\"\nExplanation: This is neither a IPv4 address nor a IPv6 address.\n\n \nConstraints:\n\nqueryIP consists only of English letters, digits and the characters '.' and ':'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(queryIP = \"192.168.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:DB8:85A3:0:0:8A2E:370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:733\") == \"IPv6\"\n assert candidate(queryIP = \"123.456.789.01\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:4567890:abcd\") == \"Neither\"\n assert candidate(queryIP = \"172.16.254.1\") == \"IPv4\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:1234\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:012:345\") == \"IPv6\"\n assert candidate(queryIP = \"0000:0000:0000:0000:0000:0000:0000:0000\") == \"IPv6\"\n assert candidate(queryIP = \"1.2.3. 4\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.abc\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:extra\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:45678:abcd\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:4567890abcd\") == \"Neither\"\n assert candidate(queryIP = \"255.255.255.255\") == \"IPv4\"\n assert candidate(queryIP = \"1.2.3.256\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.0123\") == \"Neither\"\n assert candidate(queryIP = \"123.45.67.256\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.012\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:abcd\") == \"Neither\"\n assert candidate(queryIP = \"0db8:85a3:0:0:8A2E:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:db8:85a3:8d3:1319:8a2e:370:7348\") == \"IPv6\"\n assert candidate(queryIP = \"123.45.67\") == \"Neither\"\n assert candidate(queryIP = \"192.168@1.1\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:4567890\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.256\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:8A2E:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"0:0:0:0:0:0:0:0\") == \"IPv6\"\n assert candidate(queryIP = \"1.2.3\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8A2E:0370\") == \"Neither\"\n assert candidate(queryIP = \"123.45.67.89\") == \"IPv4\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334g\") == \"Neither\"\n assert candidate(queryIP = \"256.256.256.256\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:5678\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.00\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:db8::8a2e:370:7334\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:45678901abcd\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:012:345:678:901\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8::85a3:0:0:8A2E:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:def0\") == \"IPv6\"\n assert candidate(queryIP = \"123.45.67.89.01\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:456789\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:012:345:678:901:234\") == \"IPv6\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:037g:7334\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.00\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:1234\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1\") == \"IPv4\"\n assert candidate(queryIP = \"192.168.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370\") == \"Neither\"\n assert candidate(queryIP = \"::\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.a\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"0db8:85a3:0000:0000:8a2e:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8A2E:0370:7334:1234\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:01234:4567\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.01234\") == \"Neither\"\n assert candidate(queryIP = \"192.168.01.1\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:012:345:678:901:2345\") == \"IPv6\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:00:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:733g\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:4567:abcd\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3::0:8A2E:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.012345\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:012:345678\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.0000\") == \"Neither\"\n assert candidate(queryIP = \"ffff:ffff:ffff:ffff:ffff:ffff:ffff:ffff\") == \"IPv6\"\n assert candidate(queryIP = \"192.168.1.-1\") == \"Neither\"\n assert candidate(queryIP = \"1.2.3.4.5\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:G334\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.123.456\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:4567\") == \"IPv6\"\n assert candidate(queryIP = \"2001:db8:85a3::8a2e:370:7334\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789.0\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:45678\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:4567abcd\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:1234\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:45678901:abcd\") == \"Neither\"\n assert candidate(queryIP = \"02001:0db8:85a3:0000:0000:8a2e:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:012:3456\") == \"IPv6\"\n assert candidate(queryIP = \"2001:db8::1\") == \"Neither\"\n assert candidate(queryIP = \"123.456.789\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:456789:abcd\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3::8A2E:037j:7334\") == \"Neither\"\n assert candidate(queryIP = \"1.2.3.-1\") == \"Neither\"\n assert candidate(queryIP = \"0.0.0.0\") == \"IPv4\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:0123:45678901\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:73345\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8::\") == \"Neither\"\n assert candidate(queryIP = \"123:456:789:0123:456:789:012:34567\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:000g\") == \"Neither\"\n assert candidate(queryIP = \"192.168.-1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8a2e:0370:7334:\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8::85a3:0:0:8A2E:370:7334\") == \"Neither\"\n assert candidate(queryIP = \"-1.192.168.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:733G\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"192.-1.168.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334::\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3::8A2E:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:00000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:733g\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:abcd\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1:\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:def0:1234\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"192.168.256.1\") == \"Neither\"\n assert candidate(queryIP = \"256.192.168.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3::8a2e:370:7334\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:733g\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8a2e:0370:7334:abcd\") == \"Neither\"\n assert candidate(queryIP = \"abcd:efgh:ijkl:mnop:qrst:uvwx:yza:12345\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.abc\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:12345\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:000g\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3::8A2E:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"a.192.168.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:00000\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8a2e:0370:7334:extra\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:0000:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334:7334:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:00000\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.a\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334::1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3::\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:000g\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:abz\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:extra\") == \"Neither\"\n assert candidate(queryIP = \"192.168.0.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000:0000:0000:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:73340\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:00000\") == \"Neither\"\n assert candidate(queryIP = \"2001:DB8:85A3:0:0:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"::ffff:192.168.1.1:1\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:0000\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:def0::1::\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"abcd:efgh:ijkl:mnop:qrst:uvwx:yza:1234\") == \"Neither\"\n assert candidate(queryIP = \"192.168.a.1.1\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.00\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:00000\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1::ffff\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:0000:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:000g\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.01.1\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.256\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:7334:\") == \"Neither\"\n assert candidate(queryIP = \"123.045.678.901\") == \"Neither\"\n assert candidate(queryIP = \"256.255.255.255\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.001\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.01\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.01.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:abG\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0000:0000:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8a2e:0370:73g4\") == \"Neither\"\n assert candidate(queryIP = \"0123.456.789.012\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:1:2:3:4:56789\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1a\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:extra\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000:0000:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:0000:000g\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:abcd\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334::7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"1200::AB00:1234::2552:7777:1313\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334::\") == \"Neither\"\n assert candidate(queryIP = \"192.a.168.1.1\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:def0::1\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1::1\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1::ffff:\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:00000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8a2e:0370\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.0.2.128\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:0000:00000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0DB8:85A3:0000:0000:8A2E:0370:7334\") == \"IPv6\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:abg\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:def0:1234:5678:9abc:def0\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334:7334:7334:7334:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334:000g\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1::\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:000G\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:000g\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"abcd:efgh:ijkl:mnop:qrst:uvwx:yza:\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:def0::\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:256.256.256.256\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.a.1\") == \"Neither\"\n assert candidate(queryIP = \"abcd:efgh:ijkl:mnop:qrst:uvwx:yza:1234:1234\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3::8A2E:0370:7334:\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"::ffff:192.168.1.1a\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.0000\") == \"Neither\"\n assert candidate(queryIP = \"192.256.168.1\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2e:0370:7334:0000::\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:0370:7334::\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0000:0000:8a2g:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:0000:000g\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3::8a2e:0370:7334\") == \"Neither\"\n assert candidate(queryIP = \"01.02.03.04\") == \"Neither\"\n assert candidate(queryIP = \"2001:db8:85a3:0:0:8A2E:370:7334:7334:7334:7334:7334:7334:7334:7334\") == \"Neither\"\n assert candidate(queryIP = \"1234:5678:9abc:def0:1234:5678:9abc:defg\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334:0000:0000:0000:0000:0000\") == \"Neither\"\n assert candidate(queryIP = \"2001:0db8:85a3:0:0:8A2E:0370:7334::\") == \"Neither\"\n assert candidate(queryIP = \"192.168.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1\") == \"Neither\"\n assert candidate(queryIP = \"::1\") == \"Neither\"\n"}, "metadata": {"canonical_parameter_names": ["queryIP"], "leetcode_dataset_entry_point": "Solution().validIPAddress", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var validIPAddress = function(queryIP) {", "container": null, "callable": "validIPAddress", "parameters": [{"name": "queryIP", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 472, "task_id": "concatenated-words", "difficulty": "Hard", "problem_description": "Given an array of strings words (without duplicates), return all the concatenated words in the given list of words.\nA concatenated word is defined as a string that is comprised entirely of at least two shorter words (not necessarily distinct) in the given array.\n \nExample 1:\n\nInput: words = [\"cat\",\"cats\",\"catsdogcats\",\"dog\",\"dogcatsdog\",\"hippopotamuses\",\"rat\",\"ratcatdogcat\"]\nOutput: [\"catsdogcats\",\"dogcatsdog\",\"ratcatdogcat\"]\nExplanation: \"catsdogcats\" can be concatenated by \"cats\", \"dog\" and \"cats\"; \n\"dogcatsdog\" can be concatenated by \"dog\", \"cats\" and \"dog\"; \n\"ratcatdogcat\" can be concatenated by \"rat\", \"cat\", \"dog\" and \"cat\".\nExample 2:\n\nInput: words = [\"cat\",\"dog\",\"catdog\"]\nOutput: [\"catdog\"]\n\n \nConstraints:\n\n1 <= words.length <= 104\n1 <= words[i].length <= 30\nwords[i] consists of only lowercase English letters.\nAll the strings of words are unique.\n1 <= sum(words[i].length) <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(words = ['hello', 'world', 'helloworld', 'worldhello']) == ['helloworld', 'worldhello']\n assert candidate(words = ['apple', 'banana', 'appbanana', 'banapple', 'app', 'ban']) == ['banapple', 'appbanana']\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == ['aa', 'aaa', 'aaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']\n assert candidate(words = ['cat', 'dog', 'catdog']) == ['catdog']\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa', 'aaaaa']) == ['aa', 'aaa', 'aaaa', 'aaaaa']\n assert candidate(words = ['fish', 'dog', 'cat', 'dogfishcat']) == ['dogfishcat']\n assert candidate(words = ['a', 'aa', 'aaa', 'aaaa']) == ['aa', 'aaa', 'aaaa']\n assert candidate(words = ['word', 'world', 'wordworld', 'worldword', 'wordworldword']) == ['wordworld', 'worldword', 'wordworldword']\n assert candidate(words = ['apple', 'banana', 'applepie', 'apples', 'pineapple', 'pine', 'pie']) == ['applepie', 'pineapple']\n assert candidate(words = ['ab', 'abc', 'abcd', 'abcde', 'abcdef']) == []\n assert candidate(words = ['cat', 'cats', 'catsdogcats', 'dog', 'dogcatsdog', 'hippopotamuses', 'rat', 'ratcatdogcat']) == ['dogcatsdog', 'catsdogcats', 'ratcatdogcat']\n assert candidate(words = ['hello', 'world', 'helloworld']) == ['helloworld']\n assert candidate(words = ['apple', 'banana', 'appbanana', 'banapple']) == []\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananasplit', 'applesplit', 'splitbananaapple']) == ['applebanana']\n assert candidate(words = ['a', 'b', 'ab', 'abc', 'bc', 'abcd']) == ['ab', 'abc']\n assert candidate(words = ['one', 'two', 'three', 'onetwo', 'twotwo', 'twoone', 'onetwothree', 'threetwoone', 'onetwoonetwo', 'twoonetwoone', 'onethree', 'threeone', 'onethreeone', 'threeoneone', 'threeonetwo', 'twothreeone', 'onetwothreeone', 'onetwoonetwothree']) == ['onetwo', 'twotwo', 'twoone', 'onethree', 'threeone', 'onetwothree', 'threetwoone', 'onethreeone', 'threeoneone', 'threeonetwo', 'twothreeone', 'onetwoonetwo', 'twoonetwoone', 'onetwothreeone', 'onetwoonetwothree']\n assert candidate(words = ['car', 'race', 'racecar', 'carrace', 'racecarrace', 'racecarcar']) == ['racecar', 'carrace', 'racecarcar', 'racecarrace']\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananaapple', 'grape', 'pineapple', 'pineappleapple', 'applegrapebanana']) == ['applebanana', 'bananaapple', 'pineappleapple', 'applegrapebanana']\n assert candidate(words = ['red', 'blue', 'green', 'redblue', 'bluegreen', 'greenred', 'redgreengreen', 'blueredblueblue', 'greenredblue']) == ['redblue', 'greenred', 'bluegreen', 'greenredblue', 'redgreengreen', 'blueredblueblue']\n assert candidate(words = ['base', 'ball', 'baseball', 'ballbase', 'baseballbase', 'basebaseball', 'baseballball', 'baseballbaseball']) == ['baseball', 'ballbase', 'baseballbase', 'basebaseball', 'baseballball', 'baseballbaseball']\n assert candidate(words = ['sun', 'moon', 'sunny', 'moonlight', 'sunmoon', 'moonsun', 'sunnyday', 'moonlightnight', 'sunmoonlight']) == ['sunmoon', 'moonsun', 'sunmoonlight']\n assert candidate(words = ['one', 'two', 'three', 'onetwo', 'twotwo', 'threeone', 'onetwothree', 'twothreeone', 'threeonetwo', 'onetwothreeone']) == ['onetwo', 'twotwo', 'threeone', 'onetwothree', 'twothreeone', 'threeonetwo', 'onetwothreeone']\n assert candidate(words = ['hello', 'world', 'helloworld', 'worldhello', 'hellohello', 'worldworld', 'hellohellohello', 'worldworldworld']) == ['helloworld', 'worldhello', 'hellohello', 'worldworld', 'hellohellohello', 'worldworldworld']\n assert candidate(words = ['hello', 'world', 'helloworld', 'worldhello', 'hellohello', 'worldworld', 'helloworldhello', 'worldhelloworld']) == ['helloworld', 'worldhello', 'hellohello', 'worldworld', 'helloworldhello', 'worldhelloworld']\n assert candidate(words = ['ab', 'abc', 'ababc', 'abcabc', 'aabbcc', 'aabbaabb']) == ['ababc', 'abcabc']\n assert candidate(words = ['short', 'long', 'shortlong', 'longshort', 'shortshortlong', 'longlongshort', 'shortlongshort', 'longshortlong']) == ['shortlong', 'longshort', 'longlongshort', 'longshortlong', 'shortshortlong', 'shortlongshort']\n assert candidate(words = ['prefix', 'suffix', 'prefixsuffix', 'suffixprefix', 'prefixprefix', 'suffixsuffix', 'prefixprefixsuffix', 'suffixprefixprefix']) == ['prefixsuffix', 'suffixprefix', 'prefixprefix', 'suffixsuffix', 'prefixprefixsuffix', 'suffixprefixprefix']\n assert candidate(words = ['prefix', 'suffix', 'prefixsuffix', 'suffixprefix', 'prefixsuffixprefix', 'suffixprefixsuffix', 'prefixsuffixsuffixprefix', 'suffixprefixprefixsuffix']) == ['prefixsuffix', 'suffixprefix', 'prefixsuffixprefix', 'suffixprefixsuffix', 'prefixsuffixsuffixprefix', 'suffixprefixprefixsuffix']\n assert candidate(words = ['cat', 'dog', 'catdog', 'dogcat', 'bird', 'catdogbird', 'dogcatbird', 'catbird', 'birdcat', 'dogdogcat', 'catcatdog', 'dogcatdog', 'catdogcat', 'birdbird', 'catbirdcat', 'dogcatdogcat', 'birdcatdogbird']) == ['catdog', 'dogcat', 'catbird', 'birdcat', 'birdbird', 'dogdogcat', 'catcatdog', 'dogcatdog', 'catdogcat', 'catdogbird', 'dogcatbird', 'catbirdcat', 'dogcatdogcat', 'birdcatdogbird']\n assert candidate(words = ['short', 'longer', 'longerword', 'wordlonger', 'shortword', 'wordshort', 'shortshortshort', 'longerlongerlonger']) == ['shortshortshort', 'longerlongerlonger']\n assert candidate(words = ['repetition', 'reprepetition', 'prepetition', 'rep', 'pre', 'replication', 'prepresentation', 'replicationrepetition', 'repetitionreplicationrepetition']) == ['reprepetition', 'replicationrepetition', 'repetitionreplicationrepetition']\n assert candidate(words = ['prefix', 'suffix', 'prefixsuffix', 'suffixprefix', 'prefixsuffixprefix', 'suffixprefixsuffix', 'prefixsuffixsuffixprefix', 'prefixprefixsuffix', 'suffixsuffixprefix']) == ['prefixsuffix', 'suffixprefix', 'prefixsuffixprefix', 'suffixprefixsuffix', 'prefixprefixsuffix', 'suffixsuffixprefix', 'prefixsuffixsuffixprefix']\n assert candidate(words = ['aaaa', 'aaaab', 'aaaaba', 'aaaabaaa', 'aaaabaaaa', 'aaaaa', 'aaaaaa', 'aaaaaaa', 'aaaaaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']) == ['aaaaaaaa', 'aaaabaaaa', 'aaaaaaaaa', 'aaaaaaaaaa']\n assert candidate(words = ['red', 'blue', 'redblue', 'bluered', 'redbluered', 'blueredblue', 'redredblue', 'blueredred']) == ['redblue', 'bluered', 'redbluered', 'redredblue', 'blueredred', 'blueredblue']\n assert candidate(words = ['sun', 'moon', 'star', 'sunnymoon', 'moonstar', 'star', 'sunmoonstar', 'moonmoonsun']) == ['star', 'moonstar', 'sunmoonstar', 'moonmoonsun']\n assert candidate(words = ['ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij', 'abcdefghijk', 'abcdefghijkl', 'abcdefghijklm']) == []\n assert candidate(words = ['a', 'b', 'ab', 'ba', 'aba', 'baba', 'abab', 'bababa', 'abababa', 'babababa']) == ['ab', 'ba', 'aba', 'baba', 'abab', 'bababa', 'abababa', 'babababa']\n assert candidate(words = ['abcd', 'bcde', 'cdef', 'defg', 'efgh', 'fghi', 'ghij', 'hijk', 'ijkl', 'jklm', 'klmn', 'lmno', 'mnop', 'nopq', 'opqr', 'pqrs', 'qrst', 'rstu', 'stuv', 'tuvw', 'uvwx', 'vwxy', 'wxyz', 'xyz', 'mnopqr', 'qrstuv', 'vwxyz', 'mnopqrstuv', 'mnopqrstuvwxy', 'nopqrstuvwxyz']) == ['mnopqrstuv', 'nopqrstuvwxyz']\n assert candidate(words = ['tiny', 'medium', 'mediumtiny', 'tinytiny', 'tinymedium', 'mediummedium', 'mediumtinytiny', 'tinytinytiny', 'tinytinytinytiny', 'tinytinytinytinytiny']) == ['tinytiny', 'mediumtiny', 'tinymedium', 'mediummedium', 'tinytinytiny', 'mediumtinytiny', 'tinytinytinytiny', 'tinytinytinytinytiny']\n assert candidate(words = ['word', 'concatenate', 'wordconcatenate', 'concatenateword', 'wordconcatenateword', 'wordwordconcatenate', 'concatenatethree', 'concatenateconcatenate', 'wordconcatenateconcatenate']) == ['wordconcatenate', 'concatenateword', 'wordconcatenateword', 'wordwordconcatenate', 'concatenateconcatenate', 'wordconcatenateconcatenate']\n assert candidate(words = ['alpha', 'beta', 'alphabeta', 'betabeta', 'betaalpha', 'alphabetabet', 'alphaalphabeta', 'betaalphabeta']) == ['betabeta', 'alphabeta', 'betaalpha', 'betaalphabeta', 'alphaalphabeta']\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananaapple', 'appleapplebanana', 'bananabananaapple']) == ['applebanana', 'bananaapple', 'appleapplebanana', 'bananabananaapple']\n assert candidate(words = ['aabb', 'bbaa', 'aabbcc', 'ccaabb', 'aabbaa', 'aabbccaabb', 'aabbaabbcc', 'ccccaabbaabb', 'bbccccaabbaabb', 'aabbcccaabbcccaabb']) == ['aabbccaabb', 'aabbaabbcc']\n assert candidate(words = ['one', 'two', 'three', 'onetwo', 'twotwo', 'threetwo', 'onethree', 'twothree', 'threethree', 'onetwothree', 'twothreeone', 'threetwoone', 'onetwoonetwo', 'twotwoonetwo', 'threethreethree', 'onetwothreeonetwo', 'twothreeonethree', 'threetwooneonetwo', 'onetwoonetwoonetwo']) == ['onetwo', 'twotwo', 'threetwo', 'onethree', 'twothree', 'threethree', 'onetwothree', 'twothreeone', 'threetwoone', 'onetwoonetwo', 'twotwoonetwo', 'threethreethree', 'twothreeonethree', 'onetwothreeonetwo', 'threetwooneonetwo', 'onetwoonetwoonetwo']\n assert candidate(words = ['tiny', 'small', 'tinysmall', 'smallsmall', 'tinytiny', 'tinysmalltiny']) == ['tinytiny', 'tinysmall', 'smallsmall', 'tinysmalltiny']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'abcdefg', 'abcdefabc', 'abcabcabc']) == ['abcdef', 'defabc', 'abcdefabc', 'abcabcabc']\n assert candidate(words = ['prefix', 'suffix', 'prefixsuffix', 'suffixprefix', 'prefixsuffixprefix', 'suffixprefixsuffix', 'prefixsuffixprefixsuffix']) == ['prefixsuffix', 'suffixprefix', 'prefixsuffixprefix', 'suffixprefixsuffix', 'prefixsuffixprefixsuffix']\n assert candidate(words = ['aabb', 'bbaa', 'ab', 'ba', 'aabbab', 'baabaa', 'bbaabb', 'aabbaa', 'ababab', 'babaab', 'abbaba', 'bababb', 'aabbaabb', 'bbaabaab']) == ['aabbab', 'ababab', 'babaab', 'abbaba', 'aabbaabb', 'bbaabaab']\n assert candidate(words = ['one', 'two', 'three', 'onetwo', 'twotwo', 'onetwothree', 'threethreeone', 'onetwothreeone']) == ['onetwo', 'twotwo', 'onetwothree', 'threethreeone', 'onetwothreeone']\n assert candidate(words = ['aabb', 'abab', 'bbaa', 'aabbaa', 'ababaa', 'baaabb', 'aabbab', 'bbaaab', 'aabbba', 'abababab', 'baabbaab', 'aabbaaba']) == ['abababab']\n assert candidate(words = ['abc', 'def', 'gh', 'abcdefgh', 'defgh', 'abcdefg', 'abcdefghi', 'abcdefghij', 'abcdefghijk']) == ['defgh', 'abcdefgh']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'abcabcabc', 'defdefdef', 'abcdefabcdef']) == ['abcdef', 'defabc', 'abcabcabc', 'defdefdef', 'abcdefabcdef']\n assert candidate(words = ['hello', 'world', 'helloworld', 'worldhello', 'hellotest', 'testhello', 'hellotesthello']) == ['helloworld', 'worldhello', 'hellotesthello']\n assert candidate(words = ['apple', 'apples', 'banana', 'bananas', 'applesandbananas', 'bananaapple']) == ['bananaapple']\n assert candidate(words = ['hello', 'world', 'helloworld', 'hellohello', 'worldworldhello']) == ['helloworld', 'hellohello', 'worldworldhello']\n assert candidate(words = ['one', 'onel', 'oneone', 'two', 'twotwo', 'onetwo', 'twotwoone', 'onetwoone', 'twoonetwo', 'onetwotwo', 'twoonetwotwo', 'onetwoonetwoone']) == ['oneone', 'twotwo', 'onetwo', 'twotwoone', 'onetwoone', 'twoonetwo', 'onetwotwo', 'twoonetwotwo', 'onetwoonetwoone']\n assert candidate(words = ['one', 'two', 'onetwo', 'twotwo', 'twoone', 'onetwoone', 'twoonetwo', 'onetwoonetwo']) == ['onetwo', 'twotwo', 'twoone', 'onetwoone', 'twoonetwo', 'onetwoonetwo']\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananaapple', 'grape', 'grapeapple', 'pineapple']) == ['grapeapple', 'applebanana', 'bananaapple']\n assert candidate(words = ['happy', 'sad', 'happysad', 'sadhappy', 'happyhappy', 'sadsad', 'happyhappysad', 'sadhappyhappy', 'happysadsad']) == ['sadsad', 'happysad', 'sadhappy', 'happyhappy', 'happysadsad', 'happyhappysad', 'sadhappyhappy']\n assert candidate(words = ['apple', 'banana', 'peach', 'applepie', 'bananapeach', 'peachapple']) == ['peachapple', 'bananapeach']\n assert candidate(words = ['prefix', 'suffix', 'prefixsuffix', 'suffixprefix', 'prefixprefix', 'suffixsuffix', 'prefixsuffixprefix', 'suffixprefixsuffix']) == ['prefixsuffix', 'suffixprefix', 'prefixprefix', 'suffixsuffix', 'prefixsuffixprefix', 'suffixprefixsuffix']\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananasplit', 'split', 'applebananasplit']) == ['applebanana', 'bananasplit', 'applebananasplit']\n assert candidate(words = ['abc', 'ab', 'bc', 'abcabc', 'abcab', 'ababc', 'aabbc', 'abcababc']) == ['abcab', 'ababc', 'abcabc', 'abcababc']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'abcdefdef', 'abcabcabc']) == ['abcdef', 'defabc', 'abcdefdef', 'abcabcabc']\n assert candidate(words = ['quick', 'brown', 'fox', 'quickbrown', 'brownfox', 'foxquick', 'quickbrownfox', 'brownfoxquick']) == ['brownfox', 'foxquick', 'quickbrown', 'quickbrownfox', 'brownfoxquick']\n assert candidate(words = ['tiny', 'small', 'tinytiny', 'tinysmall', 'smalltiny', 'smallsmall', 'tinytinysmall', 'tinytinysmalltiny', 'smallsml', 'tinysmalltinytiny', 'smalltinytiny', 'tinytinytiny', 'tinysmallsmallsml']) == ['tinytiny', 'tinysmall', 'smalltiny', 'smallsmall', 'tinytinytiny', 'tinytinysmall', 'smalltinytiny', 'tinytinysmalltiny', 'tinysmalltinytiny', 'tinysmallsmallsml']\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananaapple', 'appleapplebanana']) == ['applebanana', 'bananaapple', 'appleapplebanana']\n assert candidate(words = ['hello', 'world', 'helloworld', 'worldhello', 'hellohello', 'worldworld']) == ['helloworld', 'worldhello', 'hellohello', 'worldworld']\n assert candidate(words = ['repeat', 'repeated', 'repeatrepeat', 'repeatedrepeat', 'repeatrepeatedrepeat', 'repeatedrepeatrepeatedrepeat', 'repeatedrepeated', 'repeatrepeatrepeat']) == ['repeatrepeat', 'repeatedrepeat', 'repeatedrepeated', 'repeatrepeatrepeat', 'repeatrepeatedrepeat', 'repeatedrepeatrepeatedrepeat']\n assert candidate(words = ['cat', 'cats', 'catsdogcats', 'dog', 'dogcatsdog', 'hippopotamuses', 'rat', 'ratcatdogcat', 'hippo', 'popo', 'hippopop']) == ['dogcatsdog', 'catsdogcats', 'ratcatdogcat']\n assert candidate(words = ['hello', 'world', 'helloworld', 'hellohello', 'worldworld', 'hellohelloworld']) == ['helloworld', 'hellohello', 'worldworld', 'hellohelloworld']\n assert candidate(words = ['sun', 'moon', 'sunmoon', 'moonsun', 'sunsunmoon', 'moonmoonsun', 'sunmoonsunsun']) == ['sunmoon', 'moonsun', 'sunsunmoon', 'moonmoonsun', 'sunmoonsunsun']\n assert candidate(words = ['one', 'two', 'three', 'onetwo', 'twotwo', 'onethree', 'threeone', 'onetwothree', 'twothreeone']) == ['onetwo', 'twotwo', 'onethree', 'threeone', 'onetwothree', 'twothreeone']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'ghijkl', 'mnop', 'mnopqrst', 'qrst', 'mnopqrstmnopqrst', 'nopqrst', 'nopqr', 'mnopq']) == ['abcdef', 'defabc', 'mnopqrst', 'mnopqrstmnopqrst']\n assert candidate(words = ['red', 'blue', 'green', 'redblue', 'bluegreen', 'greenred', 'redbluegreen', 'bluegreenred', 'greenredblue', 'redgreenred', 'bluegreenblue', 'greenredgreen', 'redgreenbluegreen', 'bluegreenredblue', 'greenredbluegreenred']) == ['redblue', 'greenred', 'bluegreen', 'redgreenred', 'redbluegreen', 'bluegreenred', 'greenredblue', 'bluegreenblue', 'greenredgreen', 'bluegreenredblue', 'redgreenbluegreen', 'greenredbluegreenred']\n assert candidate(words = ['base', 'ball', 'baseball', 'ballbase', 'baseballbase', 'ballbaseball', 'baseballball', 'baseballbaseball']) == ['baseball', 'ballbase', 'baseballbase', 'ballbaseball', 'baseballball', 'baseballbaseball']\n assert candidate(words = ['one', 'two', 'three', 'onetwo', 'twothree', 'threeone', 'onetwothree', 'twothreeone', 'threeonetwo']) == ['onetwo', 'twothree', 'threeone', 'onetwothree', 'twothreeone', 'threeonetwo']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'abcdefghijklmnopqrstuvwxyz']) == ['abcdefghijklmnopqrstuvwxyz']\n assert candidate(words = ['apple', 'banana', 'applebanana', 'bananapple', 'bananaapplebanana']) == ['applebanana', 'bananaapplebanana']\n assert candidate(words = ['small', 'medium', 'large', 'smallmedium', 'mediumlarge', 'largesmall', 'smallmediumlarge', 'mediumlargesmall', 'largesmallmedium', 'smallmediumlargesmall']) == ['largesmall', 'smallmedium', 'mediumlarge', 'smallmediumlarge', 'mediumlargesmall', 'largesmallmedium', 'smallmediumlargesmall']\n assert candidate(words = ['a', 'ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij', 'abcdefghijk', 'abcdefghijkl', 'abcdefghijklm', 'abcdefghijklmn', 'abcdefghijklmno', 'abcdefghijklmnop', 'abcdefghijklmnopq', 'abcdefghijklmnopqr', 'abcdefghijklmnopqrs', 'abcdefghijklmnopqrst', 'abcdefghijklmnopqrstu', 'abcdefghijklmnopqrstuv', 'abcdefghijklmnopqrstuvw', 'abcdefghijklmnopqrstuvwx', 'abcdefghijklmnopqrstuvwxy', 'abcdefghijklmnopqrstuvwxyz']) == []\n assert candidate(words = ['bat', 'ball', 'batball', 'ballbat', 'batbatbat', 'ballballball', 'batballbat']) == ['batball', 'ballbat', 'batbatbat', 'batballbat', 'ballballball']\n assert candidate(words = ['partone', 'parttwo', 'partthree', 'onetwo', 'twothree', 'onetwothree', 'threeonetwo', 'twopartone', 'threeparttwo', 'onetwothreeonetwo']) == ['onetwothreeonetwo']\n assert candidate(words = ['x', 'xx', 'xxx', 'xxxx', 'xxxxx', 'xxxxxx', 'xxxxxxx', 'xxxxxxxx', 'xxxxxxxxx', 'xxxxxxxxxx']) == ['xx', 'xxx', 'xxxx', 'xxxxx', 'xxxxxx', 'xxxxxxx', 'xxxxxxxx', 'xxxxxxxxx', 'xxxxxxxxxx']\n assert candidate(words = ['alpha', 'beta', 'gamma', 'alphabeta', 'betagamma', 'alphagamma', 'betaalpha', 'gammaalpha', 'betagammabetagamma', 'gammabetagammaalpha']) == ['alphabeta', 'betagamma', 'betaalpha', 'alphagamma', 'gammaalpha', 'betagammabetagamma', 'gammabetagammaalpha']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'abcdefabc', 'abcabcabc', 'defdefdef', 'abcdefdef', 'defabcdef']) == ['abcdef', 'defabc', 'abcdefabc', 'abcabcabc', 'defdefdef', 'abcdefdef', 'defabcdef']\n assert candidate(words = ['apple', 'banana', 'appbanana', 'bananapple', 'applebananaapple']) == ['applebananaapple']\n assert candidate(words = ['sun', 'moon', 'star', 'sunset', 'moonlight', 'starlight', 'sunmoon', 'moonstar', 'sunmoonstar', 'moonstarsun']) == ['sunmoon', 'moonstar', 'sunmoonstar', 'moonstarsun']\n assert candidate(words = ['panda', 'bear', 'pandabear', 'bearpanda', 'pandapandabear', 'bearpandapanda', 'pandabearbear', 'bearbearpanda', 'pandapandapandabear', 'bearpandapandapanda']) == ['pandabear', 'bearpanda', 'pandabearbear', 'bearbearpanda', 'pandapandabear', 'bearpandapanda', 'pandapandapandabear', 'bearpandapandapanda']\n assert candidate(words = ['a', 'ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij', 'abcdefghijk', 'abcdefghijkl', 'abcdefghijklm', 'abcdefghijklmn', 'abcdefghijklmno', 'abcdefghijklmnop', 'abcdefghijklmnopq', 'abcdefghijklmnopqr', 'abcdefghijklmnopqrs', 'abcdefghijklmnopqrst']) == []\n assert candidate(words = ['abc', 'def', 'ghi', 'abcd', 'bcde', 'cdef', 'defg', 'efgh', 'fghi', 'ghij', 'hijk', 'ijkl', 'jklm', 'klmn', 'lmno', 'mnop', 'nopq', 'opqr', 'pqrs', 'qrst', 'rstu', 'stuv', 'tuvw', 'uvwxy', 'vwxyz', 'wxyzabc', 'xyzabcd', 'zabcde']) == []\n assert candidate(words = ['foo', 'bar', 'foobar', 'barfoo', 'foofoobar', 'barfoobaz', 'baz', 'foobazbar']) == ['foobar', 'barfoo', 'foofoobar', 'barfoobaz', 'foobazbar']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'ab', 'bc', 'de', 'f', 'abcd', 'cdef']) == ['def', 'abcdef', 'defabc']\n assert candidate(words = ['hello', 'world', 'helloworld', 'worldhello', 'hellohellohello', 'helloworldworld']) == ['helloworld', 'worldhello', 'hellohellohello', 'helloworldworld']\n assert candidate(words = ['apple', 'banana', 'cherry', 'applebanana', 'bananaapple', 'cherryapple', 'applecherry', 'bananaapplebanana']) == ['applebanana', 'bananaapple', 'cherryapple', 'applecherry', 'bananaapplebanana']\n assert candidate(words = ['abc', 'def', 'abcdef', 'defabc', 'fedcba', 'cab', 'bac', 'abcabc', 'defdef', 'ababab', 'defdefdef', 'abcdefgh', 'ghijklmn', 'opqrstuv', 'wxyz', 'abcdefghijk', 'lmnopqrstuv', 'wxyzabcd', 'efghijklmnopqr', 'stuvwxyzabcd']) == ['abcdef', 'defabc', 'abcabc', 'defdef', 'defdefdef']\n"}, "metadata": {"canonical_parameter_names": ["words"], "leetcode_dataset_entry_point": "Solution().findAllConcatenatedWordsInADict", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findAllConcatenatedWordsInADict = function(words) {", "container": null, "callable": "findAllConcatenatedWordsInADict", "parameters": [{"name": "words", "type": "string[]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 473, "task_id": "matchsticks-to-square", "difficulty": "Medium", "problem_description": "You are given an integer array matchsticks where matchsticks[i] is the length of the ith matchstick. You want to use all the matchsticks to make one square. You should not break any stick, but you can link them up, and each matchstick must be used exactly one time.\nReturn true if you can make this square and false otherwise.\n \nExample 1:\n\n\nInput: matchsticks = [1,1,2,2,2]\nOutput: true\nExplanation: You can form a square with length 2, one side of the square came two sticks with length 1.\n\nExample 2:\n\nInput: matchsticks = [3,3,3,3,4]\nOutput: false\nExplanation: You cannot find a way to form a square with all the matchsticks.\n\n \nConstraints:\n\n1 <= matchsticks.length <= 15\n1 <= matchsticks[i] <= 108\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(matchsticks = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3]) == True\n assert candidate(matchsticks = [10, 10, 10, 10]) == True\n assert candidate(matchsticks = [5, 5, 5, 5]) == True\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == True\n assert candidate(matchsticks = [1, 3, 3, 3, 4]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 2, 2, 2, 2]) == True\n assert candidate(matchsticks = [1, 1, 2, 2, 2]) == True\n assert candidate(matchsticks = [1, 2, 3, 4, 5]) == False\n assert candidate(matchsticks = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 4, 4, 4, 4]) == True\n assert candidate(matchsticks = [3, 3, 3, 3, 4]) == False\n assert candidate(matchsticks = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == False\n assert candidate(matchsticks = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8]) == True\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(matchsticks = [2, 2, 2, 2, 2, 2, 2, 2]) == True\n assert candidate(matchsticks = [7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == False\n assert candidate(matchsticks = [10, 20, 30, 40, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(matchsticks = [1, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == False\n assert candidate(matchsticks = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == False\n assert candidate(matchsticks = [7, 8, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12]) == False\n assert candidate(matchsticks = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) == False\n assert candidate(matchsticks = [20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 80]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 5]) == False\n assert candidate(matchsticks = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 30]) == False\n assert candidate(matchsticks = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1]) == False\n assert candidate(matchsticks = [100000000, 100000000, 100000000, 100000000, 25000000, 25000000, 25000000, 25000000]) == True\n assert candidate(matchsticks = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == False\n assert candidate(matchsticks = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8]) == False\n assert candidate(matchsticks = [15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1]) == False\n assert candidate(matchsticks = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8]) == True\n assert candidate(matchsticks = [2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 12, 13, 14, 15]) == True\n assert candidate(matchsticks = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4]) == True\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5]) == False\n assert candidate(matchsticks = [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3]) == True\n assert candidate(matchsticks = [10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(matchsticks = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8]) == True\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 100]) == False\n assert candidate(matchsticks = [10, 10, 10, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2]) == False\n assert candidate(matchsticks = [100, 100, 100, 100, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25]) == False\n assert candidate(matchsticks = [100000000, 100000000, 100000000, 100000000, 25000000, 25000000, 25000000, 25000000, 25000000, 25000000, 25000000, 25000000, 25000000, 25000000, 25000000]) == False\n assert candidate(matchsticks = [100000000, 100000000, 100000000, 100000000, 1]) == False\n assert candidate(matchsticks = [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6]) == False\n assert candidate(matchsticks = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == False\n assert candidate(matchsticks = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 5]) == False\n assert candidate(matchsticks = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 1]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == True\n assert candidate(matchsticks = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3]) == True\n assert candidate(matchsticks = [100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000, 100000000]) == False\n assert candidate(matchsticks = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == False\n assert candidate(matchsticks = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == True\n assert candidate(matchsticks = [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4]) == False\n assert candidate(matchsticks = [10, 20, 30, 40, 10, 20, 30, 40]) == True\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 28]) == False\n assert candidate(matchsticks = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 1]) == False\n assert candidate(matchsticks = [2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5]) == False\n assert candidate(matchsticks = [15, 15, 15, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 15]) == False\n assert candidate(matchsticks = [10, 20, 30, 40, 50, 15, 5, 25, 35]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == True\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]) == True\n assert candidate(matchsticks = [8, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(matchsticks = [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 32]) == False\n assert candidate(matchsticks = [15, 15, 15, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == False\n assert candidate(matchsticks = [100000000, 100000000, 100000000, 100000000]) == True\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1]) == False\n assert candidate(matchsticks = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 20]) == False\n assert candidate(matchsticks = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 1]) == False\n assert candidate(matchsticks = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1]) == False\n assert candidate(matchsticks = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 20]) == False\n assert candidate(matchsticks = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == True\n"}, "metadata": {"canonical_parameter_names": ["matchsticks"], "leetcode_dataset_entry_point": "Solution().makesquare", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var makesquare = function(matchsticks) {", "container": null, "callable": "makesquare", "parameters": [{"name": "matchsticks", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 474, "task_id": "ones-and-zeroes", "difficulty": "Medium", "problem_description": "You are given an array of binary strings strs and two integers m and n.\nReturn the size of the largest subset of strs such that there are at most m 0's and n 1's in the subset.\nA set x is a subset of a set y if all elements of x are also elements of y.\n \nExample 1:\n\nInput: strs = [\"10\",\"0001\",\"111001\",\"1\",\"0\"], m = 5, n = 3\nOutput: 4\nExplanation: The largest subset with at most 5 0's and 3 1's is {\"10\", \"0001\", \"1\", \"0\"}, so the answer is 4.\nOther valid but smaller subsets include {\"0001\", \"1\"} and {\"10\", \"1\", \"0\"}.\n{\"111001\"} is an invalid subset because it contains 4 1's, greater than the maximum of 3.\n\nExample 2:\n\nInput: strs = [\"10\",\"0\",\"1\"], m = 1, n = 1\nOutput: 2\nExplanation: The largest subset is {\"0\", \"1\"}, so the answer is 2.\n\n \nConstraints:\n\n1 <= strs.length <= 600\n1 <= strs[i].length <= 100\nstrs[i] consists only of digits '0' and '1'.\n1 <= m, n <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(strs = ['0', '0', '1', '1'],m = 2,n = 2) == 4\n assert candidate(strs = ['111', '000', '101010'],m = 3,n = 3) == 2\n assert candidate(strs = ['10', '0', '1'],m = 1,n = 1) == 2\n assert candidate(strs = ['111', '000', '1010', '0101'],m = 3,n = 3) == 2\n assert candidate(strs = ['110', '100', '001'],m = 2,n = 2) == 1\n assert candidate(strs = ['110', '100', '010'],m = 2,n = 2) == 1\n assert candidate(strs = ['1', '10', '100', '1000'],m = 4,n = 4) == 3\n assert candidate(strs = ['111111', '000000'],m = 3,n = 3) == 0\n assert candidate(strs = ['0', '0', '0', '0'],m = 0,n = 4) == 0\n assert candidate(strs = ['1111', '1010', '0101', '0000'],m = 2,n = 2) == 1\n assert candidate(strs = ['111111', '000000', '101010', '010101'],m = 3,n = 3) == 1\n assert candidate(strs = ['11111010110010001111', '01001100001100111100', '00000110011101011010', '11010011000101000011', '10011001110100010100', '00110001011100100010', '01000101110110011101'],m = 34,n = 21) == 2\n assert candidate(strs = ['0', '0', '0', '0'],m = 0,n = 0) == 0\n assert candidate(strs = ['1100', '100001111000', '000000000000001010', '11111111111111111111', '100001111000', '100001111000'],m = 31,n = 12) == 3\n assert candidate(strs = ['00', '00'],m = 1,n = 1) == 0\n assert candidate(strs = ['1101', '1101', '0010', '0000'],m = 4,n = 4) == 2\n assert candidate(strs = ['10', '0001', '111001', '1', '0'],m = 5,n = 3) == 4\n assert candidate(strs = ['101010', '010101', '110011', '001100', '111000', '000111', '1111000000', '0000111111'],m = 10,n = 10) == 3\n assert candidate(strs = ['11111', '11100', '11010', '10110', '01110', '10011', '01011', '00111', '11110', '11001', '10101', '01101'],m = 9,n = 9) == 3\n assert candidate(strs = ['111000', '000111', '111100', '000011', '111111', '000000', '101010'],m = 5,n = 5) == 1\n assert candidate(strs = ['10101010', '01010101', '11110000', '00001111', '11001100', '00110011'],m = 8,n = 8) == 2\n assert candidate(strs = ['1111110', '1010101', '0101010', '0000000', '1111111', '1000001', '0011110'],m = 6,n = 6) == 1\n assert candidate(strs = ['1010101010', '0101010101', '1111111111', '0000000000'],m = 5,n = 5) == 1\n assert candidate(strs = ['0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', '0'],m = 10,n = 10) == 10\n assert candidate(strs = ['101', '0011', '1000', '1100', '0100', '0000'],m = 5,n = 5) == 2\n assert candidate(strs = ['1010101010', '0101010101', '1111100000', '0000011111', '1100110011'],m = 10,n = 10) == 2\n assert candidate(strs = ['1010101010', '0101010101', '1110000000', '0001111111', '1100110011', '0011001100', '1011000101', '0100111010', '1111000011', '0000111100'],m = 12,n = 12) == 2\n assert candidate(strs = ['110000', '001100', '101010', '010101', '111100', '000011', '101001'],m = 6,n = 6) == 2\n assert candidate(strs = ['1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0'],m = 10,n = 10) == 20\n assert candidate(strs = ['111111111', '000000000', '101010101', '010101010', '111000011', '000111100'],m = 7,n = 7) == 1\n assert candidate(strs = ['110', '100', '001', '100', '001', '001', '010', '101', '100', '001', '001', '100', '001', '101', '010', '101', '101', '010', '100', '001'],m = 6,n = 6) == 4\n assert candidate(strs = ['1110000', '0001111', '1100110', '0011001', '1011000', '0100111', '1000000', '0111111', '1101010', '0010101'],m = 10,n = 10) == 2\n assert candidate(strs = ['1111111111', '1111111111', '1111111111', '1111111111', '1111111111', '1111111111', '1111111111', '1111111111', '1111111111', '1111111111'],m = 5,n = 5) == 0\n assert candidate(strs = ['111110', '110101', '010110', '110001', '101000', '000011', '011101'],m = 6,n = 6) == 2\n assert candidate(strs = ['1100', '1010', '0011', '0101', '1111', '0000', '1000', '0111', '1101', '1011'],m = 6,n = 6) == 3\n assert candidate(strs = ['000000', '111111', '000000', '111111', '000000', '111111', '000000', '111111', '000000', '111111', '000000', '111111', '000000', '111111', '000000', '111111'],m = 8,n = 8) == 2\n assert candidate(strs = ['1010101', '0101010', '1110000', '0001111', '1100110', '0011001', '1011000', '0100111'],m = 6,n = 6) == 1\n assert candidate(strs = ['1001', '0110', '1010', '0011', '1111', '0000', '1100', '0010', '1000', '0100'],m = 5,n = 5) == 2\n assert candidate(strs = ['11111111', '10101010', '01010101', '00000000', '11000011', '00110011', '10001100'],m = 8,n = 8) == 2\n assert candidate(strs = ['111', '110', '101', '011', '100', '010', '001', '000', '1111', '0000', '1010', '0101'],m = 7,n = 7) == 4\n assert candidate(strs = ['1101010', '1010101', '0011001', '0100110', '1110000', '0001111'],m = 8,n = 8) == 2\n assert candidate(strs = ['111110', '000011', '101010', '010101', '111000', '000111'],m = 6,n = 6) == 2\n assert candidate(strs = ['0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1', '0', '1'],m = 12,n = 12) == 24\n assert candidate(strs = ['1111111111', '1111111111', '1111111111', '1111111111', '0000000000', '0000000000', '0000000000', '0000000000', '0000000000', '0000000000'],m = 5,n = 5) == 0\n assert candidate(strs = ['11000', '10011', '00100', '01101', '11111'],m = 5,n = 5) == 2\n assert candidate(strs = ['1111111111', '0000000000', '1010101010', '0101010101', '1110000111', '0001111000'],m = 8,n = 8) == 1\n assert candidate(strs = ['1100101', '0000000', '1010101', '1110111', '0001000'],m = 5,n = 5) == 1\n assert candidate(strs = ['1010101010', '0101010101', '1111000000', '0000111111', '1100110011', '0011001100'],m = 5,n = 5) == 1\n assert candidate(strs = ['101010101010101010', '010101010101010101', '111100000000000000', '000011111111111111', '110011001100110011', '001100110011001100'],m = 10,n = 10) == 1\n assert candidate(strs = ['11011', '10010', '01001', '10000', '00111', '01010', '10001'],m = 4,n = 4) == 1\n assert candidate(strs = ['001', '010', '100', '111', '000', '110', '011'],m = 3,n = 3) == 2\n assert candidate(strs = ['1010101010101010101010101010', '0101010101010101010101010101', '1111111111111111111111111111', '0000000000000000000000000000'],m = 10,n = 10) == 0\n assert candidate(strs = ['111100', '111000', '100000', '000111', '001010', '110101'],m = 6,n = 4) == 1\n assert candidate(strs = ['11001100', '00110011', '11110000', '00001111', '10101010', '01010101'],m = 8,n = 8) == 2\n assert candidate(strs = ['11001010', '00010101', '10101010', '00110011', '10111011', '01000100'],m = 6,n = 6) == 1\n assert candidate(strs = ['1101', '0110', '1010', '0010', '1111'],m = 4,n = 3) == 1\n assert candidate(strs = ['1111000000', '0000111100', '1100110000', '0011001100', '1010101000', '0101010100', '1110001100', '0001110011'],m = 10,n = 10) == 2\n assert candidate(strs = ['1101010', '0101110', '1010101', '0011010', '1110000', '0001111', '1111100', '0000011'],m = 8,n = 8) == 2\n assert candidate(strs = ['111000111', '000111000', '110011001', '001100110', '101010101'],m = 6,n = 5) == 1\n assert candidate(strs = ['11000', '01110', '00010', '10011', '00001'],m = 5,n = 5) == 2\n assert candidate(strs = ['1110101', '0001100', '1100011', '0101010', '0010101', '1011010'],m = 8,n = 8) == 2\n assert candidate(strs = ['10101', '01010', '11001', '00110', '11111', '00000'],m = 5,n = 5) == 2\n assert candidate(strs = ['11111111', '00000000', '11000000', '00111111', '10101010', '01010101'],m = 10,n = 10) == 2\n assert candidate(strs = ['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1'],m = 10,n = 10) == 10\n assert candidate(strs = ['11111', '00000', '11000', '00111', '10101', '01010'],m = 4,n = 4) == 1\n assert candidate(strs = ['1111111111', '0000000000', '1111000000', '0000111111', '1110110011', '0001001100', '1011000101', '0100111010', '1111000011', '0000111100', '1010101010', '0101010101', '1101010010', '0010101101'],m = 10,n = 10) == 2\n assert candidate(strs = ['11111111', '00000000', '10101010', '01010101', '11001100', '00110011', '10010010', '01101101'],m = 10,n = 10) == 2\n assert candidate(strs = ['1111111111', '0000000000', '1100110011', '0011001100', '1010101010', '0101010101'],m = 8,n = 8) == 1\n assert candidate(strs = ['110000', '000011', '110000', '000011', '110000', '000011', '110000', '000011'],m = 6,n = 6) == 1\n assert candidate(strs = ['011101', '111111', '010101', '000001', '101011'],m = 5,n = 5) == 1\n assert candidate(strs = ['11110000', '00001111', '10101010', '01010101', '11001100', '00110011', '10011001', '01100110'],m = 8,n = 8) == 2\n assert candidate(strs = ['1001001', '0110110', '1111000', '0000111', '1010101', '0101010'],m = 6,n = 6) == 1\n assert candidate(strs = ['1110101', '1000110', '0111000', '0000111', '1010100', '0010011', '1001100'],m = 7,n = 7) == 1\n assert candidate(strs = ['11000', '10011', '01110', '00101', '10110', '11101'],m = 7,n = 7) == 2\n assert candidate(strs = ['111111', '000000', '111000', '000111', '101010', '010101', '110101'],m = 4,n = 5) == 1\n assert candidate(strs = ['1', '0', '11', '00', '10', '01', '1010', '0101'],m = 5,n = 5) == 6\n assert candidate(strs = ['101010101', '010101010', '111000000', '000111111', '110011001', '001100110', '100100100', '011011011'],m = 8,n = 8) == 1\n assert candidate(strs = ['111000', '000111', '110011', '010101', '101010'],m = 4,n = 4) == 1\n assert candidate(strs = ['1010101', '0101010', '1100110', '0011001', '1111000', '0000111'],m = 7,n = 7) == 2\n assert candidate(strs = ['111111', '000000', '110011', '010101', '101010', '001100', '110001', '000111'],m = 4,n = 4) == 1\n assert candidate(strs = ['1010101010', '0101010101', '1110000000', '0001111111', '1100110011', '0011001100', '1011000101', '0100111010', '1111000011', '0000111100', '1010101010', '0101010101'],m = 15,n = 15) == 3\n assert candidate(strs = ['11001100', '00110011', '10101010', '01010101', '11110000', '00001111', '10001000', '01110111'],m = 10,n = 10) == 2\n assert candidate(strs = ['101010101010', '010101010101', '111100000000', '000011111111', '110011001100', '001100110011'],m = 6,n = 6) == 1\n assert candidate(strs = ['10101010101010101010', '01010101010101010101', '11100000000000000000', '00011111111111111111', '11001100110011001100', '00110011001100110011', '10110001010101010101', '01001110101010101010', '11110000110000110000', '00001111001111001111'],m = 20,n = 20) == 2\n assert candidate(strs = ['010101010101', '101010101010', '111111000000', '000000111111', '110011001100'],m = 12,n = 12) == 2\n assert candidate(strs = ['1010101010', '0101010101', '1111000000', '0000111111', '1010101010', '0101010101', '1111000000', '0000111111'],m = 8,n = 8) == 1\n assert candidate(strs = ['110010', '010101', '100100', '111001', '001101', '110011'],m = 7,n = 6) == 2\n assert candidate(strs = ['110101', '101001', '001100', '111000', '000110'],m = 5,n = 5) == 1\n assert candidate(strs = ['110010', '1001', '110', '00010', '1'],m = 5,n = 4) == 3\n assert candidate(strs = ['1101101', '1010101', '0000001', '1111111', '0000000', '1010101'],m = 7,n = 7) == 2\n assert candidate(strs = ['110101', '100110', '101010', '111100', '000111', '010001'],m = 6,n = 6) == 2\n assert candidate(strs = ['00000', '11111', '10101', '01010', '11000', '00111'],m = 6,n = 6) == 2\n assert candidate(strs = ['010101010101', '101010101010', '111111111111', '000000000000', '110011001100', '001100110011'],m = 10,n = 10) == 1\n assert candidate(strs = ['1101010101', '1010101010', '0011001100', '1111111111', '0000000000', '1010101010', '0101010101', '1111000000'],m = 12,n = 12) == 2\n assert candidate(strs = ['1', '0', '11', '00', '101', '010', '110', '001', '111', '000'],m = 6,n = 6) == 6\n assert candidate(strs = ['111001101', '100110100', '011010101', '000111000', '111100001', '101010101', '010101010', '001001001', '110110110'],m = 9,n = 9) == 2\n assert candidate(strs = ['111000', '000111', '101010', '010101', '110011', '001100', '110100', '001011', '100110', '011001'],m = 10,n = 10) == 3\n assert candidate(strs = ['1111111111', '0000000000', '1010101010', '0101010101', '1100110011', '0011001100'],m = 8,n = 8) == 1\n assert candidate(strs = ['111000', '000111', '101010', '010101', '110010', '001101', '100100'],m = 8,n = 8) == 2\n assert candidate(strs = ['101010', '000000', '111111', '100100', '011011'],m = 5,n = 4) == 1\n assert candidate(strs = ['11110000', '00001111', '11101100', '00010011', '11010100', '00101011', '10111000', '01000111'],m = 8,n = 8) == 2\n assert candidate(strs = ['111111', '110000', '001111', '000011', '101010', '010101', '111000', '000111', '101010', '010101', '110011', '001100'],m = 12,n = 12) == 4\n assert candidate(strs = ['111111', '101010', '010101', '000000', '110011'],m = 3,n = 3) == 1\n assert candidate(strs = ['1111111', '0000000', '1110000', '0001111', '1010101', '0101010'],m = 5,n = 5) == 1\n assert candidate(strs = ['111100000', '000011111', '110011000', '001100111', '101010101', '010101010', '111000111', '000111000', '100100110', '011011001'],m = 10,n = 10) == 2\n assert candidate(strs = ['110', '100', '001', '000', '111', '011', '110', '101', '010', '100', '000', '001', '111', '101', '011', '110', '101', '010'],m = 10,n = 10) == 6\n assert candidate(strs = ['10000111', '01111000', '11100011', '00011100', '10101010', '01010101', '11010101', '00101010'],m = 12,n = 12) == 3\n assert candidate(strs = ['1100000000', '0011111111', '1010101010', '0101010101', '1110001110', '0001110001', '1101011011'],m = 7,n = 7) == 1\n assert candidate(strs = ['11001010', '1001111', '00010', '1010', '111', '0000000'],m = 6,n = 6) == 3\n assert candidate(strs = ['101010', '010101', '111111', '000000', '110000', '001100'],m = 4,n = 4) == 1\n"}, "metadata": {"canonical_parameter_names": ["strs", "m", "n"], "leetcode_dataset_entry_point": "Solution().findMaxForm", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMaxForm = function(strs, m, n) {", "container": null, "callable": "findMaxForm", "parameters": [{"name": "strs", "type": "string[]"}, {"name": "m", "type": "number"}, {"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 475, "task_id": "heaters", "difficulty": "Medium", "problem_description": "Winter is coming! During the contest, your first job is to design a standard heater with a fixed warm radius to warm all the houses.\nEvery house can be warmed, as long as the house is within the heater's warm radius range. \nGiven the positions of houses and heaters on a horizontal line, return the minimum radius standard of heaters so that those heaters could cover all houses.\nNotice that all the heaters follow your radius standard, and the warm radius will the same.\n \nExample 1:\n\nInput: houses = [1,2,3], heaters = [2]\nOutput: 1\nExplanation: The only heater was placed in the position 2, and if we use the radius 1 standard, then all the houses can be warmed.\n\nExample 2:\n\nInput: houses = [1,2,3,4], heaters = [1,4]\nOutput: 1\nExplanation: The two heaters were placed at positions 1 and 4. We need to use a radius 1 standard, then all the houses can be warmed.\n\nExample 3:\n\nInput: houses = [1,5], heaters = [2]\nOutput: 3\n\n \nConstraints:\n\n1 <= houses.length, heaters.length <= 3 * 104\n1 <= houses[i], heaters[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(houses = [1, 5],heaters = [2]) == 3\n assert candidate(houses = [1],heaters = [1]) == 0\n assert candidate(houses = [10, 20, 30, 40, 50],heaters = [15, 45]) == 15\n assert candidate(houses = [10, 20, 30, 40, 50],heaters = [5, 15, 25, 35, 45]) == 5\n assert candidate(houses = [1, 3, 5, 7, 9],heaters = [2, 6]) == 3\n assert candidate(houses = [1, 3, 5, 7, 9],heaters = [2, 6, 10]) == 1\n assert candidate(houses = [28, 8, 9, 26, 18, 25, 13, 19, 16, 11, 27, 24, 23, 17, 15, 22, 6, 10, 5, 3],heaters = [20, 1, 15, 10]) == 8\n assert candidate(houses = [10, 20, 30, 40, 50],heaters = [15, 25, 35, 45]) == 5\n assert candidate(houses = [1, 2, 3, 4, 5],heaters = [1, 5]) == 2\n assert candidate(houses = [1, 1000000000],heaters = [500000000]) == 500000000\n assert candidate(houses = [1, 2, 3],heaters = [2]) == 1\n assert candidate(houses = [1, 3, 5, 7, 9],heaters = [2, 6, 8]) == 1\n assert candidate(houses = [282475249, 622690073, 984943658, 144108930, 470211272, 101027544, 457850878, 458777923],heaters = [823564440, 115438165, 784484492, 74243042, 114807987, 137522503, 441282327, 622890097, 429201176]) == 161379218\n assert candidate(houses = [1, 3, 5, 7, 9],heaters = [2, 8]) == 3\n assert candidate(houses = [1, 2, 3, 4, 5],heaters = [3]) == 2\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],heaters = [1, 10]) == 4\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9],heaters = [1, 9]) == 4\n assert candidate(houses = [10, 20, 30, 40, 50],heaters = [15, 35]) == 15\n assert candidate(houses = [1, 2, 3, 4],heaters = [1, 4]) == 1\n assert candidate(houses = [1, 4, 6, 9],heaters = [1, 10]) == 4\n assert candidate(houses = [1, 9],heaters = [5]) == 4\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],heaters = [2, 6, 10, 14, 18]) == 1\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [5, 55, 105]) == 25\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],heaters = [25, 55, 85, 115, 145]) == 15\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],heaters = [5]) == 5\n assert candidate(houses = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97],heaters = [1, 97]) == 48\n assert candidate(houses = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [150, 350, 550, 750, 950]) == 50\n assert candidate(houses = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [200, 400, 600, 800]) == 200\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49],heaters = [25, 50]) == 24\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [10, 100]) == 40\n assert candidate(houses = [100, 150, 200, 250, 300, 350, 400, 450, 500],heaters = [200, 400]) == 100\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [15, 25, 35, 45, 55, 65, 75, 85, 95]) == 5\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],heaters = [15, 45, 75, 105, 135]) == 15\n assert candidate(houses = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000],heaters = [500000000]) == 500000000\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49],heaters = [10, 20, 30, 40]) == 9\n assert candidate(houses = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [500]) == 500\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 50],heaters = [1, 25, 50]) == 12\n assert candidate(houses = [1, 5, 10, 20, 30, 50, 60, 80, 90, 100],heaters = [15, 45, 75]) == 25\n assert candidate(houses = [1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],heaters = [10, 60, 100]) == 25\n assert candidate(houses = [1, 5, 10, 15, 20],heaters = [12, 25]) == 11\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],heaters = [10, 20, 30]) == 9\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [1, 99]) == 49\n assert candidate(houses = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],heaters = [10, 40, 70, 100]) == 15\n assert candidate(houses = [1, 100, 200, 300, 400, 500],heaters = [50, 250, 450]) == 50\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],heaters = [2, 10, 18, 26]) == 3\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],heaters = [1, 8, 15]) == 3\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],heaters = [8, 22, 48]) == 13\n assert candidate(houses = [1, 5, 9, 15, 20, 25, 30, 35, 40],heaters = [10, 20, 30]) == 10\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],heaters = [2, 6, 14, 18]) == 3\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [5, 10, 15, 20]) == 4\n assert candidate(houses = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],heaters = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 1\n assert candidate(houses = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [50, 150, 250, 350, 450, 550, 650, 750, 850, 950]) == 50\n assert candidate(houses = [5, 15, 25, 35, 45, 55],heaters = [10, 40]) == 15\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [5, 15]) == 5\n assert candidate(houses = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],heaters = [50, 150, 250]) == 50\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],heaters = [1, 3, 5, 7, 9, 11, 13, 15]) == 1\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [1, 20]) == 9\n assert candidate(houses = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [50, 550, 950]) == 250\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 0\n assert candidate(houses = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000],heaters = [500000000, 1000000000]) == 499999999\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],heaters = [2, 10, 18]) == 3\n assert candidate(houses = [100, 200, 300, 400, 500],heaters = [50, 250, 450]) == 50\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130],heaters = [25, 75, 125]) == 25\n assert candidate(houses = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [150, 450, 750]) == 250\n assert candidate(houses = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],heaters = [20, 40, 60, 80]) == 15\n assert candidate(houses = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],heaters = [5, 15, 25]) == 5\n assert candidate(houses = [1, 3, 5, 7, 9],heaters = [2, 4, 6, 8]) == 1\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],heaters = [10, 100, 190, 290]) == 40\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [10, 11]) == 9\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [10, 20]) == 9\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],heaters = [1, 15]) == 7\n assert candidate(houses = [1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49],heaters = [10, 30, 40]) == 9\n assert candidate(houses = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [5, 25, 45, 65, 85]) == 15\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],heaters = [10, 20, 30, 40, 50, 60, 70, 80, 90]) == 10\n assert candidate(houses = [1, 3, 7, 12, 17, 23, 30],heaters = [4, 9, 25]) == 8\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],heaters = [5, 10]) == 5\n assert candidate(houses = [1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120],heaters = [1, 60, 120]) == 30\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],heaters = [10, 20, 30]) == 9\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],heaters = [1, 30]) == 14\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],heaters = [1, 15]) == 7\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],heaters = [5, 100, 195]) == 45\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],heaters = [5, 100]) == 45\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [1, 20]) == 9\n assert candidate(houses = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],heaters = [10, 40, 70]) == 25\n assert candidate(houses = [1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50],heaters = [5, 25, 45]) == 10\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],heaters = [2, 4, 6, 8, 10, 12, 14, 16, 18]) == 1\n assert candidate(houses = [1, 1000000000],heaters = [500000000]) == 500000000\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],heaters = [1, 99]) == 49\n assert candidate(houses = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],heaters = [10, 30, 50, 70, 90]) == 5\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],heaters = [15, 45, 75]) == 25\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],heaters = [2, 6, 10, 14, 18, 22, 26]) == 3\n assert candidate(houses = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],heaters = [50, 100, 150, 200]) == 49\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],heaters = [5, 15, 25]) == 5\n assert candidate(houses = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],heaters = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 1\n assert candidate(houses = [1, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000],heaters = [50, 500, 5000, 50000, 500000, 5000000, 50000000, 500000000, 1500000000]) == 500000000\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],heaters = [5, 15, 20]) == 5\n assert candidate(houses = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],heaters = [150, 450, 750]) == 250\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],heaters = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31]) == 1\n assert candidate(houses = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],heaters = [10, 40, 80]) == 15\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130],heaters = [10, 130]) == 60\n assert candidate(houses = [1, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],heaters = [1, 50, 100]) == 25\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],heaters = [3, 7]) == 3\n assert candidate(houses = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],heaters = [25, 75, 125]) == 25\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],heaters = [7, 23, 37]) == 13\n assert candidate(houses = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],heaters = [5, 25, 45]) == 10\n assert candidate(houses = [50, 150, 250, 350, 450, 550, 650, 750, 850, 950],heaters = [100, 300, 500, 700, 900]) == 50\n assert candidate(houses = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],heaters = [3, 8, 13]) == 2\n assert candidate(houses = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],heaters = [5, 95, 195]) == 45\n"}, "metadata": {"canonical_parameter_names": ["houses", "heaters"], "leetcode_dataset_entry_point": "Solution().findRadius", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findRadius = function(houses, heaters) {", "container": null, "callable": "findRadius", "parameters": [{"name": "houses", "type": "number[]"}, {"name": "heaters", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 476, "task_id": "number-complement", "difficulty": "Easy", "problem_description": "The complement of an integer is the integer you get when you flip all the 0's to 1's and all the 1's to 0's in its binary representation.\n\nFor example, The integer 5 is \"101\" in binary and its complement is \"010\" which is the integer 2.\n\nGiven an integer num, return its complement.\n \nExample 1:\n\nInput: num = 5\nOutput: 2\nExplanation: The binary representation of 5 is 101 (no leading zero bits), and its complement is 010. So you need to output 2.\n\nExample 2:\n\nInput: num = 1\nOutput: 0\nExplanation: The binary representation of 1 is 1 (no leading zero bits), and its complement is 0. So you need to output 0.\n\n \nConstraints:\n\n1 <= num < 231\n\n \nNote: This question is the same as 1009: https://leetcode.com/problems/complement-of-base-10-integer/\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 31) == 0\n assert candidate(num = 10) == 5\n assert candidate(num = 32) == 31\n assert candidate(num = 5) == 2\n assert candidate(num = 1023) == 0\n assert candidate(num = 1) == 0\n assert candidate(num = 100) == 27\n assert candidate(num = 2147483647) == 0\n assert candidate(num = 15) == 0\n assert candidate(num = 8191) == 0\n assert candidate(num = 4294967295) == 0\n assert candidate(num = 33) == 30\n assert candidate(num = 4095) == 0\n assert candidate(num = 1048575) == 0\n assert candidate(num = 123456789) == 10760938\n assert candidate(num = 65535) == 0\n assert candidate(num = 500) == 11\n assert candidate(num = 2097151) == 0\n assert candidate(num = 131071) == 0\n assert candidate(num = 16777215) == 0\n assert candidate(num = 2147483646) == 1\n assert candidate(num = 134217728) == 134217727\n assert candidate(num = 4194303) == 0\n assert candidate(num = 2047) == 0\n assert candidate(num = 987654321) == 86087502\n assert candidate(num = 89123456) == 45094271\n assert candidate(num = 255) == 0\n assert candidate(num = 8388607) == 0\n assert candidate(num = 1024) == 1023\n assert candidate(num = 100000) == 31071\n assert candidate(num = 1073741823) == 0\n assert candidate(num = 262143) == 0\n assert candidate(num = 268435455) == 0\n assert candidate(num = 123456) == 7615\n assert candidate(num = 1000000) == 48575\n assert candidate(num = 8) == 7\n assert candidate(num = 32767) == 0\n assert candidate(num = 524287) == 0\n assert candidate(num = 134217727) == 0\n assert candidate(num = 4294967294) == 1\n assert candidate(num = 33554431) == 0\n assert candidate(num = 536870911) == 0\n assert candidate(num = 67108863) == 0\n assert candidate(num = 1073741824) == 1073741823\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().findComplement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findComplement = function(num) {", "container": null, "callable": "findComplement", "parameters": [{"name": "num", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 477, "task_id": "total-hamming-distance", "difficulty": "Medium", "problem_description": "The Hamming distance between two integers is the number of positions at which the corresponding bits are different.\nGiven an integer array nums, return the sum of Hamming distances between all the pairs of the integers in nums.\n \nExample 1:\n\nInput: nums = [4,14,2]\nOutput: 6\nExplanation: In binary representation, the 4 is 0100, 14 is 1110, and 2 is 0010 (just\nshowing the four bits relevant in this case).\nThe answer will be:\nHammingDistance(4, 14) + HammingDistance(4, 2) + HammingDistance(14, 2) = 2 + 2 + 2 = 6.\n\nExample 2:\n\nInput: nums = [4,14,4]\nOutput: 4\n\n \nConstraints:\n\n1 <= nums.length <= 104\n0 <= nums[i] <= 109\nThe answer for the given input will fit in a 32-bit integer.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15]) == 48\n assert candidate(nums = [4, 14, 4]) == 4\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 112\n assert candidate(nums = [31, 14, 7, 3, 1]) == 24\n assert candidate(nums = [1, 3, 5]) == 4\n assert candidate(nums = [1, 2, 4, 8, 16]) == 20\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 0\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9]) == 16\n assert candidate(nums = [1, 2, 3, 4]) == 11\n assert candidate(nums = [1, 2, 3, 4, 5]) == 18\n assert candidate(nums = [0, 1, 2, 3, 4]) == 16\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [0, 0, 0]) == 0\n assert candidate(nums = [1, 0, 1, 0, 1, 0]) == 9\n assert candidate(nums = [0, 0, 0, 0]) == 0\n assert candidate(nums = [3, 5, 6, 7, 9, 10, 11, 12]) == 62\n assert candidate(nums = [255, 128, 64, 32, 16, 8, 4, 2, 1, 0]) == 128\n assert candidate(nums = [31, 14, 7, 3]) == 13\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997]) == 32\n assert candidate(nums = [4, 14, 2]) == 6\n assert candidate(nums = [0, 1, 2, 3]) == 8\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 90\n assert candidate(nums = [123456789, 987654321, 111222333, 444555666, 777888999]) == 152\n assert candidate(nums = [536870911, 268435455, 134217727, 67108863, 33554431, 16777215, 8388607, 4194303, 2097151, 1048575]) == 165\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384]) == 210\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200]) == 304\n assert candidate(nums = [1023, 2047, 4095, 8191, 16383, 32767, 65535]) == 56\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005]) == 25\n assert candidate(nums = [134217727, 134217726, 134217725, 134217724, 134217723, 134217722, 134217721, 134217720]) == 48\n assert candidate(nums = [1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 8000000]) == 228\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 90\n assert candidate(nums = [123, 456, 789, 101112, 131415, 161718, 192021, 222324]) == 250\n assert candidate(nums = [255, 127, 63, 31, 15, 7, 3, 1]) == 84\n assert candidate(nums = [1023, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]) == 180\n assert candidate(nums = [67305985, 134611970, 269223940, 538447880, 1076895760, 2153791520]) == 140\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]) == 156\n assert candidate(nums = [123456789, 987654321, 1122334455, 5566778899, 9988776655]) == 154\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990, 999999989, 999999988, 999999987, 999999986, 999999985, 999999984, 999999983, 999999982, 999999981, 999999980]) == 456\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643]) == 16\n assert candidate(nums = [1000000, 1000001, 1000010, 1000011, 1000100, 1000101, 1000110, 1000111]) == 112\n assert candidate(nums = [128, 64, 32, 16, 8, 4, 2, 1, 255, 127, 63, 31, 15, 7, 3, 1, 0]) == 464\n assert candidate(nums = [1023, 2047, 4095, 8191, 16383]) == 20\n assert candidate(nums = [123456789, 987654321, 112233445, 556677889, 998877665, 543216789, 876543210]) == 322\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644]) == 8\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000]) == 455\n assert candidate(nums = [1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]) == 420\n assert candidate(nums = [8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096]) == 90\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643, 2147483642, 2147483641, 2147483640, 2147483639, 2147483638]) == 89\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000]) == 324\n assert candidate(nums = [131071, 131072, 131073, 131074, 131075, 131076, 131077]) == 126\n assert candidate(nums = [123456789, 987654321, 111111111, 222222222, 333333333, 444444444, 555555555, 666666666]) == 411\n assert candidate(nums = [0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912]) == 900\n assert candidate(nums = [1048575, 524287, 262143, 131071, 65535, 32767, 16383, 8191, 4095, 2047, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1]) == 1330\n assert candidate(nums = [0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 121\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643, 2147483642, 2147483641, 2147483640]) == 48\n assert candidate(nums = [536870911, 536870910, 536870909, 536870908, 536870907, 536870906]) == 25\n assert candidate(nums = [123456789, 987654321, 1122334455, 5544332211, 1357924680, 2468013579]) == 239\n assert candidate(nums = [8388607, 4194303, 2097151, 1048575, 524287, 262143, 131071, 65535, 32767, 16383, 8191, 4095, 2047, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1]) == 2024\n assert candidate(nums = [100000000, 100000001, 100000002, 100000003, 100000004, 100000005, 100000006, 100000007, 100000008, 100000009, 100000010]) == 112\n assert candidate(nums = [1023, 2047, 3071, 4095, 5119]) == 16\n assert candidate(nums = [1023, 511, 255, 127, 63, 31, 15, 7, 3, 1]) == 165\n assert candidate(nums = [33554431, 16777215, 8388607, 4194303, 2097151, 1048575, 524287, 262143]) == 84\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == 686\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000]) == 168\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643, 2147483642]) == 25\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991]) == 145\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 768\n assert candidate(nums = [8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823]) == 84\n assert candidate(nums = [123456789, 987654321, 111111111, 222222222, 333333333, 444444444, 555555555]) == 304\n assert candidate(nums = [1048575, 1048574, 1048573, 1048572, 1048571, 1048570, 1048569, 1048568]) == 48\n assert candidate(nums = [7, 77, 777, 7777, 77777, 777777, 7777777, 77777777, 777777777, 7777777777]) == 557\n assert candidate(nums = [1073741823, 536870911, 268435455, 134217727, 67108863, 33554431, 16777215, 8388607, 4194303, 2097151, 1048575, 524287, 262143, 131071, 65535, 32767, 16383, 8191, 4095, 2047, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1]) == 4495\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125]) == 634\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 512\n assert candidate(nums = [8, 4, 2, 1, 16, 8, 4, 2, 1, 32, 16, 8, 4, 2, 1, 64, 32, 16, 8, 4, 2, 1]) == 406\n assert candidate(nums = [123456789, 987654321, 1122334455, 5566778899, 9988776655, 4433221100]) == 248\n assert candidate(nums = [8388607, 8388606, 8388605, 8388604, 8388603, 8388602]) == 25\n assert candidate(nums = [500000000, 500000001, 500000002, 500000003, 500000004, 500000005, 500000006, 500000007]) == 48\n assert candidate(nums = [1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287]) == 165\n assert candidate(nums = [5318008, 4618459, 4646774, 8777780, 8777736, 6218305, 4649788, 1048585, 4649456, 4618459]) == 459\n assert candidate(nums = [134217728, 67108864, 33554432, 16777216, 8388608, 4194304, 2097152, 1048576, 524288, 262144, 131072, 65536, 32768, 16384, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1]) == 756\n assert candidate(nums = [268435455, 268435454, 268435453, 268435452, 268435451, 268435450, 268435449, 268435448, 268435447, 268435446, 268435445]) == 112\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000]) == 548\n assert candidate(nums = [1000000001, 1000000002, 1000000003, 1000000004, 1000000005, 1000000006, 1000000007, 1000000008]) == 55\n assert candidate(nums = [255, 127, 63, 31, 15, 7, 3, 1, 0]) == 120\n assert candidate(nums = [8388607, 4194303, 2097151, 1048575, 524287, 262143, 131071, 65535, 32767, 16383, 8191, 4095, 2047, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1, 0]) == 2300\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 256\n assert candidate(nums = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610]) == 392\n assert candidate(nums = [123456789, 987654321, 234567891, 1234567890, 9876543210]) == 158\n assert candidate(nums = [135792468, 246813579, 357924681, 468135792, 579246813, 681357924, 792468135, 813579246, 924681357]) == 542\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 470\n assert candidate(nums = [536870911, 536870910, 536870909, 536870908, 536870907, 536870906, 536870905, 536870904]) == 48\n assert candidate(nums = [1000000, 2000000, 3000000, 4000000, 5000000, 6000000, 7000000, 8000000, 9000000, 10000000]) == 381\n assert candidate(nums = [8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384]) == 132\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768]) == 240\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().totalHammingDistance", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var totalHammingDistance = function(nums) {", "container": null, "callable": "totalHammingDistance", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 479, "task_id": "largest-palindrome-product", "difficulty": "Hard", "problem_description": "Given an integer n, return the largest palindromic integer that can be represented as the product of two n-digits integers. Since the answer can be very large, return it modulo 1337.\n \nExample 1:\n\nInput: n = 2\nOutput: 987\nExplanation: 99 x 91 = 9009, 9009 % 1337 = 987\n\nExample 2:\n\nInput: n = 1\nOutput: 9\n\n \nConstraints:\n\n1 <= n <= 8\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == 475\n assert candidate(n = 3) == 123\n assert candidate(n = 4) == 597\n assert candidate(n = 6) == 1218\n assert candidate(n = 2) == 987\n assert candidate(n = 1) == 9\n assert candidate(n = 7) == 877\n assert candidate(n = 5) == 677\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().largestPalindrome", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var largestPalindrome = function(n) {", "container": null, "callable": "largestPalindrome", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 480, "task_id": "sliding-window-median", "difficulty": "Hard", "problem_description": "The median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. So the median is the mean of the two middle values.\n\nFor examples, if arr = [2,3,4], the median is 3.\nFor examples, if arr = [1,2,3,4], the median is (2 + 3) / 2 = 2.5.\n\nYou are given an integer array nums and an integer k. There is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position.\nReturn the median array for each window in the original array. Answers within 10-5 of the actual value will be accepted.\n \nExample 1:\n\nInput: nums = [1,3,-1,-3,5,3,6,7], k = 3\nOutput: [1.00000,-1.00000,-1.00000,3.00000,5.00000,6.00000]\nExplanation: \nWindow position Median\n--------------- -----\n[1 3 -1] -3 5 3 6 7 1\n 1 [3 -1 -3] 5 3 6 7 -1\n 1 3 [-1 -3 5] 3 6 7 -1\n 1 3 -1 [-3 5 3] 6 7 3\n 1 3 -1 -3 [5 3 6] 7 5\n 1 3 -1 -3 5 [3 6 7] 6\n\nExample 2:\n\nInput: nums = [1,2,3,4,2,3,1,4,2], k = 3\nOutput: [2.00000,3.00000,3.00000,3.00000,2.00000,3.00000,2.00000]\n\n \nConstraints:\n\n1 <= k <= nums.length <= 105\n-231 <= nums[i] <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1],k = 4) == [7.5, 6.5, 5.5, 4.5, 3.5, 2.5]\n assert candidate(nums = [1, 2, 3, 4, 2, 3, 1, 4, 2],k = 3) == [2, 3, 3, 3, 2, 3, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9],k = 5) == [3, 4, 5, 6, 7]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 3) == [-2, -3, -4, -5, -6, -7, -8, -9]\n assert candidate(nums = [1, 2, 3],k = 2) == [1.5, 2.5]\n assert candidate(nums = [1, 4, 2, 3],k = 4) == [2.5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == [3, 4, 5, 6, 7, 8]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 5) == [5, 7, 9, 11, 13, 15]\n assert candidate(nums = [1, 2, 3, 4, 5],k = 2) == [1.5, 2.5, 3.5, 4.5]\n assert candidate(nums = [1, 3, 5],k = 1) == [1, 3, 5]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == [1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1],k = 1) == [1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15],k = 8) == [8.0]\n assert candidate(nums = [5, 4, 3, 2, 1],k = 4) == [3.5, 2.5]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 1) == [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]\n assert candidate(nums = [1, 2],k = 2) == [1.5]\n assert candidate(nums = [5, 2, 2, 7, 3, 7, 9, 0, 2, 3],k = 2) == [3.5, 2.0, 4.5, 5.0, 5.0, 8.0, 4.5, 1.0, 2.5]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7],k = 3) == [1, -1, -1, 3, 5, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 2) == [1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5]\n assert candidate(nums = [1, 2, 2, 2, 2, 2, 3],k = 3) == [2, 2, 2, 2, 2]\n assert candidate(nums = [5, 2, 2, 7, 3, 7, 9, 0, 2, 3],k = 4) == [3.5, 2.5, 5.0, 7.0, 5.0, 4.5, 2.5]\n assert candidate(nums = [1, 3, 3, 3, 2, 2, 1, 1, 1, 1],k = 5) == [3, 3, 2, 2, 1, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 10) == [5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 7) == [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]\n assert candidate(nums = [1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 3) == [2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, -10, -20, -30, -40, -50, -60, -70, -80, -90, -100],k = 5) == [80, 70, 60, 50, 40, 30, 20, 10, -10, -20, -30, -40, -50, -60, -70, -80]\n assert candidate(nums = [5, 3, 8, 6, 2, 7, 4, 1, 9, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == [4.5, 5.0, 6.5, 6.5, 8.0, 10.0, 11.5, 12.5, 13.5, 14.5, 15.5]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250],k = 15) == [80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180]\n assert candidate(nums = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 6) == [3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0]\n assert candidate(nums = [3, 1, 2, 2, 3, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 7) == [2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000],k = 3) == [1000000000, 1000000000, 1000000000]\n assert candidate(nums = [-1, -100, 2, -3, 5, 3, 6, 7, 100, 0],k = 5) == [-1, 2, 3, 5, 6, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 10) == [5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, 25.5]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 7) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 10) == [5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 2) == [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 10) == [10.0, 12.0, 14.0, 16.0, 18.0, 20.0, 22.0, 24.0, 26.0, 28.0, 30.0]\n assert candidate(nums = [1, 3, 3, 3, 3, 2, 2, 2, 2, 4, 4, 4, 5, 5],k = 4) == [3.0, 3.0, 3.0, 2.5, 2.0, 2.0, 2.0, 3.0, 4.0, 4.0, 4.5]\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 7) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]\n assert candidate(nums = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 3) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [2147483647, -2147483648, 1000000000, -1000000000, 500000000, -500000000, 250000000, -250000000],k = 3) == [1000000000, -1000000000, 500000000, -500000000, 250000000, -250000000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 15) == [8, 9, 10, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 8, 8, 8]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],k = 10) == [550.0, 650.0, 750.0, 850.0, 950.0, 1050.0]\n assert candidate(nums = [1, 3, 3, 3, 2, 2, 2, 4, 4, 5],k = 3) == [3, 3, 3, 2, 2, 2, 4, 4]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 4) == [25.0, 35.0, 45.0, 55.0, 65.0, 75.0, 85.0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 1) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 7) == [6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 5) == [8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 15) == [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 1) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(nums = [5, 1, 4, 3, 6, 8, 9, 2, 7, 10],k = 4) == [3.5, 3.5, 5.0, 7.0, 7.0, 7.5, 8.0]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40],k = 20) == [10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, 25.5, 26.5, 27.5, 28.5, 29.5, 30.5]\n assert candidate(nums = [5, 2, 2, 7, 3, 1, 6, 1, 5, 4, 9, 8],k = 5) == [3, 2, 3, 3, 3, 4, 5, 5]\n assert candidate(nums = [5, 2, 2, 7, 3, 7, 9, 0, 2, 3],k = 4) == [3.5, 2.5, 5.0, 7.0, 5.0, 4.5, 2.5]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 1) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == [1, 1, 1, 1, 1, 1]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0],k = 5) == [7, 6, 5, 4, 3, 2]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],k = 6) == [35.0, 45.0, 55.0, 65.0, 75.0, 85.0, 95.0, 105.0, 115.0, 125.0, 135.0, 145.0, 155.0, 165.0, 175.0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 7) == [4, 5, 6, 7, 8, 9, 10, 11, 12]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 6) == [17.5, 16.5, 15.5, 14.5, 13.5, 12.5, 11.5, 10.5, 9.5, 8.5, 7.5, 6.5, 5.5, 4.5, 3.5]\n assert candidate(nums = [3, 1, 2, 2, 3, 1, 4, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8],k = 5) == [2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 4, 5, 5, 5, 3, 3, 3, 4, 5, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 6) == [3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5]\n assert candidate(nums = [5, 2, 2, 3, 4, 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == [3, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]\n assert candidate(nums = [9, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 2) == [5.0, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5]\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10],k = 3) == [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65],k = 11) == [38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60]\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 5) == [-3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 15) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [39, 37, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1],k = 7) == [33, 31, 29, 27, 25, 23, 21, 19, 17, 15, 13, 11, 9, 7]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 5) == [30, 40, 50, 60, 70, 80]\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300],k = 6) == [350.0, 450.0, 550.0, 650.0, 750.0, 850.0, 950.0, 1050.0]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 4) == [2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5, 23.5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35],k = 9) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 4) == [7.5, 6.5, 5.5, 4.5, 3.5, 2.5, 1.5, 0.5, -0.5, -1.5, -2.5, -3.5, -4.5, -5.5, -6.5, -7.5, -8.5]\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005],k = 3) == [1000000001, 1000000002, 1000000003, 1000000004]\n assert candidate(nums = [5, 3, 1, 2, 4, 8, 7, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 15) == [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],k = 9) == [3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 100) == [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n assert candidate(nums = [5, 2, 1, 3, 4, 6, 7, 8, 9, 10],k = 4) == [2.5, 2.5, 3.5, 5.0, 6.5, 7.5, 8.5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20],k = 6) == [7.5, 6.5, 5.5, 4.5, 3.5, 2.5, 1.5, 0.5, -0.5, -1.5, -2.5, -3.5, -4.5, -5.5, -6.5, -7.5, -8.5, -9.5, -10.5, -11.5, -12.5, -13.5, -14.5, -15.5, -16.5, -17.5]\n assert candidate(nums = [1, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5],k = 5) == [3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5]\n assert candidate(nums = [1, 3, -1, -3, 5, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 5) == [1, 3, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 9) == [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]\n assert candidate(nums = [5, 2, 2, 7, 3, 7, 9, 0, 2, 3, 2, 2, 6, 2, 8, 0, 4, 3, 6, 2, 6, 4, 8, 7, 6, 3, 7, 2, 9, 7, 4, 6, 3, 7, 2, 7, 4, 6],k = 8) == [4.0, 2.5, 3.0, 3.0, 2.5, 2.5, 2.0, 2.0, 2.0, 2.5, 2.5, 3.5, 3.5, 3.5, 4.0, 4.0, 5.0, 6.0, 6.0, 6.0, 6.0, 6.5, 7.0, 6.5, 6.0, 5.0, 6.5, 5.0, 6.5, 5.0, 5.0]\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 3, 7, 5, 1, 0, 5, 8, 2, 0, 9, 7, 4, 9, 4, 4, 5, 9, 2, 3, 0, 7, 8, 1, 6, 4, 0, 6, 2, 8, 6, 2, 0, 8, 9, 9, 8, 6, 2, 8, 0, 3, 4, 8, 2, 5, 3, 4, 2, 1, 7, 0, 6, 7],k = 15) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 6, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 5, 4, 3, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 4, 4, 3, 3, 4]\n assert candidate(nums = [1000000000, -1000000000, 500000000, 250000000, -250000000],k = 3) == [500000000, 250000000, 250000000]\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991],k = 5) == [999999998, 999999997, 999999996, 999999995, 999999994, 999999993]\n assert candidate(nums = [1000000000, -1000000000, 500000000, -500000000, 250000000, -250000000],k = 3) == [500000000, -500000000, 250000000, -250000000]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 5) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(nums = [4, 5, 1, 3, 7, 10, 2, 8, 9, 6],k = 4) == [3.5, 4.0, 5.0, 5.0, 7.5, 8.5, 7.0]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 20) == [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],k = 5) == [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == [5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 3) == [20, 30, 40, 50, 60, 70, 80, 90]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [1.0]\n assert candidate(nums = [1000000000, 999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990],k = 3) == [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 5) == [7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == [5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [8, 7, 6, 5, 4, 3]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],k = 7) == [40, 50, 60, 70, 80, 90, 100, 110, 120]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1],k = 5) == [18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3]\n assert candidate(nums = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 7) == [3, 3, 3, 3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n assert candidate(nums = [5, 2, 9, 1, 5, 6],k = 2) == [3.5, 5.5, 5.0, 3.0, 5.5]\n assert candidate(nums = [1, 3, 3, 3, 3, 3, 3, 3, 3, 3],k = 5) == [3, 3, 3, 3, 3, 3]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 15) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7],k = 5) == [2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000],k = 2) == [0.0, 0.0, 0.0, 0.0, 0.0]\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648, 2147483647, -2147483648],k = 3) == [2147483647, -2147483648, 2147483647, -2147483648]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 3) == [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 10) == [5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0, 5.0]\n assert candidate(nums = [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1],k = 3) == [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 7) == [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().medianSlidingWindow", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var medianSlidingWindow = function(nums, k) {", "container": null, "callable": "medianSlidingWindow", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 481, "task_id": "magical-string", "difficulty": "Medium", "problem_description": "A magical string s consists of only '1' and '2' and obeys the following rules:\n\nThe string s is magical because concatenating the number of contiguous occurrences of characters '1' and '2' generates the string s itself.\n\nThe first few elements of s is s = \"1221121221221121122……\". If we group the consecutive 1's and 2's in s, it will be \"1 22 11 2 1 22 1 22 11 2 11 22 ......\" and the occurrences of 1's or 2's in each group are \"1 2 2 1 1 2 1 2 2 1 2 2 ......\". You can see that the occurrence sequence is s itself.\nGiven an integer n, return the number of 1's in the first n number in the magical string s.\n \nExample 1:\n\nInput: n = 6\nOutput: 3\nExplanation: The first 6 elements of magical string s is \"122112\" and it contains three 1's, so return 3.\n\nExample 2:\n\nInput: n = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= n <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 100000) == 49972\n assert candidate(n = 100) == 49\n assert candidate(n = 15) == 7\n assert candidate(n = 10000) == 4996\n assert candidate(n = 6) == 3\n assert candidate(n = 20) == 10\n assert candidate(n = 1) == 1\n assert candidate(n = 1000) == 502\n assert candidate(n = 10) == 5\n assert candidate(n = 32000) == 15996\n assert candidate(n = 99999) == 49972\n assert candidate(n = 15000) == 7501\n assert candidate(n = 3) == 1\n assert candidate(n = 12345) == 6172\n assert candidate(n = 7500) == 3747\n assert candidate(n = 90000) == 44975\n assert candidate(n = 50000) == 24985\n assert candidate(n = 50) == 25\n assert candidate(n = 5) == 3\n assert candidate(n = 300) == 150\n assert candidate(n = 30) == 15\n assert candidate(n = 60000) == 29976\n assert candidate(n = 40) == 20\n assert candidate(n = 4) == 2\n assert candidate(n = 30000) == 14993\n assert candidate(n = 2) == 1\n assert candidate(n = 45000) == 22491\n assert candidate(n = 85000) == 42478\n assert candidate(n = 80000) == 39982\n assert candidate(n = 8) == 4\n assert candidate(n = 20000) == 9996\n assert candidate(n = 5000) == 2500\n assert candidate(n = 75000) == 37487\n assert candidate(n = 9999) == 4995\n assert candidate(n = 50001) == 24986\n assert candidate(n = 200) == 100\n assert candidate(n = 400) == 199\n assert candidate(n = 9) == 4\n assert candidate(n = 500) == 249\n assert candidate(n = 7) == 4\n assert candidate(n = 25000) == 12495\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().magicalString", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var magicalString = function(n) {", "container": null, "callable": "magicalString", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 482, "task_id": "license-key-formatting", "difficulty": "Easy", "problem_description": "You are given a license key represented as a string s that consists of only alphanumeric characters and dashes. The string is separated into n + 1 groups by n dashes. You are also given an integer k.\nWe want to reformat the string s such that each group contains exactly k characters, except for the first group, which could be shorter than k but still must contain at least one character. Furthermore, there must be a dash inserted between two groups, and you should convert all lowercase letters to uppercase.\nReturn the reformatted license key.\n \nExample 1:\n\nInput: s = \"5F3Z-2e-9-w\", k = 4\nOutput: \"5F3Z-2E9W\"\nExplanation: The string s has been split into two parts, each part has 4 characters.\nNote that the two extra dashes are not needed and can be removed.\n\nExample 2:\n\nInput: s = \"2-5g-3-J\", k = 2\nOutput: \"2-5G-3J\"\nExplanation: The string s has been split into three parts, each part has 2 characters except the first part as it could be shorter as mentioned above.\n\n \nConstraints:\n\n1 <= s.length <= 105\ns consists of English letters, digits, and dashes '-'.\n1 <= k <= 104\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"AB-CD-EF-GH-IJ\",k = 2) == \"AB-CD-EF-GH-IJ\"\n assert candidate(s = \"abcdefg-hijkl-mnopqr-stuv-wxyz\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ\"\n assert candidate(s = \"\",k = 1) == \"\"\n assert candidate(s = \"\",k = 10) == \"\"\n assert candidate(s = \"1234567890\",k = 3) == \"1-234-567-890\"\n assert candidate(s = \"2-4A0r7-4k\",k = 3) == \"24-A0R-74K\"\n assert candidate(s = \"2-5g-3-J\",k = 2) == \"2-5G-3J\"\n assert candidate(s = \"5F3Z-2e-9-w\",k = 4) == \"5F3Z-2E9W\"\n assert candidate(s = \"----\",k = 2) == \"\"\n assert candidate(s = \"abcdefg\",k = 2) == \"A-BC-DE-FG\"\n assert candidate(s = \"a-a-a-a-\",k = 1) == \"A-A-A-A\"\n assert candidate(s = \"1-23-456\",k = 2) == \"12-34-56\"\n assert candidate(s = \"ABCDEF-GHIJKL-MNOPQR-STUVWX-YZ\",k = 1) == \"A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\"\n assert candidate(s = \"-1-2-3-4-5-6-7-8-9-0-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-\",k = 6) == \"123456-7890AB-CDEFGH-IJKLMN-OPQRST-UVWXYZ\"\n assert candidate(s = \"0000-0000-0000-0000-0000-0000\",k = 8) == \"00000000-00000000-00000000\"\n assert candidate(s = \"abcdefg-hijkl-mnopqr-stuv-wxyz-1234567890\",k = 3) == \"ABC-DEF-GHI-JKL-MNO-PQR-STU-VWX-YZ1-234-567-890\"\n assert candidate(s = \"a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z\",k = 6) == \"AB-CDEFGH-IJKLMN-OPQRST-UVWXYZ\"\n assert candidate(s = \"a-\",k = 2) == \"A\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-0-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 1) == \"1-2-3-4-5-6-7-8-9-0-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\"\n assert candidate(s = \"X1-Y2-Z3\",k = 1) == \"X-1-Y-2-Z-3\"\n assert candidate(s = \"123-4567-890-ABCD-EFGH-IJKL\",k = 3) == \"1-234-567-890-ABC-DEF-GHI-JKL\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-0-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 10) == \"123456-7890ABCDEF-GHIJKLMNOP-QRSTUVWXYZ\"\n assert candidate(s = \"a-\",k = 1) == \"A\"\n assert candidate(s = \"-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ\"\n assert candidate(s = \"x-y-z\",k = 10) == \"XYZ\"\n assert candidate(s = \"123-456-789-0123-4567-8901\",k = 4) == \"1-2345-6789-0123-4567-8901\"\n assert candidate(s = \"M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 6) == \"MN-OPQRST-UVWXYZ\"\n assert candidate(s = \"1234567890\",k = 1) == \"1-2-3-4-5-6-7-8-9-0\"\n assert candidate(s = \"xXxX-xXxX-xXxX-xXxX-xXxX-xXxX-xXxX-xXxX-xXxX\",k = 5) == \"X-XXXXX-XXXXX-XXXXX-XXXXX-XXXXX-XXXXX-XXXXX\"\n assert candidate(s = \"aBcDeFgHiJkLmNoPqRsTuVwXyZ\",k = 3) == \"AB-CDE-FGH-IJK-LMN-OPQ-RST-UVW-XYZ\"\n assert candidate(s = \"----\",k = 1) == \"\"\n assert candidate(s = \"abcdefg-hijkl-mnopqr-stuv-wxyz-1234567890\",k = 7) == \"A-BCDEFGH-IJKLMNO-PQRSTUV-WXYZ123-4567890\"\n assert candidate(s = \"Z1-23X4-567-89A-BCD-EFG-HIJ-KLM-NOP-QRS-TUV-WXY-Z\",k = 3) == \"Z-123-X45-678-9AB-CDE-FGH-IJK-LMN-OPQ-RST-UVW-XYZ\"\n assert candidate(s = \"A1-B2-C3-D4-E5-F6-G7-H8-I9-J0-K1-L2-M3-N4-O5-P6-Q7-R8-S9-T0-U1-V2-W3-X4-Y5-Z6\",k = 6) == \"A1B2-C3D4E5-F6G7H8-I9J0K1-L2M3N4-O5P6Q7-R8S9T0-U1V2W3-X4Y5Z6\"\n assert candidate(s = \"a-1-b-2-c-3-d-4-e-5-f-6-g-7-h-8-i-9-j-0\",k = 2) == \"A1-B2-C3-D4-E5-F6-G7-H8-I9-J0\"\n assert candidate(s = \"a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z-0-1-2-3-4-5-6-7-8-9\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ-01234-56789\"\n assert candidate(s = \"a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z\",k = 4) == \"AB-CDEF-GHIJ-KLMN-OPQR-STUV-WXYZ\"\n assert candidate(s = \"-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-\",k = 3) == \"AB-CDE-FGH-IJK-LMN-OPQ-RST-UVW-XYZ\"\n assert candidate(s = \"aA-bB-cC-dD-eE-fF-gG-hH-iI-jJ-kK-lL-mM-nN-oO-pP-qQ-rR-sS-tT-uU-vV-wW-xX-yY-zZ\",k = 5) == \"AA-BBCCD-DEEFF-GGHHI-IJJKK-LLMMN-NOOPP-QQRRS-STTUU-VVWWX-XYYZZ\"\n assert candidate(s = \"-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z-\",k = 2) == \"AB-CD-EF-GH-IJ-KL-MN-OP-QR-ST-UV-WX-YZ\"\n assert candidate(s = \"0-0-0-0-0-0-0-0-0-0\",k = 2) == \"00-00-00-00-00\"\n assert candidate(s = \"abcdefghij-klmnopqrstuvwxyz\",k = 6) == \"AB-CDEFGH-IJKLMN-OPQRST-UVWXYZ\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-0-1-2-3-4-5-6-7-8-9-0-1-2-3-4-5-6-7-8-9-0-1-2-3-4-5-6-7-8-9-0-1-2-3-4-5-6-7-8-9-0\",k = 3) == \"12-345-678-901-234-567-890-123-456-789-012-345-678-901-234-567-890\"\n assert candidate(s = \"x-y-z-1-2-3-4-5-6-7-8-9-0-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 7) == \"XYZ1-2345678-90ABCDE-FGHIJKL-MNOPQRS-TUVWXYZ\"\n assert candidate(s = \"000-000-000-000-000\",k = 5) == \"00000-00000-00000\"\n assert candidate(s = \"123-456-7890-ABCD-EFGH-IJKL\",k = 3) == \"1-234-567-890-ABC-DEF-GHI-JKL\"\n assert candidate(s = \"2-5G-3-J-\",k = 1) == \"2-5-G-3-J\"\n assert candidate(s = \"-this-is-a-test-string-for-the-problem-description-\",k = 5) == \"T-HISIS-ATEST-STRIN-GFORT-HEPRO-BLEMD-ESCRI-PTION\"\n assert candidate(s = \"abcdefg-hijkl-mnopqr-stuv-wxyz-12345-67890\",k = 6) == \"ABCDEF-GHIJKL-MNOPQR-STUVWX-YZ1234-567890\"\n assert candidate(s = \"W3LC--DR5F--HR5P-TR22--W48P\",k = 4) == \"W3LC-DR5F-HR5P-TR22-W48P\"\n assert candidate(s = \"A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 26) == \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n assert candidate(s = \"abcdef\",k = 10) == \"ABCDEF\"\n assert candidate(s = \"---\",k = 1) == \"\"\n assert candidate(s = \"aBcDeFgHiJkLmNoPqRsTuVwXyZ\",k = 7) == \"ABCDE-FGHIJKL-MNOPQRS-TUVWXYZ\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789\",k = 4) == \"AB-CDEF-GHIJ-KLMN-OPQR-STUV-WXYZ-ABCD-EFGH-IJKL-MNOP-QRST-UVWX-YZ01-2345-6789\"\n assert candidate(s = \"---\",k = 2) == \"\"\n assert candidate(s = \"A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ\"\n assert candidate(s = \"a\",k = 2) == \"A\"\n assert candidate(s = \"-a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z-0-1-2-3-4-5-6-7-8-9---\",k = 1) == \"A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-0-1-2-3-4-5-6-7-8-9\"\n assert candidate(s = \"X-5F3Z-2E-9-W\",k = 3) == \"X5F-3Z2-E9W\"\n assert candidate(s = \"WXY-ZAB-CDE-FGH-IJK-LMN-OPQ-RST-UVW-XYZ-123-456-789\",k = 3) == \"WXY-ZAB-CDE-FGH-IJK-LMN-OPQ-RST-UVW-XYZ-123-456-789\"\n assert candidate(s = \"-\",k = 1) == \"\"\n assert candidate(s = \"1234567890-abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\",k = 10) == \"12-34567890AB-CDEFGHIJKL-MNOPQRSTUV-WXYZABCDEF-GHIJKLMNOP-QRSTUVWXYZ\"\n assert candidate(s = \"1234567890-1234567890-1234567890-1234567890\",k = 9) == \"1234-567890123-456789012-345678901-234567890\"\n assert candidate(s = \"Z1234567890123456789012345678901234567890\",k = 15) == \"Z1234567890-123456789012345-678901234567890\"\n assert candidate(s = \"a0b1-c2d3-e4f5-g6h7-i8j9-k0l1-m2n3-o4p5-q6r7-s8t9-u0v1-w2x3-y4z5\",k = 3) == \"A-0B1-C2D-3E4-F5G-6H7-I8J-9K0-L1M-2N3-O4P-5Q6-R7S-8T9-U0V-1W2-X3Y-4Z5\"\n assert candidate(s = \"-a\",k = 1) == \"A\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\",k = 13) == \"ABCDEFGHIJKLM-NOPQRSTUVWXYZ\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-0\",k = 1) == \"1-2-3-4-5-6-7-8-9-0\"\n assert candidate(s = \"---a---b---c---d---e---f---g---h---i---j---\",k = 2) == \"AB-CD-EF-GH-IJ\"\n assert candidate(s = \"abcdef-ghijklm-nopqrst-uvwxyz-012345-67890\",k = 6) == \"A-BCDEFG-HIJKLM-NOPQRS-TUVWXY-Z01234-567890\"\n assert candidate(s = \"1234567890-abcdefghij-klmnopqrstuvwxyz\",k = 6) == \"123456-7890AB-CDEFGH-IJKLMN-OPQRST-UVWXYZ\"\n assert candidate(s = \"-a-b--c-d--e-f--g-h--i-j--k-l--m-n--o-p--q-r--s-t--u-v--w-x--y-z-\",k = 4) == \"AB-CDEF-GHIJ-KLMN-OPQR-STUV-WXYZ\"\n assert candidate(s = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ-0123456789\",k = 8) == \"ABCD-EFGHIJKL-MNOPQRST-UVWXYZ01-23456789\"\n assert candidate(s = \"a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z-0-1-2-3-4-5-6-7-8-9\",k = 7) == \"A-BCDEFGH-IJKLMNO-PQRSTUV-WXYZ012-3456789\"\n assert candidate(s = \"-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-\",k = 2) == \"AB-CD-EF-GH-IJ-KL-MN-OP-QR-ST-UV-WX-YZ\"\n assert candidate(s = \"1234567890-abcdefghijklmnopqrstuvwxyz-ABCDEFGHIJKLMNOPQRSTUVWXYZ\",k = 6) == \"12-345678-90ABCD-EFGHIJ-KLMNOP-QRSTUV-WXYZAB-CDEFGH-IJKLMN-OPQRST-UVWXYZ\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 1) == \"1-2-3-4-5-6-7-8-9-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\"\n assert candidate(s = \"123-456-789-0ABC-DEF\",k = 4) == \"1234-5678-90AB-CDEF\"\n assert candidate(s = \"9876543210-zyxwvutsrqponmlkjihgfedcba-9876543210-zyxwvutsrqponmlkjihgfedcba\",k = 5) == \"98-76543-210ZY-XWVUT-SRQPO-NMLKJ-IHGFE-DCBA9-87654-3210Z-YXWVU-TSRQP-ONMLK-JIHGF-EDCBA\"\n assert candidate(s = \"123-456-789-0-ABC-DEF-GHI-JKL-MNO-PQR-STU-VWX-YZ\",k = 2) == \"12-34-56-78-90-AB-CD-EF-GH-IJ-KL-MN-OP-QR-ST-UV-WX-YZ\"\n assert candidate(s = \"0123456789\",k = 2) == \"01-23-45-67-89\"\n assert candidate(s = \"ZEBRA-1234-APPLE-5678-BANANA-9012-CHERRY\",k = 4) == \"ZE-BRA1-234A-PPLE-5678-BANA-NA90-12CH-ERRY\"\n assert candidate(s = \"-abc-def-ghi-jkl-mno-pqr-stu-vwx-yz-123-456-789-0\",k = 7) == \"A-BCDEFGH-IJKLMNO-PQRSTUV-WXYZ123-4567890\"\n assert candidate(s = \"X-Y-Z\",k = 1) == \"X-Y-Z\"\n assert candidate(s = \"-ABCD-EFGH-IJKL-MNOP-QRST-UVWX-YZ-\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ\"\n assert candidate(s = \"Z\",k = 10) == \"Z\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-0\",k = 10) == \"1234567890\"\n assert candidate(s = \"123-456-7890-ABC-DEF\",k = 3) == \"1-234-567-890-ABC-DEF\"\n assert candidate(s = \"123-456-789-0ABC-DEF\",k = 3) == \"1-234-567-890-ABC-DEF\"\n assert candidate(s = \"1234567890ABCDEFGHIJKLMNOPQRSTUVWXYZ\",k = 15) == \"123456-7890ABCDEFGHIJK-LMNOPQRSTUVWXYZ\"\n assert candidate(s = \"1234567890-abcdef-1234567890-ABCDEF\",k = 7) == \"1234-567890A-BCDEF12-3456789-0ABCDEF\"\n assert candidate(s = \"0000-0000-0000-0000\",k = 4) == \"0000-0000-0000-0000\"\n assert candidate(s = \"--a-b--c-d--e-f--g-h--i-j--\",k = 2) == \"AB-CD-EF-GH-IJ\"\n assert candidate(s = \"Z\",k = 1) == \"Z\"\n assert candidate(s = \"a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z\",k = 27) == \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\"\n assert candidate(s = \"A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z\",k = 4) == \"AB-CDEF-GHIJ-KLMN-OPQR-STUV-WXYZ\"\n assert candidate(s = \"-A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--S--T--U--V--W--X--Y--Z-\",k = 2) == \"AB-CD-EF-GH-IJ-KL-MN-OP-QR-ST-UV-WX-YZ\"\n assert candidate(s = \"-A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-0-1-2-3-4-5-6-7-8-9-\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ-01234-56789\"\n assert candidate(s = \"LICENSE-KEY-FOR-EXAMPLE-1234567\",k = 7) == \"LICENS-EKEYFOR-EXAMPLE-1234567\"\n assert candidate(s = \"a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a\",k = 2) == \"A-AA-AA-AA-AA-AA-AA-AA-AA-AA-AA-AA-AA-AA-AA-AA\"\n assert candidate(s = \"---a---b---c---d---e---f---g---h---i---j---k---l---m---n---o---p---q---r---s---t---u---v---w---x---y---z---\",k = 5) == \"A-BCDEF-GHIJK-LMNOP-QRSTU-VWXYZ\"\n assert candidate(s = \"0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0\",k = 4) == \"00-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000\"\n assert candidate(s = \"1-2-3-4-5-6-7-8-9-0-1-2-3-4-5-6-7-8-9-0-1-2-3-4-5-6-7-8-9-0\",k = 10) == \"1234567890-1234567890-1234567890\"\n assert candidate(s = \"a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z\",k = 3) == \"AB-CDE-FGH-IJK-LMN-OPQ-RST-UVW-XYZ\"\n"}, "metadata": {"canonical_parameter_names": ["s", "k"], "leetcode_dataset_entry_point": "Solution().licenseKeyFormatting", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var licenseKeyFormatting = function(s, k) {", "container": null, "callable": "licenseKeyFormatting", "parameters": [{"name": "s", "type": "string"}, {"name": "k", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 483, "task_id": "smallest-good-base", "difficulty": "Hard", "problem_description": "Given an integer n represented as a string, return the smallest good base of n.\nWe call k >= 2 a good base of n, if all digits of n base k are 1's.\n \nExample 1:\n\nInput: n = \"13\"\nOutput: \"3\"\nExplanation: 13 base 3 is 111.\n\nExample 2:\n\nInput: n = \"4681\"\nOutput: \"8\"\nExplanation: 4681 base 8 is 11111.\n\nExample 3:\n\nInput: n = \"1000000000000000000\"\nOutput: \"999999999999999999\"\nExplanation: 1000000000000000000 base 999999999999999999 is 11.\n\n \nConstraints:\n\nn is an integer in the range [3, 1018].\nn does not contain any leading zeros.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = \"4681\") == \"8\"\n assert candidate(n = \"9\") == \"8\"\n assert candidate(n = \"104729\") == \"104728\"\n assert candidate(n = \"15\") == \"2\"\n assert candidate(n = \"218\") == \"217\"\n assert candidate(n = \"13\") == \"3\"\n assert candidate(n = \"81\") == \"80\"\n assert candidate(n = \"7\") == \"2\"\n assert candidate(n = \"3\") == \"2\"\n assert candidate(n = \"4\") == \"3\"\n assert candidate(n = \"121\") == \"3\"\n assert candidate(n = \"8\") == \"7\"\n assert candidate(n = \"21\") == \"4\"\n assert candidate(n = \"1023\") == \"2\"\n assert candidate(n = \"255\") == \"2\"\n assert candidate(n = \"91\") == \"9\"\n assert candidate(n = \"1000\") == \"999\"\n assert candidate(n = \"999\") == \"998\"\n assert candidate(n = \"1000000000000000000\") == \"999999999999999999\"\n assert candidate(n = \"2187\") == \"2186\"\n assert candidate(n = \"100\") == \"99\"\n assert candidate(n = \"343\") == \"18\"\n assert candidate(n = \"1801088541\") == \"1801088540\"\n assert candidate(n = \"2222222222222222222\") == \"2222222222222222221\"\n assert candidate(n = \"14348907\") == \"14348906\"\n assert candidate(n = \"59048\") == \"59047\"\n assert candidate(n = \"1125899906842623\") == \"2\"\n assert candidate(n = \"100000000\") == \"99999999\"\n assert candidate(n = \"79228162514264337593543950336\") == \"79228162514264337593543950335\"\n assert candidate(n = \"348678440099710752\") == \"348678440099710751\"\n assert candidate(n = \"222222222222222222\") == \"222222222222222221\"\n assert candidate(n = \"1234567890123456789\") == \"1234567890123456788\"\n assert candidate(n = \"617673396283947\") == \"617673396283946\"\n assert candidate(n = \"1000000000\") == \"999999999\"\n assert candidate(n = \"987654321\") == \"987654320\"\n assert candidate(n = \"298023223876953125\") == \"298023223876953124\"\n assert candidate(n = \"98765432109876543\") == \"98765432109876542\"\n assert candidate(n = \"3486784401\") == \"3486784400\"\n assert candidate(n = \"8191\") == \"2\"\n assert candidate(n = \"19683\") == \"19682\"\n assert candidate(n = \"12345678987654321\") == \"12345678987654320\"\n assert candidate(n = \"68719476736\") == \"68719476735\"\n assert candidate(n = \"549755813888\") == \"549755813887\"\n assert candidate(n = \"99999999999999999999999999999999999999999999999999999999999999999999999999999999999\") == \"99999999999999999999999999999999999999999999999999999999999999999999999999999999998\"\n assert candidate(n = \"3125\") == \"3124\"\n assert candidate(n = \"555555555555555555\") == \"555555555555555554\"\n assert candidate(n = \"281474976710656\") == \"281474976710655\"\n assert candidate(n = \"10000000000000000000000000000000000000000000000000000\") == \"9999999999999999999999999999999999999999999999999999\"\n assert candidate(n = \"18446744073709551615\") == \"2\"\n assert candidate(n = \"18014398509481984\") == \"18014398509481983\"\n assert candidate(n = \"193836733056657\") == \"193836733056656\"\n assert candidate(n = \"387420488\") == \"387420487\"\n assert candidate(n = \"8916100448256\") == \"8916100448255\"\n assert candidate(n = \"98765432109876543210987654321\") == \"98765432109876543210987654320\"\n assert candidate(n = \"6789101112131415161718192021222324252627282930\") == \"6789101112131415161718192021222324252627282929\"\n assert candidate(n = \"68719476735\") == \"2\"\n assert candidate(n = \"2357947691\") == \"2357947690\"\n assert candidate(n = \"1000000000000000000000000000000\") == \"999999999999999999999999999999\"\n assert candidate(n = \"4095\") == \"2\"\n assert candidate(n = \"65535\") == \"2\"\n assert candidate(n = \"16777216\") == \"16777215\"\n assert candidate(n = \"65537\") == \"65536\"\n assert candidate(n = \"111111111\") == \"10\"\n assert candidate(n = \"4398046511104\") == \"4398046511103\"\n assert candidate(n = \"111111111111111111\") == \"10\"\n assert candidate(n = \"823543\") == \"823542\"\n assert candidate(n = \"123456789101112131415\") == \"123456789101112131414\"\n assert candidate(n = \"101110111\") == \"101110110\"\n assert candidate(n = \"1111111111111111111\") == \"10\"\n assert candidate(n = \"38127987654321\") == \"38127987654320\"\n assert candidate(n = \"1111111111111111111111111111111\") == \"10\"\n assert candidate(n = \"161051\") == \"161050\"\n assert candidate(n = \"4294967295\") == \"2\"\n assert candidate(n = \"2305843009213693952\") == \"2305843009213693951\"\n assert candidate(n = \"1134903170\") == \"1134903169\"\n assert candidate(n = \"797161\") == \"3\"\n assert candidate(n = \"59049\") == \"59048\"\n assert candidate(n = \"678223072849\") == \"678223072848\"\n assert candidate(n = \"134217728\") == \"134217727\"\n assert candidate(n = \"999999999999999998\") == \"999999999999999997\"\n assert candidate(n = \"2000000000000000000\") == \"1999999999999999999\"\n assert candidate(n = \"999999999999999997\") == \"999999999999999996\"\n assert candidate(n = \"9223372036854775807\") == \"2\"\n assert candidate(n = \"123456789012345678\") == \"123456789012345677\"\n assert candidate(n = \"987654321987654321\") == \"987654321987654320\"\n assert candidate(n = \"515377520732011329\") == \"515377520732011328\"\n assert candidate(n = \"387420489\") == \"387420488\"\n assert candidate(n = \"282429536481\") == \"282429536480\"\n assert candidate(n = \"57896044618658097711785492504343953926634992332820282019728792003956564819949\") == \"57896044618658097711785492504343953926634992332820282019728792003956564819948\"\n assert candidate(n = \"268435455\") == \"2\"\n assert candidate(n = \"999999999\") == \"999999998\"\n assert candidate(n = \"9811\") == \"9810\"\n assert candidate(n = \"123456789\") == \"123456788\"\n assert candidate(n = \"3689348814741910323\") == \"3689348814741910322\"\n assert candidate(n = \"5555555555555555555\") == \"5555555555555555554\"\n assert candidate(n = \"999999999999999981\") == \"999999999999999980\"\n assert candidate(n = \"1024\") == \"1023\"\n assert candidate(n = \"1010101010101010101\") == \"100\"\n assert candidate(n = \"1111111111111111112\") == \"1111111111111111111\"\n assert candidate(n = \"555555555555555555555555555555\") == \"555555555555555555555555555554\"\n assert candidate(n = \"1000000000000000001\") == \"1000000000000000000\"\n assert candidate(n = \"78364164096\") == \"78364164095\"\n assert candidate(n = \"123456789012345678901234567890\") == \"123456789012345678901234567889\"\n assert candidate(n = \"1125899906842624\") == \"1125899906842623\"\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().smallestGoodBase", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var smallestGoodBase = function(n) {", "container": null, "callable": "smallestGoodBase", "parameters": [{"name": "n", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 485, "task_id": "max-consecutive-ones", "difficulty": "Easy", "problem_description": "Given a binary array nums, return the maximum number of consecutive 1's in the array.\n \nExample 1:\n\nInput: nums = [1,1,0,1,1,1]\nOutput: 3\nExplanation: The first two digits or the last three digits are consecutive 1s. The maximum number of consecutive 1s is 3.\n\nExample 2:\n\nInput: nums = [1,0,1,1,0,1]\nOutput: 2\n\n \nConstraints:\n\n1 <= nums.length <= 105\nnums[i] is either 0 or 1.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 0, 0, 0, 1, 0, 0, 1, 1, 0]) == 2\n assert candidate(nums = [1, 0, 1, 1, 0, 1]) == 2\n assert candidate(nums = [1]) == 1\n assert candidate(nums = [1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0]) == 4\n assert candidate(nums = [1, 0]) == 1\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]) == 4\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 1]) == 1\n assert candidate(nums = [0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1]) == 3\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [0]) == 0\n assert candidate(nums = [1, 1, 0, 1, 1, 1]) == 3\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [1, 0, 1]) == 1\n assert candidate(nums = [0, 0, 0, 0]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 0, 0, 0, 0, 1]) == 1\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 1, 0, 1, 1]) == 3\n assert candidate(nums = [1, 1, 1, 1, 1, 1]) == 6\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 0]) == 9\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1]) == 4\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0]) == 2\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 9\n assert candidate(nums = [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 29\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 2\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 2\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1]) == 3\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0]) == 37\n assert candidate(nums = [1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1]) == 3\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]) == 5\n assert candidate(nums = [1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0]) == 4\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 2\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 10\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1]) == 6\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]) == 7\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0]) == 7\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 15\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 14\n assert candidate(nums = [1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]) == 2\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 39\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 17\n assert candidate(nums = [1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1]) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]) == 29\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 20\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 11\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 38\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]) == 6\n assert candidate(nums = [0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]) == 3\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]) == 2\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 1\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]) == 4\n assert candidate(nums = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]) == 1\n assert candidate(nums = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]) == 3\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 20\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 17\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 30\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]) == 8\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 2\n assert candidate(nums = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1]) == 7\n assert candidate(nums = [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 29\n assert candidate(nums = [1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1]) == 5\n assert candidate(nums = [1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1]) == 3\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 2\n assert candidate(nums = [1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 18\n assert candidate(nums = [1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]) == 28\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]) == 6\n assert candidate(nums = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]) == 6\n assert candidate(nums = [0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 5\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1]) == 5\n assert candidate(nums = [1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0]) == 3\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 1\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findMaxConsecutiveOnes", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMaxConsecutiveOnes = function(nums) {", "container": null, "callable": "findMaxConsecutiveOnes", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 486, "task_id": "predict-the-winner", "difficulty": "Medium", "problem_description": "You are given an integer array nums. Two players are playing a game with this array: player 1 and player 2.\nPlayer 1 and player 2 take turns, with player 1 starting first. Both players start the game with a score of 0. At each turn, the player takes one of the numbers from either end of the array (i.e., nums[0] or nums[nums.length - 1]) which reduces the size of the array by 1. The player adds the chosen number to their score. The game ends when there are no more elements in the array.\nReturn true if Player 1 can win the game. If the scores of both players are equal, then player 1 is still the winner, and you should also return true. You may assume that both players are playing optimally.\n \nExample 1:\n\nInput: nums = [1,5,2]\nOutput: false\nExplanation: Initially, player 1 can choose between 1 and 2. \nIf he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5, then player 1 will be left with 1 (or 2). \nSo, final score of player 1 is 1 + 2 = 3, and player 2 is 5. \nHence, player 1 will never be the winner and you need to return false.\n\nExample 2:\n\nInput: nums = [1,5,233,7]\nOutput: true\nExplanation: Player 1 first chooses 1. Then player 2 has to choose between 5 and 7. No matter which number player 2 choose, player 1 can choose 233.\nFinally, player 1 has more score (234) than player 2 (12), so you need to return True representing player1 can win.\n\n \nConstraints:\n\n1 <= nums.length <= 20\n0 <= nums[i] <= 107\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [10, 10, 10, 10]) == True\n assert candidate(nums = [1, 5, 2]) == False\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [10]) == True\n assert candidate(nums = [1]) == True\n assert candidate(nums = [5, 17, 100, 11]) == True\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [1, 2, 3, 4]) == True\n assert candidate(nums = [1, 2, 3, 4, 5]) == True\n assert candidate(nums = [1, 2, 3, 7]) == True\n assert candidate(nums = [0, 0, 7, 6, 5, 6, 1]) == False\n assert candidate(nums = [5, 18, 6, 3, 1, 19, 2, 4, 10, 11]) == True\n assert candidate(nums = [1, 5, 233, 7]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [0, 0, 0, 0]) == True\n assert candidate(nums = [8, 15, 3, 7]) == True\n assert candidate(nums = [10, 10]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8]) == True\n assert candidate(nums = [1, 2]) == True\n assert candidate(nums = [1, 2, 3]) == True\n assert candidate(nums = [1, 3, 1]) == False\n assert candidate(nums = [5, 18, 4, 3, 9, 13, 13, 17]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41]) == True\n assert candidate(nums = [8, 15, 3, 7, 25, 10]) == True\n assert candidate(nums = [10000000, 9999999, 9999998, 9999997, 9999996, 9999995, 9999994, 9999993, 9999992, 9999991]) == True\n assert candidate(nums = [10000000, 1000000, 100000, 10000, 1000, 100, 10, 1, 0]) == True\n assert candidate(nums = [23, 17, 10, 14, 3, 8, 15, 21]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16]) == True\n assert candidate(nums = [1, 100, 1, 100, 1, 100, 1, 100]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [10, 20, 30, 40, 50]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [1000, 100, 10, 1, 1, 10, 100, 1000]) == True\n assert candidate(nums = [3, 1, 5, 4, 2]) == True\n assert candidate(nums = [1, 2, 3, 6, 5, 4, 3]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [10000000, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80]) == True\n assert candidate(nums = [10, 2, 5, 6, 7, 8]) == True\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == True\n assert candidate(nums = [8, 15, 3, 7, 10, 12, 14, 13]) == True\n assert candidate(nums = [10, 80, 90, 30, 50]) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == True\n assert candidate(nums = [100, 50, 200, 250, 300, 150, 100, 50, 200, 250, 300]) == True\n assert candidate(nums = [10, 80, 60, 20, 40, 30]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10000000]) == True\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == True\n assert candidate(nums = [23, 19, 45, 3, 12, 67, 2, 9, 15, 18, 21, 34, 56, 78, 90]) == True\n assert candidate(nums = [12, 5, 7, 23, 19, 18, 15, 10]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == True\n assert candidate(nums = [5, 2, 3, 4, 1, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [1, 5, 2, 4, 6, 8, 10]) == True\n assert candidate(nums = [1, 2, 100, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60]) == True\n assert candidate(nums = [8, 15, 3, 7, 10]) == False\n assert candidate(nums = [19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == True\n assert candidate(nums = [8, 15, 3, 7, 6, 12]) == True\n assert candidate(nums = [3, 4, 6, 10, 2, 1, 5, 9, 7, 8]) == True\n assert candidate(nums = [10000000, 1, 10000000, 1, 10000000, 1, 10000000, 1]) == True\n assert candidate(nums = [7, 10, 12, 5, 8, 7, 3, 9]) == True\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == True\n assert candidate(nums = [10000000, 9999999, 9999998, 9999997, 9999996]) == True\n assert candidate(nums = [30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == True\n assert candidate(nums = [10, 20, 15, 10, 5]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == True\n assert candidate(nums = [50, 40, 30, 20, 10, 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40]) == True\n assert candidate(nums = [23, 12, 32, 4, 55, 2, 3]) == False\n assert candidate(nums = [3, 1, 5, 4, 2, 9, 10, 6, 8, 7]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == True\n assert candidate(nums = [10000000, 0, 10000000, 0, 10000000, 0, 10000000, 0, 10000000, 0]) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == True\n assert candidate(nums = [8, 15, 3, 7, 10, 12]) == True\n assert candidate(nums = [2, 8, 5, 3, 7, 1, 9, 4]) == True\n assert candidate(nums = [20, 10, 3, 8, 5, 2, 7, 6, 1, 4]) == True\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35]) == True\n assert candidate(nums = [10000000, 1, 10000000, 1, 10000000, 1, 10000000, 1, 10000000, 1]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == True\n assert candidate(nums = [100, 200, 150, 100, 50, 25]) == True\n assert candidate(nums = [8, 15, 3, 7, 11, 12]) == True\n assert candidate(nums = [23, 15, 56, 7, 98, 1]) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == True\n assert candidate(nums = [3, 30, 27, 5, 20, 10]) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21]) == True\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == True\n assert candidate(nums = [5, 23, 7, 1, 9, 15, 3, 18, 11, 17, 2, 14, 6, 12, 8, 10, 4, 13, 16, 19]) == True\n assert candidate(nums = [23, 11, 17, 19, 21, 13, 5, 3, 2, 8]) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == True\n assert candidate(nums = [1, 100, 50, 25, 20, 10, 5, 1]) == True\n assert candidate(nums = [3, 1, 5, 8, 9, 2]) == True\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == True\n assert candidate(nums = [3, 9, 1, 2]) == True\n assert candidate(nums = [1, 23, 45, 6, 78, 90, 12, 34]) == True\n assert candidate(nums = [10000000, 9000000, 8000000, 7000000, 6000000, 5000000, 4000000, 3000000, 2000000, 1000000]) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == True\n assert candidate(nums = [1, 3, 1, 5, 2, 4]) == True\n assert candidate(nums = [10, 8, 6, 4, 2, 1, 3, 5, 7, 9]) == True\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().predictTheWinner", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var predictTheWinner = function(nums) {", "container": null, "callable": "predictTheWinner", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 488, "task_id": "zuma-game", "difficulty": "Hard", "problem_description": "You are playing a variation of the game Zuma.\nIn this variation of Zuma, there is a single row of colored balls on a board, where each ball can be colored red 'R', yellow 'Y', blue 'B', green 'G', or white 'W'. You also have several colored balls in your hand.\nYour goal is to clear all of the balls from the board. On each turn:\n\nPick any ball from your hand and insert it in between two balls in the row or on either end of the row.\nIf there is a group of three or more consecutive balls of the same color, remove the group of balls from the board.\n\t\nIf this removal causes more groups of three or more of the same color to form, then continue removing each group until there are none left.\n\n\nIf there are no more balls on the board, then you win the game.\nRepeat this process until you either win or do not have any more balls in your hand.\n\nGiven a string board, representing the row of balls on the board, and a string hand, representing the balls in your hand, return the minimum number of balls you have to insert to clear all the balls from the board. If you cannot clear all the balls from the board using the balls in your hand, return -1.\n \nExample 1:\n\nInput: board = \"WRRBBW\", hand = \"RB\"\nOutput: -1\nExplanation: It is impossible to clear all the balls. The best you can do is:\n- Insert 'R' so the board becomes WRRRBBW. WRRRBBW -> WBBW.\n- Insert 'B' so the board becomes WBBBW. WBBBW -> WW.\nThere are still balls remaining on the board, and you are out of balls to insert.\nExample 2:\n\nInput: board = \"WWRRBBWW\", hand = \"WRBRW\"\nOutput: 2\nExplanation: To make the board empty:\n- Insert 'R' so the board becomes WWRRRBBWW. WWRRRBBWW -> WWBBWW.\n- Insert 'B' so the board becomes WWBBBWW. WWBBBWW -> WWWW -> empty.\n2 balls from your hand were needed to clear the board.\n\nExample 3:\n\nInput: board = \"G\", hand = \"GGGGG\"\nOutput: 2\nExplanation: To make the board empty:\n- Insert 'G' so the board becomes GG.\n- Insert 'G' so the board becomes GGG. GGG -> empty.\n2 balls from your hand were needed to clear the board.\n\n \nConstraints:\n\n1 <= board.length <= 16\n1 <= hand.length <= 5\nboard and hand consist of the characters 'R', 'Y', 'B', 'G', and 'W'.\nThe initial row of balls on the board will not have any groups of three or more consecutive balls of the same color.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = \"RRYYGG\",hand = \"\") == -1\n"}, "metadata": {"canonical_parameter_names": ["board", "hand"], "leetcode_dataset_entry_point": "Solution().findMinStep", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMinStep = function(board, hand) {", "container": null, "callable": "findMinStep", "parameters": [{"name": "board", "type": "string"}, {"name": "hand", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 491, "task_id": "non-decreasing-subsequences", "difficulty": "Medium", "problem_description": "Given an integer array nums, return all the different possible non-decreasing subsequences of the given array with at least two elements. You may return the answer in any order.\n \nExample 1:\n\nInput: nums = [4,6,7,7]\nOutput: [[4,6],[4,6,7],[4,6,7,7],[4,7],[4,7,7],[6,7],[6,7,7],[7,7]]\n\nExample 2:\n\nInput: nums = [4,4,3,2,1]\nOutput: [[4,4]]\n\n \nConstraints:\n\n1 <= nums.length <= 15\n-100 <= nums[i] <= 100\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 3, 2, 4, 5]) == [[1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 4, 5], [1, 4], [1, 5], [3, 4, 5], [3, 4], [3, 5], [2, 4, 5], [2, 4], [2, 5], [4, 5]]\n assert candidate(nums = [1, 2, 2, 3]) == [[1, 2, 2, 3], [1, 2, 2], [1, 2, 3], [1, 2], [1, 3], [2, 2, 3], [2, 2], [2, 3]]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4]) == [[1, 2, 2, 2, 3, 3, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4], [1, 3], [1, 4], [2, 2, 2, 3, 3, 4], [2, 2, 2, 3, 3], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4], [2, 2, 2], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4], [2, 3], [2, 4], [3, 3, 4], [3, 3], [3, 4]]\n assert candidate(nums = [3, 2, 1, 2, 3, 4, 2, 2, 3, 4]) == [[3, 3, 4, 4], [3, 3, 3, 4], [3, 3, 3], [2, 2, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 4, 4], [2, 2, 2, 2, 3, 4], [2, 2, 2, 2, 3], [2, 2, 2, 2, 4], [2, 2, 2, 2], [1, 2, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 4, 4], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], [1, 3], [1, 4], [2, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 4, 4], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4], [2, 2, 2], [3, 4, 4], [3, 3, 4], [3, 3], [4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [2, 3, 4], [2, 3], [2, 4], [3, 4]]\n assert candidate(nums = [10, 9, 2, 5, 3, 7, 101, 18]) == [[10, 101], [10, 18], [9, 101], [9, 18], [2, 5, 7, 101], [2, 5, 7, 18], [2, 5, 7], [2, 5, 101], [2, 5, 18], [2, 5], [2, 3, 7, 101], [2, 3, 7, 18], [2, 3, 7], [2, 3, 101], [2, 3, 18], [2, 3], [2, 7, 101], [2, 7, 18], [2, 7], [2, 101], [2, 18], [5, 7, 101], [5, 7, 18], [5, 7], [5, 101], [5, 18], [3, 7, 101], [3, 7, 18], [3, 7], [3, 101], [3, 18], [7, 101], [7, 18]]\n assert candidate(nums = [1, 2, 2, 3, 4, 4]) == [[1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4], [1, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4], [2, 4], [3, 4, 4], [3, 4], [4, 4]]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8], [1, 2, 4, 9, 10], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 9, 10], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 7], [1, 2, 6, 8, 9, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 8], [1, 2, 6, 9, 10], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 8], [1, 2, 7, 9, 10], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7], [1, 2, 8, 9, 10], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8], [1, 2, 9, 10], [1, 2, 9], [1, 2, 10], [1, 2], [1, 3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 9, 10], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 10], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8, 9, 10], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 8, 10], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 9, 10], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 10], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7, 8, 9, 10], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 7, 8, 10], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 9, 10], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8, 9, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9, 10], [1, 3, 4, 5, 9], [1, 3, 4, 5, 10], [1, 3, 4, 5], [1, 3, 4, 6, 7, 8, 9, 10], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 6, 7, 8, 10], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 9, 10], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8, 9, 10], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9, 10], [1, 3, 4, 6, 9], [1, 3, 4, 6, 10], [1, 3, 4, 6], [1, 3, 4, 7, 8, 9, 10], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 7], [1, 3, 4, 8, 9, 10], [1, 3, 4, 8, 9], [1, 3, 4, 8, 10], [1, 3, 4, 8], [1, 3, 4, 9, 10], [1, 3, 4, 9], [1, 3, 4, 10], [1, 3, 4], [1, 3, 5, 6, 7, 8, 9, 10], [1, 3, 5, 6, 7, 8, 9], [1, 3, 5, 6, 7, 8, 10], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 9, 10], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8, 9, 10], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9, 10], [1, 3, 5, 6, 9], [1, 3, 5, 6, 10], [1, 3, 5, 6], [1, 3, 5, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 3, 5, 7, 8, 10], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 9], [1, 3, 5, 7, 10], [1, 3, 5, 7], [1, 3, 5, 8, 9, 10], [1, 3, 5, 8, 9], [1, 3, 5, 8, 10], [1, 3, 5, 8], [1, 3, 5, 9, 10], [1, 3, 5, 9], [1, 3, 5, 10], [1, 3, 5], [1, 3, 6, 7, 8, 9, 10], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9, 10], [1, 3, 6, 7, 9], [1, 3, 6, 7, 10], [1, 3, 6, 7], [1, 3, 6, 8, 9, 10], [1, 3, 6, 8, 9], [1, 3, 6, 8, 10], [1, 3, 6, 8], [1, 3, 6, 9, 10], [1, 3, 6, 9], [1, 3, 6, 10], [1, 3, 6], [1, 3, 7, 8, 9, 10], [1, 3, 7, 8, 9], [1, 3, 7, 8, 10], [1, 3, 7, 8], [1, 3, 7, 9, 10], [1, 3, 7, 9], [1, 3, 7, 10], [1, 3, 7], [1, 3, 8, 9, 10], [1, 3, 8, 9], [1, 3, 8, 10], [1, 3, 8], [1, 3, 9, 10], [1, 3, 9], [1, 3, 10], [1, 3], [1, 4, 5, 6, 7, 8, 9, 10], [1, 4, 5, 6, 7, 8, 9], [1, 4, 5, 6, 7, 8, 10], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 9, 10], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8, 9, 10], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9, 10], [1, 4, 5, 6, 9], [1, 4, 5, 6, 10], [1, 4, 5, 6], [1, 4, 5, 7, 8, 9, 10], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 9], [1, 4, 5, 7, 10], [1, 4, 5, 7], [1, 4, 5, 8, 9, 10], [1, 4, 5, 8, 9], [1, 4, 5, 8, 10], [1, 4, 5, 8], [1, 4, 5, 9, 10], [1, 4, 5, 9], [1, 4, 5, 10], [1, 4, 5], [1, 4, 6, 7, 8, 9, 10], [1, 4, 6, 7, 8, 9], [1, 4, 6, 7, 8, 10], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9, 10], [1, 4, 6, 7, 9], [1, 4, 6, 7, 10], [1, 4, 6, 7], [1, 4, 6, 8, 9, 10], [1, 4, 6, 8, 9], [1, 4, 6, 8, 10], [1, 4, 6, 8], [1, 4, 6, 9, 10], [1, 4, 6, 9], [1, 4, 6, 10], [1, 4, 6], [1, 4, 7, 8, 9, 10], [1, 4, 7, 8, 9], [1, 4, 7, 8, 10], [1, 4, 7, 8], [1, 4, 7, 9, 10], [1, 4, 7, 9], [1, 4, 7, 10], [1, 4, 7], [1, 4, 8, 9, 10], [1, 4, 8, 9], [1, 4, 8, 10], [1, 4, 8], [1, 4, 9, 10], [1, 4, 9], [1, 4, 10], [1, 4], [1, 5, 6, 7, 8, 9, 10], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9, 10], [1, 5, 6, 7, 9], [1, 5, 6, 7, 10], [1, 5, 6, 7], [1, 5, 6, 8, 9, 10], [1, 5, 6, 8, 9], [1, 5, 6, 8, 10], [1, 5, 6, 8], [1, 5, 6, 9, 10], [1, 5, 6, 9], [1, 5, 6, 10], [1, 5, 6], [1, 5, 7, 8, 9, 10], [1, 5, 7, 8, 9], [1, 5, 7, 8, 10], [1, 5, 7, 8], [1, 5, 7, 9, 10], [1, 5, 7, 9], [1, 5, 7, 10], [1, 5, 7], [1, 5, 8, 9, 10], [1, 5, 8, 9], [1, 5, 8, 10], [1, 5, 8], [1, 5, 9, 10], [1, 5, 9], [1, 5, 10], [1, 5], [1, 6, 7, 8, 9, 10], [1, 6, 7, 8, 9], [1, 6, 7, 8, 10], [1, 6, 7, 8], [1, 6, 7, 9, 10], [1, 6, 7, 9], [1, 6, 7, 10], [1, 6, 7], [1, 6, 8, 9, 10], [1, 6, 8, 9], [1, 6, 8, 10], [1, 6, 8], [1, 6, 9, 10], [1, 6, 9], [1, 6, 10], [1, 6], [1, 7, 8, 9, 10], [1, 7, 8, 9], [1, 7, 8, 10], [1, 7, 8], [1, 7, 9, 10], [1, 7, 9], [1, 7, 10], [1, 7], [1, 8, 9, 10], [1, 8, 9], [1, 8, 10], [1, 8], [1, 9, 10], [1, 9], [1, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9], [2, 3, 4, 5, 6, 7, 8, 10], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 9, 10], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 10], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8, 9, 10], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 8, 10], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 9, 10], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7, 8, 9, 10], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 7, 8, 10], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 9, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8, 9, 10], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 8, 10], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9, 10], [2, 3, 4, 5, 9], [2, 3, 4, 5, 10], [2, 3, 4, 5], [2, 3, 4, 6, 7, 8, 9, 10], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 6, 7, 8, 10], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 9, 10], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 10], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8, 9, 10], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 9], [2, 3, 4, 6, 10], [2, 3, 4, 6], [2, 3, 4, 7, 8, 9, 10], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 9], [2, 3, 4, 7, 10], [2, 3, 4, 7], [2, 3, 4, 8, 9, 10], [2, 3, 4, 8, 9], [2, 3, 4, 8, 10], [2, 3, 4, 8], [2, 3, 4, 9, 10], [2, 3, 4, 9], [2, 3, 4, 10], [2, 3, 4], [2, 3, 5, 6, 7, 8, 9, 10], [2, 3, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 10], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8, 9, 10], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 8, 10], [2, 3, 5, 6, 8], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 9], [2, 3, 5, 6, 10], [2, 3, 5, 6], [2, 3, 5, 7, 8, 9, 10], [2, 3, 5, 7, 8, 9], [2, 3, 5, 7, 8, 10], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 9], [2, 3, 5, 7, 10], [2, 3, 5, 7], [2, 3, 5, 8, 9, 10], [2, 3, 5, 8, 9], [2, 3, 5, 8, 10], [2, 3, 5, 8], [2, 3, 5, 9, 10], [2, 3, 5, 9], [2, 3, 5, 10], [2, 3, 5], [2, 3, 6, 7, 8, 9, 10], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 9], [2, 3, 6, 7, 10], [2, 3, 6, 7], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 10], [2, 3, 6, 8], [2, 3, 6, 9, 10], [2, 3, 6, 9], [2, 3, 6, 10], [2, 3, 6], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 10], [2, 3, 7, 8], [2, 3, 7, 9, 10], [2, 3, 7, 9], [2, 3, 7, 10], [2, 3, 7], [2, 3, 8, 9, 10], [2, 3, 8, 9], [2, 3, 8, 10], [2, 3, 8], [2, 3, 9, 10], [2, 3, 9], [2, 3, 10], [2, 3], [2, 4, 5, 6, 7, 8, 9, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9], [2, 4, 5, 6, 10], [2, 4, 5, 6], [2, 4, 5, 7, 8, 9, 10], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9], [2, 4, 5, 7, 10], [2, 4, 5, 7], [2, 4, 5, 8, 9, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 10], [2, 4, 5, 8], [2, 4, 5, 9, 10], [2, 4, 5, 9], [2, 4, 5, 10], [2, 4, 5], [2, 4, 6, 7, 8, 9, 10], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 9], [2, 4, 6, 7, 10], [2, 4, 6, 7], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 10], [2, 4, 6, 8], [2, 4, 6, 9, 10], [2, 4, 6, 9], [2, 4, 6, 10], [2, 4, 6], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 10], [2, 4, 7, 8], [2, 4, 7, 9, 10], [2, 4, 7, 9], [2, 4, 7, 10], [2, 4, 7], [2, 4, 8, 9, 10], [2, 4, 8, 9], [2, 4, 8, 10], [2, 4, 8], [2, 4, 9, 10], [2, 4, 9], [2, 4, 10], [2, 4], [2, 5, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 10], [2, 5, 6, 7], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 10], [2, 5, 6, 8], [2, 5, 6, 9, 10], [2, 5, 6, 9], [2, 5, 6, 10], [2, 5, 6], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 10], [2, 5, 7, 8], [2, 5, 7, 9, 10], [2, 5, 7, 9], [2, 5, 7, 10], [2, 5, 7], [2, 5, 8, 9, 10], [2, 5, 8, 9], [2, 5, 8, 10], [2, 5, 8], [2, 5, 9, 10], [2, 5, 9], [2, 5, 10], [2, 5], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 10], [2, 6, 7, 8], [2, 6, 7, 9, 10], [2, 6, 7, 9], [2, 6, 7, 10], [2, 6, 7], [2, 6, 8, 9, 10], [2, 6, 8, 9], [2, 6, 8, 10], [2, 6, 8], [2, 6, 9, 10], [2, 6, 9], [2, 6, 10], [2, 6], [2, 7, 8, 9, 10], [2, 7, 8, 9], [2, 7, 8, 10], [2, 7, 8], [2, 7, 9, 10], [2, 7, 9], [2, 7, 10], [2, 7], [2, 8, 9, 10], [2, 8, 9], [2, 8, 10], [2, 8], [2, 9, 10], [2, 9], [2, 10], [3, 4, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 10], [3, 4, 5, 6], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 10], [3, 4, 5, 7], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 10], [3, 4, 5, 8], [3, 4, 5, 9, 10], [3, 4, 5, 9], [3, 4, 5, 10], [3, 4, 5], [3, 4, 6, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 10], [3, 4, 6, 7], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 10], [3, 4, 6, 8], [3, 4, 6, 9, 10], [3, 4, 6, 9], [3, 4, 6, 10], [3, 4, 6], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 10], [3, 4, 7, 8], [3, 4, 7, 9, 10], [3, 4, 7, 9], [3, 4, 7, 10], [3, 4, 7], [3, 4, 8, 9, 10], [3, 4, 8, 9], [3, 4, 8, 10], [3, 4, 8], [3, 4, 9, 10], [3, 4, 9], [3, 4, 10], [3, 4], [3, 5, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 10], [3, 5, 6, 7], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 10], [3, 5, 6, 8], [3, 5, 6, 9, 10], [3, 5, 6, 9], [3, 5, 6, 10], [3, 5, 6], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 10], [3, 5, 7, 8], [3, 5, 7, 9, 10], [3, 5, 7, 9], [3, 5, 7, 10], [3, 5, 7], [3, 5, 8, 9, 10], [3, 5, 8, 9], [3, 5, 8, 10], [3, 5, 8], [3, 5, 9, 10], [3, 5, 9], [3, 5, 10], [3, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8], [3, 6, 9, 10], [3, 6, 9], [3, 6, 10], [3, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8], [3, 7, 9, 10], [3, 7, 9], [3, 7, 10], [3, 7], [3, 8, 9, 10], [3, 8, 9], [3, 8, 10], [3, 8], [3, 9, 10], [3, 9], [3, 10], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [8, 9, 10], [8, 9], [8, 10], [9, 10]]\n assert candidate(nums = [4, 6, 7, 7]) == [[4, 6, 7, 7], [4, 6, 7], [4, 6], [4, 7, 7], [4, 7], [6, 7, 7], [6, 7], [7, 7]]\n assert candidate(nums = [1, 2, 3, 4]) == [[1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], [1, 3], [1, 4], [2, 3, 4], [2, 3], [2, 4], [3, 4]]\n assert candidate(nums = [-1, 0, 1, 0, -1]) == [[-1, 0, 1], [-1, 0, 0], [-1, 1], [-1, 0], [-1, -1], [0, 1], [0, 0]]\n assert candidate(nums = [1, 3, 2, 4, 3, 5]) == [[1, 3, 4, 5], [1, 3, 4], [1, 3, 3, 5], [1, 3, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 5], [1, 2], [1, 4, 5], [1, 4], [1, 3, 5], [1, 3], [1, 5], [3, 4, 5], [3, 4], [3, 3, 5], [3, 3], [2, 4, 5], [2, 4], [2, 3, 5], [2, 3], [2, 5], [4, 5], [3, 5]]\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 4, 3, 2, 1]) == [[1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3, 4], [1, 3, 3], [1, 4, 5, 5], [1, 4, 5], [1, 4, 4], [1, 5, 5], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 4, 5, 5], [2, 4, 5], [2, 4, 4], [2, 5, 5], [2, 5], [2, 4], [2, 3], [2, 2], [3, 4, 5, 5], [3, 4, 5], [3, 4, 4], [3, 5, 5], [3, 5], [3, 4], [3, 3], [4, 5, 5], [4, 5], [4, 4], [5, 5]]\n assert candidate(nums = [5, 5, 5, 5]) == [[5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [3, 4, 5], [3, 4], [3, 5], [4, 5]]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1]) == [[1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 3, 4], [1, 3, 3], [1, 4], [1, 3], [1, 2], [1, 1], [2, 3, 4], [2, 3, 3], [2, 4], [2, 3], [2, 2], [3, 4], [3, 3]]\n assert candidate(nums = [1, 2, 2, 2, 3, 4]) == [[1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], [1, 3], [1, 4], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4], [2, 2, 2], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [2, 3, 4], [2, 3], [2, 4], [3, 4]]\n assert candidate(nums = [-1, 0, 1, 0, -1, -1]) == [[-1, 0, 1], [-1, 0, 0], [-1, 1], [-1, 0], [-1, -1, -1], [0, 1], [0, 0], [-1, -1]]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1]) == [[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [-10, -9, -8, -7, -6, -5, -4, -3, -2], [-10, -9, -8, -7, -6, -5, -4, -3, -1], [-10, -9, -8, -7, -6, -5, -4, -3], [-10, -9, -8, -7, -6, -5, -4, -2, -1], [-10, -9, -8, -7, -6, -5, -4, -2], [-10, -9, -8, -7, -6, -5, -4, -1], [-10, -9, -8, -7, -6, -5, -4], [-10, -9, -8, -7, -6, -5, -3, -2, -1], [-10, -9, -8, -7, -6, -5, -3, -2], [-10, -9, -8, -7, -6, -5, -3, -1], [-10, -9, -8, -7, -6, -5, -3], [-10, -9, -8, -7, -6, -5, -2, -1], [-10, -9, -8, -7, -6, -5, -2], [-10, -9, -8, -7, -6, -5, -1], [-10, -9, -8, -7, -6, -5], [-10, -9, -8, -7, -6, -4, -3, -2, -1], [-10, -9, -8, -7, -6, -4, -3, -2], [-10, -9, -8, -7, -6, -4, -3, -1], [-10, -9, -8, -7, -6, -4, -3], [-10, -9, -8, -7, -6, -4, -2, -1], [-10, -9, -8, -7, -6, -4, -2], [-10, -9, -8, -7, -6, -4, -1], [-10, -9, -8, -7, -6, -4], [-10, -9, -8, -7, -6, -3, -2, -1], [-10, -9, -8, -7, -6, -3, -2], [-10, -9, -8, -7, -6, -3, -1], [-10, -9, -8, -7, -6, -3], [-10, -9, -8, -7, -6, -2, -1], [-10, -9, -8, -7, -6, -2], [-10, -9, -8, -7, -6, -1], [-10, -9, -8, -7, -6], [-10, -9, -8, -7, -5, -4, -3, -2, -1], [-10, -9, -8, -7, -5, -4, -3, -2], [-10, -9, -8, -7, -5, -4, -3, -1], [-10, -9, -8, -7, -5, -4, -3], [-10, -9, -8, -7, -5, -4, -2, -1], [-10, -9, -8, -7, -5, -4, -2], [-10, -9, -8, -7, -5, -4, -1], [-10, -9, -8, -7, -5, -4], [-10, -9, -8, -7, -5, -3, -2, -1], [-10, -9, -8, -7, -5, -3, -2], [-10, -9, -8, -7, -5, -3, -1], [-10, -9, -8, -7, -5, -3], [-10, -9, -8, -7, -5, -2, -1], [-10, -9, -8, -7, -5, -2], [-10, -9, -8, -7, -5, -1], [-10, -9, -8, -7, -5], [-10, -9, -8, -7, -4, -3, -2, -1], [-10, -9, -8, -7, -4, -3, -2], [-10, -9, -8, -7, -4, -3, -1], [-10, -9, -8, -7, -4, -3], [-10, -9, -8, -7, -4, -2, -1], [-10, -9, -8, -7, -4, -2], [-10, -9, -8, -7, -4, -1], [-10, -9, -8, -7, -4], [-10, -9, -8, -7, -3, -2, -1], [-10, -9, -8, -7, -3, -2], [-10, -9, -8, -7, -3, -1], [-10, -9, -8, -7, -3], [-10, -9, -8, -7, -2, -1], [-10, -9, -8, -7, -2], [-10, -9, -8, -7, -1], [-10, -9, -8, -7], [-10, -9, -8, -6, -5, -4, -3, -2, -1], [-10, -9, -8, -6, -5, -4, -3, -2], [-10, -9, -8, -6, -5, -4, -3, -1], [-10, -9, -8, -6, -5, -4, -3], [-10, -9, -8, -6, -5, -4, -2, -1], [-10, -9, -8, -6, -5, -4, -2], [-10, -9, -8, -6, -5, -4, -1], [-10, -9, -8, -6, -5, -4], [-10, -9, -8, -6, -5, -3, -2, -1], [-10, -9, -8, -6, -5, -3, -2], [-10, -9, -8, -6, -5, -3, -1], [-10, -9, -8, -6, -5, -3], [-10, -9, -8, -6, -5, -2, -1], [-10, -9, -8, -6, -5, -2], [-10, -9, -8, -6, -5, -1], [-10, -9, -8, -6, -5], [-10, -9, -8, -6, -4, -3, -2, -1], [-10, -9, -8, -6, -4, -3, -2], [-10, -9, -8, -6, -4, -3, -1], [-10, -9, -8, -6, -4, -3], [-10, -9, -8, -6, -4, -2, -1], [-10, -9, -8, -6, -4, -2], [-10, -9, -8, -6, -4, -1], [-10, -9, -8, -6, -4], [-10, -9, -8, -6, -3, -2, -1], [-10, -9, -8, -6, -3, -2], [-10, -9, -8, -6, -3, -1], [-10, -9, -8, -6, -3], [-10, -9, -8, -6, -2, -1], [-10, -9, -8, -6, -2], [-10, -9, -8, -6, -1], [-10, -9, -8, -6], [-10, -9, -8, -5, -4, -3, -2, -1], [-10, -9, -8, -5, -4, -3, -2], [-10, -9, -8, -5, -4, -3, -1], [-10, -9, -8, -5, -4, -3], [-10, -9, -8, -5, -4, -2, -1], [-10, -9, -8, -5, -4, -2], [-10, -9, -8, -5, -4, -1], [-10, -9, -8, -5, -4], [-10, -9, -8, -5, -3, -2, -1], [-10, -9, -8, -5, -3, -2], [-10, -9, -8, -5, -3, -1], [-10, -9, -8, -5, -3], [-10, -9, -8, -5, -2, -1], [-10, -9, -8, -5, -2], [-10, -9, -8, -5, -1], [-10, -9, -8, -5], [-10, -9, -8, -4, -3, -2, -1], [-10, -9, -8, -4, -3, -2], [-10, -9, -8, -4, -3, -1], [-10, -9, -8, -4, -3], [-10, -9, -8, -4, -2, -1], [-10, -9, -8, -4, -2], [-10, -9, -8, -4, -1], [-10, -9, -8, -4], [-10, -9, -8, -3, -2, -1], [-10, -9, -8, -3, -2], [-10, -9, -8, -3, -1], [-10, -9, -8, -3], [-10, -9, -8, -2, -1], [-10, -9, -8, -2], [-10, -9, -8, -1], [-10, -9, -8], [-10, -9, -7, -6, -5, -4, -3, -2, -1], [-10, -9, -7, -6, -5, -4, -3, -2], [-10, -9, -7, -6, -5, -4, -3, -1], [-10, -9, -7, -6, -5, -4, -3], [-10, -9, -7, -6, -5, -4, -2, -1], [-10, -9, -7, -6, -5, -4, -2], [-10, -9, -7, -6, -5, -4, -1], [-10, -9, -7, -6, -5, -4], [-10, -9, -7, -6, -5, -3, -2, -1], [-10, -9, -7, -6, -5, -3, -2], [-10, -9, -7, -6, -5, -3, -1], [-10, -9, -7, -6, -5, -3], [-10, -9, -7, -6, -5, -2, -1], [-10, -9, -7, -6, -5, -2], [-10, -9, -7, -6, -5, -1], [-10, -9, -7, -6, -5], [-10, -9, -7, -6, -4, -3, -2, -1], [-10, -9, -7, -6, -4, -3, -2], [-10, -9, -7, -6, -4, -3, -1], [-10, -9, -7, -6, -4, -3], [-10, -9, -7, -6, -4, -2, -1], [-10, -9, -7, -6, -4, -2], [-10, -9, -7, -6, -4, -1], [-10, -9, -7, -6, -4], [-10, -9, -7, -6, -3, -2, -1], [-10, -9, -7, -6, -3, -2], [-10, -9, -7, -6, -3, -1], [-10, -9, -7, -6, -3], [-10, -9, -7, -6, -2, -1], [-10, -9, -7, -6, -2], [-10, -9, -7, -6, -1], [-10, -9, -7, -6], [-10, -9, -7, -5, -4, -3, -2, -1], [-10, -9, -7, -5, -4, -3, -2], [-10, -9, -7, -5, -4, -3, -1], [-10, -9, -7, -5, -4, -3], [-10, -9, -7, -5, -4, -2, -1], [-10, -9, -7, -5, -4, -2], [-10, -9, -7, -5, -4, -1], [-10, -9, -7, -5, -4], [-10, -9, -7, -5, -3, -2, -1], [-10, -9, -7, -5, -3, -2], [-10, -9, -7, -5, -3, -1], [-10, -9, -7, -5, -3], [-10, -9, -7, -5, -2, -1], [-10, -9, -7, -5, -2], [-10, -9, -7, -5, -1], [-10, -9, -7, -5], [-10, -9, -7, -4, -3, -2, -1], [-10, -9, -7, -4, -3, -2], [-10, -9, -7, -4, -3, -1], [-10, -9, -7, -4, -3], [-10, -9, -7, -4, -2, -1], [-10, -9, -7, -4, -2], [-10, -9, -7, -4, -1], [-10, -9, -7, -4], [-10, -9, -7, -3, -2, -1], [-10, -9, -7, -3, -2], [-10, -9, -7, -3, -1], [-10, -9, -7, -3], [-10, -9, -7, -2, -1], [-10, -9, -7, -2], [-10, -9, -7, -1], [-10, -9, -7], [-10, -9, -6, -5, -4, -3, -2, -1], [-10, -9, -6, -5, -4, -3, -2], [-10, -9, -6, -5, -4, -3, -1], [-10, -9, -6, -5, -4, -3], [-10, -9, -6, -5, -4, -2, -1], [-10, -9, -6, -5, -4, -2], [-10, -9, -6, -5, -4, -1], [-10, -9, -6, -5, -4], [-10, -9, -6, -5, -3, -2, -1], [-10, -9, -6, -5, -3, -2], [-10, -9, -6, -5, -3, -1], [-10, -9, -6, -5, -3], [-10, -9, -6, -5, -2, -1], [-10, -9, -6, -5, -2], [-10, -9, -6, -5, -1], [-10, -9, -6, -5], [-10, -9, -6, -4, -3, -2, -1], [-10, -9, -6, -4, -3, -2], [-10, -9, -6, -4, -3, -1], [-10, -9, -6, -4, -3], [-10, -9, -6, -4, -2, -1], [-10, -9, -6, -4, -2], [-10, -9, -6, -4, -1], [-10, -9, -6, -4], [-10, -9, -6, -3, -2, -1], [-10, -9, -6, -3, -2], [-10, -9, -6, -3, -1], [-10, -9, -6, -3], [-10, -9, -6, -2, -1], [-10, -9, -6, -2], [-10, -9, -6, -1], [-10, -9, -6], [-10, -9, -5, -4, -3, -2, -1], [-10, -9, -5, -4, -3, -2], [-10, -9, -5, -4, -3, -1], [-10, -9, -5, -4, -3], [-10, -9, -5, -4, -2, -1], [-10, -9, -5, -4, -2], [-10, -9, -5, -4, -1], [-10, -9, -5, -4], [-10, -9, -5, -3, -2, -1], [-10, -9, -5, -3, -2], [-10, -9, -5, -3, -1], [-10, -9, -5, -3], [-10, -9, -5, -2, -1], [-10, -9, -5, -2], [-10, -9, -5, -1], [-10, -9, -5], [-10, -9, -4, -3, -2, -1], [-10, -9, -4, -3, -2], [-10, -9, -4, -3, -1], [-10, -9, -4, -3], [-10, -9, -4, -2, -1], [-10, -9, -4, -2], [-10, -9, -4, -1], [-10, -9, -4], [-10, -9, -3, -2, -1], [-10, -9, -3, -2], [-10, -9, -3, -1], [-10, -9, -3], [-10, -9, -2, -1], [-10, -9, -2], [-10, -9, -1], [-10, -9], [-10, -8, -7, -6, -5, -4, -3, -2, -1], [-10, -8, -7, -6, -5, -4, -3, -2], [-10, -8, -7, -6, -5, -4, -3, -1], [-10, -8, -7, -6, -5, -4, -3], [-10, -8, -7, -6, -5, -4, -2, -1], [-10, -8, -7, -6, -5, -4, -2], [-10, -8, -7, -6, -5, -4, -1], [-10, -8, -7, -6, -5, -4], [-10, -8, -7, -6, -5, -3, -2, -1], [-10, -8, -7, -6, -5, -3, -2], [-10, -8, -7, -6, -5, -3, -1], [-10, -8, -7, -6, -5, -3], [-10, -8, -7, -6, -5, -2, -1], [-10, -8, -7, -6, -5, -2], [-10, -8, -7, -6, -5, -1], [-10, -8, -7, -6, -5], [-10, -8, -7, -6, -4, -3, -2, -1], [-10, -8, -7, -6, -4, -3, -2], [-10, -8, -7, -6, -4, -3, -1], [-10, -8, -7, -6, -4, -3], [-10, -8, -7, -6, -4, -2, -1], [-10, -8, -7, -6, -4, -2], [-10, -8, -7, -6, -4, -1], [-10, -8, -7, -6, -4], [-10, -8, -7, -6, -3, -2, -1], [-10, -8, -7, -6, -3, -2], [-10, -8, -7, -6, -3, -1], [-10, -8, -7, -6, -3], [-10, -8, -7, -6, -2, -1], [-10, -8, -7, -6, -2], [-10, -8, -7, -6, -1], [-10, -8, -7, -6], [-10, -8, -7, -5, -4, -3, -2, -1], [-10, -8, -7, -5, -4, -3, -2], [-10, -8, -7, -5, -4, -3, -1], [-10, -8, -7, -5, -4, -3], [-10, -8, -7, -5, -4, -2, -1], [-10, -8, -7, -5, -4, -2], [-10, -8, -7, -5, -4, -1], [-10, -8, -7, -5, -4], [-10, -8, -7, -5, -3, -2, -1], [-10, -8, -7, -5, -3, -2], [-10, -8, -7, -5, -3, -1], [-10, -8, -7, -5, -3], [-10, -8, -7, -5, -2, -1], [-10, -8, -7, -5, -2], [-10, -8, -7, -5, -1], [-10, -8, -7, -5], [-10, -8, -7, -4, -3, -2, -1], [-10, -8, -7, -4, -3, -2], [-10, -8, -7, -4, -3, -1], [-10, -8, -7, -4, -3], [-10, -8, -7, -4, -2, -1], [-10, -8, -7, -4, -2], [-10, -8, -7, -4, -1], [-10, -8, -7, -4], [-10, -8, -7, -3, -2, -1], [-10, -8, -7, -3, -2], [-10, -8, -7, -3, -1], [-10, -8, -7, -3], [-10, -8, -7, -2, -1], [-10, -8, -7, -2], [-10, -8, -7, -1], [-10, -8, -7], [-10, -8, -6, -5, -4, -3, -2, -1], [-10, -8, -6, -5, -4, -3, -2], [-10, -8, -6, -5, -4, -3, -1], [-10, -8, -6, -5, -4, -3], [-10, -8, -6, -5, -4, -2, -1], [-10, -8, -6, -5, -4, -2], [-10, -8, -6, -5, -4, -1], [-10, -8, -6, -5, -4], [-10, -8, -6, -5, -3, -2, -1], [-10, -8, -6, -5, -3, -2], [-10, -8, -6, -5, -3, -1], [-10, -8, -6, -5, -3], [-10, -8, -6, -5, -2, -1], [-10, -8, -6, -5, -2], [-10, -8, -6, -5, -1], [-10, -8, -6, -5], [-10, -8, -6, -4, -3, -2, -1], [-10, -8, -6, -4, -3, -2], [-10, -8, -6, -4, -3, -1], [-10, -8, -6, -4, -3], [-10, -8, -6, -4, -2, -1], [-10, -8, -6, -4, -2], [-10, -8, -6, -4, -1], [-10, -8, -6, -4], [-10, -8, -6, -3, -2, -1], [-10, -8, -6, -3, -2], [-10, -8, -6, -3, -1], [-10, -8, -6, -3], [-10, -8, -6, -2, -1], 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-7, -5, -3, -2, -1], [-8, -7, -5, -3, -2], [-8, -7, -5, -3, -1], [-8, -7, -5, -3], [-8, -7, -5, -2, -1], [-8, -7, -5, -2], [-8, -7, -5, -1], [-8, -7, -5], [-8, -7, -4, -3, -2, -1], [-8, -7, -4, -3, -2], [-8, -7, -4, -3, -1], [-8, -7, -4, -3], [-8, -7, -4, -2, -1], [-8, -7, -4, -2], [-8, -7, -4, -1], [-8, -7, -4], [-8, -7, -3, -2, -1], [-8, -7, -3, -2], [-8, -7, -3, -1], [-8, -7, -3], [-8, -7, -2, -1], [-8, -7, -2], [-8, -7, -1], [-8, -7], [-8, -6, -5, -4, -3, -2, -1], [-8, -6, -5, -4, -3, -2], [-8, -6, -5, -4, -3, -1], [-8, -6, -5, -4, -3], [-8, -6, -5, -4, -2, -1], [-8, -6, -5, -4, -2], [-8, -6, -5, -4, -1], [-8, -6, -5, -4], [-8, -6, -5, -3, -2, -1], [-8, -6, -5, -3, -2], [-8, -6, -5, -3, -1], [-8, -6, -5, -3], [-8, -6, -5, -2, -1], [-8, -6, -5, -2], [-8, -6, -5, -1], [-8, -6, -5], [-8, -6, -4, -3, -2, -1], [-8, -6, -4, -3, -2], [-8, -6, -4, -3, -1], [-8, -6, -4, -3], [-8, -6, -4, -2, -1], [-8, -6, -4, -2], [-8, -6, -4, -1], [-8, -6, -4], [-8, -6, -3, -2, -1], [-8, -6, -3, -2], [-8, -6, -3, -1], [-8, -6, -3], [-8, -6, -2, -1], [-8, -6, -2], [-8, -6, -1], [-8, -6], [-8, -5, -4, -3, -2, -1], [-8, -5, -4, -3, -2], [-8, -5, -4, -3, -1], [-8, -5, -4, -3], [-8, -5, -4, -2, -1], [-8, -5, -4, -2], [-8, -5, -4, -1], [-8, -5, -4], [-8, -5, -3, -2, -1], [-8, -5, -3, -2], [-8, -5, -3, -1], [-8, -5, -3], [-8, -5, -2, -1], [-8, -5, -2], [-8, -5, -1], [-8, -5], [-8, -4, -3, -2, -1], [-8, -4, -3, -2], [-8, -4, -3, -1], [-8, -4, -3], [-8, -4, -2, -1], [-8, -4, -2], [-8, -4, -1], [-8, -4], [-8, -3, -2, -1], [-8, -3, -2], [-8, -3, -1], [-8, -3], [-8, -2, -1], [-8, -2], [-8, -1], [-7, -6, -5, -4, -3, -2, -1], [-7, -6, -5, -4, -3, -2], [-7, -6, -5, -4, -3, -1], [-7, -6, -5, -4, -3], [-7, -6, -5, -4, -2, -1], [-7, -6, -5, -4, -2], [-7, -6, -5, -4, -1], [-7, -6, -5, -4], [-7, -6, -5, -3, -2, -1], [-7, -6, -5, -3, -2], [-7, -6, -5, -3, -1], [-7, -6, -5, -3], [-7, -6, -5, -2, -1], [-7, -6, -5, -2], [-7, -6, -5, -1], [-7, -6, -5], [-7, -6, -4, -3, -2, -1], [-7, -6, -4, -3, -2], [-7, -6, -4, -3, -1], [-7, -6, -4, -3], [-7, -6, -4, -2, -1], [-7, -6, -4, -2], [-7, -6, -4, -1], [-7, -6, -4], [-7, -6, -3, -2, -1], [-7, -6, -3, -2], [-7, -6, -3, -1], [-7, -6, -3], [-7, -6, -2, -1], [-7, -6, -2], [-7, -6, -1], [-7, -6], [-7, -5, -4, -3, -2, -1], [-7, -5, -4, -3, -2], [-7, -5, -4, -3, -1], [-7, -5, -4, -3], [-7, -5, -4, -2, -1], [-7, -5, -4, -2], [-7, -5, -4, -1], [-7, -5, -4], [-7, -5, -3, -2, -1], [-7, -5, -3, -2], [-7, -5, -3, -1], [-7, -5, -3], [-7, -5, -2, -1], [-7, -5, -2], [-7, -5, -1], [-7, -5], [-7, -4, -3, -2, -1], [-7, -4, -3, -2], [-7, -4, -3, -1], [-7, -4, -3], [-7, -4, -2, -1], [-7, -4, -2], [-7, -4, -1], [-7, -4], [-7, -3, -2, -1], [-7, -3, -2], [-7, -3, -1], [-7, -3], [-7, -2, -1], [-7, -2], [-7, -1], [-6, -5, -4, -3, -2, -1], [-6, -5, -4, -3, -2], [-6, -5, -4, -3, -1], [-6, -5, -4, -3], [-6, -5, -4, -2, -1], [-6, -5, -4, -2], [-6, -5, -4, -1], [-6, -5, -4], [-6, -5, -3, -2, -1], [-6, -5, -3, -2], [-6, -5, -3, -1], [-6, -5, -3], [-6, -5, -2, -1], [-6, -5, -2], [-6, -5, -1], [-6, -5], [-6, -4, -3, -2, -1], [-6, -4, -3, -2], [-6, -4, -3, -1], [-6, -4, -3], [-6, -4, -2, -1], [-6, -4, -2], [-6, -4, -1], [-6, -4], [-6, -3, -2, -1], [-6, -3, -2], [-6, -3, -1], [-6, -3], [-6, -2, -1], [-6, -2], [-6, -1], [-5, -4, -3, -2, -1], [-5, -4, -3, -2], [-5, -4, -3, -1], [-5, -4, -3], [-5, -4, -2, -1], [-5, -4, -2], [-5, -4, -1], [-5, -4], [-5, -3, -2, -1], [-5, -3, -2], [-5, -3, -1], [-5, -3], [-5, -2, -1], [-5, -2], [-5, -1], [-4, -3, -2, -1], [-4, -3, -2], [-4, -3, -1], [-4, -3], [-4, -2, -1], [-4, -2], [-4, -1], [-3, -2, -1], [-3, -2], [-3, -1], [-2, -1]]\n assert candidate(nums = [1, 1, 1, 1, 1]) == [[1, 1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1], [1, 1]]\n assert candidate(nums = [5, 5, 4, 4, 3, 3]) == [[5, 5], [4, 4], [3, 3]]\n assert candidate(nums = [3, 2, 1]) == []\n assert candidate(nums = [1, 3, 2, 4, 3]) == [[1, 3, 4], [1, 3, 3], [1, 2, 4], [1, 2, 3], [1, 2], [1, 4], [1, 3], [3, 4], [3, 3], [2, 4], [2, 3]]\n assert candidate(nums = [7, 7, 7, 7]) == [[7, 7, 7, 7], [7, 7, 7], [7, 7]]\n assert candidate(nums = [1, 2, 3]) == [[1, 2, 3], [1, 2], [1, 3], [2, 3]]\n assert candidate(nums = [1, 2, 3, 2, 1]) == [[1, 2, 3], [1, 2, 2], [1, 3], [1, 2], [1, 1], [2, 3], [2, 2]]\n assert candidate(nums = [4, 4, 3, 2, 1]) == [[4, 4]]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4]) == [[1, 2, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3], [1, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 1, 2, 3, 4], [1, 1, 2, 3], [1, 1, 2, 4], [1, 1, 2], [1, 1, 3, 4], [1, 1, 3], [1, 1, 4], [1, 1], [2, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3], [2, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4], [2, 2, 2], [3, 4, 4], [3, 3, 3, 4], [3, 3, 3], [4, 4], [3, 3, 4], [3, 3], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], [1, 3], [1, 4], [2, 3, 4], [2, 3], [2, 4], [3, 4]]\n assert candidate(nums = [100, -100, 0, 0]) == [[-100, 0, 0], [-100, 0], [0, 0]]\n assert candidate(nums = [3, 1, 2, 4, 3, 5, 1, 2, 4, 5, 6, 2, 3, 4, 5]) == [[3, 4, 5, 5, 6], [3, 4, 5, 5, 5], [3, 4, 4, 5, 6], [3, 4, 4, 5, 5], [3, 4, 4, 6], [3, 4, 4, 4, 5], [3, 4, 4, 4], [3, 3, 5, 5, 6], [3, 3, 5, 5, 5], [3, 3, 4, 5, 6], [3, 3, 4, 5, 5], [3, 3, 4, 6], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 5, 6], [3, 3, 5, 5], [3, 3, 6], [3, 3, 3, 4, 5], [3, 3, 3, 4], [3, 3, 3, 5], [3, 3, 3], [1, 2, 4, 5, 5, 6], [1, 2, 4, 5, 5, 5], [1, 2, 4, 4, 5, 6], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 6], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4], [1, 2, 3, 5, 5, 6], [1, 2, 3, 5, 5, 5], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5, 6], [1, 2, 3, 5, 5], [1, 2, 3, 6], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 5, 5, 6], [1, 2, 5, 5, 5], [1, 2, 2, 4, 5, 6], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 6], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 5, 6], [1, 2, 2, 5, 5], [1, 2, 2, 6], [1, 2, 2, 2, 3, 4, 5], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 5], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4, 5], [1, 2, 2, 2, 4], [1, 2, 2, 2, 5], [1, 2, 2, 2], [1, 4, 5, 5, 6], [1, 4, 5, 5, 5], [1, 4, 4, 5, 6], [1, 4, 4, 5, 5], [1, 4, 4, 6], [1, 4, 4, 4, 5], [1, 4, 4, 4], [1, 3, 5, 5, 6], [1, 3, 5, 5, 5], [1, 3, 4, 5, 6], [1, 3, 4, 5, 5], [1, 3, 4, 6], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 5, 6], [1, 3, 5, 5], [1, 3, 6], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5], [1, 3, 3], [1, 5, 5, 6], [1, 5, 5, 5], [1, 1, 2, 4, 5, 6], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 6], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 5, 6], [1, 1, 2, 5, 5], [1, 1, 2, 6], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 4, 5, 6], [1, 1, 4, 5, 5], [1, 1, 4, 6], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 5, 6], [1, 1, 5, 5], [1, 1, 6], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5], [1, 1], [2, 4, 5, 5, 6], [2, 4, 5, 5, 5], [2, 4, 4, 5, 6], [2, 4, 4, 5, 5], [2, 4, 4, 6], [2, 4, 4, 4, 5], [2, 4, 4, 4], [2, 3, 5, 5, 6], [2, 3, 5, 5, 5], [2, 3, 4, 5, 6], [2, 3, 4, 5, 5], [2, 3, 4, 6], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 5, 6], [2, 3, 5, 5], [2, 3, 6], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5], [2, 3, 3], [2, 5, 5, 6], [2, 5, 5, 5], [2, 2, 4, 5, 6], [2, 2, 4, 5, 5], [2, 2, 4, 6], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 5, 6], [2, 2, 5, 5], [2, 2, 6], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 4], [2, 2, 2, 3, 5], [2, 2, 2, 3], [2, 2, 2, 4, 5], [2, 2, 2, 4], [2, 2, 2, 5], [2, 2, 2], [4, 5, 5, 6], [4, 5, 5, 5], [4, 4, 5, 6], [4, 4, 5, 5], [4, 4, 6], [4, 4, 4, 5], [4, 4, 4], [3, 5, 5, 6], [3, 5, 5, 5], [3, 4, 5, 6], [3, 4, 5, 5], [3, 4, 6], [3, 4, 4, 5], [3, 4, 4], [3, 5, 6], [3, 5, 5], [3, 6], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5], [3, 3], [5, 5, 6], [5, 5, 5], [1, 2, 4, 5, 6], [1, 2, 4, 5, 5], [1, 2, 4, 6], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 5, 6], [1, 2, 5, 5], [1, 2, 6], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5], [1, 2, 2], [1, 4, 5, 6], [1, 4, 5, 5], [1, 4, 6], [1, 4, 4, 5], [1, 4, 4], [1, 5, 6], [1, 5, 5], [1, 6], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [2, 4, 5, 6], [2, 4, 5, 5], [2, 4, 6], [2, 4, 4, 5], [2, 4, 4], [2, 5, 6], [2, 5, 5], [2, 6], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [4, 5, 6], [4, 5, 5], [4, 6], [4, 4, 5], [4, 4], [5, 6], [5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [3, 4, 5], [3, 4], [3, 5], [4, 5]]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [[3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3], [3, 3, 3], [3, 3]]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5]) == [[1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 3, 3, 3, 4, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 3, 4, 5], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3, 5, 5, 5], [1, 2, 2, 3, 3, 3, 5, 5], [1, 2, 2, 3, 3, 3, 5], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5, 5], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5, 5], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5, 5, 5], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5, 5], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5, 5], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5, 5, 5], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5, 5], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5, 5], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 3, 4, 4, 5], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 4, 5, 5, 5], [1, 2, 3, 3, 3, 4, 5, 5], [1, 2, 3, 3, 3, 4, 5], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 5, 5, 5], [1, 2, 3, 3, 3, 5, 5], [1, 2, 3, 3, 3, 5], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4, 4, 5, 5, 5], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5, 5], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5, 5], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5, 5, 5], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5, 5], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5, 5], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5, 5, 5], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5, 5], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5, 5], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 3, 4, 4, 5, 5, 5], [1, 3, 3, 3, 4, 4, 5, 5], [1, 3, 3, 3, 4, 4, 5], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 4, 5, 5, 5], [1, 3, 3, 3, 4, 5, 5], [1, 3, 3, 3, 4, 5], [1, 3, 3, 3, 4], [1, 3, 3, 3, 5, 5, 5], [1, 3, 3, 3, 5, 5], [1, 3, 3, 3, 5], [1, 3, 3, 3], [1, 3, 3, 4, 4, 5, 5, 5], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5, 5], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5, 5], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5, 5, 5], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5, 5], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5, 5], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 5, 5, 5], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5, 5], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5, 5], [1, 5, 5], [1, 5], [2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [2, 2, 3, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 3, 4, 4, 5], [2, 2, 3, 3, 3, 4, 4], [2, 2, 3, 3, 3, 4, 5, 5, 5], [2, 2, 3, 3, 3, 4, 5, 5], [2, 2, 3, 3, 3, 4, 5], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3, 5, 5, 5], [2, 2, 3, 3, 3, 5, 5], [2, 2, 3, 3, 3, 5], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 5, 5, 5], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5, 5], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5, 5], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5, 5, 5], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5, 5], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5, 5], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5, 5, 5], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5, 5], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5, 5], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 3, 4, 4, 5, 5, 5], [2, 3, 3, 3, 4, 4, 5, 5], [2, 3, 3, 3, 4, 4, 5], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4, 5, 5, 5], [2, 3, 3, 3, 4, 5, 5], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 5, 5, 5], [2, 3, 3, 3, 5, 5], [2, 3, 3, 3, 5], [2, 3, 3, 3], [2, 3, 3, 4, 4, 5, 5, 5], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5, 5], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5, 5], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5, 5, 5], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5, 5], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5, 5], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 5, 5, 5], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5, 5], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5, 5], [2, 5, 5], [2, 5], [3, 3, 3, 4, 4, 5, 5, 5], [3, 3, 3, 4, 4, 5, 5], [3, 3, 3, 4, 4, 5], [3, 3, 3, 4, 4], [3, 3, 3, 4, 5, 5, 5], [3, 3, 3, 4, 5, 5], [3, 3, 3, 4, 5], [3, 3, 3, 4], [3, 3, 3, 5, 5, 5], [3, 3, 3, 5, 5], [3, 3, 3, 5], [3, 3, 3], [3, 3, 4, 4, 5, 5, 5], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5, 5], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5, 5], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 5, 5, 5], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5, 5], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5, 5], [3, 5, 5], [3, 5], [4, 4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5, 5], [4, 5, 5], [4, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [3, 8, 7, 1, 2, 1, 5, 6, 7, 8, 10]) == [[3, 8, 8, 10], [3, 8, 8], [3, 7, 7, 8, 10], [3, 7, 7, 8], [3, 7, 7, 10], [3, 7, 7], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 10], [3, 5, 6, 7], [3, 5, 6, 8, 10], [3, 5, 6, 8], [3, 5, 6, 10], [3, 5, 6], [3, 5, 7, 8, 10], [3, 5, 7, 8], [3, 5, 7, 10], [3, 5, 7], [3, 5, 8, 10], [3, 5, 8], [3, 5, 10], [3, 5], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 10], [3, 6, 8], [3, 6, 10], [3, 6], [3, 7, 8, 10], [3, 7, 8], [3, 7, 10], [3, 7], [3, 8, 10], [3, 8], [3, 10], [8, 8, 10], [8, 8], [7, 7, 8, 10], [7, 7, 8], [7, 7, 10], [7, 7], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 10], [1, 2, 6, 7], [1, 2, 6, 8, 10], [1, 2, 6, 8], [1, 2, 6, 10], [1, 2, 6], [1, 2, 7, 8, 10], [1, 2, 7, 8], [1, 2, 7, 10], [1, 2, 7], [1, 2, 8, 10], [1, 2, 8], [1, 2, 10], [1, 2], [1, 1, 5, 6, 7, 8, 10], [1, 1, 5, 6, 7, 8], [1, 1, 5, 6, 7, 10], [1, 1, 5, 6, 7], [1, 1, 5, 6, 8, 10], [1, 1, 5, 6, 8], [1, 1, 5, 6, 10], [1, 1, 5, 6], [1, 1, 5, 7, 8, 10], [1, 1, 5, 7, 8], [1, 1, 5, 7, 10], [1, 1, 5, 7], [1, 1, 5, 8, 10], [1, 1, 5, 8], [1, 1, 5, 10], [1, 1, 5], [1, 1, 6, 7, 8, 10], [1, 1, 6, 7, 8], [1, 1, 6, 7, 10], [1, 1, 6, 7], [1, 1, 6, 8, 10], [1, 1, 6, 8], [1, 1, 6, 10], [1, 1, 6], [1, 1, 7, 8, 10], [1, 1, 7, 8], [1, 1, 7, 10], [1, 1, 7], [1, 1, 8, 10], [1, 1, 8], [1, 1, 10], [1, 1], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 10], [2, 5, 6, 7], [2, 5, 6, 8, 10], [2, 5, 6, 8], [2, 5, 6, 10], [2, 5, 6], [2, 5, 7, 8, 10], [2, 5, 7, 8], [2, 5, 7, 10], [2, 5, 7], [2, 5, 8, 10], [2, 5, 8], [2, 5, 10], [2, 5], [2, 6, 7, 8, 10], [2, 6, 7, 8], [2, 6, 7, 10], [2, 6, 7], [2, 6, 8, 10], [2, 6, 8], [2, 6, 10], [2, 6], [2, 7, 8, 10], [2, 7, 8], [2, 7, 10], [2, 7], [2, 8, 10], [2, 8], [2, 10], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 10], [1, 5, 6, 7], [1, 5, 6, 8, 10], [1, 5, 6, 8], [1, 5, 6, 10], [1, 5, 6], [1, 5, 7, 8, 10], [1, 5, 7, 8], [1, 5, 7, 10], [1, 5, 7], [1, 5, 8, 10], [1, 5, 8], [1, 5, 10], [1, 5], [1, 6, 7, 8, 10], [1, 6, 7, 8], [1, 6, 7, 10], [1, 6, 7], [1, 6, 8, 10], [1, 6, 8], [1, 6, 10], [1, 6], [1, 7, 8, 10], [1, 7, 8], [1, 7, 10], [1, 7], [1, 8, 10], [1, 8], [1, 10], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 10], [5, 6, 8], [5, 6, 10], [5, 6], [5, 7, 8, 10], [5, 7, 8], [5, 7, 10], [5, 7], [5, 8, 10], [5, 8], [5, 10], [6, 7, 8, 10], [6, 7, 8], [6, 7, 10], [6, 7], [6, 8, 10], [6, 8], [6, 10], [7, 8, 10], [7, 8], [7, 10], [8, 10]]\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == [[1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [1, 2, 2, 2, 2], [1, 1, 2, 2, 2], [1, 1, 1, 2, 2], [1, 1, 1, 1, 2], [1, 1, 1, 1, 1], [2, 2, 2, 2], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1, 1], [2, 2, 2], [1, 2, 2], [1, 1, 2], [1, 1, 1], [2, 2], [1, 2], [1, 1]]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == [[10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10], [10, 10, 10, 10], [10, 10, 10], [10, 10]]\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9]) == [[1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 7, 9], [1, 3, 4, 5, 6, 7, 7], [1, 3, 4, 5, 6, 6, 8, 9], [1, 3, 4, 5, 6, 6, 8], [1, 3, 4, 5, 6, 6, 7, 9], [1, 3, 4, 5, 6, 6, 7], [1, 3, 4, 5, 6, 6, 9], [1, 3, 4, 5, 6, 6], [1, 3, 4, 5, 5, 7, 8, 9], [1, 3, 4, 5, 5, 7, 8], [1, 3, 4, 5, 5, 7, 7, 9], [1, 3, 4, 5, 5, 7, 7], [1, 3, 4, 5, 5, 6, 8, 9], [1, 3, 4, 5, 5, 6, 8], [1, 3, 4, 5, 5, 6, 7, 9], [1, 3, 4, 5, 5, 6, 7], [1, 3, 4, 5, 5, 6, 9], [1, 3, 4, 5, 5, 6], [1, 3, 4, 5, 5, 8, 9], [1, 3, 4, 5, 5, 8], [1, 3, 4, 5, 5, 7, 9], [1, 3, 4, 5, 5, 7], [1, 3, 4, 5, 5, 9], [1, 3, 4, 5, 5], [1, 3, 4, 4, 6, 7, 8, 9], [1, 3, 4, 4, 6, 7, 8], [1, 3, 4, 4, 6, 7, 7, 9], [1, 3, 4, 4, 6, 7, 7], [1, 3, 4, 4, 6, 6, 8, 9], [1, 3, 4, 4, 6, 6, 8], [1, 3, 4, 4, 6, 6, 7, 9], [1, 3, 4, 4, 6, 6, 7], [1, 3, 4, 4, 6, 6, 9], [1, 3, 4, 4, 6, 6], [1, 3, 4, 4, 5, 7, 8, 9], [1, 3, 4, 4, 5, 7, 8], [1, 3, 4, 4, 5, 7, 7, 9], [1, 3, 4, 4, 5, 7, 7], [1, 3, 4, 4, 5, 6, 8, 9], [1, 3, 4, 4, 5, 6, 8], [1, 3, 4, 4, 5, 6, 7, 9], [1, 3, 4, 4, 5, 6, 7], [1, 3, 4, 4, 5, 6, 9], [1, 3, 4, 4, 5, 6], [1, 3, 4, 4, 5, 8, 9], [1, 3, 4, 4, 5, 8], [1, 3, 4, 4, 5, 7, 9], [1, 3, 4, 4, 5, 7], [1, 3, 4, 4, 5, 9], [1, 3, 4, 4, 5], [1, 3, 4, 4, 7, 8, 9], [1, 3, 4, 4, 7, 8], [1, 3, 4, 4, 7, 7, 9], [1, 3, 4, 4, 7, 7], [1, 3, 4, 4, 6, 8, 9], [1, 3, 4, 4, 6, 8], [1, 3, 4, 4, 6, 7, 9], [1, 3, 4, 4, 6, 7], [1, 3, 4, 4, 6, 9], [1, 3, 4, 4, 6], [1, 3, 4, 4, 8, 9], [1, 3, 4, 4, 8], [1, 3, 4, 4, 7, 9], [1, 3, 4, 4, 7], [1, 3, 4, 4, 9], [1, 3, 4, 4], [1, 3, 3, 5, 6, 7, 8, 9], [1, 3, 3, 5, 6, 7, 8], [1, 3, 3, 5, 6, 7, 7, 9], [1, 3, 3, 5, 6, 7, 7], [1, 3, 3, 5, 6, 6, 8, 9], [1, 3, 3, 5, 6, 6, 8], [1, 3, 3, 5, 6, 6, 7, 9], [1, 3, 3, 5, 6, 6, 7], [1, 3, 3, 5, 6, 6, 9], [1, 3, 3, 5, 6, 6], [1, 3, 3, 5, 5, 7, 8, 9], [1, 3, 3, 5, 5, 7, 8], [1, 3, 3, 5, 5, 7, 7, 9], [1, 3, 3, 5, 5, 7, 7], [1, 3, 3, 5, 5, 6, 8, 9], [1, 3, 3, 5, 5, 6, 8], [1, 3, 3, 5, 5, 6, 7, 9], [1, 3, 3, 5, 5, 6, 7], [1, 3, 3, 5, 5, 6, 9], [1, 3, 3, 5, 5, 6], [1, 3, 3, 5, 5, 8, 9], [1, 3, 3, 5, 5, 8], [1, 3, 3, 5, 5, 7, 9], [1, 3, 3, 5, 5, 7], [1, 3, 3, 5, 5, 9], [1, 3, 3, 5, 5], [1, 3, 3, 4, 6, 7, 8, 9], [1, 3, 3, 4, 6, 7, 8], [1, 3, 3, 4, 6, 7, 7, 9], [1, 3, 3, 4, 6, 7, 7], [1, 3, 3, 4, 6, 6, 8, 9], [1, 3, 3, 4, 6, 6, 8], [1, 3, 3, 4, 6, 6, 7, 9], [1, 3, 3, 4, 6, 6, 7], [1, 3, 3, 4, 6, 6, 9], [1, 3, 3, 4, 6, 6], [1, 3, 3, 4, 5, 7, 8, 9], [1, 3, 3, 4, 5, 7, 8], [1, 3, 3, 4, 5, 7, 7, 9], [1, 3, 3, 4, 5, 7, 7], [1, 3, 3, 4, 5, 6, 8, 9], [1, 3, 3, 4, 5, 6, 8], [1, 3, 3, 4, 5, 6, 7, 9], [1, 3, 3, 4, 5, 6, 7], [1, 3, 3, 4, 5, 6, 9], [1, 3, 3, 4, 5, 6], [1, 3, 3, 4, 5, 8, 9], [1, 3, 3, 4, 5, 8], [1, 3, 3, 4, 5, 7, 9], [1, 3, 3, 4, 5, 7], [1, 3, 3, 4, 5, 9], [1, 3, 3, 4, 5], [1, 3, 3, 4, 7, 8, 9], [1, 3, 3, 4, 7, 8], [1, 3, 3, 4, 7, 7, 9], [1, 3, 3, 4, 7, 7], [1, 3, 3, 4, 6, 8, 9], [1, 3, 3, 4, 6, 8], [1, 3, 3, 4, 6, 7, 9], [1, 3, 3, 4, 6, 7], [1, 3, 3, 4, 6, 9], [1, 3, 3, 4, 6], [1, 3, 3, 4, 8, 9], [1, 3, 3, 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5, 5, 7, 8], [4, 5, 5, 7, 7, 9], [4, 5, 5, 7, 7], [4, 5, 5, 6, 8, 9], [4, 5, 5, 6, 8], [4, 5, 5, 6, 7, 9], [4, 5, 5, 6, 7], [4, 5, 5, 6, 9], [4, 5, 5, 6], [4, 5, 5, 8, 9], [4, 5, 5, 8], [4, 5, 5, 7, 9], [4, 5, 5, 7], [4, 5, 5, 9], [4, 5, 5], [4, 4, 6, 7, 8, 9], [4, 4, 6, 7, 8], [4, 4, 6, 7, 7, 9], [4, 4, 6, 7, 7], [4, 4, 6, 6, 8, 9], [4, 4, 6, 6, 8], [4, 4, 6, 6, 7, 9], [4, 4, 6, 6, 7], [4, 4, 6, 6, 9], [4, 4, 6, 6], [4, 4, 5, 7, 8, 9], [4, 4, 5, 7, 8], [4, 4, 5, 7, 7, 9], [4, 4, 5, 7, 7], [4, 4, 5, 6, 8, 9], [4, 4, 5, 6, 8], [4, 4, 5, 6, 7, 9], [4, 4, 5, 6, 7], [4, 4, 5, 6, 9], [4, 4, 5, 6], [4, 4, 5, 8, 9], [4, 4, 5, 8], [4, 4, 5, 7, 9], [4, 4, 5, 7], [4, 4, 5, 9], [4, 4, 5], [4, 4, 7, 8, 9], [4, 4, 7, 8], [4, 4, 7, 7, 9], [4, 4, 7, 7], [4, 4, 6, 8, 9], [4, 4, 6, 8], [4, 4, 6, 7, 9], [4, 4, 6, 7], [4, 4, 6, 9], [4, 4, 6], [4, 4, 8, 9], [4, 4, 8], [4, 4, 7, 9], [4, 4, 7], [4, 4, 9], [4, 4], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8], [3, 5, 6, 7, 7, 9], [3, 5, 6, 7, 7], [3, 5, 6, 6, 8, 9], [3, 5, 6, 6, 8], [3, 5, 6, 6, 7, 9], [3, 5, 6, 6, 7], [3, 5, 6, 6, 9], [3, 5, 6, 6], [3, 5, 5, 7, 8, 9], [3, 5, 5, 7, 8], [3, 5, 5, 7, 7, 9], [3, 5, 5, 7, 7], [3, 5, 5, 6, 8, 9], [3, 5, 5, 6, 8], [3, 5, 5, 6, 7, 9], [3, 5, 5, 6, 7], [3, 5, 5, 6, 9], [3, 5, 5, 6], [3, 5, 5, 8, 9], [3, 5, 5, 8], [3, 5, 5, 7, 9], [3, 5, 5, 7], [3, 5, 5, 9], [3, 5, 5], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8], [3, 4, 6, 7, 7, 9], [3, 4, 6, 7, 7], [3, 4, 6, 6, 8, 9], [3, 4, 6, 6, 8], [3, 4, 6, 6, 7, 9], [3, 4, 6, 6, 7], [3, 4, 6, 6, 9], [3, 4, 6, 6], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8], [3, 4, 5, 7, 7, 9], [3, 4, 5, 7, 7], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7], [3, 4, 5, 6, 9], [3, 4, 5, 6], [3, 4, 5, 8, 9], [3, 4, 5, 8], [3, 4, 5, 7, 9], [3, 4, 5, 7], [3, 4, 5, 9], [3, 4, 5], [3, 4, 7, 8, 9], [3, 4, 7, 8], [3, 4, 7, 7, 9], [3, 4, 7, 7], [3, 4, 6, 8, 9], [3, 4, 6, 8], [3, 4, 6, 7, 9], [3, 4, 6, 7], [3, 4, 6, 9], [3, 4, 6], [3, 4, 8, 9], [3, 4, 8], [3, 4, 7, 9], [3, 4, 7], [3, 4, 9], [3, 4], [3, 6, 7, 8, 9], [3, 6, 7, 8], [3, 6, 7, 7, 9], [3, 6, 7, 7], [3, 6, 6, 8, 9], [3, 6, 6, 8], [3, 6, 6, 7, 9], [3, 6, 6, 7], [3, 6, 6, 9], [3, 6, 6], [3, 5, 7, 8, 9], [3, 5, 7, 8], [3, 5, 7, 7, 9], [3, 5, 7, 7], [3, 5, 6, 8, 9], [3, 5, 6, 8], [3, 5, 6, 7, 9], [3, 5, 6, 7], [3, 5, 6, 9], [3, 5, 6], [3, 5, 8, 9], [3, 5, 8], [3, 5, 7, 9], [3, 5, 7], [3, 5, 9], [3, 5], [3, 7, 8, 9], [3, 7, 8], [3, 7, 7, 9], [3, 7, 7], [3, 6, 8, 9], [3, 6, 8], [3, 6, 7, 9], [3, 6, 7], [3, 6, 9], [3, 6], [3, 8, 9], [3, 8], [3, 7, 9], [3, 7], [3, 9], [5, 6, 7, 8, 9], [5, 6, 7, 8], [5, 6, 7, 7, 9], [5, 6, 7, 7], [5, 6, 6, 8, 9], [5, 6, 6, 8], [5, 6, 6, 7, 9], [5, 6, 6, 7], [5, 6, 6, 9], [5, 6, 6], [5, 5, 7, 8, 9], [5, 5, 7, 8], [5, 5, 7, 7, 9], [5, 5, 7, 7], [5, 5, 6, 8, 9], [5, 5, 6, 8], [5, 5, 6, 7, 9], [5, 5, 6, 7], [5, 5, 6, 9], [5, 5, 6], [5, 5, 8, 9], [5, 5, 8], [5, 5, 7, 9], [5, 5, 7], [5, 5, 9], [5, 5], [4, 6, 7, 8, 9], [4, 6, 7, 8], [4, 6, 7, 7, 9], [4, 6, 7, 7], [4, 6, 6, 8, 9], [4, 6, 6, 8], [4, 6, 6, 7, 9], [4, 6, 6, 7], [4, 6, 6, 9], [4, 6, 6], [4, 5, 7, 8, 9], [4, 5, 7, 8], [4, 5, 7, 7, 9], [4, 5, 7, 7], [4, 5, 6, 8, 9], [4, 5, 6, 8], [4, 5, 6, 7, 9], [4, 5, 6, 7], [4, 5, 6, 9], [4, 5, 6], [4, 5, 8, 9], [4, 5, 8], [4, 5, 7, 9], [4, 5, 7], [4, 5, 9], [4, 5], [4, 7, 8, 9], [4, 7, 8], [4, 7, 7, 9], [4, 7, 7], [4, 6, 8, 9], [4, 6, 8], [4, 6, 7, 9], [4, 6, 7], [4, 6, 9], [4, 6], [4, 8, 9], [4, 8], [4, 7, 9], [4, 7], [4, 9], [6, 7, 8, 9], [6, 7, 8], [6, 7, 7, 9], [6, 7, 7], [6, 6, 8, 9], [6, 6, 8], [6, 6, 7, 9], [6, 6, 7], [6, 6, 9], [6, 6], [5, 7, 8, 9], [5, 7, 8], [5, 7, 7, 9], [5, 7, 7], [5, 6, 8, 9], [5, 6, 8], [5, 6, 7, 9], [5, 6, 7], [5, 6, 9], [5, 6], [5, 8, 9], [5, 8], [5, 7, 9], [5, 7], [5, 9], [7, 8, 9], [7, 8], [7, 7, 9], [7, 7], [6, 8, 9], [6, 8], [6, 7, 9], [6, 7], [6, 9], [8, 9], [7, 9]]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == [[5, 5], [4, 4, 5], [4, 4], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5], [3, 3], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5], [1, 1], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [3, 4, 5], [3, 4], [3, 5], [4, 5]]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == []\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5, 5, 5], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 4, 5], [1, 2, 3, 4, 4, 4], [1, 2, 3, 5, 5, 5], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 3, 4, 5], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 5], [1, 2, 3, 3, 3], [1, 2, 4, 5, 5, 5], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4], [1, 2, 5, 5, 5], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 5, 5], [1, 2, 2, 2, 3, 4, 5], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 5], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4, 5], [1, 2, 2, 2, 4], [1, 2, 2, 2, 5], [1, 2, 2, 2], [1, 3, 4, 5, 5, 5], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 4, 5], [1, 3, 4, 4, 4], [1, 3, 5, 5, 5], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 5, 5], [1, 3, 3, 3, 4, 5], [1, 3, 3, 3, 4], [1, 3, 3, 3, 5], [1, 3, 3, 3], [1, 4, 5, 5, 5], [1, 4, 4, 5, 5], [1, 4, 4, 4, 5], [1, 4, 4, 4], [1, 5, 5, 5], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 5, 5], [1, 1, 1, 2, 3, 4, 5], [1, 1, 1, 2, 3, 4], [1, 1, 1, 2, 3, 5], [1, 1, 1, 2, 3], [1, 1, 1, 2, 4, 5], [1, 1, 1, 2, 4], [1, 1, 1, 2, 5], [1, 1, 1, 2], [1, 1, 1, 3, 4, 5], [1, 1, 1, 3, 4], [1, 1, 1, 3, 5], [1, 1, 1, 3], [1, 1, 1, 4, 5], [1, 1, 1, 4], [1, 1, 1, 5], [1, 1, 1], [2, 3, 4, 5, 5, 5], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4], [2, 3, 5, 5, 5], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 5, 5], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 5], [2, 3, 3, 3], [2, 4, 5, 5, 5], [2, 4, 4, 5, 5], [2, 4, 4, 4, 5], [2, 4, 4, 4], [2, 5, 5, 5], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 5, 5], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 4], [2, 2, 2, 3, 5], [2, 2, 2, 3], [2, 2, 2, 4, 5], [2, 2, 2, 4], [2, 2, 2, 5], [2, 2, 2], [3, 4, 5, 5, 5], [3, 4, 4, 5, 5], [3, 4, 4, 4, 5], [3, 4, 4, 4], [3, 5, 5, 5], [3, 3, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 5, 5], [3, 3, 3, 4, 5], [3, 3, 3, 4], [3, 3, 3, 5], [3, 3, 3], [4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [5, 5, 5], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5], [1, 2, 2], [1, 3, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5], [1, 3, 3], [1, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5], [1, 1], [2, 3, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5], [2, 3, 3], [2, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [3, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5], [3, 3], [4, 5, 5], [4, 4, 5], [4, 4], [5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [3, 4, 5], [3, 4], [3, 5], [4, 5]]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == []\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == [[1, 2, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 3, 3, 3, 3], [1, 1, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 3, 3], [1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1], [2, 3, 3, 3, 3], [2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2], [3, 3, 3, 3], [1, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3], [1, 1, 1], [2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [3, 3, 3], [1, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3], [1, 1], [2, 3, 3], [2, 2, 3], [2, 2], [3, 3], [1, 2, 3], [1, 2], [1, 3], [2, 3]]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1]) == [[1, 2, 3, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4, 5], [1, 2, 4, 4], [1, 2, 5], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 3, 4, 5], [1, 3, 4, 4], [1, 3, 5], [1, 3, 4], [1, 3, 3], [1, 4, 5], [1, 4, 4], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1], [2, 3, 4, 5], [2, 3, 4, 4], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 4, 5], [2, 4, 4], [2, 5], [2, 4], [2, 3], [2, 2], [3, 4, 5], [3, 4, 4], [3, 5], [3, 4], [3, 3], [4, 5], [4, 4]]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]) == [[1, 2, 2, 3, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4, 4], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4, 4], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4, 4], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4, 4], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 3, 4, 4, 4, 4], [1, 3, 3, 3, 4, 4, 4], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3], [1, 3, 3, 4, 4, 4, 4], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4, 4], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4, 4], [1, 4, 4, 4], [1, 4, 4], [1, 4], [2, 2, 3, 3, 3, 4, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 4, 4], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4, 4], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4, 4], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 3, 4, 4, 4, 4], [2, 3, 3, 3, 4, 4, 4], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3], [2, 3, 3, 4, 4, 4, 4], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4, 4], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4, 4], [2, 4, 4, 4], [2, 4, 4], [2, 4], [3, 3, 3, 4, 4, 4, 4], [3, 3, 3, 4, 4, 4], [3, 3, 3, 4, 4], [3, 3, 3, 4], [3, 3, 3], [3, 3, 4, 4, 4, 4], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4, 4], [3, 4, 4, 4], [3, 4, 4], [3, 4], [4, 4, 4, 4], [4, 4, 4], [4, 4]]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3]) == [[1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 4, 4, 5], [1, 2, 3, 4, 4, 4, 4], [1, 2, 3, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4, 4], [1, 2, 3, 3, 3, 4, 5], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 5], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 3], [1, 2, 4, 5, 5], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4, 4], [1, 2, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4, 4], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 2, 2, 3, 4, 5], [1, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 3, 5], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 4, 5], [1, 2, 2, 2, 4, 4], [1, 2, 2, 2, 5], [1, 2, 2, 2, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 3, 4, 5, 5], [1, 3, 4, 4, 4, 5], [1, 3, 4, 4, 4, 4], [1, 3, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4, 4], [1, 3, 3, 3, 4, 5], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 5], [1, 3, 3, 3, 4], [1, 3, 3, 3, 3], [1, 4, 5, 5], [1, 4, 4, 4, 5], [1, 4, 4, 4, 4], [1, 5, 5], [1, 4, 4, 5], [1, 4, 4, 4], [1, 3, 3, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 5], [1, 3, 3, 4], [1, 3, 3, 3], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 5], [1, 2, 2, 4], [1, 2, 2, 3], [1, 2, 2], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 3], [1, 1, 2, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 5], [1, 1, 2, 4], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 5], [1, 1, 3, 4], [1, 1, 3, 3], [1, 1, 4, 5], [1, 1, 4, 4], [1, 1, 5], [1, 1, 4], [1, 1, 3], [1, 1], [2, 3, 4, 5, 5], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4, 4], [2, 3, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4, 4], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 3], [2, 4, 5, 5], [2, 4, 4, 4, 5], [2, 4, 4, 4, 4], [2, 5, 5], [2, 4, 4, 5], [2, 4, 4, 4], [2, 3, 3, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 5], [2, 3, 3, 4], [2, 3, 3, 3], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 4, 4], [2, 2, 2, 3, 5], [2, 2, 2, 3, 4], [2, 2, 2, 3, 3], [2, 2, 2, 4, 5], [2, 2, 2, 4, 4], [2, 2, 2, 5], [2, 2, 2, 4], [2, 2, 2, 3], [2, 2, 2], [3, 4, 5, 5], [3, 4, 4, 4, 5], [3, 4, 4, 4, 4], [3, 5, 5], [3, 4, 4, 5], [3, 4, 4, 4], [3, 3, 3, 4, 5], [3, 3, 3, 4, 4], [3, 3, 3, 5], [3, 3, 3, 4], [3, 3, 3, 3], [4, 5, 5], [4, 4, 4, 5], [4, 4, 4, 4], [5, 5], [4, 4, 5], [4, 4, 4], [3, 3, 4, 5], [3, 3, 4, 4], [3, 3, 5], [3, 3, 4], [3, 3, 3], [2, 2, 3, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 5], [2, 2, 3, 4], [2, 2, 3, 3], [2, 2, 4, 5], [2, 2, 4, 4], [2, 2, 5], [2, 2, 4], [2, 2, 3], [2, 2], [1, 2, 3, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4, 5], [1, 2, 4, 4], [1, 2, 5], [1, 2, 4], [1, 2, 3], [1, 2], [1, 3, 4, 5], [1, 3, 4, 4], [1, 3, 5], [1, 3, 4], [1, 3, 3], [1, 4, 5], [1, 4, 4], [1, 5], [1, 4], [1, 3], [2, 3, 4, 5], [2, 3, 4, 4], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 4, 5], [2, 4, 4], [2, 5], [2, 4], [2, 3], [3, 4, 5], [3, 4, 4], [3, 5], [3, 4], [3, 3], [4, 5], [4, 4]]\n assert candidate(nums = [1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == [[1, 1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1], [1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [1, 2, 2, 2, 2], [1, 1, 2, 2, 2], [1, 1, 1, 2, 2], [1, 1, 1, 1, 2], [1, 1, 1, 1], [2, 2, 2, 2], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1], [2, 2, 2], [1, 2, 2], [1, 1, 2], [1, 1], [2, 2], [1, 2]]\n assert candidate(nums = [7, 7, 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4]) == [[7, 7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7], [7, 7], [6, 6, 6, 6], [6, 6, 6], [6, 6], [5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == [[10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10], [10, 10, 10, 10], [10, 10, 10], [10, 10]]\n assert candidate(nums = [3, 2, 1, 2, 3, 4, 3, 2, 1]) == [[3, 3, 4], [3, 3, 3], [2, 2, 3, 4], [2, 2, 3, 3], [2, 2, 4], [2, 2, 3], [2, 2, 2], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 3, 4], [1, 3, 3], [1, 4], [1, 3], [1, 2], [1, 1], [2, 3, 4], [2, 3, 3], [2, 4], [2, 3], [2, 2], [3, 4], [3, 3]]\n assert candidate(nums = [100, -100, 100, -100, 100, -100]) == [[100, 100, 100], [-100, 100, 100], [-100, -100, 100], [-100, -100, -100], [100, 100], [-100, 100], [-100, -100]]\n assert candidate(nums = [1, 2, 3, 2, 3, 4, 5, 4, 5, 6]) == [[1, 2, 3, 3, 4, 5, 5, 6], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5, 6], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4, 6], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 5, 5, 6], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 4, 5, 6], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4, 6], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 6], [1, 2, 3, 3, 5], [1, 2, 3, 3, 6], [1, 2, 3, 3], [1, 2, 2, 3, 4, 5, 5, 6], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5, 6], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4, 6], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 5, 5, 6], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 4, 5, 6], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4, 6], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 6], [1, 2, 2, 3, 5], [1, 2, 2, 3, 6], [1, 2, 2, 3], [1, 2, 2, 4, 5, 5, 6], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 4, 5, 6], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4, 6], [1, 2, 2, 4, 4], [1, 2, 2, 5, 5, 6], [1, 2, 2, 5, 5], [1, 2, 2, 4, 5, 6], [1, 2, 2, 4, 5], [1, 2, 2, 4, 6], [1, 2, 2, 4], [1, 2, 2, 5, 6], [1, 2, 2, 5], [1, 2, 2, 6], [1, 2, 2], [1, 3, 3, 4, 5, 5, 6], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 4, 5, 6], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4, 6], [1, 3, 3, 4, 4], [1, 3, 3, 5, 5, 6], [1, 3, 3, 5, 5], [1, 3, 3, 4, 5, 6], [1, 3, 3, 4, 5], [1, 3, 3, 4, 6], [1, 3, 3, 4], [1, 3, 3, 5, 6], [1, 3, 3, 5], [1, 3, 3, 6], [1, 3, 3], [1, 2, 3, 4, 5, 5, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 4, 5, 6], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4, 6], [1, 2, 3, 4, 4], [1, 2, 3, 5, 5, 6], [1, 2, 3, 5, 5], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6], [1, 2, 3, 4], [1, 2, 3, 5, 6], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3], [1, 2, 4, 5, 5, 6], [1, 2, 4, 5, 5], [1, 2, 4, 4, 5, 6], [1, 2, 4, 4, 5], [1, 2, 4, 4, 6], [1, 2, 4, 4], [1, 2, 5, 5, 6], [1, 2, 5, 5], [1, 2, 4, 5, 6], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4], [1, 2, 5, 6], [1, 2, 5], [1, 2, 6], [1, 2], [1, 3, 4, 5, 5, 6], [1, 3, 4, 5, 5], [1, 3, 4, 4, 5, 6], [1, 3, 4, 4, 5], [1, 3, 4, 4, 6], [1, 3, 4, 4], [1, 3, 5, 5, 6], [1, 3, 5, 5], [1, 3, 4, 5, 6], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4], [1, 3, 5, 6], [1, 3, 5], [1, 3, 6], [1, 3], [1, 4, 5, 5, 6], [1, 4, 5, 5], [1, 4, 4, 5, 6], [1, 4, 4, 5], [1, 4, 4, 6], [1, 4, 4], [1, 5, 5, 6], [1, 5, 5], [1, 4, 5, 6], [1, 4, 5], [1, 4, 6], [1, 4], [1, 5, 6], [1, 5], [1, 6], [2, 3, 3, 4, 5, 5, 6], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 4, 5, 6], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4, 6], [2, 3, 3, 4, 4], [2, 3, 3, 5, 5, 6], [2, 3, 3, 5, 5], [2, 3, 3, 4, 5, 6], [2, 3, 3, 4, 5], [2, 3, 3, 4, 6], [2, 3, 3, 4], [2, 3, 3, 5, 6], [2, 3, 3, 5], [2, 3, 3, 6], [2, 3, 3], [2, 2, 3, 4, 5, 5, 6], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 4, 5, 6], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4, 6], [2, 2, 3, 4, 4], [2, 2, 3, 5, 5, 6], [2, 2, 3, 5, 5], [2, 2, 3, 4, 5, 6], [2, 2, 3, 4, 5], [2, 2, 3, 4, 6], [2, 2, 3, 4], [2, 2, 3, 5, 6], [2, 2, 3, 5], [2, 2, 3, 6], [2, 2, 3], [2, 2, 4, 5, 5, 6], [2, 2, 4, 5, 5], [2, 2, 4, 4, 5, 6], [2, 2, 4, 4, 5], [2, 2, 4, 4, 6], [2, 2, 4, 4], [2, 2, 5, 5, 6], [2, 2, 5, 5], [2, 2, 4, 5, 6], [2, 2, 4, 5], [2, 2, 4, 6], [2, 2, 4], [2, 2, 5, 6], [2, 2, 5], [2, 2, 6], [2, 2], [3, 3, 4, 5, 5, 6], [3, 3, 4, 5, 5], [3, 3, 4, 4, 5, 6], [3, 3, 4, 4, 5], [3, 3, 4, 4, 6], [3, 3, 4, 4], [3, 3, 5, 5, 6], [3, 3, 5, 5], [3, 3, 4, 5, 6], [3, 3, 4, 5], [3, 3, 4, 6], [3, 3, 4], [3, 3, 5, 6], [3, 3, 5], [3, 3, 6], [3, 3], [2, 3, 4, 5, 5, 6], [2, 3, 4, 5, 5], [2, 3, 4, 4, 5, 6], [2, 3, 4, 4, 5], [2, 3, 4, 4, 6], [2, 3, 4, 4], [2, 3, 5, 5, 6], [2, 3, 5, 5], [2, 3, 4, 5, 6], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4], [2, 3, 5, 6], [2, 3, 5], [2, 3, 6], [2, 3], [2, 4, 5, 5, 6], [2, 4, 5, 5], [2, 4, 4, 5, 6], [2, 4, 4, 5], [2, 4, 4, 6], [2, 4, 4], [2, 5, 5, 6], [2, 5, 5], [2, 4, 5, 6], [2, 4, 5], [2, 4, 6], [2, 4], [2, 5, 6], [2, 5], [2, 6], [3, 4, 5, 5, 6], [3, 4, 5, 5], [3, 4, 4, 5, 6], [3, 4, 4, 5], [3, 4, 4, 6], [3, 4, 4], [3, 5, 5, 6], [3, 5, 5], [3, 4, 5, 6], [3, 4, 5], [3, 4, 6], [3, 4], [3, 5, 6], [3, 5], [3, 6], [4, 5, 5, 6], [4, 5, 5], [4, 4, 5, 6], [4, 4, 5], [4, 4, 6], [4, 4], [5, 5, 6], [5, 5], [4, 5, 6], [4, 5], [4, 6], [5, 6]]\n assert candidate(nums = [1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5, 3, 1, 3, 5]) == [[1, 3, 5, 5, 5, 5], [1, 3, 3, 3, 5, 5, 5], [1, 3, 3, 3, 3, 3, 5, 5], [1, 3, 3, 3, 3, 3, 3, 3, 5], [1, 3, 3, 3, 3, 3, 3, 3], [1, 5, 5, 5, 5], [1, 3, 3, 5, 5, 5], [1, 3, 3, 3, 3, 5, 5], [1, 3, 3, 3, 3, 3, 3, 5], [1, 3, 3, 3, 3, 3, 3], [1, 1, 3, 5, 5, 5], [1, 1, 3, 3, 3, 5, 5], [1, 1, 3, 3, 3, 3, 3, 5], [1, 1, 3, 3, 3, 3, 3], [1, 1, 5, 5, 5], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 3, 3, 5], [1, 1, 3, 3, 3, 3], [1, 1, 1, 3, 5, 5], [1, 1, 1, 3, 3, 3, 5], [1, 1, 1, 3, 3, 3], [1, 1, 1, 5, 5], [1, 1, 1, 3, 3, 5], [1, 1, 1, 3, 3], [1, 1, 1, 1, 3, 5], [1, 1, 1, 1, 3], [1, 1, 1, 1, 5], [1, 1, 1, 1], [3, 5, 5, 5, 5], [3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3, 3], [5, 5, 5, 5], [3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3], [1, 3, 5, 5, 5], [1, 3, 3, 3, 5, 5], [1, 3, 3, 3, 3, 3, 5], [1, 3, 3, 3, 3, 3], [1, 5, 5, 5], [1, 3, 3, 5, 5], [1, 3, 3, 3, 3, 5], [1, 3, 3, 3, 3], [1, 1, 3, 5, 5], [1, 1, 3, 3, 3, 5], [1, 1, 3, 3, 3], [1, 1, 5, 5], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 1, 3, 5], [1, 1, 1, 3], [1, 1, 1, 5], [1, 1, 1], [3, 5, 5, 5], [3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3], [5, 5, 5], [3, 3, 5, 5], [3, 3, 3, 3, 5], [3, 3, 3, 3], [1, 3, 5, 5], [1, 3, 3, 3, 5], [1, 3, 3, 3], [1, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 1, 3, 5], [1, 1, 3], [1, 1, 5], [1, 1], [3, 5, 5], [3, 3, 3, 5], [3, 3, 3], [5, 5], [3, 3, 5], [3, 3], [1, 3, 5], [1, 3], [1, 5], [3, 5]]\n assert candidate(nums = [100, -100, 0, 50, -50, 25, -25, 75, -75, 50, 0, -100, 100, 50, -50]) == [[100, 100], [-100, 0, 50, 75, 100], [-100, 0, 50, 75], [-100, 0, 50, 50, 100], [-100, 0, 50, 50, 50], [-100, 0, 25, 75, 100], [-100, 0, 25, 75], [-100, 0, 25, 50, 100], [-100, 0, 25, 50, 50], [-100, 0, 25, 100], [-100, 0, 25, 50], [-100, 0, 25], [-100, 0, 75, 100], [-100, 0, 75], [-100, 0, 50, 100], [-100, 0, 50, 50], [-100, 0, 0, 100], [-100, 0, 0, 50], [-100, 0, 0], [-100, 50, 75, 100], [-100, 50, 75], [-100, 50, 50, 100], [-100, 50, 50, 50], [-100, -50, 25, 75, 100], [-100, -50, 25, 75], [-100, -50, 25, 50, 100], [-100, -50, 25, 50, 50], [-100, -50, 25, 100], [-100, -50, 25, 50], [-100, -50, 25], [-100, -50, -25, 75, 100], [-100, -50, -25, 75], [-100, -50, -25, 50, 100], [-100, -50, -25, 50, 50], [-100, -50, -25, 0, 100], [-100, -50, -25, 0, 50], [-100, -50, -25, 0], [-100, -50, -25, 100], [-100, -50, -25, 50], [-100, -50, -25], [-100, -50, 75, 100], [-100, -50, 75], [-100, -50, 50, 100], [-100, -50, 50, 50], [-100, -50, 0, 100], [-100, -50, 0, 50], [-100, -50, 0], [-100, -50, 100], [-100, -50, 50], [-100, -50, -50], [-100, 25, 75, 100], [-100, 25, 75], [-100, 25, 50, 100], [-100, 25, 50, 50], [-100, 25, 100], [-100, 25, 50], [-100, 25], [-100, -25, 75, 100], [-100, -25, 75], [-100, -25, 50, 100], [-100, -25, 50, 50], [-100, -25, 0, 100], [-100, -25, 0, 50], [-100, -25, 0], [-100, -25, 100], [-100, -25, 50], [-100, -25], [-100, 75, 100], [-100, 75], [-100, -75, 50, 100], [-100, -75, 50, 50], [-100, -75, 0, 100], [-100, -75, 0, 50], [-100, -75, 0], [-100, -75, 100], [-100, -75, 50], [-100, -75, -50], [-100, -75], [-100, 50, 100], [-100, 50, 50], [-100, 0, 100], [-100, 0, 50], [-100, 0], [-100, -100, 100], [-100, -100, 50], [-100, -100, -50], [-100, -100], [0, 50, 75, 100], [0, 50, 75], [0, 50, 50, 100], [0, 50, 50, 50], [0, 25, 75, 100], [0, 25, 75], [0, 25, 50, 100], [0, 25, 50, 50], [0, 25, 100], [0, 25, 50], [0, 25], [0, 75, 100], [0, 75], [0, 50, 100], [0, 50, 50], [0, 0, 100], [0, 0, 50], [0, 0], [50, 75, 100], [50, 75], [50, 50, 100], [50, 50, 50], [-50, 25, 75, 100], [-50, 25, 75], [-50, 25, 50, 100], [-50, 25, 50, 50], [-50, 25, 100], [-50, 25, 50], [-50, 25], [-50, -25, 75, 100], [-50, -25, 75], [-50, -25, 50, 100], [-50, -25, 50, 50], [-50, -25, 0, 100], [-50, -25, 0, 50], [-50, -25, 0], [-50, -25, 100], [-50, -25, 50], [-50, -25], [-50, 75, 100], [-50, 75], [-50, 50, 100], [-50, 50, 50], [-50, 0, 100], [-50, 0, 50], [-50, 0], [-50, 100], [-50, 50], [-50, -50], [25, 75, 100], [25, 75], [25, 50, 100], [25, 50, 50], [25, 100], [25, 50], [-25, 75, 100], [-25, 75], [-25, 50, 100], [-25, 50, 50], [-25, 0, 100], [-25, 0, 50], [-25, 0], [-25, 100], [-25, 50], [75, 100], [-75, 50, 100], [-75, 50, 50], [-75, 0, 100], [-75, 0, 50], [-75, 0], [-75, 100], [-75, 50], [-75, -50], [50, 100], [50, 50], [0, 100], [0, 50], [-100, 100], [-100, 50], [-100, -50]]\n assert candidate(nums = [1, 3, 2, 4, 2, 3, 4]) == [[1, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 2, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4], [1, 2, 2], [1, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4], [1, 2], [1, 3, 4], [1, 3], [1, 4], [3, 4, 4], [3, 3, 4], [3, 3], [2, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4], [2, 2], [4, 4], [2, 3, 4], [2, 3], [2, 4], [3, 4]]\n assert candidate(nums = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == [[0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5], [0, 0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 5], [0, 0, 1, 1, 2, 2, 3, 3, 4, 5], [0, 0, 1, 1, 2, 2, 3, 3, 4], [0, 0, 1, 1, 2, 2, 3, 3, 5, 5], [0, 0, 1, 1, 2, 2, 3, 3, 5], [0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 5], [0, 0, 1, 1, 2, 2, 3, 4, 4, 5], [0, 0, 1, 1, 2, 2, 3, 4, 4], [0, 0, 1, 1, 2, 2, 3, 4, 5, 5], [0, 0, 1, 1, 2, 2, 3, 4, 5], [0, 0, 1, 1, 2, 2, 3, 4], [0, 0, 1, 1, 2, 2, 3, 5, 5], [0, 0, 1, 1, 2, 2, 3, 5], [0, 0, 1, 1, 2, 2, 3], [0, 0, 1, 1, 2, 2, 4, 4, 5, 5], [0, 0, 1, 1, 2, 2, 4, 4, 5], [0, 0, 1, 1, 2, 2, 4, 4], [0, 0, 1, 1, 2, 2, 4, 5, 5], [0, 0, 1, 1, 2, 2, 4, 5], [0, 0, 1, 1, 2, 2, 4], [0, 0, 1, 1, 2, 2, 5, 5], [0, 0, 1, 1, 2, 2, 5], [0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 5], [0, 0, 1, 1, 2, 3, 3, 4, 4, 5], [0, 0, 1, 1, 2, 3, 3, 4, 4], [0, 0, 1, 1, 2, 3, 3, 4, 5, 5], [0, 0, 1, 1, 2, 3, 3, 4, 5], [0, 0, 1, 1, 2, 3, 3, 4], [0, 0, 1, 1, 2, 3, 3, 5, 5], [0, 0, 1, 1, 2, 3, 3, 5], [0, 0, 1, 1, 2, 3, 3], [0, 0, 1, 1, 2, 3, 4, 4, 5, 5], [0, 0, 1, 1, 2, 3, 4, 4, 5], [0, 0, 1, 1, 2, 3, 4, 4], [0, 0, 1, 1, 2, 3, 4, 5, 5], [0, 0, 1, 1, 2, 3, 4, 5], [0, 0, 1, 1, 2, 3, 4], [0, 0, 1, 1, 2, 3, 5, 5], [0, 0, 1, 1, 2, 3, 5], [0, 0, 1, 1, 2, 3], [0, 0, 1, 1, 2, 4, 4, 5, 5], [0, 0, 1, 1, 2, 4, 4, 5], [0, 0, 1, 1, 2, 4, 4], [0, 0, 1, 1, 2, 4, 5, 5], [0, 0, 1, 1, 2, 4, 5], [0, 0, 1, 1, 2, 4], [0, 0, 1, 1, 2, 5, 5], [0, 0, 1, 1, 2, 5], [0, 0, 1, 1, 2], [0, 0, 1, 1, 3, 3, 4, 4, 5, 5], [0, 0, 1, 1, 3, 3, 4, 4, 5], [0, 0, 1, 1, 3, 3, 4, 4], [0, 0, 1, 1, 3, 3, 4, 5, 5], [0, 0, 1, 1, 3, 3, 4, 5], [0, 0, 1, 1, 3, 3, 4], [0, 0, 1, 1, 3, 3, 5, 5], [0, 0, 1, 1, 3, 3, 5], [0, 0, 1, 1, 3, 3], [0, 0, 1, 1, 3, 4, 4, 5, 5], [0, 0, 1, 1, 3, 4, 4, 5], [0, 0, 1, 1, 3, 4, 4], [0, 0, 1, 1, 3, 4, 5, 5], [0, 0, 1, 1, 3, 4, 5], [0, 0, 1, 1, 3, 4], [0, 0, 1, 1, 3, 5, 5], [0, 0, 1, 1, 3, 5], [0, 0, 1, 1, 3], [0, 0, 1, 1, 4, 4, 5, 5], [0, 0, 1, 1, 4, 4, 5], [0, 0, 1, 1, 4, 4], [0, 0, 1, 1, 4, 5, 5], [0, 0, 1, 1, 4, 5], [0, 0, 1, 1, 4], [0, 0, 1, 1, 5, 5], [0, 0, 1, 1, 5], [0, 0, 1, 1], [0, 0, 1, 2, 2, 3, 3, 4, 4, 5, 5], [0, 0, 1, 2, 2, 3, 3, 4, 4, 5], [0, 0, 1, 2, 2, 3, 3, 4, 4], [0, 0, 1, 2, 2, 3, 3, 4, 5, 5], [0, 0, 1, 2, 2, 3, 3, 4, 5], [0, 0, 1, 2, 2, 3, 3, 4], [0, 0, 1, 2, 2, 3, 3, 5, 5], [0, 0, 1, 2, 2, 3, 3, 5], [0, 0, 1, 2, 2, 3, 3], [0, 0, 1, 2, 2, 3, 4, 4, 5, 5], [0, 0, 1, 2, 2, 3, 4, 4, 5], [0, 0, 1, 2, 2, 3, 4, 4], [0, 0, 1, 2, 2, 3, 4, 5, 5], [0, 0, 1, 2, 2, 3, 4, 5], [0, 0, 1, 2, 2, 3, 4], [0, 0, 1, 2, 2, 3, 5, 5], [0, 0, 1, 2, 2, 3, 5], [0, 0, 1, 2, 2, 3], [0, 0, 1, 2, 2, 4, 4, 5, 5], [0, 0, 1, 2, 2, 4, 4, 5], [0, 0, 1, 2, 2, 4, 4], [0, 0, 1, 2, 2, 4, 5, 5], [0, 0, 1, 2, 2, 4, 5], [0, 0, 1, 2, 2, 4], [0, 0, 1, 2, 2, 5, 5], [0, 0, 1, 2, 2, 5], [0, 0, 1, 2, 2], [0, 0, 1, 2, 3, 3, 4, 4, 5, 5], [0, 0, 1, 2, 3, 3, 4, 4, 5], [0, 0, 1, 2, 3, 3, 4, 4], [0, 0, 1, 2, 3, 3, 4, 5, 5], [0, 0, 1, 2, 3, 3, 4, 5], [0, 0, 1, 2, 3, 3, 4], [0, 0, 1, 2, 3, 3, 5, 5], [0, 0, 1, 2, 3, 3, 5], [0, 0, 1, 2, 3, 3], [0, 0, 1, 2, 3, 4, 4, 5, 5], [0, 0, 1, 2, 3, 4, 4, 5], [0, 0, 1, 2, 3, 4, 4], [0, 0, 1, 2, 3, 4, 5, 5], [0, 0, 1, 2, 3, 4, 5], [0, 0, 1, 2, 3, 4], [0, 0, 1, 2, 3, 5, 5], [0, 0, 1, 2, 3, 5], [0, 0, 1, 2, 3], [0, 0, 1, 2, 4, 4, 5, 5], [0, 0, 1, 2, 4, 4, 5], [0, 0, 1, 2, 4, 4], [0, 0, 1, 2, 4, 5, 5], [0, 0, 1, 2, 4, 5], [0, 0, 1, 2, 4], [0, 0, 1, 2, 5, 5], [0, 0, 1, 2, 5], [0, 0, 1, 2], [0, 0, 1, 3, 3, 4, 4, 5, 5], [0, 0, 1, 3, 3, 4, 4, 5], [0, 0, 1, 3, 3, 4, 4], [0, 0, 1, 3, 3, 4, 5, 5], [0, 0, 1, 3, 3, 4, 5], [0, 0, 1, 3, 3, 4], [0, 0, 1, 3, 3, 5, 5], [0, 0, 1, 3, 3, 5], [0, 0, 1, 3, 3], [0, 0, 1, 3, 4, 4, 5, 5], [0, 0, 1, 3, 4, 4, 5], [0, 0, 1, 3, 4, 4], [0, 0, 1, 3, 4, 5, 5], [0, 0, 1, 3, 4, 5], [0, 0, 1, 3, 4], [0, 0, 1, 3, 5, 5], [0, 0, 1, 3, 5], [0, 0, 1, 3], [0, 0, 1, 4, 4, 5, 5], [0, 0, 1, 4, 4, 5], [0, 0, 1, 4, 4], [0, 0, 1, 4, 5, 5], [0, 0, 1, 4, 5], [0, 0, 1, 4], [0, 0, 1, 5, 5], [0, 0, 1, 5], [0, 0, 1], [0, 0, 2, 2, 3, 3, 4, 4, 5, 5], [0, 0, 2, 2, 3, 3, 4, 4, 5], [0, 0, 2, 2, 3, 3, 4, 4], [0, 0, 2, 2, 3, 3, 4, 5, 5], [0, 0, 2, 2, 3, 3, 4, 5], [0, 0, 2, 2, 3, 3, 4], [0, 0, 2, 2, 3, 3, 5, 5], [0, 0, 2, 2, 3, 3, 5], [0, 0, 2, 2, 3, 3], [0, 0, 2, 2, 3, 4, 4, 5, 5], [0, 0, 2, 2, 3, 4, 4, 5], [0, 0, 2, 2, 3, 4, 4], [0, 0, 2, 2, 3, 4, 5, 5], [0, 0, 2, 2, 3, 4, 5], [0, 0, 2, 2, 3, 4], [0, 0, 2, 2, 3, 5, 5], [0, 0, 2, 2, 3, 5], [0, 0, 2, 2, 3], [0, 0, 2, 2, 4, 4, 5, 5], [0, 0, 2, 2, 4, 4, 5], [0, 0, 2, 2, 4, 4], [0, 0, 2, 2, 4, 5, 5], [0, 0, 2, 2, 4, 5], [0, 0, 2, 2, 4], [0, 0, 2, 2, 5, 5], [0, 0, 2, 2, 5], [0, 0, 2, 2], [0, 0, 2, 3, 3, 4, 4, 5, 5], [0, 0, 2, 3, 3, 4, 4, 5], [0, 0, 2, 3, 3, 4, 4], [0, 0, 2, 3, 3, 4, 5, 5], [0, 0, 2, 3, 3, 4, 5], [0, 0, 2, 3, 3, 4], [0, 0, 2, 3, 3, 5, 5], [0, 0, 2, 3, 3, 5], [0, 0, 2, 3, 3], [0, 0, 2, 3, 4, 4, 5, 5], [0, 0, 2, 3, 4, 4, 5], [0, 0, 2, 3, 4, 4], [0, 0, 2, 3, 4, 5, 5], [0, 0, 2, 3, 4, 5], [0, 0, 2, 3, 4], [0, 0, 2, 3, 5, 5], [0, 0, 2, 3, 5], [0, 0, 2, 3], [0, 0, 2, 4, 4, 5, 5], [0, 0, 2, 4, 4, 5], [0, 0, 2, 4, 4], [0, 0, 2, 4, 5, 5], [0, 0, 2, 4, 5], [0, 0, 2, 4], [0, 0, 2, 5, 5], [0, 0, 2, 5], [0, 0, 2], [0, 0, 3, 3, 4, 4, 5, 5], [0, 0, 3, 3, 4, 4, 5], [0, 0, 3, 3, 4, 4], [0, 0, 3, 3, 4, 5, 5], [0, 0, 3, 3, 4, 5], [0, 0, 3, 3, 4], [0, 0, 3, 3, 5, 5], [0, 0, 3, 3, 5], [0, 0, 3, 3], [0, 0, 3, 4, 4, 5, 5], [0, 0, 3, 4, 4, 5], [0, 0, 3, 4, 4], [0, 0, 3, 4, 5, 5], [0, 0, 3, 4, 5], [0, 0, 3, 4], [0, 0, 3, 5, 5], [0, 0, 3, 5], [0, 0, 3], [0, 0, 4, 4, 5, 5], [0, 0, 4, 4, 5], [0, 0, 4, 4], [0, 0, 4, 5, 5], [0, 0, 4, 5], [0, 0, 4], [0, 0, 5, 5], [0, 0, 5], [0, 0], [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [0, 1, 1, 2, 2, 3, 3, 4, 4, 5], [0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 1, 1, 2, 2, 3, 3, 4, 5, 5], [0, 1, 1, 2, 2, 3, 3, 4, 5], [0, 1, 1, 2, 2, 3, 3, 4], [0, 1, 1, 2, 2, 3, 3, 5, 5], [0, 1, 1, 2, 2, 3, 3, 5], [0, 1, 1, 2, 2, 3, 3], [0, 1, 1, 2, 2, 3, 4, 4, 5, 5], [0, 1, 1, 2, 2, 3, 4, 4, 5], [0, 1, 1, 2, 2, 3, 4, 4], [0, 1, 1, 2, 2, 3, 4, 5, 5], [0, 1, 1, 2, 2, 3, 4, 5], [0, 1, 1, 2, 2, 3, 4], [0, 1, 1, 2, 2, 3, 5, 5], [0, 1, 1, 2, 2, 3, 5], [0, 1, 1, 2, 2, 3], [0, 1, 1, 2, 2, 4, 4, 5, 5], [0, 1, 1, 2, 2, 4, 4, 5], [0, 1, 1, 2, 2, 4, 4], [0, 1, 1, 2, 2, 4, 5, 5], [0, 1, 1, 2, 2, 4, 5], [0, 1, 1, 2, 2, 4], [0, 1, 1, 2, 2, 5, 5], [0, 1, 1, 2, 2, 5], [0, 1, 1, 2, 2], [0, 1, 1, 2, 3, 3, 4, 4, 5, 5], [0, 1, 1, 2, 3, 3, 4, 4, 5], [0, 1, 1, 2, 3, 3, 4, 4], [0, 1, 1, 2, 3, 3, 4, 5, 5], [0, 1, 1, 2, 3, 3, 4, 5], [0, 1, 1, 2, 3, 3, 4], [0, 1, 1, 2, 3, 3, 5, 5], [0, 1, 1, 2, 3, 3, 5], [0, 1, 1, 2, 3, 3], [0, 1, 1, 2, 3, 4, 4, 5, 5], [0, 1, 1, 2, 3, 4, 4, 5], [0, 1, 1, 2, 3, 4, 4], [0, 1, 1, 2, 3, 4, 5, 5], [0, 1, 1, 2, 3, 4, 5], [0, 1, 1, 2, 3, 4], [0, 1, 1, 2, 3, 5, 5], [0, 1, 1, 2, 3, 5], [0, 1, 1, 2, 3], [0, 1, 1, 2, 4, 4, 5, 5], [0, 1, 1, 2, 4, 4, 5], [0, 1, 1, 2, 4, 4], [0, 1, 1, 2, 4, 5, 5], [0, 1, 1, 2, 4, 5], [0, 1, 1, 2, 4], [0, 1, 1, 2, 5, 5], [0, 1, 1, 2, 5], [0, 1, 1, 2], [0, 1, 1, 3, 3, 4, 4, 5, 5], [0, 1, 1, 3, 3, 4, 4, 5], [0, 1, 1, 3, 3, 4, 4], [0, 1, 1, 3, 3, 4, 5, 5], [0, 1, 1, 3, 3, 4, 5], [0, 1, 1, 3, 3, 4], [0, 1, 1, 3, 3, 5, 5], [0, 1, 1, 3, 3, 5], [0, 1, 1, 3, 3], [0, 1, 1, 3, 4, 4, 5, 5], [0, 1, 1, 3, 4, 4, 5], [0, 1, 1, 3, 4, 4], [0, 1, 1, 3, 4, 5, 5], [0, 1, 1, 3, 4, 5], [0, 1, 1, 3, 4], [0, 1, 1, 3, 5, 5], [0, 1, 1, 3, 5], [0, 1, 1, 3], [0, 1, 1, 4, 4, 5, 5], [0, 1, 1, 4, 4, 5], [0, 1, 1, 4, 4], [0, 1, 1, 4, 5, 5], [0, 1, 1, 4, 5], [0, 1, 1, 4], [0, 1, 1, 5, 5], [0, 1, 1, 5], [0, 1, 1], [0, 1, 2, 2, 3, 3, 4, 4, 5, 5], [0, 1, 2, 2, 3, 3, 4, 4, 5], [0, 1, 2, 2, 3, 3, 4, 4], [0, 1, 2, 2, 3, 3, 4, 5, 5], [0, 1, 2, 2, 3, 3, 4, 5], [0, 1, 2, 2, 3, 3, 4], [0, 1, 2, 2, 3, 3, 5, 5], [0, 1, 2, 2, 3, 3, 5], [0, 1, 2, 2, 3, 3], [0, 1, 2, 2, 3, 4, 4, 5, 5], [0, 1, 2, 2, 3, 4, 4, 5], [0, 1, 2, 2, 3, 4, 4], [0, 1, 2, 2, 3, 4, 5, 5], [0, 1, 2, 2, 3, 4, 5], [0, 1, 2, 2, 3, 4], [0, 1, 2, 2, 3, 5, 5], [0, 1, 2, 2, 3, 5], [0, 1, 2, 2, 3], [0, 1, 2, 2, 4, 4, 5, 5], [0, 1, 2, 2, 4, 4, 5], [0, 1, 2, 2, 4, 4], [0, 1, 2, 2, 4, 5, 5], [0, 1, 2, 2, 4, 5], [0, 1, 2, 2, 4], [0, 1, 2, 2, 5, 5], [0, 1, 2, 2, 5], [0, 1, 2, 2], [0, 1, 2, 3, 3, 4, 4, 5, 5], [0, 1, 2, 3, 3, 4, 4, 5], [0, 1, 2, 3, 3, 4, 4], [0, 1, 2, 3, 3, 4, 5, 5], [0, 1, 2, 3, 3, 4, 5], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 3, 5, 5], [0, 1, 2, 3, 3, 5], [0, 1, 2, 3, 3], [0, 1, 2, 3, 4, 4, 5, 5], [0, 1, 2, 3, 4, 4, 5], [0, 1, 2, 3, 4, 4], [0, 1, 2, 3, 4, 5, 5], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5, 5], [0, 1, 2, 3, 5], [0, 1, 2, 3], [0, 1, 2, 4, 4, 5, 5], [0, 1, 2, 4, 4, 5], [0, 1, 2, 4, 4], [0, 1, 2, 4, 5, 5], [0, 1, 2, 4, 5], [0, 1, 2, 4], [0, 1, 2, 5, 5], [0, 1, 2, 5], [0, 1, 2], [0, 1, 3, 3, 4, 4, 5, 5], [0, 1, 3, 3, 4, 4, 5], [0, 1, 3, 3, 4, 4], [0, 1, 3, 3, 4, 5, 5], [0, 1, 3, 3, 4, 5], [0, 1, 3, 3, 4], [0, 1, 3, 3, 5, 5], [0, 1, 3, 3, 5], [0, 1, 3, 3], [0, 1, 3, 4, 4, 5, 5], [0, 1, 3, 4, 4, 5], [0, 1, 3, 4, 4], [0, 1, 3, 4, 5, 5], [0, 1, 3, 4, 5], [0, 1, 3, 4], [0, 1, 3, 5, 5], [0, 1, 3, 5], [0, 1, 3], [0, 1, 4, 4, 5, 5], [0, 1, 4, 4, 5], [0, 1, 4, 4], [0, 1, 4, 5, 5], [0, 1, 4, 5], [0, 1, 4], [0, 1, 5, 5], [0, 1, 5], [0, 1], [0, 2, 2, 3, 3, 4, 4, 5, 5], [0, 2, 2, 3, 3, 4, 4, 5], [0, 2, 2, 3, 3, 4, 4], [0, 2, 2, 3, 3, 4, 5, 5], [0, 2, 2, 3, 3, 4, 5], [0, 2, 2, 3, 3, 4], [0, 2, 2, 3, 3, 5, 5], [0, 2, 2, 3, 3, 5], [0, 2, 2, 3, 3], [0, 2, 2, 3, 4, 4, 5, 5], [0, 2, 2, 3, 4, 4, 5], [0, 2, 2, 3, 4, 4], [0, 2, 2, 3, 4, 5, 5], [0, 2, 2, 3, 4, 5], [0, 2, 2, 3, 4], [0, 2, 2, 3, 5, 5], [0, 2, 2, 3, 5], [0, 2, 2, 3], [0, 2, 2, 4, 4, 5, 5], [0, 2, 2, 4, 4, 5], [0, 2, 2, 4, 4], [0, 2, 2, 4, 5, 5], [0, 2, 2, 4, 5], [0, 2, 2, 4], [0, 2, 2, 5, 5], [0, 2, 2, 5], [0, 2, 2], [0, 2, 3, 3, 4, 4, 5, 5], [0, 2, 3, 3, 4, 4, 5], [0, 2, 3, 3, 4, 4], [0, 2, 3, 3, 4, 5, 5], [0, 2, 3, 3, 4, 5], [0, 2, 3, 3, 4], [0, 2, 3, 3, 5, 5], [0, 2, 3, 3, 5], [0, 2, 3, 3], [0, 2, 3, 4, 4, 5, 5], [0, 2, 3, 4, 4, 5], [0, 2, 3, 4, 4], [0, 2, 3, 4, 5, 5], [0, 2, 3, 4, 5], [0, 2, 3, 4], [0, 2, 3, 5, 5], [0, 2, 3, 5], [0, 2, 3], [0, 2, 4, 4, 5, 5], [0, 2, 4, 4, 5], [0, 2, 4, 4], [0, 2, 4, 5, 5], [0, 2, 4, 5], [0, 2, 4], [0, 2, 5, 5], [0, 2, 5], [0, 2], [0, 3, 3, 4, 4, 5, 5], [0, 3, 3, 4, 4, 5], [0, 3, 3, 4, 4], [0, 3, 3, 4, 5, 5], [0, 3, 3, 4, 5], [0, 3, 3, 4], [0, 3, 3, 5, 5], [0, 3, 3, 5], [0, 3, 3], [0, 3, 4, 4, 5, 5], [0, 3, 4, 4, 5], [0, 3, 4, 4], [0, 3, 4, 5, 5], [0, 3, 4, 5], [0, 3, 4], [0, 3, 5, 5], [0, 3, 5], [0, 3], [0, 4, 4, 5, 5], [0, 4, 4, 5], [0, 4, 4], [0, 4, 5, 5], [0, 4, 5], [0, 4], [0, 5, 5], [0, 5], [1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 2, 2, 3, 3, 5], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5, 5], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 2, 2, 4, 4, 5], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4, 5, 5], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5, 5], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 2, 3, 3, 4, 4, 5, 5], [1, 1, 2, 3, 3, 4, 4, 5], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5, 5], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5, 5], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 3, 4, 4, 5, 5], [1, 1, 3, 3, 4, 4, 5], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5, 5], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 3, 4, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5, 5], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 4, 5, 5], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5, 5], [1, 1, 5], [1, 1], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5, 5], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 4, 5, 5], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5, 5], [1, 2, 5], [1, 2], [1, 3, 3, 4, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5, 5], [1, 3, 3, 5], [1, 3, 3], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 4, 5, 5], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5, 5], [1, 3, 5], [1, 3], [1, 4, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 4, 5, 5], [1, 4, 5], [1, 4], [1, 5, 5], [1, 5], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5], [2, 5], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5], [3, 5], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5], [4, 5], [5, 5]]\n assert candidate(nums = [1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3]) == [[1, 2, 3, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3, 3], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2], [1, 3, 3, 3, 3, 3], [1, 1, 2, 3, 3, 3, 3], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 3], [1, 1, 2, 2, 2, 2], [1, 1, 3, 3, 3, 3], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2], [1, 1, 1, 3, 3, 3], [1, 1, 1, 1, 2, 3, 3], [1, 1, 1, 1, 2, 2, 3], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1], [2, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2], [3, 3, 3, 3, 3], [1, 2, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 3, 3, 3, 3], [1, 1, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 3, 3], [1, 1, 1, 1, 2, 3], [1, 1, 1, 1, 2], [1, 1, 1, 1, 3], [1, 1, 1, 1], [2, 3, 3, 3, 3], [2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2], [3, 3, 3, 3], [1, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3], [1, 1, 1], [2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [3, 3, 3], [1, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3], [1, 1], [2, 3, 3], [2, 2, 3], [2, 2], [3, 3], [1, 2, 3], [1, 2], [1, 3], [2, 3]]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4]) == [[9, 9], [8, 9], [8, 8], [7, 9], [7, 8], [7, 7], [6, 9], [6, 8], [6, 7], [6, 6], [5, 9], [5, 8], [5, 7], [5, 6], [5, 5], [4, 9], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [3, 9], [3, 8], [3, 7], [3, 6], [3, 5], [3, 4], [2, 9], [2, 8], [2, 7], [2, 6], [2, 5], [2, 4], [1, 9], [1, 8], [1, 7], [1, 6], [1, 5], [1, 4]]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1]) == [[1, 1, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 3], [1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 2, 3, 3, 3, 3], [1, 1, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2, 2, 2], [1, 1, 3, 3, 3, 3], [1, 1, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2, 2, 2], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2, 2, 2], [1, 1, 1, 1, 3, 3], [1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2], [1, 1, 1, 1, 1], [1, 2, 2, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2, 2], [1, 2, 3, 3, 3, 3], [1, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2], [1, 3, 3, 3, 3], [1, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2, 2, 2], [1, 2, 3, 3], [1, 2, 3], [1, 2, 2, 2], [1, 1, 1, 3, 3], [1, 1, 1, 3], [1, 1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1, 1], [2, 2, 3, 3, 3, 3], [2, 2, 3, 3, 3], [2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2], [2, 3, 3, 3, 3], [2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2, 2, 2], [3, 3, 3, 3], [3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2, 2, 2], [2, 3, 3], [2, 3], [2, 2, 2], [1, 1, 3, 3], [1, 1, 3], [1, 1, 2, 2], [1, 1, 2], [1, 1, 1], [1, 3, 3], [1, 3], [1, 2, 2], [1, 2], [1, 1], [3, 3], [2, 2]]\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1], [1, 1]]\n assert candidate(nums = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == [[5, 5, 5], [4, 5, 5], [4, 4, 5], [4, 4, 4], [3, 5, 5], [3, 4, 5], [3, 4, 4], [3, 3, 5], [3, 3, 4], [3, 3, 3], [2, 5, 5], [2, 4, 5], [2, 4, 4], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 2, 5], [2, 2, 4], [2, 2, 3], [2, 2, 2], [1, 5, 5], [1, 4, 5], [1, 4, 4], [1, 3, 5], [1, 3, 4], [1, 3, 3], [1, 2, 5], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 1, 5], [1, 1, 4], [1, 1, 3], [1, 1, 2], [1, 1, 1], [5, 5], [4, 5], [4, 4], [3, 5], [3, 4], [3, 3], [2, 5], [2, 4], [2, 3], [2, 2], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1]]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3]) == [[1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3, 3, 3], [1, 1, 1, 2, 3, 3, 3, 3], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3, 3, 3], [1, 1, 1, 3, 3, 3, 3], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3], [1, 1, 1, 3], [1, 1, 1], [1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3], [1, 1, 2, 2, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 2, 3], [1, 1, 2, 2, 2, 2], [1, 1, 2, 2, 2, 3, 3, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 3, 3, 3], [1, 1, 2, 2, 3, 3, 3, 3], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 2, 3, 3, 3, 3, 3], [1, 1, 2, 3, 3, 3, 3], [1, 1, 2, 3, 3, 3], [1, 1, 2, 3, 3], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3, 3, 3, 3, 3], [1, 1, 3, 3, 3, 3], [1, 1, 3, 3, 3], [1, 1, 3, 3], [1, 1, 3], [1, 1], [1, 2, 2, 2, 2, 3, 3, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 2, 2, 2, 3, 3, 3, 3, 3], [1, 2, 2, 2, 3, 3, 3, 3], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3, 3], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3, 3, 3], [1, 2, 3, 3, 3, 3], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3, 3, 3], [1, 3, 3, 3, 3], [1, 3, 3, 3], [1, 3, 3], [1, 3], [2, 2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2], [2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3], [2, 3, 3, 3], [2, 3, 3], [2, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3], [3, 3, 3], [3, 3]]\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 4, 4, 4]) == [[1, 2, 2, 2, 3, 3, 4, 4, 4, 4], [1, 2, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 2, 3, 3, 4, 4], [1, 2, 2, 2, 3, 3, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3, 4, 4, 4, 4], [1, 2, 2, 2, 3, 4, 4, 4], [1, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4, 4, 4, 4], [1, 2, 2, 2, 4, 4, 4], [1, 2, 2, 2, 4, 4], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 2, 2, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4, 4], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4, 4], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4, 4], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4, 4], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 4, 4, 4, 4], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4, 4], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4, 4], [1, 4, 4, 4], [1, 4, 4], [1, 4], [2, 2, 2, 3, 3, 4, 4, 4, 4], [2, 2, 2, 3, 3, 4, 4, 4], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 4], [2, 2, 2, 3, 3], [2, 2, 2, 3, 4, 4, 4, 4], [2, 2, 2, 3, 4, 4, 4], [2, 2, 2, 3, 4, 4], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4, 4, 4, 4], [2, 2, 2, 4, 4, 4], [2, 2, 2, 4, 4], [2, 2, 2, 4], [2, 2, 2], [2, 2, 3, 3, 4, 4, 4, 4], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4, 4], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4, 4], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 4, 4, 4, 4], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4, 4], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4, 4], [2, 4, 4, 4], [2, 4, 4], [2, 4], [3, 3, 4, 4, 4, 4], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4, 4], [3, 4, 4, 4], [3, 4, 4], [3, 4], [4, 4, 4, 4], [4, 4, 4], [4, 4]]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3]) == [[1, 2, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 3, 3], [1, 2, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3, 3, 3], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2, 2], [1, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3, 3, 3], [1, 4, 4], [1, 3, 3, 4], [1, 3, 3, 3, 3], [1, 2, 2, 3, 4], [1, 2, 2, 3, 3, 3], [1, 2, 2, 4], [1, 2, 2, 3, 3], [1, 2, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 1, 2, 3, 4], [1, 1, 2, 3, 3, 3], [1, 1, 2, 4], [1, 1, 2, 3, 3], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2], [1, 1, 3, 4], [1, 1, 3, 3, 3], [1, 1, 4], [1, 1, 3, 3], [1, 1, 2, 2, 3], [1, 1, 2, 2], [1, 1, 1, 2, 3], [1, 1, 1, 2], [1, 1, 1, 3], [1, 1, 1], [2, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3, 3, 3], [2, 4, 4], [2, 3, 3, 4], [2, 3, 3, 3, 3], [2, 2, 2, 3, 4], [2, 2, 2, 3, 3, 3], [2, 2, 2, 4], [2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2], [3, 4, 4], [3, 3, 3, 4], [3, 3, 3, 3, 3], [4, 4], [3, 3, 4], [3, 3, 3, 3], [2, 2, 3, 4], [2, 2, 3, 3, 3], [2, 2, 4], [2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2], [1, 2, 3, 4], [1, 2, 3, 3, 3], [1, 2, 4], [1, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 3, 4], [1, 3, 3, 3], [1, 4], [1, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 1, 2, 3], [1, 1, 2], [1, 1, 3], [1, 1], [2, 3, 4], [2, 3, 3, 3], [2, 4], [2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [3, 4], [3, 3, 3], [3, 3], [2, 2, 3], [2, 2], [1, 2, 3], [1, 2], [1, 3], [2, 3]]\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1]) == [[1, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 3, 3], [1, 2, 2, 3], [1, 2, 2, 2], [1, 1, 2, 3], [1, 1, 2, 2], [1, 1, 3], [1, 1, 2], [1, 1, 1], [2, 3, 3], [2, 2, 2, 3], [2, 2, 2, 2], [3, 3], [2, 2, 3], [2, 2, 2], [1, 2, 3], [1, 2, 2], [1, 3], [1, 2], [1, 1], [2, 3], [2, 2]]\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == [[1, 2, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2, 2], [1, 1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2, 2], [1, 2, 2, 2, 2, 2], [1, 1, 2, 2, 2, 2], [1, 1, 1, 2, 2, 2], [1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 1, 1], [2, 2, 2, 2, 2], [1, 2, 2, 2, 2], [1, 1, 2, 2, 2], [1, 1, 1, 2, 2], [1, 1, 1, 1, 2], [1, 1, 1, 1, 1], [2, 2, 2, 2], [1, 2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1, 1], [2, 2, 2], [1, 2, 2], [1, 1, 2], [1, 1, 1], [2, 2], [1, 2], [1, 1]]\n assert candidate(nums = [0, 1, 0, 2, 1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6]) == [[0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6, 6], [0, 1, 2, 3, 4, 5, 5, 7], [0, 1, 2, 3, 4, 5, 5, 6], [0, 1, 2, 3, 4, 5, 5], [0, 1, 2, 3, 4, 4, 6, 7], [0, 1, 2, 3, 4, 4, 6, 6], [0, 1, 2, 3, 4, 4, 5, 7], [0, 1, 2, 3, 4, 4, 5, 6], [0, 1, 2, 3, 4, 4, 5], [0, 1, 2, 3, 4, 4, 7], [0, 1, 2, 3, 4, 4, 6], [0, 1, 2, 3, 4, 4], [0, 1, 2, 3, 3, 5, 6, 7], [0, 1, 2, 3, 3, 5, 6, 6], [0, 1, 2, 3, 3, 5, 5, 7], [0, 1, 2, 3, 3, 5, 5, 6], [0, 1, 2, 3, 3, 5, 5], [0, 1, 2, 3, 3, 4, 6, 7], [0, 1, 2, 3, 3, 4, 6, 6], [0, 1, 2, 3, 3, 4, 5, 7], [0, 1, 2, 3, 3, 4, 5, 6], [0, 1, 2, 3, 3, 4, 5], [0, 1, 2, 3, 3, 4, 7], [0, 1, 2, 3, 3, 4, 6], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 3, 6, 7], [0, 1, 2, 3, 3, 6, 6], [0, 1, 2, 3, 3, 5, 7], [0, 1, 2, 3, 3, 5, 6], [0, 1, 2, 3, 3, 5], [0, 1, 2, 3, 3, 7], [0, 1, 2, 3, 3, 6], [0, 1, 2, 3, 3], [0, 1, 2, 2, 4, 5, 6, 7], [0, 1, 2, 2, 4, 5, 6, 6], [0, 1, 2, 2, 4, 5, 5, 7], [0, 1, 2, 2, 4, 5, 5, 6], [0, 1, 2, 2, 4, 5, 5], [0, 1, 2, 2, 4, 4, 6, 7], [0, 1, 2, 2, 4, 4, 6, 6], [0, 1, 2, 2, 4, 4, 5, 7], [0, 1, 2, 2, 4, 4, 5, 6], [0, 1, 2, 2, 4, 4, 5], [0, 1, 2, 2, 4, 4, 7], [0, 1, 2, 2, 4, 4, 6], [0, 1, 2, 2, 4, 4], [0, 1, 2, 2, 3, 5, 6, 7], [0, 1, 2, 2, 3, 5, 6, 6], [0, 1, 2, 2, 3, 5, 5, 7], [0, 1, 2, 2, 3, 5, 5, 6], [0, 1, 2, 2, 3, 5, 5], [0, 1, 2, 2, 3, 4, 6, 7], [0, 1, 2, 2, 3, 4, 6, 6], [0, 1, 2, 2, 3, 4, 5, 7], [0, 1, 2, 2, 3, 4, 5, 6], [0, 1, 2, 2, 3, 4, 5], [0, 1, 2, 2, 3, 4, 7], [0, 1, 2, 2, 3, 4, 6], [0, 1, 2, 2, 3, 4], [0, 1, 2, 2, 3, 6, 7], [0, 1, 2, 2, 3, 6, 6], [0, 1, 2, 2, 3, 5, 7], [0, 1, 2, 2, 3, 5, 6], [0, 1, 2, 2, 3, 5], [0, 1, 2, 2, 3, 7], [0, 1, 2, 2, 3, 6], [0, 1, 2, 2, 3], [0, 1, 2, 2, 5, 6, 7], [0, 1, 2, 2, 5, 6, 6], [0, 1, 2, 2, 5, 5, 7], [0, 1, 2, 2, 5, 5, 6], [0, 1, 2, 2, 5, 5], [0, 1, 2, 2, 4, 6, 7], [0, 1, 2, 2, 4, 6, 6], [0, 1, 2, 2, 4, 5, 7], [0, 1, 2, 2, 4, 5, 6], [0, 1, 2, 2, 4, 5], [0, 1, 2, 2, 4, 7], [0, 1, 2, 2, 4, 6], [0, 1, 2, 2, 4], [0, 1, 2, 2, 6, 7], [0, 1, 2, 2, 6, 6], [0, 1, 2, 2, 5, 7], [0, 1, 2, 2, 5, 6], [0, 1, 2, 2, 5], [0, 1, 2, 2, 7], [0, 1, 2, 2, 6], [0, 1, 2, 2], [0, 1, 1, 3, 4, 5, 6, 7], [0, 1, 1, 3, 4, 5, 6, 6], [0, 1, 1, 3, 4, 5, 5, 7], [0, 1, 1, 3, 4, 5, 5, 6], [0, 1, 1, 3, 4, 5, 5], [0, 1, 1, 3, 4, 4, 6, 7], [0, 1, 1, 3, 4, 4, 6, 6], [0, 1, 1, 3, 4, 4, 5, 7], [0, 1, 1, 3, 4, 4, 5, 6], [0, 1, 1, 3, 4, 4, 5], [0, 1, 1, 3, 4, 4, 7], [0, 1, 1, 3, 4, 4, 6], [0, 1, 1, 3, 4, 4], [0, 1, 1, 3, 3, 5, 6, 7], [0, 1, 1, 3, 3, 5, 6, 6], [0, 1, 1, 3, 3, 5, 5, 7], [0, 1, 1, 3, 3, 5, 5, 6], [0, 1, 1, 3, 3, 5, 5], [0, 1, 1, 3, 3, 4, 6, 7], [0, 1, 1, 3, 3, 4, 6, 6], [0, 1, 1, 3, 3, 4, 5, 7], [0, 1, 1, 3, 3, 4, 5, 6], [0, 1, 1, 3, 3, 4, 5], [0, 1, 1, 3, 3, 4, 7], [0, 1, 1, 3, 3, 4, 6], [0, 1, 1, 3, 3, 4], [0, 1, 1, 3, 3, 6, 7], [0, 1, 1, 3, 3, 6, 6], [0, 1, 1, 3, 3, 5, 7], [0, 1, 1, 3, 3, 5, 6], [0, 1, 1, 3, 3, 5], [0, 1, 1, 3, 3, 7], [0, 1, 1, 3, 3, 6], [0, 1, 1, 3, 3], [0, 1, 1, 2, 4, 5, 6, 7], [0, 1, 1, 2, 4, 5, 6, 6], [0, 1, 1, 2, 4, 5, 5, 7], [0, 1, 1, 2, 4, 5, 5, 6], [0, 1, 1, 2, 4, 5, 5], [0, 1, 1, 2, 4, 4, 6, 7], [0, 1, 1, 2, 4, 4, 6, 6], [0, 1, 1, 2, 4, 4, 5, 7], [0, 1, 1, 2, 4, 4, 5, 6], [0, 1, 1, 2, 4, 4, 5], [0, 1, 1, 2, 4, 4, 7], [0, 1, 1, 2, 4, 4, 6], [0, 1, 1, 2, 4, 4], [0, 1, 1, 2, 3, 5, 6, 7], [0, 1, 1, 2, 3, 5, 6, 6], [0, 1, 1, 2, 3, 5, 5, 7], [0, 1, 1, 2, 3, 5, 5, 6], [0, 1, 1, 2, 3, 5, 5], [0, 1, 1, 2, 3, 4, 6, 7], [0, 1, 1, 2, 3, 4, 6, 6], [0, 1, 1, 2, 3, 4, 5, 7], [0, 1, 1, 2, 3, 4, 5, 6], [0, 1, 1, 2, 3, 4, 5], [0, 1, 1, 2, 3, 4, 7], [0, 1, 1, 2, 3, 4, 6], [0, 1, 1, 2, 3, 4], [0, 1, 1, 2, 3, 6, 7], [0, 1, 1, 2, 3, 6, 6], [0, 1, 1, 2, 3, 5, 7], [0, 1, 1, 2, 3, 5, 6], [0, 1, 1, 2, 3, 5], [0, 1, 1, 2, 3, 7], [0, 1, 1, 2, 3, 6], [0, 1, 1, 2, 3], [0, 1, 1, 2, 5, 6, 7], [0, 1, 1, 2, 5, 6, 6], [0, 1, 1, 2, 5, 5, 7], [0, 1, 1, 2, 5, 5, 6], [0, 1, 1, 2, 5, 5], [0, 1, 1, 2, 4, 6, 7], [0, 1, 1, 2, 4, 6, 6], [0, 1, 1, 2, 4, 5, 7], [0, 1, 1, 2, 4, 5, 6], [0, 1, 1, 2, 4, 5], [0, 1, 1, 2, 4, 7], [0, 1, 1, 2, 4, 6], [0, 1, 1, 2, 4], [0, 1, 1, 2, 6, 7], [0, 1, 1, 2, 6, 6], [0, 1, 1, 2, 5, 7], [0, 1, 1, 2, 5, 6], [0, 1, 1, 2, 5], [0, 1, 1, 2, 7], [0, 1, 1, 2, 6], [0, 1, 1, 2], [0, 1, 1, 4, 5, 6, 7], [0, 1, 1, 4, 5, 6, 6], [0, 1, 1, 4, 5, 5, 7], [0, 1, 1, 4, 5, 5, 6], [0, 1, 1, 4, 5, 5], [0, 1, 1, 4, 4, 6, 7], [0, 1, 1, 4, 4, 6, 6], [0, 1, 1, 4, 4, 5, 7], [0, 1, 1, 4, 4, 5, 6], [0, 1, 1, 4, 4, 5], [0, 1, 1, 4, 4, 7], [0, 1, 1, 4, 4, 6], [0, 1, 1, 4, 4], [0, 1, 1, 3, 5, 6, 7], [0, 1, 1, 3, 5, 6, 6], [0, 1, 1, 3, 5, 5, 7], [0, 1, 1, 3, 5, 5, 6], [0, 1, 1, 3, 5, 5], [0, 1, 1, 3, 4, 6, 7], [0, 1, 1, 3, 4, 6, 6], [0, 1, 1, 3, 4, 5, 7], [0, 1, 1, 3, 4, 5, 6], [0, 1, 1, 3, 4, 5], [0, 1, 1, 3, 4, 7], [0, 1, 1, 3, 4, 6], [0, 1, 1, 3, 4], [0, 1, 1, 3, 6, 7], [0, 1, 1, 3, 6, 6], [0, 1, 1, 3, 5, 7], [0, 1, 1, 3, 5, 6], [0, 1, 1, 3, 5], [0, 1, 1, 3, 7], [0, 1, 1, 3, 6], [0, 1, 1, 3], [0, 1, 1, 5, 6, 7], [0, 1, 1, 5, 6, 6], [0, 1, 1, 5, 5, 7], [0, 1, 1, 5, 5, 6], [0, 1, 1, 5, 5], [0, 1, 1, 4, 6, 7], [0, 1, 1, 4, 6, 6], [0, 1, 1, 4, 5, 7], [0, 1, 1, 4, 5, 6], [0, 1, 1, 4, 5], [0, 1, 1, 4, 7], [0, 1, 1, 4, 6], [0, 1, 1, 4], [0, 1, 1, 6, 7], [0, 1, 1, 6, 6], [0, 1, 1, 5, 7], [0, 1, 1, 5, 6], [0, 1, 1, 5], [0, 1, 1, 7], [0, 1, 1, 6], [0, 1, 1], [0, 0, 2, 3, 4, 5, 6, 7], [0, 0, 2, 3, 4, 5, 6, 6], [0, 0, 2, 3, 4, 5, 5, 7], [0, 0, 2, 3, 4, 5, 5, 6], [0, 0, 2, 3, 4, 5, 5], [0, 0, 2, 3, 4, 4, 6, 7], [0, 0, 2, 3, 4, 4, 6, 6], [0, 0, 2, 3, 4, 4, 5, 7], [0, 0, 2, 3, 4, 4, 5, 6], [0, 0, 2, 3, 4, 4, 5], [0, 0, 2, 3, 4, 4, 7], [0, 0, 2, 3, 4, 4, 6], [0, 0, 2, 3, 4, 4], [0, 0, 2, 3, 3, 5, 6, 7], [0, 0, 2, 3, 3, 5, 6, 6], [0, 0, 2, 3, 3, 5, 5, 7], [0, 0, 2, 3, 3, 5, 5, 6], [0, 0, 2, 3, 3, 5, 5], [0, 0, 2, 3, 3, 4, 6, 7], [0, 0, 2, 3, 3, 4, 6, 6], [0, 0, 2, 3, 3, 4, 5, 7], [0, 0, 2, 3, 3, 4, 5, 6], [0, 0, 2, 3, 3, 4, 5], [0, 0, 2, 3, 3, 4, 7], [0, 0, 2, 3, 3, 4, 6], [0, 0, 2, 3, 3, 4], [0, 0, 2, 3, 3, 6, 7], [0, 0, 2, 3, 3, 6, 6], [0, 0, 2, 3, 3, 5, 7], [0, 0, 2, 3, 3, 5, 6], [0, 0, 2, 3, 3, 5], [0, 0, 2, 3, 3, 7], [0, 0, 2, 3, 3, 6], [0, 0, 2, 3, 3], [0, 0, 2, 2, 4, 5, 6, 7], [0, 0, 2, 2, 4, 5, 6, 6], [0, 0, 2, 2, 4, 5, 5, 7], [0, 0, 2, 2, 4, 5, 5, 6], [0, 0, 2, 2, 4, 5, 5], [0, 0, 2, 2, 4, 4, 6, 7], [0, 0, 2, 2, 4, 4, 6, 6], [0, 0, 2, 2, 4, 4, 5, 7], [0, 0, 2, 2, 4, 4, 5, 6], [0, 0, 2, 2, 4, 4, 5], [0, 0, 2, 2, 4, 4, 7], [0, 0, 2, 2, 4, 4, 6], [0, 0, 2, 2, 4, 4], [0, 0, 2, 2, 3, 5, 6, 7], [0, 0, 2, 2, 3, 5, 6, 6], [0, 0, 2, 2, 3, 5, 5, 7], [0, 0, 2, 2, 3, 5, 5, 6], [0, 0, 2, 2, 3, 5, 5], [0, 0, 2, 2, 3, 4, 6, 7], [0, 0, 2, 2, 3, 4, 6, 6], [0, 0, 2, 2, 3, 4, 5, 7], [0, 0, 2, 2, 3, 4, 5, 6], [0, 0, 2, 2, 3, 4, 5], [0, 0, 2, 2, 3, 4, 7], [0, 0, 2, 2, 3, 4, 6], [0, 0, 2, 2, 3, 4], [0, 0, 2, 2, 3, 6, 7], [0, 0, 2, 2, 3, 6, 6], [0, 0, 2, 2, 3, 5, 7], [0, 0, 2, 2, 3, 5, 6], [0, 0, 2, 2, 3, 5], [0, 0, 2, 2, 3, 7], [0, 0, 2, 2, 3, 6], [0, 0, 2, 2, 3], [0, 0, 2, 2, 5, 6, 7], [0, 0, 2, 2, 5, 6, 6], [0, 0, 2, 2, 5, 5, 7], [0, 0, 2, 2, 5, 5, 6], [0, 0, 2, 2, 5, 5], [0, 0, 2, 2, 4, 6, 7], [0, 0, 2, 2, 4, 6, 6], [0, 0, 2, 2, 4, 5, 7], [0, 0, 2, 2, 4, 5, 6], [0, 0, 2, 2, 4, 5], [0, 0, 2, 2, 4, 7], [0, 0, 2, 2, 4, 6], [0, 0, 2, 2, 4], [0, 0, 2, 2, 6, 7], [0, 0, 2, 2, 6, 6], [0, 0, 2, 2, 5, 7], [0, 0, 2, 2, 5, 6], [0, 0, 2, 2, 5], [0, 0, 2, 2, 7], [0, 0, 2, 2, 6], [0, 0, 2, 2], [0, 0, 1, 3, 4, 5, 6, 7], [0, 0, 1, 3, 4, 5, 6, 6], [0, 0, 1, 3, 4, 5, 5, 7], [0, 0, 1, 3, 4, 5, 5, 6], [0, 0, 1, 3, 4, 5, 5], [0, 0, 1, 3, 4, 4, 6, 7], [0, 0, 1, 3, 4, 4, 6, 6], [0, 0, 1, 3, 4, 4, 5, 7], [0, 0, 1, 3, 4, 4, 5, 6], [0, 0, 1, 3, 4, 4, 5], [0, 0, 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5, 5, 7], [2, 4, 5, 5, 6], [2, 4, 5, 5], [2, 4, 4, 6, 7], [2, 4, 4, 6, 6], [2, 4, 4, 5, 7], [2, 4, 4, 5, 6], [2, 4, 4, 5], [2, 4, 4, 7], [2, 4, 4, 6], [2, 4, 4], [2, 3, 5, 6, 7], [2, 3, 5, 6, 6], [2, 3, 5, 5, 7], [2, 3, 5, 5, 6], [2, 3, 5, 5], [2, 3, 4, 6, 7], [2, 3, 4, 6, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5, 6], [2, 3, 4, 5], [2, 3, 4, 7], [2, 3, 4, 6], [2, 3, 4], [2, 3, 6, 7], [2, 3, 6, 6], [2, 3, 5, 7], [2, 3, 5, 6], [2, 3, 5], [2, 3, 7], [2, 3, 6], [2, 3], [2, 5, 6, 7], [2, 5, 6, 6], [2, 5, 5, 7], [2, 5, 5, 6], [2, 5, 5], [2, 4, 6, 7], [2, 4, 6, 6], [2, 4, 5, 7], [2, 4, 5, 6], [2, 4, 5], [2, 4, 7], [2, 4, 6], [2, 4], [2, 6, 7], [2, 6, 6], [2, 5, 7], [2, 5, 6], [2, 5], [2, 7], [2, 6], [4, 5, 6, 7], [4, 5, 6, 6], [4, 5, 5, 7], [4, 5, 5, 6], [4, 5, 5], [4, 4, 6, 7], [4, 4, 6, 6], [4, 4, 5, 7], [4, 4, 5, 6], [4, 4, 5], [4, 4, 7], [4, 4, 6], [4, 4], [3, 5, 6, 7], [3, 5, 6, 6], [3, 5, 5, 7], [3, 5, 5, 6], [3, 5, 5], [3, 4, 6, 7], [3, 4, 6, 6], [3, 4, 5, 7], [3, 4, 5, 6], [3, 4, 5], [3, 4, 7], [3, 4, 6], [3, 4], [3, 6, 7], [3, 6, 6], [3, 5, 7], [3, 5, 6], [3, 5], [3, 7], [3, 6], [5, 6, 7], [5, 6, 6], [5, 5, 7], [5, 5, 6], [5, 5], [4, 6, 7], [4, 6, 6], [4, 5, 7], [4, 5, 6], [4, 5], [4, 7], [4, 6], [6, 7], [6, 6], [5, 7], [5, 6]]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [100, -100, 50, -50, 25, -25, 0, 0, 0, 0]) == [[-100, 50], [-100, -50, 25], [-100, -50, -25, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0], [-100, -50, -25, 0, 0], [-100, -50, -25, 0], [-100, -50, -25], [-100, -50, 0, 0, 0, 0], [-100, -50, 0, 0, 0], [-100, -50, 0, 0], [-100, -50, 0], [-100, -50], [-100, 25], [-100, -25, 0, 0, 0, 0], [-100, -25, 0, 0, 0], [-100, -25, 0, 0], [-100, -25, 0], [-100, -25], [-100, 0, 0, 0, 0], [-100, 0, 0, 0], [-100, 0, 0], [-100, 0], [-50, 25], [-50, -25, 0, 0, 0, 0], [-50, -25, 0, 0, 0], [-50, -25, 0, 0], [-50, -25, 0], [-50, -25], [-50, 0, 0, 0, 0], [-50, 0, 0, 0], [-50, 0, 0], [-50, 0], [-25, 0, 0, 0, 0], [-25, 0, 0, 0], [-25, 0, 0], [-25, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0]]\n assert candidate(nums = [5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == []\n assert candidate(nums = [-10, 10, -10, 10, -10, 10, -10, 10, -10, 10]) == [[-10, 10, 10, 10, 10, 10], [-10, -10, 10, 10, 10, 10], [-10, -10, -10, 10, 10, 10], [-10, -10, -10, -10, 10, 10], [-10, -10, -10, -10, -10, 10], [-10, -10, -10, -10, -10], [10, 10, 10, 10, 10], [-10, 10, 10, 10, 10], [-10, -10, 10, 10, 10], [-10, -10, -10, 10, 10], [-10, -10, -10, -10, 10], [-10, -10, -10, -10], [10, 10, 10, 10], [-10, 10, 10, 10], [-10, -10, 10, 10], [-10, -10, -10, 10], [-10, -10, -10], [10, 10, 10], [-10, 10, 10], [-10, -10, 10], [-10, -10], [10, 10], [-10, 10]]\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == [[1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4, 5], [1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 5, 5, 5], [1, 2, 2, 3, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 3, 4, 5], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 5, 5, 5, 5], [1, 2, 2, 3, 3, 3, 5, 5, 5], [1, 2, 2, 3, 3, 3, 5, 5], [1, 2, 2, 3, 3, 3, 5], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 2, 2, 3, 3, 4, 4, 5], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 5, 5, 5, 5], [1, 2, 2, 3, 3, 4, 5, 5, 5], [1, 2, 2, 3, 3, 4, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5, 5, 5, 5, 5], [1, 2, 2, 3, 3, 5, 5, 5, 5], [1, 2, 2, 3, 3, 5, 5, 5], [1, 2, 2, 3, 3, 5, 5], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5], [1, 2, 2, 3, 4, 4, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 4, 4, 5], [1, 2, 2, 3, 4, 4, 4, 4], [1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 4, 4, 4, 5, 5, 5], [1, 2, 2, 3, 4, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 4, 5], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 4, 4, 5, 5, 5, 5], [1, 2, 2, 3, 4, 4, 5, 5, 5], [1, 2, 2, 3, 4, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4, 5, 5, 5, 5, 5], [1, 2, 2, 3, 4, 5, 5, 5, 5], [1, 2, 2, 3, 4, 5, 5, 5], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5, 5, 5, 5, 5], [1, 2, 2, 3, 5, 5, 5, 5], [1, 2, 2, 3, 5, 5, 5], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 4, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 4, 4, 4, 4, 5, 5, 5], [1, 2, 2, 4, 4, 4, 4, 5, 5], [1, 2, 2, 4, 4, 4, 4, 5], [1, 2, 2, 4, 4, 4, 4], [1, 2, 2, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 4, 4, 4, 5, 5, 5, 5], [1, 2, 2, 4, 4, 4, 5, 5, 5], [1, 2, 2, 4, 4, 4, 5, 5], [1, 2, 2, 4, 4, 4, 5], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4, 5, 5, 5, 5, 5], [1, 2, 2, 4, 4, 5, 5, 5, 5], [1, 2, 2, 4, 4, 5, 5, 5], [1, 2, 2, 4, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 4, 5, 5, 5, 5, 5], [1, 2, 2, 4, 5, 5, 5, 5], [1, 2, 2, 4, 5, 5, 5], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5, 5, 5, 5, 5], [1, 2, 2, 5, 5, 5, 5], [1, 2, 2, 5, 5, 5], [1, 2, 2, 5, 5], [1, 2, 2, 5], [1, 2, 2], [1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 4, 5], [1, 2, 3, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 2, 3, 3, 3, 4, 4, 4, 5], [1, 2, 3, 3, 3, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 2, 3, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 3, 4, 4, 5], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 5, 5, 5, 5], [1, 2, 3, 3, 3, 4, 5, 5, 5], [1, 2, 3, 3, 3, 4, 5, 5], [1, 2, 3, 3, 3, 4, 5], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 5, 5, 5, 5, 5], [1, 2, 3, 3, 3, 5, 5, 5, 5], [1, 2, 3, 3, 3, 5, 5, 5], [1, 2, 3, 3, 3, 5, 5], [1, 2, 3, 3, 3, 5], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5], [1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5], [1, 2, 3, 3, 4, 4, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 4, 4, 5], [1, 2, 3, 3, 4, 4, 4, 4], [1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5], [1, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 2, 3, 3, 4, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 4, 5], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5], [1, 2, 3, 3, 4, 4, 5, 5, 5, 5], [1, 2, 3, 3, 4, 4, 5, 5, 5], [1, 2, 3, 3, 4, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 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5, 5], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5, 5, 5, 5], [3, 4, 5, 5, 5, 5], [3, 4, 5, 5, 5], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5, 5, 5, 5], [3, 5, 5, 5, 5], [3, 5, 5, 5], [3, 5, 5], [3, 5], [4, 4, 4, 4, 5, 5, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5, 5], [4, 4, 4, 4, 5, 5, 5], [4, 4, 4, 4, 5, 5], [4, 4, 4, 4, 5], [4, 4, 4, 4], [4, 4, 4, 5, 5, 5, 5, 5], [4, 4, 4, 5, 5, 5, 5], [4, 4, 4, 5, 5, 5], [4, 4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [4, 4, 5, 5, 5, 5, 5], [4, 4, 5, 5, 5, 5], [4, 4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5, 5, 5, 5], [4, 5, 5, 5, 5], [4, 5, 5, 5], [4, 5, 5], [4, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9], [1, 2, 4, 7, 10], [1, 2, 4, 7], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9], [1, 2, 4, 8, 10], [1, 2, 4, 8], [1, 2, 4, 9, 10], [1, 2, 4, 9], [1, 2, 4, 10], [1, 2, 4], [1, 2, 5, 6, 7, 8, 9, 10], [1, 2, 5, 6, 7, 8, 9], [1, 2, 5, 6, 7, 8, 10], [1, 2, 5, 6, 7, 8], [1, 2, 5, 6, 7, 9, 10], [1, 2, 5, 6, 7, 9], [1, 2, 5, 6, 7, 10], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8, 9, 10], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9, 10], [1, 2, 5, 6, 9], [1, 2, 5, 6, 10], [1, 2, 5, 6], [1, 2, 5, 7, 8, 9, 10], [1, 2, 5, 7, 8, 9], [1, 2, 5, 7, 8, 10], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9, 10], [1, 2, 5, 7, 9], [1, 2, 5, 7, 10], [1, 2, 5, 7], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9], [1, 2, 5, 8, 10], [1, 2, 5, 8], [1, 2, 5, 9, 10], [1, 2, 5, 9], [1, 2, 5, 10], [1, 2, 5], [1, 2, 6, 7, 8, 9, 10], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9, 10], [1, 2, 6, 7, 9], [1, 2, 6, 7, 10], [1, 2, 6, 7], [1, 2, 6, 8, 9, 10], [1, 2, 6, 8, 9], [1, 2, 6, 8, 10], [1, 2, 6, 8], [1, 2, 6, 9, 10], [1, 2, 6, 9], [1, 2, 6, 10], [1, 2, 6], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9], [1, 2, 7, 8, 10], [1, 2, 7, 8], [1, 2, 7, 9, 10], [1, 2, 7, 9], [1, 2, 7, 10], [1, 2, 7], [1, 2, 8, 9, 10], [1, 2, 8, 9], [1, 2, 8, 10], [1, 2, 8], [1, 2, 9, 10], [1, 2, 9], [1, 2, 10], [1, 2], [1, 3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 4, 5, 6, 7, 8, 9], [1, 3, 4, 5, 6, 7, 8, 10], [1, 3, 4, 5, 6, 7, 8], [1, 3, 4, 5, 6, 7, 9, 10], [1, 3, 4, 5, 6, 7, 9], [1, 3, 4, 5, 6, 7, 10], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8, 9, 10], [1, 3, 4, 5, 6, 8, 9], [1, 3, 4, 5, 6, 8, 10], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 9, 10], [1, 3, 4, 5, 6, 9], [1, 3, 4, 5, 6, 10], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7, 8, 9, 10], [1, 3, 4, 5, 7, 8, 9], [1, 3, 4, 5, 7, 8, 10], [1, 3, 4, 5, 7, 8], [1, 3, 4, 5, 7, 9, 10], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7], [1, 3, 4, 5, 8, 9, 10], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8], [1, 3, 4, 5, 9, 10], [1, 3, 4, 5, 9], [1, 3, 4, 5, 10], [1, 3, 4, 5], [1, 3, 4, 6, 7, 8, 9, 10], [1, 3, 4, 6, 7, 8, 9], [1, 3, 4, 6, 7, 8, 10], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 9, 10], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 7], [1, 3, 4, 6, 8, 9, 10], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9, 10], [1, 3, 4, 6, 9], [1, 3, 4, 6, 10], [1, 3, 4, 6], [1, 3, 4, 7, 8, 9, 10], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 9], [1, 3, 4, 7, 10], [1, 3, 4, 7], [1, 3, 4, 8, 9, 10], [1, 3, 4, 8, 9], [1, 3, 4, 8, 10], [1, 3, 4, 8], [1, 3, 4, 9, 10], [1, 3, 4, 9], [1, 3, 4, 10], [1, 3, 4], [1, 3, 5, 6, 7, 8, 9, 10], [1, 3, 5, 6, 7, 8, 9], [1, 3, 5, 6, 7, 8, 10], [1, 3, 5, 6, 7, 8], [1, 3, 5, 6, 7, 9, 10], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7], [1, 3, 5, 6, 8, 9, 10], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8], [1, 3, 5, 6, 9, 10], [1, 3, 5, 6, 9], [1, 3, 5, 6, 10], [1, 3, 5, 6], [1, 3, 5, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 3, 5, 7, 8, 10], [1, 3, 5, 7, 8], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 9], [1, 3, 5, 7, 10], [1, 3, 5, 7], [1, 3, 5, 8, 9, 10], [1, 3, 5, 8, 9], [1, 3, 5, 8, 10], [1, 3, 5, 8], [1, 3, 5, 9, 10], [1, 3, 5, 9], [1, 3, 5, 10], [1, 3, 5], [1, 3, 6, 7, 8, 9, 10], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9, 10], [1, 3, 6, 7, 9], [1, 3, 6, 7, 10], [1, 3, 6, 7], [1, 3, 6, 8, 9, 10], [1, 3, 6, 8, 9], [1, 3, 6, 8, 10], [1, 3, 6, 8], [1, 3, 6, 9, 10], [1, 3, 6, 9], [1, 3, 6, 10], [1, 3, 6], [1, 3, 7, 8, 9, 10], [1, 3, 7, 8, 9], [1, 3, 7, 8, 10], [1, 3, 7, 8], [1, 3, 7, 9, 10], [1, 3, 7, 9], [1, 3, 7, 10], [1, 3, 7], [1, 3, 8, 9, 10], [1, 3, 8, 9], [1, 3, 8, 10], [1, 3, 8], [1, 3, 9, 10], [1, 3, 9], [1, 3, 10], [1, 3], [1, 4, 5, 6, 7, 8, 9, 10], [1, 4, 5, 6, 7, 8, 9], [1, 4, 5, 6, 7, 8, 10], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 9, 10], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8, 9, 10], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9, 10], [1, 4, 5, 6, 9], [1, 4, 5, 6, 10], [1, 4, 5, 6], [1, 4, 5, 7, 8, 9, 10], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 9], [1, 4, 5, 7, 10], [1, 4, 5, 7], [1, 4, 5, 8, 9, 10], [1, 4, 5, 8, 9], [1, 4, 5, 8, 10], [1, 4, 5, 8], [1, 4, 5, 9, 10], [1, 4, 5, 9], [1, 4, 5, 10], [1, 4, 5], [1, 4, 6, 7, 8, 9, 10], [1, 4, 6, 7, 8, 9], [1, 4, 6, 7, 8, 10], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9, 10], [1, 4, 6, 7, 9], [1, 4, 6, 7, 10], [1, 4, 6, 7], [1, 4, 6, 8, 9, 10], [1, 4, 6, 8, 9], [1, 4, 6, 8, 10], [1, 4, 6, 8], [1, 4, 6, 9, 10], [1, 4, 6, 9], [1, 4, 6, 10], [1, 4, 6], [1, 4, 7, 8, 9, 10], [1, 4, 7, 8, 9], [1, 4, 7, 8, 10], [1, 4, 7, 8], [1, 4, 7, 9, 10], [1, 4, 7, 9], [1, 4, 7, 10], [1, 4, 7], [1, 4, 8, 9, 10], [1, 4, 8, 9], [1, 4, 8, 10], [1, 4, 8], [1, 4, 9, 10], [1, 4, 9], [1, 4, 10], [1, 4], [1, 5, 6, 7, 8, 9, 10], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9, 10], [1, 5, 6, 7, 9], [1, 5, 6, 7, 10], [1, 5, 6, 7], [1, 5, 6, 8, 9, 10], [1, 5, 6, 8, 9], [1, 5, 6, 8, 10], [1, 5, 6, 8], [1, 5, 6, 9, 10], [1, 5, 6, 9], [1, 5, 6, 10], [1, 5, 6], [1, 5, 7, 8, 9, 10], [1, 5, 7, 8, 9], [1, 5, 7, 8, 10], [1, 5, 7, 8], [1, 5, 7, 9, 10], [1, 5, 7, 9], [1, 5, 7, 10], [1, 5, 7], [1, 5, 8, 9, 10], [1, 5, 8, 9], [1, 5, 8, 10], [1, 5, 8], [1, 5, 9, 10], [1, 5, 9], [1, 5, 10], [1, 5], [1, 6, 7, 8, 9, 10], [1, 6, 7, 8, 9], [1, 6, 7, 8, 10], [1, 6, 7, 8], [1, 6, 7, 9, 10], [1, 6, 7, 9], [1, 6, 7, 10], [1, 6, 7], [1, 6, 8, 9, 10], [1, 6, 8, 9], [1, 6, 8, 10], [1, 6, 8], [1, 6, 9, 10], [1, 6, 9], [1, 6, 10], [1, 6], [1, 7, 8, 9, 10], [1, 7, 8, 9], [1, 7, 8, 10], [1, 7, 8], [1, 7, 9, 10], [1, 7, 9], [1, 7, 10], [1, 7], [1, 8, 9, 10], [1, 8, 9], [1, 8, 10], [1, 8], [1, 9, 10], [1, 9], [1, 10], [2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 6, 7, 8, 9], [2, 3, 4, 5, 6, 7, 8, 10], [2, 3, 4, 5, 6, 7, 8], [2, 3, 4, 5, 6, 7, 9, 10], [2, 3, 4, 5, 6, 7, 9], [2, 3, 4, 5, 6, 7, 10], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 8, 9, 10], [2, 3, 4, 5, 6, 8, 9], [2, 3, 4, 5, 6, 8, 10], [2, 3, 4, 5, 6, 8], [2, 3, 4, 5, 6, 9, 10], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7, 8, 9, 10], [2, 3, 4, 5, 7, 8, 9], [2, 3, 4, 5, 7, 8, 10], [2, 3, 4, 5, 7, 8], [2, 3, 4, 5, 7, 9, 10], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7], [2, 3, 4, 5, 8, 9, 10], [2, 3, 4, 5, 8, 9], [2, 3, 4, 5, 8, 10], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9, 10], [2, 3, 4, 5, 9], [2, 3, 4, 5, 10], [2, 3, 4, 5], [2, 3, 4, 6, 7, 8, 9, 10], [2, 3, 4, 6, 7, 8, 9], [2, 3, 4, 6, 7, 8, 10], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 9, 10], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 7, 10], [2, 3, 4, 6, 7], [2, 3, 4, 6, 8, 9, 10], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 9], [2, 3, 4, 6, 10], [2, 3, 4, 6], [2, 3, 4, 7, 8, 9, 10], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 9], [2, 3, 4, 7, 10], [2, 3, 4, 7], [2, 3, 4, 8, 9, 10], [2, 3, 4, 8, 9], [2, 3, 4, 8, 10], [2, 3, 4, 8], [2, 3, 4, 9, 10], [2, 3, 4, 9], [2, 3, 4, 10], [2, 3, 4], [2, 3, 5, 6, 7, 8, 9, 10], [2, 3, 5, 6, 7, 8, 9], [2, 3, 5, 6, 7, 8, 10], [2, 3, 5, 6, 7, 8], [2, 3, 5, 6, 7, 9, 10], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8, 9, 10], [2, 3, 5, 6, 8, 9], [2, 3, 5, 6, 8, 10], [2, 3, 5, 6, 8], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 9], [2, 3, 5, 6, 10], [2, 3, 5, 6], [2, 3, 5, 7, 8, 9, 10], [2, 3, 5, 7, 8, 9], [2, 3, 5, 7, 8, 10], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 9], [2, 3, 5, 7, 10], [2, 3, 5, 7], [2, 3, 5, 8, 9, 10], [2, 3, 5, 8, 9], [2, 3, 5, 8, 10], [2, 3, 5, 8], [2, 3, 5, 9, 10], [2, 3, 5, 9], [2, 3, 5, 10], [2, 3, 5], [2, 3, 6, 7, 8, 9, 10], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 9], [2, 3, 6, 7, 10], [2, 3, 6, 7], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 10], [2, 3, 6, 8], [2, 3, 6, 9, 10], [2, 3, 6, 9], [2, 3, 6, 10], [2, 3, 6], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 10], [2, 3, 7, 8], [2, 3, 7, 9, 10], [2, 3, 7, 9], [2, 3, 7, 10], [2, 3, 7], [2, 3, 8, 9, 10], [2, 3, 8, 9], [2, 3, 8, 10], [2, 3, 8], [2, 3, 9, 10], [2, 3, 9], [2, 3, 10], [2, 3], [2, 4, 5, 6, 7, 8, 9, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9], [2, 4, 5, 6, 10], [2, 4, 5, 6], [2, 4, 5, 7, 8, 9, 10], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9], [2, 4, 5, 7, 10], [2, 4, 5, 7], [2, 4, 5, 8, 9, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 10], [2, 4, 5, 8], [2, 4, 5, 9, 10], [2, 4, 5, 9], [2, 4, 5, 10], [2, 4, 5], [2, 4, 6, 7, 8, 9, 10], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 9], [2, 4, 6, 7, 10], [2, 4, 6, 7], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 10], [2, 4, 6, 8], [2, 4, 6, 9, 10], [2, 4, 6, 9], [2, 4, 6, 10], [2, 4, 6], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 10], [2, 4, 7, 8], [2, 4, 7, 9, 10], [2, 4, 7, 9], [2, 4, 7, 10], [2, 4, 7], [2, 4, 8, 9, 10], [2, 4, 8, 9], [2, 4, 8, 10], [2, 4, 8], [2, 4, 9, 10], [2, 4, 9], [2, 4, 10], [2, 4], [2, 5, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 10], [2, 5, 6, 7], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 10], [2, 5, 6, 8], [2, 5, 6, 9, 10], [2, 5, 6, 9], [2, 5, 6, 10], [2, 5, 6], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 10], [2, 5, 7, 8], [2, 5, 7, 9, 10], [2, 5, 7, 9], [2, 5, 7, 10], [2, 5, 7], [2, 5, 8, 9, 10], [2, 5, 8, 9], [2, 5, 8, 10], [2, 5, 8], [2, 5, 9, 10], [2, 5, 9], [2, 5, 10], [2, 5], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 10], [2, 6, 7, 8], [2, 6, 7, 9, 10], [2, 6, 7, 9], [2, 6, 7, 10], [2, 6, 7], [2, 6, 8, 9, 10], [2, 6, 8, 9], [2, 6, 8, 10], [2, 6, 8], [2, 6, 9, 10], [2, 6, 9], [2, 6, 10], [2, 6], [2, 7, 8, 9, 10], [2, 7, 8, 9], [2, 7, 8, 10], [2, 7, 8], [2, 7, 9, 10], [2, 7, 9], [2, 7, 10], [2, 7], [2, 8, 9, 10], [2, 8, 9], [2, 8, 10], [2, 8], [2, 9, 10], [2, 9], [2, 10], [3, 4, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 10], [3, 4, 5, 6], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 10], [3, 4, 5, 7], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 10], [3, 4, 5, 8], [3, 4, 5, 9, 10], [3, 4, 5, 9], [3, 4, 5, 10], [3, 4, 5], [3, 4, 6, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 10], [3, 4, 6, 7], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 10], [3, 4, 6, 8], [3, 4, 6, 9, 10], [3, 4, 6, 9], [3, 4, 6, 10], [3, 4, 6], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 10], [3, 4, 7, 8], [3, 4, 7, 9, 10], [3, 4, 7, 9], [3, 4, 7, 10], [3, 4, 7], [3, 4, 8, 9, 10], [3, 4, 8, 9], [3, 4, 8, 10], [3, 4, 8], [3, 4, 9, 10], [3, 4, 9], [3, 4, 10], [3, 4], [3, 5, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 10], [3, 5, 6, 7], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 10], [3, 5, 6, 8], [3, 5, 6, 9, 10], [3, 5, 6, 9], [3, 5, 6, 10], [3, 5, 6], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 10], [3, 5, 7, 8], [3, 5, 7, 9, 10], [3, 5, 7, 9], [3, 5, 7, 10], [3, 5, 7], [3, 5, 8, 9, 10], [3, 5, 8, 9], [3, 5, 8, 10], [3, 5, 8], [3, 5, 9, 10], [3, 5, 9], [3, 5, 10], [3, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8], [3, 6, 9, 10], [3, 6, 9], [3, 6, 10], [3, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8], [3, 7, 9, 10], [3, 7, 9], [3, 7, 10], [3, 7], [3, 8, 9, 10], [3, 8, 9], [3, 8, 10], [3, 8], [3, 9, 10], [3, 9], [3, 10], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [8, 9, 10], [8, 9], [8, 10], [9, 10]]\n assert candidate(nums = [9, 8, 7, 7, 7, 6, 5, 4, 4, 3, 2, 1]) == [[7, 7, 7], [7, 7], [4, 4]]\n assert candidate(nums = [5, 3, 5, 7, 5, 3, 7, 3, 5, 3, 5, 3, 5, 3, 5]) == [[5, 5, 7, 7], [5, 5, 5, 7], [5, 5, 5, 5, 5, 5, 5], [3, 5, 7, 7], [3, 5, 5, 7], [3, 5, 5, 5, 5, 5, 5], [3, 7, 7], [3, 5, 7], [3, 5, 5, 5, 5, 5], [3, 3, 7], [3, 3, 3, 5, 5, 5, 5], [3, 3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3, 3], [5, 7, 7], [5, 5, 7], [5, 5, 5, 5, 5, 5], [7, 7], [5, 7], [5, 5, 5, 5, 5], [3, 7], [3, 3, 5, 5, 5, 5], [3, 3, 3, 5, 5, 5], [3, 3, 3, 3, 5, 5], [3, 3, 3, 3, 3, 5], [3, 3, 3, 3, 3], [3, 5, 5, 5, 5], [3, 3, 5, 5, 5], [3, 3, 3, 5, 5], [3, 3, 3, 3, 5], [3, 3, 3, 3], [5, 5, 5, 5], [3, 5, 5, 5], [3, 3, 5, 5], [3, 3, 3, 5], [3, 3, 3], [5, 5, 5], [3, 5, 5], [3, 3, 5], [3, 3], [5, 5], [3, 5]]\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7, 6]) == [[1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 6], [1, 3, 4, 5, 5, 7], [1, 3, 4, 5, 5, 6], [1, 3, 4, 5, 5], [1, 3, 4, 4, 6, 7], [1, 3, 4, 4, 6, 6], [1, 3, 4, 4, 5, 7], [1, 3, 4, 4, 5, 6], [1, 3, 4, 4, 5], [1, 3, 4, 4, 7], [1, 3, 4, 4, 6], [1, 3, 4, 4], [1, 3, 3, 5, 6, 7], [1, 3, 3, 5, 6, 6], [1, 3, 3, 5, 5, 7], [1, 3, 3, 5, 5, 6], [1, 3, 3, 5, 5], [1, 3, 3, 4, 6, 7], [1, 3, 3, 4, 6, 6], [1, 3, 3, 4, 5, 7], [1, 3, 3, 4, 5, 6], [1, 3, 3, 4, 5], [1, 3, 3, 4, 7], [1, 3, 3, 4, 6], [1, 3, 3, 4], [1, 3, 3, 6, 7], [1, 3, 3, 6, 6], [1, 3, 3, 5, 7], [1, 3, 3, 5, 6], [1, 3, 3, 5], [1, 3, 3, 7], [1, 3, 3, 6], [1, 3, 3], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 6], [1, 2, 4, 5, 5, 7], [1, 2, 4, 5, 5, 6], [1, 2, 4, 5, 5], [1, 2, 4, 4, 6, 7], [1, 2, 4, 4, 6, 6], [1, 2, 4, 4, 5, 7], [1, 2, 4, 4, 5, 6], [1, 2, 4, 4, 5], [1, 2, 4, 4, 7], [1, 2, 4, 4, 6], [1, 2, 4, 4], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 6], [1, 2, 3, 5, 5, 7], [1, 2, 3, 5, 5, 6], [1, 2, 3, 5, 5], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5], [1, 2, 3, 4, 7], [1, 2, 3, 4, 6], [1, 2, 3, 4], [1, 2, 3, 6, 7], [1, 2, 3, 6, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5, 6], [1, 2, 3, 5], [1, 2, 3, 7], [1, 2, 3, 6], [1, 2, 3], [1, 2, 5, 6, 7], [1, 2, 5, 6, 6], [1, 2, 5, 5, 7], [1, 2, 5, 5, 6], [1, 2, 5, 5], [1, 2, 4, 6, 7], [1, 2, 4, 6, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5, 6], [1, 2, 4, 5], [1, 2, 4, 7], [1, 2, 4, 6], [1, 2, 4], [1, 2, 6, 7], [1, 2, 6, 6], [1, 2, 5, 7], [1, 2, 5, 6], [1, 2, 5], [1, 2, 7], [1, 2, 6], [1, 2], [1, 4, 5, 6, 7], [1, 4, 5, 6, 6], [1, 4, 5, 5, 7], [1, 4, 5, 5, 6], [1, 4, 5, 5], [1, 4, 4, 6, 7], [1, 4, 4, 6, 6], [1, 4, 4, 5, 7], [1, 4, 4, 5, 6], [1, 4, 4, 5], [1, 4, 4, 7], [1, 4, 4, 6], [1, 4, 4], [1, 3, 5, 6, 7], [1, 3, 5, 6, 6], [1, 3, 5, 5, 7], [1, 3, 5, 5, 6], [1, 3, 5, 5], [1, 3, 4, 6, 7], [1, 3, 4, 6, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5, 6], [1, 3, 4, 5], [1, 3, 4, 7], [1, 3, 4, 6], [1, 3, 4], [1, 3, 6, 7], [1, 3, 6, 6], [1, 3, 5, 7], [1, 3, 5, 6], [1, 3, 5], [1, 3, 7], [1, 3, 6], [1, 3], [1, 5, 6, 7], [1, 5, 6, 6], [1, 5, 5, 7], [1, 5, 5, 6], [1, 5, 5], [1, 4, 6, 7], [1, 4, 6, 6], [1, 4, 5, 7], [1, 4, 5, 6], [1, 4, 5], [1, 4, 7], [1, 4, 6], [1, 4], [1, 6, 7], [1, 6, 6], [1, 5, 7], [1, 5, 6], [1, 5], [1, 7], [1, 6], [3, 4, 5, 6, 7], [3, 4, 5, 6, 6], [3, 4, 5, 5, 7], [3, 4, 5, 5, 6], [3, 4, 5, 5], [3, 4, 4, 6, 7], [3, 4, 4, 6, 6], [3, 4, 4, 5, 7], [3, 4, 4, 5, 6], [3, 4, 4, 5], [3, 4, 4, 7], [3, 4, 4, 6], [3, 4, 4], [3, 3, 5, 6, 7], [3, 3, 5, 6, 6], [3, 3, 5, 5, 7], [3, 3, 5, 5, 6], [3, 3, 5, 5], [3, 3, 4, 6, 7], [3, 3, 4, 6, 6], [3, 3, 4, 5, 7], [3, 3, 4, 5, 6], [3, 3, 4, 5], [3, 3, 4, 7], [3, 3, 4, 6], [3, 3, 4], [3, 3, 6, 7], [3, 3, 6, 6], [3, 3, 5, 7], [3, 3, 5, 6], [3, 3, 5], [3, 3, 7], [3, 3, 6], [3, 3], [2, 4, 5, 6, 7], [2, 4, 5, 6, 6], [2, 4, 5, 5, 7], [2, 4, 5, 5, 6], [2, 4, 5, 5], [2, 4, 4, 6, 7], [2, 4, 4, 6, 6], [2, 4, 4, 5, 7], [2, 4, 4, 5, 6], [2, 4, 4, 5], [2, 4, 4, 7], [2, 4, 4, 6], [2, 4, 4], [2, 3, 5, 6, 7], [2, 3, 5, 6, 6], [2, 3, 5, 5, 7], [2, 3, 5, 5, 6], [2, 3, 5, 5], [2, 3, 4, 6, 7], [2, 3, 4, 6, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5, 6], [2, 3, 4, 5], [2, 3, 4, 7], [2, 3, 4, 6], [2, 3, 4], [2, 3, 6, 7], [2, 3, 6, 6], [2, 3, 5, 7], [2, 3, 5, 6], [2, 3, 5], [2, 3, 7], [2, 3, 6], [2, 3], [2, 5, 6, 7], [2, 5, 6, 6], [2, 5, 5, 7], [2, 5, 5, 6], [2, 5, 5], [2, 4, 6, 7], [2, 4, 6, 6], [2, 4, 5, 7], [2, 4, 5, 6], [2, 4, 5], [2, 4, 7], [2, 4, 6], [2, 4], [2, 6, 7], [2, 6, 6], [2, 5, 7], [2, 5, 6], [2, 5], [2, 7], [2, 6], [4, 5, 6, 7], [4, 5, 6, 6], [4, 5, 5, 7], [4, 5, 5, 6], [4, 5, 5], [4, 4, 6, 7], [4, 4, 6, 6], [4, 4, 5, 7], [4, 4, 5, 6], [4, 4, 5], [4, 4, 7], [4, 4, 6], [4, 4], [3, 5, 6, 7], [3, 5, 6, 6], [3, 5, 5, 7], [3, 5, 5, 6], [3, 5, 5], [3, 4, 6, 7], [3, 4, 6, 6], [3, 4, 5, 7], [3, 4, 5, 6], [3, 4, 5], [3, 4, 7], [3, 4, 6], [3, 4], [3, 6, 7], [3, 6, 6], [3, 5, 7], [3, 5, 6], [3, 5], [3, 7], [3, 6], [5, 6, 7], [5, 6, 6], [5, 5, 7], [5, 5, 6], [5, 5], [4, 6, 7], [4, 6, 6], [4, 5, 7], [4, 5, 6], [4, 5], [4, 7], [4, 6], [6, 7], [6, 6], [5, 7], [5, 6]]\n assert candidate(nums = [9, 7, 5, 3, 1, 9, 7, 5, 3, 1, 9, 7, 5, 3, 1]) == [[9, 9, 9], [7, 9, 9], [7, 7, 9], [7, 7, 7], [5, 9, 9], [5, 7, 9], [5, 7, 7], [5, 5, 9], [5, 5, 7], [5, 5, 5], [3, 9, 9], [3, 7, 9], [3, 7, 7], [3, 5, 9], [3, 5, 7], [3, 5, 5], [3, 3, 9], [3, 3, 7], [3, 3, 5], [3, 3, 3], [1, 9, 9], [1, 7, 9], [1, 7, 7], [1, 5, 9], [1, 5, 7], [1, 5, 5], [1, 3, 9], [1, 3, 7], [1, 3, 5], [1, 3, 3], [1, 1, 9], [1, 1, 7], [1, 1, 5], [1, 1, 3], [1, 1, 1], [9, 9], [7, 9], [7, 7], [5, 9], [5, 7], [5, 5], [3, 9], [3, 7], [3, 5], [3, 3], [1, 9], [1, 7], [1, 5], [1, 3], [1, 1]]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == [[1, 2, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 3], [1, 2, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3, 3], [1, 4, 4], [1, 3, 3, 4], [1, 3, 3, 3], [1, 2, 2, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 4], [1, 2, 2, 3], [1, 2, 2, 2], [1, 1, 2, 3, 4], [1, 1, 2, 3, 3], [1, 1, 2, 4], [1, 1, 2, 3], [1, 1, 2, 2], [1, 1, 3, 4], [1, 1, 3, 3], [1, 1, 4], [1, 1, 3], [1, 1, 2], [1, 1, 1], [2, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3, 3], [2, 4, 4], [2, 3, 3, 4], [2, 3, 3, 3], [2, 2, 2, 3, 4], [2, 2, 2, 3, 3], [2, 2, 2, 4], [2, 2, 2, 3], [2, 2, 2, 2], [3, 4, 4], [3, 3, 3, 4], [3, 3, 3, 3], [4, 4], [3, 3, 4], [3, 3, 3], [2, 2, 3, 4], [2, 2, 3, 3], [2, 2, 4], [2, 2, 3], [2, 2, 2], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 3, 4], [1, 3, 3], [1, 4], [1, 3], [1, 2], [1, 1], [2, 3, 4], [2, 3, 3], [2, 4], [2, 3], [2, 2], [3, 4], [3, 3]]\n assert candidate(nums = [5, 4, 3, 2, 1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == [[5, 5, 5], [4, 5, 5], [4, 4, 5], [4, 4, 4], [3, 5, 5], [3, 4, 5], [3, 4, 4], [3, 3, 5], [3, 3, 4], [3, 3, 3], [2, 5, 5], [2, 4, 5], [2, 4, 4], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 2, 5], [2, 2, 4], [2, 2, 3], [2, 2, 2], [1, 5, 5], [1, 4, 5], [1, 4, 4], [1, 3, 5], [1, 3, 4], [1, 3, 3], [1, 2, 5], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 1, 5], [1, 1, 4], [1, 1, 3], [1, 1, 2], [1, 1, 1], [5, 5], [4, 5], [4, 4], [3, 5], [3, 4], [3, 3], [2, 5], [2, 4], [2, 3], [2, 2], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1]]\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0]]\n assert candidate(nums = [3, 3, 3, 1, 2, 2, 2, 3, 3, 3]) == [[3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3], [3, 3, 3, 3], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3], [1, 2, 2, 2], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3], [1, 2, 2, 3], [1, 2, 2], [1, 2, 3, 3, 3], [1, 2, 3, 3], [1, 2, 3], [1, 2], [1, 3, 3, 3], [1, 3, 3], [1, 3], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [2, 2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 3], [2, 2], [2, 3, 3, 3], [2, 3, 3], [2, 3], [3, 3, 3], [3, 3]]\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5]) == [[1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3, 5], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4, 5], [1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 5, 5], [1, 1, 1, 2, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4, 5], [1, 1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 5, 5], [1, 1, 1, 2, 2, 2, 3, 4, 5], [1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 2, 2, 2, 3, 5, 5, 5], [1, 1, 1, 2, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 2, 3, 5], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 4, 5], [1, 1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 1, 2, 2, 2, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 5, 5], [1, 1, 1, 2, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 2, 4, 4], [1, 1, 1, 2, 2, 2, 4, 5, 5, 5], [1, 1, 1, 2, 2, 2, 4, 5, 5], [1, 1, 1, 2, 2, 2, 4, 5], [1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 2, 2, 2, 5, 5, 5], [1, 1, 1, 2, 2, 2, 5, 5], [1, 1, 1, 2, 2, 2, 5], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4, 5], [1, 1, 1, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 5, 5], [1, 1, 1, 2, 2, 3, 3, 3, 5], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 3, 4, 5], [1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 5, 5, 5], [1, 1, 1, 2, 2, 3, 3, 5, 5], [1, 1, 1, 2, 2, 3, 3, 5], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 4, 5], [1, 1, 1, 2, 2, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 5, 5], [1, 1, 1, 2, 2, 3, 4, 4, 5], [1, 1, 1, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 3, 4, 5, 5, 5], [1, 1, 1, 2, 2, 3, 4, 5, 5], [1, 1, 1, 2, 2, 3, 4, 5], [1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 2, 2, 3, 5, 5, 5], [1, 1, 1, 2, 2, 3, 5, 5], [1, 1, 1, 2, 2, 3, 5], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2, 4, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 4, 4, 4, 5, 5], [1, 1, 1, 2, 2, 4, 4, 4, 5], [1, 1, 1, 2, 2, 4, 4, 4], [1, 1, 1, 2, 2, 4, 4, 5, 5, 5], [1, 1, 1, 2, 2, 4, 4, 5, 5], [1, 1, 1, 2, 2, 4, 4, 5], [1, 1, 1, 2, 2, 4, 4], [1, 1, 1, 2, 2, 4, 5, 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2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 4, 5, 5, 5], [2, 2, 3, 3, 4, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 4, 5], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4, 5, 5, 5], [2, 2, 3, 3, 4, 4, 5, 5], [2, 2, 3, 3, 4, 4, 5], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4, 5, 5, 5], [2, 2, 3, 3, 4, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5, 5, 5], [2, 2, 3, 3, 5, 5], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4, 5, 5, 5], [2, 2, 3, 4, 4, 4, 5, 5], [2, 2, 3, 4, 4, 4, 5], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4, 5, 5, 5], [2, 2, 3, 4, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 4, 5, 5, 5], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5, 5, 5], [2, 2, 3, 5, 5], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 4, 4, 5, 5, 5], [2, 2, 4, 4, 4, 5, 5], [2, 2, 4, 4, 4, 5], [2, 2, 4, 4, 4], [2, 2, 4, 4, 5, 5, 5], [2, 2, 4, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 4, 5, 5, 5], [2, 2, 4, 5, 5], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5, 5, 5], [2, 2, 5, 5], [2, 2, 5], [2, 2], [2, 3, 3, 3, 4, 4, 4, 5, 5, 5], [2, 3, 3, 3, 4, 4, 4, 5, 5], [2, 3, 3, 3, 4, 4, 4, 5], [2, 3, 3, 3, 4, 4, 4], [2, 3, 3, 3, 4, 4, 5, 5, 5], [2, 3, 3, 3, 4, 4, 5, 5], [2, 3, 3, 3, 4, 4, 5], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4, 5, 5, 5], [2, 3, 3, 3, 4, 5, 5], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 5, 5, 5], [2, 3, 3, 3, 5, 5], [2, 3, 3, 3, 5], [2, 3, 3, 3], [2, 3, 3, 4, 4, 4, 5, 5, 5], [2, 3, 3, 4, 4, 4, 5, 5], [2, 3, 3, 4, 4, 4, 5], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4, 5, 5, 5], [2, 3, 3, 4, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 4, 5, 5, 5], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5, 5, 5], [2, 3, 3, 5, 5], [2, 3, 3, 5], [2, 3, 3], [2, 3, 4, 4, 4, 5, 5, 5], [2, 3, 4, 4, 4, 5, 5], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4], [2, 3, 4, 4, 5, 5, 5], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 4, 5, 5, 5], [2, 3, 4, 5, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5, 5, 5], [2, 3, 5, 5], [2, 3, 5], [2, 3], [2, 4, 4, 4, 5, 5, 5], [2, 4, 4, 4, 5, 5], [2, 4, 4, 4, 5], [2, 4, 4, 4], [2, 4, 4, 5, 5, 5], [2, 4, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 4, 5, 5, 5], [2, 4, 5, 5], [2, 4, 5], [2, 4], [2, 5, 5, 5], [2, 5, 5], [2, 5], [3, 3, 3, 4, 4, 4, 5, 5, 5], [3, 3, 3, 4, 4, 4, 5, 5], [3, 3, 3, 4, 4, 4, 5], [3, 3, 3, 4, 4, 4], [3, 3, 3, 4, 4, 5, 5, 5], [3, 3, 3, 4, 4, 5, 5], [3, 3, 3, 4, 4, 5], [3, 3, 3, 4, 4], [3, 3, 3, 4, 5, 5, 5], [3, 3, 3, 4, 5, 5], [3, 3, 3, 4, 5], [3, 3, 3, 4], [3, 3, 3, 5, 5, 5], [3, 3, 3, 5, 5], [3, 3, 3, 5], [3, 3, 3], [3, 3, 4, 4, 4, 5, 5, 5], [3, 3, 4, 4, 4, 5, 5], [3, 3, 4, 4, 4, 5], [3, 3, 4, 4, 4], [3, 3, 4, 4, 5, 5, 5], [3, 3, 4, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 4, 5, 5, 5], [3, 3, 4, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5, 5, 5], [3, 3, 5, 5], [3, 3, 5], [3, 3], [3, 4, 4, 4, 5, 5, 5], [3, 4, 4, 4, 5, 5], [3, 4, 4, 4, 5], [3, 4, 4, 4], [3, 4, 4, 5, 5, 5], [3, 4, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 4, 5, 5, 5], [3, 4, 5, 5], [3, 4, 5], [3, 4], [3, 5, 5, 5], [3, 5, 5], [3, 5], [4, 4, 4, 5, 5, 5], [4, 4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [4, 4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 5], [4, 4], [4, 5, 5, 5], [4, 5, 5], [4, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [1, 2, 3, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == [[1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 3, 5], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 3], [1, 2, 3, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 2, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 2, 5], [1, 2, 2, 2, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 2], [1, 3, 3, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 3, 5], [1, 3, 3, 3, 4], [1, 3, 3, 3, 3], [1, 3, 4, 5], [1, 3, 4, 4], [1, 3, 3, 5], [1, 3, 3, 4], [1, 3, 3, 3], [1, 2, 4, 5], [1, 2, 4, 4], [1, 2, 3, 5], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 2, 5], [1, 2, 2, 4], [1, 2, 2, 3], [1, 2, 2, 2], [1, 1, 4, 5], [1, 1, 4, 4], [1, 1, 3, 5], [1, 1, 3, 4], [1, 1, 3, 3], [1, 1, 2, 5], [1, 1, 2, 4], [1, 1, 2, 3], [1, 1, 2, 2], [1, 1, 1, 5], [1, 1, 1, 4], [1, 1, 1, 3], [1, 1, 1, 2], [1, 1, 1, 1], [2, 3, 3, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 3, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 3], [2, 3, 4, 5], [2, 3, 4, 4], [2, 3, 3, 5], [2, 3, 3, 4], [2, 3, 3, 3], [2, 2, 4, 5], [2, 2, 4, 4], [2, 2, 3, 5], [2, 2, 3, 4], [2, 2, 3, 3], [2, 2, 2, 5], [2, 2, 2, 4], [2, 2, 2, 3], [2, 2, 2, 2], [3, 3, 4, 5], [3, 3, 4, 4], [3, 3, 3, 5], [3, 3, 3, 4], [3, 3, 3, 3], [3, 4, 5], [3, 4, 4], [3, 3, 5], [3, 3, 4], [3, 3, 3], [2, 4, 5], [2, 4, 4], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 2, 5], [2, 2, 4], [2, 2, 3], [2, 2, 2], [1, 4, 5], [1, 4, 4], [1, 3, 5], [1, 3, 4], [1, 3, 3], [1, 2, 5], [1, 2, 4], [1, 2, 3], [1, 2, 2], [1, 1, 5], [1, 1, 4], [1, 1, 3], [1, 1, 2], [1, 1, 1], [4, 5], [4, 4], [3, 5], [3, 4], [3, 3], [2, 5], [2, 4], [2, 3], [2, 2], [1, 5], [1, 4], [1, 3], [1, 2], [1, 1]]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == []\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5, 5, 5], [1, 2, 3, 4, 4, 5, 5], [1, 2, 3, 4, 4, 4, 5], [1, 2, 3, 4, 4, 4], [1, 2, 3, 5, 5, 5], [1, 2, 3, 3, 4, 5, 5], [1, 2, 3, 3, 4, 4, 5], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 5, 5], [1, 2, 3, 3, 3, 4, 5], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3, 5], [1, 2, 3, 3, 3], [1, 2, 4, 5, 5, 5], [1, 2, 4, 4, 5, 5], [1, 2, 4, 4, 4, 5], [1, 2, 4, 4, 4], [1, 2, 5, 5, 5], [1, 2, 2, 3, 4, 5, 5], [1, 2, 2, 3, 4, 4, 5], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 5, 5], [1, 2, 2, 3, 3, 4, 5], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3, 5], [1, 2, 2, 3, 3], [1, 2, 2, 4, 5, 5], [1, 2, 2, 4, 4, 5], [1, 2, 2, 4, 4], [1, 2, 2, 5, 5], [1, 2, 2, 2, 3, 4, 5], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3, 5], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4, 5], [1, 2, 2, 2, 4], [1, 2, 2, 2, 5], [1, 2, 2, 2], [1, 3, 4, 5, 5, 5], [1, 3, 4, 4, 5, 5], [1, 3, 4, 4, 4, 5], [1, 3, 4, 4, 4], [1, 3, 5, 5, 5], [1, 3, 3, 4, 5, 5], [1, 3, 3, 4, 4, 5], [1, 3, 3, 4, 4], [1, 3, 3, 5, 5], [1, 3, 3, 3, 4, 5], [1, 3, 3, 3, 4], [1, 3, 3, 3, 5], [1, 3, 3, 3], [1, 4, 5, 5, 5], [1, 4, 4, 5, 5], [1, 4, 4, 4, 5], [1, 4, 4, 4], [1, 5, 5, 5], [1, 1, 2, 3, 4, 5, 5], [1, 1, 2, 3, 4, 4, 5], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 5, 5], [1, 1, 2, 3, 3, 4, 5], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3, 5], [1, 1, 2, 3, 3], [1, 1, 2, 4, 5, 5], [1, 1, 2, 4, 4, 5], [1, 1, 2, 4, 4], [1, 1, 2, 5, 5], [1, 1, 2, 2, 3, 4, 5], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3, 5], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 5], [1, 1, 2, 2, 4], [1, 1, 2, 2, 5], [1, 1, 2, 2], [1, 1, 3, 4, 5, 5], [1, 1, 3, 4, 4, 5], [1, 1, 3, 4, 4], [1, 1, 3, 5, 5], [1, 1, 3, 3, 4, 5], [1, 1, 3, 3, 4], [1, 1, 3, 3, 5], [1, 1, 3, 3], [1, 1, 4, 5, 5], [1, 1, 4, 4, 5], [1, 1, 4, 4], [1, 1, 5, 5], [1, 1, 1, 2, 3, 4, 5], [1, 1, 1, 2, 3, 4], [1, 1, 1, 2, 3, 5], [1, 1, 1, 2, 3], [1, 1, 1, 2, 4, 5], [1, 1, 1, 2, 4], [1, 1, 1, 2, 5], [1, 1, 1, 2], [1, 1, 1, 3, 4, 5], [1, 1, 1, 3, 4], [1, 1, 1, 3, 5], [1, 1, 1, 3], [1, 1, 1, 4, 5], [1, 1, 1, 4], [1, 1, 1, 5], [1, 1, 1], [2, 3, 4, 5, 5, 5], [2, 3, 4, 4, 5, 5], [2, 3, 4, 4, 4, 5], [2, 3, 4, 4, 4], [2, 3, 5, 5, 5], [2, 3, 3, 4, 5, 5], [2, 3, 3, 4, 4, 5], [2, 3, 3, 4, 4], [2, 3, 3, 5, 5], [2, 3, 3, 3, 4, 5], [2, 3, 3, 3, 4], [2, 3, 3, 3, 5], [2, 3, 3, 3], [2, 4, 5, 5, 5], [2, 4, 4, 5, 5], [2, 4, 4, 4, 5], [2, 4, 4, 4], [2, 5, 5, 5], [2, 2, 3, 4, 5, 5], [2, 2, 3, 4, 4, 5], [2, 2, 3, 4, 4], [2, 2, 3, 5, 5], [2, 2, 3, 3, 4, 5], [2, 2, 3, 3, 4], [2, 2, 3, 3, 5], [2, 2, 3, 3], [2, 2, 4, 5, 5], [2, 2, 4, 4, 5], [2, 2, 4, 4], [2, 2, 5, 5], [2, 2, 2, 3, 4, 5], [2, 2, 2, 3, 4], [2, 2, 2, 3, 5], [2, 2, 2, 3], [2, 2, 2, 4, 5], [2, 2, 2, 4], [2, 2, 2, 5], [2, 2, 2], [3, 4, 5, 5, 5], [3, 4, 4, 5, 5], [3, 4, 4, 4, 5], [3, 4, 4, 4], [3, 5, 5, 5], [3, 3, 4, 5, 5], [3, 3, 4, 4, 5], [3, 3, 4, 4], [3, 3, 5, 5], [3, 3, 3, 4, 5], [3, 3, 3, 4], [3, 3, 3, 5], [3, 3, 3], [4, 5, 5, 5], [4, 4, 5, 5], [4, 4, 4, 5], [4, 4, 4], [5, 5, 5], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5, 5], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 4, 5, 5], [1, 2, 4, 4, 5], [1, 2, 4, 4], [1, 2, 5, 5], [1, 2, 2, 3, 4, 5], [1, 2, 2, 3, 4], [1, 2, 2, 3, 5], [1, 2, 2, 3], [1, 2, 2, 4, 5], [1, 2, 2, 4], [1, 2, 2, 5], [1, 2, 2], [1, 3, 4, 5, 5], [1, 3, 4, 4, 5], [1, 3, 4, 4], [1, 3, 5, 5], [1, 3, 3, 4, 5], [1, 3, 3, 4], [1, 3, 3, 5], [1, 3, 3], [1, 4, 5, 5], [1, 4, 4, 5], [1, 4, 4], [1, 5, 5], [1, 1, 2, 3, 4, 5], [1, 1, 2, 3, 4], [1, 1, 2, 3, 5], [1, 1, 2, 3], [1, 1, 2, 4, 5], [1, 1, 2, 4], [1, 1, 2, 5], [1, 1, 2], [1, 1, 3, 4, 5], [1, 1, 3, 4], [1, 1, 3, 5], [1, 1, 3], [1, 1, 4, 5], [1, 1, 4], [1, 1, 5], [1, 1], [2, 3, 4, 5, 5], [2, 3, 4, 4, 5], [2, 3, 4, 4], [2, 3, 5, 5], [2, 3, 3, 4, 5], [2, 3, 3, 4], [2, 3, 3, 5], [2, 3, 3], [2, 4, 5, 5], [2, 4, 4, 5], [2, 4, 4], [2, 5, 5], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [3, 4, 5, 5], [3, 4, 4, 5], [3, 4, 4], [3, 5, 5], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5], [3, 3], [4, 5, 5], [4, 4, 5], [4, 4], [5, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [3, 4, 5], [3, 4], [3, 5], [4, 5]]\n assert candidate(nums = [10, 5, 10, 5, 10, 5, 10, 5, 10, 5]) == [[10, 10, 10, 10, 10], [5, 10, 10, 10, 10], [5, 5, 10, 10, 10], [5, 5, 5, 10, 10], [5, 5, 5, 5, 10], [5, 5, 5, 5, 5], [10, 10, 10, 10], [5, 10, 10, 10], [5, 5, 10, 10], [5, 5, 5, 10], [5, 5, 5, 5], [10, 10, 10], [5, 10, 10], [5, 5, 10], [5, 5, 5], [10, 10], [5, 10], [5, 5]]\n assert candidate(nums = [-10, 10, -20, 20, -30, 30, -40, 40, -50, 50, 0, 0, 0, 0, 0]) == [[-10, 10, 20, 30, 40, 50], [-10, 10, 20, 30, 40], [-10, 10, 20, 30, 50], [-10, 10, 20, 30], [-10, 10, 20, 40, 50], [-10, 10, 20, 40], [-10, 10, 20, 50], [-10, 10, 20], [-10, 10, 30, 40, 50], [-10, 10, 30, 40], [-10, 10, 30, 50], [-10, 10, 30], [-10, 10, 40, 50], [-10, 10, 40], [-10, 10, 50], [-10, 10], [-10, 20, 30, 40, 50], [-10, 20, 30, 40], [-10, 20, 30, 50], [-10, 20, 30], [-10, 20, 40, 50], [-10, 20, 40], [-10, 20, 50], [-10, 20], [-10, 30, 40, 50], [-10, 30, 40], [-10, 30, 50], [-10, 30], [-10, 40, 50], [-10, 40], [-10, 50], [-10, 0, 0, 0, 0, 0], [-10, 0, 0, 0, 0], [-10, 0, 0, 0], [-10, 0, 0], [-10, 0], [10, 20, 30, 40, 50], [10, 20, 30, 40], [10, 20, 30, 50], [10, 20, 30], [10, 20, 40, 50], [10, 20, 40], [10, 20, 50], [10, 20], [10, 30, 40, 50], [10, 30, 40], [10, 30, 50], [10, 30], [10, 40, 50], [10, 40], [10, 50], [-20, 20, 30, 40, 50], [-20, 20, 30, 40], [-20, 20, 30, 50], [-20, 20, 30], [-20, 20, 40, 50], [-20, 20, 40], [-20, 20, 50], [-20, 20], [-20, 30, 40, 50], [-20, 30, 40], [-20, 30, 50], [-20, 30], [-20, 40, 50], [-20, 40], [-20, 50], [-20, 0, 0, 0, 0, 0], [-20, 0, 0, 0, 0], [-20, 0, 0, 0], [-20, 0, 0], [-20, 0], [20, 30, 40, 50], [20, 30, 40], [20, 30, 50], [20, 30], [20, 40, 50], [20, 40], [20, 50], [-30, 30, 40, 50], [-30, 30, 40], [-30, 30, 50], [-30, 30], [-30, 40, 50], [-30, 40], [-30, 50], [-30, 0, 0, 0, 0, 0], [-30, 0, 0, 0, 0], [-30, 0, 0, 0], [-30, 0, 0], [-30, 0], [30, 40, 50], [30, 40], [30, 50], [-40, 40, 50], [-40, 40], [-40, 50], [-40, 0, 0, 0, 0, 0], [-40, 0, 0, 0, 0], [-40, 0, 0, 0], [-40, 0, 0], [-40, 0], [40, 50], [-50, 50], [-50, 0, 0, 0, 0, 0], [-50, 0, 0, 0, 0], [-50, 0, 0, 0], [-50, 0, 0], [-50, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0]]\n assert candidate(nums = [1, 2, 1, 1, 2, 1, 2, 1]) == [[1, 2, 2, 2], [1, 1, 1, 2, 2], [1, 1, 1, 1, 2], [1, 1, 1, 1, 1], [2, 2, 2], [1, 1, 2, 2], [1, 1, 1, 2], [1, 1, 1, 1], [1, 2, 2], [1, 1, 2], [1, 1, 1], [2, 2], [1, 2], [1, 1]]\n assert candidate(nums = [100, -100, 50, -50, 25, -25, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == [[-100, 50], [-100, -50, 25], [-100, -50, -25, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0, 0, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0, 0], [-100, -50, -25, 0, 0, 0], [-100, -50, -25, 0, 0], [-100, -50, -25, 0], [-100, -50, -25], [-100, -50, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-100, -50, 0, 0, 0, 0, 0, 0, 0, 0], [-100, -50, 0, 0, 0, 0, 0, 0, 0], [-100, -50, 0, 0, 0, 0, 0, 0], [-100, -50, 0, 0, 0, 0, 0], [-100, -50, 0, 0, 0, 0], [-100, -50, 0, 0, 0], [-100, -50, 0, 0], [-100, -50, 0], [-100, -50], [-100, 25], [-100, -25, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-100, -25, 0, 0, 0, 0, 0, 0, 0, 0], [-100, -25, 0, 0, 0, 0, 0, 0, 0], [-100, -25, 0, 0, 0, 0, 0, 0], [-100, -25, 0, 0, 0, 0, 0], [-100, -25, 0, 0, 0, 0], [-100, -25, 0, 0, 0], [-100, -25, 0, 0], [-100, -25, 0], [-100, -25], [-100, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-100, 0, 0, 0, 0, 0, 0, 0, 0], [-100, 0, 0, 0, 0, 0, 0, 0], [-100, 0, 0, 0, 0, 0, 0], [-100, 0, 0, 0, 0, 0], [-100, 0, 0, 0, 0], [-100, 0, 0, 0], [-100, 0, 0], [-100, 0], [-50, 25], [-50, -25, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-50, -25, 0, 0, 0, 0, 0, 0, 0, 0], [-50, -25, 0, 0, 0, 0, 0, 0, 0], [-50, -25, 0, 0, 0, 0, 0, 0], [-50, -25, 0, 0, 0, 0, 0], [-50, -25, 0, 0, 0, 0], [-50, -25, 0, 0, 0], [-50, -25, 0, 0], [-50, -25, 0], [-50, -25], [-50, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-50, 0, 0, 0, 0, 0, 0, 0, 0], [-50, 0, 0, 0, 0, 0, 0, 0], [-50, 0, 0, 0, 0, 0, 0], [-50, 0, 0, 0, 0, 0], [-50, 0, 0, 0, 0], [-50, 0, 0, 0], [-50, 0, 0], [-50, 0], [-25, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0, 0], [-25, 0, 0, 0, 0], [-25, 0, 0, 0], [-25, 0, 0], [-25, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0], [0, 0]]\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]) == [[0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 3], [0, 0, 0, 1, 1, 1, 2, 2, 2, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2, 4], [0, 0, 0, 1, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3, 4], [0, 0, 0, 1, 1, 1, 2, 2, 3], [0, 0, 0, 1, 1, 1, 2, 2, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 4, 4], [0, 0, 0, 1, 1, 1, 2, 2, 4], [0, 0, 0, 1, 1, 1, 2, 2], [0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 4], [0, 0, 0, 1, 1, 1, 2, 3, 3, 3], [0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 3, 3, 4], [0, 0, 0, 1, 1, 1, 2, 3, 3], [0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 3, 4, 4], [0, 0, 0, 1, 1, 1, 2, 3, 4], [0, 0, 0, 1, 1, 1, 2, 3], [0, 0, 0, 1, 1, 1, 2, 4, 4, 4], [0, 0, 0, 1, 1, 1, 2, 4, 4], [0, 0, 0, 1, 1, 1, 2, 4], [0, 0, 0, 1, 1, 1, 2], [0, 0, 0, 1, 1, 1, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 3, 3, 3, 4], [0, 0, 0, 1, 1, 1, 3, 3, 3], [0, 0, 0, 1, 1, 1, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 3, 3, 4, 4], [0, 0, 0, 1, 1, 1, 3, 3, 4], [0, 0, 0, 1, 1, 1, 3, 3], [0, 0, 0, 1, 1, 1, 3, 4, 4, 4], [0, 0, 0, 1, 1, 1, 3, 4, 4], [0, 0, 0, 1, 1, 1, 3, 4], [0, 0, 0, 1, 1, 1, 3], [0, 0, 0, 1, 1, 1, 4, 4, 4], [0, 0, 0, 1, 1, 1, 4, 4], [0, 0, 0, 1, 1, 1, 4], [0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 2, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3, 4], [0, 0, 0, 1, 1, 2, 2, 2, 3], [0, 0, 0, 1, 1, 2, 2, 2, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 4, 4], [0, 0, 0, 1, 1, 2, 2, 2, 4], [0, 0, 0, 1, 1, 2, 2, 2], [0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 4], [0, 0, 0, 1, 1, 2, 2, 3, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4], [0, 0, 0, 1, 1, 2, 2, 3, 3, 4], [0, 0, 0, 1, 1, 2, 2, 3, 3], [0, 0, 0, 1, 1, 2, 2, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 3, 4, 4], [0, 0, 0, 1, 1, 2, 2, 3, 4], [0, 0, 0, 1, 1, 2, 2, 3], [0, 0, 0, 1, 1, 2, 2, 4, 4, 4], [0, 0, 0, 1, 1, 2, 2, 4, 4], [0, 0, 0, 1, 1, 2, 2, 4], [0, 0, 0, 1, 1, 2, 2], [0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 2, 3, 3, 3, 4], [0, 0, 0, 1, 1, 2, 3, 3, 3], [0, 0, 0, 1, 1, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 3, 3, 4, 4], [0, 0, 0, 1, 1, 2, 3, 3, 4], [0, 0, 0, 1, 1, 2, 3, 3], [0, 0, 0, 1, 1, 2, 3, 4, 4, 4], [0, 0, 0, 1, 1, 2, 3, 4, 4], [0, 0, 0, 1, 1, 2, 3, 4], [0, 0, 0, 1, 1, 2, 3], [0, 0, 0, 1, 1, 2, 4, 4, 4], [0, 0, 0, 1, 1, 2, 4, 4], [0, 0, 0, 1, 1, 2, 4], [0, 0, 0, 1, 1, 2], [0, 0, 0, 1, 1, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 3, 3, 3, 4, 4], [0, 0, 0, 1, 1, 3, 3, 3, 4], [0, 0, 0, 1, 1, 3, 3, 3], [0, 0, 0, 1, 1, 3, 3, 4, 4, 4], [0, 0, 0, 1, 1, 3, 3, 4, 4], [0, 0, 0, 1, 1, 3, 3, 4], [0, 0, 0, 1, 1, 3, 3], [0, 0, 0, 1, 1, 3, 4, 4, 4], [0, 0, 0, 1, 1, 3, 4, 4], [0, 0, 0, 1, 1, 3, 4], [0, 0, 0, 1, 1, 3], [0, 0, 0, 1, 1, 4, 4, 4], [0, 0, 0, 1, 1, 4, 4], [0, 0, 0, 1, 1, 4], [0, 0, 0, 1, 1], [0, 0, 0, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 2, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 2, 2, 2, 3, 3, 3, 4], [0, 0, 0, 1, 2, 2, 2, 3, 3, 3], [0, 0, 0, 1, 2, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 2, 2, 2, 3, 3, 4, 4], [0, 0, 0, 1, 2, 2, 2, 3, 3, 4], [0, 0, 0, 1, 2, 2, 2, 3, 3], [0, 0, 0, 1, 2, 2, 2, 3, 4, 4, 4], [0, 0, 0, 1, 2, 2, 2, 3, 4, 4], [0, 0, 0, 1, 2, 2, 2, 3, 4], [0, 0, 0, 1, 2, 2, 2, 3], [0, 0, 0, 1, 2, 2, 2, 4, 4, 4], [0, 0, 0, 1, 2, 2, 2, 4, 4], [0, 0, 0, 1, 2, 2, 2, 4], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 2, 2, 3, 3, 3, 4], [0, 0, 0, 1, 2, 2, 3, 3, 3], [0, 0, 0, 1, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 2, 2, 3, 3, 4, 4], [0, 0, 0, 1, 2, 2, 3, 3, 4], [0, 0, 0, 1, 2, 2, 3, 3], [0, 0, 0, 1, 2, 2, 3, 4, 4, 4], [0, 0, 0, 1, 2, 2, 3, 4, 4], [0, 0, 0, 1, 2, 2, 3, 4], [0, 0, 0, 1, 2, 2, 3], [0, 0, 0, 1, 2, 2, 4, 4, 4], [0, 0, 0, 1, 2, 2, 4, 4], [0, 0, 0, 1, 2, 2, 4], [0, 0, 0, 1, 2, 2], [0, 0, 0, 1, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 2, 3, 3, 3, 4, 4], [0, 0, 0, 1, 2, 3, 3, 3, 4], [0, 0, 0, 1, 2, 3, 3, 3], [0, 0, 0, 1, 2, 3, 3, 4, 4, 4], [0, 0, 0, 1, 2, 3, 3, 4, 4], [0, 0, 0, 1, 2, 3, 3, 4], [0, 0, 0, 1, 2, 3, 3], [0, 0, 0, 1, 2, 3, 4, 4, 4], [0, 0, 0, 1, 2, 3, 4, 4], [0, 0, 0, 1, 2, 3, 4], [0, 0, 0, 1, 2, 3], [0, 0, 0, 1, 2, 4, 4, 4], [0, 0, 0, 1, 2, 4, 4], [0, 0, 0, 1, 2, 4], [0, 0, 0, 1, 2], [0, 0, 0, 1, 3, 3, 3, 4, 4, 4], [0, 0, 0, 1, 3, 3, 3, 4, 4], [0, 0, 0, 1, 3, 3, 3, 4], [0, 0, 0, 1, 3, 3, 3], [0, 0, 0, 1, 3, 3, 4, 4, 4], [0, 0, 0, 1, 3, 3, 4, 4], [0, 0, 0, 1, 3, 3, 4], [0, 0, 0, 1, 3, 3], [0, 0, 0, 1, 3, 4, 4, 4], [0, 0, 0, 1, 3, 4, 4], [0, 0, 0, 1, 3, 4], [0, 0, 0, 1, 3], [0, 0, 0, 1, 4, 4, 4], [0, 0, 0, 1, 4, 4], [0, 0, 0, 1, 4], [0, 0, 0, 1], [0, 0, 0, 2, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 2, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 2, 2, 2, 3, 3, 3, 4], [0, 0, 0, 2, 2, 2, 3, 3, 3], [0, 0, 0, 2, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 2, 2, 2, 3, 3, 4, 4], [0, 0, 0, 2, 2, 2, 3, 3, 4], [0, 0, 0, 2, 2, 2, 3, 3], [0, 0, 0, 2, 2, 2, 3, 4, 4, 4], [0, 0, 0, 2, 2, 2, 3, 4, 4], [0, 0, 0, 2, 2, 2, 3, 4], [0, 0, 0, 2, 2, 2, 3], [0, 0, 0, 2, 2, 2, 4, 4, 4], [0, 0, 0, 2, 2, 2, 4, 4], [0, 0, 0, 2, 2, 2, 4], [0, 0, 0, 2, 2, 2], [0, 0, 0, 2, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 2, 2, 3, 3, 3, 4, 4], [0, 0, 0, 2, 2, 3, 3, 3, 4], [0, 0, 0, 2, 2, 3, 3, 3], [0, 0, 0, 2, 2, 3, 3, 4, 4, 4], [0, 0, 0, 2, 2, 3, 3, 4, 4], [0, 0, 0, 2, 2, 3, 3, 4], [0, 0, 0, 2, 2, 3, 3], [0, 0, 0, 2, 2, 3, 4, 4, 4], [0, 0, 0, 2, 2, 3, 4, 4], [0, 0, 0, 2, 2, 3, 4], [0, 0, 0, 2, 2, 3], [0, 0, 0, 2, 2, 4, 4, 4], [0, 0, 0, 2, 2, 4, 4], [0, 0, 0, 2, 2, 4], [0, 0, 0, 2, 2], [0, 0, 0, 2, 3, 3, 3, 4, 4, 4], [0, 0, 0, 2, 3, 3, 3, 4, 4], [0, 0, 0, 2, 3, 3, 3, 4], [0, 0, 0, 2, 3, 3, 3], [0, 0, 0, 2, 3, 3, 4, 4, 4], [0, 0, 0, 2, 3, 3, 4, 4], [0, 0, 0, 2, 3, 3, 4], [0, 0, 0, 2, 3, 3], [0, 0, 0, 2, 3, 4, 4, 4], [0, 0, 0, 2, 3, 4, 4], [0, 0, 0, 2, 3, 4], [0, 0, 0, 2, 3], [0, 0, 0, 2, 4, 4, 4], [0, 0, 0, 2, 4, 4], [0, 0, 0, 2, 4], [0, 0, 0, 2], [0, 0, 0, 3, 3, 3, 4, 4, 4], [0, 0, 0, 3, 3, 3, 4, 4], [0, 0, 0, 3, 3, 3, 4], [0, 0, 0, 3, 3, 3], [0, 0, 0, 3, 3, 4, 4, 4], [0, 0, 0, 3, 3, 4, 4], [0, 0, 0, 3, 3, 4], [0, 0, 0, 3, 3], [0, 0, 0, 3, 4, 4, 4], [0, 0, 0, 3, 4, 4], [0, 0, 0, 3, 4], [0, 0, 0, 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4], [0, 2, 2, 3, 4, 4], [0, 2, 2, 3, 4], [0, 2, 2, 3], [0, 2, 2, 4, 4, 4], [0, 2, 2, 4, 4], [0, 2, 2, 4], [0, 2, 2], [0, 2, 3, 3, 3, 4, 4, 4], [0, 2, 3, 3, 3, 4, 4], [0, 2, 3, 3, 3, 4], [0, 2, 3, 3, 3], [0, 2, 3, 3, 4, 4, 4], [0, 2, 3, 3, 4, 4], [0, 2, 3, 3, 4], [0, 2, 3, 3], [0, 2, 3, 4, 4, 4], [0, 2, 3, 4, 4], [0, 2, 3, 4], [0, 2, 3], [0, 2, 4, 4, 4], [0, 2, 4, 4], [0, 2, 4], [0, 2], [0, 3, 3, 3, 4, 4, 4], [0, 3, 3, 3, 4, 4], [0, 3, 3, 3, 4], [0, 3, 3, 3], [0, 3, 3, 4, 4, 4], [0, 3, 3, 4, 4], [0, 3, 3, 4], [0, 3, 3], [0, 3, 4, 4, 4], [0, 3, 4, 4], [0, 3, 4], [0, 3], [0, 4, 4, 4], [0, 4, 4], [0, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 2, 3, 3], [1, 1, 1, 2, 2, 2, 3, 4, 4, 4], [1, 1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 2, 3, 4], [1, 1, 1, 2, 2, 2, 3], [1, 1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 1, 2, 2, 2, 4, 4], [1, 1, 1, 2, 2, 2, 4], [1, 1, 1, 2, 2, 2], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 2, 3, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3, 3], [1, 1, 1, 2, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 1, 2, 2, 3, 3, 4], [1, 1, 1, 2, 2, 3, 3], [1, 1, 1, 2, 2, 3, 4, 4, 4], [1, 1, 1, 2, 2, 3, 4, 4], [1, 1, 1, 2, 2, 3, 4], [1, 1, 1, 2, 2, 3], [1, 1, 1, 2, 2, 4, 4, 4], [1, 1, 1, 2, 2, 4, 4], [1, 1, 1, 2, 2, 4], [1, 1, 1, 2, 2], [1, 1, 1, 2, 3, 3, 3, 4, 4, 4], [1, 1, 1, 2, 3, 3, 3, 4, 4], [1, 1, 1, 2, 3, 3, 3, 4], [1, 1, 1, 2, 3, 3, 3], [1, 1, 1, 2, 3, 3, 4, 4, 4], [1, 1, 1, 2, 3, 3, 4, 4], [1, 1, 1, 2, 3, 3, 4], [1, 1, 1, 2, 3, 3], [1, 1, 1, 2, 3, 4, 4, 4], [1, 1, 1, 2, 3, 4, 4], [1, 1, 1, 2, 3, 4], [1, 1, 1, 2, 3], [1, 1, 1, 2, 4, 4, 4], [1, 1, 1, 2, 4, 4], [1, 1, 1, 2, 4], [1, 1, 1, 2], [1, 1, 1, 3, 3, 3, 4, 4, 4], [1, 1, 1, 3, 3, 3, 4, 4], [1, 1, 1, 3, 3, 3, 4], [1, 1, 1, 3, 3, 3], [1, 1, 1, 3, 3, 4, 4, 4], [1, 1, 1, 3, 3, 4, 4], [1, 1, 1, 3, 3, 4], [1, 1, 1, 3, 3], [1, 1, 1, 3, 4, 4, 4], [1, 1, 1, 3, 4, 4], [1, 1, 1, 3, 4], [1, 1, 1, 3], [1, 1, 1, 4, 4, 4], [1, 1, 1, 4, 4], [1, 1, 1, 4], [1, 1, 1], [1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 2, 2, 2, 3, 3, 3, 4, 4], [1, 1, 2, 2, 2, 3, 3, 3, 4], [1, 1, 2, 2, 2, 3, 3, 3], [1, 1, 2, 2, 2, 3, 3, 4, 4, 4], [1, 1, 2, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 2, 3, 3, 4], [1, 1, 2, 2, 2, 3, 3], [1, 1, 2, 2, 2, 3, 4, 4, 4], [1, 1, 2, 2, 2, 3, 4, 4], [1, 1, 2, 2, 2, 3, 4], [1, 1, 2, 2, 2, 3], [1, 1, 2, 2, 2, 4, 4, 4], [1, 1, 2, 2, 2, 4, 4], [1, 1, 2, 2, 2, 4], [1, 1, 2, 2, 2], [1, 1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 1, 2, 2, 3, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 3, 4], [1, 1, 2, 2, 3, 3, 3], [1, 1, 2, 2, 3, 3, 4, 4, 4], [1, 1, 2, 2, 3, 3, 4, 4], [1, 1, 2, 2, 3, 3, 4], [1, 1, 2, 2, 3, 3], [1, 1, 2, 2, 3, 4, 4, 4], [1, 1, 2, 2, 3, 4, 4], [1, 1, 2, 2, 3, 4], [1, 1, 2, 2, 3], [1, 1, 2, 2, 4, 4, 4], [1, 1, 2, 2, 4, 4], [1, 1, 2, 2, 4], [1, 1, 2, 2], [1, 1, 2, 3, 3, 3, 4, 4, 4], [1, 1, 2, 3, 3, 3, 4, 4], [1, 1, 2, 3, 3, 3, 4], [1, 1, 2, 3, 3, 3], [1, 1, 2, 3, 3, 4, 4, 4], [1, 1, 2, 3, 3, 4, 4], [1, 1, 2, 3, 3, 4], [1, 1, 2, 3, 3], [1, 1, 2, 3, 4, 4, 4], [1, 1, 2, 3, 4, 4], [1, 1, 2, 3, 4], [1, 1, 2, 3], [1, 1, 2, 4, 4, 4], [1, 1, 2, 4, 4], [1, 1, 2, 4], [1, 1, 2], [1, 1, 3, 3, 3, 4, 4, 4], [1, 1, 3, 3, 3, 4, 4], [1, 1, 3, 3, 3, 4], [1, 1, 3, 3, 3], [1, 1, 3, 3, 4, 4, 4], [1, 1, 3, 3, 4, 4], [1, 1, 3, 3, 4], [1, 1, 3, 3], [1, 1, 3, 4, 4, 4], [1, 1, 3, 4, 4], [1, 1, 3, 4], [1, 1, 3], [1, 1, 4, 4, 4], [1, 1, 4, 4], [1, 1, 4], [1, 1], [1, 2, 2, 2, 3, 3, 3, 4, 4, 4], [1, 2, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 2, 3, 3, 3, 4], [1, 2, 2, 2, 3, 3, 3], [1, 2, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 2, 3, 3, 4, 4], [1, 2, 2, 2, 3, 3, 4], [1, 2, 2, 2, 3, 3], [1, 2, 2, 2, 3, 4, 4, 4], [1, 2, 2, 2, 3, 4, 4], [1, 2, 2, 2, 3, 4], [1, 2, 2, 2, 3], [1, 2, 2, 2, 4, 4, 4], [1, 2, 2, 2, 4, 4], [1, 2, 2, 2, 4], [1, 2, 2, 2], [1, 2, 2, 3, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 3, 4, 4], [1, 2, 2, 3, 3, 3, 4], [1, 2, 2, 3, 3, 3], [1, 2, 2, 3, 3, 4, 4, 4], [1, 2, 2, 3, 3, 4, 4], [1, 2, 2, 3, 3, 4], [1, 2, 2, 3, 3], [1, 2, 2, 3, 4, 4, 4], [1, 2, 2, 3, 4, 4], [1, 2, 2, 3, 4], [1, 2, 2, 3], [1, 2, 2, 4, 4, 4], [1, 2, 2, 4, 4], [1, 2, 2, 4], [1, 2, 2], [1, 2, 3, 3, 3, 4, 4, 4], [1, 2, 3, 3, 3, 4, 4], [1, 2, 3, 3, 3, 4], [1, 2, 3, 3, 3], [1, 2, 3, 3, 4, 4, 4], [1, 2, 3, 3, 4, 4], [1, 2, 3, 3, 4], [1, 2, 3, 3], [1, 2, 3, 4, 4, 4], [1, 2, 3, 4, 4], [1, 2, 3, 4], [1, 2, 3], [1, 2, 4, 4, 4], [1, 2, 4, 4], [1, 2, 4], [1, 2], [1, 3, 3, 3, 4, 4, 4], [1, 3, 3, 3, 4, 4], [1, 3, 3, 3, 4], [1, 3, 3, 3], [1, 3, 3, 4, 4, 4], [1, 3, 3, 4, 4], [1, 3, 3, 4], [1, 3, 3], [1, 3, 4, 4, 4], [1, 3, 4, 4], [1, 3, 4], [1, 3], [1, 4, 4, 4], [1, 4, 4], [1, 4], [2, 2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 2, 3, 3, 3, 4, 4], [2, 2, 2, 3, 3, 3, 4], [2, 2, 2, 3, 3, 3], [2, 2, 2, 3, 3, 4, 4, 4], [2, 2, 2, 3, 3, 4, 4], [2, 2, 2, 3, 3, 4], [2, 2, 2, 3, 3], [2, 2, 2, 3, 4, 4, 4], [2, 2, 2, 3, 4, 4], [2, 2, 2, 3, 4], [2, 2, 2, 3], [2, 2, 2, 4, 4, 4], [2, 2, 2, 4, 4], [2, 2, 2, 4], [2, 2, 2], [2, 2, 3, 3, 3, 4, 4, 4], [2, 2, 3, 3, 3, 4, 4], [2, 2, 3, 3, 3, 4], [2, 2, 3, 3, 3], [2, 2, 3, 3, 4, 4, 4], [2, 2, 3, 3, 4, 4], [2, 2, 3, 3, 4], [2, 2, 3, 3], [2, 2, 3, 4, 4, 4], [2, 2, 3, 4, 4], [2, 2, 3, 4], [2, 2, 3], [2, 2, 4, 4, 4], [2, 2, 4, 4], [2, 2, 4], [2, 2], [2, 3, 3, 3, 4, 4, 4], [2, 3, 3, 3, 4, 4], [2, 3, 3, 3, 4], [2, 3, 3, 3], [2, 3, 3, 4, 4, 4], [2, 3, 3, 4, 4], [2, 3, 3, 4], [2, 3, 3], [2, 3, 4, 4, 4], [2, 3, 4, 4], [2, 3, 4], [2, 3], [2, 4, 4, 4], [2, 4, 4], [2, 4], [3, 3, 3, 4, 4, 4], [3, 3, 3, 4, 4], [3, 3, 3, 4], [3, 3, 3], [3, 3, 4, 4, 4], [3, 3, 4, 4], [3, 3, 4], [3, 3], [3, 4, 4, 4], [3, 4, 4], [3, 4], [4, 4, 4], [4, 4]]\n assert candidate(nums = [100, -100, 100, -100, 100]) == [[100, 100, 100], [-100, 100, 100], [-100, -100, 100], [-100, -100], [100, 100], [-100, 100]]\n assert candidate(nums = [-10, -5, -3, -1, 0, 1, 3, 5, 7, 9]) == [[-10, -5, -3, -1, 0, 1, 3, 5, 7, 9], [-10, -5, -3, -1, 0, 1, 3, 5, 7], [-10, -5, -3, -1, 0, 1, 3, 5, 9], [-10, -5, -3, -1, 0, 1, 3, 5], [-10, -5, -3, -1, 0, 1, 3, 7, 9], [-10, -5, -3, -1, 0, 1, 3, 7], [-10, -5, -3, -1, 0, 1, 3, 9], [-10, -5, -3, -1, 0, 1, 3], [-10, -5, -3, -1, 0, 1, 5, 7, 9], [-10, -5, -3, -1, 0, 1, 5, 7], [-10, -5, -3, -1, 0, 1, 5, 9], [-10, -5, -3, -1, 0, 1, 5], [-10, -5, -3, -1, 0, 1, 7, 9], [-10, -5, -3, -1, 0, 1, 7], [-10, -5, -3, -1, 0, 1, 9], [-10, -5, -3, -1, 0, 1], [-10, -5, -3, -1, 0, 3, 5, 7, 9], [-10, -5, -3, -1, 0, 3, 5, 7], [-10, -5, -3, -1, 0, 3, 5, 9], [-10, -5, -3, -1, 0, 3, 5], [-10, -5, -3, -1, 0, 3, 7, 9], [-10, -5, -3, -1, 0, 3, 7], [-10, -5, -3, -1, 0, 3, 9], [-10, -5, -3, -1, 0, 3], [-10, -5, -3, -1, 0, 5, 7, 9], [-10, -5, -3, -1, 0, 5, 7], [-10, -5, -3, -1, 0, 5, 9], [-10, -5, -3, -1, 0, 5], [-10, -5, -3, -1, 0, 7, 9], [-10, -5, -3, -1, 0, 7], [-10, -5, -3, -1, 0, 9], [-10, -5, -3, -1, 0], [-10, -5, -3, -1, 1, 3, 5, 7, 9], [-10, -5, -3, -1, 1, 3, 5, 7], [-10, -5, -3, -1, 1, 3, 5, 9], [-10, -5, -3, -1, 1, 3, 5], [-10, -5, -3, -1, 1, 3, 7, 9], [-10, -5, -3, -1, 1, 3, 7], [-10, -5, -3, -1, 1, 3, 9], [-10, -5, -3, -1, 1, 3], [-10, -5, -3, -1, 1, 5, 7, 9], [-10, -5, -3, -1, 1, 5, 7], [-10, -5, -3, -1, 1, 5, 9], [-10, -5, -3, -1, 1, 5], [-10, -5, -3, -1, 1, 7, 9], [-10, -5, -3, -1, 1, 7], [-10, -5, -3, -1, 1, 9], [-10, -5, -3, -1, 1], [-10, -5, -3, -1, 3, 5, 7, 9], [-10, -5, -3, -1, 3, 5, 7], [-10, -5, -3, -1, 3, 5, 9], [-10, -5, -3, -1, 3, 5], [-10, -5, -3, -1, 3, 7, 9], [-10, -5, -3, -1, 3, 7], [-10, -5, -3, -1, 3, 9], [-10, -5, -3, -1, 3], [-10, -5, -3, -1, 5, 7, 9], [-10, -5, -3, -1, 5, 7], [-10, -5, -3, -1, 5, 9], [-10, -5, -3, -1, 5], [-10, -5, -3, -1, 7, 9], [-10, -5, -3, -1, 7], [-10, -5, -3, -1, 9], [-10, -5, -3, -1], [-10, -5, -3, 0, 1, 3, 5, 7, 9], [-10, -5, -3, 0, 1, 3, 5, 7], [-10, -5, -3, 0, 1, 3, 5, 9], [-10, -5, -3, 0, 1, 3, 5], [-10, -5, -3, 0, 1, 3, 7, 9], [-10, -5, -3, 0, 1, 3, 7], [-10, -5, -3, 0, 1, 3, 9], [-10, -5, -3, 0, 1, 3], [-10, -5, -3, 0, 1, 5, 7, 9], [-10, -5, -3, 0, 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[-5, -3, 0, 1], [-5, -3, 0, 3, 5, 7, 9], [-5, -3, 0, 3, 5, 7], [-5, -3, 0, 3, 5, 9], [-5, -3, 0, 3, 5], [-5, -3, 0, 3, 7, 9], [-5, -3, 0, 3, 7], [-5, -3, 0, 3, 9], [-5, -3, 0, 3], [-5, -3, 0, 5, 7, 9], [-5, -3, 0, 5, 7], [-5, -3, 0, 5, 9], [-5, -3, 0, 5], [-5, -3, 0, 7, 9], [-5, -3, 0, 7], [-5, -3, 0, 9], [-5, -3, 0], [-5, -3, 1, 3, 5, 7, 9], [-5, -3, 1, 3, 5, 7], [-5, -3, 1, 3, 5, 9], [-5, -3, 1, 3, 5], [-5, -3, 1, 3, 7, 9], [-5, -3, 1, 3, 7], [-5, -3, 1, 3, 9], [-5, -3, 1, 3], [-5, -3, 1, 5, 7, 9], [-5, -3, 1, 5, 7], [-5, -3, 1, 5, 9], [-5, -3, 1, 5], [-5, -3, 1, 7, 9], [-5, -3, 1, 7], [-5, -3, 1, 9], [-5, -3, 1], [-5, -3, 3, 5, 7, 9], [-5, -3, 3, 5, 7], [-5, -3, 3, 5, 9], [-5, -3, 3, 5], [-5, -3, 3, 7, 9], [-5, -3, 3, 7], [-5, -3, 3, 9], [-5, -3, 3], [-5, -3, 5, 7, 9], [-5, -3, 5, 7], [-5, -3, 5, 9], [-5, -3, 5], [-5, -3, 7, 9], [-5, -3, 7], [-5, -3, 9], [-5, -3], [-5, -1, 0, 1, 3, 5, 7, 9], [-5, -1, 0, 1, 3, 5, 7], [-5, -1, 0, 1, 3, 5, 9], [-5, -1, 0, 1, 3, 5], [-5, -1, 0, 1, 3, 7, 9], [-5, -1, 0, 1, 3, 7], [-5, -1, 0, 1, 3, 9], [-5, -1, 0, 1, 3], [-5, -1, 0, 1, 5, 7, 9], [-5, -1, 0, 1, 5, 7], [-5, -1, 0, 1, 5, 9], [-5, -1, 0, 1, 5], [-5, -1, 0, 1, 7, 9], [-5, -1, 0, 1, 7], [-5, -1, 0, 1, 9], [-5, -1, 0, 1], [-5, -1, 0, 3, 5, 7, 9], [-5, -1, 0, 3, 5, 7], [-5, -1, 0, 3, 5, 9], [-5, -1, 0, 3, 5], [-5, -1, 0, 3, 7, 9], [-5, -1, 0, 3, 7], [-5, -1, 0, 3, 9], [-5, -1, 0, 3], [-5, -1, 0, 5, 7, 9], [-5, -1, 0, 5, 7], [-5, -1, 0, 5, 9], [-5, -1, 0, 5], [-5, -1, 0, 7, 9], [-5, -1, 0, 7], [-5, -1, 0, 9], [-5, -1, 0], [-5, -1, 1, 3, 5, 7, 9], [-5, -1, 1, 3, 5, 7], [-5, -1, 1, 3, 5, 9], [-5, -1, 1, 3, 5], [-5, -1, 1, 3, 7, 9], [-5, -1, 1, 3, 7], [-5, -1, 1, 3, 9], [-5, -1, 1, 3], [-5, -1, 1, 5, 7, 9], [-5, -1, 1, 5, 7], [-5, -1, 1, 5, 9], [-5, -1, 1, 5], [-5, -1, 1, 7, 9], [-5, -1, 1, 7], [-5, -1, 1, 9], [-5, -1, 1], [-5, -1, 3, 5, 7, 9], [-5, -1, 3, 5, 7], [-5, -1, 3, 5, 9], [-5, -1, 3, 5], [-5, -1, 3, 7, 9], [-5, -1, 3, 7], [-5, -1, 3, 9], [-5, -1, 3], [-5, -1, 5, 7, 9], [-5, -1, 5, 7], [-5, -1, 5, 9], [-5, -1, 5], [-5, -1, 7, 9], [-5, -1, 7], [-5, -1, 9], [-5, -1], [-5, 0, 1, 3, 5, 7, 9], [-5, 0, 1, 3, 5, 7], [-5, 0, 1, 3, 5, 9], [-5, 0, 1, 3, 5], [-5, 0, 1, 3, 7, 9], [-5, 0, 1, 3, 7], [-5, 0, 1, 3, 9], [-5, 0, 1, 3], [-5, 0, 1, 5, 7, 9], [-5, 0, 1, 5, 7], [-5, 0, 1, 5, 9], [-5, 0, 1, 5], [-5, 0, 1, 7, 9], [-5, 0, 1, 7], [-5, 0, 1, 9], [-5, 0, 1], [-5, 0, 3, 5, 7, 9], [-5, 0, 3, 5, 7], [-5, 0, 3, 5, 9], [-5, 0, 3, 5], [-5, 0, 3, 7, 9], [-5, 0, 3, 7], [-5, 0, 3, 9], [-5, 0, 3], [-5, 0, 5, 7, 9], [-5, 0, 5, 7], [-5, 0, 5, 9], [-5, 0, 5], [-5, 0, 7, 9], [-5, 0, 7], [-5, 0, 9], [-5, 0], [-5, 1, 3, 5, 7, 9], [-5, 1, 3, 5, 7], [-5, 1, 3, 5, 9], [-5, 1, 3, 5], [-5, 1, 3, 7, 9], [-5, 1, 3, 7], [-5, 1, 3, 9], [-5, 1, 3], [-5, 1, 5, 7, 9], [-5, 1, 5, 7], [-5, 1, 5, 9], [-5, 1, 5], [-5, 1, 7, 9], [-5, 1, 7], [-5, 1, 9], [-5, 1], [-5, 3, 5, 7, 9], [-5, 3, 5, 7], [-5, 3, 5, 9], [-5, 3, 5], [-5, 3, 7, 9], [-5, 3, 7], [-5, 3, 9], [-5, 3], [-5, 5, 7, 9], [-5, 5, 7], [-5, 5, 9], [-5, 5], [-5, 7, 9], [-5, 7], [-5, 9], [-3, -1, 0, 1, 3, 5, 7, 9], [-3, -1, 0, 1, 3, 5, 7], [-3, -1, 0, 1, 3, 5, 9], [-3, -1, 0, 1, 3, 5], [-3, -1, 0, 1, 3, 7, 9], [-3, -1, 0, 1, 3, 7], [-3, -1, 0, 1, 3, 9], [-3, -1, 0, 1, 3], [-3, -1, 0, 1, 5, 7, 9], [-3, -1, 0, 1, 5, 7], [-3, -1, 0, 1, 5, 9], [-3, -1, 0, 1, 5], [-3, -1, 0, 1, 7, 9], [-3, -1, 0, 1, 7], [-3, -1, 0, 1, 9], [-3, -1, 0, 1], [-3, -1, 0, 3, 5, 7, 9], [-3, -1, 0, 3, 5, 7], [-3, -1, 0, 3, 5, 9], [-3, -1, 0, 3, 5], [-3, -1, 0, 3, 7, 9], [-3, -1, 0, 3, 7], [-3, -1, 0, 3, 9], [-3, -1, 0, 3], [-3, -1, 0, 5, 7, 9], [-3, -1, 0, 5, 7], [-3, -1, 0, 5, 9], [-3, -1, 0, 5], [-3, -1, 0, 7, 9], [-3, -1, 0, 7], [-3, -1, 0, 9], [-3, -1, 0], [-3, -1, 1, 3, 5, 7, 9], [-3, -1, 1, 3, 5, 7], [-3, -1, 1, 3, 5, 9], [-3, -1, 1, 3, 5], [-3, -1, 1, 3, 7, 9], [-3, -1, 1, 3, 7], [-3, -1, 1, 3, 9], [-3, -1, 1, 3], [-3, -1, 1, 5, 7, 9], [-3, -1, 1, 5, 7], [-3, -1, 1, 5, 9], [-3, -1, 1, 5], [-3, -1, 1, 7, 9], [-3, -1, 1, 7], [-3, -1, 1, 9], [-3, -1, 1], [-3, -1, 3, 5, 7, 9], [-3, -1, 3, 5, 7], [-3, -1, 3, 5, 9], [-3, -1, 3, 5], [-3, -1, 3, 7, 9], [-3, -1, 3, 7], [-3, -1, 3, 9], [-3, -1, 3], [-3, -1, 5, 7, 9], [-3, -1, 5, 7], [-3, -1, 5, 9], [-3, -1, 5], [-3, -1, 7, 9], [-3, -1, 7], [-3, -1, 9], [-3, -1], [-3, 0, 1, 3, 5, 7, 9], [-3, 0, 1, 3, 5, 7], [-3, 0, 1, 3, 5, 9], [-3, 0, 1, 3, 5], [-3, 0, 1, 3, 7, 9], [-3, 0, 1, 3, 7], [-3, 0, 1, 3, 9], [-3, 0, 1, 3], [-3, 0, 1, 5, 7, 9], [-3, 0, 1, 5, 7], [-3, 0, 1, 5, 9], [-3, 0, 1, 5], [-3, 0, 1, 7, 9], [-3, 0, 1, 7], [-3, 0, 1, 9], [-3, 0, 1], [-3, 0, 3, 5, 7, 9], [-3, 0, 3, 5, 7], [-3, 0, 3, 5, 9], [-3, 0, 3, 5], [-3, 0, 3, 7, 9], [-3, 0, 3, 7], [-3, 0, 3, 9], [-3, 0, 3], [-3, 0, 5, 7, 9], [-3, 0, 5, 7], [-3, 0, 5, 9], [-3, 0, 5], [-3, 0, 7, 9], [-3, 0, 7], [-3, 0, 9], [-3, 0], [-3, 1, 3, 5, 7, 9], [-3, 1, 3, 5, 7], [-3, 1, 3, 5, 9], [-3, 1, 3, 5], [-3, 1, 3, 7, 9], [-3, 1, 3, 7], [-3, 1, 3, 9], [-3, 1, 3], [-3, 1, 5, 7, 9], [-3, 1, 5, 7], [-3, 1, 5, 9], [-3, 1, 5], [-3, 1, 7, 9], [-3, 1, 7], [-3, 1, 9], [-3, 1], [-3, 3, 5, 7, 9], [-3, 3, 5, 7], [-3, 3, 5, 9], [-3, 3, 5], [-3, 3, 7, 9], [-3, 3, 7], [-3, 3, 9], [-3, 3], [-3, 5, 7, 9], [-3, 5, 7], [-3, 5, 9], [-3, 5], [-3, 7, 9], [-3, 7], [-3, 9], [-1, 0, 1, 3, 5, 7, 9], [-1, 0, 1, 3, 5, 7], [-1, 0, 1, 3, 5, 9], [-1, 0, 1, 3, 5], [-1, 0, 1, 3, 7, 9], [-1, 0, 1, 3, 7], [-1, 0, 1, 3, 9], [-1, 0, 1, 3], [-1, 0, 1, 5, 7, 9], [-1, 0, 1, 5, 7], [-1, 0, 1, 5, 9], [-1, 0, 1, 5], [-1, 0, 1, 7, 9], [-1, 0, 1, 7], [-1, 0, 1, 9], [-1, 0, 1], [-1, 0, 3, 5, 7, 9], [-1, 0, 3, 5, 7], [-1, 0, 3, 5, 9], [-1, 0, 3, 5], [-1, 0, 3, 7, 9], [-1, 0, 3, 7], [-1, 0, 3, 9], [-1, 0, 3], [-1, 0, 5, 7, 9], [-1, 0, 5, 7], [-1, 0, 5, 9], [-1, 0, 5], [-1, 0, 7, 9], [-1, 0, 7], [-1, 0, 9], [-1, 0], [-1, 1, 3, 5, 7, 9], [-1, 1, 3, 5, 7], [-1, 1, 3, 5, 9], [-1, 1, 3, 5], [-1, 1, 3, 7, 9], [-1, 1, 3, 7], [-1, 1, 3, 9], [-1, 1, 3], [-1, 1, 5, 7, 9], [-1, 1, 5, 7], [-1, 1, 5, 9], [-1, 1, 5], [-1, 1, 7, 9], [-1, 1, 7], [-1, 1, 9], [-1, 1], [-1, 3, 5, 7, 9], [-1, 3, 5, 7], [-1, 3, 5, 9], [-1, 3, 5], [-1, 3, 7, 9], [-1, 3, 7], [-1, 3, 9], [-1, 3], [-1, 5, 7, 9], [-1, 5, 7], [-1, 5, 9], [-1, 5], [-1, 7, 9], [-1, 7], [-1, 9], [0, 1, 3, 5, 7, 9], [0, 1, 3, 5, 7], [0, 1, 3, 5, 9], [0, 1, 3, 5], [0, 1, 3, 7, 9], [0, 1, 3, 7], [0, 1, 3, 9], [0, 1, 3], [0, 1, 5, 7, 9], [0, 1, 5, 7], [0, 1, 5, 9], [0, 1, 5], [0, 1, 7, 9], [0, 1, 7], [0, 1, 9], [0, 1], [0, 3, 5, 7, 9], [0, 3, 5, 7], [0, 3, 5, 9], [0, 3, 5], [0, 3, 7, 9], [0, 3, 7], [0, 3, 9], [0, 3], [0, 5, 7, 9], [0, 5, 7], [0, 5, 9], [0, 5], [0, 7, 9], [0, 7], [0, 9], [1, 3, 5, 7, 9], [1, 3, 5, 7], [1, 3, 5, 9], [1, 3, 5], [1, 3, 7, 9], [1, 3, 7], [1, 3, 9], [1, 3], [1, 5, 7, 9], [1, 5, 7], [1, 5, 9], [1, 5], [1, 7, 9], [1, 7], [1, 9], [3, 5, 7, 9], [3, 5, 7], [3, 5, 9], [3, 5], [3, 7, 9], [3, 7], [3, 9], [5, 7, 9], [5, 7], [5, 9], [7, 9]]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [-1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1]) == [[-1, 0, 1, 1, 1, 1, 1], [-1, 0, 0, 1, 1, 1, 1], [-1, 0, 0, 0, 1, 1, 1], [-1, 0, 0, 0, 0, 1, 1], [-1, 0, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 0, 0], [-1, 1, 1, 1, 1, 1], [-1, -1, 0, 1, 1, 1, 1], [-1, -1, 0, 0, 1, 1, 1], [-1, -1, 0, 0, 0, 1, 1], [-1, -1, 0, 0, 0, 0, 1], [-1, -1, 0, 0, 0, 0], [-1, -1, 1, 1, 1, 1], [-1, -1, -1, 0, 1, 1, 1], [-1, -1, -1, 0, 0, 1, 1], [-1, -1, -1, 0, 0, 0, 1], [-1, -1, -1, 0, 0, 0], [-1, -1, -1, 1, 1, 1], [-1, -1, -1, -1, 0, 1, 1], [-1, -1, -1, -1, 0, 0, 1], [-1, -1, -1, -1, 0, 0], [-1, -1, -1, -1, 1, 1], [-1, -1, -1, -1, -1, 0, 1], [-1, -1, -1, -1, -1, 0], [-1, -1, -1, -1, -1, 1], [-1, -1, -1, -1, -1], [0, 1, 1, 1, 1, 1], [0, 0, 1, 1, 1, 1], [0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0], [1, 1, 1, 1, 1], [-1, 0, 1, 1, 1, 1], [-1, 0, 0, 1, 1, 1], [-1, 0, 0, 0, 1, 1], [-1, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 0], [-1, 1, 1, 1, 1], [-1, -1, 0, 1, 1, 1], [-1, -1, 0, 0, 1, 1], [-1, -1, 0, 0, 0, 1], [-1, -1, 0, 0, 0], [-1, -1, 1, 1, 1], [-1, -1, -1, 0, 1, 1], [-1, -1, -1, 0, 0, 1], [-1, -1, -1, 0, 0], [-1, -1, -1, 1, 1], [-1, -1, -1, -1, 0, 1], [-1, -1, -1, -1, 0], [-1, -1, -1, -1, 1], [-1, -1, -1, -1], [0, 1, 1, 1, 1], [0, 0, 1, 1, 1], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1], [0, 0, 0, 0], [1, 1, 1, 1], [-1, 0, 1, 1, 1], [-1, 0, 0, 1, 1], [-1, 0, 0, 0, 1], [-1, 0, 0, 0], [-1, 1, 1, 1], [-1, -1, 0, 1, 1], [-1, -1, 0, 0, 1], [-1, -1, 0, 0], [-1, -1, 1, 1], [-1, -1, -1, 0, 1], [-1, -1, -1, 0], [-1, -1, -1, 1], [-1, -1, -1], [0, 1, 1, 1], [0, 0, 1, 1], [0, 0, 0, 1], [0, 0, 0], [1, 1, 1], [-1, 0, 1, 1], [-1, 0, 0, 1], [-1, 0, 0], [-1, 1, 1], [-1, -1, 0, 1], [-1, -1, 0], [-1, -1, 1], [-1, -1], [0, 1, 1], [0, 0, 1], [0, 0], [1, 1], [-1, 0, 1], [-1, 0], [-1, 1], [0, 1]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9], [1, 2, 3, 10], [1, 2, 3, 3, 4, 5], [1, 2, 3, 3, 4], [1, 2, 3, 3, 5], [1, 2, 3, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7], [1, 2, 4, 6, 8, 9, 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4, 8, 9, 10], [2, 4, 8, 9], [2, 4, 8, 10], [2, 4, 8], [2, 4, 9, 10], [2, 4, 9], [2, 4, 10], [2, 4, 4, 5], [2, 4, 4], [2, 5, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 10], [2, 5, 6, 7], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 10], [2, 5, 6, 8], [2, 5, 6, 9, 10], [2, 5, 6, 9], [2, 5, 6, 10], [2, 5, 6], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 10], [2, 5, 7, 8], [2, 5, 7, 9, 10], [2, 5, 7, 9], [2, 5, 7, 10], [2, 5, 7], [2, 5, 8, 9, 10], [2, 5, 8, 9], [2, 5, 8, 10], [2, 5, 8], [2, 5, 9, 10], [2, 5, 9], [2, 5, 10], [2, 5, 5], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 10], [2, 6, 7, 8], [2, 6, 7, 9, 10], [2, 6, 7, 9], [2, 6, 7, 10], [2, 6, 7], [2, 6, 8, 9, 10], [2, 6, 8, 9], [2, 6, 8, 10], [2, 6, 8], [2, 6, 9, 10], [2, 6, 9], [2, 6, 10], [2, 6], [2, 7, 8, 9, 10], [2, 7, 8, 9], [2, 7, 8, 10], [2, 7, 8], [2, 7, 9, 10], [2, 7, 9], [2, 7, 10], [2, 7], [2, 8, 9, 10], [2, 8, 9], [2, 8, 10], [2, 8], [2, 9, 10], [2, 9], [2, 10], [2, 2, 3, 4, 5], [2, 2, 3, 4], [2, 2, 3, 5], [2, 2, 3], [2, 2, 4, 5], [2, 2, 4], [2, 2, 5], [2, 2], [3, 4, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 10], [3, 4, 5, 6], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 10], [3, 4, 5, 7], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 10], [3, 4, 5, 8], [3, 4, 5, 9, 10], [3, 4, 5, 9], [3, 4, 5, 10], [3, 4, 5, 5], [3, 4, 6, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 10], [3, 4, 6, 7], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 10], [3, 4, 6, 8], [3, 4, 6, 9, 10], [3, 4, 6, 9], [3, 4, 6, 10], [3, 4, 6], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 10], [3, 4, 7, 8], [3, 4, 7, 9, 10], [3, 4, 7, 9], [3, 4, 7, 10], [3, 4, 7], [3, 4, 8, 9, 10], [3, 4, 8, 9], [3, 4, 8, 10], [3, 4, 8], [3, 4, 9, 10], [3, 4, 9], [3, 4, 10], [3, 4, 4, 5], [3, 4, 4], [3, 5, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 10], [3, 5, 6, 7], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 10], [3, 5, 6, 8], [3, 5, 6, 9, 10], [3, 5, 6, 9], [3, 5, 6, 10], [3, 5, 6], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 10], [3, 5, 7, 8], [3, 5, 7, 9, 10], [3, 5, 7, 9], [3, 5, 7, 10], [3, 5, 7], [3, 5, 8, 9, 10], [3, 5, 8, 9], [3, 5, 8, 10], [3, 5, 8], [3, 5, 9, 10], [3, 5, 9], [3, 5, 10], [3, 5, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9], [3, 6, 7, 10], [3, 6, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9], [3, 6, 8, 10], [3, 6, 8], [3, 6, 9, 10], [3, 6, 9], [3, 6, 10], [3, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9], [3, 7, 8, 10], [3, 7, 8], [3, 7, 9, 10], [3, 7, 9], [3, 7, 10], [3, 7], [3, 8, 9, 10], [3, 8, 9], [3, 8, 10], [3, 8], [3, 9, 10], [3, 9], [3, 10], [3, 3, 4, 5], [3, 3, 4], [3, 3, 5], [3, 3], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9], [4, 5, 6, 10], [4, 5, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9], [4, 5, 7, 10], [4, 5, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9], [4, 5, 8, 10], [4, 5, 8], [4, 5, 9, 10], [4, 5, 9], [4, 5, 10], [4, 5, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9], [4, 6, 7, 10], [4, 6, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9], [4, 6, 8, 10], [4, 6, 8], [4, 6, 9, 10], [4, 6, 9], [4, 6, 10], [4, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9], [4, 7, 8, 10], [4, 7, 8], [4, 7, 9, 10], [4, 7, 9], [4, 7, 10], [4, 7], [4, 8, 9, 10], [4, 8, 9], [4, 8, 10], [4, 8], [4, 9, 10], [4, 9], [4, 10], [4, 4, 5], [4, 4], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9], [5, 6, 7, 10], [5, 6, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9], [5, 6, 8, 10], [5, 6, 8], [5, 6, 9, 10], [5, 6, 9], [5, 6, 10], [5, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9], [5, 7, 8, 10], [5, 7, 8], [5, 7, 9, 10], [5, 7, 9], [5, 7, 10], [5, 7], [5, 8, 9, 10], [5, 8, 9], [5, 8, 10], [5, 8], [5, 9, 10], [5, 9], [5, 10], [5, 5], [6, 7, 8, 9, 10], [6, 7, 8, 9], [6, 7, 8, 10], [6, 7, 8], [6, 7, 9, 10], [6, 7, 9], [6, 7, 10], [6, 7], [6, 8, 9, 10], [6, 8, 9], [6, 8, 10], [6, 8], [6, 9, 10], [6, 9], [6, 10], [7, 8, 9, 10], [7, 8, 9], [7, 8, 10], [7, 8], [7, 9, 10], [7, 9], [7, 10], [8, 9, 10], [8, 9], [8, 10], [9, 10], [1, 2, 3, 4, 5], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3], [1, 2, 4, 5], [1, 2, 4], [1, 2, 5], [1, 2], [1, 3, 4, 5], [1, 3, 4], [1, 3, 5], [1, 3], [1, 4, 5], [1, 4], [1, 5], [2, 3, 4, 5], [2, 3, 4], [2, 3, 5], [2, 3], [2, 4, 5], [2, 4], [2, 5], [3, 4, 5], [3, 4], [3, 5], [4, 5]]\n assert candidate(nums = [3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3]) == [[3, 3, 3, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2, 2], [3, 3, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2, 2], [3, 3, 3, 3, 3, 3], [2, 3, 3, 3, 3, 3], [2, 2, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3], [2, 2, 2, 2, 3, 3], [2, 2, 2, 2, 2, 3], [2, 2, 2, 2, 2], [3, 3, 3, 3, 3], [2, 3, 3, 3, 3], [2, 2, 3, 3, 3], [2, 2, 2, 3, 3], [2, 2, 2, 2, 3], [2, 2, 2, 2], [3, 3, 3, 3], [2, 3, 3, 3], [2, 2, 3, 3], [2, 2, 2, 3], [2, 2, 2], [3, 3, 3], [2, 3, 3], [2, 2, 3], [2, 2], [3, 3], [2, 3]]\n assert candidate(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0]) == [[0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2, 3, 4, 5, 6], [0, 1, 2, 3, 4, 5, 7], [0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 6, 7], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4], [0, 1, 2, 3, 5, 6, 7], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 7], [0, 1, 2, 3, 5], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6], [0, 1, 2, 3, 7], [0, 1, 2, 3], [0, 1, 2, 4, 5, 6, 7], [0, 1, 2, 4, 5, 6], [0, 1, 2, 4, 5, 7], [0, 1, 2, 4, 5], [0, 1, 2, 4, 6, 7], [0, 1, 2, 4, 6], [0, 1, 2, 4, 7], [0, 1, 2, 4], [0, 1, 2, 5, 6, 7], [0, 1, 2, 5, 6], [0, 1, 2, 5, 7], [0, 1, 2, 5], [0, 1, 2, 6, 7], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 2], [0, 1, 3, 4, 5, 6, 7], [0, 1, 3, 4, 5, 6], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6], [0, 1, 3, 4, 7], [0, 1, 3, 4], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6], [0, 1, 3, 5, 7], [0, 1, 3, 5], [0, 1, 3, 6, 7], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 3], [0, 1, 4, 5, 6, 7], [0, 1, 4, 5, 6], [0, 1, 4, 5, 7], [0, 1, 4, 5], [0, 1, 4, 6, 7], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 4], [0, 1, 5, 6, 7], [0, 1, 5, 6], [0, 1, 5, 7], [0, 1, 5], [0, 1, 6, 7], [0, 1, 6], [0, 1, 7], [0, 1], [0, 0, 2, 3, 4, 5, 6, 7], [0, 0, 2, 3, 4, 5, 6], [0, 0, 2, 3, 4, 5, 7], [0, 0, 2, 3, 4, 5], [0, 0, 2, 3, 4, 6, 7], [0, 0, 2, 3, 4, 6], [0, 0, 2, 3, 4, 7], [0, 0, 2, 3, 4], [0, 0, 2, 3, 5, 6, 7], [0, 0, 2, 3, 5, 6], [0, 0, 2, 3, 5, 7], [0, 0, 2, 3, 5], [0, 0, 2, 3, 6, 7], [0, 0, 2, 3, 6], [0, 0, 2, 3, 7], [0, 0, 2, 3], [0, 0, 2, 4, 5, 6, 7], [0, 0, 2, 4, 5, 6], [0, 0, 2, 4, 5, 7], [0, 0, 2, 4, 5], [0, 0, 2, 4, 6, 7], [0, 0, 2, 4, 6], [0, 0, 2, 4, 7], [0, 0, 2, 4], [0, 0, 2, 5, 6, 7], [0, 0, 2, 5, 6], [0, 0, 2, 5, 7], [0, 0, 2, 5], [0, 0, 2, 6, 7], [0, 0, 2, 6], [0, 0, 2, 7], [0, 0, 2], [0, 0, 0, 3, 4, 5, 6, 7], [0, 0, 0, 3, 4, 5, 6], [0, 0, 0, 3, 4, 5, 7], [0, 0, 0, 3, 4, 5], [0, 0, 0, 3, 4, 6, 7], [0, 0, 0, 3, 4, 6], [0, 0, 0, 3, 4, 7], [0, 0, 0, 3, 4], [0, 0, 0, 3, 5, 6, 7], [0, 0, 0, 3, 5, 6], [0, 0, 0, 3, 5, 7], [0, 0, 0, 3, 5], [0, 0, 0, 3, 6, 7], [0, 0, 0, 3, 6], [0, 0, 0, 3, 7], [0, 0, 0, 3], [0, 0, 0, 0, 4, 5, 6, 7], [0, 0, 0, 0, 4, 5, 6], [0, 0, 0, 0, 4, 5, 7], [0, 0, 0, 0, 4, 5], [0, 0, 0, 0, 4, 6, 7], [0, 0, 0, 0, 4, 6], [0, 0, 0, 0, 4, 7], [0, 0, 0, 0, 4], [0, 0, 0, 0, 0, 5, 6, 7], [0, 0, 0, 0, 0, 5, 6], [0, 0, 0, 0, 0, 5, 7], [0, 0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 0, 6, 7], [0, 0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6], [1, 2, 3, 4, 7], [1, 2, 3, 4], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5], [1, 2, 3, 6, 7], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6], [1, 2, 4, 5, 7], [1, 2, 4, 5], [1, 2, 4, 6, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4], [1, 2, 5, 6, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5], [1, 2, 6, 7], [1, 2, 6], [1, 2, 7], [1, 2], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5], [1, 3, 4, 6, 7], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4], [1, 3, 5, 6, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5], [1, 3, 6, 7], [1, 3, 6], [1, 3, 7], [1, 3], [1, 4, 5, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5], [1, 4, 6, 7], [1, 4, 6], [1, 4, 7], [1, 4], [1, 5, 6, 7], [1, 5, 6], [1, 5, 7], [1, 5], [1, 6, 7], [1, 6], [1, 7], [0, 2, 3, 4, 5, 6, 7], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 7], [0, 2, 3, 4, 5], [0, 2, 3, 4, 6, 7], [0, 2, 3, 4, 6], [0, 2, 3, 4, 7], [0, 2, 3, 4], [0, 2, 3, 5, 6, 7], [0, 2, 3, 5, 6], [0, 2, 3, 5, 7], [0, 2, 3, 5], [0, 2, 3, 6, 7], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 3], [0, 2, 4, 5, 6, 7], [0, 2, 4, 5, 6], [0, 2, 4, 5, 7], [0, 2, 4, 5], [0, 2, 4, 6, 7], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 4], [0, 2, 5, 6, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 5], [0, 2, 6, 7], [0, 2, 6], [0, 2, 7], [0, 2], [0, 0, 3, 4, 5, 6, 7], [0, 0, 3, 4, 5, 6], [0, 0, 3, 4, 5, 7], [0, 0, 3, 4, 5], [0, 0, 3, 4, 6, 7], [0, 0, 3, 4, 6], [0, 0, 3, 4, 7], [0, 0, 3, 4], [0, 0, 3, 5, 6, 7], [0, 0, 3, 5, 6], [0, 0, 3, 5, 7], [0, 0, 3, 5], [0, 0, 3, 6, 7], [0, 0, 3, 6], [0, 0, 3, 7], [0, 0, 3], [0, 0, 0, 4, 5, 6, 7], [0, 0, 0, 4, 5, 6], [0, 0, 0, 4, 5, 7], [0, 0, 0, 4, 5], [0, 0, 0, 4, 6, 7], [0, 0, 0, 4, 6], [0, 0, 0, 4, 7], [0, 0, 0, 4], [0, 0, 0, 0, 5, 6, 7], [0, 0, 0, 0, 5, 6], [0, 0, 0, 0, 5, 7], [0, 0, 0, 0, 5], [0, 0, 0, 0, 0, 6, 7], [0, 0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0, 0], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6], [2, 3, 4, 5, 7], [2, 3, 4, 5], [2, 3, 4, 6, 7], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4], [2, 3, 5, 6, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5], [2, 3, 6, 7], [2, 3, 6], [2, 3, 7], [2, 3], [2, 4, 5, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5], [2, 4, 6, 7], [2, 4, 6], [2, 4, 7], [2, 4], [2, 5, 6, 7], [2, 5, 6], [2, 5, 7], [2, 5], [2, 6, 7], [2, 6], [2, 7], [0, 3, 4, 5, 6, 7], [0, 3, 4, 5, 6], [0, 3, 4, 5, 7], [0, 3, 4, 5], [0, 3, 4, 6, 7], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 4], [0, 3, 5, 6, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 5], [0, 3, 6, 7], [0, 3, 6], [0, 3, 7], [0, 3], [0, 0, 4, 5, 6, 7], [0, 0, 4, 5, 6], [0, 0, 4, 5, 7], [0, 0, 4, 5], [0, 0, 4, 6, 7], [0, 0, 4, 6], [0, 0, 4, 7], [0, 0, 4], [0, 0, 0, 5, 6, 7], [0, 0, 0, 5, 6], [0, 0, 0, 5, 7], [0, 0, 0, 5], [0, 0, 0, 0, 6, 7], [0, 0, 0, 0, 6], [0, 0, 0, 0, 0, 7], [0, 0, 0, 0, 0, 0], [3, 4, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5], [3, 4, 6, 7], [3, 4, 6], [3, 4, 7], [3, 4], [3, 5, 6, 7], [3, 5, 6], [3, 5, 7], [3, 5], [3, 6, 7], [3, 6], [3, 7], [0, 4, 5, 6, 7], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 5], [0, 4, 6, 7], [0, 4, 6], [0, 4, 7], [0, 4], [0, 0, 5, 6, 7], [0, 0, 5, 6], [0, 0, 5, 7], [0, 0, 5], [0, 0, 0, 6, 7], [0, 0, 0, 6], [0, 0, 0, 0, 7], [0, 0, 0, 0, 0], [4, 5, 6, 7], [4, 5, 6], [4, 5, 7], [4, 5], [4, 6, 7], [4, 6], [4, 7], [0, 5, 6, 7], [0, 5, 6], [0, 5, 7], [0, 5], [0, 0, 6, 7], [0, 0, 6], [0, 0, 0, 7], [0, 0, 0, 0], [5, 6, 7], [5, 6], [5, 7], [0, 6, 7], [0, 6], [0, 0, 7], [0, 0, 0], [6, 7], [0, 7], [0, 0]]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9, 9], [1, 2, 3, 4, 5, 6, 7, 8, 10], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2, 3, 4, 5, 6, 7, 8, 8], [1, 2, 3, 4, 5, 6, 7, 9, 10], [1, 2, 3, 4, 5, 6, 7, 9, 9], [1, 2, 3, 4, 5, 6, 7, 10], [1, 2, 3, 4, 5, 6, 7, 9], [1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 3, 4, 5, 6, 7, 7], [1, 2, 3, 4, 5, 6, 8, 9, 10], [1, 2, 3, 4, 5, 6, 8, 9, 9], [1, 2, 3, 4, 5, 6, 8, 10], [1, 2, 3, 4, 5, 6, 8, 9], [1, 2, 3, 4, 5, 6, 8, 8], [1, 2, 3, 4, 5, 6, 9, 10], [1, 2, 3, 4, 5, 6, 9, 9], [1, 2, 3, 4, 5, 6, 10], [1, 2, 3, 4, 5, 6, 9], [1, 2, 3, 4, 5, 6, 8], [1, 2, 3, 4, 5, 6, 7], [1, 2, 3, 4, 5, 6, 6], [1, 2, 3, 4, 5, 7, 8, 9, 10], [1, 2, 3, 4, 5, 7, 8, 9, 9], [1, 2, 3, 4, 5, 7, 8, 10], [1, 2, 3, 4, 5, 7, 8, 9], [1, 2, 3, 4, 5, 7, 8, 8], [1, 2, 3, 4, 5, 7, 9, 10], [1, 2, 3, 4, 5, 7, 9, 9], [1, 2, 3, 4, 5, 7, 10], [1, 2, 3, 4, 5, 7, 9], [1, 2, 3, 4, 5, 7, 8], [1, 2, 3, 4, 5, 7, 7], [1, 2, 3, 4, 5, 8, 9, 10], [1, 2, 3, 4, 5, 8, 9, 9], [1, 2, 3, 4, 5, 8, 10], [1, 2, 3, 4, 5, 8, 9], [1, 2, 3, 4, 5, 8, 8], [1, 2, 3, 4, 5, 9, 10], [1, 2, 3, 4, 5, 9, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 8], [1, 2, 3, 4, 5, 7], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 5], [1, 2, 3, 4, 6, 7, 8, 9, 10], [1, 2, 3, 4, 6, 7, 8, 9, 9], [1, 2, 3, 4, 6, 7, 8, 10], [1, 2, 3, 4, 6, 7, 8, 9], [1, 2, 3, 4, 6, 7, 8, 8], [1, 2, 3, 4, 6, 7, 9, 10], [1, 2, 3, 4, 6, 7, 9, 9], [1, 2, 3, 4, 6, 7, 10], [1, 2, 3, 4, 6, 7, 9], [1, 2, 3, 4, 6, 7, 8], [1, 2, 3, 4, 6, 7, 7], [1, 2, 3, 4, 6, 8, 9, 10], [1, 2, 3, 4, 6, 8, 9, 9], [1, 2, 3, 4, 6, 8, 10], [1, 2, 3, 4, 6, 8, 9], [1, 2, 3, 4, 6, 8, 8], [1, 2, 3, 4, 6, 9, 10], [1, 2, 3, 4, 6, 9, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 6], [1, 2, 3, 4, 7, 8, 9, 10], [1, 2, 3, 4, 7, 8, 9, 9], [1, 2, 3, 4, 7, 8, 10], [1, 2, 3, 4, 7, 8, 9], [1, 2, 3, 4, 7, 8, 8], [1, 2, 3, 4, 7, 9, 10], [1, 2, 3, 4, 7, 9, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 8], [1, 2, 3, 4, 7, 7], [1, 2, 3, 4, 8, 9, 10], [1, 2, 3, 4, 8, 9, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 8], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 9, 9], [1, 2, 3, 4, 10], [1, 2, 3, 4, 9], [1, 2, 3, 4, 8], [1, 2, 3, 4, 7], [1, 2, 3, 4, 6], [1, 2, 3, 4, 5], [1, 2, 3, 4, 4], [1, 2, 3, 5, 6, 7, 8, 9, 10], [1, 2, 3, 5, 6, 7, 8, 9, 9], [1, 2, 3, 5, 6, 7, 8, 10], [1, 2, 3, 5, 6, 7, 8, 9], [1, 2, 3, 5, 6, 7, 8, 8], [1, 2, 3, 5, 6, 7, 9, 10], [1, 2, 3, 5, 6, 7, 9, 9], [1, 2, 3, 5, 6, 7, 10], [1, 2, 3, 5, 6, 7, 9], [1, 2, 3, 5, 6, 7, 8], [1, 2, 3, 5, 6, 7, 7], [1, 2, 3, 5, 6, 8, 9, 10], [1, 2, 3, 5, 6, 8, 9, 9], [1, 2, 3, 5, 6, 8, 10], [1, 2, 3, 5, 6, 8, 9], [1, 2, 3, 5, 6, 8, 8], [1, 2, 3, 5, 6, 9, 10], [1, 2, 3, 5, 6, 9, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 8], [1, 2, 3, 5, 6, 7], [1, 2, 3, 5, 6, 6], [1, 2, 3, 5, 7, 8, 9, 10], [1, 2, 3, 5, 7, 8, 9, 9], [1, 2, 3, 5, 7, 8, 10], [1, 2, 3, 5, 7, 8, 9], [1, 2, 3, 5, 7, 8, 8], [1, 2, 3, 5, 7, 9, 10], [1, 2, 3, 5, 7, 9, 9], [1, 2, 3, 5, 7, 10], [1, 2, 3, 5, 7, 9], [1, 2, 3, 5, 7, 8], [1, 2, 3, 5, 7, 7], [1, 2, 3, 5, 8, 9, 10], [1, 2, 3, 5, 8, 9, 9], [1, 2, 3, 5, 8, 10], [1, 2, 3, 5, 8, 9], [1, 2, 3, 5, 8, 8], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9, 9], [1, 2, 3, 5, 10], [1, 2, 3, 5, 9], [1, 2, 3, 5, 8], [1, 2, 3, 5, 7], [1, 2, 3, 5, 6], [1, 2, 3, 5, 5], [1, 2, 3, 6, 7, 8, 9, 10], [1, 2, 3, 6, 7, 8, 9, 9], [1, 2, 3, 6, 7, 8, 10], [1, 2, 3, 6, 7, 8, 9], [1, 2, 3, 6, 7, 8, 8], [1, 2, 3, 6, 7, 9, 10], [1, 2, 3, 6, 7, 9, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 8], [1, 2, 3, 6, 7, 7], [1, 2, 3, 6, 8, 9, 10], [1, 2, 3, 6, 8, 9, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 8], [1, 2, 3, 6, 9, 10], [1, 2, 3, 6, 9, 9], [1, 2, 3, 6, 10], [1, 2, 3, 6, 9], [1, 2, 3, 6, 8], [1, 2, 3, 6, 7], [1, 2, 3, 6, 6], [1, 2, 3, 7, 8, 9, 10], [1, 2, 3, 7, 8, 9, 9], [1, 2, 3, 7, 8, 10], [1, 2, 3, 7, 8, 9], [1, 2, 3, 7, 8, 8], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9, 9], [1, 2, 3, 7, 10], [1, 2, 3, 7, 9], [1, 2, 3, 7, 8], [1, 2, 3, 7, 7], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9, 9], [1, 2, 3, 8, 10], [1, 2, 3, 8, 9], [1, 2, 3, 8, 8], [1, 2, 3, 9, 10], [1, 2, 3, 9, 9], [1, 2, 3, 10], [1, 2, 3, 9], [1, 2, 3, 8], [1, 2, 3, 7], [1, 2, 3, 6], [1, 2, 3, 5], [1, 2, 3, 4], [1, 2, 3, 3], [1, 2, 4, 5, 6, 7, 8, 9, 10], [1, 2, 4, 5, 6, 7, 8, 9, 9], [1, 2, 4, 5, 6, 7, 8, 10], [1, 2, 4, 5, 6, 7, 8, 9], [1, 2, 4, 5, 6, 7, 8, 8], [1, 2, 4, 5, 6, 7, 9, 10], [1, 2, 4, 5, 6, 7, 9, 9], [1, 2, 4, 5, 6, 7, 10], [1, 2, 4, 5, 6, 7, 9], [1, 2, 4, 5, 6, 7, 8], [1, 2, 4, 5, 6, 7, 7], [1, 2, 4, 5, 6, 8, 9, 10], [1, 2, 4, 5, 6, 8, 9, 9], [1, 2, 4, 5, 6, 8, 10], [1, 2, 4, 5, 6, 8, 9], [1, 2, 4, 5, 6, 8, 8], [1, 2, 4, 5, 6, 9, 10], [1, 2, 4, 5, 6, 9, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 7], [1, 2, 4, 5, 6, 6], [1, 2, 4, 5, 7, 8, 9, 10], [1, 2, 4, 5, 7, 8, 9, 9], [1, 2, 4, 5, 7, 8, 10], [1, 2, 4, 5, 7, 8, 9], [1, 2, 4, 5, 7, 8, 8], [1, 2, 4, 5, 7, 9, 10], [1, 2, 4, 5, 7, 9, 9], [1, 2, 4, 5, 7, 10], [1, 2, 4, 5, 7, 9], [1, 2, 4, 5, 7, 8], [1, 2, 4, 5, 7, 7], [1, 2, 4, 5, 8, 9, 10], [1, 2, 4, 5, 8, 9, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 8], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9, 9], [1, 2, 4, 5, 10], [1, 2, 4, 5, 9], [1, 2, 4, 5, 8], [1, 2, 4, 5, 7], [1, 2, 4, 5, 6], [1, 2, 4, 5, 5], [1, 2, 4, 6, 7, 8, 9, 10], [1, 2, 4, 6, 7, 8, 9, 9], [1, 2, 4, 6, 7, 8, 10], [1, 2, 4, 6, 7, 8, 9], [1, 2, 4, 6, 7, 8, 8], [1, 2, 4, 6, 7, 9, 10], [1, 2, 4, 6, 7, 9, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 7], [1, 2, 4, 6, 8, 9, 10], [1, 2, 4, 6, 8, 9, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 8], [1, 2, 4, 6, 9, 10], [1, 2, 4, 6, 9, 9], [1, 2, 4, 6, 10], [1, 2, 4, 6, 9], [1, 2, 4, 6, 8], [1, 2, 4, 6, 7], [1, 2, 4, 6, 6], [1, 2, 4, 7, 8, 9, 10], [1, 2, 4, 7, 8, 9, 9], 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6, 7, 9, 10], [2, 3, 6, 7, 9, 9], [2, 3, 6, 7, 10], [2, 3, 6, 7, 9], [2, 3, 6, 7, 8], [2, 3, 6, 7, 7], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 9, 9], [2, 3, 6, 8, 10], [2, 3, 6, 8, 9], [2, 3, 6, 8, 8], [2, 3, 6, 9, 10], [2, 3, 6, 9, 9], [2, 3, 6, 10], [2, 3, 6, 9], [2, 3, 6, 8], [2, 3, 6, 7], [2, 3, 6, 6], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9, 9], [2, 3, 7, 8, 10], [2, 3, 7, 8, 9], [2, 3, 7, 8, 8], [2, 3, 7, 9, 10], [2, 3, 7, 9, 9], [2, 3, 7, 10], [2, 3, 7, 9], [2, 3, 7, 8], [2, 3, 7, 7], [2, 3, 8, 9, 10], [2, 3, 8, 9, 9], [2, 3, 8, 10], [2, 3, 8, 9], [2, 3, 8, 8], [2, 3, 9, 10], [2, 3, 9, 9], [2, 3, 10], [2, 3, 9], [2, 3, 8], [2, 3, 7], [2, 3, 6], [2, 3, 5], [2, 3, 4], [2, 3, 3], [2, 4, 5, 6, 7, 8, 9, 10], [2, 4, 5, 6, 7, 8, 9, 9], [2, 4, 5, 6, 7, 8, 10], [2, 4, 5, 6, 7, 8, 9], [2, 4, 5, 6, 7, 8, 8], [2, 4, 5, 6, 7, 9, 10], [2, 4, 5, 6, 7, 9, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 7], [2, 4, 5, 6, 8, 9, 10], [2, 4, 5, 6, 8, 9, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 8], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9, 9], [2, 4, 5, 6, 10], [2, 4, 5, 6, 9], [2, 4, 5, 6, 8], [2, 4, 5, 6, 7], [2, 4, 5, 6, 6], [2, 4, 5, 7, 8, 9, 10], [2, 4, 5, 7, 8, 9, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 8], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9, 9], [2, 4, 5, 7, 10], [2, 4, 5, 7, 9], [2, 4, 5, 7, 8], [2, 4, 5, 7, 7], [2, 4, 5, 8, 9, 10], [2, 4, 5, 8, 9, 9], [2, 4, 5, 8, 10], [2, 4, 5, 8, 9], [2, 4, 5, 8, 8], [2, 4, 5, 9, 10], [2, 4, 5, 9, 9], [2, 4, 5, 10], [2, 4, 5, 9], [2, 4, 5, 8], [2, 4, 5, 7], [2, 4, 5, 6], [2, 4, 5, 5], [2, 4, 6, 7, 8, 9, 10], [2, 4, 6, 7, 8, 9, 9], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 8, 9], [2, 4, 6, 7, 8, 8], [2, 4, 6, 7, 9, 10], [2, 4, 6, 7, 9, 9], [2, 4, 6, 7, 10], [2, 4, 6, 7, 9], [2, 4, 6, 7, 8], [2, 4, 6, 7, 7], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 9, 9], [2, 4, 6, 8, 10], [2, 4, 6, 8, 9], [2, 4, 6, 8, 8], [2, 4, 6, 9, 10], [2, 4, 6, 9, 9], [2, 4, 6, 10], [2, 4, 6, 9], [2, 4, 6, 8], [2, 4, 6, 7], [2, 4, 6, 6], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 9, 9], [2, 4, 7, 8, 10], [2, 4, 7, 8, 9], [2, 4, 7, 8, 8], [2, 4, 7, 9, 10], [2, 4, 7, 9, 9], [2, 4, 7, 10], [2, 4, 7, 9], [2, 4, 7, 8], [2, 4, 7, 7], [2, 4, 8, 9, 10], [2, 4, 8, 9, 9], [2, 4, 8, 10], [2, 4, 8, 9], [2, 4, 8, 8], [2, 4, 9, 10], [2, 4, 9, 9], [2, 4, 10], [2, 4, 9], [2, 4, 8], [2, 4, 7], [2, 4, 6], [2, 4, 5], [2, 4, 4], [2, 5, 6, 7, 8, 9, 10], [2, 5, 6, 7, 8, 9, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 8], [2, 5, 6, 7, 9, 10], [2, 5, 6, 7, 9, 9], [2, 5, 6, 7, 10], [2, 5, 6, 7, 9], [2, 5, 6, 7, 8], [2, 5, 6, 7, 7], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 9, 9], [2, 5, 6, 8, 10], [2, 5, 6, 8, 9], [2, 5, 6, 8, 8], [2, 5, 6, 9, 10], [2, 5, 6, 9, 9], [2, 5, 6, 10], [2, 5, 6, 9], [2, 5, 6, 8], [2, 5, 6, 7], [2, 5, 6, 6], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9, 9], [2, 5, 7, 8, 10], [2, 5, 7, 8, 9], [2, 5, 7, 8, 8], [2, 5, 7, 9, 10], [2, 5, 7, 9, 9], [2, 5, 7, 10], [2, 5, 7, 9], [2, 5, 7, 8], [2, 5, 7, 7], [2, 5, 8, 9, 10], [2, 5, 8, 9, 9], [2, 5, 8, 10], [2, 5, 8, 9], [2, 5, 8, 8], [2, 5, 9, 10], [2, 5, 9, 9], [2, 5, 10], [2, 5, 9], [2, 5, 8], [2, 5, 7], [2, 5, 6], [2, 5, 5], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 9, 9], [2, 6, 7, 8, 10], [2, 6, 7, 8, 9], [2, 6, 7, 8, 8], [2, 6, 7, 9, 10], [2, 6, 7, 9, 9], [2, 6, 7, 10], [2, 6, 7, 9], [2, 6, 7, 8], [2, 6, 7, 7], [2, 6, 8, 9, 10], [2, 6, 8, 9, 9], [2, 6, 8, 10], [2, 6, 8, 9], [2, 6, 8, 8], [2, 6, 9, 10], [2, 6, 9, 9], [2, 6, 10], [2, 6, 9], [2, 6, 8], [2, 6, 7], [2, 6, 6], [2, 7, 8, 9, 10], [2, 7, 8, 9, 9], [2, 7, 8, 10], [2, 7, 8, 9], [2, 7, 8, 8], [2, 7, 9, 10], [2, 7, 9, 9], [2, 7, 10], [2, 7, 9], [2, 7, 8], [2, 7, 7], [2, 8, 9, 10], [2, 8, 9, 9], [2, 8, 10], [2, 8, 9], [2, 8, 8], [2, 9, 10], [2, 9, 9], [2, 10], [2, 9], [2, 8], [2, 7], [2, 6], [2, 5], [2, 4], [2, 3], [2, 2], [3, 4, 5, 6, 7, 8, 9, 10], [3, 4, 5, 6, 7, 8, 9, 9], [3, 4, 5, 6, 7, 8, 10], [3, 4, 5, 6, 7, 8, 9], [3, 4, 5, 6, 7, 8, 8], [3, 4, 5, 6, 7, 9, 10], [3, 4, 5, 6, 7, 9, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 7], [3, 4, 5, 6, 8, 9, 10], [3, 4, 5, 6, 8, 9, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 8], [3, 4, 5, 6, 9, 10], [3, 4, 5, 6, 9, 9], [3, 4, 5, 6, 10], [3, 4, 5, 6, 9], [3, 4, 5, 6, 8], [3, 4, 5, 6, 7], [3, 4, 5, 6, 6], [3, 4, 5, 7, 8, 9, 10], [3, 4, 5, 7, 8, 9, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 8], [3, 4, 5, 7, 9, 10], [3, 4, 5, 7, 9, 9], [3, 4, 5, 7, 10], [3, 4, 5, 7, 9], [3, 4, 5, 7, 8], [3, 4, 5, 7, 7], [3, 4, 5, 8, 9, 10], [3, 4, 5, 8, 9, 9], [3, 4, 5, 8, 10], [3, 4, 5, 8, 9], [3, 4, 5, 8, 8], [3, 4, 5, 9, 10], [3, 4, 5, 9, 9], [3, 4, 5, 10], [3, 4, 5, 9], [3, 4, 5, 8], [3, 4, 5, 7], [3, 4, 5, 6], [3, 4, 5, 5], [3, 4, 6, 7, 8, 9, 10], [3, 4, 6, 7, 8, 9, 9], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 8, 9], [3, 4, 6, 7, 8, 8], [3, 4, 6, 7, 9, 10], [3, 4, 6, 7, 9, 9], [3, 4, 6, 7, 10], [3, 4, 6, 7, 9], [3, 4, 6, 7, 8], [3, 4, 6, 7, 7], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 9, 9], [3, 4, 6, 8, 10], [3, 4, 6, 8, 9], [3, 4, 6, 8, 8], [3, 4, 6, 9, 10], [3, 4, 6, 9, 9], [3, 4, 6, 10], [3, 4, 6, 9], [3, 4, 6, 8], [3, 4, 6, 7], [3, 4, 6, 6], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 9, 9], [3, 4, 7, 8, 10], [3, 4, 7, 8, 9], [3, 4, 7, 8, 8], [3, 4, 7, 9, 10], [3, 4, 7, 9, 9], [3, 4, 7, 10], [3, 4, 7, 9], [3, 4, 7, 8], [3, 4, 7, 7], [3, 4, 8, 9, 10], [3, 4, 8, 9, 9], [3, 4, 8, 10], [3, 4, 8, 9], [3, 4, 8, 8], [3, 4, 9, 10], [3, 4, 9, 9], [3, 4, 10], [3, 4, 9], [3, 4, 8], [3, 4, 7], [3, 4, 6], [3, 4, 5], [3, 4, 4], [3, 5, 6, 7, 8, 9, 10], [3, 5, 6, 7, 8, 9, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 8], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9, 9], [3, 5, 6, 7, 10], [3, 5, 6, 7, 9], [3, 5, 6, 7, 8], [3, 5, 6, 7, 7], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 9, 9], [3, 5, 6, 8, 10], [3, 5, 6, 8, 9], [3, 5, 6, 8, 8], [3, 5, 6, 9, 10], [3, 5, 6, 9, 9], [3, 5, 6, 10], [3, 5, 6, 9], [3, 5, 6, 8], [3, 5, 6, 7], [3, 5, 6, 6], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9, 9], [3, 5, 7, 8, 10], [3, 5, 7, 8, 9], [3, 5, 7, 8, 8], [3, 5, 7, 9, 10], [3, 5, 7, 9, 9], [3, 5, 7, 10], [3, 5, 7, 9], [3, 5, 7, 8], [3, 5, 7, 7], [3, 5, 8, 9, 10], [3, 5, 8, 9, 9], [3, 5, 8, 10], [3, 5, 8, 9], [3, 5, 8, 8], [3, 5, 9, 10], [3, 5, 9, 9], [3, 5, 10], [3, 5, 9], [3, 5, 8], [3, 5, 7], [3, 5, 6], [3, 5, 5], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 9, 9], [3, 6, 7, 8, 10], [3, 6, 7, 8, 9], [3, 6, 7, 8, 8], [3, 6, 7, 9, 10], [3, 6, 7, 9, 9], [3, 6, 7, 10], [3, 6, 7, 9], [3, 6, 7, 8], [3, 6, 7, 7], [3, 6, 8, 9, 10], [3, 6, 8, 9, 9], [3, 6, 8, 10], [3, 6, 8, 9], [3, 6, 8, 8], [3, 6, 9, 10], [3, 6, 9, 9], [3, 6, 10], [3, 6, 9], [3, 6, 8], [3, 6, 7], [3, 6, 6], [3, 7, 8, 9, 10], [3, 7, 8, 9, 9], [3, 7, 8, 10], [3, 7, 8, 9], [3, 7, 8, 8], [3, 7, 9, 10], [3, 7, 9, 9], [3, 7, 10], [3, 7, 9], [3, 7, 8], [3, 7, 7], [3, 8, 9, 10], [3, 8, 9, 9], [3, 8, 10], [3, 8, 9], [3, 8, 8], [3, 9, 10], [3, 9, 9], [3, 10], [3, 9], [3, 8], [3, 7], [3, 6], [3, 5], [3, 4], [3, 3], [4, 5, 6, 7, 8, 9, 10], [4, 5, 6, 7, 8, 9, 9], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 8, 9], [4, 5, 6, 7, 8, 8], [4, 5, 6, 7, 9, 10], [4, 5, 6, 7, 9, 9], [4, 5, 6, 7, 10], [4, 5, 6, 7, 9], [4, 5, 6, 7, 8], [4, 5, 6, 7, 7], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 9, 9], [4, 5, 6, 8, 10], [4, 5, 6, 8, 9], [4, 5, 6, 8, 8], [4, 5, 6, 9, 10], [4, 5, 6, 9, 9], [4, 5, 6, 10], [4, 5, 6, 9], [4, 5, 6, 8], [4, 5, 6, 7], [4, 5, 6, 6], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 9, 9], [4, 5, 7, 8, 10], [4, 5, 7, 8, 9], [4, 5, 7, 8, 8], [4, 5, 7, 9, 10], [4, 5, 7, 9, 9], [4, 5, 7, 10], [4, 5, 7, 9], [4, 5, 7, 8], [4, 5, 7, 7], [4, 5, 8, 9, 10], [4, 5, 8, 9, 9], [4, 5, 8, 10], [4, 5, 8, 9], [4, 5, 8, 8], [4, 5, 9, 10], [4, 5, 9, 9], [4, 5, 10], [4, 5, 9], [4, 5, 8], [4, 5, 7], [4, 5, 6], [4, 5, 5], [4, 6, 7, 8, 9, 10], [4, 6, 7, 8, 9, 9], [4, 6, 7, 8, 10], [4, 6, 7, 8, 9], [4, 6, 7, 8, 8], [4, 6, 7, 9, 10], [4, 6, 7, 9, 9], [4, 6, 7, 10], [4, 6, 7, 9], [4, 6, 7, 8], [4, 6, 7, 7], [4, 6, 8, 9, 10], [4, 6, 8, 9, 9], [4, 6, 8, 10], [4, 6, 8, 9], [4, 6, 8, 8], [4, 6, 9, 10], [4, 6, 9, 9], [4, 6, 10], [4, 6, 9], [4, 6, 8], [4, 6, 7], [4, 6, 6], [4, 7, 8, 9, 10], [4, 7, 8, 9, 9], [4, 7, 8, 10], [4, 7, 8, 9], [4, 7, 8, 8], [4, 7, 9, 10], [4, 7, 9, 9], [4, 7, 10], [4, 7, 9], [4, 7, 8], [4, 7, 7], [4, 8, 9, 10], [4, 8, 9, 9], [4, 8, 10], [4, 8, 9], [4, 8, 8], [4, 9, 10], [4, 9, 9], [4, 10], [4, 9], [4, 8], [4, 7], [4, 6], [4, 5], [4, 4], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 9, 9], [5, 6, 7, 8, 10], [5, 6, 7, 8, 9], [5, 6, 7, 8, 8], [5, 6, 7, 9, 10], [5, 6, 7, 9, 9], [5, 6, 7, 10], [5, 6, 7, 9], [5, 6, 7, 8], [5, 6, 7, 7], [5, 6, 8, 9, 10], [5, 6, 8, 9, 9], [5, 6, 8, 10], [5, 6, 8, 9], [5, 6, 8, 8], [5, 6, 9, 10], [5, 6, 9, 9], [5, 6, 10], [5, 6, 9], [5, 6, 8], [5, 6, 7], [5, 6, 6], [5, 7, 8, 9, 10], [5, 7, 8, 9, 9], [5, 7, 8, 10], [5, 7, 8, 9], [5, 7, 8, 8], [5, 7, 9, 10], [5, 7, 9, 9], [5, 7, 10], [5, 7, 9], [5, 7, 8], [5, 7, 7], [5, 8, 9, 10], [5, 8, 9, 9], [5, 8, 10], [5, 8, 9], [5, 8, 8], [5, 9, 10], [5, 9, 9], [5, 10], [5, 9], [5, 8], [5, 7], [5, 6], [5, 5], [6, 7, 8, 9, 10], [6, 7, 8, 9, 9], [6, 7, 8, 10], [6, 7, 8, 9], [6, 7, 8, 8], [6, 7, 9, 10], [6, 7, 9, 9], [6, 7, 10], [6, 7, 9], [6, 7, 8], [6, 7, 7], [6, 8, 9, 10], [6, 8, 9, 9], [6, 8, 10], [6, 8, 9], [6, 8, 8], [6, 9, 10], [6, 9, 9], [6, 10], [6, 9], [6, 8], [6, 7], [6, 6], [7, 8, 9, 10], [7, 8, 9, 9], [7, 8, 10], [7, 8, 9], [7, 8, 8], [7, 9, 10], [7, 9, 9], [7, 10], [7, 9], [7, 8], [7, 7], [8, 9, 10], [8, 9, 9], [8, 10], [8, 9], [8, 8], [9, 10], [9, 9]]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [[5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5, 5], [5, 5, 5, 5, 5], [5, 5, 5, 5], [5, 5, 5], [5, 5]]\n assert candidate(nums = [3, 3, 3, 2, 2, 2, 1, 1, 1, 0, 0, 0, -1, -1, -1]) == [[3, 3, 3], [3, 3], [2, 2, 2], [2, 2], [1, 1, 1], [1, 1], [0, 0, 0], [0, 0], [-1, -1, -1], [-1, -1]]\n assert candidate(nums = [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7]) == [[7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7, 7], [7, 7, 7, 7, 7], [7, 7, 7, 7], [7, 7, 7], [7, 7]]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findSubsequences", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findSubsequences = function(nums) {", "container": null, "callable": "findSubsequences", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 492, "task_id": "construct-the-rectangle", "difficulty": "Easy", "problem_description": "A web developer needs to know how to design a web page's size. So, given a specific rectangular web page’s area, your job by now is to design a rectangular web page, whose length L and width W satisfy the following requirements:\n\nThe area of the rectangular web page you designed must equal to the given target area.\nThe width W should not be larger than the length L, which means L >= W.\nThe difference between length L and width W should be as small as possible.\n\nReturn an array [L, W] where L and W are the length and width of the web page you designed in sequence.\n \nExample 1:\n\nInput: area = 4\nOutput: [2,2]\nExplanation: The target area is 4, and all the possible ways to construct it are [1,4], [2,2], [4,1]. \nBut according to requirement 2, [1,4] is illegal; according to requirement 3, [4,1] is not optimal compared to [2,2]. So the length L is 2, and the width W is 2.\n\nExample 2:\n\nInput: area = 37\nOutput: [37,1]\n\nExample 3:\n\nInput: area = 122122\nOutput: [427,286]\n\n \nConstraints:\n\n1 <= area <= 107\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(area = 81) == [9, 9]\n assert candidate(area = 122122) == [427, 286]\n assert candidate(area = 37) == [37, 1]\n assert candidate(area = 10000000) == [3200, 3125]\n assert candidate(area = 1) == [1, 1]\n assert candidate(area = 4) == [2, 2]\n assert candidate(area = 50) == [10, 5]\n assert candidate(area = 10000) == [100, 100]\n assert candidate(area = 999999) == [1001, 999]\n assert candidate(area = 60) == [10, 6]\n assert candidate(area = 987654321) == [379721, 2601]\n assert candidate(area = 314159) == [314159, 1]\n assert candidate(area = 9876543) == [14503, 681]\n assert candidate(area = 7920) == [90, 88]\n assert candidate(area = 131072) == [512, 256]\n assert candidate(area = 87654321) == [14631, 5991]\n assert candidate(area = 841) == [29, 29]\n assert candidate(area = 98765) == [19753, 5]\n assert candidate(area = 625) == [25, 25]\n assert candidate(area = 123456789) == [11409, 10821]\n assert candidate(area = 1024) == [32, 32]\n assert candidate(area = 8281) == [91, 91]\n assert candidate(area = 86400) == [300, 288]\n assert candidate(area = 12345678) == [14593, 846]\n assert candidate(area = 1000000000) == [32000, 31250]\n assert candidate(area = 12345) == [823, 15]\n assert candidate(area = 50000000) == [8000, 6250]\n assert candidate(area = 1000000) == [1000, 1000]\n assert candidate(area = 100000000) == [10000, 10000]\n assert candidate(area = 20000000) == [5000, 4000]\n assert candidate(area = 8192) == [128, 64]\n assert candidate(area = 432432) == [693, 624]\n assert candidate(area = 121) == [11, 11]\n assert candidate(area = 333333) == [693, 481]\n assert candidate(area = 1048576) == [1024, 1024]\n assert candidate(area = 54321) == [953, 57]\n assert candidate(area = 250000) == [500, 500]\n assert candidate(area = 9801) == [99, 99]\n assert candidate(area = 135895476) == [11324623, 12]\n assert candidate(area = 2345678) == [50993, 46]\n assert candidate(area = 1111111) == [4649, 239]\n assert candidate(area = 9999999) == [4649, 2151]\n assert candidate(area = 987654) == [1697, 582]\n assert candidate(area = 84100) == [290, 290]\n assert candidate(area = 9999997) == [1428571, 7]\n assert candidate(area = 500500) == [715, 700]\n assert candidate(area = 9999991) == [9999991, 1]\n assert candidate(area = 102400) == [320, 320]\n assert candidate(area = 49) == [7, 7]\n assert candidate(area = 7654321) == [402859, 19]\n assert candidate(area = 1413721) == [1189, 1189]\n assert candidate(area = 216000000) == [15000, 14400]\n assert candidate(area = 5000000) == [2500, 2000]\n assert candidate(area = 123456) == [643, 192]\n assert candidate(area = 9765625) == [3125, 3125]\n assert candidate(area = 100) == [10, 10]\n assert candidate(area = 555555) == [777, 715]\n assert candidate(area = 169) == [13, 13]\n assert candidate(area = 100000001) == [5882353, 17]\n assert candidate(area = 720) == [30, 24]\n assert candidate(area = 2000000) == [1600, 1250]\n assert candidate(area = 67600) == [260, 260]\n assert candidate(area = 676) == [26, 26]\n assert candidate(area = 1234567) == [9721, 127]\n assert candidate(area = 3199128) == [7841, 408]\n assert candidate(area = 111111) == [407, 273]\n assert candidate(area = 1524157875) == [44019, 34625]\n assert candidate(area = 134217728) == [16384, 8192]\n assert candidate(area = 2048) == [64, 32]\n assert candidate(area = 65536) == [256, 256]\n assert candidate(area = 789456123) == [41487, 19029]\n assert candidate(area = 567890123) == [28151, 20173]\n assert candidate(area = 73456) == [4591, 16]\n assert candidate(area = 1000001) == [9901, 101]\n"}, "metadata": {"canonical_parameter_names": ["area"], "leetcode_dataset_entry_point": "Solution().constructRectangle", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var constructRectangle = function(area) {", "container": null, "callable": "constructRectangle", "parameters": [{"name": "area", "type": "number"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 493, "task_id": "reverse-pairs", "difficulty": "Hard", "problem_description": "Given an integer array nums, return the number of reverse pairs in the array.\nA reverse pair is a pair (i, j) where:\n\n0 <= i < j < nums.length and\nnums[i] > 2 * nums[j].\n\n \nExample 1:\n\nInput: nums = [1,3,2,3,1]\nOutput: 2\nExplanation: The reverse pairs are:\n(1, 4) --> nums[1] = 3, nums[4] = 1, 3 > 2 * 1\n(3, 4) --> nums[3] = 3, nums[4] = 1, 3 > 2 * 1\n\nExample 2:\n\nInput: nums = [2,4,3,5,1]\nOutput: 3\nExplanation: The reverse pairs are:\n(1, 4) --> nums[1] = 4, nums[4] = 1, 4 > 2 * 1\n(2, 4) --> nums[2] = 3, nums[4] = 1, 3 > 2 * 1\n(3, 4) --> nums[3] = 5, nums[4] = 1, 5 > 2 * 1\n\n \nConstraints:\n\n1 <= nums.length <= 5 * 104\n-231 <= nums[i] <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [8, 6, 4, 2, 1, 3, 5, 7, 9]) == 6\n assert candidate(nums = [2147483647, -2147483648, 0, 1, -1]) == 6\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 20\n assert candidate(nums = [1, 5, 3, 4, 2]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 0\n assert candidate(nums = [1, 3, 2, 3, 1]) == 2\n assert candidate(nums = [1, 2, 3, 0, -1, -2, -3]) == 18\n assert candidate(nums = [1]) == 0\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 90\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 0\n assert candidate(nums = [-1, -2, -3, -4, -5]) == 10\n assert candidate(nums = [10, 20, 30, 40, 50]) == 0\n assert candidate(nums = [-1, -2, -3, -4, -5]) == 10\n assert candidate(nums = [-5, -4, -3, -2, -1]) == 4\n assert candidate(nums = [0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5]) == 0\n assert candidate(nums = [2147483647, -2147483648, 2147483647, -2147483648]) == 4\n assert candidate(nums = [5, 2, 6, 1]) == 3\n assert candidate(nums = [0]) == 0\n assert candidate(nums = [1000000000, -1000000000, 2000000000, -2000000000]) == 4\n assert candidate(nums = [5, 4, 3, 2, 1]) == 4\n assert candidate(nums = [2, 4, 3, 5, 1]) == 3\n assert candidate(nums = [-5, -4, -3, -2, -1]) == 4\n assert candidate(nums = [1, 5, 3, 7, 9, 2, 4, 6, 8]) == 4\n assert candidate(nums = [2, 2, 2, 2, 2]) == 0\n assert candidate(nums = [50, 40, 30, 20, 10]) == 4\n assert candidate(nums = [5, -5, 15, -15, 25, -25, 35, -35]) == 16\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]) == 0\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 500000000, 500000000, 500000000, 500000000, 500000000]) == 0\n assert candidate(nums = [0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5]) == 25\n assert candidate(nums = [-1000000000, -1000000001, -1000000002, -1000000003, -1000000004, -1000000005]) == 15\n assert candidate(nums = [1, 4, 2, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19]) == 0\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 90\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 11, 13, 15, 12, 14, 16, 18, 17, 19, 20]) == 4\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 0]) == 13\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 0\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 49\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5]) == 0\n assert candidate(nums = [5, 2, 6, 1, 4, 3, 8, 7]) == 3\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 49\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == 0\n assert candidate(nums = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9, 7, 9, 3, 2, 3, 8, 4, 6]) == 25\n assert candidate(nums = [1000000000, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]) == 19\n assert candidate(nums = [2147483647, -2147483648, 2147483646, -2147483647, 2147483645]) == 4\n assert candidate(nums = [10, 20, 30, 40, 50, 1, 2, 3, 4, 5]) == 24\n assert candidate(nums = [1, 5, 4, 3, 2, 1, 5, 4, 3, 2, 1]) == 12\n assert candidate(nums = [5, 3, 10, 20, 1, 8, 15, 6, 11]) == 7\n assert candidate(nums = [-5, -3, -1, 1, 3, 5, -4, -2, 0, 2, 4, 6, -3, -1, 1, 3, 5, 7]) == 40\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 5, 15, 25, 35, 45]) == 6\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == 4\n assert candidate(nums = [2147483647, -2147483648, 1073741823, -1073741824, 536870911, -536870912]) == 9\n assert candidate(nums = [5, 5, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 2, 2, 1]) == 22\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -2, -3, -4, -5]) == 60\n assert candidate(nums = [-2147483648, 2147483647, -2147483648, 2147483647, -2147483648, 2147483647, -2147483648, 2147483647, -2147483648, 2147483647]) == 20\n assert candidate(nums = [-2147483648, -2147483647, -2147483646, -2147483645, -2147483644, -2147483643, -2147483642, -2147483641]) == 28\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19]) == 190\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]) == 0\n assert candidate(nums = [1, 9, 2, 8, 3, 7, 4, 6, 5, 0]) == 13\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125]) == 36\n assert candidate(nums = [3, 1, 2, 2, 2, 3, 1, 2, 3, 1]) == 6\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == 185\n assert candidate(nums = [1, 4, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 0\n assert candidate(nums = [-1000000000, -500000000, -250000000, -125000000, -62500000, -31250000, -15625000, -7812500, -3906250, -1953125]) == 0\n assert candidate(nums = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38]) == 0\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125]) == 36\n assert candidate(nums = [2147483647, 2147483646, 2147483645, 2147483644, 2147483643, 2147483642, 2147483641, 2147483640]) == 0\n assert candidate(nums = [-1, 1, -1, 1, -1, 1]) == 6\n assert candidate(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 20, 19, 18, 17, 16, 15, 14, 13, 12]) == 5\n assert candidate(nums = [1, 5, 2, 6, 3, 7, 4, 8, 5, 9]) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]) == 0\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 49\n assert candidate(nums = [1, 5, 3, 4, 2, 8, 6, 7]) == 1\n assert candidate(nums = [1, 10, 2, 9, 3, 8, 4, 7, 5, 6, 11, 20, 12, 19, 13, 18, 14, 17, 15, 16]) == 5\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 20\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10]) == 100\n assert candidate(nums = [9, 4, 2, 10, 7, 3, 8, 1, 5, 6]) == 11\n assert candidate(nums = [0, -1, -2, -3, -4, 0, 1, 2, 3, 4]) == 10\n assert candidate(nums = [38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0]) == 100\n assert candidate(nums = [512, 256, 128, 64, 32, 16, 8, 4, 2, 1]) == 36\n assert candidate(nums = [1, 2, 3, 4, 5, 10, 20, 30, 40, 50, 100, 200, 300, 400, 500]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 0\n assert candidate(nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 0\n assert candidate(nums = [4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647]) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(nums = [3, 1, 2, 4, 5, 10, 9, 8, 7, 6]) == 1\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == 0\n assert candidate(nums = [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0]) == 55\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(nums = [999999999, 999999998, 999999997, 999999996, 999999995, 999999994, 999999993, 999999992, 999999991, 999999990]) == 0\n assert candidate(nums = [3, 3, 3, 2, 2, 1, 1, 5, 5, 4, 4]) == 6\n assert candidate(nums = [1000000000, 1000000001, 1000000002, 1000000003, 1000000004, 1000000005]) == 0\n assert candidate(nums = [-1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8, 8, -9, 9, -10, 10]) == 90\n assert candidate(nums = [30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16]) == 0\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == 49\n assert candidate(nums = [-1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1]) == 40\n assert candidate(nums = [100, 200, 300, 400, 500, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 50\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 0\n assert candidate(nums = [5, 2, 6, 1, 8, 7, 3, 4, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 25\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20]) == 20\n assert candidate(nums = [1000000000, 500000000, 250000000, 125000000, 62500000, 31250000, 15625000, 7812500, 3906250, 1953125, 976562, 488281, 244140, 122070, 61035, 30517, 15258, 7629, 3814, 1907]) == 176\n assert candidate(nums = [9, 18, 27, 36, 45, 4, 8, 12, 16, 20]) == 15\n assert candidate(nums = [2, 4, 6, 8, 10, 1, 3, 5, 7, 9]) == 6\n assert candidate(nums = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 0\n assert candidate(nums = [-2147483648, 2147483647, -2147483647, 2147483646, -2147483646, 2147483645, -2147483645, 2147483644, -2147483644, 2147483643]) == 20\n assert candidate(nums = [1, -1, 2, -2, 3, -3, 4, -4, 5, -5]) == 25\n assert candidate(nums = [5, 2, 6, 1, 9, 4, 3, 7]) == 5\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95]) == 25\n assert candidate(nums = [1, 3, 2, 3, 1, 4, 5, 6, 7, 8]) == 2\n assert candidate(nums = [1, 3, 2, 3, 1, 4, 2, 3, 1, 4, 2, 3, 1, 4, 2]) == 12\n assert candidate(nums = [5, 2, 6, 1, 3, 4]) == 3\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == 25\n assert candidate(nums = [2147483647, 1073741823, 536870911, 268435455, 134217727, 67108863, 33554431, 16777215, 8388607, 4194303, 2097151, 1048575, 524287, 262143, 131071, 65535, 32767, 16383, 8191, 4095]) == 190\n assert candidate(nums = [1, 3, 2, 3, 1, 4, 2, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15]) == 2\n assert candidate(nums = [1, 2, 3, 2, 1, 4, 5, 4, 3, 2, 1]) == 7\n assert candidate(nums = [45, 40, 35, 30, 25, 20, 15, 10, 5, 0]) == 25\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().reversePairs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var reversePairs = function(nums) {", "container": null, "callable": "reversePairs", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 494, "task_id": "target-sum", "difficulty": "Medium", "problem_description": "You are given an integer array nums and an integer target.\nYou want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.\n\nFor example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression \"+2-1\".\n\nReturn the number of different expressions that you can build, which evaluates to target.\n \nExample 1:\n\nInput: nums = [1,1,1,1,1], target = 3\nOutput: 5\nExplanation: There are 5 ways to assign symbols to make the sum of nums be target 3.\n-1 + 1 + 1 + 1 + 1 = 3\n+1 - 1 + 1 + 1 + 1 = 3\n+1 + 1 - 1 + 1 + 1 = 3\n+1 + 1 + 1 - 1 + 1 = 3\n+1 + 1 + 1 + 1 - 1 = 3\n\nExample 2:\n\nInput: nums = [1], target = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= nums.length <= 20\n0 <= nums[i] <= 1000\n0 <= sum(nums[i]) <= 1000\n-1000 <= target <= 1000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [10, 20, 30],target = 60) == 1\n assert candidate(nums = [1, 2, 3, 4, 5],target = 3) == 3\n assert candidate(nums = [0, 0, 0, 0, 0],target = 0) == 32\n assert candidate(nums = [1000],target = 1000) == 1\n assert candidate(nums = [1],target = 1) == 1\n assert candidate(nums = [1, 2, 3, 4, 5],target = 10) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],target = 0) == 1024\n assert candidate(nums = [10, 20, 30, 40, 50],target = 100) == 0\n assert candidate(nums = [1, 2, 3, 4, 5],target = 3) == 3\n assert candidate(nums = [5, 5, 5, 5, 5],target = 15) == 5\n assert candidate(nums = [10, 20, 30, 40, 50],target = 15) == 0\n assert candidate(nums = [1, 1, 1, 1, 1],target = 3) == 5\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 5) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],target = 1000) == 10\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = -250) == 20\n assert candidate(nums = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50],target = 250) == 0\n assert candidate(nums = [100, 200, 300, 400, 500],target = 500) == 3\n assert candidate(nums = [20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400],target = 2000) == 2865\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 300) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 3000) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],target = 1) == 524288\n assert candidate(nums = [33, 49, 84, 43, 22, 14, 15, 57, 31, 30, 83, 84, 29, 3, 23, 76, 69, 38, 83, 12],target = 21) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 2) == 167960\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 0) == 184756\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 1) == 0\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19],target = 20) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 100) == 2865\n assert candidate(nums = [100, 50, 25, 12, 6, 3, 1],target = 100) == 0\n assert candidate(nums = [1, 1, 2, 3, 5],target = 3) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 1000) == 2865\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 5) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 0) == 0\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],target = 0) == 76\n assert candidate(nums = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105],target = 525) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 1500) == 31\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = -5) == 39\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 10) == 15504\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 250) == 20\n assert candidate(nums = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500],target = 1000) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 10) == 15504\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 250) == 20\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],target = 100) == 5126\n assert candidate(nums = [500, 500, 500, 500, 500],target = 1000) == 0\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 550) == 1969\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],target = 0) == 29504\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 0) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 10) == 15029\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],target = 5) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 1) == 40\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70],target = 100) == 6\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = -500) == 10206\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 500) == 10206\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],target = 20) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 5000) == 0\n assert candidate(nums = [999, 1000, 999, 1000, 999, 1000],target = 0) == 0\n assert candidate(nums = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],target = 2) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 1000) == 2865\n assert candidate(nums = [9, 7, 5, 3, 1],target = 3) == 1\n assert candidate(nums = [25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25],target = 250) == 15504\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10],target = 50) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 30) == 0\n assert candidate(nums = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100],target = 500) == 2865\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 20) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 2500) == 20\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5],target = 15) == 1062\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],target = 5) == 0\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],target = 45) == 0\n assert candidate(nums = [2, 10, 3, 5, 6, 9, 8],target = 20) == 0\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 15) == 0\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],target = 15) == 0\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],target = 1500) == 31\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],target = 0) == 184756\n assert candidate(nums = [100, 200, 300, 400, 500],target = 1500) == 1\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],target = 0) == 252\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 50) == 10206\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 25) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],target = 5) == 39\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 20) == 14326\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],target = 550) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],target = 0) == 15272\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],target = 15) == 34\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],target = 10) == 21\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],target = 0) == 15272\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],target = 200) == 2865\n assert candidate(nums = [5, 10, 15, 20, 25, 30],target = 50) == 0\n"}, "metadata": {"canonical_parameter_names": ["nums", "target"], "leetcode_dataset_entry_point": "Solution().findTargetSumWays", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findTargetSumWays = function(nums, target) {", "container": null, "callable": "findTargetSumWays", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "target", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 495, "task_id": "teemo-attacking", "difficulty": "Easy", "problem_description": "Our hero Teemo is attacking an enemy Ashe with poison attacks! When Teemo attacks Ashe, Ashe gets poisoned for a exactly duration seconds. More formally, an attack at second t will mean Ashe is poisoned during the inclusive time interval [t, t + duration - 1]. If Teemo attacks again before the poison effect ends, the timer for it is reset, and the poison effect will end duration seconds after the new attack.\nYou are given a non-decreasing integer array timeSeries, where timeSeries[i] denotes that Teemo attacks Ashe at second timeSeries[i], and an integer duration.\nReturn the total number of seconds that Ashe is poisoned.\n \nExample 1:\n\nInput: timeSeries = [1,4], duration = 2\nOutput: 4\nExplanation: Teemo's attacks on Ashe go as follows:\n- At second 1, Teemo attacks, and Ashe is poisoned for seconds 1 and 2.\n- At second 4, Teemo attacks, and Ashe is poisoned for seconds 4 and 5.\nAshe is poisoned for seconds 1, 2, 4, and 5, which is 4 seconds in total.\n\nExample 2:\n\nInput: timeSeries = [1,2], duration = 2\nOutput: 3\nExplanation: Teemo's attacks on Ashe go as follows:\n- At second 1, Teemo attacks, and Ashe is poisoned for seconds 1 and 2.\n- At second 2 however, Teemo attacks again and resets the poison timer. Ashe is poisoned for seconds 2 and 3.\nAshe is poisoned for seconds 1, 2, and 3, which is 3 seconds in total.\n \nConstraints:\n\n1 <= timeSeries.length <= 104\n0 <= timeSeries[i], duration <= 107\ntimeSeries is sorted in non-decreasing order.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(timeSeries = [0, 1, 2, 3, 4, 5],duration = 1) == 6\n assert candidate(timeSeries = [1, 5, 9],duration = 4) == 12\n assert candidate(timeSeries = [1],duration = 5) == 5\n assert candidate(timeSeries = [10, 14, 15],duration = 5) == 10\n assert candidate(timeSeries = [0, 1, 2, 3, 4],duration = 1) == 5\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],duration = 1) == 10\n assert candidate(timeSeries = [1, 2, 3, 4, 5],duration = 1) == 5\n assert candidate(timeSeries = [0, 5, 10, 15],duration = 5) == 20\n assert candidate(timeSeries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],duration = 1) == 10\n assert candidate(timeSeries = [10, 14, 15],duration = 4) == 9\n assert candidate(timeSeries = [1, 1, 1, 1],duration = 2) == 2\n assert candidate(timeSeries = [1, 2],duration = 2) == 3\n assert candidate(timeSeries = [1, 4],duration = 2) == 4\n assert candidate(timeSeries = [10, 20, 30, 40, 50],duration = 10) == 50\n assert candidate(timeSeries = [1, 10, 15, 20, 25],duration = 5) == 25\n assert candidate(timeSeries = [5, 7, 8, 10],duration = 3) == 8\n assert candidate(timeSeries = [1, 100, 200, 300, 400, 500],duration = 10) == 60\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],duration = 8) == 53\n assert candidate(timeSeries = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],duration = 100) == 427\n assert candidate(timeSeries = [1, 3, 5, 6, 10, 12, 15],duration = 3) == 16\n assert candidate(timeSeries = [1, 3, 6, 10],duration = 3) == 11\n assert candidate(timeSeries = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],duration = 1) == 1\n assert candidate(timeSeries = [1, 2, 3, 5, 8, 13, 21, 34, 55],duration = 5) == 32\n assert candidate(timeSeries = [0, 2, 4, 6, 8, 10],duration = 2) == 12\n assert candidate(timeSeries = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109],duration = 10) == 19\n assert candidate(timeSeries = [5, 10, 15, 20, 25],duration = 3) == 15\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90],duration = 8) == 80\n assert candidate(timeSeries = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],duration = 3) == 30\n assert candidate(timeSeries = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109],duration = 1) == 10\n assert candidate(timeSeries = [1, 2, 4, 5, 7, 8, 10, 11, 13, 14],duration = 2) == 15\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],duration = 1) == 10\n assert candidate(timeSeries = [1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],duration = 50) == 249\n assert candidate(timeSeries = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89],duration = 7) == 47\n assert candidate(timeSeries = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],duration = 2) == 30\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],duration = 7) == 52\n assert candidate(timeSeries = [0, 1, 3, 6, 10, 15, 21, 28, 36, 45],duration = 8) == 52\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30],duration = 7) == 32\n assert candidate(timeSeries = [1, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40],duration = 5) == 44\n assert candidate(timeSeries = [2, 3, 5, 6, 8, 9, 11],duration = 2) == 11\n assert candidate(timeSeries = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],duration = 2) == 30\n assert candidate(timeSeries = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],duration = 1) == 11\n assert candidate(timeSeries = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],duration = 5) == 23\n assert candidate(timeSeries = [0, 2, 5, 10, 15, 20, 25],duration = 5) == 30\n assert candidate(timeSeries = [0, 5, 10, 15, 20, 25, 30, 35, 40],duration = 5) == 45\n assert candidate(timeSeries = [1, 4, 7, 10, 13, 16],duration = 3) == 18\n assert candidate(timeSeries = [0, 2, 5, 9, 12, 15, 18, 21, 24, 27],duration = 5) == 32\n assert candidate(timeSeries = [100, 200, 300, 400, 500],duration = 150) == 550\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30],duration = 7) == 32\n assert candidate(timeSeries = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31],duration = 3) == 33\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],duration = 4) == 18\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],duration = 10) == 109\n assert candidate(timeSeries = [10, 12, 15, 17, 18, 20, 25, 30],duration = 4) == 22\n assert candidate(timeSeries = [1, 3, 5, 7, 9],duration = 3) == 11\n assert candidate(timeSeries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14],duration = 2) == 16\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],duration = 2) == 16\n assert candidate(timeSeries = [100, 101, 102, 103, 104, 105],duration = 5) == 10\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],duration = 1) == 20\n assert candidate(timeSeries = [2, 5, 10, 15, 20],duration = 6) == 24\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30],duration = 3) == 18\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],duration = 15) == 60\n assert candidate(timeSeries = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60],duration = 10) == 60\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90],duration = 10) == 99\n assert candidate(timeSeries = [1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 8, 9],duration = 3) == 11\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],duration = 10) == 39\n assert candidate(timeSeries = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],duration = 2) == 40\n assert candidate(timeSeries = [1, 2, 3, 5, 7, 9, 12, 15, 20, 25],duration = 2) == 18\n assert candidate(timeSeries = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300],duration = 15) == 305\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90],duration = 15) == 104\n assert candidate(timeSeries = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],duration = 2) == 20\n assert candidate(timeSeries = [0, 2, 5, 10, 15, 20, 25, 30],duration = 10) == 40\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],duration = 3) == 12\n assert candidate(timeSeries = [1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26],duration = 4) == 29\n assert candidate(timeSeries = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95],duration = 10) == 100\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],duration = 1) == 20\n assert candidate(timeSeries = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],duration = 10) == 100\n assert candidate(timeSeries = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28],duration = 2) == 20\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15],duration = 3) == 15\n assert candidate(timeSeries = [100, 102, 105, 110, 115, 121, 128, 136, 145, 155],duration = 15) == 70\n assert candidate(timeSeries = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],duration = 1) == 1\n assert candidate(timeSeries = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],duration = 2) == 20\n assert candidate(timeSeries = [5, 10, 15, 20, 25],duration = 5) == 25\n assert candidate(timeSeries = [0, 0, 0, 0, 0],duration = 10000) == 10000\n assert candidate(timeSeries = [0, 2, 4, 6, 8, 10, 12, 14],duration = 2) == 16\n assert candidate(timeSeries = [1000, 1005, 1010, 1015, 1020, 1025],duration = 5) == 30\n assert candidate(timeSeries = [100, 150, 200, 250, 300, 350, 400, 450, 500, 550],duration = 50) == 500\n assert candidate(timeSeries = [2, 2, 2, 2, 2],duration = 5) == 5\n assert candidate(timeSeries = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],duration = 5) == 5\n assert candidate(timeSeries = [2, 4, 8, 12, 16, 20, 24, 28],duration = 6) == 32\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30],duration = 5) == 30\n assert candidate(timeSeries = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512],duration = 50) == 263\n assert candidate(timeSeries = [1, 3, 6, 10, 15],duration = 3) == 14\n assert candidate(timeSeries = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],duration = 5) == 25\n assert candidate(timeSeries = [1, 3, 5, 6, 8, 10, 12, 15],duration = 4) == 18\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],duration = 2) == 11\n assert candidate(timeSeries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],duration = 3) == 33\n assert candidate(timeSeries = [1, 3, 6, 10, 15, 21, 28, 36, 45],duration = 7) == 48\n assert candidate(timeSeries = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],duration = 10) == 100\n assert candidate(timeSeries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],duration = 3) == 13\n assert candidate(timeSeries = [5, 15, 25, 35, 45, 55],duration = 10) == 60\n assert candidate(timeSeries = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],duration = 10) == 110\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140],duration = 10) == 149\n assert candidate(timeSeries = [1, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],duration = 100) == 1099\n assert candidate(timeSeries = [1, 4, 10, 20, 30, 40, 50, 60, 70, 80, 90],duration = 5) == 53\n assert candidate(timeSeries = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20],duration = 3) == 23\n assert candidate(timeSeries = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],duration = 5) == 14\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75],duration = 8) == 78\n assert candidate(timeSeries = [1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43],duration = 3) == 45\n assert candidate(timeSeries = [1, 10, 19, 28, 37, 46, 55, 64, 73, 82],duration = 9) == 90\n assert candidate(timeSeries = [5, 10, 15, 20, 25, 30, 35, 40],duration = 10) == 45\n assert candidate(timeSeries = [1, 4, 8, 12, 16],duration = 3) == 15\n assert candidate(timeSeries = [100, 200, 300, 400, 500],duration = 150) == 550\n assert candidate(timeSeries = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],duration = 50) == 500\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],duration = 50) == 249\n assert candidate(timeSeries = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],duration = 100) == 100\n assert candidate(timeSeries = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],duration = 15) == 105\n assert candidate(timeSeries = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70],duration = 7) == 77\n assert candidate(timeSeries = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],duration = 10) == 10\n assert candidate(timeSeries = [1, 2, 3, 10, 15, 20],duration = 5) == 22\n assert candidate(timeSeries = [1, 10, 20, 30, 40, 50, 60, 70, 80, 90],duration = 9) == 90\n assert candidate(timeSeries = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],duration = 2) == 27\n"}, "metadata": {"canonical_parameter_names": ["timeSeries", "duration"], "leetcode_dataset_entry_point": "Solution().findPoisonedDuration", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findPoisonedDuration = function(timeSeries, duration) {", "container": null, "callable": "findPoisonedDuration", "parameters": [{"name": "timeSeries", "type": "number[]"}, {"name": "duration", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 496, "task_id": "next-greater-element-i", "difficulty": "Easy", "problem_description": "The next greater element of some element x in an array is the first greater element that is to the right of x in the same array.\nYou are given two distinct 0-indexed integer arrays nums1 and nums2, where nums1 is a subset of nums2.\nFor each 0 <= i < nums1.length, find the index j such that nums1[i] == nums2[j] and determine the next greater element of nums2[j] in nums2. If there is no next greater element, then the answer for this query is -1.\nReturn an array ans of length nums1.length such that ans[i] is the next greater element as described above.\n \nExample 1:\n\nInput: nums1 = [4,1,2], nums2 = [1,3,4,2]\nOutput: [-1,3,-1]\nExplanation: The next greater element for each value of nums1 is as follows:\n- 4 is underlined in nums2 = [1,3,4,2]. There is no next greater element, so the answer is -1.\n- 1 is underlined in nums2 = [1,3,4,2]. The next greater element is 3.\n- 2 is underlined in nums2 = [1,3,4,2]. There is no next greater element, so the answer is -1.\n\nExample 2:\n\nInput: nums1 = [2,4], nums2 = [1,2,3,4]\nOutput: [3,-1]\nExplanation: The next greater element for each value of nums1 is as follows:\n- 2 is underlined in nums2 = [1,2,3,4]. The next greater element is 3.\n- 4 is underlined in nums2 = [1,2,3,4]. There is no next greater element, so the answer is -1.\n\n \nConstraints:\n\n1 <= nums1.length <= nums2.length <= 1000\n0 <= nums1[i], nums2[i] <= 104\nAll integers in nums1 and nums2 are unique.\nAll the integers of nums1 also appear in nums2.\n\n \nFollow up: Could you find an O(nums1.length + nums2.length) solution?", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums1 = [2, 3, 5, 6],nums2 = [5, 6, 2, 3, 8, 9]) == [3, 8, 6, 8]\n assert candidate(nums1 = [1, 2],nums2 = [2, 1]) == [-1, -1]\n assert candidate(nums1 = [1, 2, 3, 4],nums2 = [4, 3, 2, 1]) == [-1, -1, -1, -1]\n assert candidate(nums1 = [5],nums2 = [5]) == [-1]\n assert candidate(nums1 = [1, 6, 4, 8],nums2 = [4, 5, 1, 8, 6, 7, 9]) == [8, 7, 5, 9]\n assert candidate(nums1 = [5, 2, 6],nums2 = [4, 1, 5, 2, 3, 6]) == [6, 3, -1]\n assert candidate(nums1 = [2, 4],nums2 = [1, 2, 3, 4]) == [3, -1]\n assert candidate(nums1 = [4, 1, 2],nums2 = [1, 3, 4, 2]) == [-1, 3, -1]\n assert candidate(nums1 = [10, 5, 6],nums2 = [3, 4, 2, 1, 5, 7, 8, 9, 10, 6]) == [-1, 7, -1]\n assert candidate(nums1 = [2],nums2 = [1, 2]) == [-1]\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [1, 2, 3, 4, 5, 6, 7, 8]) == [2, 4, 6, 8]\n assert candidate(nums1 = [3, 5, 8],nums2 = [2, 3, 4, 5, 7, 8, 10]) == [4, 7, 10]\n assert candidate(nums1 = [1],nums2 = [3, 2, 1]) == [-1]\n assert candidate(nums1 = [9, 8, 7],nums2 = [8, 9, 7, 6, 5, 4, 3, 2, 1]) == [-1, 9, -1]\n assert candidate(nums1 = [3, 5, 8],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [4, 6, 9]\n assert candidate(nums1 = [9, 10, 7],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [10, -1, 8]\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [7, 5, 3, 1, 9, 11, 13]) == [9, 9, 9, 9]\n assert candidate(nums1 = [1],nums2 = [1]) == [-1]\n assert candidate(nums1 = [1, 3],nums2 = [2, 1, 3, 4]) == [3, 4]\n assert candidate(nums1 = [10, 8, 6],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) == [11, 9, 7]\n assert candidate(nums1 = [9, 7, 3],nums2 = [3, 6, 9, 12, 15, 7]) == [12, -1, 6]\n assert candidate(nums1 = [10, 9, 8],nums2 = [8, 9, 10, 5, 7]) == [-1, 10, 9]\n assert candidate(nums1 = [100, 90, 80, 70],nums2 = [70, 80, 90, 100, 110, 120, 130, 140, 150]) == [110, 100, 90, 80]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [2, 4, 6, 8, 10, 1, 3, 5, 7, 9]) == [3, 5, 7, 9, -1]\n assert candidate(nums1 = [33, 22, 11],nums2 = [11, 22, 33, 44, 55, 66, 77, 88, 99]) == [44, 33, 22]\n assert candidate(nums1 = [100, 99, 98, 97],nums2 = [98, 100, 97, 99, 96, 95, 94, 93, 92]) == [-1, -1, 100, 99]\n assert candidate(nums1 = [3, 5, 2, 1],nums2 = [1, 2, 3, 5, 4]) == [5, -1, 3, 2]\n assert candidate(nums1 = [3, 5, 2, 4, 9],nums2 = [8, 5, 3, 9, 2, 4, 7, 6]) == [9, 9, 4, 7, -1]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1]) == [-1, -1, -1, -1, -1]\n assert candidate(nums1 = [7, 8, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [8, 9, -1]\n assert candidate(nums1 = [3, 8, 9],nums2 = [10, 11, 7, 8, 6, 5, 3, 4, 9, 2, 1]) == [4, 9, -1]\n assert candidate(nums1 = [5, 7, 3, 9, 1],nums2 = [11, 14, 8, 15, 13, 2, 11, 5, 12, 7, 9, 3, 6, 10, 4, 1]) == [12, 9, 6, 10, -1]\n assert candidate(nums1 = [6, 2, 8, 9],nums2 = [6, 5, 4, 3, 2, 1, 10, 11, 8, 9, 7]) == [10, 10, 9, -1]\n assert candidate(nums1 = [11, 13, 15, 17],nums2 = [17, 15, 13, 11, 19, 21, 23]) == [19, 19, 19, 19]\n assert candidate(nums1 = [9, 8, 7, 6, 5],nums2 = [5, 6, 7, 8, 9]) == [-1, 9, 8, 7, 6]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 6, 7]) == [6, 6, 6, 6, 6]\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [7, 5, 3, 1, 2, 4, 6, 8, 10]) == [2, 4, 6, 8]\n assert candidate(nums1 = [3, 6, 9, 12, 15],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [4, 7, 10, 13, -1]\n assert candidate(nums1 = [3, 5, 7, 9],nums2 = [9, 7, 5, 3, 1, 2, 4, 6, 8, 10]) == [4, 6, 8, 10]\n assert candidate(nums1 = [15, 25, 35],nums2 = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]) == [20, 30, 40]\n assert candidate(nums1 = [6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [7, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [100, 90, 80, 70],nums2 = [70, 80, 90, 100, 110]) == [110, 100, 90, 80]\n assert candidate(nums1 = [10, 20, 30, 40],nums2 = [40, 10, 20, 30, 50, 60, 70]) == [20, 30, 50, 50]\n assert candidate(nums1 = [6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6]) == [-1, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [3, 2, 1],nums2 = [5, 3, 2, 1, 6, 4]) == [6, 6, 6]\n assert candidate(nums1 = [23, 56, 78, 90],nums2 = [90, 78, 56, 23, 12, 34, 45, 67, 89, 100]) == [34, 67, 89, 100]\n assert candidate(nums1 = [42, 55, 66, 77],nums2 = [42, 77, 55, 88, 66, 99, 100]) == [77, 88, 99, 88]\n assert candidate(nums1 = [8, 6, 4, 2],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [9, 7, 5, 3]\n assert candidate(nums1 = [100, 90, 80],nums2 = [70, 80, 90, 100, 60, 50, 40, 30, 20, 10]) == [-1, 100, 90]\n assert candidate(nums1 = [10, 20, 30],nums2 = [10, 20, 30, 25, 15, 5, 40, 35, 33, 31]) == [20, 30, 40]\n assert candidate(nums1 = [6, 7, 8, 9, 10],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [7, 8, 9, 10, -1]\n assert candidate(nums1 = [7, 3, 2],nums2 = [5, 7, 3, 2, 1, 8]) == [8, 8, 8]\n assert candidate(nums1 = [12, 14, 13, 11, 15],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [13, 15, 14, 12, -1]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11]) == [11, 11, 11, 11, 11, 11, 11, 11, 11, 11]\n assert candidate(nums1 = [8, 10, 4, 3],nums2 = [1, 11, 10, 4, 8, 3, 7]) == [-1, -1, 8, 7]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, -1, -1, -1, -1]\n assert candidate(nums1 = [7, 6, 5, 4, 3, 2, 1],nums2 = [2, 1, 3, 6, 5, 4, 7]) == [-1, 7, 7, 7, 6, 3, 3]\n assert candidate(nums1 = [2, 6, 4, 5, 3],nums2 = [3, 1, 2, 5, 4, 7, 6]) == [5, -1, 7, 7, 5]\n assert candidate(nums1 = [8, 9, 10, 11],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [9, 10, 11, 12]\n assert candidate(nums1 = [3, 6, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]) == [4, 7, 10]\n assert candidate(nums1 = [3, 5, 7, 9],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [4, 6, 8, -1]\n assert candidate(nums1 = [7, 5, 3, 1],nums2 = [9, 7, 5, 3, 1, 2, 4, 6, 8, 10]) == [8, 6, 4, 2]\n assert candidate(nums1 = [100, 90, 80, 70],nums2 = [70, 80, 90, 100, 110, 120, 130]) == [110, 100, 90, 80]\n assert candidate(nums1 = [1, 3, 5, 7, 9],nums2 = [9, 7, 5, 3, 1, 2, 4, 6, 8, 10]) == [2, 4, 6, 8, 10]\n assert candidate(nums1 = [3, 5, 2, 4, 9],nums2 = [9, 1, 2, 5, 3, 7, 8, 4, 6]) == [7, 7, 5, 6, -1]\n assert candidate(nums1 = [42, 23, 14, 5, 1],nums2 = [1, 5, 14, 23, 42, 3, 7, 11, 13, 19, 21, 27]) == [-1, 42, 23, 14, 5]\n assert candidate(nums1 = [1, 3, 5, 7, 9, 11, 13, 15, 17],nums2 = [15, 13, 11, 9, 7, 5, 3, 1, 17, 19]) == [17, 17, 17, 17, 17, 17, 17, 17, 19]\n assert candidate(nums1 = [5, 10, 15, 20],nums2 = [20, 15, 10, 5, 25, 30, 35, 40]) == [25, 25, 25, 25]\n assert candidate(nums1 = [7, 3, 9, 1],nums2 = [1, 3, 5, 7, 9]) == [9, 5, -1, 3]\n assert candidate(nums1 = [15, 10, 5],nums2 = [1, 2, 3, 4, 5, 10, 15, 20, 25]) == [20, 15, 10]\n assert candidate(nums1 = [10, 11, 12, 13],nums2 = [13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, -1, -1, -1]\n assert candidate(nums1 = [7, 6, 5, 4, 3, 2, 1],nums2 = [1, 2, 3, 4, 5, 6, 7]) == [-1, 7, 6, 5, 4, 3, 2]\n assert candidate(nums1 = [6, 7, 8],nums2 = [1, 2, 3, 6, 7, 8, 5, 4]) == [7, 8, -1]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [5, 4, 3, 2, 1, 6]) == [6, 6, 6, 6, 6]\n assert candidate(nums1 = [7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, -1, -1]\n assert candidate(nums1 = [1, 10, 100, 1000],nums2 = [100, 1, 1000, 10, 200, 300, 400, 500]) == [1000, 200, 1000, -1]\n assert candidate(nums1 = [3, 6, 1, 4],nums2 = [9, 3, 8, 1, 7, 6, 5, 4, 2]) == [8, -1, 7, -1]\n assert candidate(nums1 = [15, 12, 11, 13],nums2 = [15, 12, 11, 14, 10, 9, 8, 13, 16]) == [16, 14, 14, 16]\n assert candidate(nums1 = [100, 99, 98, 97, 96],nums2 = [96, 97, 98, 99, 100, 101, 102, 103]) == [101, 100, 99, 98, 97]\n assert candidate(nums1 = [9, 7, 5, 3, 1],nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [11, 9, 7, 5, 3]\n assert candidate(nums1 = [1, 7, 4, 2, 10],nums2 = [2, 1, 10, 7, 4, 5, 3]) == [10, -1, 5, 10, -1]\n assert candidate(nums1 = [11, 13, 7, 5, 3, 1],nums2 = [1, 3, 5, 7, 9, 11, 13, 15]) == [13, 15, 9, 7, 5, 3]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],nums2 = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 12, 13, 14, 15]) == [11, 11, 11, 11, 11, 11, 11, 11, 11, 11]\n assert candidate(nums1 = [10, 20, 30],nums2 = [30, 20, 10, 40, 50, 60]) == [40, 40, 40]\n assert candidate(nums1 = [9, 8, 7, 6, 5, 4, 3, 2, 1],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(nums1 = [10, 20, 30],nums2 = [10, 15, 20, 25, 30]) == [15, 25, -1]\n assert candidate(nums1 = [6, 4, 1],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [7, 5, 2]\n assert candidate(nums1 = [7, 5, 9],nums2 = [9, 4, 7, 3, 5, 1, 8, 6, 2]) == [8, 8, -1]\n assert candidate(nums1 = [7, 6, 5],nums2 = [5, 1, 2, 3, 4, 6, 7]) == [-1, 7, 6]\n assert candidate(nums1 = [3, 11, 17, 19],nums2 = [3, 19, 23, 11, 17, 29, 21, 25]) == [19, 17, 29, 23]\n assert candidate(nums1 = [1, 7, 3, 4, 5, 6],nums2 = [3, 4, 1, 6, 8, 9, 5, 2, 7]) == [6, -1, 4, 6, 7, 8]\n assert candidate(nums1 = [2, 5, 10, 15, 20],nums2 = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2]) == [-1, 7, -1, 17, -1]\n assert candidate(nums1 = [15, 10, 18, 23, 5],nums2 = [18, 10, 15, 5, 23, 2, 11, 17, 3, 12]) == [23, 15, 23, -1, 23]\n assert candidate(nums1 = [11, 12, 13],nums2 = [5, 11, 9, 12, 13, 8, 7, 6, 10]) == [12, 13, -1]\n assert candidate(nums1 = [50, 60, 70, 80, 90],nums2 = [90, 80, 70, 60, 50, 40, 30, 20, 10]) == [-1, -1, -1, -1, -1]\n assert candidate(nums1 = [100, 200, 300, 400],nums2 = [400, 300, 200, 100, 50, 150, 250, 350, 450]) == [150, 250, 350, 450]\n assert candidate(nums1 = [1, 6, 11, 13],nums2 = [1, 3, 5, 7, 9, 11, 13, 2, 4, 6, 8, 10, 12, 14]) == [3, 8, 13, 14]\n assert candidate(nums1 = [15, 25, 35],nums2 = [10, 20, 30, 40, 50, 60, 70, 80, 90, 15, 25, 35]) == [25, 35, -1]\n assert candidate(nums1 = [7, 5, 3, 1],nums2 = [1, 3, 5, 7, 9]) == [9, 7, 5, 3]\n assert candidate(nums1 = [5, 8, 12, 15],nums2 = [15, 12, 5, 8, 20, 25, 30, 35]) == [8, 20, 20, 20]\n assert candidate(nums1 = [5, 1, 4],nums2 = [2, 6, 4, 5, 1, 9]) == [9, 9, 5]\n assert candidate(nums1 = [9, 10, 11],nums2 = [3, 4, 5, 1, 6, 9, 7, 8, 11, 10, 2]) == [11, -1, -1]\n assert candidate(nums1 = [9, 8, 7, 6],nums2 = [1, 2, 3, 4, 5, 6, 7, 8, 9]) == [-1, 9, 8, 7]\n assert candidate(nums1 = [4, 3, 2, 1],nums2 = [1, 2, 3, 4]) == [-1, 4, 3, 2]\n assert candidate(nums1 = [4, 3, 2, 1, 0],nums2 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [5, 4, 3, 2, 1]\n assert candidate(nums1 = [8, 6, 4, 2],nums2 = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30]) == [10, 8, 6, 4]\n assert candidate(nums1 = [2, 6, 4, 5, 7, 3],nums2 = [3, 5, 4, 6, 2, 1, 7, 9, 8]) == [7, 7, 6, 6, 9, 5]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 10]) == [10, 10, 10, 10, 10, 10, 10, 10, 10]\n assert candidate(nums1 = [1, 3, 5, 7],nums2 = [2, 4, 6, 8, 1, 3, 5, 7]) == [3, 5, 7, -1]\n assert candidate(nums1 = [11, 22, 33],nums2 = [33, 22, 11, 44, 55, 66, 77]) == [44, 44, 44]\n assert candidate(nums1 = [10, 20, 30, 40, 50],nums2 = [50, 40, 30, 20, 10, 60, 70, 80, 90]) == [60, 60, 60, 60, 60]\n assert candidate(nums1 = [4, 1, 3, 7, 6, 2, 5],nums2 = [7, 8, 2, 3, 4, 1, 6, 5, 9]) == [6, 6, 4, 8, 9, 3, 9]\n assert candidate(nums1 = [1, 2, 3, 4, 5, 6, 7, 8, 9],nums2 = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 12]) == [11, 11, 11, 11, 11, 11, 11, 11, 11]\n assert candidate(nums1 = [1, 2, 3, 4, 5],nums2 = [3, 4, 5, 1, 2]) == [2, -1, 4, 5, -1]\n assert candidate(nums1 = [1, 10, 5, 3],nums2 = [3, 1, 10, 5, 9, 7, 4, 6, 8]) == [10, -1, 9, 10]\n assert candidate(nums1 = [5, 10, 20],nums2 = [20, 10, 5, 25, 15, 30]) == [25, 25, 25]\n assert candidate(nums1 = [7, 5, 3, 2],nums2 = [3, 2, 7, 5, 4]) == [-1, -1, 7, 7]\n assert candidate(nums1 = [1, 7, 4, 3],nums2 = [3, 4, 1, 5, 7, 8, 9]) == [5, 8, 5, 4]\n"}, "metadata": {"canonical_parameter_names": ["nums1", "nums2"], "leetcode_dataset_entry_point": "Solution().nextGreaterElement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var nextGreaterElement = function(nums1, nums2) {", "container": null, "callable": "nextGreaterElement", "parameters": [{"name": "nums1", "type": "number[]"}, {"name": "nums2", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 498, "task_id": "diagonal-traverse", "difficulty": "Medium", "problem_description": "Given an m x n matrix mat, return an array of all the elements of the array in a diagonal order.\n \nExample 1:\n\n\nInput: mat = [[1,2,3],[4,5,6],[7,8,9]]\nOutput: [1,2,4,7,5,3,6,8,9]\n\nExample 2:\n\nInput: mat = [[1,2],[3,4]]\nOutput: [1,2,3,4]\n\n \nConstraints:\n\nm == mat.length\nn == mat[i].length\n1 <= m, n <= 104\n1 <= m * n <= 104\n-105 <= mat[i][j] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(mat = [[1, 2], [3, 4]]) == [1, 2, 3, 4]\n assert candidate(mat = [[1]]) == [1]\n assert candidate(mat = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]) == [1, 2, 5, 9, 6, 3, 4, 7, 10, 11, 8, 12]\n assert candidate(mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]) == [1, 2, 4, 7, 5, 3, 6, 8, 9]\n assert candidate(mat = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20]]) == [1, 2, 6, 11, 7, 3, 4, 8, 12, 16, 17, 13, 9, 5, 10, 14, 18, 19, 15, 20]\n assert candidate(mat = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]]) == [1, 3, 10, 23, 11, 5, 7, 16, 30, 34, 20, 60]\n assert candidate(mat = [[10000, 9999, 9998], [9997, 9996, 9995], [9994, 9993, 9992], [9991, 9990, 9989]]) == [10000, 9999, 9997, 9994, 9996, 9998, 9995, 9993, 9991, 9990, 9992, 9989]\n assert candidate(mat = [[1000, 2000, 3000], [4000, 5000, 6000], [7000, 8000, 9000], [10000, 11000, 12000]]) == [1000, 2000, 4000, 7000, 5000, 3000, 6000, 8000, 10000, 11000, 9000, 12000]\n assert candidate(mat = [[-10, 20, -30, 40], [-50, 60, -70, 80], [-90, 100, -110, 120]]) == [-10, 20, -50, -90, 60, -30, 40, -70, 100, -110, 80, 120]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28], [29, 30, 31, 32, 33, 34, 35]]) == [1, 2, 8, 15, 9, 3, 4, 10, 16, 22, 29, 23, 17, 11, 5, 6, 12, 18, 24, 30, 31, 25, 19, 13, 7, 14, 20, 26, 32, 33, 27, 21, 28, 34, 35]\n assert candidate(mat = [[100, 200, 300, 400, 500], [600, 700, 800, 900, 1000], [1100, 1200, 1300, 1400, 1500]]) == [100, 200, 600, 1100, 700, 300, 400, 800, 1200, 1300, 900, 500, 1000, 1400, 1500]\n assert candidate(mat = [[10, 20, 30, 40, 50, 60, 70], [80, 90, 100, 110, 120, 130, 140], [150, 160, 170, 180, 190, 200, 210], [220, 230, 240, 250, 260, 270, 280]]) == [10, 20, 80, 150, 90, 30, 40, 100, 160, 220, 230, 170, 110, 50, 60, 120, 180, 240, 250, 190, 130, 70, 140, 200, 260, 270, 210, 280]\n assert candidate(mat = [[-10, -9, -8, -7, -6], [-5, -4, -3, -2, -1], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]]) == [-10, -9, -5, 0, -4, -8, -7, -3, 1, 5, 10, 6, 2, -2, -6, -1, 3, 7, 11, 12, 8, 4, 9, 13, 14]\n assert candidate(mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15], [16, 17, 18], [19, 20, 21], [22, 23, 24]]) == [1, 2, 4, 7, 5, 3, 6, 8, 10, 13, 11, 9, 12, 14, 16, 19, 17, 15, 18, 20, 22, 23, 21, 24]\n assert candidate(mat = [[-1, -2, -3, -4, -5], [-6, -7, -8, -9, -10], [-11, -12, -13, -14, -15], [-16, -17, -18, -19, -20]]) == [-1, -2, -6, -11, -7, -3, -4, -8, -12, -16, -17, -13, -9, -5, -10, -14, -18, -19, -15, -20]\n assert candidate(mat = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]) == [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n assert candidate(mat = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20], [21, 22], [23, 24], [25, 26], [27, 28], [29, 30]]) == [1, 2, 3, 5, 4, 6, 7, 9, 8, 10, 11, 13, 12, 14, 15, 17, 16, 18, 19, 21, 20, 22, 23, 25, 24, 26, 27, 29, 28, 30]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(mat = [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50], [51, 52, 53, 54, 55, 56, 57, 58, 59, 60]]) == [1, 2, 11, 21, 12, 3, 4, 13, 22, 31, 41, 32, 23, 14, 5, 6, 15, 24, 33, 42, 51, 52, 43, 34, 25, 16, 7, 8, 17, 26, 35, 44, 53, 54, 45, 36, 27, 18, 9, 10, 19, 28, 37, 46, 55, 56, 47, 38, 29, 20, 30, 39, 48, 57, 58, 49, 40, 50, 59, 60]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54]]) == [1, 2, 10, 19, 11, 3, 4, 12, 20, 28, 37, 29, 21, 13, 5, 6, 14, 22, 30, 38, 46, 47, 39, 31, 23, 15, 7, 8, 16, 24, 32, 40, 48, 49, 41, 33, 25, 17, 9, 18, 26, 34, 42, 50, 51, 43, 35, 27, 36, 44, 52, 53, 45, 54]\n assert candidate(mat = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35], [36, 37, 38, 39, 40], [41, 42, 43, 44, 45]]) == [1, 2, 6, 11, 7, 3, 4, 8, 12, 16, 21, 17, 13, 9, 5, 10, 14, 18, 22, 26, 31, 27, 23, 19, 15, 20, 24, 28, 32, 36, 41, 37, 33, 29, 25, 30, 34, 38, 42, 43, 39, 35, 40, 44, 45]\n assert candidate(mat = [[-1, -2, -3, -4], [-5, -6, -7, -8], [-9, -10, -11, -12], [-13, -14, -15, -16]]) == [-1, -2, -5, -9, -6, -3, -4, -7, -10, -13, -14, -11, -8, -12, -15, -16]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28]]) == [1, 2, 8, 15, 9, 3, 4, 10, 16, 22, 23, 17, 11, 5, 6, 12, 18, 24, 25, 19, 13, 7, 14, 20, 26, 27, 21, 28]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32]]) == [1, 2, 9, 17, 10, 3, 4, 11, 18, 25, 26, 19, 12, 5, 6, 13, 20, 27, 28, 21, 14, 7, 8, 15, 22, 29, 30, 23, 16, 24, 31, 32]\n assert candidate(mat = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]]) == [1, 2, 3, 5, 4, 6, 7, 9, 8, 10]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48, 49, 50]]) == [1, 2, 11, 21, 12, 3, 4, 13, 22, 31, 41, 32, 23, 14, 5, 6, 15, 24, 33, 42, 43, 34, 25, 16, 7, 8, 17, 26, 35, 44, 45, 36, 27, 18, 9, 10, 19, 28, 37, 46, 47, 38, 29, 20, 30, 39, 48, 49, 40, 50]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45]]) == [1, 2, 10, 19, 11, 3, 4, 12, 20, 28, 37, 29, 21, 13, 5, 6, 14, 22, 30, 38, 39, 31, 23, 15, 7, 8, 16, 24, 32, 40, 41, 33, 25, 17, 9, 18, 26, 34, 42, 43, 35, 27, 36, 44, 45]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30]]) == [1, 2, 7, 13, 8, 3, 4, 9, 14, 19, 25, 20, 15, 10, 5, 6, 11, 16, 21, 26, 27, 22, 17, 12, 18, 23, 28, 29, 24, 30]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54], [55, 56, 57, 58, 59, 60, 61, 62, 63]]) == [1, 2, 10, 19, 11, 3, 4, 12, 20, 28, 37, 29, 21, 13, 5, 6, 14, 22, 30, 38, 46, 55, 47, 39, 31, 23, 15, 7, 8, 16, 24, 32, 40, 48, 56, 57, 49, 41, 33, 25, 17, 9, 18, 26, 34, 42, 50, 58, 59, 51, 43, 35, 27, 36, 44, 52, 60, 61, 53, 45, 54, 62, 63]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36, 37, 38, 39, 40]]) == [1, 2, 11, 21, 12, 3, 4, 13, 22, 31, 32, 23, 14, 5, 6, 15, 24, 33, 34, 25, 16, 7, 8, 17, 26, 35, 36, 27, 18, 9, 10, 19, 28, 37, 38, 29, 20, 30, 39, 40]\n assert candidate(mat = [[5, 10, 15, 20, 25], [30, 35, 40, 45, 50], [55, 60, 65, 70, 75], [80, 85, 90, 95, 100], [105, 110, 115, 120, 125], [130, 135, 140, 145, 150]]) == [5, 10, 30, 55, 35, 15, 20, 40, 60, 80, 105, 85, 65, 45, 25, 50, 70, 90, 110, 130, 135, 115, 95, 75, 100, 120, 140, 145, 125, 150]\n assert candidate(mat = [[-10, -20, -30, -40], [-50, -60, -70, -80], [-90, -100, -110, -120], [-130, -140, -150, -160]]) == [-10, -20, -50, -90, -60, -30, -40, -70, -100, -130, -140, -110, -80, -120, -150, -160]\n assert candidate(mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15], [16, 17, 18]]) == [1, 2, 4, 7, 5, 3, 6, 8, 10, 13, 11, 9, 12, 14, 16, 17, 15, 18]\n assert candidate(mat = [[-10, -20, -30, -40], [-50, -60, -70, -80], [-90, -100, -110, -120], [-130, -140, -150, -160], [-170, -180, -190, -200], [-210, -220, -230, -240], [-250, -260, -270, -280], [-290, -300, -310, -320]]) == [-10, -20, -50, -90, -60, -30, -40, -70, -100, -130, -170, -140, -110, -80, -120, -150, -180, -210, -250, -220, -190, -160, -200, -230, -260, -290, -300, -270, -240, -280, -310, -320]\n assert candidate(mat = [[1, 2, 3, 4, 5], [6, 7, 8, 9, 10], [11, 12, 13, 14, 15], [16, 17, 18, 19, 20], [21, 22, 23, 24, 25], [26, 27, 28, 29, 30], [31, 32, 33, 34, 35]]) == [1, 2, 6, 11, 7, 3, 4, 8, 12, 16, 21, 17, 13, 9, 5, 10, 14, 18, 22, 26, 31, 27, 23, 19, 15, 20, 24, 28, 32, 33, 29, 25, 30, 34, 35]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42], [43, 44, 45, 46, 47, 48], [49, 50, 51, 52, 53, 54], [55, 56, 57, 58, 59, 60]]) == [1, 2, 7, 13, 8, 3, 4, 9, 14, 19, 25, 20, 15, 10, 5, 6, 11, 16, 21, 26, 31, 37, 32, 27, 22, 17, 12, 18, 23, 28, 33, 38, 43, 49, 44, 39, 34, 29, 24, 30, 35, 40, 45, 50, 55, 56, 51, 46, 41, 36, 42, 47, 52, 57, 58, 53, 48, 54, 59, 60]\n assert candidate(mat = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16]]) == [1, 2, 3, 5, 4, 6, 7, 9, 8, 10, 11, 13, 12, 14, 15, 16]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12], [13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30], [31, 32, 33, 34, 35, 36]]) == [1, 2, 7, 13, 8, 3, 4, 9, 14, 19, 25, 20, 15, 10, 5, 6, 11, 16, 21, 26, 31, 32, 27, 22, 17, 12, 18, 23, 28, 33, 34, 29, 24, 30, 35, 36]\n assert candidate(mat = [[-10, -9, -8, -7], [-6, -5, -4, -3], [-2, -1, 0, 1], [2, 3, 4, 5], [6, 7, 8, 9], [10, 11, 12, 13]]) == [-10, -9, -6, -2, -5, -8, -7, -4, -1, 2, 6, 3, 0, -3, 1, 4, 7, 10, 11, 8, 5, 9, 12, 13]\n assert candidate(mat = [[1, 0, -1, 2, 3, 4], [0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 6], [2, 3, 4, 5, 6, 7], [3, 4, 5, 6, 7, 8]]) == [1, 0, 0, 1, 1, -1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8]\n assert candidate(mat = [[-10, -9, -8, -7, -6, -5], [-4, -3, -2, -1, 0, 1], [2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13], [14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24, 25]]) == [-10, -9, -4, 2, -3, -8, -7, -2, 3, 8, 14, 9, 4, -1, -6, -5, 0, 5, 10, 15, 20, 21, 16, 11, 6, 1, 7, 12, 17, 22, 23, 18, 13, 19, 24, 25]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36]]) == [1, 2, 10, 19, 11, 3, 4, 12, 20, 28, 29, 21, 13, 5, 6, 14, 22, 30, 31, 23, 15, 7, 8, 16, 24, 32, 33, 25, 17, 9, 18, 26, 34, 35, 27, 36]\n assert candidate(mat = [[0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 2, 0, 0], [0, 0, 0, 3, 0], [0, 0, 0, 0, 4]]) == [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 4]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32], [33, 34, 35, 36, 37, 38, 39, 40], [41, 42, 43, 44, 45, 46, 47, 48], [49, 50, 51, 52, 53, 54, 55, 56], [57, 58, 59, 60, 61, 62, 63, 64]]) == [1, 2, 9, 17, 10, 3, 4, 11, 18, 25, 33, 26, 19, 12, 5, 6, 13, 20, 27, 34, 41, 49, 42, 35, 28, 21, 14, 7, 8, 15, 22, 29, 36, 43, 50, 57, 58, 51, 44, 37, 30, 23, 16, 24, 31, 38, 45, 52, 59, 60, 53, 46, 39, 32, 40, 47, 54, 61, 62, 55, 48, 56, 63, 64]\n assert candidate(mat = [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12], [13, 14], [15, 16], [17, 18], [19, 20]]) == [1, 2, 3, 5, 4, 6, 7, 9, 8, 10, 11, 13, 12, 14, 15, 17, 16, 18, 19, 20]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28], [29, 30, 31, 32, 33, 34, 35], [36, 37, 38, 39, 40, 41, 42]]) == [1, 2, 8, 15, 9, 3, 4, 10, 16, 22, 29, 23, 17, 11, 5, 6, 12, 18, 24, 30, 36, 37, 31, 25, 19, 13, 7, 14, 20, 26, 32, 38, 39, 33, 27, 21, 28, 34, 40, 41, 35, 42]\n assert candidate(mat = [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15], [16, 17, 18], [19, 20, 21]]) == [1, 2, 4, 7, 5, 3, 6, 8, 10, 13, 11, 9, 12, 14, 16, 19, 17, 15, 18, 20, 21]\n assert candidate(mat = [[-5, 3, -10, 1], [-7, -1, -2, -4], [-9, -4, -5, -8]]) == [-5, 3, -7, -9, -1, -10, 1, -2, -4, -5, -4, -8]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18], [19, 20, 21, 22, 23, 24, 25, 26, 27], [28, 29, 30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40, 41, 42, 43, 44, 45], [46, 47, 48, 49, 50, 51, 52, 53, 54], [55, 56, 57, 58, 59, 60, 61, 62, 63], [64, 65, 66, 67, 68, 69, 70, 71, 72], [73, 74, 75, 76, 77, 78, 79, 80, 81]]) == [1, 2, 10, 19, 11, 3, 4, 12, 20, 28, 37, 29, 21, 13, 5, 6, 14, 22, 30, 38, 46, 55, 47, 39, 31, 23, 15, 7, 8, 16, 24, 32, 40, 48, 56, 64, 73, 65, 57, 49, 41, 33, 25, 17, 9, 18, 26, 34, 42, 50, 58, 66, 74, 75, 67, 59, 51, 43, 35, 27, 36, 44, 52, 60, 68, 76, 77, 69, 61, 53, 45, 54, 62, 70, 78, 79, 71, 63, 72, 80, 81]\n assert candidate(mat = [[-1, -2, -3], [-4, -5, -6], [-7, -8, -9], [-10, -11, -12]]) == [-1, -2, -4, -7, -5, -3, -6, -8, -10, -11, -9, -12]\n assert candidate(mat = [[1, 4, 7, 10, 13], [2, 5, 8, 11, 14], [3, 6, 9, 12, 15], [16, 19, 22, 25, 28], [17, 20, 23, 26, 29], [18, 21, 24, 27, 30]]) == [1, 4, 2, 3, 5, 7, 10, 8, 6, 16, 17, 19, 9, 11, 13, 14, 12, 22, 20, 18, 21, 23, 25, 15, 28, 26, 24, 27, 29, 30]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]\n assert candidate(mat = [[10, -5, 23, 45, 67], [-10, 20, 5, -6, 78], [2, 4, 6, 8, -100], [9, 3, 7, -4, -88], [12, 14, 16, 18, 20]]) == [10, -5, -10, 2, 20, 23, 45, 5, 4, 9, 12, 3, 6, -6, 67, 78, 8, 7, 14, 16, -4, -100, -88, 18, 20]\n assert candidate(mat = [[5, 10, 15, 20, 25, 30], [35, 40, 45, 50, 55, 60], [65, 70, 75, 80, 85, 90], [95, 100, 105, 110, 115, 120]]) == [5, 10, 35, 65, 40, 15, 20, 45, 70, 95, 100, 75, 50, 25, 30, 55, 80, 105, 110, 85, 60, 90, 115, 120]\n assert candidate(mat = [[100, 200, 300], [400, 500, 600], [700, 800, 900], [1000, 1100, 1200], [1300, 1400, 1500]]) == [100, 200, 400, 700, 500, 300, 600, 800, 1000, 1300, 1100, 900, 1200, 1400, 1500]\n assert candidate(mat = [[1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 29]]) == [1, 4, 2, 3, 5, 7, 11, 8, 6, 10, 18, 13, 9, 12, 15, 19, 16, 14, 21, 23, 17, 22, 24, 26, 29]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 12, 13, 14], [15, 16, 17, 18, 19, 20, 21], [22, 23, 24, 25, 26, 27, 28], [29, 30, 31, 32, 33, 34, 35], [36, 37, 38, 39, 40, 41, 42], [43, 44, 45, 46, 47, 48, 49]]) == [1, 2, 8, 15, 9, 3, 4, 10, 16, 22, 29, 23, 17, 11, 5, 6, 12, 18, 24, 30, 36, 43, 37, 31, 25, 19, 13, 7, 14, 20, 26, 32, 38, 44, 45, 39, 33, 27, 21, 28, 34, 40, 46, 47, 41, 35, 42, 48, 49]\n assert candidate(mat = [[1, 2, 3, 4, 5, 6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16], [17, 18, 19, 20, 21, 22, 23, 24], [25, 26, 27, 28, 29, 30, 31, 32], [33, 34, 35, 36, 37, 38, 39, 40]]) == [1, 2, 9, 17, 10, 3, 4, 11, 18, 25, 33, 26, 19, 12, 5, 6, 13, 20, 27, 34, 35, 28, 21, 14, 7, 8, 15, 22, 29, 36, 37, 30, 23, 16, 24, 31, 38, 39, 32, 40]\n"}, "metadata": {"canonical_parameter_names": ["mat"], "leetcode_dataset_entry_point": "Solution().findDiagonalOrder", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findDiagonalOrder = function(mat) {", "container": null, "callable": "findDiagonalOrder", "parameters": [{"name": "mat", "type": "number[][]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 500, "task_id": "keyboard-row", "difficulty": "Easy", "problem_description": "Given an array of strings words, return the words that can be typed using letters of the alphabet on only one row of American keyboard like the image below.\nNote that the strings are case-insensitive, both lowercased and uppercased of the same letter are treated as if they are at the same row.\nIn the American keyboard:\n\nthe first row consists of the characters \"qwertyuiop\",\nthe second row consists of the characters \"asdfghjkl\", and\nthe third row consists of the characters \"zxcvbnm\".\n\n\n \nExample 1:\n\nInput: words = [\"Hello\",\"Alaska\",\"Dad\",\"Peace\"]\nOutput: [\"Alaska\",\"Dad\"]\nExplanation:\nBoth \"a\" and \"A\" are in the 2nd row of the American keyboard due to case insensitivity.\n\nExample 2:\n\nInput: words = [\"omk\"]\nOutput: []\n\nExample 3:\n\nInput: words = [\"adsdf\",\"sfd\"]\nOutput: [\"adsdf\",\"sfd\"]\n\n \nConstraints:\n\n1 <= words.length <= 20\n1 <= words[i].length <= 100\nwords[i] consists of English letters (both lowercase and uppercase). \n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(words = ['Hello', 'Alaska', 'Dad', 'Peace']) == ['Alaska', 'Dad']\n assert candidate(words = ['qwerty', 'ASDFGH', 'zxcvbN']) == ['qwerty', 'ASDFGH', 'zxcvbN']\n assert candidate(words = ['QwErTy', 'aSdF', 'zXcV']) == ['QwErTy', 'aSdF', 'zXcV']\n assert candidate(words = ['AAAAA', 'eeeee', 'QQQqq', 'zzzzz']) == ['AAAAA', 'eeeee', 'QQQqq', 'zzzzz']\n assert candidate(words = ['QwErTy', 'AsDfGh', 'ZxCvBn']) == ['QwErTy', 'AsDfGh', 'ZxCvBn']\n assert candidate(words = ['omk']) == []\n assert candidate(words = ['adsdf', 'sfd']) == ['adsdf', 'sfd']\n assert candidate(words = ['Flask', 'kite', 'BAT']) == ['Flask']\n assert candidate(words = ['Unbelievable', 'Incomprehensible', 'Supernatural', 'Phenomenal', 'Transcendent', 'Metaphysical', 'Ethereal', 'Mystical', 'Enigmatic', 'Paradoxical']) == []\n assert candidate(words = ['MixedCASE', 'Keyboard', 'TESTING', 'qwerty', 'ASDF', 'ZXCV', 'QwErTy', 'AsDf', 'ZxCv']) == ['qwerty', 'ASDF', 'ZXCV', 'QwErTy', 'AsDf', 'ZxCv']\n assert candidate(words = ['Programming', 'Python', 'Keyboard', 'Typing', 'Challenge']) == []\n assert candidate(words = ['quick', 'brown', 'fox', 'jumps', 'over', 'lazy', 'dogs', 'cat', 'bat', 'rat', 'mat', 'hat', 'sat', 'van', 'pan', 'tan', 'man', 'can', 'fan', 'fan']) == []\n assert candidate(words = ['helloWorld', 'pythonProgramming', 'dataScience', 'machineLearning', 'artificialIntelligence']) == []\n assert candidate(words = ['The', 'Quick', 'Brown', 'Fox', 'Jumps', 'Over', 'Lazy', 'Dog', 'Zoology']) == []\n assert candidate(words = ['a', 'A', 'b', 'B', 'c', 'C', 'd', 'D', 'e', 'E', 'f', 'F', 'g', 'G', 'h', 'H', 'i', 'I', 'j', 'J', 'k', 'K', 'l', 'L', 'm', 'M', 'n', 'N', 'o', 'O', 'p', 'P', 'q', 'Q', 'r', 'R', 's', 'S', 't', 'T', 'u', 'U', 'v', 'V', 'w', 'W', 'x', 'X', 'y', 'Y', 'z', 'Z']) == ['a', 'A', 'b', 'B', 'c', 'C', 'd', 'D', 'e', 'E', 'f', 'F', 'g', 'G', 'h', 'H', 'i', 'I', 'j', 'J', 'k', 'K', 'l', 'L', 'm', 'M', 'n', 'N', 'o', 'O', 'p', 'P', 'q', 'Q', 'r', 'R', 's', 'S', 't', 'T', 'u', 'U', 'v', 'V', 'w', 'W', 'x', 'X', 'y', 'Y', 'z', 'Z']\n assert candidate(words = ['qwerty', 'ASDFGH', 'ZXCVBNM', 'QwErTy', 'AsDfGh', 'ZxCvBnM']) == ['qwerty', 'ASDFGH', 'ZXCVBNM', 'QwErTy', 'AsDfGh', 'ZxCvBnM']\n assert candidate(words = ['developer', 'programming', 'software', 'engineer', 'algorithm', 'datastructure']) == []\n assert candidate(words = ['qwertyuiopq', 'asdfghjklasdf', 'zxcvbnmzxcvbnm', 'qwertyuiopqwertyuiop', 'asdfghjklasdfghjkl', 'zxcvbnmzxcvbnmzxcvbnm']) == ['qwertyuiopq', 'asdfghjklasdf', 'zxcvbnmzxcvbnm', 'qwertyuiopqwertyuiop', 'asdfghjklasdfghjkl', 'zxcvbnmzxcvbnmzxcvbnm']\n assert candidate(words = ['neurotransmitter', 'photosynthesis', 'biochemistry', 'mitochondria', 'cytoplasm', 'hypothalamus', 'glucose', 'enzymes', 'photosynthetic', 'photosynthesis']) == []\n assert candidate(words = ['MixedCaseWords', 'CamelCase', 'PascalCase', 'SnakeCase', 'KebabCase']) == []\n assert candidate(words = ['Programming', 'Python', 'Keyboard', 'Layout', 'Challenges']) == []\n assert candidate(words = ['supercalifragilisticexpialidocious', 'antidisestablishmentarianism', 'honorificabilitudinitatibus', 'floccinaucinihilipilification', 'pneumonoultramicroscopicsilicovolcanoconiosis', 'supercalifragilisticexpialidocious', 'antidisestablishmentarianism']) == []\n assert candidate(words = ['HELLOworld', 'aLpHa', 'KEYbOArD', 'OnEtwOthReE', 'QuICkBrOWnFoXJUMPsOvErLAZYdOG', 'PYtHoNcOdInG']) == []\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']) == ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']\n assert candidate(words = ['Mississippi', 'Delaware', 'Washington', 'California', 'Texas', 'Alabama', 'Georgia', 'Virginia', 'Florida']) == []\n assert candidate(words = ['Typewriter', 'Keyboard', 'Mouse', 'Monitor', 'Motherboard']) == ['Typewriter']\n assert candidate(words = ['Python', 'Java', 'C++', 'JavaScript', 'Ruby', 'Go', 'Swift', 'Kotlin']) == []\n assert candidate(words = ['Quickly', 'Brown', 'Fox', 'Jumps', 'Over', 'Lazy', 'Dog']) == []\n assert candidate(words = ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM', 'qazwsxedcrfvtgbyhnujmikolp', 'poiuytrewqlkjhgfdsamnbvcxz', 'mnbvcxzlkjhgfdsapoiuytrewq', 'abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz', 'zzzyyxxwwvvuuttrrssqqppoonnmmllkkjjiihhggffeeddccbbaa']) == ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM']\n assert candidate(words = ['International', 'Pineapple', 'Keyboard', 'Queen', 'Zebra', 'Alphabet', 'Quick', 'Brown', 'Fox', 'Lazy']) == []\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'ZYXWVUTSRQPONMLKJIHGFEDCBA', 'QwErTyUiOpAsDfGhJkLzXcVbNm']) == []\n assert candidate(words = ['Mississippi', 'Alabama', 'Hawaii', 'Delaware', 'Alaska', 'Florida']) == ['Alaska']\n assert candidate(words = ['OneRow', 'TwoRows', 'ThreeRows', 'FourRows', 'FiveRows']) == []\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'ZYXWVUTSRQPONMLKJIHGFEDCBA', 'QwErTyUiOpAsDfGhJkLzXcVbNm', 'mnbvcxzlkjhgfdsapoiuytrewq']) == []\n assert candidate(words = ['Supercalifragilisticexpialidocious', 'Pneumonoultramicroscopicsilicovolcanoconiosis', 'Honorificabilitudinitatibus', 'Antidisestablishmentarianism', 'Floccinaucinihilipilification']) == []\n assert candidate(words = ['qwerty', 'asdfgh', 'zxcvbnm', 'QWERTY', 'ASDFGH', 'ZXCVBNM']) == ['qwerty', 'asdfgh', 'zxcvbnm', 'QWERTY', 'ASDFGH', 'ZXCVBNM']\n assert candidate(words = ['Quick', 'Brown', 'Fox', 'Jumps', 'Over', 'Lazy', 'Dog']) == []\n assert candidate(words = ['helloWorld', 'OpenAI', 'Python', 'Java', 'CSharp', 'JavaScript', 'TypeScript']) == []\n assert candidate(words = ['Python', 'Keyboard', 'Alphabet', 'Row', 'Line']) == ['Row']\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']\n assert candidate(words = ['Shift', 'Ctrl', 'Alt', 'Fn', 'Enter', 'Space', 'Backspace', 'Tab', 'CapsLock', 'Esc', 'PrintScreen', 'ScrollLock', 'Pause', 'Insert', 'Delete', 'Home', 'End', 'PageUp', 'PageDown', 'ArrowUp', 'ArrowDown', 'ArrowLeft', 'ArrowRight']) == []\n assert candidate(words = ['aaaaabbbbcccccdddddeeeeefffffggggghhhhhiiiiiijjjjjkkkkklllllmnnnnnooooo', 'pppppqqqqqrrrrrssssstttttuuuuuvvvvvwwwwwxxxxyyyyyzzzzz']) == []\n assert candidate(words = ['asdfghjklASDFGHJKL', 'zxcvbnmZXCVBNM', 'qwertyuiopQWERTYUIOP']) == ['asdfghjklASDFGHJKL', 'zxcvbnmZXCVBNM', 'qwertyuiopQWERTYUIOP']\n assert candidate(words = ['RowOne', 'RowTwo', 'RowThree', 'roWONe', 'roWTWo', 'roWTHrEE', 'ONE', 'TWO', 'THREE', 'one', 'two', 'three']) == ['RowTwo', 'roWTWo', 'TWO', 'two']\n assert candidate(words = ['Alphabet', 'Zebra', 'Python', 'Java', 'CSharp', 'Ruby']) == []\n assert candidate(words = ['racecar', 'madam', 'refer', 'deed', 'level', 'noon', 'rotor']) == ['rotor']\n assert candidate(words = ['single', 'double', 'triple', 'quadruple', 'quintuple', 'sextuple', 'septuple', 'octuple', 'nonuple', 'decuple']) == []\n assert candidate(words = ['aaaaaaaaa', 'bbbbbbbbb', 'ccccccccc', 'ddddddddd', 'eeeeeeeee', 'fffffffff', 'ggggggggg', 'hhhhhhhhh', 'iiiiiiiii', 'jjjjjjjjj', 'kkkkkkkkk', 'lllllllll', 'mmmmmmmmm', 'nnnnnnnnn', 'ooooooooo', 'ppppppppp', 'qqqqqqqqq', 'rrrrrrrrr', 'sssssssss', 'ttttttttt', 'uuuuuuuuu', 'vvvvvvvvv', 'wwwwwwwww', 'xxxxxxxxx', 'yyyyyyyyy', 'zzzzzzzzz']) == ['aaaaaaaaa', 'bbbbbbbbb', 'ccccccccc', 'ddddddddd', 'eeeeeeeee', 'fffffffff', 'ggggggggg', 'hhhhhhhhh', 'iiiiiiiii', 'jjjjjjjjj', 'kkkkkkkkk', 'lllllllll', 'mmmmmmmmm', 'nnnnnnnnn', 'ooooooooo', 'ppppppppp', 'qqqqqqqqq', 'rrrrrrrrr', 'sssssssss', 'ttttttttt', 'uuuuuuuuu', 'vvvvvvvvv', 'wwwwwwwww', 'xxxxxxxxx', 'yyyyyyyyy', 'zzzzzzzzz']\n assert candidate(words = ['Mississippi', 'Delaware', 'California', 'Texas', 'Montana', 'Alaska', 'Hawaii', 'Vermont', 'Wyoming', 'RhodeIsland', 'NewJersey', 'Connecticut', 'Pennsylvania', 'NewYork', 'Ohio', 'Michigan', 'Illinois', 'Indiana', 'Wisconsin', 'Minnesota', 'Iowa', 'Kansas', 'Nebraska', 'NorthDakota', 'SouthDakota', 'NorthCarolina', 'SouthCarolina', 'Georgia', 'Florida', 'Alabama', 'Missouri', 'Kentucky', 'Tennessee', 'Virginia', 'WestVirginia', 'Maryland', 'Delaware', 'NewHampshire', 'RhodeIsland', 'Massachusetts', 'Connecticut', 'Vermont', 'NewHampshire', 'Maine']) == ['Alaska']\n assert candidate(words = ['unique', 'characters', 'strings', 'keyboard', 'input', 'typing', 'fast']) == []\n assert candidate(words = ['supercalifragilisticexpialidocious', 'antidisestablishmentarianism', 'honorificabilitudinitatibus', 'floccinaucinihilipilification']) == []\n assert candidate(words = ['Supercalifragilisticexpialidocious', 'abcdefghijklmnopqrstuvwxyz', 'ABCDEFGHIJKLMNOPQRSTUVWXYZ']) == []\n assert candidate(words = ['gaming', 'console', 'controller', 'joystick', 'keyboard', 'monitor']) == []\n assert candidate(words = ['Alaska', 'AlaskaAlaska', 'DadDadDad', 'PeacePeacePeace']) == ['Alaska', 'AlaskaAlaska', 'DadDadDad']\n assert candidate(words = ['AaAaAaAaAaAa', 'BbBbBbBbBbBb', 'CcCcCcCcCcCc', 'DdDdDdDdDdDd', 'EeEeEeEeEeEe', 'FfFfFfFfFfFf', 'GgGgGgGgGgGg', 'HhHhHhHhHhHh', 'IiIiIiIiIiIi', 'JjJjJjJjJjJj', 'KkKkKkKkKkKk', 'LlLlLlLlLlLl', 'MmMmMmMmMmMm', 'NnNnNnNnNnNn', 'OoOoOoOoOoOo', 'PpPpPpPpPpPp', 'QqQqQqQqQqQq', 'RrRrRrRrRrRr', 'SsSsSsSsSsSs', 'TtTtTtTtTtTt', 'UuUuUuUuUuUu', 'VvVvVvVvVvVv', 'WwWwWwWwWwWw', 'XxXxXxXxXxXx', 'YyYyYyYyYyYy', 'ZzZzZzZzZzZz']) == ['AaAaAaAaAaAa', 'BbBbBbBbBbBb', 'CcCcCcCcCcCc', 'DdDdDdDdDdDd', 'EeEeEeEeEeEe', 'FfFfFfFfFfFf', 'GgGgGgGgGgGg', 'HhHhHhHhHhHh', 'IiIiIiIiIiIi', 'JjJjJjJjJjJj', 'KkKkKkKkKkKk', 'LlLlLlLlLlLl', 'MmMmMmMmMmMm', 'NnNnNnNnNnNn', 'OoOoOoOoOoOo', 'PpPpPpPpPpPp', 'QqQqQqQqQqQq', 'RrRrRrRrRrRr', 'SsSsSsSsSsSs', 'TtTtTtTtTtTt', 'UuUuUuUuUuUu', 'VvVvVvVvVvVv', 'WwWwWwWwWwWw', 'XxXxXxXxXxXx', 'YyYyYyYyYyYy', 'ZzZzZzZzZzZz']\n assert candidate(words = ['Consistency', 'Maintainability', 'Scalability', 'Performance', 'Efficiency', 'Optimization', 'Debugging', 'Testing', 'Deployment', 'Maintenance']) == []\n assert candidate(words = ['aAbBcCdDeEfFgGhHiIjJkKlLmMnNoOpPqQrRsStTuUvVwWxXyYzZ']) == []\n assert candidate(words = ['Quick', 'Brown', 'Fox', 'Jumps', 'Over', 'Lazy', 'Dogs']) == []\n assert candidate(words = ['aA', 'bB', 'cC', 'dD', 'eE', 'fF', 'gG', 'hH', 'iI', 'jJ', 'kK', 'lL', 'mM', 'nN', 'oO', 'pP', 'qQ', 'rR', 'sS', 'tT', 'uU', 'vV', 'wW', 'xX', 'yY', 'zZ']) == ['aA', 'bB', 'cC', 'dD', 'eE', 'fF', 'gG', 'hH', 'iI', 'jJ', 'kK', 'lL', 'mM', 'nN', 'oO', 'pP', 'qQ', 'rR', 'sS', 'tT', 'uU', 'vV', 'wW', 'xX', 'yY', 'zZ']\n assert candidate(words = ['qwertyuiop', 'ASDFGHJKL', 'zxcvbnm', 'QwErTyUiOp', 'AsDfGhJkL', 'Zx Cv Bn M']) == ['qwertyuiop', 'ASDFGHJKL', 'zxcvbnm', 'QwErTyUiOp', 'AsDfGhJkL']\n assert candidate(words = ['supercalifragilisticexpialidocious', 'antidisestablishmentarianism', 'floccinaucinihilipilification', 'pneumonoultramicroscopicsilicovolcanoconiosis', 'thyroparathyroidectomized']) == []\n assert candidate(words = ['aBcDeFgHiJ', 'klMnOpQrSt', 'uVwXyZ', 'AeIoU', 'bcd', 'fgh', 'jkl', 'mno', 'pqr', 'stv', 'wxy', 'z']) == ['fgh', 'jkl', 'pqr', 'z']\n assert candidate(words = ['Super', 'Califragilisticexpialidocious', 'ExpiAlIdoCious', 'Antidisestablishmentarianism', 'Pneumonoultramicroscopicsilicovolcanoconiosis']) == []\n assert candidate(words = ['MIXED', 'CaSe', 'sEnSiTiViTy', 'UpPeR', 'LoWeR']) == ['UpPeR']\n assert candidate(words = ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM']) == ['qwertyuiop', 'asdfghjkl', 'zxcvbnm', 'QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM']\n assert candidate(words = ['ASDFG', 'ZXCVBNM', 'QWERTYUIOP', 'alabama', 'kentucky', 'delaware']) == ['ASDFG', 'ZXCVBNM', 'QWERTYUIOP']\n assert candidate(words = ['qwertyuiop', 'Qwertyuiop', 'asdfghjkl', 'Asdfghjkl', 'zxcvbnm', 'Zxcvbnm', 'QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM', 'qQwWeErRtTyYuUiIoOpP', 'aAsSdDfFgGhHjJkKlL', 'zZxXcCvVbBnNmM']) == ['qwertyuiop', 'Qwertyuiop', 'asdfghjkl', 'Asdfghjkl', 'zxcvbnm', 'Zxcvbnm', 'QWERTYUIOP', 'ASDFGHJKL', 'ZXCVBNM', 'qQwWeErRtTyYuUiIoOpP', 'aAsSdDfFgGhHjJkKlL', 'zZxXcCvVbBnNmM']\n assert candidate(words = ['Quick', 'Brown', 'Fox', 'Jumps', 'Over', 'Lazy', 'Dog']) == []\n assert candidate(words = ['qwertyuiopasdfghjklzxcvbnmqwertyuiop', 'asdfghjklzxcvbnmqwertyuiopasdfghjkl', 'zxcvbnmqwertyuiopasdfghjklzxcvbnm']) == []\n assert candidate(words = ['Shift', 'Ctrl', 'Alt', 'Enter', 'Space', 'Esc', 'Tab', 'Backspace', 'Delete', 'Insert', 'Home', 'End', 'PageUp', 'PageDown', 'F1', 'F2', 'F3', 'F4', 'F5', 'F6', 'F7', 'F8', 'F9', 'F10', 'F11', 'F12']) == []\n assert candidate(words = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']\n assert candidate(words = ['aAaAaAaAaA', 'bBbBbBbBbB', 'cCcCcCcCcC', 'dDdDdDdDdD', 'eEeEeEeEeE', 'fFfFfFfFfF', 'gGgGgGgGgG', 'hHhHhHhHhH', 'iIiIiIiIiI', 'jJjJjJjJjJ', 'kKkKkKkKkK', 'lLlLlLlLlL', 'mMmMmMmMmM', 'nNnNnNnNnN', 'oOoOoOoOoO', 'pPpPpPpPpP', 'qQqQqQqQqQ', 'rRrRrRrRrR', 'sSsSsSsSsS', 'tTtTtTtTtT', 'uUuUuUuUuU', 'vVvVvVvVvV', 'wWwWwWwWwW', 'xXxXxXxXxX', 'yYyYyYyYyY', 'zZzZzZzZzZ']) == ['aAaAaAaAaA', 'bBbBbBbBbB', 'cCcCcCcCcC', 'dDdDdDdDdD', 'eEeEeEeEeE', 'fFfFfFfFfF', 'gGgGgGgGgG', 'hHhHhHhHhH', 'iIiIiIiIiI', 'jJjJjJjJjJ', 'kKkKkKkKkK', 'lLlLlLlLlL', 'mMmMmMmMmM', 'nNnNnNnNnN', 'oOoOoOoOoO', 'pPpPpPpPpP', 'qQqQqQqQqQ', 'rRrRrRrRrR', 'sSsSsSsSsS', 'tTtTtTtTtT', 'uUuUuUuUuU', 'vVvVvVvVvV', 'wWwWwWwWwW', 'xXxXxXxXxX', 'yYyYyYyYyY', 'zZzZzZzZzZ']\n assert candidate(words = ['abcdefghij', 'klmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'mnopqrstu', 'vwxyz', 'qazwsxedcrfvtgbyhnujmiklop', 'lkjhgfdsapoiuytrewq', 'poiuytrewqazxcvbnm', 'mnbvcxzlkjhgfdsapoiuytrewq']) == []\n assert candidate(words = ['Quick', 'brown', 'fox', 'jumps', 'over', 'lazy', 'dogs']) == []\n assert candidate(words = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'qwertyuiopasdfghjklzxcvbnm', 'mnbvcxzlkjhgfdsapoiuytrewq']) == []\n assert candidate(words = ['RowOne', 'RowTWO', 'ROWthree', 'rOWFOUR', 'RoWFIVe', 'ROWsiX', 'ROWseVE', 'ROWeiGHT', 'ROWniNE', 'ROWten']) == ['RowTWO']\n assert candidate(words = ['qwerty', 'asdfghjkl', 'zxcvbnm', 'QWERTY', 'ASDFGHJKL', 'ZXCVBNM', 'QwErTyUiOp', 'AsDfGhJkL', 'ZxCvBnM']) == ['qwerty', 'asdfghjkl', 'zxcvbnm', 'QWERTY', 'ASDFGHJKL', 'ZXCVBNM', 'QwErTyUiOp', 'AsDfGhJkL', 'ZxCvBnM']\n assert candidate(words = ['Programming', 'Language', 'Python', 'Java', 'CSharp', 'Ruby']) == []\n assert candidate(words = ['abcdefghij', 'klmnopqrstu', 'vwxyz', 'ABCDEFGHIJ', 'KLMNOPQRSTU', 'VWXYZ']) == []\n assert candidate(words = ['aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', 'bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb', 'cccccccccccccccccccccccccccccccccccccc', 'dddddddddddddddddddddddddddddddddddddd', 'eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee', 'ffffffffffffffffffffffffffffffffffffffff', 'gggggggggggggggggggggggggggggggggggggggg', 'hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh', 'iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii', 'jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj', 'kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk', 'llllllllllllllllllllllllllllllllllllll', 'mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm', 'nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn', 'oooooooooooooooooooooooooooooooooooooo', 'pppppppppppppppppppppppppppppppppppppp', 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', 'rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr', 'ssssssssssssssssssssssssssssssssssssss', 'tttttttttttttttttttttttttttttttttttttt', 'uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu', 'vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv', 'wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww', 'xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx', 'yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy', 'zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz']) == ['aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', 'bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb', 'cccccccccccccccccccccccccccccccccccccc', 'dddddddddddddddddddddddddddddddddddddd', 'eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee', 'ffffffffffffffffffffffffffffffffffffffff', 'gggggggggggggggggggggggggggggggggggggggg', 'hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh', 'iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii', 'jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj', 'kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk', 'llllllllllllllllllllllllllllllllllllll', 'mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm', 'nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn', 'oooooooooooooooooooooooooooooooooooooo', 'pppppppppppppppppppppppppppppppppppppp', 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', 'rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr', 'ssssssssssssssssssssssssssssssssssssss', 'tttttttttttttttttttttttttttttttttttttt', 'uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu', 'vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv', 'wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww', 'xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx', 'yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy', 'zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz']\n assert candidate(words = ['Typewriter', 'Keyboard', 'Mouse', 'Monitor', 'qwerty', 'zxcvbnm']) == ['Typewriter', 'qwerty', 'zxcvbnm']\n"}, "metadata": {"canonical_parameter_names": ["words"], "leetcode_dataset_entry_point": "Solution().findWords", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findWords = function(words) {", "container": null, "callable": "findWords", "parameters": [{"name": "words", "type": "string[]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 501, "task_id": "find-mode-in-binary-search-tree", "difficulty": "Easy", "problem_description": "Given the root of a binary search tree (BST) with duplicates, return all the mode(s) (i.e., the most frequently occurred element) in it.\nIf the tree has more than one mode, return them in any order.\nAssume a BST is defined as follows:\n\nThe left subtree of a node contains only nodes with keys less than or equal to the node's key.\nThe right subtree of a node contains only nodes with keys greater than or equal to the node's key.\nBoth the left and right subtrees must also be binary search trees.\n\n \nExample 1:\n\n\nInput: root = [1,null,2,2]\nOutput: [2]\n\nExample 2:\n\nInput: root = [0]\nOutput: [0]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 104].\n-105 <= Node.val <= 105\n\n \nFollow up: Could you do that without using any extra space? (Assume that the implicit stack space incurred due to recursion does not count).", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, None, None, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([5, 2, 5, None, None, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([3, 1, 4, 1, 3, None, 5])) == [1, 3]\n assert candidate(root = tree_node([2, 1, 2])) == [2]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([2, 2, 2])) == [2]\n assert candidate(root = tree_node([1, None, 1, None, 1, None, 1])) == [1]\n assert candidate(root = tree_node([0])) == [0]\n assert candidate(root = tree_node([5, 2, 5, 1, 3, 5, 7])) == [5]\n assert candidate(root = tree_node([1, None, 3, 2, 4, None, 5, None, None, 3, 4])) == [1, 2, 3, 5, 4, 3, 4]\n assert candidate(root = tree_node([1, 1, 2, 2, 3])) == [2, 1, 3, 1, 2]\n assert candidate(root = tree_node([2, 1, 2, 1, 2])) == [2]\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 2, 6])) == [2, 6]\n assert candidate(root = tree_node([1, 1, 2, 2, 3, 3])) == [2, 1, 3, 1, 3, 2]\n assert candidate(root = tree_node([1, 1, 2, 2, 3, 3, 4, 4])) == [4, 2, 1, 3, 1, 3, 2, 4]\n assert candidate(root = tree_node([1, None, 2, 2])) == [2]\n assert candidate(root = tree_node([1, None, 2, None, None, 3, 3])) == [1, 2]\n assert candidate(root = tree_node([1, 1, 2, 2, 3, 3, 3])) == [2, 1, 3, 1, 3, 2, 3]\n assert candidate(root = tree_node([1, None, 2, None, 3])) == [1, 2, 3]\n assert candidate(root = tree_node([50, 25, 75, 10, 35, 55, 85, 5, 15, 30, 40, 50, 60, 70, 90, 3, 7, 12, 18, 28, 32, 42, 48, 58, 62, 72, 82, 88, 93, 97])) == [3, 5, 7, 10, 12, 15, 18, 25, 28, 30, 32, 35, 42, 40, 48, 50, 58, 50, 62, 55, 72, 60, 82, 75, 88, 70, 93, 85, 97, 90]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 10, 18, 12, 17, 16, 19])) == [3, 7, 9, 15, 12, 10, 17, 20, 16, 18, 19]\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 23, 27, 32, 37, 42, 3, 7, 11, 13, 16, 19, 22, 24, 26, 28, 31, 33, 36, 38, 41, 43, 1, 4, 6, 8, 9, 14, 15, 17, 21, 29, 34, 35, 39, 40, 44, 45])) == [1, 3, 4, 5, 6, 7, 8, 10, 9, 11, 14, 12, 15, 13, 17, 15, 21, 16, 29, 18, 34, 19, 35, 20, 39, 22, 40, 23, 44, 24, 45, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10])) == [9, 5, 9, 3, 10, 5, 10, 2, 6, 3, 6, 1, 7, 4, 7, 2, 8, 4, 8]\n assert candidate(root = tree_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 18, 23, 27, 32, 37, 1, 3, 6, 8, 11, 13, 17, 19, 22, 24, 26, 28, 31, 33, 36, 38])) == [1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38]\n assert candidate(root = tree_node([7, 3, 10, 2, 5, 9, 12, 1, 4, 6, 8, 11, 13, None, None, None, None, None, None, None, None, None, None])) == [1, 2, 4, 3, 6, 5, 8, 7, 11, 9, 13, 10, 12]\n assert candidate(root = tree_node([50, 20, 60, 10, 30, 55, 70, 5, 15, 25, 35, 53, 57, 65, 75, 3, 7, 13, 17, 23, 27, 33, 37, 52, 54, 56, 58, 63, 67, 72, 77, 4, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38, 51, 59, 61, 69, 71, 73, 78, 1, 9, 11, 19, 21, 29, 31, 39, 49, 62, 64, 68, 74, 76, 79, 0])) == [64, 4, 68, 3, 74, 6, 76, 5, 79, 8, 0, 7, 12, 10, 14, 13, 16, 15, 18, 17, 22, 20, 24, 23, 26, 25, 28, 27, 32, 30, 34, 33, 36, 35, 38, 37, 51, 50, 59, 52, 61, 53, 69, 54, 71, 55, 73, 56, 78, 57, 1, 58, 9, 60, 11, 63, 19, 65, 21, 67, 29, 70, 31, 72, 39, 75, 49, 77, 62]\n assert candidate(root = tree_node([2, 0, 3, None, 1, None, None, 0, 1])) == [0, 1]\n assert candidate(root = tree_node([1, 2, 3, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3])) == [3]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, 8, 10, 11, 16, 17, 25, 23, 28, 22, 24, 27, 29, 26])) == [3, 7, 26, 17, 8, 25, 9, 23, 10, 28, 15, 22, 11, 24, 20, 27, 16, 29]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37, 1, 4, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38])) == [1, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 37, 38]\n assert candidate(root = tree_node([2, 1, 3, None, None, 1, 3, None, None, 1, 3])) == [3]\n assert candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, 7, 9, 11, 13, 14, 17, 18, 22, 21, 23, 24, 26])) == [21, 7, 23, 8, 24, 9, 26, 10, 11, 12, 13, 15, 14, 16, 17, 20, 18, 25, 22]\n assert candidate(root = tree_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7])) == [7]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 10])) == [9, 5, 9, 3, 10, 5, 10, 2, 10, 6, 10, 3, 10, 6, 1, 7, 4, 7, 2, 8, 4, 8]\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 2, 6, None, None, None, None, None, 10])) == [2, 6]\n assert candidate(root = tree_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, 4, 6, 8, None, None, 2, None, None, 16, 19])) == [2, 1, 3, 4, 16, 5, 19, 6, 7, 8, 10, 15, 18]\n assert candidate(root = tree_node([1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2])) == [2]\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85])) == [10, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85]\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == [0, 0, 0, 0, 0, 0]\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, None, 2, 4, 4, 4, 4, 4])) == [4]\n assert candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13])) == [1, 3, 4, 6, 7, 8, 10, 13, 14]\n assert candidate(root = tree_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])) == [2]\n assert candidate(root = tree_node([8, 5, 10, 3, 7, 9, 12, 1, 4, 6, 8, 11, 13, None, None, None, None, None, None, None, None, None, None])) == [8]\n assert candidate(root = tree_node([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])) == [2]\n assert candidate(root = tree_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75, 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69, 71, 79])) == [1, 5, 9, 10, 11, 15, 19, 20, 21, 25, 29, 30, 31, 35, 39, 40, 41, 45, 49, 50, 51, 55, 59, 60, 61, 65, 69, 70, 71, 75, 79]\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n assert candidate(root = tree_node([1, 1, 2, 1, 1, None, 2, 1, 1, None, None, 2, 2])) == [1]\n assert candidate(root = tree_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, 4, 6, 8, 12, 14, 17, 19, 2, 9, 11, 16, 20])) == [2, 1, 9, 3, 11, 4, 16, 5, 20, 6, 7, 8, 10, 12, 13, 14, 15, 17, 18, 19]\n assert candidate(root = tree_node([5, 1, 5, None, 2, None, 5])) == [5]\n assert candidate(root = tree_node([15, 10, 20, 5, 12, 17, 25, 2, 6, 8, 11, 14, 16, 18, 22, 1, 3, 4, 7, 9, None, None, None, None, None, 13])) == [1, 2, 3, 5, 4, 6, 7, 10, 9, 8, 12, 11, 15, 14, 17, 13, 16, 20, 18, 25, 22]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, 4, 6, 8, None, None, None, None, 12, 17, 16, 19, 20, 21, 22])) == [1, 3, 22, 12, 4, 17, 5, 16, 6, 19, 7, 20, 8, 21, 10, 15, 18]\n assert candidate(root = tree_node([8, 4, 10, 2, 6, 9, 12, 1, 3, 5, 7, 11, 13])) == [1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 13, 10, 12]\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7, 1, 2, 3, 4, 5, 6, 7, 8])) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7, 0, 1, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([4, 2, 5, 2, 3, 4, 6, 2, 3, None, None, 4, 5])) == [4]\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 8, 10, 16, 21, 17, 18, 19])) == [3, 7, 9, 15, 19, 16, 8, 21, 20, 17, 10, 18]\n assert candidate(root = tree_node([25, 10, 30, 5, 20, None, None, 3, 7, 15, 22, None, None, 13, 17, 19, 21])) == [3, 5, 13, 7, 17, 10, 19, 15, 21, 20, 22, 25, 30]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, 4, 6, 8, 11, 14, 16, 19, 0, 2, None, None, None, None, None, None, None, None, 9, 12, 17, 20])) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 9, 14, 12, 15, 17, 16, 20, 18, 19]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, None, 6, 8, 14, 16, 19, 12, 13, 17, 15, 11])) == [16, 1, 19, 3, 5, 7, 12, 6, 13, 10, 15, 17, 8, 15, 18, 11, 14]\n assert candidate(root = tree_node([1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2])) == [1]\n assert candidate(root = tree_node([1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6])) == [6, 4, 6, 2, 6, 4, 6, 1, 6, 4, 6, 3, 5, 1, 5, 3, 6, 2, 6, 4, 6]\n assert candidate(root = tree_node([4, 2, 6, 1, 3, 5, 7, 0, 1, 4, 6, 8, 9, 2, 5, 3, 5, 6, 7, 8, 9])) == [3, 0, 5, 1, 6, 1, 7, 2, 8, 4, 9, 3, 6, 4, 8, 5, 9, 6, 2, 7, 5]\n assert candidate(root = tree_node([1, 1, 1, 1, 1, None, None, None, None, None, None])) == [1]\n assert candidate(root = tree_node([7, 3, 15, 2, 5, 10, 17, 1, 4, 6, 8, 12, 16, 14, 18])) == [1, 2, 4, 3, 6, 5, 8, 7, 12, 10, 16, 15, 14, 17, 18]\n assert candidate(root = tree_node([1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [16, 8, 17, 4, 18, 9, 19, 2, 20, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, 7, None, 12, 18, 23, 28, 33, None, 3, 6, 9, 11, 13, 16, 17, 19, 22, 24, 26, 29, 32, 34, 36])) == [1, 34, 3, 36, 5, 6, 7, 9, 10, 15, 11, 12, 13, 20, 16, 18, 17, 25, 19, 23, 22, 30, 24, 28, 26, 35, 29, 33, 32]\n assert candidate(root = tree_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, 6, 9, 11, 13, 14, 18, 22, 30, 4, 7, 5, 17, 19, 21, 23, 24, 26, 27, 28, 29])) == [4, 6, 7, 8, 5, 9, 17, 10, 19, 11, 21, 12, 23, 13, 24, 15, 26, 14, 27, 16, 28, 18, 29, 20, 22, 25, 30]\n assert candidate(root = tree_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7])) == [7]\n assert candidate(root = tree_node([7, 4, 8, 2, 6, 7, 9, 1, None, 3, 5, 7, 8, None, None, None, None, 10])) == [7]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, 4, 6, 8, 11, 13, 17, 19])) == [1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 18, 19]\n assert candidate(root = tree_node([1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 3])) == [1, 2, 2, 2, 3]\n assert candidate(root = tree_node([5, 3, 6, 3, 5, 6, 7, 3, 3, 5, 5, 6, 6, 6, 7, 3, 3, 5, 5, 5, 6, 6, 6, 7, 3, 3, 5, 5, 5, 6, 6, 6, 7])) == [3]\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 1, 6, 11, 17, 22, 27, 32, 38, 0, 3, 7, 8, 12, 14, 18, 21, 23, 26, 28, 31, 33, 36, 39, 4, 9, 10, 13, 16, 19, 24, 29, 30, 34, 37, 40, 2, 5, 12, 14, 18, 20, 23, 26, 28, 31, 33, 36, 39])) == [20, 23, 26]\n assert candidate(root = tree_node([1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8])) == [8, 6, 8, 4, 8, 6, 8, 3, 8, 6, 4, 6, 2, 6, 4, 6, 3, 7, 5, 7, 1, 7, 5, 7, 3, 7, 5, 7, 2, 7, 5, 8, 4, 8, 5, 8]\n assert candidate(root = tree_node([1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 3, 4, 3, 3])) == [3]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == [1, 3, 5, 6, 7, 10, 15, 18]\n assert candidate(root = tree_node([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 4, 8, 12, 14, 17, 19])) == [1, 3, 5, 4, 7, 8, 10, 12, 13, 14, 15, 17, 18, 19]\n assert candidate(root = tree_node([6, 3, 6, 2, 4, None, 7, 1, None, 3, 5, None, None, 8])) == [3, 6]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().findMode", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMode = function(root) {", "container": null, "callable": "findMode", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 502, "task_id": "ipo", "difficulty": "Hard", "problem_description": "Suppose LeetCode will start its IPO soon. In order to sell a good price of its shares to Venture Capital, LeetCode would like to work on some projects to increase its capital before the IPO. Since it has limited resources, it can only finish at most k distinct projects before the IPO. Help LeetCode design the best way to maximize its total capital after finishing at most k distinct projects.\nYou are given n projects where the ith project has a pure profit profits[i] and a minimum capital of capital[i] is needed to start it.\nInitially, you have w capital. When you finish a project, you will obtain its pure profit and the profit will be added to your total capital.\nPick a list of at most k distinct projects from given projects to maximize your final capital, and return the final maximized capital.\nThe answer is guaranteed to fit in a 32-bit signed integer.\n \nExample 1:\n\nInput: k = 2, w = 0, profits = [1,2,3], capital = [0,1,1]\nOutput: 4\nExplanation: Since your initial capital is 0, you can only start the project indexed 0.\nAfter finishing it you will obtain profit 1 and your capital becomes 1.\nWith capital 1, you can either start the project indexed 1 or the project indexed 2.\nSince you can choose at most 2 projects, you need to finish the project indexed 2 to get the maximum capital.\nTherefore, output the final maximized capital, which is 0 + 1 + 3 = 4.\n\nExample 2:\n\nInput: k = 3, w = 0, profits = [1,2,3], capital = [0,1,2]\nOutput: 6\n\n \nConstraints:\n\n1 <= k <= 105\n0 <= w <= 109\nn == profits.length\nn == capital.length\n1 <= n <= 105\n0 <= profits[i] <= 104\n0 <= capital[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(k = 1,w = 10,profits = [5, 6],capital = [4, 0]) == 16\n assert candidate(k = 5,w = 10,profits = [5, 4, 3, 2, 1],capital = [1, 2, 3, 4, 5]) == 25\n assert candidate(k = 2,w = 3,profits = [8, 10, 6],capital = [2, 5, 0]) == 21\n assert candidate(k = 4,w = 0,profits = [1, 1, 1, 1],capital = [0, 0, 0, 0]) == 4\n assert candidate(k = 5,w = 0,profits = [1, 2, 3, 4, 5],capital = [0, 1, 2, 3, 4]) == 15\n assert candidate(k = 5,w = 0,profits = [10, 20, 30, 40, 50],capital = [0, 0, 0, 0, 0]) == 150\n assert candidate(k = 1,w = 10,profits = [1, 2, 3],capital = [5, 5, 5]) == 13\n assert candidate(k = 1,w = 5,profits = [1, 2, 3],capital = [3, 4, 5]) == 8\n assert candidate(k = 3,w = 0,profits = [1, 2, 3],capital = [0, 1, 2]) == 6\n assert candidate(k = 3,w = 0,profits = [10, 20, 30],capital = [0, 0, 0]) == 60\n assert candidate(k = 2,w = 1,profits = [1, 2, 3],capital = [1, 1, 2]) == 6\n assert candidate(k = 1,w = 100,profits = [1000, 2000, 3000],capital = [1000, 2000, 3000]) == 100\n assert candidate(k = 3,w = 3,profits = [1, 2, 3, 4, 5],capital = [0, 1, 2, 3, 4]) == 15\n assert candidate(k = 2,w = 0,profits = [1, 2, 3],capital = [0, 1, 1]) == 4\n assert candidate(k = 10,w = 1,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 11\n assert candidate(k = 2,w = 3,profits = [5, 6, 4, 3, 2],capital = [2, 3, 4, 5, 6]) == 14\n assert candidate(k = 3,w = 2,profits = [5, 4, 3, 2, 1],capital = [5, 4, 3, 2, 1]) == 13\n assert candidate(k = 2,w = 5,profits = [100, 200, 300, 400, 500],capital = [0, 0, 0, 0, 0]) == 905\n assert candidate(k = 5,w = 20,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],capital = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == 3720\n assert candidate(k = 6,w = 1,profits = [1, 2, 3, 4, 5, 6, 7],capital = [0, 1, 2, 3, 4, 5, 6]) == 28\n assert candidate(k = 3,w = 0,profits = [10, 10, 10, 10, 10],capital = [0, 0, 0, 0, 0]) == 30\n assert candidate(k = 5,w = 100,profits = [10, 20, 30, 40, 50],capital = [10, 20, 30, 40, 50]) == 250\n assert candidate(k = 4,w = 0,profits = [100, 200, 300, 400, 500],capital = [0, 1, 2, 3, 4]) == 1300\n assert candidate(k = 1,w = 1,profits = [100, 200, 300, 400, 500],capital = [0, 0, 0, 0, 0]) == 501\n assert candidate(k = 10,w = 10000,profits = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000],capital = [0, 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000]) == 65000\n assert candidate(k = 4,w = 0,profits = [10, 20, 30, 40],capital = [0, 10, 20, 30]) == 100\n assert candidate(k = 20,w = 1000,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000],capital = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == 22000\n assert candidate(k = 3,w = 1,profits = [10, 20, 30, 40, 50],capital = [1, 2, 3, 4, 5]) == 101\n assert candidate(k = 5,w = 0,profits = [1, 10, 100, 1000, 10000],capital = [0, 0, 0, 0, 0]) == 11111\n assert candidate(k = 4,w = 10,profits = [100, 200, 300, 400],capital = [50, 50, 50, 50]) == 10\n assert candidate(k = 3,w = 50,profits = [100, 200, 300, 400, 500],capital = [50, 50, 50, 50, 50]) == 1250\n assert candidate(k = 5,w = 0,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],capital = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 4000\n assert candidate(k = 7,w = 50,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 540\n assert candidate(k = 7,w = 5,profits = [5, 10, 15, 20, 25, 30, 35, 40],capital = [0, 1, 2, 3, 4, 5, 6, 7]) == 180\n assert candidate(k = 10,w = 50000,profits = [10000, 20000, 30000, 40000, 50000, 60000, 70000, 80000, 90000, 100000],capital = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]) == 600000\n assert candidate(k = 3,w = 3,profits = [1, 1, 1, 1, 1],capital = [0, 1, 2, 3, 4]) == 6\n assert candidate(k = 10,w = 5,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 15\n assert candidate(k = 5,w = 5,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 405\n assert candidate(k = 1,w = 0,profits = [10000, 9000, 8000, 7000, 6000],capital = [0, 1000, 2000, 3000, 4000]) == 10000\n assert candidate(k = 4,w = 1500,profits = [500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500],capital = [1000, 1200, 1400, 1600, 1800, 2000, 2200, 2400, 2600]) == 15000\n assert candidate(k = 10,w = 1,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],capital = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 5501\n assert candidate(k = 5,w = 1,profits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],capital = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 1\n assert candidate(k = 5,w = 1,profits = [1, 2, 3, 4, 5],capital = [0, 1, 2, 3, 4]) == 16\n assert candidate(k = 10,w = 0,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 10\n assert candidate(k = 10,w = 100,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],capital = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 5600\n assert candidate(k = 7,w = 5,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 495\n assert candidate(k = 10,w = 5,profits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],capital = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 60\n assert candidate(k = 3,w = 10,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 280\n assert candidate(k = 3,w = 15,profits = [5, 10, 15, 20, 25],capital = [5, 10, 15, 20, 25]) == 75\n assert candidate(k = 3,w = 20,profits = [10, 10, 10, 10, 10],capital = [15, 15, 15, 15, 15]) == 50\n assert candidate(k = 5,w = 1000,profits = [5000, 1000, 2000, 1500, 3000, 4000, 6000, 7000, 8000, 9000],capital = [0, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500]) == 36000\n assert candidate(k = 15,w = 10,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],capital = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75]) == 1210\n assert candidate(k = 5,w = 0,profits = [500, 400, 300, 200, 100],capital = [100, 200, 300, 400, 500]) == 0\n assert candidate(k = 4,w = 10,profits = [5, 2, 10, 8, 1],capital = [3, 4, 1, 10, 5]) == 35\n assert candidate(k = 3,w = 1,profits = [5, 4, 3, 2, 1],capital = [0, 1, 2, 3, 4]) == 13\n assert candidate(k = 4,w = 2,profits = [1, 2, 3, 4, 5, 6, 7, 8],capital = [0, 1, 2, 3, 4, 5, 6, 7]) == 26\n assert candidate(k = 5,w = 10,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == 15\n assert candidate(k = 7,w = 0,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],capital = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == 0\n assert candidate(k = 3,w = 1000,profits = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],capital = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]) == 1100\n assert candidate(k = 3,w = 0,profits = [10, 20, 30, 40, 50],capital = [0, 0, 0, 0, 0]) == 120\n assert candidate(k = 3,w = 5,profits = [10, 15, 20, 25, 30],capital = [0, 0, 0, 0, 0]) == 80\n assert candidate(k = 3,w = 100,profits = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500],capital = [50, 50, 50, 50, 50, 50, 50, 50, 50, 50]) == 1450\n assert candidate(k = 1,w = 0,profits = [10000, 20000, 30000],capital = [10000, 20000, 30000]) == 0\n assert candidate(k = 5,w = 1000,profits = [500, 750, 1000, 1250, 1500],capital = [250, 500, 750, 1000, 1250]) == 6000\n assert candidate(k = 4,w = 10,profits = [5, 5, 5, 5, 5, 5],capital = [0, 0, 0, 0, 0, 0]) == 30\n assert candidate(k = 3,w = 20,profits = [100, 200, 300, 400, 500],capital = [10, 20, 30, 40, 50]) == 1120\n assert candidate(k = 10,w = 100,profits = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],capital = [0, 10, 20, 30, 40, 50, 60, 70, 80, 90]) == 375\n assert candidate(k = 10,w = 10,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 560\n assert candidate(k = 4,w = 10,profits = [5, 8, 7, 10, 9, 12],capital = [0, 5, 4, 9, 8, 10]) == 49\n assert candidate(k = 3,w = 10,profits = [50, 40, 30, 20, 10],capital = [5, 10, 15, 20, 25]) == 130\n assert candidate(k = 5,w = 20,profits = [100, 200, 300, 400, 500, 600],capital = [150, 250, 350, 450, 550, 650]) == 20\n assert candidate(k = 2,w = 0,profits = [5, 5, 5, 5, 5, 5],capital = [1, 2, 3, 4, 5, 6]) == 0\n assert candidate(k = 3,w = 5,profits = [1, 3, 2, 5, 4],capital = [0, 2, 3, 6, 4]) == 17\n assert candidate(k = 3,w = 10,profits = [5, 4, 3, 2, 1],capital = [10, 20, 30, 40, 50]) == 15\n assert candidate(k = 6,w = 5,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 11\n assert candidate(k = 7,w = 5,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [0, 5, 10, 15, 20, 25, 30, 35, 40, 45]) == 475\n assert candidate(k = 3,w = 5,profits = [6, 7, 8, 9, 10, 11],capital = [0, 1, 2, 3, 4, 5]) == 35\n assert candidate(k = 10,w = 0,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(k = 2,w = 100,profits = [50, 75, 25, 100, 125],capital = [0, 100, 50, 200, 150]) == 300\n assert candidate(k = 5,w = 5,profits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],capital = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 5\n assert candidate(k = 2,w = 3,profits = [1, 2, 3, 4, 5],capital = [2, 3, 4, 5, 6]) == 9\n assert candidate(k = 5,w = 100,profits = [10, 20, 30, 40, 50],capital = [50, 50, 50, 50, 50]) == 250\n assert candidate(k = 3,w = 50,profits = [100, 200, 300, 400, 500],capital = [50, 100, 150, 200, 250]) == 950\n assert candidate(k = 3,w = 0,profits = [100, 200, 300, 400, 500],capital = [50, 100, 150, 200, 250]) == 0\n assert candidate(k = 3,w = 10,profits = [100, 200, 300, 400, 500],capital = [0, 0, 0, 0, 0]) == 1210\n assert candidate(k = 2,w = 500,profits = [150, 250, 350, 450, 550],capital = [50, 150, 250, 350, 450]) == 1500\n assert candidate(k = 5,w = 10,profits = [5, 6, 7, 8, 9],capital = [2, 3, 4, 5, 6]) == 45\n assert candidate(k = 7,w = 2,profits = [1, 2, 3, 4, 5, 6, 7, 8],capital = [0, 1, 2, 3, 4, 5, 6, 7]) == 37\n assert candidate(k = 5,w = 0,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 5\n assert candidate(k = 6,w = 3,profits = [1, 2, 3, 4, 5, 6, 7],capital = [1, 2, 3, 4, 5, 6, 7]) == 30\n assert candidate(k = 3,w = 10,profits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],capital = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 37\n assert candidate(k = 5,w = 5,profits = [3, 4, 5, 1, 2],capital = [1, 2, 3, 4, 5]) == 20\n assert candidate(k = 3,w = 5,profits = [10, 20, 30, 40, 50],capital = [0, 1, 2, 3, 4]) == 125\n assert candidate(k = 5,w = 100,profits = [200, 300, 400, 500, 600],capital = [50, 100, 150, 200, 250]) == 2100\n assert candidate(k = 100,w = 0,profits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],capital = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 55\n assert candidate(k = 3,w = 20,profits = [10, 20, 30, 40, 50],capital = [5, 10, 15, 20, 25]) == 140\n assert candidate(k = 3,w = 1,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 4\n assert candidate(k = 1,w = 1000000000,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000]) == 1000000001\n assert candidate(k = 1,w = 100,profits = [1, 2, 3, 4, 5],capital = [0, 0, 0, 0, 0]) == 105\n assert candidate(k = 3,w = 5,profits = [2, 3, 5, 6, 8],capital = [1, 2, 3, 5, 6]) == 24\n assert candidate(k = 5,w = 0,profits = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50],capital = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == 0\n assert candidate(k = 5,w = 10,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == 15\n assert candidate(k = 2,w = 100,profits = [100, 200, 300, 400, 500],capital = [0, 0, 0, 0, 0]) == 1000\n assert candidate(k = 4,w = 2,profits = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],capital = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 12\n assert candidate(k = 3,w = 500,profits = [100, 200, 300, 400, 500, 600, 700, 800],capital = [0, 100, 200, 300, 400, 500, 600, 700]) == 2600\n assert candidate(k = 5,w = 10,profits = [100, 200, 300, 400, 500],capital = [1, 2, 3, 4, 5]) == 1510\n assert candidate(k = 2,w = 5,profits = [10, 15, 20, 25, 30],capital = [0, 5, 10, 15, 20]) == 50\n assert candidate(k = 5,w = 0,profits = [10, 20, 30, 40, 50],capital = [100, 50, 200, 300, 400]) == 0\n assert candidate(k = 2,w = 5,profits = [10, 10, 10, 10, 10],capital = [0, 0, 0, 0, 0]) == 25\n assert candidate(k = 5,w = 0,profits = [1, 2, 3, 4, 5, 6],capital = [0, 1, 1, 2, 2, 3]) == 19\n assert candidate(k = 5,w = 500,profits = [100, 200, 300, 400, 500],capital = [0, 0, 0, 0, 0]) == 2000\n assert candidate(k = 6,w = 10,profits = [1, 2, 3, 4, 5, 6],capital = [0, 2, 4, 6, 8, 10]) == 31\n assert candidate(k = 5,w = 3,profits = [10, 2, 11, 1, 4],capital = [3, 1, 5, 0, 2]) == 31\n assert candidate(k = 4,w = 0,profits = [100, 200, 300, 400],capital = [50, 150, 250, 350]) == 0\n assert candidate(k = 5,w = 50,profits = [10, 20, 30, 40, 50],capital = [10, 20, 30, 40, 50]) == 200\n assert candidate(k = 5,w = 50,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],capital = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == 450\n assert candidate(k = 4,w = 5,profits = [6, 7, 8, 9, 10],capital = [0, 5, 10, 15, 20]) == 39\n assert candidate(k = 5,w = 10,profits = [1, 3, 5, 7, 9],capital = [0, 2, 3, 5, 8]) == 35\n assert candidate(k = 3,w = 5,profits = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],capital = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 5\n assert candidate(k = 4,w = 10,profits = [10, 20, 30, 40, 50],capital = [0, 10, 20, 30, 40]) == 150\n assert candidate(k = 3,w = 10,profits = [15, 25, 35, 45, 55, 65, 75, 85, 95],capital = [0, 0, 0, 0, 0, 0, 0, 0, 0]) == 265\n assert candidate(k = 2,w = 1000,profits = [1000, 1000, 1000, 1000, 1000],capital = [0, 100, 200, 300, 400]) == 3000\n assert candidate(k = 4,w = 1,profits = [4, 5, 6, 7, 8, 9],capital = [2, 3, 4, 5, 6, 7]) == 1\n assert candidate(k = 4,w = 10,profits = [1, 5, 7, 10, 12],capital = [3, 7, 10, 14, 17]) == 44\n assert candidate(k = 5,w = 100,profits = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150],capital = [50, 40, 30, 20, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 750\n assert candidate(k = 3,w = 1000,profits = [300, 500, 700, 100, 200, 400, 600, 800],capital = [0, 500, 1000, 1500, 2000, 2500, 3000, 3500]) == 2500\n assert candidate(k = 4,w = 1000,profits = [900, 800, 700, 600, 500],capital = [500, 600, 700, 800, 900]) == 4000\n assert candidate(k = 3,w = 0,profits = [10, 20, 30, 40, 50],capital = [1, 2, 3, 4, 5]) == 0\n assert candidate(k = 15,w = 500,profits = [50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750],capital = [200, 150, 100, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 6500\n assert candidate(k = 2,w = 5,profits = [10, 20, 30, 40, 50],capital = [1, 2, 3, 4, 5]) == 95\n assert candidate(k = 5,w = 10,profits = [10, 20, 30, 40, 50],capital = [5, 15, 25, 35, 45]) == 160\n"}, "metadata": {"canonical_parameter_names": ["k", "w", "profits", "capital"], "leetcode_dataset_entry_point": "Solution().findMaximizedCapital", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMaximizedCapital = function(k, w, profits, capital) {", "container": null, "callable": "findMaximizedCapital", "parameters": [{"name": "k", "type": "number"}, {"name": "w", "type": "number"}, {"name": "profits", "type": "number[]"}, {"name": "capital", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 503, "task_id": "next-greater-element-ii", "difficulty": "Medium", "problem_description": "Given a circular integer array nums (i.e., the next element of nums[nums.length - 1] is nums[0]), return the next greater number for every element in nums.\nThe next greater number of a number x is the first greater number to its traversing-order next in the array, which means you could search circularly to find its next greater number. If it doesn't exist, return -1 for this number.\n \nExample 1:\n\nInput: nums = [1,2,1]\nOutput: [2,-1,2]\nExplanation: The first 1's next greater number is 2; \nThe number 2 can't find next greater number. \nThe second 1's next greater number needs to search circularly, which is also 2.\n\nExample 2:\n\nInput: nums = [1,2,3,4,3]\nOutput: [2,3,4,-1,4]\n\n \nConstraints:\n\n1 <= nums.length <= 104\n-109 <= nums[i] <= 109\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [5, 4, 3, 2, 1]) == [-1, 5, 5, 5, 5]\n assert candidate(nums = [1]) == [-1]\n assert candidate(nums = [3, 10, 4, 3, 2, 1, 5]) == [10, -1, 5, 5, 5, 5, 10]\n assert candidate(nums = [10, 5, 7, 3, 6, 2]) == [-1, 7, 10, 6, 10, 10]\n assert candidate(nums = [1, 5, 4, 3, 2, 6]) == [5, 6, 6, 6, 6, -1]\n assert candidate(nums = [7, 8, 9, 10, 1, 2, 3, 4, 5, 6]) == [8, 9, 10, -1, 2, 3, 4, 5, 6, 7]\n assert candidate(nums = [1, 1, 1, 1, 1]) == [-1, -1, -1, -1, -1]\n assert candidate(nums = [3, 8, 4, 1, 2]) == [8, -1, 8, 2, 3]\n assert candidate(nums = [10, 5, 15, 20, 25, 5, 10]) == [15, 15, 20, 25, -1, 10, 15]\n assert candidate(nums = [1, 2, 3, 4, 5]) == [2, 3, 4, 5, -1]\n assert candidate(nums = [5, 1, 2, 3, 4]) == [-1, 2, 3, 4, 5]\n assert candidate(nums = [3, 1, 2]) == [-1, 2, 3]\n assert candidate(nums = [1, 2, 1]) == [2, -1, 2]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, 10, 10, 10, 10, 10, 10, 10, 10, 10]\n assert candidate(nums = [1, 5, 4, 3, 2]) == [5, -1, 5, 5, 5]\n assert candidate(nums = [1, 2, 3, 4, 3]) == [2, 3, 4, -1, 4]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, -1]\n assert candidate(nums = [1, 10, 100, 1000, 10000, 1, 10, 100, 1000, 10000, 1, 10, 100, 1000, 10000]) == [10, 100, 1000, 10000, -1, 10, 100, 1000, 10000, -1, 10, 100, 1000, 10000, -1]\n assert candidate(nums = [5, 4, 3, 2, 1, 10]) == [10, 10, 10, 10, 10, -1]\n assert candidate(nums = [5, 1, 4, 3, 2, 8, 6, 7, 10, 9, 11, 12]) == [8, 4, 8, 8, 8, 10, 7, 10, 11, 11, 12, -1]\n assert candidate(nums = [3, 8, 4, 12, 5, 10, 6, 7, 1, 2]) == [8, 12, 12, -1, 10, 12, 7, 8, 2, 3]\n assert candidate(nums = [1, 2, 3, 2, 1, 1, 2, 3, 2, 1]) == [2, 3, -1, 3, 2, 2, 3, -1, 3, 2]\n assert candidate(nums = [5, 4, 3, 2, 1, 6, 7, 8, 9, 10, 1]) == [6, 6, 6, 6, 6, 7, 8, 9, 10, -1, 5]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 2]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1]\n assert candidate(nums = [3, 3, 3, 3, 3, 1, 2, 1, 2, 1, 2]) == [-1, -1, -1, -1, -1, 2, 3, 2, 3, 2, 3]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(nums = [3, 8, 4, 12, 5, 10, 6, 7]) == [8, 12, 12, -1, 10, 12, 7, 8]\n assert candidate(nums = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [-1, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15]\n assert candidate(nums = [7, 6, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1]) == [-1, 7, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, 7, -1, -1, 7, 7, 7, 7, 7, 7]\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1]) == [2, 3, 4, 5, -1, 2, 3, 4, 5, -1, 2, 3, 4, 5, -1, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5]) == [2, 3, 4, 5, -1, 2, 3, 4, 5, -1]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]\n assert candidate(nums = [8, 7, 6, 5, 4, 3, 2, 1, 9, 0]) == [9, 9, 9, 9, 9, 9, 9, 9, -1, 8]\n assert candidate(nums = [5, 7, 1, 2, 6, 4, 5, 9, 1, 2]) == [7, 9, 2, 6, 9, 5, 9, -1, 2, 5]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 110]) == [110, 110, 110, 110, 110, 110, 110, 110, 110, 110, -1]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 20]) == [-1, 20, 20, 20, 20, 20, 20, 20, 20, 20, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [2, 3, 4, 5, 9, 9, 9, 9, 9, 9, -1, 9, 9, 9, 9, 5, 4, 3, 2, 1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 10, 9, 8, 7, 6, 5, 4, 3, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, -1, 2]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10]) == [-1, 10, 10, 10, 10, 10, 10, 10, 10, 10, -1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 1]) == [3, 5, 7, 9, 11, 13, 15, 17, 19, -1, 3]\n assert candidate(nums = [2, 3, 1, 5, 4, 8, 7, 6, 9, 10, 11, 12, 13, 14, 1]) == [3, 5, 5, 8, 8, 9, 9, 9, 10, 11, 12, 13, 14, -1, 2]\n assert candidate(nums = [73, 74, 75, 71, 69, 72, 76, 73]) == [74, 75, 76, 72, 72, 76, -1, 74]\n assert candidate(nums = [10, 5, 2, 6, 10, 3, 4, 8, 1, 9]) == [-1, 6, 6, 10, -1, 4, 8, 9, 9, 10]\n assert candidate(nums = [1, 3, 2, 4, 3, 5, 4, 6, 5, 7]) == [3, 4, 4, 5, 5, 6, 6, 7, 7, -1]\n assert candidate(nums = [8, 7, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, 8, 8, 8, 8, 8, 8, 8, -1, 8, 8, 8, 8, 8, 8, 8, -1, 8, 8, 8, 8, 8, 8, 8, -1, 8, 8, 8, 8, 8, 8, 8]\n assert candidate(nums = [4, 2, 5, 1, 2, 3, 6, 4, 7]) == [5, 5, 6, 2, 3, 6, 7, 7, -1]\n assert candidate(nums = [3, 3, 2, 2, 1, 6, 5, 4, 3, 2, 1, 6]) == [6, 6, 6, 6, 6, -1, 6, 6, 6, 6, 6, -1]\n assert candidate(nums = [1, 1, 2, 3, 3, 2, 2, 3, 1, 1]) == [2, 2, 3, -1, -1, 3, 3, -1, 2, 2]\n assert candidate(nums = [1, 2, 3, 4, 5, 5, 5, 5, 5, 1, 2, 3, 4, 5]) == [2, 3, 4, 5, -1, -1, -1, -1, -1, 2, 3, 4, 5, -1]\n assert candidate(nums = [1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000, 1000000000, -1000000000]) == [-1, 1000000000, -1, 1000000000, -1, 1000000000, -1, 1000000000, -1, 1000000000]\n assert candidate(nums = [1, 2, 1, 3, 4, 3, 2, 4, 5, 6, 5, 4, 6, 5, 7, 8, 9, 0]) == [2, 3, 3, 4, 5, 4, 4, 5, 6, 7, 6, 6, 7, 7, 8, 9, -1, 1]\n assert candidate(nums = [5, 3, 2, 1, 4, 5, 6, 7, 8, 9]) == [6, 4, 4, 4, 5, 6, 7, 8, 9, -1]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == [2, 3, 4, -1, 4, 3, 2, 3, 4, -1, 4, 3, 2, 3, 4, -1, 4, 3, 2]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5]) == [2, 2, 3, 3, 4, 4, 5, 5, -1, -1]\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]) == [-1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [1, 10, 11, 1, 10, 11, 1]) == [10, 11, -1, 10, 11, -1, 10]\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]) == [2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, -1, -1]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == [3, 5, 7, 9, 11, 13, 15, 17, 19, -1]\n assert candidate(nums = [5, 5, 4, 4, 3, 3, 2, 2, 1, 1]) == [-1, -1, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5]) == [-1, 5, 4, 3, 2, 1, 2, 3, 4, 5, -1, 5, 4, 3, 2, 1, 2, 3, 4, 5, -1]\n assert candidate(nums = [2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 2]) == [3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1, 3]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 10]) == [10, 10, 10, 10, 10, 10, 10, 10, 10, -1]\n assert candidate(nums = [3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4]) == [4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1]\n assert candidate(nums = [1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11, 13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 25, 27, 26, 28, 30, 29, 31, 33, 32, 34, 36, 35, 37, 39, 38, 40, 42, 41, 43, 45, 44, 46, 48, 47, 49, 50]) == [3, 4, 4, 6, 7, 7, 9, 10, 10, 12, 13, 13, 15, 16, 16, 18, 19, 19, 21, 22, 22, 24, 25, 25, 27, 28, 28, 30, 31, 31, 33, 34, 34, 36, 37, 37, 39, 40, 40, 42, 43, 43, 45, 46, 46, 48, 49, 49, 50, -1]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(nums = [9, 0, 1, 2, 3, 4, 5, 6, 7, 8]) == [-1, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 12, 13]) == [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 13, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 3, 4, 5, 6, 7, 8, 9, 10, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1]\n assert candidate(nums = [7, 1, 5, 2, 6, 3, 4, 8, 9, 0]) == [8, 5, 6, 6, 8, 4, 8, 9, -1, 7]\n assert candidate(nums = [3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 2, 1]) == [4, 2, 4, 5, 6, 7, 8, 9, 10, -1, 3, 3]\n assert candidate(nums = [5, 5, 5, 5, 5, 1, 2, 3, 4, 5, 5, 5, 5, 5]) == [-1, -1, -1, -1, -1, 2, 3, 4, 5, -1, -1, -1, -1, -1]\n assert candidate(nums = [5, 4, 3, 2, 1, 6, 7, 8, 9, 10]) == [6, 6, 6, 6, 6, 7, 8, 9, 10, -1]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == [-1, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, -1, -1, 9, 9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums = [5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5]) == [-1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 9]) == [10, 9, 8, 7, 6, 5, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, -1, 10]\n assert candidate(nums = [1, 3, 2, 1, 3, 2, 1, 3, 2, 1]) == [3, -1, 3, 3, -1, 3, 3, -1, 3, 3]\n assert candidate(nums = [3, 1, 2, 4, 3, 1, 2, 4, 3, 1]) == [4, 2, 4, -1, 4, 2, 4, -1, 4, 3]\n assert candidate(nums = [3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2]) == [-1, -1, -1, -1, 2, 2, 2, 2, 3, 3, 3, 3]\n assert candidate(nums = [3, 8, 4, 1, 2, 7, 5, 6, 10, 9]) == [8, 10, 7, 2, 7, 10, 6, 10, -1, 10]\n assert candidate(nums = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [-1, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100]\n assert candidate(nums = [1, 3, 2, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5, 6]) == [3, 4, 4, 5, 6, 5, 4, 3, 2, 2, 3, 4, 5, 6, -1]\n assert candidate(nums = [10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5]) == [-1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10, -1, 10]\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]) == [20, 30, 40, 50, 60, 70, 80, 90, 100, -1]\n assert candidate(nums = [0, 1, 0, 2, 0, 3, 0, 4, 0, 5]) == [1, 2, 2, 3, 3, 4, 4, 5, 5, -1]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 100]) == [-1, 100, 100, 100, 100, 100, 100, 100, 100, 100, -1]\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, -1]\n assert candidate(nums = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21]) == [21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -1]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == [-1, 9, 9, 9, 9, 9, 9, 9, 9, 9]\n assert candidate(nums = [1, 3, 2, 4, 6, 5, 7, 9, 8, 10]) == [3, 4, 4, 6, 7, 7, 9, 10, 10, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 2, 3, 4, 5, 6, 7, 8, 9, 10, -1]\n assert candidate(nums = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11]) == [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -1]\n assert candidate(nums = [3, 8, 4, 12, 5, 10, 6, 7, 9, 2, 1, 11]) == [8, 12, 12, -1, 10, 11, 7, 9, 11, 11, 11, 12]\n assert candidate(nums = [7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8]) == [8, 9, 10, -1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(nums = [1, 2, 2, 1, 2, 1, 2, 1, 2, 1]) == [2, -1, -1, 2, -1, 2, -1, 2, -1, 2]\n assert candidate(nums = [1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3]) == [2, 3, -1, 3, 2, 3, -1, 3, 2, 3, -1, 3, 2, 3, -1]\n assert candidate(nums = [9, 7, 5, 3, 1, 2, 4, 6, 8, 10]) == [10, 8, 6, 4, 2, 4, 6, 8, 10, -1]\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == [-1, 100, 100, 100, 100, 100, 100, 100, 100, 100]\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(nums = [1, 3, 2, 4, 5, 1, 3, 2, 4, 5]) == [3, 4, 4, 5, -1, 3, 4, 4, 5, -1]\n assert candidate(nums = [9, 8, 7, 6, 5, 4, 3, 2, 1, 9]) == [-1, 9, 9, 9, 9, 9, 9, 9, 9, -1]\n assert candidate(nums = [3, 8, 4, 1, 2, 7, 6, 5, 1, 4, 9]) == [8, 9, 7, 2, 7, 9, 9, 9, 4, 9, -1]\n assert candidate(nums = [1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 1]) == [2, 3, 4, -1, 4, 3, 2, 3, 4, -1, 4, 3, 2]\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == [3, 5, 7, 9, 11, 13, 15, 17, 19, -1, 19, 17, 15, 13, 11, 9, 7, 5, 3]\n assert candidate(nums = [1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == [3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1]\n assert candidate(nums = [3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4]) == [4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1, 4, 2, 4, -1]\n assert candidate(nums = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]\n assert candidate(nums = [1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 2, 3, 4, 5]) == [2, 3, 4, 5, -1, 5, 4, 3, 2, 2, 3, 4, 5, -1]\n assert candidate(nums = [5, 4, 3, 2, 1, 2, 3, 4, 5]) == [-1, 5, 4, 3, 2, 3, 4, 5, -1]\n assert candidate(nums = [3, 1, 2, 4, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15]) == [4, 2, 4, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, -1, 16]\n assert candidate(nums = [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]) == [-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, -1]\n assert candidate(nums = [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]) == [2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1]\n assert candidate(nums = [5, 4, 3, 2, 1, 10, 9, 8, 7, 6]) == [10, 10, 10, 10, 10, -1, 10, 10, 10, 10]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, -1, 2, 3, 4, 5, 6]\n assert candidate(nums = [19, 17, 15, 13, 11, 9, 7, 5, 3, 1]) == [-1, 19, 19, 19, 19, 19, 19, 19, 19, 19]\n assert candidate(nums = [10, 20, 30, 40, 50, 15, 25, 35, 45, 55, 5, 1, 6, 11, 16, 21, 26, 31, 36, 41, 46]) == [20, 30, 40, 50, 55, 25, 35, 45, 55, -1, 6, 6, 11, 16, 21, 26, 31, 36, 41, 46, 50]\n assert candidate(nums = [5, 5, 5, 5, 5, 1, 2, 3, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 1, 2, 3, 4, 5]) == [6, 6, 6, 6, 6, 2, 3, 4, 5, 6, 6, 6, 6, 6, -1, -1, -1, -1, -1, 2, 3, 4, 5, 6]\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1]) == [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, -1, 2]\n assert candidate(nums = [1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]) == [2, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2]\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().nextGreaterElements", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var nextGreaterElements = function(nums) {", "container": null, "callable": "nextGreaterElements", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 504, "task_id": "base-7", "difficulty": "Easy", "problem_description": "Given an integer num, return a string of its base 7 representation.\n \nExample 1:\nInput: num = 100\nOutput: \"202\"\nExample 2:\nInput: num = -7\nOutput: \"-10\"\n\n \nConstraints:\n\n-107 <= num <= 107\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = -1000000) == \"-11333311\"\n assert candidate(num = 49) == \"100\"\n assert candidate(num = 165) == \"324\"\n assert candidate(num = -10000000) == \"-150666343\"\n assert candidate(num = 0) == \"0\"\n assert candidate(num = 10000000) == \"150666343\"\n assert candidate(num = 16807) == \"100000\"\n assert candidate(num = 100) == \"202\"\n assert candidate(num = -7) == \"-10\"\n assert candidate(num = 16) == \"22\"\n assert candidate(num = 500000) == \"4151504\"\n assert candidate(num = -40353607) == \"-1000000000\"\n assert candidate(num = 1234567) == \"13331215\"\n assert candidate(num = -9999999) == \"-150666342\"\n assert candidate(num = -4826464) == \"-56011216\"\n assert candidate(num = -9876543) == \"-146643405\"\n assert candidate(num = 823543) == \"10000000\"\n assert candidate(num = -5764801) == \"-100000000\"\n assert candidate(num = -987654) == \"-11252313\"\n assert candidate(num = -500000) == \"-4151504\"\n assert candidate(num = -1) == \"-1\"\n assert candidate(num = 117649) == \"1000000\"\n assert candidate(num = 40353607) == \"1000000000\"\n assert candidate(num = -2401) == \"-10000\"\n assert candidate(num = 5764801) == \"100000000\"\n assert candidate(num = -117649) == \"-1000000\"\n assert candidate(num = -16807) == \"-100000\"\n assert candidate(num = -1234567) == \"-13331215\"\n assert candidate(num = -343) == \"-1000\"\n assert candidate(num = 2401) == \"10000\"\n assert candidate(num = 1049600) == \"11631026\"\n assert candidate(num = 7) == \"10\"\n assert candidate(num = -823543) == \"-10000000\"\n assert candidate(num = 9999999) == \"150666342\"\n assert candidate(num = 1) == \"1\"\n assert candidate(num = 6827346) == \"112013541\"\n assert candidate(num = 343) == \"1000\"\n assert candidate(num = 9876543) == \"146643405\"\n assert candidate(num = -282475249) == \"-10000000000\"\n assert candidate(num = -49) == \"-100\"\n assert candidate(num = 1000000) == \"11333311\"\n assert candidate(num = 4826464) == \"56011216\"\n assert candidate(num = 282475249) == \"10000000000\"\n assert candidate(num = -64) == \"-121\"\n assert candidate(num = 64) == \"121\"\n assert candidate(num = 117648) == \"666666\"\n assert candidate(num = -6827346) == \"-112013541\"\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().convertToBase7", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var convertToBase7 = function(num) {", "container": null, "callable": "convertToBase7", "parameters": [{"name": "num", "type": "number"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 506, "task_id": "relative-ranks", "difficulty": "Easy", "problem_description": "You are given an integer array score of size n, where score[i] is the score of the ith athlete in a competition. All the scores are guaranteed to be unique.\nThe athletes are placed based on their scores, where the 1st place athlete has the highest score, the 2nd place athlete has the 2nd highest score, and so on. The placement of each athlete determines their rank:\n\nThe 1st place athlete's rank is \"Gold Medal\".\nThe 2nd place athlete's rank is \"Silver Medal\".\nThe 3rd place athlete's rank is \"Bronze Medal\".\nFor the 4th place to the nth place athlete, their rank is their placement number (i.e., the xth place athlete's rank is \"x\").\n\nReturn an array answer of size n where answer[i] is the rank of the ith athlete.\n \nExample 1:\n\nInput: score = [5,4,3,2,1]\nOutput: [\"Gold Medal\",\"Silver Medal\",\"Bronze Medal\",\"4\",\"5\"]\nExplanation: The placements are [1st, 2nd, 3rd, 4th, 5th].\nExample 2:\n\nInput: score = [10,3,8,9,4]\nOutput: [\"Gold Medal\",\"5\",\"Bronze Medal\",\"Silver Medal\",\"4\"]\nExplanation: The placements are [1st, 5th, 3rd, 2nd, 4th].\n\n\n \nConstraints:\n\nn == score.length\n1 <= n <= 104\n0 <= score[i] <= 106\nAll the values in score are unique.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(score = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10']\n assert candidate(score = [5, 4, 3, 2, 1]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5']\n assert candidate(score = [0, 1000000]) == ['Silver Medal', 'Gold Medal']\n assert candidate(score = [100, 90, 95, 80, 75]) == ['Gold Medal', 'Bronze Medal', 'Silver Medal', '4', '5']\n assert candidate(score = [10, 3, 8, 9, 4]) == ['Gold Medal', '5', 'Bronze Medal', 'Silver Medal', '4']\n assert candidate(score = [100]) == ['Gold Medal']\n assert candidate(score = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == ['10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [40, 10, 30, 20]) == ['Gold Medal', '4', 'Silver Medal', 'Bronze Medal']\n assert candidate(score = [42]) == ['Gold Medal']\n assert candidate(score = [20, 10, 30, 50, 40]) == ['4', '5', 'Bronze Medal', 'Gold Medal', 'Silver Medal']\n assert candidate(score = [40, 10, 20, 30]) == ['Gold Medal', '4', 'Bronze Medal', 'Silver Medal']\n assert candidate(score = [1000000, 0, 500000, 250000, 750000]) == ['Gold Medal', '5', 'Bronze Medal', '4', 'Silver Medal']\n assert candidate(score = [33, 27, 22, 15, 6]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5']\n assert candidate(score = [1]) == ['Gold Medal']\n assert candidate(score = [1, 2, 3, 4, 5]) == ['5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [5, 20, 15, 10, 25]) == ['5', 'Silver Medal', 'Bronze Medal', '4', 'Gold Medal']\n assert candidate(score = [3, 1, 2]) == ['Gold Medal', 'Bronze Medal', 'Silver Medal']\n assert candidate(score = [3, 1, 2, 5, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == ['13', '15', '14', '11', '12', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [34, 7, 23, 32, 5, 62]) == ['Silver Medal', '5', '4', 'Bronze Medal', '6', 'Gold Medal']\n assert candidate(score = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', '30', '31', '32', '33', '34', '35', '36', '37', '38', '39', '40', '41', '42', '43', '44', '45', '46', '47', '48', '49', '50', '51', '52', '53', '54', '55', '56', '57', '58', '59', '60', '61', '62', '63', '64', '65', '66', '67', '68', '69', '70', '71', '72', '73', '74', '75', '76', '77', '78', '79', '80', '81', '82', '83', '84', '85', '86', '87', '88', '89', '90', '91', '92', '93', '94', '95', '96', '97', '98', '99', '100']\n assert candidate(score = [123, 456, 789, 101112, 131415, 161718, 192021, 222324, 252627, 282930]) == ['10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [50, 20, 30, 10, 40, 60]) == ['Silver Medal', '5', '4', '6', 'Bronze Medal', 'Gold Medal']\n assert candidate(score = [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22']\n assert candidate(score = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29]) == ['15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1000000, 999999, 999998, 999997, 999996]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5']\n assert candidate(score = [789, 654, 321, 987, 456, 123, 890, 567, 234]) == ['Bronze Medal', '4', '7', 'Gold Medal', '6', '9', 'Silver Medal', '5', '8']\n assert candidate(score = [12345, 12346, 12347, 12348, 12349, 12350, 12351, 12352, 12353, 12354]) == ['10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105]) == ['15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [100, 90, 95, 85, 70, 60, 50, 40, 30, 20, 10]) == ['Gold Medal', 'Bronze Medal', 'Silver Medal', '4', '5', '6', '7', '8', '9', '10', '11']\n assert candidate(score = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000]) == ['20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [23, 34, 12, 45, 56, 78, 89, 90, 101, 112, 134, 145, 156, 167, 178]) == ['14', '13', '15', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [8, 6, 7, 5, 3, 0, 9, 10, 12, 14, 13, 11, 15, 17, 16, 18, 20, 19, 21, 23, 22, 24, 26, 25, 27, 29, 28, 30]) == ['23', '25', '24', '26', '27', '28', '22', '21', '19', '17', '18', '20', '16', '14', '15', '13', '11', '12', '10', '8', '9', '7', '5', '6', '4', 'Silver Medal', 'Bronze Medal', 'Gold Medal']\n assert candidate(score = [33, 11, 44, 22, 55, 66, 77, 88, 99, 100]) == ['8', '10', '7', '9', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]) == ['100', '99', '98', '97', '96', '95', '94', '93', '92', '91', '90', '89', '88', '87', '86', '85', '84', '83', '82', '81', '80', '79', '78', '77', '76', '75', '74', '73', '72', '71', '70', '69', '68', '67', '66', '65', '64', '63', '62', '61', '60', '59', '58', '57', '56', '55', '54', '53', '52', '51', '50', '49', '48', '47', '46', '45', '44', '43', '42', '41', '40', '39', '38', '37', '36', '35', '34', '33', '32', '31', '30', '29', '28', '27', '26', '25', '24', '23', '22', '21', '20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [3456, 1234, 7890, 4567, 8901, 2345, 5678]) == ['5', '7', 'Silver Medal', '4', 'Gold Medal', '6', 'Bronze Medal']\n assert candidate(score = [54321, 65432, 76543, 87654, 98765, 43210, 32109, 21098, 10987, 9876, 8765, 7654, 6543, 5432, 4321, 3210, 2109, 1098, 987, 876, 765, 654, 543, 432, 321, 210, 109, 98, 87, 76, 65, 54, 43, 32, 21, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == ['5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', '30', '31', '32', '33', '34', '35', '36', '37', '38', '39', '40', '41', '42', '43', '44', '45']\n assert candidate(score = [9999, 8888, 7777, 6666, 5555, 4444, 3333, 2222, 1111, 0]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10']\n assert candidate(score = [1, 10, 100, 1000, 10000, 100000, 1000000, 999999, 99999, 9999, 999, 99, 9]) == ['13', '11', '9', '7', '5', 'Bronze Medal', 'Gold Medal', 'Silver Medal', '4', '6', '8', '10', '12']\n assert candidate(score = [100000, 1, 10000, 1000, 100, 10, 0]) == ['Gold Medal', '6', 'Silver Medal', 'Bronze Medal', '4', '5', '7']\n assert candidate(score = [5, 20, 15, 10, 25, 30, 35, 40, 45, 50]) == ['10', '7', '8', '9', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300]) == ['30', '29', '28', '27', '26', '25', '24', '23', '22', '21', '20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [42, 23, 35, 56, 78, 89, 12, 34, 56, 78, 90, 101, 112, 134, 145]) == ['11', '14', '12', '9', '7', '6', '15', '13', '10', '8', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1000000, 999999, 999998, 999997, 999996, 999995, 999994, 999993, 999992, 999991]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10']\n assert candidate(score = [5, 15, 25, 35, 45, 55, 65, 75, 85, 95, 105, 115, 125, 135, 145]) == ['15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630]) == ['15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17']\n assert candidate(score = [1000000, 0, 500000, 250000, 750000, 125000]) == ['Gold Medal', '6', 'Bronze Medal', '4', 'Silver Medal', '5']\n assert candidate(score = [23, 15, 45, 67, 89, 12, 34]) == ['5', '6', 'Bronze Medal', 'Silver Medal', 'Gold Medal', '7', '4']\n assert candidate(score = [999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 100000, 100001, 100002, 100003, 100004, 100005, 100006, 100007, 100008, 100009, 100010]) == ['30', '29', '28', '27', '26', '25', '24', '23', '22', '21', '20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [99, 34, 23, 44, 55, 12, 67, 89, 100]) == ['Silver Medal', '7', '8', '6', '5', '9', '4', 'Bronze Medal', 'Gold Medal']\n assert candidate(score = [300, 290, 280, 270, 260, 250, 240, 230, 220, 210, 200, 190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', '30']\n assert candidate(score = [5, 999, 1000, 9999, 10000, 99999, 100000, 999999, 1000000]) == ['9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]) == ['20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1, 1000, 10, 100, 10000]) == ['5', 'Silver Medal', '4', 'Bronze Medal', 'Gold Medal']\n assert candidate(score = [88, 77, 66, 55, 44, 33, 22, 11]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8']\n assert candidate(score = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]) == ['7', '10', '6', '11', 'Bronze Medal', 'Gold Medal', '9', 'Silver Medal', '4', '8', '5']\n assert candidate(score = [30, 40, 20, 10, 50, 60, 70, 80, 90, 100]) == ['8', '7', '9', '10', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [5]) == ['Gold Medal']\n assert candidate(score = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000]) == ['20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [123, 456, 789, 101, 202, 303, 404, 505, 606, 707, 808, 909]) == ['11', '7', 'Bronze Medal', '12', '10', '9', '8', '6', '5', '4', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150]) == ['15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [85, 67, 92, 78, 99, 56, 88, 77, 100, 95]) == ['6', '9', '4', '7', 'Silver Medal', '10', '5', '8', 'Gold Medal', 'Bronze Medal']\n assert candidate(score = [1, 3, 6, 9, 12, 15, 18, 21, 24, 27]) == ['10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [23, 45, 12, 67, 34, 89, 90, 11, 2, 3, 5, 7, 9, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99]) == ['42', '30', '48', '19', '36', '7', '6', '49', '54', '53', '52', '51', '50', '47', '46', '45', '44', '43', '41', '40', '39', '38', '37', '35', '34', '33', '32', '31', '29', '28', '27', '26', '25', '24', '23', '22', '21', '20', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1000000, 0, 500000, 250000, 750000]) == ['Gold Medal', '5', 'Bronze Medal', '4', 'Silver Medal']\n assert candidate(score = [88, 1, 56, 91, 67, 29, 42, 74, 35, 81, 100, 23, 64, 50, 79, 38, 95, 47, 61, 85]) == ['4', '20', '12', 'Bronze Medal', '9', '18', '15', '8', '17', '6', 'Gold Medal', '19', '10', '13', '7', '16', 'Silver Medal', '14', '11', '5']\n assert candidate(score = [100000, 50000, 25000, 12500, 6250, 3125, 1562, 781, 390, 195]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10']\n assert candidate(score = [1, 1000000, 500000, 250000, 750000, 100000, 600000, 300000, 800000, 400000, 900000]) == ['11', 'Gold Medal', '6', '9', '4', '10', '5', '8', 'Bronze Medal', '7', 'Silver Medal']\n assert candidate(score = [1, 10000, 1000, 100, 10, 100000, 1000000]) == ['7', 'Bronze Medal', '4', '5', '6', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10']\n assert candidate(score = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200]) == ['20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1, 100, 1000, 10000, 100000]) == ['5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 999999999, 99999999, 9999999, 999999, 99999, 9999, 999, 99, 9]) == ['19', '17', '15', '13', '11', '9', '7', '5', 'Bronze Medal', 'Gold Medal', 'Silver Medal', '4', '6', '8', '10', '12', '14', '16', '18']\n assert candidate(score = [8, 1, 3, 7, 4, 6, 5, 2]) == ['Gold Medal', '8', '6', 'Silver Medal', '5', 'Bronze Medal', '4', '7']\n assert candidate(score = [78, 56, 34, 12, 90, 67, 45, 23, 89, 10]) == ['Bronze Medal', '5', '7', '9', 'Gold Medal', '4', '6', '8', 'Silver Medal', '10']\n assert candidate(score = [9, 3, 15, 12, 6, 24, 18, 30, 27, 21]) == ['8', '10', '6', '7', '9', 'Bronze Medal', '5', 'Gold Medal', 'Silver Medal', '4']\n assert candidate(score = [7, 6, 5, 4, 3, 2, 1, 0]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8']\n assert candidate(score = [87, 68, 94, 78, 85, 91, 89, 76, 82, 93]) == ['5', '10', 'Gold Medal', '8', '6', 'Bronze Medal', '4', '9', '7', 'Silver Medal']\n assert candidate(score = [100, 200, 150, 300, 250, 400, 350, 500, 450, 600, 550, 700, 650, 800, 750, 900, 850, 1000, 950, 1100, 1050]) == ['21', '19', '20', '17', '18', '15', '16', '13', '14', '11', '12', '9', '10', '7', '8', '5', '6', 'Bronze Medal', '4', 'Gold Medal', 'Silver Medal']\n assert candidate(score = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210]) == ['20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [100000, 90000, 80000, 70000, 60000, 50000, 40000, 30000, 20000, 10000]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10']\n assert candidate(score = [20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == ['Gold Medal', 'Silver Medal', 'Bronze Medal', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20']\n assert candidate(score = [999999, 0, 500000, 250000, 750000, 100000]) == ['Gold Medal', '6', 'Bronze Medal', '4', 'Silver Medal', '5']\n assert candidate(score = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000]) == ['10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [987, 654, 321, 123, 456, 789, 111, 222, 333, 444, 555, 666, 777, 888, 999]) == ['Silver Medal', '7', '12', '14', '9', '4', '15', '13', '11', '10', '8', '6', '5', 'Bronze Medal', 'Gold Medal']\n assert candidate(score = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000, 21000, 22000, 23000, 24000, 25000, 26000, 27000, 28000, 29000, 30000, 31000, 32000, 33000, 34000, 35000, 36000, 37000, 38000, 39000, 40000, 41000, 42000, 43000, 44000, 45000, 46000, 47000, 48000, 49000, 50000]) == ['50', '49', '48', '47', '46', '45', '44', '43', '42', '41', '40', '39', '38', '37', '36', '35', '34', '33', '32', '31', '30', '29', '28', '27', '26', '25', '24', '23', '22', '21', '20', '19', '18', '17', '16', '15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [50, 20, 30, 10, 40]) == ['Gold Medal', '4', 'Bronze Medal', '5', 'Silver Medal']\n assert candidate(score = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500]) == ['15', '14', '13', '12', '11', '10', '9', '8', '7', '6', '5', '4', 'Bronze Medal', 'Silver Medal', 'Gold Medal']\n assert candidate(score = [42, 24, 66, 100, 35, 90, 28, 72, 55, 88]) == ['7', '10', '5', 'Gold Medal', '8', 'Silver Medal', '9', '4', '6', 'Bronze Medal']\n"}, "metadata": {"canonical_parameter_names": ["score"], "leetcode_dataset_entry_point": "Solution().findRelativeRanks", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findRelativeRanks = function(score) {", "container": null, "callable": "findRelativeRanks", "parameters": [{"name": "score", "type": "number[]"}], "return_type": "string[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 507, "task_id": "perfect-number", "difficulty": "Easy", "problem_description": "A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. A divisor of an integer x is an integer that can divide x evenly.\nGiven an integer n, return true if n is a perfect number, otherwise return false.\n \nExample 1:\n\nInput: num = 28\nOutput: true\nExplanation: 28 = 1 + 2 + 4 + 7 + 14\n1, 2, 4, 7, and 14 are all divisors of 28.\n\nExample 2:\n\nInput: num = 7\nOutput: false\n\n \nConstraints:\n\n1 <= num <= 108\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num = 8128) == True\n assert candidate(num = 10) == False\n assert candidate(num = 100000000) == False\n assert candidate(num = 28) == True\n assert candidate(num = 12) == False\n assert candidate(num = 7) == False\n assert candidate(num = 6) == True\n assert candidate(num = 33550336) == True\n assert candidate(num = 27) == False\n assert candidate(num = 1) == False\n assert candidate(num = 100) == False\n assert candidate(num = 496) == True\n assert candidate(num = 99999999) == False\n assert candidate(num = 1046527) == False\n assert candidate(num = 1234567) == False\n assert candidate(num = 99999998) == False\n assert candidate(num = 10000000) == False\n assert candidate(num = 56949850) == False\n assert candidate(num = 81284288) == False\n assert candidate(num = 37) == False\n assert candidate(num = 82589933) == False\n assert candidate(num = 672280688) == False\n assert candidate(num = 2096128) == False\n assert candidate(num = 67891011) == False\n assert candidate(num = 32766) == False\n assert candidate(num = 496000) == False\n assert candidate(num = 96141120) == False\n assert candidate(num = 11111111) == False\n assert candidate(num = 497) == False\n assert candidate(num = 987654321) == False\n assert candidate(num = 33550337) == False\n assert candidate(num = 1048576) == False\n assert candidate(num = 2) == False\n assert candidate(num = 495) == False\n assert candidate(num = 2147483647) == False\n assert candidate(num = 4690) == False\n assert candidate(num = 8128000) == False\n assert candidate(num = 100000) == False\n assert candidate(num = 1073741823) == False\n assert candidate(num = 600851475143) == False\n assert candidate(num = 672) == False\n assert candidate(num = 50000000) == False\n assert candidate(num = 67229820) == False\n assert candidate(num = 56456456) == False\n assert candidate(num = 98304) == False\n assert candidate(num = 1073741824) == False\n assert candidate(num = 98765432) == False\n assert candidate(num = 10000) == False\n assert candidate(num = 119439360) == False\n"}, "metadata": {"canonical_parameter_names": ["num"], "leetcode_dataset_entry_point": "Solution().checkPerfectNumber", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var checkPerfectNumber = function(num) {", "container": null, "callable": "checkPerfectNumber", "parameters": [{"name": "num", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 508, "task_id": "most-frequent-subtree-sum", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, return the most frequent subtree sum. If there is a tie, return all the values with the highest frequency in any order.\nThe subtree sum of a node is defined as the sum of all the node values formed by the subtree rooted at that node (including the node itself).\n \nExample 1:\n\n\nInput: root = [5,2,-3]\nOutput: [2,-3,4]\n\nExample 2:\n\n\nInput: root = [5,2,-5]\nOutput: [2]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 104].\n-105 <= Node.val <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([-1, -2, -3, -4, -5])) == [-4, -5, -11, -3, -15]\n assert candidate(root = tree_node([0, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([1, 2, 3, 4, 5])) == [4, 5, 11, 3, 15]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [5, 9, 12, 14, 15]\n assert candidate(root = tree_node([5, 2, -5])) == [2]\n assert candidate(root = tree_node([5, 2, -3])) == [2, -3, 4]\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1])) == [3]\n assert candidate(root = tree_node([0, 1, -1])) == [1, -1, 0]\n assert candidate(root = tree_node([5])) == [5]\n assert candidate(root = tree_node([1])) == [1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [4, 5, 11, 6, 7, 16, 28]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, None, 8, None, 9, None, 10])) == [10, 17, 21, 8, 13, 36, 9, 15, 18, 55]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14])) == [-7, -8, -18, -9, -10, -23, -42, -11, -12, -28, -13, -14, -33, -63, -105]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [10, 19, 27, 34, 40, 45, 49, 52, 54, 55]\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, None, None, 4, None, None, 4])) == [3, 5, 4, 8, 11, 13, 19]\n assert candidate(root = tree_node([5, 3, 2, 1, -1, -2, -3])) == [-3]\n assert candidate(root = tree_node([7, -1, -10, None, 5, None, -3, None, -2, None, 1, None, -4, None, 2])) == [-4, -6, -1, -2, 2, 3, 0, -10, -5]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3])) == [3]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25])) == [16, 17, 41, 18, 19, 46, 91, 20, 21, 51, 22, 23, 56, 112, 205, 24, 25, 61, 13, 80, 14, 15, 36, 119, 325]\n assert candidate(root = tree_node([5, 2, -5, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7])) == [2]\n assert candidate(root = tree_node([100, 98, 102, None, 99, None, 105, 97, None, None, 101, None, 106])) == [106, 203, 302, 400, 101, 206, 308, 808]\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, None, None, 4])) == [4, 7, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, 8, None, 10, None, 11, None, 12, None, 13])) == [12, 20, 24, 26, 13, 23, 29, 11, 18, 50, 77]\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 0, 6, None, -1, 8])) == [6]\n assert candidate(root = tree_node([100, -50, -50, 30, 20, -30, -20, 10, 5, -10, -5, 3, -3, 2, -2])) == [5, 0]\n assert candidate(root = tree_node([-1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15])) == [-6, -8]\n assert candidate(root = tree_node([3, 2, 3, None, 3, None, 3, None, 3, None, 3, None, 3, None, 3])) == [3, 6, 9]\n assert candidate(root = tree_node([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])) == [7, 8, 18, 9, 10, 23, 42, 11, 12, 28, 13, 14, 33, 63, 105]\n assert candidate(root = tree_node([100, 50, -25, 20, 30, -10, -15, 10, 5, 3, 2, -1, -2])) == [35]\n assert candidate(root = tree_node([-10, -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])) == [3, 8, 6]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 3, 4, None, None, 5, None, None, 5, None, None])) == [5, 14]\n assert candidate(root = tree_node([100, 50, 50, 25, 25, 25, 25, 12, 13, 14, 15, 16, 17, 18, 19])) == [12, 13, 50, 14, 15, 54, 154, 16, 17, 58, 18, 19, 62, 170, 424]\n assert candidate(root = tree_node([10, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80, 90, -90, 100, -100])) == [-60]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])) == [91]\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, -1, -1, 0, 0])) == [0, 3, -1]\n assert candidate(root = tree_node([100, 50, -50, 25, 25, -25, -25, 12, 13, -12, -13, 12, 13, -12, -13])) == [12, 13, -12, -13, 0, 100]\n assert candidate(root = tree_node([10, 10, -10, 5, 5, None, -5, None, None, None, None, 2, 3])) == [5, 20]\n assert candidate(root = tree_node([0, 1, -1, 2, -2, 3, -3])) == [2, -2, 1, 3, -3, -1, 0]\n assert candidate(root = tree_node([7, 3, -3, 2, -1, None, -4, 1, -2, None, -5, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([-10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10])) == [10, -10]\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, -1, 1, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([5, 2, -3, 1, 0, -2, 1])) == [1]\n assert candidate(root = tree_node([1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1])) == [1]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, None, None, None, 8])) == [7, 11, 13, 5, 8, 14, 22, 36]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25])) == [25, 49, 72, 94, 115, 135, 154, 172, 189, 205, 220, 234, 247, 259, 270, 280, 289, 297, 304, 310, 315, 319, 322, 324, 325]\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7])) == [-4, -5, -11, -6, -7, -16, -28]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, 8, 9])) == [4, 5, 11, 6, 8, 9, 24, 33, 45]\n assert candidate(root = tree_node([1, -1, 1, -1, 1, -1, 1])) == [1]\n assert candidate(root = tree_node([5, 15, 10, 7, -5, -3, 2, None, -1, None, None, None, None, None, None])) == [-1, 6, -5, 16, -3, 2, 9, 30]\n assert candidate(root = tree_node([5, 2, -3, 4, 1, -1, -4, 6, 0, None, None, None, None, 2, None])) == [6, 0, 10, 1, 13, -1, 2, -2, -6, 12]\n assert candidate(root = tree_node([0, 1, 1, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([5, 2, -3, 2, -2, 1, -1, 3, -3, 4, -4])) == [-3, 2, 4]\n assert candidate(root = tree_node([5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 4, 4, None, None, None, None, 5, 5, 5, 5, 5])) == [5]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [9, 17, 24, 30, 35, 39, 42, 44, 45]\n assert candidate(root = tree_node([5, 15, -10, 20, -20, 30, -30, 40, -40, 50, -50, 60, -60, 70, -70, 80, -80, 90, -90, 100, -100])) == [80, -80, 40, 90, -90, -40, 20, 100, -100, 50, -50, -20, 15, 60, -60, 30, 70, -70, -30, -10, 10]\n assert candidate(root = tree_node([-10, -20, -30, -40, -50, -60, -70, -80, -90, -100, -110, -120, -130, -140, -150])) == [-80, -90, -210, -100, -110, -260, -490, -120, -130, -310, -140, -150, -360, -700, -1200]\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([0, 1, 1, 1, 1, 1, 1])) == [1]\n assert candidate(root = tree_node([-1, -2, -3, 1, 2, 3, 4, -4, -3, -2, -1, 0, 1, 2, 3])) == [-1, 0]\n assert candidate(root = tree_node([100, -50, 50, None, 50, None, -50, None, 25, None, -25, None, 25, None, -25])) == [50, 100, -50]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, 2, 6, 8, 11, 13, 19, 21])) == [6, 21]\n assert candidate(root = tree_node([-10, 9, 20, None, None, 15, 7])) == [9, 15, 7, 42, 41]\n assert candidate(root = tree_node([-10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10, -10])) == [-10]\n assert candidate(root = tree_node([-10, -5, 0, 5, 10])) == [10, 0]\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20])) == [-46]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])) == [16, 17, 41, 18, 19, 46, 91, 20, 21, 51, 22, 23, 56, 112, 205, 24, 25, 61, 26, 27, 66, 133, 28, 29, 71, 30, 45, 123, 259, 465]\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == [-8, -9, -21, -10, -11, -26, -49, -12, -13, -31, -14, -15, -36, -70, -120]\n assert candidate(root = tree_node([0, 1, 1, 0, 0, 0, 1, -1, None, -1, None, None, None, -1])) == [-1]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20, None, 21, None, 22, None, 23, None, 24, None, 25, None, 26, None, 27, None, 28, None, 29, None, 30, None, 31, None, 32, None, 33, None, 34, None, 35, None, 36, None, 37, None, 38, None, 39, None, 40])) == [40, 79, 117, 154, 190, 225, 259, 292, 324, 355, 385, 414, 442, 469, 495, 520, 544, 567, 589, 610, 630, 649, 667, 684, 700, 715, 729, 742, 754, 765, 775, 784, 792, 799, 805, 810, 814, 817, 819, 820]\n assert candidate(root = tree_node([5, 2, -5, 1, -4, 0, -6, 2, -1, -3, -5, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [46]\n assert candidate(root = tree_node([1, 2, 3, 4, None, 6, 7, 8, 9, 10, 11, None, None, 14, 15, None, None, 18, None, 20])) == [14, 15, 37, 9, 50, 52, 18, 28, 20, 31, 65, 7, 75, 128]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])) == [5, 6, 14, 7, 8, 19, 35, 9, 10, 22, 11, 12, 27, 51, 87]\n assert candidate(root = tree_node([100, -50, -50, 25, 25, -25, -25, 12, -12, 12, -12, 12, -12, 12, -12])) == [12, -12]\n assert candidate(root = tree_node([0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10])) == [8, -8, 4, 9, -9, -4, 2, 10, -10, 5, -5, -2, 1, 6, -6, 3, 7, -7, -3, -1, 0]\n assert candidate(root = tree_node([10, -10, 0, 5, -5, 5, -5, 3, -3, 3, -3, 3, -3, 3, -3])) == [3, -3]\n assert candidate(root = tree_node([5, 2, -5, 1, 3, None, -2, 4, None, -1, None, 2])) == [2, 9]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [8, 9, 21, 10, 11, 26, 49, 12, 13, 31, 14, 15, 36, 70, 120]\n assert candidate(root = tree_node([10, 15, 3, 7, -2, 9, 12, -1, 4])) == [-1, 4, 10, -2, 23, 9, 12, 24, 57]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4])) == [4]\n assert candidate(root = tree_node([10, 10, -10, 10, -10, 10, -10])) == [10]\n assert candidate(root = tree_node([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])) == [0]\n assert candidate(root = tree_node([1, -1, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0])) == [0]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().findFrequentTreeSum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findFrequentTreeSum = function(root) {", "container": null, "callable": "findFrequentTreeSum", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 509, "task_id": "fibonacci-number", "difficulty": "Easy", "problem_description": "The Fibonacci numbers, commonly denoted F(n) form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,\n\nF(0) = 0, F(1) = 1\nF(n) = F(n - 1) + F(n - 2), for n > 1.\n\nGiven n, calculate F(n).\n \nExample 1:\n\nInput: n = 2\nOutput: 1\nExplanation: F(2) = F(1) + F(0) = 1 + 0 = 1.\n\nExample 2:\n\nInput: n = 3\nOutput: 2\nExplanation: F(3) = F(2) + F(1) = 1 + 1 = 2.\n\nExample 3:\n\nInput: n = 4\nOutput: 3\nExplanation: F(4) = F(3) + F(2) = 2 + 1 = 3.\n\n \nConstraints:\n\n0 <= n <= 30\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 0) == 0\n assert candidate(n = 3) == 2\n assert candidate(n = 30) == 832040\n assert candidate(n = 4) == 3\n assert candidate(n = 2) == 1\n assert candidate(n = 20) == 6765\n assert candidate(n = 1) == 1\n assert candidate(n = 10) == 55\n assert candidate(n = 5) == 5\n assert candidate(n = 8) == 21\n assert candidate(n = 29) == 514229\n assert candidate(n = 15) == 610\n assert candidate(n = 12) == 144\n assert candidate(n = 18) == 2584\n assert candidate(n = 6) == 8\n assert candidate(n = 25) == 75025\n assert candidate(n = 28) == 317811\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().fib", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var fib = function(n) {", "container": null, "callable": "fib", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 513, "task_id": "find-bottom-left-tree-value", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, return the leftmost value in the last row of the tree.\n \nExample 1:\n\n\nInput: root = [2,1,3]\nOutput: 1\n\nExample 2:\n\n\nInput: root = [1,2,3,4,null,5,6,null,null,7]\nOutput: 7\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [1, 104].\n-231 <= Node.val <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([2, 1, 3])) == 1\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, None, None, 7])) == 7\n assert candidate(root = tree_node([0, None, 1])) == 1\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == 15\n assert candidate(root = tree_node([1])) == 1\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, 1, None, None, None, None, None, None, 9])) == 1\n assert candidate(root = tree_node([2, 2, 2, 3, None, 3, None, 4, None, 4, None, 5, None, 5, None, 6])) == 6\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 10\n assert candidate(root = tree_node([1, -2, -3, -4, None, -5, -6, None, None, None, -7])) == -7\n assert candidate(root = tree_node([1, 2, None, 3, 4, None, 5, None, None, 6, None, 7])) == 7\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == 3\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 4, 4])) == 4\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 7, None, None, None, None, None, None, 8])) == 4\n assert candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13])) == 4\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 0, 7, 5, None, None, 8, 6, None, None, None, 11, None, 13, None, None, None, 14])) == 14\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 90, 110, 140, 160, 190])) == 10\n assert candidate(root = tree_node([6, 2, 8, 0, 4, 7, 9, None, None, 3, 5])) == 3\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 9\n assert candidate(root = tree_node([1, 2, 3, None, 5, None, 6, 7, None, 8, 9, None, None, 10])) == 10\n assert candidate(root = tree_node([1, 2, 3, 4, None, 5, 6, 7, None, 8, 9, None, None, None, 10, None, 11])) == 10\n assert candidate(root = tree_node([0, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15])) == -8\n assert candidate(root = tree_node([1, None, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14])) == 9\n assert candidate(root = tree_node([8, 5, 1, 6, 9, None, None, 7, None, 10, 11])) == 7\n assert candidate(root = tree_node([50, 25, 75, 10, 35, 55, 85, 5, 15, 30, 40, 52, 60, 70, 90])) == 5\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, None, 7, 8, 9, 10, None, None, 11, 12, 13, None, None, None, None, 14])) == 14\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, None, 7, 8, None, None, 9])) == 8\n assert candidate(root = tree_node([100, 50, 150, 25, 75, None, 175, 10, 35, 65, 85, None, None, None, None, None, 200, 15, 40, 60, 80, 90, 110, 130, 180, 250])) == 90\n assert candidate(root = tree_node([8, 15, 1, None, -98, 75, None, 94, 93, None, -82, None, -70, None, -52])) == -70\n assert candidate(root = tree_node([2, 2, 2, 3, None, 3, None, 4, None, 4, None, 5, None, 5, None, 6, None, 6, None, 7, None, 7])) == 7\n assert candidate(root = tree_node([1, None, 3, 2, 4, None, None, 5, None, 6])) == 6\n assert candidate(root = tree_node([1, None, 3, None, None, 2])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, None, None, 9])) == 8\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7])) == -4\n assert candidate(root = tree_node([1, None, 2, 3, None, None, 4, None, None, 5])) == 4\n assert candidate(root = tree_node([0, -1, -2, -3, None, -4, -5, -6, None, None, None, -7, -8])) == -6\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, None, 1])) == 7\n assert candidate(root = tree_node([5, 3, 8, 1, 4, None, 9, None, 2, None, None, None, 6, None, 10, 7, None, 11, 12])) == 11\n assert candidate(root = tree_node([20, 15, 25, 10, 17, 22, 30, 5, 12, None, 18, 21, 24, 28, 35, 3, None, 11, 14, 16, None, 19, None, None, 23, 27, 31, None, None, None, None, 33, None, 36, 37])) == 33\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, None, 15])) == 8\n assert candidate(root = tree_node([25, 20, 30, 15, 22, 28, 35, 10, None, 18, 24, None, None, 26, 29, None, None, 5, None, None, None, None, None, None, 12])) == 5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == 8\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, None, None, None, None, 9, 10, 11, 12])) == 12\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5])) == 5\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6])) == 1\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 5\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, 8, None, 16, 18, 19, 21])) == 19\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, 7, 1, None, None, None, None, None, None, 8])) == 8\n assert candidate(root = tree_node([5, None, 6, None, 7, None, 8, None, 9, None, 10])) == 10\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == 3\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])) == 15\n assert candidate(root = tree_node([2147483647])) == 2147483647\n assert candidate(root = tree_node([2, 1, 3, 4, 5, 6, 7, 8, 9, 10, None, None, 11, 12, None, 13, None, None, 14])) == 13\n assert candidate(root = tree_node([4, 2, 7, 1, 3, 6, 9, None, None, None, None, None, None, 8, 10])) == 8\n assert candidate(root = tree_node([-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15])) == -8\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, 4, 6, 8, 11, 13, 18, 25, None, None, None, None, 5.5, 9, 10.5, None, None, 14, 16, 22, None, None, 17, None, None, None, None, None, None, None, None, None, None, 19])) == 19\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, None, 17, 23, None, 27, None, 18])) == 18\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, None, None, 11, None, 12])) == 8\n assert candidate(root = tree_node([0, 0, 0, 0, None, None, 0, None, 0, None, None, 0])) == 0\n assert candidate(root = tree_node([1, 2, 3, 4, 5, None, 6, 7, 8, None, None, 9, 10, None, None, 11])) == 11\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15, None, 16, None, 17, None, 18, None, 19, None, 20])) == 20\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4])) == 4\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, None, 6])) == 1\n assert candidate(root = tree_node([1, 2, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == 8\n assert candidate(root = tree_node([2, 3, 4, 5, None, 6, 7, 8, None, None, None, None, None, None, 9])) == 9\n assert candidate(root = tree_node([5, 3, 8, 2, 4, 7, 9, 1, None, None, None, None, 10])) == 1\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, 18, 28, None, 38, 45])) == 5\n assert candidate(root = tree_node([30, 15, 45, 7, 22, 35, 50, 3, 11, 18, 27, 32, 42, 48, 55, 1, 5, 9, 13, 17, 20, 24, 26, 29, 31, 34, 38, 41, 44, 46, 49, 52, 54, 57, 60, 2, 4, 6, 8, 10, 12, 14, 16, 19, 21, 23, 25, 28, 30, 33, 36, 39, 43, 45, 47, 50, 53, 56, 58, 61, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 62])) == 62\n assert candidate(root = tree_node([5, 3, 8, 2, 4, 6, 9, 1, None, None, None, 5, None, 7, 10])) == 1\n assert candidate(root = tree_node([-2147483648, None, 2147483647, -2147483647])) == -2147483647\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180, 5, None, None, 20, 35, 55, 70, None, None, None, None, None, 105, 130, 135, 145, None, None, 155, 175, 185, None, None, None, None, None, None, None, 7])) == 155\n assert candidate(root = tree_node([1, 2, 3, None, 5, 6, None, 7, 8, 9, 10, None, 11, 12])) == 11\n assert candidate(root = tree_node([1, 2, 2, 3, None, None, 3, 4, 4, None, None, 5, 5])) == 5\n assert candidate(root = tree_node([1, 2, 3, None, None, 4, 5, None, None, 6, 7, None, None, 8, 9, None, None, None, None, None, 10])) == 8\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, None, None, 5, 5])) == 5\n assert candidate(root = tree_node([1, 2, 3, None, 4, 5, 6, None, None, 7, 8, None, None, 9, 10])) == 9\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85])) == 10\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 18, 1, None, 6, 9, 11, 13, 17, 20])) == 1\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11])) == 11\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20, None, None, None, 30, 25, 35])) == 25\n assert candidate(root = tree_node([10, 5, -3, 3, 2, None, 11, 3, -2, None, 1])) == 3\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, None])) == 8\n assert candidate(root = tree_node([1, None, 2, None, None, 3, None, None, None, 4, None, None, None, None, 5])) == 2\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, 4, 6, 8, 11, 13, 18, 25])) == 1\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3, 5, 5, None, None, 6, 6, None, None, 7, 7])) == 7\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().findBottomLeftValue", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findBottomLeftValue = function(root) {", "container": null, "callable": "findBottomLeftValue", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 514, "task_id": "freedom-trail", "difficulty": "Hard", "problem_description": "In the video game Fallout 4, the quest \"Road to Freedom\" requires players to reach a metal dial called the \"Freedom Trail Ring\" and use the dial to spell a specific keyword to open the door.\nGiven a string ring that represents the code engraved on the outer ring and another string key that represents the keyword that needs to be spelled, return the minimum number of steps to spell all the characters in the keyword.\nInitially, the first character of the ring is aligned at the \"12:00\" direction. You should spell all the characters in key one by one by rotating ring clockwise or anticlockwise to make each character of the string key aligned at the \"12:00\" direction and then by pressing the center button.\nAt the stage of rotating the ring to spell the key character key[i]:\n\nYou can rotate the ring clockwise or anticlockwise by one place, which counts as one step. The final purpose of the rotation is to align one of ring's characters at the \"12:00\" direction, where this character must equal key[i].\nIf the character key[i] has been aligned at the \"12:00\" direction, press the center button to spell, which also counts as one step. After the pressing, you could begin to spell the next character in the key (next stage). Otherwise, you have finished all the spelling.\n\n \nExample 1:\n\n\nInput: ring = \"godding\", key = \"gd\"\nOutput: 4\nExplanation:\nFor the first key character 'g', since it is already in place, we just need 1 step to spell this character. \nFor the second key character 'd', we need to rotate the ring \"godding\" anticlockwise by two steps to make it become \"ddinggo\".\nAlso, we need 1 more step for spelling.\nSo the final output is 4.\n\nExample 2:\n\nInput: ring = \"godding\", key = \"godding\"\nOutput: 13\n\n \nConstraints:\n\n1 <= ring.length, key.length <= 100\nring and key consist of only lower case English letters.\nIt is guaranteed that key could always be spelled by rotating ring.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(ring = \"caotmcaataijjxi\",key = \"oatjiioijjjxxxcx\") == 42\n assert candidate(ring = \"godding\",key = \"gd\") == 4\n assert candidate(ring = \"pqwcx\",key = \"cpqwx\") == 13\n assert candidate(ring = \"edcba\",key = \"abc\") == 6\n assert candidate(ring = \"ababcabc\",key = \"abc\") == 6\n assert candidate(ring = \"iotfo\",key = \"fio\") == 8\n assert candidate(ring = \"abcdefghijklmnopqrstuvwxyz\",key = \"zyxwvutsrqponmlkjihgfedcba\") == 52\n assert candidate(ring = \"iaadddfef\",key = \"dd\") == 5\n assert candidate(ring = \"abcdefghijklmnopqrstuvwxyz\",key = \"cba\") == 7\n assert candidate(ring = \"abcdefg\",key = \"fa\") == 6\n assert candidate(ring = \"iaejfhfihjdghfihdddddddhddcfjghjgddf\",key = \"did\") == 9\n assert candidate(ring = \"xyxzyzyxy\",key = \"xzyxz\") == 12\n assert candidate(ring = \"godding\",key = \"godding\") == 13\n assert candidate(ring = \"caotmcaataijjxi\",key = \"oatjiioijia\") == 35\n assert candidate(ring = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",key = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 66\n assert candidate(ring = \"lkjhgfedcbazyxwvutsrqponml\",key = \"abcdefghijklmnopqrstuvwxyz\") == inf\n assert candidate(ring = \"mississippi\",key = \"ppiiisssmm\") == 18\n assert candidate(ring = \"uniquecharacters\",key = \"unique\") == 11\n assert candidate(ring = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",key = \"zyxwvutsrqponmlkjihgfedcba\") == 77\n assert candidate(ring = \"mississippi\",key = \"missis\") == 10\n assert candidate(ring = \"noonnoonnoonnoonnoonnoon\",key = \"noonnoon\") == 12\n assert candidate(ring = \"abacabadabacabadabacabadabacabad\",key = \"badabadabacaba\") == 28\n assert candidate(ring = \"thistimeitsshouldbeaveryunusualring\",key = \"unusualring\") == 30\n assert candidate(ring = \"thisisaverylongringwithmanysamecharacters\",key = \"thisisaverylongring\") == 37\n assert candidate(ring = \"encyclopedia\",key = \"pediaencyclopedia\") == 38\n assert candidate(ring = \"abcabcabcabcabcabcabcabcabcabcabcabcabcabcabc\",key = \"ac\") == 3\n assert candidate(ring = \"rotor\",key = \"rotorrotor\") == 18\n assert candidate(ring = \"abcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefgabcdefg\",key = \"gfedcba\") == 14\n assert candidate(ring = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",key = \"zzzaa\") == 7\n assert candidate(ring = \"abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz\",key = \"zyxwvutsrqponmlkjihgfedcba\") == 52\n assert candidate(ring = \"abababababababababab\",key = \"bababa\") == 12\n assert candidate(ring = \"abacabadabacaba\",key = \"abcabcabc\") == 20\n assert candidate(ring = \"rhythms\",key = \"rhythmrhythmsrhythmrhythms\") == 53\n assert candidate(ring = \"abcdefghijklmnopqrstuvwxyzaabcdefghijklmnopqrstuvwxyza\",key = \"abcdefghijklmnopqrstuvwxyz\") == 51\n assert candidate(ring = \"floccinaucinihilipilification\",key = \"floccinaucinihilipilification\") == 57\n assert candidate(ring = \"abcdefghijabcdefghijabcdefghij\",key = \"jjiihhggffeeddccba\") == 28\n assert candidate(ring = \"bcaacbcaacbcaac\",key = \"abcabc\") == 15\n assert candidate(ring = \"qwertyuiopasdfghjklzxcvbnm\",key = \"lkjhgfdsa\") == 25\n assert candidate(ring = \"abcabcabcabcabcabcabcabc\",key = \"abcabcabc\") == 17\n assert candidate(ring = \"ringwithrepeatedcharactersrrrr\",key = \"ringwithrepeatedcharacters\") == 51\n assert candidate(ring = \"repetition\",key = \"rep\") == 5\n assert candidate(ring = \"abcdefgabcdefgabcdefgabcdefgabcdefg\",key = \"abcdefgabcdefgabcdefgabcdefg\") == 55\n assert candidate(ring = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",key = \"zzzyyxxwvuttsrqponmlkjihgfedcba\") == 82\n assert candidate(ring = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",key = \"zzyyxxwvuttsrqponmlkjihgfedcba\") == 81\n assert candidate(ring = \"abracadabra\",key = \"abcabcabc\") == 25\n assert candidate(ring = \"qwertyuiopasdfghjklzxcvbnmqwertyuiop\",key = \"programming\") == 87\n assert candidate(ring = \"thisisaverylongstringthatweneedtocheckanditsrepeatedthisisaverylongstringthatweneedtocheck\",key = \"check\") == 12\n assert candidate(ring = \"thisisaverylongstringthatweneedtocheck\",key = \"string\") == 26\n assert candidate(ring = \"rhythm\",key = \"myrhth\") == 16\n assert candidate(ring = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",key = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 52\n assert candidate(ring = \"pqrsyzxcvbnmlkjhgfedwatpoiuy\",key = \"python\") == 42\n assert candidate(ring = \"mnbvcxzlkjhgfdsapoiuytrewq\",key = \"qwertyuiop\") == 20\n assert candidate(ring = \"mississippi\",key = \"mississippimississippi\") == 41\n assert candidate(ring = \"qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\",key = \"mnbvcxzlkjhgfdsapoiuytrewq\") == 52\n assert candidate(ring = \"abcdefgabcdefgabcdefgabcdefg\",key = \"aceg\") == 10\n assert candidate(ring = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",key = \"zzz\") == 3\n assert candidate(ring = \"repeatedrepeatedrepeated\",key = \"repeat\") == 11\n assert candidate(ring = \"aaabbbcccdddeeefffggghhhiii\",key = \"abcdefghi\") == 33\n assert candidate(ring = \"aaaaabbbbbcccccdddddeeeeefffffggggghhhhhiiiii\",key = \"abcdefghi\") == 49\n assert candidate(ring = \"rotorrotorrotor\",key = \"rotor\") == 9\n assert candidate(ring = \"qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm\",key = \"qzam\") == 31\n assert candidate(ring = \"abcdefghijklmnopqrstuvwxyz\",key = \"abcdefghijklmnopqrstuvwxyz\") == 51\n assert candidate(ring = \"aaabbbbccccddddeeeeffffgggg\",key = \"abcdefg\") == 30\n assert candidate(ring = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",key = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == 60\n assert candidate(ring = \"abcdefabcdefabcdefabcdefabcdefabcdefabcdef\",key = \"abcdefabcdefabcdefabcdefabcdefabcdefabcdef\") == 83\n assert candidate(ring = \"abacabadabacabadabacabad\",key = \"abad\") == 7\n assert candidate(ring = \"lmnopqrstuvwxyzabcdefghijkl\",key = \"key\") == 17\n assert candidate(ring = \"xylophone\",key = \"oxylphoen\") == 24\n assert candidate(ring = \"aaaaabbbbcccccdddddeeeeeffffffggggghhhhhhiiiiijjjjjjkkkkkkllllllmmmmmmnnnnnnooooooppppppqqqqqqrrrrrrssssssttttttuuuuuuvvvvvvwwwwwwwxxxxxxxxxyyyyyyyzzzzzzz\",key = \"zyxwvutsrqponmlkjihgfedcba\") == 176\n assert candidate(ring = \"mississippi\",key = \"issi\") == 7\n"}, "metadata": {"canonical_parameter_names": ["ring", "key"], "leetcode_dataset_entry_point": "Solution().findRotateSteps", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findRotateSteps = function(ring, key) {", "container": null, "callable": "findRotateSteps", "parameters": [{"name": "ring", "type": "string"}, {"name": "key", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 515, "task_id": "find-largest-value-in-each-tree-row", "difficulty": "Medium", "problem_description": "Given the root of a binary tree, return an array of the largest value in each row of the tree (0-indexed).\n \nExample 1:\n\n\nInput: root = [1,3,2,5,3,null,9]\nOutput: [1,3,9]\n\nExample 2:\n\nInput: root = [1,2,3]\nOutput: [1,3]\n\n \nConstraints:\n\nThe number of nodes in the tree will be in the range [0, 104].\n-231 <= Node.val <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == [1, 2, 3, 4, 5]\n assert candidate(root = tree_node([1, 2, 3])) == [1, 3]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9])) == [1, 3, 9]\n assert candidate(root = tree_node([0])) == [0]\n assert candidate(root = tree_node([])) == []\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7])) == [1, 3, 7]\n assert candidate(root = tree_node([3, 1, 4, 3, None, 1, 5])) == [3, 4, 5]\n assert candidate(root = tree_node([3, 1, 4, None, 2])) == [3, 4, 2]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, 8, 9, 10, 11, 12, 13, None, None, 14])) == [1, 3, 7, 13, 14]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, None, None, 8, 9, 10, 11, None, None, None, 12, None, None, 13, None, None, 14, None, None, 15])) == [1, 3, 7, 11, 14, 15]\n assert candidate(root = tree_node([0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14])) == [0, -1, -3, -7]\n assert candidate(root = tree_node([3, 1, 4, None, None, 2])) == [3, 4, 2]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, 9, 7, 8, 6, 4, None, 11, 13, None, 10, None, None, 12])) == [1, 3, 9, 13, 12]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n assert candidate(root = tree_node([100, 90, 80, 70, 60, 50, 40, 30, 20, 10, -10, -20, -30, -40, -50])) == [100, 90, 70, 30]\n assert candidate(root = tree_node([1, None, 3, 2, 4, None, 5, 6, None, None, 7])) == [1, 3, 4, 6, 7]\n assert candidate(root = tree_node([2147483647, -2147483648, None, 2147483647])) == [2147483647, -2147483648, 2147483647]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, None, 7, None, 10, None, None, 8])) == [1, 3, 9, 10, 8]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7, None, None, 8, 12])) == [3, 20, 15, 12]\n assert candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, None, None, 2, None, None, None, None, 10])) == [5, 8, 9, 10]\n assert candidate(root = tree_node([-10, -5, -3, -6, -20, 0, 5, None, None, -8, None, -15, -1])) == [-10, -3, 5, -1]\n assert candidate(root = tree_node([2, 1, 3, 0, 7, 9, 1, 2, None, 1, 0, None, None, 8, 8, None, None, None, None, 7])) == [2, 3, 9, 8, 7]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, 7, None, None, None, None, 8, 10, 11, 12, 13, 14, 15])) == [1, 3, 9, 7, 12, 15]\n assert candidate(root = tree_node([-10, -5, -15, -3, -8, -18, -12, -20, -4, -7, -17, -13, None, -6])) == [-10, -5, -3, -4]\n assert candidate(root = tree_node([3, 9, 20, None, None, 15, 7])) == [3, 20, 15]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40])) == [1, 3, 7, 15, 31, 40]\n assert candidate(root = tree_node([10, 5, 15, None, None, 6, 20])) == [10, 15, 20]\n assert candidate(root = tree_node([1, None, 3, None, 5, None, 7, None, 9, None, 11, None, 13])) == [1, 3, 5, 7, 9, 11, 13]\n assert candidate(root = tree_node([100, -100, 50, -50, 25, 0, 25, None, None, -25, 0, 25, None, None, None, -25, None, None, 25])) == [100, 50, 25, 25, 25]\n assert candidate(root = tree_node([0, 0, 0, None, 0, 0, None, None, 0, 0, None, None, 0])) == [0, 0, 0, 0, 0]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, 9, 8, 6, 7, 4, 10])) == [1, 3, 9, 10]\n assert candidate(root = tree_node([5, 3, 9, 1, 7, 8, 10, 0, 2, 6, 4, None, None, None, None, None, 11])) == [5, 9, 10, 6, 11]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == [10, 15, 18]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 12, 20, 1, None, 6, None, None, None, 14, 18])) == [10, 15, 20, 18]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, None, None, 4, 4, 4, 4])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([10, 5, 15, 3, 7, 13, 18, 1, 4, 6, 8, 12, 14, 17, 20])) == [10, 15, 18, 20]\n assert candidate(root = tree_node([1000000000, 999999999, 1000000001, 999999998, 999999997, 1000000002, 1000000003])) == [1000000000, 1000000001, 1000000003]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, None, None, None, None, 21])) == [1, 3, 7, 15, 21]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7])) == [1, 2, 3, 4, 5, 6, 7]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, None, 8, None, 10, None, 11, None, 12, -13, None, -14, None, -15])) == [1, 3, 9, 10, 12, -15]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == [1, 2, 3, 4, 5, 6, 7, 8, 9]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, 7])) == [1, 3, 9, 7]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, 7, None, None, None, None, 8, 10])) == [1, 3, 9, 7, 10]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, 7, None, None, None, 11, 12, None, 13, 14])) == [1, 3, 9, 11, 14]\n assert candidate(root = tree_node([5, 1, None, 4, None, 2, None, None, 3])) == [5, 1, 4, 2, 3]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, None, 8, None, 10, None, 11, None, 12])) == [1, 3, 9, 10, 12]\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8])) == [1, 2, 3, 4, 5, 6, 7, 8]\n assert candidate(root = tree_node([5, 1, 4, None, None, 3, 6])) == [5, 4, 6]\n assert candidate(root = tree_node([7, 5, 8, 3, 6, 9, 10, None, None, 4, None, None, 11])) == [7, 8, 10, 11]\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180])) == [100, 150, 175, 180]\n assert candidate(root = tree_node([2147483647])) == [2147483647]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, None, 7, None, 10, None, None, None, 11])) == [1, 3, 9, 10, 11]\n assert candidate(root = tree_node([9, 3, 12, None, None, 11, 13])) == [9, 12, 13]\n assert candidate(root = tree_node([-100, 50, -50, 25, 75, -25, 25])) == [-100, 50, 75]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 7, 8, None, 10, None, 12, None, 14, None, 16])) == [1, 3, 7, 10, 14, 16]\n assert candidate(root = tree_node([7, 10, None, 5, None, 1, None, None, -1, None, -3, None, 6, None, None, -5, None])) == [7, 10, 5, 1, -1, -3, 6]\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, 7])) == [5, 6, 7]\n assert candidate(root = tree_node([1, 2, 3, 4, None, None, 5, 6, None, 7, None, 8, None, 9])) == [1, 3, 5, 7, 9]\n assert candidate(root = tree_node([2147483647, -2147483648, None, -2147483648, None, None, 2147483647])) == [2147483647, -2147483648, -2147483648, 2147483647]\n assert candidate(root = tree_node([1, 3, 2, 5, 3, None, 9, 6, 7, None, None, None, 8])) == [1, 3, 9, 8]\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8, None, None, None, None, None, None, None, 9])) == [5, 7, 8, 9]\n assert candidate(root = tree_node([-10, -20, -30, -40, -50, -60, -70, -80, -90, -100])) == [-10, -20, -40, -80]\n assert candidate(root = tree_node([10, None, 5, None, None, None, 15, None, 7])) == [10, 5]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20])) == [1, 3, 7, 15, 20]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == [1, 3, 7, 15]\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190])) == [100, 150, 175, 190]\n assert candidate(root = tree_node([1, 2, 2, 3, 4, 4, 3])) == [1, 2, 4]\n assert candidate(root = tree_node([1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4])) == [1, 2, 3, 4]\n assert candidate(root = tree_node([5, 3, 6, 2, 4, None, None, 1])) == [5, 6, 4, 1]\n assert candidate(root = tree_node([5, 3, 9, -10, None, 2, 8, 6, None, None, None, None, 4, None, None, -1])) == [5, 9, 8, 6, -1]\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31])) == [1, 3, 7, 15, 31]\n assert candidate(root = tree_node([-1, -2, -3, -4, None, -5, -6])) == [-1, -2, -4]\n assert candidate(root = tree_node([5, 8, 5, 8, None, None, 5, None, 4, None, 9, 7, 6])) == [5, 8, 8, 9, 7]\n assert candidate(root = tree_node([1, None, None, 2, None, None, 3, None, None, 4, None, None, 5, None, None, 6, None, None, 7, None, None, 8, None, None, 9])) == [1]\n assert candidate(root = tree_node([1, None, 3, None, None, 2, None, None, 4, None, None, None, 5, None, None, None, None, None, 6])) == [1, 3]\n assert candidate(root = tree_node([-100, -200, -300, -400, None, -500, -600])) == [-100, -200, -400]\n assert candidate(root = tree_node([5, 4, 8, 11, None, 13, 4, 7, 2, None, None, 5, 1])) == [5, 8, 13, 7]\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().largestValues", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var largestValues = function(root) {", "container": null, "callable": "largestValues", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number[]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 516, "task_id": "longest-palindromic-subsequence", "difficulty": "Medium", "problem_description": "Given a string s, find the longest palindromic subsequence's length in s.\nA subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.\n \nExample 1:\n\nInput: s = \"bbbab\"\nOutput: 4\nExplanation: One possible longest palindromic subsequence is \"bbbb\".\n\nExample 2:\n\nInput: s = \"cbbd\"\nOutput: 2\nExplanation: One possible longest palindromic subsequence is \"bb\".\n\n \nConstraints:\n\n1 <= s.length <= 1000\ns consists only of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"abcba\") == 5\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\") == 1\n assert candidate(s = \"abcdcba\") == 7\n assert candidate(s = \"abcdedcba\") == 9\n assert candidate(s = \"noonhighnoon\") == 11\n assert candidate(s = \"a\") == 1\n assert candidate(s = \"cbbd\") == 2\n assert candidate(s = \"ab\") == 1\n assert candidate(s = \"aabaa\") == 5\n assert candidate(s = \"abcde\") == 1\n assert candidate(s = \"racecar\") == 7\n assert candidate(s = \"abcb\") == 3\n assert candidate(s = \"bcbab\") == 3\n assert candidate(s = \"noon\") == 4\n assert candidate(s = \"banana\") == 5\n assert candidate(s = \"deeee\") == 4\n assert candidate(s = \"agbdba\") == 5\n assert candidate(s = \"abccba\") == 6\n assert candidate(s = \"aaaa\") == 4\n assert candidate(s = \"character\") == 5\n assert candidate(s = \"level\") == 5\n assert candidate(s = \"bbbab\") == 4\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\") == 1\n assert candidate(s = \"abcdefg\") == 1\n assert candidate(s = \"aabcdefggfedcbagfedcba\") == 16\n assert candidate(s = \"noonappa\") == 4\n assert candidate(s = \"aacaagttaccagtcacaagttaacaagttaccagtcacaagttaac\") == 33\n assert candidate(s = \"abbdbba\") == 7\n assert candidate(s = \"abracadabra\") == 7\n assert candidate(s = \"abcabcabcabc\") == 7\n assert candidate(s = \"levelmadam\") == 5\n assert candidate(s = \"abbaababa\") == 8\n assert candidate(s = \"abcdaedcba\") == 9\n assert candidate(s = \"babbbabbbbabbb\") == 12\n assert candidate(s = \"tattarrattat\") == 12\n assert candidate(s = \"aaaabaaaa\") == 9\n assert candidate(s = \"noonnoon\") == 8\n assert candidate(s = \"abccbaabccba\") == 12\n assert candidate(s = ('elrmenmet',)) == 1\n assert candidate(s = \"aabbccddeeaabbccddeeff\") == 6\n assert candidate(s = \"madamracecar\") == 7\n assert candidate(s = \"nogood\") == 3\n assert candidate(s = \"abcdcbazxyzyxcba\") == 11\n assert candidate(s = \"epelppel\") == 5\n assert candidate(s = \"aabaaabbabaaabbbaabaa\") == 19\n assert candidate(s = \"abcdaabcd\") == 4\n assert candidate(s = \"zazalxlkjlkjlkjljlkjljlkjlkjljlkjljlkjljlkjljlkjljlkjljlkjljlkjlkjljlkjljlkjljlkjljlkjljlkjlkjljlkjljlkjljlkjl\") == 81\n assert candidate(s = \"xyzabcba\") == 5\n assert candidate(s = \"aabacbebebe\") == 5\n assert candidate(s = \"kayak\") == 5\n assert candidate(s = \"rotorotor\") == 9\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyzzyxwvutsrqponmlkjihgfedcba\") == 52\n assert candidate(s = \"zyxzyxzyxzyxzyx\") == 9\n assert candidate(s = \"elkfaodfnofowefwaefewfafwefawfawfawfawfawfawfawfawfawfawfaw\") == 35\n assert candidate(s = \"abcdefggfedcba\") == 14\n assert candidate(s = \"attacking\") == 4\n assert candidate(s = \"nursesrun\") == 9\n assert candidate(s = \"aabbccddeeaabbccddeeaabbccddeeaabbccddeeaabbccddeeaabbccddeeaabbccdd\") == 26\n assert candidate(s = \"aibohphobia\") == 11\n assert candidate(s = \"abcaebcabcbcabcbc\") == 11\n assert candidate(s = \"deeeeved\") == 7\n assert candidate(s = \"madam\") == 5\n assert candidate(s = \"ababababababa\") == 13\n assert candidate(s = \"radar\") == 5\n assert candidate(s = \"pwwkew\") == 3\n assert candidate(s = \"aabbccddeeeffggghhhhiiii\") == 4\n assert candidate(s = \"bcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbcbc\") == 109\n assert candidate(s = \"abcdefghikjlmnopqrstuvwxyz\") == 1\n assert candidate(s = \"xyzabcdedcbazyx\") == 15\n assert candidate(s = \"aabcbab\") == 5\n assert candidate(s = \"abcadacaabc\") == 7\n assert candidate(s = \"aabaaa\") == 5\n assert candidate(s = \"anana\") == 5\n assert candidate(s = \"aabbabbaaabbabbaaabbabbaaabbabba\") == 31\n assert candidate(s = \"aabbccddeeffgg\") == 2\n assert candidate(s = \"xyzyxzyxzyxzyxzyx\") == 13\n assert candidate(s = \"aabaaaabaaabaaaba\") == 15\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\") == 2\n assert candidate(s = \"longestpalindromicsubsequence\") == 9\n assert candidate(s = \"zxcvbnnbvxcz\") == 10\n assert candidate(s = \"racecarannakayak\") == 8\n assert candidate(s = \"abcdefghgfedcba\") == 15\n assert candidate(s = \"abcdefghiijkmlkjihgfedcba\") == 23\n assert candidate(s = \"mimimum\") == 5\n assert candidate(s = \"aannnaaaa\") == 7\n assert candidate(s = \"repaper\") == 7\n assert candidate(s = \"mamadmim\") == 5\n assert candidate(s = \"mamad\") == 3\n assert candidate(s = \"abacdfgdcaba\") == 11\n assert candidate(s = \"abcddcba\") == 8\n assert candidate(s = \"civic\") == 5\n assert candidate(s = \"rotor\") == 5\n assert candidate(s = \"abcdefghihgfedcba\") == 17\n assert candidate(s = \"intersubjective\") == 7\n assert candidate(s = \"lrfipxxl\") == 4\n assert candidate(s = \"mississippi\") == 7\n assert candidate(s = \"madaminnadamsandnoon\") == 10\n assert candidate(s = \"forgeeksskeegfor\") == 12\n assert candidate(s = \"aaaaabbbbbccccc\") == 5\n assert candidate(s = \"refer\") == 5\n"}, "metadata": {"canonical_parameter_names": ["s"], "leetcode_dataset_entry_point": "Solution().longestPalindromeSubseq", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var longestPalindromeSubseq = function(s) {", "container": null, "callable": "longestPalindromeSubseq", "parameters": [{"name": "s", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 517, "task_id": "super-washing-machines", "difficulty": "Hard", "problem_description": "You have n super washing machines on a line. Initially, each washing machine has some dresses or is empty.\nFor each move, you could choose any m (1 <= m <= n) washing machines, and pass one dress of each washing machine to one of its adjacent washing machines at the same time.\nGiven an integer array machines representing the number of dresses in each washing machine from left to right on the line, return the minimum number of moves to make all the washing machines have the same number of dresses. If it is not possible to do it, return -1.\n \nExample 1:\n\nInput: machines = [1,0,5]\nOutput: 3\nExplanation:\n1st move: 1 0 <-- 5 => 1 1 4\n2nd move: 1 <-- 1 <-- 4 => 2 1 3\n3rd move: 2 1 <-- 3 => 2 2 2\n\nExample 2:\n\nInput: machines = [0,3,0]\nOutput: 2\nExplanation:\n1st move: 0 <-- 3 0 => 1 2 0\n2nd move: 1 2 --> 0 => 1 1 1\n\nExample 3:\n\nInput: machines = [0,2,0]\nOutput: -1\nExplanation:\nIt's impossible to make all three washing machines have the same number of dresses.\n\n \nConstraints:\n\nn == machines.length\n1 <= n <= 104\n0 <= machines[i] <= 105\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(machines = [0, 2, 0]) == -1\n assert candidate(machines = [9, 1, 8, 8, 9]) == 4\n assert candidate(machines = [0, 0, 18]) == 12\n assert candidate(machines = [1, 0, 0, 3, 0, 2, 0]) == -1\n assert candidate(machines = [100000]) == 0\n assert candidate(machines = [0, 0, 0, 0, 0]) == 0\n assert candidate(machines = [4, 0, 0, 4]) == 2\n assert candidate(machines = [5, 5, 5, 5, 5]) == 0\n assert candidate(machines = [1]) == 0\n assert candidate(machines = [1, 1, 1, 1]) == 0\n assert candidate(machines = [1, 0, 5]) == 3\n assert candidate(machines = [0, 3, 0]) == 2\n assert candidate(machines = [10, 10, 10, 10]) == 0\n assert candidate(machines = [1, 2, 3, 4, 5]) == 3\n assert candidate(machines = [1, 0, 0, 3, 0, 0, 2, 0]) == -1\n assert candidate(machines = [0, 0, 11, 5]) == 8\n assert candidate(machines = [1, 0, 5, 4, 0, 0, 2, 3]) == -1\n assert candidate(machines = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 0\n assert candidate(machines = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == -1\n assert candidate(machines = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == -1\n assert candidate(machines = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) == -1\n assert candidate(machines = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000]) == 12500\n assert candidate(machines = [100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 95\n assert candidate(machines = [2, 2, 2, 2, 1, 2, 2, 2, 2]) == -1\n assert candidate(machines = [0, 0, 0, 0, 0, 0, 0, 0, 0, 10]) == 9\n assert candidate(machines = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(machines = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2]) == -1\n assert candidate(machines = [10000, 9000, 8000, 7000, 6000, 5000, 4000, 3000, 2000, 1000]) == 12500\n assert candidate(machines = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]) == -1\n assert candidate(machines = [1, 0, 0, 0, 0, 5]) == 4\n assert candidate(machines = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100]) == -1\n assert candidate(machines = [20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 19\n assert candidate(machines = [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]) == 0\n assert candidate(machines = [4, 5, 6, 7, 8]) == 3\n assert candidate(machines = [10, 15, 10, 15, 10, 15, 10]) == -1\n assert candidate(machines = [0, 0, 0, 0, 0, 0, 21, 0]) == -1\n assert candidate(machines = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100]) == 95\n assert candidate(machines = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == -1\n assert candidate(machines = [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]) == 28\n assert candidate(machines = [10, 1, 1, 1, 10]) == -1\n assert candidate(machines = [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) == 0\n assert candidate(machines = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 28\n assert candidate(machines = [1, 0, 0, 0, 0, 10, 0, 0, 0, 0, 1]) == -1\n assert candidate(machines = [0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100]) == -1\n assert candidate(machines = [5, 5, 5, 5, 5, 5, 5, 5]) == 0\n assert candidate(machines = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(machines = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 0\n assert candidate(machines = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(machines = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10]) == 0\n assert candidate(machines = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 0\n assert candidate(machines = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100]) == 95\n assert candidate(machines = [50, 45, 40, 35, 30, 25, 20, 15, 10, 5]) == -1\n assert candidate(machines = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == -1\n"}, "metadata": {"canonical_parameter_names": ["machines"], "leetcode_dataset_entry_point": "Solution().findMinMoves", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMinMoves = function(machines) {", "container": null, "callable": "findMinMoves", "parameters": [{"name": "machines", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 518, "task_id": "coin-change-ii", "difficulty": "Medium", "problem_description": "You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.\nReturn the number of combinations that make up that amount. If that amount of money cannot be made up by any combination of the coins, return 0.\nYou may assume that you have an infinite number of each kind of coin.\nThe answer is guaranteed to fit into a signed 32-bit integer.\n \nExample 1:\n\nInput: amount = 5, coins = [1,2,5]\nOutput: 4\nExplanation: there are four ways to make up the amount:\n5=5\n5=2+2+1\n5=2+1+1+1\n5=1+1+1+1+1\n\nExample 2:\n\nInput: amount = 3, coins = [2]\nOutput: 0\nExplanation: the amount of 3 cannot be made up just with coins of 2.\n\nExample 3:\n\nInput: amount = 10, coins = [10]\nOutput: 1\n\n \nConstraints:\n\n1 <= coins.length <= 300\n1 <= coins[i] <= 5000\nAll the values of coins are unique.\n0 <= amount <= 5000\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(amount = 20,coins = [1, 5, 10]) == 9\n assert candidate(amount = 1,coins = [1]) == 1\n assert candidate(amount = 0,coins = [1, 2, 5]) == 1\n assert candidate(amount = 5000,coins = [1, 5, 10, 25, 50]) == 432699251\n assert candidate(amount = 100,coins = [3, 7, 40, 9]) == 48\n assert candidate(amount = 6249,coins = [186, 419, 83, 408]) == 19\n assert candidate(amount = 15,coins = [1, 3, 5, 7]) == 19\n assert candidate(amount = 10,coins = [1, 3, 4, 5]) == 12\n assert candidate(amount = 10,coins = [10]) == 1\n assert candidate(amount = 50,coins = [1, 18, 27, 34, 50]) == 7\n assert candidate(amount = 5000,coins = [3, 5, 7, 8, 9, 10]) == 351757492460\n assert candidate(amount = 100,coins = [3, 6, 9]) == 0\n assert candidate(amount = 3,coins = [2]) == 0\n assert candidate(amount = 25,coins = [1, 2, 5]) == 42\n assert candidate(amount = 5,coins = [1, 2, 5]) == 4\n assert candidate(amount = 100,coins = [1, 2, 5, 10, 20, 50]) == 4562\n assert candidate(amount = 1000,coins = [3, 5, 7, 8, 9, 10, 11]) == 1952879228\n assert candidate(amount = 3000,coins = [4, 12, 23, 34, 51]) == 1913606\n assert candidate(amount = 1800,coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 120836624716\n assert candidate(amount = 3500,coins = [50, 100, 150, 200, 250, 300, 350]) == 94425\n assert candidate(amount = 2500,coins = [11, 22, 33, 44, 55, 66, 77, 88, 99]) == 0\n assert candidate(amount = 2500,coins = [13, 17, 19, 23, 29, 31]) == 10673219\n assert candidate(amount = 4500,coins = [23, 47, 61, 83, 97, 101]) == 358270\n assert candidate(amount = 4200,coins = [11, 22, 33, 44, 55, 66, 77, 88, 99]) == 0\n assert candidate(amount = 4000,coins = [3, 9, 18, 36, 72, 144]) == 0\n assert candidate(amount = 8000,coins = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 0\n assert candidate(amount = 3333,coins = [3, 6, 9, 12, 15, 18, 21, 24, 27]) == 186150339220814\n assert candidate(amount = 1200,coins = [2, 5, 10, 25, 50, 100]) == 2459925\n assert candidate(amount = 4500,coins = [11, 22, 33, 44, 55]) == 0\n assert candidate(amount = 2000,coins = [11, 17, 29, 31]) == 8465\n assert candidate(amount = 3000,coins = [4, 9, 15, 25, 30, 50, 75]) == 816870821\n assert candidate(amount = 3750,coins = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 6877248457909551\n assert candidate(amount = 4800,coins = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]) == 402020904793077\n assert candidate(amount = 3500,coins = [1, 2, 5, 10, 20, 50, 100]) == 298945088016\n assert candidate(amount = 10000,coins = [2, 3, 5, 7, 11, 13, 17, 19, 23]) == 11569288968418829417\n assert candidate(amount = 3750,coins = [125, 250, 500, 1000, 2000]) == 166\n assert candidate(amount = 2750,coins = [4, 9, 14, 19, 24, 29, 34, 39, 44, 49]) == 1980385268761\n assert candidate(amount = 6000,coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512]) == 1608946754650872\n assert candidate(amount = 4500,coins = [2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000]) == 17776167706\n assert candidate(amount = 4500,coins = [5, 10, 20, 50, 100, 200]) == 94862488\n assert candidate(amount = 6000,coins = [11, 22, 33, 44, 55, 66]) == 0\n assert candidate(amount = 5555,coins = [7, 14, 21, 28, 35, 42, 49, 56, 63]) == 0\n assert candidate(amount = 2048,coins = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 2320518947\n assert candidate(amount = 4000,coins = [1, 11, 13, 19, 21, 31, 37]) == 95941704933\n assert candidate(amount = 2700,coins = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 385226325096527\n assert candidate(amount = 4999,coins = [1, 2, 5, 10, 25, 50, 100, 200, 500]) == 14978475244405\n assert candidate(amount = 700,coins = [3, 7, 11, 13, 17, 19, 23, 29]) == 45005473\n assert candidate(amount = 4500,coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048]) == 171076578684392\n assert candidate(amount = 2500,coins = [2, 3, 5, 7, 11, 13]) == 28227697415\n assert candidate(amount = 500,coins = [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]) == 0\n assert candidate(amount = 3500,coins = [7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]) == 1916917910649679\n assert candidate(amount = 500,coins = [11, 22, 33, 44, 55]) == 0\n assert candidate(amount = 8000,coins = [1, 2, 5, 10, 20, 50, 100]) == 39042657518121\n assert candidate(amount = 1500,coins = [3, 5, 7, 11, 13, 17, 19, 23]) == 38017360391\n assert candidate(amount = 3500,coins = [17, 23, 29, 31, 37]) == 519429\n assert candidate(amount = 2700,coins = [3, 6, 9, 12, 15, 18, 21, 24, 27]) == 35818551286815\n assert candidate(amount = 1500,coins = [50, 200, 500, 1000]) == 22\n assert candidate(amount = 500,coins = [11, 19, 29, 37, 47, 59, 71, 83]) == 3292\n assert candidate(amount = 2000,coins = [1, 3, 7, 11]) == 5867703\n assert candidate(amount = 3000,coins = [15, 25, 35, 45, 55]) == 582580\n assert candidate(amount = 5000,coins = [1, 4, 9, 16, 25, 36, 49]) == 928443384056\n assert candidate(amount = 2500,coins = [7, 17, 27, 37, 47, 57, 67, 77]) == 115681732\n assert candidate(amount = 2000,coins = [1, 3, 4, 12, 24, 48]) == 1799991438\n assert candidate(amount = 3000,coins = [2, 5, 10, 20, 50, 100]) == 238303231\n assert candidate(amount = 5000,coins = [20, 25, 50, 100, 200, 500]) == 831886\n assert candidate(amount = 4000,coins = [2, 4, 6, 8, 10, 12, 14, 16, 18]) == 19131722793601739\n assert candidate(amount = 3000,coins = [33, 66, 99, 132, 165, 198, 231, 264, 297]) == 0\n assert candidate(amount = 2222,coins = [2, 4, 6, 8, 10, 12, 14, 16, 18]) == 186150339220814\n assert candidate(amount = 200,coins = [1, 3, 5, 7, 9]) == 89740\n assert candidate(amount = 4567,coins = [2, 5, 10, 20, 50]) == 188174063\n assert candidate(amount = 800,coins = [10, 20, 50, 100, 200, 500]) == 2064\n assert candidate(amount = 3333,coins = [13, 23, 33, 43, 53, 63, 73, 83, 93, 103]) == 3570286683\n assert candidate(amount = 2000,coins = [10, 25, 50, 100, 200, 500]) == 29674\n assert candidate(amount = 1500,coins = [5, 11, 17, 23, 29]) == 378081\n assert candidate(amount = 6000,coins = [1, 2, 3, 5, 11, 23, 37, 41]) == 5179949524521356\n assert candidate(amount = 3000,coins = [1, 10, 25, 50, 100, 200]) == 11051256\n assert candidate(amount = 4999,coins = [1, 3, 9, 27, 81, 243, 729, 2187, 6561]) == 3946672836\n assert candidate(amount = 1200,coins = [4, 8, 15, 16, 23, 42]) == 3481694\n assert candidate(amount = 999,coins = [1, 4, 9, 16, 25, 36, 49, 64, 81]) == 528165615\n assert candidate(amount = 1111,coins = [1, 4, 9, 16, 25, 36, 49, 64, 81]) == 1122054398\n assert candidate(amount = 6666,coins = [1, 2, 3, 5, 8, 13, 21, 34, 55]) == 858790214643388609\n assert candidate(amount = 4000,coins = [3, 5, 7, 9, 11, 13, 15]) == 2941614132296\n assert candidate(amount = 1234,coins = [13, 21, 34, 55, 89, 144, 233, 377, 610, 987]) == 10948\n assert candidate(amount = 3500,coins = [1, 2, 4, 8, 16, 32, 64]) == 1356535733168\n assert candidate(amount = 1500,coins = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100]) == 23221589514\n assert candidate(amount = 1200,coins = [5, 15, 25, 50, 100, 200]) == 115862\n assert candidate(amount = 3000,coins = [1, 3, 4, 10, 20, 50]) == 18144427661\n assert candidate(amount = 3000,coins = [2, 5, 11, 23, 47]) == 30080239\n assert candidate(amount = 3456,coins = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]) == 35362292367933393\n assert candidate(amount = 800,coins = [5, 10, 20, 50, 100, 200]) == 38835\n assert candidate(amount = 1234,coins = [1, 2, 5, 10, 20, 50, 100]) == 754797589\n assert candidate(amount = 4000,coins = [11, 22, 33, 44, 55]) == 0\n assert candidate(amount = 2000,coins = [7, 11, 13, 17, 19, 23]) == 40067247\n assert candidate(amount = 1800,coins = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]) == 1067122993784732\n assert candidate(amount = 7000,coins = [1, 5, 10, 25, 50, 100, 200, 500]) == 399576201827\n assert candidate(amount = 4000,coins = [8, 16, 24, 32, 40, 48, 56]) == 5078412464\n assert candidate(amount = 1500,coins = [2, 5, 11, 25, 40, 60]) == 12079534\n assert candidate(amount = 1800,coins = [2, 6, 12, 18, 24, 30]) == 192387751\n assert candidate(amount = 1500,coins = [7, 11, 13, 17, 19]) == 712518\n assert candidate(amount = 3500,coins = [5, 15, 25, 35, 45, 55, 65, 75]) == 10998232465\n assert candidate(amount = 1234,coins = [3, 5, 7, 11, 13, 17, 19]) == 1209189166\n assert candidate(amount = 750,coins = [7, 14, 21, 28, 35, 42]) == 0\n assert candidate(amount = 2000,coins = [1, 3, 5, 7, 9, 11, 13]) == 707531982781\n assert candidate(amount = 4000,coins = [5, 11, 17, 23, 29, 35, 41, 47, 53, 59]) == 7799502297011\n assert candidate(amount = 4000,coins = [5, 10, 25, 50, 100]) == 9370181\n assert candidate(amount = 1800,coins = [15, 25, 35, 45, 55, 65, 75, 85, 95, 105]) == 79077323\n assert candidate(amount = 7777,coins = [13, 26, 39, 52, 65, 78, 91, 104, 117]) == 0\n assert candidate(amount = 9000,coins = [15, 25, 35, 45, 55, 65]) == 1244874855\n assert candidate(amount = 4000,coins = [7, 14, 21, 28, 35]) == 0\n assert candidate(amount = 4321,coins = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) == 8412107116918783059141522248\n assert candidate(amount = 2000,coins = [101, 103, 107, 109]) == 0\n assert candidate(amount = 2500,coins = [2, 5, 11, 17, 23, 29, 35, 41, 47]) == 623719935720\n assert candidate(amount = 500,coins = [1, 2, 5, 10, 20, 50, 100]) == 5824071\n assert candidate(amount = 5000,coins = [1, 2, 5, 10, 20, 50, 100, 200, 500]) == 18682149631801\n assert candidate(amount = 2000,coins = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024]) == 264830889564\n assert candidate(amount = 4500,coins = [7, 13, 19, 23, 37, 41]) == 275308289\n assert candidate(amount = 8888,coins = [11, 22, 33, 44, 55, 66, 77, 88, 99]) == 15453068500547\n assert candidate(amount = 1500,coins = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]) == 0\n assert candidate(amount = 7000,coins = [3, 5, 7, 11, 13, 17, 19]) == 34788754338474\n assert candidate(amount = 3000,coins = [1, 3, 5, 10, 25, 50]) == 11669586691\n assert candidate(amount = 1999,coins = [111, 222, 333, 444, 555, 666, 777, 888]) == 0\n assert candidate(amount = 999,coins = [1, 2, 4, 8, 16, 32, 64]) == 944362512\n assert candidate(amount = 6000,coins = [3, 6, 12, 24, 48, 96]) == 8807842176\n assert candidate(amount = 5000,coins = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]) == 1027087367648016934506457070508\n"}, "metadata": {"canonical_parameter_names": ["amount", "coins"], "leetcode_dataset_entry_point": "Solution().change", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var change = function(amount, coins) {", "container": null, "callable": "change", "parameters": [{"name": "amount", "type": "number"}, {"name": "coins", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 520, "task_id": "detect-capital", "difficulty": "Easy", "problem_description": "We define the usage of capitals in a word to be right when one of the following cases holds:\n\nAll letters in this word are capitals, like \"USA\".\nAll letters in this word are not capitals, like \"leetcode\".\nOnly the first letter in this word is capital, like \"Google\".\n\nGiven a string word, return true if the usage of capitals in it is right.\n \nExample 1:\nInput: word = \"USA\"\nOutput: true\nExample 2:\nInput: word = \"FlaG\"\nOutput: false\n\n \nConstraints:\n\n1 <= word.length <= 100\nword consists of lowercase and uppercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(word = \"AB\") == True\n assert candidate(word = \"Python\") == True\n assert candidate(word = \"python\") == True\n assert candidate(word = \"USA\") == True\n assert candidate(word = \"ab\") == True\n assert candidate(word = \"hello\") == True\n assert candidate(word = \"gOOgle\") == False\n assert candidate(word = \"Leetcode\") == True\n assert candidate(word = \"ABcD\") == False\n assert candidate(word = \"Google\") == True\n assert candidate(word = \"AbcD\") == False\n assert candidate(word = \"a\") == True\n assert candidate(word = \"A\") == True\n assert candidate(word = \"leetcode\") == True\n assert candidate(word = \"HELLO\") == True\n assert candidate(word = \"HelloWorld\") == False\n assert candidate(word = \"FlaG\") == False\n assert candidate(word = \"HELloworld\") == False\n assert candidate(word = \"INSTAGRAMSERVICES\") == True\n assert candidate(word = \"mNoPqR\") == False\n assert candidate(word = \"FACEBOOK\") == True\n assert candidate(word = \"cYbErSeCUrIty\") == False\n assert candidate(word = \"RoaDmAP\") == False\n assert candidate(word = \"AmaZoN\") == False\n assert candidate(word = \"Aaaaaaaaa\") == True\n assert candidate(word = \"QwErTyUiOp\") == False\n assert candidate(word = \"abcdefghij\") == True\n assert candidate(word = \"INTERNET\") == True\n assert candidate(word = \"M\") == True\n assert candidate(word = \"pRoGrAmMiNg\") == False\n assert candidate(word = \"rANDOMIZE\") == False\n assert candidate(word = \"aMAzOaN\") == False\n assert candidate(word = \"aNIMaTiOn\") == False\n assert candidate(word = \"dEveLopMeNt\") == False\n assert candidate(word = \"SNAPCHATWEB\") == True\n assert candidate(word = \"SiMpLe\") == False\n assert candidate(word = \"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz\") == False\n assert candidate(word = \"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ\") == False\n assert candidate(word = \"aBCdEfGhI\") == False\n assert candidate(word = \"AbCdEfGh\") == False\n assert candidate(word = \"wEb\") == False\n assert candidate(word = \"sWift\") == False\n assert candidate(word = \"TeChNiCaL\") == False\n assert candidate(word = \"bUG\") == False\n assert candidate(word = \"sUpErCaLiFrAgIlIsTiCcExPiAlIdOiCiOuS\") == False\n assert candidate(word = \"GoogleIsAmazing\") == False\n assert candidate(word = \"AlibabaCloud\") == False\n assert candidate(word = \"AbCdEfGhIj\") == False\n assert candidate(word = \"flag\") == True\n assert candidate(word = \"SNAPCHAT\") == True\n assert candidate(word = \"alibaba\") == True\n assert candidate(word = \"lower\") == True\n assert candidate(word = \"internationalization\") == True\n assert candidate(word = \"ABCDEFGHijklmnopqrstuvwxyz\") == False\n assert candidate(word = \"cLoudCOmPUTInG\") == False\n assert candidate(word = \"world\") == True\n assert candidate(word = \"AbcDefGhIjKlMnopQrstUvWxyZ\") == False\n assert candidate(word = \"TitleCase\") == False\n assert candidate(word = \"FLICKRWEB\") == True\n assert candidate(word = \"HaRdWaRE\") == False\n assert candidate(word = \"fAceBoOk\") == False\n assert candidate(word = \"JupyTeR\") == False\n assert candidate(word = \"PYTHON\") == True\n assert candidate(word = \"CdEf\") == False\n assert candidate(word = \"SuperCalifragilisticexpialidocious\") == False\n assert candidate(word = \"MachiNeLEARNING\") == False\n assert candidate(word = \"Internationalization\") == True\n assert candidate(word = \"APPLECOMPUTER\") == True\n assert candidate(word = \"eNd\") == False\n assert candidate(word = \"machinelearning\") == True\n assert candidate(word = \"AuDiO\") == False\n assert candidate(word = \"aAaAaA\") == False\n assert candidate(word = \"AbCdEfGhIjKlMnOpQrStUvWxYzA\") == False\n assert candidate(word = \"iNTERNATIONALIZATION\") == False\n assert candidate(word = \"pRoJeCt\") == False\n assert candidate(word = \"FLICKR\") == True\n assert candidate(word = \"qwen\") == True\n assert candidate(word = \"lAnGuAgE\") == False\n assert candidate(word = \"physICs\") == False\n assert candidate(word = \"cSHaRp\") == False\n assert candidate(word = \"EDiToR\") == False\n assert candidate(word = \"FaCeBoOk\") == False\n assert candidate(word = \"aB\") == False\n assert candidate(word = \"oNE\") == False\n assert candidate(word = \"aNATOMy\") == False\n assert candidate(word = \"QwErTyUiOpAsDfGhJkLzXcVbNm\") == False\n assert candidate(word = \"FACEBOOKINSTAGRAM\") == True\n assert candidate(word = \"aBcDeFgHiJkLmNoPqRsTuVwXyZ\") == False\n assert candidate(word = \"MaChInE\") == False\n assert candidate(word = \"ABc\") == False\n assert candidate(word = \"java\") == True\n assert candidate(word = \"CoMpLiCATED\") == False\n assert candidate(word = \"gOOGLE\") == False\n assert candidate(word = \"AMAZONWEB\") == True\n assert candidate(word = \"Alibaba\") == True\n assert candidate(word = \"pROGRaMMiNG\") == False\n assert candidate(word = \"xMl\") == False\n assert candidate(word = \"RaDIo\") == False\n assert candidate(word = \"INternationalization\") == False\n assert candidate(word = \"iNtErNaTioNaL\") == False\n assert candidate(word = \"uSeR\") == False\n assert candidate(word = \"INSTAGRAM\") == True\n assert candidate(word = \"AbCdEfGhIjKlMnOpQrSt\") == False\n assert candidate(word = \"ABCDEFGHIjklmnopqr\") == False\n assert candidate(word = \"Zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\") == True\n assert candidate(word = \"lowercase\") == True\n assert candidate(word = \"MuSiC\") == False\n assert candidate(word = \"fAcEboOk\") == False\n assert candidate(word = \"YOUTUBESERVICES\") == True\n assert candidate(word = \"aPpLiCaTiOn\") == False\n assert candidate(word = \"Ba\") == True\n assert candidate(word = \"s\") == True\n assert candidate(word = \"AbCdEfGhIjKlMnOp\") == False\n assert candidate(word = \"yOuTuBe\") == False\n assert candidate(word = \"fRoM\") == False\n assert candidate(word = \"gRaphIcS\") == False\n assert candidate(word = \"cGraPhIcs\") == False\n assert candidate(word = \"eCONoMiCS\") == False\n assert candidate(word = \"SiNgEr\") == False\n assert candidate(word = \"abcdefgh\") == True\n assert candidate(word = \"PRoDUCeR\") == False\n assert candidate(word = \"vIdEoGaMe\") == False\n assert candidate(word = \"GOOGLESERVICES\") == True\n assert candidate(word = \"Z\") == True\n assert candidate(word = \"z\") == True\n assert candidate(word = \"BuSINESSiNTelligence\") == False\n assert candidate(word = \"EBAY\") == True\n assert candidate(word = \"rEddIt\") == False\n assert candidate(word = \"CAPITALIZATION\") == True\n assert candidate(word = \"wOrLd\") == False\n assert candidate(word = \"abcdefghijKlmnopqrSTUVWXyz\") == False\n assert candidate(word = \"InValid\") == False\n assert candidate(word = \"data\") == True\n assert candidate(word = \"TWo\") == False\n assert candidate(word = \"wEbDeVeLopMeNt\") == False\n assert candidate(word = \"cDEF\") == False\n assert candidate(word = \"RUsT\") == False\n assert candidate(word = \"MICROSOFTAZURE\") == True\n assert candidate(word = \"MiCROsOfT\") == False\n assert candidate(word = \"UPPERlower\") == False\n assert candidate(word = \"MICROSOFTCLOUD\") == True\n assert candidate(word = \"openAI\") == False\n assert candidate(word = \"ViDIoGraPhEr\") == False\n assert candidate(word = \"YouTube\") == False\n assert candidate(word = \"hACK\") == False\n assert candidate(word = \"Ab\") == True\n assert candidate(word = \"jSoN\") == False\n assert candidate(word = \"DiReCtOr\") == False\n assert candidate(word = \"aPPlE\") == False\n assert candidate(word = \"ZyxWvuTsRqPoNmLkJiHgFeDcBa\") == False\n assert candidate(word = \"FACEBOOKWEB\") == True\n assert candidate(word = \"AbcDefGhIjKlMnopQrstUvWxyz\") == False\n assert candidate(word = \"WRiTeR\") == False\n assert candidate(word = \"tELEviSiOn\") == False\n assert candidate(word = \"FLICKRSERVICES\") == True\n assert candidate(word = \"YOUTUBE\") == True\n assert candidate(word = \"ai\") == True\n assert candidate(word = \"TUMBLRSERVICES\") == True\n assert candidate(word = \"artificialintelligence\") == True\n assert candidate(word = \"bUiLd\") == False\n assert candidate(word = \"gAmEs\") == False\n assert candidate(word = \"GOOGLEWEB\") == True\n assert candidate(word = \"PHp\") == False\n assert candidate(word = \"applecomputer\") == True\n assert candidate(word = \"openai\") == True\n assert candidate(word = \"LoWeRuPPeR\") == False\n assert candidate(word = \"ArtificialIntelligence\") == False\n assert candidate(word = \"qwenai\") == True\n assert candidate(word = \"TyPeScRiPT\") == False\n assert candidate(word = \"wEbSiTe\") == False\n assert candidate(word = \"pRoGrAmMaR\") == False\n assert candidate(word = \"AMericA\") == False\n assert candidate(word = \"AbCdEfGhIjKl\") == False\n assert candidate(word = \"cOdInG\") == False\n assert candidate(word = \"SPSS\") == True\n assert candidate(word = \"JAVA\") == True\n assert candidate(word = \"hELLO\") == False\n assert candidate(word = \"PsYCHOLOgY\") == False\n assert candidate(word = \"aBcDeFgHiJ\") == False\n assert candidate(word = \"allUPPER\") == False\n assert candidate(word = \"Defg\") == True\n assert candidate(word = \"tHISISATEST\") == False\n assert candidate(word = \"TUMBLR\") == True\n assert candidate(word = \"OpenAI\") == False\n assert candidate(word = \"wHiTtEr\") == False\n assert candidate(word = \"PyThOnPrOgRaM\") == False\n assert candidate(word = \"LeArNiNg\") == False\n assert candidate(word = \"AMAZONWEBSERVICES\") == True\n assert candidate(word = \"iOS\") == False\n assert candidate(word = \"FLaG\") == False\n assert candidate(word = \"QWENAI\") == True\n assert candidate(word = \"bAcK\") == False\n assert candidate(word = \"ALLUPPERCASE\") == True\n assert candidate(word = \"SAP\") == True\n assert candidate(word = \"UPPERCASE\") == True\n assert candidate(word = \"STATA\") == True\n assert candidate(word = \"FlAG\") == False\n assert candidate(word = \"SlAcK\") == False\n assert candidate(word = \"NeWs\") == False\n assert candidate(word = \"vIsUAlsTuDiOs\") == False\n assert candidate(word = \"tWItTeR\") == False\n assert candidate(word = \"LINKEDINSERVICES\") == True\n assert candidate(word = \"RuBuY\") == False\n assert candidate(word = \"THISISATEST\") == True\n assert candidate(word = \"ThIsIsAtEsT\") == False\n assert candidate(word = \"AAAAAAAAA\") == True\n assert candidate(word = \"AlLcaPslOcK\") == False\n assert candidate(word = \"gOOgLE\") == False\n assert candidate(word = \"PyThOn\") == False\n assert candidate(word = \"HELLOworld\") == False\n assert candidate(word = \"MaThS\") == False\n assert candidate(word = \"AbCdEfGhIjKlMnOpQrStUvWx\") == False\n assert candidate(word = \"tHIsSHOULDBEFalse\") == False\n assert candidate(word = \"Qwen\") == True\n assert candidate(word = \"INTERNationalIZATION\") == False\n assert candidate(word = \"PhYSIOlOGy\") == False\n assert candidate(word = \"dEfInE\") == False\n assert candidate(word = \"MiXeD123\") == False\n assert candidate(word = \"SNAPCHATSERVICES\") == True\n assert candidate(word = \"AbCDeFgHiJkLmNoPqRsTuVwXyZ\") == False\n assert candidate(word = \"GOOGLE\") == True\n assert candidate(word = \"WRiTEr\") == False\n assert candidate(word = \"AcTReSS\") == False\n assert candidate(word = \"gOOD\") == False\n assert candidate(word = \"AbCdEfGhIjKlMnOpQrStUvWxYz\") == False\n assert candidate(word = \"ArTIFICiALiNTelligence\") == False\n assert candidate(word = \"AbCd\") == False\n assert candidate(word = \"ValidCapital\") == False\n assert candidate(word = \"microsoft\") == True\n assert candidate(word = \"LINKEDIN\") == True\n assert candidate(word = \"EBAYSERVICES\") == True\n assert candidate(word = \"AMAZON\") == True\n assert candidate(word = \"AbCdEf\") == False\n assert candidate(word = \"ORAcLe\") == False\n assert candidate(word = \"AMaZiNg\") == False\n assert candidate(word = \"NeURALnETWORKS\") == False\n assert candidate(word = \"mNopQr\") == False\n assert candidate(word = \"ALIBABA\") == True\n assert candidate(word = \"america\") == True\n assert candidate(word = \"cOdE\") == False\n assert candidate(word = \"HTmL\") == False\n assert candidate(word = \"GoogleSearch\") == False\n assert candidate(word = \"ThisIsATest\") == False\n assert candidate(word = \"DROPBOXWEB\") == True\n assert candidate(word = \"MACHINELEARNING\") == True\n assert candidate(word = \"Go\") == True\n assert candidate(word = \"tEsT\") == False\n assert candidate(word = \"gRaPhiCs\") == False\n assert candidate(word = \"OPENAI\") == True\n assert candidate(word = \"DataSCIENCE\") == False\n assert candidate(word = \"hISToRY\") == False\n assert candidate(word = \"oneTWOthreeFOUR\") == False\n assert candidate(word = \"TUMBLRWEB\") == True\n assert candidate(word = \"MaNaGeR\") == False\n assert candidate(word = \"mAkE\") == False\n assert candidate(word = \"mEsSeNger\") == False\n assert candidate(word = \"RoBOtIcs\") == False\n assert candidate(word = \"sUPERCALIFRAGILISTICEXPIALIDOCIOUS\") == False\n assert candidate(word = \"AbCdEfGhIjKlMnOpQr\") == False\n assert candidate(word = \"m\") == True\n assert candidate(word = \"sOFTwaRE\") == False\n assert candidate(word = \"AbCdEfGhIjKlMn\") == False\n assert candidate(word = \"AI\") == True\n assert candidate(word = \"RaCT\") == False\n assert candidate(word = \"BingSearchEngine\") == False\n assert candidate(word = \"ARTIFICIALINTELLIGENCE\") == True\n assert candidate(word = \"oPeN\") == False\n assert candidate(word = \"mOVie\") == False\n assert candidate(word = \"AA\") == True\n assert candidate(word = \"mnopqr\") == True\n assert candidate(word = \"Aa\") == True\n assert candidate(word = \"abc\") == True\n assert candidate(word = \"TWITTER\") == True\n assert candidate(word = \"aLGoRiTHMs\") == False\n assert candidate(word = \"tO\") == False\n assert candidate(word = \"ZzZ\") == False\n assert candidate(word = \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\") == True\n assert candidate(word = \"MACHINE\") == True\n assert candidate(word = \"GoOgLe\") == False\n assert candidate(word = \"INFORMATIONtechnology\") == False\n assert candidate(word = \"JSAvAsCrIpT\") == False\n assert candidate(word = \"kOTlIN\") == False\n assert candidate(word = \"MuSiCiAn\") == False\n assert candidate(word = \"machine\") == True\n assert candidate(word = \"tIKtOk\") == False\n assert candidate(word = \"mnopQR\") == False\n assert candidate(word = \"yAmL\") == False\n assert candidate(word = \"abCdEfGhIjKlMnOpQrStUvWxYz\") == False\n assert candidate(word = \"singleLETTER\") == False\n assert candidate(word = \"youtube\") == True\n assert candidate(word = \"sNAPcHaT\") == False\n assert candidate(word = \"apple\") == True\n assert candidate(word = \"AbCdEfGhIjKlMnOpQrStUv\") == False\n assert candidate(word = \"cODe\") == False\n assert candidate(word = \"cINeMa\") == False\n assert candidate(word = \"MICROSOFTWEB\") == True\n assert candidate(word = \"alllower\") == True\n assert candidate(word = \"THISisAteSt\") == False\n assert candidate(word = \"FLAG\") == True\n assert candidate(word = \"Data\") == True\n assert candidate(word = \"OnEtwOthReEfOuR\") == False\n assert candidate(word = \"pRoGrEsS\") == False\n assert candidate(word = \"ABCDEFGH\") == True\n assert candidate(word = \"TWITTERWEB\") == True\n assert candidate(word = \"leetCODe\") == False\n assert candidate(word = \"fLAG\") == False\n assert candidate(word = \"bA\") == False\n assert candidate(word = \"abcdefghijKLMNOPQR\") == False\n assert candidate(word = \"DISCoRd\") == False\n assert candidate(word = \"MakE\") == False\n assert candidate(word = \"bing\") == True\n assert candidate(word = \"gOOGLe\") == False\n assert candidate(word = \"vErSiOn\") == False\n assert candidate(word = \"eXpEriEnCe\") == False\n assert candidate(word = \"ThrEE\") == False\n assert candidate(word = \"wItH\") == False\n assert candidate(word = \"mICROSOFT\") == False\n assert candidate(word = \"MaCHiNeViSiOn\") == False\n assert candidate(word = \"qUaNtuMCoMpUtInG\") == False\n assert candidate(word = \"APPLEpie\") == False\n assert candidate(word = \"AaAaAa\") == False\n assert candidate(word = \"SAS\") == True\n assert candidate(word = \"MicroSoft\") == False\n assert candidate(word = \"DaTaANaLYsIS\") == False\n assert candidate(word = \"EBAYWEB\") == True\n assert candidate(word = \"MiXeDLoWeRuPpEr\") == False\n assert candidate(word = \"MATLAB\") == True\n assert candidate(word = \"CamelCase\") == False\n assert candidate(word = \"micro\") == True\n assert candidate(word = \"onELETTER\") == False\n assert candidate(word = \"MiCroSoFt\") == False\n assert candidate(word = \"fACeBoOk\") == False\n assert candidate(word = \"DATA\") == True\n assert candidate(word = \"TWITTERSERVICES\") == True\n assert candidate(word = \"sOuRcE\") == False\n assert candidate(word = \"DEFG\") == True\n assert candidate(word = \"CAPITAL\") == True\n assert candidate(word = \"JAVa\") == False\n assert candidate(word = \"dEsIgN\") == False\n assert candidate(word = \"FLAGship\") == False\n assert candidate(word = \"BING\") == True\n assert candidate(word = \"QwertyUiopAsDfGhJkLzXcVbNm\") == False\n assert candidate(word = \"GOOGLECLOUD\") == True\n assert candidate(word = \"alibabacloud\") == True\n assert candidate(word = \"DeBuGgInG\") == False\n assert candidate(word = \"MIXEDcase\") == False\n assert candidate(word = \"ApPlE\") == False\n assert candidate(word = \"TwItTeR\") == False\n assert candidate(word = \"ONE\") == True\n assert candidate(word = \"cOMPUTERsCIENCE\") == False\n assert candidate(word = \"PythonProgram\") == False\n assert candidate(word = \"zXcVbNmKlJ\") == False\n assert candidate(word = \"QwenAI\") == False\n assert candidate(word = \"NeTwORkS\") == False\n assert candidate(word = \"ZePpElIn\") == False\n assert candidate(word = \"AcTOr\") == False\n assert candidate(word = \"zYxWVuTsRqPoNmLkJiHgFeDcBa\") == False\n assert candidate(word = \"vIsIoN\") == False\n assert candidate(word = \"Three\") == True\n assert candidate(word = \"INSTaGram\") == False\n assert candidate(word = \"two\") == True\n assert candidate(word = \"AMERICA\") == True\n assert candidate(word = \"MixedCASE\") == False\n assert candidate(word = \"jOuRnaLiSm\") == False\n assert candidate(word = \"lInKeDin\") == False\n assert candidate(word = \"AlGoRiThMs\") == False\n assert candidate(word = \"JaVaScRiPt\") == False\n assert candidate(word = \"INSTAGRAMFACEBOOK\") == True\n assert candidate(word = \"DeEPLEaRNING\") == False\n assert candidate(word = \"APPLE\") == True\n assert candidate(word = \"aNdRoId\") == False\n assert candidate(word = \"LeetCode\") == False\n assert candidate(word = \"DROPBOX\") == True\n assert candidate(word = \"Valid\") == True\n assert candidate(word = \"LINKEDINWEB\") == True\n assert candidate(word = \"INSTAGRAMWEB\") == True\n assert candidate(word = \"abcdefghijklmnopqrstuvwxyz\") == True\n assert candidate(word = \"MachineLearning\") == False\n assert candidate(word = \"ALIBABACLOUD\") == True\n assert candidate(word = \"DataScience\") == False\n assert candidate(word = \"CAPITALS\") == True\n assert candidate(word = \"oneTWOthree\") == False\n assert candidate(word = \"YOUTUBEWEB\") == True\n assert candidate(word = \"LEETCODE\") == True\n assert candidate(word = \"tWiTtEr\") == False\n assert candidate(word = \"thisisatest\") == True\n assert candidate(word = \"sCALA\") == False\n assert candidate(word = \"bLoGgInG\") == False\n assert candidate(word = \"alllowercase\") == True\n assert candidate(word = \"TeStCaSe\") == False\n assert candidate(word = \"QWEN\") == True\n assert candidate(word = \"cSs\") == False\n assert candidate(word = \"aAaAaAaAaA\") == False\n assert candidate(word = \"Supercalifragilisticexpialidocious\") == True\n assert candidate(word = \"ABCDEFGHIJ\") == True\n assert candidate(word = \"INfOrMaTiOnSYsTEMS\") == False\n assert candidate(word = \"pInTeReSt\") == False\n assert candidate(word = \"DROPBOXSERVICES\") == True\n assert candidate(word = \"nOcaPslOcK\") == False\n assert candidate(word = \"PERL\") == True\n assert candidate(word = \"CoMpUtEr\") == False\n"}, "metadata": {"canonical_parameter_names": ["word"], "leetcode_dataset_entry_point": "Solution().detectCapitalUse", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var detectCapitalUse = function(word) {", "container": null, "callable": "detectCapitalUse", "parameters": [{"name": "word", "type": "string"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 521, "task_id": "longest-uncommon-subsequence-i", "difficulty": "Easy", "problem_description": "Given two strings a and b, return the length of the longest uncommon subsequence between a and b. If no such uncommon subsequence exists, return -1.\nAn uncommon subsequence between two strings is a string that is a subsequence of exactly one of them.\n \nExample 1:\n\nInput: a = \"aba\", b = \"cdc\"\nOutput: 3\nExplanation: One longest uncommon subsequence is \"aba\" because \"aba\" is a subsequence of \"aba\" but not \"cdc\".\nNote that \"cdc\" is also a longest uncommon subsequence.\n\nExample 2:\n\nInput: a = \"aaa\", b = \"bbb\"\nOutput: 3\nExplanation: The longest uncommon subsequences are \"aaa\" and \"bbb\".\n\nExample 3:\n\nInput: a = \"aaa\", b = \"aaa\"\nOutput: -1\nExplanation: Every subsequence of string a is also a subsequence of string b. Similarly, every subsequence of string b is also a subsequence of string a. So the answer would be -1.\n\n \nConstraints:\n\n1 <= a.length, b.length <= 100\na and b consist of lower-case English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(a = \"aaa\",b = \"bbb\") == 3\n assert candidate(a = \"same\",b = \"same\") == -1\n assert candidate(a = \"test\",b = \"testing\") == 7\n assert candidate(a = \"a\",b = \"b\") == 1\n assert candidate(a = \"abcde\",b = \"fghij\") == 5\n assert candidate(a = \"abc\",b = \"abcde\") == 5\n assert candidate(a = \"a\",b = \"a\") == -1\n assert candidate(a = \"abab\",b = \"baba\") == 4\n assert candidate(a = \"abcabc\",b = \"abc\") == 6\n assert candidate(a = \"abcd\",b = \"ab\") == 4\n assert candidate(a = \"aaa\",b = \"aaa\") == -1\n assert candidate(a = \"aba\",b = \"cdc\") == 3\n assert candidate(a = \"aaaa\",b = \"aa\") == 4\n assert candidate(a = \"abcd\",b = \"dcba\") == 4\n assert candidate(a = \"xyz\",b = \"zyx\") == 3\n assert candidate(a = \"hello\",b = \"world\") == 5\n assert candidate(a = \"\",b = \"\") == -1\n assert candidate(a = \"abc\",b = \"def\") == 3\n assert candidate(a = \"samecharacters\",b = \"samecharacters\") == -1\n assert candidate(a = \"aabbccddeeffgghhii\",b = \"abcabcabcabcabcabcabcabcabcabc\") == 30\n assert candidate(a = \"sameple\",b = \"sample\") == 7\n assert candidate(a = \"aaaaabbbb\",b = \"bbbbbaaaa\") == 9\n assert candidate(a = \"pqrstuvwxyz\",b = \"mnopqrstuvwxyz\") == 14\n assert candidate(a = \"mississippi\",b = \"mississippiiss\") == 14\n assert candidate(a = \"xylophone\",b = \"polymorph\") == 9\n assert candidate(a = \"aabbcc\",b = \"bbccaa\") == 6\n assert candidate(a = \"pqr\",b = \"pqrstu\") == 6\n assert candidate(a = \"abcdabcdabcd\",b = \"dcba\") == 12\n assert candidate(a = \"abcdefgh\",b = \"abcd\") == 8\n assert candidate(a = \"thisisatest\",b = \"thisisatesting\") == 14\n assert candidate(a = \"uniquecharacters\",b = \"differentcharacters\") == 19\n assert candidate(a = \"abc\",b = \"defg\") == 4\n assert candidate(a = \"aaaaabbbb\",b = \"bbbbbcccc\") == 9\n assert candidate(a = \"abracadabra\",b = \"avadakedavra\") == 12\n assert candidate(a = \"mississippi\",b = \"ississippi\") == 11\n assert candidate(a = \"patternmatching\",b = \"ternmpahcinoat\") == 15\n assert candidate(a = \"aaaaaaaab\",b = \"bbbbbbbba\") == 9\n assert candidate(a = \"uniquecharacters\",b = \"distinctcharacters\") == 18\n assert candidate(a = \"abcabcabcabc\",b = \"defdefdefdef\") == 12\n assert candidate(a = \"aaaaaaa\",b = \"aaaaaaaa\") == 8\n assert candidate(a = \"aabbccddeeff\",b = \"ffeeddccbaa\") == 12\n assert candidate(a = \"abacabadabacaba\",b = \"abcabcabcabc\") == 15\n assert candidate(a = \"aabbccddeeffgghhii\",b = \"jklmnopqrstuvwxyzz\") == 18\n assert candidate(a = \"abcdefghijk\",b = \"mnopqrstuvw\") == 11\n assert candidate(a = \"abacabadabacaba\",b = \"abacabadabacab\") == 15\n assert candidate(a = \"abcabcabc\",b = \"bcabcabca\") == 9\n assert candidate(a = \"aabbccddeeffgg\",b = \"ffggeeccddbbbaaa\") == 16\n assert candidate(a = \"aaaaaaaaaa\",b = \"bbbbbbbbbb\") == 10\n assert candidate(a = \"abcabcabc\",b = \"abcabc\") == 9\n assert candidate(a = \"aabbccddeeffgghhii\",b = \"aabbccddeeffgghhii\") == -1\n assert candidate(a = \"abcabcabcabc\",b = \"abcabcabc\") == 12\n assert candidate(a = \"\",b = \"abcdef\") == 6\n assert candidate(a = \"abcabcabcabcabcabcabcabcabcabc\",b = \"defdefdefdefdefdefdefdefdefdef\") == 30\n assert candidate(a = \"abababab\",b = \"babababa\") == 8\n assert candidate(a = \"xyzabc\",b = \"xyzdef\") == 6\n assert candidate(a = \"abcabcabc\",b = \"defdefdef\") == 9\n assert candidate(a = \"repeatedrepeated\",b = \"repeatedrepeatt\") == 16\n assert candidate(a = \"abcabcabc\",b = \"abc\") == 9\n assert candidate(a = \"xyxyxyxyxy\",b = \"yxyxyxyxyx\") == 10\n assert candidate(a = \"\",b = \"a\") == 1\n assert candidate(a = \"longestuncommonsubsequence\",b = \"short\") == 26\n assert candidate(a = \"abcdefghijklmnopqrstuvwxyz\",b = \"zyxwvutsrqponmlkjihgfedcba\") == 26\n assert candidate(a = \"mississippi\",b = \"mississipp\") == 11\n assert candidate(a = \"abacax\",b = \"bacxab\") == 6\n assert candidate(a = \"abracadabra\",b = \"cabracadabr\") == 11\n assert candidate(a = \"pneumonoultramicroscopicsilicovolcanoconiosis\",b = \"antidisestablishmentarianism\") == 45\n assert candidate(a = \"thisisatest\",b = \"isatestthis\") == 11\n assert candidate(a = \"aabbccddeeff\",b = \"aabbccddeeffgghh\") == 16\n assert candidate(a = \"xyzxyz\",b = \"zyxzyx\") == 6\n assert candidate(a = \"abcdexyz\",b = \"abcdexyz\") == -1\n assert candidate(a = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",b = \"zzyyxxwwvvuuttssrrqqppoonnmmllkkjjiihhggffeeddccbbaa\") == 52\n assert candidate(a = \"differentstrings\",b = \"different\") == 16\n assert candidate(a = \"abacabadabacaba\",b = \"bacabadabacabaa\") == 15\n assert candidate(a = \"repeatedrepeated\",b = \"repeated\") == 16\n assert candidate(a = \"aaaaaaabbbbcccc\",b = \"ccccbbbbaaaaaa\") == 15\n assert candidate(a = \"abcabcabcabc\",b = \"abcabc\") == 12\n assert candidate(a = \"differentstring\",b = \"differentstringxyz\") == 18\n assert candidate(a = \"abcd\",b = \"abcdabcd\") == 8\n assert candidate(a = \"abracadabra\",b = \"abracadabrac\") == 12\n assert candidate(a = \"aaaaa\",b = \"baaaa\") == 5\n assert candidate(a = \"repeatedsubstringrepeatedsubstring\",b = \"substring\") == 34\n assert candidate(a = \"aaabbbcccdddeee\",b = \"eeeedddcccbbbbaaa\") == 17\n assert candidate(a = \"abcdefghijabcdefghij\",b = \"jihgfedcbajihgfedcba\") == 20\n assert candidate(a = \"abcdefg\",b = \"ghijklm\") == 7\n assert candidate(a = \"aaaabbbbcccc\",b = \"ccccbbbbaaaa\") == 12\n assert candidate(a = \"abcdeabcdeabcde\",b = \"deabcdeabcdeabc\") == 15\n assert candidate(a = \"aaaaaa\",b = \"aaaaa\") == 6\n assert candidate(a = \"abcdabcdabcd\",b = \"dcbaabdc\") == 12\n assert candidate(a = \"aaaaaaab\",b = \"aaaaaaac\") == 8\n assert candidate(a = \"samestring\",b = \"samestring\") == -1\n assert candidate(a = \"abcde\",b = \"edcba\") == 5\n assert candidate(a = \"aaaabaaa\",b = \"aaabaaaa\") == 8\n assert candidate(a = \"abcdef\",b = \"ghijkl\") == 6\n assert candidate(a = \"abacabadabacaba\",b = \"babacabadabacab\") == 15\n assert candidate(a = \"unique\",b = \"distinct\") == 8\n assert candidate(a = \"abababababababab\",b = \"babababababababa\") == 16\n assert candidate(a = \"aabbccddeeff\",b = \"ffeeddccbbaa\") == 12\n assert candidate(a = \"aaaaaabbbbbbbbbbcccccc\",b = \"ccccccdddddeeeeeeffffff\") == 23\n assert candidate(a = \"aaaaaaaab\",b = \"aaaaaaaac\") == 9\n assert candidate(a = \"longestuncommonsubsequence\",b = \"subsequencelongestuncom\") == 26\n assert candidate(a = \"a\",b = \"\") == 1\n assert candidate(a = \"banana\",b = \"bananab\") == 7\n assert candidate(a = \"aabbccddeeffgghhiijj\",b = \"bbccddeeffgghhiijjkk\") == 20\n assert candidate(a = \"aabbcc\",b = \"ccbbaa\") == 6\n assert candidate(a = \"aaaaabaaaaabaaaaab\",b = \"baaaaabaaaaabaaaaa\") == 18\n assert candidate(a = \"aaaaaabbbbb\",b = \"bbbbbaaaaaa\") == 11\n assert candidate(a = \"longestuncommonsubsequence\",b = \"longestcommonsubsequence\") == 26\n assert candidate(a = \"longerstringexample\",b = \"short\") == 19\n assert candidate(a = \"thisisatest\",b = \"testthisis\") == 11\n assert candidate(a = \"abcdabcdabcd\",b = \"dcbaabcdabcd\") == 12\n assert candidate(a = \"uniqueuncommonstring\",b = \"stringuncommonunique\") == 20\n assert candidate(a = \"aaaaabbbbb\",b = \"bbbbbccccc\") == 10\n assert candidate(a = \"overlappingcharactersoverlap\",b = \"overlapoverlappingcharacters\") == 28\n assert candidate(a = \"abcabcabcabc\",b = \"abcabcabcabcabcabc\") == 18\n assert candidate(a = \"aabbccddeeffgghhii\",b = \"aabbccddeeffgg\") == 18\n assert candidate(a = \"aabbcc\",b = \"abbccc\") == 6\n assert candidate(a = \"aaaaaaa\",b = \"aaaaaab\") == 7\n assert candidate(a = \"abcdabcd\",b = \"dcba\") == 8\n assert candidate(a = \"identicalstrings\",b = \"identicalstrings\") == -1\n assert candidate(a = \"abcdabcdabcd\",b = \"cdabcdabcdab\") == 12\n assert candidate(a = \"aaaaa\",b = \"bbbbb\") == 5\n assert candidate(a = \"aabbccddeeffgg\",b = \"ggffeeeeddccbaaabb\") == 18\n assert candidate(a = \"longerstring\",b = \"longerstringabc\") == 15\n assert candidate(a = \"xyzabc\",b = \"abcxyz\") == 6\n assert candidate(a = \"aabbccddeeffgghhii\",b = \"zzzzzzzzzzzzzzzzzzzzzzzz\") == 24\n"}, "metadata": {"canonical_parameter_names": ["a", "b"], "leetcode_dataset_entry_point": "Solution().findLUSlength", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findLUSlength = function(a, b) {", "container": null, "callable": "findLUSlength", "parameters": [{"name": "a", "type": "string"}, {"name": "b", "type": "string"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 522, "task_id": "longest-uncommon-subsequence-ii", "difficulty": "Medium", "problem_description": "Given an array of strings strs, return the length of the longest uncommon subsequence between them. If the longest uncommon subsequence does not exist, return -1.\nAn uncommon subsequence between an array of strings is a string that is a subsequence of one string but not the others.\nA subsequence of a string s is a string that can be obtained after deleting any number of characters from s.\n\nFor example, \"abc\" is a subsequence of \"aebdc\" because you can delete the underlined characters in \"aebdc\" to get \"abc\". Other subsequences of \"aebdc\" include \"aebdc\", \"aeb\", and \"\" (empty string).\n\n \nExample 1:\nInput: strs = [\"aba\",\"cdc\",\"eae\"]\nOutput: 3\nExample 2:\nInput: strs = [\"aaa\",\"aaa\",\"aa\"]\nOutput: -1\n\n \nConstraints:\n\n2 <= strs.length <= 50\n1 <= strs[i].length <= 10\nstrs[i] consists of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(strs = ['aaa', 'aaa', 'aa']) == -1\n assert candidate(strs = ['a', 'b', 'c', 'd', 'e']) == 1\n assert candidate(strs = ['a', 'a', 'a', 'a']) == -1\n assert candidate(strs = ['xyz', 'xy', 'xz', 'yzz']) == 3\n assert candidate(strs = ['aabbcc', 'abc', 'aabbc', 'aabc']) == 6\n assert candidate(strs = ['abcd', 'abcde', 'ab', 'abc']) == 5\n assert candidate(strs = ['abcd', 'ab', 'bc', 'cd']) == 4\n assert candidate(strs = ['abc', 'abc', 'abcd']) == 4\n assert candidate(strs = ['aabbcc', 'abc', 'abbc', 'aabbc']) == 6\n assert candidate(strs = ['abc', 'def', 'ghi']) == 3\n assert candidate(strs = ['abcde', 'abc', 'de', 'a']) == 5\n assert candidate(strs = ['aba', 'cdc', 'eae']) == 3\n assert candidate(strs = ['a', 'b', 'c']) == 1\n assert candidate(strs = ['xyz', 'zyx', 'yxz', 'xzy', 'yzx', 'zxy', 'xyz', 'zyx']) == 3\n assert candidate(strs = ['aaaaa', 'bbbbb', 'ccccc', 'ddddd', 'eeeee', 'ffffff']) == 6\n assert candidate(strs = ['abcd', 'dcba', 'abcd', 'dcba', 'abcd', 'dcba', 'abcd', 'dcba']) == -1\n assert candidate(strs = ['abcd', 'abdc', 'acbd', 'dacb', 'cadb', 'bacd']) == 4\n assert candidate(strs = ['apple', 'apples', 'applesauce', 'appl', 'applf', 'applfs', 'applfsa', 'applfsau', 'applfsauc']) == 10\n assert candidate(strs = ['programming', 'programing', 'progamming', 'programmig', 'proogramming', 'programmiing']) == 12\n assert candidate(strs = ['mississippi', 'mississipi', 'mississipp', 'mississip', 'mississi', 'mississ', 'missis', 'missi', 'misi', 'msi', 'mi', 'm']) == 11\n assert candidate(strs = ['abcde', 'abxde', 'axcde', 'abxde', 'abcde', 'abcde']) == 5\n assert candidate(strs = ['abac', 'bca', 'cab', 'aaa', 'bbb', 'ccc']) == 4\n assert candidate(strs = ['banana', 'bananb', 'bananc', 'bandan', 'bandna', 'bandan', 'bandnaa', 'bandnaab', 'bandnaabc']) == 9\n assert candidate(strs = ['abcd', 'abdc', 'aebc', 'aecb', 'acbe']) == 4\n assert candidate(strs = ['abcd', 'abc', 'ab', 'a', 'aaaa', 'aaa', 'aa', 'a']) == 4\n assert candidate(strs = ['mnopqr', 'nopqrm', 'opqrmn', 'pqrmno', 'qrmnop', 'rmnopq']) == 6\n assert candidate(strs = ['abc', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij']) == 10\n assert candidate(strs = ['pqr', 'pqrs', 'pqs', 'prs', 'qs', 'qrs', 'qr', 'rs', 'r', 's']) == 4\n assert candidate(strs = ['hello', 'world', 'hold', 'hero']) == 5\n assert candidate(strs = ['abcde', 'edcba', 'abdec', 'cabde', 'deabc', 'eabcd']) == 5\n assert candidate(strs = ['aabbcc', 'aabbbc', 'aabbcccc', 'aabbccdd', 'aabbccdde', 'aabbccddee']) == 10\n assert candidate(strs = ['aabbcc', 'abcabc', 'aabcbc', 'abacbc', 'aabbcc', 'aacbbc', 'aabbbc']) == 6\n assert candidate(strs = ['xxyy', 'xyxy', 'yxyx', 'xyyx', 'yxxxy', 'xyxxy', 'xxyxy', 'xyxyx']) == 5\n assert candidate(strs = ['abcabc', 'bcabca', 'cababc', 'abacbc', 'bcbcab', 'acbcab']) == 6\n assert candidate(strs = ['hello', 'hallo', 'hxllo', 'hell', 'helo', 'helo', 'heo', 'he', 'h', 'o']) == 5\n assert candidate(strs = ['abacax', 'bacaxa', 'caxaba', 'axabac', 'xacaba', 'cabaxa']) == 6\n assert candidate(strs = ['pqrst', 'pqrstu', 'pqrstu', 'pqrstu', 'pqr', 'pq', 'p']) == -1\n assert candidate(strs = ['unique', 'uniqe', 'unque', 'uniqu', 'uqnie', 'unieq', 'unqiue']) == 6\n assert candidate(strs = ['aab', 'aac', 'baa', 'bca', 'caa', 'cab', 'abc', 'acb']) == 3\n assert candidate(strs = ['x', 'xy', 'xyz', 'xyzz', 'xyzzz', 'xyzzzz', 'xyzzzzz', 'xyzzzzzz']) == 8\n assert candidate(strs = ['abcd', 'abcde', 'abcdef', 'ab', 'abcd']) == 6\n assert candidate(strs = ['aabbcc', 'bbaacc', 'ccabba', 'aaccbb', 'cabbba', 'bccaba']) == 6\n assert candidate(strs = ['aaaaa', 'aaaba', 'aabaa', 'abaab', 'abbaa']) == 5\n assert candidate(strs = ['abcdefg', 'bcdefga', 'cdefgab', 'defgabc', 'efgabcd', 'fgabcde']) == 7\n assert candidate(strs = ['abcde', 'edcba', 'bcdea', 'cdeab', 'decba']) == 5\n assert candidate(strs = ['hello', 'hallo', 'hxllo', 'hexlo', 'helxo']) == 5\n assert candidate(strs = ['abab', 'baba', 'abba', 'baab', 'abba']) == 4\n assert candidate(strs = ['abcdabcd', 'abcdeabc', 'abdcabdc', 'dacbdacb', 'dabcdbac', 'bacdabcd', 'abcdabdc']) == 8\n assert candidate(strs = ['aabbcc', 'aabcbc', 'abacbc', 'abcabc', 'abcbac', 'abccba']) == 6\n assert candidate(strs = ['banana', 'anana', 'nana', 'ana', 'na', 'a']) == 6\n assert candidate(strs = ['aaaaa', 'aaaba', 'aabaa', 'abaaa', 'baaaa']) == 5\n assert candidate(strs = ['abcde', 'abc', 'ab', 'a']) == 5\n assert candidate(strs = ['abc', 'acb', 'bac', 'bca', 'cab', 'cba', 'abcd', 'abdc', 'acbd', 'acdb', 'adbc', 'adcb', 'bacd', 'badc', 'bcad', 'bcda', 'bdac', 'bdca', 'cabd', 'cadb', 'cbad', 'cbda', 'cdab', 'cdba', 'dabc', 'dacb', 'dbac', 'dbca', 'dcab', 'dcba', 'abcd']) == 4\n assert candidate(strs = ['banana', 'anana', 'nana', 'ana', 'na', 'a', 'b']) == 6\n assert candidate(strs = ['longstring', 'longerstring', 'longeststring', 'longstringer', 'longstringest', 'longstringerer']) == 14\n assert candidate(strs = ['abcdef', 'abcfed', 'bacdef', 'badcfe', 'bcadef', 'bcdafe']) == 6\n assert candidate(strs = ['aaaa', 'aaab', 'aaba', 'abaa', 'abab', 'abba', 'bbaa', 'baab', 'baba', 'bbaa']) == 4\n assert candidate(strs = ['abcabc', 'bcabc', 'cabc', 'abc', 'ab', 'a', 'b', 'c']) == 6\n assert candidate(strs = ['aaaaa', 'aaab', 'aab', 'aba', 'baa', 'aaa']) == 5\n assert candidate(strs = ['mississippi', 'missisipi', 'missippi', 'mssippi', 'msissippi']) == 11\n assert candidate(strs = ['abcdefg', 'bcdefga', 'cdefgab', 'defgabc', 'efgabcd', 'fgabcde', 'gabcdef']) == 7\n assert candidate(strs = ['cat', 'dog', 'caterpillar', 'cattle', 'tall']) == 11\n assert candidate(strs = ['hello', 'hallo', 'hullo', 'hellu', 'hullo', 'helou']) == 5\n assert candidate(strs = ['aabbcc', 'abbccc', 'aabccc', 'aaabcc', 'aabbcc', 'aabbbc', 'aabbbc', 'aabccc', 'abbccc', 'abaccc']) == 6\n assert candidate(strs = ['abcd', 'abac', 'abca', 'acba', 'acab', 'aabc', 'abbc', 'aabb', 'abbb', 'bbbb']) == 4\n assert candidate(strs = ['ab', 'abc', 'abcd', 'abcde', 'abcdef', 'abcdefg']) == 7\n assert candidate(strs = ['abcd', 'abdc', 'acbd', 'dabc', 'dacb']) == 4\n assert candidate(strs = ['abcabc', 'ababc', 'abc', 'abcd', 'abcde']) == 6\n assert candidate(strs = ['abcd', 'abdc', 'acbd', 'acdb', 'adbc', 'adcb', 'bacd', 'badc', 'bcad', 'bcda', 'bdac', 'bdca', 'cabd', 'cadb', 'cbad', 'cbda', 'cdab', 'cdba', 'dabc', 'dacb', 'dbac', 'dbca', 'dcab', 'dcba']) == 4\n assert candidate(strs = ['abcdef', 'abdefc', 'acdefb', 'adefbc', 'aebcdf', 'afedcb']) == 6\n assert candidate(strs = ['hello', 'world', 'hold', 'wolf', 'hold', 'hold']) == 5\n assert candidate(strs = ['abcdefgh', 'bghcdefa', 'cdefghba', 'defghbac', 'efghbacd', 'fghbacde']) == 8\n assert candidate(strs = ['abcde', 'abced', 'acbed', 'acbde', 'adbec', 'adebc']) == 5\n assert candidate(strs = ['abc', 'acb', 'bac', 'bca', 'cab', 'cba']) == 3\n assert candidate(strs = ['abcde', 'edcba', 'cbade', 'badce', 'aecdb', 'bcdea', 'abced']) == 5\n assert candidate(strs = ['abcdefgh', 'bcdefgh', 'cdefgh', 'defgh', 'efgh', 'fgh', 'gh', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']) == 8\n assert candidate(strs = ['aaaa', 'aaab', 'aaba', 'abaa', 'baaa']) == 4\n assert candidate(strs = ['abcd', 'abdc', 'acbd', 'dacb', 'cabd']) == 4\n assert candidate(strs = ['aaaa', 'aaab', 'aabb', 'abbb', 'bbbb']) == 4\n assert candidate(strs = ['xyz', 'zyx', 'yz', 'zx', 'yx', 'x', 'y', 'z', '']) == 3\n assert candidate(strs = ['abcd', 'abcde', 'ab', 'abc', 'a', 'abcd', 'abcde', 'ab', 'abc', 'a']) == -1\n assert candidate(strs = ['aab', 'abc', 'abcd', 'abcde', 'abcdef']) == 6\n assert candidate(strs = ['abcd', 'abdc', 'acbd', 'adcb', 'bacd']) == 4\n assert candidate(strs = ['xyzz', 'zyxz', 'xzyz', 'zxzy', 'xzzy', 'zzxy']) == 4\n assert candidate(strs = ['banana', 'bandana', 'bandanna', 'band', 'anana']) == 8\n assert candidate(strs = ['aabbcc', 'aabbc', 'aabc', 'abc', 'aab', 'ab', 'ac', 'a', 'b', 'c', 'd']) == 6\n assert candidate(strs = ['abc', 'abc', 'abc', 'abcd']) == 4\n assert candidate(strs = ['apple', 'ale', 'app', 'appl', 'ample']) == 5\n assert candidate(strs = ['zzzzzzzzzz', 'zzzzzzzzz', 'zzzzzzzz', 'zzzzzzz', 'zzzzzz', 'zzzzz', 'zzzz', 'zzz', 'zz', 'z']) == 10\n assert candidate(strs = ['unique', 'distinct', 'different', 'separate', 'unequal', 'unique', 'distinct', 'different', 'separate', 'unequal']) == -1\n assert candidate(strs = ['sequence', 'subsequence', 'subseq', 'seq', 'sequencee']) == 11\n assert candidate(strs = ['aaaaa', 'aaaab', 'aaaba', 'aabaa', 'abaaa', 'baaaa', 'aabba', 'aabra', 'abaab', 'baaab', 'ababa', 'babaa', 'abaab', 'baaba', 'abaaa', 'baaaa', 'aabaa', 'abaaa', 'baaba', 'abaab']) == 5\n assert candidate(strs = ['zzzz', 'zzzzz', 'zzzzzz', 'zzzzzzz', 'zzzzzzzz', 'zzzzzzzzz', 'zzzzzzzzzz']) == 10\n assert candidate(strs = ['abcd', 'abdc', 'acbd', 'dacb', 'cdab', 'cabd']) == 4\n assert candidate(strs = ['xyz', 'xyx', 'xyy', 'xzy', 'yzy', 'yzz', 'zzy', 'zzyz', 'zzzy', 'zzzz']) == 4\n assert candidate(strs = ['apple', 'aple', 'appl', 'pple', 'aplp']) == 5\n assert candidate(strs = ['hello', 'hallo', 'hxllo', 'hexlo', 'hxllo', 'hxllo']) == 5\n assert candidate(strs = ['aaaabbbb', 'aaabbb', 'aabbb', 'abbb', 'bbb', 'bb', 'b']) == 8\n assert candidate(strs = ['pqr', 'qrp', 'rpq', 'prq', 'rqp', 'qpr', 'ppp', 'qqq', 'rrr']) == 3\n assert candidate(strs = ['qwerty', 'qwertyuiop', 'qwertyuio', 'qwertyui', 'qwer']) == 10\n assert candidate(strs = ['aaabbb', 'aabbbb', 'abbbbb', 'aaabbbb', 'aabbbbbb', 'abbbbbbb']) == 8\n assert candidate(strs = ['abcabcabc', 'abc', 'bc', 'c', 'bca', 'cab', 'bac', 'acb', 'cba', 'abcabc']) == 9\n assert candidate(strs = ['pqr', 'pqrs', 'pqrst', 'pqrstu', 'pqrstuv', 'pqrstuvw', 'pqrstuvwx', 'pqrstuvwxy']) == 10\n assert candidate(strs = ['xyz', 'xy', 'xz', 'yz', 'x', 'y', 'z', 'xyx', 'yzy', 'zxz']) == 3\n assert candidate(strs = ['xyz', 'xyx', 'xzy', 'yxz', 'yzy', 'zyx', 'zyz']) == 3\n assert candidate(strs = ['abcdefghij', 'abcdefghi', 'abcdefgh', 'abcdefg', 'abcdef', 'abcde', 'abcd', 'abc', 'ab', 'a']) == 10\n"}, "metadata": {"canonical_parameter_names": ["strs"], "leetcode_dataset_entry_point": "Solution().findLUSlength", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findLUSlength = function(strs) {", "container": null, "callable": "findLUSlength", "parameters": [{"name": "strs", "type": "string[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 523, "task_id": "continuous-subarray-sum", "difficulty": "Medium", "problem_description": "Given an integer array nums and an integer k, return true if nums has a good subarray or false otherwise.\nA good subarray is a subarray where:\n\nits length is at least two, and\nthe sum of the elements of the subarray is a multiple of k.\n\nNote that:\n\nA subarray is a contiguous part of the array.\nAn integer x is a multiple of k if there exists an integer n such that x = n * k. 0 is always a multiple of k.\n\n \nExample 1:\n\nInput: nums = [23,2,4,6,7], k = 6\nOutput: true\nExplanation: [2, 4] is a continuous subarray of size 2 whose elements sum up to 6.\n\nExample 2:\n\nInput: nums = [23,2,6,4,7], k = 6\nOutput: true\nExplanation: [23, 2, 6, 4, 7] is an continuous subarray of size 5 whose elements sum up to 42.\n42 is a multiple of 6 because 42 = 7 * 6 and 7 is an integer.\n\nExample 3:\n\nInput: nums = [23,2,6,4,7], k = 13\nOutput: false\n\n \nConstraints:\n\n1 <= nums.length <= 105\n0 <= nums[i] <= 109\n0 <= sum(nums[i]) <= 231 - 1\n1 <= k <= 231 - 1\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [2, 5, 31, 4, 5, 1],k = 5) == True\n assert candidate(nums = [1, 2, 3, 4, 5],k = 9) == True\n assert candidate(nums = [23, 2, 6, 4, 7],k = 6) == True\n assert candidate(nums = [2, 5, 4, 5, 10],k = 3) == True\n assert candidate(nums = [1, 0, 1, 0, 1],k = 2) == True\n assert candidate(nums = [23, 2, 4, 6, 7],k = 6) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6],k = 10) == True\n assert candidate(nums = [23, 2, 6, 4, 7],k = 13) == False\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == True\n assert candidate(nums = [5, 0, 0, 0],k = 3) == True\n assert candidate(nums = [23, 2, 4, 6, 6],k = 7) == True\n assert candidate(nums = [1, 2, 1, 2, 1, 2],k = 6) == True\n assert candidate(nums = [0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [2, 2, 2, 2, 2, 2],k = 10) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 11],k = 5) == True\n assert candidate(nums = [23, 2, 4, 6, 7],k = 1) == True\n assert candidate(nums = [1, 2, 12],k = 6) == False\n assert candidate(nums = [0, 0],k = 1) == True\n assert candidate(nums = [0, 1, 0],k = 1) == True\n assert candidate(nums = [1, 2, 3, 4, 5],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5],k = 15) == True\n assert candidate(nums = [28, 29, 49, 0, 48, 50, 52, 51, 52, 53, 54, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 25) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30],k = 11) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000],k = 1) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 20) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [21, 2, 19, 2, 20, 3],k = 6) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 11) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7],k = 21) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == True\n assert candidate(nums = [2, 5, 10, 15, 20, 25, 30],k = 25) == True\n assert candidate(nums = [23, 2, 6, 8, 1, 4, 7],k = 10) == True\n assert candidate(nums = [10, 5, 2, 7, 1, 9, 2, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5],k = 15) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 19) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 10, 11, 12],k = 13) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 2) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7],k = 5) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 10) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 10) == True\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47],k = 17) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 25) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000],k = 500000000) == True\n assert candidate(nums = [23, 2, 6, 4, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 55) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 1, 2, 4, 6, 7],k = 10) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 23, 2, 4, 6, 7, 23, 2, 4, 6, 7, 23, 2, 4, 6, 7],k = 14) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 10, 11, 12],k = 6) == True\n assert candidate(nums = [9, 10, 7, 3, 9, 6, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 6) == True\n assert candidate(nums = [21, 26, 29, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100],k = 11) == True\n assert candidate(nums = [3, 2, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 4) == True\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1],k = 2) == True\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 55) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1],k = 2) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 5, 3, 9, 10],k = 12) == True\n assert candidate(nums = [29, 23, 17, 13, 11, 7, 5, 3, 2, 1, 1, 2, 3, 5, 7, 11, 13, 17, 23, 29],k = 20) == True\n assert candidate(nums = [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9],k = 18) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],k = 24) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 22) == True\n assert candidate(nums = [10, 20, 30, 40, 50],k = 15) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 20) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 8, 10, 11, 12],k = 6) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 10) == True\n assert candidate(nums = [0, 1, 0, 3, 0, 4, 0, 5, 0, 6],k = 2) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [10, 5, 0, 0, 3, 1, 0, 0, 8, 0, 0, 6],k = 10) == True\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0],k = 2) == True\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13],k = 10) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 29) == True\n assert candidate(nums = [10, 5, 0, 0, 0, 10, 5],k = 5) == True\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0],k = 2) == True\n assert candidate(nums = [5, 8, 9, 12, 16, 1, 3, 1, 4, 6, 7, 8, 9, 10, 11, 12],k = 27) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 33) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000],k = 2000000000) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 15) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 19) == True\n assert candidate(nums = [0, 1, 0, 1, 0],k = 1) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 36) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 8, 10],k = 6) == True\n assert candidate(nums = [2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 13) == True\n assert candidate(nums = [1, 1000000000, 1, 1000000000, 1, 1000000000],k = 2000000000) == False\n assert candidate(nums = [23, 2, 4, 6, 7, 8, 10, 12],k = 9) == True\n assert candidate(nums = [1, 0, 1, 0, 1, 0],k = 2) == True\n assert candidate(nums = [0, 1, 0, 3, 0, 4, 0, 5, 0, 6],k = 3) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 21) == True\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0],k = 1) == True\n assert candidate(nums = [28, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22],k = 21) == True\n assert candidate(nums = [1, 3, 5, 0, 2, 4, 6],k = 5) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 8, 10],k = 13) == True\n assert candidate(nums = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29],k = 100) == True\n assert candidate(nums = [23, 2, 4, 6, 6, 7],k = 6) == True\n assert candidate(nums = [23, 2, 6, 4, 7, 2, 4, 6, 7],k = 13) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000, 1000000000, 1000000000],k = 1000000000) == True\n assert candidate(nums = [1, 10, 100, 1000, 10000, 100000],k = 111111) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 25) == True\n assert candidate(nums = [1000000000, 1000000000, 1000000000, 1000000000],k = 2000000000) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7, 1, 2, 4, 6, 7],k = 1) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 2) == True\n assert candidate(nums = [29, 7, 21, 20, 12, 28, 8, 5, 4, 1, 20, 4, 11, 15, 7, 12, 9, 7, 4, 15, 1, 3, 15, 11, 7, 12, 3, 7, 15, 11, 12, 9, 10, 7, 6, 6, 3, 14, 12, 4, 14, 16, 7, 10, 2, 9, 14, 9, 7, 15, 14, 1, 15, 13, 8, 6, 2, 14, 8, 2, 13, 1, 10, 6, 15, 9, 11, 16, 8, 15, 10, 7, 9, 20, 14, 14, 16, 4, 10, 9, 7, 8, 9, 13, 14, 14, 10, 6, 2, 3, 8, 15, 2, 9, 7, 10, 15, 11, 12, 9, 10, 7, 6, 6, 3, 14, 12, 4, 14, 16, 7, 10, 2, 9, 14, 9, 7, 15, 14, 1, 15, 13, 8, 6, 2, 14, 8, 2, 13],k = 59) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 1, 2, 4],k = 6) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30],k = 13) == True\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20],k = 5) == True\n assert candidate(nums = [29, 23, 17, 3, 19, 11, 25, 2, 9, 28, 15, 18, 11, 22, 24, 24, 20, 11, 10, 22, 5, 26, 8, 6, 19, 25, 28, 15, 27, 18],k = 29) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == True\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 5) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 10, 11, 12],k = 1) == True\n assert candidate(nums = [2, 3, 1, 2, 4, 3, 5, 4, 5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 10) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 5, 3, 9, 10, 15, 20, 25, 30, 35, 40],k = 17) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 1, 3, 5, 8, 10],k = 12) == True\n assert candidate(nums = [23, 2, 6, 4, 7, 23, 2, 6, 4, 7],k = 6) == True\n assert candidate(nums = [3, 1, 7, 5, 6, 9],k = 10) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 5, 3, 1, 2, 4, 5, 6],k = 15) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 60) == True\n assert candidate(nums = [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26],k = 13) == True\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 100) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 5, 3, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115],k = 13) == True\n assert candidate(nums = [9, 7, 5, 3, 1, 2, 4, 6, 8, 10],k = 12) == True\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],k = 150) == True\n assert candidate(nums = [23, 2, 4, 6, 7, 0, 0, 0, 0, 0],k = 6) == True\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().checkSubarraySum", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var checkSubarraySum = function(nums, k) {", "container": null, "callable": "checkSubarraySum", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "boolean", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 524, "task_id": "longest-word-in-dictionary-through-deleting", "difficulty": "Medium", "problem_description": "Given a string s and a string array dictionary, return the longest string in the dictionary that can be formed by deleting some of the given string characters. If there is more than one possible result, return the longest word with the smallest lexicographical order. If there is no possible result, return the empty string.\n \nExample 1:\n\nInput: s = \"abpcplea\", dictionary = [\"ale\",\"apple\",\"monkey\",\"plea\"]\nOutput: \"apple\"\n\nExample 2:\n\nInput: s = \"abpcplea\", dictionary = [\"a\",\"b\",\"c\"]\nOutput: \"a\"\n\n \nConstraints:\n\n1 <= s.length <= 1000\n1 <= dictionary.length <= 1000\n1 <= dictionary[i].length <= 1000\ns and dictionary[i] consist of lowercase English letters.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(s = \"\",dictionary = ['a', 'b', 'c']) == \"\"\n assert candidate(s = \"a\",dictionary = ['b', 'c', 'd']) == \"\"\n assert candidate(s = \"zcfzdb\",dictionary = ['a', 'b', 'c']) == \"b\"\n assert candidate(s = \"aaaaaaa\",dictionary = ['aaa', 'aaaa']) == \"aaaa\"\n assert candidate(s = \"aaaaaaa\",dictionary = ['aaaaaaa', 'aa', 'a', '']) == \"aaaaaaa\"\n assert candidate(s = \"xyz\",dictionary = ['x', 'y', 'z', 'xy', 'xyz']) == \"xyz\"\n assert candidate(s = \"apple\",dictionary = ['app', 'appl', 'applep']) == \"appl\"\n assert candidate(s = \"aaaa\",dictionary = ['aa', 'aaa', 'aaaa']) == \"aaaa\"\n assert candidate(s = \"abpcplea\",dictionary = ['a', 'b', 'c']) == \"a\"\n assert candidate(s = \"abcd\",dictionary = ['db', 'abc', 'ab', 'b']) == \"abc\"\n assert candidate(s = \"\",dictionary = ['a', 'b', 'c']) == \"\"\n assert candidate(s = \"aaa\",dictionary = ['a', 'aa', 'aaa']) == \"aaa\"\n assert candidate(s = \"xyz\",dictionary = ['x', 'y', 'z', 'xy', 'yz', 'xyz']) == \"xyz\"\n assert candidate(s = \"aewfafwafjlwajflwajflwafj\",dictionary = ['apple', 'ewaf', 'awefawfwaf', 'awef', 'awefe', 'ewafeffewafewf']) == \"ewaf\"\n assert candidate(s = \"abpcplea\",dictionary = ['ale', 'apple', 'monkey', 'plea']) == \"apple\"\n assert candidate(s = \"abcd\",dictionary = []) == \"\"\n assert candidate(s = \"abcd\",dictionary = ['db', 'dc', 'bd', 'ac', 'cad']) == \"ac\"\n assert candidate(s = \"aewfafwafjlwajflwajflwafjlwafjl\",dictionary = ['apple', 'ewaf', 'awefawfwaf', 'awef', 'awefe', 'ewafeffewafewf']) == \"ewaf\"\n assert candidate(s = \"xyz\",dictionary = ['xyzz', 'zxy', 'zyx']) == \"\"\n assert candidate(s = \"abcdabcdabcd\",dictionary = ['abcd', 'abc', 'ab', 'a', 'bc', 'bcd', 'abcdabcd', 'abcdabcdabcd', 'abcdabcda', 'bcdabcdabcd', 'abcabcabc']) == \"abcdabcdabcd\"\n assert candidate(s = \"abracadabra\",dictionary = ['ab', 'abc', 'abrac', 'abraca', 'abracadabra', 'cadabra', 'rac']) == \"abracadabra\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['zyxwvutsrqponmlkjihgfedcba', 'abcdefghijklmnopqrstuvwxyz', 'mnopqrstuv']) == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"banana\",dictionary = ['an', 'banana', 'anana', 'nana', 'ba', 'ana', 'aaa', 'aa', 'a', 'b']) == \"banana\"\n assert candidate(s = \"thequickbrownfoxjumpsoverthelazydog\",dictionary = ['the', 'quick', 'brown', 'fox', 'jumps', 'over', 'lazy', 'dog', 'hello', 'world', 'python']) == \"brown\"\n assert candidate(s = \"mississippi\",dictionary = ['issi', 'ppis', 'miss', 'ssip', 'isip', 'mississippi', 'mis', 'sip', 'iss', 'piss']) == \"mississippi\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'ab', 'cd']) == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"vvvvvvvvvv\",dictionary = ['v', 'vv', 'vvv', 'vvvv', 'vvvvv', 'vvvvvv', 'vvvvvvv', 'vvvvvvvv', 'vvvvvvvvv', 'vvvvvvvvvv']) == \"vvvvvvvvvv\"\n assert candidate(s = \"mississippi\",dictionary = ['issi', 'miss', 'pissi', 'ppi', 'issipi', 'ississi', 'mississi', 'issippi']) == \"mississi\"\n assert candidate(s = \"abracadabra\",dictionary = ['abc', 'abcd', 'abrac', 'cadabra', 'abra']) == \"cadabra\"\n assert candidate(s = \"abcabcabc\",dictionary = ['abc', 'abca', 'abcb', 'abcc', 'aabbcc', 'abcabc', 'abcabca', 'abcaabc']) == \"abcaabc\"\n assert candidate(s = \"mississippi\",dictionary = ['issi', 'miss', 'mississ', 'issippi', 'issippis']) == \"issippi\"\n assert candidate(s = \"abracadabra\",dictionary = ['abc', 'abcd', 'abracadabra', 'racad', 'abraca', 'cadabra', 'dabra', 'bra']) == \"abracadabra\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\",dictionary = ['zyx', 'wvu', 'tsr', 'pon', 'mlk', 'jih', 'gfed', 'cba', 'zyxwvut', 'srqponmlkjihgfedcba']) == \"srqponmlkjihgfedcba\"\n assert candidate(s = \"babgbagagbagagbagagbag\",dictionary = ['bag', 'bags', 'bagga', 'baggage', 'bagag', 'bagagag', 'bagagaga', 'bagagagag', 'bagagagaga']) == \"bagagagaga\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['abc', 'def', 'ghijk', 'lmnop', 'qrstuv', 'wxyz']) == \"qrstuv\"\n assert candidate(s = \"abcdeffedcba\",dictionary = ['abcd', 'abce', 'abcf', 'abde', 'abdf', 'acde', 'acdf', 'adef', 'bcde', 'bcdf', 'bcef', 'bdef', 'cdef']) == \"abcd\"\n assert candidate(s = \"aabbbccddeeff\",dictionary = ['abc', 'abcd', 'abde', 'acde', 'aabbccddeeff', 'abcde']) == \"aabbccddeeff\"\n assert candidate(s = \"bananaanananannanana\",dictionary = ['ana', 'anan', 'anana', 'ananas', 'banana', 'bananana', 'ananan', 'nananan']) == \"bananana\"\n assert candidate(s = \"aaaabaaaabaaaaabaaaabaaaab\",dictionary = ['ab', 'aba', 'abab', 'ababa', 'ababab', 'abababa', 'abababab']) == \"abababab\"\n assert candidate(s = \"mississippi\",dictionary = ['is', 'ppi', 'missi', 'missis', 'mississi', 'mississipp']) == \"mississipp\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",dictionary = ['abcdefghij', 'klmnopqrstu', 'vwxyz', 'mnop', 'abcd', 'mnopqr', 'ghijkl', 'efgh', 'mnopqrstuv', 'vwxyzabc']) == \"klmnopqrstu\"\n assert candidate(s = \"abcdeabcdeabcde\",dictionary = ['abcde', 'abcdee', 'abcd', 'abcdeeabcde', 'abcdeabcdeabcde']) == \"abcdeabcdeabcde\"\n assert candidate(s = \"abcdefghijklmno\",dictionary = ['abc', 'abcd', 'abcde', 'abcdef', 'abcdefg', 'abcdefgh', 'abcdefghi', 'abcdefghij', 'abcdefghijk', 'abcdefghijkl', 'abcdefghijklm', 'abcdefghijklmn', 'abcdefghijklmno']) == \"abcdefghijklmno\"\n assert candidate(s = \"longwordwithmanycharacters\",dictionary = ['long', 'word', 'with', 'many', 'characters', 'longword', 'longwordwith', 'withmany', 'manycharacters', 'longwordwithmany', 'wordwithmany', 'wordwithmanycharacters']) == \"wordwithmanycharacters\"\n assert candidate(s = \"leetcode\",dictionary = ['leet', 'leetc', 'lee', 'code', 'leetcod', 'cod', 'ode', 'leetode', 'leetcoded', 'teecode']) == \"leetcod\"\n assert candidate(s = \"abcxyz\",dictionary = ['abc', 'bca', 'cab', 'xyz', 'zyx']) == \"abc\"\n assert candidate(s = \"thisisaverylongstringthatwilltestourfunction\",dictionary = ['this', 'is', 'a', 'very', 'long', 'string', 'that', 'will', 'test', 'our', 'function', 'thisisaverylongstringthatwilltestourfunction']) == \"thisisaverylongstringthatwilltestourfunction\"\n assert candidate(s = \"abacaxbabax\",dictionary = ['aba', 'abacax', 'bacab', 'cab', 'bacabc', 'abcabc']) == \"abacax\"\n assert candidate(s = \"mississippi\",dictionary = ['mis', 'issi', 'issip', 'ippi', 'ppi', 'pip', 'pis', 'is', 'i']) == \"issip\"\n assert candidate(s = \"mississippi\",dictionary = ['issi', 'miss', 'pippi', 'mippi', 'mississippi']) == \"mississippi\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\",dictionary = ['zyx', 'zyxwv', 'zyxwvutsrqponmlkjihgfedcba', 'zyxwvutsrqponmlkjihgfedcb', 'zyxwvutsrqponmlkjihgfedc', 'zyxwvutsrqponmlkjihgfed', 'zyxwvutsrqponmlkjihgfe', 'zyxwvutsrqponmlkjihgf', 'zyxwvutsrqponmlkjihg', 'zyxwvutsrqponmlkjih', 'zyxwvutsrqponmlkji', 'zyxwvutsrqponmlkj', 'zyxwvutsrqponmlk', 'zyxwvutsrqponml', 'zyxwvutsrqponm', 'zyxwvutsrqpon', 'zyxwvutsrqpo', 'zyxwvutsrqp', 'zyxwvutsrq', 'zyxwvutsr', 'zyxwvuts', 'zyxwvut', 'zyxwvu', 'zyxwv', 'zyxw', 'zyx', 'zy', 'z']) == \"zyxwvutsrqponmlkjihgfedcba\"\n assert candidate(s = \"aaaaabbbbcccc\",dictionary = ['abc', 'acb', 'bac', 'bca', 'cab', 'cba', 'aaa', 'bbb', 'ccc', 'aabb', 'abcc', 'bbcc', 'aabbcc', 'ab', 'bc', 'ca', 'bb', 'cc', 'aa']) == \"aabbcc\"\n assert candidate(s = \"programmingisfun\",dictionary = ['pro', 'gram', 'ming', 'is', 'fun', 'program', 'programming', 'programmin', 'programmingi', 'programmingis', 'programmingisf', 'programmingisfu', 'programmingisfun', 'programmingisfunn', 'programmingisfuns']) == \"programmingisfun\"\n assert candidate(s = \"mississippi\",dictionary = ['miss', 'piss', 'misp', 'issi', 'issipp']) == \"issipp\"\n assert candidate(s = \"zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\",dictionary = ['zzzzzzzzzz', 'zzzzzzzz', 'zzzzzzz', 'zzzzzz', 'zzzzz', 'zzzz', 'zzz', 'zz', 'z']) == \"zzzzzzzzzz\"\n assert candidate(s = \"babgbag\",dictionary = ['bag', 'bgb', 'ggb', 'bbag', 'baggb']) == \"bbag\"\n assert candidate(s = \"bananaaa\",dictionary = ['baaa', 'ban', 'anana', 'nana', 'banan', 'anan', 'na', 'n', 'a', 'b', 'ba', 'ban', 'bana', 'banan', 'banana', 'bananaa']) == \"bananaa\"\n assert candidate(s = \"mississippi\",dictionary = ['issi', 'missi', 'issipi', 'mississippi', 'mis', 'pi']) == \"mississippi\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['zyxwvutsrqponmlkjihgfedcba', 'abcdefghijklmnopqrstuvwxyz', 'abcdefghijklmnopqrstuvwxy']) == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['zyx', 'yxz', 'xyz', 'abcdefghijklmnopqrstuvwxyzz', 'abcdefghijklmnopqrstuvwxyz']) == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"abracadabra\",dictionary = ['bra', 'abr', 'cad', 'acad', 'a', 'abracadabra']) == \"abracadabra\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",dictionary = ['abc', 'def', 'ghi', 'jkl', 'mno', 'pqr', 'stu', 'vwx', 'yz', 'zzyx']) == \"abc\"\n assert candidate(s = \"abcdefghij\",dictionary = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'abcdefghij', 'abcdefghijk', 'abcdefghi', 'abcdefgh', 'abcdefg', 'abcdef', 'abcde', 'abcd', 'abc', 'ab', 'a']) == \"abcdefghij\"\n assert candidate(s = \"xxyyzz\",dictionary = ['xyz', 'xyzz', 'xzyz', 'xzy', 'yzx', 'zyx', 'zx', 'yx', 'xz', 'zy']) == \"xyzz\"\n assert candidate(s = \"babbbbaabbaaaaabbaabbbabbbaaabbbbbabababbbababbbbbbbbbaabbaaaabbabbbaababbaabbbaaaabbbbbbaaaabbabbbaaaabbaaabbaabba\",dictionary = ['babbbbaabbaaaaaaba', 'babbbaaabbbaabbbba', 'bbbaabbbaaaaaababb', 'bbbabbbbaabbaaaaaabb', 'abababbaabbbaababa', 'bbbbbabbaabbaaaaaa', 'babbbbaaaabbaaaaaa', 'abbbbabbaaaabbaabaa', 'baabaaaabaaabaaaab']) == \"bbbabbbbaabbaaaaaabb\"\n assert candidate(s = \"kfkfkfkfkfkfkfkfkfkfkfkfkfkfkfkf\",dictionary = ['kfk', 'fkf', 'kfkf', 'fkfk', 'kfkfkf', 'fkfkfk']) == \"fkfkfk\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",dictionary = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba', 'abcdefghijklmnopqrstuvwxy', 'qrstuvwxy', 'wxyz', 'uvw', 'vw', 'w']) == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",dictionary = ['aabbcc', 'ddeeff', 'gghhiijj', 'kkllmm', 'nnoopp', 'qqrrst', 'tuuvvw', 'xxyyzz', 'zzzyyx']) == \"gghhiijj\"\n assert candidate(s = \"a\",dictionary = ['b', 'c', 'd', 'e', 'f', 'g']) == \"\"\n assert candidate(s = \"leetcodeisgreat\",dictionary = ['leet', 'code', 'is', 'great', 'leetcode', 'leetcodes', 'leetcodeis', 'leetcodeisgreat', 'etcodeisgreat']) == \"leetcodeisgreat\"\n assert candidate(s = \"aabbaabbaabbaabbaabbaabbaabbaabbaabbaabb\",dictionary = ['aabba', 'aabbaabb', 'aabbaabbaabb', 'aabbaabbaabbaabb', 'aabbaabbaabbaabbaabb', 'aabbaabbaabbaabbaabbaabb']) == \"aabbaabbaabbaabbaabbaabb\"\n assert candidate(s = \"longestwordinadictionary\",dictionary = ['longestword', 'word', 'dictionary', 'in', 'a', 'longest', 'long']) == \"longestword\"\n assert candidate(s = \"llllllllllllllllllllllllllllllllllllllllll\",dictionary = ['l', 'll', 'lll', 'llll', 'lllll', 'llllll', 'lllllll', 'llllllll', 'lllllllll', 'llllllllll', 'lllllllllll', 'llllllllllll', 'lllllllllllll', 'llllllllllllll', 'lllllllllllllll', 'llllllllllllllll', 'lllllllllllllllll', 'llllllllllllllllll']) == \"llllllllllllllllll\"\n assert candidate(s = \"aaabbcccddd\",dictionary = ['aabbbcccddd', 'aabbbccc', 'aabbcc', 'aabc', 'abc', 'a', 'b', 'c']) == \"aabbcc\"\n assert candidate(s = \"ababcababc\",dictionary = ['ab', 'abc', 'ababc', 'aabbcc', 'aabbc', 'abab', 'abba', 'ababab', 'babab', 'abcabcabc']) == \"ababab\"\n assert candidate(s = \"ababcabcabc\",dictionary = ['abc', 'abca', 'abcab', 'abcabc', 'abcabcd']) == \"abcabc\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['zyxwvutsrqponmlkjihgfedcba', 'nopqrstuvwxy', 'mnopqrstuvwx', 'lmnopqrstu', 'klmnopqr', 'jklmnop', 'ijklmno', 'ijklm', 'ijkl', 'ijk', 'ij', 'i']) == \"mnopqrstuvwx\"\n assert candidate(s = \"aaaaaaa\",dictionary = ['aaaa', 'aa', 'a', 'aaa', 'aaaaa', 'aaaaaa']) == \"aaaaaa\"\n assert candidate(s = \"zyxwvutsrqponmlkjihgfedcba\",dictionary = ['zyx', 'wvut', 'srqpo', 'nmlkj', 'ihgfedcba', 'mnopqrstu', 'zyxwvutsrqponmlkjihgfedcba']) == \"zyxwvutsrqponmlkjihgfedcba\"\n assert candidate(s = \"longestword\",dictionary = ['long', 'longer', 'longest', 'longestw', 'longestwo', 'longestwor', 'longestword', 'longestworde']) == \"longestword\"\n assert candidate(s = \"qwertyuiopasdfghjklzxcvbnm\",dictionary = ['qwerty', 'asdfgh', 'zxcvbn', 'mnbvcxz', 'lkjhgfdsa', 'poiuytrewq', 'uytrewqpo', 'uytres', 'yuiop', 'poiuyt', 'poiuy', 'poiu', 'po', 'p', 'zxcvbn', 'qwerty', 'asdfghjklzxcvbnm', 'qwertyuiopasdfghjklzxcvbnm', 'qwertyuiopasdfghjklzzzzzzzz', 'zxcvbnmlkjhgfdsapoiuytrewq']) == \"qwertyuiopasdfghjklzxcvbnm\"\n assert candidate(s = \"aaaaaaaaaabbbbbbbbbbccccccccccdddddddddd\",dictionary = ['aaaabbbbccccddd', 'bbbccccddd', 'ccccddd', 'ddd', 'ccc', 'bbb', 'aaa', 'aaabbb', 'bbcccc', 'ccccdd', 'ddd']) == \"aaaabbbbccccddd\"\n assert candidate(s = \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\",dictionary = ['abcdabcdabcdabcdabcdabcdabcdabcdabcdabcd', 'abcdabcdabcdabcdabcdabcdabcdabcdabcdabc', 'abcdabcdabcdabcdabcdabcdabcdabcdabcdab', 'abcdabcdabcdabcdabcdabcdabcdabcdabcd', 'abcdabcdabcdabcdabcdabcdabcdabcdabc', 'abcdabcdabcdabcdabcdabcdabcdabcdab', 'abcdabcdabcdabcdabcdabcdabcdabcd']) == \"abcdabcdabcdabcdabcdabcdabcdabcdabcdabcd\"\n assert candidate(s = \"lletscodeleet\",dictionary = ['code', 'let', 'lets', 'leetc', 'leet', 'leetcode', 'ccode', 'lcode']) == \"lcode\"\n assert candidate(s = \"aabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\",dictionary = ['zz', 'yy', 'xx', 'ww', 'vv', 'uu', 'tt', 'ss', 'rr', 'qq', 'pp', 'oo', 'nn', 'mm', 'll', 'kk', 'jj', 'ii', 'hh', 'gg', 'ff', 'ee', 'dd', 'cc', 'bb', 'aa']) == \"aa\"\n assert candidate(s = \"mississippi\",dictionary = ['miss', 'missi', 'missis', 'mississ', 'mississi', 'mississip', 'mississipp', 'mississippi']) == \"mississippi\"\n assert candidate(s = \"aaaabbbbcccc\",dictionary = ['abc', 'aab', 'bbcc', 'aabbcc', 'aaabbbccc', 'ccccbbbbaaa', 'aaaabbbbcccc']) == \"aaaabbbbcccc\"\n assert candidate(s = \"abcdefghij\",dictionary = ['abc', 'def', 'ghi', 'j', 'abcdefghij', 'abcd', 'efgh', 'ijkl', 'ghij']) == \"abcdefghij\"\n assert candidate(s = \"supercalifragilisticexpialidocious\",dictionary = ['super', 'cali', 'fragilistic', 'expialidocious', 'docious', 'ocious', 'cious', 'ious', 'ous', 'us', 's', 'ex', 'pi', 'li', 'tic', 'exp', 'cal', 'sup', 'era', 'istic']) == \"expialidocious\"\n assert candidate(s = \"pppqqqrrrsssttt\",dictionary = ['ppqrs', 'pqr', 'pppp', 'qqqq', 'rrrr', 'ssss', 'tttt', 'pqqqrrrsttt', 'pppqqqrrrssttt']) == \"pppqqqrrrssttt\"\n assert candidate(s = \"abcdabcdabcd\",dictionary = ['abcd', 'abc', 'ab', 'a', 'abcdabcdabcd', 'abcdabcd', 'bcd', 'cd', 'd', 'abcdabcda', 'bcdabcd', 'cdabcd', 'dabcd']) == \"abcdabcdabcd\"\n assert candidate(s = \"abcdefghijklmnopqrstuvwxyz\",dictionary = ['abcdefghijklmnopqrstuvwxyz', 'zyxwvutsrqponmlkjihgfedcba']) == \"abcdefghijklmnopqrstuvwxyz\"\n assert candidate(s = \"banana\",dictionary = ['ban', 'banana', 'banan', 'bananas', 'anana', 'ana', 'nana', 'na', 'a']) == \"banana\"\n assert candidate(s = \"banana\",dictionary = ['ban', 'anana', 'nana', 'banan', 'anan', 'na', 'n', 'a', 'b', 'ba', 'ban', 'bana', 'banan', 'banana']) == \"banana\"\n"}, "metadata": {"canonical_parameter_names": ["s", "dictionary"], "leetcode_dataset_entry_point": "Solution().findLongestWord", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findLongestWord = function(s, dictionary) {", "container": null, "callable": "findLongestWord", "parameters": [{"name": "s", "type": "string"}, {"name": "dictionary", "type": "string[]"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 525, "task_id": "contiguous-array", "difficulty": "Medium", "problem_description": "Given a binary array nums, return the maximum length of a contiguous subarray with an equal number of 0 and 1.\n \nExample 1:\n\nInput: nums = [0,1]\nOutput: 2\nExplanation: [0, 1] is the longest contiguous subarray with an equal number of 0 and 1.\n\nExample 2:\n\nInput: nums = [0,1,0]\nOutput: 2\nExplanation: [0, 1] (or [1, 0]) is a longest contiguous subarray with equal number of 0 and 1.\n\nExample 3:\n\nInput: nums = [0,1,1,1,1,1,0,0,0]\nOutput: 6\nExplanation: [1,1,1,0,0,0] is the longest contiguous subarray with equal number of 0 and 1.\n\n \nConstraints:\n\n1 <= nums.length <= 105\nnums[i] is either 0 or 1.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [0, 1, 1, 0, 1, 1, 0, 0]) == 8\n assert candidate(nums = [1, 0, 0, 1, 0, 1, 1]) == 6\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0]) == 8\n assert candidate(nums = [0, 1, 1, 1, 1, 1, 0, 0, 0]) == 6\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 0, 0, 0, 0]) == 8\n assert candidate(nums = [1, 1, 0, 1, 0, 1, 0, 0, 1, 1]) == 8\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0]) == 8\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 1]) == 8\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 12\n assert candidate(nums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]) == 12\n assert candidate(nums = [0, 1]) == 2\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 10\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0]) == 10\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 12\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0]) == 8\n assert candidate(nums = [0, 1, 1, 0, 1, 1, 1, 0, 0, 1]) == 6\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 10\n assert candidate(nums = [1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1]) == 12\n assert candidate(nums = [0, 0, 1, 1, 0, 0, 1, 1]) == 8\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1]) == 8\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 0, 0]) == 8\n assert candidate(nums = [0, 1, 0]) == 2\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1]) == 8\n assert candidate(nums = [1, 0, 0, 1, 0, 0, 1, 1]) == 8\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 8\n assert candidate(nums = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1]) == 10\n assert candidate(nums = [0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0]) == 10\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1]) == 6\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 26\n assert candidate(nums = [1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0]) == 28\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 22\n assert candidate(nums = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]) == 20\n assert candidate(nums = [0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 14\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]) == 40\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 44\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 22\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 20\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]) == 24\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0]) == 18\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 38\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]) == 40\n assert candidate(nums = [0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]) == 24\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]) == 30\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 38\n assert candidate(nums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]) == 42\n assert candidate(nums = [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0]) == 54\n assert candidate(nums = [0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0]) == 16\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 46\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 44\n assert candidate(nums = [0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1]) == 20\n assert candidate(nums = [0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 34\n assert candidate(nums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]) == 30\n assert candidate(nums = [1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]) == 14\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 20\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 34\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 32\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 28\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]) == 24\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 46\n assert candidate(nums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]) == 18\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 20\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 48\n assert candidate(nums = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0]) == 4\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]) == 30\n assert candidate(nums = [0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0]) == 22\n assert candidate(nums = [1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]) == 30\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]) == 48\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]) == 24\n assert candidate(nums = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 48\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 26\n assert candidate(nums = [0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1]) == 30\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 20\n assert candidate(nums = [0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 44\n assert candidate(nums = [0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]) == 26\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 40\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 24\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 68\n assert candidate(nums = [0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 16\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 22\n assert candidate(nums = [1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 22\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 62\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1]) == 26\n assert candidate(nums = [0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 22\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 26\n assert candidate(nums = [0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1]) == 30\n assert candidate(nums = [1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0]) == 4\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]) == 16\n assert candidate(nums = [1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]) == 26\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]) == 20\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]) == 20\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 28\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) == 40\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 26\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 44\n assert candidate(nums = [0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0]) == 14\n assert candidate(nums = [0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 14\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 38\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 40\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1]) == 24\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]) == 16\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0]) == 30\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1]) == 20\n assert candidate(nums = [1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1]) == 20\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) == 22\n assert candidate(nums = [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 24\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 28\n assert candidate(nums = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1]) == 20\n assert candidate(nums = [1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]) == 16\n assert candidate(nums = [1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1]) == 24\n assert candidate(nums = [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]) == 24\n assert candidate(nums = [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1]) == 30\n"}, "metadata": {"canonical_parameter_names": ["nums"], "leetcode_dataset_entry_point": "Solution().findMaxLength", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMaxLength = function(nums) {", "container": null, "callable": "findMaxLength", "parameters": [{"name": "nums", "type": "number[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 526, "task_id": "beautiful-arrangement", "difficulty": "Medium", "problem_description": "Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true:\n\nperm[i] is divisible by i.\ni is divisible by perm[i].\n\nGiven an integer n, return the number of the beautiful arrangements that you can construct.\n \nExample 1:\n\nInput: n = 2\nOutput: 2\nExplanation: \nThe first beautiful arrangement is [1,2]:\n - perm[1] = 1 is divisible by i = 1\n - perm[2] = 2 is divisible by i = 2\nThe second beautiful arrangement is [2,1]:\n - perm[1] = 2 is divisible by i = 1\n - i = 2 is divisible by perm[2] = 1\n\nExample 2:\n\nInput: n = 1\nOutput: 1\n\n \nConstraints:\n\n1 <= n <= 15\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(n = 8) == 132\n assert candidate(n = 3) == 3\n assert candidate(n = 11) == 750\n assert candidate(n = 15) == 24679\n assert candidate(n = 4) == 8\n assert candidate(n = 12) == 4010\n assert candidate(n = 14) == 10680\n assert candidate(n = 9) == 250\n assert candidate(n = 13) == 4237\n assert candidate(n = 6) == 36\n assert candidate(n = 2) == 2\n assert candidate(n = 1) == 1\n assert candidate(n = 7) == 41\n assert candidate(n = 10) == 700\n assert candidate(n = 5) == 10\n"}, "metadata": {"canonical_parameter_names": ["n"], "leetcode_dataset_entry_point": "Solution().countArrangement", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var countArrangement = function(n) {", "container": null, "callable": "countArrangement", "parameters": [{"name": "n", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 529, "task_id": "minesweeper", "difficulty": "Medium", "problem_description": "Let's play the minesweeper game (Wikipedia, online game)!\nYou are given an m x n char matrix board representing the game board where:\n\n'M' represents an unrevealed mine,\n'E' represents an unrevealed empty square,\n'B' represents a revealed blank square that has no adjacent mines (i.e., above, below, left, right, and all 4 diagonals),\ndigit ('1' to '8') represents how many mines are adjacent to this revealed square, and\n'X' represents a revealed mine.\n\nYou are also given an integer array click where click = [clickr, clickc] represents the next click position among all the unrevealed squares ('M' or 'E').\nReturn the board after revealing this position according to the following rules:\n\nIf a mine 'M' is revealed, then the game is over. You should change it to 'X'.\nIf an empty square 'E' with no adjacent mines is revealed, then change it to a revealed blank 'B' and all of its adjacent unrevealed squares should be revealed recursively.\nIf an empty square 'E' with at least one adjacent mine is revealed, then change it to a digit ('1' to '8') representing the number of adjacent mines.\nReturn the board when no more squares will be revealed.\n\n \nExample 1:\n\n\nInput: board = [[\"E\",\"E\",\"E\",\"E\",\"E\"],[\"E\",\"E\",\"M\",\"E\",\"E\"],[\"E\",\"E\",\"E\",\"E\",\"E\"],[\"E\",\"E\",\"E\",\"E\",\"E\"]], click = [3,0]\nOutput: [[\"B\",\"1\",\"E\",\"1\",\"B\"],[\"B\",\"1\",\"M\",\"1\",\"B\"],[\"B\",\"1\",\"1\",\"1\",\"B\"],[\"B\",\"B\",\"B\",\"B\",\"B\"]]\n\nExample 2:\n\n\nInput: board = [[\"B\",\"1\",\"E\",\"1\",\"B\"],[\"B\",\"1\",\"M\",\"1\",\"B\"],[\"B\",\"1\",\"1\",\"1\",\"B\"],[\"B\",\"B\",\"B\",\"B\",\"B\"]], click = [1,2]\nOutput: [[\"B\",\"1\",\"E\",\"1\",\"B\"],[\"B\",\"1\",\"X\",\"1\",\"B\"],[\"B\",\"1\",\"1\",\"1\",\"B\"],[\"B\",\"B\",\"B\",\"B\",\"B\"]]\n\n \nConstraints:\n\nm == board.length\nn == board[i].length\n1 <= m, n <= 50\nboard[i][j] is either 'M', 'E', 'B', or a digit from '1' to '8'.\nclick.length == 2\n0 <= clickr < m\n0 <= clickc < n\nboard[clickr][clickc] is either 'M' or 'E'.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [3, 0]) == [['B', '1', 'E', '1', 'B'], ['B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', '1', '1', '1'], ['B', 'B', '1', 'M', 'E']]\n assert candidate(board = [['B', '1', 'E', '1', 'B'], ['B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']],click = [1, 2]) == [['B', '1', 'E', '1', 'B'], ['B', '1', 'X', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E'], ['E', 'E', 'E'], ['E', 'M', 'E']],click = [1, 1]) == [['E', 'E', 'E'], ['E', '1', 'E'], ['E', 'M', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E']],click = [2, 1]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', '1', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E']]\n assert candidate(board = [['E']],click = [0, 0]) == [['B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [3, 0]) == [['B', '1', 'E', '1', 'B'], ['B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 1]) == [['E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'E']],click = [1, 2]) == [['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'X', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'E']]\n assert candidate(board = [['M']],click = [0, 0]) == [['X']]\n assert candidate(board = [['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'M', 'E', 'E'], ['E', '2', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B'], ['B', '1', '1', '1'], ['B', '1', 'M', 'E']]\n assert candidate(board = [['M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['X', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['X', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['B', '1', 'E', '1', 'B'], ['B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']],click = [1, 2]) == [['B', '1', 'E', '1', 'B'], ['B', '1', 'X', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', '2', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 1]) == [['E', '1', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'M', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [1, 3]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', '2', 'E'], ['E', 'E', 'E', 'M', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', '1', '2', '3', '2', '1', 'B', 'B'], ['B', 'B', '1', 'M', 'M', 'M', '1', 'B', 'B'], ['B', 'B', '1', '2', '3', '2', '1', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', '1', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', '1', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', '1', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [4, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E'], ['E', 'E', 'E', 'E']],click = [2, 1]) == [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'X', 'M', 'E'], ['E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'E', 'E', 'E']],click = [7, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'M', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 1]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', '1', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [6, 6]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', '1', '2', '3', '2', '1', 'B', 'B', 'B'], ['B', 'B', '1', 'M', 'M', 'M', '1', 'B', 'B', 'B'], ['B', 'B', '1', '2', '3', '2', '1', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M'], ['E', 'E', 'E', 'E'], ['M', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M'], ['E', 'E', '1', 'E'], ['M', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'M', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', '1', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 4]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', '1', '1', '1', 'B', 'B', '1', '1', '1', 'B'], ['B', '1', 'M', '1', 'B', 'B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B', 'B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E']],click = [4, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [4, 5]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', '2', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [1, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [4, 4]) == [['B', 'B', 'B', 'B', 'B'], ['B', '1', '1', '1', 'B'], ['B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', '2', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', '1', 'M', 'E'], ['B', 'B', '1', '1', '1'], ['1', '1', 'B', 'B', 'B'], ['M', '1', 'B', 'B', 'B'], ['E', '1', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 6]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', '1', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', '1', 'E', 'E', 'E'], ['B', '1', 'M', 'M', 'E'], ['B', '1', '2', '2', '1'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B', 'B'], ['B', '1', '1', '1', 'B', 'B'], ['B', '1', 'M', '1', 'B', 'B'], ['B', '1', '1', '2', '1', '1'], ['B', 'B', 'B', '1', 'M', 'E'], ['B', 'B', 'B', '1', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', '1', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['M', 'M', 'M', 'M', 'M'], ['E', 'E', 'E', 'E', 'E']],click = [4, 0]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['M', 'M', 'M', 'M', 'M'], ['2', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M']],click = [2, 1]) == [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', '1', 'M', '1', 'B', 'B', 'B', 'B'], ['B', '1', '1', '2', '1', '1', '1', '1', '1', 'B'], ['B', '1', 'M', '1', 'B', 'B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B', 'B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', '1', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', '1', '2', '2', '1'], ['B', '1', 'M', 'M', 'E'], ['B', '1', '2', '2', '1'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', '1', '1', '1', 'B', 'B'], ['B', 'B', 'B', '1', 'M', '1', 'B', 'B'], ['B', 'B', 'B', '1', '1', '1', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'M'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'M', 'M'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E']],click = [2, 1]) == [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E'], ['E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'M', 'E', 'M', 'E', 'E'], ['E', 'E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'M', '8', 'M', 'E', 'E'], ['E', 'E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['M', 'E', 'E', 'E', 'M'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['1', '1', 'B', '1', '1'], ['M', '1', 'B', '1', 'M'], ['E', '1', 'B', '1', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['1', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E']],click = [7, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['1', '2', '2', '1', 'B'], ['E', 'M', 'M', '1', 'B'], ['E', 'E', 'E', '1', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [4, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 8]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', '1', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E']],click = [1, 2]) == [['E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E'], ['E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['1', '1', '2', '1', '1'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E']],click = [4, 4]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', '1']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [1, 3]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', '1', 'E', 'E'], ['E', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M']],click = [2, 2]) == [['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E'], ['M', 'E', 'X', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [3, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E', 'M', 'E', 'M']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['1', '1', '2', '1', '2', '1', '2', '1'], ['E', 'M', 'E', 'M', 'E', 'M', 'E', 'M']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', '1', 'M', '1', 'B'], ['B', 'B', 'B', 'B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [5, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['M', 'M', 'M', 'M', 'M', 'M', 'M'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', '3', 'E', 'E', 'E', 'E'], ['M', 'M', 'M', 'M', 'M', 'M', 'M'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E'], ['E', 'E', '3', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'E', 'E', 'E'], ['E', '1', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'M', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['M', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['X', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [5, 1]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'X', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', '1', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [5, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [4, 4]) == [['B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [0, 8]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', '1', '2', '3', '2', '1', 'B', 'B'], ['B', 'B', '1', 'M', 'M', 'M', '1', 'B', 'B'], ['B', 'B', '1', '2', '3', '2', '1', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'X', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 1]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'X', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['M', 'E', 'E', 'E', 'E', 'E', 'E', 'M']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['1', '1', 'B', 'B', 'B', 'B', '1', '1'], ['M', '1', 'B', 'B', 'B', 'B', '1', 'M']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'M']],click = [4, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'M', 'M']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['M', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E']],click = [2, 2]) == [['B', 'B', 'B', 'B', 'B', 'B'], ['1', '1', 'B', '1', '1', '1'], ['M', '1', 'B', '1', 'M', 'E'], ['E', '2', '1', '2', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'M', 'M', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'M', 'M', 'M', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [4, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'M', 'M', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'M', 'M', 'M', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', '1', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'M', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'M', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', '2', 'E', 'E'], ['E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', '1', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'M']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['B', 'B', 'B', 'B', 'B'], ['1', '1', '1', '1', '1'], ['E', 'M', 'E', 'E', 'M']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 7]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', '1', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'M'], ['E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'M'], ['E', 'E', 'M', 'E'], ['E', 'E', '2', 'E'], ['E', 'M', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['B', 'B', 'B', 'B', 'B'], ['B', 'B', '1', '1', '1'], ['B', 'B', '1', 'M', 'E'], ['B', 'B', '1', '1', '1'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [4, 4]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [1, 2]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['M', 'E', 'E', 'E', 'M'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['B', 'B', 'B', 'B', 'B'], ['1', '1', 'B', '1', '1'], ['M', '1', 'B', '1', 'M'], ['1', '1', 'B', '1', '1'], ['B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['M', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [0, 0]) == [['X', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'X', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E', 'E'], ['E', 'M', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E'], ['E', 'E', 'M', 'M', 'E'], ['E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E'], ['E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E']],click = [1, 1]) == [['E', 'E', 'E', 'E'], ['E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [3, 3]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'M', 'E', 'E'], ['E', 'E', 'E', '2', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [2, 2]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', '2', 'E', 'E', 'E'], ['E', 'M', 'M', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']],click = [2, 3]) == [['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'X', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E']],click = [4, 3]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', '1', '1', '1', 'B', 'B', '1', '1', '1', 'B'], ['B', '1', 'M', '1', 'B', 'B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', 'B', 'B', '1', '1', '1', 'B'], ['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B']]\n assert candidate(board = [['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'M', 'E', 'E', 'E', 'E', 'M', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E', 'E'], ['E', 'E', 'E', 'E', 'E', 'M', 'E', 'E', 'E', 'E']],click = [0, 8]) == [['B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B', 'B'], ['B', '1', '1', '1', 'B', 'B', '1', '1', '1', 'B'], ['B', '1', 'M', '1', 'B', 'B', '1', 'M', '1', 'B'], ['B', '1', '1', '1', '1', '1', '2', '1', '1', 'B'], ['B', 'B', 'B', 'B', '1', 'M', '1', 'B', 'B', 'B']]\n"}, "metadata": {"canonical_parameter_names": ["board", "click"], "leetcode_dataset_entry_point": "Solution().updateBoard", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var updateBoard = function(board, click) {", "container": null, "callable": "updateBoard", "parameters": [{"name": "board", "type": "character[][]"}, {"name": "click", "type": "number[]"}], "return_type": "character[][]", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 530, "task_id": "minimum-absolute-difference-in-bst", "difficulty": "Easy", "problem_description": "Given the root of a Binary Search Tree (BST), return the minimum absolute difference between the values of any two different nodes in the tree.\n \nExample 1:\n\n\nInput: root = [4,2,6,1,3]\nOutput: 1\n\nExample 2:\n\n\nInput: root = [1,0,48,null,null,12,49]\nOutput: 1\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [2, 104].\n0 <= Node.val <= 105\n\n \nNote: This question is the same as 783: https://leetcode.com/problems/minimum-distance-between-bst-nodes/\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(root = tree_node([4, 2, 6, 1, 3])) == 1\n assert candidate(root = tree_node([1, 30, None, 10, None, None, 15, None, 18])) == -29\n assert candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])) == 1\n assert candidate(root = tree_node([236, 104, 701, None, 227, None, 911])) == 9\n assert candidate(root = tree_node([5, 4, 7])) == 1\n assert candidate(root = tree_node([1, 0, 48, None, None, 12, 49])) == 1\n assert candidate(root = tree_node([5, 3, 7, 2, 4, 6, 8])) == 1\n assert candidate(root = tree_node([50, 25, 75, 15, 35, 65, 85, 10, 20, 30, 40, 60, 70, 80, 90])) == 5\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 80, 110, 140, 160, 190])) == 5\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, 4, 6, 8])) == 1\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])) == 2\n assert candidate(root = tree_node([60, 20, 80, 10, 30, 70, 90, 5, 15, 25, 35, 65, 75, 85, 95, 2, 8, 12, 18, 27, 33, 37, 55, 68, 72, 77, 82, 88, 92, 97, 98])) == -3\n assert candidate(root = tree_node([10, 9, 20, None, None, 15, 21])) == 1\n assert candidate(root = tree_node([25, 10, 30, 5, 15, 26, 40, 2, 7, 12, 18, 27, 35, 38, 45])) == -5\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 17, 22, 35, 43, 48, 55])) == 2\n assert candidate(root = tree_node([10, 5, 15, None, None, 12, 20, 11, None, None, 14])) == -6\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 90, 110, 140, 160, 190])) == 5\n assert candidate(root = tree_node([60, 30, 90, 10, 40, 80, 100, 5, 15, 35, 45, 75, 85, 95, 105])) == 5\n assert candidate(root = tree_node([10000, 5000, 15000, 2500, 7500, 12500, 17500, 1250, 3750, 5875, 8625, 11250, 15250, 16750, 18250])) == -250\n assert candidate(root = tree_node([8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15])) == 1\n assert candidate(root = tree_node([10, 5, 15, 2, None, 11, 18, 1, None, None, 13])) == 1\n assert candidate(root = tree_node([999, 499, 1499, 249, 749, 1249, 1749, 125, 375, 587, 862, 1124, 1524, 1674, 1824])) == -25\n assert candidate(root = tree_node([150, 75, 225, 37, 112, 188, 263, 18, 56, 87, 100, 163, 200, 242, 284])) == -12\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 17, 22, 27, 32, 37])) == 2\n assert candidate(root = tree_node([9, 3, 15, None, 8, 12, 20, 4, 7, 11, 13, 18, 25])) == -1\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, None, 17])) == -3\n assert candidate(root = tree_node([70, 35, 105, 20, 50, 85, 125, 10, 25, 40, 60, 80, 90, 110, 130])) == 5\n assert candidate(root = tree_node([20, 15, 30, 10, 18, 25, 35, 5, 12, 16, 19, 23, 27, 32, 38])) == 1\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 17, 22, 37, 42, 47, 52])) == 2\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 18, 23, 28, 33, 38])) == 2\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180, 5, 15, 22, 32, 42, 58, 68, 78, 88, 108, 118, 138, 158, 178, 190])) == -12\n assert candidate(root = tree_node([90, 45, 135, 20, 60, 110, 160, 10, 30, 50, 70, 100, 120, 140, 170])) == 5\n assert candidate(root = tree_node([8, 3, 13, None, 7, 10, 18, None, None, 9, 11, None, 15, 19, 22])) == -12\n assert candidate(root = tree_node([8, 3, 13, None, 7, 10, 17, None, None, 9, 12, 14, 16, 18, 20])) == -10\n assert candidate(root = tree_node([250, 125, 375, 62, 188, 312, 438, 31, 93, 156, 220, 275, 356, 400, 480])) == 19\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 12, 18, 23, 28, 33, 37])) == 2\n assert candidate(root = tree_node([15, 10, 20, 5, 12, None, None, 2, None, 11, 14])) == 1\n assert candidate(root = tree_node([30, 10, 50, 5, 20, 40, 60, 1, None, 15, 25, 35, 45, 55, 65])) == 4\n assert candidate(root = tree_node([15, 10, 20, 5, 12, 18, 25, 3, 8, 11, 14, 17, 22, 24, 30])) == -2\n assert candidate(root = tree_node([50, 25, 75, 15, 35, 65, 85, 5, 20, 30, 40, 60, 70, 80, 90])) == 5\n assert candidate(root = tree_node([15, 10, 20, 8, 12, 17, 25, 7, 9, 11, 13, 16, 18, 23, 27, 6, None, 10, None, 14, None, None, 19, 21, 26, 30, None, None, None, None, None, None, None, None, 1])) == -12\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 43, 55, 60])) == -5\n assert candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])) == -10\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 13, 18, 23, 28, 33, 37])) == 2\n assert candidate(root = tree_node([2, None, 3, None, 4, None, 5])) == 1\n assert candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 2, None, 6, 8, 17, 19])) == 1\n assert candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 17, 22, 27, 32, 37, 42])) == 2\n assert candidate(root = tree_node([500, 250, 750, 125, 375, 625, 875, 63, 188, 288, 469, 513, 688, 763, 938, 31, 94, 134, 225, 334, 409, 494, 569, 654, 729, 794, 859, 904, 964, 987])) == -141\n assert candidate(root = tree_node([50, 25, 75, 10, 35, 60, 85, 5, 15, 30, 40, 55, 65, 80, 90, 3, 7, 12, 18, 28, 32, 45, 52, 63, 68, 77, 82, 88, 93, 2, 4, 6, 8, 11, 13, 14, 17, 19, 27, 29, 31, 33, 39, 43, 48, 51, 54, 57, 62, 67, 70, 76, 79, 81, 83, 87, 89, 92, 95, 97, 1, 9, 16, 20, 23, 26, 34, 36, 38, 41, 42, 44, 46, 47, 49, 50, 53, 56, 58, 59, 61, 64, 66, 69, 71, 72, 73, 74, 75, 78, 80, 84, 86, 91, 94, 96, 98, 99])) == -95\n assert candidate(root = tree_node([9, 4, 17, 2, 6, 12, 22, 1, 3, 5, 7, 11, 13, 18, 25])) == 1\n assert candidate(root = tree_node([50, 25, 75, 10, 30, 60, 80, 5, 15, 27, 35, 55, 65, 77, 85])) == 2\n assert candidate(root = tree_node([20, 10, None, 5, 15, None, 25, 2, None, 13, 18, None, None, 16, None])) == -8\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37, 1, 4, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38])) == 1\n assert candidate(root = tree_node([50, 25, 75, 10, 35, 60, 85, 5, 15, 30, 40, 55, 65, 80, 90])) == 5\n assert candidate(root = tree_node([50, 25, 75, 12, 37, 63, 87, 6, 18, 30, 45, 58, 60, 72, 90])) == -3\n assert candidate(root = tree_node([7, 3, 15, None, None, 9, 20, None, None, None, 18])) == -2\n assert candidate(root = tree_node([500, 250, 750, 125, 375, 625, 875, 62, 188, 312, 438, 563, 712, 813, 938])) == 38\n assert candidate(root = tree_node([60, 30, 90, 20, 40, 70, 100, 15, 25, 35, 45, 65, 75, 85, 105])) == -5\n assert candidate(root = tree_node([99, 98, 102, 97, None, 101, 103, 96, None, None, None, None, None, None])) == 1\n assert candidate(root = tree_node([90, 60, 120, 30, 75, 100, 150, 20, 40, 65, 80, 95, 110, 140, 160])) == 5\n assert candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75])) == 5\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 90, 110, 140, 160, 190])) == 10\n assert candidate(root = tree_node([60, 30, 90, 20, 40, 70, 100, 15, 25, 35, 45, 65, 75, 85, 95, 10, 18, 23, 32, 43, 58, 63, 72, 78, 83, 92, 98, 110, 120, 130, 140, 150])) == -140\n assert candidate(root = tree_node([2, 1, 3, None, None, None, 4, None, None, None, None, None, None, 5])) == 1\n assert candidate(root = tree_node([10, 5, 15, None, None, 12, 20, None, None, None, None, 13, 18])) == 2\n assert candidate(root = tree_node([70, 35, 105, 15, 50, 85, 120, 10, 25, 40, 60, 80, 90, 110, 130])) == 5\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37])) == 2\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 90, 110, 140, 160, 180])) == 5\n assert candidate(root = tree_node([7, 3, 15, None, 4, 9, 20, None, None, None, None, 18, 22])) == 1\n assert candidate(root = tree_node([90, 45, 135, 22, 67, 112, 178, 11, 33, 55, 82, 100, 123, 165, 190])) == 8\n assert candidate(root = tree_node([75, 50, 100, 25, 62, 87, 125, 10, 38, 56, 65, 82, 93, 112, 138])) == 3\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 25, 35, 42, 48, 55])) == 2\n assert candidate(root = tree_node([8, 3, 13, 1, None, 7, 15, 0, 2, 6, 9, 14, 17, None, None, None, None, None, None, None, None])) == -2\n assert candidate(root = tree_node([30, 15, None, 10, 20, 18, 25])) == -10\n assert candidate(root = tree_node([75, 40, 100, 30, 55, 85, 110, 20, 35, 50, 60, 80, 90, 105, 115])) == 5\n assert candidate(root = tree_node([30, 10, 50, 5, 25, 40, 60, None, 15, None, 20, 35, 45, 55, 65])) == -5\n assert candidate(root = tree_node([2, 1, None])) == 1\n assert candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 85])) == 5\n assert candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 17, 22, 28, 33, 40])) == 2\n assert candidate(root = tree_node([40, 20, 60, 10, 30, 50, 70, 5, 15, 25, 35, 45, 55, 65, 75, 1, 9, 13, 22, 28, 33, 42, 48, 53, 57, 63, 68, 73, 77, 80, 83, 88, 93, 98, 100])) == -90\n assert candidate(root = tree_node([1, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])) == -1\n assert candidate(root = tree_node([99, 49, 149, 24, 74, 124, 174, 12, 37, 62, 87, 112, 137, 162, 187, 6, 22, 31, 43, 56, 71, 82, 93, 103, 118, 132, 143, 158, 168, 178, 182, 193])) == -187\n assert candidate(root = tree_node([50, 25, 75, 15, 35, 60, 85, 10, 20, 30, 40, 55, 65, 80, 90])) == 5\n assert candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 180])) == 5\n assert candidate(root = tree_node([30, 20, 40, 10, None, 35, 45, 5, None, None, 38, None, 47])) == 2\n assert candidate(root = tree_node([1000, 500, 1500, 250, 750, 1250, 1750, 125, 375, 625, 875, 1125, 1375, 1625, 1875, 63, 225, 313, 438, 563, 688, 763, 894, 1063, 1188, 1313, 1438, 1563, 1688, 1813, 1938])) == 13\n assert candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 17, 25, 35, 47, 49, 55])) == -2\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().getMinimumDifference", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var getMinimumDifference = function(root) {", "container": null, "callable": "getMinimumDifference", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 532, "task_id": "k-diff-pairs-in-an-array", "difficulty": "Medium", "problem_description": "Given an array of integers nums and an integer k, return the number of unique k-diff pairs in the array.\nA k-diff pair is an integer pair (nums[i], nums[j]), where the following are true:\n\n0 <= i, j < nums.length\ni != j\n|nums[i] - nums[j]| == k\n\nNotice that |val| denotes the absolute value of val.\n \nExample 1:\n\nInput: nums = [3,1,4,1,5], k = 2\nOutput: 2\nExplanation: There are two 2-diff pairs in the array, (1, 3) and (3, 5).\nAlthough we have two 1s in the input, we should only return the number of unique pairs.\n\nExample 2:\n\nInput: nums = [1,2,3,4,5], k = 1\nOutput: 4\nExplanation: There are four 1-diff pairs in the array, (1, 2), (2, 3), (3, 4) and (4, 5).\n\nExample 3:\n\nInput: nums = [1,3,1,5,4], k = 0\nOutput: 1\nExplanation: There is one 0-diff pair in the array, (1, 1).\n\n \nConstraints:\n\n1 <= nums.length <= 104\n-107 <= nums[i] <= 107\n0 <= k <= 107\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(nums = [1, 2, 3, 4, 5],k = 3) == 2\n assert candidate(nums = [6, 3, 5, 7, 2, 3, 3, 8, 2, 4],k = 2) == 5\n assert candidate(nums = [10, 20, 30, 40, 50],k = 10) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == 5\n assert candidate(nums = [1, 3, 1, 5, 4],k = 0) == 1\n assert candidate(nums = [1, 1, 1, 1, 1],k = 0) == 1\n assert candidate(nums = [-1, -1, -1, 2, 2, 2],k = 3) == 1\n assert candidate(nums = [-1, -2, -3, -4, -5],k = 1) == 4\n assert candidate(nums = [1, 1, 2, 2, 3, 3],k = 1) == 2\n assert candidate(nums = [3, 1, 4, 1, 5],k = 2) == 2\n assert candidate(nums = [1, 2, 2, 3, 3, 4, 4],k = 2) == 2\n assert candidate(nums = [1, 3, 5, 7, 9],k = 2) == 4\n assert candidate(nums = [0, 0, 0, 0, 0],k = 0) == 1\n assert candidate(nums = [1, 2, 3, 4, 5],k = 1) == 4\n assert candidate(nums = [-10000000, -9999999, -9999998, -9999997, -9999996, -9999995, -9999994, -9999993, -9999992, -9999991],k = 1) == 9\n assert candidate(nums = [-1, -2, -3, -1, -2, -3, -4, -5, -6, -7, -8, -9],k = 1) == 8\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 0) == 1\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3],k = 1) == 2\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 19) == 1\n assert candidate(nums = [100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110],k = 1) == 10\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 0) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 0) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == 7\n assert candidate(nums = [10000000, 9999999, 9999998, 9999997, 9999996, 9999995, 9999994, 9999993, 9999992, 9999991],k = 1) == 9\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],k = 2) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 11) == 0\n assert candidate(nums = [-5, -5, -5, -5, 5, 5, 5, 5, 10, 10, 10, 10, 15, 15, 15, 15],k = 10) == 2\n assert candidate(nums = [1, 5, 3, 4, 2],k = 3) == 2\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 0) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 0) == 0\n assert candidate(nums = [10000000, -10000000, 0, 5000000, -5000000],k = 20000000) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 4) == 18\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],k = 10) == 25\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],k = 1) == 9\n assert candidate(nums = [10, 2, 2, 10, 10, 3, 3, 3, 4, 4, 5, 5, 5, 5],k = 3) == 1\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 10) == 9\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 2) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 3) == 12\n assert candidate(nums = [1, 3, 1, 3, 5, 7, 5, 9, 7, 9, 11, 13, 11],k = 2) == 6\n assert candidate(nums = [5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10, 10, 10],k = 1) == 5\n assert candidate(nums = [9, 2, 9, 8, 3, 3, 6, 9, 1, 7, 4, 10, 6, 3, 7, 8, 4, 3, 9, 6],k = 2) == 6\n assert candidate(nums = [10, 20, 30, 40, 50, 10, 20, 30, 40, 50],k = 10) == 4\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14],k = 1) == 13\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 2) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5],k = 0) == 5\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],k = 30) == 7\n assert candidate(nums = [-10, -10, -10, -10, -10, -10, -10, -10, -10, -10],k = 0) == 1\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 50, 150, 250, 350, 450, 550, 650, 750, 850, 950],k = 100) == 18\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 10) == 9\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5],k = 0) == 5\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 3) == 17\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19],k = 0) == 0\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 0) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 1) == 19\n assert candidate(nums = [-1, -2, -2, -3, -3, -3, -4, -4, -4, -4, -5, -5, -5, -5, -5],k = 1) == 4\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 1) == 14\n assert candidate(nums = [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3],k = 1) == 2\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 1) == 0\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 2) == 8\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5],k = 2) == 8\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 1) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == 15\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],k = 2) == 19\n assert candidate(nums = [5, 3, 1, 5, 7, 9, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],k = 4) == 13\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000],k = 150) == 0\n assert candidate(nums = [10000000, -10000000, 5000000, -5000000, 0],k = 15000000) == 2\n assert candidate(nums = [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3],k = 1) == 2\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 1) == 0\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 9) == 11\n assert candidate(nums = [100, 90, 80, 70, 60, 50, 40, 30, 20, 10],k = 10) == 9\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 2) == 8\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],k = 1) == 9\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 0) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],k = 0) == 10\n assert candidate(nums = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5],k = 1) == 4\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 3) == 7\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20],k = 1) == 19\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 19) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 1) == 0\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 0) == 1\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 2) == 17\n assert candidate(nums = [1, 2, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 8, 9, 10],k = 1) == 9\n assert candidate(nums = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500],k = 100) == 14\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],k = 5) == 10\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 2) == 18\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2],k = 1) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14],k = 0) == 14\n assert candidate(nums = [10000000, -10000000, 5000000, -5000000, 0, 2500000, -2500000],k = 15000000) == 2\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 0) == 1\n assert candidate(nums = [10000000, 9999999, 9999998, 9999997, 9999996, 9999995, 9999994, 9999993, 9999992, 9999991],k = 1) == 9\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == 15\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25],k = 5) == 20\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 5) == 5\n assert candidate(nums = [-10, -20, -30, -40, -50, -60, -70, -80, -90, -100],k = 10) == 9\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 0) == 1\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10],k = 0) == 10\n assert candidate(nums = [-1, -2, -3, -1, -4, -2, -5, -6, -7, -8],k = 1) == 7\n assert candidate(nums = [-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10],k = 1) == 9\n assert candidate(nums = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],k = 0) == 1\n assert candidate(nums = [1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15],k = 2) == 13\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29],k = 4) == 13\n assert candidate(nums = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5],k = 2) == 9\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10],k = 0) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],k = 3) == 7\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == 10\n assert candidate(nums = [100, 200, 300, 200, 100, 400, 500, 600, 700, 800],k = 100) == 7\n assert candidate(nums = [10000000, 9999999, 9999998, 9999997, 9999996],k = 1) == 4\n assert candidate(nums = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20],k = 1) == 19\n assert candidate(nums = [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10],k = 1) == 9\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 5) == 16\n assert candidate(nums = [-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 2) == 20\n assert candidate(nums = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],k = 0) == 1\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39],k = 2) == 19\n assert candidate(nums = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5],k = 0) == 1\n assert candidate(nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20],k = 10) == 10\n assert candidate(nums = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59],k = 3) == 0\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200],k = 10) == 19\n assert candidate(nums = [-1000, -2000, -3000, -4000, -5000, -6000, -7000, -8000, -9000, -10000],k = 1000) == 9\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 15) == 0\n assert candidate(nums = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5],k = 1) == 4\n assert candidate(nums = [10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20],k = 10) == 1\n assert candidate(nums = [10000000, 9999999, 9999998, 10000001, 10000000, 9999999, 9999998, 10000001],k = 1) == 3\n assert candidate(nums = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100],k = 20) == 8\n assert candidate(nums = [1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000],k = 1000) == 19\n assert candidate(nums = [2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40],k = 4) == 18\n assert candidate(nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],k = 1) == 9\n"}, "metadata": {"canonical_parameter_names": ["nums", "k"], "leetcode_dataset_entry_point": "Solution().findPairs", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findPairs = function(nums, k) {", "container": null, "callable": "findPairs", "parameters": [{"name": "nums", "type": "number[]"}, {"name": "k", "type": "number"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 537, "task_id": "complex-number-multiplication", "difficulty": "Medium", "problem_description": "A complex number can be represented as a string on the form \"real+imaginaryi\" where:\n\nreal is the real part and is an integer in the range [-100, 100].\nimaginary is the imaginary part and is an integer in the range [-100, 100].\ni2 == -1.\n\nGiven two complex numbers num1 and num2 as strings, return a string of the complex number that represents their multiplications.\n \nExample 1:\n\nInput: num1 = \"1+1i\", num2 = \"1+1i\"\nOutput: \"0+2i\"\nExplanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, and you need convert it to the form of 0+2i.\n\nExample 2:\n\nInput: num1 = \"1+-1i\", num2 = \"1+-1i\"\nOutput: \"0+-2i\"\nExplanation: (1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.\n\n \nConstraints:\n\nnum1 and num2 are valid complex numbers.\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(num1 = \"100+0i\",num2 = \"0+100i\") == \"0+10000i\"\n assert candidate(num1 = \"7+-8i\",num2 = \"-9+2i\") == \"-47+86i\"\n assert candidate(num1 = \"-50+-50i\",num2 = \"50+50i\") == \"0+-5000i\"\n assert candidate(num1 = \"1+-1i\",num2 = \"1+-1i\") == \"0+-2i\"\n assert candidate(num1 = \"1+1i\",num2 = \"1+1i\") == \"0+2i\"\n assert candidate(num1 = \"2+3i\",num2 = \"3+4i\") == \"-6+17i\"\n assert candidate(num1 = \"-100+-100i\",num2 = \"100+100i\") == \"0+-20000i\"\n assert candidate(num1 = \"50+50i\",num2 = \"50+50i\") == \"0+5000i\"\n assert candidate(num1 = \"33+-50i\",num2 = \"-20+77i\") == \"3190+3541i\"\n assert candidate(num1 = \"0+0i\",num2 = \"0+0i\") == \"0+0i\"\n assert candidate(num1 = \"0+0i\",num2 = \"5+6i\") == \"0+0i\"\n assert candidate(num1 = \"3+4i\",num2 = \"-4+3i\") == \"-24+-7i\"\n assert candidate(num1 = \"-1+2i\",num2 = \"3+-4i\") == \"5+10i\"\n assert candidate(num1 = \"2+3i\",num2 = \"3+2i\") == \"0+13i\"\n assert candidate(num1 = \"10+-10i\",num2 = \"-10+10i\") == \"0+200i\"\n assert candidate(num1 = \"100+100i\",num2 = \"-100+-100i\") == \"0+-20000i\"\n assert candidate(num1 = \"-1+1i\",num2 = \"1+1i\") == \"-2+0i\"\n assert candidate(num1 = \"-1+-1i\",num2 = \"-1+-1i\") == \"0+2i\"\n assert candidate(num1 = \"12+34i\",num2 = \"56+78i\") == \"-1980+2840i\"\n assert candidate(num1 = \"25+75i\",num2 = \"-75+25i\") == \"-3750+-5000i\"\n assert candidate(num1 = \"-50+50i\",num2 = \"50+50i\") == \"-5000+0i\"\n assert candidate(num1 = \"1+0i\",num2 = \"1+0i\") == \"1+0i\"\n assert candidate(num1 = \"0+0i\",num2 = \"100+100i\") == \"0+0i\"\n assert candidate(num1 = \"100+0i\",num2 = \"-100+0i\") == \"-10000+0i\"\n assert candidate(num1 = \"-25+25i\",num2 = \"25+25i\") == \"-1250+0i\"\n assert candidate(num1 = \"42+0i\",num2 = \"0+42i\") == \"0+1764i\"\n assert candidate(num1 = \"0+1i\",num2 = \"1+0i\") == \"0+1i\"\n assert candidate(num1 = \"0+50i\",num2 = \"50+0i\") == \"0+2500i\"\n assert candidate(num1 = \"-50+0i\",num2 = \"0+-50i\") == \"0+2500i\"\n assert candidate(num1 = \"50+0i\",num2 = \"-50+0i\") == \"-2500+0i\"\n assert candidate(num1 = \"88+11i\",num2 = \"-44+22i\") == \"-4114+1452i\"\n assert candidate(num1 = \"50+30i\",num2 = \"-20+40i\") == \"-2200+1400i\"\n assert candidate(num1 = \"-99+99i\",num2 = \"99+99i\") == \"-19602+0i\"\n assert candidate(num1 = \"75+25i\",num2 = \"-25+75i\") == \"-3750+5000i\"\n assert candidate(num1 = \"-99+-99i\",num2 = \"99+99i\") == \"0+-19602i\"\n assert candidate(num1 = \"-1011+789i\",num2 = \"456+123i\") == \"-558063+235431i\"\n assert candidate(num1 = \"88+88i\",num2 = \"11+11i\") == \"0+1936i\"\n assert candidate(num1 = \"-100+0i\",num2 = \"-100+0i\") == \"10000+0i\"\n assert candidate(num1 = \"123+-456i\",num2 = \"-789+101i\") == \"-50991+372207i\"\n assert candidate(num1 = \"-1+0i\",num2 = \"-1+0i\") == \"1+0i\"\n assert candidate(num1 = \"50+0i\",num2 = \"0+50i\") == \"0+2500i\"\n assert candidate(num1 = \"-89+34i\",num2 = \"56+-23i\") == \"-4202+3951i\"\n assert candidate(num1 = \"0+-50i\",num2 = \"-50+0i\") == \"0+2500i\"\n assert candidate(num1 = \"-100+0i\",num2 = \"0+100i\") == \"0+-10000i\"\n assert candidate(num1 = \"66+88i\",num2 = \"88+66i\") == \"0+12100i\"\n assert candidate(num1 = \"99+99i\",num2 = \"1+1i\") == \"0+198i\"\n assert candidate(num1 = \"-1+1i\",num2 = \"-1+1i\") == \"0+-2i\"\n assert candidate(num1 = \"34+56i\",num2 = \"-78+90i\") == \"-7692+-1308i\"\n assert candidate(num1 = \"-100+0i\",num2 = \"0+-100i\") == \"0+10000i\"\n assert candidate(num1 = \"0+0i\",num2 = \"-100+-100i\") == \"0+0i\"\n assert candidate(num1 = \"50+-50i\",num2 = \"-50+50i\") == \"0+5000i\"\n assert candidate(num1 = \"99+99i\",num2 = \"-99+99i\") == \"-19602+0i\"\n assert candidate(num1 = \"0+100i\",num2 = \"0+100i\") == \"-10000+0i\"\n assert candidate(num1 = \"-10+-20i\",num2 = \"10+20i\") == \"300+-400i\"\n assert candidate(num1 = \"0+-100i\",num2 = \"0+-100i\") == \"-10000+0i\"\n assert candidate(num1 = \"100+0i\",num2 = \"100+0i\") == \"10000+0i\"\n assert candidate(num1 = \"-20+-30i\",num2 = \"20+30i\") == \"500+-1200i\"\n assert candidate(num1 = \"1+0i\",num2 = \"-1+0i\") == \"-1+0i\"\n assert candidate(num1 = \"1+0i\",num2 = \"0+1i\") == \"0+1i\"\n assert candidate(num1 = \"99+1i\",num2 = \"1+99i\") == \"0+9802i\"\n assert candidate(num1 = \"0+100i\",num2 = \"100+0i\") == \"0+10000i\"\n assert candidate(num1 = \"1+-1i\",num2 = \"-100+100i\") == \"0+200i\"\n"}, "metadata": {"canonical_parameter_names": ["num1", "num2"], "leetcode_dataset_entry_point": "Solution().complexNumberMultiply", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var complexNumberMultiply = function(num1, num2) {", "container": null, "callable": "complexNumberMultiply", "parameters": [{"name": "num1", "type": "string"}, {"name": "num2", "type": "string"}], "return_type": "string", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 538, "task_id": "convert-bst-to-greater-tree", "difficulty": "Medium", "problem_description": "Given the root of a Binary Search Tree (BST), convert it to a Greater Tree such that every key of the original BST is changed to the original key plus the sum of all keys greater than the original key in BST.\nAs a reminder, a binary search tree is a tree that satisfies these constraints:\n\nThe left subtree of a node contains only nodes with keys less than the node's key.\nThe right subtree of a node contains only nodes with keys greater than the node's key.\nBoth the left and right subtrees must also be binary search trees.\n\n \nExample 1:\n\n\nInput: root = [4,1,6,0,2,5,7,null,null,null,3,null,null,null,8]\nOutput: [30,36,21,36,35,26,15,null,null,null,33,null,null,null,8]\n\nExample 2:\n\nInput: root = [0,null,1]\nOutput: [1,null,1]\n\n \nConstraints:\n\nThe number of nodes in the tree is in the range [0, 104].\n-104 <= Node.val <= 104\nAll the values in the tree are unique.\nroot is guaranteed to be a valid binary search tree.\n\n \nNote: This question is the same as 1038: https://leetcode.com/problems/binary-search-tree-to-greater-sum-tree/\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert is_same_tree(candidate(root = tree_node([3, 1, 4, None, 2])), tree_node([7, 10, 4, None, 9]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5])), tree_node([15, None, 14, None, 12, None, 9, None, 5]))\n assert is_same_tree(candidate(root = tree_node([5, 2, 13])), tree_node([18, 20, 13]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18])), tree_node([43, 55, 33, 58, 50, None, 18]))\n assert is_same_tree(candidate(root = tree_node([1, None, 3, None, None, 2])), tree_node([4, None, 3]))\n assert is_same_tree(candidate(root = tree_node([3, 2, 4, 1])), tree_node([7, 9, 4, 10]))\n assert is_same_tree(candidate(root = tree_node([5, None, 14])), tree_node([19, None, 14]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175])), tree_node([550, 675, 325, 700, 625, 450, 175]))\n assert is_same_tree(candidate(root = tree_node([4, 1, 6, 0, 2, 5, 7, None, None, None, 3, None, None, None, 8])), tree_node([30, 36, 21, 36, 35, 26, 15, None, None, None, 33, None, None, None, 8]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3])), tree_node([6, None, 5, None, 3]))\n assert is_same_tree(candidate(root = tree_node([0, None, 1])), tree_node([1, None, 1]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, None, 7, 13, None, None, 8])), tree_node([38, 58, 15, None, 53, 28, None, None, 46]))\n assert candidate(root = tree_node([])) == None\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 130, 160, 180])), tree_node([1130, 1395, 665, 1450, 1285, 920, 355, 1460, 1425, 1345, 1210, 1030, 795, 515, 180]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 2, 7, 12, 18, 23, 27, 32, 37])), tree_node([229, 284, 134, 296, 262, 186, 72, 298, 291, 274, 247, 209, 161, 104, 37]))\n assert is_same_tree(candidate(root = tree_node([2, 1, 4, None, None, 3, 5])), tree_node([14, 15, 9, None, None, 12, 5]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 8, 2, 4, 6, 9, 1, None, None, None, None, None, None, 10])), tree_node([38, 45, 27, 47, 42, 33, 19, 48, None, None, None, None, None, None, 10]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10])), tree_node([55, None, 54, None, 52, None, 49, None, 45, None, 40, None, 34, None, 27, None, 19, None, 10]))\n assert is_same_tree(candidate(root = tree_node([9, 4, 17, 3, 7, 12, 22, 1, 5, None, 8, 11, 15, 18, 26])), tree_node([130, 149, 83, 157, 145, 110, 48, 158, 154, None, 138, 121, 98, 66, 26]))\n assert is_same_tree(candidate(root = tree_node([15, 7, 20, None, 10, 18, 23, None, None, 9, 11, 16, 19, None, None, None, None, None, 17])), tree_node([148, 165, 95, None, 158, 124, 42, None, None, 133, 106, 75, 19, None, None, None, None, None, 59]))\n assert is_same_tree(candidate(root = tree_node([-2147483648, None, 2147483647])), tree_node([-1, None, 2147483647]))\n assert is_same_tree(candidate(root = tree_node([30, 10, 50, 5, 15, 40, 60, 2, 7, 12, 18, 35, 45, 55, 65])), tree_node([380, 435, 230, 447, 413, 315, 125, 449, 442, 425, 398, 350, 275, 180, 65]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 190])), tree_node([1150, 1415, 675, 1470, 1305, 940, 365, 1480, 1445, 1365, 1230, 1050, 815, 525, 190]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, None, 12, 20])), tree_node([75, 93, 65, 96, 82, None, 38, 97, None, 88, None, 50, 20]))\n assert is_same_tree(candidate(root = tree_node([12, 7, 17, 4, 9, 14, 20, 2, 5, 8, 11, 13, 16, 18, 22, None, None, None, None, 6, None, 10, None, None, None, None, None, None, None, 15, 19, None, None, 21, None, 23])), tree_node([189, 261, 134, 270, 240, 164, 99, 272, 266, 248, 200, 177, 150, 117, 41, None, None, None, None, 254, None, 210, None, None, None, None, None, None, None, 56, 19, None, None, 231, None, 79]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13])), tree_node([45, 65, 37, 66, 58, None, 14, None, None, 62, 52, 27]))\n assert is_same_tree(candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, 6, 9, 11, 13, 18, 22, 28])), tree_node([144, 190, 73, 207, 169, 111, 25, 213, 199, 180, 157, 129, 95, 53]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 8, 2, 4, 7, 9, 1, None, None, None, 6, None, None, 10])), tree_node([45, 52, 27, 54, 49, 34, 19, 55, None, None, None, 40, None, None, 10]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13, None, 14, None, 15])), tree_node([120, None, 119, None, 117, None, 114, None, 110, None, 105, None, 99, None, 92, None, 84, None, 75, None, 65, None, 54, None, 42, None, 29, None, 15]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9])), tree_node([45, None, 44, None, 42, None, 39, None, 35, None, 30, None, 24, None, 17, None, 9]))\n assert is_same_tree(candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 18, 22, 28, 32, 38, 45])), tree_node([273, 348, 158, 370, 315, 220, 85, 375, 360, 333, 295, 248, 190, 123, 45]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, 4, 7, 9, 13, None, None, None, None, None, None, None, 12, 15])), tree_node([72, 97, 64, 102, 87, None, 14, None, 101, 94, 81, 42, None, None, None, None, None, None, None, 54, 29]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 130, 160, 180, None, None, None, None, None, None, 12, None, 35, None, None, None, None, 95, None, None, 145, None, 190])), tree_node([1450, 1872, 760, 1927, 1762, 1015, 355, 1937, 1902, 1822, 1530, 1125, 890, 610, 180, None, None, None, None, None, None, 1542, None, 1160, None, None, None, None, 450, None, None, 1687, None, 1350]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, 1, 5, 9, 20, None, None, 2, 6, None, 12, None, None, None, None, 8, 11, 13, 19, 21])), tree_node([95, 151, 35, 152, 146, 88, 20, None, None, 148, 112, None, 66, None, None, None, None, 120, 106, 79, 54, 141]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, None, 4, 7, 13, None, None, None, None, None, 11])), tree_node([56, 76, 48, 77, 69, None, 14, None, None, 73, 63, 27, None, None, None, None, None, 38]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, 1, 5, 9, 20, None, None, 4, 6, 8, 13, None, None, 17, 22])), tree_node([72, 129, 35, 130, 83, 57, 20, None, None, 109, 78, 65, 48, None, None, 126, 105]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, None, 35, 45, 55, 65, None, 75, None, 90])), tree_node([455, 605, 225, 625, 540, 350, 155, 725, None, 575, 500, 405, 290, None, 75, None, 715]))\n assert is_same_tree(candidate(root = tree_node([1, 0, 2, None, -1])), tree_node([3, 2, 2, None, 2]))\n assert is_same_tree(candidate(root = tree_node([-10, -5, 0, None, -8, -3, -1])), tree_node([-14, -27, -1, None, -22, -4, -1]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, None, 6, 9, 12, None, 5, 7, 11, 13])), tree_node([70, 84, 35, None, 81, 55, 12, None, 75, 62, 46, 25]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, 1, 3, 6, 8, None, None, None, None, None, 17])), tree_node([45, 71, 35, 93, 60, None, 20, 94, 91, 66, 53, None, None, None, None, None, 88]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 10, 40, 60, 80, 5, 20, None, 45, 55, 65, 75, 90])), tree_node([545, 660, 315, 690, 630, 440, 170, 695, 680, None, 590, 495, 380, 245, 90]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8, 13, 17])), tree_node([73, 99, 63, 102, 88, None, 35, 103, None, 94, 81, 48, 17]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, 1, None, 9, 20, None, 2, None, 18])), tree_node([69, 72, 35, 75, None, 62, 20, None, 74, None, 53]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 9, 14, 17, 20])), tree_node([74, 101, 64, 104, 90, None, 35, 105, None, 96, 83, 49, 17, 125]))\n assert is_same_tree(candidate(root = tree_node([2, 1, 3])), tree_node([5, 6, 3]))\n assert is_same_tree(candidate(root = tree_node([5, None, -3, 2, None, None, -1, None, 4])), tree_node([7, None, -3, 2, None, None, 0, None, 1]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 12, 18, 23, 28, 33, 38])), tree_node([232, 287, 136, 299, 265, 189, 73, 302, 294, 277, 250, 212, 164, 106, 38]))\n assert is_same_tree(candidate(root = tree_node([-10, 5, None, 3, 7, -3, None, -5, None, None, 8])), tree_node([-10, -3, None, 0, -3, 5, None, -8, None, None, 8]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 18, None, 30, 5, 13, 16, 19, None, 28, 35])), tree_node([103, 171, 83, 194, 140, None, 58, 199, 184, 156, 122, None, 28, 234]))\n assert is_same_tree(candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 17, 22, 28, 33, 38, 45])), tree_node([274, 348, 158, 370, 316, 221, 85, 375, 360, 333, 296, 249, 191, 123, 45]))\n assert is_same_tree(candidate(root = tree_node([60, 30, 90, 15, 45, 75, 105, 5, 25, 40, 55, 70, 85, 100, 110])), tree_node([695, 865, 405, 905, 795, 565, 215, 910, 890, 835, 750, 635, 490, 315, 110]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8, None, None, None, None, 14, 19])), tree_node([43, 102, 33, 105, 58, None, 18, 106, None, 83, 51, None, None, None, None, 97, 77]))\n assert is_same_tree(candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, 5, 9, 11, 13, 14, 18, 22, 27])), tree_node([157, 203, 94, 220, 182, 128, 52, 225, 212, 193, 170, 142, 112, 74, 27]))\n assert is_same_tree(candidate(root = tree_node([15, 9, 20, 7, 12, 17, 25, 5, 8, 11, 13, 16, 19, 23, 27])), tree_node([162, 207, 95, 222, 187, 131, 52, 227, 215, 198, 175, 147, 114, 75, 27]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15])), tree_node([71, 99, 39, 112, 87, 58, 22, 120, 108, 97, 82, 70, 52, 36, 15]))\n assert is_same_tree(candidate(root = tree_node([21, 7, 32, 3, 14, 28, 37, 2, 5, 9, 16, 24, 30, 35, 40])), tree_node([247, 293, 144, 301, 277, 202, 77, 303, 298, 286, 263, 226, 174, 112, 40]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 30, 10, 17, 25, 35, 5, 12, 16, 18, 22, 28, 33, 40])), tree_node([233, 299, 138, 321, 268, 191, 75, 326, 311, 284, 251, 213, 166, 108, 40]))\n assert is_same_tree(candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 17, 22, 27, 32, 37, 42])), tree_node([268, 342, 154, 364, 310, 216, 82, 369, 354, 327, 290, 243, 186, 119, 42]))\n assert is_same_tree(candidate(root = tree_node([50, 20, 70, 10, 30, 60, 80, 5, 15, 25, 35, 55, 65, 75, 85])), tree_node([540, 650, 310, 675, 605, 435, 165, 680, 665, 630, 575, 490, 375, 240, 85]))\n assert is_same_tree(candidate(root = tree_node([30, 20, 40, 15, 25, 35, 45, 10, 18, 23, 28, 32, 38, 43, 48])), tree_node([311, 407, 176, 440, 364, 249, 93, 450, 425, 387, 339, 281, 214, 136, 48]))\n assert is_same_tree(candidate(root = tree_node([5, 2, 13, 1, 4, 9, 21, 0, None, None, 6, 8, 11, 19, None])), tree_node([86, 98, 53, 99, 96, 73, 21, 99, None, None, 92, 81, 64, 40]))\n assert is_same_tree(candidate(root = tree_node([5, 2, 13, 1, 4, 9, 18, None, None, 3, 6, 7, 12, 15, None, None, None, None, None, None, 14, 19])), tree_node([112, 127, 46, 128, 122, 86, 18, None, None, 125, 118, 107, 58, 33, None, None, None, None, None, None, 100, 77]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 40, 60, 90, 110, 140, 160, 190, 5, 15, 28, 45, 65, 85, 105, 135, 155, 178, 188, 200])), tree_node([1871, 2536, 675, 2674, 2276, 1328, 365, 2699, 2621, 2421, 2096, 1616, 1015, 525, 190, 2704, 2689, 2649, 2581, 2486, 2361, 2201, 2006, 1771, 1506, 1203, 875]))\n assert is_same_tree(candidate(root = tree_node([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), tree_node([17, 34, 10, 47, 22, 16, 7, 55, 43, 32]))\n assert is_same_tree(candidate(root = tree_node([5, 3, 8, 1, 4, 7, 9, None, 2, None, None, None, None, None, 10])), tree_node([39, 46, 27, 49, 43, 34, 19, None, 48, None, None, None, None, None, 10]))\n assert is_same_tree(candidate(root = tree_node([3, 2, 5, 1, None, 4, 6, None, None, None, None, None, 7])), tree_node([25, 27, 18, 28, None, 22, 13, None, None, None, None, None, 7]))\n assert is_same_tree(candidate(root = tree_node([20, 10, 30, 5, 15, 25, 35, 3, 7, 13, 17, 23, 27, 33, 37, 1, 4, 6, 8, 11, 14, 16, 19, 21, 24, 26, 29, 31, 34, 36, 39, 41, 43, 44])), tree_node([470, 585, 275, 611, 537, 382, 147, 662, 600, 564, 506, 429, 331, 214, 76, 706, 615, 606, 593, 575, 551, 522, 489, 450, 406, 357, 304, 245, 181, 112, 39, 747, 705, 659]))\n assert is_same_tree(candidate(root = tree_node([50, 25, 75, 10, 30, 60, 90, 5, 15, 20, 35, 55, 65, 85, 100])), tree_node([580, 690, 350, 715, 645, 475, 190, 720, 705, 665, 615, 530, 415, 275, 100]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 80, 110, 140, 160, 190, 5, 15, 20, 35, 55, 65, 70, 85, 105, 115, 135, 145, 155, 170, 180, 195, None, None, None, None, None, None, None, None, None, None, 40, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 120])), tree_node([2470, 3050, 1495, 3160, 2780, 2040, 860, 3185, 3115, 2945, 2635, 2265, 1780, 1190, 505, 3190, 3175, 3135, 3085, 3000, 2845, 2705, 2555, 2370, 2155, 1915, 1640, 1345, 1030, 685, 195, None, None, None, None, None, None, None, None, None, None, 2885, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, None, 315]))\n assert is_same_tree(candidate(root = tree_node([50, 20, 70, 10, 30, 60, 80, 5, 15, 25, 35, 55, 65, 75, 85, None, None, None, None, None, None, None, 1, None, None, None, None, None, 4, 8, 9, None, None, 17, 33, 34, 36, None, None, None, 76, None, None, 86, None, None, 95, None, None, 99])), tree_node([1037, 1148, 807, 1173, 1103, 932, 532, 1178, 1163, 1128, 1073, 987, 872, 737, 94, None, None, None, None, None, None, None, 1038, None, None, None, None, None, 569, 233, 9, None, None, 662, 565, 267, 225, None, None, None, 645, None, None, 353, None, None, 189, None, None, 452]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 35, 60, 90, 110, 140, 160, 190])), tree_node([1150, 1425, 675, 1485, 1315, 940, 365, 1495, 1460, 1375, 1240, 1050, 815, 525, 190]))\n assert is_same_tree(candidate(root = tree_node([2147483647])), tree_node([2147483647]))\n assert is_same_tree(candidate(root = tree_node([5, 2, 13, 1, 3, 9, 21, None, None, None, None, 7, 15, None, None, 17, None, None, None, 25])), tree_node([112, 117, 34, 118, 115, 58, 21, None, None, None, None, 65, 49, None, None, 82, None, None, None, 107]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, 1, 5, None, 20, None, None, 4, 6])), tree_node([42, 60, 35, 61, 53, None, 20, None, None, 57, 48]))\n assert is_same_tree(candidate(root = tree_node([20, 15, 25, 10, 18, 22, 30, 5, 12, 16, 19, 21, 24, 27, 35])), tree_node([204, 272, 117, 294, 241, 163, 65, 299, 284, 257, 223, 184, 141, 92, 35]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 13, None, 7, 10, 17, 1, None, None, 8, None, None, 11, 14])), tree_node([56, 92, 30, None, 63, 48, 17, 78, None, None, 38, None, None, 89, 77]))\n assert is_same_tree(candidate(root = tree_node([90, 45, 135, 20, 70, 110, 160, 10, 30, 50, 80, 105, 125, 145, 175])), tree_node([1045, 1290, 615, 1340, 1195, 850, 335, 1350, 1320, 1245, 1125, 955, 740, 480, 175]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 13, 1, 5, 10, 18, 0, 2, 4, 7, 9, 11, 14, 20, None, None, None, None, None, 6])), tree_node([103, 128, 65, 131, 115, 86, 38, 131, 130, 125, 110, 95, 76, 52, 20, None, None, None, None, None, 121]))\n assert is_same_tree(candidate(root = tree_node([30, 15, 45, 10, 20, 40, 50, 5, 12, 18, 23, 35, 43, 48, 55])), tree_node([346, 422, 198, 444, 389, 281, 105, 449, 434, 407, 369, 316, 241, 153, 55]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, 6, 8])), tree_node([43, 69, 33, 72, 58, None, 18, 73, None, 64, 51]))\n assert is_same_tree(candidate(root = tree_node([12, 7, 15, 5, 8, 13, 18, 3, 6, 9, 11, 14, 17, 20])), tree_node([109, 144, 53, 155, 128, 83, 18, 158, 150, 137, 120, 97, 70, 38]))\n assert is_same_tree(candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, 17, 22, 28, 32, 38, 45])), tree_node([273, 347, 158, 369, 315, 220, 85, 374, 359, 332, 295, 248, 190, 123, 45]))\n assert is_same_tree(candidate(root = tree_node([100, 50, 150, 25, 75, 125, 175, 10, 30, 60, 85, 110, 140, 160, 190])), tree_node([1150, 1420, 675, 1475, 1310, 940, 365, 1485, 1450, 1370, 1235, 1050, 815, 525, 190]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, 1, 5, 9, 20, None, 2, 4, 6, 8, 12, 17, 25])), tree_node([113, 131, 77, 134, 124, 98, 45, None, 133, 128, 119, 106, 89, 62, 25]))\n assert is_same_tree(candidate(root = tree_node([25, 15, 35, 10, 20, 30, 40, 5, 12, None, 17, 22, 28, 33, 45])), tree_node([258, 310, 153, 332, 295, 211, 85, 337, 322, None, 275, 233, 181, 118, 45]))\n assert is_same_tree(candidate(root = tree_node([75, 35, 115, 15, 55, 85, 145, 10, 25, 45, 65, 78, 105, 135, 165])), tree_node([903, 1103, 560, 1143, 1023, 750, 310, 1153, 1128, 1068, 968, 828, 665, 445, 165]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 13, None, 7, 10, 17, 1, None, 5, 9, 12, 15, None, 16])), tree_node([89, 116, 57, None, 96, 76, 32, 113, None, 81, 66, 44, 15, None, 112]))\n assert is_same_tree(candidate(root = tree_node([1, None, 2, None, 3, None, 4, None, 5, None, 6, None, 7, None, 8, None, 9, None, 10, None, 11, None, 12, None, 13])), tree_node([91, None, 90, None, 88, None, 85, None, 81, None, 76, None, 70, None, 63, None, 55, None, 46, None, 36, None, 25, None, 13]))\n assert is_same_tree(candidate(root = tree_node([7, 3, 15, None, 5, 9, 20, None, None, 4, 6, 8, 11, 19, 25, None, 17, 18, 21, 23, 27, 26, 28, None, None, None, None, None, 22, None, None, 24, None, None, None, None, None, None, 29, None, None, 30])), tree_node([389, 397, 219, None, 394, 251, 135, None, None, 280, 242, 164, 38, 356, 276, None, 236, 204, 156, 61, 27, 382, 337, None, None, None, None, None, 186, None, None, 85, None, None, None, None, None, None, 309, None, None, 115]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 3, 7, None, 18, 1, None, None, 6, None, 19])), tree_node([62, 80, 52, 83, 75, None, 37, 84, None, None, 68, None, 19]))\n assert is_same_tree(candidate(root = tree_node([15, 10, 20, 8, 12, 16, 25, 5, 9, 11, 13, 17, 22, 28])), tree_node([143, 189, 73, 206, 168, 111, 25, 211, 198, 179, 156, 128, 95, 53]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, 4, 7, 13, None, None, 9])), tree_node([32, 61, 24, 75, 51, None, 14, None, 65, 58, 45, None, None, 74]))\n assert is_same_tree(candidate(root = tree_node([8, 3, 10, 1, 6, None, 14, None, 4, 7, 13, None, None, 11, 15])), tree_node([32, 61, 24, 92, 51, None, 14, None, 80, 58, 45, None, None, 91, 76]))\n assert is_same_tree(candidate(root = tree_node([12, 7, 17, 5, 9, 14, 20, 3, 6, 8, 11, 13, 16, 19, 22])), tree_node([133, 168, 78, 179, 153, 108, 42, 182, 174, 161, 144, 121, 94, 61, 22]))\n assert is_same_tree(candidate(root = tree_node([50, 30, 70, 20, 40, 60, 80, 10, 25, 35, 45, 55, 65, 75, 90])), tree_node([545, 695, 315, 740, 630, 440, 170, 750, 720, 665, 590, 495, 380, 245, 90]))\n assert is_same_tree(candidate(root = tree_node([10, 5, 15, 2, 7, None, 20, 1, None, 6, None, None, None, 18])), tree_node([45, 63, 35, 65, 52, None, 20, 66, None, 58, None, None, None, 84]))\n"}, "metadata": {"canonical_parameter_names": ["root"], "leetcode_dataset_entry_point": "Solution().convertBST", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var convertBST = function(root) {", "container": null, "callable": "convertBST", "parameters": [{"name": "root", "type": "TreeNode"}], "return_type": "TreeNode", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}} +{"question_id": 539, "task_id": "minimum-time-difference", "difficulty": "Medium", "problem_description": "Given a list of 24-hour clock time points in \"HH:MM\" format, return the minimum minutes difference between any two time-points in the list.\n \nExample 1:\nInput: timePoints = [\"23:59\",\"00:00\"]\nOutput: 1\nExample 2:\nInput: timePoints = [\"00:00\",\"23:59\",\"00:00\"]\nOutput: 0\n\n \nConstraints:\n\n2 <= timePoints.length <= 2 * 104\ntimePoints[i] is in the format \"HH:MM\".\n\n", "canonical_tests": {"language": "python", "source": "def check(candidate):\n assert candidate(timePoints = ['01:01', '02:02', '03:03', '23:23']) == 61\n assert candidate(timePoints = ['12:34', '12:34', '12:34']) == 0\n assert candidate(timePoints = ['14:59', '15:00', '15:01', '15:02', '15:03']) == 1\n assert candidate(timePoints = ['23:59', '00:00']) == 1\n assert candidate(timePoints = ['14:50', '14:52', '15:50', '15:51', '16:00', '16:05', '16:10']) == 1\n assert candidate(timePoints = ['01:01', '02:02', '03:03', '04:04', '05:05', '06:06', '07:07', '08:08', '09:09', '10:10', '11:11', '12:12', '13:13', '14:14', '15:15', '16:16', '17:17', '18:18', '19:19', '20:20', '21:21', '22:22', '23:23', '00:00']) == 37\n assert candidate(timePoints = ['23:58', '23:59', '00:00', '00:01']) == 1\n assert candidate(timePoints = ['11:11', '11:12', '11:13', '11:14', '11:15']) == 1\n assert candidate(timePoints = ['00:00', '00:01', '00:02', '00:03']) == 1\n assert candidate(timePoints = ['12:34', '23:45', '01:02', '12:34']) == 0\n assert candidate(timePoints = ['00:00', '23:59', '00:00']) == 0\n assert candidate(timePoints = ['12:00', '00:00', '12:00']) == 0\n assert candidate(timePoints = ['12:34', '23:45', '00:12', '01:23']) == 27\n assert candidate(timePoints = ['14:50', '14:51', '00:00', '23:59']) == 1\n assert candidate(timePoints = ['00:01', '00:02', '00:03']) == 1\n assert candidate(timePoints = ['00:01', '00:02', '00:03', '00:04']) == 1\n assert candidate(timePoints = ['01:01', '02:02', '03:03', '23:59', '00:00']) == 1\n assert candidate(timePoints = ['01:01', '01:01', '01:01', '01:01', '01:02', '01:02', '01:03', '01:04']) == 0\n assert candidate(timePoints = ['00:00', '00:01', '00:02', '00:03', '00:04', '00:05', '00:06', '00:07', '00:08', '00:09', '00:10', '00:11', '00:12', '00:13', '00:14', '00:15', '00:16', '00:17', '00:18', '00:19', '00:20', '00:21', '00:22', '00:23', '00:24', '00:25', '00:26', '00:27', '00:28', '00:29', '00:30', '00:31', '00:32', '00:33', '00:34', '00:35', '00:36', '00:37', '00:38', '00:39', '00:40', '00:41', '00:42', '00:43', '00:44', '00:45', '00:46', '00:47', '00:48', '00:49', '00:50', '00:51', '00:52', '00:53', '00:54', '00:55', '00:56', '00:57', '00:58', '00:59']) == 1\n assert candidate(timePoints = ['00:01', '23:59', '12:34', '12:35', '00:00']) == 1\n assert candidate(timePoints = ['11:11', '11:12', '11:13', '11:14', '11:15', '11:16', '11:17', '11:18', '11:19', '11:20', '11:21', '11:22', '11:23', '11:24', '11:25', '11:26', '11:27', '11:28', '11:29', '11:30']) == 1\n assert candidate(timePoints = ['00:00', '06:30', '12:00', '18:00', '23:59']) == 1\n assert candidate(timePoints = ['00:00', '01:15', '02:30', '03:45', '05:00', '06:15', '07:30', '08:45', '10:00', '11:15', '12:30', '13:45', '15:00', '16:15', '17:30', '18:45', '19:00', '20:15', '21:30', '22:45', '23:59']) == 1\n assert candidate(timePoints = ['01:23', '02:45', '03:56', '05:17', '06:38', '07:59', '09:20', '10:41', '12:02', '13:23', '14:45', '16:06', '17:27', '18:48', '20:09', '21:30', '22:51', '24:12']) == 71\n assert candidate(timePoints = ['15:30', '15:30', '15:30', '15:30', '15:30']) == 0\n assert candidate(timePoints = ['12:34', '12:35', '12:36', '12:37', '12:38', '12:39']) == 1\n assert candidate(timePoints = ['14:30', '22:45', '09:15', '00:01', '08:59', '12:00']) == 16\n assert candidate(timePoints = ['00:01', '00:02', '00:03', '00:04', '00:05']) == 1\n assert candidate(timePoints = ['23:55', '23:56', '23:57', '23:58', '23:59', '00:00', '00:01', '00:02', '00:03', '00:04']) == 1\n assert candidate(timePoints = ['12:34', '12:35', '12:36', '12:37', '12:38', '12:39', '12:40', '12:41', '12:42', '12:43', '12:44', '12:45', '12:46', '12:47', '12:48', '12:49', '12:50', '12:51', '12:52', '12:53', '12:54', '12:55', '12:56', '12:57', '12:58', '12:59']) == 1\n assert candidate(timePoints = ['00:01', '00:02', '00:03', '23:58', '23:59']) == 1\n assert candidate(timePoints = ['08:00', '08:10', '08:20', '08:30', '08:40', '08:50', '09:00']) == 10\n assert candidate(timePoints = ['11:11', '11:12', '11:13', '11:14', '11:15', '11:16', '11:17', '11:18', '11:19', '11:20']) == 1\n assert candidate(timePoints = ['01:01', '02:02', '03:03', '04:04', '05:05', '23:23']) == 61\n assert candidate(timePoints = ['23:58', '00:02', '12:34', '12:35', '12:36']) == 1\n assert candidate(timePoints = ['00:00', '12:00', '23:59', '11:59', '12:01', '00:01']) == 1\n assert candidate(timePoints = ['11:59', '23:58', '23:57', '00:01', '00:02', '00:03', '00:04', '00:05']) == 1\n assert candidate(timePoints = ['11:59', '23:58', '23:59', '00:00', '00:01']) == 1\n assert candidate(timePoints = ['00:00', '04:30', '09:00', '13:30', '18:00', '22:30']) == 90\n assert candidate(timePoints = ['13:30', '14:30', '15:30', '16:30', '17:30', '18:30', '19:30', '20:30', '21:30', '22:30', '23:30', '00:30']) == 60\n assert candidate(timePoints = ['01:10', '01:10', '02:20', '03:30', '04:40']) == 0\n assert candidate(timePoints = ['00:00', '00:01', '00:02', '00:03', '23:59']) == 1\n assert candidate(timePoints = ['12:00', '12:01', '12:02', '12:03', '12:04', '12:05', '12:06', '12:07', '12:08', '12:09', '12:10', '12:11', '12:12', '12:13', '12:14', '12:15', '12:16', '12:17', '12:18', '12:19']) == 1\n assert candidate(timePoints = ['07:07', '07:07', '07:07', '07:08', '07:09', '07:10', '07:11', '07:12']) == 0\n assert candidate(timePoints = ['09:45', '09:46', '09:47', '09:48', '09:49', '09:50', '09:51', '09:52', '09:53', '09:54']) == 1\n assert candidate(timePoints = ['05:30', '05:31', '05:32', '05:33', '05:34']) == 1\n assert candidate(timePoints = ['06:06', '06:07', '06:08', '06:09', '06:10', '06:11', '06:12', '06:13', '06:14', '06:15']) == 1\n assert candidate(timePoints = ['11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22', '11:11', '22:22']) == 0\n assert candidate(timePoints = ['00:00', '00:01', '23:58', '23:59', '12:00']) == 1\n assert candidate(timePoints = ['23:59', '00:01', '00:02', '00:03', '00:04', '00:05', '00:06', '00:07', '00:08', '00:09']) == 1\n assert candidate(timePoints = ['01:23', '02:45', '03:30', '04:15', '05:00', '23:50']) == 45\n assert candidate(timePoints = ['11:59', '12:00', '12:01', '12:02', '12:03', '12:04']) == 1\n assert candidate(timePoints = ['10:10', '10:10', '10:11', '10:11', '10:12', '10:12', '10:13', '10:13', '10:14', '10:14']) == 0\n assert candidate(timePoints = ['00:00', '00:01', '00:02', '00:03', '00:04', '00:05', '00:06', '00:07', '00:08', '00:09', '00:10', '00:11', '00:12', '00:13', '00:14', '00:15', '00:16', '00:17', '00:18', '00:19', '00:20', '00:21', '00:22', '00:23', '00:24', '00:25', '00:26', '00:27', '00:28', '00:29', '00:30', '00:31', '00:32', '00:33', '00:34', '00:35', '00:36', '00:37', '00:38', '00:39', '00:40', '00:41', '00:42', '00:43', '00:44', '00:45', '00:46', '00:47', '00:48', '00:49', '00:50', '00:51', '00:52', '00:53', '00:54', '00:55', '00:56', '00:57', '00:58', '00:59', '23:00', '23:01', '23:02', '23:03', '23:04', '23:05', '23:06', '23:07', '23:08', '23:09', '23:10', '23:11', '23:12', '23:13', '23:14', '23:15', '23:16', '23:17', '23:18', '23:19', '23:20', '23:21', '23:22', '23:23', '23:24', '23:25', '23:26', '23:27', '23:28', '23:29', '23:30', '23:31', '23:32', '23:33', '23:34', '23:35', '23:36', '23:37', '23:38', '23:39', '23:40', '23:41', '23:42', '23:43', '23:44', '23:45', '23:46', '23:47', '23:48', '23:49', '23:50', '23:51', '23:52', '23:53', '23:54', '23:55', '23:56', '23:57', '23:58', '23:59']) == 1\n assert candidate(timePoints = ['00:00', '00:01', '23:59', '23:58', '00:02', '23:57']) == 1\n assert candidate(timePoints = ['14:30', '14:31', '14:32', '14:33', '14:34', '14:35', '14:36', '14:37', '14:38', '14:39']) == 1\n assert candidate(timePoints = ['14:00', '14:01', '14:02', '14:03', '14:04', '14:05', '14:06', '14:07', '14:08', '14:09', '14:10']) == 1\n assert candidate(timePoints = ['01:01', '01:02', '01:03', '01:04', '01:05']) == 1\n assert candidate(timePoints = ['00:00', '23:59', '12:34', '12:35', '12:36', '12:37', '12:38', '12:39', '12:40', '12:41']) == 1\n assert candidate(timePoints = ['23:59', '23:58', '23:57', '23:56', '23:55', '23:54', '23:53', '23:52', '23:51', '23:50', '23:49', '23:48', '23:47', '23:46', '23:45', '23:44', '23:43', '23:42', '23:41', '23:40', '23:39', '23:38', '23:37', '23:36', '23:35', '23:34', '23:33', '23:32', '23:31', '23:30', '23:29', '23:28', '23:27', '23:26', '23:25', '23:24', '23:23', '23:22', '23:21', '23:20', '23:19', '23:18', '23:17', '23:16', '23:15', '23:14', '23:13', '23:12', '23:11', '23:10', '23:09', '23:08', '23:07', '23:06', '23:05', '23:04', '23:03', '23:02', '23:01', '00:00']) == 1\n assert candidate(timePoints = ['05:45', '05:46', '10:10', '10:09', '23:59', '00:00']) == 1\n assert candidate(timePoints = ['23:58', '23:59', '00:00', '00:01', '00:02', '00:03', '00:04', '00:05']) == 1\n assert candidate(timePoints = ['00:00', '00:10', '00:20', '00:30', '00:40', '00:50']) == 10\n assert candidate(timePoints = ['23:58', '23:59', '00:00', '00:01', '00:02']) == 1\n assert candidate(timePoints = ['00:00', '00:10', '00:20', '00:30', '00:40', '00:50', '01:00', '01:10', '01:20', '01:30', '01:40', '01:50', '02:00', '02:10', '02:20', '02:30', '02:40', '02:50', '03:00']) == 10\n assert candidate(timePoints = ['09:09', '18:18', '09:09', '18:18', '09:09', '18:18']) == 0\n assert candidate(timePoints = ['00:00', '04:00', '08:00', '12:00', '16:00', '20:00', '23:59']) == 1\n assert candidate(timePoints = ['00:00', '01:00', '02:00', '03:00', '04:00', '05:00', '06:00', '07:00', '08:00', '09:00', '10:00', '11:00', '12:00', '13:00', '14:00', '15:00', '16:00', '17:00', '18:00', '19:00', '20:00', '21:00', '22:00', '23:00']) == 60\n assert candidate(timePoints = ['00:01', '23:59', '12:34', '01:02', '12:34']) == 0\n assert candidate(timePoints = ['00:01', '00:02', '00:03', '23:59', '00:04']) == 1\n assert candidate(timePoints = ['12:30', '13:30', '14:30', '15:30', '16:30']) == 60\n assert candidate(timePoints = ['00:15', '01:15', '02:15', '03:15', '04:15', '05:15', '06:15', '07:15', '08:15', '09:15', '10:15', '11:15', '12:15', '13:15', '14:15', '15:15', '16:15', '17:15', '18:15', '19:15', '20:15', '21:15', '22:15', '23:15']) == 60\n assert candidate(timePoints = ['09:09', '10:10', '11:11', '12:12', '13:13', '14:14', '15:15', '16:16', '17:17', '18:18', '19:19', '20:20', '21:21', '22:22', '23:23', '00:00']) == 37\n assert candidate(timePoints = ['12:00', '12:01', '12:02', '12:03', '12:04', '12:05', '12:06', '12:07', '12:08', '12:09', '12:10', '12:11', '12:12', '12:13', '12:14', '12:15', '12:16', '12:17', '12:18', '12:19', '12:20', '12:21', '12:22', '12:23', '12:24', '12:25', '12:26', '12:27', '12:28', '12:29', '12:30', '12:31', '12:32', '12:33', '12:34', '12:35', '12:36', '12:37', '12:38', '12:39', '12:40', '12:41', '12:42', '12:43', '12:44', '12:45', '12:46', '12:47', '12:48', '12:49', '12:50', '12:51', '12:52', '12:53', '12:54', '12:55', '12:56', '12:57', '12:58', '12:59']) == 1\n assert candidate(timePoints = ['00:00', '00:05', '00:10', '00:15', '00:20', '00:25', '00:30', '00:35', '00:40', '00:45', '00:50', '00:55', '01:00']) == 5\n assert candidate(timePoints = ['01:00', '02:00', '03:00', '04:00', '05:00', '06:00', '07:00', '08:00', '09:00', '10:00', '11:00', '12:00', '13:00', '14:00', '15:00', '16:00', '17:00', '18:00', '19:00', '20:00', '21:00', '22:00', '23:00']) == 60\n assert candidate(timePoints = ['12:00', '12:10', '12:20', '12:30', '12:40', '12:50']) == 10\n assert candidate(timePoints = ['23:00', '00:01', '00:02', '00:03', '22:58', '22:59']) == 1\n assert candidate(timePoints = ['01:30', '02:30', '03:30', '04:30', '05:30', '06:30', '07:30', '08:30', '09:30', '10:30', '11:30', '12:30', '13:30', '14:30', '15:30', '16:30', '17:30', '18:30', '19:30', '20:30', '21:30', '22:30', '23:30']) == 60\n assert candidate(timePoints = ['15:22', '15:22', '15:23', '15:23', '15:24', '15:24', '15:25', '15:25', '15:26', '15:26', '15:27', '15:27', '15:28', '15:28', '15:29', '15:29', '15:30', '15:30', '15:31', '15:31']) == 0\n assert candidate(timePoints = ['13:40', '13:41', '13:42', '13:43', '13:44', '13:45']) == 1\n assert candidate(timePoints = ['11:59', '12:00', '12:01', '12:02', '12:03', '12:04', '12:05', '12:06', '12:07', '12:08', '12:09', '12:10']) == 1\n assert candidate(timePoints = ['00:01', '00:02', '00:03', '00:04', '00:05', '00:06', '00:07', '00:08', '00:09', '00:10']) == 1\n assert candidate(timePoints = ['13:45', '02:50', '06:12', '19:34', '08:43', '21:01', '15:23', '03:30', '17:56', '10:14', '04:26', '18:38', '09:51', '20:49', '14:07', '07:19', '16:32', '11:25', '05:37', '12:48', '01:06', '00:52', '13:45']) == 0\n"}, "metadata": {"canonical_parameter_names": ["timePoints"], "leetcode_dataset_entry_point": "Solution().findMinDifference", "problem_source": "newfacade/LeetCodeDataset", "interface_source": "leetcode/codeSnippets"}, "language": "javascript", "interface": {"raw_signature": "var findMinDifference = function(timePoints) {", "container": null, "callable": "findMinDifference", "parameters": [{"name": "timePoints", "type": "string[]"}], "return_type": "number", "signature_source": "leetcode/codeSnippets", "type_source": "leetcode/codeSnippets"}}